over pressure

13

2The Interrelationships betweenOverpressure Mechanisms andIn-Situ StressesT. W. MillerKnowledge Systems Inc.,Stafford, Texas

C. H. LukRetired from ExxonMobil Upstream Research Company,Houston, Texas

D. L. OlgaardExxonMobil Upstream Research Company,Houston, Texas

A B S T R A C T

In this chapter, we discuss how the two different excess pore-pressure–generating mechanisms that areprimarily associated with burial affect stresses in different ways. We, and others before us, term thesetwo mechanisms as either “compaction disequilibrium” or “source mechanisms.” Rapid burial rates inassociation with low permeabilities are attributed to the former, whereas aquathermal expansion, smec-tite/illite diagenesis (or other diagenetic processes), kerogen maturation, and hydrocarbon cracking areexamples of the latter.The compaction disequilibrium mechanism is fundamentally different from the source mechanism.

In the compaction disequilibrium case, pore-pressure increases are primarily a reaction of the fluid topore-volume decreases that are a result of increased vertical loading (assuming minimal tectonicstresses). The magnitude of the pressure increase depends on the load increase and the relative mag-nitudes of the sediment pore-volume and pore-fluid compressibilities. Regardless of the magnitude ofthe pore-pressure increase, mechanical equilibrium requires that the effective stresses of the sedimentincrease. As a result, both the horizontal and vertical (effective and total) stresses of a given sedimentpackage increase as its burial depth increases, and pore-pressure increases due to burial are less thanthe increase in the overburden stress. In the source case, pore-pressure increases are a response toincreases in the pore-fluid specific volume. In a source-dominated system, the sediment pore volumeincreases, and, consequently, the effective stresses decrease. In these cases, the pore pressures increasefaster than the effective stresses decrease, and the horizontal and vertical total stresses increase. Becausepore volumes increase, the increases in pore pressure can be larger than increases in overburden stress.

Miller, T. W., C. H. Luk, and D. L. Olgaard, 2002, The Interrelationships between Overpressure Mechanisms and In-Situ Stresses, in A. R.Huffman and G. L. Bowers, eds., Pressure regimes in sedimentary basins and their prediction: AAPG Memoir 76, p. 13–20.

14 M I L L E R E T A L .

I N T R O D U C T I O N

Although there are many mechanisms that cause ov-erpressures, these mechanisms can be classified in gen-eral groups based on whether they are directlyassociated with burial and how they affect in-situstresses. Compaction disequilibrium, aquathermal ex-pansion, smectite/illite diagenesis (or other diageneticprocesses), kerogen maturation, and hydrocarboncracking are examples of overpressuring mechanismsassociated with burial-depth increases. Shear failure(Yassir, 1989) and geometric factors such as large, tiltedsand bodies (Flemings et al., 1998) are examples ofother mechanisms that are not covered in this chapter.This chapter focuses on those excess pore-pressure–

generating mechanisms commonly associated withburial-depth increases and the fundamental differ-ences between compaction disequilibrium and theother mechanisms. Of course, all of these mechanismsact simultaneously, so each mechanism contributes toexcess pore pressures to some degree. When we iden-tify a mechanism as the cause of overpressures, wemean that the particular mechanism is the dominantcause of overpressures. To identify the dominantmechanism, we should look at how the differentmech-anisms affect in-situ stresses and pore pressures.Whether compaction disequilibrium or source

mechanisms are the dominant cause of overpressuresis ultimately due to the relative magnitudes of manyfactors such as burial rate, sediment permeability, me-chanical behavior, and the thermal environment. Thesefactors are compared via simple considerations of fluidflow and the sediment’s mechanical behavior that arediscussed in the following section. For simplicity, weassume one-dimensional fluid flow and deformation.Many of the conclusions are not strongly affected bythis assumption. Some are, however, so the conclu-sions presented in this chapter should be carefullyevaluated when one-dimensional assumptions are notappropriate.

T H E O R E T I C A L B A C K G R O U N D

Fluid-Flow Considerations

The basic equation that describes fluid flow in asediment undergoing burial provides key insights intohow compaction disequilibrium and source mecha-nisms affect in-situ stresses. Following Luo andVasseur(1992), using terms added to account for sediment-grainvolume changes, the fluid-flow equation can bewrittenin terms of the time rates of change in total stress andeither the pore pressure or the effective stress. When

the equation is written in terms of the pore pressure,p, and the total vertical stress, sv, it is clear that thepore pressure increases with an increase in burialdepth (sv), inward Darcy flows, an increase in tem-perature, and with active fluid sources.We assume compressive stresses and strains are

positive and use the shorthand convention of a dotover the variable to mean the time differential of thatvariable.

1p � � �c �c�cp f s

1 qk ˙c s � �• �(p�qgz)�(� �� )T�q (1)p v f s� � ��q l

The variables T, q, �, and z are temperature, fluid-specific volume source, porosity, and true verticaldepth, respectively. Material constants cp, cs, cf, k, q,l, �f, and �s are, respectively, the one-dimensionalcompressibilities of the sediment pores and solid con-stituents, the fluid compressibility, the sediment per-meability, the fluid density and viscosity, and thecoefficients of thermal expansion of the fluid andsolids; g is the acceleration of gravity. The pore com-pressibility, cp, depends on �, cs, and the rock’s one-dimensional bulk compressibility, cb: cp � (cb—cs)/�.The first term in the curly brackets {} defines the rate

of pressure increase due to burial-depth increases. Thefirst term in the square brackets governs Darcy flowand is positive for fluid flows into the system. The sec-ond term in the square brackets describes aquathermalexpansion, and the third term (in the square brackets)describes any other source such as smectite/illite dia-genesis or kerogen maturation. Either of these latterterms in the square brackets can be thought of as asource mechanism.Equation 1 demonstrates that both active source

mechanisms and increasing burial depths tend to in-crease pore pressures. This is not the casewith effectivestresses, r, which may tend to increase or decrease de-pending on the mechanism that causes overpressures.Because the basic fluid-flow and compaction equationsinvolve porosity changes, we use the Terzaghi effectivestress (Carroll, 1980), defined as

r � s � p (2)

where s is the total compressive stress.Combining equations 1 and 2 gives the following

relationship for the effective vertical stress in terms ofthe total vertical stress and the various fluid sourceterms:

The Interrelationships between Overpressure Mechanisms and In-Situ Stresses 15

Figure 1. Schematic illustrating porosity vs. depth for a clas-tic sediment under two loading conditions. Porosity is re-duced irreversibly during virgin compaction but rebounds/re-compacts reversibly during unloading/reloading.

1s �v � �c �c�cp f s

1 qk ˙(c�c )s � �• �(p�qgz)�(� �� )T�q (3)f s v f s� �� q l

Whether rv increases or decreases depends on therelative strengths of the source terms, the system’s per-meability, and the burial rate. Under one-dimensionalvertical strain condition, the horizontal stresses re-spond directly to changes in the vertical effective stressand the pore pressure. As we show in the followingsection, both the magnitude of the horizontal stressand the relationship between horizontal and verticalstresses change depending on whether the effectivestresses increase or decrease.

Stress-Strain Considerations

A sediment compacts inelastically (irreversibly) orelastically (reversibly) depending on its loading his-tory. Figure 1 shows porosity vs. depth for virgin com-

paction (inelastic) and unloading/reloading (elastic)paths for normally pressured rocks. Porosity changefollows the virgin compaction curve as long as the sed-iment’s effective stress is increasing and at its maxi-mum value. Porosity change follows the unloading/reloading curve, which is tied to the porosity at thesediment’s maximum effective stress, whenever the ef-fective stress is less than its previous maximum value.This latter response can be caused either by uplift anderosion or by active source terms.The various loading behaviors can bemodeledmath-

ematically with a modified Cam-Clay model from criti-cal state soil mechanics (Atkinson and Bransby, 1978).Here we modify the basic Cam-Clay log-linear plasticvolume-change relationship to one based on a generalAthy-type exponential compaction curve in which

� � � exp(�kd) (4)0

where � is the porosity; �0 is the porosity at the top ofthe sediment column, d is the depth, and k is an em-pirical coefficient. The porosity actually depends on

Figure 2. Overpressures caused by compaction disequilib-rium (solid lines) increase both pore pressures, p, and totalhorizontal stresses, sh. Normal pressures (dotted line)shown for reference.


Figure 4. In sediments that are highly overpressured bycompaction disequilibrium, p � sh � sv.

the vertical effective stress. An appropriate functionaldependence between � and rv can be found from suchAthy relationships for normally pressured sediments.We call that function the compaction function, whichis defined as

� � C(r ) (5)v

This compaction function applies whenever the sedi-ment is at its maximum rv. In this case, the one-dimensional deformation assumption leads to

s � k s (6)h 0 v

(Atkinson and Bransby, 1978). We assume equality inequation 6 because this condition ignores only a smallthermoplastic effect. The parameter k0 depends on thetype of sediment. Experiments have shown (Karig andHou, 1992; Vasseur et al., 1995) that k0 remains con-stant over a wide range of stresses. Although it is notstrictly a material property in that its value is a con-sequence of other material properties, it can be treatedas one for uniaxial deformation conditions.

The parameter k0 is not related to Poisson’s ratio,m, which should be considered as an elastic propertyonly. In fact, the values of Poisson’s ratio (m*) in-ferred from measured values of k0 via the Eaton(1975) equation

k0m* � (7)1�k0

are approximately twice those measured in appropri-ate, drained stress-strain tests. For example, k0 isaround 0.70 for most shales and 0.55 for many uncon-solidated sands. Thus the inferred Poisson’s ratios forthese materials would be 0.41 and 0.35, respectively,compared to reported elastic values of 0.25 and 0.20,respectively. Clearly misapplication of the apparentproperty into the incorrect governing equation couldlead to large errors in calculated stresses.The previous discussion points out the important

differences between assuming elastic and inelastic me-chanical responses. While the sediment is activelycompacting, it behaves inelastically, but at stresses lessthan the maximum, sediments behave mechanicallymore like elastic materials. It follows (Miller, 1995)then that during unloading/reloading,

Figure 3. Overpressures caused by compaction disequilib-rium decrease total vertical stresses, sv. Other symbols thesame as in Figure 2.


Figure 5. Total stresses, sv and sh, and pore pressures, p, ina sediment column of shale overlain by sand.

Figure 6. Stress reversals can be caused by changes in li-thology without unloading (rv � rvmax).

� � [(1��)c �c ]s and (8)b s v

˙1 c (1�2v) �Tss � vs � p� (9)h v� � ��1�m c cb s

The value of m for this equation cannot be determinedfrom stress data, and the inelastic bulk compressibilityimplicit in equation 5 is typically an order of magni-tude greater than the equivalent elastic constant, cb, inequations 8 and 9.

R E S U L T S

The following examples demonstrate some of the keydifferences in the distribution and magnitudes of porepressures and in-situ stress conditions resulting fromcompaction disequilibrium and source-pressuringmechanisms. The results presented in this chapterwere calculated using a one-dimensional simulatorthat calculates pressure, temperature, and stress his-tories of a sediment column. In addition to the basicequations described previously, this model couplesfluid properties to temperature and pressure and in-cludes a permeability vs. porosity algorithm that re-

sults in shale permeability predictions consistent withthe average values given by Neuzil (1994).

Compaction Disequilibrium

Excess pore pressures resulting from compaction dis-equilibrium lead to porosities higher than, total verti-cal stresses less than, and total horizontal stressesgreater than those found in equivalent normally pres-sured settings. Although the pressures can be highunder rapid burial conditions, pore pressures and hor-izontal stresses cannot exceed the overburden stress.Figures 2 and 3, respectively, show that overpres-

sures increase the total horizontal stress, sh, and de-crease the overburden or total vertical stress, sv. Thetotal vertical stress is less than in the normally pres-sured case because the excess pressures inhibit porosityreduction, resulting in a less dense overburden. The to-tal horizontal stress increases with fluid pressure be-cause of a combination of several factors, but the mostimportant is that lateral strains are constrained byadjacent rocks, which prevent free horizontal defor-mations. Consequently, horizontal loads (and totalstresses) increase or decrease where lateral deforma-tions are, respectively, inward or outward. Therefore,


Figure 7. With a small fluid source in the shale, unload-ing (rv � rvmax) occurs because of the increase in porepressure.

increased pore pressures, which tend to expand therock, increase the horizontal total stresses.In addition, because the vertical effective stress at

any given location has always increased in time, rh canbe calculated from equation 6 and hence is always lessthan rv.Because the pore-pressure increases are caused by

compression of the pores, mechanical equilibrium dic-tates that any increase in pore pressure resulting fromburial-depth increases cannot exceed the increase in to-tal vertical stress. This effect is illustrated in Figure 4.The stresses and pore pressure follow the same trendestablished in Figures 2 and 3, in which increasing porepressures lead to decreased overburden stresses and in-creased horizontal stresses. Note that these simulationscould be repeated with a higher burial rate (or lowerpermeability), and the horizontal and vertical stresseswould approach the limiting condition of p � sh � sv.Figure 5 is a plot of the pore pressures and vertical

and horizontal total stresses of a sediment column thatis predominantly shale in the lower half and pre-dominantly sand in the upper half. In this example,

both the sand and shale were buried at a constant rateof 1.5 km/Ma. Here the pore pressures and stresses inthe sand are as expected for normally pressured sedi-ments, and the elevated pore pressures and changedstresses are as expected in the shale. The general pore-pressure and stress conditions shown in Figure 5 arecommonly mistaken for unloading because a plot ofporosity vs. depth would show an increase in porositybelow the sand/shale interface. Figure 6 is a plot of thecurrent and maximum vertical and the current hori-zontal effective stresses vs. depth for the same sedi-ment whose total stresses are shown in Figure 5. Theseeffective-stress plots show that the current and maxi-mum vertical stresses are the same, a result that indi-cates unloading has not occurred despite the effectivestresses decreasing with depth.

Sources and Unloading

For unloading to occur, an active source, fluid inflows,or fluid expansion are required (equation 3). Althoughthe relative rate of decrease in the horizontal and ver-tical effective stresses during unloading varies as afunction of mechanical properties, source intensity,and temperature, the vertical effective stress tends todecrease faster than the horizontal effective stress(equations 8 and 9). Eventually, the horizontal totalstresses may exceed the overburden stress. Further-more, pore pressures can also increase, at least in prin-ciple if rock fracture would not occur, above theoverburden stress. As a practical matter, leak-off testsin such an environment would generate horizontalfractures, and one can erroneously conclude that thehorizontal stress would equal the vertical stress in-stead of exceeding it.Figures 7 and 8 are plots of the current and maxi-

mum vertical and current horizontal effective stressesfor the same sand-over-shale sediment package shownin Figures 5 and 6, but with a recently active source inthe shale. For the small source case, shown in Figure6, unloading has occurred because the current verticaleffective stress is less than its maximum value, and thedifference between the vertical and horizontal stressesis less than in the no-source case. The vertical effectivestress, however, is still greater than the horizontal ef-fective stress. For the larger source case, shown in Fig-ure 8, the shale has unloaded further, and the verticaleffective stress has decreased below the horizontal ef-fective stress at depth, that is, horizontal total stressesexceed the overburden, and pore pressures almostequal the overburden, that is, rv � 0. High pore pres-sures are not by themselves conclusive evidence of anyone overpressuring mechanism (Figure 9).


Figure 8. With a large fluid source in the shale, unloadingoccurs to such an extent that rv � rh is possible.

Figure 9. Pore pressure, p, vs. depth for no fluid source,small fluid source, and large fluid source magnitudes in theshale (see Figures 6–8).

D I S C U S S I O N

The previous examples show that the compaction dis-equilibrium and source-dominated overpressuringmechanisms affect in-situ stresses in fundamentally dif-ferent ways. In the case of compaction disequilibrium:

• The overburden stress (sv) is less than in the nor-mal pressure case

• Current stresses (rv, rh, sv, and sh) are always attheir maximum value

• Horizontal stresses (rh and sh) are less than therespective vertical stresses

• Pore pressures are always less than theoverburden

In the case of fluid sources:

• The total overburden stress is virtually un-changed

• Current effective stresses are less than their max-imum values

• Horizontal (effective and total) stresses can ex-ceed their respective vertical stresses

• Pore pressures can exceed the overburden stress

R E F E R E N C E S C I T E D

Atkinson, J. H., and P. L. Bransby, 1978, The mechanics ofsoils: London, McGraw-Hill, 450 p.

Carroll, M. M., 1980, Mechanical response of fluid-saturatedporous materials, in F. Rimrott and B. Tabarrok, eds.,Theoretical and applied mechanics: Proceedings of 15thInternational Congress of Theoretical and Applied Me-chanics, p. 251–262.

Eaton, B. A., 1975, The equation for geopressure predictionfromwell-logs: Society of Petroleum Engineers Paper 5544.

Flemings, P., B. B. Stump, T. Finkbeiner, and M. D. Zoback,1998, Pressure differences between overpressured sandsand bounding shales of the Eugene Island 330 field (off-shore Louisiana, U.S.A.) with implications for fluid flowinduced by sediment loading: Proceedings of the Ameri-can Association of Drilling Engineers Industry Forum onPressure Regimes in Sedimentary Basins and Their Pre-diction.


Karig, D., and G. Hou, 1992, High-stress consolidation ex-periments and their geologic implications: Journal of Geo-physical Research, v. 97, no. B1, p. 289–300.

Luo, X., and G. Vasseur, 1992, Contributions of compactionand aquathermal pressuring to geopressure and the influ-ence of environmental conditions: AAPG Bulletin, v. 76,no. 10, p. 1550–1559.

Miller, T. W., 1995, New insight on natural hydraulic frac-tures induced by abnormally high pore pressures: AAPGBulletin, v. 79, no. 7, p. 1005–1018.

Neuzil, C. E., 1994, How permeable are clays and shales?:Water Resources Research, v. 30, no. 2, p. 145–150.

Vasseur, G., I. Djeran-Maigre, D. Grunberger, G. Rousset,D. Tessier, and B. Velde, 1995, Evolution of structural andphysical parameters of clays during experimental compac-tion: Marine Petroleum Geology, v. 12, no. 8, p. 941–954.

Yassir, N. A., 1989, Undrained shear characteristics of clay athigh total stress, in V. Maury and C. Fourmaintraux, eds.,Rock at great depth: Proceedings of the InternationalSymposium on Rock Mechanics, v. 2, p. 907–913.

21

3The Primary Controls overSediment CompactionPhil HolbrookForce Balanced Petrophysics, Houston, Texas

A B S T R A C T

Mineralogic composition is the primary control over sediment compaction. Near-surface sediments andsedimentary rocks compact in proportion to the effective stress load applied to the grain matrix frame-work. The load borne by the grain framework is a volumetric force-balance relationship within andbetween solid particles. Mineral ionic bonds bear the load within particles and across direct grain-graincontacts. Electrostatic repulsive forces between negatively charged clay mineral particles also bears apart of the effective stress load.

A strong correlation exists between average particle size and initial porosity of natural marinesediments. Compaction resistance is also strongly correlated to average particle size. Clay mineral in-terparticle repulsive force explains both correlations. The relationship of particle size vs. compactionresistance is continuous from coarse sands to the finest particle-size clays. Graded bedding due toindividual particle settling velocity sorting places mineral grains of similar size and mechanical prop-erties together.

Five mineral-specific compaction functions were determined from in-situ petrophysical data. Av-erage mineral ionic bond strength controls mineral hardness, solubility, and the plastic compactionintercept at zero porosity. Clay minerals have an additional interparticle electrostatic repulsive forcethat is inversely proportional to sedimentary clay particle size and directly proportional to clay surfacearea in a given rock volume. All these factors are simultaneously accounted for by two power-lawcompaction coefficients (rmax and �).

Solidity (1.0 � porosity) is an end-of-plastic-compaction in-situ strain parameter. The (solidity �1.0) intercept (rmax) incorporates both elastic and plastic grain matrix strain into volumetric in-situstrain. The power-law compaction exponent (�) captures the interparticle and intraparticle compactionresistances mentioned previously with respect to (rmax).

S T R U C T U R E , I O N I C B O N D S T R E N G T H ,A N D C H A R G E D I S T R I B U T I O N O F T H EC O M M O N S E D I M E N T A R Y M I N E R A L S

Figure 1 shows the crystal lattice structures of the fourmost common sedimentary mineral types. The com-mon nonclay minerals have a directionally neutral

internal charge distribution. Positive and negativecharges are equal on the angstrom scale within themineral. Contacts between nonclay mineral particlesare on the much larger micron scale and therefore haveno net electrostatic charge. Adjacent nonclay mineralparticles and those in direct contact have no net elec-trostatic repulsive forces between them.Sedimentary clay minerals all possess a layered

structure of dominantly silicon-centered tetrahedraand aluminum-centered octahedra as shown in Figure1. The positively charged (�) aluminum, silicon, and

Holbrook, Phil, 2002, The Primary Controls over Sediment Compaction, in A. R.Huffman and G. L. Bowers, eds., Pressure regimes in sedimentary basins andtheir prediction: AAPG Memoir 76, p. 21–32.

22 H O L B R O O K

Figure 1. Crystal lattices of the four most common sedimentary mineral types. Quartz, muscovite (representative 2:1 clay), calcite,and halite (rock salt) are shown. All minerals have a net neutral internal change balance. The nonclay minerals cleave in alldirections presenting net neutrally changed mineral grain surfaces. The clay minerals cleave preferentially perpendicular to thec axis presenting a negatively charged oxygen anion layer at the clay particle surface. Adapted from Berry and Mason (1959).

other high positive valence ions are sandwiched be-tween negatively charged (�) oxygen layers.Clays cleave preferentially normal to their c axis ex-

posing large surfaces of negatively charged (�) oxygenanions. Sedimentary clay particles are thin plateletswith negatively charged faces and positively chargededges. The negative to positive charge ratio over theentire surface of sedimentary clay mineral platelets isvery large (Scott, 1963).

I O N I C B O N D F O R C E B A L A N C EW I T H I N M I N E R A L P A R T I C L E SA N D A C R O S S N O N C L A Y M I N E R A LG R A I N C O N T A C T S

Nonclayminerals resist compaction through theirmin-eral lattice and at direct grain contacts with other non-clay minerals. A given particle is in contact with itsneighbors over a fractional area of that particle. Parti-

The Primary Controls over Sediment Compaction 23

Figure 2. (a) Microscopic scale diagram showing the com-paction of a spherical grain matrix from 40 to 0% porosity.Solid mass is conserved through pressure solution compac-tion. During compaction minerals are dissolved preferen-tially at grain-grain contacts and reprecipitated in the localpore space. The microscopic examination of quartz grain-stones and intergranular cement look very much like Figure2a as porosity is reduced from 40 to 0%. (b) Sedimentaryparticles and forms of water in a low-porosity clay soil. F �free or bulk water; E � external or intercluster water; Im �Interlammelar or intercluster water; S � silt; K � kaolinite;I � illite; Sm � smectite (modified from Hueckel, 1992).(c) Bound water occurs adjacent to negatively charged claymineral surfaces. Two opposing negatively charged claymineral oxygen anionic surfaces shown at the atomic scale.Negative charge density diminishes with distance from theoxygen anionic mineral surface. Negative charge densityboth orients the nearby water dipole molecules and repelsother negatively charged clay mineral surfaces.

cle contact area limits are from zero in a particle fluidsuspension to 1.0 where intergranular porosity is re-duced to zero.Force balance across the fractional contact area is the

product of the number and strength of mineral ionicbonds. Harderminerals with stronger ionic bonds suchas quartz can bear a given load over a smaller area thansoft minerals like halite. Particle contact area varies inproportion to volumetric solidity. Both particle areaand solid volume reach 1.0 at the sedimentary rock’supper plastic compaction limit (rmax).

D I R E C T N O N C L A Y M I N E R A L G R A I NC O N T A C T P R E S S U R E S O L U T I O NC O M P A C T I O N M E C H A N I S M

Pressure solution (dissolution of grains at highlystressed intergranular contact points) is a major com-paction mechanism on a geologic time scale. On a geo-logic time scale the mineral grain matrix tends tobehave like an ideal plastic. Higher stress across neu-trally charged grain-grain contacts is gradually equal-ized through pressure solution and generally localreprecipitation.Mineral solubility in water can be related to hard-

ness via an inverse power law function (Carmichael,1982). All are fundamentally controlled by averagemineral ionic bond strength.Stress is everywhere proportional to strain in the

earth’s mechanical systems. The stress field is three-dimensional, and the coordination number of adjacentsolid load-bearing grains is n-dimensional. The load-ing limb and unloading limb stress/strain relation-ships for porous granular solids are multidimensional,that is, power-law functions.

C O M P A C T I O N O F N O N C L A Y G R A N U L A RS E D I M E N T S

Figure 2a shows a representative transition of neutrallycharged spherical grains from initial grain contact tocomplete consolidation. The initial depositional poros-ity of rounded sedimentary grains is about 40%. Theleft border of the diagram represents the point of initialgravitational grain-grain contact. Zero effective stressexists at initial contact. Physically this represents thesurface of the earth overlain by fluid or air. The right-most edge of Figure 2a is the plastic compaction limit(solidity � 1.0 at rmax).Figure 2a represents solid volume conserved com-

paction of rounded neutrally charged mineral grains.As the grains are forced together, minerals are dis-solved preferentially at the more highly stressed grain-

24 H O L B R O O K

grain contacts and reprecipitated in the nearby porespace. Net pore volume is indicated in white in Figure2a. Idealized pore shape changes progressively froman inverse sphere toward small isolated sphereswhereporosity reduction is accompanied by pressure solu-tion followed by local reprecipitation.Initial grain volume is not reduced from left to right

in Figure 2a. The compaction portrayed is accom-plished entirely by transporting mineral matter fromhigher stress grain-grain contacts into the availablepore space. Natural quartz grains have different initialshapes. Mineral grains may be fractured, rehealed, andrearranged during compaction. If there is no net min-eral volume added or subtracted, however, the volu-metric strain of the grain framework is necessarily thesame as the idealized case of Figure 2a.Quartz cement has the same mineral lattice struc-

ture and the same load-bearing capacity as the quartzgrain from which it was dissolved. Through pressuresolution the neutrally charged grain matrix increasesthe number of mineral ionic bonds at each grain-graincontact to support the average effective stress load. Theremainder of the total load is borne by pore-fluid pres-sure. Although an agglomerated grain matrix hassome finite porosity, the total confining load is sharedbetween (1) solid net neutrally charged mineral ionicbonds, (2), interparticle electrostatic repulsive forces,and (3) pore-fluid pressure.

S E D I M E N T A R Y C L A Y M I N E R A L P A R T I C L ES I Z E V S . E L E C T R O S T A T I C I N T E R P A R T I C L ER E P U L S I V E F O R C E R E L A T I O N S H I P

Most natural sediments and sedimentary rocks are amixture of clay and nonclay minerals. Electrostatic in-terparticle repulsion is an important factor in the com-paction of these natural sediments. Figure 2b shows amicroscopic representation of a low-porosity claydominated soil. The clay mineral packets shown (ka-olinite, illite, and smectite) have similar particle-size/shape-aspect ratios. Clays are commonly sedimentedwith varying percentages of neutrally charged siltgrains also shown. The net compaction resistance of anaturally deposited sedimentary mixture is themineralogically weighted average of the individualgrain compaction resistances (Holbrook et al., 1995).Figure 2c is a molecular scale representation of the

space between two adjacent clay mineral particles. Thewater dipoles are held tightly to the electrostaticallycharged clay mineral oxygen anionic surface as shown.Water dipoles oscillate more randomly as the negativecharge density originating from the clay mineral sur-face falls to zero.The different clay minerals shown in Figure 2b, c

have important internal structural and compositional

differences. These different minerals, however, havevery similar micromechanical properties that are all re-lated to particle size as indicated in Figure 3. An es-sentially 1:1 power-law relationship exists betweenclay mineral specific surface area and cation exchangecapacity (CEC). Clay mineral particle size decreases asspecific surface area and CEC increase, as shown inFigure 3.Both clay and nonclay mineral particle size at initial

sedimentation is determined by particle settling veloc-ity. The clay mineral CEC–particle-size continuumshown in Figure 3 is an extension of the general Rey-nolds number particle-size settling velocity continuumfor all particles that are settled gravitationally (Scott,1963).The dominant underlying control over clay mineral

electrostatic repulsive forces and mechanical proper-ties is also clay mineral particle size. This relationshipis set gravitationally at the moment of initial particlesettling agglomeration at the earth’s surface. Naturalmarine sediments with longer water columns bestdemonstrate the particle size, initial porosity, and in-terparticle repulsive force relationships. (Liquid limitis the water content at which a clay starts behaving likea liquid; water content is the weight of water in theclay divided by the weight of the dry clay solids.)

M I N E R A L - D E P E N D E N T G R A I N S I Z E –I N T E R P A R T I C L E R E P U L S I V E F O R C E –I N I T I A L P O R O S I T Y R E L A T I O N S H I P S

The zero effective stress compaction starting point forgranular sediments can be determined from porosity–mineralogy–particle-size relationships in marine sedi-ments at the sea floor (Shumway, 1960; Skempton,1970). The approximately 10 cm below the surface lineprovides a sample that is close to zero effective stress.Figure 4 shows the interrelationships between ob-served initial depositional porosity, laboratory-mea-sured liquid limit, and observed in-situ compactionalstress/strain relationships. (Liquid limit is the watercontent at which a clay starts behaving like a liquid;water content is the weight of water in the clay dividedby the weight of the dry clay solids.) Effective verticalstress is on the horizontal axis, and the two more com-mon measures of strain, void ratio and porosity, areshown on the vertical axis. Liquid limit is strongly cor-related to CEC (Nagaraj and Murthy, 1983). Thereforethe effective stress compactional relationships shownin Figure 4 are also particle-size dependent.Figure 5, adapted from Shumway (1960), shows the

average sediment particle diameter (left-hand axis)plotted on the phi scale (right-hand axis) vs. surfacedepositional porosity. The conversion from particle di-ameter (mm) to phi scale value (not to be confused


Figure 3. Specific surface area vs. CEC for various clay min-erals. This strong correlation suggests that the surfacecharge density of a clay mineral portrayed in Figure 2c is es-sentially an areal constant. Given this, the dominant under-lying control over clay mineral physical properties is mostlikely average clay mineral particle size. Taken from Revil etal. (1997), reprinted with permission from the GeologicalSociety Publishing House. Numbers in parentheses refer toreferences, which are listed in Revil et al. (1977).

with porosity) is phi� �log(particle diameter)/log(2)(Bates and Jackson, 1987). The figure shows a system-atic semi–log-linear relationship between almost pureclay mineral deposits with more than 80% depositionalporosity and an average 2 lm particle size to an almostpure quartz sand deposit with an average particle sizeof more than 500 lm and a depositional porosity ofonly 40%. The highly correlated depositional porosityand particle-size distributions of the near-surface ma-rine sediment are controlled by mineral particle set-tling velocity.The grain density of quartz and clay are approxi-

mately equal, and the effective stress gravitational loadin the uppermost meter of the sea floor is very low.The difference between 80% porosity for fine clay de-posits and 40% porosity for medium quartz sand de-posits is due to the repulsive force between individualclay particles. The interparticle repulsive force is weakbut persistent with increasing effective stress compac-tion as indicated in Figure 4. The Figure 5 particle-sizecrossplot coincides with the 10 cm line in Figure 4.Nagaraj and Murthy (1983) later explained Skemp-

ton’s entire compactional relationship mechanically

in terms of negatively charged mineral surface area.The CEC is essentially a direct measure of clay min-eral negatively charged (�) oxygen anion surfacearea. The average electrostatic repulsive force be-tween clay particles is also proportional to CEC. Thecompactional relationships of all clay minerals werenormalized to the same curve based upon their av-erage CEC.Adjacent particles in a sedimentary layer have fallen

through the same water medium at about the samespeed. Clay particles in the sand size range have pro-portionally lower external surface area and thereforelower average interparticle repulsive force. Gradedbedding places grains of like size and interparticle re-pulsive force adjacent to each other. Particle size andnegative surface charge area work together in the ma-rine environment to generate the strong interdepen-dent relationship shown in Figures 3, 4, and 5.

G E N E R A L M I N E R A L O G I C S T R E S S / S T R A I NL O A D I N G F O R G R A N U L A R S O L I D S

Here, voumentric strain is represented by the comple-ment of porosity (1 � �), termed “solidity.” Solidityis assumed to follow a power law effective stress re-lation of the form proposed by Baldwin and Butler(1985). Figure 6 (adapted from Holbrook, 1999) showsthe volumetric effective stress loading-limb compac-tional relationships for natural single mineral sedi-mentary deposits over the entire depth range ofdrilling interest. The loading-limb stress/strain rela-tionships are global in nature, dependent principallyupon mineralogic composition (Holbrook, 1995).The effective stress compactional relationships were

measured in situ considering overburden and pore-pressure force balance (Terzaghi, 1923). The volumetriceffective stress theorem (Carroll, 1980)was also honored(Holbrook, 1999). These macromechanical stress/strainrelationships are a composite of the micromechanicalrelationships (Figures 1–5) previously discussed. Thecomposite of many microscale power-law relationshipsresults in a macro–power-law relationship.The four neutrally charged nonclay minerals—

quartz, calcite, anhydrite, and halite—have subparallelpower-law loading-limb effective stress/strain coeffi-cients (�). These neutrally charged single-mineralstress/strain relationships are offset from each other inproportion to their plastic compaction intercepts(rmax). The compaction intercept (rmax) is positivelyrelated to mineral hardness and inversely related tomineral solubility (Table 1). All three are measures ofthe average interionic bond strength of these sedimen-tary minerals.Naturally sedimented clay minerals also have

power-law loading-limb effective stress/strain coeffi-

26 H O L B R O O K

Figure 4. Relationships of in-situcompactional effective stress(kg/cm2) to strain (void ratio)from many different basinsworldwide. Compactional strainis proportional to the laboratorymeasured liquid limit (LL) of thereconstructed solid. The liquidlimit is fundamentally controlledby clay mineralogy and averageclay content and can be relatedto depositional porosity approxi-mately 10 cm below the seafloor. Taken from Skempton(1970), reprinted with permis-sion from the Geological SocietyPublishing House.

cients (�) and a plastic compaction intercept (rmax). Asshown in Figure 6, the (rmax) compaction intercept iswell below granular quartz and above granular calcite.This corresponds to clay mineral ordinal rankings be-tween quartz and calcite on the hardness and solubilityphysical property scales. This supports the conclusionthat (rmax) is a mineralogic compactional stress/strainphysical property.The average sedimentary claystone effective stress/

strain coefficients (�) is distinctly different from thefour neutrally charged minerals: quartz, calcite, an-

hydrite, and halite. So long as clay minerals have wa-ter-wet surfaces, the additional electrostatic repulsiveforces between adjacent clay particles are effective.These electrostatic repulsive forces tend to oppose di-rect grain-to-grain contact, especially during initialcompaction, which, in comparison to other sedimenttypes, leads to the lower compaction coefficients (�)and the greater ductility observed in natural clay sed-iments and claystones.This clay mineral repulsive force particle-size effect

is shown by Skempton (1970) (Figure 4), Shumway

Figure 5. Mean sediment diameter vs. porosity forsurface marine sediments taken from Shumway(1960); reprinted with permission from the Societyof Exploration Geophysicists. Samples are from 10cm below the sea floor. Depositional porosity rangesuniformly from 40% for (0.5 mm) quartz sands to90% for a very fine (0.001 mm) sedimentary clay.Porosity at very low effective stress is a function ofparticle size and clay mineral interparticle repulsion.

1.0

.50

.250

.125

.0625

.031

.016

.008

.004

.002

.001.90 .80 .70 .60 .50 .40 .30

Depositional Porosity at very low Effective Stress

Mea

n S

edim

ent d

iam

eter

(m

illim

eter

s)

.80 .70 .60 .50 .40 .30


(1960) (Figure 5), and rationalized by Nagaraj andMurthy (1983). This relative mineralogic compactionalrelationship is also observed in corresponding non–force-balanced depth vs. porosity relationships asshown subsequently.

T H E G R A N U L A R Q U A R T Z V S . C L A Y S T O N EG R A V I T A T I O N A L C O M P A C T I O NC R O S S O V E R

The porosities of gravitationally compacted granularquartz sediments and clay-rich sediments cross overeach other in virtually all subsiding basins. Figure 7shows average quartz sandstone and shale porosity vs.depth relationships from a well in the Gulf Coast.Above 2000 ft in Figure 7, clay-rich sediments havehigher porosity than quartz sands. Below 2000 ft eachof the two mineralogic end members continue alongtheir own compaction gradients, and the curves di-verge with increasing depth. Each mineralogic endmember follows its own smooth continuous compac-

tion vs. depth trend throughout the burial historyshown.Figure 6 has a corresponding mineralogic effective

stress/strain crossover at about 300 psi and 35% po-rosity. With increasing effective stress the quartz grain-stone and worldwide claystone compactional stress/strain relationships diverge as they do in Figure 7.Skempton’s Figure 4 data also indicate a convergencein this same effective stress/strain region. Figures 4and 6 show the effective stress data and force-balancedstress/strain relationships. Compactional porosity vs.depth data such as shown in Figure 7 correspond tothe convergence and crossover shown on the effectivestress functions of Figures 4 and 6.This crossover occurs because of the claystone in-

terparticle repulsive force. Quartz grainstones settle tothe sea floor with about 40% porosity or less. Depend-ing on particle size and related interparticle repulsiveforce, clay particles settle with an initial porosity of 50to 95% (Lambe and Whitman, 1969). The individualquartz grains are much harder than clay minerals andhave high compaction resistance. Claystone electrostaticinterparticle repulsion and the minerals themselves aresofter by comparison and therefore compact more eas-ily. The primary controls over sediment compaction arethese mineral-specific physical properties.If effective stress were properly accounted for in

Figure 7, the claystone points would plot on the world-wide claystone stress/strain power-law relationshipwhether they are overpressured or not. The samewould be true of the quartz grainstone data points. Thedashed line extensions of compaction trends in Figure7 are entirely speculative. They do not consider thechanging overburden load conditions nor do they con-sider the load borne by pore pressure. Plotting depthagainst porosity makes no mechanical sense, yet it isdone frequently.The power-law effective stress and strain axes of

Figure 6 account for sediment compaction or lack of itin a mechanically sensible way. The compaction cross-over, so-called normal compaction, and overpressuredretracement are both related to average effective stress.Figure 6 explains both compaction features shown inFigure 7 as a simple mechanical system that is depen-dent on mineral physical properties.

L O A D I N G L I M B C O M P A C T I O NV I S U A L I Z A T I O N

Figure 8 shows the three most common mineralogicend members as a stacked ternary diagram. The ver-tical axis of this diagram is effective stress on a loga-rithmic scale. The logarithmic scale linearizes the

% Strain (1. – φφφφ)

σave = σ

σ

m ax (1.0 – Φ) α

End-member claystones(Baldw in & Butler, 1 985)

Clean (rounded quartz)Gulf C oast sandstones

Calcite G ra instonesAnhydrite

H alite1 00

1 00 ,0 00

10 ,000

100806040 50 70 90

1,000

Eff

ecti

ve S

tres

s (p

si)

in situ

ave

Figure 6. The first fundamental in-situ stress/strain relation-ship for the five most common single mineral sedimentaryrocks. Average effective stress is borne by mineral ionicbonds and sedimentary clay mineral interparticle repulsiveforce. Average effective stress (rave) is calculated directlyfrom volumetric in-situ strain (1.0 � �) for single mineraland mixed mineral sedimentary rocks. The power-law effec-tive stress/strain coefficients (rmax and �) are sedimentarymineral grain properties that are independent of geologicage, depth, and pressure. The power-law compaction expo-nent (�) incorporates interparticle repulsion in proportionto clay volume. Adapted from Holbrook (1999).

28 H O L B R O O K

power-law effective stress/strain relationship on thevertical scale. The horizontal quartz-calcite-clay planeis linear. Isoporosity lines are drawn on the surface ofthe two visible bimineral surfaces shown. The lime-stone-claystone continuum is on the left face of the di-agram, and the quartz grainstone-claystone continuumis on the right.The data supporting this diagram are about 300 con-

tinuous petrophysical logs from Normal Fault RegimeBasins worldwide (Holbrook, 1996). In-situ–measuredporosity, mineralogy, and effective stress were cali-brated at each location. Porosity was estimated from

an appropriately transformed density or resistivity log.Lithostratigraphic sequence type, limestone-claystone(L), or quartz grainstone-claystone (S) were assignedby an operator using local knowledge. Relative clayfraction (0 to 1.0) was assigned based upon a baseline-normalized gamma-ray log. Holbrook et al. (1995) de-scribes these procedures.The features and relative compactional relation-

ships shown in Figure 8 were observed on all 300 pe-trophysical logs and are reasoned to be global innature. The limestone-claystone face (L) of Figure 8 ischaracterized by a high-gamma-ray–high-porosity re-lationship. The quartz grainstone-claystone face (S) ofFigure 8 is characterized by a high-gamma-ray–low-porosity relationship. These two lithostratigraphic se-quence types produce parallel and hourglass patternson petrophysical log suites as shown in Figure 9.

T H E C O M P A C T I O N C R O S S O V E R I N T H EQ U A R T Z G R A I N S T O N E - C L A Y S T O N EL I T H O S T R A T I G R A P H I C S E Q U E N C E

The isoporosity lines in Figure 8 are traces of isopo-rosity surfaces that pass through the ternary mixedmineralogy solid. This three mineral idealization isreasonably close to the gross mineralogic compositionof many sedimentary rocks. Many of the patterns thatare observed on petrophysical logs are explained bythese mineralogic power-law linear compactional re-lationships.The quartz grainstone-claystone compaction cross-

over occurs at about 300–500 psi on the right face ofFigure 8. The 35% isoporosity line is parallel with ef-fective stress on the quartz grainstone-claystone sur-face. This parallel stress/strain relationship is thephysically representative equivalent of a compactioncrossover.Claystones compact more than quartz grainstones

at effective stresses above 500 psi. This corresponds tothe porosity divergence observed in the depth functionshown in Figure 7. Any occurrence of calcite in a quartz

0 10 20 30 40 50 60 70

TOP GEOPRESSUREZONE

POROSITY (percent)

0

4000

8000

12,000

16,000

0

1000

2000

3000

4000

5000

100 90 80 70 60 50 40 30

SOLIDITY (1 .- φφφφ) STRAIN (percent)Increas ing STRAIN toward the plastic limit

QUARTZSANDSTONE

CLAYSTONE

Dep

th (

feet

)

Dep

th (

met

ers)

in-situ

Figure 7. Quartz sand and shale porosity vs. depth compac-tion functions in the Gulf Coast. Modified from Stuart(1970). Shales have higher � plastic compressibility than doquartz sandstones. The two mineral-specific in-situ compac-tion curves cross at about 1000 ft.

Table 1. Power-Law Compaction Coefficients, Hardness, and Solubility for Naturally Sedimented Single-Mineral Grainstonesand End-Member Claystones*

Mineral (or Rock) rmax (psi) Plastic Limit � Compaction Exponent Hardness (mhos) Solubility (ppm)

Quartz sand 130,000 13.849 7.0 6End-member claystone 18,461 9.348 3.0� 20Calcite sand 12,000 13.637 3.0 120Anhydrite 1585 20.646 2.5 3000Halite 85 32.564 2.0 350,000

*Holbrook et al. (1995).


grainstone-claystone lithostratigraphic sequence tendsto reduce rock porosity. Calcite has significantly lowerload-bearing capacity than either quartz or sedimen-tary clays.

Granular Quartz–Calcite Mineralogic Mixtures

Thin isolated limestones commonly occur in domi-nantly quartz grainstone-claystone stratigraphic se-quences. Where these thin limestones occur, theyinvariably have lower porosity than the neighboringquartz grainstones. This is because calcite (hardness 3)has much lower compaction resistance than quartz(hardness 7). The calcite-quartz mineralogic contin-uum is on the back face of the diagram shown in Figure8, and the expected porosities are shown along the8000 psi edge of the diagram.

Calcite cement in quartz grainstones invariably re-duces porosity. This too is a natural consequence of thesofter calcite’s low compaction resistance. Whether thecalcite mineral is a secondary deposit or not, the softercalcite would yield to the much harder quartz uponloading. Should a calcite grain be recrystallized or betransported from high to low stress locations by pres-sure solution, calcite would appear to be cement. Themechanical properties of the minerals present should beconsidered using the grain-cement nomenclature com-monly used to describe relative compaction.The calcite mineral lattice has the same load-bearing

capacity whether it be recognized as grain or cement.The same is true of quartz. Minerals bear the averageeffective stress load through their crystalline lattice ir-respective of their geometry. The whole load is borneby the whole rock that is composed of these minerals.

StrainStrain

1510

5

5

10

8000 psi

4000 psi

2000 psi

1000 psi

300 psi

POROSITYLINES

30

30

35

15

10

15

20

20

36

25

20

15

10 25

30

5

End MemberEnd MemberCLAYSTONECLAYSTONE

QUARTZ SANDSTONEQUARTZ SANDSTONE(rounded)(rounded)

LIMESTONELIMESTONE

35

25

1.0 - Porosity

Figure 8. Ternary limestone-clay-stone-quartz grainstone mineral-ogic compaction resistancediagram. The vertical axis of thisdiagram is effective stress on alogarithmic scale. Isoporosity linesare drawn on the surface of thetwo lithostratigraphic continuashown. The limestone-claystonecontinuum is on the left face ofthe diagram, and the quartz grain-stone-claystone continuum is onthe right. Figure taken from Hol-brook, 2001.

30 H O L B R O O K

Limestone-Claystone Lithostratigraphic Sequences

Calcite grainstones, chalk, and marl are rock typesin the limestone-claystone lithostratigraphic contin-uum. Porosity is positively correlated to clay contentin these sequences. Clay minerals are slightly harderthan calcite so clay minerals have a slightly higherload-bearing capacity than calcite. Clay mineral inter-particle repulsion, however, accounts for most of theincreased porosity with respect to calcite. Much of thewater in the marl pore space is probably electrostati-cally bound as shown in Figure 2c.Pore pressure in limestone-claystone lithostrati-

graphic sequences can be significant. Loads borne byfluids are the other physical control of sedimentaryrock compaction.

L O G E X A M P L E O F L I T H O S T R A T I G R A P H I CC O N T R O L S O V E R C O M P A C T I O N O FS E D I M E N T A R Y R O C K S

Figure 9 is a composite petrophysical log that showsboth lithostratigraphic sequence types and their rep-resentative log patterns. Track 3 is a lithologic columnshowing fractional clay volume as an offset dash pat-tern. Quartz grainstone volume is shown by the dotpattern. Calcite volume is shown as a limestone blockpattern. Porosity indicated as either boundwater (grayshade) or free water (white) is the remainder of wholerock volume in track 3.The raw gamma-ray and raw resistivity logs in

tracks 1 and 2 move parallel in quartz grainstone-clay-stone lithostratigraphic sequences. They move oppo-

Figure 9. Composite wire-lineand real-time log showing twolithostratigraphic sequence types.The quartz grainstone-claystonelithostratigraphic sequence hasthe opposite log pattern. Theraw gamma-ray and raw resistiv-ity logs in tracks 1 and 2 moveparallel in quartz grainstone-clay-stone sequences. They move op-posite in an hourglass pattern inlimestone-claystone lithostrati-graphic sequences. Figure takenfrom Holbrook, 1995.


site in an hourglass pattern in limestone-claystonelithostratigraphic sequences. This is the individual bedscale manifestation of the general power-law compac-tional relationships portrayed in Figures 6 and 8. Be-low the compaction crossover, quartz grainstones aremore compaction resistant than claystones, and calciteis less compaction resistant than quartz and claystones.The parallel and hourglass log patterns observed onmost petrophysical logs are related to these (Figures 6,8) mineralogic compaction resistance relationships.

C O N C L U S I O N S

The compaction of sedimentary particles is explainedin terms of mineral particle physical properties. Theintraparticle load is borne within the mineral’s latticeand across electrostatically neutral mineral grain con-tacts. Compaction of electrostatically neutral particlesoccurs at each of the n contacts with other particles. Apower-law stress/strain relationship captures bulkcompaction of n-coordinated particulate solids.The repulsive electrostatic field between negatively

charged clay mineral surfaces is also load bearing. Themagnitude of this repulsive field is power-law relatedto clay particle surface area within a rock volume (Fig-ure 3). Interparticle repulsive force is also a power-lawfunction of distance between clay mineral surfaces(Figure 2c). The sum of these clay mineral power-lawfunctions and the electrostatically neutral power-lawfunction is a composite power-law function.The net effects of interparticle and intraparticle load

types on volumetric in-situ strain (1.0 � �) are cap-tured with two power-law compactional stress/straincoefficients (rmax and �). The power-law compactioncoefficients for the five most common sedimentaryminerals were measured from in-situ strain after prop-erly accounting for effective stress. Peak granular solidcompaction resistance (rmax) is positively correlated tomineral hardness and negatively correlated to mineralsolubility. All three are power-law relationships.End-member sedimentary claystones have a signifi-

cantly lower � value than the electrostatically neutralminerals. The unusually high 40–95% initial porosityof clay-rich sediments is power-law related to the logof average sediment particle size. Whole rock com-paction is the volume-weighted average (rmax and �)of its individual mineral specific stress/strain coeffi-cients.This general mineralogic (rmax and �) sedimentary

rock stress/strain compactional relationship has beentested in more than 300 wells in normal fault regimebasins worldwide. Large-scale compaction trends (Fig-ures 6, 7) are explained by this force-balanced stress/

strain relationship. Observed sedimentary bed-scalecompactional differences (Figures 4, 8, 9) are also ex-plained by the same compactional relationship.The entire load placed upon a sedimentary rock

volume is borne by interparticle repulsion, intraparti-cle resistance, and pore-fluid pressure. Intraparticlecompaction resistance is related to rmax and hardness.Interparticle repulsion contributes additional compac-tional resistance to � in proportion to clay mineral sur-face area. Mineral ionic bond strength and claymineralinterparticle repulsion are believed to be primary con-trols over sediment compaction.

A C K N O W L E D G M E N T S

Figure 9 is reprinted with permission of the Society of Pro-fessional Well Log Analysts.


Baldwin, B., and C. O. Butler, 1985, Compaction curves:AAPG Bulletin, v. 69, no. 4, p. 622–626.

Bates, R. L., and J. Jackson, eds., 1987, 3d ed., Glossary ofgeology: Falls Church, Virginia, American Geological In-stitute, 788 p.

Berry, L. G., and B. Mason, 1959, Mineralogy, concepts, de-scriptions, determinations: San Francisco and London,W. H. Freeman and Company, 630 p.

Carmichael, R. S., 1982, Handbook of physical properties ofrocks: Boca Raton, CRC Press, 404 p.

Carroll, M.M., 1980, Compaction of dry or fluid-filledporousmaterials: Journal of Engineering Mechanics Division,Proceedings of the American Society of Civil Engineers,v. 106, no. EM5, p. 969–990.

Holbrook, P. W., 1995, The relationship between porosity,mineralogy and effective stress in granular sedimentaryrocks: Society of Professional Well Log Analysts 36th An-nual Logging Symposium, paper AA, 14 p.

Holbrook, P. W., 1996, The use of petrophysical data for wellplanning, drilling safety and efficiency: Society of Profes-sional Well Log Analysts 37th Annual Logging Sympo-sium, paper X, 14 p.

Holbrook, P. W., 1999, A simple closed-form force}balancedsolution for pore pressure, overburden and the principaleffective stresses in the earth: Journal of Marine and Pe-troleum Geology, v. 16, p. 303–319.

Holbrook, P. W., 2001, Pore pressure through Earth mechan-ical systems: Houston, Texas, Force Balanced Press, 135 p.

Holbrook, P. W., D. A. Maggiori, and R. Hensley, 1995, Real-time pore pressure and fracture pressure determinationin all sedimentary lithologies: Society of Petroleum En-gineers Formation Evaluation, v. 10, n. 4, p. 215–222.

Hueckel, T. A., 1992, Water-mineral interaction in hygro-mechanics of clays exposed to environmental loads: amixture-theory approach: CanadianGeotechnical Journal,v. 29, p. 1071–1086.

Lambe, T. W., and R. V. Whitman, 1969, Soil mechanics: NewYork, John Wiley & Sons, 553 p.

Nagaraj, T. S., and B. R. S. Murthy, 1983, Rationalization ofSkempton’s compressibility equation: Geophysique, v. 33,no. 4, p. 433–443.

Revil, A. P., A. Pezard, and M. Darot, 1997, Electrical con-ductivity, spontaneous potential and ionic diffusion in po-rous media, in M. A. Lovell and P. K. Harvey, eds.,Developments in petrophysics: Geological Society SpecialPublication 122, p. 253–275.

Scott, R. F., 1963, Principles of soil mechanics: Reading, Mas-sachusetts, Addison-Wesley, 550 p.

Shumway, G., 1960, Sound speed and absorption studies ofmarine sediments by resonance method—part II: Geo-physics, v. 25, p. 659–682.

Skempton, A. W., 1970, The consolidation of clays by gravi-tational compaction: Quarterly Journal of the GeologicalSociety of London, v. 125, pt. 3, p. 373–411.

Stuart, C. A., 1970, Geopressures: Proceedings of the SecondSymposium on Abnormal Subsurface Pressure, 121 p.

Terzaghi, K. von, 1923, Die Berechnung der Durchassigkeits-ziffer des Tones aus dem Verlauf der hydrodynamischenSpannungserscheinungen: Sitzungsberichte Akademie derWissenschaften, Vienna,Mathematisch-Naturwissenschaft-liche Klasse, abt. 2a, v. 132, p. 125–138.

32 H O L B R O O K

33

4Critical-Porosity ModelsJack DvorkinStanford University,Stanford, California

Amos NurStanford University,Stanford, California

A B S T R A C T

Anomalous velocity and porosity are common indicators of abnormal pore pressure. Therefore, it isimportant to be able to link velocity to porosity and rock texture in a rational, first-principle–basedmanner. The critical-porosity concept allows for building such rock physics models. Critical porosity isthe porosity above which the rock can exist only as a suspension. In sandstones the critical porosity is36–40%, that is, the porosity of a random close pack of well-sorted rounded quartz grains. This packis commonly the starting point for the formation of consolidated sandstones. Using this starting pointfor effective medium modeling, rational models can be built that relate velocity to porosity dependingon rock texture and lithology.

I N T R O D U C T I O N A N D C R I T I C A L - P O R O S I T YC O N C E P T

Porosity is one of the desired reservoir parameters thatcan be used, for example, for reserve estimation, res-ervoir simulation, and pore-pressure prediction. Der-ivation of porosity from such seismic observableproperties as impedance or velocity requires a veloc-ity-porosity relation. Such relations vary depending onlithology and rock texture. To appreciate the effect oftexture on velocity, consider Figure 1, where P- and S-wave velocity are plotted vs. the total porosity for rela-tively clay-free gas-saturated sands at the differentialpressure (confining minus pore pressure) of about 20MPa.All sandstone data points in Figure 1 represent

rock that is mainly quartz with clay content not ex-ceeding 10%. Yet, in the same porosity range, the

Dvorkin, Jack, and Amos Nur, 2002, Critical-Porosity Models, in A. R. Huffmanand G. L. Bowers, eds., Pressure regimes in sedimentary basins and theirprediction: AAPG Memoir 76, p. 33–41.

P-wave velocity may span from 1.5 to more than 3km/s, and the S-wave velocity from 1 to more than 2km/s. One apparent reason for this large velocity dif-ference between mineralogically similar samples isrock texture—the arrangement of the sand grains andpore-filling material in the pore space. In the sand-stone samples from S. Strandenes (1991, unpublisheddata), the grains appear to be slightly cemented attheir contacts, whereas the samples from Blangy(1992) are friable sands.The velocity in the well-log data (Dvorkin et al.,

1999b) is even smaller than that in the friable sands.These rocks are elastically similar to a handmade mix-ture of Ottawa sand and kaolinite where the small ka-olinite particles fill the pore space without noticeablyaffecting the velocity.We can create rational effective medium models to

explain and predict the observed velocity-porosity be-havior by examining the textural nature of sandstones.Consider Figure 2a where the compressional modulus(bulk density times the compressional-wave-velocitysquared) of water-saturated clean sandstones andquartz marine sediment (suspensions) is plotted vs.

34 D V O R K I N A N D N U R

Figure 1. (a) P- (Vp) and (b) S-wave velocity (Vs) in rocks withgas at 20 MPa differential pres-sure. Circles represent laboratorydata obtained on high-porosityfast (S. Strandenes, 1991, un-published data) and slow(Blangy, 1992) sands; both datasets are from the North Sea. Graysymbols are from a Gulf Coastgas well. The filled square is fora handmade mixture of Ottawasand and 10% kaolinite (Yin,1993). Clay content for thesedata does not exceed 10%.

Figure 2. (a) Compressionalmodulus vs. porosity in cleanwater saturated sandstones andmarine sediment. (b) Compres-sional and shear moduli ofroom-dry sandstones vs. poros-ity. The data used are discussedin Nur et al. (1998).

porosity. The porosity of 36–40% is the point wherethe modulus-porosity trend abruptly changes. In thelower porosity domain, the stiffness of the sandstoneis determined by the framework of contacting quartzgrains. In the higher porosity domain, the grains arenot in contact anymore and are suspended in water. Inthis case, the stiffness of the sediment is determinedby the pore fluid.We call this threshold porosity “critical porosity”

(Nur et al., 1998). The rocks where the solid phase isspatially continuous and dominates the stiffness of therock have porosity that is smaller than the critical po-rosity. This fact is illustrated in Figure 2b where thecompressional and shear moduli of many sandstonesamples (room dry at 30–40 MPa differential pressure)are plotted vs. porosity.

The critical-porosity concept is valid not only forsandstones but also for other natural and artificialrocks. An example is given in Figure 3 where the com-pressional modulus is plotted vs. porosity for crackedigneous rocks and pumice (Nur et al., 1998). In the firstcase, the critical porosity is as small as 6%, whereas inthe second case it reaches 70%. The reason is the pe-culiar microstructural topology of the rocks under ex-amination. The igneous rocks are permeated by cracksthat percolate and make the solid phase lose its spatialcontinuity at very small porosity. In the pumice, thehoneycomb structure of the solid ensures its spatialcontinuity at high-porosity values. Nur et al. (1998)summarize the critical-porosity values for variousrocks as shown in Table 1. In the following sections,we introduce the critical-concentration concept andde-

Critical-Porosity Models 35

Figure 3. Compressional modulus vs. porosity in cracked ig-neous rocks and pumice. The data used are discussed inNur et al. (1998).

Table 1. Critical-Porosity Values*

Material Critical Porosity

Sandstones 40%Limestones 40%Dolomites 40%Pumice 70%Chalks 65%Rock salt 40%Cracked igneous rocks 5%Oceanic basalts 20%Sintered glass beads 40%Glass foam 90%

*Data from Nur et al. (1998).

Figure 4. (a) Porosity, (b) elastic moduli, and (c) dynamicPoisson’s ratio vs. volumetric clay content in Ottawa sandmixed with kaolinite at room-dry conditions and 20 MPadifferential pressure (modified from Yin, 1993).

scribe several effective medium models that are basedon the critical-porosity concept.

C R I T I C A L - C O N C E N T R A T I O N C O N C E P T

The critical-porosity concept leads to the “critical-concentration” concept that Marion (1990) and Yin(1993)used todescribe thepropertiesof sandswithshale.Consider the experimentaldata fromYin (1993)obtainedon synthetic rocksmade bymixingOttawa sand and ka-olinite at room-dry conditions. The volumetric clay con-tent in the samples ranged from 0 to 100%.The total porosity at 20 MPa differential pressure is

plotted vs. the volumetric clay content in Figure 4a.

The two end members of the data set are the porosityof Ottawa sand at zero clay content and porosity ofkaolinite at 100% clay content. The porosity of the mix-ture reaches its minimum at the point where the vol-umetric concentration of clay equals the porosity ofOttawa sand (which is close to the critical porosity forsandstones). This clay content is called “critical clayconcentration.”The critical concentration affects not only the total

porosity but also the dynamic (velocity-derived) elasticmoduli of the mixture (Figure 4b). The elastic moduliof the mixture are maximum at the critical concentra-tion and decrease as the clay content increases or de-creases from the critical-concentration value. Dynamicdry Poisson’s ratios behave in a similar way (Figure 4c).The elastic properties of the synthetic mixture of Ot-

tawa sand and kaolinite are plotted vs. the total po-rosity in Figure 5. The nonuniqueness of the elasticmoduli, and, especially, Poisson’s ratio in the cross-plots is due to the grain-scale texture of the rock.


Figure 5. (a) Elastic moduli and(b) dynamic Poisson’s ratio vs.total porosity in room-dry Ottawasand mixed with kaolinite atroom-dry conditions and 20 MPadifferential pressure (modifiedfrom Yin, 1993). The arrowsshow increasing clay content.

This effect has to be considered when examiningwell-log data. In Figure 6a and b, we plot the bulkdensity and P-wave impedance vs. the gamma-ray val-ues for a well in Colombia (M. Gutierrez, 1998, per-sonal communication). Different trends are apparentfor the low–gamma-ray and the high–gamma-raybranches. This effect depends on the rock’s microstruc-ture and results in nonuniqueness as the P-wave im-pedance is plotted vs. the bulk density and porosity(Figure 6c, d). Being aware of the physical reason un-derlying these nonunique crossplots allows the log an-alyst to separate the trends and arrive at accurateimpedance-porosity transforms.

M O D E L S F O R H I G H - P O R O S I T YS A N D S T O N E S

The initial building point for effective mediummodelsthat describe high-porosity sandstones should be un-consolidated well-sorted sand, as proposed by thecritical-porosity concept. In mathematical modeling,such sand is approximated by a dense pack of identicalelastic spheres (Figure 7).The contact-cement model (Dvorkin and Nur, 1996)

assumes that porosity decreases from the initial criti-cal-porosity value due to the uniform deposition of ce-ment layers on the surface of the grains. This cementmay be diagenetic quartz, calcite, or reactive clay (suchas illite). The diagenetic cement dramatically increasesthe stiffness of the sand by reinforcing the grain con-tacts (Figure 8). The mathematical model is based on arigorous contact-problem solution by Dvorkin et al.(1994).In this model, the effective bulk (Kdry) and shear

(Gdry) moduli of dry rock are

K � n(1�� )M S /6dry c c n (1)G � 3K /5�3n(1�� )G S /20dry dry c c s

where �c is critical porosity; Kc and Gc are the bulkand shear moduli of the cement material, respectively;Mc � Kc �4Gc/3 is the compressional modulus of thecement; and n is the coordination number (averagenumber of contacts per grain is 8–9). The variables Snand Ss are

2S � A (K )� � B (K )� � C (K )n n n n n n n

�1.3646A (K ) � �0.024153Kn n n

�0.89008B (K ) � 0.20405Kn n n

�1.9864C (K ) � 0.00024649Kn n n

2S � A (K , m )� � B (K , m )� � C (K , m )s s s s s s s s s s

�2 2A (K , m ) � �10 (2.26m � 2.07ms s s s s20.079m �0.1754m �1.342s s� 2.3)Ks

2B (K , m ) � (0.0573m � 0.0937ms s s s s20.0274m �0.0529m �0.8765s s� 0.202)Ks

�4 2C (K , m ) � 10 (9.654m � 4.945ms s s s s20.01867m �0.4011m �1.8186s s� 3.1)Ks

K � 2G (1�m )(1�m )/[pG (1�2m )]n c s c s c

K � G /(pG )s c s

0.5� � [(2/3)(� ��)/(1�� )]c c

m � 0.5(K /G �2/3)/(K /G �1/3)c c c c c


Figure 6. Well-log data. (a) Bulk density and (b) P impedance vs. gamma ray; P impedance vs. (c) bulk density and (c) totalporosity.

m � 0.5(K /G �2/3)/(K /G �1/3)s s s s s

where Ks and Gs are the bulk and shear moduli of thegrain material. A detailed explanation of these equa-tions and their derivation are given in Dvorkin andNur (1996).The contact-cement theory allows one to accurately

model the velocity in fast high-porosity sands (Figure9). One may find that the contact-cement model is ap-propriate for describing sands in high-energy deposi-tional environments where the grains are well sortedand not covered by organic matter.

Figure 7. Approximating sand by a sphere pack. Micropho-tographs of (a) well-sorted sand and (b) a glass-bead pack.


