spwla-2003-w

SPWLA 44 th Annual Logging Symposium, June 22-25, 2003

METHODS OF SATURATION MODELING USING CAPILLARY PRESSURE AVERAGING AND PSEUDOS

Nick A. Wiltgen, Jo~l Le Calvez, and Keith Owen Schhmaberger

ABSTRACT To generate an accurate integrated formation evaluation, it is necessary to know, for as many locations as possible, the original reservoir fluid saturation value. This highly variable parameter can be best determined when well log data are adequately combined with core analysis data. From the core analysis, the key parameter capillary pressure, which relates directly to the water saturation, can be extracted. From the well logs, the reservoir scale of both vertical and lateral variations in reservoir rock properties can be determined.

There is never enough hard reservoir data to rely upon; thus, there is always a need to extrapolate the reservoir rock properties obtained from a few well logs and core analysis data points to the entire reservoir. These data can then be used to initialize the original fluid saturation distribution in a reservoir model simulation.

This paper is a review of several capillary pressure models using averaging and pseudos that are intended to model the original reservoir fluid saturations within the entire reservoir on the basis of a few data points.

The models are Leverette 'J' function, lambda functions for saturation modeling, FOIL functions (Bulk Volume Water vs. Free-Water Level), Johnson method "pseudo- permeability", pseudo-porosity method (capillary porosity), Guthrie polynomial method, Thomeer and Swanson method, Heseldin method and its derivatives, and Skelt and Harrison method. Only the Thomeer and Swanson method can generate synthetic capillary pressure curves for reservoir description when no actual capillary pressure data are available. If porosity, log- derived water saturation, and permeability are known, porosity can be used as total interconnected pore volume with an estimated pore geometrical factor to solve for displacement pressure to predict the down-dip water level.

A review of these methods leads to the conclusion that none is intrinsically better than another if all the rock types are the same. However most reservoirs have more than one rock type, and these variations are best

handled by building a robust, non-linear formulation and optimization method, designed so that each term in the function can be related directly to a physical parameter. Therefore if the following are available m high-pressure mercury injection (HPMI) capillary data, well logs and their associated water level, and a good knowledge of the rock quality--then the Skelt and Harrison method in relation to the pseudo-porosity method can be used with confidence.

INTRODUCTION There are essentially three methods available to the engineer to determine connate or interstitial water saturations. These methods are to core formations with oil-base or tracer bearing fluids, to calculate values from petrophysical log analysis, and to determine values from capillary pressure data.

A correlation between water saturation and air permeability for cores obtained with oil-base mud shows a general trend of increasing water saturation with decreasing permeability. It is accepted from field and experimental evidence that the water content determined from cores cut with oil-base mud reflects closely the water saturation that exists in a reservoir. However, in the transition zones where some of the interstitial water is replaced by filtrate or displaced by gas expansion conditions this is not true (Leverett, 1941; Amyx et al., 1960). Even though there is no general correlation applicable to all fields, an approximately linear correlation between connate water saturation and the logarithm of permeability exists for each field. The general trend of the correlation is usually decreasing connate water with increasing permeability.

If capillary pressure data are to be used for determining fluid saturations, the saturation values obtained from core should be similar to those calculated with other methods. Water distributions determined from petrophysical logs and capillary pressure data are usually in good agreement with one another. In a gas/oil/water zone case where the gas-bearing portion of the formation is above the transition zone, there is no significant variation in water saturation with depth. However, in the

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S P W L A 44 th Annual Logging Symposium, June 22-25, 2003

oil-bearing portion of the rock there is significant variation in the water saturation with depth depending on the method used. In all cases, the oil segment is almost entirely in the oil/water transition zone. Variations in water saturation with depth within that zone must be taken into account to accurately determine average reservoir connate or interstitial water saturations.

LEVERETTE ' J ' FUNCTION The 'J' function correlating term uses the physical reservoir properties of the rock and fluid and is expressed as in Figure 1. Nomenclature is as follows: P c is the capillary pressure in dynes/cm 2, ~ is the interracial tension in dynes/cm, k is the permeability in cm 2, and ~b is the fractional porosity. Some authors alter the expression by including cos 0, where 0 is the contact angle as in Figure 1.

The 'J' function was originally proposed as a means of converting all capillary pressure data into a universal curve, which it is not. There are significant differences in correlation of the 'J' function with water saturation from formation to formation, so no universal curve can be obtained (Leverett, 1941).

This method will work with only one rock type; otherwise there must be a 'J' function for each rock type. Therefore using only one 'J' function will not provide an accurate initialization of the original fluid saturation distribution in a reservoir model simulation.

L A M B D A FUNCTIONS In the 'J' function, a relationship between permeability and porosity is needed along with knowledge of the areal variations of these parameters. Other functions used for saturation call for only the porosity with a simple hyperbolic fit to saturation. The quality of the rock is divided into effective porosity classes. The porosity classes address the areal variation in rock quality.