The friable sand model (Dvorkin and Nur, 1996) as-sumes that porosity decreases from the initial critical-porosity value due to the deposition of the solid matteraway from the grain contacts. Such a diagenetic processof porosity reduction may correspond to deterioratinggrain sorting. This noncontact additional solid matterweakly affects the stiffness of the rock (Figure 8b).The theoretical effective-medium model connects

two end points in the elastic-modulus-porosity plane.One end point is at critical porosity. The elastic moduliof the dry rock at that point are assumed to be the sameas of an elastic sphere pack subject to confining pres-sure. These moduli are given by the Hertz-Mindlin(Mindlin, 1949) theory:

12 2 2n (1�� ) G 3cK � PHM � �2 218p (1�m)

(2)12 2 25�4m 3n (1�� ) G 3cG � PHM � �2 25(2�m) 2p (1�m)

where KHM and GHM are the bulk and shear moduliat critical porosity �c, respectively; P is the differential

pressure (total confining pressure minus pore pres-sure); G and m are the bulk and shear moduli of thesolid phase, and its Poisson’s ratio, respectively; and nis the coordination number.The other end point is at zero porosity and has the

bulk (K) and shear (G) moduli of the pure solid phase.These two points in the porosity-moduli plane are con-nected with the curves that have the algebraic expres-sions of the lower Hashin-Shtrikman (1963) bound(bulk and shear moduli) for the mixture of two com-ponents: the pure solid phase and the phase that is thesphere pack. The reasoning is that in unconsolidatedsediment, the softest component (the sphere pack) en-

Figure 8. Schematic depiction ofthree effective-medium modelsfor high-porosity sandstones andcorresponding diagenetic trans-formations. (a) Contact-cementmodel, (b) friable sand model,and (c) constant-cement model.

Figure 9. P-wave velocity vs. po-rosity. (a) Water-saturated-rockdata based on laboratory mea-surements of fast high-porosityNorth Sea sandstones by S.Strandenes (1991, unpublisheddata). Solid black circles are forvery clean samples. Solid graycircles are for samples with someclay. The curves are from thecontact-cement model for purequartz grains with quartz andclay cement. (b) Well-log data.The clean sand interval is satu-rated with water. The curve isfrom the contact-cement theoryfor pure quartz grains with quartzcement.

Figure 10. Hashin-Shtrikman arrangements of sphere pack,solid, and void.


velopes the stiffest component (the solid) in theHashin-Shtrikman fashion (Figure 10).At porosity � the concentration of the pure solid

phase (added to the sphere pack to decrease porosity)in the rock is 1 � �/�c and that of the sphere-packphase is �/�c. Then the bulk (Kdry) and shear (Gdry)moduli of the dry frame are

�1�/� 1��/� 4c cK � � � GDry HM� �4 4 3K � G K� GHM HM HM3 3

�1�/� 1��/�c cG � � �z (3)Dry � �G �z G�zHM

G 9K �8GHM HM HMz � � �6 K �2GHM HM

The friable sandmodel allows one to accurately pre-dict velocity in soft high-porosity sands (Figure 11).This model is appropriate for describing sands wherecontact-cement deposition was inhibited by organicmatter deposited on the grain surface.The constant-cement model (Avseth et al., 1998) as-

sumes that the initial porosity reduction from criticalporosity is due to the contact-cement deposition. Atsome high porosity, this diagenetic process stops, andafter that porosity reduces because of the deposition ofthe solid phase away from the grain contacts as in thefriable sand model (Figure 8c). This model is mathe-matically analogous to the friable sand model exceptthat the high-porosity end-point bulk and shear mod-uli (Kb and Gb, respectively) are calculated at some ce-

mented porosity �b from the contact-cement model.Then the dry-rock bulk and shear moduli are

�1�/� 1��/�b bK � � �4G /3dry b� �K �4G /3 K �4G /3b b s b

�1�/� 1��/�b bG � � �z (4)dry � �G �z G �zb s

G 9K �8Gb b bz � � �6 K �2Gb b

Figure 11. Velocity vs. porosity.(a) Water-saturated-rock databased on laboratory measure-ments of soft high-porosityNorth Sea sandstones by Blangy(1992). (b) Well-log data (Av-seth et al., 1998) for oil-satu-rated pay zone. The curves arefrom the friable sand model.

Figure 12. Velocity vs. porosity. Well-log data (Avseth et al.,1998) for oil-saturated pay zone. The curve is from the con-stant-cement model.


An example of applying this model to well-log data isgiven in Figure 12.

M O D E L S F O R U N C O N S O L I D A T E D M A R I N ES E D I M E N T

This model (Dvorkin et al., 1999a) is analogous to thefriable sand model but covers the porosity range abovecritical porosity. One end point is the critical porositywhere the elastic moduli of the sphere pack are givenby equation 2. To arrive at higher porosity, we addempty voids to the sphere pack (Figure 10). In this casethe voids are placed inside the pack in the Hashin-Shtrikman fashion. Now the pack is the stiffest com-ponent, so we have to use the upper Hashin-Shtrikmanlimit.

At porosity � � �c, the concentration of the voidphase is (� – �c)/(1 – �c) and that of the sphere-packphase is (1 – �)/(1 – �c). Then the effective dry-rockframe bulk and shear moduli are

�1(1��)/(1�� ) (�� )/(1�� )c c c 4�K � � GDry HM4 4 3� �K � G GHM HM HM3 3

�1(1��)/(1�� ) (�� )/(1�� )c c cG � � �z (5)Dry � �G �z zHM

G 9K �8GHM HM HMz � � �6 K �2GHM HM

Figure 13. Deep Sea Drilling Pro-ject (DSDP) Well 974. (a) Neu-tron porosity vs. depth; mbsf �meters below sea floor. (b) Ve-locity vs. depth: data, our model,and suspension model. Allcurves are smoothed.

Figure 14. Velocity vs. porosity.Theoretical curves superimposedon data allow one to identify therock type. (a) Data from Figures9a and 11a. (b) Data from Fig-ures 11b and 12.


The saturated-rock elastic moduli can be calculatedusing Gassmann’s (1951) equation.An example of applying this model to log data is

given in Figure 13 (Dvorkin et al., 1999a). A goodagreement between the model and the data is appar-ent. At the same time, the commonly used suspensionmodel fails to correctly mimic the data. This model’sdeparture from the data increases with depth, whichis due to the effect of confining pressure that adds stiff-ness to the dry frame of the sediment, thus making thesuspension model inadequate.

C O N C L U S I O N

The critical-porosity and critical-concentration conceptsallow the geophysicist to better understand the diver-sity of well-log and core-elastic data. Effective-mediummodels built on the basis of the critical-porosity conceptcan accurately model data. By superimposing theoreti-cal model curves on velocity-porosity and elastic-moduli-porosity crossplots, one may mathematicallydiagnose rock, that is, determine the texture of the sed-iment (e.g., contact-cemented vs. friable). Rock-physicsdiagnostic can be conducted with velocity, impedance,or elastic moduli. Examples of diagnostic rock curvesare given in Figure 14. Such diagnostic curves have im-plications for fluid detection (Avseth et al., 1998) andstrength and permeability estimation (Dvorkin and Bre-vik, 1999). Moreover, the rock physics diagnostic maybe crucial for pore-pressure prediction from velocity be-cause at the same pressure, velocity may vary depend-ing on rock texture (Dvorkin et al., 1999c). As a result,texture-related velocity variations may be mistakenlyattributed to pore-pressure anomalies.


This work was supported by the Stanford Rock Physics Lab-oratory.


Avseth, P., J. Dvorkin, G. Mavko, and J. Rykkje, 1998, Diag-nosing high-porosity sands for reservoir characterizationusing sonic and seismic: Society of Exploration Geophys-icists 66th Annual Meeting, Expanded Abstracts, p. 1024–1025.

Blangy, J. P., 1992, Integrated seismic lithologic interpreta-tion: the petrophysical basis: Ph.D. thesis, Stanford Uni-versity, Stanford, California, 357 p.

Dvorkin, J., and I. Brevik, 1999, Diagnosing high-porositysandstones: strength and permeability from porosity andvelocity: Geophysics, v. 64, p. 795–799.

Dvorkin, J., and A. Nur, 1996, Elasticity of high-porositysandstones: theory for two North Sea datasets: Geophys-ics, v. 61, p. 1363–1370.

Dvorkin, J., A. Nur, and H. Yin, 1994, Effective properties ofcemented granular materials: Mechanics of Materials,v. 18, p. 351–366.

Dvorkin, J., M. Prasad, A. Sakai, and D. Lavoie, 1999a, Elas-ticity of marine sediments: Geophysical Research Letters,v. 26, p. 1781–1784.

Dvorkin, J., D. Moos, J. Packwood, and A. Nur, 1999b, Iden-tifying patchy saturation from well logs: Geophysics,v. 64, p. 1–5.

Dvorkin, J., G. Mavko, and A. Nur, 1999c, Overpressure de-tection from compressional- and shear-wave data: Geo-physical Research Letters, v. 26, p. 3417–3420.

Gassman, F., 1951, Elasticity of porousmedia—Uber die elas-tizitat poroser medien: Vierteljahrsschrift der Naturfor-schenden Gesselschaft, v. 96, p. 1–23.

Hashin, Z., and S. Shtrikman, 1963, A variational approachto the elastic behavior of multiphase materials: Journal ofMechanics and Physics of Solids, v. 11, p. 127–140.

Marion, D., 1990, Acoustical, mechanical, and transportproperties of sediments and granular materials: Ph.D. the-sis, Stanford University, Stanford, California, 136 p.

Mindlin, R. D., 1949, Compliance of elastic bodies in contact:Journal of Applied Mechanics, v. 16, p. 259–268.

Nur, A., G. Mavko, J. Dvorkin, andD. Galmudi, 1998, Criticalporosity: a key to relating physical properties to porosityin rocks: The Leading Edge, v. 17, p. 357–362.

Yin, H., 1993, Acoustic velocity and attenuation of rocks: isot-ropy, intrinsic anisotropy, and stress induced anisotropy:Ph.D. thesis, Stanford University, Stanford, California,227 p.

43

5The Role of Shale Pore Structureon the Sensitivity of Wire-LineLogs to OverpressureG. L. BowersApplied Mechanics Technologies,Houston, Texas

T. John KatsubeGeological Survey of Canada,Ottawa, Ontario, Canada

A B S T R A C T

Petrophysical characteristics of shales have been analyzed to improve our understanding of wire-linelog response to overpressure. Bulk density and neutron porosity logs sometimes mask pore-pressureincreases that are clearly evident on sonic and resistivity logs. This may be because sonic and resistivitylogs respond to transport properties, whereas neutron and density logs reflect bulk properties.

Results of this study indicate that shale pore structure can be characterized by a storage-connectingpore system, with connecting pore sizes on the order of 2–20 nm. Laboratory compaction tests indicatethat connecting pores are mechanically more flexible compared to storage pores and are likely to havelower aspect ratios. Consequently, connecting pores are likely to undergo more elastic rebound (wid-ening) compared to storage pores as a result of effective stress reductions caused by overpressure.

Essentially, these results provide evidence that suggest sonic and resistivity logs respond to trans-port properties, whereas neutron and density logs reflect bulk properties, as previously proposed. Thissuggests that, whereas overpressure resulting from compaction disequilibrium may be detected by allfour logs, fluid expansion overpressure may be best detected by sonic and resistivity logs.


Pore-pressure increases are sometimes masked by thedensity log (Carstens and Dypvik, 1981; Grauls andCassignol, 1993; Hermanrud et al., 1998). Fortunately,from the standpoint of overpressure detection, sonicvelocity and resistivity commonly respond to pore-pressure changes where the density log does not. Infact, a drop in sonic velocity and electrical resistivity

Bowers, G. L., and T. John Katsube, 2002, The Role of Shale Pore Structure onthe Sensitivity of Wire-Line Logs to Overpressure, in A. R. Huffman and G. L.Bowers, eds., Pressure regimes in sedimentary basins and their prediction:AAPG Memoir 76, p. 43–60.

without a comparable decrease in density is commonlyan indication of severe overpressure. Figure 1 showsan example of this from the Gulf of Mexico (GOM).Hermanrud et al. (1998) investigated the relative

sensitivity of sonic, resistivity, density, and neutronporosity logs to overpressure in the Haltenbanken areaof offshore Norway. They were able to track wire-linedata from the same shale across 28 wells in which thepore pressure of the shale ranged from normal to rela-tively high overpressure (up to 1.8 g/cm3 [15.0 lb/gal]equivalent mud weight).They found no significant differences between the

responses for normal pressure and overpressure fromdensity and neutron porosity logs. Sonic velocities and

44 B O W E R S A N D K A T S U B E

Figure 2. Wire-line density, sonic velocity, and resistivity for the Not formation in Haltenbanken, offshore middle Norway (Her-manrud et al., 1998). “Low Press.,” “Moderate Press.,” and “High Press.” imply overpressures of less than 7.5 MPa, 7.5–20 MPa,and more than 20 MPa, respectively.

Figure 1. Wire-line data from an overpressured well in which sonic velocity and resistivity show a greater response to the onsetof overpressure than bulk density data. The curve labeled “R” is the raw resistivity data; the curve labeled “R200” is the resistivitydata normalized to a common temperature of 200�F (93�C).

resistivities in the higher pressure wells (�1.4 g/cm3

[11.7 lb/gal] equivalent mud weight), however, weresubstantially below the trends for lower pressures (Fig-ure 2). Because the data were collected from similardepths over an area in which the shale shows littlelateral variation, Hermanrud et al. (1998) ruled outlithologic/diagenetic differences as important factorsin these log responses.Hermanrud et al. (1998) recognized that sonic and

resistivity logs both respond to changes in transportproperties, whereas neutron and density logs reflectbulk properties. This led them to suggest that the sonic

and resistivity logs were sensing textural changes in-duced by overpressure. Sonic velocity decreases werethought to result from a reduction in intergranularcontact stresses, whereas resistivity decreases were at-tributed to enhanced fluid connectivity, possibly dueto microfracturing.Hermanrud et al. (1998) also explored possible

causes of the overpressure at Haltenbanken but wereunable to draw any definite conclusions. Actually, theirexplanation for the pressure sensitivity of the sonic andresistivity logs limits the possible overpressure causesto internal, sourcelikemechanisms. Stress-relatedmech-

The Role of Shale Pore Structure on the Sensitivity of Wire-Line Logs to Overpressure 45

anisms (undercompaction, tectonic compression, tec-tonic extension) are not viable. Undercompactioncannot cause stress reductions, and neither can tectoniccompression, unless it is accompanied by uplift and ero-sion, which appears not to be the case in the Halten-banken area (Hermanrud et al., 1998). Tectonicextension can cause stress reductions and fracturing,but not overpressure.Most internal pressure sources can be grouped into

the category called fluid expansion mechanisms (Bow-ers, 1995), which includes lateral transfer, aquathermalpressuring, hydrocarbon generation, and the expul-sion/expansion of bound water during clay diagene-sis. Load transfer from smectite grains to pore waterduring clay diagenesis (Lahann, 1998) can also beviewed as an internal pressure mechanism because itcan generate overpressure without a change in the in-situ total stress state. Precisely which mechanisms areinvolved at Haltenbanken remains an open question.Figure 4 of Hermanrud et al. (1998) indicates that

the pore pressures in their study area are all well belowthe overburden stress curve. Consequently, the log re-sponses are unlikely to be due to pressure-inducedmi-crofracturing, because as discussed by Miller (1995), atincipient fracturing conditions, the pore pressureshould be close to, and in principle, possibly evengreater than the overburden stress. Pore pressures nearthe overburden stress would also be required to keeppreviously formed microfractures from closing. Thesensitivity of transport properties to internal pressuresources, however, can be explained without invokingmicrofracturing. Such effects could also result from thewidening of preexisting void spaces.Toksoz et al. (1976) and Cheng and Toksoz (1979)

analyzed the pressure sensitivity of porous media bymodeling pores as oblate spheroids. Their relationssuggest that pores with aspect ratios (minimum di-mension over maximum dimension) in the range of0.001 to 0.10 should be most responsive to internalpressuring. Pores with aspect ratios (�) greater than0.10 (possibly representative of vugs and intergranularpores) are too rigid. And cracklike pores with very lowaspect ratios are too flexible; they close at low stresslevels and require pressures near the fracturing levelto reopen. On the basis of these, we divide the poresinto three types: elastically rigid (� � 0.1), elasticallyflexible (� � 0.001–0.1), and collapsing, cracklike pores(� � 0.001).Evidence (Katsube et al., 1992) exists that rock pore

structures are a combination of relatively large, highaspect ratio storage pores linked together by a networkof smaller, lower aspect ratio connecting pores, withtransport properties controlled by the connectingpores. Recent studies (Katsube et al., 1999b) further in-

dicate that connecting pores have a much higher sen-sitivity to laboratory stress changes than do storagepores, particularly in well-consolidated rocks. The ob-late spheroid pore model (Toksoz et al., 1976; Chengand Toksoz, 1979) suggests that storage pores tend tohave higher aspect ratios than connecting pores.Therefore, we propose that differences between the

sensitivity of transport properties and bulk propertiesto overpressure can be explained by this storage pore/connecting pore model. With bulk properties (density,porosity), the contributions of storage pores and con-necting pores are weighted equally. With transportproperties, the two pore types are in series, which im-plies connecting pores are a more dominant factor.Storage pores are more resistant to volumetric changesthan connecting pores. By the same token, volumetriclosses in storage pores tend to be permanent, whereasthe more flexible connecting pores are capable of elas-tic rebound.These results suggest that bulk and transport prop-

erties should be equally responsive to overpressurecaused by undercompaction because pressuring sim-ply slows down or arrests the compaction process.Mismatches between the response of bulk and trans-port properties to pressure changes occur where over-pressure is internally generated. The excess pressurewidens the flexible connecting pores without signifi-cantly altering the more rigid storage pores.In this chapter, first we present petrophysical evi-

dence that supports the storage/connecting poremodel. Second, we present relevant pore-structure the-ory (equations) and experimental and analytical pro-cedures, including some new analytical techniques,used to obtain the connecting/storage porosity vs.pressure data that was used in this study. Finally, wediscuss the shale storage/connecting pore character-istics and their implication on overpressure effect tolog responses.

B A S I C P O R E - S T R U C T U R E C O N C E P T S A N DM O D E L S

Pore-Structure Models

Effective porosity of a rock represents the pore-spaceof all interconnected pores, excluding isolated pores.Total porosity represents all pore space in a rock, in-cluding isolated pores. Effective porosity is comprisedof a three-dimensional network of void spaces thatcan vary in size and shape from sheetlike cracks tospherical chambers. Bulk density and effective poros-ity only depend on net pore volume. Transport prop-erties such as permeability, resistivity, and sonic


STORAGE PORES

JOINTPORES

VUGULARPORES

INTER-GRANULAR

GENERALIZED FORM

MODEL OF ROCK PORES

CONNECTING PORE

Number ofCracks = nClY

lZ

lX

lY

dc

φs = τIXl

C

φc = = nCdCτ (nClY )dCl

ClZ

(lXlYlZ)

Sc= = 2nCτ 2(nClY )lCl

Z

(lXlYlZ)

τ2

φcF =

= φS + φCφE

φc3

3τ2Sc2

k =

(a)

(b)

Figure 3. Some pore-structure models used for characteriz-ing shales (Katsube and Williamson, 1994, 1998): (a) stor-age-connecting pore model, and (b) tortuous connectingand storage pore model (modified from Katsube and Kami-neni, 1983).

velocity, however, are sensitive to pore sizes, shapes,and how the pores are interconnected. These proper-ties are grouped into a category called “pore struc-ture.”Pore-size distributions are investigated through

mercury porosimetry (Washburn, 1921). These testsalso provide information on how the pore structure isdivided between pores that control flow and pores thatdo not (Wardlaw and Taylor, 1976). Katsube and Wil-liamson (1994) call the first group connecting poresand the second group storage pores. In the literature,connecting and storage pores are commonly referredto as “throats” and “pores,” respectively.Storage pores consist of relatively large, interior

void spaces that can only be accessed through smallerconnecting pores, or blind pores that branch off fromthe interconnected pore network (Katsube and Mares-chal, 1993). The flow of fluid and electrical currentthrough a rock is assumed to be controlled by the net-work of connecting pores (see Figure 3a). The sheetlikeconnecting pores in Figure 3 are simplified represen-tations of connecting pores with aspect ratios of lessthan 0.001 to about 0.1. The volume fraction of storagepores (�S) plus connecting pores (�c) must equal theeffective porosity (�E):

� � � � � (1)E S C

Permeability and electrical resistivity measure-ments provide information on the connecting porosity,connecting pore size, and tortuosity. Katsube andWil-liamson (1994) interpret these data using a pore-struc-ture model in which connecting pores are idealized asa series of parallel, possibly saw-toothed–shapedcracks of uniform width (see Figure 3b). Storage poresare assumed to have no impact on flow properties;they are treated as nodes along the connecting porenetwork.

Mercury Injection/Withdrawal Porosimetry Tests

Pore-size distributions are determined from mercuryporosimetry injection tests (Washburn, 1921). Mercuryis forced into a rock sample in a series of pressure in-crements, and the volume injected during each step isrecorded (Figure 4a). The latest pore size invaded dur-ing each injection step is estimated from the equation(Washburn, 1921):

d � (4 c cosh) / (P � P ) (2)Hg AIR0

where d is the equivalent diameter of the pore, PHg isthe mercury pressure of the injection step, c is the sur-


1.0

01.0 10 10 10 102 3 4

Pore size d (nm)

Par

tial P

oros

ity(%

)aφ

(a)

(b)

10

1.0

0.1

0.01100 50 0

Percent Pore Volume Hg Saturated

Pre

ssur

e (M

Pa)

VI

VR

Withdrawal

Injection

φrr = 100 x VR / VI

WE = 100 - φrr

Figure 4. Diagram modified from (a) Wardlaw and Taylor(1976) describing the mercury intrusion and extrusioncurves and explaining the definitions and methods for de-termining withdrawal efficiency (WE) and storage porosityratio (�rr), and (b) typical pore-size distribution for tightshales (Katsube and Williamson, 1994, 1998). VI and VR arethe total mercury intrusion volume and total residual vol-ume, respectively.

face tension of the air/mercury meniscus, h is the anglethe meniscus makes with the pore wall, and PAIR0 isthe air pressure at the start of the test. The total volumeof pores with a diameter d is equated to the volume ofmercury injected during that step. The net result is apore-size distribution plot (Figure 4b).After the maximum injection pressure is reached,

additional pore-structure information can be obtainedby monitoring the volume of mercury expelled as theconfining pressure is reduced (Figure 4a), termedwith-drawal (Wardlaw and Taylor, 1976). We interpret the

volume of mercury that is not recovered to representthe volume of storage pores and the volume of mer-cury that is recovered to represent the volume of con-necting pores. The fractional part of the effectiveporosity comprised of storage pores is referred to asthe residual porosity ratio (�rr), where

� � � / � (3)rr S E

The �rr values for shales are generally in the range of0.4–0.8 (e.g., Katsube et al., 1999b), a range of valuesthat provides proof of the existence of the two types ofpores: storage and connecting pores. Further details ofthe principles of this method are described in Appen-dix 1.

Permeability/Formation Factor

The interpretation of permeability/formation factordata begins with the one-dimensional flow modelshown in Figure 3b. As discussed previously, storagepores are assumed to have little impact on either elec-trical or fluid flow properties. Connecting pores arerepresented by a set of parallel cracks of uniformwidthdC (Katsube and Williamson, 1994). The number ofcracks per unit distance perpendicular to the directionof flow is termed the flow-path density gC. Tortuosity(s) is the ratio of the length of the actual flow pathfollowed through a porous medium divided by thelength of the assumed straight-line flow path. With theflow model in Figure 3b, tortuosity can be consideredas giving the cracks a saw-toothed shape.The actual network of connecting pores in a natural

rock can be a very complex, three-dimensional struc-ture. To make the analysis tractable, however, wemodel the connecting pore network as three mutuallyperpendicular sets of cracks (Figure 5), with identicaltortuosities, crack widths, and flow-path densities(Katsube et al., 1991). Therefore, the total connectingporosity �C, and SC, the connecting pore-surface areaper unit bulk volume, are (Figure 3b):

� � n d s (4)C C C

S � 2n s (5)C C

where

n � 3g (6)C C

is the total number of cracks in all three dimensionsper unit length.


Figure 5. Three-dimensional ex-tension of the tortuous connect-ing and storage pore model.

Formation Factor (Electrical Current)

IX = I1 + I2

V/ρX = V/ρ1 + V/ρ2 (Ohm's Law)

ρW/ρX = 1/FX = 1/F1 + 1/F2

Porosity

φC = φC1 + φC2 + φC3

For Isotropic Cracks

φC1 = φC2 = φC3 = τ2/F1

φC = 3φC1= 3τ2/F1

1/FX = 2/F1

φC = 1.5τ2/FX

I1

I2

X

Y

Z

2

13

∼V

This model leads to the following relationships for�C, �E, �S, and dC as a function of s, permeability (k),and formation factor (F):

2� � b s /F (7)C 1

2� � � � b s /F (8)E S 1

d � Z(12Fk) (9)C

Appendix 2 shows the derivation of equations 7–9. Theparameter b1 equals

b � 3/N (10)1

where N depends on the amount of coupling betweenmutually perpendicular crack sets. The planar crackmodel shown in Figure 5 corresponds to N � 2, b1 �1.5 (Katsube et al., 1991). A pore network with moreout-of-plane branching than the model in Figure 5would have N closer to 3 and b1 near 1. Values for b1are chosen based on the assumed configuration of theconnecting pore network.Of the seven parameters in equations 7–9, �E, F, and

k are measured, and the rest are derived or interpreted.As illustrated in Figure 6, the product b1s2 is obtainedby linear regression of �E vs. 1/F data obtained at mul-tiple effective confining pressures (Pe) (Katsube, 2000)using equation 8. The �C and �S values are then de-rived by inserting the F and F and �E values for each

pressure step into equations 7 and 8, respectively, us-ing the b1s2 value. The connecting pore width (dC) isderived by inserting the F and k values, for each pres-sure step, into equation 9. Tortuosity (s) can be com-puted from b1s

2 using an assumed value for b1.Linear �E � 1/F trends indicate that �S and s are

both, on average, constant (see equation 8). Nonlinear�E � 1/F trends imply that �S and/or s change witheffective pressure. To interpret nonlinear trends, suchas the data in Figure 7a, the following relations for �Sand s are substituted into equation 8:

� � � exp(�eP ) (11)S S0 e

s � s exp(xP ) (12)0 e

Equations 11 and 12 follow from equation 8, and theobservations of Rubey and Hubbert (1959) and Kat-sube (2000), respectively, that �E and F can be approx-imated as exponential functions of effective stress. Anonlinear curve fitting tool in Excel (“Solver”) is usedto find b1, �S0, e, s0, and x values that best fit the �E� 1/F data. Tortuosity is then analytically calculatedfrom equation 12, whereas �S and �C are computed ateach pressure step from equations 7, 8, and 12. Figure7 illustrates the process. It should be noted that thisapproach is new and still under evaluation. For thelaboratory data presented subsequently, only thesample of sea floor mud (VSF-1) required a nonlinearanalysis.


Figure 6. Pore-structure analyses for multiple confining pressure tests: (a) effective porosity �E, (b) formation factor F, and (c)permeability k are measured at multiple effective stresses Pe; (d) tortuosity s is determined from the slope of a crossplot of �Evs. 1/F; b1 is a constant, typically assumed equal to 1.5; (d, e) connecting porosity �C � 100 b1s

2/F; storage porosity �S ��E � �C; (f) connecting pore width dc is calculated from F and k. The original data source is Katsube et al. (1996a).

E X P E R I M E N T A L A P P R O A C H

Petrophysical Data and Samples

Physical data used in this study have been previouslypublished (e.g., Katsube, 2000). The samples used toproduce these data were commonly obtained from 1-in.plugs taken from 4-in. (101.6 mm) split-core samplesfrom various wells in North America. A typical sam-pling procedure that was used is documented in theliterature (Katsube et al., 1991). Several disc specimens,0.5–1.5 cm in thickness, were cut from each of theseplugs for the permeability and formation factor mea-surements. Cuttings, disks, or partial disk specimensfrom the same samples were used for the other mea-surements (e.g., porosity and shale texture includingscanning electron microscopy and x-ray diffraction).

Pore-Size Distributions

Pore-size distributions were calculated from mer-cury porosimetry injection tests using equation 2. Val-ues typically used for the surface tension c andcontact angle h are 0.48 N/m and 140�, respectively(Katsube et al., 1991). Injection pressures covered arange of 0.14–420 MPa, with equilibration times of45 s for each high-pressure step and 10 s for low-pressure steps.The maximum injection pressure of 420 MPa that

was used should theoretically be capable of invadinga minimum pore size of 3–4 nm, so the populations ofsmaller nanopores may be missed. Storage poresshielded frommercury invasion by smaller connectingpores have their volumes inadvertently included in thepopulation of the pore size that controls invasion.


Figure 7. Storage porosity/connecting porosity analysis for nonlinear �E � 1/F trends; �S and s are assumed to be exponentialfunctions of effective stress, associated parameters are found by nonlinear curve fit of �E � 1/F algorithm. Tortuosity is thenanalytically calculated and used to find �C and �S from 1/F and �E data. Original data source is Katsube (2000).

Effective Porosity/Residual Porosity Ratio

Immersion, helium porosimetry, and mercury-injec-tion porosimetry methods have been used to deter-mine effective porosity (�E) (e.g., Katsube et al., 1992)using cuttings (5–10 g) from core samples. As previ-ously discussed, the residual porosity ratio (�rr) is de-termined from mercury porosimetry withdrawal testsby taking the ratio of the total mercury residual vol-ume (VR), after extrusion, over the total intrusion vol-ume (VI) (Figure 4) (Wardlaw and Taylor, 1976).Effective porosities were also measured at multiple

confining pressures under drained (constant pore pres-sure) conditions. Thin disc specimens of 0.5–1.5 cm inthickness were used to minimize pore-pressure equil-ibration times. Initial porosities were found from mer-cury immersion bulk volume and helium porosimetergrain volume measurements. The pore volume changecaused by each confining pressure increment wasequated to the volume of brine squeezed out of thesample, with each load step held until the flow of brinestopped. Details of the testing and sampling proce-dures can be found in the original references (e.g., Lo-man et al., 1993).

Formation Factor

The multiple confining pressure tests typically in-cluded 1000 Hz bulk electrical resistivity measure-ments. Formation factors computed directly fromthese data include pore-surface conductivity effects,whereas equations 7–9 require true formation factor (F)data free of pore-surface conductivity effects. Sucheffects are routinely eliminated using a well-docu-

mented procedure (e.g., Patnode andWyllie, 1950; Kat-sube et al., 1991), but this technique is difficult to applyto tests run at multiple confining pressures.Therefore, pore-surface conductivity effectswere re-

moved through a new analytical technique developedby Katsube (1999). The technique is based on the as-sumption that F can be represented by an exponentialfunction of effective pressure (Pe):

F � F exp(bP ) (13)0 e

where F0 is the true formation factor at atmosphericpressure, and b is a coefficient. This expression is jus-tified by the fact that permeability (k) is generally anexponential function of Pe (Katsube and Coyner, 1994)and that both k and F are determined by the connectingpore configuration. Further details of this procedureare described in Appendix 3.

Permeability

Permeability at atmospheric pressure (k0) is commonlyextrapolated from measurements made at higher pres-sures (Katsube and Coyner, 1994) by the transientpulse technique (Brace et al., 1968), using the followingequation (Katsube et al., 1991):

k � k exp(mP ) (14)0 e

where k0 and k are the fluid permeabilities at atmo-spheric pressure and at given effective pressures Pe,respectively, and m is a coefficient.


Figure 8. Mercury porosimetrydata: effective porosity (�Hg),mean pore size (dHg), and pore-size distribution (d) as functionof depth for shale samples fromthree wells in the Beaufort-Mac-kenzie basin (Northern Canada)(Katsube and Issler, 1993).

P O R E - S T R U C T U R E D A T A

Pore-Structure Evolution during Burial

Figure 8 illustrates pore-structure evolution duringburial under normal pressure conditions using mer-cury porosimetry data from three wells in the Beau-fort-Mackenzie basin. On the left are plotted effectiveporosities (�E) and mean pore sizes (dHg) vs. depth. Tothe right are pore-size (d) distributions for samples ob-tained from the depths marked by shaded horizontallines.Pore-size distributions are unimodal at all depths

but have larger porosities and pore sizes at shallower

depths. Effective porosities decrease from 30% at 952m to 7% at 2460 m. The mean pore size starts out inthe vicinity of 230 nm at 952 m, abruptly drops to 32nm by 1640 m, and then remains in the 20–40 nm rangefrom there on. The mode (peak value) of each pore-size distribution changes more with depth than themean, decreasing from roughly 800 nm at 952 m toapproximately 8 nm at 2460 m. As previously men-tioned, however, the mode could be biased by smallerpores that shield larger pores from mercury invasion.Storage porosities (�s), and residual porosity ratios

(�rr) were also determined for these samples. Residualporosity ratios show no apparent depth dependence.Values for most samples lie between 0.45 and 0.60; the


Figure 9. (a) Porosity-effectivestress trends developed from he-lium porosimetry measurementsfor Beaufort-Mackenzie shales inFigure 7; possible low-stresstrends represented by GOM soildata; (b) effective stress trends in(a) compared with laboratorycompaction tests for a sea floormud (VSF-1) and a Beaufort-Mackenzie shale (B-TG-6b) (Kat-sube et al., 1996a). Behavior ofsea floor mud is consistent within-situ profiles; the B-TG-6b sam-ple shows no evidence of inelas-tic deformation even whereloaded well beyond its estimatedin-situ stress state.

Table 1. Mercury and Helium Porosimetry Data from the Beaufort Mackenzie Basin

Sample Depth (m) dmean (nm) dmode (nm) �E (%) �C (%) �S (%) �rr �He

B-TG-1 952 229 800 29.5 13.3 16.2 0.55 29.5B-TG-2 1350 115 100 22.8 8.9 13.9 0.61 24.5B-TG-3 1640 32 32 18.6 10.2 8.4 0.45 18.4B-TG-4 2075 26 20 12.6 5.9 6.7 0.53 17.3B-TG-6 2460 36 8 6.92 1.62 5.3 0.77 10.6

*dmean � mean of the pore-size distribution; dmode � mode (peak value) of the pore-size distribution; �Ehg � effective porosity determinedfrom mercury injection; �C � connecting porosity � volume of mercury recovered/sample bulk volume; �S � storage porosity � �E � �C;�rr � residual porosity ratio � �S/�E; and �Ehe � effective porosity determined from helium injection. Data from Issler and Katsube, 1994.

exception is the sample at 2460m, for which�rr � 0.77.Table 1 summarizes these results and also lists poros-ities obtained from helium porosimetry measure-ments. Helium porosities tend to be higher thanmercury injection values because helium can penetratesmaller pore sizes than mercury.

In-Situ Porosity-Effective Stress Trends

Figure 9a shows possible fits of porosity-effectivestress data derived from the helium porosity measure-ments in Table 1. Effective stresses were estimated bysubtracting a 0.0104 MPa/m (0.46 psi/ft) normal pres-sure profile from an overburden stress curve calcu-lated from the helium porosities in Table 1 and fromshallow core density data from the GOM shelf. Poros-ities derived from the GOM shallow core data are alsoplotted in Figure 9a.For low to intermediate effective stresses, we used

the following form of a porosity-effective stress rela-tion proposed by Butterfield (1979) for soils and byBaldwin and Butler (1985) for shales:

k� � 1� lr (15)E

where r is the vertical effective stress, and l and k arecoefficients. For intermediate to high stresses, weswitched to a generalized version of the Rubey andHubbert equation (1959):

� � � � � exp(�fr) (16)E MIN 0

where �MIN, �0, and f are all coefficients.Results of using two versions of equation 16 are

shown (Figure 9); one with �MIN � 0 and a secondwith �MIN � 5%. The second case represents the Kat-sube and Williamson (1994) hypothesis that at poros-ities somewhere between 5 and 10%, the dominantcause of porosity loss in shales changes from mechan-ical compaction to diagenetic/chemical processes. La-hann (1998) also advocates a nonzero minimumporosity, with �MIN lying somewhere between 3 and10%, for rocks of smectite and illite composition.


Laboratory Compaction Behavior vs. In-Situ Trends

Figure 9b compares the estimated in-situ porosity-effective stress trends in Figure 9a with two laboratorycompaction tests. Sample B-TG-6b is the Beaufort-Mac-kenzie sample from 2460 m whose pore-size distribu-tion is plotted in Figure 8; VSF-1 is a sea floor mudsample from offshore Nova Scotia (Katsube et al.,1996b). The B-TG-6b data follow a much flatter com-paction trend than either the in-situ profiles or the seafloor mud.To a certain extent, this difference is expected. Com-

paction, especially in shales, is predominately an in-elastic process. As a result, only a small amount ofelastic rebound occurs when the effective stress actingon a formation is reduced. During reloading, the de-formation remains elastic until the past maximum ef-fective stress is exceeded. This means that inelasticdeformation cannot occur in the laboratory until theeffective confining pressure exceeds the maximum in-situ stress. Sample B-TG-6b has an estimated in-situvertical effective stress of 29 MPa � 4200 psi, whereasVSF-1 is essentially being compacted for the first time.Therefore, it is not surprising that VSF-1 would un-dergo substantially more inelastic deformation at lowpressures in the lab than B-TG-6b.This does not explain, however, why the B-TG-6b

sample appears to continue deforming elastically afterits in-situ effective stress is exceeded. Such an effectcould be caused by cementation, but no cement wasfound in this sample. Another possible explanationcould be the several orders of magnitude differencebetween laboratory and geologic loading rates. Labo-ratory tests also do not account for effects such assmectite dehydration (Bird, 1984; Colten-Bradley,1987), clay diagenesis (Lahann, 1998), and pressure so-

lution (Houseknecht, 1987). Exactly why these discrep-ancies occur remains an open question.Regardless of whether a sample has undergone elas-

tic rebound during its burial history, it certainly willhave experienced elastic rebound after coring. There-fore, at effective confining pressures below the maxi-mum in-situ stress state, and possibly at higher levels,laboratory compaction data reflect only elastic behav-ior. This, however, is precisely the deformation regimewe are interested in, because our focus is pore-struc-ture response during elastic rebound.We make the assumption that the effective stress

path followed by a pore-structure parameter duringelastic reloading in the laboratory is indicative of thepath that would be tracked during elastic rebound in-duced by overpressure. We realize that laboratory sam-ples may contain artificial fractures caused by coring,drying, and handling. These effects, however, can com-monly be identified, and they provide additional infor-mation on the response of bulk and transport propertiesto the opening and closing of cracklike void spaces.

Laboratory Compaction Data

Numerous data have been published (Coyner et al.,1993; Loman et al., 1993; Katsube and Coyner, 1994;Katsube et al., 1996a, b, 1999b) on the pressure char-acteristics of effective porosity (�E), formation factor(F), and permeability (k) for shales. Compaction testresults for samples B-TG-6b, VSF-1, and four addi-tional samples are presented here. Samples VSF-1, V-7, V-8, and V-9 are from offshore eastern Canada,whereas samples B-TG-6b and EJA-2 are fromnorthernCanada.Table 2 lists in-situ depths and the available x-ray

diffraction mineralogy data for these samples. The

Table 2. Mineral content (XRD wt. %) of Laboratory Compaction Test Samples*

Sample Depth (m) �E** (%) Total Clay Qz Fld Ca Dl Sd Py Kl Ch Il/Mc Il/Sm

VSF-1† 7.6 37.8EJA-2 896.4 33.3 25 70 5 0 0 0 0 5 3 15 2B-TG-6b†† 2460 12.2 50 38 1 0.3 0.9 6.3 0.2 7 3 - 40V-8 5270 7.7 20 73 5 Tr 0 0 2 0 10 7 3V-7 5270 7.2 24 70 4 Tr 0 tr 2 0 7 12 5V-9 5550 10 2 0 4 4 10 3

*Data taken from Katsube et al. (1996b, 1999b), Block and Issler (1996), and Katsube and Williamson (1994).Qz � quartz; Dl � dolomite; Kl � kaolinite; Mc � mica; Fld � feldspar; Sd � siderite; Ch � chlorite; Sm � smectite; Ca � calcite; Py �

pyrite; Il � illite.**Effective porosity measured after the first load step, which corresponded to an effective confining pressure of 3.5 MPa � 508 psi forsamples VSF-1, EJA-2, B-TG-6b, V-8, V-7; 4.4 MPa � 638 psi for sample V-9.†No XRD data available.††No XRD data available; values shown are for a sample from 2530 m in the same well.


Figure 10. Laboratory compaction data: (a) effective porosity (�E), (b) inverse formation factor (1/F), and (c) permeability (k)as a function of effective stress (Pe); (d, e, f) data normalized to the measurement recorded after the first the load step. Origi-nal data source is Katsube (2000).

mineralogy data shown for sample B-TG-6b are actuallyfrom a sample obtained 70 m deeper in the same well.By GOM shale standards, most of these samples havevery low clay contents. Sample B-TG-6b has the largestclay content (50%); the other samples contain less than25% clay.All tests were run at drained conditions, with each

confining pressure increment held constant until thepore pressure and sample had stabilized. During the�E and F tests the pore pressure was vented to theatmosphere, whereas base pore pressures of 5–10 MPa(725–1450 psi) were used for the permeability tests.True formation factors (F) were determined from pub-lished apparent formation factor (Fa) data (Loman etal., 1993; Katsube et al., 1996a) using the technique de-scribed in Appendix 3 (Katsube, 1999).The sensitivity of effective porosity (�E), formation

factor (plotted as 1/F), and permeability (k) to effectivepressure (Pe) changes are displayed in Figure 10. Fig-ure 10a, b, c presents the data in their original form,while Figure 10d, e, f replots the data normalized to

the measurement made after the first load step. Onlythe sea floor mud sample (VSF-1) displays a significantchange in effective porosity (�E) with increased Pe; theother samples appear to undergo primarily elastic de-formation.The 1/F values for all samples show considerable

change with increased effective stress (Figure 10b, e),and the permeability data are even more responsive(Figure 10c, f). All of the permeability curves undergoa reduction in slope somewhere between 6 and 25MPa(870–7250 psi), which could reflect closure of fracturesinduced by coring and handling. The three sampleswith the steepest permeability curves in the low stressrange (VSF-1, EJA-2, B-TG-6b) are the only samplesthat have not experienced diagenetic cementation.The �E vs. 1/F trends for samples VSF-1, EJA-2, and

B-TG-6b, and the storage porosity (�S) and connectingporosity (�C) estimates derived from these data aredisplayed in Figure 11a, b, c. Similar plots for samplesB-TG-6b, V-8, V-7, and V-9 are presented in Figure 11d,e, f. The connecting porosities all decrease with in-


Figure 11. Storage porosity (�S)/connecting porosity (�C) analyses: (a, d) �E vs. b1/F; (b, e) �S vs. Pe; and (c, f) �C vs. Pe. Linear�E � b1/F trends imply constant tortuosity, and on average, constant storage porosity; the curved �E � b1/F trend for sampleVSF-1 suggests tortuosity and storage porosity may both change with effective stress.

creasing effective stress, whereas the storage porositiesfor every sample except VSF-1 (the sea floor mud)show little, if any, change.Figure 12a, b, c shows the input data and results for

the connecting pore width (dC) analyses for samplesVSF-1, EJA-2, and B-TG-6b; corresponding data forsamples B-TG-6b, V-8, V-7, and V-9 are presented inFigure 12d, e, f. The dC values range considerably, aswould be expected, because these samples range fromcoarse-grained framework supported sandy shales (V-8) to finer grained framework-supported silty shales(V-7, EJA-2) or matrix-supported shales (V-9, B-TG-6b)(Katsube and Williamson, 1994; Katsube et al., 1996a,1999a, b). The coarse-grained sandy shale (V-8) showsthe largest dC values. As with the permeability data(Figure 12e), the dC curves for all samples in Figure 12fundergo a slope reduction after the first 6–25 MPa ofloading, which, again, we believe reflect sample dam-age effects.

Surprising is that the samples from the shallowestburial depths, VSF-1 (sea floor mud) and EJA-2 (896.4m), show the smallest dC values (Figure 12c). These twosamples have not experienced any diagenetic cemen-tation, their clay contents show no indications of beinghigher than the rest (Table 2), and their silt content ishigh (�50–60 wt. % (Katsube et al., 1996b; Katsube etal., 1999b). The location of the clay particles within thetexture of the rocks from shallower burial depth (VSF-1 and EJA-2) may be different (Katsube et al., 1999b)compared to those of the deeply buried rocks that haveundergone diagenesis and have pore surfaces coatedwith authogenic clays (Katsube and Williamson, 1994).The textures of these samples are now being investi-gated using a scanning electron microscope.In Table 3, the values of �E, �S,�C, and dC in Figures

10–12 are compared with those determined by mercuryporosimetry. The s and b1 values for the �E � 1/F dataare also listed. All of the mercury porosimetry-based


Figure 12. Connecting pore width (dC) analyses: (a, d) F vs. Pe; (b, e) k vs. Pe; and (c, f) dC vs. Pe.

data in Table 3, except dCHg, are measured values; thedCHg values represent the modes of calculated pore-size distributions. With the compaction tests, only �Eis measured; the remaining data are calculated from F,k, and �E. Having two independent methods to deter-mine the same pore-structure parameter providescredibility to the results.With the exception of sample EJA-2, the two sets of

�S and �C values show the same consistency as the �Emeasurements. The reason for the relatively large dis-crepancy between the two EJA-2 storage porosity es-timates is still being explored. The two sets offlow-path size estimates agree to within the same orderof magnitude, which is the level of accuracy expected.The laboratory compaction data indicate that shaleconnecting pore sizes are in the range of 2–20 nm,whereas the mercury porosimetry tests produce valuesin the range of 4–8 nm.

D I S C U S S I O N

Pressure Sensitivity of Bulk and Transport Properties

The formation factor and permeability data in Figure10 both show a much stronger response to elastic re-loading than the effective porositymeasurements. Thissuggests that elastic rebound induced by internal over-pressuring would cause a greater change in transportproperties (at least resistivity and permeability) thanbulk properties. Such behavior is consistent with thewire-line log responses observed by Hermanrud et al.(1998) at Haltenbanken (see Figure 2).

Storage and Connecting Pore Properties

The �S � Pe and �C � Pe data for sample VSF-1(Figure 11b, c) demonstrate that both storage and con-


necting pores can undergo significant volume de-creases during first-time compaction. The data for theother samples in Figure 11, however, indicate that po-rosity changes during elastic reloading are almost en-tirely due to connecting porosity. Consequently, itappears that volume reductions in storage pores tendto be permanent, whereas connecting pores are moreflexible and capable of elastic rebound. The oblatespheroid pore model (Toksoz et al., 1976; Cheng andToksoz, 1979) would further suggest that connectingpores generally have lower aspect ratios than storagepores, possibly something like the shapes drawn inFigure 3a.

Wire-Line Log Responses to Overpressure

Because connecting pores appear to be mechanicallyflexible, they are likely to open up or widen when theeffective stress decreases due to fluid expansion. Stor-age pores, however, are expected to remain essentiallyunchanged. Compaction disequilibrium cannot causeeffective stress reductions, so this pressure mechanismis not capable of causing either the connecting or thestorage pores to undergo widening.This study has provided evidence that the contri-

butions of storage pores and connecting pores to bulkproperties (density, porosity) are weighted equally.With transport properties, however, the two poretypes are in a series relationship, implying the effect ofconnecting pores is dominant. Bulk and transportproperties should be equally responsive to overpres-sure caused by compaction disequilibrium, which canonly slow down or arrest the compaction process. Mis-matches between the response of bulk and transportproperties to pressure changes occur where overpres-

sure is internally generated, such as by fluid expan-sion. The excess pressure widens connecting poreswithout significantly altering storage pores.


Results of this study indicate that shale pore structurecan be characterized by a storage-connecting pore sys-tem, with connecting pore sizes on the order of 2–20nm. Laboratory compaction tests show connecting po-rosity (�C) decreasing during elastic reloading,whereas storage porosity (�S) remains essentially con-stant. This suggests that connecting pores are mechan-ically more flexible than storage pores and aretherefore likely to have lower aspect ratios. Conse-quently, connecting pores would be expected to un-dergo more elastic rebound (widening) than storagepores where fluid expansion mechanisms cause effec-tive stress reductions.This study shows evidence that the contributions

of storage pores and connecting pores to bulk prop-erties (density, porosity) are weighted equally. Withtransport properties, however, the two pore types arein a series relationship, implying that the effect ofconnecting pores is dominant. Bulk and transportproperties should be equally responsive to overpres-sure caused by compaction disequilibrium becausethis pressure mechanism can only slow down or ar-rest the compaction process. Mismatches between theresponse of bulk and transport properties to pressurechanges occur where overpressure is internally gen-erated, such as by fluid expansion. The excess pres-sure widens connecting pores without significantlyaltering storage pores.

Table 3. Pore-Structure Parameters Computed from Mercury Porosimetry (Subscript “Hg”) vs. Range of Values Determinedfrom Laboratory Compaction Tests (Subscript “Pe”)*

Effective Porosity(�E) Storage Porosity (�S)

Connecting Porosity(�C) Flow Path Size (dC) Tortuosity

Sample �EHg (%) �EPe (%) �SHg (%) �SPe (%) �CHg (%) �CPe (%) dCHg (nm) dCPe (nm) (s) b1

VSF-1 – 37.8–2.7 – 18–1.3 – 20–1.4 – 2–4 1–2.1 1EJA-2 29.5** 33.3–24.5 12 24 17.5 9–1.4 5; 250† 4–2 1 1.2B-TG-6b 7.8 12.2–9.3 5.3 9 2.5 3–0.4 8 20–5 1.9 1.5V-8 9.1 7.7–6.4 3.9 6 5.2 1.8–0.2 7 19–14 2.3 1.5V-7 5.9 7.2–6.8 3.2 7 2.7 0.5–0.1 6 10–4 1.5 1.5V-9 2.3 2.0–1.3 0.4 1 1.3 1.8–0.1 6 6–4 2.6 1.5

*Tortuosity and the b1 parameter are only obtained from compaction tests. The basic data used for these determinations were taken fromother publications (Katsube et al., 1996 a, b, 1999b, 2000).**Effective porosity measured by helium porosimetry.†Sample exhibited bimodal pore-size distribution.



We express our sincere thanks to S. Connell (Geological Sur-vey of Canada) for drafting and preparing many of the dia-grams contained in this chapter.

A P P E N D I X 1 : M E R C U R Y P O R O S I M E T R YT E S T S

Because mercury is a nonwetting liquid, mercury invasion is re-sisted by menisci that form at the entrances to pores. Surfacetension enables a meniscus to support a pressure differential,termed the capillary pressure (Pc), which from equilibrium con-siderations, is equal to

P � P – P � (c cosh) � C/A (17)c Hg AIR

where PHg is the pressure of the mercury, PAIR is the pressureof the air inside the pore, c is the meniscus’ surface tension, h isthe angle the meniscus makes with the pore wall, and C and Aare the pore’s perimeter and cross sectional area, respectively.Mercury injection data are commonly interpreted by modelingthe pores as cylindrical capillary tubes. From equation 17, thepressure PHgi required to invade a specific cylindrical pore withdiameter di is

P � P � (4 c cosh)/d (18)Hgi AIR0 i

where PAIR0 is the air pressure at the start of the test. Throughequation 18, the latest pore size invaded during each injectionstep can be estimated as follows:

d � (4 c cosh)/(P � P ) (19)i Hgi AIR0

The total volume of pores with that diameter is assumed to equalthe volume of mercury that is injected during that step. The netresult is a pore-size distribution plot, like the one shown in Fig-ure 4b. A limitation of this technique is that large pores shieldedfrom invasion by smaller pores are included in the volume es-timates for the smaller pores (Wardlaw and Taylor, 1976).

Mercury expulsion during withdrawal results from the ex-pansion of trapped air; the air expands to keep equation 17 sat-isfied as the confining pressure is reduced. A pore becomesmercury free when its air pressure returns to PAIR0, and equation18 is once again satisfied. Consequently, mercury recovery suc-cessively occurs from smallest to largest pores.

For a system of parallel, constant diameter capillary tubes,all of the mercury that is injected would be recovered. Largeinterior pores that can only be accessed through smaller pores,however, may not be able to empty (Wardlaw and Taylor, 1976).If mercury continuity is broken, the smaller pores expel theirmercury first and leave behind menisci where they join a largerpore. By the time this occurs, the pressure of the mercury is toolow to cause reinvasion of the smaller pores, so the mercury inthe large pore becomes trapped.

The volume of mercury that is not recovered, including alltypes of trapped mercury, is interpreted to represent the volume

of storage pores. The fractional part of the effective porosity,referred to as residual porosity ratio (�rr)

� � � /� (20)rr S E

is related to withdrawal efficiency (WE) in the literature (Ward-law and Taylor, 1976) by

W � 1 � � (21)E rr

A P P E N D I X 2 : P E R M E A B I L I T Y / F O R M A T I O NF A C T O R R E L A T I O N S

Wyllie and Spangler (1952) adapted the general solution for fluidflow in a pipe to derive the following version of the Kozeny-Carman equation for permeability (k) as a function of porosity(�), pore-surface area per unit bulk volume (S), and tortuosity(s):

3 2 2k � � /(S s c ) (22)0

The parameter c0 is a shape factor that generally falls somewherein the range of 2.5–3.5 (Wyllie and Spangler, 1952); Walsh andBrace (1984) assumed c0 � 3.0.

Walsh and Brace (1984) followed a similar approach to obtaina relation for formation factor (F) as a function of s and �

2F � s /� (23)

In this model, a porous medium has a higher resistivity than avolume of water of the same dimensions because the electricalflow path followed through pores (1) is longer, (2) has a smallercross sectional area, and (3) is generally oriented at an angle fromthe assumed direction of flow.

Equations 22 and 23 are adapted to our pore-structuremodelby replacing � with connecting porosity �C. Likewise, S is takenas the surface area of the connecting pores per unit bulk volume(SC). Equations 4 and 5 give the relationships for �C and SC asa function of connecting pore width (dC), tortuosity (s), andthree-dimensional crack density (nC).

Equations 22 and 23 are assumed to define the porosity-per-meability and porosity–formation factor relationships for one setof cracks. To account for three-dimensional effects, a constant b1is introduced into the formation factor relationship:

2F � b s /� (24)1 C

where b1 is defined in equation 10. The b1 term accounts for thefact that all three crack sets contribute to porosity, whereas lessthan three may contribute to flow along a principal flow direc-tion (X, Y, and Z axes in Figure 5). By similar logic, b1 is alsorequired in the denominator of the permeability relation, soequation 22 becomes the following:

3 2 2k � [� /(S s c )]/ b (25)C 0 1


With c0 � 3.0, equations 4, 5, and 25 yield the following relationfor permeability:

2 2k � � d /(12b s ) (26)C C 1

Finally, through equations 4, 5, 24, and 26, all of the key con-necting pore parameters (dC, �C, nC, SC) can be expressed solelyin terms of F, k, and s:

2� � b s /F (27)C 1

d � Z(12Fk) (28)C

2 3S � 2 b s /Z(12F k) (29)C 1

3n � b s /Z(12F k) (30)C 1

A P P E N D I X 3 : F O R M A T I O N F A C T O RD E T E R M I N A T I O N

In principle, the formation factor, F, is determined from the bulk-rock electrical resistivity, qr, and the electrical resistivity, qw, ofthe pore fluid that saturates the rock using the Archie (1942)equation:

q � F q (31)r a/ w

where Fa is the apparent formation factor. Because Fa is not al-ways equal to F due to conductive layers existing on the poresurfaces, equation 31 is replaced with the Patnode and Wyllie(1950) equation:

1/q � 1/(Fq ) � 1/q (32)r w c

where qc is the pore-surface resistivity. A value of F free fromsurface conduction effects can be obtained by (1) measuring qrfor several pore-fluid solutions having different values of qw, (2)crossplotting 1/qr as a function of 1/qw, and (3) performing alinear regression on the results. The slope equals 1/F, whereasthe intercept corresponds to 1/qc.

The true formation factor (F) has been successfully deter-mined for various types of rocks (e.g., Katsube andWalsh, 1987),including shales (Katsube et al., 1991), using this method. Withlow-permeability shales, however, it can be extremely time con-suming and costly to repeat this technique at multiple pressures.To overcome this problem, a new method proposed by Katsube(1999) assumes F to be an exponential function of the effectivepressure Pe:

F � F exp(bP ) (33)0 e

where F0 is the true formation factor at atmospheric pressure,and b is a coefficient. This is based on the observation that per-meability (k) appears to be generally an exponential function ofPe (Katsube and Coyner, 1994) and that both k and F are deter-mined by the connecting pore configuration. Equations 32 and

33 suggest that with the correct qc value, a semi-log plot of (1/qr � 1/qc) vs. Pe should follow a straight line, that is,

1/q � 1/q � exp(�bP )/(q F ) (34)r c e w 0

Therefore, an iterative procedure is used to find a pore-surfaceresistivity that does the best job of aligning (1/qr � 1/qc) vs. Pedata along a semi-log straight-line trend. This qc value and theqW of the pore fluid used during the tests are then substitutedinto equation 32 to find the value of F.


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Bowers, G. L., 1995, Pore pressure estimation from velocitydata: accounting for overpressure mechanisms besidesundercompaction: Society of Petroleum Engineers Drill-ing and Completion, June, p. 89–95.

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Carstens, C., andH. Dypvik, 1981, Abnormal formationpres-sure and shale porosity: AAPG Bulletin, v. 65, p. 344–350.

Cheng, H. C., and M. N. Toksoz, 1979, Inversion of seismicvelocities for the pore aspect ratio spectrum of rock: Jour-nal of Geophysical Research, v. 84, no. 813, p. 7533–7543.

Colten-Bradley, V. A., 1987, Role of pressure in smectite de-hydration-effects on geopressure and smectite-illite trans-formation: AAPG Bulletin, v. 71, p. 1414–1427.

Coyner, K., T. J. Katsube, M. E. Best, and M. Williamson,1993, Gas and water permeability of tight shales from theVenture gas field offshore Nova Scotia: Geological Surveyof Canada, Current Research, no. 1993-D, p. 129–136.

Grauls, D., and C. Cassignol, 1993, Identification of a zone offluid pressure-induced fractures from log and seismicdata—a case history: First Break, v. 11, no. 2, p. 59–68.

Hermanrud, C., L. Wensaas, G. M. G. Teige, H. M. NordgardBolas, S. Hansen and E. Vik, 1998, Shale porosities fromwell logs on Haltenbanken (offshore mid-Norway) showno influence of overpressuring, in B. E. Law, G. F. Ulmi-shek, and V. I. Slavin, eds., Abnormal pressures in hydro-carbon environments: AAPG Memoir 70, p. 65–85.

Houseknecht, D. W., 1987, Assessing the relative importanceof compaction processes and cementation to reduction ofporosity in sandstones: AAPG Bulletin, v. 71, p. 633–642.


Issler, D. R., and T. J. Katsube, 1994, Effective porosity ofshale samples from the Beaufort-MacKenzie basin: Geo-logical Survey of Canada, Current Research, no. 1994-1B,p. 19–26.

Katsube, T. J., 1999, True formation factor determination bynon-linear curve fitting: Geological Survey of Canada,Current Research, no. 1999-D, p. 27–34.

Katsube, T. J., 2000, Shale permeability and pore-structureevolution characteristics: Geological Survey of Canada,Current Research, no. 2000-E15, 9 p.

Katsube, T. J., and K. Coyner, 1994, Determination of per-meability(k)-compaction relationship from interpretationof k-stress data for shales from eastern and northern Can-ada: Geological Survey of Canada, Current Research,no. 1994-D, p. 169–177.

Katsube, T. J., and D. R. Issler, 1993, Pore-size distribution ofshales from the Beaufort-MacKenzie basin, northern Can-ada: Geological Survey of Canada, Current Research,no. 1993-E, p. 123–132.

Katsube, T. J., and D. C. Kamineni, 1983, Effect of alterationon pore structure of crystalline rocks: core samples fromAtikokan, Ontario: Canadian Mineralogist, v. 21, p. 637–646.

Katsube, T. J., and M. Mareschal, 1993, Petrophysical modelof deep electrical conductors: graphite lining as a sourceand its disconnection due to uplift: Journal of GeophysicalResearch, v. 98, no. B5, p. 8019–8030.

Katsube, T. J., and J. B. Walsh, 1987, Effective aperture forfluid flow in microcracks: International Journal of RockMechanics and Mining Sciences and Geomechanics Ab-stracts, v. 24, p. 175–183.

Katsube, T. J., and M. A. Williamson, 1994, Effects of diagen-esis on shale nano-pore structure and implications forsealing capacity: Clay Minerals, v. 29, p. 451–461.

Katsube, T. J., and M. A. Williamson, 1998, Shale petrophys-ical characteristics: permeability history of subsidingshales, in J. Schiber, W. Zimmerle, and P. S. Sethi, eds.,Shales and mudstones II: Stattgard, Germany, E. Schweiz-erbart’sche Verlagslouchhandlung, p. 69–91.

Katsube, T. J., M. E. Best, and B. S. Mudford, 1991, Petro-physical characteristics of shales from the Scotian Shelf:Geophysics, v. 56, p. 1681–1688.

Katsube, T. J., M. Williamson, and M. E. Best, 1992, Shalepore structure evolution and its effect on permeability,in Thirty-third annual symposium of the Society ofProfessional Well Log Analysts (SPWLA), symposiumv. 3: Society of Core Analysts Preprints, Paper SCA-9214,p. 1–22.

Katsube, T. J., D. R. Issler, and K. Coyner, 1996a, Petrophys-ical characteristics of shales from the Beaufort-MacKenziebasin, northern Canada: permeability, formation factorand porosity versus pressure: Geological Survey of Can-ada, Current Research, no. 1996-B, p. 45–50.

Katsube, T. J., G. N. Boitnott, P. J. Lindsay, and M. William-son, 1996b, Pore structure evolution of compacting muds

from the sea floor offshoreNova Scotia: Geological Surveyof Canada, Current Research, no. 1996-D: p. 17–26.

Katsube, T. J., J. Bloch, and W. C. Cox, 1999a, The effect ofdiagenetic alteration on shale pore-structure and its im-plications for abnormal pressures and geophysical sig-natures, in A. Mitchell and D. Grauls, eds., Overpressurein petroleum exploration—Proc. Workshop: Bulletin Cen-tre Recherche Elf Exploration and Production, Memoir 22,p. 49–54.

Katsube, T. J., S. R. Dallimore, T. Uchida, K. A. Jenner, T. S.Collett, and S. Connell, 1999b, Petrophysical environ-ment of sediments hosting gas-hydrate, JAPEX/JNOC/GSC Mallik 2L-38 gas hydrate research well, in S. R.Dallimore, T. Uchida, and T. S. Collett, eds., Scientific re-sults from JAPEX/JNOC/GSC Mallik 2L-38 gas hydrateresearch well, Mackenzie Delta, North West Territories,Canada: Geological Survey of Canada Bulletin 544,p. 109–124.

Lahann, R., 1998, Impact of smectite diagenesis of compac-tion profiles and compaction equilibrium: AmericanAssociation of Drilling Engineers Industry Forum: Pres-sure Regimes in Sedimentary Basins and Their Prediction,6 p.

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61

6Impact of Smectite Diagenesis onCompaction Modeling andCompaction EquilibriumRichard LahannConoco Exploration Production Technology,Houston, Texas

A B S T R A C T

Shale compaction models employed in pore-pressure interpretation and prediction generally do notconsider the effects of changing shale mineralogy with depth. The conversion of smectite to illite reducesthe amount of bound water in the shale. This change reduces the equilibrium porosity associated withan effective stress. If dewatering does not accompany the mineralogical transformation, excess pressuredevelops. This pressure-generating mechanism is independent of the volume change associated withthe clay reaction.

Three examples from the United States Gulf Coast show that application of smectitic and illiticcompaction models allows improved interpretation of pore-pressure variation with depth. The com-bination of both porosity and compaction model changing with depth can create a pattern of effectivestress and velocity variation that resembles unloading.


Studies of shale porosity/overpressure commonlymodel shale porosity (U) as in equation 1.

�BrU � U e (1)0

where U0 is the surface intercept porosity, B is an em-pirical constant, and r is effective stress (Athy, 1930;Rubey and Hubbert, 1959). Hart et al. (1995) used twoequations of this form, with different B values, tomodel shale porosity and pressure in Pleistocene strataof the Gulf of Mexico. Rearrangement of equation 1allows calculation of effective stress as a function ofshale porosity.

One of the features of equation 1 is that increasingeffective stress causes shale porosity to approach 0, as

Lahann, Richard, 2002, Impact of Smectite Diagenesis on Compaction Modelingand Compaction Equilibrium, in A. R. Huffman and G. L. Bowers, eds., Pressureregimes in sedimentary basins and their prediction: AAPG Memoir 76, p. 61–72.

shown in Figure 1. The curves displayed in this figureare the two shale porosity-stress relationships fromHart et al. (1995). Note that the two calibrations indi-cate porosity from 6 to 1% at 50 MPa, which is roughlyequivalent to normal pressure at about 4500 m. Thedeep calibration value is probably unreasonably lowfor natural materials.

The porosity term in equation 1 includes intergran-ular porosity and water associated with mineral sur-faces (either external or clay interlayer surfaces). Thewater associated with shale mineral surfaces persistsuntil diagenesis/metamorphism have annealed theminerals into a much coarser grained assemblage.Equation 2,

�BrU � U � U e (2)m 0

allows porosity to decline to a minimum value, Um,based on the grain size/surface area characteristics ofthe shale. Within this study, Um is referred to as

62 L A H A N N

Figure 1. Porosity effective stress plots of shallow and deep shale compaction algorithms published in Hart et al. (1995). Notethat both expressions approach zero porosity at large values of effective stress.

“bound” water. The concept of clay-associated (bound)water being distinct from intergranular water was usedby Brown and Ransom (1996) in calculating the appro-priate porosity for compaction/pressure analysis.

The empirical constants B and U0 are commonly ob-tained by curve fitting in the shallow, near normallypressured part of a well. For sediments in the Gulf ofMexico the depth of the calibration zone is substan-tially above the depth at which smectite begins totransform to illite. Thus the Um value in equation 2should correspond to the surface or bound-water char-acteristic of a smectitic shale (where calibrated to theshallow part of Gulf of Mexico wells). At greater depthand temperature, following conversion of smectite toillite, the surface or bound water can be expected to bemuch lower than for a smectitic shale. The value of Umshould also be lower as a result.

Several previous works have used the concept ofbound water and bound-water release during diagen-

esis in pressure calculations. Dutta (1986) describes abasin model in which compaction is a function of bothstress and temperature. By making the shale equilib-rium void ratio (porosity) a function of temperature(as well as stress), Dutta incorporated the conversionof bound water to intergranular water by illite for-mation in the fluid-pressure calculation. The model de-scribed in following sections allows evaluation of thepressure effect of illitization without conducting a ba-sin modeling analysis.

Audet (1995) concluded that conversion of smectiteto illite could increase excess pore pressure by as muchas 30% by increasing the volume of free water. Thatanalysis maintained the same compaction (stress/po-rosity) relationship for before and after the bound-wa-ter conversion. The pressure contribution could begreater than the 30% value quoted by Audet if the re-sultant illitic shale is more compactible than its smec-titic precursor. This work incorporates probable

Impact of Smectite Diagenesis on Compaction Modeling and Compaction Equilibrium 63

changes in the compaction relationship as a result ofthe mineral conversion.

M O D E L

Calibration of equation 2 to shallow-water data requiresan evaluation of the Um term. This value includes waterassociated with clay and other mineral surfaces and alsowater in smectite interlayers. Colten-Bradley (1987)showed that for normal (hydrostatic) pressure condi-tions, smectite retains two water layers to depths rang-ing from 1100 to 2200 m. If fluid pressures were greaterthan hydrostatic pressures, the stability of the two-layersystem would extend to greater depths. These depthscorrespond to temperatures between 50 and 75� C,which are associated with conversion of smectite to il-lite. Based on these data, I assume that shales above thesmectite-illite transition contain smectites with two wa-

ter layers. A complete analysis would include three-wa-ter complexes in the shallow subsurface; this complexityis not dealt with in this chapter.

Hunt et al. (1998) suggest that shales with small in-ternal surface areas stop compacting at about 3% po-rosity and that shales with mixed-layer water stopcompacting at about 10% porosity. The 7% porositydifference cited by Hunt et al. (1998) is close to thevalue that can be calculated based on preservation oftwo-water layers in smectite in Gulf of Mexico shales.Data from Hower et al. (1976) suggest that typical, di-agenetically immature, Gulf of Mexico shales containabout 50% clay minerals relative to the total volume ofsolids, and the clays are about 50% smectite. The vol-ume fraction of compacted (and illitized) smectite at3% intergranular porosity is about 24%. If the illiticclays were expanded by the volume ratio of two-waterlayer smectite to illite (14/10), the shale volume wouldincrease by 10% because the 24 vol. % of illite would

Figure 2. Smectitic and illitic compaction profiles fitted to data from Plumley (1980). Note the substantially lower effectivestress associated with the illitic curve.

64 L A H A N N

now occupy about 34 volume units (24 � (14/10). Theporosity fraction of the expanded volume would be12%, intergranular porosity would be 3%, and inter-layer, smectite-associated porosity would be 9%. Forthis study, the Um value of smectitic shales is fixed at12%, and the Um value of illitic shales is set at 3%.

The values of B and U0 for smectitic shale are de-termined empirically by fitting model porosities tomeasured porosities. For this study, I assume initiallythat B and U0 are identical for smectitic and illiticshales. This assumption implies that the only differ-ences in the compactional properties of the two shaletypes is due to the retention of interlayer porosity inthe smectitic model.

Figure 2 shows porosity/effective stress plots forsmectitic and illitic shales derived from data in Plum-ley (1980) (discussed in the next section). Note that theeffective stress required to produce a given shale po-rosity is always lower for illitic shale than for smectiticshale. The calculated fluid pressure for a given poros-

ity is lower if the smectitic model is used than if theillitic curve is employed. In terms of Figure 2, the effectof illitization is to move the mineral system horizon-tally from the smectitic curve toward the illitic curve.The transition from one curve to the next occurs gra-dationally as the reaction proceeds.

The smectite-illite reaction may be usefully viewedas one of crystal growth and bound-water reduction.At any point along the smectite curve in Figure 2, theporosity is a combination of bound water (the 12%Um value) and intergranular water. The formation ofillite eliminates substantial amounts of smectitic inter-layer surface, which was hydrated when the clay wasa smectite. As a result the amount of bound water(Um) decreases and intergranular water increases. Ifthe smectitic shale was in compactional equilibrium,conversion to illite increases intergranular water. Ifthe intergranular water cannot escape to maintaincompactional equilibrium, then excess fluid pressureresults.

Figure 3. Depth variation of observed porosity for well B described in Plumley (1980). The top of the clay transition and topof excess pressure are also shown. All data replotted from Plumley (1980, figure 5).


The relationship between illitization and effectivestress described in Figure 2 is independent of any vol-ume change associated with illitization. If the specificvolume of intergranular water is greater than smectiticinterlayer water, then the pressure effect of illitizationwould be greater than shown in Figure 2. Alterna-tively, a decrease in specific volume would decreasethe pressure effect indicated in Figure 2.

Osborne and Swarbrick (1997) argued that the smec-tite-illite conversion is not a significant pressure sourcebecause the maximum likely volume change betweeninterlayer and intergranular water increases the vol-ume of intergranular water by a very small amount. If,for example, both intergranular and interlayer waterare 9 vol. %, an expansion of the interlayer water by10% during illitization increases the porosity from 18to 18.9%, a change of only 0.9%. Given reasonable val-ues for seal permeability, the pressure increase wouldbe small. If the interlayer water is viewed as bound

water, however, illitization increases the volume of in-tergranular water from 9 to 18%, a far more substantialchange. The models in Figure 2 suggest that the dif-ference in fluid pressure can be substantial.

Applications

The pressure/porosity/clay mineralogy concepts de-veloped in previous sections are tested in this sectionwith three data sets taken from the literature. Detailsof the pressure tests are not known, and so no attemptis made to adjust the pressures measured in the sandsfor centroid or hydrocarbon column effects. The sim-plistic assumption is made that the measured pres-sures reflect shale pressures at that point.

Data Set 1The data published in Plumley (1980) provide shaleporosity data from 1400 to 4200 m, a top of excess fluid

Figure 4. Observed shale porosity (replotted from Plumley, 1980, figure 5), smectitic, hybrid and illitic shale compaction modelsas function of hydrostatic effective stress, calculated by assuming constant overburden and hydrostatic fluid pressure.Divergenceof observed porosity and smectitic model at high porosity is probably due to overestimation of effective stress due to assumptionof constant overburden.

66 L A H A N N

pressure, a top of clay transition, and a pressure mea-surement within the excess pressure zone. The poros-ity/depth data from Plumley are displayed in Figure3. By assuming a constant overburden gradient (22.6MPa/km), effective stress values can be calculated cor-responding to each of the porosity points. From thesedata a plot of effective stress vs. porosity can be made,and the values of U0 and B can be solved empiricallyfor a smectitic model. This plot is shown in Figure 4 asthe smectitic trend. The mismatch between the smec-titic model and data at high porosity is due in part tothe assumption of a constant overburden. A betteroverburden model would reduce the effective stresscalculated at shallow depth and result in a better matchof model and observation. The porosity effective stresstrend generated by changing U0 to 0.34 (9% shift) isidentified as the hybrid model; the derivation of theillitic model is discussed subsequently.

Figure 5 displays the calculated pressure profiles,based on the effective stress relationships shown in Fig-ure 4 and the observed porosity profile in Figure 3.

From the surface down to about 3050 m, the top of theclay transition, the pressure is best interpreted with thesmectitic model (solid line in Figure 5). The smectiticmodel (Um � 0.12, U0 � 0.43, B � 0.0624) agrees rea-sonably well with the top of excess fluid pressure at3000 m. The excess pressure predicted by the smectiticmodel at depths less than 2000 m is probably due to er-ror in estimation of the overburden, as discussed pre-viously.

Below 3000 m (within the clay transition) the modeldiscussed in previous sections predicts that fluid pres-sure should begin to shift toward the hybrid line. Thedashed line in Figure 5 (Um � 0.03, U0 � 0.43, B �0.0624) is termed a hybrid because it has a Um value ap-propriate for illite and U0 and B values taken from thesmectitic model. The pressure measurement at about4200 m is about 6 MPa greater than predicted by thehybrid model and far in excess of that predicted by thesmectitic model.

The pressure measurement at 4200 m is about 1150m below the top of the clay transition. Based on the

Figure 5. Fluid pressure predicted by smectitic, hybrid, and illitic shale compaction models. Note that the smectitic model predictsminor excess fluid pressure down to about 3000 m. The observed fluid pressure at 4100 m (from Plumley, 1980, figure 5) isgreater than predicted by the hybrid model and far in excess of the pressure predicted by the smectitic model.


clay-transition profiles in Hower et al. (1976) and Bruce(1984), 1000 m is a typical thickness for completion ofsmectite conversion to low expandability illite.

A very good match can be made between an illiticcompaction model and the observed pressure if B isincreased to 0.1015 (dotted line, illitic model). Thismodel attributes low bound water to the illitic shale,Um � 0.03, and greater compactibility because B isgreater for illite than for smectite. Compaction modelscan be generated that match the observed pressure byreduction of the U0 value to less than 0.03. These mod-els, however, yield unrealistically low porosity valuesat low effective stress values. These low porosity val-ues also create problems in calculating pressures insystems with high preserved shale porosity at depth.

Data Set 2Berg and Habeck (1982) provide shale porosity, claymineralogy, and pressure data from about 600 to 4500m depth. The data set is from Oligocene sediments in

the McAllen ranch area of south Texas. The shale po-rosity/depth data were used to calibrate (empirically)smectitic and hybrid porosity/effective stress relation-ships (Figure 6). A good match is possible between asmectitic model (Um � 0.12, U0 � 0.48, and B � 0.087;solid line in Figure 6) and the observed porosities atseveral points in the shallow part of the section. Hy-brid (Um � 0.03, U0 � 0.48, and B � 0.087) and illitic(Um � 0.03, U0 � 0.48, and B � 0.142) effective stressmodels are also displayed in Figure 6 as dashed anddotted lines, respectively. The illitic model was gen-erated by increasing the B value in the same ratio aswas done for the Plumley illitic model.

Figure 7 displays the predicted pressures based onthe porosity/effective stress models in Figure 6 andtwo observed pressures. The smectitic model agreesextremely well with the measured pressure near 2000m, which is above the top of the transition zone. Theillitic pressure agrees within 1 MPa with the observedpressure at 3400 m. Data in Berg and Habeck (1982)

Figure 6. Observed shale porosity calculated from density data in figure 8 of Berg and Habeck (1982), smectitic and illitic shalecompaction models as function of hydrostatic effective stress, calculated by assuming constant overburden and hydrostatic fluidpressure. The smectitic model was empirically fitted to match the porosity data at low effective stress.

68 L A H A N N

indicate that the clay transition is nearly complete atthis depth.

Data Set 3Hart et al. (1995) provide shale porosity and eight pres-sure data points from between 400 and 3600 m fromPleistocene sediments from the Eugene Island Block330 area. The depth to the top of the clay transition inthe Eugene Island 330 A20ST (Pathfinder) well appearsto be at about 1500 m (Figure 8), based on data con-tained in Losh et al. (1999). This depth, as discussed byLosh et al. (1999) is anomalously shallow for the ageand temperature of the sediments. Model calculationsfor the top of the clay transition, using the method de-scribed by Gordon and Flemings (1998), place the topof the transition near 2000 m.

The shale porosity and effective stress data fromHart et al. (1995) were used to calibrate smectitic (Um� 0.12, U0 � 0.27, and B � 0.055), and illitic porosity/effective stress relationships as in Figure 9. The illitic

(Um � 0.03, U0 � 0.27, and B � 0.088) model wasgenerated as described previously. The smectiticmodel provides a close match to the measured poros-ities in the shallow section of the well. Because the claycomposition data (Figure 9) indicates that the most il-litic phases present retain about 40% smectite layers, atransition model was generated with Um, U0 and Bvalues (Um � 0.075, U0 � 0.27, and B � 0.071) be-tween those used for the smectite and illite models.

Measured pressures and the fluid pressures calcu-lated by the relationships in Figure 9 are displayed inFigure 10. The smectitic model agrees extremely wellwith the measured pressures at 1300 and 1500 m. Thetransition model predicts a fluid pressure in excellentagreement with measured pressures at 2100–2200 m.Hart et al. (1995) and Gordon and Flemings (1998) sug-gest that thermal expansion of pore fluids and claysourced fluids may account for up to 20% of the excesspressure in Eugene Island wells. The data in Figure 10account for the pressure increase by changes in the

Figure 7. Fluid pressure predicted by smectitic and illitic shale compaction models. Note that the smectitic model agrees ex-tremely well with measured pressure (taken from Berg and Habeck, 1982, figure 8) near 2000 m. The illitic model closelymatches the measured pressure at 3400 m.


compaction model for the reacting shales, without ap-pealing to volume expansion during the clay reactions.

Based on these model/pressure correlations, a fluidpressure between 24 and 32 MPa, the values predictedfor the smectitic and transition models, is anticipatedat 1950 m. The measured pressure at 1950 m is about23 MPa, well below the anticipated shale pressure andconsistent with the smectitic model.

An alternative interpretation for the data in Figure10 is that the smectitic model matches the observedpressure data down to a depth of 1950 m, followed bya reasonable match between the transition model andmeasured data at 2100–2200 m. This interpretation re-quires that the measured clay expandability data (Loshet al., 1999) be in error between 1500 and 1900 m andalso requires a dramatic change in shale compactionproperties between 1950 and 2100 m.

D I S C U S S I O N A N D C O N C L U S I O N S

A procedure has been developed and demonstrated forusing porosity/effective stress relationships in the shal-low part of wells to predict fluid-pressure profiles be-low the clay transition. In the three examples examined

in this study, the shallow smectitic part of the well wasused to define a smectitic compaction curve with a min-imum porosity of 12%. In all three cases, the observedpressure below the top of the clay transition was fargreater than could be predicted either from the smectiticmodel or from a single traditional expression with nominimum porosity (see Plumley, 1980; Hart et al., 1995).

The procedure for generating an illitic model, devel-oped from the Plumley data, provides an excellent es-timate of the pressure reported by Berg and Habeck(1982) in the illitic zone of the well. The transitionalmodel generated for the Hart et al. (1995) data providesan excellent pressure match to the deep (2100–2200 m)pressure data in the Pathfinder well. The transitionalmodel is also consistent with the presence of about 50%smectite in the mixed-layer clay at that depth.

In the three cases discussed, the top of the clay tran-sition was known from sample analyses. Ideally, in anexploration mode the top and base of the clay transi-tion would be estimated from thermal modeling (seeGordon and Flemings, 1998) or from offset data. Asmectitic compaction profile could then be applieddown to the top of the clay transition and an illiticprofile from the base of the transition onward. Withinthe transition zone stepwise application of transitional

Figure 8. Depth variation of mixed-layer clay expandability, smectite/smectite � illite (S/S � I) for the Pathfinder well. Datafrom table 1 of Losh et al. (1999). Note that below 1500 m the maximum smectite fraction is .7, substantially less than themaximum value above 1500 m. A top of the clay transition of 1500 m is interpreted for this well.

70 L A H A N N

models can provide reasonably accurate pore-pressureestimates.

The three smectitic models generated in this studyhad U0 values ranging from 0.27 to 0.48 and B valuesranging from 0.055 to 0.087. These ranges may indicatedifferences in shale/clay properties or may reflect sys-tematic differences in the methods used to calculateporosities. The lowest porosity value is associated witha sonic-log–based porosity transformation (data set 3),whereas the other two models were density-log based.Spatial and temporal variations in clay and shale prop-erties certainly occur in natural geologic materials andcontribute uncertainty to the analysis.

Variation in mineralogy and compaction modelswith depth can produce changes in velocity/effectivestress models used to predict pore pressure from seis-mic data. Figure 11 contains plots of velocity/effectivestress for the smectitic, transition, and illitic models inFigure 8. The velocity corresponding to a porosity/ef-

fective stress pair was determined with the sonic/po-rosity relationship of Issler (1992) as detailed in Hartet al. (1995). The progression with depth from a smec-titic to a mixed-layer mineralogy requires a shift fromthe smectitic effective stress velocity relationship to-ward the transitional relationship.

The depth/porosity relationship for the Pathfinderwell (Hart et al., 1995) was combined with a depth/mineralogy relationship to produce the velocity/effec-tive stress relationship shown in Figure 11. In thismodel effective stress was assumed to be hydrostaticdown to 1900 m, which generally agrees with Figure10. An effective stress model was created, whichranged from smectitic at 1900 m to the transitionalmodel at 2500 m. This model would honor the mea-sured pressure points in Figure 10. The effectivestress/velocity trend resembles an unloading curve asdiscussed in Bowers (1994). In this case the loadingcurve begins at about 12 MPa because no sonic logs

Figure 9. Observed shale porosity (taken from Hart et al., 1995, figure 3), smectitic, transitional and illitic shale compactionmodels as function of hydrostatic effective stress, calculated by subtracting hydrostatic pressure from overburden data providedby Hart et al. (1995). The smectitic model was empirically fitted to match the low effective stress porosity data.


are available until almost 2000 m. The greater velocity,for an effective stress value, on the unloading curvereflects the changing mineralogy that requires less ef-fective stress for a given degree of compaction (poros-ity). The unloading is not due to fluid expansion butload transfer from hydrated solids (smectites) to freewater during the mineral transition.


Athy, L. F., 1930, Density, porosity, and compaction of sed-imentary rocks: AAPG Bulletin, v. 56, p. 1–22.

Audet, D. M., 1995, Mathematical modeling of gravitationalcompaction and clay dehydration in thick sediment lay-ers: Geophysics Journal International, v. 122, p. 283–298.

Berg, R. R., and M. F. Habeck, 1982, Abnormal pressures inthe lower Vicksburg, McAllen Ranch field, south Texas:Transactions of the Gulf Coast Association of GeologicalSocieties, v. 32, p. 247–253.

Bowers, G., 1994, Pore pressure estimation from velocitydata: accounting for overpressure mechanisms besidesundercompaction: International Association of DrillingContractors/Society of Petroleum Engineers DrillingConference, no. 27488, p. 515–530.

Brown, K. M., and B. Ransom, 1996, Porosity corrections forsmectite-rich sediments: impact on studies of compaction,fluid generation, and tectonic history: Geology, v. 24,p. 843–846.

Bruce, C., 1984, Smectite dehydration—its relation to struc-tural development and hydrocarbon accumulation innorthern Gulf of Mexico Basin: AAPG Bulletin, v. 68,p. 673–683.

Colten-Bradley, V. A., 1987, Role of pressure in smectite de-hydration—effects on geopressure and smectite-illitetransformation: AAPG Bulletin, v. 71, p. 1414–1427.

Dutta, N. C, 1986, Shale compaction, burial diagenesis, andgeopressures: a dynamic model, solution and some re-sults, in J. Burrus, ed., Thermal modeling in sedimentarybasins: Carcans, France, Editions Technip, p. 149–172.

Figure 10. Fluid pressure predicted by smectitic, transitional, and illitic compaction models for the Pathfinder well. Note that thesmectitic model agrees well with measured pressures at 1300 and 1500 m and that the transitional model agrees well withmeasured pressures between 2100 and 2200 m (pressure data from Hart et al., 1995).

72 L A H A N N

Figure 11. Effective stress/velocity crossplot for smectitic, transition, and illitic models of the Pathfinder well data. Also shownis an interpretation of the effective stress/velocity trend for the Pathfinder well (velocity and stress data taken from Hart et al.,1995), assuming top clay transition occurs at 1900 m. Note that the Pathfinder data resemble an unloading curve as describedin Bowers (1994).

Gordon, D. S., and P. B. Flemings, 1998, Generation of over-pressure and compaction-driven fluid flow in a Plio-Pleis-tocene growth-faulted basin, Eugene Island 330, offshoreLouisiana: Basin Research, v. 10, p. 177–196.

Hart, B. S., P. B. Flemings, and A. Deshpande, 1995, Porosityand pressure: role of compaction disequilibrium in thedevelopment of geopressures in a Gulf Coast Pleistocenebasin: Geology, v. 23, p. 45–48.

Hower, J., E. V. Eslinger, M. E. Hower, and E. A. Perry, 1976,Mechanism of burial metamorphism, 1: mineralogical andchemical evidence: Geological Society of America Bulle-tin, v. 87, p. 725–737.

Hunt, J. M., J. K. Whelan, L. B. Eglinton, and L. M. CathlesIII, 1998, Relation of shale porosities, gas generation, andcompaction to deep overpressures in the U.S. Gulf Coast,in B. E. Law, G. F. Ulmishek, and V. I. Slavin, eds., Ab-normal pressures in hydrocarbon environments: AAPGMemoir 70, p. 87–104.

Issler, D. R., 1992, A new approach to shale compaction andstratigraphic restoration, Beaufort-MacKenzie basin andMacKenzie Corridor, northern Canada: AAPG Bulletin,v. 76, p. 289–300.

Losh, S., L. Eglinton, M. Schoell, and J. Wood, 1999, Verticaland lateral fluid flow related to a large growth fault, SouthEugene Island Block 330 field, offshore Louisiana: AAPGBulletin, v. 83, p. 244–276.

Osborne, M. J., and R. E. Swarbrick, 1997, Mechanisms forgenerating overpressure in sedimentary basins: a reeval-uation: AAPG Bulletin, v. 81, p. 1023–1041.

Plumley, W. J., 1980, Abnormally high fluid pressures: surveyof some basic principles: AAPG Bulletin, v. 64, p. 414–422.

Rubey, W. W., and M. K. Hubbert, 1959, Overthrust belt ingeosynclinal area of western Wyoming in light of fluid-pressure hypothesis, 2: role of fluid pressure in mechanicsof overthrust faulting: Geological Society of America Bul-letin, v. 70, p. 167–205.

73

7Effect of Gas on PoroelasticResponse to Burial or ErosionK. W. KataharaBP America Inc., Houston, Texas

J. D. CorriganWilliams Energy Services,Tulsa, Oklahoma

A B S T R A C T

Where hydraulically isolated rock is either buried or erosionally unloaded, its pore pressure dependson differences in compressibility and thermal expansivity between the pore fluid and the solid skeleton.Pore pressure in gas-saturated rock changes relatively little compared to water-saturated rock becausegas has a much higher compressibility than water. For the same reason, escape of pore fluid throughsurrounding seals affects pressure less in gas-filled than in water-filled rocks. This effect is accentuatedwhere the rock is well consolidated and has a stiff skeleton. One implication is that erosional unloadingmay contribute to overpressuring in tight-gas sandstones, where gas saturation is high, the rock is stiff,and the surrounding rocks have low permeability.


Barker (1972) suggested that thermal expansion of porewater during burial could cause overpressure. Thissuggestion stimulated a series of articles on the ther-moelastic response of rock to burial or erosion (for in-stance, see Dutta [1987] for a brief review andreferences; Neuzil and Pollock, 1982; Shi and Wang,1986; Luo and Vasseur, 1992, 1993; Miller and Luk,1993). These articles primarily consider only water asthe pore fluid. A notable exception was Barker (1987),who recognized that reservoirs charged early with bio-genic gas would behave differently under burial thanwould water-saturated reservoirs. In this chapter, weuse laboratory data on rock compressibility to evaluatehow gas affects the development of abnormal pres-sures in well-consolidated rocks during burial or ero-

Katahara, K. W., and J. D. Corrigan, 2002, Effect of Gas on Poroelastic Responseto Burial or Erosion, in A. R. Huffman and G. L. Bowers, eds., Pressure regimesin sedimentary basins and their prediction: AAPG Memoir 76, p. 73–78.

sion. We conclude that the high compressibility of gashas strong effects on how pore pressure responds tochanges in overburden and that these effects should beconsidered in models of pore-pressure evolution intight-gas sands.

The basic idea can be illustrated by the followingthought experiment. Consider a well-consolidatedsandstone that is initially at 3000mdepth, at hydrostaticpore pressure (�31 MPa or 4500 psi), and encased inessentially impermeable shales. If 1500m of overburdenis eroded away, we might expect the pore volume ofthe sandstone to increase slightly, say by 1% more thanits initial value. Ignore thermal effects for the moment,and assume that the pore space is filled with water. Be-cause the compressibility of water is about 0.36 GPa�1

(2� 10�6 psi�1), a 1% increase inwater volume impliesa decrease in pore pressure of about 28 MPa (4000 psi).So the pore pressure at 5000 ft (1524 m) is only about 3MPa (500 psi). If the pores are filled with gas of com-pressibility 10�4 psi�1, however, the pore pressure de-creases by about 1 MPa, to 30 MPa (about 4400 psi).Thus the erosion causes subnormal pressure if water is

74 K A T A H A R A A N D C O R R I G A N

DEPTH

PRESSURE

LITHOSTATIC

HYDROSTATIC ( B = 0.4 - 0.5 )

B = 1

B << 1

Figure 1. Schematic diagram of pressure variations withburial or erosion in undrained rocks. Where only poroelasticprocesses are considered, pressure is governed by Skemp-ton’s B coefficient. A low B value implies that pore pressurevaries little with burial or erosion. A B value equal to 1 im-plies that the pore pressure varies along the lithostatic gra-dient. Where B is equal to the ratio of the hydrostaticgradient to the lithostatic gradient, typically 0.4–0.5, thepore pressure varies along a hydrostatic gradient.

Isothermal B at 31 MPa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40

Porosity, %

wet

80% gas

BT

Figure 2. Skempton’s isothermal coefficient B at a porepressure of 31 MPa (4500 psi) and a temperature of 93�C(200�F) plotted against porosity. Where thermal effects areignored, B is small for gas-bearing sands with low porosity.Because B falls below the hydrostatic range, 0.4–0.5, fortight gas sands, erosional unloading causes overpressure.For wet sands, B is generally above the hydrostatic range,which implies that unloading causes subnormal pressure.These values have been computed from laboratory data asdescribed in the Appendix. Most of the data are for tight-gassands. A few points have been added for unconsolidatedsands to illustrate that B approaches 1 at high porosity. TheB value also approaches 1 in the limit of vanishing porosity.

the pore fluid and overpressure if gas is the pore fluid.Furthermore, because the compressibility of gas is sohigh, leakage of a small volume of pore fluid throughthe surrounding shales has much less effect on pressurein the gas-filled sand as compared to the water-filledsand.

R O C K C O M P R E S S I B I L I T Y A N DS K E M P T O N ’ S C O E F F I C I E N T

Assume that the rocks are undrained, that is, thatchanges in pore pressure occur at a rate much fasterthan can be relaxed by flow to or from surroundingrocks. According to Biot’s theory of poroelasticity(Biot, 1941; Rice and Cleary, 1976), a change in confin-ing stress, DS, in an undrained rock is accompanied bya change in pore pressure, DP, according to

DP � B DS (1)

The parameter B is the undrained pore-pressurebuildup coefficient, called “Skempton’s coefficient” insoil mechanics. The value of B depends on the prop-erties of the rock skeleton and pore fluid, and it canrange from nearly 0 to about 1. In the earth, a typicaloverburden gradient is 3.5 kPa/m (1 psi/ft), and a typ-ical hydrostatic pressure gradient is 1.6 kPa/m (0.45psi/ft). A B value of 0.45 then implies that a change inoverburden stress causes the pore pressure to changealong a near-hydrostatic gradient, even if the rock isencapsulated in a perfect seal. If B is much less than0.45, then the pore pressure in an isolated rock is nearlyindependent of overburden. If B is approximatelyequal to 1, then changes in pore pressure are the sameas changes in overburden stress. These scenarios areshown schematically in Figure 1.

Ignore thermal effects for the moment. The isother-mal coefficient BT depends on pore-fluid propertiesand degree of consolidation. A BT value equal to 1 isa good approximation in unconsolidated water-satu-rated sediments, but BT can be significantly lower forwell-lithified rock. Berge (1998) lists values from 0.55to 0.99 for water-saturated sandstones. FurthermoreBTmust approach 1 with vanishing porosity. Figure 2shows BT values estimated from laboratory measure-ments of sandstone static compressibility, as describedin the Appendix.

The value of BT decreases with increasing compress-ibility of the pore fluid and is generally between 0.5and 1 when water is the pore fluid. The value of BT,however, is much smaller when gas is present, asshown by the open squares in Figure 2. Oil saturationimplies values intermediate between water and gas.

Effect of Gas on Poroelastic Response to Burial or Erosion 75

Geothermal B at 31 MPa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40

Porosity, %

wet

80% gasBG

Figure 3. Skempton’s coefficient B along a geotherm, at apore pressure of 31 MPa (4500 psi) and a temperature of93�C (200�F). In comparison to Figure 2, B values for gassands are higher but still well below the hydrostatic rangeof 0.4–0.5. At this pressure, thermal effects reduce abnor-mal pressure in gas sands due to erosional unloading.

Geothermal B at 16 MPa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40

Porosity, %

wet

80% gas

BG

Figure 4. Skempton’s coefficient, B, along a geotherm at apore pressure of 16 MPa (2250 psi) and at a temperatureof 57�C (135�F). At this pressure the gas compressibility ishigh enough that thermal effects are minor in comparison.For tight gas sands B is about 0.1, which is significantly be-low the hydrostatic range (0.4–0.5).

When the pore pressure is low, the gas compressibilityis very high, so only a small fraction of the pore spaceneeds to be occupied by gas in order for BT to be nearlythe same as for a completely gas-saturated rock. Formuch the same reason, seismic compressional veloci-ties respond similarly to low gas saturation as to highgas saturation. Unlike the dynamic seismic case, how-ever, the static pressure response described in thischapter is the same whether the gas exists as a gas capover water or is distributed throughout the reservoir.

Now consider thermal effects. An increase in over-burden stress is generally accompanied by an increasein temperature. Thermal expansion of the pore fluid,which is greater than thermal expansion of the gran-ular skeleton, augments any pore-pressure incrementdue to confining stress alone. Thus B is greater alonga geotherm than along an isotherm. The Appendix de-fines a modified coefficient, BG, for a geothermal tem-perature gradient. The value of BG has been computedfor two pore-pressure (P) and temperature (T) states:first for P � 31 MPa (4500 psi) and T � 93�C (200�F),and second for P � 16 MPa (2250 psi) and T � 57�C(135�F). The overburden gradient is assumed to be 3.5kPa/m (1 psi/ft), and the temperature gradient is as-sumed to be 24�C/km (1.3�F/100 ft). Figures 3 and 4show BG values computed for these two states.

Figure 3 shows that, at 31 MPa (4500 psi) and 93�C(200�F), BG is roughly 0.2 for tight gas sands. This valueis well below the hydrostatic range (0.4–0.5). In otherwords, temperature effects only partially cancel out theeffects of high gas compressibility for these gas-bear-ing sandstones. The undrained thermoelastic response

to erosion is that pore pressure decreases at about halfthe hydrostatic gradient. At the lower pressure andtemperature shown in Figure 4, BG is even smaller,about 0.1 for tight gas sands, well below the hydro-static range. Undrained gas sands with low pore pres-sure have steeper pressure gradients than gas sandswith high pore pressure.

Finally, Figure 5 shows some modeled pore-pres-sure trajectories for a tight-gas sand during erosion.Each trajectory starts at hydrostatic pressure at a dif-ferent depth. The sand is assumed to have 12% poros-ity and a static drained bulk modulus of 12 GPa,independent of depth. As depth decreases with in-creasing erosion, pore pressure decreases along eachtrajectory. The rate of pressure decrease is less thanhydrostatic, so excess pressure increases. The trajec-tories become less steep with increasing pressure be-cause the gas compressibility decreases.

D I S C U S S I O N A N D C O N C L U S I O N S

Poroelastic response in gas-bearing sands is very dif-ferent from the response of water-saturated sands.Although erosional unloading tends to induce subnor-mal pressure in isolated water sands, it tends to induceoverpressure in gas sands. We have only consideredthe undrained case in this chapter. Obviously theremust be some fluid leakage through surrounding for-mations. A small fluid loss (or gain) causes a largepressure drop (or increase) in water-saturated rockand may largely negate poroelastic effects. But a small


fluid-volume loss causes relatively little pressurechange in a gas reservoir because of the much greatercompressibility of the gas.

We conclude that poroelastic effects in gas sandsdeserve further consideration. For instance, overpres-sure is common in tight-gas sandstone reservoirsthroughout basins in the Rocky Mountain region(Spencer, 1985; 1989). Active charging of these reser-voirs by ongoing generation of gas from adjacent coalor carbonaceous shale formations has been invoked toexplain the development of overpressure in such res-ervoirs (e.g., Law and Dickinson, 1985; Spencer, 1987;Surdam et al., 1994). Rocky Mountain area basins,however, have experienced net erosion during thepost-Laramide (post-Eocene) (Burgess et al., 1997). Es-timates of overburden removed for some of these ba-sins are on the order of several thousand feet (e.g.,Nuncio and Johnson, 1984; Nuncio, 1990; Naeser,1992). Active gas generation from source facies wouldhave essentially shut down as a result of decreasingformation temperature upon commencement of ero-sion. Consequently, development and maintenance ofoverpressure via active, or recently active, gas charg-ing seems unlikely for tight-gas sands in these basins.

Poroelastic effects may contribute to, or largely be re-sponsible for, overpressuring developed in tight-gassands in these and other basins subjected to recent ero-sional unloading. This effectwould bemost accentuatedin gas-bearing, well-consolidated sandstone bodieswithlow B values encased by very low permeability shalethat have been subjected to rapid decrease in overbur-den stress. Poroelastic underpressuring effects are lesslikely to be significant during burial because effectivestress tends to increase to the point where inelastic com-paction occurs.

We have ignored several effects that should be con-sidered in a more complete treatment. These includepressure- and temperature-dependent solubility of gasin brine, the difference between overburden stress andmean confining stress, and possible differences in Bvalue at laboratory vs. geological strain rates. A real-istic treatment requires careful consideration of othermechanisms such as gas generation and disequilib-rium compaction and of how rates of erosion or burialbalance off against fluid flow through sealing forma-tions.


We thank Vastar and ARCO for permission to publish, AltonBrown, Chuan Yin, Steve Crews, and Bill Kilsdonk for valu-able comments, and Pat Berge for a timely preprint.

A P P E N D I X

The parameter B in equation 1 is defined (Rice and Cleary,1976) to be

1B � (2)T

b �bf �1 � � � �b�bs

where bf � isothermal pore-fluid compressibility; bs � iso-thermal solid grain compressibility; b� � isothermal pore-space compressibility at constant differential stress; b �isothermal bulk rock drained compressibility. The parameterBT is known as Skempton’s coefficient, or as the undrainedisothermal pore-pressure buildup coefficient. In the specialcase where the rock is monomineralic and the only mineralis elastically isotropic, b� � bs, so that

1B � (3)T

b �bf s1 � � � �b�bs

For well-lithified rocks of primary interest in this chapter, bs� b � bf. Where gas is present, b �� bf, which implies BT�� 1, except when porosities approach 0.

Figure 5. Pore pressure during undrained erosion for amodel tight-gas sand with 12% porosity and a staticdrained bulk modulus of 12 GPa. Several cases are shownfor different starting depths. Also shown for reference arehydrostatic (dashed) and lithostatic (heavy solid) lines. Inall cases the excess pore pressure increases with erosion.The increase is steepest where the starting pore pressure islowest because the gas compressibility is highest. The porepressure could conceivably increase to the point where hy-draulic fractures occur. Temperature was assumed to line-arly increase at 0.013�F per foot from a surface temperatureof 70�F.

Effect of Gas on Poroelastic Response to Burial or Erosion 77

Recent studies indicate that b� may be significantly higherthan bs (e.g., Berge et al., 1993; Berge, 1998). Thus BT valuescomputed using b� � bs may be too low. Although this effectmay be significant for wet rocks, our computations indicatethat the effects of b� � bs are negligible for gas-bearing rocks.

Because gas compressibility varies strongly with tem-perature and pressure, BT for gas-bearing rocks also dependson pressure and temperature. It will be higher for lower tem-peratures and higher pressures.

Where temperature is not constant but varies along ageotherm, a modified geothermal B coefficient can be definedas (e.g., see Miller, 1995, equation 4)

� �� DTfB � B 1 � � (4)G T � �b�b DSs

where �f is the thermal expansivity of the fluid, � is the ther-mal expansivity of the drained rock, and DT is the tempera-ture increment corresponding to an increment of confiningstress, DS, during burial or erosion.

Measured b values were from Jizba (1991), Tutuncu andSharma (1992), Tutuncu et al., (1993), G. G. Ramos (1995,unpublished data), and T. E. Scott (1995, unpublished data).Fluid properties were computed as in Batzle and Wang(1992), assuming a gas of gravity 0.6 and water salinity of50,000 ppm NaCl. The expression � � 3 � 10�5 �C�1 wasassumed for sandstones (Miller, 1995).

The previous computations have also neglected the sol-ubility of gas in water or oil and the dependence of that sol-ubility on pressure and temperature. Solubility of gas inwater increases with increasing pressure and decreasingtemperature.


Barker, C., 1972, Aquathermal pressuring: role of tempera-ture in development of abnormal pressure zones: AAPGBulletin, v. 56, p. 2068–2071.

Barker, C., 1987, Development of abnormal and subnormalpressures in reservoirs containing bacterially generatedgas: AAPG Bulletin, v. 71, p. 1404–1413.

Batzle, M. L., and Z. Wang, 1992, Seismic properties of porefluids: Geophysics, v. 57, p. 1396–1408.

Berge, P. A., 1998, Pore compressibility in rocks in J.-F.Thimus, Y. Abousleiman, A. H.-D. Cheng, O. Coussy, andE. Detournay, eds., Poromechanics: Rotteram, Balkema,p. 351–356.

Berge, P. A., H. F. Wang, B. P. Bonner, 1993, Pore pressurebuildup coefficient in synthetic and natural sandstones:International Journal of Rock Mechanics and Mining Sci-ences, v. 30, p. 1135–1141.

Biot, M. A., 1941, General theory of three-dimensional con-solidation: Journal of Applied Physics, v. 12, p. 155–164.

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processes: Geological Society of America Bulletin, v. 108,p. 1515–1535.

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Naeser, N. D., 1992, Miocene cooling in the southwesternPowder River basin, Wyoming: preliminary evidencefrom apatite fission-track analysis: U.S. Geological SurveyBulletin, B 1917-O, p. O1–O17.

Neuzil, C. E., and D. W. Pollock, 1982, Erosional unloadingand fluid pressures in hydraulically “tight” rock: Journalof Geology, v. 91, p. 179–193.

Nuncio, V. F., 1990, Burial, thermal, and petroleum genera-tion history of the Upper Cretaceous Steele Member ofthe Cody Shale (Shannon Sandstone Bed horizon), Pow-der River basin, Wyoming: U.S. Geological Survey Bul-letin, B 1917-A, p. A1–A17.

Nuncio, V. F., and R. C. Johnson, 1984, Thermal maturationand burial history of the Upper Cretaceous MesaverdeGroup, including the Multiwell Experiment (MWX), Pi-ceance Creek basin, Colorado, in C. W. Spencer and C. W.Keighin, eds., Geologic studies in support of the U.S. De-partment of Energy Multiwell Experiment, GarfieldCounty, Colorado: U.S. Geological Survey Open-File Re-port 84-757, p. 102–109.

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Spencer, C. W., 1989, Review of characteristics of low-per-meability gas reservoirs in western United States: AAPGBulletin, v. 73, p. 613–629.

Surdam, R. C., Z. S. Jiao, and R. S. Martinsen, 1994, The re-gional pressure regime in Cretaceous sandstones andshales in the Powder River basin, in P. Ortoleva and Z.Al-Shaieb, eds., Pressure compartments and seals: AAPGMemoir 61, p. 213–233.

Tutuncu, A. N., and M. M. Sharma, 1992, Relating static andultrasonic laboratory measurements to acoustic log mea-

surements in tight gas sands: 67th Annual Technical Con-ference and Exhibition of the Society of PetroleumEngineers, Society of Petroleum Engineers paper 24689,p. 299–311.

Tutuncu, A. N., A. L. Podio, and M. M. Sharma, 1993, Strainamplitude and stress dependence of static moduli insandstones and limestones, in P. P. Nelson and S. E.Laubach, eds., Rock mechanics: Rotterdam, Balkema,p. 489–496.

79

8Relationships between PorePressure and Stress in DifferentTectonic SettingsNajwa YassirRijswijk, Netherlandsformerly with CSIRO Petroleum,Melbourne, Australia

M. Anthony AddisShell, SIEP,Rijswijk, Netherlands;formerly with CSIRO Petroleum,Melbourne, Australia

A B S T R A C T

This chapter discusses the effect of different overpressure mechanisms and tectonic settings on the pore-pressure–stress relationship. We demonstrate that the two are intrinsically linked and that a change ofone affects the other. Vertical and horizontal stress increases result in overpressuring in normally con-solidated low-permeability sediments; overpressuring due to tectonic stresses can be far higher thanthat generated by rapid sedimentary loading. Pore-pressure increase, however, causes a change in thestresses and fracture gradient if deformation is constrained in any direction. We present a theoreticalmodel, based on field observations, which suggests that overpressuring by a fluid source tends to renderthe stresses more isotropic. The variability of porosity and pore-pressure–stress relationships for dif-ferent overpressure mechanisms and tectonic settings means that methods that consider risk and un-certainty in pressure-fracture gradient prediction need to be developed for geologically complex areas.


The knowledge of pore-pressure and fracture gradient(minimum principal stress) is crucial in all aspects ofthe upstream petroleum industry. In exploration, amajor consideration in bidding for a permit in an ov-erpressured area is the so-called window between thepressure and fracture gradients. If the pressure is highenough, it can approach theminimum stress and result

Yassir, Najwa, and M. Anthony Addis, 2002, Relationships between PorePressure and Stress in Different Tectonic Settings, in A. R. Huffman and G. L.Bowers, eds., Pressure regimes in sedimentary basins and their prediction:AAPG Memoir 76, p. 79–88.

in seal breach by fracture reopening or possibly by nat-ural hydraulic fracturing. In drilling, it is important todefine the window between the two to design casingpoints and a safe mud weight that will prevent blow-outs (during underbalanced drilling) and mud losses(during overbalanced drilling). An understanding ofthe relationship between pore pressure and stress isalso important during production. Depletion of over-pressured reservoirs results in dramatic stress changesthat have an impact on reservoir productivity, subsi-dence, seismicity, and, in some cases, well integrity.Overpressuring is known to occur by several different

mechanisms related to burial, tectonism, hydrocarbongeneration, mineral transformation, and temperature

80 Y A S S I R A N D A D D I S

increase, among other sources. The geological detailsof most of the individual mechanisms are exhaustivelydescribed in the literature and are not discussed indetail here (see reviews by Fertl, 1976; Mouchet andMitchell, 1989; Yassir, 1989; Osborne and Swarbrick,1997). The main topic of this chapter is the coupledrelationship between the pore-fluid pressure (PP) andfracture gradient (FG), which varies according to over-pressure mechanism. The impact of this relationshipon sediment porosity is also discussed.Overpressure mechanisms are divided into two cate-

gories in this chapter: overpressuring caused by stress(including sedimentary loading and tectonic loading)and overpressuring caused by a fluid source or fluidexpansion (including hydrocarbon generation, osmosis,smectite dehydration, and thermal pressuring).

S T R E S S E S C A U S I N G O V E R P R E S S U R E

Two types of overpressure are caused by increases instresses: undercompaction that results from rapid ver-tical loading (commonly sedimentary), and tectonicloading, leading to undrained shear. Undercompac-tion is by far the best understood of the overpressuremechanisms and is predominantly used to explain andquantify overpressures. Tectonic loading, however, ispoorly understood and has been underrated in the lit-erature, mainly because it is a difficult mechanism toquantify. Emphasis in this chapter is therefore placedon how overpressure generated by tectonic loading isdifferent from undercompaction and on its possiblemanifestations in exploration.

Rapid Vertical Loading

Overpressuring is commonly associated with Tertiarybasins where rapid deposition and subsidence occur,such as the Mississippi, Orinoco, and Niger delta re-gions (type areas for the development of pore-pressureprediction methods). In these regions, the fluid pres-sure (PP) increases in response to an increase in totalvertical stress (rV) in low-permeability sediments. Ac-cording to Terzaghi’s equation, an increase in rV istaken up partly by the rock matrix and partly by thepore fluid (Terzaghi and Peck, 1948),

r � r � � P (1)V V P

assuming a Biot constant of 1, where rV� is the effectivevertical stress.In the extreme case, where vertical loading occurs

without any fluid escape, the load is taken up totally

by the pore fluid, and the pressure response is ex-pressed as

C � DP / Dr (2)P V

C is a constant for uniaxial strain conditions, which isrelated to sediment saturation and system compressi-bility (see Lambe and Whitman, 1979). C commonlyhas values of 1 for saturated clays (Lambe and Whit-man, 1979) and greater than 0.95 for shales (Yassir,1989).This mechanism of overpressuring is most common

in young sediments where anomalously high porosi-ties for depth of burial are preserved. Older, normallyconsolidated, sediments can become overpressured ina similar manner, however. Rapid vertical loading bytectonic subsidence or overthrusting is mechanisticallyakin to undercompaction in that the addition of verti-cal load is reflected by a pore-pressure increase. Al-though the original porosity may have been normal,the sudden addition of load renders the sediment tech-nically undercompacted for its depth of burial. If themechanism also involves changes in the lateral stresses(and therefore the shear stress in the rock), however,this too will have an important effect on the pore pres-sure, as discussed in the following section.

Tectonic Loading

Tectonic loading, long recognized as a potential causeof overpressuring (e.g., Higgins and Saunders, 1974;Unruh et al., 1992), is far less considered in the litera-ture as an overpressure mechanism than sedimentaryloading, even in tectonically active basins. Yet globaloccurrences of overpressuring show, with a few nota-ble exceptions, a strong relationship between over-pressure and present-day compressional tectonics(Figure 1). Some examples include Trinidad (Higginsand Saunders, 1974), Papua New Guinea (Hennig etal., 2002), California (Unruh et al., 1992) and the Gulfor Alaska (Hottman et al., 1979). In the Gulf of Alaska,the onset of overpressuring coincides with a stress re-versal from normal faulting (or strike slip) to com-pressional faulting (Hottman et al., 1979). Thepressures in the San Andreas fault region have a dis-tribution that is strongly associated with the geometryof the fault and is thought by some workers to be re-lated to fault activity (e.g., Unruh et al., 1992). The su-perlithostatic (PP � rV) overpressures observed intectonically active regions (e.g., Bigelow, 1994) and theeruption of deep-seated mud volcanoes in earthquakeregions (Figure 1) are further indications of the strongrelationship between tectonic stress and overpressure.

Relationships between Pore Pressure and Stress in Different Tectonic Settings 81

Figure 1. Schematic map ofglobal overpressure occurrences(shading), areas of Cenozoicfolding (lines), and deep-seatedmud volcanoes (triangles). Modi-fied from Mouchet and Mitchell(1989), Yassir (1989), and Hig-gins and Saunders (1974).

Recently, overpressure models have begun to con-sider tectonic stresses (Van Balen and Cloetingh, 1995).To date, however, the models treat the pressure re-sponse to a horizontal load in the same manner de-scribed in equations 1 and 2, that is, the pressureincrease is caused by a unidirectional increase in stress,in this case horizontal rather than vertical. The impor-tant difference between the twomechanisms, however,is the shear stress—the difference between maximumand minimum total stresses (rMAX � rMIN). In thecase of sedimentary loading in a passive basin, the sed-iments are laterally constrained by the basin, so an in-crease in vertical stress (rV) is countered by a partialincrease in horizontal stress (rH). Under such condi-tions, the sediments do not experience critical shearstresses (shear failure) with increasing vertical stress(Figure 2a). With lateral tectonic loading, however, thesediments experience very high shear stresses becausethe horizontal stress increases without significant con-straint in the vertical stress (overburden) direction. Theshear stresses are capable of generating pore pressuresgreater than those generated by undercompaction(Figure 2b). To our knowledge, the relationship be-tween shear stress and pore pressure is not consideredin overpressure models.

Pressure Response to Shear Stress and the Concept ofA ValuesIn a compressional basin (r1 � rH), the sediments un-dergo changes in the shear stress that, if undrained,also result in a pore-pressure change described by

A � (DP – Dr )/(Dr – Dr ) (3)P 3 1 3

Or, if we assume that the overburden weight remainsconstant during shearing, the shear stress can increase(to failure) through an increase in rH, and the relation-ship simplifies to

A � DP / Dr (4)P H

where A is Skempton’s parameter describing the pore-pressure response to shear stress (see Lambe andWhit-man, 1979). The parameter A is not a constant, and,unlike the parameter C for most rocks, it commonlyexceeds 1, that is, the pore-pressure increment can ex-ceed the increment of applied load (Dr). Where a low-permeability sediment is subjected to shearing, thesediment structure or matrix deforms without signifi-cant fluid escape. This transfers some of the load to thefluid and results in overpressuring (Yassir, 1990). Thehigher the porosity, the greater the potential for therock matrix to rearrange itself under shear and to gen-erate larger pore-pressure responses.Figure 3 shows typical experimentally derived val-

ues of A for different sediment types: claystones (Yas-sir, 1990), a smectitic shale (Wu, 1987), a cementedshale (Ohtsuki et al., 1981), high porosity chalks (Led-dra and Jones, 1989), and sand (Bishop et al., 1965). Inthese tests, the sedimentwas consolidated isotropically(r1� � r3�) or anisotropically (r3�/r1� � K) to a certainmean effective stress before being subjected to shearstresses in an undrained state (no fluid escape) untilfailure is reached. Each point in the figure plots theratio of the total pore-pressure change divided by thetotal applied shear stress versus the initial mean stress.All the sediment types show a positive A value,

which means that the application of shear stress to a


Figure 2. Schematic illustrationof the different shear stresses(rMAX � rMIN) acting in a pas-sive basin and in a compres-sional basin. (a) Sedimentaryloading; (b) tectonic loading. Inthe passive basin, the increase inboth vertical and horizontalstress means that no criticalshear stresses are reached andthe pore pressures are controlledby the maximum vertical stress.In the compressional basin, theincrease in horizontal stress andthe relatively constant verticalstress means that the sedimentcan reach critical shear stresses.The pore-pressure increase inthis case is related to these shearstresses and can therefore bevery high.

range of sediments in an undrained state results in ov-erpressuring. Many of the results in Figure 3 give Avalues far greater than 1, that is, an increment of pore-pressure increase greater than the increment of appliedshear stress. In the case of the chalks at low mean ef-fective stresses (high porosities), extremely high A val-ues are recorded (up to 8), reverting back to around 1at the higher consolidation stresses. Figure 3 clearlyshows that overpressuring is achieved not only inhigh-porosity sediments but also in low-porosity sed-iments consolidated to high mean effective stresses. Acomparison between isotropic and anisotropic loadingin the sand and the claystones indicates that the stress

path during consolidation also has an effect on the Avalue, the anisotropically loaded samples giving thehigher A values (�1).An important implication of the data in Figure 3 is

that large overpressures can be generated by shearing,even in low-porosity normally consolidated materials.Bearing in mind that the stresses in a compressionalsedimentary basin are far higher than those in a pas-sive basin, the shear-induced pore-pressure magni-tudes relative to the overburden stress are higher.To illustrate this, take a normally consolidated sed-

iment buried to a depth of 1500 m in a passive basin;the vertical stress is approximately 33.9 MPa and the

Figure 3. Variation in A valueswith mean effective stress for avariety of sediment types: clay-stones (Yassir, 1990), an over-consolidated smectitic shale(Wu, 1987), a cemented shale(Ohtsuki et al., 1981), high-po-rosity chalks (Leddra and Jones,1989), and sand (Bishop et al.,1965).


Figure 4. Schematic illustration of the relationship betweenstress and pore pressure during undrained loading. If thesediment is normally or underconsolidated, the pore-pressure response is positive; if it is overconsolidated, theresponse is negative, leading to dilation.

hydrostatic pressure is 15.3 MPa. If undercompactionstarts at this depth the overpressure increases mono-tonically with the increase in the vertical total stress(DPP/DrV � C � 1; equation 2); it never reaches thetotal vertical (overburden) stress. The application of ahorizontal stress, which takes the basin to inversion,however, results in an increase in shear stress and ac-companying pore pressure at a constant depth. If wetake a lower bound fault friction angle of 15� and aPoisson’s ratio of 0.35 for the shale, the expected hor-izontal stress increase is 1.15rV� (Addis et al., 1996).Using an A value of 1, the overpressures at 1500 mdepth are 36.9 MPa, that is, exceeding the overburden(vertical) stress at that depth. For the undercompactioncase to reach the same overpressure, undrained burialto 2460 m is required.

Liquefaction: A Manifestation of Overpressure byShear StressA values far exceeding 1 are observed in Figure 3. Thisbehavior is related to the phenomenon of pore collapse(Addis, 1987), where thematrix of a high-porosity, com-monly cemented, sediment collapses under stress.Where this occurs in an undrained state, or under rapidcyclic loading, such as in an earthquake, all the stresscarried by the structure or matrix is transferred to thepore fluid, generating overpressures and causing liq-uefaction (see Lambe and Whitman, 1979). At the sur-face, liquefaction is observed in loose sands andsensitive clays (see Lambe andWhitman, 1979), and theexcess pressure is quickly dissipated. At depth, how-ever, where permeabilities decrease significantly, thegenerated overpressure could be preserved. Evidenceof liquefaction at depth includes chalks in the North Sea(Addis, 1987; Leddra and Jones, 1989). It is also themechanism bywhichmany deep-seatedmudvolcanoeserupt (Yassir, 1989). Deep-seated mud volcanoes are al-most always associated with areas of Cenozoic folding(Higgins and Saunders, 1974). They mostly appearalong compressional faults and fold axes, for example,Trinidad (Higgins and Saunders, 1974), New Zealand(Ridd, 1970), andAzerbaijan (Jakubov et al., 1971). Theireruption is also commonly coincident with earthquakes(Ridd, 1970; Jakubov et al., 1971).

A Note on Loading of Overconsolidated SedimentsThe previously mentioned relationships between load-ing and pore-pressure increase apply only to normallyconsolidated or underconsolidated sediments. Sedi-ments that have experienced higher stresses/depthsthan present have abnormally low porosities for depthof burial and are termed overconsolidated. These sed-iments cannot be overpressured by rapid loading orundrained shear unless the imposed stress change ex-

ceeds the historic stresses. In fact, undrained shear ofoverconsolidated sediment results in dilation andtherefore a reduction in pore pressure (Figure 4) (seeLambe and Whitman, 1979).The rock mechanics literature has, until recently,

largely concentrated on strong, low-porosity rocks,which display this dilatant behavior. This has, un-fortunately, colored our view of the importance ofshearing as an overpressure mechanism in sedimen-tary basins.The previous section dealt with overpressure mech-

anismswhere a stress increase results in overpressuring.The next section deals with the opposite phenomenonof overpressuring by a fluid source causing an increasein fracture gradient.

O V E R P R E S S U R E C A U S I N G S T R E S SC H A N G E S

Fluid source overpressure mechanisms are related tofluid generation at depth, either by hydrocarbon gen-eration, smectite dehydration, or any such internalpressuring mechanism. These overpressure mecha-nisms also show a pressure-stress relationship, but un-like the sedimentary and tectonic loading cases, thepressure is not generated by stress, but instead causesa change in the total stress regime (Yassir and Bell,1994, 1996; Engelder and Fischer, 1994). According toTerzaghi’s effective stress equation (equation 1), achange in pore pressure causes a change in the effec-tive stress, without affecting the total stress, if strainsare allowed in all directions. Under field boundaryconditions where the rock is constrained in a direc-tion, however, the pore-pressure changes can also af-fect the total stresses. The simplest example is the


elastic zero-lateral strain (eH � 0) boundary assump-tion commonly applied to passive basins. The assump-tion is not entirely accurate for passive basins, but it isused to illustrate the effect of purely vertical compac-tion. In this case, the increase in pore pressure resultsin a partial increase in horizontal stress, as defined bythe relationship in equation 5

m 1�2mr � r � P (5)h m P� � � �1�m 1�m

where m � Poisson’s ratio.The horizontal stress (commonly the fracture gra-

dient in sedimentary basins) increases in this case be-cause the rock cannot strain (or so-called bulge) in thehorizontal direction to accommodate the pore-pres-sure increase and the accompanying volume increasein the rock unit. Vertically, the strain boundary is free,and, in the absence of structural effects, there is no cor-responding increase in total vertical stress.Qualitatively there is a great deal of evidence in the

literature to suggest that overpressured rock in sedi-mentary basins is associated with a minimumhorizon-tal stress increase (Breckels and van Eekelen, 1981;Yassir and Bell, 1994; Addis et al., 1996; Engelder andFischer, 1994). Evidence also exists that underpres-sured rock is associated with abnormally low horizon-tal stress (Breckels and van Eekelen, 1981). Fieldmeasurements of reservoir pressures and fracture gra-dients during depletion further illustrate the decreasein fracture gradient with decreasing pore pressure(Teufel et al., 1991; Addis, 1997).The passive-basin equation (equation 5) assumes

that the horizontal stresses are isotropic. Yet it isknown that in most sedimentary basins, there is sig-nificant anisotropy in the horizontal stresses (rH �rh), as indicated by the occurrence of faulting. Herewe consider the effect of overpressuring by a fluidsource at depth on normal faulting (stress systemcausing fault: rv � rH � rh) and thrust faulting(stress system causing fault: rH � rh � rV). In bothcases, it is assumed that the rock block is bounded byan active fault, with an additional tectonic componentof the horizontal stress resulting from fault friction,which has to be overcome before the fault is mobi-lized. The same pressure in the fault plane and intactrock, a plane strain boundary normal to the fault anda constant vertical stress are also assumed. Using elas-ticity theory and the Mohr-Coulomb failure criterionfor slippage on the fault, the relationship betweenhorizontal stresses and pore pressure during mobili-zation of normal and thrust faulting is (Addis et al.,1996)

r 2m P PH P PNormal faulting: � 1� � (6)� �r 1�sin U r rh h h

r 1HThrust faulting: �r m(K �1)h p

PPK � [K (1�m)�m] (7)p p� �rh

where U � internal friction angle of the fault; Kp �Mohr-Coulomb passive coefficient� (1� sinU)/(1�sinU); (Fault cohesion is assumed to be zero in bothequations).The horizontal stress–pore-pressure relationship is

illustrated for both normal and thrust faulting in Fig-ure 5a and b, respectively. In both cases, the ratio ofhorizontal stresses becomes more isotropic with in-creasing pore pressure until PP � rV, at which pointall stresses become isotropic. In the normal faultingcase, the stresses increase with pore-pressure increase,but, depending on the fault friction angle and on theorientation of rH, the maximum horizontal stress canbe parallel or perpendicular with the fault (Figure 5a).In the thrust-faulting case, the stresses decrease withpore-pressure increase, to converge with the verticalstress (Figure 5b).This illustrates, using a simple mechanical model,

the potential integration of pore-pressure and fracturegradients in faulted regimes.

L I M I T S T O P O R E - P R E S S U R E I N C R E A S EA N D F L U I D M I G R A T I O N

The minimum stress is generally accepted as the upperlimit to the pore pressure in a rock (Grauls, 1997). Theminimum stress is the minimum horizontal stress (rh)in normal and strike-slip faulting regimes and can berV or rh in a thrust-fault regime (Addis et al., 1996).As illustrated previously for normal-faulting andstrike-slip faulting regimes, however, where assumingrock elasticity, the pore pressure in a layer can increaseto the value of the vertical stress, causing a correspond-ing increase in rh in that layer. This suggests that it ispotentially difficult for the pore pressure to reach thefracture pressure. The theory is qualitatively sup-ported by field observations of high fracture gradientsin association with high pore-pressure gradients in tec-tonically passive basins (Breckels and van Eekelen,1981; Yassir and Bell, 1994). Yet, it is known from leak-off and hydraulic fracture tests that rock can be hy-draulically fractured at pressures far lower than rV,and from field studies, that fluid pressures can frac-


Figure 5. The relationship be-tween horizontal stress ratio(rH/rh) and pressure gradientfor (a) normal faulting and (b)thrust faulting for different valuesof fault friction angle (U). Here,rH is assumed to be the stressparallel with the fault plane; un-der certain friction angles, it canbecome smaller than the hori-zontal stress normal to the fault(rh) (Addis et al., 1996). rV gra-dient � 1 psi/ft; Poisson’s ratiom � 0.3.

ture, or open fractures, in the overburden, leading tomassive fluid migration.In this discussion, it is important to distinguish be-

tween PP-FG relationships (1) on a regional vs. a lo-calized scale and (2) in different sediment layers. In aleak-off test a local rapid increase in drilling mud pres-sure in the wellbore does not affect the far-field mini-mum stress; a fracture opens where the minimumstress (fracture pressure) is reached, as long as the ten-sile strength of the rock is exceeded (Enever et al.,1996). If the pore pressure increases in a sedimentarylayer, by hydrocarbon generation, for example, this re-sults in a corresponding increase in the fracture gra-dient in that layer. The fracture gradient of thenormally pressured overlying rocks can remain unaf-fected. This means that hydraulic fracturing of theoverburden occurs if the overpressure in the layer ex-ceeds the minimum stress and tensile strength of theoverburden. This is evoked as an effective method ofhydrocarbon leakage in petroleum basins (Grauls,1997). To summarize, although pore pressure is cou-pled with the fracture gradient within one layer, it isuncoupled with the fracture gradient of the overbur-den. It is the minimum stress in the overburden thatcontrols the maximum pore pressure in a layer.Furthermore, on a regional scale, the horizontal

stress is controlled not only by the pore pressure, butalso by a tectonic (or structural) component. The min-imum stress in the overburden can be tectonically re-duced, causing fracturing, seal breach, and massivemigration of overpressured fluids (J. Cosgrove, 1996,personal communication).A note should be made here of references in the lit-

erature to pressures exceeding the overburden stress.For example, in the Himalayan foothills in Pakistan,pressures reach 7000 psi at a depth of 1646 m (Bigelow,1994), amounting to a gradient of 1.3 psi/ft—poten-tially 1.3 times the expected overburden gradient.

These superlithostatic pressures are unstable and canonly be localized (i.e., they are impossible on a regionalscale). They can be accounted for in a thrust-fault stressregime, where rV � r3, the minimum stress, and then,only if the tensile strength of the rock exceeds the porepressure and the vertical stress. In these cases, how-ever, the vertical stress can be greater than the weightof the overburden due to tectonic flexure.

O V E R P R E S S U R E D E T E C T I O N I ND I F F E R E N T T E C T O N I C S E T T I N G S

Standard pore-pressure prediction methods, predomi-nantly developed and calibrated in the soft undercon-solidated Tertiary sediments of the Gulf of Mexico, arebased on finding a porosity anomaly in the overpres-sured sediment, manifested in deviation of velocity,resistivity, and so on, from a normal trend with depth.The previous discussion illustrated that high porepressure can be generated in completely differentstress environments and that the overpressure can in-fluence the stress regime. Each overpressure mecha-nism therefore has a unique geomechanical signature,which is manifested in its porosity.

Porosity–Effective Stress Relationships for DifferentOverpressure Mechanisms

In the absence of shear strain, porosity reduction onlyoccurs with an increase in effective stress (Terzaghiand Peck, 1948). If the effective stress remains constantduring loading, so does the porosity. This is the prin-ciple used in pore-pressure estimation. Further as-sumed in most pressure prediction methodologies isthat overpressure preserves a porosity that is uniquelyrelated to the maximum effective stress experiencedby the sediment, that is, that unloading (by uplift for


example) has little effect on porosity. Knowledge of thenormal compaction trend for the sediment is thereforedeemed sufficient for the estimation of the pore pres-sure from porosity. Figure 6 demonstrates that theseassumptions do not apply to all overpressure mecha-nisms.

Rapid Vertical LoadingThe relationship between porosity and effective stressis defined by the normal compaction curve for the sed-iment (Figure 6). If no compaction occurs during bur-ial, the sediment remains at the same point on itscompaction curve (Figure 6), that is, the pore pressureand porosity become uncommonly high for depth ofburial.

Fluid SourceThe sediment is buried to depth with normal compac-tion (i.e., normal pressure), then is injected with a fluidto a certain overpressure. Here, we can have the samepore pressure at the same depth as the previous case,but the conditions are different. The load on the sedi-ment is constant (no additional burial), but the porepressure increases internally. This decreases the effec-tive stress, which is manifested in unloading of the sed-iment. Because compaction is an inelastic, irreversibleprocess, porosity rebound is below the compactiontrend (Figure 6). Bowers (1994) addressed this unload-ing effect on pore-pressure prediction in basins wherea fluid source is the overpressure mechanism andnoted the less pronounced porosity anomaly associ-ated with this mechanism. Yassir and Bell (1996) madethe same observation for the Scotian Shelf.