The resulting equations are

2 = ea+b*ln(¢e/lO0) (1)

D T h = F W L - e (C+¢e)/d, (2)

where a, b, c, and d are fitting functions and t~e the effective porosity in percent. The lambda fimction is )~. Therefore, the effective water saturation is

Sw = (Pc/Pe) -~ = ( S w - Sw i ) /O- Swi) (3)

which can also be written as

Sw = [(FWL - rVD)/(FWL - Drh)l-Z × (100 - Swi)+ Swi,

(4)

where P e =

Pc = Sw = S w i =

F W L =

T V D =

D T h =

entry pressure capillary pressure total water saturation irreducible water saturation free-water level true vertical depth of the calculation depth where P c equals Pe .

This method involving effective porosity classes works for one Swi only. Since a single Swi does not characterize a reservoir, this method can not provide an accurate initialization of the original fluid saturation distribution in a reservoir model simulation.

FOIL FUNCTIONS (B VW vs. Z F W D

A simple convincing function was developed that calculates water saturation as a function of the height above the free-water-level zone. This function, which is virtually independent of the porosity and permeability of the rock, is based on the bulk volume of water (the product of porosity and water saturation). The derivation is simpler than with classical functions because there is no porosity banding. It uses the Leverett 'J' function and the bulk volume of water equation (B VI~:

B V W = S w ( ¢ ) (6)

_ act cos 0 S w p - g ( p w _ p g ) h F ~ 4 ¢ / K (7)

yielding to

aer cos 0 B V W = g ( p w _ p g ) h F w L 4 q k / K ,

where ot and [3= 0 = ( y - -

K =

constants from the 'J' function contact angle (deg) interracial tension (dyne/cm) permeability (cm 2)

(8)


g = acceleration of gravity (m/s 2) 9w = density of the water phase (g/cm 3) 9g = density of the gas phase (g/cm 3) hyrvL = height above free-water level (ft). This equation suggests that the bulk volume of water at a certain height above the free-water level is virtually independent of rock properties such as porosity and permeability. This implies that a saturation height (Swh) function based on the bulk volume of water avoids the problems associated with porosity banding and variance of the gas/water contact (GWC) from FWL. This type of Swh function has been called the "FOIL" fimction (Cuddy et al., 1993)"

BVW = I - A x H B, (9)

where A and B =constants B VW =Sw x d~(FOIL) H =height above the free-water level.

This method relies upon the observation that bulk volume water (Swxqb) is constant regardless of the porosity at any elevation in the trap in question. This is not always true. It fails to honor the uniqueness of FWL, estimating it within +30 ft, and like the other models fails to recognize different rock types.

JOHNSON "PSEUDO-PERMEABILITY" This method mathematically relates water saturations derived from standard laboratory capillary measurements to permeability and capillary pressure.

The relationship between water saturation and permeability on a log/log plot is reasonably linear and can be described by an equation of the form

log Sw - A x log K + B, (10)

where A =slope of the capillary pressure data set B =relationship between the intercept B" and Pc.

A bi-logarithmic plot function of B" versus Pc of the entire capillary pressure data set generates an equation in the form

B ' = a x P c -b, (11)

which results in the f'mal relationship

log(Swn )= A x log K + (ax Pc -b ) (12)

It is difficult to relate the various parameters A, B, a, and b because of not knowing the exact effect of each. This averaged "pseudo-permeability" capillary analysis technique (Figure 2) shows itself to be a fairly simple yet robust method of incorporating capillary data into various aspects of log analysis and field study work. It does not rely on any profound theoretical basis but is merely a practical technique, which has evolved in response to a number of operational requirements (Johnson, 1987). It does require permeability mapping.

If the relationship between water saturation and permeability is not linear, then this method cannot be used.

PSEUDO-POROSITY (CAPILLARY POROSITY) The pseudo-porosity method mathematically relates water saturations derived from standard laboratory capillary measurements to porosity and capillary pressure. This is similar to the Johnson "pseudo- permeability" technique, in which permeability is used instead of porosity for the mathematical relation in the form

log Sw = A x Ht B + C log ~b, (13)

where A, B, and C are constants and Ht is mid-zone height above the water contact.

Ht and Sw are derived from a specific capillary pressure data curve. The well log-derived zonal average water saturation and mid-zone height above the field hydrocarbon water contact are used to determine the capillary porosity (dPcAP) from

log ~bcA e = (A/C)x Ht B +(1/C)logSwAv G . (14)

Now one is able to map ~CAP and determine the average water saturation (SwArt) at each grid node from $cA? and mid-zone height by using the Equation (14) and apply this to the mapped porosity to calculate the hydrocarbon pore volume (HCPV).

If the mathematical relationship between water saturation and porosity cannot be shown to be valid then this method cannot be used.

GUTHRIE POLYNOMIAL Another way of evaluating capillary pressure data is to analyze a number of representative samples and treat them statistically to derive correlations. These added to the porosity and permeability distribution data can be 117


used to compute the connate-water saturations for a field.