Undrained Tectonic ShearingThe sediment is normally consolidated to depth, andthen it is sheared by tectonic forces, resulting in over-pressure. The shearing occurs without drainage (lowpermeability), so the sediment experiences little or noporosity change with reduction of effective stress (Fig-ure 6) (Yassir and Bell, 1996). The porosity response toa change in effective stress is not expected in this casebecause it involves shear strains (Terzaghi and Peck,1948). This mechanism can therefore achieve overpres-suring without a significant porosity anomaly.Even if the three overpressure mechanisms result in

the same pressure at the same depth, the porosity isdifferent for the three cases. In the rapid loading case,the porosity can be used to estimate the effective stress(and therefore pore pressure) using the normal com-paction trend for the sediment. In the case of a fluidsource, a porosity anomaly is registered but it gives anunderestimate of pore pressure with standard predic-tion techniques (Bowers, 1994; Yassir and Bell, 1996).

In the tectonic shearing case, however, the porosity canpotentially remain constant so that the overpressurecan go undetected (Yassir and Bell, 1996).

Pore-Pressure Prediction in Sheared Sediments

The previous discussion suggests that the lack ofporosity anomaly in sediments sheared in a low-per-meability environment renders prediction difficult. Sofar, however, the different overpressure mechanismshave been discussed independently of one another,whereas more than one mechanism can act in one area.Overpressuring by undrained shear is particularly ef-fective in sediments with high porosity (Figure 3),which renders abruptly deposited undercompactedsediments in a compressional basin ideal candidatesfor this mechanism (Yassir, 1989). Furthermore, com-pression is locally associated with overthrusting (e.g.,Barbados Ridge complex, Westbrook and Smith, 1983),which involves the addition of overburden load in amanner not unlike rapid sedimentary loading. Thisshould be possible to detect by geophysical anomalies.In other areas (e.g., Trinidad) (Yassir, 1989), the com-pression is accompanied by significant hydrocarbongeneration, which also contributes to an overpressuresignature.If the shearing mechanism is acting alone, detection

is difficult. Even so, there are cases in which it is pos-sible: shearing can occur under drained or partiallydrained conditions, resulting in fluid migration andpotential overpressuring of adjacent sediments. This isillustrated in Figure 6, which shows the relationshipbetween pore pressure and shear stress for the twolimiting cases (drained/undrained) and the expectedcorresponding porosity–effective stress relationship.Figure 6 shows that the porosity can remain constant,or it can be further reduced by shear-related compac-tion. In other words, overpressuring can also be asso-ciated with abnormally low porosity. Evidence for thiswas presented by Fertl and Chilingarian (1989) in thePripyatskiy Deep, Byelorussia. They found that the Bu-rejskiy shales, which overlie overpressured reservoirs,are highly compacted with an associated increase inresistivity. Theoretically, therefore, tectonic overpres-sures can, in some lithologies, be detected by a depar-ture from the compaction curve that is opposite to thatexpected from the other overpressure mechanisms.

Relationships between Pressure and Fracture Gradients forPrediction

The fracture gradient in a sedimentary basin is com-monly estimated from the pore-pressure and overbur-den gradients. This is done by making an assumption


Figure 6. The relationship be-tween porosity and effectivestress for different pore-pressuremechanisms. Undercompactionis the only mechanism that re-sults in a correct identification ofoverpressure magnitude. A fluidsource mechanism shows a loganomaly, but if undercompactionis assumed, pressure magnitudeis underestimated (Bowers,1994; Yassir and Bell, 1996). Un-drained tectonic shear can resultin overpressuring without an im-pact on shale log properties(Hennig et al., 2002). If tectonicshearing is occurring with partialdrainage, this results in an ab-normally low porosity anomalyin association with overpressure(Fertl and Chilingarian, 1989;Yassir, 1998).

on the stress regime (commonly a variation on the pas-sive-basin assumption, equation 5) or by obtaining anempirical relationship between measured PP and rh(e.g., Breckels and van Eekelen, 1981; Gaarenstrom etal., 1993; and see review in Mouchet and Mitchell,1989). Either approach is valid where confirmed byrepeatable measurements in a particular basin. Theprevious discussion, however, demonstrates that pore-pressure–stress relationships are highly dependent onthe stress regime and the field boundary conditions.Addis et al. (1996) use field data from Breckels and vanEekelen (1981) to compare the effect of different stressconditions on the in-situ PP/rh ratio. They find thatthe commonly used passive-basin assumption can giveunrealistic stress values in some cases. Yassir and Bell(1996) further demonstrate that, for the same basinwith identical passive-basin conditions (equation 5),the same pressure increase by sedimentary loading ora fluid source mechanism results in different PP/rhratios. In that context, methods of estimation of oneparameter from the other should consider the geology,stress system, stress history, and mechanisms of over-pressure.

C O N C L U D I N G R E M A R K S

This chapter illustrates that the pore-pressure and frac-ture gradient in a sediment are intrinsically coupled sothat an increase in one results in an increase in theother. Special emphasis was placed on undrained

shearing as a largely ignored yet potentially importantoverpressure mechanism not only in tectonically activebasins, but in basins experiencing high shear stressescaused by inversion, diapirism, or overthrusting. Thischapter also illustrates that sediment porosity and thePP-FG relationship vary according to tectonic settingand overpressure mechanism. In an era of explorationin less accessible andmore complex geology, therefore,new methods of quantifying the risk and uncertaintyin PP-FG prediction need to be developed.


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89

9Pore-Pressure Estimation in an ActiveThrust Region and Its Impact onExploration and DrillingAllison HennigCSIRO Petroleum,Perth, Australia

Najwa YassirCSIRO Petroleum,Melbourne, Australia

M. Anthony AddisShell, SIEP,Rijswijk, Netherlands;formerly, CSIRO Petroleum,Melbourne, Australia

Andrew WarringtonBP Developments Australia Ltd.,Melbourne, Australia

A B S T R A C T

A study of overpressuring is presented for the fold belt and foreland basin of PapuaNewGuinea (PNG),where pore pressures are known to be highly variable and compartmentalized. The project was initiatedto identify a methodology for predicting pore pressures in PNG, as all the standard approaches to pore-pressure prediction had failed to provide adequate estimates. Ten wells were selected for this study,including normally pressured and highly overpressured wells. Central to this study were the Hidesfield wells. Pore-pressure data are presented from formation pressure tests (repeat formation tests anddrillstem tests) and from kicks calculated from mud weights and shut-in drill-pipe pressures. By de-signing an interactive database, the pressure data were analyzed with respect to topographic variations,the corresponding geology, drilling, and electrical logs and by using drilling events.

The pressure regimes in the overburden and reservoir sections were generally found to be unre-lated. The reservoir pressures were analyzed using different methods both to evaluate the source of thepressures and to quantify the pressures.

The problems encountered with pressure prediction in the shales in this part of PNG are commonto argillaceous sedimentary rocks in uplifted regions. These include the absence of a recognizable nor-mal compaction trend from log data, the presence of uplift, the potential influence of fracturing andshearing on overpressure development and on the compaction trend, and a water table several hundred

Hennig, Allison, Najwa Yassir, M. Anthony Addis, and Andrew Warrington, 2002, Pore-Pressure Estimation in an Active Thrust Region and ItsImpact on Exploration and Drilling, in A. R. Huffman and G. L. Bowers, eds., Pressure regimes in sedimentary basins and their prediction: AAPGMemoir 76, p. 89–105.

90 H E N N I G E T A L .

meters below the drill floor. Poor-quality log data, due to the presence of wellbore damage, exacerbatesthe difficulties of overpressure detection and quantification in the shale formations. Data from theHideswells are used to illustrate the effect of wellbore instability on pore-pressure prediction from electricallogs.

No obvious correlation was observed between the pore pressures and the shale sonic transit times,resistivity, or other electrical and drilling logs because the sedimentary rocks where kicks have beenobserved during drilling do not display significant log anomalies. Standard methodologies of pressuredetection based predominantly on a porosity-related anomaly cannot therefore be applied effectivelyin this region.

Comparing well data was complicated by differences of well elevations, formation depths, andthicknesses. The use of the appropriate datum for comparing pressure data is crucial in identifying thecause of the overpressures. A geomechanical approach was used to assess the sensitivity of electricaland drilling logs to the effective stress in the shales in an attempt to circumvent the problems raisedby elevation differences and highly variable formation thicknesses. The advantage of using effectivestress is that it corrects for the effect of topography on the pore-pressure data. Preliminary results showthat the logs have a weak relationship with effective stress.

The important lesson from this study is that conventional pore-pressure detection techniques inshales cannot be used with confidence in tectonically active regions. The development of an interactivedatabase that captures significant events and conditions in offset wells has proved invaluable in un-derstanding the complexity of the pore-pressure regime in the Hides region and its impact on drilling.The approaches adopted here move some way toward more effective pressure-detection methodologyin complex geological areas.


One of the major challenges for exploration and drill-ing in the Highlands of Papua New Guinea (PNG) isto understand the variability and distribution of thefluid pressures in the area. Both the overburden section(Ieru formation) and the reservoir (Toro formation) canbe highly overpressured, but the fluid pressures arevariable and compartmentalized. The standard meth-odologies for overpressure detection and predictionhave not worked well in the area because they rely onthe identification of anomalous porosities, principallyassociatedwith overpressuring by rapid burial and un-dercompaction. In an area like PNG, tectonic activityand related faulting and fracturing are likely to havean overriding effect on pressure distributions, and thesediments might not be expected to display significantporosity anomalies. In such environments, standardapproaches to overpressure detection and quantifica-tion may be inappropriate. Poor overpressure detec-tion leads to problems in well design (mudweight andcasing point selection) that, in turn, results in large un-certainties and a greater risk of experiencing kicks.Furthermore, it impacts significantly on assessments ofseal breach risk and fluid migration pathways.The scope of this study is to comprehensively re-

view data and drilling experiences for 10 wells in thegeneral vicinity of the Hides field (Figure 1). Most ofthe wells are located in the Papuan fold belt (Hides-1,Hides-2, Hides-3, Angore-1A, SE Mananda-1X, SE

Mananda-2X, Paua-1X, and Kutubu-1X) but two fore-land basin wells (Elevala-1 and Ketu-1) were also in-cluded for comparison (Figure 1). To this end, a welldatabase was created that includes pressure data(kicks/flows, repeat formation tests [RFTs], drillstemtests [DSTs]), fracture data (leak-off tests, formation in-tegrity tests), lithology, stratigraphy, biostratigraphy,and all available electrical logs and mud logs, as wellas drilling events. The database was designed to allowvisual comparison among all the different parameters.The aim of the database was to capture the experiencesfrom offset wells, as well as to identify correlations (ifany) between overpressuring, geology, logs, and/orsignificant drilling events.The chapter discusses variations in pressure distri-

bution in the shaly Ieru formation and the Toro/Im-buru reservoir sections and the difficulties experiencedin detecting and quantifying the overpressures. Thecorrelations between pressures and logs for pore-pres-sure prediction purposes are reviewed, and possiblecontrols on the observed overpressures are discussed.

G E O L O G Y O F T H E A R E A

The Papuan fold belt is a northwest-southeast–trend-ing mountain range that rises to about 3500 m andfaces southwest toward a lowland foreland basin sit-ting approximately at sea level. The fold belt was cre-ated by the Pliocene–Holocene oblique collision of the

Pore-Pressure Estimation in an Active Thrust Region and Its Impact on Exploration and Drilling 91

Figure 1. Map of the studyarea showing general welllocations.

Australian and Pacific plates (Hill, 1991; Eisenberg,1993). The collision and accompanying deformationcaused the inversion of the Papuan sedimentary basin;a Mesozoic rift/passive margin marine sequence anda Cenozoic foreland basin (Hill et al., 1993; Phelps andDenison, 1993; Eisenberg et al., 1994). The major com-mercial hydrocarbon discoveries of PNG are associ-ated with this deformation belt and are located in aseries of thrust-related northwest- to southeast-trend-ing en echelon anticlines formed during this period.Figure 2 is a simplified, representative cross sectionthrough the fold belt, showing the direction of thrustfaulting in the study area.The major units in the region include the Toro for-

mation, which is the main hydrocarbon target, the Ieruformation, and Darai limestone formation. This se-quence is overlain by Quaternary clastics in some lo-calities.

Toro Formation

The Toro formation comprises a series of stacked,areally extensive, gas-rich sand bodies deposited in awave-dominated shelf environment. This formationhas been informally separated into threemembers. Theupper and lower members consist predominantly offine- to coarse-grained sandstone, interbedded withmudstone and siltstone. The middle member is pre-dominantly mudstone and siltstone, with minor inter-bedded sandstone. The Toro is known at outcrop inseveral locations and elevations throughout the foldbelt and foreland basin (Hill, 1991; Eisenberg, 1993). Inthe study area it crops out in the Muller anticlinorium(Figure 1). The Toro formation is overpressured insome areas and normally pressured in others, which

implies that the reservoir has been compartmentalizedby the thrust faulting. The Toro formation is underlainby the shaly Imburu formation, which is not discussedin this chapter.

Ieru Formation

The Cretaceous Ieru formation conformably overliesthe Toro reservoir and acts as a regional seal. It consistsof interbeds of mudstone, siltstone, and sandstone. Thelower section is divided into three members, which indecreasing age are the Alene, the Juha, and the Bawia.These are predominantly comprised of mudstone li-thologies with interbedded siltstone and occasionalminor sandstones. The upper section of the Ieru is di-vided into the Giero, Ubea, and the Haito members,again with decreasing age.The Giero member is further subdivided into the

Giero A, B, and C units. The upper section is sandierbut is generally dominated by mudstone with inter-bedded sandstone and siltstone. Only the Giero C unitis consistently sandstone. The mudstones and silt-stones are generally massive or blocky and soft to firmin texture. They range from moderately to very calcar-eous and are generally glauconitic. The sandstones aremoderately to well sorted, very fine to fine-grainedquartz. Divisions in the Ieru are based on palynologicalassemblages and lithology changes.The Ieru formation was deposited during the Tu-

ronian and Berriasian prior to the opening of the CoralSea and the collision of the Australian and Pacificplates. During the collision the Ieru formation was up-lifted and exposed to erosion. It is known to outcropin places within the fold belt and unconformably un-derlies the Darai limestone (Phelps andDenison, 1993).


Figure 2. Schematic structuralcross section through thePapuan fold belt (modifiedafter British Petroleum).

The Ieru formation is commonly associated with se-vere drilling problems, including gas shows, kicks,wellbore instability, and mud losses.

Darai Formation

The Darai limestone is a thick (up to 2500 m), shallow-marine sequence deposited during the middle to lateMiocene period; it unconformably overlies the Ieru for-mation (Daniels, 1993). Deposition commenced priorto the collision of the Australian and Pacific plates andcontinued during the subsequent inversion of the Pap-uan basin that led to the development of the fold andthrust belt (Phelps and Denison, 1993). At outcrop, thislimestone unit is deeply karstified, which has, until re-cently, prevented acquisition of high-quality seismicdata in the fold belt (Hill et al., 1996). Thus outcropand well information have formed the basis for struc-tural models and have provided the only means ofunderstanding and predicting subsurface pressure dis-tributions.

P R E S S U R E R E G I M E S

The pressure data measured in the 10 wells selectedfor this study (Figure 1; Table 1) illustrate the signifi-cant pressure variability across the area, both withinindividual formations and between overburden andreservoir. Pressure data are presented in MPa (1 MPa� 145 psi), and pressure gradients (equivalent mudweights [EMWs]) are presented in terms of their spe-cific gravity (s.g.). Note that 1 s.g. unit � 9.81 kPa/m� 0.433 psi/ft.

Summary of Well Pressures

In the Hides field and Angore-1X, the Ieru formationis more overpressured than the reservoir. Kicks have

been recorded in the Giero B and C units in thesewells,but not in the lower part of the formation (Juha/Alenemembers) in which the pressures are unknown. Theuncertainty regarding the continuation of overpressur-ing in the lower Ieru section in these wells renders cas-ing design problematic.The pressure system in the southeast Mananda

wells is very different: the Ieru formation is sandierand seems to be only slightly overpressured, withmoderate overpressuring in the reservoir. The sameapplies to Paua-1X, but reservoir pressures reach avalue of 2.19 s.g.—the highest recorded pressure gra-dient in this study (Table 1). Further to the southeast(Figure 1), Kutubu-1X shows severe overpressuring inthe Ieru formation again, but the pressures appear tobe normal down to the top of the Juha/Alene mem-bers, where kicks occur at pressures exceeding 2 s.g.The high overpressures continue into the Toro forma-tion in this well (Table 1).Considerable variability in the pressure profiles of

the wells in the fold belt is apparent. By contrast, thetwo foreland wells have thin, sand-rich, normally tomildly overpressured Ieru formations and a normallypressured reservoir (Table 1).In the following section, we examine the pressures

in the overburden and the reservoir separately. As isillustrated in the following section, comparisons be-tween wells in this type of terrain are difficult, as theselection of the appropriate datum is not obvious. Forexample, choosing a kelly bushing (or drill floor) leveldatum is inappropriate for comparing pressure data ifthe overpressures have an artesian origin (connectionto an elevated outcrop). Depending on the datumused, pressure-depth plots of the composite well datacan lead to very different interpretations. The identi-fication of a correct datum depth at which to plot pres-sure data is therefore crucial for an understanding ofthe source of the overpressures. Pressure analyses arefurther complicated by steeply dipping beds, three-


Table 1. Elevation and Formation Thickness for Wells in the Study Area and Their Equivalent Formation Pressure*

Well Name Latitude (S) Longitude (E)

KellyBushingElevation(m AMSL)

Depth ofWaterTable(m RKB)

Depthto Ieru

Formation(m RKB)

Depthto ToroFormation(m RKB)

Max.PressureGradientin Ieru

Formation(s.g.)

Max.PressureGradientin Toro/ImburuFormation(s.g.)

Fold BeltAngore-1A �5� 58� 3.55� 142� 53� 3.66� 1610 200 2547 3994 1.73 1.26Hides-1 �5� 55� 51.76� 142� 42� 49.97� 2698 962 1094 2999 1.64 1.31Hides-2 �5� 56� 56.18� 142� 43� 52.26� 2454 665 1254 2725 1.68 1.4Hides-3 �5� 56� 59.51� 142� 44� 40.76� 2264 632 1232 3019 1.85 1.31Kutubu-1X �6� 27� 55.8� 143� 20� 57.6� 1260 525 847 2062 2.03 1.99Paua-1X �6� 14� 54.06� 143� 10� 25.14� 1594 520 454 2759 1.42 2.19SE Mananda-1X �6� 16� 19.46� 143� 2� 30.63� 1541 350 1045 2024 1.13 1.34SE Mananda-2X �6� 15� 56.87� 143� 0� 59.71� 1708 617 1064 2179 1.10 1.26

Foreland BasinElevala-1 �6� 9� 4.92� 141� 45� 57.42� 64 20 2329 3102 1.34 1.02Ketu-1 �6� 2� 15.62� 141� 47� 20.34� 101 7 2451 3334 0.99 1.00

*AMSL � above mean sea level; RKB � relative to kelly bushing; 1 s.g. � 0.43 psi/ft.

dimensional structural closures, reservoir outcrop atseveral elevations, and pressure compartmentaliza-tion.

A Note on Datum Selection

In such mountainous terrain, difficulties arise in di-rectly comparing pressures between two wells. Thereis variability in topographic elevation, depth to variousformations and their thickness, dip, structure, andeven in the top of the saturated zone (water table—with the additional complexity of seasonally changingwater-table elevations). Close attention therefore needsto be paid to the datum used in pressure analysis. Thiscan be a formation top, sea level, ground level, or thewater table, depending on the type of analysis requiredand the prevailing geological conditions.

Reservoir Pressures

To illustrate the importance of datum selection, Figure3 is a plot of RFT/DST pressures in the Toro and Im-buru formations plotted relative to kelly bushing (Fig-ure 3a) and to sea level (Figure 3b). Ieru formationpressures in Elevala-1 and Paua-1X were measured byRFTs, and these are also noted for comparison.Figure 3a shows clearly that the Kutubu-1X and

Paua-1X reservoir sections had to be drilled with highmud weights (�2 s.g.). Note that the Ieru formationpressures in Paua-1X are subhydrostatic (�1 s.g.),which can be explained by the low water table, re-

corded at 520 m below kelly bushing, (i.e., within theIeru formation, Table 1). The Ketu-1 and Elevala-1wells are hydrostatically pressured in the Toro,whereas the remaining well data indicate only mod-erately overpressured reservoirs, with pressure gradi-ents less than 1.5 s.g.Where the data are plotted relative to sea level (Fig-

ure 3b), the interpretation is different. The wells in theforeland basin Ketu-1 and Elevala-1 still lie on thefreshwater hydrostatic gradient because their kellybushing is close to sea level. This may indicate thatthese wells are connected to a Toro outcrop lying closeto sea level. In the fold belt the Toro formation out-crops at much higher elevations. The outcrop at theMuller anticlinorium (Figure 1) occurs at approxi-mately 2350 m above mean sea level (AMSL) (Grainge,1993), Figure 3b. Southeast Mananda-1X and -2X pres-sures seem to be hydrostatic and are possibly in pres-sure communication with the outcrop, as suggested bythe hydrostatic water gradient between them (Figure3b). The pressures measured in the Hides and Kutubu-1X wells are similar in magnitude and plot at the samedepth relative to sea level (Figure 3b). Because of thedifference in well elevations, however, the Toro for-mation pressures in the Hides wells appeared onlymildly overpressured during drilling, whereas in Ku-tubu-1X, they are associated with very high mudweights (1.8 s.g.) (Figure 3a). Figure 3b also clearlyshows that the Toro pressures in the foreland wells(Ketu-1 and Elevala-1) appear unrelated to the pres-sures in the fold belt.


Figure 3. Reservoir RFT/DSTpressures in all wells plottedrelative to (a) kelly bushing(RKB) and (b) sea level (RSL).Where Ieru formation pressuresare plotted, these are labeled(1 MPa � 145 psi).

Pore Pressures in the Overburden

Pressure estimation in argillaceous formations is no-toriously difficult because of the low permeability ofthe rock. Accurate pressure measurements are alwayssparse and associated with high-permeability string-ers. The Ieru formation is no doubt overpressured inmany wells, but the degree and extent of overpressur-ing is unknown except where a kick is taken whendrilling a sandy layer and, uncommonly, where RFT/DST measurements are taken (Elevala-1, Paua-1X).Many of the recorded influxes are gas, which indicatesthat the Ieru is not completely water saturated. Thisrenders the application of pressure detection technol-ogy more difficult because (1) it is dependent on theassumption of a saturated, undercompacted shale se-quence, and (2) some electrical logs used for detectionmay need to be corrected for the presence of gas.Pressure determination is further complicated by

the occurrence of stress-induced wellbore instability(Twynam et al., 1994; Addis et al., 1998), which can bemistaken for overpressuring.All kicks and flows recorded in the wells included

in this study are listed in Table 2. The pressures re-corded during the kicks in the Ieru formation are plot-ted relative to the kelly bushing in Figure 4a andrelative to the top of the Ieru in Figure 4b to illustratethe lack of any relationship between the observed pres-sures and the datum.The pattern of overpressuring in the shales is incon-

sistent even for wells within the same field. The threeHides wells all experienced kicks while being drilled inthe Ieru. In these wells, the depth to the top of the res-ervoir and the thickness of the overburden varies byonly 200 m, with Hides-1 being the deepest and Hides-

3 the shallowest (Table 1). The kicks range in value be-tween 1.64 s.g and 1.90 s.g. The kicks taken in the GieroC sandstone in Hides-1 and Hides-3 were 1.64 and 1.85s.g., respectively, although the two wells are located insimilar locations, on the crest of the Hides anticline.In contrast, the foreland basin well, Elevala-1, which

has a similar depth to the top of the reservoir (Table1), was drilled with much lower mud weights and ex-perienced a kick of 1.34 s.g. in the Ieru.Overpressures in the overburden have been esti-

mated and discussed here based on kicks only. Mudweights have not been used because they are not reli-able indications of the pore pressures where wellboreinstability occurs.

P O R E - P R E S S U R E P R E D I C T I O N I N P N GF R O M L O G S

The pressures measured in stringers are normallytaken as representative of the pressures in the juxta-posed argillaceous sediments. In the absence of suchdata, the pressures in argillaceous sedimentary rocksneed to be understood and evaluated by other means.This is commonly achieved through the use of drillinginformation and log data. Where seismic data areavailable, interval velocities can be correlated to thedrilling and log data to estimate the likely pore pres-sures. No seismic data were available for this study.The use of the log-based data to achieve an under-

standing of the overpressures in the shale and mud-stone lithologies of the PNG fold belt is now discussed.The structural complexity and the topographical vari-ations of the region again make interpretation of porepressures in the shales difficult.


Table 2. Kick/Flow Pressures and Parameters for Wells in the Study Area*

Well Name Kick Depth (m RKB) Kick EMW (s.g.) Kick Pressure (MPa) Formation Influx Fluid

Angore-1A 3511 1.73 59.47 Ieru/Giero C Gas4107 1.26 50.67 Toro ?Gas4226 1.33 55.03 Imburu ?Gas

Elevala-1 2426 1.34 31.83 Imburu GasHides-1 2305 1.64 37.01 Ieru/Giero C Gas

3002 1.31 38.50 Toro GasHides-2 1906 1.68 31.35 Ieru/Giero B GasHides-3 2038 1.90 37.91 Ieru/Giero B Water

2258 1.85 40.90 Ieru/Giero C WaterHides-3 sidetrack 3000 1.40 41.06 Ieru/Alene GasKutubu-1X 1857 1.88 34.18 Ieru/Juha Water

2029 2.03 40.33 Ieru/Alene ?2065 1.99 40.23 Toro ?

Paua-1X 2767 1.68��1.99 45.51��53.91 Toro Water2888 2.08 58.58 Imburu ?3138.7 2.19 66.83 Imburu ?

*RKB � relative to kelly bushing; EMW � equivalent mud weight; ? � unknown.

Figure 4. Ieru formation pressures from kicks and some RFT data, plotted (a) with mud weight as EMW (equivalent mudweight) vs. depth relative to kelly bushing; (b) as pressure vs. depth relative to the top of the Ieru.

Electrical Log Anomalies

Pore-pressure prediction from logs traditionally relieson the identification of a normal compaction trend ina lithologically uniform and thick shale sequence. Anormal compaction curve based on local data, or a ge-neric global curve, can be used for the analysis(Mouchet and Mitchell, 1989). The latter normally re-quires local calibration to well data. These methods of

pressure detection identify the onset of overpressuringwith the occurrence of an anomalously high porosity(undercompaction) for the depth. Overpressuring ap-pears as a reversal or deviation from the normal com-paction trend line. The extent of the deviation from thenormal trend is used to quantify the overpressure.This methodology works well in young basins wherethe depositional environment is stable and continuous.The method commonly relies on the presence of a


uniform shale lithology—where only one compactioncurve needs to be identified. Where sediment sourceshave varied over time and led to differing shale li-thologies andmineral assemblages, the compaction be-havior (Aplin and Yang, 1995) and the resultant logresponse with depth varies. Accurate pore-pressureprediction then relies on identifying numerous com-paction trends—one for each shale or mudstone li-thology.In the PNG fold belt the validity of using a com-

paction trend-line approach to pore-pressure predic-tion in shales is questionable, as many of the criteriaunderlying this pore-pressure predictionmethodologyare violated:

1. Discontinuous shale and mudstone deposition,with variable lithologies

2. A thick (up to 1000 m) limestone overlies theshale, which would have significantly enhancedcompaction

3. The rocks have been heavily deformed and up-lifted, which leads to pervasive fracturing, andaffects not only formation porosity but fluid pres-sures as well (Yassir and Addis, 2002)

As mentioned previously, the Cretaceous Ieru forma-tion, although thick in some areas, comprises interbed-ded shale and thick sandstone units and is known tohave undergone major tectonic uplift and deformationin the late Tertiary. Under the circumstances, the ov-erpressuring observed in the Ieru formation may notbe the result of undercompaction. Any study of pore-pressure estimation in shales based on wire-line logsis further complicated by the occurrence of wellboreinstability (breakouts), particularly in tectonic regions.In the Ieru, wellbore instability is known to have oc-curred during drilling. Nevertheless, the ability to es-timate the pore pressures in the Ieru shales from logdata was addressed along with an assessment of thepotential errors introduced into the analysis due to thepresence of wellbore instability and wellbore damage.Figure 5 shows drilling and pressure data for

Hides-1 and the corresponding wire-line log curvesthat are commonly used to determine normal compac-tion gradients for pore-pressure evaluation: resistivityand transit time, and a gamma-ray log for shale iden-tification. The well location does not contain a thicksection of pure shales from which to define a normalcompaction trend, a problem common to all of thewells in this study. The transit time increases withdepth into the Ieru formation then abruptly decreaseswith depth at around 2000 m relative to kelly bushing.The initial increase in transit time (slowness) could beinterpreted as the onset of overpressuring; however, it

corresponds to wellbore instability problems encoun-tered in the upper Ieru sections (Figure 5). Note alsothat the transit-time response decreases with depth to-ward the Giero C unit, which is known to be highlyoverpressured in this well. This is contrary to whatwould be expected. A similar observation was madefor the resistivity logs (Figure 5).

Generic Compaction Curves for Pore-Pressure Prediction

The absence of a normal compaction trend line in log-based data has led to the use of generic trend lines, orcompaction curves, which are considered to be glob-ally applicable. This approach to pore-pressure predic-tion has been widely adopted (Eaton, 1972; Mouchetand Mitchell, 1989; Holbrook, 1995).Generic compaction curves define the change of

some porosity-related property; resistivity, sonic tran-sit time, and so on, with effective stress. The variationof the parameter from the generic curves indicateslower effective stress acting on the rock, and, by im-plication, higher pore pressures. Because the detectionand quantification of pore pressure is based on thepresence of a porosity anomaly, this method is mostsuccessful in detecting overpressures caused by un-dercompaction (Bowers, 1995; Yassir and Addis, 2002).The generic compaction curves are lithology specific,and large variations in the back-calculated pore pres-sures can occur, depending upon the mineralogical as-semblage (Skempton, 1970; Baldwin and Butler, 1985).As a result, calibration of these global techniques tolocal well experience is commonly necessary. The useof generic compaction curves for pore-pressure detec-tion and evaluation has the same underlying assump-tions as the compaction trend-line–based approachthat uses local data. Consequently, the use of genericcompaction curves to calculate pore pressures is the-oretically inconsistent with the geological develop-ment of a tectonic region, where uplift and lateral shearare dominant geological processes.These potential shortcomings were illustrated

where the pore pressures in the Hides wells were eval-uated using the Eaton method, the most commonlyused of the generic relationships. Sonic-log compactiontrend lines were superimposed on the data fromHides-1, Hides-3, and Elevala-1. The Eaton curveswere calibrated to kick data observed in the Hides-3(Figure 6a) and Elevala-1 (Figure 6b) wells. Shale sonicvalues were used that are within 1–2 m from the kicklocation, with the assumption that the shale layershave the same pore pressure as calculated for the kick.Three wells are shown in Figure 6: Hides-1, Hides-

3, and Elevala-1. The Hides-3 data are used to calibratethe Eaton curves, in preference to Hides-1, as the for-


Figure 5. Hides-1 generalizedstratigraphy showing pressuremeasurements and e-logs. Deltatransit time (DT) in ls/ft; induc-tion resistivity deep (ILD)/laterolog deep (LLD) in ohms;gamma ray (GR) in API units.K denotes kick (an influx offormation fluid).

mer contains fewer artifacts arising from wellbore in-stability. The data from these three wells allow acomparison between pore-pressure prediction in theuplifted wells of Hides and the Elevala-1 well, whichhas undergone less uplift. The data also allow a com-parison between the Hides-1 and Hides-3 wells, whichare the most geologically similar on the Hides struc-ture. Using these comparisons the likely success of thecompaction-curve approach for pore-pressure estima-tion in this area was assessed.The location of the normal compaction trend line

varies quite considerably depending upon the choiceof the pore pressure taken for the calibration. Usingthe Elevala-1 kick to construct the normal compactioncurve results in large errors in pore-pressure predic-tions in the uplifted Hides wells. More seriously, con-structing the compaction trend line based on the kickin Hides-3 leads to large errors when predicting thepore pressures in the adjacent Hides-1 well. Errors arein the order of 0.2–0.3 s.g., which are unacceptable forwell design and for drilling purposes. The shortcom-ings of this approach are not expected to be limited toEaton’s curves but to the use of any generic compac-tion curve that relies on a porosity-related anomaly asa measure of the overpressure.The use of standard log-based methods for pore-

pressure prediction in the Hides area by BP has been

unsuccessful and was the basis for initiating the pro-ject. The approach described here is consistent withBP’s experience. Consequently, a broader approach toidentifying pore pressures and hole problems whiledrilling was adopted by generating a database ofevents.

Pore-Pressure Prediction in Uplifted Shale Formations

Pore-pressure prediction in areas that have experi-enced uplift requires corrections to standard pore-pressure methodologies and techniques. Using thestandard trend line or a generic compaction-curve ap-proach, the correction entails displacing the compac-tion curves to different depths. This is equivalent tounloading with no relaxation—zero porosity change—which is a conservative approach, particularly wherethe uplift has been accompanied by major tectonicshearing, faulting, and natural fracturing. We arguethat, having gone through uplift and shearing, the sed-iments no longer resemble the preuplift and preshearsediments in terms of their compaction state, mechan-ical properties, and porosity profile.Pore-pressure evaluations that incorporate the ef-

fects of unloading have been discussed by Bowers(1995) and Ward et al. (1995). Unloading curves weredeveloped that account for increases in porosity with


Figure 6. Comparison of pres-sure prediction using Eaton’strend lines calibrated with (a)Hides-3 and (b) Elevala-1 datawith observed kicks.

reduction of effective stress. Both studies require thatregional unloading responses of the logs are definedfor the overpressured sections. Bowers (1995) andWard et al. (1995) consider mechanical unloading–ef-fective stress decreases resulting from overpressuregeneration at depth. The physical unloading experi-enced in PNG requires a different approach, especiallyas the tectonic forces driving the uplift physicallychange rocks and their mechanical behavior.To summarize, the detection of overpressures using

compaction trend lines based on a monotonically de-creasing porosity with stress (or depth) appears inap-propriate in the Papuan fold belt. Depth-correctedcompaction curves, which aim to consider the effectsof physical uplift, inherently assume that the magni-

tudes of overpressure can be quantified using the un-dercompaction-based curves. This ignores anygeological processes that have accompanied uplift.Bowers (1995) shows the shortcomings of this ap-proach for less complicated unloading scenarios andgeological environments.

G E O M E C H A N I C A L A P P R O A C H T OP R E S S U R E E V A L U A T I O N

The discussion of pore-pressure detection has centeredon the difficulties experienced when working in amountainous area that has been uplifted, where thewells have different elevations, where formation thick-


Figure 7. Effective stresses(curves) from kicks and EMWplotted with delta transit time(DT, shown as symbols) againstnormalized depth (top Bawiashale, Ieru formation) for fivewells from the study area.

nesses vary, and where the cause of overpressuring isunknown. The use of undercompaction-based meth-odologies for quantifying the magnitudes of the over-pressures has been hampered by the lack of anynormal compaction trend line and is deemed inappro-priate for this complex geological region. To start toaddress some of this complexity and specifically theproblem of appropriate datum selection, a geomechan-ical approach was used to assess whether any im-provement in the analysis could be achieved.Rock properties such as porosity are highly depen-

dent on overburden thickness and stress, and this hasto be corrected for when comparing wells in this re-gion. Using the vertical effective stress (overburden to-tal stress minus pore pressure) normalizes the resultswith respect to the overburden. This enables the mostdirect comparison of data between wells of differentelevations. Mud weights and kick pressures for theIeru formation were used to calculate the vertical ef-fective stress in the Hides wells, Elevala-1, and Ku-tubu-1X, using an overburden gradient of 1 psi/ft asan estimate. Wells with the highest pore pressureshave the lowest effective stress, and those with thelowest pressures have the highest effective stress. Be-cause of highly variable Ieru thickness, the datumdepth used in Figure 7 is the center of the Ieru for-mation, which allows direct comparison of the log anddrilling data between wells. Sand units were removedfrom the transit-time curves, leaving only the mud-stones and siltstones for evaluation.The estimated effective stress values presented in

Figure 7 show that, as expected, the normally toslightly overpressured Elevala-1 has the highest effec-

tive stress, the overpressured Hides wells have thelowest, and Kutubu-1X, which is also normally tomildly overpressured, lies between. In contrast to this,the sonic response for the Hides and Elevala-1 wellsare similar throughout the Ieru formation regardlessof the significant variation in effective stress. The tran-sit time of Kutubu-1X is lower (faster) and almost con-stant with depth. It would be expected that if the soniclogs were accurately representing the pressures foundin the Ieru formation, the relative positions of the tran-sit-time curves would correspond better with the ef-fective stress data. Instead, this is not seen because thesonic response of three of the fold-belt wells is almostoverlain by the sonic response of the foreland wells,despite the significant difference in the calculated ef-fective stress.Figure 8 is a plot of effective stress based on pres-

sure measurements in shale vs. sonic transit time forall of the wells in this study. Despite the previous find-ings, Figure 8 does show a weak relationship of de-creasing effective stress with increasing transit time(higher porosity). This suggests that the sonic log mayhave some sensitivity to the overpressure; however,the relationship cannot as yet be used in a predictivesense because of the significant scatter of the sonic re-sponse. The same finding was confirmed for the den-sity logs and the neutron logs.The failure of the sonic logs to reflect the measured

pore pressures suggests that overpressuring is notnecessarily associated with a porosity-related anomalyin this area. Consequently, the factor of undercompac-tion in overpressure generation is considered to beminor. This is consistent with overpressures produced


Figure 8. Effective stress values from shales in the Ieru forall wells from the study area plotted against delta transittime (DT).

by tectonic shearing, which commonly go undetected(Yassir and Addis, 2002). Although standard pore-pres-sure analysis and prediction techniques do not workwell in the study area, rigorous geomechanical corre-lation between wire-line logs and effective stresses maybe of value in improving pressure prediction.

E F F E C T O F W E L L B O R E I N S T A B I L I T Y O NP R E S S U R E D E T E C T I O N F R O M E L E C T R I C A LL O G S

A further complication in pore-pressure detection inshale sections is the occurrence of wellbore instability(McLean and Addis, 1990). Instability occurs in thema-jority of shale formations in hydrocarbon explorationwells and particularly in areas of high stress, such asPNG. Wellbore instability is recognized in most com-pressive areas throughout the world, for example, inPNG (Twynam et al., 1994; Addis et al., 1998), offshoreBali (Ramos et al., 1998), in the Canadian Rockies(Woodland, 1990), and in Colombia (Addis et al., 1993;Last and McLean, 1995; Last et al., 1996).Wellbore instability commonly manifests itself as

breakouts: elliptically shaped, overgauge holes cre-ated by anisotropic compressive stresses, which areaccompanied by the development of cavings.Wellboreinstability occurs during both overbalanced and un-derbalanced drilling and has the same signature inboth cases: shale sloughing, cavings, mud-weight in-creases, and gas increases. Consequently, none of thesecan be used as true pore-pressure indicators in shaleformations. More significantly for pore-pressure detec-tion, electrical logs, even where corrected for hole size,

are highly sensitive to borehole condition (Addis et al.,1998). This has been recognized in the Colombian foot-hills, where stress-related hole problems were initiallyattributed to overpressures. Electric logs are correctedfor borehole size but not for the change in the rockfabric in the unstable and damaged wellbore wall (Ad-dis et al., 1990). Wellbore damage has been recognizedin both in-gauge holes and out-of-gauge holes. Thereis a wealth of literature describing the electric-log re-sponse due to wellbore damage and mud-shale inter-action (Hornby and Chang, 1985; Wu et al., 1993;Winkler, 1997; Boonen et al., 1998; Hsu et al., 1998).Two questions are addressed in this chapter. (1)

How significant is the effect of wellbore damage onpore-pressure detection and quantification? (2) Doeswellbore damage influence the pore-pressure evalua-tion in PNG?To address the first question, time-lapse logging

data from five separate logging runs of a long-spacedsonic tool were used to determine the potential errorin pore-pressure estimation resulting from boreholedamage (Figure 9). The data come from an offshorewell where wellbore stresses and mud-shale interac-tion have affected the wellbore (Blakeman, 1982).Changes in the interval transit-time response of up to23 ls/ft (0.3 m) were recorded over a period of 35 days.If these altered sonic data were used for pore-pressureevaluation a significant error would be introduced.This is illustrated using Eaton’s relationships to quan-tify the resultant apparent pore pressures. The altera-tion of the sonic values of 5–20 ls/ft (0.3 m), due towellbore damage, results in a normally pressured for-mation having an apparent pore pressure of 1.19 to1.54 s.g. Electric logs are not commonly rerun repeat-edly over the same interval with significant time inter-vals between each run, which makes removing suchartifacts from pore-pressure analysis difficult. Asstated previously, the mud weights offer little help indistinguishing between pore pressures and instability-related log anomalies.The occurrence of wellbore instability in the Papuan

fold belt is well known, and the geological stresses act-ing in the area, as well as the mud types used in theearlier wells, are know to have contributed to the in-stability (Twynam et al., 1994). The effect of instabilityon the log response for Hides-1 is shown in Figure 10a,which is a plot of the sonic log against the caliper datain the 8.5 in. section. Hides-1 is known to have expe-rienced wellbore instability problems, confirmed bythe elliptical-shaped hole on the four-arm caliper data.Figure 10a shows a scatter of data with an increase inthe minimum sonic traveltime with larger borehole di-ameters. Figure 10b shows the corresponding sonic-logvalues for Hides-3, which experienced few hole prob-


lems. A similar response is also observed in the resis-tivity log for the same hole sections for these twowells.Figure 11 shows the difference in the distributions

of sonic values from Hides-1 to Hides-3. The two wellsare considered to be very similar geologically and aregeographically the closest wells in the Hides area. Theshift in the sonic transit-time distribution to higher val-ues in Hides-1 is considered to be a result of the well-bore damage and instability. This shift in sonic valuesof approximately 20 ls/ft (0.3 m) from 91 to 112 ls/ft(0.3 m) gives rise to apparent pore pressures. Theseshifts are consistent with altered sonic traveltimes re-ported by Hornby and Chang (1985). Using the sameapproach as previously, for a true pore-pressure gra-dient in the Ieru shales of 1.8 s.g., the shift in the sonic-log response of 20 ls/ft (0.3 m) would give rise to anapparent pore pressure of approximately 2.05 s.g.The deviation of transit times from a normal com-

paction trend, which is used to identify overpressur-ing, can therefore sometimes be purely an artifact of

wellbore instability. The occurrence of wellbore insta-bility and the effect of wellbore damage on the sonic-log response give rise to large errors in pore-pressureprediction. In-gauge boreholes can contain incipientbreakouts (Brereton and Evans, 1987; Hornby andChang, 1985; Addis et al., 1990), which also result in aporosity increase of the borehole wall. These effectswould be particularly seen in areas of high tectonicstresses.For the reliable use of porosity-based log data (e.g.,

sonic, resistivity, density) the data quality of the logdata can only be assured by eliminating the possibilityof wellbore instability or wellbore damage. This is alsoessential where mud-weight data are used as an indi-cator of pore pressure, particularly in a tectonically ac-tive region such as PNG.

P O S S I B L E C A U S E S O F O V E R P R E S S U R I N GI N T H E P A P U A N F O L D B E L T

Several overpressure mechanisms are briefly consid-ered in this chapter as possible causes of overpressur-ing in PNG. We also refer readers to a detailed reviewin Kota et al. (1996). Note that the driving mechanismsbehind the pressures in the Ieru may be different fromthose defining the Toro pressures. The following sec-tions constitute preliminary views based on the limiteddata set used in this project.Reservoir connection to a recharge area at high to-

pographic elevation is the most obvious potentialcause of overpressure in the reservoir in a mountain-ous terrain. This possibly explains the SEMananda res-ervoir pressures (Figure 3b). Reservoir connection to arecharge area at high topographic elevation is also thegenerally accepted interpretation of the reservoir pres-sures in the Hides-Angore structure (Grainge, 1993; Ei-senberg, 1993; Kotaka, 1996), although the gas-watercontact (GWC) has not yet been penetrated. Maximumreservoir water heads in Kutubu-1X and Paua-1X,however, are 3000 m and more than 5500 m, respec-tively. In the absence of Toro outcrops at these eleva-tions, the pressures would be controlled by otherfactors.Compaction disequilibrium associated with rapid

sedimentary loading is a common cause of overpres-suring in young sedimentary basins. Unlikely, how-ever, is that the high overpressures observed in someof the wells in this study are related to this mechanism,because the geological conditions necessary for thisform of overpressuring are absent. Ideally, compactiondisequilibrium occurs in thick, abruptly deposited, pref-erably Tertiary, shale sequences. The Cretaceous Ierusection can be thick in places but contains dominant

Figure 9. Effect of wellbore alteration with time for foursections of a well on the (a) sonic response of a long-spaced sonic tool (from Blakeman, 1982) and (b) thecalculated apparent pore pressures.


Figure 10. The relationship be-tween the sonic transit time(slowness) and the average holesize encountered in (a) Hides-1and (b) Hides-3. Both intervalswere drilled with 8.5 in.diameter drill bits.

Figure 11. The sonic transit-time frequencydistributions for Hides-1 and Hides-3 acrossthe Ieru formation.

0

1

2

3

4

5

6

1 2 0 1 4 0 1 6 0

Sonic Travel Time (µs/ft)

No

rmal

ized

Fre

qu

ency

(%

) Hides 1

Hides 3

Change with Overgauge hole

800 20 40 10060

sandstone layers (which would have assisted compac-tion) and is overlain by a massive carbonate sequence.Furthermore, the Ieru formation has been subjected tosevere uplift and deformation, which not only radi-cally affects the fluid pressure, but also the porosityand log signature of the sediments. Not surprising,therefore, is that the Ieru formation does not displayclassic undercompaction anomalies, such as repeatablesonic-velocity reversals on all wells. Discrete reversalsin electrical and drilling logs are observed in places,which may reflect some undercompaction, but theseare not meaningful in the absence of a compactiontrend. They could just as easily be caused by litholog-ical variations, fracturing, or wellbore instability. Un-der these conditions, undercompaction may beconsidered a secondary mechanism at best. The pre-

vious comments only apply to observations made ofthe wells in this study; undercompaction may be animportant mechanism in geologically recent deposi-tional areas in PNG (e.g., Eastern Gulf of Papua).Papua New Guinea is a tectonically active area,

which is an important consideration in studying for-mation pressures. Tectonic shearing of low-permeabil-ity sediments can result in significant localizedoverpressures (Yassir and Addis, 2002); unfortunately,these are not commonly associated with porosityanomalies (Yassir and Bell 1996; Yassir and Addis,2002). Tectonic shearing could be an important over-pressure mechanism in PNG, as it seems to be in otheroverpressured regions, for example, Trinidad, Azer-baijan, and the Gulf of Alaska (Yassir andAddis, 2002).Another component of this mechanism is tectonic


overburden loading (Kota et al., 1996). This involvesaddition of overburden load by overthrusting, whichcould result in a porosity anomaly.The volumetric expansion of fluids at depth, related

to hydrocarbon generation (or, less likely, smectite de-hydration), can result in significant pressuring withsome associated porosity increase (Yassir and Bell,1996). The possibility that oil and gas generation hascontributed to the overpressures should not be ig-nored. A formation can also become overpressuredthrough connection to a pressure source. In PNG, thisis most likely to occur by tectonic squeezing of a for-mation, which causes fluid migration and entrapmentinto a structure. The shallow pressure gradients asso-ciated with hydrocarbon columns result in pressureanomalies at depth, which could be mistaken for over-pressure, especially if there is connectivity between thehydrocarbon column in the reservoir and overburdenformation pressures. This is the generally accepted in-terpretation of the high reservoir pressures in theHides-Angore structure (Grainge, 1993; Eisenberg,1993; Kotaka, 1996).Uplift is commonly cited as a potential overpressure

mechanism. In theory, a formation with hydrostaticpressures can be uplifted, rendering its pressure out ofequilibrium with the shallower depth. This requiresthe seal to perfectly maintain its volume to preventpressure equilibration. In practice, however, all geo-logical seals expand and can commonly fracturewherethey are subjected to a reduction in effective stresses(through uplift in this case). Minimal expansion resultsin pressure dissipation and even underpressuring insome cases. Uplift as an overpressuremechanism is notproposed for PNG.


The previous discussion has demonstrated the diffi-culty of understanding the pressure environment inthe Papuan fold belt. It is a geologically complex areawith locally compartmentalized pressures. Also, res-ervoir pressures appear unrelated to the Ieru overbur-den pressures.Correct selection of a reference datum, from which

to plot any measured data, is crucial to correct inter-pretation where surface elevations are not constantand where high structural dips and pressure compart-mentalization occur. A conventional approach to wellplanning, which assumes the wellhead to be close tosea level, is not applicable to pressure prediction andevaluation in a mountainous terrain. To make analysisof pressure data from a number of wells meaningful

for the shales, the effect of overburden should be con-sidered.Using different pressure-depth plots, this study has

found some pressures to be linked to surface outcropand others to be compartmentalized. Reservoir pres-sures of two foreland wells (Ketu-1 and Elevala-1) areshown to be hydrostatic, and two of the fold-belt wells,SE Mananda-1X and SE Mananda-2X, are likely con-nected to outcrop of reservoir formations high in thefold belt, which explains their mild overpressure.Paua-1X and Kutubu-1X, however, are most likelycompartmentalized.In the course of this study, it was found that stan-

dard pressure-prediction techniques using wire-linelogs are ineffective in this area. One reason for this isthe lack of suitable conditions necessary for reliable loginterpretations, specifically, the absence of a relativelyuniform and thick shale zone to establish representa-tive compaction trend lines. The use of generic com-paction curves is also seen to be of limited use in thisarea.Nevertheless, comparison of the sonic-log responses

from wells within the same field, wells spatially dis-tant, wells from the active fold belt, and wells from theforeland basin showed little absolute difference in logresponse. Wellbore instability is likely to be an im-portant influence on log response in these areas andintroduces significant errors into the pore-pressureanalysis. Another important consideration is the originof the overpressure, which influences its log response.Undercompaction is unlikely responsible for overpres-suring in the area; instead, the large, horizontalstresses acting in this area are likely to be a predomi-nant factor in controlling the pressure. A weak rela-tionship between log response and effective stress wasobserved for the shaly units, which suggests some geo-mechanical control on the log response. The data, how-ever, are too sparse to be effectively used for pressureprediction at this stage.The main conclusion of this study is that in a com-

plex, tectonically active area, such as the Papuan foldbelt, normal methods of pressure prediction may notapply, but rigorous analysis and correlation betweendata can still yield valuable information on the pres-sure regime.


Wewould like to thank BP Developments Australia Pty. Ltd.and CSIRO Petroleum for their support of this research. Thechapter has also benefited from technical reviews by PhilipCaldwell, Mick McWalter, and three anonymous reviewers.



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107

10Geological Controls and Variability inPore Pressure in the Deep-WaterGulf of MexicoMichael A. SmithMinerals Management Service, New Orleans, Louisiana

A B S T R A C T

In most areas of the world, pressure-related drilling problems are the leading cause for abandoning adeep-water well or else requiring expensive remedial changes in the drilling and casing programs toreach its targeted reservoir depths. This chapter discusses geological controls and trends in the onsetof geopressure in the deep-water Gulf of Mexico, shallow water flow from overpressured sands in thetop-hole section, and other pressure-related problems unique to deep water. Pore-pressure predictionhas become a subject of intense current interest with several joint industry projects and predictivemodels now available for government and company participation.


As exploration moves into deeper water in the Gulf ofMexico, pore-pressure prediction and the correct an-ticipation of overpressured sands becomes more andmore critical to the effective evaluation of federal outercontinental shelf (OCS) lease blocks. Since 1992, thegrowth in deep-water activity has been reflected in nu-merous leasing, drilling, and production statistics. Thenumber of exploratory wells drilled and the numberof Exploration Plans filed for deep-water lease blockshave increased by about a factor of 5 since 1994, butmany of these leases will expire without being drilled.In addition, many deep-water blocks, initially leasedafter the OCS Deep Water Royalty Relief (DWRR) Actin 1996 provided economic incentives to develop deep-water fields, will be available by 2006. During the lasteight years of the 1990s, the number of deep-water ac-

Smith, Michael A., 2002, Geological Controls and Variability in Pore Pressure inthe Deep-Water Gulf of Mexico, in A. R. Huffman and G. L. Bowers, eds.,Pressure regimes in sedimentary basins and their prediction: AAPG Memoir 76,p. 107–113.

tive leases increased from about 1500 to nearly 3900(Figure 1), about half of the active present-day OCSblocks, including a record number of lease blocks since1996 in ultradeep water (�5000 ft [1524 m]). Baud etal. (2000) noted that, in the 1990s, the average Gulf ofMexico field size in more than 1500 ft (457 m) of waterwas 60 million BOE, 12 times the average shallow-wa-ter discovery. Deep-water oil now provides more thanhalf of the region’s production, and increases in gasproduction have also offset the shallow-water declinein recent years, with much of new volume comingfrom subsea completions.

In this chapter, we look at the occurrence of geo-pressure in about 100 wells in deep water from VioscaKnoll to Alaminos Canyon, most of them drilled inmore than 2000 ft (610 m) of water during the last fiveyears. We also analyze shallow water-flow encountersand trends in these areas. As exploratory drilling be-gins in previously untested geological trends in ultra-deep water, new technology and equipment will beneeded to control unique pressure-related drillingproblems encountered in the exploration and devel-opment of hydrocarbon resources in this emergingprovince.

108 S M I T H

Figure 1. Deep-water (�1000 ft [305 m]) and ultradeep-water (�5000 ft [1524 m]) active leases in the Gulf of Mexico.

P O R E - P R E S S U R E G R A D I E N T S

Minerals Management Service (MMS) geological re-views of exploration and development plans and ap-plications for permit to drill on Gulf of Mexico OCSleases include a discussion of possible abnormal pres-sure zones. Geopressure is defined as the situationwhere pore fluid pressure exceeds normal hydrostaticpressure (Fertl, 1976; Dutta, 1987). This onset of mod-erate overpressure in continental shelf deltaic sedi-ment occurs where pore pressures are equivalent to12.5 pound per gallon (ppg) mud weights. In deep wa-ter, however, the fracture gradient and shallow casingshoe tests are lower, and the onset of even mild over-pressures of 9.5 to 12.0 ppg contributes to many drill-ing problems such as shallow water flow. Burial rates,geothermal gradients, compaction, and diagenetic re-actions are the primary factors affecting the occurrenceof geopressure (Law et al., 1998). In deep-water wells,the large seawater column also results in greater

depths to abnormal pressure, so depths below themudline (bml) or sea floor were used in this study in placeof vertical subsea depths. Geological factors that con-trol the deposition of turbidite systems, sequence stra-tigraphy, major faults, unconformities, and salt alsoaffect pore pressure. In complexly faulted structures,formation pressures may be compartmentalized andmay vary between different sands.

We analyzed predicted and actual pore pressures,sedimentation rates, and formation temperatures inthe deep-water Gulf of Mexico and prepared trendmaps of the occurrence of geopressure for this prov-ince. The top of geopressure was defined as the depthat which pore-pressure equivalent mud weights, ref-erenced to kelly bushing elevation, exceeded 12.5 ppg.The wells in this study are located in four deep-watersections that include, from east to west, Viosca Knoll/Mississippi Canyon/Atwater Valley, Green Canyon,Garden Banks, and East Breaks/Alaminos Canyon.The upper slope (less than 1000 m of water) in Missis-

Geological Controls and Variability in Pore Pressure in the Deep-Water Gulf of Mexico 109

Figure 2. Average depth and stratigraphic interval for the occurrence of moderate overpressures (12.5 ppg pore pressure), deep-water Gulf of Mexico.

sippi Canyon has a thicker Pliocene sectionwith a shal-lower top of geopressure, an average of about 6950 ft(2118 m) bml, than the deeper water parts of this area.In deeper water, the average top of geopressure occursin the Miocene at about 10,700 ft (3261 m) bml. In theyounger Pliocene–Pleistocene section to the west inGreen Canyon, Garden Banks, and East Breaks, the av-erage top of geopressure occurs at about 8700 ft (2652m) bml. In the deeper water sections in Green Canyon,Garden Banks, and Alaminos Canyon to the south andsoutheast, however, the top of geopressure occurs inthe Miocene at an average depth of about 11,200 ft(3414m) bml. Throughout the deep-water Gulf ofMex-ico, as shown in Figure 2, it appears that older andmore compacted strata have a deeper top of geopres-sure than occurs in younger strata.

Except for the northeastern corner of MississippiCanyon, the thermal gradient in the eastern study areais lower than that of deep-water areas to the west, gen-erally about 1.05�F/100 ft (0.58�C/30.5 m). The thermal

gradient falls from an average of 1.25�F/100 ft (0.69�C/30.5 m) in East Breaks to about 1.0�F/100 ft (0.555�C/30.5 m) in Garden Banks, and in Green Canyon thetemperature gradient appears to decrease from 1.3 to0.8�F/100 ft (from 0.72 to 0.44�C/30.5 m) to the south-east with greater water depths. These observationssuggest that lower thermal gradients may correspondto a deeper top of geopressure.

Salt domes and ridges that form the boundaries ofsalt-withdrawal minibasins cause increased pore pres-sure in the surrounding sediment. This fact results inanomalously high pore pressures in wells drilled onthe flanks of a salt dome relative to wells drilledthrough equivalent strata toward the center of the ba-sin. Pore-pressure ramps or steep increases also occuradjacent to salt masses, and some deep-water explor-atory wells have had to be abandoned during attemptsto drill through overpressured fractured shale associ-ated with a salt diapir before the reservoir interval wasreached. Below tabular salt sheets, formations can be

110 S M I T H

overpressured because of an effective seal, and in somesubsalt wells a pressure kick has been encountered inthe rubble zone below salt. In general, however, thetop of subsalt geopressure occurs at greater depths anddeeper in the stratigraphic section than in wells with-out salt.

S H A L L O W W A T E R - F L O W S A N D S

Water flow from an overpressured shallow aquifer oc-curring above the first pressure-containing casingstring can significantly impact drilling and cementingpractices in addition to the setting depth and numberof shallow casing points. This shallow subsurface geo-hazard may even cause an operator to change a surfacelocation or lose a well. Shallow water-flow sands weredeposited as continental slope/fan sequences duringupper Pleistocene progradation, the building out ofprodelta sandy zones. Since 1984, shallow water-flowoccurrences have been reported in about 70 Gulf ofMexico lease blocks covering 55 oil and gas fields orprospects. With a few exceptions, water-flow incidentsoccur at water depths exceeding 1700 ft (518 m) witha mean value at about 3000 ft (914 m) of water. Water-flow problem sands also typically occur from 950 to2000 ft (290–610 m) bml but have been reported from450 to 3500 ft (137–1067 m) below the sea floor. Individ-ual channel-sand units display slumping zones or de-bris flows with a chaotic seismic character and, in somecases, tilted and rotated slump blocks. In theMississippiCanyon and southern Viosca Knoll areas, some of theshallowest channel sands can be identified as part of aparticular distributary system such as the old TimbalierChannel, Southwest Pass Canyon, or Einstein levee/channel system. High-sedimentation rates and an im-permeable mud or clay seal from a condensed sectionare the main factors contributing to overpressures inshallow water-flow sands (Alberty et al., 1997). Thesesands occur in several depositional subbasins that aregenerally bounded by salt ridges or walls. No signifi-cant water-flow occurrence, however, is found over tab-ular salt sills that are 1000 to 10,000 ft (305–3048 m)below the sea floor in some areas. This fact may suggestthat communication with the deeper stratigraphic sec-tion contributes to abnormal pressures in shallow sandsor that the salt forms a positive sea floor topographicfeature, preventing sediment loading that might con-tribute to the generation of overpressures.

The integration of high-resolutionmultichannel andreprocessed conventional two-dimensional (2-D) andthree-dimensional (3-D) seismic data for the top-holesection, further refined by seismic facies analysis, canidentify sand bodies with moderate or high shallow

water-flow potential. In assessing shallow water-flowrisk, information from surrounding wells and shallowborehole tests also provides important data for drillingprogram design. The MMS Notice to Lessees and Op-erators (NTL) on shallow hazards requirements for theGulf of Mexico OCS, NTL 98–20, is currently under-going extensive revisions (Stauffer et al., 1999). The up-dated NTL will accommodate the shifting focus ofdrilling into deeper water and the improved technol-ogy and data now available to mitigate deep-watergeohazards such as shallow water flow.

Mitigating approaches that have been used in thedrilling of shallow water-flow areas include measure-ment while drilling (MWD) logging plus an annularpressure measurement while drilling (PWD) tool,monitoring and confirming shallow water-flow occur-rences with remotely operated vehicles (ROV), anddrilling the shallow section as a pilot hole. Additionalcasing strings and quick-setting foam cements, bore-hole tests to 1500 to 5000 ft (457–1524 m) bml beforedevelopment drilling, and other geophysical and en-gineering techniques that are currently under devel-opment have also been employed. The loss of integrityplus buckling or collapse of shallow casing strings indevelopment wells has caused serious economic lossin several cases. Establishing a database of known shal-low water-flow occurrences and the most effectivemethods for controlling them will greatly advance thepartnership between the MMS and offshore operatorsin containing this critical deep-water hazard (Smith,1999).

O V E R P R E S S U R E D S A N D S I N U L T R A D E E PW A T E R

In low-margin deep-water drilling areas with abruptlyincreasing pore pressures and weak fracture gradients,extra casing strings are needed to maintain control inthe shallower part of the well. A conventional single-gradient mud system and marine riser maintain bot-tom-hole pressure with a single mud density from therig to the bottom of the well, which may require extracasing strings to prevent weaker formations from frac-turing. In addition, loop currents or other strong deep-water currents might limit drilling at times because ofhigh riser loads. With a dual-gradient system, how-ever, mud is diverted to separate riser return lineswiththe effect of replacing the mud from the drilling riserwith seawater and referencing pressure gradients rela-tive to the sea floor (Smith and Gault, 2002). The largerhole size maintained at total depth with this technol-ogy also allows more completion and production op-tions for deep-water reservoirs.


Figure 3. Established and frontier deep-water Gulf of Mexico hydrocarbon plays.

The northern Gulf of Mexico Basin can be dividedinto various arcuate tectonic provinces that parallel theshelf/slope break (Diegel et al., 1995; Karlo and Shoup,1999). Salt-withdrawal minibasins on the continentalslope, such as those in the Green Canyon and GardenBanks areas, are bounded by salt walls and filled withthe ponded turbidite sands that provide reservoirs formost of the earlier deep-water Gulf of Mexico discov-eries. A tabular salt canopy tectonic province occurs ina basinward direction in Walker Ridge and KeathleyCanyon, and the Sigsbee Escarpment defines its extent.The middle to lower continental slope contains fold/thrust belts with large prospective geological struc-tures that are the focus of current deep-water drillingand include several recent discoveries (Peel, 1999;Rowan et al., 2000). Figure 3 shows the distribution of

hydrocarbon plays in the deep-water Gulf of Mexico,including untested plays in ultradeep water.

In the centroid concept, pore pressure in a reservoirsand at the crest of a high-relief overpressured struc-ture can exceed pore pressure in the bounding shale.Deep-water areas with extensive shallow faulting areparticularly vulnerable to low-margin drilling condi-tions that require extra casing strings. The top of alarge, high-relief fold or anticlinal structure at variousdepths in an exploratory well may contain fluid pres-sures that approach the fracture gradient in adjacentshale (Traugott, 1997). The mud log from a 1996 ultra-deep-water well (Figure 4) provides an example ofsubstantial pore-pressure increases that requiredclosely spaced additional casing strings in the shallowsection. This exploratory well was abandoned less than

112 S M I T H

Figure 4. Ultradeep-water exploratory well that encountered rapid pore-pressure buildup requiring extra shallow casingstrings. Higher values in the Total Gas track are marked with an x.

3000 ft (914 m) bml because of the narrow margin be-tween pore-pressure and fracture gradient in additionto its small hole size well above the prospective targetinterval. The use of a dual-gradient/riserless drillingapproach and other innovative casing and divertersystems that are under development, however, maycontribute the new technologies required for success-ful exploration in the deepest Gulf of Mexico leases.


Many of the serious and costly drilling problems indeep water are related to the pore-pressure/fracture-gradient relationship. Other pressure-related hazards,such as shallow water flow, require better predrillidentification and quantification of overpressuredproblem sands. In many Gulf of Mexico frontier deep-water areas, a lack of offset wells mandates better pres-sure models that incorporate all available geologicaldata. Operations geologists and geophysicists in the

MMS are working with deep-water operators to estab-lish databases and methodologies that will improveindustry’s success in dealing with deep-water geoha-zards well into the new millennium.


This project was initiated as a result of excellent presenta-tions at the 1998 American Association of Drilling EngineersIndustry Forum on Pressure Regimes in Sedimentary Basinsand their Prediction. Preliminary results were presented atthe 1998 MMS Information Transfer Meeting and the 1999AAPG International Conference in Birmingham, England. Ithank two anonymous reviewers and, particularly, James C.Niemann for their insightful comments, which greatly im-proved this chapter. Some of the ideas presented here wereclarified by discussions with Jim Bridges, Matt Czerniak, Na-der Dutta, Pete Harrison, Alan Huffman, Bob Peterson, PaulPost, and Selim Shaker. Finally, I am grateful to the MMSGulf of Mexico Region, especially to Darcel Waguespack,Fred Times, and Wayne Plaisance, for help and support inthe preparation of this chapter.



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Smith, K. L., and A. D. Gault, 2002, Subsea mudlift drilling:a new technology for ultradeep-water environments, inA. R. Huffman and G. L. Bowers, eds., Pressure regimesin sedimentary basins and their prediction: AAPG Mem-oir 76, p. 171–175.

Stauffer, K. E., A. Ahmed, R. C. Kuzela, and M. A. Smith,1999, Revised MMS regulations on shallow geohazards inthe Gulf of Mexico: Offshore Technology Conference Pro-ceedings Paper OTC 10728, v. 1, p. 79–81.

Traugott, M., 1997, Pore/fracture pressure determinations indeep water: World Oil, v. 218, no. 8, p. 68–70.

115

11An Easily Derived OverburdenModel Is Essential for the Predictionof Pore-Pressure Gradients and FractureGradients for Wildcat Explorationin the Gulf of MexicoFred R. HolasekDiamond Offshore Team Solutions, Inc., Houston, Texas

A B S T R A C T

Analysis of overburden and Poisson’s ratio profiles, in addition to being essential to pore-pressure andfracture-gradient analysis, is critical to calculation of maximum pore pressure where using amicrobasinfluid-migration model to predict the pore pressure for a proposed well. A review of the sensitivity ofpore-pressure analysis to a range of overburden and Poisson’s ratio profiles has been made. A modelis presented that is currently being successfully used in the Gulf of Mexico.


Exploration for oil and gas has led our industry intonew areas including deep water. This has given ourindustry new challenges and made us revisit neglectedtheories.Two immediate challenges that greet us in new ar-

eas of the Gulf of Mexico including deep water are thatthe pore-pressure and fracture-gradient predictiontechniques are not as reliable as desired. The purposeof this chapter is to suggest a method to estimate theoverburden and Poisson’s ratio profiles for an area ofinterest. This method is currently being used with amicrobasin fluid-migration model to successfully pre-dict pore pressure and fracture gradient for proposedwildcat wells.

B A C K G R O U N D

In the past, exploration for oil and gas has led ourindustry to drill deeper and to move offshore. Whenpore-pressure and fracture-gradient prediction gainedincreased importance, methods based on sound theorywere developed to meet these needs for specific areas.For many years, these methods worked reasonablywellwhere applied to specific areas. When our industrymoved to different areas, including deep-water areas,not surprisingly, the methods did not work as well asdesired.Two primary reasons exist for the failure of these

techniques. One reason for failure is that the tolerancefor error is greatly reduced in new frontiers of explo-ration of deeper wells and deeper water. The secondreason is that the existing techniques did not present areliable method of predicting pore pressure prior to thedrilling of a proposed wildcat well in a way that hon-ored geological events.Some work has been done with seismic stacking ve-

locities. Working closely with many major exploration

Holasek, Fred R., 2002, An Easily Derived Overburden Model Is Essential for thePrediction of Pore-Pressure Gradients and Fracture Gradients for WildcatExploration in the Gulf of Mexico, in A. R. Huffman and G. L. Bowers, eds.,Pressure regimes in sedimentary basins and their prediction: AAPG Memoir 76,p. 115–124.

116 H O L A S E K

Figure 1. Integrated specificgravity vs. depth.

corporations, I have noted a general disappointmentwith the results. Using the refined overburden modeland honoring all geological events dramatically im-proves the results of stacking-velocity analysis.I have noted in the past four years that many of the

major exploration corporations are using and perfectingmicrobasin fluid-migrationmodels to estimate the pore-pressure profile for proposed wells. The concept of ac-tive fluid migration from the deeply buried Mesozoic

carbonate source rocks in the Gulf of Mexico appears tobe becoming widely accepted (Sassen, 1993).To get the desired results from the models, all geo-

logical events must be honored including the pressureat which active fluid migration occurs. This requires agood estimate of overburden at the proposed drillinglocation.The objective of the chapter is to present a general

overburden model that is currently being successfully

An Easily Derived Overburden Model Is Essential for the Prediction of Pore-Pressure Gradients and Fracture Gradients for Wildcat Exploration 117

Figure 2. Poisson’s ratio vs.depth. KB � kelly bushing;WD � water depth.

used in the Gulf of Mexico to estimate overburden inconjunction with estimation of pore pressure for rankwildcat drilling locations.

T H E O R Y

One of the most popular theories for fracture-gradientprediction was developed by Eaton. Eaton’s equation(restated in Eaton and Eaton, 1997) is

F/D � [m/(1 � m)] [(S/D) � (p/D)] � (p/D) (1)

where F � fracture extension pressure (psi); p � pore-pressure (psi); S � overburden pressure (psi); D �true vertical depth; and m � Poisson’s ratio (dimen-sionless). The use of this equation to produce a fracturegradient vs. true vertical depth requires

1. Pore-pressure gradient (p/D) vs. true verticaldepth

2. Overburden pressure gradient (S/D) vs. true ver-tical depth

3. Poisson’s ratio vs. true vertical depth

118 H O L A S E K

Figure 3. Resistivity vs. pore-pressure equivalent mud weight.Company: confidential; well:confidential; location: confiden-tial, offshore Texas. KB � kellybushing; WD � water depth.Reasons for the curve jumps areaddressed in Holasek (2002).

One of the most popular theories for deriving for-mation pore pressure from well logs was developedby Eaton (1975). Eaton’s equations for formation pore-pressure gradient prediction using shale resistivity(Ro), conductivity (Co), and interval transit time Dtoare

ap/D � (S/D) � [(S/D) � (p /D) ] [R /R ] (2)n n o n

ap/D � (S/D) � [(S/D) � (p /D)] [C /C ] (3)n n o

bp/D � (S/D) � [(S/D) � (p /D)] [Dt /Dt ] (4)n n o

where p/D � formation pore-pressure gradient (psi/ft); S/D � overburden pressure gradient (psi/ft); pn/

D � normal pore-pressure gradient (0.465) psi/ft; Ro� shale resistivity (X m); Rn � normal compaction-line shale resistivity (X m); Co � shale conductivityfrom well log (mmho/m); Cn � normal shale conduc-tivity (mX/m); Dto � interval transit time throughshale (ls/ft);Dtn� normal interval transit time throughshale (ls/ft); a is given as a constant with a value of 1.2;b is given as a constant with a value of 3.0.

D I S C U S S I O N

Close examination of the equations for pore-pressureequations suggest that they would be very sensitive to


Figure 4. Interval transit time vs.pore-pressure equivalent mudweight. Company: confidential;well: confidential; location: confi-dential, offshore Louisiana. KB �kelly bushing; WD � waterdepth. Reasons for the curvejumps are addressed in Holasek(2002).

changes in overburden profile. Examination of thefracture-gradient equation suggests that it would bevery sensitive to changes in overburden and to a lesserdegree, changes in Poisson’s ratio profile.Immediately, five questions arise:

1. How much does the overburden profile changein the Gulf of Mexico?

2. How much does the Poisson’s ratio profilechange in the Gulf of Mexico?

3. How much do the observed changes in over-burden profile change the resistivity vs. pore-pressure relationship?

4. How much do the observed changes in overbur-den profile change the interval transit time vs.pore-pressure relationship?

5. How much do the observed changes in overbur-den profile and Poisson’s ratio profile change thefracture-gradient profile?

G E N E R A L C O N C E P T

Ideally, hundreds of high-quality density logs frommud line to more than 20,000 ft (�6096 m) should beanalyzed, and the resulting overburden profiles should

120 H O L A S E K

Figure 5. Resistivity vs. pore-pressure equivalent mud weight.17 ppg curves vs. comparisonfactor C3. KB � kelly bushing;WD � water depth.

be related. Very few high-quality density logs frommud line to more than 20,000 ft (�6096 m) exist.Another approach was taken. A general overburden

modelwas developed from the few available andusabledensity logs. Also, a general Poisson’s ratio model wasdeveloped using the associated drilling data. The gen-eral overburdenmodel and the pore-pressure equationswere used to develop a real-time interactive graphicalprogram to allow matching of actual data. The generaloverburden model, the general Poisson’s ratio model,

and the fracture-gradient equation were combined in aprogram to allow matching of actual data.The general concept was to assume an overburden

profile and analyze the logs and well data to producea pore-pressure profile. Then the pore-pressure profilewas used in the fracture-gradient model and the over-burden and Poisson’s ratio models were modified tomatch actual data. The new overburden profile wasused to reanalyze the log and well data to produce asecond pore-pressure profile. This process was re-


Figure 6. Interval transit time vs.pore-pressure equivalent mudweight. 17 ppg curves vs. com-parison factor C3. KB � kellybushing; WD � water depth.

peated to yield a unique solution for the overburdenprofile and Poisson’s ratio profile.

G E N E R A L O V E R B U R D E N M O D E L

Briefly reviewing the basics, the overburden for anygiven point is the sum of weight of air from kelly bush-ing (KB) to mean sea level, plus the weight of seawaterfrom mean sea level to mud line, plus the weight ofthe sediments from mud line to the point of interest.Where used in the gradient form, the reference pointis the KB. The general equation for overburden is

TVDmud line

OB � f (Spg )d(TVD)sw�TVDMSL

TVD0

� f (Spg )d(TVD) (5)sed�TVDmud line

where OB � integrated overburden specific gravity;Spgsw � specific gravity of sea water; Spgsed � spe-cific gravity of the sediment at TVD; TVDMSL � truevertical depth from KB to mean sea level; TVDmud line� true vertical depth from KB to mud line; and TVDo� true vertical depth at point of interest.

122 H O L A S E K

Figure 7. Fracture gradient vs.overburden comparison factor(OCF) C3. KB � kelly bushing;WD � water depth.

Please note that the overburden is presented usingspecific gravity. I have found that the advantages ofusing specific gravity to relate to closely associated dis-ciplines outweigh any minor inconveniences. Depth ispresented in feet, which is the convention in the Gulfof Mexico (metric values in parentheses).The overburden of air from KB to sea level is as-

sumed to be negligible. The calculation of contributionto overburden of seawater is assumed to approach the

linear function of seawater specific gravity in the areaof interest. The remaining part of the overburden isestimating the specific gravity of the sedimentary rocksto the point of interest.Define Spgintg as

Spgintg

(6)TVD0

� f (Spg )d(TVD) /TVDBMLsed 0�� TVDmud line


TBDBML0Spg � (Spg )D(TVDBML) /intg sed�� TVDBMLmud line

TVDBML0 (7)

where Spgintg � integrated specific gravity of forma-tion sediment; TVDBML � true vertical depth belowmud line; TVDBMLmud line � 0 ft; TVDBMLo � truevertical depth below mud line at the point of interest.The overburden stress can then be written as

S � 0.4335 (Spg WD � Spg TVDBML ) (8)SW intg o

where WD is water depth (ft), and 0.4335 is a conver-sion factor from specific gravity to psi/ft.Formation density logs in digital form were evalu-

ated for Spgintg. I noted that the profile varied fromarea to area and block to block. I also noted that Spgintgcould bematchedwith the following generalized equa-tion.

Spg � Cintg 1(0.8)(n)� (C � C )/(exp(C /(TVDBML) ) (9)2 1 3

where C1 � Spgintg at the mud line. In the evaluationof many wells, this factor did not deviate significantlyfrom a value of 2.13. C2 equals Spgintg at infinity. Inthe evaluation of many wells, this factor has rarely de-viated from a value of 2.8. Nearby salt (halite) can re-duce the value. C3 is the comparison factor, andTVDBML is measured in feet. In the evaluation ofmany wells, this factor has ranged from as small as1000 ft (305 m) to as much as 6000 ft (1829 m). Thevariable n is the exponential modifier. In the evaluationof many wells, this factor did not deviate from thevalue of 1.0 with the exception of below a salt raft. Notethat integration of the overburden functionmust honordiscontinuities such as halite.

Question No. 1—How Much Does the Overburden ProfileChange in the Gulf of Mexico?

A plot of integrated specific gravity vs. depth for C3comparison factors ranging from 1000 ft (305 m) tomore than 6000 ft (�1829 m) was prepared and is pre-sented in Figure 1. In general, wells with a C3 com-parison factor greater than 4000 ft (1219 m) were inareas of higher depositional rates. Wells with a C3comparison factor less than 3000 ft (914 m) were inareas of low depositional rates, that is, older stratanearer the mud line.The majority of the wells drilled in the Gulf of Mex-

ico should be contained within the plotted limits of theC3 comparison factor. To put the range of Spgintg

curves into perspective, a constant overburden gradi-ent of 1 psi/ft below mud line would plot as a verticalline with a Spgintg of 2.3.

General Poisson’s Ratio ModelThe Poisson’s ratio model was developed from wellsanalyzed with a useful density log to derive a uniqueoverburden equation. The Poisson’s ratio model wasdeveloped to match leak-off tests. The Poisson’s ratiomodel is represented by the following general equa-tion:

m � B1(1.16)(n)� (B � B )/(exp(B /(TVDBML) ) (10)2 1 3

where B1 � m at the mud line. In the evaluation ofmany wells, this factor generally could be estimatedusing the following relationship:

2B � 0.37 � 0.0056(C /1000) (11)1 3

where B2 � m at infinity. In the evaluation of manywells, this factor did not deviate from the value of0.497. B3 is the comparison factor, and TVDBML ismeasured in feet. In the evaluation of many wells, thisfactor generally is equal to C3. The variable n is theexponential modifier. In the evaluation of many wells,this factor rarely deviated from the value of 1.0.

Question No. 2—How Much Does the Poisson’s Ratio ProfileChange in the Gulf of Mexico?

A plot of Poisson’s ratio vs. depth for B3 comparisonfactors ranging from 1000 ft to 6000 ft (305–1829 m) ispresented in Figure 2.

Pore-Pressure AnalysisTwo interactive graphic programs were developedfor pore-pressure analysis. One was based on Eaton’sresistivity vs. pore-pressure equation, and the otherwas based on the Eaton’s interval transit time vs. pore-pressure equation.Each model has a provision for three different base

lines, sometimes referred to as normal pressure (0.465psi/ft � 8.94 ppg) lines. Each base line is an equationfor a straight line on a semi-log base, with intercept atmud line and slope available for modification. Theequation for each base line is:

(b)(depth)base line � a(10 ) (12)

where a � the intercept of the base line at the mudline, and b � the slope of the base line.

124 H O L A S E K

Eaton’s equations were solved for a series of con-stant pore-pressure gradient curves from 10–20 ppg,incorporating the base line and general overburdenequation, and allowing for the exponentwithin Eaton’sequation to be modified.The interactive graphic program also plotted actual

mud weights used and known pressure data such asrepeat formation tests, bottom-hole pressure survey re-sults, or estimated bottom-hole pressure from well-kick data.An example of the resistivity vs. pore-pressure plot

is shown in Figure 3. An example of the interval transittime vs. pore-pressure plot is shown in Figure 4. Re-viewing Figures 3 and 4, it is readily apparent that abase trend is not necessary for pore-pressure analysis.Most of the wells encountered multiple geological

units with different base-line slopes and intercepts.The geological units appeared to have different andcomplex depositional and fluid-migration histories.

Question No. 3—How Much Do the Observed Changes inOverburden Profile Change the Resistivity vs. Pore-PressureRelationship?

A resistivity vs. pore-pressure plot was preparedshowing only the 17 ppg pore-pressure curve for afixed set of variables. Without changing any other vari-ables, a 17 ppg curve was prepared for different C3comparison factors from 1000 ft to 6000 ft (305–1829m) (Figure 5). A significant difference exists betweenthe curves. Constant pressure curves less than 17 ppghad progressively less difference. Conversely, constantpressure curves greater than 17 ppg had progressivelygreater differences. Clearly, resistivity vs. pore pres-sure equations are very sensitive to the changes in theoverburden profile seen in the Gulf of Mexico.

Question No. 4—How Much Do the Observed Changes inOverburden Profile Change the Interval Transit Time vs.Pore-Pressure Relationship?

A plot of interval transit time vs. pore pressure wasprepared showing only the 17 ppg pore-pressure curvefor a fixed set of variables. Without changing any othervariables, a 17 ppg curve was prepared for differentC3 comparison factors from 1000 ft to 6000 ft (305–1829m) (Figure 6) .A significant difference exists between the curves.

Constant pressure curves less than 17 ppg had pro-gressively less difference. Conversely, constant pres-sure curves greater than 17 ppg had progressivelygreater differences. Clearly, interval transit time vs.

pore-pressure equations are very sensitive to thechanges in the overburden profile seen the Gulf ofMexico.

Question No. 5—How Much Do the Observed Changes inOverburden Profile and Poisson’s Ratio Profile Change theFracture-Gradient Profile?

A set of fracture-gradient profiles was calculated for agiven pore-pressure profile for different C3 compari-son factors from 1000 ft to 6000 ft (305–1829 m). Thenoted relationships for B1 and B3 were used for thisplot.For this chapter, C3 has been defined as the “over-

burden comparison factor” (Figure 7). There is asignificant difference between the curves. Clearly,fracture-gradient equations are very sensitive tochanges in the overburden profile seen in the Gulf ofMexico.


The sensitivity of Eaton’s pore-pressure and fracture-gradient equations can easily be used to refine an over-burden profile for a given area. Honoring all geologicalevents, an overburden profile can be easily derived fora proposed drilling location using conventional inte-gration techniques. Using the derived overburden pro-file and a fluid-migration model, a pore-pressureprofile can be derived for the proposed well. Using thederived overburden profile and a derived interval ve-locity profile, an analysis of the seismic stacking veloc-ity for pore pressure can be made.


Eaton, B. A., 1975, The equation for geopressured predictionfrom well logs: Society of Petroleum Engineers Paper5544, 5 p.

Eaton, B. A., and T. L. Eaton, 1997, Fracture gradient predic-tion for the new generation: World Oil, v. 218, no. 10 (Oc-tober), p. 93–100.

Holasek, F., 2002, Evaluation of deepwater drilling prospectsusing new concepts to identify, quantify, and mitigate(IQM) risks for well design: Society of Professional Engi-neers Paper 74489.

Sassen, R., 1993, Association of oil seeps and chemosyntheticcommunities with oil discoveries upper continental slope,Gulf of Mexico, in N. C. Rosen, ed., Transactions of the43rd annual convention of the Gulf Coast Association ofGeological Societies: GCAGS, v. 43, p. 349–355.

125

12Fracture-Gradient Predictions inDepleted Sands in the Gulf CoastSedimentary BasinBaldeo SinghUnocal, Indonesia, Balikpapan, Indonesia

Nelson EmeryUnocal, Lafayette, Louisiana

A B S T R A C T

The primary objective of this work was to estimate fracture gradients in depleted sands. This infor-mation is necessary in predicting lost-circulation zones and optimizing drilling plans. Large reservesare known to exist in deeper horizons underneath mature fields in several basins in the United States,such as the Gulf Coast, the Permian basin, and the West Coast.

Historically, fracture-gradient predictions are made for shales to enable selection of casing points.In this chapter, the shale fracture gradients are related to the fracture gradient in sands (virgin condi-tions) using a lithology factor. The lithology factor is a function of Poisson’s ratio, a physical propertyconsidered to be the most significant rock-mechanical property in lithology determination. For ease ofapplication, Poisson’s ratio is related to the shaliness of the sand. The fracture gradient so computed isthen discounted to account for pressure depletion using a field correlation from the literature.

Although the method of fracture-gradient prediction has only been tested on Gulf Coast wells, theformulation is general and may have application in other basins. In its partial form, this procedure mayalso be used to predict contrast between shale and sand fracture gradients to design stimulation jobs.

F R A C T U R E G R A D I E N T S I N T H E E A R T H

Several techniques have been suggested for estimatingfracture gradients in the earth (Matthews and Kelly,1967; Pennebaker, 1968; Eaton, 1969; Christman, 1973).They all attempt to relate the overburden gradient andpore pressure to the horizontal stress gradient (or frac-ture gradient). For a gravity-dominated system, suchas the Gulf Coast, the basic equation is written as

[G – G ] � K[G – G ] (1)f p ob p

Singh, Baldeo, and Nelson Emery, 2002, Fracture-Gradient Predictions inDepleted Sands in the Gulf Coast Sedimentary Basin, in A. R. Huffman andG. L. Bowers, eds., Pressure regimes in sedimentary basins and their prediction:AAPG Memoir 76, p. 125–129.

where Gf is the fracture gradient of shale, Gob is theoverburden gradient, Gp is the pore-pressure gradi-ent of the formation, and K is the stress factor. Theproportionality factor, K (stress factor), relates thevertical effective stress to the horizontal effectivestress being generated due to compaction. The stressfactor is essentially an empirical function that ac-counts for the complexity of lithology and diagene-sis processes as the rock is buried in the ground.Pilkington (1978) reviewed the published data onfracture gradients (Matthews and Kelly, 1967; Pen-nebaker, 1968; Eaton, 1969; Christman, 1973). Hefound that all of these data could be normalized toproduce a single stress-factor curve. This observationhas been used widely in making predictions for frac-ture gradients.

126 S I N G H A N D E M E R Y

Table 1. Summary of Important Parameters in Predicting Lost Circulation through Depleted Sands, Gulf Coast, United States

Gamma-Ray Log

Pore Pressure(ppg) Fracture Gradients (ppg) Mud Remarks:

Field NameValue forSand

VirginSand

DepletedSand Shale

VirginSand

DepletedSand

Weight(ppg)

LostCirculation?

Ship Shoal–208(E–14) 30 12.6 1.9 17.1 15.2 11.1 12.7 YesNorth Fresh Water Bayou(F–20) 30 14.9 9.5 18.5 17.0 14.5 15.7 YesNorth Fresh Water Bayou(E–9) 30 13.8 9.4 18.5 16.5 14.5 17.0 YesWest Cameron–196(A–4) 30 9.72 6.98 16.7 13.7 12.7 12.0 NoWest Cameron–280(A–4 ST) 30 8.2 4.2 16.7 13.1 11.6 11.2 NoWest Cameron–280(A–4 ST) 30 9.7 3.4 16.7 13.7 11.4 11.2 NoVermillion–39(12) 30 8.8 0.72 16.3 13.1 10.3 10.0 NoSouth Marsh Island–48(C–2) 40 10.2 2.6 17.6 15.0 12.0 11.0 NoLake Pagie(B–17) 30 11.0 2.4 17.9 15.0 11.6 14.5 Yes

P R O P O S E D M O D I F I C A T I O N

In the proposed model, the stress factor, K, is subdi-vided into two factors: one to account for lithology,and the other to account for the nonlinearity of thestress pattern found in the earth. The lithology factoris based on the plane-strain solution from elasticitytheory for horizontal effective stress as a function ofvertical effective stress and is a function of Poisson’sratio. It is equal to m /(1 � m), where, in this chapter,m is Poisson’s ratio for shale. Poisson’s ratio is consid-ered to be the most significant rock-mechanical prop-erty in lithology determination. All other nonlineareffects due to factors such as diagenesis and compac-tion are lumped in the second stress-correction term,Kc. This correction term, Kc, is expected to be area spe-cific and represents the characteristics of that particularregion. The resulting equation may now be written as

[G � G ] � K [m /(1 � m)][G � G ] (2)f p c ob p

By doing so, we have incorporated the effects of li-thology explicitly, through Poisson’s ratio. Althoughthe previous formulation was written for shale, it isgeneral in nature and can be easily modified to rep-resent sand by using the Poisson’s ratio of sand. Alsonote that the correction term, Kc, is independent of li-thology.

We write, explicitly, an equation for the fracturegradient of a sand adjacent to the shale:

sd sd sd[G – G ] � K [m / (1 – m )][G – G ] (3)f p c ob p

where Gfsd is the fracture gradient in the sand, and msd

is Poisson’s ratio of the xsand.

Dividing equation 2 by equation 3, we get

sd[G � G ]/[G � G ]f p f psd sd� [m/(1 � m)][ (1 � m )/m ] (4)

By this manipulation, we are able to relate the fracturegradients in shale to the fracture gradient in sand usingPoisson’s ratio. This is a very useful result and is usedin this chapter in computing fracture gradients insands at virgin pore-pressure conditions where thefracture gradient in an adjacent shale is known. His-torically, good correlations exist in the literature to pre-dict fracture gradients in shales, such as Eaton’srelation (1969) for the Gulf Coast. Alternatively, thesemay be obtained fromwell-characterized leak-off tests.

E S T I M A T I O N O F P O I S S O N ’ S R A T I OU S I N G G A M M A - R A Y – L O G V A L U E S

The ultimate objective here is to relate Poisson’s ratioto gamma-ray–log values, which, unlike Poisson’s ra-tio, are readily available. A linear model is used to re-late the two.

Typical formation sand is a mixture of numerousminerals, such as clays, quartz, and dolomite. For sim-plicity of modeling, however, we have assumed thatthe two dominant constituents comprising sands arepure shales (primarily clays) and pure sand (primarilyquartz). For a given shaliness, fsh, Poisson’s ratio of theformation sand is then computed as follows:

sd qz sm � (1 � f )m � (f ) m (5)sh sh

where mqz and ms are Poisson’s ratio for quartz andclean shale, respectively. These are assumed constant

Fracture-Gradient Predictions in Depleted Sands in the Gulf Coast Sedimentary Basin 127

Figure 1. Nomogram to compute fracture gradients in sand (Gulf Coast sedimentary basin). Figure used with permission ofUnocal.

128 S I N G H A N D E M E R Y

and are chosen as 0.125 and 0.25 for sand and shale,respectively. Note that these values may vary and areregion specific. The shaliness of a sand, fsh, reflects therelative amount of contamination of the sand by shaleand is estimated using linear interpolation as follows:

f � (GR � GR )/(GR � GR ) (6)sh qz sh qz

where GR is the gamma-ray–log count in the sand un-der consideration, GRsh is the gamma-ray–log count inclean shale, and GRqz is the gamma-ray–log count inclean sand; GRsh and GRqz are considered fixed andare area specific. These values are obtained as de-scribed in the following paragraphs.

First, base lines are established for clean shale andclean sand for a specific region. Only thick sections ofshales (representative of the clean shale found in theformation) are used. Because thick sections of shalesare abundant in fields, these data are readily available.Based on the logs from the Gulf Coast, a value of 80

API units is the gamma-ray–log value typically usedfor GRsh.

But the task of obtaining a base-line gamma valuefor pure (uncontaminated) sand is not a trivial one.Most sand sections are contaminated to some degree.Ideally, a sand unit made out of quartz only has agamma-ray–log value close to 0. But because of inher-ent presence of minute amounts of contamination,along with logging instrument resolution, a value of10 API units is selected to represent a gamma value ofpure sand (made out of quartz), GRqz. The results are,however, found to be rather insensitive to minor vari-ation in these values.

F R A C T U R E G R A D I E N T S I N D E P L E T E DS A N D S

Salz (1977) measured fracture gradients in several res-ervoirs (including depleted reservoirs) in the Vicks-

Figure 2. Comparison of fracture-gradient prediction in depleted reservoir and mud weight used. Losses occured for SS-208,NFWB-F20, NFWB-E9, LP. No losses occured for WC-196, WC-280, VER-39, SMI-48. Dep � depleted; Vir � virgin; SS � ShipShoal; NFWB � North Fresh Water Bayou; WC � West Cameron; VER � Vermillion; SMI � South Marsh Island; LP � LakePagie.

Fracture-Gradient Predictions in Depleted Sands in the Gulf Coast Sedimentary Basin 129

burg Formation at the McAllen Ranch area, southTexas. To start with, some of these reservoirs werehighly abnormally pressured to a pressure gradient ofabout 0.96 psi/ft. The reservoirs were depleted to pres-sures as low as 0.2 ppg. Salz measured in-situ stressby conducting well-characterized fracturing tests. Thefracture gradients were measured before and after thedepletion. Based on more than 70 fracture treatments,he developed a correlation that could predict fracturegradient of a depleted reservoir if the fracture gradientin the virgin formation was known.

Salz’s correlation is used in this chapter for predict-ing fracture gradient in the depleted sand. The corre-lation can be written as follows:

sd sdG [Dep] � G [Vir] � exp[�0.57(P – P )] (7)f f i f

where Gfsd [Dep] is the fracture gradient in depleted

sand (ppg), Gfsd[Vir] is the fracture gradient in virgin

sand (ppg),Pi is initial formationpressuregradient (psi/ft), and Pf is final formation pressure gradient (psi/ft).

C A S E H I S T O R I E S — F R A C T U R E - G R A D I E N TP R E D I C T I O N I N D E P L E T E D S A N D S I N T H EG U L F C O A S T R E S E R V O I R S

Table 1 presents lost-circulation data in depleted sandsfrom seven lost-circulation–prone Unocal fields in theGulf Coast. Fracture-gradient predictions in nine de-pleted sands from eight wells are compared with themud weights that were used while drilling.

First, fracture gradients in adjacent shales were es-timated using Eaton’s (1969) correlation. Then, equa-tions 4, 5, and 6 were used to calculate the fracturegradient for a virgin sand using gamma values for thesand. This estimate was then corrected for depletionusing Salz’s correlation, equation 7.

For simplicity and ease of application, a nomogramwas developed incorporating the previous steps. Thenomogram is shown in Figure 1. An example, includedin the nomogram, illustrates how to use it.

R E S U L T S A N D D I S C U S S I O N

Excellent agreement was found between the predictedvs. observed lost-circulation cases for the depletedfield data in Table 1 (nine sands from seven Gulf Coastfields). Lost circulation was observed in all of the caseswhere the predicted fracture gradient was less than themud weight. The results are shown graphically in Fig-ure 2. Note also the change in the fracture gradients ofthe depleted sands as compared with the virgin sands.In its partial form, this fracture-gradient predictionprocedure may also be used to predict the contrast be-tween the shale and the sand fracture gradients andthus improve the design of stimulation jobs.


Christman, S. A., 1973, Offshore fracture gradients: Journalof Petroleum Technology, v. 25, p. 910–914.

Eaton, B. A., 1969, Fracture gradient prediction and its ap-plication in oilfield operations: Journal of PetroleumTech-nology, v. 21, p. 1353–1360.

Matthews, M. K., and J. Kelly, 1967, How to predict forma-tion pressure and fracture gradient: Oil & Gas Journal,v. 65, no. 8, p. 92–106.

Pennebaker, E. S., 1968, An engineering interpretation ofseismic data: Society of Petroleum Engineers 43rd AnnualFall Meeting, SPE 2165, 12 p.

Pilkington, P. E., 1978, Fracture gradient estimates in Tertiarybasins: Petroleum Engineer International, v. 50, no. 5,p. 138–148.

Salz, L. B., 1977, Relationship between fracture propagationpressure and pore pressure: Society of Petroleum Engi-neers 52nd Annual Fall Meeting, SPE 6870, 8 p.

131

13Consolidation State, Permeability, and StressRatio as Determined from Uniaxial StrainExperiments on Mudstone Samples from theEugene Island 330 Area, Offshore Louisiana

Beth B. StumpTexaco Worldwide Exploration and Production,New Orleans, Louisiana

Peter B. FlemingsPennsylvania State University,University Park, Pennsylvania

A B S T R A C T

Uniaxial strain experiments conducted on mudstone cores from overpressured horizons in EugeneIsland Block 330 (Gulf of Mexico) reveal information about consolidation state, compaction behavior,and permeability. Maximum past effective stresses for two mudstone samples were experimentallyderived and are within 200 psi of porosity-based estimates of in-situ stress. Laboratory measurementsof stress ratio (K0 � 0.85) compare well with in-situ measurements made during leak-off and stresstests (K0 � 0.84 � 0.91). The high K0 values suggest that the sediment deformation is primarily plasticat in-situ levels of effective stress. A slope change on the stress-strain curve supports the observationof primarily plastic deformation following yield. Direct measurements of mudstone permeability atestimated in-situ levels of effective stress reveal layer-parallel and layer-perpendicular permeability of5.32 � 10�4 md (5.25 � 10�19 m2) and 1.17 � 10�4 md (1.15 � 10�19 m2), respectively.


Strain in a geologic basin is typically assumed to occuruniaxially (Roegiers, 1989). We use this uniaxial strainassumption to replicate geologic deformation in thelaboratory (Karig and Hou, 1992; Karig, 1996). Defor-mation behavior of an uncemented sample depends onstress history and physical properties. Uniaxial strain

Stump, Beth B., and Peter B. Flemings, 2002, Consolidation State, Permeability,and Stress Ratio as Determined from Uniaxial Strain Experiments on MudstoneSamples from the Eugene Island 330 Area, Offshore Louisiana, in A. R. Huffmanand G. L. Bowers, eds., Pressure regimes in sedimentary basins and theirprediction: AAPG Memoir 76, p. 131–144.

experiments provide an estimate of the maximum paststress of an undisturbed sample. Using this estimate ofmaximum past stress, we assess the consolidation stateand stress history of the sample.Laboratory tests on undisturbed samples provide

further insight into compaction behavior and elasticproperties by providing continuous measurements ofstress ratio, K0, defined here as the ratio of change inhorizontal effective stress to change in vertical effectivestress (Karig and Morgan, 1994). We compare experi-mental values of K0 with stress ratios calculated fromleak-off tests and fracture completions in this area. No-menclature and symbols used in this chapter are pre-sented in Table 1.

132 S T U M P A N D F L E M I N G S

Table 1. Nomenclature

Variable Property Units*

A sample cross sectional area L2

e void ratio L3/L3

f acoustic formation factor dimensionlessg gravitational acceleration L/T2

h hydraulic head Lk permeability L2

K hydraulic conductivity L/TK0 stress ratio dimensionlessl sample length Lp’ mean effective stress M/LT2

Pf fluid pressure M/LT2

q differential stress M/LT2

Q volumetric flow rate L3/TSv vertical stress M/LT2

vp compressional-wave velocity L/TdPf Pf difference across the sample M/LT2

dt wire-line–measured transit time T/Ldtma matrix transit time T/Le strain L3/L3

� porosity L3/L3

�i initial sample porosity L3/L3

l fluid viscosity M/LTm Poisson’s ratio dimensionlessqf fluid density M/L3

rc preconsolidation stress M/LT2

rh horizontal effective stress M/LT2

rv vertical effective stress M/LT2

*L � length; T � time; M � mass.

Figure 1. Basemap locates cored wells from which labora-tory samples were taken. Circles indicate bottom-holelocation.

We describe our methodologies for uniaxial strainexperiments and permeability tests. We then presentour experimental results and draw comparisons to in-situ estimates and previous studies. Finally, we discussfactors that affect laboratory and in-situmeasurementsand close with implications of our findings.

M E T H O D S

Sample Description

Conventional core taken from two wells in the EugeneIsland 330 field (Figure 1) provided mudstone samplesfor the deformation experiments. The Pennzoil 330 A-20ST2 (Pathfinder) well was cored in 1993; 343 ft (104.5m) of core was recovered (95% recovery). In 1994, 43.2ft (13.1 m) of core was recovered from the Pennzoil 316A-12 well (34% recovery). All of the 4 in. (101.6 mm)diameter cores were cut into 3 ft (.914 m) sections andthen stabilized in the core barrels using a quick-hard-ening epoxy resin. Cores were then slabbed into one-

third and two-thirds parts. Laboratory samples weretaken from the two-thirds part. Slabs were archived incold storage at Core Labs (Houston) and then movedto Penn State University, where they are stored in ahumid, chilled room. The A-20ST2 core was sealed inwax to preserve moisture.The pressure regime (Figure 2) of the Eugene Island

330 area consists of a shallow, sand-rich, hydrostaticallypressured zone overlying an interbedded transitionzone of moderate overpressure (12 lb/gal equivalent-mudweight [EMW]) and a severely overpressured sec-tion (�14 lb/gal EMW) at depth. The samples for thedeformation experiments were taken from the severelyoverpressured outer neritic mudstone section adjacentto the Lentic 1 sand (Figure 3). Alexander and Flemings(1995) present a detailed description of the geologic evo-lution of this field. Table 2 provides a summary of es-timated in-situ fluid pressures and effective stress, aswell as the composition of the core samples.The A-12 core was subsampled between the Lentic

1 upper and lower sands (Figure 3a). The Lentic 1 sandhas been interpreted as a turbidite/distal shelf deposit(Alexander and Flemings, 1995). At the onset of the K0experiment, the A-12 mudstone (T96) sample was 63.5mm long and 31.01 mm in diameter, with an initialporosity of 0.39. The samplewas taken from core barrel1 and contains 38% quartz, 39% clay, and small frac-tions of potassium feldspar, plagioclase, and calcite(Core Laboratories, 1994). See Table 2 for a detailed

Consolidation State, Permeability, and Stress Ratio in Mudstone Samples from the Eugene Island 330 Area, Offshore Louisiana 133

Figure 2. A pressure regime typi-cal of the Eugene Island 330area is shown for the A-20ST2well. (a) Gamma ray showsdepths of key sands. (b) Pres-sure track is bounded by hydro-static (0.465 psi/ft) andlithostatic gradients. Dashed linerepresents pressure calculatedfrom drilling mud weights, graydots indicate fluid pressure cal-culated from porosity in themudstones, and circles are mea-sured fluid pressures in adjacentsands.

composition description. Laser particle size analysisrevealed 2.5% fine-grained, 15.4% very fine grained,62.1% silt-size, and 20.0% clay-size particles.Fluid pressure (Pf) in the mudstone overlying the

Lentic 1 sand in the A-12 well is estimated as 35.0 MPa(5080 psi; 14.6 lb/gal EMW) from a porosity-effectivestress method (Hart et al., 1995). Vertical (overburden)stress (Sv) is calculated by integrating the bulk densitylog and is 42.1 MPa (6105 psi). The estimated in-situvertical effective stress (rv) is 7.1 MPa (1025 psi), asdefined by equation 1 (Terzaghi, 1925).

r � S �P (1)m m f

The A-20ST2 (T77) sample (Figure 3b) was taken be-tween the Cris S flooding surface and the Lentic 1 sand(Alexander and Flemings, 1995). Losh (1998) providesa discussion of the structural analysis of the A-20ST2core. The A-20ST2 sample had an initial length of 52.73mm, a diameter of 30.94 mm, and an initial porosity of0.37. The sample contains 35% quartz and 54% clay(Table 2) (Losh et al., 1994). Estimated fluid pressure

in this mudstone interval is 39.5 MPa (5730 psi; 15.0lb/gal EMW). Calculated Sv is 46.8 MPa (6782 psi). Theestimated in-situ vertical effective stress in theA-20ST2at 2240 m (7350 ft) is 7.3 MPa (1052 psi).

Experiment Description

K0 TestsK0 tests, defined here as consolidation experimentsconducted under uniaxial strain conditions, were con-ducted in a triaxial servohydraulic load frame con-trolled by computers at Cornell University (see Karig[1996] for a photograph of the configuration). An initialisotropic stress state at the onset of the experiment, ateffective-stress levels well below anticipated sampleyield, was used to minimize preshearing of the sample(Mesri and Hayat, 1993). After the sample was stabi-lized in a period of 24–48 hr, the experiment proceededunder uniaxial strain conditions. Experiment durationwas determined, in part, by the length of time neces-sary to reach yield. The durations of the T96 (A-12) andT77 (A-20ST2) experiments were 8 and 13 days, re-spectively.


Figure 3. Cylindrical laboratorysamples were drilled perpendicu-lar to bedding at locations de-noted with circles. Gray arearepresents entire cored interval.(a) 316 A-12; (b) 330 A-20ST2.

Table 2. Sample Descriptions

Well, SampleSubsea TrueVertical Depth Composition

Sonic-DerivedIn-Situ Pf (psi)

EstimatedIn-Situ rv (psi)

EstimatedIn-Situ K0

316 A-12 T96 6690 ft(2039 m)

38% quartz, 5% potassiumfeldspar, 9% plagioclase, 3%calcite, 1% dolomite, and 39%clay (48% illite, 38% smectite,7% kaolinite, 8% chlorite)

5080(35.0 MPa)

1025(7.1 MPa)

0.91(6690 ft)

316 A-12 P01, P03 6781 ft(2067 m)

40% quartz, 1% potassiumfeldspar, 9% plagioclase, 2%pyrite, and 48% clays (45% illite,35% smectite, 7% kaolinite, 12%chlorite)

5166(35.6 MPa)

1045(7.2 MPa)

0.43(6798 ft)

330 A-20ST2 T77 7350 ft(2240 m)

35% quartz, , 8% potassiumfeldspar, 3% plagioclase, and54% clay (52% illite, 32%smectite, 15% kaolinite, 1%chlorite)

5730(39.5 MPa)

1052(7.3 MPa)

�0.84(7277 ft)


All experiments were run under controlled axialload at a rate of 0.1 psi/min, which approximates aninitial strain rate of 1 � 10�7 s�1. A controlled loadexperiment was used to allow fluid dissipation in theselow-permeability samples. As consolidation increaseswith increasing axial load and the sample compresses,sample compressibility decreases, which in turn causesthe strain rate to decrease. Within the apparatus, sin-tered titanium disks with 2 lm pore spaces allow fluiddrainage from the top and bottom of the cell duringconsolidation. Linear variable-displacement transduc-ers (LVDT) measure axial strain. Karig (1996) pre-sented a full description of the apparatus used in theseexperiments.Jacob’s (1949) relation provides a method for cal-

culating porosity changes from strain, e (compressionpositive), during these experiments:

�d�e � (2)

1��

By substituting d� � � � �i and rearranging, weget an expression for porosity as a function of initialporosity (�i) and axial strain:

� �ei� � (3)

1�e

Initial porosity (�i) is calculated in the laboratoryusing initial bulk density, pycnometer-derived graindensity, and an assumed fluid (brine) density of 1.07g/cm3.Void ratio (e), used to graphically determine con-

solidation state, is a function of porosity:

�e � (4)

1��

Permeability TestsMudstones in the Eugene Island 330 area act as sealsto pressure and hydrocarbon migration. Permeabilitymeasurements in mudstone allow us to evaluate sealintegrity and estimate time scales of overpressure dis-sipation. Permeability is determined directly in the lab-oratory from the rate of fluid flow through a sampleof known length, using a constant-head test.During this experiment, constant fluid pressure is

held at one end of the sample; the outflow end is keptat atmospheric pressure. We calculate hydraulic con-ductivity, K, from Darcy’s law.

Q Dh� �K (5)� �A Dl

Using the definition of hydraulic head, h, and sub-stituting the expression for hydraulic conductivity(equation 6) into equation 5, we get an expression forpermeability, k (equation 7).

kq gfK � (6)l

Ql Dlk � (7)

A DPf

Laboratory measurements of permeability in low-permeability sediments are difficult. The identificationand elimination of potential errors are the keys to ac-curate direct-permeability measurements (Tavenas etal., 1983). Leakage through the external fitting is per-haps the largest and most unavoidable source of error.We attempt to quantify this error by running leak-ratetests in the cell containing no sample. Stump (1998)detailed methods used to decrease error in these con-solidation experiments. Such methods include sur-rounding the sample with silicone oil to reduceosmotic effects and maintaining a confining pressureon the sample to minimize preferred flow between thelatex sleeve and the sample.Our experiments were run using an inflow fluid

pressure ranging from 49 to 150 psi to redissolve anygas bubbles that exsolved during core retrieval. Wealso used saline brine (35 ppt) to minimize osmotic ef-fects that can decrease apparent permeability (Neuzil,1986). Last, to account for the transient nature of theflow at the beginning of the test (Olsen et al., 1985), weallow the test to equilibrate and reach steady-state flowbefore measuring flow rate.

R E S U L T S

Determination of Maximum Past Stress

Preconsolidation stress (rc), defined as the maximumpast effective stress, was determined using the graph-ical Casagrande method (1936) (Figure 4a). If the lab-oratory experiment replicates the burial-induceddeformation path, and the sample is relatively undis-turbed and uncemented, the observed yield stress cor-responds to the sample’s preconsolidation stress(Karig and Morgan, 1994). Sample yield is defined asthe break in slope of the stress-strain curve, which


Figure 4. Maximum past stress (preconsolidation stress,rc), is determined using Casagrande’s (1936) graphicalmethod. Estimated in-situ rv is calculated from integratedbulk density and fluid pressure estimated by a porosity-effective stress method. (a) For the A-12 (T96), rc is within0.2 MPa (25 psi) of estimated in-situ rv. (b) In the A-20ST2(T77), experimental rc is approximately 1.4 MPa (200 psi)greater than estimated in-situ rv.

denotes the transition from elastic reconsolidation tofirst-time consolidation (Karig and Morgan, 1994).The preconsolidation stress for the A-12 mud (T96)

sample was experimentally determined as 7.2 MPa(1046 psi) (Figure 4a), which is within 0.1 MPa (21 psi)of the estimated in-situ rv of 7.1 MPa (1025 psi), cal-culated from integrated bulk density and pressure de-rived from a porosity-effective stress analysis. For theA-20ST2 sample (T77), the experimentally derivedrc is 8.6 MPa (1248 psi) (Figure 4b), which is 1.3 MPa(196 psi) greater than estimated in-situ rv of 7.3 MPa(1052 psi), based on porosity-effective stress method.Table 3 presents a summary of results from the K0experiments.

Stress Ratio, K0

The stress ratio, K0, referred to as the coefficient ofearth pressure at rest (Brooker and Ireland, 1965), isthe ratio between horizontal effective stress and ver-tical effective stress under uniaxial strain conditions(Jones, 1994). We calculate K0 as the slope of the rh �rv curve (equation 8).

DrhK � (8)0 Drn

K0 increased in the A-12 (T96) and A-20ST2 (T77)experiments following sample yield (Figure 5). In theA-12 (T96) sample (Figure 5a), at vertical effectivestresses less than rc, K0 was 0.52. At larger values ofvertical effective stress, K0 was 0.86. Similarly, in theA-20ST2 (T77), K0 increased from 0.63 to 0.85 followingrc (Figure 5b).

Permeability

Constant-head permeability tests on samples from theA-12 well provided estimates of layer-parallel (P01)and layer-perpendicular (P03) mudstone permeability.Flow rates through the layer-parallel (P01) samplewere measured using two pressure differences (DPf)across the length of the sample: 0.34 and 0.66 MPa (49and 96 psi, respectively) (Figure 6a). Confining pres-sure remained at 6.9 MPa (1000 psi) for the duration

Table 3. Summary of Deformation Experiment Results

Well SampleSubsea TrueVertical Depth rc (psi) Preyield K0 Postyield K0

316 A-12 T96 6690 ft (2039 m) 1046 (7.2 MPa) 0.52 m � 0.34 0.86 m � 0.46330 A-20ST2 T77 7350 ft (2240 m) 1248 (8.6 MPa) 0.63 m � 0.39 0.85 m � 0.46


Figure 6. (a) Direct measurements of layer-parallel (P01)permeability yield an average permeability of 5.25 � 10�19

m2 (5.32 � 10�4 md). Initial porosity of P01 sample is0.40; final porosity was difficult to determine because sam-ple was misshapen upon removal from cell. (b) Averagelayer-perpendicular permeability (P03) is 1.15 � 10�19 m2

(1.17 � 10�4 md). During the P03 experiment, porositydecreased from 0.48 to 0.38.

Figure 5. Stress ratio K0 is calculated throughout the defor-mation experiments as the slope of horizontal vs. verticaleffective stress. (a) In the A-12 (T96), pre-rc K0 is 0.52;post-rc K0 is 0.86. The dotted line denotes in-situ rv andthe circle represents experimental rc. (b) In the A-20ST2(T77) sample, K0 increased from 0.63 to 0.85.

of the experiment. Average layer-parallel permeabilityat the two pressure differences is 5.25� 10�19 m2 (5.32� 10�4 md). The layer-perpendicular sample, P03,was tested at four pressure differences of 0.35, 0.52,0.70, and 1.03 MPa (51, 75, 100, 150 psi, respectively)(Figure 6b). Confining pressure for the P03 experimentwas 800 psi. Layer-perpendicular permeability mea-

surements averaged 1.15� 10�19 m2 (1.17� 10�4 md),ranging from 9.29 � 10�20 m2 to 1.43 � 10�19 m2.Two leak-rate tests, run at a variety ofDPf, identified

leak rates of 0.042 and 0.048 mL/hr. Correcting for theleak rate of the system, the values for layer-parallel andlayer-perpendicular permeability are 3.82 � 10�19 m2

and 6.47 � 10�20 m2 (3.87 � 10�4 and 6.56 � 10�5

md), respectively.


Figure 7. Compressional velocity increases with increasingvertical effective stress during all three K0 tests. Symbolsrepresent velocity measurements taken during T96 (�) andT77 (�) experiments. The change in velocity with verticaleffective stress (i.e., the slope of linear regressions throughthese data) is 1.91 � 10�2 for the T96 (A-12) and 1.04 �10�2 for T77 (A-20ST2). Vertical lines are shown at the ex-perimental preconsolidation stresses for the A-12 and A-20ST2 samples (1046 and 1248 psi, respectively).

Figure 8. A generalized mudstone deformation path in-cludes primary compaction (1–2). As effective stress de-creases (2–3), sample experiences some porosity rebound,but does not decompact along the original deformationpath. Upon reloading (3–4), sample follows similar pathuntil it reaches maximum past stress. Deformation at higherstresses (4–5) tracks along a primary compaction path.

Velocity

Compressional-wave velocity (vp) was measured dur-ing K0 experiments on the A-12 andA-20ST2mud sam-ples. Compressional waves at a frequency of 400 kHzwere generated along the core axis (i.e., perpendicularto bedding). Velocity measurements have an accuracy

of�0.02 km/s (Karig, 1996). As vertical effective stressincreases and the sediment compacts, vp increases (Fig-ure 7). At rc, compressional velocity in the A-12 (T96)sample was 2234 m/s (delta transit time [DT] � 136ls/ft). The A-20ST2 (T77) velocity at rc was 2101 m/s(DT � 145 ls/ft). By comparison, in-situ wire-linesonic traveltime measurements at core sample depthswere 155 ls/ft in the A-12 and 149 ls/ft in the A-20ST2.

D I S C U S S I O N

Assessment of Consolidation State

A normally consolidated sediment has never been sub-jected to a higher stress than its current stress (Jones,1994). An overconsolidated sediment is one that has amaximum past effective stress that is greater than thecurrent effective stress. We determined the maximumpast stress experimentally by observing the change indeformation behavior during the uniaxial strain ex-periment. Mudstone compaction is largely irreversiblebecause deformation is primarily plastic with a smallelastic component. When a sample is brought fromdepth to the surface, it experiences a decrease in effec-tive stress and a consequent rebound in void ratio(point 3 on Figure 8). This rebound results from elasticexpansion and opening of microcracks (Karig andHou, 1992). As the sample is reloaded in the labora-tory, the deformation path follows a slope similar to,but not identical with, the unloading path until thestress reaches the maximum past stress (point 4 in Fig-ure 8). Mesri and Choi (1985) demonstrated the effec-tiveness of the void ratio–effective stress relationshipin determining maximum past stress experimentally.As the vertical effective stress increases beyond themaximum past effective stress, the slope of the voidratio–effective stress curve changes, reflecting a changefrom primarily elastic to primarily plastic deformation(Turcotte and Schubert, 1982; Atkinson, 1993). On atraditional stress-strain plot the elastic to plastic tran-sition is manifested by a change from linear to nonlin-ear behavior.Our experimentally derived rc values are within 0.2

and 1.4 MPa (25 and 200 psi) of our prediction of thein-situ stresses based on a porosity-effective stressmethod. The agreement between these different ap-proaches suggests that both approaches are imagingthe preconsolidation stress of the sample. Unfortu-nately, neither approach taken independently can de-termine if these sediments are overconsolidated.Bowers (1994) refers to overconsolidation, or a late-stage decrease in effective stress, as “unloading.”


Cementation vs. Overconsolidation

One possible way to determine if the sediment is over-consolidated is illustrated on plots of mean effectivestress (p� � (2rh � rv)/3) vs. differential stress(q � rv – rh). A normally consolidated sample exhibits

a bilinear behavior on a p�-q plot, whereas both over-consolidated and cemented samples exhibit more com-plicated behavior (Figure 9a, adapted from Karig[1996]). One interpretation of the A-12 sample behav-ior is that this sediment is normally consolidated,whereas the A-20ST2 sediment is overconsolidated

Figure 9. Crossplots of mean effective stress (p�) with differential stress (q) can illuminate the difference between cementationand a state of overconsolidation. (a) A generalized figure (adapted from Karig, 1996) shows the p�-q signatures for cemented,uncemented normally consolidated, and uncemented overconsolidated sediments. (b) A-12 (T96) sample shows a bilineardeformation path, indicative of uncemented, normally consolidated sediment. Vertical lines denote mean effective stress atexperimental yield (rm � 727; rv � 1046, rh � 567 psi) and from in-situ estimates (rm � 889; rv � 1025, rh � 820 psi).(c) The A-20ST2 (T77) p�-q signature suggests that this sample may be overconsolidated. Mean effective stress at yield in theT77 experiment was 977 psi (rv � 1248, rh � 842 psi); in-situ estimate of mean effective stress is 940 psi (rv � 1052, rh �884 psi).


(Figure 9b, c). Neither sample demonstrated a decreasein differential stress indicative of cement breakdown.This observation is consistent with the lack of typicalcements like calcite in these samples (Core Laborato-ries, 1994; Losh et al., 1994).Although we used the Casagrande method, Bryant

et al. (1986a) suggested that this method may under-predict the maximum past stress by as much as 35%.They proposed an alternative method of computingregressions through the reloading and first-time com-paction curves. In this method the intersection of thetwo lines identifies the maximum past stress. Blum etal. (1996), however, observed no systematic differencebetween the Casagrande and Bryant methods in de-termining the preconsolidation stress of their samples.A few potential sources of error are inherent in our

calculations because of our assumptions. First, we as-sume that geologic deformation is approximately uni-axial. We then consider uniaxial strain experiments tobe a replication of sediment burial in a geologic basinand therefore presume the experimental yield stress tobe indicative of the maximum past stress. In an exten-sional basin such as the Eugene Island 330 area the

assumption of pure uniaxial strain may cause themax-imum past vertical effective stress observed in the lab-oratory to differ from the in-situ maximum pastvertical effective stress.Second, we assume that the deformation experi-

ments are run under drained conditions. That is, weassume that strain rates are sufficiently slow to allowexcess fluid pressure to dissipate, such that the fluidpressure in the sample is constant. If this assumptionis invalid and the excess fluid is not drained from thesediments during the experiments, we are overesti-mating effective stress for a given porosity. Prelimi-nary calculations indicate that for an average strainrate of 1 � 10�7 s�1 in a sample with permeability of1 � 10�19 m2 (1 � 10�4 md) the accumulated excesspressure is negligible (Pf/Sv � 0.05). As the A-12 mud-permeability measurements are in the range of 1 �10�19 m2, we consider all of these tests to be represen-tative of drained behavior and therefore that no over-pressure was induced in the samples during theexperiments.

Stress Ratio, K0

Experimentally derived K0 values at vertical stressesabove the preconsolidation stress for the A-12 (T96)and A-20ST2 (T77) samples agree well with in-situstress ratios calculated from leak-off test and stress-testdata (Stump, 1998). A stress test in the A-20ST2 wellprovided an in-situ estimate of horizontal effectivestress, rh (Flemings et al., 1994). Vertical effectivestress was calculated using bulk density and sonic-de-rived estimates of fluid pressure (Stump and Flemings,2000). The calculated in-situ stress ratio in the A-20ST2well is 0.84, which is nearly identical with the postyieldK0 value (0.85). A leak-off test close to the A-12 wellprovided an in-situ stress ratio at sample depth of 0.91(Finkbeiner, 1998; Finkbeiner et al., 2001). This in-situstress ratio is slightly higher than the experimentalpostyield K0 of 0.86. The mudstone K0 values mea-sured in our experiments are slightly higher than val-ues of K0 presented in previous studies (Table 4).Both the A-12 and the A-20ST2 mud samples

showed an increase in K0 following yield. The sharpincrease following yield results from a change in de-formation. Prior to yield, during the reloaded phase,deformation is recoverable (elastic). Following yield,as the sample consolidates along its first-time compac-tion path, deformation is mostly plastic. Karig andHou (1992) measured K0 values of 0.35 and 0.62 for theelastic and first-time consolidation phases of defor-mation in silty clays, respectively.In isotropic sediments, during elastic deformation

under uniaxial strain conditions, the stress ratio is a

Table 4. Comparison of Postyield K0 Values with PreviousWork

Sediment Type Composition K0

A-12 mud (this study) 38% quartz, 39% clay,some potassiumfeldspar, plagioclase,calcite

0.86

A-20ST2 mud (thisstudy)

35% quartz, 54% clay 0.85

Ottawa sand mixture(Karig and Hou, 1992)


silty clay (Karig andHou, 1992)

50% silica powder(including quartz,potassium feldspar),50% clay

0.62

Boston blue clay (Mesriand Hayat, 1993)

35% quartz, 30% clay,23% plagioclase, 8%potassium feldspar

0.56

St. Alban clay (Mesriand Hayat, 1993)

25% quartz, 26% clay,33% plagioclase, 11%potassium feldspar

0.49

Bearpaw Shale (Brookerand Ireland, 1965)

30% quartz, 65% clay,5% potassium feldspar

0.70

London clay (Brookerand Ireland, 1965)


Weald clay (Brooker andIreland, 1965)


Goose Lake flour(Brooker and Ireland,1965)



direct function of Poisson’s ratio. We recognize theanisotropy of clays, but estimate an average Poisson’sratio using the experimental K0. Equation 9 is derivedfrom Hooke’s Law.

Dr mhK � � (9)0 Dr 1�mn

By rearranging, we calculate the Poisson’s ratio ofthese samples from the experimentalK0measured dur-ing the reload (elastic) phase of consolidation.

K0m � (10)1�K0

In the A-12 sample the K0 of the reloaded phase is0.52, corresponding to a Poisson’s ratio of 0.34. Dy-namic Poisson’s ratio, calculated from wire-line dipolesonic measurements at the depth of the A-12mud sam-ple, is 0.39. The relationship used to calculate dynamicPoisson’s ratio from wire-line logs is m � [(Dts/Dtc)2 –2 ]/[2(Dts/Dtc)2 – 2], where Dts is shear-wave travel-time and Dtc is compressional-wave traveltime.

Figure 10. Comparison plot ofporosity-permeability data pub-lished by previous authors showsthat our permeability measure-ments (black circles) comparewell with previous measure-ments made in similar sedi-ments. Plus symbols (�)represent modeled results fromBryant et al. (1986a) and Gordonand Flemings (1998) for Gulf ofMexico mudstones. Indirect per-meability measurements, madeduring consolidation tests, areshown as asterisks (*), �s, andfilled symbols. Empty symbolsdenote direct measurements ofpermeability (constant-head andflow-pump tests).


In the A-20ST2, the pre-rc K0 of 0.63 corresponds toa Poisson’s ratio of 0.39. A Poisson’s ratio measuredduring a uniaxial stress test on a mudstone samplefrom the A-20ST2 well (D. Karig, 1998, personal com-munication) was 0.35.

Permeability

Permeability calculations (5.32 � 10�4 md, 1.17 �10�4 md) from constant-head tests on samples fromthe A-12 well fall in the range of measurements madein previous studies (Figure 10). Dewhurst et al. (1998)measured an average permeability of 7.5 � 10�3 md(7.4 � 10�18 m2) for a silt-rich (40% clay) sample with34% porosity. Measurements of permeability duringconsolidation tests on deep-water core from the PigmyBasin, Gulf of Mexico, yielded an average value of 3� 10�4 md (3 � 10�19 m2) (Bryant et al., 1986b).Wetzel (1990) measured an average permeability of 8.6� 10�3 md (8.5� 10�18 m2) for turbidites taken fromseveral hundred feet below the sea floor. Bryant et al.(1975) evaluated permeability from consolidation testson various Gulf ofMexico sediments. For sampleswithcomposition and porosity similar to our samples, per-meability ranged from 6.6 � 10�4 md (6.5 � 10�19

m2) to 9.6 � 10�4 md (9.5 � 10�19 m2) (Bryant et al.,1975).The ratio of layer-parallel to layer-perpendicular

permeability, a ratio of 4.5 for our data, is due to the

anisotropy of the mudstone. Vasseur et al. (1995)showed that the difference between layer-parallel andlayer-perpendicular permeabilities increases for in-creasing levels of compaction. Taylor and Fisher (1993)also observed anisotropy in their permeability mea-surements of sediments from the Nankai accretionaryprism.The permeability of amudstone layer in a basinmay

exceed laboratory estimates of permeability because ofthe influence of fractures. Neuzil (1994) recognized thedifferences between laboratory and regional estimatesfor the Pierre shale and some clay till, but also ob-served that several muds showed very similar valuesfor both laboratory and regional permeability.

Velocity

The porosity-velocity relationships from these defor-mation experiments (Figure 11) correlate well with arelationship developed by Raymer et al. (1980) and en-hanced by Raiga-Clemenceau et al. (1986).

1/fDtma� � 1� (11)� �Dt

Issler (1992) calculated an acoustic formation factor,f, of 2.19 and a Dtma of 67 ls/ft for noncalcareous, lowtotal organic carbon shale. As shown in Figure 11, val-ues calculated during our K0 tests on the A-12 and

Figure 11. Crossplot of porosityand compressional velocity datais used to determine acousticformation factor (f) and matrixvelocity (Dtma) (equation 11).Specifically, the slope of the re-gression line is 1/f. The y inter-cept of the line is equal to (1/f)log (Dtma). The correlationcoefficients (R2) for T77 and T96were 0.9850 and 0.9962, respec-tively. For reference, Issler’s(1992) relationship is shown.


A-20ST2 mudstone samples correlate well with Issler’s(1992) values. Linear regression of the T77 (A-20ST2)data reveals f � 2.18 and Dtma � 59 ls/ft. T96 (A-12)data yields an f value of 2.19 and a Dtma value of 56ls/ft. The observations that both the experimentallyderived porosity-velocity relationship and the acousticformation factor values agree with Raiga-Clemenceauet al. (1986) and Issler (1992), respectively, is significantbecause the in-situ fluid pressures in the mudstoneswere calculated from sonic-derived porosities, usingequation 11 and Issler’s (1992) values.


Deformation experiments conducted on twomudstonesamples from the Eugene Island 330 area are relativelycompatible with estimated in-situ behavior. Experi-mentally observed yield stresses agree with porosity-derived estimates of in-situ vertical effective stresses.Experimental stress ratios following sample yield cor-relate well with in-situ measurements. Constant-headtests reveal mudstone-permeability estimates of 5.32�10�4 and 1.17 � 10�4 md.


This research was supported by the Gas Research Institute(Contract 5095-260-3558) and the Penn State GeoFluids Con-sortium. We thank Pennzoil for donating the core used inthese experiments. The A-20ST2 (Pathfinder) core was re-trieved by the Global Basins Research Network (funded byDOE and industry partners). We especially thank Dan Karigfor both conducting these experiments and for critically re-viewing this chapter. We thank Alan Huffman for providingvaluable feedback on this chapter. We also thank HeatherJohnson for assistance with figures.


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145

14Method for Determining RegionalForce-Balanced Loading and UnloadingPore-Pressure Regimes and ApplyingThem in Well Planning andReal-Time DrillingPhil HolbrookForce Balanced Petrophysics, Houston, Texas

A B S T R A C T

Fluid-expansion effective-stress unloading requires a very low net permeability seal and a relativelyhigh (�25�C/km) regional geothermal gradient. Transition from loading-limb to unloading-limb pore-pressure calibration depends upon the recognition of the regional seal in each well. A regional unload-ing-limb stress-strain coefficient is calibrated below the regional sealing surface.

The depth to fluid-expansion unloading in 16 worldwide basins ranges from 2 to 6 km. The onsetof fluid-expansion unloading occurs between the 90 and 120�C isotherms in these basins. The occurrenceof a regional seal to contain fluid expansion is determined from a regional overburden, high fracture-propagation pressure correspondence. These factors control net (intergranular � fracture) permeabilitythat is required to form an effective fluid-expansion pressure seal.

In each well within a region, pore pressures above this seal can be determined from a force-balancedloading-limb stress-strain relationship. The loading-limb stress-strain coefficients sigmamax (rmax) andalpha exponent (�) are dependent only onmineralogic constants. These coefficients are compositephysi-cal properties of minerals that are independent of depth or location. Loading-limb pore-fluid pressurecould be considerably above hydrostatic pressure before encountering the unloading pore-pressureregime.

The optimum regional unloading-limb in-situ stress-strain relationship is determined from an ap-propriate correspondence between measured pore pressures with respect to petrophysically measuredstrain. A common regional unloading-limb stress-strain exponent (�offset) is determined with respect tothe fluid-expansion seal in each well.

Each petrophysical sensor has a different nonlinear response that is not readily transformed toporosity through single-mineral chart book functions. Petrophysical sensor to porosity transforms de-pend upon the physical properties of the mineral grains. Each petrophysical sensor has its own boreholeenvironmental problems. If sensor- and mineral-specific porosities are different for a given foot, thediscrepancy should be resolved before the (strain � 1.0 � porosity) determination is made. The detailsof the sensor- and mineral-specific nonlinear porosity transforms for resistivity, c-c density, and transittime for water-saturated sedimentary rocks are described.

Holbrook, Phil, 2002, Method for Determining Regional Force-Balanced Loading and Unloading Pore-Pressure Regimes and Applying Them inWell Planning and Real-Time Drilling, in A. R. Huffman and G. L. Bowers, eds., Pressure regimes in sedimentary basins and their prediction:AAPG Memoir 76, p. 145–157.

146 H O L B R O O K

The regional unloading-limb stress-strain exponent (�offset) joins the loading limb (�) at the region-ally extensive seal. This stress-strain fitting approach maintains a mechanically sensible fluid pressureto strain proportionality throughout the regionally confined unloading-limb pressure regime. Detailedfluid-pressure comparisons in many stacked unloading-limb pressure compartments indicate that thisis commonly the case.

Field experience has shown that there is no unique unloading-limb exponent (�offset). Differingregional temperature gradients and complex hydrocarbon richness exert strong influences on in-situhydrocarbon cracking. The liquid- to gas-phase change accompanying complex hydrocarbon crackingis the dominant fluid-expansion mechanism.

Mineral grain dissolution can return unloaded sedimentary rocks to the gravitational loading limb,but not beyond. The overlying Newtonian gravitational loading-limb stress-strain coefficients (rmax and�) are mineralogically general throughout approximately biaxial normal fault regime basins. The un-derlying unloading-limb stress-strain exponent (�offset), however, is region specific and needs to bedetermined empirically as described previously.

P O R E P R E S S U R E A N D F R A C T U R EP R E S S U R E D E R I V E D S I M U L T A N E O U S L YF R O M F O R C E - B A L A N C E D S T R E S S - S T R A I NP H Y S I C S

Pore pressure is the fluid load-sharing element in thesubsurface. Solid mineral grains bear the remainingload. The entire load is both generated and borne bythe Earth’s solid and fluid matter. The effective stresstheorem is the force-balanced physical-mathematicalexpression for porous granular solids that compose theEarth’s sedimentary crust. In this rigorous physical ex-pression, the fluid scalar pore pressure (PP) is the dif-ference between the two solid element scalars, averageconfining load (Save), and average effective stress(rave), that is, PP � Save� rave.

The Earth’s sedimentary crust is a continuous closed-form solid-fluid mechanical system. The (Save) and(rave) terms of the effective stress theorem are interde-pendent within the Earth through constant mineral andfluid coefficients. Holbrook (2002), in chapter 3 of thisvolume, presents and explains a Newtonian force-bal-anced in-situ strain-linked system of equations that ap-plies to both loading and unloading pressure regimesin the subsurface. Both loading and unloading pore-pressure regimes depend on overburden, mineralogy,and in-situ strain. The only difference between loading-limb and unloading-limb pressure regimes is their dif-ferent stress-strain coefficients (�) or (�offset).

There are dynamic interactions within the Earth’sclosed mechanical system that regulate pore-fluidpressure in both the loading and unloading pore-fluidpressure regimes. On a geologic time scale, fluids arethe continuous pore-pressure transmission system.The containing solid granular matrix and fracture sys-tem regulates pore-pressure profiles in the subsurface(Holbrook, 1998).

A regional stratigraphic column can be characterizedas a series of moderate-permeability pressure com-

partments with interlayered low-permeability pressure-regulating seals. On a geologic time scale, fluids withina continuous moderately permeable lithostratigraphicbody reach a seal relative hydrostatic pressure gradient.The overriding pressure regulation dynamics are thatpore pressure at a partially sealing cap rock’s minimumwork leak point can be no greater than the fracturepropagation pressure of the overlying cap rock at thatleak point. Intergranular Darcy flow regulates porepressures where fluid pressures are below the force-bal-anced fracture-propagation pressure limit.

The keys to understanding and quantitatively pre-dicting loading vs. unloading pore-pressure regimesare the subsurface dynamic interactions of theseforce�balanced terms. The first key to unloading-limbpore-pressure determination is the recognition of a re-gional caprock seal. This is the tie point of the loadingand unloading limbs in stress-strain space. The secondkey requirement is a regionally calibrated unloading-limb stress-strain exponent (�offset) below that seal.These two key factors are interdependent. They varyfrom region to region and must be calibrated from off-set wells on that scale.

S T R E S S - S T R A I N L O A D I N G A N DU N L O A D I N G H Y S T E R E S I S F O RG R A N U L A R S O L I D S

The loading limb defines the relationships betweenstress and strain for sediments that are currently attheir maximum state of compaction. The loading-limbpore-pressure regime contains hydrostatic and dis-equilibrium compaction suprahydrostatic fluid pres-sures. Minerals are the discrete solid load-bearingelements of the Earth. The loading-limb stress-strain co-efficients (rmax and �) are global in nature dependentprincipally upon mineralogic composition (Holbrook,1995). Each mineral has only two volumetric plastic

Method for Determining Regional Force-Balanced Loading and Unloading Pore-Pressure Regimes and Applying Them in Well Planning and Real-Time Drilling 147

Figure 1. Regional in-situ loading and unloading effectivestress–strain angular relationships. The relative in-situ un-loading-limb angle effective stress–strain response ispower-law linear within plastic and elastic limits. Adaptedfrom Holbrook, 2001.

stress-strain coefficients that are operative during gran-ular consolidation under effective-stress loading.

Each mineralogic end member has a unique volu-metric elastic stress-strain coefficient (J � bulk mod-ulus). A porous sedimentary rock has a proportionallylower bulk modulus (Holbrook et al., 1999). Stress-strain unloading-reloading hysteresis loops are cen-tered about the porous rock or sediment bulkmodulus. Hysteresis loops are wider at faster unload-ing-reloading rates (Holbrook, 1996). The unloading-reloading stress paths approach singularity at geologicstrain rates (see figure 1 in Holbrook, 1996).

Geologic loading rate volumetric effective-stresscompaction is assumed to be power-law proportionalto volumetric in-situ strain (1.0 � �) (Holbrook, 2002).The (rmax) mineralogic coefficients are related to theaverage bond strength and hardness of the mineral’scrystalline lattice (Holbrook, 2002). The reversible ther-mal and elastic stress-strain properties of mineralswere measured in laboratories decades ago (Carmi-chael, 1982). The elastic properties of sedimentaryrocks are related to and limited by the elastic proper-ties of the minerals of which they are composed.

Figure 1 is a power-law linear effective stress–straindiagram. The plastic loading-limb coefficients (� andrmax) of the first fundamental in-situ effective stress–strain relationship are shown. The plastic and elasticstress-strain limits join at the peak loading-limb point.The geologic unloading-limb angular offset (�offset)

falls between the elastic and plastic limits with respectto the peak loading-limb point.

During natural loading, sedimentary grains arebrought closer together, and contact area betweengrains is increased. The solid element load is borne atthese grain contacts and through the mineral lattice tothe neighboring grains. Under increasing loads, elasticenergy is accumulated in the mineral lattice in propor-tion to strain. Elastic strain is a miniscule fraction oftotal strain, which is dominantly plastic.

Also during natural loading, the grain contact area isincreased irreversibly following a plastic stress-strainrelationship (Holbrook, 2002). The limit of plastic gran-ular consolidation is where all fluid-filled porosity isgone and the rock is totally solid. Solidity (1.0 � po-rosity) is a direct measure of volumetric in-situ strain.Plastic compaction of granular solids ends where solid-ity � 1.0. The volumetric strain of zero porosity rocksinvolves only thermal and elastic coefficients.

The grain contact area necessary to support the av-erage effective-stress load over geologic time is also afunction of the average mineralogic crystalline latticebond strength.Weakermineral ionic bonds at grain con-tacts require proportionally more area to bear the sameload and vice versa. Grain external contacts and internalmineral lattices bear loads from all directions. Grainme-chanical and pressure solution adjustment to force bal-ance is volumetric. Volumetric power-law stress-straincoefficients represent the composite intergrain contactareaplusvolumetric intragrain forcebalance in thesolid.Pore pressure bears the remaining load.

The two grain matrix mechanical limits in the sub-surface are (1) the plastic compactional loading limb;and (2) the elastic unloading limb. The two crucial ele-ments of regional pore-pressure calibration are (1) thelocation of the peak loading point in the subsurfaceand (2) the slope of the geologic unloading-limb effec-tive stress–strain exponent (�offset) below the continu-ous, regional, peak loading-limb surface.

Log and Crossplot Example

The unloading limb joins the peak loading limb in aregion that is a continuous surface. Individual wellswithin a region define points on this surface. Figure 2is a Gulf Coast example demonstrating how both thepeak loading-limb point and the regional unloading-limb stress-strain exponent (�offset) are related. The en-tire database represents about 14,200 1-ft (0.3 m)samples of effective-stress and strain data. The upperloading-limb segment is about 9700 ft (2957 m) and thelower unloading-limb segment is about 4500 ft (1372m).

The first panels show the complete stress-strain dataset. For clarity, the loading-limb and unloading-limb

148 H O L B R O O K

segments are shown separately as panels. The loading-limb stress-strain relationship is shown in the top twopanels. The regional unloading-limb stress-strain rela-tionship joins the loading limb at the peak loading-limbpoint. This point is shown on the logs and crossplots ofall three panels.

The loading-limb exponent (�) and unloading-limbstress-strain exponent (�offset) are distinctly different.The average mineralogic compactional loading limb an-gle tan�1 (�) is more than 80� (� � 5.7) and is plastic(see Holbrook, 2002). The average unloading limb an-gle, tan�1 (�offset), is 89.2� which corresponds to �offset� 71.615. The unloading exponent (�offset) is very closeto the bulk modulus mineralogic elastic stress-strainlimit. A slight but measurable increase in porosity existsdue to in-situ elastic mineral contraction in response tofluid-expansion unloading. Allowable force-balance–dependent pore-fluid pressure measuring relationshipsmust fall between the plastic loading-limb and elasticunloading-limb limits. The data shown in Figure 2 rep-resent an extreme but commonly encountered case offluid-expansion unloading that is near the elastic min-eralogic limit.

The location of the peak loading-limb point is clearlydiscernible on both the stress-strain crossplots and theindividual stress and strain logs shown to the side. Thepeak loading-limb point is the point of highest solidityin this well. This peak solidity point intersects the re-gionally continuous fluid-expansion unloading pore-pressure seal.

Regional seals are known to cross stratigraphicboundaries in the North Sea Central Graben as de-scribed by Ward et al. (1995, figure 3). High solidity isthe common interregional fluid-expansion seal recog-nition criteria in the North Sea, Gulf Coast, and FarEast. All three regions have approximately biaxial nor-mal fault regime stress fields. The same force-balancedphysical relationships regulate pore-fluid pressure inall three places. The horizontal/vertical stress ratio inbiaxial normal fault regime basins is apparently equalto solidity irrespective of depth and mineralogy (Hol-brook, 1996). Solidity (strain) is proportional to the av-erage and principal stresses in the Earth’s closed formforce balance (Holbrook, 1999).

Force balance determines the upper limit pore-fluidpressure sealing capacity of all cap rocks (Holbrook,2001). Cap rocks above continuous permeable reser-voirs can hold no more pore-fluid pressure than theminimum principal stress at the cap rock’s minimumwork leak point (where the reservoir pressure is high-est with respect to the sum of the cap rock’s fracturepropagation and capillary entry pressures). The mini-mum work leak point is on the same surface as thepeak loading-limb point in a particular well that pen-etrates a particular pressure compartment. A regionalcaprock seal operates in accordance with solid-fluidforce balance and can be recognized by its regionallycontinuous high solidity. Sealing caprock mechanicsare the same in both loading and unloading pressureregimes.

Figure 2. Raw in-situ effectivestress–strain relationships. Load-ing and unloading stress-strainrelationships from a Gulf Coastwell showing the peak loading-limb point. Most of the scatter inthe data is caused by groupingsedimentary rocks of differentaverage mineralogic compositionwith correspondingly differentstress-strain coefficients. Takenfrom Holbrook, 2001.


F A C T O R S A F F E C T I N G T H E C A L C U L A T I O NO F P O R O S I T Y F R O M P E T R O P H Y S I C A LS E N S O R S

The calculation of very accurate porosity (�) from pe-trophysical sensor data is equivalent to the calculationof very accurate in-situ strain (1 � �) for further rock-mechanics calculations. For calculation purposes thereare several mineral coefficients that are essentially con-stant (� 0.04%) under natural in-situ PV/T conditions.Clay mineral grain density, however, varies by asmuch as 16% under natural subsurface conditions(Grim, 1968).

Most subsurface sedimentary rocks contain sodiumchloride brine under different PV/T x-salinity condi-tions. Under the known range of geothermal gradientsin sedimentary basins, (1) the velocity of sodium chlo-ride brine varies by up to 27%, (2) the density of sodiumchloride brine ranges from 0.92 to 1.26 g/cm3 (also27%), and (3) the compressibility of sodium chloridebrines varies by as much as 61% under known in-situconditions (Holbrook et al., 1999). The electrical con-ductivity of sodium chloride brines (Cw) varies by fiveorders of magnitude. All this natural subsurface vari-ability should be considered if one expects to calculateporosity accurately from any petrophysical sensor.

C L A Y S T O N E D I A G E N E T I C E F F E C T S O ND E N S I T Y , C A L C U L A T E D P O R O S I T Y , A N DO V E R B U R D E N

During burial diagenesis clay minerals are trans-formed from low-density highly disordered weather-ing products into well-crystallizedmetamorphicmicasand chlorites. In moderate to high geothermal gradientareas this complete diagenetic transformation occursin the upper 5000 m of the Earth’s crust. The averagegrain density of clay minerals in mudstones increasesfrom about 2.64 to 3.15 g/cm3 as theminerals are trans-formed primarily through increasing temperature (Ajaand Rosenberg, 1992).

Huang et al. (1991) successfully modeled smectite toillite clay mineral transformation as a thermokineticprocess in many basins with different geothermal gra-dients. Aja and Rosenberg (1992) went further, show-ing data supporting thermodynamic equilibriumbetween clay minerals during this primarily tempera-ture-controlled diagenetic transformation.

Within a given region, the zero porosity averageclay mineral grain matrix (qclay) density/depthgradient is estimated. Quartz and calcite have essen-tially constant densities of 2.65 and 2.71 g/cm3 insubsurface sedimentary rocks over all known geo-

thermal gradients. Whole rock grain density changesfor each sample interval in proportion to the volume-weighted average of clay and nonclay minerals pres-ent. Where applied, this procedure reconciles most ofthe differences between resistivity sensor and c-cdensity sensor-calculated porosities. Accounting forthe regional qclay/depth density gradient, results ingreatly improved porosity, overburden, effectivestress, and pore-pressure calculations no matter whatpetrophysical sensor is used for the primary porositydetermination.

P O R O S I T Y F R O M c - c D E N S I T Y S E N S O RI N P U T

Both average mineral grain density (qmin) and averagedownhole fluid density (qfluid) must be used to obtainaccurate porosity (�) calculations from bulk density(qbulk) sensor input. Average clay volume of the solidfraction commonly varies considerably with depth. Aborehole attenuation-corrected natural gamma-raysignal from the formation is used to estimate clay vol-ume (Vclay) as a fraction of solid for each foot (Hol-brook, 1989). Depending upon the stratigraphicsequence type, average mineral grain matrix density iscalculated in one of two ways. The average grain ma-trix density (qmatrix) used in quartz sand–claystonestratigraphic sequences is

(q ) � [(1.0 � V ) � 2.65]matrix clay

� (V � q ) (1)clay clay

In a calcite–claystone stratigraphic sequence, calcitedensity (2.71 g/cm3) is substituted for quartz density(2.65 g/cm3) in the previous equation. The averageclaystone grain matrix density (qclay) increases grad-ually with depth determined from the regional geo-thermal (qclay/depth) profile.

Fluid density (qfluid) is estimated from a regionalPV/T x-sodium chloride salinity profile. The densityand bulk modulus coefficients of sodium chloridebrines were extracted from voluminousmeasuredden-sity and velocity data by Archer (1992). Archer’s equa-tion-of-state thermodynamic molecular interactioncoefficients were recast as third-order functions of so-dium chloride brine density, pressure, temperature,and molality. The third-order PV/T x-sodium chlorideregression of theNaCl brine equation-of-state providesvery accurate physically consistent fluid coefficientsfor porosity (�) from c-c bulk density (qbulk) measure-ments estimation and for Gassmann equation forwardand inversemodeling (Holbrook et al., 1999). Using the

150 H O L B R O O K

appropriate downhole density coefficients, porosity iscalculated from bulk density using the equation

� � (q � q )/(q � q ) (2)bulk matrix fluid matrix

This procedure incorporates the best knowledge wehave of grain matrix and fluid densities into the po-rosity from bulk-density calculation.

P O R O S I T Y F R O M R E S I S T I V I T Y S E N S O RI N P U T

The common sedimentary mineral grains are infinitelyresistive to electric current. Sedimentary rocks conductelectricity primarily through the motion of chargedNa� and Cl� ions in the dominantly sodium chloridebrine–filled pore space. The formation resistivity factor(F) relates formation water conductivity (Cw) to mea-sured true rock conductivity (Ct). Where porosity (�)equals 1.0, F equals 1.0, and Cw equals Ct.

F � C /C (3)w t

Archie (1941) found a power-law relationshipbetween porosity and formation factor for many sed-imentary rocks. The combined intergranular tortuos-ity-cementation exponent (m) varies with porosity andmineral grain shape in the Archie equation:

(�1.0/m)� � F (4)

Most subsurface brines have salinities equal to orabove normal salinity seawater. At these salinities, al-most all the total conductivity (Ct) is through thecharged Na� and Cl� ions in the water phase (Cw).Variability in the tortuosity-cementation exponent (m)is the pore geometric factor in estimating porosity fromresistivity. The power law exponent (m) is a measureof the electrical length/actual length of an insulatingporous granular solid. It is a complex function of in-tergranular pore volume, continuity, and shape.

Figure 3 shows a set of three measured formationfactor vs. porosity relationships for the three mostcommon sedimentary minerals. Implicit in each ofthese curves is the natural grain shape (aspect ratio) ofthat insulating mineral as it occurs naturally. Grain as-pect ratio ranges from 1:1 for perfectly rounded quartzgrains to more than 500:1 for an average sedimentaryclay. The electrical path though a claystone is manytimes longer than the electrical path through a quartzgrainstone. Considering mineralogically variable tor-tuosity-cementation (m), the formation factor for a 10%porosity grainstone is 50. The formation factor for a

10% porosity claystone is 240. The inappropriate useof a quartz sandstone formation factor to estimate po-rosity in a claystone would result in (15/10 PU) or 50%overestimate of claystone porosity.

Mao et al. (1995) determined the quartz grainstoneArchie function from laboratory measurements on 155quartz grainstone core samples. Mao et al.’s data set ismany times larger than the earlier Archie or Humbledata sets. The value of m increases nonlinearly withdecreasing porosity in all three single-mineral empir-ical formation-factor relationships.

Borai (1987) developed an empirical formation-fac-tor vs. porosity relationship for an equally large coresample data set for pure limestones in Abu Dhubi. Theformation factor trend in Borai’s data set is offset tohigher m values than for quartz grainstones. Minera-logically pure limestones are composed of more platyorganic particles. Their average aspect ratio is com-monly higher than the generally equant quartz grains.The increased tortuosity-cementation exponent m isevident over the entire range of observed porositiesbetween the rounded quartz and platy limestone datasets (Figure 3).

Holbrook (1996, unpublished data) calculated end-member claystone formation factors from density andresistivity logs on five wells containing only quartzgrainstones and claystones. The depth range was from1000 to 20,000 ft (305–6096 m) covering a wide rangeof quartz and claystone porosities. The density logsshowed unequivocally that the claystones had muchlower porosities than the approximately depth equiv-alent quartz grainstones. A formation-factor ratio(Fclaystone/Fquartz grainstone) was developed from thisdata set. The claystone formation factors were lever-aged from the well-determined quartz grainstone for-mation factors. The result is the uppermost m variableclaystone formation-factor relationship shown on Fig-ure 3.

All three of the mineralogic end-member formation-factor vs. porosity relationships were determined fromlarge modern data sets. All three relationships are tor-tuosity-cementation m variable in the same sense. Allthree are in relative m agreement considering the in-tergranular tortuosity expected from their different in-sulating mineral grain aspect ratios. Further details onhow porosity is calculated from resistivity measure-ments can be found in Holbrook et al. (1995).

P O R O S I T Y F R O M A C O U S T I C T R A N S I T -T I M E S E N S O R I N P U T

Sonic logs are commonly used to estimate porosityfrom transit-time measurements. Generally, there is


High Gamma-ray claystonerelationship back calculated from density logs

Por

osity

loga

rithm

ic s

cale

1.0

0.1

0.011.0 10. 100. 1000.

Formation Resistivity Factor

Mao formula forquartz

grainstones

Borai limestoneformula

Form

atio

n re

sistiv

ity fa

ctor

and

tortu

osity

-cem

enta

tion

expo

nent

(m)

incr

ease

is n

on-li

near

with

incr

easin

g

insu

latin

g pa

rticle

asp

ect r

atio Figure 3. Formation resistivity

factor vs. porosity for mineral par-ticles of different aspect ratios.Laboratory sample data was usedby Borai (1987) and Mao (1995)to define the m variable func-tions. The claystone m variablefunction was back calculatedfrom in-situ log data using quartzgrainstone density log porositydata as a formation-factorreference.

agreement between the velocity-porosity measure-ments made on laboratory cores at ultrasonic fre-quencies and that observed with downhole-loggingsondes. Almost every study, however, shows a largemineralogic effect, particularly with respect to clayminerals, on measured acoustic velocities (Holbrook etal., 1999).

The propagation of compressional and shear wavesthrough unfractured sedimentary rocks closely followsthe extended elastic equations. The Gassmann (1951)equations, Woods equation, and Hashin-Schtrikman(1963) equations, and Archer’s (1992) sodium chloridebrine relationships are all forms of Hooke’s law (Hol-brook et al., 1999).

Figure 4 shows the composite elastic coefficients–mineralogy–porosity–Vp

2 � Vs2 relationships for the

common sedimentary rocks. The Vp2 and Vs

2 axes ofthe plot correspond to the bulk modulus (J), shearmodulus (l), and bulk density (qbulk) terms in accor-dance with Gassmann’s (1951) granular solid elasticequations.

In-situ claystone elastic coefficients and velocitieshave been poorly understood. To fill this informationgap Goldberg and Gurevich (1998) performed a seriesof Hashin-Schtrikman inversions onmixedmineralogyVp

2 and Vs2 full waveform log data sets. Their average

water-wet end-member (zero porosity) claystone elas-tic coefficients (velocities) fall into a very narrow rangeshown in Figure 4. This is the same Vp

2 � Vs2 region

where electrostatically neutral grainstones pass from

a slurry suspension into an amalgamated granularsolid.

Though a different physics is involved, there is acorrespondence between the convergent formation-factor region (37 � 3% porosity) in Figure 3 with thatof Wood’s equation to Gassmann’s equation transitionregion in Figure 4. In both Figures 3 and 4 the single-mineral curves converge as sediments of any miner-alogy consolidate from a separate particle slurry to agranular solid.

The measurement axes in Figure 4 are Vp2 and Vs

2.Adjacent to each axis are the Hooke’s law coefficients,bulk modulus, shear modulus, and bulk density thatare equivalent to those squared velocities. The pointbeing emphasized is elastic-wave velocities for porousgranular sedimentary rocks and slurries closely followHooke’s law extended elastic equations over the entire(0 to 100%) porosity range.

The log data sets from which the claystone elasticcoefficients were extracted had porosities ranging from38 to 2%. All these lithologies were reasonably hardrocks, not slurries. The general slurrylike acoustic be-havior for low-porosity claystones is reasonable consid-ering the acoustic-wave travel path on the molecularscale. Each clay particle has an associated interlammelarelectrostatically bound-water layer.

An elastic wave propagating through water-wetclay in any direction must pass through the muchslower water phase in the interlammelar pore space.Even in very hard claystones, the individual clay la-

152 H O L B R O O K

Figure 4. Extended elastic equation velocities (Vp2 – Vs

2)crossplot of single-mineral grainstones and claystones withNaCl brine. Elastic coefficients–mineralogy–porosity–(Vp

2 �Vs

2) relationships. This figure is modified from Kreif et al.(1990). The average zero porosity claystone coefficientswere derived from Vp � Vs sonic data through Hashin-Schtrikman modulus decomposition by Goldberg and Gur-evich (1998). The claystone velocities and elasticcoefficients fall in the same initial slurry to granular solidamalgamation zone as do the nonclay minerals.

mellae are generally not in direct solid-solid contact.Water-wet claystone elastic behavior is overall slurry-like, as each clay lamella is encased in its own electro-statically bound-water layer. The effective elasticmodulus of water-wet claystones includes electrostat-ically bound water until almost all porosity is lost. Wa-ter-wet claystones are only slightly above theHashin-Schtrikman lower grain contact limit in severallarge log data sets.

The extended elastic equations portrayed in Figure4 can be used to invert porosity from Vp

2 and/or Vs2

in-situ petrophysical data where used in concert withpetrophysically measured bulk density (qbulk) andmineralogy (Vclay) from natural gamma-ray petro-physical data (Holbrook et al., 1999).

P E T R O P H Y S I C A L S E N S O R - D E R I V E DP O R O S I T Y ( � ) L I N K A G E T O N E W T O N I A NI N - S I T U F O R C E B A L A N C E A N D S T R A I N( 1 . 0 � � )

Figure 5 shows a flowchart to calculate in-situ forcebalance from petrophysical measurements. The upper

region contains three vertical sensor specific flowpathsthat calculate porosity with respect to mineralogy.Each vertical flow path uses the appropriate in-situdensity, conductivity, and elastic coefficients of theminerals and fluid that compose a sedimentary rock.

The grain framework bulk modulus elastic limit isa parameter in the porosity from sonic Dt flow path.The PV/T – x variable sodium chloride brine coeffi-cients are shown across the three sensor-specific flowpaths. The diagenetic clay mineral grain density is anadjustable parameter in the porosity from c-c densitysensor flow path. Mineral and fluid coefficients in allthe sensor flow paths are consistent across the upperhalf elastic stress-strain domain.

The resistivity and sonic sensor flow paths containnonlinear pore volume and shape coefficients as men-tioned in the sensor to porosity transforms sections. Ifthe three vertical sensor to porosity transforms are exe-cuted properly and there is no significant boreholewall damage, all three sensor-specific flow pathsshould indicate the same in-situ true rock porosity ofwater-filled sedimentary rocks. True rock porosity isthe most important petrophysically derived reservoirparameter and is also the central force balance vs. in-situ strain (1.0 � �) consideration in Figure 5.

Below the true rock porosity midpoint in Figure 5is the Newtonian closed-form force-balance load vs.strain relationship for normal fault regime approxi-mately biaxial basins. The load elements of the New-tonian closed formulation are on the left side of theindividually force-balanced equations. On the left, con-fining loads are denoted with an “S.” Force-balancedcorresponding effective-stress loads are denoted witha “r.” Both S and r are subscripted vectors. The “v”subscripts denote vertical gravitational loads, and “h”subscripts denote the two corresponding orthogonalhorizontal vectorial loads. Average confining load(Save) and average effective stress (rave) are force-balanced scalars.

The effective stress theorem is the fifth equation inthe Newtonian force-balanced closed formulation. Thescalar pore pressure (Pp) is calculated as the differencebetween the two load scalars [(Save)� (rave)]. Fracturepropagation pressure (PF � Pp � rh � Sh) is there-after calculated in the sixth equation using force-bal-anced pore pressure (Pp) calculated using the effectivestress theorem. All the load terms (S, rh, and Pp) to theleft of the diagonal load vs. strain (�) signs are a New-tonian closed-form force balance.

All the earth strain terms are on the right side of theequal signs in Figure 5. Absolute volumetric in-situstrain (1.0 � �) is in each of the individually force-balanced stress-strain equations. The descending ar-row in the strain region of Figure 5 indicates thealgebraic linkage of these equations to petrophysically


Figure 5. Linkage of petrophysi-cal sensor readings through min-eralogically sensitive porositytransforms to the Newtonianclosed-form force-balancedstress-strain relationship in nor-mal fault regime approximatelybiaxial basins. Taken from Hol-brook, 2001.

measurable strain. The remaining strain terms (q, rmax,and �) are mineral and fluid coefficients that are com-positionally linked to each other.

The equal (�) signs denoted by background shad-ing divide in Figure 5 mathematically relate force-bal-anced loads to absolute in-situ strain in the earth. Forcebalance–measurable strain linkage is unique to thisNewtonian formulation and leads to simplicity and ac-curacy of calibration, prediction, and detection of porepressure.

Regional Effective-Stress Calibration and Real-Time Pore-Pressure Prediction

Six wells in a Far East area were used to establish aregional unloading-limb stress-strain exponent (�offset).Three porosity-sensitive sensors, resistivity, bulk den-sity, and P-wave interval transit time were used to de-termine in-situ strain (solidity). A base-line–normalizedgamma-ray sensor reading was used to estimate solidfraction shale volume. A regional average shale grain-density profile and formation-water conductivity pro-file were established. Mud-weight profiles and repeatformation testers (RFTs) were available to calibrate rela-tive and absolute pore-fluid pressure. Leak-off testswere available to calibrate fracture propagation pres-

sure. Pore-pressure and fracture-pressure data from allsix wells were evaluated and weighted equally to de-termine the regional mechanical and petrophysical re-lationships. Holbrook (1996) described this calibrationprocedure up to the point of unloading-limb seal rec-ognition and regional stress-strain exponent (�offset) cal-ibration.

Figure 6 shows one of the six regional calibrationwells used. Mineralogy sensitive raw and normalizedgamma-ray readings are shown in track 1. Porosityand mineralogy sensitive bulk density and transit-timereadings are also shown in track 1. Porosity from them variable resistivity is shown in track 1 on the same0–50 porosity units scale as porosity from bulk density.If the separate sensor–porosity transforms are correct,and there are no borehole-related sensor problems, theseparate sensor porosity curves should be identical.

Porosity was calculated from resistivity using thesecond-order Archie relationship that accounts for thevariable mineralogy dependent tortuosity-cementa-tion m coefficient. Petrophysical sensor conflicts are re-solved. The best calculated porosity enters both thepower law effective-stress scalar (rave) calculation andthe integrated bulk density overburden (Sv) calcula-tions. The raw Dt log is displayed as a blue trace intrack 1. The raw Dt log tracks the red m variable Archie

154 H O L B R O O K

Figure 6. Loading- and unload-ing-limb force-balanced calibra-tion well-log example. Shalevolume and porosity, the comple-ment of strain, are displayed intrack 1. The deep resistivity datashown in track 2 is converted toporosity using a second-order mvariable Archie relationship thataccounts for the mineralogic tor-tuosity-cementation effect onelectrical conductivity. The effec-tive stress–strain loading- and un-loading-limb intervals both usepower-law linear stress-strain co-efficient (�t) or (�offset) to calcu-late pore-fluid pressure. The peakloading point shown on the logsseparates the loading and un-loading effective-stress–fluid-pressure regimes. The peakloading point is on the regionalhigh fracture propagation pres-sure-sealing surface.

porosity log in shales. This correspondence tends toconfirm that the input Cw profile used to calculate po-rosity from resistivity is correct.

Track 3 displays overburden, fracture-propagationpressure, mud weight, and pore-fluid pressure in ppgas fluid-pressure gradients. The calculated traces areclosed-form force balanced. Leak-off tests andRFTs areannotated in track 3 to demonstrate the combinedborehole pressure measurements match the closed-form force-balanced calibration. The RFTs closelymatch the force-balance calculated pore pressures. Themud-weight profile is generally greater than the cal-culated pore-fluid pressure. The green fracture pres-

sure trace exactly matches the upper leak-off test,indicating that initial overburden is correct.

Evaluating all the traces, the comparable loading-limb, peak loading point, unloading-limb featuresfrom Figure 1 are readily interpreted. The porosity-sensitive sensors all indicate a decreasing porositytrend to the peak loading point followed by an increas-ing porosity trend. As in Figure 2, the peak loading-limb point is where the calculated effective stressreaches a maximum, and the calculated porosityreaches a minimum.

The five other calibration wells had these same rec-ognizable features but at different depths. Considering


the regional unloading pressure regime as a whole, a2.0� (�offset) relative unloading-limb stress-strain ex-ponent angle was determined. Force-balanced pore-pressure, fracture-gradient, and overburden values inFigure 6 were calculated from the 2.0� unloading-limbstress-strain exponent (�offset) joined at the peak load-ing point.

Figure 6 shows a long interval of increasingly un-derbalanced drilling from 3000 to 3500 m. This was alsotrue in several other calibration wells. Drilling mud gasdid not provide adequate warning of underbalanceddrilling in these wells or the well that was logged mea-sured while drilling (MWD). Some of the calibrationwells were shut in to control unpredicted pore pressure.One of these wells required hole abandonment and sidetracking to reach their drilling objective.

Pore-Pressure and Fracture-Gradient Prediction from MWDData

Figure 7 shows the final log generated from combinedwire-line and MWD petrophysical data. No adjust-ments were made to any of the regionally derived con-stants or control profiles for the entire duration of thiswell. This well also shows the same upper global min-eralogic stress-strain loading-limb interval. An easilyrecognizable peak loading point is annotated in Figure7. The same 2.0� relative unloading-limb stress-strainexponent (�offset) was used below the peak loading-limb point.

Some initial skepticism in the force�balancedmethod was removed by three predicted gas cut mudincidents. The real-time pore-pressure log indicatedunderbalanced mud weight at 3380 m. The first gas-cut mud incidents occurred at 3400 m. The kill weightof 10.5 ppg was in agreement with that predicted bythe real-time pore pressure log.

Mud weight was raised again to 10.7 ppg at 3480 min preparation for setting casing. The primary objectiveof setting casing in the overpressured interval wasachieved. Note that the onset of elevated pore pressureoccurred 200 m below the peak loading-limb point and200 m below the resistivity reversal on the raw resis-tivity log. Based upon the previously mentioned mudcut and kill weights the regional 2.0� unloading-limbstress-strain calibration was correct.

Mud weight was raised to 11.6 ppg after casing wasset. A sharp pore-pressure increase to 11.6 ppg oc-curred at 3725m. Underbalancedmudweightwas pre-dicted at 3750 m. This preceded gas-cut mud, andmudweight was raised to 12.3 ppg that temporarily con-trolled the mud gas cut.

Heavy gas mud cut occurred again at 3800 m. Theeventual kill weight for this gas cut mud was 14.8 ppg

in agreement with the real-time pore pressure. Theflow and kill mud weights bracketed the force-balancecalculated pore pressure to 0.2 ppg accuracy.


Pore-pressure estimation accuracy resulted from theapplication of the closed-form force-balanced calcula-tion method. The method corresponds to a regionalloading-limb regime over a fluid-expansion pressureregime that was related to petrophysical data. The pre-dictions were made through a regionally calibratedclosed-form mechanical system. Both wire-line mea-sured andMWD petrophysical data were used asmea-surement input to the mechanical system.

Drilling efficiency benefits were as follows: (1) thegas-cut mud incidents were circulated out withoutwell shut-in; (2) the operator was able to safely reachhis drilling objective with one less casing string by set-ting casing in the upper part of the unloading-limbpressure transition zone. Safety and cost objectiveswere met by applying force-balanced physics in thecalculation of pore pressure.

Using force-balanced stress-strain physical relation-ships to directly determine pore pressure is a sounddrilling engineering choice. Pore pressure is mechani-cally related to porosity, mineralogy, and density thatcan be estimated from several petrophysical sensors inthe closed mathematical form described. The calcula-tion procedure applied incorporates known rockstress-strain relationships with Newtonian physicsthat is mathematically related to absolute in-situ strain.This is the only pore-pressure method that involves adefined mechanical stress-strain system.

Loading- and unloading-limb pore-pressure re-gimes have distinct separate stress-strain exponents (�)and (�offset). The loading-limb/unloading-limb re-gimes join along a surface that corresponds to a con-tinuous high-solidity cap rock that partially seals anexpanding fluid phase pore pressure. Pore pressuresin both regimes are treated with mechanically sensiblemineralogic stress-strain relationships.

Closed-form force balance comprehensively ac-counts for both fluid- and solid-borne subsurfaceloads. Pore pressure below the peak loading-limb sur-face is limited by the minimum work fracture propa-gation pressure of the sealing cap rock. Pore pressurein both loading and unloading regimes is determinedfrom regionally calibrated effective stress–strainmath-ematical functions.

Pore pressure in the subsurface results from a force-balanced mineral and fluid load-sharing relationship.The Newtonian stress-strain formulation is also a

156 H O L B R O O K

Figure 7. Real-time force-bal-anced logs in the same format asFigure 6. All petrophysical cali-bration constants are identicalwith the regional calibrationused for Figure 6. The only oper-ator intervention applied duringthe entire well was to switch tothe regionally calibrated 2.0�(�offset) unloading-limb stress-strain coefficient at the peakloading-limb point shown.

closed-form solution to many other oilfieldmechanicalproblems that inherently depend on in-situ boreholevs. Earth formation force balance.


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Mao, Z. Q., C. G. Zhang, C. Z. Lin, J. Ouyang, Q. Wang, andC. J. Yan, 1995, The effects of pore structure and electricalproperties of core samples from various sandstone res-ervoirs in Tarim Basin: Society of Professional Well LogAnalysts 36th Annual Logging Symposium.

Ward, C. D., K. Coghill, and M. D. Broussard, 1995, The ap-plication of petrophysical data to improve pore pressureand fracture pressure determination in North Sea CentralGraben HPHT wells: Society of Petroleum Engineers An-nual Technical Conference and Exhibition, SPE paper28297.

159

15Forward Modeling of Log Response inGeopressured Formations Reveals ValuableInsights to the Various Pore-PressurePrediction TechniquesJ. C. RasmusSchlumberger Product Center,Sugar Land, Texas

A B S T R A C T

A forward model for log response in a geopressured shale is developed. The state of compaction,lithology, water depths, salinity profiles, compaction coefficients, and clay characteristics are all usermodifiable. Effective-stress relationships for geopressured shales that are currently widely practiced inthe industry all assume constant log response is indicative of constant porosity and, therefore, constanteffective stress. This modeling reveals that, although the porosity of a geopressured shale may remainconstant for a constant effective stress, its log reponse does not. Therefore, this chapter illustrates thatany effective-stress technique that uses the log response directly cannot be used to accurately computethe effective-stress state of the shale. Instead, the log response must first be characterized in terms oflithology, salinity profile, fluid moduli, water depth, and compaction coefficients. The modeling showsthat this is much more critical for resistivity than velocity measurements.


A self-consistent model of a sedimentary formation invarious stages of undercompaction has been devel-oped to forward model various logging-tool re-sponses. The sedimentary formation model includesuser-modifiable expressions for temperature, clay con-tent, lithology, salinity, sediment water volume, waterdepth, and compacting stress as a function of sedimentburial depth below the mud line. The formationmodelis input to various logging-tool response equations topredict log response as a function of any of the modelcharacteristics. Valuable insight is gained by compar-

Rasmus, J. C., 2002, Forward Modeling of Log Response in GeopressuredFormations Reveals Valuable Insights to the Various Pore-Pressure PredictionTechniques, in A. R. Huffman and G. L. Bowers, eds., Pressure regimes insedimentary basins and their prediction: AAPG Memoir 76, p. 159–164.

ing these modeled logs to those expected from con-ventional pore-pressure interpretation techniques.

M E T H O D

The geopressure formation forward model consists ofuser-modifiable expressions for lithology, porosity,pore fluid temperature, salinity, and bulk modulusproperties as a function of sediment vertical depth be-low the mud line. The formation is taken to be com-posed of quartz, wet clay, and effective (filled withmoveable fluids) porosity. This is the porosity that con-tains the interstitial water that escapes from the for-mation while it is being compacted. The relationship,rock depth � C � 10 (�b�) is used to model the effec-tive porosity of the formation with depth, where rockdepth is the depth below mud line (Rasmus, 1991).

C is the depth at which � equals 0, and b is the rate ofcompaction. Water depth and air-gap parameters areinput so that true vertical depth relative to kelly bush-ing (TVD RKB) can be plotted. The solids (1 � �) areplaced in the volume that is not taken up by porosity.They are divided into quartz and wet clay and repre-sented by a parameter that is the ratio of quartz to clay,staying constant with depth to accurately reflect thefact that the solids mass is conserved. The temperatureis modeled with an offset (surface temperature) and agradient. An expression for the salinity fluid property

allows it to range from seawater at the mud line to saltsaturated at a given depth. The fluid bulk modulus ismodeled as a function of pressure, temperature, andsalinity. A model has also been developed for the com-pressional and shear dry frame modulus as a functionof porosity and lithology.The volumes and parameters from this forward

model as a function of depth are input to the variouslogging-tool response equations containing thesemod-eled parameters and volumes. The response of resis-tivity, density, gamma ray, and neutron log vs. depth

Figure 1. Forward-modeled re-sistivity vs. depth for variouspore-pressure equivalent mudweights for a water depth of 0 ftand a quartz/wet clay ratio of1.0. Notice how the resistivitytrends are similar to other pub-lished overlays. True verticaldepth (TVD) is in feet; resistivityis in ohm m.

Figure 2. Resistivity vs. depth forvarious pore-pressure equivalentmud weights for a water depth of2000 ft (610 m) and a quartz/wetclay ratio of 0.25. The deviationfrom Figure 1 is significant and il-lustrates the importance of propercharacterization of the lithologyand water depth for pore-pressurecomputations. True vertical depth(TVD) is in feet; resistivity is inohm m.

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

102

101

100

101

TVD RKB Depth

For

war

d M

odel

ed R

esis

tivity

for

919

PP

G

9 PPG

19 PPG

-

Forward Modeling of Log Response in Geopressured Formations Reveals Valuable Insights to the Various Pore-Pressure Prediction Techniques 161

can then be computed and displayed. The sonic com-pressional and shear response is modeled using Gass-mann’s equations (Gassmann, 1951). The modeledformation bulk density is integrated to compute theoverburden pressure as a function of air gap, waterdepth, and sediment depth.

R E S U L T S

Forward-Modeled Resistivity

Figure 1 shows the forwardmodel of resistivity for vari-ous pore-pressure equivalent mud weights vs. TVDRKB using a water depth of zero. The lines representpore-pressure equivalent mud weights ranging from 9to 19 ppg, with 19 ppg being the right-most line. Noticehow the constant equivalent mud weight lines have asimilar appearance to the resistivity overlays developedby past authors (Matthews and Kelly, 1967) when shal-low waters were being drilled. The resistivity risesquickly at shallow depths as the decreasing porosity ef-fect outweighs the increasing salinity effect then risesmore gradually as the porosity decrease becomes morelinear. The difficulty in drawing a straight-line normaltrend as required for some techniques can be seen atshallow depths. At depths greater than several thou-sand feet below the mud line and for intervals of lessthan 5000 ft (1524 m), however, the normal trend isfairly linear on this typical logarithmic resistivity scale.Figure 2 shows the effect of changing the quartz/wetclay ratio from 1.0 (0.5/0.5) in Figure 1 to 0.25 (0.2/0.8)and the water depth to 2000 ft (610 m). Notice how theslopes of the resistivity curves for each equivalent mudweight have changed, as well as the values at any par-

ticular TVD. It is these changes in lithology that causeshifts in the normal trend lines and canmake these plotslook noisy when real data are plotted at this scale. Thatis why previous authors have stressed that consistent-lithology shale points be plotted on these charts. Plotslike Figures 1 and 2 using the forward-modeled resis-tivity allow a prediction of pore pressure as a functionof lithology, water depth, and resistivity before drillinga well and help in defining the normal trend for othertechniques.

Forward-Modeled Velocity

Figure 3 shows a plot of compressional velocity vs.depth for the various pore-pressure equivalent mudweights. Figure 4 is the same data plotted vs. effectivestress, the difference between overburden stress andpore pressure. Normally, the velocity is assumed to bea function of effective stress independent of the valueof pore pressure. In this case there would be only oneline on this plot with all of the pore pressures lying ontop of each other. Note that for the higher pore pres-sures, this is not the case. This is because the fluid bulkmodulus, being a function of temperature, salinity, andpressure, can be different for the same effective stress.Consider two formations with equal effective stress, oneshallow at normal pressure and one deeper with over-pressure. The deeper one has a greater overburden, tem-perature, pore pressure, and possibly salinity. The fluidmodulus is therefore larger at the deeper depth becauseof these environmental differences. A larger fluid mod-ulus (less compressibility) gives rise to a greater velocityfor the deeper formation although the effective stress isthe same. This phenomenon has the same signature asunloading reported by others (Bowers, 1994). Figure 5

Figure 3. Velocity vs. depth forvarious pore-pressure equivalentmud weights for a water depthof 0 ft and a quartz/wet clay ra-tio of 1.0. Total vertical depth(TVD) is measured in feet, andvelocity is in ft/sec.

162 R A S M U S

Figure 4. Velocity vs. effectivestress for various pore-pressureequivalent mud weights for awater depth of 0 ft and a quartz/wet clay ratio of 1.0. The velocitydepends not only on the effec-tive stress but also on the fluidproperties at any particular effec-tive-stress state. This means thatthe velocity is a function of botheffective stress and depth andhas not been addressed in otherpore-pressure techniques todate. Effective stress is measuredin psi, and velocity is measuredin ft/sec. Temperature in allcases was assumed to linearlyincrease at 1.0�F/100 ft from asurface temperature of 50�F.

shows the effect of changing the water depth to 2000 ft(610 m) and the quartz/wet clay ratio from 1.0 to 0.25as was done for Figure 2. The large effect of relativelysmall changes in lithology can be seen.

I N S I G H T S I N T O O T H E R T E C H N I Q U E S

The dependence of velocity on both effective stress anddepth affects other pore-pressure techniques as follows.In an undercompacted shale, the effective stress of the

rock is the difference between the overburden and porepressures. The equivalent-depth technique assumes thattwo formations with equal effective stresses have thesame porosity and therefore the same log response. Thefirst assumption is logical and valid, but the second isnot as shown in Figure 4. The result is that these tech-niques underestimate pore pressures. Below about 15ppg, however, and over limited depth ranges, thesetechniques should give good results. Other techniques(Eaton, 1975) use the ratio of an observed to normal logresponse to compute pore pressures. In the following

Figure 5. Velocity vs. effectivestress for various pore-pressureequivalent mud weights for awater depth of 2000 ft (610 m)and a quartz/wet clay ratio of0.25. Effective stress is measuredin psi, and velocity is measuredin ft/sec. Temperature in allcases was assumed to linearlyincrease at 1.0�F/100 ft from asurface temperature of 50�F.

Forward Modeling of Log Response in Geopressured Formations Reveals Valuable Insights to the Various Pore-Pressure Prediction Techniques 163

paragraphs, I show that this is not an entirely indepen-dent technique from the equivalent-depth technique.The definition of the equivalent depth method is

that the effective stress of a geopressured rock at depthD2 is assumed to be equal to the effective stress of thesame type rock at a shallower, normally pressureddepthD1. This is the definition of the equivalent-depthmethod, sometimes referred to as a vertical method(Traugott, 1997). One can compute the pore pressureof the rock at depth D2 knowing the overburden pres-sures and normal water pressure. An expression forthe equivalent-depth method is

P � P (1)eff2 eff1

or

P � P � P � P (2)ovb2 wpore2 ovb1 wnor1

where Peff is effective pressure, subscripts 1 and 2 referto depths D1 at normal pore pressure and a deeperdepth D2 at a higher pore pressure. Pwpore is the porepressure atD2, Pwnor is the normal water pressure, andPovb is the overburden pressure. Dividing by D2, thiscan be rewritten as

P /D � P /Dwpore2 2 ovb2 2

� (P � P )/D (3)ovb1 wnor1 2

Figure 6. Resistivity ratio vs. ef-fective stress ratio for variouspore-pressure equivalent mudweights for a water depth of 0 ftand a quartz/wet clay ratio of1.0. Effective stress ratio is di-mensionless and is the right sideof equation 5. Resistivity ratio isdimensionless and is the leftside of equation 5. The fact thatthe curves are double valuedand unique for each pore pres-sure illustrates the futility of us-ing resistivity ratios foreffective-stress and pore-pressure calculations.

Figure 7. Velocity ratio vs. effec-tive stress ratio for various pore-pressure equivalent mudweights for a water depth of 0 ftand a quartz/wet clay ratio of1.0. Effective stress ratio is di-mensionless and is the right sideof equation 5. This plot illus-trates that velocity ratios in mod-erate pore pressures can beused for effective-stress andpore-pressure calculations.

164 R A S M U S

which can be compared to Eaton’s equation

P /D � P /D � ((Pwpore2 2 ovb2 2 ovb2(Y)� P )/D )(X /X ) (4)wnor2 2 obs nor

where Xobs and Xnor are the observed and expectednormal log responses at a given depth. The two ex-pressions are equivalent if set as

(Y)(X /X ) � (Pobs nor ovb1

� P )/(P � P ) (5)wnor1 ovb2 wnor2

The right-hand side of this equation is the ratio of thenormal effective stresses, which is also equivalent toD1/D2 when the slopes of the overburden stress andnormal pore-pressure curves are constant with depth.Therefore

(Y)(X /X ) � D /D (6)obs nor 1 2

Thus, Eaton’s method is an attempt to map the nor-mal and observed log response (sometimes called ahorizontal technique [Traugott, 1997]) at one particulardepth to the ratio of depths at equal effective stresses(sometimes called a vertical technique). This meansthat Eaton’s method relies on the validity of the equiv-alent-depth method. Previously, it was shown that theequivalent-depth method is valid only over limiteddepth ranges due to the fact that fluid propertieschange with depth, causing the log response to changewith depth even when the porosity (or effective stress)stays constant. Therefore Eaton’s method is under thesame limitations. The widespread success of Eaton’smethod lends credence to the equivalent-depth tech-nique. As pointed out in Figure 4, however, the equiv-alent-depth method’s assumption of constant logresponse for constant effective stress is not alwaysvalid and may explain why Eaton’s exponent (Y) and/or normal trend lines may sometimes have to be al-tered to compute the correct pore pressure. The limi-tations of the equivalent-depth technique can beshown graphically by plotting data in the format givenby equation 5. Plotting (Xobs/Xnor) vs. (Povb1 �Pwnor1)/(Povb2 � Pwnor2) on a log-log plot should re-sult in a straight line with a slope of Y. Figure 6 showsthe results of plotting forward-modeled resistivitydatarepresenting a depth range from mud line to 40,000 ft(12,192 m) and pore-pressure equivalent mud weightsfrom normal to 19 ppg. Where the pore pressure isnormal, the effective-stress ratio and Xobs/Xnor areboth unity, and all of the normally pressured data ateach depth level plots at this point as seen on the plotin Figure 6. The various lines plotting away from this

point represent pore-pressure equivalent mudweightsfrom 9 to 19 ppg at various depth levels. The lines notonly have changing slopes but go through a reversaland are doubled valued for a given resistivity ratio.This essentially shows that resistivity cannot be usedin an equivalent-depth method. Figure 7, however,shows that velocity is better behaved and better suitedthan resistivity for use in an equivalent-depth tech-nique. This is because the lines of constant pore pres-sure are close to each other and have similar slopes.


1. Forward modeling is used to produce overlaysfor a particular formation model and waterdepth. For shallow water depths, these overlaysmimic the trends seen in earlier empirical over-lays.

2. Forward modeling has shown that logging-toolresponse is not always constant with constantporosity and effective stress as heretofore as-sumed because of the temperature, pressure,and salinity changes that occur as a geopres-sured shale is buried deeper. Techniques usingthe equivalent-depth method are affected by thisphenomena.

3. Horizontal techniques or those that use ratios ofobserved to normal log response are in reality anapproximation to the equivalent-depth methodand are under the same limitations.


Bowers, G. L., 1994, Pore pressure estimation from velocitydata: accounting for overpressure mechanisms besidesundercompaction: International Association of DrillingContractors/Society of Petroleum Engineers 27488, p. 515–530.

Eaton, B. A., 1975, The equation for geopressure predictionfrom well logs: Society of Petroleum Engineers 50th An-nual Fall Meeting Proceedings, SPE 5544, 11 p.

Gassmann, F., 1951, Uber die Elastizitat poroser Medien:Vier. der Natur. Gesellschaft, v. 96, p. 1–23.

Matthews, W. R., and J. Kelly, 1967, How to predict forma-tion pressure and fracture gradient: Oil & Gas Journal,February 20, p. 92–106.

Rasmus, J. C., 1991, The use of real time pore pressure anddrilling derived rock strength to optimize ROP: Society ofPetroleum Engineers Drilling Engineer, v. 6, no. 4, p. 264–272.

Traugott, M. O., 1997, Pore/fracture pressure determinationin deep water: Deepwater Technology 218 (8), supple-ment to World Oil, p. 68–70.

165

16Pore Pressure ahead of the Bit:An Integrated ApproachNader C. DuttaWesternGeco, Houston, Texas

William H. BorlandSchlumberger Wireline and Testing Services, Gatwick, United Kingdom

W. Scott LeaneySchlumberger Wireline and Testing Services, Gatwick, United Kingdom

Richard MeehanSchlumberger Wireline and Testing Services, Sugar Land, Texas

W. Les NuttSchlumberger Wireline and Testing Services, Fuchinobe, Japan

A B S T R A C T

Undercompacted shales generally have a lower acoustic impedance (product of density and velocity)than those that follow a normal compaction trend. Departure from the normal compaction trend mayindicate potential drilling hazards due to overpressure. Techniques that canmonitor acoustic impedancecan be used to indicate the existence of such potential hazards, and thereby, help in designing the casingand mud program.

Prediction of pressure ahead of the bit starts with the best predrill model. In frontier wells, com-monly seismic data are the only data available. Seismic velocities from analysis of stacking velocitiesand impedances from reflection sequence analyses, in conjunction with a predrill rock model, can beused to develop a predrill pressure vs. depth profile. This has been used with considerable success indeep-water wells. The limitations, however, are the lack of resolution in the reflection seismic data anduncalibrated velocity models. Thus, a strategy is developed that can update this so-called static modelin real time using borehole data.

Conventional wire-line vertical seismic profile (VSP) measurements are commonly used to providehigh-quality reflection data within and below the bottom of the well. Inversion of VSP data for acousticimpedance has been demonstrated to be a reliable way to accurately predict acoustic impedance belowthe bit, with more resolution than the conventional velocity data from stacking-velocity analyses. Thishas been found to yield pressure vs. depth profiles, at the bit level, with more resolution. Downtimeon the rig is required to acquire the wire-line data.

Vertical seismic profile inversion allows the location of the overpressured zone to be accuratelydetermined in two-way traveltime. This time estimate can be converted to depth if the formation acous-tic velocity ahead of the bit is known. The drill bit seismic technique, which uses a working drill bit asthe seismic source, provides continuous time to depth information. These data can be used to estimatethe formation acoustic velocity continuously, in real time, and to calibrate seismic velocity at the bit

Dutta, Nader C., William H. Borland, W. Scott Leaney, Richard Meehan, and W. Les Nutt, 2002, Pore Pressure ahead of the Bit: An IntegratedApproach, in A. R. Huffman and G. L. Bowers, eds., Pressure regimes in sedimentary basins and their prediction: AAPG Memoir 76, p. 165–169.

166 D U T T A E T A L .

level and hence allow an accurate, continuously updated, prediction of the depth to the overpressurehazard in real time at the well site.

In this chapter we present a methodology to quantify and predict overpressure hazards ahead ofthe bit using surface seismic, VSP, and drill bit seismic.


Prediction of pore pressure is critical at several stagesin the exploration and development process. Duringexploration it can be used to assess seal effectivenessand map hydrocarbon migration pathways. It can as-sist in analyzing trap configuration and basin geome-try and provide calibration to basin modeling. Duringthe exploration, appraisal, and development drillingphases, accurate pore-pressure prediction can be vitalfor safe and economic drilling. It is essential for opti-mized casing and mud-weight programs and helpsavoid well-control problems. This chapter discussestechniques for predicting overpressure both before andduring the drilling phase. The first part concentrateson the predrill problem, whereas the second looks atwhile-drilling methods.

P R E D R I L L

Conventional pressure-prediction techniques relatesome measurable attribute, commonly a porosity in-dicator, to fluid pressure. A set of calibration curvesfor a particular region are established, relating devi-ation from the normal trend of that attribute tochanges in pore pressure (Hottman and Johnson,1965). In frontier areas, commonly the only data avail-able are the surface seismic data. A new integratedgeological and geophysical technique (Dutta, 1997)that uses surface seismic data is presented in thischapter.The development of overpressure suggests that

fluid movement is retarded, both vertically and hori-zontally. This can be due to the rapid burial of sedi-ments, or lithology change, or both. Some of theimportant mechanisms that cause overpressure are asfollows:

• Mechanical compaction disequilibrium (under-compaction) (Hubbert and Rubey, 1956)

• Clay dehydration and alteration due to burialdiagenesis (Dutta, 1987)

• Dipping or lenticular permeable beds embeddedin shales (Fertl, 1976)

• Buoyancy (Fertl, 1976)• Tectonism (Dutta, 1987)• Aquathermal pressuring (Dutta, 1987)

The method of pressure prediction discussed in thischapter uses a model that includes the first four ofthese mechanisms.The velocity of a given lithology is related directly

to effective stress and temperature. This relationship isbased on BP’s extensive database of wire-line logs,cores, and repeat formation tester (RFT)measurementsin the Gulf of Mexico. The data have been carefullyquality controlled and corrected for environmental ef-fects. Two fundamental relations were developed: (1)bulk density vs. slowness for a given lithology and (2)velocity vs. effective stress and temperature for a givenlithology. The first relationship enables the calculationof bulk density, and hence overburden pressure, fromvelocity data. The second gives effective stress directlyfrom velocity. Pore pressure is then given as the dif-ference between overburden pressure and effectivestress.Figure 1 shows the prediction procedure. The qual-

ity of the prediction is heavily dependent on the ac-curacy of the interval velocities calculated from thesurface seismic data. Where well data are available, theprocess can be better constrained, and the calculatedinterval velocities can be validated. Examples of thisapproach can be found in Dutta (1997).Although the results of this type of processing are

encouraging, the lack of resolution in the seismic dataand the difficulties involved in correctly identifyingtrue interval velocities in areas of velocity anisotropymean that the technique is in general limited to large-scale applications. To address the while-drilling prob-lem, higher resolution techniques must be employed.

V E R T I C A L S E I S M I C P R O F I L E ( V S P )I N V E R S I O N

One of the most popular and important applicationsof traditional borehole seismic VSP data is the predic-tion of overpressure ahead of an intermediate totaldepth (TD). This is achieved by inverting the VSP datafor acoustic impedance. The VSP data are more suit-able for this task than surface seismic data because theycommonly have higher bandwidths and better signal-to-noise ratios (SNR), and therefore, greater verticalresolution capabilities. A seismic trace is an indicationof variations in acoustic impedance (velocity timesdensity). These variations depend upon formation ve-

Pore Pressure ahead of the Bit: An Integrated Approach 167

Effective stressOverburden stress

Pore pressure

VelocityTemperature

Gross Lithology

bulk densityoverburden

VelocityLithology

VelocityLithology

effective stresstemperature

Input

Transform

Output

Figure 1. A schematic showing the procedure for the pre-diction of pore pressures from surface seismic data.

locity and density. In undercompaction environments,a decrease in acoustic impedance can indicate an in-crease in porosity, hence a potential overpressuredzone.Various techniques exist for inverting VSP data for

acoustic impedance. In general they require that thedata have a good SNR and contain low frequencies.The output is generally in the form of a prediction ofacoustic impedance vs. two-way traveltime. Using anempirical velocity-density relationship, such as thatproposed by Gardner (Gardner et al., 1985), calibratedby data from nearby wells if available, allows theacoustic-impedance profile to be converted to intervalvelocities. The formation velocity prediction can betransformed to a pore-pressure estimate, or minimummud-weight recommendation, by using local infor-mation on the relationship between formation veloci-ties (or slownesses) and pore pressure. If there areinsufficient local data, various empirical methods havebeen suggested in the literature, for example, the well-known Hottmann-Johnson (Hottmann and Johnson,1965) relationship.The resultant pore-pressure vs. two-way traveltime

profile can be converted to a pore-pressure vs. depth

profile by using the calculated formation velocities.The accuracy of the predicted depth to the interpretedoverpressure zone depends upon the validity of theassumptions in the velocity-density relationship andthe efficacy of the VSP inversion technique. The accu-racy of this depth prediction can be greatly enhancedby actually measuring the local formation velocity asdrilling progresses. This can be achieved by using thedrill bit seismic technique.

D R I L L B I T S E I S M I C

Drill bit seismic uses the acoustic energy radiated by aworking rollercone drill bit to determine the seismictime to depth ratio as the well is being drilled. Theenergy required for drilling is supplied to the bit byrotation of the drillstring, causing the cones to roll overthe bottom of the hole. As the cones roll over, the teethpenetrate and gouge the formation, destroying therock. Each tooth impact applies an axial force to thebottom of the hole and an equal and opposite force tothe drillstring. The succession of axial impacts as thebit drills radiate compressional or P waves into the for-mation and cause axial vibrations to travel up thedrillstring. The bit acts as a dipole source for P waves(Hardage, 1992), radiating energy upward toward thesurface and downward ahead of the bit. At the surfacefor land wells, and at the sea floor for offshore wells,geophones, hydrophones, or a combination of both areused to detect the P waves. Accelerometers, placednear the top of the drillstring, detect the axial vibra-tions traveling up the drill pipe. See Meehan et al.(1998) for a detailed description of this technique.The bit-generated signal is continuous in nature,

and timing information must be extracted. Referring toFigure 2, correlating the drillstring sensor signal withthe seismic sensor signals gives the traveltime differ-ence between the formation path and the drillstringpath. Once DTrel is known, if the time taken for theaxial vibrations to travel along the drillstring,DTds, canbe determined, the absolute traveltime from bit to sur-face, DTf, can be calculated.The time-to-depth ratio is calculated using the direct

radiation from the drill bit to the surface. The energythat propagates downward ahead of the bit is reflectedback to the surface by impedance changes in the for-mation. This energy can also be detected and pro-cessed to produce a seismic image of the formationahead of the bit. Where used in combination with thesurface seismic, such look-ahead images allow the ap-proach to critical horizons to be monitored as drillingprogresses.Although simple in concept, significant technical

hurdles must be overcome to produce a robust and

168 D U T T A E T A L .

∆Trel = ∆Tf - ∆Tds

form

atio

n pa

th ∆

Tf

drill

stri

ng p

ath

∆Tds

drillstringsensor

geophones/hydrophones

cross correlation of drillstring sensor and geophone signals

Figure 2. A schematic of the drill bit seismic system. Corre-lation of the rig sensor signal with the seismic sensors givesthe relative traveltime difference between the formationpath and the drillstring path. If the drillstring traveltime isknown, the traveltime from the bit to the surface throughthe formation can be determined.

Aco

ust

ic Im

ped

ance

1.8 1.9 2 2.1 2.2 2.3

2000

2200

2400

2600

2800

3000

two-way time (seconds)

dep

th (

met

ers)

updated hazard depth 2753 meters

initial hazard depth 2707

meters

interpreted onset of

overpressure

initial drill-bit dataupdated drill-bit data

Figure 3. An example of the depth-to-hazard predictiontechnique.

reliable measurement technique. The most importantinformation derived is the formation traveltime, and itis essential that all factors that affect the accuracy, bothrelative and absolute, of this measurement are under-stood. Quantifying the size of the possible timing er-rors gives confidence in the measurement and helpsensure the technique is correctly applied (Meehan etal., 1998). Particular attention must be paid to thedrillstring traveltime measurement and to the effectsof processing on the phase of the signals. Working rigscreate a great deal of noise, and sophisticated signal-processing methods must be employed to extract thedrill-bit signal (Meehan et al., 1998). Differentiation ofthe time to depth measurement with respect to depthgives an estimate of the local formation velocity.The drill bit seismic technique can be used in con-

junction with a conventional wire-line VSP to enablereal-time prediction of the depth to overpressuredzones. Figure 3 shows an example of this. The top partof the plot is an acoustic-impedance inversion of anintermediate wire-line VSP acquired at a TD of 2000m. The sudden drop in acoustic impedance just before2.2 s two-way traveltime is interpreted as the onset of

overpressure. The bottom section of the plot showshow the time-to-depth information from the drill bitseismic is used to update the predicted depth to thetop of the overpressured zone. Where the bit hasreached a depth of 2200 m, the hazard depth is pre-dicted to be at 2707 m (using a least-squares extrapo-lation). As drilling progresses, more time to depthinformation becomes available. Where the bit hasreached 2400 m, the new depth-to-hazard prediction is2753 m. The closer the bit approaches the hazard, themore accurate the prediction becomes.This technique relies upon a successful inversion of

the wire-line VSP data and the updating of the currenttime to depth ratio using the drill bit seismic data. Ifthe drill bit seismic look-ahead image could be in-verted for acoustic impedance, it would be more con-venient, eliminating the need for the intermediatewire-line VSP. The poorer SNR of the drill bit seismicdata and the lack of control over the source signature,however, mean that the data are not commonly suit-able for inversion. As the methodologies for acquiringand processing drill bit seismic data improve andevolve, this situation will change.


In undercompacted areas, where pore pressure can berelated to changes in porosity, seismic techniques canprovide valuable pressure-prediction tools. For the

Pore Pressure ahead of the Bit: An Integrated Approach 169

predrill situation, this can be at the basin scale usingsurface seismic data or at the reservoir scale wheresurface seismic data are combined with borehole in-formation. For real time, while-drilling prediction, acombination of the well-established wire-line bore-hole seismic techniques and the emerging seismicwhile-drilling technologies, can be used. Togetherthese methods provide an accurate, continuously up-dated depth to overpressure hazard prediction in realtime.


Dutta, N. C., ed., 1987, Geopressure: Society of ExplorationGeophysicists Geophysical Reprint Series 7, 365 p.

Dutta, N. C., 1997, Pressure prediction from seismic data:implications for seal distribution and hydrocarbon explo-ration and exploitation in the deepwater Gulf of Mexico:

Norwegian Petroleum Foundation Special Publication 7,p. 187–199.

Fertl, H.W., 1976, Abnormal formation pressures: NewYork,Elsevier, 382 p.

Gardner, G. H. F., L. W. Gardner, and A. R. Gregory, 1985,Formation velocity and density—the diagnostic basics forstratigraphic traps: Geophysics, v. 50, no. 11, p. 2085–2095.

Hardage, B. A., 1992, Crosswell seismology and reverse VSP:London, Geophysical Press, 41 p.

Hottmann, C. E., and R. K. Johnson, 1965, Estimation of for-mation pressures from log-derived shale properties: Jour-nal of Petroleum Technology, v. 17, p. 717–722.

Hubbert, M. K., and W. W. Rubey, 1956, Role of fluid pres-sure in mechanics of overthrust faulting: Geological So-ciety of America Bulletin, v. 70, p. 115–166.

Meehan, R., L. Nutt, and N. Dutta, 1998, Drill-bit seismic: adrilling optimisation tool: Proceedings of the Interna-tional Association of Drilling Contractors/Society of Pe-troleum Engineers Drilling Conference, SPE 39312, p. 177–190.

177

18Velocity Estimation forPore-Pressure Prediction

David W. BellConoco Inc., Ponca City, Oklahoma

A B S T R A C T

The speed of propagation of compressional-wave energy in the subsurface, known simply as “formationvelocity,” is strongly influenced by compaction, particularly in young clastic basins. Because pore pres-sures affect compaction, changes in velocity can be calibrated to changes in pore pressure. Velocitiesderived from surface seismic data provide indirect pressure measurements at undrilled locations. Theaccuracy depends on the validity of the relationship between pressure and velocity, the quality of thevelocity measurements at enough points to perform the calibration and prediction, and the reliabilityof average velocities to correctly convert from seismic time to depth.

A key step is construction of a velocity profile with depth that simultaneously defines both thecompaction characteristics and a valid time-depth curve. A linear fit to the logarithm of the sonic transittime with depth is commonly assumed to represent the normal compaction trend. Such a velocity-depthtrend, however, does not produce a time-depth relationship that accurately converts seismic measure-ments in time to depth. A linear fit of velocity with time provides a consistent fit to both time-depthand velocity-depth data and is a better empirical representation of the normal compaction trend. Thelinear velocity-time model can be used to smooth through inaccuracies in seismic stacking-velocity pickswhere applied to geologically consistent units.

This chapter illustrates relationships between velocity and the geologic setting and establishes anempirical model for the normal compaction trend. It then reviews various assumptions and techniquesfor converting seismic stacking velocities into representative formation velocities. It concludes with astep-by-step recommendation for estimation and calibration of velocity from seismic data.

V E L O C I T Y - P R E S S U R E R E L A T I O N S H I P S

A starting point for pressure prediction from seismicvelocity is to invoke an empirical relationship betweenvelocity and effective pressure. Effective pressure, Pe,is the difference between the overburden, or confining,pressure, Pc, and the pore pressure, Pp. In zones ofnormal compaction, the overburden pressure is ob-tained by integrating a density function, whereas thepore pressure is obtained simply from the weight of a

Bell, David W., 2002, Velocity Estimation for Pore-Pressure Prediction, in A. R.Huffman and G. L. Bowers, eds., Pressure regimes in sedimentary basins andtheir prediction: AAPG Memoir 76, p. 177–215.

unit volume of the fluid times the total depth. Sub-tracting these two qualities gives values of effectivepressure that can be crossplotted against velocity mea-surements over the same region. A curve fitted to thesedata provides a calibration between effective pressureand velocity. Pore pressure in anomalous zones canthen be deduced from additional velocity measure-ments at that location or anywhere in the basin wherethe initial calibration curve is valid. Figure 1 illustratesthese concepts with synthetic data.

In Figure 1A, velocity increases uniformly withdepth in a zone of normal compaction and then de-creases with depth where overpressure is encountered.Figure 1B plots effective pressure, pore pressure, and

178 B E L L

Figure 1. Velocity-pressure relationships. Parts A, B, and C illustrate the relationships between depth and velocity, depth andpressure, and velocity and effective pressure under the assumptions of compaction disequilibrium and the equivalent depthmethod. Parts D, E, and F show the behavior attributed to unloading.

overburden pressure over the same depth interval.Note that points at different depths that have the samevelocity also have the same effective pressure. Velocityplotted vs. effective pressure defines a single, depth-independent curve (Figure 1C). No similar one-to-onecorrespondence to either the pore pressure or the over-burden pressure exists.

The graphical scheme for pore-pressure predictionimplied by Figure 1A and B is known as the equiva-lent-depth method. The velocity at a point with un-known pore pressure is projected vertically upward

until it intersects the normal trend line at a shallowerdepth. The effective pressure at the new depth isequated to the effective pressure at the point of inter-est. Similar results can be obtained from Figure 1C, oranalytically from the curve fit; however, no universallyaccepted functional form for the relationship betweenvelocity and effective pressure exists. Some functionsin use are concave, as implied in Figure 1C. Others areconvex. To a large extent, the functional form assignedto the velocity-pressure relationship is dependent onthe assumed form of the normal trend line for velocity

Velocity Estimation for Pore-Pressure Prediction 179

vs. depth. This chapter reviews those relationships andsuggests that some are more appropriate than others.In particular, the common assumption that the loga-rithm of velocity is linear in depth is not consistentwith check shot data.

A single, definitive relationship between velocityand pressure is difficult to establish for various rea-sons. One is that the true variation of velocity withdepth is not as simple as shown in Figure 1A. Varia-tions caused by lithology exhibit large positive andnegative excursions from the trend. Plots as simple asthe one in Figure 1C are obtained only if the velocitydata are significantly smoothed. A second reason isthat several functions yield similar residuals where fitto a few noisy data points over a limited range of theindependent variable. Any empirical technique thatworks is difficult to criticize. A third reason is that sucha function may not physically exist.

The assumption of a one-to-one relationship be-tween velocity and effective pressure is not alwaysvalid. The approximation appears to hold wheneverthe cause of abnormal pressure is simple compactiondisequilibrium. Processes such as clay diagenesis, or-ganic maturation, or aquathermal pressuring can mod-ify the velocity-pressure relationship, as can unloadingcaused by uplift and erosion. Figure 1 also illustratesa case where the velocity-pressure relationship in theoverpressure region differs from that of the normalcompaction curve.

Figure 1D postulates the same velocity-depth valuesas Figure 1A. The effective pressure in Figure 1E, how-ever, is no longer the same as that at a shallower depthwith the same velocity (the equivalent-depth point). Ve-locities in the overpressure zone no longer retrace thevelocity-effective stress curve of the normal compactiontrend (Figure 1F). Application of the equivalent-depthmethod predicts too large an effective pressure andthereby underestimates the pore pressure.

Two points related to the normal trend are identi-fied in Figure 1D that can be used to recalibrate thedata. Bowers (1995) assumes a functional form for theunloading curve that is based on the equivalent-depthsolution and the effective pressure at the start of thereversal. His technique reproduces the behavior of Fig-ure 1C whenever an exponent is set to 1. For largervalues of the exponent, it produces a curve similar tothat shown in green in Figure 1F. The Eaton (1975)technique is based on extrapolated values of velocityand pressure along the normal trend line at the samedepth as the point in question. Allowing the exponentin the Eaton equation to vary produces a curve similarto that shown in pink in Figure 1F.

Figure 2 uses real data to demonstrate some of theconcepts introduced in Figure 1. Figure 2A shows the

sonic velocities from two wells in the same basin, albeitmore than 100 km apart. One is in shallow water, andthe other is in deep water. A second set of curves inFigure 2A represents sonic values smoothed to extractthe low-frequency compaction trend from high-fre-quency variations caused by lithology. Triangles andsquares superimposed on the curves indicate depthsat which pore-pressure measurements are available.The pore pressure in the shallow-water well follows ahydrostatic gradient, whereas the pore pressure in thedeep-water well rises above hydrostatic pressure as thedepth increases (Figure 2B). Figure 2C shows the den-sity curves from the two wells. Fitting a curve to themeasured densities allows extrapolation of the sedi-ment density to the sea floor. Integration of the densityfunction from sea level provides an estimate of the to-tal overburden pressure, Pc. Subtracting the measuredpore pressures from the calculated overburden pres-sure yields the effective pressure, Pe (Figure 2D). Nowsufficient information is available to determine the re-lationship between velocity and pressure. Figure 2Eplots smoothed velocity vs. pore pressure, whereasFigure 2F plots smoothed velocity vs. effective pres-sure. No simple relationship exists between velocityand pore pressure that connects one well with theother. A common trend in effective pressure exists thatmatches the assumed form in Figure 1C.

The previous discussion reveals that accurate pre-diction of pore pressure from velocity requires twocritical sets of information. One is an accurate velocitytrend. The other is sufficient data to calculate the ef-fective pressure at enough points to establish and cal-ibrate a relationship between velocity and effectivepressure. That in turn requires density and pore-pres-sure measurements in a similar setting. The rest of thischapter concentrates on the characteristics of velocity-depth functions and how to accurately determine themfrom surface seismic data. Remember, however, thatvelocity is only one piece of the puzzle.

V E L O C I T Y - D E P T H - T I M E R E L A T I O N S H I P S

Figure 1A implies that the presence of overpressurecan be deduced from a reversal in the velocity-depthcurve. That is commonly the case in young clastic ba-sins, but velocity reversals can also be caused bychanges in lithology, particularly where salt, carbon-ates, or volcanics are present. Figure 2A demonstratesthat significant overpressure can be encountered evenif no velocity reversal occurs. Therefore, it is instructiveto review several velocity-depth curves to determineclues to overpressure that are useful for quality controlof seismic velocities.

180 B E L L

Figure 2. Examples of velocity-pressure relationships. (A) Sonicvelocity vs. depth; (B) pore pres-sure vs. depth; (C) density log vs.depth; (D) overburden and effec-tive pressure vs. depth; (E) porepressure vs. smoothed velocity; (F)effective pressure vs. smoothed ve-locity. SL � sea level.

5000

6000

7000

8000

9000

10000

11000

12000

2000 4000 6000 8000

Pore Pressure (psi)

Sm

oo

thed

Vel

oci

ty (

ft/s

)

E

0

2000

4000

6000

8000

10000

12000

14000

16000

2.0 2.2 2.4 2.6

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Dep

th r

e S

L (

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5000

6000

7000

8000

9000

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11000

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0 2000 4000 6000

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oo

thed

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oci

ty (

ft/s

)

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0

2000

4000

6000

8000

10000

12000

14000

16000

5000 7500 10000 12500

Sonic Velocity (ft/s)

Dep

th r

e S

L (

ft)

A

0

2000

4000

6000

8000

10000

12000

14000

16000

0 4000 8000 12000

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Dep

th r

e S

L (

ft)

B

0

2000

4000

6000

8000

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12000

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0 4000 8000 12000

Overburden & Effective Pressure (psi)

Dep

th r

e S

L (

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D

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shallow water well

deep water well

C

Sonic logs in Figure 3 illustrate velocity trends infour wells. Diamonds indicates overpressure zones.Two of the wells are from Africa, and two are fromIndonesia. Figure 3A demonstrates a typical profile ina young clastic basin. The velocity increases uniformlywith depth according to a smooth empirical compac-tion trend. Near a depth of 9000 ft (2743 m) there is anabrupt decrease in velocity away from the trend linewhere the wellbore intersects a fault. The region of lowvelocity below the fault corresponds to a region of highpressure.

Figure 3B shows a similar velocity decrease around11,000 ft (3353 m) that again correlates with overpres-sure in a clastic sequence. Also, there is a positive breakin the trend line at a major unconformity near 5000 ft(1524 m). Sediments below the unconformity have ex-perienced tectonic uplift and therefore exhibit a highervelocity for a given depth than expected from the com-paction trend evident above the unconformity. Theanalysis in Figure 1A–C, neglected the influence of achange in the history of the effective stress. The pos-sibility of multiple compaction curves in the same well


0

2

4

6

8

10

12

Velocity (kft/s)

Dep

th (

kft)

0.6

1.2

1.8

2.4

3.0

3.6

Depth (km

)

A B C D

Fault

Unconformity

Figure 3. Sonic velocity vs. depthfor four wells, A, B, C, and D. Ap-proximate normal compactiontrends shown as smooth lines.Overpressure zones indicatedby diamonds. kft � feet inthousands.

suggests that accurate pore-pressure prediction re-quires an understanding of the depositional and tec-tonic history of an area.

The velocity profile in the third well (Figure 3C) iscomplicated by variations in lithology. The velocity de-crease near 6000 ft (1829 m) reflects a change from car-bonates to clastics, rather than a change in pressure. Asecond velocity break near 9000 ft (2743 m) does resultfrom excess pore pressure. Changes in lithology com-plicate pressure prediction from seismic velocities. Inthis example, the presence of carbonates is easily in-ferred from large seismic stacking velocities at shallowdepths. The shallow, high-velocity zone, however, alsointerferes with accurate seismic velocity measurementat greater depths. Accurate pressure prediction fromsurface seismic data is difficult under such circum-stances.

Not all velocity changes due to overpressure are asabrupt as those shown in the first three examples. Thefourth well (Figure 3D) shows a modest deviationfrom the normal velocity trend near 2000 ft (610 m)that represents a change in mud weight from 9 to 11 lb(4–5 kg).

The fourth well was also chosen as a counterpointto the previous examples. Near 7000 ft (2133 m), anincrease in pressure correlates with a thick sand unitwhose velocity is greater than the overlying shale.Sonic, density, and resistivity data in this well all in-dicate continued compaction within the deeper over-pressure zone. Mechanisms that induce overpressure

after compaction, and possible cementation, do notnecessarily lower the velocity sufficiently to producean obvious imprint.

Average Velocity

Normally, pressure predictions are based on pointmeasurements, that is, formation velocities at particu-lar depths. Various relationships dealing with averagevelocity also provide useful insights. Average velocityrepresents the total depth from a datum divided by thetotal one-way transit time of a seismic signal. (See Ta-ble 1 for a comparison of velocity terms.)

Average velocity is closely akin to seismic stackingvelocity. Stacking velocity does not always need to beconverted to interval velocity to infer pressure anom-alies. Knowing the influence of overpressure on aver-age velocity aids in picking and quality control ofstacking velocities for pressure prediction, particularlyin the presence of noise.

Figure 4 shows the average-velocity curves derivedfrom the wells in Figure 3. All of the important trendsobserved in interval velocity are manifest as slopechanges in the average velocity. An increase in slope(toward the vertical) indicates a reduction in intervalvelocity. A decrease in slope (toward the horizontal)indicates an increase in interval velocity. A sharp slopebreak indicates an abrupt interval-velocity change. Asmooth transition in the slope of the average velocityimplies the same in interval velocity.

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0

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4

6

8

10

12

Average Velocity (kft/s)

Dep

th (

kft)

0.6

1.2

1.8

2.4

3.0

3.6

Depth (km

)

1A 1B 1C

1D

PressureBreak

DepositionalBreak

LithologyBreak

PressureBreak

PressureBreak

PressureBreak

Figure 4. Average-velocity curvesfor wells from Figure 3. Slopebreaks indicate changes in inter-val-velocity trends associated withchanges in deposition, lithology,and pore pressure. kft � feet inthousands.

Interval velocities used in pressure prediction arecommonly smoothed. A normal trend line is one formof smoothing, but deviations from the trend are alsocommonly smoothed to prevent the predicted pressureprofile from exhibiting the large, rapid fluctuationsseen in a sonic log. Average-velocity curves are a formof smoothing and provide guidelines for other filteringprocesses. Smoothing interval-velocity excursions isappropriate within regions where the slope of the av-erage-velocity curve is reasonably constant. Velocityfidelity is compromised if averaging is performedacross major slope breaks in the average-velocitycurve.

Time-Depth-Velocity Relationships from Check Shots

Accurate prediction of the depth to a pressure anomalyfrom seismic velocities requires a valid time-depth re-lationship. Check shots provide the most accuratetime-to-depth information. Check shots are directtransmission measurements at seismic frequencies oftraveltime from a surface source to a receiver at aknown depth. Uniformly spaced check shots at smalldepth intervals are characteristic of vertical seismicprofiles (VSPs). (Processed VSPs also provide a seismictrace that ties waveform changes in time to formationboundaries in depth).

Figure 5 plots the time-depth relationship (Figure5A), the average velocity (Figure 5B) , and the interval

velocity (Figure 5C) derived from a VSP in a shallow-water Gulf of Mexico well. The onset of overpressureis manifest on a time-depth curve as a deviation fromthe trend in the shallower data. The effect, however, ismore pronounced if the check shots are converted toaverage velocity, Va � z/t. The break in slope of theaverage velocity is correlated with overpressure simi-lar to the curves in Figure 4. Note that check shotsprovide more accurate average-velocity informationthan sonic logs alone. Missing sonic values at shallowdepths, in washout zones, or near casing points leadto uncertainty in time-depth relationships because adepth integration is required over all intervals. Eachcheck shot is an independent measurement. Errors inshallow measurements do not affect deeper values.

Average velocities calculated from good-quality,vertical-incident check shots are accurate within 0.5%or less. Interval velocities between closely spacedcheck shots are subject to much greater uncertainty.The time difference between two levels in a VSP ap-proaches the sample rate. A picking error that is smallrelative to the total time can be large compared withthe differential time. Extreme interval-velocity excur-sions implied by check shot data should be verifiedwith the sonic log data. Check shot velocity informa-tion should be smoothed before being used to calibratethe sonic log. Nevertheless, overall velocity trendsshould still be evident in an interval-velocity curve de-rived from check shots (Figure 5C). Check shots also

184 B E L L

Figure 5. (A) Time-depth, (B)average velocity–depth, and(C) interval velocity–depth rela-tionships from check shots in aGulf of Mexico well. Seismic pre-diction of depth to overpressurerequires accurate time-depthconversion. Check shots providethe best time-depth calibration.Casing points and mud weightsare shown in decimal numbers.Major pressure transitionsoccur across faults. kft � feetin thousands.

0

2

4

6

8

10

12

14

16

18

4000 6000 8000 10000 12000

Vi (ft/s)

0

1

2

3

4

5

1219 1829 2438 3048 3657

Vi (m/s)

Dep

th (

km)

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5Vertical two-way traveltime (s)

Dep

th (

kft)

0

2

4

6

8

10

12

14

16

18

5000 6000 7000 8000 9000

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provide data very well suited to test various equationsused to represent the normal compaction trend for ve-locity vs. depth.

Various properties are desired of an empiricalmodel used to characterize noisy data. First, the modelparameters should be fairly insensitive to the range ofthe data and the number and placement of individualdata points. A corollary is that the model can be usedto confidently extrapolate data into regions where themodel applies but data are lacking. Second, the differ-ences between the values predicted by the model andthe actual data points (the residuals) should be smalland randomly distributed about zero. Third, consistentvalues of the parameters should be obtained where fit-ting the data with mathematically equivalent state-ments, for example, using sonic transit time (ds) ratherthan Vi. A fourth criterion is a bias toward a smallnumber of parameters. Any given data series can be fitperfectly with enough degrees of freedom, but extraparameters commonly fit noise rather than signal andtend to violate the previous criteria.

This chapter examines four two-parameter models,all of which yield a reasonable starting value, V0, atzero depth: an exponential curve, linear on a semi-logplot

bzV � V e (1)i 0

a power law, linear on a log-log plot

nV � V � z (2)i 0

a linear model, exponential in time (see equation 10)

V � V � kz (3)i 0

and a square-root model, linear in time (see equa-tion 7)

2 1/2V � (V � 4Az) (4)i 0

Because velocity is the rate of change of distance tra-versed for a given unit of time (dz/dt), the previousexpressions can be used to obtain formulas for equiv-alent time-depth and time–average-velocity curves,provided that the zero datum is consistent with themodel (see following paragraphs).

Figure 6 displays how well the various modelsmatch the data from Figure 5C. The data are displayedboth as velocity on a linear scale (Figure 6B) and as dson a semi-log plot (Figure 6A). Coefficients for thecurves were determined from least-squares fits of theoriginal check shot time-depth data from 3000 to 12,000ft (914–3658 m). Near 9000 ft (2743 m), all the curvespredict approximately the same velocity value. Belowthat point they begin to diverge significantly. That hasimplications for pore-pressure prediction schemesbased on the ratio of the normal trend and actual valueat a given depth (Eaton, 1975), or the difference be-tween the two (Hottmann and Johnson, 1965).

In Figure 6A, the exponential model (blue curve)yields a straight line. Close examination of the figure,particularly at a larger scale, suggests that a differentslope better fits the velocity data over the range used


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Figure 6. Comparison of checkshot velocities with various trendlines fit to time-depth data (Fig-ure 5A) from 3000 to 12,000 ft(914–3658 m). Blue � expo-nential; red � linear depth;green � power law; pink � lin-ear time. Note significant varia-tions in predicted values inoverpressured region below13,000 ft (3962 m). (A) sonictransit time with a log scale;(B) velocity with a linear scale.kft � feet in thousands; lsec �microseconds.

to calculate the coefficients. Figure 7 shows that such isindeed the case. The difference in implied velocity inthe overpressure zone is significant. Of the four modelsunder consideration, only the exponential expressionshows such a large variation where fitting mathemati-cally equivalent expressions for vertical two-way trav-eltime vs. depth rather than velocity vs. depth.

Figure 8 shows how well the various curves predictaverage velocity as a function of time. The input datarange was approximately 1.0–3.0 s two-way travel-time. Once again there is significant variation in valuesextrapolated into the region of overpressure. Theexponential model using parameters fit to intervalvelocity vs. depth from Figure 7 is clearly a poor rep-resentation of the data in this form. Restated, the ve-locity profile obtained from fitting the exponentialfunction to velocity-depth data does not yield a suit-able equation for converting from seismic time todepth.

The best visual fit appears to be the square-root pa-rameterization, which yields a straight line as a func-tion of time. Also, there is an indication for this wellthat none of the curves adequately represent the dataat both shallow and intermediate depths. That couldbe due either to a change in the depositional history,that is, the rate of compaction, or a shortcoming of theempirical models. Additional data imply the former

and support the linear time relationship as the bestoverall empirical fit for both time-depth conversionand prediction of Vi trends within zones of normalpressure.

Figure 9 presents data from 12 wells in a shallow-water area in the Gulf of Mexico. Coefficients for themodels were determined for each well based on least-squares fits to check shot time-depth data from 3000 to7000 ft (914–2134 m). The plots are of residual error,that is, the difference between predicted depths andactual depths. The prediction was extended by another2000 ft (610 m) in each direction to test the ability ofthe models to accurately forecast trends into regions ofknown data in normally pressured formations. Over ashort enough range, the data and all the models ap-proach linearity. The coefficients of a robust modelshould not be unduly sensitive to either the range orthe sample interval of the data available for curvefitting.

A perfect model including random noise wouldhave the residuals randomly distributed about zeroover the entire region fit by the model, not just overthe range of data used to determine the coefficients. Insuch a case, the magnitude of the residual indicates theuncertainty in the input measurements. Figure 9A il-lustrates such behavior. A single function for each wellbased on a square-root variation of velocity with depth

186 B E L L

Figure 7. Comparison of expo-nential trend lines: (A) transittime with a log scale; (B) velocitywith a linear scale. Coefficientsfor blue line determined frombest statistical fit to time-depthdata from 3000 to 12,000 ft(914–3658 m). Coefficients forbrown line determined from bestfit to interval-velocity data oversame depth range. Lack of con-sistency implies exponential ap-proximation is not a goodempirical fit to the data. Notelarge velocity difference in over-pressured zone. kft � feetin thousands; lsec � micro-seconds.

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can reproduce the check shot data from depths of1000–9000 ft (2743 m) to within 50 ft (15.3 m). Giventhe expected error in the check shot data itself, the ac-curacy of the model is probably within 20 ft (6.1 m).At 5000 ft (1524 m), that is less than one-half of 1% ofthe true value. Because the residuals fluctuate aroundzero, addition of more variables to the model wouldserve only to fit the noise. That is, three-parameterequations (e.g. Marsden et al., 1995) do not appear nec-essary to characterize either the time-depth or velocity-depth relationships representing normal compaction.

The depth residuals from the linear depth-velocitymodel (Figure 9B) are still relatively small. Note, how-ever, that the residuals vary from positive to negativeand back to positive. That implies structure in the datathat is not explained by the model and the possibilitythat additional degrees of freedom would improve thefit. The same behavior is displayed in the residualsfrom the exponential model (Figure 9C). The residualsare still relatively small, particularly over the rangeused to determine the coefficients, but grow more thanthree times as large as those from the first model. Thedifference in predicted interval velocity is similar tothat shown in Figure 6. At a depth of 9000 ft (2743 m),the difference is around 800 ft/s (244 m/s), from 9670ft/s (2947 m/s) for the square-root model to 10,470 ft/

s (3191 m/s) for the exponential model using a well inthe middle of the distribution.

Figures 6–9 demonstrate that the square-root modelis a better mathematical representation of the data thanthe exponential model. Both the square-root and linearmodels are commonly used by geophysicists for time-depth conversion, with about the same degree of suc-cess, particularly over limited depth ranges. The powerlaw is a generalization of the linear fit. Empirically, thecoefficient n is close to 1, and the power-law curve fallsbetween the linear and square-root models. The powerlaw is not as useful for time-to-depth conversion as theothers because there is not a simple, closed-form eval-uation of the integral of velocity for a general value ofn (Kaufman, 1953).

The exponential model is somewhat a standard forpore-pressure analysis, although various authors, (e.g.Kumar, 1979; Heasler and Kharitonova, 1996) havenoted problems with the formulation. An ever-increas-ing velocity gradient with depth is counterintuitive.The popularity of the exponential model apparentlyarose from the acceptance of Athy’s formula relatingporosity to depth (Korvin, 1984) and the simple as-sumption that sonic transit time for shale is propor-tional to porosity. The wide scatter in sonic data andthe contraction effect of a log plot commonly provides


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VVVVaaaa (((( ffff tttt //// ssss))))

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Figure 8. Comparison of trend lines with average-velocitydata (Figure 5B) displayed as functions of vertical two-waytraveltime. Brown curve is exponential model fit to interval-velocity data. It should not be used for time-to-depth con-version. Coefficients for other curves determined by fit totime-depth data. Blue: exponential, green: linear depth,pink: linear time. Note that linear time model predicts thatboth Vi and Va are linear with vertical two-way traveltime.

a satisfactory visual fit where the traveltime implica-tions are omitted. In the end, calibration of velocitywith pressure is needed to account for several vagariesin the underlying assumptions. The accuracy of thoseassumptions is a distinctively different subject fromthe accuracy of the input velocities that this chapteraddresses. For the purposes of this discussion, empir-ical trends are used to constrain the velocity in poordata zones, as indicators of changes in lithology as wellas pressure, and to produce accurate depth predictionsfrom seismic data. Eaton (1975) in his conclusion notedthat the methodology “used to establish normal trendsvaries as much as the number of people who do it.”The square-root model is one such variant that de-serves closer examination.

That the best mathematical fit relating velocity todepth also gives the simplest expressions for workingwith seismic velocities in time is fortuitous. If it is as-sumed that

2 1/2V � (V � 4Az)i 0

then given that Vi � dz/dt � dz/d(T/2),

2z � V T/2 � A(T/2) (5)0

V � V � AT/2 (6)a 0

and

V � V � AT (7)i 0

where T � vertical two-way traveltime. Alternatively,if it is assumed that

V � V � kzi 0

then

z � (V /k) exp(kT/2 � 1) (8)0

V � (2V /kT) exp(kT/2 � 1) (9)a 0

and

V � V exp(kT/2) (10)i 0

The first set of equations gives depth, average veloc-ity, and interval velocity as functions of vertical two-way traveltime for the square-root model. Extra factorsof 2 and 4 arise from using two-way traveltime in an-ticipation of comparisons with seismic data. The time-depth curve is a simple quadratic. Both the interval

velocity and average velocity are linear functions oftime with Va having one-half the slope of the Vi curve.This behavior simplifies interpretation of seismic ve-locities. The time expressions in the second set of equa-tions are derived from the linear velocity-depth modeland are not as easy to visualize or manipulate. (Thelinear depth model is preferred in some geophysicalapplications because traveltimes and travel paths areeasier to calculate as a function of offset.)

Effect of the Water Column

Variations from basin to basin in the normal compactioncoefficients should be considered. Before that is done,however, it is advantageous to remove the effect of thewater column. In normally pressured areas, the heightof the water column does not directly influence the

188 B E L L

Figure 9. Comparison of deptherrors obtained by individually fit-ting various velocity models tocheck shots in 12 GOM wells.Statistical fit of data from 3000 to7000 ft. Values extrapolated out-side of those bounds. (A) lineartime model; (B) linear depthmodel; (C) exponential model.

trend in the formation velocity, other than to shift thedatum to the mud line. (The effective stress is zero atthe sea floor regardless of the water depth.) The waterdepth does impact the time-depth curve, the averagevelocity, and the seismic stacking velocity. Changingthe velocity datum to the mud line makes it easier toinfer geographic variations in formation velocity di-rectly from average or stacking velocities. Figure 10demonstrates the effect using check shot data from aregion of the Gulf of Mexico where there are significantchanges in water depth.

Geographical Variations in Compaction Trends

Figure 11 displays average velocities from check shotsfrom five areas in two different basins. Data from sev-eral of the wells have already been shown in pre-

vious displays. All of the data are referenced to the seafloor. The orange, blue, and purple data are from shal-low-water locations that exhibit a well-defined normalcompaction trend before encountering overpressure.The brown and green data represent deep-water wells.Most of the deep-water wells begin to build abnormalpressure at relatively shallow depths. Some of thesehave a second, abrupt, pressure build across faults.

Within the normal compaction zone of each of theshallow-water areas, both the intercept, V0, and thegradient, A, vary only slightly. A single curve fit to allof the wells in a given area is not as accurate as indi-vidual curves for each well, but in general the depthresiduals are still less than 100 ft (30.5 m) over the en-tire normally compacted depth range. That is withinthe accuracy expected from seismic velocities. Becausethe wells are separated by up to 20 mi (32 km), the


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Figure 10. Effect of water col-umn on time-depth and average-velocity curves. Variable waterdepth obscures compaction rela-tionships. (A) time-depth curvewith regard to sea level; (B) av-erage velocity with regard to sealevel; (C) time-depth curve withregard to sea floor; (D) averagevelocity with regard to sea floor.TWT � vertical two-way travel-time; SL � sea level.

implication is that velocity tracks depth rather than lo-cal lithologic, stratigraphic, or structural trends. Thatis, the formation velocity of a given sand or shalewithin a depositional sequence is not constant fromwell to well but varies with depth. The velocity canbe reasonably constant across a fault although rocksof different ages and lithologies are juxtaposed. Asingle time-depth curve referenced to the sea floorcan commonly be used to the top of overpressure.These observations are used in a following section to

justify both vertical and lateral smoothing of seismicvelocities.

Effects of Sand/Shale Ratio, Age, and Burial Rate

Several techniques are available, ranging from drill-ing rates to resistivity logs, for predicting pore pres-sure on the basis of a deviation from a normalcompaction trend. Although direct pressure measure-ments are normally made in sands, most prediction

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Figure 11. Geographic variation in average-velocity trends. Basin 1-A (blue diamond), basin 1-B (pink square), basin 1-C(green triangle), basin 2-A (orange square), and basin 2-B (brown square). TWT � vertical two-way traveltime.

techniques, including sonic methods, define empiricaltrends based on measurements in shale. Presumably,porosity and density variations with depth are betterdefined for the shales. Seismic velocity measurementsusing differences in moveout, however, seldom havethe resolution necessary to separate lithology on a finescale. Fortunately, velocity-depth trends for sand andshale are similar enough that lithology affects tend toaverage out unless thick, seismically resolvable unitsare present.

Shale velocities tend to fall between those of high-porosity sands containing compressible hydrocarbonsand well-cemented, low-porosity, water-saturatedsands. Statistically, for deposits of a given age, there isa depth at which the velocity of water-saturated sandstransition from slower than shale to faster (Neidell and

Berry, 1989). Given the wide range in both sand andshale velocities possible at a given depth, however,such a sand/shale crossover is hard to observe on asingle sonic log. Figure 12 shows the variability of ve-locity with sand/shale ratio using the sonic log fromthe shallow-water well in Figure 2A.

D E T E R M I N I N G V E L O C I T Y F R O M M O V E O U TO N S E I S M I C G A T H E R S

Now that expectations have been established with welldata, it is appropriate to determine how accurately theresults can be reproduced using velocities determinedfrom surface seismic data. Figure 13 compares well ve-locities with seismic velocities for the well shown in


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Figure 12. Sonic velocity as function of depth and lithology.Sands are in yellow. Shales are in green. kft � feet in thou-sands.

Figure 5. The seismic velocity data are taken from thethree processing contractor velocity analysis locationsclosest to the well. The average-velocity trends aresimilar although the seismic values tend to be slightlyfaster than the sonic values. The interval velocities cor-rectly locate the first pressure break in depth (around12,500 ft [3810 m]). The difference in velocity betweenthe three curves provides an estimate of the uncer-tainty in the technique. Also, note that the second pres-sure break near 14,500 ft (4420 m) has not beenresolved. Seismic processors commonly err on the highside where there is uncertainty in the stacking-velocitytrend. Otherwise, there is a danger of stacking multi-ply reflected energy in poor data zones. In this case,deeper picks were extrapolated such that the resultinginterval velocities increased rather than decreased.Those values were excluded from the plot. Generally,velocities used to process seismic data reveal majorpressure breaks. They may be, however, inadequatefor detailed pressure prediction work. That is particu-larly true for speculative processing or fast track vol-umes. Ideally, seismic velocities should be repicked forthe express purpose of pressure prediction, which canbe costly and time consuming unless the appropriatedata are saved during the original processing. At the

very least, contractor picking of velocities should bequality controlled by someone familiar with the con-cepts of pressure prediction.

Several seismic-processing procedures derive veloc-ity estimates to account for the moveout in reflectiontime observed with offset. The most common sorts thedata into a common midpoint (CMP) gather and de-termines the best-fit normal moveout velocity, Vnmo,as a function of vertical two-way traveltime (T) foreach major reflector. Vnmo assumes that the measuredtraveltime is a hyperbolic function of the offset dis-tance between seismic sources and receivers. Themoveout velocity is used to remove the traveltime var-iations, that is, to flatten the event at the zero-offsettime, prior to stacking the data to obtain a seismic im-age. Generally, the stacking velocity, Vstack, is an esti-mate of Vnmo obtained by systematic repetition of thestacking procedure involving examination of varia-tions in gather flatness, semblance across the gather,and stacked image continuity. (Refer to Table 1 for acomparison of velocity terms.)

Figure 14 shows common seismic velocity analysisdisplays from a good-quality, deep-water location.Figure 14B and C show a CMP gather both before andafter moveout correction. Events should be flat afterthe moveout correction. All of the traces after moveoutare then summed to form a single trace for that CMPlocation. The semblance contours in Figure 14A are ameasure of stacked amplitude in a sliding T windowfor a large number of trial stacking velocities. The sem-blance is high where events are correctly flattened andlow where they are not. The windowing process meansthat semblance maximums do not always directly cor-respond to event times seen on the CMP gather. Figure14D shows the result of stacking several CMPs withconstant velocities around the analysis location. Con-tinuity of events at a given time is another indicationthat the correct stacking velocity has been obtained. Inpoor data areas, which unfortunately are commonlyassociated with overpressure, distinct events may notbe seen on the CMP gathers. In those cases, constant-velocity stacks are an important tool.

Note the slope break at 5.5 s seen in the stacking-velocity trend in Figure 14A. Although no wells havebeen drilled in this area, it probably indicates over-pressure. The trend above 5.5 s is not linear as expectedbecause of the large depth of water. It is linear if thedata are datumed to the sea floor. The resulting inter-val-velocity curve does reveal a linear trend down tothe velocity reversal indicative of pressure. The lineartrend in interval velocity results somewhat from a biasin the picking. Minor changes in stacking velocitywithin the contours of high semblance have little influ-ence on the final stack but can cause large changes inthe interval velocities, particularly if the picks are close

192 B E L L

Figure 13. Comparison of checkshot and seismic velocities usingwell data from Figure 5. Seismicstacking velocities from three lo-cations near the well convertedto Va and Vi. Two-way traveltimeconverted to depth. (A) Averagevelocity vs. two-way traveltime;(B) interval velocity vs. depth.

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together. Commonly, an unreasonably high excursionis immediately followed by a very slow interval veloc-ity, or vice versa. The stacking velocity picks in thiscase have been adjusted to remove interval-velocitypairs that fluctuate about the trend. The thick, low-velocity water layer also impacts the sensitivity of theinterval-velocity determination near the water bottom.In this example, a 1% change in the value of the firststacking velocity pick below the water bottom leads toa 20% change in the corresponding interval velocity.

Figure 15 shows additional semblance panels andCMP gathers to demonstrate how the quality of stack-ing velocity information can vary over relatively shortdistances. The semblance panel at the first location(CMP1) shows numerous distinct events that can betracked both on the seismic section and the gather. Thequality of the semblance picks begins to deteriorate atthe second location. At the third location, little confi-dence should be placed on the deeper semblance picks.Events on the seismic section are chaotic and difficultto interpret. Coherent multiples interfere with primar-ies on the CMP gather. In areas such as these, it is im-portant that the pressure analyst understand thevariable uncertainty in the seismic velocities.

Calculating Interval Velocity from Stacking Velocity

For a single horizontal layer with constant velocity, theformation velocity at each depth, the interval velocity

across the unit, the average velocity to any depth be-low the surface, and the normal moveout velocityfor the base of the unit are all the same. All other situa-tions require adjustments to the stacking velocity toobtain an appropriate representation of the formationvelocity.

The conventional method to convert from Vstack inmeasured two-way traveltime to Vi vs. depth is to usethe Dix equation to determine Vi between adjacentstacking velocities and then to multiply the intervalone-way time by Vi to obtain a layer thickness. Therunning sum of the thickness for each of the precedinglayers gives the depth. The Dix equation (Sheriff, 1991)for the interval velocity of the nth layer is as follows:

2 2V � [(V T �V T )/in stackn n stackn�1 n�11/2(T �T )] (11)n n�1

where Vstackn and Tn are the stacking velocity and ver-tical two-way traveltime, respectively, for the top ofthe nth layer.

The Dix equation is founded on two assumptions.First is that the earth is composed of multiple horizon-tal layers of constant velocity. Ray bending due to acontinuous change of velocity with depth, as impliedby compaction, causes the calculated interval velocitiesto be slightly too high. Anisotropy (a difference

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Figure 14. Determination of optimum stacking velocity from seismic data. (A) Semblance panel with stacking-velocity picks andresulting interval velocities; contours plot semblance as a function of stacking velocity and vertical two-way traveltime; (B) CMPgather showing hyperbolic moveout with offset; (C) CMP gather after normal moveout correction using stacking-velocity picks;(D) constant stacking velocity stacks at 1600 (left), 1650 (middle), and 1700 (right) m/s. Moveout curves properly fit by thosestacking velocities appear flat.

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Figure 15. Seismic line (top) with velocity scan locations. Semblance panels (middle) and gathers (bottom) at selected loca-tions. Confidence in velocity information decreases from left to right. Deeper coherent events in CMP 3 are multiples.


between the horizontal and vertical velocity at thesame point) also introduces errors, as do dipping ho-rizons and other lateral velocity variations.

The second, related, assumption made in derivingthe Dix equation is that stacking velocity is the sameas the root-mean-square (rms) velocity, Vrms. The rmsvelocity variations mimic the average-velocity behav-ior noted previously but is always slightly higher be-cause rms averaging is biased toward higher velocities.The Dix equation accounts for that part of the differ-ence between stacking velocity and average velocity,but only if the velocity is truly constant within the in-terval. Additionally, the moveout curves for multiplelayers, even if flat and of constant velocity, are nolonger strictly hyperbolic. This introduces a positivebias that depends on offset and the relative velocitychanges between layers. In places, higher order termsare added to the moveout equation to better flattenevents at long offsets. The Dix equation is more appro-priate in the limit of short offsets.

Figure 16 illustrates the application of the Dix equa-tion to a single 4000 ft (1219 m) flat layer with foursimple variations of velocity within the layer. Figure16A plots the four different velocity functions, all ofwhich have the same vertical traveltime and averageinterval velocity of 6427 ft/s (1959 m/s). The first issimply a constant velocity. The second is a series offour constant-velocity steps. The velocity in the thirdexample varies as the square root of the depth as perthe linear time model in Figure 9. The fourth case is asingle anisotropic layer with a vertical velocity of 6427ft/s (1959 m/s) and a horizontal velocity of 7712 ft/s(2351 m/s).

Anisotropy with a vertical axis of symmetry, alsoknown as transverse isotropy, is easy to think of interms of vertical and horizontal velocities. Four param-eters are necessary, however, to characterize such amedium (Alkhalifah and Tsvankin, 1995). A commonparameterization consists of the vertical compression-wave velocity, the vertical shear-wave velocity, andtwo additional constants, d and e. In simple terms, thedifference between d and e controls the stacking veloc-ity. If d equals e, the moveout is exactly hyperbolic,and the stacking velocity for a single flat horizon givesthe horizontal velocity. If d does not equal e, the move-out curve diverges from a hyperbola. Two cases areillustrated in Figure 16, both with the same vertical andhorizontal velocities. Open triangles represent d �0.219 and e � 0.22. Filled triangles represent d � 0.1and e � 0.22.

Figure 16B shows the moveout curves. (These werecalculated analytically except for the four-step func-tion, which was ray traced.) Hyperbolas were fit to themoveout curves over offset ranges of 0–4000 ft (0–1219m) and 0–10,000 ft (0–3048 m). As expected, the Dix

equation yields the true velocity, independent of offsetfor the constant-velocity case. The Dix estimated ve-locity is too high for the two cases of a vertical velocityincrease within the layer. The error in the estimate alsogrows as a function of the offset range over which themoveout curves are fit. The Dix equation applied tothe anisotropic layer where d nearly equals e yields thehorizontal velocity rather than the vertical velocity.Where d does not equal e, the velocity from the Dixequation falls between the vertical and horizontal ve-locities and depends noticeably on offset.

The raypaths for both the constant-velocity and an-isotropic cases are straight (Figure 16C), which was theassumption used to derive the Dix equation. Raypathsegments for the four-step function are straight linesthat bend, or refract, at the velocity discontinuitiessuch that the overall traveltime is minimized. A con-tinuous variation in velocity with depth results in con-tinuous ray bending. In the presence of ray bending,Dix velocities in the zero offset limit more closely ap-proximate rms interval velocities rather than averageinterval velocities.

The cause of the variation of stacking velocity, andhence the Dix velocity, with offset is shown in Figure16D. The difference between the best fit hyperbola andthe actual moveout is plotted. The residuals are zerofor the constant-velocity case and almost so for thebrown anisotropic curve. The residuals are similar forthe two cases with vertical velocity variations and arelarge enough to influence the stacking-velocity esti-mate without unduly impacting the image quality (4ms is a normal wavelet trace sampling). If the offsetrange is large compared with the reflector depth, thedeviation represented by the orange anisotropic casecan impact the imaging. Unfortunately, the correct ver-tical velocity cannot be derived solely from the move-out curve.

Although the velocity differences in this simple ex-ample appear minor, the effect of velocity layering onestimation of true interval velocities from seismicstacking velocity are almost always noticeable (5–10%),more so if significant anisotropy is involved. An ac-curate prediction of the depth of an overpressure zonerequires calibration of the Dix velocity function withcheck shots. Even so, the effects of vertical variationsin velocity tend to be small compared to those intro-duced by lateral structural variations.

Effect of Structure on Seismic Velocity

Significant errors in the Dix estimation of interval ve-locity from stacking velocity arise where the earth de-parts from the simple flat layered model. Figure 17compares a flat layer geometry with that of a dipping

196 B E L L

Figure 16. Effect of velocitymodel on interval velocities de-rived from seismic moveout. (A)Color-coded models all withsame vertical average interval ve-locity. Blue � constant velocity;green � four velocity layers; pink� velocity gradient; orange �transversely isotropic velocity.(B) Corresponding moveoutcurves and derived interval veloc-ities for each model with two off-set ranges. kft � feet inthousands. (C) Correspondingraypath plots. (D) Residual move-out curves (deviation of moveoutfrom assumed hyperbola) forthree of the models. TWT �two-way traveltime.


OFFSET DISTANCE

RAYPATH PLOTS ON DEPTH MODELS CMP TRACE GATHERS SEMBLANCE PANELS

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Figure 17. Influence of dip onnormal moveout and effect ofDMO. (A) Flat-layer model;(B) dip effects; (C) effect ofDMO. TWT � two-waytraveltime.

event. For a single interface, the stacking velocity isincreased proportional to the cosine of the dip angle.For stacked layers with variable dips, simple correc-tions based on analytical expressions are not possible.Interpretation is further complicated where a changein dip occurs within a cable length. In Figure 17B, thedipping interface has a higher moveout velocity thanthe horizontal interface. If a single velocity pick ismade for the pair of events, one or the other, or neither,stack correctly. If a velocity pick is made for each event,the Dix equation imposes an apparent velocity changewhere none actually exists.

Also note in Figure 17B that the rays representativeof seismic energy for different offsets no longer con-verge at a single point directly beneath the midpointof the gather. A seismic velocity profile does not al-ways represent vertical sampling of the earth. Migra-tion is a process applied during seismic imaging to

correct for various items, including lateral positioningof events. Several types of migration algorithms existthat vary in their cost and ability to handle lateral ve-locity changes. All migration codes require an inputvelocity field. Commonly, migration velocities avail-able from the seismic processor have been smoothedtoo much for detailed pressure work. In general, pres-sure analysis should be performed using stacking ve-locities picked after dip moveout (DMO) correction(Figure 15C).

The DMO is a prestack process that does a reason-able job of removing dip effects so that flat and dippingevents can be stacked with the same velocity (see Der-egowski [1986] and Liner [1999]). Application of DMOrequires an initial estimate of the velocity field, but theoperator is relatively insensitive to the velocity. A con-stant-velocity DMO operator is normally adequate forstacking purposes. If transverse isotropy is present,

198 B E L L

however, constant-velocity DMO does not yield thebest image. The difference in moveout between a dip-ping event and a flat event can be used to estimate thetransverse isotropy (TI) parameters (Alkhalifah andTsvankin, 1995).

If neither DMO nor more sophisticated prestack mi-gration processes have been applied to the data priorto NMO analysis (uncommon in modern data process-ing), then the pressure analyst should concentrate onareas in the seismic section that are flat over the lengthof a seismic cable. Velocities from those locations maythen be extrapolated to prospect locations using geo-logic insight.

Although DMO does a reasonable job of removingdip effects, it does not correct for lateral changes invelocity. An important example for pressure work ishow stacking velocities vary across a fault that boundsa velocity decrease due to overpressure.

Figure 18 shows how a simple fault model distortsthe stacking velocity. The effect of a lateral velocitychange is first seen on the far offsets of a CMP (Figure18A). Successive CMPs are influenced to a greater ex-tent until the middle of the spread moves past the dis-continuity. Figure 18B shows how the moveout of theevent at CMP 7 differs from the constant-velocity caseat CMP 5. Similarly, the moveout at CMP 11 is notice-ably different from the moveout for the constant-ve-locity case at CMP 15 (Figure 18C). Figure 18D tracksthe lateral change in stacking velocity. For imagingpurposes, it is important to honor such changes. Forpressure work, it is commonly appropriate to extendlateral velocity trends up to the fault rather than tohonor stacking-velocity picks within a cable length ofan implied velocity discontinuity. This can be difficultwhere the target is a fault block that is smaller thantypical cable lengths of 6 km. In such a case it is some-times useful to carefully pick the location of the veloc-ity analysis and to discard long offsets.

Figure 18D also illustrates another display useful invelocity work. If semblance calculations are made atclose CMP spacing, it is possible to sort the data basedon a digitized horizon and produce a plot of semblancevs. velocity and CMP location for a single event.

The lateral smearing of velocity information over acable length has other implications with regard to ve-locity analysis. Velocity analysis for pressure work istypically done with a CMP interval of 1 km or so. Be-cause that is already well below the length of a seismiccable, the velocity information from one point to thenext is not independent. Velocity analysis at closerCMP spacing can provide useful statistical informationbut seldom provides increased lateral resolution usingthe Dix equation. Abrupt changes in stacking velocity

from one profile to the next are suspect. Finer samplingmay be warranted using tomographic techniques, butthat is another topic.

Shooting geometries commonly deploy more re-ceivers per shot than are sorted into a CMP bin. Ad-jacent CMP gathers may contain only every other oreven every fourth offset. Because velocity informationis already smeared laterally because of the cable lengthand reflector dip, it is commonly appropriate to com-bine several adjacent CMP profiles into one super-gather prior to velocity analysis. See Figure 19.

The previous discussion of structural affects as-sumes that hyperbolic NMO velocities are still appro-priate for stacking but illustrates situations where thebest stacking velocity may not be appropriate for Dixderivation of interval velocities. If reflector moveoutobserved during velocity analysis cannot be reason-ably flattened with a hyperbolic fit, then the conceptsof NMO and the Dix equation are no longer appropri-ate. Depth migration is then required. Depth migrationis appropriate whenever there are large abruptchanges in lateral velocity, for example, under theflanks of salt domes (see Lines et al. [1993] and Whit-more and Garing [1993]).

Figure 20 shows examples of displays used to de-termine velocities for depth migration. An initialmodel consisting of two layers with vertical velocitygradients is shown as a blue line in Figure 20A. Themodel is then used to migrate the data. If the velocityfield is correct, then all events in a common imagepoint (CIP) gather should be at the same depth. (A CIPgather represents a single reflection point in the earthdirectly below the surface location. Reflections on aCMP may arise from several locations away from thecenter, as in the dipping-layer example of Figure 17B.)Figure 20A displays the depth error in both verticaland horizontal semblance. After a tomographic updateto the velocity model, the maximum semblance valuesare near zero residual depth, and the events in the mi-grated gather appear flat. Tomography (Sheriff, 1991)is a procedure in which a velocity model is automati-cally adjusted to simultaneously minimize the errorbetween multiple horizon picks on multiple offsetsand the values predicted by the model.

C A S E S T U D Y : S E I S M I C V E L O C I T YA N A L Y S I S

Figure 21 shows a seismic line with two wells. Well Awas drilled first and did not encounter significant over-pressure. There were problems completing well B afterit encountered abnormal pressures across a fault. The


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Figure 18. Effect of lateral velocitychange across fault on event move-out and corresponding stacking ve-locities. (A) Cross section of depthmodel showing ray path distortion atCMP 7 due to fault; kft � feet inthousands; (B) moveout curves atCMP locations 5 and 7; (C) moveoutcurves at CMP locations 11 and 15;(D) cross section of velocity sem-blance picks vs. CMP locations.TWT � two-way traveltime.

sonic log for this well is shown in Figure 3A. Note thechange in reflection continuity in the center of the sec-tion. As a rule of thumb, such changes in image qualityare commonly associated with overpressure. Unfortu-nately, this also implies that reliable velocity estimatesare more difficult to extract from those regions.

Figure 21B shows the CMP locations where velocityanalysis was performed. Figure 22 shows the velocityanalysis panel near the well B location. Only a limitednumber of picks are shown to prevent obscuring theevent moveout seen on the CMP gather. Note that the

slope break in the stacking-velocity trend occurs at theknown location of the pressure transition.

Figure 23 compares the Dix derived interval veloc-ities (blue stair step) with the sonic log (gray curve)from well B, both in time and in depth. The originalinterval velocities displayed in time (Figure 23A) cor-rectly predict the decrease in velocity seen on the soniclog just above 2.5 s. Where those velocities are used fortime-to-depth conversion (Figure 23B), however, thepressure transition is mislocated by several hundredft. As indicated in the previous discussion, such a

200 B E L L

CMP 1CMP 2

Shot 3 Shot 2 Shot 1Offsets:

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Figure 19. Common shooting geometrics result in adjacent CMP gathers having different offset distributions. Velocity analysiscan be improved if supergathers are formed that contain all available offsets.

result is expected because of several factors that imparta positive bias to the Dix estimates.

Figure 23A also compares the original Dix calcu-lated average velocity (pink curve) with check shot val-ues in the same well (green points). To demonstrateanalysis techniques ahead of the bit, check shots fromwell A were used to calibrate the average-velocitycurve at the well B location. The calibrated curve (inred) is consistent with known well B values and cor-rects the error in the depth display of the interval ve-locity (Figure 23B). The final difference between thesonic and the calibrated Dix interval velocities is anindication of the uncertainty in the velocity analysistechnique and the low resolution of seismic moveoutvelocities compared with sonic values.

To some extent, the Dix assumption that the earthis composed of a finite number of constant-velocity

layers is at odds with the concept of a smoothly vary-ing normal compaction trend. Pressure analysts some-times use Dix velocities only at the midpoint of thelayer to produce a smooth trend in the predicted pres-sures. Reality lies between the two simplistic models.A useful compromise is to regard the earth as a seriesof layers with velocity gradients. Constant-velocitylayers simply have zero gradients, whereas all layerswithin a normally compacted region have the samegradient. Such a view fosters the concept of verticaland lateral smoothing of stacking velocities withingeologic units to reduce the uncertainty in both time-to-depth conversion and pressure predictions. The gra-dient can be based on any analytic expression thoughtto represent the proper velocity-depth relationship.The key criterion is that the chosen expression is con-sistent with the stacking-velocity information.


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Figure 20. Horizon-keyed veloc-ity analysis in the depth domain.(A) Diagnostic plots using initiallayered velocity model; (B) diag-nostic plots after tomographicupdate of velocity model.

202 B E L L

Figure 21. Seismic data from study area. (A) Interpreted section with well locations in red. (B) Section with location of velocitypicks shown as blue squares. Sonic log for well B is first curve in Figure 3. Overpressure encountered after cutting second fault.Vertical axes are vertical two-way traveltime in seconds.


Figure 22. Seismic cross section, semblance panel, and CMP at overpressured well B location. Sparse picks indicate trend. Notechange in slope of stacking-velocity curve at event just above 2.5 s corresponding to location of fault. Common vertical axes aretwo-way traveltime in seconds.

Figure 24 compares conventional Dix velocity pro-files (Figure 24B) with gradient profiles (Figure 24C)for the six velocity functions that sample the structurearound well B in Figure 21. Figure 24A identifies thehorizons that were picked in the initial analysis alongwith zones where the velocity gradient might be ex-pected to change, for example, fault blocks and majorunconformities.

Figure 25 plots velocity data from the six locationsin Figure 24 on common axes. Figure 25A and B showboth the final stacking-velocity picks and the calcu-lated Dix interval velocities color coded by location.Note that the software package used for the velocityanalysis allowed interactive adjustment of both thestacking velocity and the interval-velocity values rela-tive to preliminary picks at the other locations. In otherwords, the consistency of the interval velocities in theshallow section already reflects an interpretive biasbased on tracking chosen horizons and multiple passesthrough the data.

Each stacking-velocity function in Figure 25A canbe closely approximated by a linear function in time

from the surface down to the individual slope breaksbelow 2 s. That would have the effect of replacing thestair steps in Figure 25B with a straight line at eachlocation. Such action amounts to vertical smoothing ofthe stacking-velocity picks.

Figure 25C and D display the same data color codedby geologic unit. The interval-velocity steps from Figure25B have been plotted as single midpoint values in Fig-ure 25D. Both plots suggest that a single, laterally in-variant function is appropriate for the first three layers,whereas a separate function is appropriate for layers 4and 5. The derived interval velocities show considerablescatter in the low-velocity overpressure regions (layers6 and 7). Part of that scatter is attributed to the poorseismic data quality in those areas. A linear fit to thestacking-velocity data in those zones produces a betterapproximation of the true velocity field. Such smooth-ing is appropriate provided the adjusted picks still flat-ten the observed moveouts. The gradient curves inFigure 24C were obtained by fitting straight lines to thestacking-velocity picks within each zone prior to Dixconversion to interval velocity.

204 B E L L

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Figure 23. Comparison of seismic velocities with log data from well B. Time-depth information from well A used forcalibration.

Figure 26 compares the calibrated Dix velocity pro-file from Figure 23 with the calibrated gradient profilefrom Figure 24 at the well B location. The gradient pro-file is obviously an acceptable alternative to the Dixdisplay.

Figure 27 compares various ways to display seismicvelocity information in cross section. Figure 27A showsthe stacking-velocity field interpolated laterally. Suchdisplays offer a few clues to the interval-velocity be-havior. Constant thickness stacking velocity contoursimply a uniformly increasing velocity with depth. Indeep-water areas, those bands most likely follow theshape of the water bottom. An increase in the spacingof the color contours indicates a change in gradient ofthe stacking velocity.

If the stacking velocities are smoothed, either ver-tically and/or horizontally, as in the previous dis-cussion, a display of the gradient of the stacking

velocity commonly gives a rough indication of slowvelocity zones that correlate with overpressure(Figure 27B).

Figure 27C and D are color analogs of the individualfunction displays shown in Figure 24C and B. The ve-locity field in Figure 27C is represented by vertical gra-dients that are allowed to vary according to geologicstructure. Figure 27D imposes a laterally varying, con-stant vertical velocity within each layer. Both represen-tations are correct in the sense that they produce thesame vertical time-depth curve at the indicated bound-aries. The gradient display, however, is probably a bet-ter representation of the true picture. Recall that thelateral consistency of average velocities from the checkshots (Figure 11) implies that velocity contours com-monly cut horizon boundaries and faults. Reilly (1993)discussed additional reasons for preferring the gradi-ent view to the Dix conceptualization.


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Figure 24. Comparison of velocity functions referenced tohorizons. (A) Geologic units. (B) Dix interval velocities tiedto horizon picks. (C) Gradient functions tied to unit bound-aries. TWT � vertical two-way traveltime in seconds.

H O R I Z O N - B A S E D S M O O T H I N G O FS E I S M I C S T A C K I N G V E L O C I T I E S

The concept of horizon-based smoothing of seismicstacking velocities is important enough to justify ad-ditional discussion. If used judiciously, it can improveconfidence in seismically derived formation velocities.If misused, it can obscure or destroy information con-tained in moveout variations.

Figure 28 shows various ways to interpret fivestacking-velocity profiles close to a proposed well lo-

cation. Each point is within 0.5 km of the well, andgiven a 6 km cable, should sample a similar velocityfield. The stacking velocities were generated by a re-liable processing contractor. Analysis of the stackingvelocities for time-depth conversion and regional pres-sure prediction was begun at the same time as the geo-logic interpretation. Four major horizon boundariessubsequently supplied by the interpreter are indicatedon several of the plots.

A pronounced change in slope of the stacking ve-locities shown in Figure 28A suggests a possible pres-sure transition beneath horizon 2. Picks below thehorizon show considerable scatter due to a poor signal-to-noise ratio and difficult imaging.

The processing geophysicist was asked to pick allreliable primary semblance events. Considerable scat-ter in the interval velocity estimates is expected whenthe Dix equation is used to convert closely spacedstacking velocities. Although each stacking-velocitypick represents a valid moveout velocity, the interval-velocity calculation is very sensitive to small time er-rors where the time interval itself is very small.

Figure 28B shows the raw Dix interval velocities.Several of the velocity values are physically unrealistic,and the large amount of scatter suggests that none ofthe deeper values should be used for pressure predic-tion without further analysis.

One way to reduce the sensitivity of the Dix equa-tion to small intervals is to consistently make picks onhorizons that are well separated in time. If that ap-proach is taken, both well and seismic data should bereviewed beforehand to insure that the chosen inter-faces are adequate to describe important variations inthe velocity field. Figure 28C shows a limited choice ofdata points based on horizons that correspond to slopebreaks in the original picks. The corresponding Dix in-terval velocities (Figure 28D) are now more consistent.Averaging the midpoint values of interval velocityfrom the decimated stacking velocities could result inan acceptable pressure prediction.

Note that the apparent improvement in the interval-velocity functions in Figure 28D did not arise fromchanging the individual stacking-velocity picks. Thestacking-velocity picks that were rejected are probablyjust as valid as the ones retained. The final velocityinterpretation should be better constrained if all thepicks are considered.

One way to examine the additional data would beto choose other sets of similarly separated stacking ve-locities and then to interleave the resulting Dix intervalvelocities. Also, stacking-velocity picks for additionalclosely spaced horizons can be interactively tweakedto produce reasonable interval-velocity profiles. Thatwas the procedure used to obtain the interval-velocity

206 B E L L

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Figure 25. Comparison of (A) stacking velocity and (B) Dix interval velocity color coded by surface location with (C) stackingvelocity and (D) midpoint interval velocity color coded by geologic unit. Curve fitting within units with a laterally constant velocity–depth relationship reduces uncertainty in individual Dix derived interval velocities. TWT � vertical two-way traveltime in seconds.


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Figure 26. Comparison of Dix interval-velocity profile withgradient model.

curves shown in the previous example (Figure 25B).This technique, however, can be time consuming andsubject to interpreter bias.

Also, it is possible to employ simple statistical tech-niques to extract robust interval-velocity estimatesfrom closely spaced stacking-velocity picks. Simplecurves may be fit over geologically consistent units, aswas done to derive the gradient curves in Figure 24C.

Figure 28E demonstrates yet another technique forsmoothing the stacking velocities. The individualstacking-velocity functions in Figure 28A were linearlyinterpolated in time to a uniform sampling interval. Amedian filter was then applied to the collection of fivedata points at each time sample. That operation pro-duced a single stacking-velocity function smoothedover location. A running median filter was then ap-plied along the time axis to smooth the data vertically.The final result is a smoothed version of the originaldata (Figure 28E). Median filters are better suited tosuch operations than averages. Median filters rejectlarge spurious events that could skew an average. Me-

dian filters also preserve slope changes and distinctlayers that are longer than half of the filter window.

Figure 28F shows the result of applying the Dixequation to the smoothed stacking velocities in Figure28E. The result adds appropriate detail to the stair stepfunction in Figure 28D and is easily reproduced byanyone starting with the same stacking-velocity picks.Anytime stacking-velocity picks are modified, how-ever, it is appropriate, if possible, to use the smoothedstacking-velocity function to apply normal moveout tothe original gather. If the seismic events are not rea-sonably flat, then further analysis is needed.

Before lateral smoothing is applied to stacking-ve-locity functions in regions of variable water depth, it isimportant to remove the influence of the water layer(recall Figure 10). Figure 29A shows three widely sepa-rated stacking-velocity functions from a three-dimen-sional survey. The water depth ranges from 480 to 919m. Lateral smoothing of these functions is inappropri-ate. Figure 29B shows the same data after the effect ofthe water column is removed. Now, it is now apparentthat the three functions follow the same initial trend butdeviate from the trend at different times. Such infor-mation suggests that a single velocity-time curve can beused to aid velocity interpretation throughout the area.

Measured stacking velocities can be datumed to themud line if the water velocity, Vw, and two-way trav-eltime to the water bottom, Twb, are known:

2 2V � (V Tstack new stack old old2� V T )/(T � T ) (12)w wb old wb

T � T � Tnew old wb

The previous equations cause stacking velocitiesmeasured from the surface to coalesce if the only dif-ference is a constant-velocity medium above the com-paction datum. They do not have the same effect if thevelocity intercept changes due to uplift and/or erosionor if multiple geologic units have the same depth ref-erence but different velocity gradients. Both time anddepth equations can be derived to extract compactioncurves where such effects are present. Changes in in-tercept between locations with the same velocity gra-dient can be used to infer the amount of erosion and/or uplift. (Magara, 1976; Poix, 1998) Such interpreta-tions are beyond the scope of this chapter other thanto suggest that it is best to work in the depth domainfor such applications. Although mathematically equiv-alent expressions for velocity vs. time can be written,compaction trends are physically connected to depthrather than traveltime. Thinking in time for simplesituations is advantageous because the initial seismicvelocities are in that space. In complicated cases,

208 B E L L

B

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Gradient (m/ms2):

Figure 27. Comparison of velocity displays. (A) Stacking velocity. (B) Gradient of stacking velocity. (C) Layer velocities representedby gradients between horizons. (D) Layer velocities constant between horizons. Vertical traveltimes at boundaries are the samein C and D. Vertical axes are vertical two-way traveltime.

however, the time behavior is not intuitive and can bemisleading.

The data analysis presented in this chapter wasdone using spreadsheets and generic statistical soft-ware. Commercial software packages are also availablethat are designed to apply such concepts. They com-

bine statistical analysis of stacking velocities, soniclogs, check shots, and horizon picks to produce a ve-locity field for time-to-depth conversion. They have theability to characterize the expected error in each dataset and to determine if changes in analytic coefficientsfit to the data represent reliable variations in velocity


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Figure 28. Effect of smoothing.(A) Raw stacking-velocity picks inred at a proposed well locationalong with the four nearestneighbor functions from a 0.5km grid. Note that interpretedhorizons do not correspond toslope breaks. (B) Resulting scat-ter in Dix interval velocities.(C) Picks decimated to majorslope breaks. (D) Dix intervalvelocities from decimated picks.These are more consistent thanthose in part B (curves withoutsymbols). (E) Result of linear in-terpolation followed by medianfilters in both time and position.The filtering effectively fits asmooth curve to the raw stack-ing-velocity picks. (F) The result-ing interval-velocity profilecompared with the interval ve-locities computed in step D(stair-step curves). TWT �vertical two-way traveltime.

210 B E L L

Figure 29. Removing effect ofwater depth on stacking velocityreveals common trend and aidsanalysis, particularly curve fittingin regions of similar gradient.(A) Three stacking-velocity func-tions with water depths of480 m (blue), 714 m (green),and 919 m (red). Surface loca-tions are separated by 10 km.(B) Same data after correctionfor the water layer. TWT � verti-cal two-way traveltime. SL � sealevel.

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or simply scatter in the measurements (See Al-Chalabi,1997). Such modules should be used to refine velocityestimations for pressure work beyond the traditionalreliance on a simple Dix inversion.

P O S T S T A C K I N V E R S I O N

The previous discussion concentrated on deriving for-mation velocities from differences in event moveout onoffset seismic gathers. Velocity information can also beextracted from reflection amplitudes. Figure 30 re-views the basics of poststack inversion of seismictraces. A stacked seismic trace can be modeled as theconvolution of a wavelet with a reflection coefficientseries (Sheriff, 1991). The zero-offset reflection coeffi-cient at each point in the series is given by the differ-ence in seismic impedance divided by the sum of theimpedances. Impedance is the product of velocity anddensity.

Figure 30A–F shows the forward modeling of a seis-mic trace. The goal of inversion is to reproduce theoriginal impedance log. Various techniques are avail-able to estimate the impedance, but they all have tocontend with the band-limited nature of the seismictrace. The fine detail in the impedance log is not re-solved at typical seismic frequencies and cannot be re-covered unambiguously from the seismic data.Low-frequency data is similarly absent from the seis-mic trace but can be recovered from the stacking ve-locities or added from well control.

Figure 30G shows the result of inverting the mod-eled seismic trace in Figure 30F. Where the missing

low-frequency information (Figure 30H) is added andadjustments are made between velocity and impe-dance, it is possible to reproduce much of the finestructure in the sonic log (Figure 30I). The invertedtrace is obviously a more detailed representation of thesonic log than the previous results shown in Figure 26.Poststack, or newer prestack, inversions are recom-mended for detailed lithology interpretation based onseismic velocity and are also suited for detailed pres-sure predictions. The critical information for pressurework, however, is contained in the missing low-fre-quency signal. All of the preceding concerns are stillpertinent and must be considered in the derivation andinterpretation of an inverted trace.

S U G G E S T E D P R O C E D U R E F O R V E L O C I T YA N A L Y S I S F O R P R E S S U R E P R E D I C T I O N

By way of conclusion, the following 11 steps condensethe previous material into a guideline for velocity anal-ysis using seismic data. Application to pore-pressureprediction by tying existing well control to a proposedwell location is assumed, but the recommendations arealso appropriate with slight modifications to regionalpressure studies without nearby well control.

1. Determine What Software Is Available for VelocityAnalysis and Collect the Appropriate Data

The software available for velocity picking, display,and analysis influences the way data is manipulated

Figure 30. Review of poststack inversion. (A) Velocity multiplied by (B) density gives (C) impedance. (D) The reflectioncoefficientseries is given by the difference in impedance at an interface divided by the sum of the impedances. Poststack inversion assumesthat a (F) stacked seismic trace is the convolution of the reflection coefficient series with (E) a known wavelet. (G) Inversion ofthe seismic trace gives a band-limited estimate of the velocity after removing the density term. (I) The final velocity estimaterequires addition of (H) a low-frequency trend obtained independently from well logs or stacking velocities. TWT � vertical two-way traveltime.

212 B E L L

and the quality of the final result. Seismic-processingsystems have basic routines for picking stacking veloc-ity based on normal moveout of CMP gathers. Sem-blance panels and constant-velocity stacks arecommon tools. Such tools are appropriate in good dataareas with simple velocity fields. The CMP traces areinput at select locations. Simple calculations such asDix conversion to interval velocity and interpolationare commonly included, but detailed analysis of thestacking velocities and calibration with well controlnormally require transfer of the basic data to a separatesoftware package.

Spreadsheets or generic statistical packages arecommonly adequate for further analysis of stacking ve-locities. Software designed for seismic time-to-depthconversion, however, may offer easier data input andsimpler access to robust tools for statistical analysisand comparisons with sonic logs, check shots, and ho-rizon times. Regardless of the software used, effort isrequired to collect and format the various data typesfor input. (Ideally, various modules will draw from thesame database and share data via common formats,but that is not always reality, particularly where mod-ules from different vendors are chosen for particularfeatures.)

More sophisticated processing packages offer to-mographic inversion, ray-trace modeling, and depthmigration tools to account for structural complexity.Such programs work with an entire prestack data setand contain advanced tools for estimating interval ve-locity based on matching nonhyperbolic moveout. In-terpreted horizons may be input into such systems orpicked as part of the analysis. Calibration of the veloc-ities with well control is still needed. Although suchtools are based on advanced theoretical techniques,data quality in difficult areas may still be insufficientto provide velocities without a relatively large degreeof uncertainty.

2. Select the Appropriate Seismic Lines and VelocityAnalysis Locations

Any nearby wells available for velocity and pressurecalibrations should be tied to the proposed drilling lo-cation via a series of velocity analysis locations alonglines having the same acquisition geometry and pro-cessing history. Spacings of 0.5–1.0 km are appropri-ate. Additional velocity locations should be selected tooptimize analysis near the wells, particularly if thetraps are small fault blocks less than a cable length inextent. If possible, line ties should avoid poor recordareas, such as salt diapirs, that prevent direct horizonties between the wells. For two-dimensional (2-D) data,dip lines are preferred to strike lines (2-D DMO and

migration cannot correct for out-of-plane dip effects).Velocity analysis at 2-D line crossings near the welllocations helps quantify the potential error in the finalvelocity result. Ideally, gathers from separate lines thathave the same midpoint location should sample thesame velocity field. Differences between velocities atsuch locations can be diagnostic of problems at otherlocations that might otherwise escape notice.

The detailed velocity analysis needed for pore-pres-sure prediction is also ideally suited for time-to-depthconversion. Additional analysis points may be usefulfor that purpose.

3. Determine Whether Prestack Seismic Data Are Available

If prestack seismic data are available, stacking veloci-ties should be repicked for the express purpose ofpressure prediction and time-to-depth conversion. Ifprestack data are not available, then previous contrac-tor stacking velocities should be critically examined tosee if they contain the desired level of information.

The contractor stacking velocities should have beenpicked after DMO. Avoid picks that have been inter-polated to a regular time interval because it is thendifficult to determine which values correspond to ac-tual moveout information. Processors sometimes makephantom picks deep in the section, particularly if thesignal-to-noise ratio is poor. Such picks will adverselyeffect the analysis if they are used to interpolate inter-vening values. Also avoid picks that have beensmoothed laterally, as is commonly done for poststackmigration.

4. If the Stacking Velocities Are to Be Repicked, Sort theData into Supergathers after Appropriate Preprocessing

Data at the chosen velocity analysis sites should bebinned to include all available offsets. Velocity analysisshould follow DMO and mild passes at removing mul-tiple reflections. Strong multiples that obscure primaryevents should be suppressed. If the multiple removalis too robust, however, slope breaks indicative of ve-locity reversals may be eliminated.

Use of data after prestack time migration is also ap-propriate, or superior, provided moveout has been re-stored to reconstituted gathers. If prestack time, ordepth migration, or tomographic techniques are to beused for the velocity analysis, then DMO should notbe applied.

5. Examine Sonic and Check Shot Information

Sonic and check shot information should be examinedto identify major velocity units and the expected im-


print of pressure on velocity. Sonic logs should becheck shot corrected and displayed in two-way trav-eltime for comparison with events picked on seismictime sections. Look for assumed compaction trends,offsets in the compaction trends, thick units with rela-tively constant velocity, velocity reversals associatedwith lithology, and velocity reversals associated withoverpressure. Look for consistent velocity units at dif-ferent well locations and units that change velocitywith location. Display well data as average velocity vs.time to mimic the behavior expected of stacking-veloc-ity picks. In particular, notice how changes in intervalvelocity correspond to changes in slope of the average-velocity curve.

6. Review Geologic Interpretations of Existing Seismic Data

Extrapolate the observations made at the wells to theproposed location based on the latest interpretation.The seismic interpreter, the seismic processor, the ve-locity analyst, and the pressure analyst (or at least asmany of those who are separate people) should discussexpectations prior to the detailed velocity work. Typ-ically, the interpreter concentrates only on a limitednumber of horizons of geologic interest. The velocityanalyst needs to be aware of geologic changes in theunits that most impact the stacking-velocity field.

7. Make a Preliminary Pass at Picking the StackingVelocities

Getting an overall feel for variations in both stackingvelocities and data quality, particularly if well controlis limited or absent, is useful. Commonly, the area ofexploration interest corresponds to a region of poordata quality. After the initial pass, it may be useful torethink the preprocessing and selection of analysis lo-cations prior to detailed work. Additional CMPs canbe added to the bin gather to improve the signal-to-noise ratio if needed. If event moveout is not hyper-bolic, depth migration should be considered.

8. Decide on Criteria for Picking Events

In good data areas, it is possible to minimize subse-quent analysis if stacking-velocity picks are limited toa set of predetermined horizons that include the majorvelocity interfaces identified from the well logs. Track-ing such events is easier if an interpreted seismic sec-tion is displayed concurrently with the semblancepanel and CMP gather. Note that horizon times maynot correspond to a maximum in the semblance. Thatis, it may be necessary to visually interpolate a pick tothe selected horizon. Interference between reflection

events in the semblance window may shift the maxi-mum. More importantly, the event in the CMP maynot necessarily be from the same subsurface point asthe horizon pick on the migrated data. A first passthrough the data should concentrate on flatteningevents in the gather. Subsequent passes should com-pare interval-velocity plots to either side of a givenanalysis location so that minor adjustments to thestacking velocity can be made to insure consistency inthe final interval-velocity field. The last step is an in-terpretation rather than a deterministic exercise andmay require several iterations around a loop tied towell control, particularly if the time separation be-tween events is small. Phantom picks may be neededto maintain horizon consistency near faults and in poordata areas.

An alternative approach limits stacking-velocitypicks to those events with unambiguous moveout butmakes as many such picks as is reasonable, withoutconcern for horizon consistency or the time differencebetween the points. The intent is to accumulate asmuch valid information as possible and to avoid mak-ing phantom picks that could later skew statisticalanalyses. Scarcity of picks in a given zone implies in-creased uncertainty in the final velocity interpretation.This approach initially avoids the problem of eventsthat come and go or that are hard to correlate acrossfaults. It is quicker than horizon-keyed picking andmore reproducible. The procedure is appropriate if thevelocity picking is to be done in a processing shop bysomeone other than the person doing the final velocityinterpretation or if a geologic interpretation of the datahas not been completed. Horizon consistency is im-posed after the picks are made rather than as part ofthe picking exercise.

9. Analyze Velocities for Geologically Consistent Trends

Data redundancy and statistical analysis can be usedin several ways to improve the accuracy of velocitypredictions. Data should be analyzed for verticaltrends and horizontal consistency within geologicallysimilar units, for example, between major unconfor-mities. The effort needed depends on the geologic set-ting and the quality of the seismic data. Workingdirectly with the stacking velocities is generally betterthan beginning with the derived interval velocities.

Plot numerous stacking-velocity curves on the samevelocity-time plot. Determine if a single compactioncurve is appropriate for the shallow section. In deepwater, first datum the stacking velocities to the seafloor. (Similar information can be obtained by plottingthe Dix interval velocity vs. the interval midpoint timerelative to the vertical two-way traveltime from the sea

214 B E L L

floor. The scatter in the Dix velocities, however, maynot be representative of the quality of the moveout in-formation if the events are close together in time.)

If there is a common trend in the shallow section,look for changes in the slope of the stacking-velocitytrends that represent velocity changes with depth. Ifpossible, correlate the slope change with a geologic ho-rizon or fault. Fit stacking-velocity curves to pointsabove the slope change. Check that curve coefficientsat any one location are consistent with the statistics offitting data from several locations at once. The stack-ing-velocity curve may then be converted to intervalvelocity either analytically or by applying the Dix for-mula at regularly sampled intervals along the curve.

If there is an areal variation in the stacking velocityin the shallow section, look for a plausible geologicexplanation. A subtle slope change in the stacking ve-locity may have been overlooked. Variations can alsoarise from uplift and erosion (in which case the normalcompaction trend has a different datum at each loca-tion) or from gradual changes in overpressure withdepth (in which case there is no well-defined normaltrend). Fitting a curve to several points within a unitat a given location, but not including points from ad-jacent locations, may be appropriate. Check that avail-able well control is consistent with the assumed cause,but be alert to changes that are not represented by lim-ited well sampling.

Apply similar analyses unit by unit for deeperevents. Ideally, the standard deviations for a fittedcurve should be within the uncertainty of the picks.Interpolated or smoothed stacking velocities should beused to apply normal moveout to the gathers at criticallocations. If the interpreted velocity does not flattendistinct hyperbolic events (at least at near offsets), thenthe results are suspect. If distinct events are absent, thatis, the data are poor, then a corresponding uncertaintyshould be placed on subsequent pressure predictions.

10. Calibrate Well with Well Control

At this stage, vertical two-way traveltimes of bound-aries between major velocity units should match rea-sonably well with the check shot–corrected sonic logsdisplayed in time, but the velocities are probably toohigh to produce an accurate time-depth conversion.The seismic interval velocities should be converted toaverage velocity and compared with average velocitiesfrom check shots. A time-dependent calibration shouldbe determined to correct the former to the latter. Ide-ally, a similar calibration should apply at all availablewells. If not, geologic insight can be applied to deter-mine a lateral variation in the calibration. The cali-brated average velocities should then be convertedback to interval velocity.

11. Apply Time-Depth Conversion

The final step is to convert the calibrated interval ve-locities from functions of time to functions of depth.Any remaining differences in interval velocity betweenthe seismic functions and the well logs should be fac-tored into the uncertainty in the pressure prediction ata proposed location.

A P P E N D I X

Definitions of some common velocity analysis terms (adaptedfrom Sheriff, 1991; Bates and Jackson, 1980):

common midpoint (CMP)—Having the same midpoint locationbetween the source and the geophone.

gather—A side-by-side display of seismic traces that have anacquisition coordinate in common; for example, a commonmidpoint.

geophone—An instrument that measures the passage of seismicenergy. The output record is called a trace.

moveout—A change in the traveltimes recorded by differentsource/geophone locations for the same seismic event. Nor-mal moveout is the two-way traveltime change that occursas the distance between the source and the geophone is var-ied assuming a flat reflector model. Dip moveout is the two-way traveltime change that occurs assuming a reflection froma dipping plane.

multiple reflection—A seismic pulse that has been reflectedmore than once. Commonly referred to as a multiple.

offset—The distance between a source and a geophone.primary reflection—A seismic pulse that has only been reflected

once. Commonly referred to as a primary.source—A device that releases a pulse of seismic energy.stack—n. A composite record made by adding together several

traces. v. Adding together several traces.trace—A single seismic record, normally amplitude vs. two-way

traveltime, that represents the subsurface seismic responsefor a real or hypothetical source/geophone geometry eitherbefore or after various processes are applied to improve theimage.

traveltime—The time it takes a seismic pulse to travel from onereference location to another.

two-way traveltime—The time it takes a seismic pulse to travelfrom its source to a reflector and back to a geophone.

vertical two-way traveltime—The two-way traveltime calcu-lated for a hypothetical seismic pulse that travels straightdown and up.

wavelet—A seismic pulse.


Alan Huffman provided encouragement to produce thischapter and useful suggestions during the editing. Bob Lank-ston edited the final draft. Glenn Bowers helped clarify con-cepts relating pressure and velocity. Rob Meek provided theexample in Figure 20. The other real-data examples come


from productive interactions with numerous Conoco col-leagues who have provided me with challenging opportu-nities and guidance in learning a trade that continues toevolve. Thanks to all.


Al-Chalabi, M., 1997, Parameter nonuniqueness in velocityversus depth functions: Geophysics, v. 62, p. 970–979.

Alkhalifah, T., and I. Tsvankin, 1995, Velocity analysis fortranversely isotropic media: Geophysics, v. 60, p. 1550–1566.

Bates, R. L., and J. Jackson, eds., 1987, Glossary of geology,3d edition: American Geological Institute, 788 p.

Bowers, G. L., 1995, Pore pressure estimation from velocitydata: accounting for overpressure mechanisms besidesundercompaction: Society of Petroleum Engineers Drill-ing and Completions, v. 4, no. 10, p. 89–95.

Deregowski, S. M., 1986, What is DMO?: First Break, v. 4, no.7, p. 7–24.

Eaton, B. A., 1975, The equation for geopressure predictionfrom well logs: 50th Annual Fall Meeting of the Societyof Petroleum Engineers, SPE paper 5544, unpaginated.

Heasler, H. P., and N. A. Kharitonova, 1996, Analysis of sonicwell logs applied to erosion estimates in the Bighorn ba-sin, Wyoming: AAPG Bulletin, v. 80, p. 630–646.

Hottmann, C. E., and R. K. Johnson, 1965, Estimation of for-mation pressures from log-derived shale properties: Jour-nal of Petroleum Technology, v. 17, p. 717–722.

Kaufman, H., 1953, Velocity functions in seismic prospecting:Geophysics, v. 18, p. 289–297.

Korvin, G., 1984, Shale compaction and statistical physics:Geophys. J. R. astr. Soc. v. 78, p. 35–50.

Kumar, N., 1979, Thickness of removed sedimentary rocks,paleopore pressure, and paleotemperature, southwesternpart of Western Canada basin: discussion: AAPG Bulletin,v. 63, p. 812–814.

Liner, C. L., 1999, Concepts of normal and dip moveout:Geophysics, v. 64, p. 1637–1647.

Lines, L. R., F. Rahimian, and K. R. Kelly, 1993, A model-based comparison of modern velocity analysis methods:The Leading Edge, v. 12, no. 7, p. 750–754.

Magara, K., 1976, Thickness of removed sedimentary rocks,paleopore pressure, and paleotemperature, southwesternpart of Western Canada basin: AAPG Bulletin, v. 60,p. 554–565.

Marsden, D., M. D. Bush, and D. S. Johng, 1995, Analytic ve-locity functions: The Leading Edge, v. 14, no. 7, p. 775–782.

Neidell, N. S., and N. Berry, 1989, Documenting the sand/shale crossover: Geophysics, v. 54, p. 1430–1434.

Poix, O., 1998, Sonic anomalies, a means to quantifying ov-erpressures, in Mitchell and Grauls, eds., Overpressuresin petroleum exploration: Bulletin Centre Recherche ElfExploration and Production, Memoir 22, p. 207–211.

Reilly, J. M., 1993, Integration of well and seismic data for3D velocity model building: First Break, v. 11, no. 6,p. 247–260.

Sheriff, R. E., 1991, Encyclopedic dictionary of explorationgeophysics, 3d edition: Society of Exploration Geophysics,384 p.

Whitmore, N. D., and J. D. Garing, 1993, Interval velocityestimation using iterative prestack depth migration in theconstant angle domain: The Leading Edge, v. 12, no. 7,p. 757–762.

217

19The Future of Pressure PredictionUsing Geophysical Methods

Alan R. HuffmanConoco Inc., Houston, Texas

A B S T R A C T

The technology of pore-pressure prediction has advanced significantly in recent years. In the future,new methods for pore-pressure prediction will routinely use shear-wave data gathered using multi-component seismic technology. Overburden and fracture gradient will be predicted in three dimensionsusing gravity and magnetic inversion technology. Seismic inversion, both prestack and poststack, willprovide refined estimates of the velocity field in the subsurface, and new seismic-processing methodswill allow velocity anisotropy to be predicted accurately so that it can be used to predict both porepressure and real triaxial stress fields in the earth. These new methods will be used to make advancesin the prediction of pressures in nonclastic rocks and to extract information that can be used to accuratelypredict structural hyperpressuring in reservoirs to assist in drilling difficult wells. Pressure predictionwill become a standard tool in basin-scale and prospect-scale evaluation of the hydrocarbon systemand will be used to guide the exploration process. In the production environment, pore-pressure pre-diction will be used routinely to provide a three-dimensional model for the pressure regime in thesubsurface that will be critical to effective reservoir simulation and reservoir management.

Despite all these advances, however, pore-pressure prediction will still be limited by the quality ofseismic data acquisition and processing technology that is used to prepare the data and by the structuralcomplexity of the subsurface that is to be imaged. Predictions will continue to be limited by the lack ofpredrill information about the state of compaction in the subsurface that is critical to a robust pressureprediction. Lastly, prediction accuracy will continue to be limited by the presence of secondary pressurein situations where velocity reversals are difficult to detect on seismic data.


Predrill pressure prediction using geophysical data andmethods has historically been done using very simplemodels and overly simplistic estimates of the Earth’svelocity field. The methods commonly incorporate a lo-cally calibrated set of curves for pressure that containedimbedded assumptions about the cause of pressure inthe geologic section sampled by the control wells. Theadvent of the effective-stress concept and the pressure-

Huffman, Alan R., 2002, The Future of Pressure Prediction Using GeophysicalMethods, in A. R. Huffman and G. L. Bowers, eds., Pressure regimes insedimentary basins and their prediction: AAPG Memoir 76, p. 217–233.

prediction and the pressure-predictionmethods that de-veloped from that concept led to a much neededinclusion of fundamental physics into the art of pressureprediction. The use of effective-stress methods has be-come the standard for pressure prediction with manyvariants including the Eaton method (Eaton, 1975), theBowers method (Bowers, 1994), and the Sperry Sunmethod (Holbrook and Hauck, 1987), to name a few.The range of software available for pressure predictionhas grown significantly in recent years, along with thesophistication of the parameters used. Still, weaknessesremain because of (1) the limitations of the seismic ve-locities themselves, (2) the lack of understanding of thebasic causes of pressure, and (3) the effects of pressure

218 H U F F M A N

on physical properties, including velocity, density, andporosity, of the rocks. Despite the level of sophisticationthat is used in pressure prediction today, most practi-tioners are concerned primarily with predrill predictionand overlook the vast significance of pressure variationsat the basin and prospect scale. This chapter discussessome of these issues and tries to put them into context.

E F F E C T I V E - S T R E S S A N D L O A D I N G - P A T HD E P E N D E N C Y O F P R E S S U R E

The functional relationship between pore pressure andvelocity has been generally recognized for many years.The level of understanding about the relationships be-tween various physical properties and pore pressure,however, varies widely. Many people still are unawarethat there is more than one cause of pressure and thatpresent-day pressure regimes are the result of the com-plete loading path that a rock has undergone since itsdeposition.The causes of abnormal pressure can be divided into

two types. Undercompaction, also known as compac-tion disequilibrium, is related to the compaction pro-cess itself and occurs where the rates of deposition andburial are sufficiently great relative to the vertical per-meability of the sediments. Where large loading ratesare applied to rocks such as shales with relatively low-vertical permeability, the confined fluids in the rockmass cannot escape abruptly enough to maintain a hy-drostatic fluid pressure gradient. This type of abnor-mal pressure is observed in many young Tertiarybasins worldwide and is commonly recognized in seis-mic-velocity data by the slow decrease in the velocitygradient with depth.The other class of abnormal pressure mechanisms is

not associatedwith the compaction process, and occurswhere the pressure of the fluid in the rock mass is al-lowed to increase relative to hydrostatic pressurethrough one of several mechanisms (Plumley, 1980).Thesemechanisms include (1) aquathermal fluid expan-sion (Magara, 1975), (2) hydrocarbon sourcematurationand fluid expulsion (Spencer, 1987), (3) clay diagenesis(Bruce, 1984), (4) fluid pumping from deeper pressuredintervals during fluid migration, and (5) decreases inoverburden caused by tectonic activity. Although eachone of these mechanisms are distinctly different in theirbehavior, they all produce a similar effect in pressuredrocks in that they work to cause a decrease in the effec-tive stress on the formation for a given porosity. In par-ticular, clay diagenesis, aquathermal expansion, andsource maturation occur at elevated temperatures sothat cold sediments should not be affected by thesemechanisms. In contrast, fluid pumping and overbur-

den decreases can occur in any sediments. Where sec-ondary pressure occurs, it is commonly manifestedthrough a reversal in the velocity trend with depthwithout an increase in porosity. Although not all veloc-ity reversals are caused by secondary pressure, it is im-portant to remember that reversals caused by secondarypressure contain some of the most severe pressure in-creases. Thus, it is prudent to treat velocity reversals asif they are caused by secondary pressure unless there isclear evidence from well data that the velocity reversalsare due to undercompaction, lithology changes, or otherpossible causes. Also, velocity reversals, if not recog-nized as being due to secondary pressure, overestimateporosity if it is assumed that the rocks are simply un-dercompacted.To understand the relationships between effective

stress, porosity, and velocity, consider the concept ofcritical porosity that was first defined by Marion et al.(1992). Figure 1 shows the relationship between poros-ity and velocity for clastic materials from laboratory ex-periments. The boundary between Wood’s equationbehavior and the loading-bearing behavior occurs at po-rosities of 38 to 50% and is defined as the critical po-rosity. The trend of velocity with porosity shows twodominant trends that follow (1) Wood’s equation(Wood, 1941) at porosities above the critical porosityand (2) a modified Voigt-Reuss behavior at porositiesbelow the critical porosity (Nar et al., 1991). TheWood’sequation behavior is characteristic of slurries, and themodified Voigt-Reuss behavior is characteristic offrame-bearing solids, including clastic rocks undersignificant effective-stress conditions. Figure 1 showshow velocity increases as porosity decreases. This trendcorrelates with the degree of compaction that the ma-terial has undergone and is part of the reason that somepressure methods use porosity as a proxy in determin-ing the compaction state of a material.We must also consider the relationship between ve-

locity and effective stress that defines the normal com-paction trend. Tosaya (1982) performed experiments onclastic rocks to demonstrate the critical factor of the ef-fective stress. Figure 2 shows that the velocity of thematerial follows the effective stress nearly perfectly re-gardless of the total overburden stress that is applied.This experimental result is an excellent demonstrationthat Terzhagi’s effective-stress relationship is valid andcan be correlated with velocity changes in clastic ma-terials.One way to think about the two causes of abnormal

pressure is to recognize that the velocity of any rockin the subsurface is a direct function of its depositionaland burial history. Figure 3 shows a hypotheticalloading path for a rock in a clastic basin in porosity–velocity–effective-stress space. This diagram is a three-

The Future of Pressure Prediction Using Geophysical Methods 219

Figure 1. Velocity-porosity rela-tionships in clastic sedimentarymaterials. Note the change inbehavior caused by the inceptionof load-bearing capability at thecritical porosity point (about40% porosity). At porosities lessthan critical porosity, the mate-rial behaves like a Voigt-Reussmaterial. Also note the shear-wave behavior and how abruptlyit changes from zero to nonzeroas you pass the critical porosity.Figure modified from Marion etal. (1992).

dimensional composite of Figures 1 and 2 thatdemonstrates the interplay between velocity, porosity,and effective stress. The loading path starts at an ef-fective stress of zero, and the velocity increases andporosity decreases until the material changes overfrom a Wood’s equation material to a frame-bearingclastic rock that can support an effective stress on thegrains. The Wood’s equation part of the loading path(blue curve) occurs as thematerial is initially depositedand compacted near the surface. Once the critical po-rosity is reached, the material follows the primarycompaction curve (black curve), achieving eithera compacted or undercompacted state. If allowed tocompact normally with fluid draining out of the porespaces, a rock continues up the normal loading path,velocity increases, and porosity decreases. Both ofthese properties are dependent on the effective stresson the grains that are bearing the external load. If atsome point the fluid is prevented from escaping, therate of ascent up the normal pressure curve decreasesso that the rock has a lower velocity and effective stress

than would be expected at normal pressure conditionsat a given depth of burial. This condition is known asundercompaction or compaction disequilibrium. Thekey to understanding undercompaction is to recognizethat a rock under these conditions still remains on thenormal compaction trend, only it is not as compactedas you would expect it to be at that depth of burialunder normal hydrostatic pressure.Unlike undercompaction, a rock subjected to sec-

ondary pressure cannot stay on the normal compactioncurve. Where fluid is pumped into a rock or expandswithin the pore spaces in the rock, the compaction pro-cess is arrested, and the rock begins to display a formof hysteresis behavior in velocity–effective-stress space.Where this occurs, the porosity essentially does notchange except for some minor elastic rebound (Moosand Zwart, 1998), and the velocity behavior is strictlycontrolled by the contact area and the grain-to-graincontact stresses in the rock. Because there is essentiallyno porosity change, the net effect is to flatten out thevelocity–effective-stress trend and produce an unload-

220 H U F F M A N

Figure 2. Experimental resultsfrom Tosaya (1982) demonstrat-ing the relationship between ef-fective stress and velocity in agranular material of approxi-mately constant porosity. Theschematic equation below thediagrams represents the ob-served stresses that are appliedto the grains where total stress isapplied as an external force tothe rock volume, and pore pres-sure counteracts the total stressresulting in a net grain load thatis equal to the effective stress.

=-

Pore Pressure Effective StressTotal Stress

Figure 3. A three-dimensionaldiagram showing the loadinghistory of a hypothetical shalematerial in terms of effectivestress, velocity, and porosity. Theactual three-dimensional normalcompaction trend and unloadinglimbs are projected into the ve-locity–effective stress plane tothe left, which is the same dis-play shown in Figure 4B.

ing trend that is different from the primary compactiontrend. The unloading curve must start from the veloc-ity–porosity–effective stress point on the primary com-paction curve where the unloading begins (Bowers,1994). This is why unloading (red curves on Figure 3)always starts from a porosity–velocity–effective-stresspoint on the primary compaction curve. Note that the

unloading paths occur essentially in the velocity–effec-tive-stress plane as the porosity decrease associatedwith compaction is arrested during unloading andverylittle elastic rebound (less than 1 porosity unit) occursduring the unloading process. As the effective stressdecreases because of higher fluid pressures at fixedoverburden, the velocity decreases in direct relation to


the stress change. Once a rock is on an unloading path,the rock does not change porosity unless other phenom-ena such as diagenesis or cementation are occurring con-currently with the pressure changes. For the rock tobegin compacting again, the secondary pressures mustfirst bleed off, or the overburden must increase suffi-cientlybyadditional sediment loadingtocounterbalancethe secondaryfluidpressures thatwereaddedwithintherockmass. In either case, the rock responds to the changein effective stress andmoves backup theunloadingpathuntil it contacts the normal compaction curve again.Once the effective stress has exceeded the value whereunloading began, the rock can begin to compact again.If the stress never reaches this level, the rock remains onthe unloading path indefinitely. Important to recognizein this context is that thenormal compaction curve is alsothemaximumcompaction,maximumvelocity, andmin-imum porosity that a material can achieve at normalpressure for a given effective stress.To properly predict pressure ahead of the bit, it is

essential to know not only the normal compactiontrend, but also the slope of the secondary pressurecurve and the maximum stress-velocity state that wasachieved before unloading began. Important to rec-ognize is that the presence of two possible pressuremechanisms and a range of possible maximum veloc-ities for unloading leads to a range of possible pre-dicted pressures according to which mechanism isassumed to be at work and where unloading began.For any velocity (Figure 4), there are a range of possiblepressures that are a function of the normal trend, themaximum velocity attained by the rock, and the un-loading curve slope. In practical terms, for any ob-served velocity value, the minimum pressure case isrepresented by the effective stress at the equivalentdepth of burial on the normal trend curve, and themaximum pressure case is represented by the greatestreasonable maximum velocity on the normal trend andthe slope of the unloading curve from that point backto the observed velocity value. Thus, it is imperativethat the pressure-prediction expert be aware of bothcauses of pressure and also recognize when and howto apply unloading corrections to the velocity data.Figure 4A is the velocity-depth plot that is used to pre-dict pressure, and Figure 4B is the velocity–effective-stress plot that is used to show the normal compactiontrend and unloading behavior. Point D in Figure 4Arepresents the velocity in the zone being determinedin the analysis and correlates with the velocity D inFigure 4B. Point A represents the maximum loadingcase where the material has been completely unloadedfrom the normal compaction state. Point B representsthe case where the velocity zone just above the un-loaded interval represents the maximum compaction

state. Point C represents the equivalent-depth pointabove the unloaded zone (point D) that would have tobe used if the material displayed no unloading char-acteristics in the zone.

L I M I T A T I O N S O N V E L O C I T Y A N A L Y S I SW I T H D I F F E R E N T M E T H O D S

Velocity analysis has been used for many years to pre-dict pressures prior to drilling. The level of under-standing of the various velocity tools and theirapplicability to pressure prediction, however, is not al-ways adequate to achieve the best results. A standardapproach for pressure prediction is to use conventionalstacking-velocity analysis and convert the stacking ve-locities to Dix equation–corrected interval velocities(Bell, 2002). Beyond this simple approach to velocityanalysis lies a range of more sophisticated techniquesincluding horizon-keyed velocity analysis, refractionand reflection tomography, and prestack inversion(Bell, 2002). These techniques can increase the accuracyof the velocity analysis but require additional analysisand processing, commonly at higher cost. The questionis which technique is appropriate for a given situation.Also important to recognize is that geologic and inter-preter input to the velocity analysis is essential to agood pressure prediction.

Preprocessing of Seismic Data for Pressure Prediction

As the complexity of the subsurface increases, the needfor increased effort in velocity analysis becomes im-portant. The simplified Dix model becomes progres-sively more problematic in the presence of steeplydipping and complexly structured geology. In addi-tion, velocity analysis becomes difficult where multi-ple reflections of the same seismic pulse are severeenough to overwhelm first arrivals (primaries), andwhere anisotropy is present. Where large lateral andvertical velocity gradients and significant raypath dis-tortion are encountered near salt bodies, volcanics, orother diapiric and nonstratigraphic features, it may be-come difficult to get any good velocity information.Where structural complexity increases, it is also nec-

essary to increase the amount of effort that goes intopreparing the data for velocity analysis. Prestack timemigration, demultiple, and other techniques are com-monly required to clean up the seismic data so that itis suitable for analysis. These techniques improve thequality of the seismic data in most cases, but they alsodrive up the cost of the process significantly. The ad-vanced methods for seismic imaging can improve thequality of the seismic data to facilitate pressure pre-

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Figure 4. An example of the range of possible maximum compaction stresses that can result in the same velocity being tiedto different effective stresses. (A) Velocity vs. depth; (B) effective stress vs. velocity.

diction. If applied carelessly or improperly, however,these methods can remove seismic events that are criti-cal to a robust pressure prediction. Consider the casein Figure 4A and suppose that a velocity reversal oc-curs in the seismic data. If this seismic line has severemultiple reflection problems, a routine preprocessingstream might include a radon or frequency-wavenum-ber (f-k) demultiple step that removes or suppressesthe multiple. If that multiple has the same or fastervelocity as point D in Figure 4A, then the demultiplestep removes both the multiple and the primary re-flection event that allows the velocity in interval D tobe picked properly. If this happens, the velocity ana-lyst is not able to pick this event because it no longerexists in the data. In this case, the analyst would mostlikely make no velocity pick or would pick a fastervelocity that will underpredict the actual pressure inthe formation. All seismic data used for pressure pre-diction should be processed and quality controlled bysomeone with expertise in seismic processing specifi-cally for pressure prediction. Standard processingstreams may be poorly suited for the purpose, and ad-vanced methods must also be used with caution.The vertical resolution and accuracy of velocity

analysis varies with the technique applied. For exam-ple, a sonic log has a resolution of around 1 ft (0.3 m),but seismic-velocity analysis at great depths may havea resolution of greater than 500 ft (152.4 m). Each co-herent event on a seismic section provides an indepen-

dent estimate of the average velocity where examinedprestack and corrected for various geometric effects.Analysis of all reliable events helps to constrain thefinal velocity interpretation. Care must be exercised,however, where applying the Dix equation to derivean interval velocity between closely spaced events.Small timing errors inherent in picking each event cancause significant uncertainty in the interval velocitywhere the total time separation is small. The conven-tional approach to this problem is to use the Dix equa-tion only for events greater than about 200 ms apart.A more robust approach involves careful smoothing ofthe stacking-velocity picks before the interval-velocitycalculation is performed.

Poststack Inversion

Poststack inversion is one alternative to conventionalvelocity analysis that provides higher resolution by in-verting for impedance from the reflection strength(Bell, 2002). Poststack inversion allows the analyst toseparate the seismic wavelet from the reflection seriesrepresented by the geologic formations and results inan estimate of residual impedance for each layer. Post-stack inversion can be applied using only the stackedseismic data or can be calibrated with well logs, checkshot surveys, VSP data, and seismic-velocity data.Where calibrated properly, the analysis can be used togenerate an estimate of the absolute impedance or its


components of velocity and density. This requires agood set of density-velocity relationships for the li-thologies encountered in the wells so that these twocomponents can be separated effectively. This exerciseis not trivial, however, because the poststack-inversiontechnique ignores the fact that offset-dependent be-havior (amplitude vs. offset) is buried in the stackedresponse and can cause significant perturbation of theresults. One way to overcome this limitation and alsoboost resolution of the results at the same time is touse only the near-offset traces for the analysis. This isa good method to use because it provides higher res-olution results due to the removal of far-offset datathat are degraded by normal moveout (NMO) stretch.Near-stack inversion also gives the most robust cali-bration to well logs that are essentially measuring thesame vertical-incident information. Figure 5 shows anexample of the difference in resolution between con-ventional velocity analysis and poststack inversion.One of the challenges of poststack inversion is that

the method does not normally include a low-frequencytrend for velocity, but instead predicts variations in re-sidual impedance that must be separated into velocityand density trends using well log data. Incorporating alow-frequency velocity trend in the analysis is possible,but it is commonly observed that the low-frequencytrend, where combined with the residual impedanceson the seismic data, does not match the predicted im-pedances from thewell logs. Thus, the calibration of thismethod still remains problematic in many cases.

P R E S T A C K I N V E R S I O N I N P R E S S U R EP R E D I C T I O N

The techniques employed to get reliable velocity datafor pressure prediction will undergo a revolution inthe next 10 years. The availability of faster computersat lower cost will allow the use of prestack inversionfor pressure prediction. Prestack inversion of seismicdata will take us to the next level in accuracy and mayallow us to predict pressure at a scale that was notachievable in the past. Prestack inversion can estimatethe P-wave velocity, shear-wave velocity, and densitysimultaneously by using the near-offset reflectivityand amplitude vs. offset behavior of each reflection inthe subsurface. This allows the user to estimate theoverburden and effective stress from the same data set.The resolution limits for prestack inversion are ap-proximately at the tuning thickness of the individualformations, so pressure data can be generated for lay-ers on the order of 100–200 ft (30.5–61 m) at moderatedepths in clastic basins.The biggest drawback to prestack inversion at this

time other than cost is its extreme sensitivity to data

quality. A robust inversion requires data that are rela-tively clean, uncontaminated by multiples and noise,and in areas of little structural complexity. In addition,the resolution and accuracy of prestack inversion isonly as good as the quality of the reflection events inthe data. If there are pressure cells that do not havereflections associated with them, no velocity or reflec-tion-amplitude technique including inversion willidentify those zones.The use of calibrated prestack inversion, especially

where multicomponent (shear and compressional ve-locity) data are available, allows the estimation of den-sity and velocity simultaneously along a line. Thisallows predictions to be made that consider the lateralvariations in density that accompany changes in pres-sure. At present, most methods of pressure predictionassume that the overburden from the control well rep-resents overburden globally, which is false in general.Prestack inversion helps to remedy this problem bypredicting the density from the seismic data and allow-ing the pressure interpreter to make judgements aboutthe density using the seismic and well data and his orher own intuition. Figure 6 shows a result from a pre-stack inversion of the same seismic line shown in Fig-ure 5. Note that the analysis results in a P-wave sectionand a shear-wave section that can each be used to pre-dict pressure in the presence of the proper calibration.Prestack inversion allows isolation of velocities for

individual sand packages so that the user can deter-mine where disequilibrium may exist between thesand-bearing formations and massive shales and iso-late the velocity and density effect of hydrocarbon-bearing reservoirs on the velocity field around them.At present, most methods lump these effects intothicker stratigraphic intervals that have a single veloc-ity attached to them and hide the effect. These errorscan cause predictions to overestimate or underestimatepressures significantly, which leads to less effectivewell planning. This problem is shown in Figure 7.In the future, prestack inversion may allow the user

to compensate for the effects of anisotropy using theinitial velocity analysis and well data as constraints. Atpresent, anisotropy is ignored in nearly all pressureanalysis. In the future, prestack inversion will be ableto separate the anisotropy effect from the isotropicZoeppritz reflectivity effects (Sheriff, 1991) at the in-terface and allow a more robust estimate of the verticalvelocity and density field.In essence, prestack inversion with low-frequency

information is the ultimate tool to allow the user toget the most out of the prestack seismic data for pres-sure prediction and other purposes. The greatest lim-itations to this powerful technique at present are thecost of application, the data quality limitations men-tioned previously, and the continuing problem with

224 H U F F M A N

Figure 5. Comparison of conven-tional horizon-keyed velocityanalysis (A) with seismic tracesshown and poststack inversion(B). Note the higher resolutionof the inversion results.

the low-frequency component. As computers improvein price performance, and we learn to deal more effec-tively with complex imaging problems, the use of pre-stack inversion for pressure prediction should increasedramatically.

P R E S S U R E P R E D I C T I O N U S I N GM U L T I C O M P O N E N T D A T A

Recent developments in multicomponent seismic ac-quisition and processing suggest that this new tech-nology will be increasing dramatically in use in the

future. This growth in multicomponent technologywillcreate an opportunity to use mode-converted and directshear-wave velocities for pressure prediction. Shear ve-locities provide another type of velocity data for pres-sure prediction that may turn out to be particularlyvaluable for shallow, grossly undercompacted sedi-ments (Huffman and Castagna, 2000) and for zones ofsevere unloading where effective stress drops back tonear zero. The variation of the shear-wave velocity withchanges at low effective stresses has been demonstratedto be much greater than P-wave velocity variation,which may provide additional data and greater sensi-tivity for pressure prediction. Shear-wave data will also


Figure 6. Prestack inversion resultsfor the same seismic line shown inFigure 5. Note the differences inthe (A) P-wave and (B) Poisson’sratio results from the inversion.

Figure 7. Comparison of velocitydata from stacking-velocity analy-sis (dashed line on part A) andprestack inversion with the low-frequency component fromstacking velocities (solid line) ina hydrocarbon-bearing zone withinterbedded shales. Note thetemporal averaging in the stack-ing-velocity analysis that pre-vents the gas-bearing zones frombeing isolated in the pressureanalysis on part B.

226 H U F F M A N

be valuable in areas where gas chimneys distort thecompressional-wave velocity data and prevent robustvelocity analysis. Shear-wave data also provides asecond measurement of pore pressure in cases wherehydrocarbons in a reservoir distort the compressional-wave velocity field. The fact that the shear waves aremuch less affected by fluid variations (Gregory, 1977)permits pressure prediction to be performed withoutworrying about how to correct for Gassmann effects inthe reservoir as must be done for compressional-wavedata.

O V E R B U R D E N P R E D I C T I O N U S I N GG R A V I T Y D A T A

One of the greatest limitations on robust pore-pressureprediction is the fact that the density data used to con-strain the overburden and fracture gradient are com-monly from one to two wells in the best circumstances.In some cases, little to no density data exist, and re-gional curves have to be used to predict overburdenand fracture gradient. In all these cases, the pressureanalysis relies on one-dimensional data to solve athree-dimensional problem.One method for determining densities in the sub-

surface that has recently come into its own is gravityinversion. Recent developments in this area pioneeredby Conoco (Jorgensen and Kisabeth, 2000) have re-vealed that gravity inversion using conventional grav-ity data and full tensor gradiometry data can be usedto constrain the density field in three dimensions quiteaccurately for pressure prediction. Although themethod was initially developed for determining thebase of anomalous bodies such as salt and volcanics, itcan also solve for lateral variations in sediment densitydue to variations in the compaction state. This methodalso allows the analyst to overcome one of the weak-nesses of the velocity-based prediction methods in thatit can see some of the density variations due to changesin pressure regime that can not be distinguished withvelocity data alone because of the nonuniqueness ofvelocity–effective-stress relationships.Figure 8 shows amodel example of how critical grav-

ity inversion results can be to a robust pressure analysisin areas where subsalt wells are to be drilled. The finaldensity model from the inversion including the pre-dicted anomalous salt bodies is integrated to get anoverburden estimate. Note how the overburden stressdecreases under the salt due to the effect of the lighterdensities in the anomalous body. In many cases, a welldrilled in the basin adjacent to the salt body might beused to predict the overburden gradient in planning for

a subsalt well. If that approach is taken and the analystdoes not correct for the density effect of the salt body,the well will be grossly overbalanced where it drills outof the salt. The gravity inversion result is especiallysuited to this problem because it allows a two-dimen-sional or three-dimensional prediction of the densityand overburden that includes the variations due to theanomalous body and any variations in sediment densitywhere no anomalous nonclastic bodies exist. In somecases, the sediments below the salt are observed to beanomalous relative to the regional density trend be-cause of a local or regional salt seal. The method solvesthis problem by allowing the salt to be constrained fromthe inversion and seismic data alongwith the sedimentseverywhere but below the salt, so that variations relatedto pressure can be predicted from a second iteration ofthe gravity inversion. The gravity inversion results arealso totally independent of the seismic-velocity infor-mation and thus provide additional data that can notbe obtained by other means.

P R E S S U R E P R E D I C T I O N I N B A S I NA N A L Y S I S

Today, only a handful of companies are using seismic-based pressure prediction as an end constraint in basinanalysis andmodeling. Pressure prediction at the basinscale can be very powerful in (1) determining wheresource rocks are actively maturing, (2) determiningwhere large-scale fluid migration is occurring in a ba-sin, (3) predicting the behavior of large regional faultsand structures, (4) identifying the presence of second-ary-pressured areas, (5) constraining the porositymodel for the basin, and (6) evaluating the integrity ofvertical seals in the basin. Such a case is shown in Fig-ure 9.Note that large-scale exploration already makes

routine use of seismic-velocity data for time-depthconversion, but very few people are using these datafor determining pressure and using this as an end con-straint on basin models. This is truly ironic as it is oneof the basinwide parameters that we can measure di-rectly from seismic data.Also, it should be possible to work the inverse prob-

lem and go backward from current-day conditions tothe start of basin formation using the pressure pre-diction as the starting point. This approach would besimilar to the current technology for palinspastic re-construction used routinely by structural geologistsbut would require the added complexity of reverse en-gineering the basin loading history and compactionprocesses.


Figure 8. A two-dimensionalgravity model for salt bodies im-bedded in sediment showing (A)the calculated gravity and mag-netic fields over anomalous saltbodies, (B) the final densitymodel with the salt bodies, and(C) the overburden stress esti-mated by integrating the densityfunction at each vertical locationin the model.

P R E S S U R E P R E D I C T I O N A T T H EP R O S P E C T S C A L E

Like basin analysis, only a handful of companies todayare using pressure prediction for prospect analysis.Considering the importance of pressure in establishingthe fluid migration pathways and reservoir properties,it is quite surprising that this technique has not beenmore heavily used for this purpose. At the prospectscale, pressure prediction as currently applied can beused to (1) constrain the porosity and pressure regimessurrounding accumulations of hydrocarbons, (2) de-termine the sealing characteristics of faults, (3) evalu-

ate vertical and lateral pressure seal properties, (4)evaluate the risk of structural effects on pressure inreservoirs, and (5) determine the production drivemechanism for a given reservoir based on its locationrelative to pressure. If prestack inversion is used at theprospect scale in pressure prediction, it may be possi-ble to (1) isolate the pressure behavior of specific res-ervoirs and determine the centroid effect (Heppardand Traugott, 1998) in them, (2) identify cases wherethe sands are not in pressure equilibrium with the en-casing shales, and (3) isolate and understand localizedeffects such as cementation, nonclastic rock units, andother factors on pressure prediction.

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Figure 9. Example of (A) an in-terpreted seismic line and (B)the resulting horizon-keyed pres-sure prediction showing the seal-ing behavior of faults andpressure compartmentalization.Note the two faults on the farleft that show fault seal failure inthe deep section (red color) andcompare this to the major faultin the center that acts as a pres-sure barrier between the red andyellow pressure isobars. The faulton the far right also appears tobe a conduit for pressure pump-ing from deep in the section.

At the prospect scale, we are not currently using theresults of pressure prediction in coordination with hy-drogeologic modeling to predict fluid flow, migrationpathways, and rates of hydrocarbon charging. Amerger of hydrogeologic methods with pressure pre-diction could dramatically improve our ability to un-derstand the hydrocarbon system at both the basin andprospect scale. Such an understanding would un-doubtedly improve our exploration results by elimi-nating areas where migration and hydrocarboncharging are not viable. The combination of robust ef-fective-stress methods, prestack inversion, and ad-vanced hydrogeologic modeling may allow pressureprediction to become a routine part of the geophysicalprospect evaluation process. Proper integration ofpressure analysis with other geophysical tools andstratigraphic and structural analysis at the prospectscale should improve the industry’s ability to success-fully identify and produce economic accumulations ofhydrocarbons in the future.

U N A N S W E R E D I S S U E S

Many issues still need to be addressed in pressure pre-diction. These issues have been viewed in the past assecondary concerns that were not critical to the anal-

ysis but are now becoming primary issues as we refineour methods for pressure prediction.

Pressure Prediction in Nonclastic Rocks

How do we predict pressure in nonclastic rocks aheadof the drill bit? Presently, the methods employed in theindustry work fairly well for clastic rocks because thenormal compaction trend has a sufficiently large gra-dient in velocity–effective-stress space to allow a robustcalibration. Other rocks such as carbonates, however,are not as forgiving as clastic rocks. Carbonates in par-ticular have a very flat velocity–effective-stress gradientso that there is very little velocity sensitivity to changesin pressure in these rocks (Figure 10). Furthermore, thehysteresis effect related to unloading in carbonates pro-duces virtually no velocity change, which allows car-bonates to sustain severe secondary pressure conditionswith very little velocity change. At present, most work-ers use the encasing shales to infer the pressures in thecarbonates, but this has proven to be very dangerous inmany cases.

Pressure Prediction in the Presence of Velocity Anisotropy

Another issue is the effect of anisotropy on the mea-sured velocity field. It was noted previously in this


Figure 10. Velocity vs. effective stress plot showing normalcompaction and unloading curves for clastic and carbonatematerials showing the relative differences in their sensitivity.Note the large difference between points A and B for clasticrocks compared to the difference between A� and B� forcarbonates. Also note the larger contrast between the un-loading paths in clastic rocks vs. carbonates.

chapter that there are anisotropic migration and veloc-ity analysis programs available to handle this issue. Inthe real world of clastic basins, anisotropy most com-monly occurs as transverse isotropy (TI) but can some-times occur as full anisotropy where the velocity variesin all three dimensions. Full anisotropy can be fractureinduced, stress induced, and lithologically induced,singly or in combination. Distinguishing which type isoperating can be important for pressure and fracture-gradient prediction. Once anisotropy is identified, theissue becomes one of determining the cause and thenhow to correct for it or use it properly in pressurework. In most of the young Tertiary basins that pres-sure prediction is applied to, the cause of anisotropyis commonly a mixture of thin-bed anisotropy, intrin-sic shale anisotropy, and other forms.Unfortunately, nearly all of the algorithms available

today are designed to either ignore anisotropy or han-dle one form of anisotropy, TI, which is the case wherethe velocity field varies between the vertical and hor-izontal but does not vary with azimuth. Transverseisotropy requires two additional parameters to accu-rately produce vertical velocity as a function of depthfrom seismic moveout. Estimates of one parameter canbe made from the seismic data itself and used to im-prove the seismic image. The moveout, however, is in-sensitive to the vertical velocity. Well data are neededto produce an accurate depth prediction. Transverse

isotropy is one of several complications that can behandled if well data are available for calibration. With-out such data, the ability of the seismic data to discernthe anisotropy in the subsurface is limited (Bell, 2002).To make matters worse, the velocity effects related toanisotropy are commonly superimposed with other ef-fects such as dip or cable feathering that makes theanalysis even more difficult.Velocity anisotropy that is related to fracturing

presents an additional problem because it is not easilytransposed into velocities that can be used for pressureprediction. In this sense, fractures are analogous to theproblem caused by nonclastic rocks and hydrocarbonsbecause it is an effect that must be removed from thevelocity field before a pressure prediction can be per-formed. In theory, if a single set of oriented fracturesexist in a formation, it should be possible to do a ve-locity analysis parallel with the fractures and get a ve-locity result that does not include the influence of thefractures. This is uncommonly the case, however, inreal rocks. In practice, it is also very difficult to assurea priori that the seismic data are acquired in a way thatmeet this criterion for velocity analysis.

Stress State of Basins and Its Effect on Pressure Prediction

Large deviatoric or differential stresses in tectonicallyactive areas can cause significant variation in horizontalstresses, and hence in fracture gradient, that can have acritical impact on the accuracy of a pressure prediction.The effects of the stress field are observed on both thevelocity field through stress-induced anisotropy, andonthe fracture gradient and induced fracture orientationfor the basin. To consider these effects, we must look atsimple models for the three dominant types of basinsettings and their resultant stress fields (Figure 11).In an extensional basin (e.g., Gulf of Mexico and Ba-

sin and Range province), the stress field is such that theminimum principal stress is horizontal and the maxi-mum principal stress is vertical. The magnitude of thedifferential stress in extensional basins is commonlysmall, and the intermediate and minimum principalstresses are commonly close to the same value. In thiscase, the stress-induced maximum velocity is vertical,and the stress-induced minimum velocity is horizontal.This presents a significant problem in that the stress-induced anisotropy offsets some of the other forms ofanisotropy acting in these basins as defined previously.This also implies that the velocity field measured fromseismic data generally correlates reasonably with thevelocities measured from vertical seismic profiles orcheck shots and from dispersion-corrected sonic logs.The degree of stress-induced velocity anisotropy in thistype of basin is commonly sufficiently small that it is

230 H U F F M A N

Figure 11. Models for stress regimes in basins showing the three principal stress orientations and their effect on the fractureorientation. Note that all of the stresses are positive so that true tensile stresses are not observed in nature.

within the measurement error of the velocity analysismethods and thus is not a significant problem in pres-sure prediction. Stress-induced velocity anisotropy isalso offset by the presence of anisotropy (TI) that tendsto occur in shale-prone basins. Fracture gradients in ex-tensional basins are commonly slightly less than theoverburden calculated from integration of the densitylogs. This is intuitively reasonable because the maxi-mum principal stress is vertical and themean stress (theaverage of the three principal stresses) is commonly notmuch less than the maximum principal stress. The frac-ture gradient is commonly controlled by the minimumprincipal stress, whereas the overburden is tied moreclosely to the mean stress. The orientation of inducedfractures is normally parallel with the greatest principalstress and perpendicular to the minimum principalstress. For extensional basins, this implies that inducedfractures will be vertical in orientation. As a result, se-

vere induced fractures can propagate vertically throughthe formation and potentially undermine the cement jobabove the casing shoe.In a compressional basin (e.g., Rocky Mountains,

Zagros Mountains), the stress field is such that themaximum principal stress is horizontal and the mini-mum principal stress is vertical. The magnitude of thedifferential stress in compressional basins is signifi-cantly larger that in extensional basins due to the factthat rocks tend to be stronger in compression and thussupport larger compressional loads. In this case, thestress-induced maximum velocity will be horizontaland the stress-induced minimum velocity is vertical.The degree of stress-induced velocity anisotropy inthis type of basin can be significant and much largerthan the measurement error of the velocity analysismethods. Fracture gradients in compressional basinscan actually be greater than the overburden calculated


from integration of the density logs. This can result intoo conservative an estimate of the fracture gradientand lead to suboptimal well design. Obtaining goodleak-off test (LOT) data in such areas to be sure thatthe fracture-gradient relationship to overburden iswell understood before drilling additional wells is im-portant. For compressional basins, induced fracturesare commonly horizontal in orientation away from thewellbore. This orientation implies that fractures in-duced by drilling fluids pose less of a threat to casingand cement integrity because they will not propagatepast the casing shoe. The local stress field around thewellbore, however, commonly induces a fracture thatstarts out vertical as in the other basin stress fields. Thisinitial fracture can still pose a threat if it runs suffi-ciently far in the vertical direction along the wellboreto get past the cement job. If the fracture runs suffi-ciently outward from the well to get past the localstress field at the well, it can rotate to align itself withthe regional stress field, which can add complexity tothe interpretation of test data.In a strike-slip or listric basin (e.g., San Andreas

fault region), the stress field is such that the maximumand minimum principal stresses are both horizontaland the intermediate principal stress is vertical. Themagnitude of the differential stress in listric basins canalso be significantly larger than in extensional basins.In this case, both the stress-inducedmaximumvelocityand the stress-induced minimum velocity are horizon-tal. The degree of stress-induced velocity anisotropy inthis type of basin can also be significant. This againpresents a significant problem for anisotropy-process-ing algorithms because the velocity varies predomi-nantly with azimuth in listric basins. This requires notonly that the interpreter be able to process properly foranisotropy, but also that the subsurface be sampledwith a range of azimuths, which has not been donehistorically except on some land seismic surveys. Frac-ture gradients in listric basins can vary over a widerange but are commonly found to be close to the meanstress, which is commonly close to the intermediateprincipal stress that is commonly vertical in this typeof basin. For listric basins, induced fractures are com-monly vertical in orientation. As with the extensionalbasin case, severe induced fractures can propagate ver-tically through the formation and potentially under-mine the cement job above the casing shoe.

Structural Hyperpressuring in Reservoirs

Several authors (e.g., Heppard and Traugott, 1998;Stump et al., 1998) have addressed the centroid effect onpressures in structurally positioned reservoirs. This ef-fect can be significant enough to cause seal failures and

serious drilling problems if it is not recognized predrill.To date, however, the industry has not tackled the issueof how to detect this effect predrill using seismic data.Again, the use of poststack and prestack inversion maygive us a significant advantage by being able to isolatethe seismic behavior of a reservoir and evaluating it indetail as a function of structural position. This, however,requires sufficient knowledge of the physics of the pro-cess and its effect on both the reservoir and sealing rocksso that we can model the effect and interpret it in theseismic data. It also requires a good knowledge or def-inition of the reservoir geometry.For water-bearing reservoirs, there are two factors

that must be considered in dealing with structural hy-perpressuring. The first factor is the possibility that thedegree of compaction may change from the top to thebottom of the reservoir with large amounts of structuralrelief. In this situation, the centroid pressure profile ob-served in the velocity data may be magnified by thevertical change in compaction state of the reservoir. Thesecond factor is the possibility that the reservoir hasbeen breached by a fault or other conduit that allowsfluids to escape from or recharge into the reservoir. Inthis case, it is possible that the centroid position in thereservoir may be shifted significantly. Also importantto recognize is that the seal rocks adjacent to the reser-voir can be affected by breaching a reservoir. For ex-ample, if a reservoir is drained slowly and thenrecharged, seal rocks adjacent to the reservoir may alsoundergo some compaction and reduction of fluid pres-sures. This results in a compaction halowhose thicknessdepends on the elapsed time for the drained condition.Once the reservoir is recharged, this halo stabilizes andpreserves evidence of the drainage event that can beseen as a local increase in velocity and density in theseal rocks. This is important for inversion analysis be-cause the local halo affects the reflection coefficients be-tween the shale and reservoir and could result inmisleading data. The halo also produces shale velocitiesand densities that are not the same as those further fromthe reservoir. This effect can be detected in inversionbut would bemissed by a conventional velocity analysisthat measures the velocities more coarsely.For hydrocarbon-bearing reservoirs, the effect of the

hydrocarbons on the velocity field must also be consid-ered in estimating the reservoir pressures. In this case,either the hydrocarbon effect must be calculated andremoved by performing a Gassmann fluid replacementcalculation, or the reservoir pressure calibration itselfmust be adjusted to include the hydrocarbon effect. Ineither case, enough must be known about the reservoirand its fluids to permit these adjustments to be made.Recent work in deep-water drilling hazards has also

suggested that shallow water flows (SWF) are the

232 H U F F M A N

result of structural hyperpressuring (Huffman andCastagna, 2000). These shallow sands commonly occurwithin a few thousand feet of the mud line in abruptlydepositing basins and exhibit pore pressures close tofracture gradient and near-zero effective stresses. Theyare probably the most significant hazard currently fac-ing deepwater drilling and should be studied in thecontext of pressure prediction.

Identifying the Top of Secondary Pressure Zones

One of the most difficult issues in pressure predictionis knowing how to identify the correct maximum ve-locity–effective-stress point for a velocity reversal thatis attributed to secondary pressure (see Figure 4). Thetechnique for handling a velocity reversal requires thatthe maximum compaction state be known to estimatethe correct unloading path for the interval. The selec-tion of this maximum velocity determines the densityand porosity in the unloaded interval, as well as thepressure that is attained for a given velocity (Bowers,1994). The most common practice for determining themaximum velocity is to use the velocity of the intervaldirectly above the unloaded interval. This is problem-atic, however, in that it assumes that there is continuityin loading history across this pressure boundary,which may not be correct. The maximum velocity thatshould be achievable for a given depth is the velocitythat is on the normal pressure curve for the greatestdepth of burial that the interval achieved because thisis the maximum compaction state that any rock canattain. Selecting this velocity as the maximum velocityfor any velocity inversion yields the maximum possi-ble pore pressure that can be attained for that unload-ing condition. In most cases where the maximumvelocity value is not well constrained, it is prudent toprovide a worst case scenario using this approach.Overpredicting pressure is possible by using a sec-ondary pressuring estimate where one is not needed.The minimum pressure case can be provided by sim-ply assuming no unloading and treating the reversalas an undercompacted interval. The problem is know-ing where unloading is actually occurring and whatvelocity point to tie it back to, which is a reflection ofthe loading history of the particular formation beinganalyzed.This issue can be addressed in part by density data.

If unloading is present, the compaction process is ar-rested by the secondary pressure. In that case, densityshould not continue to increase and porosity shouldnot continue to decrease with depth. Therefore, collect-ing density and/or porosity data in real time can beinvaluable in determining whether a velocity reversalrepresents secondary pressure conditions or under-

compacted conditions and what maximum compactionpoint to tie the unloaded zone to. In the absence of un-usual diagenetic alteration or cementation, the densityof the formation gives a good indication of the maxi-mum compaction achieved by the rocks. In general, ifthe velocity reverses and the density also decreases, thismost likely indicates undercompaction as the cause. Ifthe velocity decreases and the density and porosity re-main the same, secondary pressure is likely to be thecause.


The future of pressure prediction will see dramaticchanges in the purpose for whichwe use the technique,the types of data that are used, and the type of analysisthat is employed to get more detailed high-resolutionvelocity data. Pressure prediction will become part ofthe holistic discipline of basin analysis andwill be usedto determine the present pressure state of a basin as acontrol on both forward and inverse basin modeling.Pressure prediction will also be used at the subregionalto prospect scale to determine critical aspects about thehydrocarbon migration and trapping process, faultleak/seal, and source maturation.Despite all of these new technologies and tech-

niques for improving estimates of velocity and density,we will still be forced to cope with our lack of under-standing of the nature of pressure and fluid movementin shale-dominated basins and the various physicalprocesses that cause pressure. Future research willhave to focus on these basic physical processes so thatwe can properly interpret the data that we are becom-ing so masterful at acquiring in large quantities.


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