A first approximation for the correlation of capillary pressure data is to plot water saturation against the logarithm of permeability for constant values of capillary pressure. An approximately linear relationship usually results. A straight line can be fitted to the data for each value of capillary pressure, and average capillary pressure curves are computed from the permeability distribution data for the field. The resulting straight line takes the general form

Sw = a log K + C, (15)

where a and C are constants determined from the sample data (Guthrie and Greenburger, 1955).

There are indications, however, that water saturation at constant capillary pressure is not only a function of permeability but also some function of porosity as suggested by

Sw= al~+ a 2 logK +C, (16)

where al, a2, and C are constants determined from the sample data. The method of least squares can be used to determine the constants of the best fitting lines. The effect of ignoring the porosity is the prediction of lower water saturations for low-permeability materials. The polynomial form is shown in Figure 3.

It should be noted that the sample data are based on plug data, not averaged water saturation and porosity data (Amyx et al., 1960).

If the mathematical relationship, from Equation (16) between water saturation, permeability, and porosity, cannot be shown to be valid then this method cannot be used.

THOMEER AND SWANSON The Thomeer and Swanson method, in principle, can predict water levels from a combination of capillary pressure data and porosity, water saturation, and permeability. In the model, regression analysis is used to find the water level that best honors all available log and core data in a reservoir (Figure 4 shows a graphical representation for this technique).

In 1960, Thomeer proposed that mercury capillary pressure data could be described with hyperbolic curves employing the three parameters as follows (Figure 5):

-Fg /log(Pc/Pd ) Sb/Sb~ =e . (17)

If it is assumed that Sb® is porosity and Sb is the product of porosity and hydrocarbon saturation. Then the equation can be written

log Pc = -Fg ~In 0 - Sw)+ log Pal. (18)

Swanson (1981) demonstrated that the coordinates from a special point A on the capillary pressure curve could be related to air permeability. This relationship is the following:

PcA . (19)

Thomeer (1983) reported the following empirical relationship for which a graphical representation of the equation is shown in Figure 6:

ka = 3.8068Fg -13334 (Sb~ /Pd) 2° , (20)

where F g =

k~ Pc = Pd = Sb = Shoo -"

pore geometrical factor (dimensionless) Fg is also called G in some texts air permeability (md) mercury capillary pressure (psi) mercury displacement pressure (psi) bulk volume occupied by mercury (%) bulk volume occupied by mercury at inf'mite pressure (%).

The missing link was a practical means of determining Pc and Sw at point A, which are called PCA and SwA, respectively. In 1992, Pittman provided the link by demonstrating a relation between the pore-throat radius at point A and air permeability in sandstones as follows:

log rapex = 0.226 + 0.466 log ka, (21)

where rapex is the pore throat radius at point A (gm). The technique was fully described by Smith (1992).

Also Hawkins et al. (1993) made many improvements with the use of regression theory. This further algebraic manipulation resulted in the following:

Fg = Iln(5.21 ka°'1254)]2~.03~ (22)

Pd = 937.8/(ka°'34°6 )qk (23)


h= Pc (O'r c O S O r ) ( 2 4 )

0.433(Pw --ph) O'l cosO l '

where h = height above the flee-water level (ft) 0r = contact angle between the water and reservoir

rock (0 °) 0t = contact angle between mercury and the rock in

the laboratory ( 140 °) cyr = interfacial tension between the fluids in the

reservoir (dynes/cm) ct = interfacial tension for mercury in the

laboratory (480 dynes/cm) 9w = formation water density (g/mL) 9h = formation hydrocarbon density (g/mL).

The bulk volume Sb/Sboo or Pc,~ and SWA determination does not have a unique solution (see Figure 5).

At each depth level, there are four observed variables: depth or Pc, porosity, water saturation, and air permeability. Although some or all of the last three values may be calculated from logs rather than measured on cores, the interpretation from log-derived porosities, permeabilities, and water saturations should be in good agreement with the core values.

If any three of the four basic quantities (porosity, permeability, water saturation, and capillary pressure) are known, then the fourth can be calculated. If the water level is known and porosity and permeability are available, then a water saturation profile can be derived. Another application is the calculation of permeability values when the water level, porosity, and water saturation values are known with confidence.

Haynes (1995) made the following conclusions in an evaluation of the method:

• The capillary pressure model requires permeability, porosity, and water saturation to predict FWL.

• The capillary pressure model can reliably predict FWL in a reservoir if the sand is in a transition zone.

• The capillary pressure model can reasonably predict permeabilities if porosities, saturations, and FWL are known with confidence.

• The capillary pressure model can be used as a check of log-derived water saturation values

when porosity, permeability, and FWL are known. The model can be used to check the consistency of capillary pressure data at the displacement pressure and the shape of the curve in the high-pressure region.

Not knowing how to map Fg, Pd, and Sboo, it is difficult to apply this method to populate the original reservoir fluid saturations cell by cell

HESELDIN METHOD AND ITS DERIVATIVES The Heseldin method, linking the Pc/Sw relationship to other reservoir rock properties, plots porosity vs. bulk volume hydrocarbon (BVH) at a constant value of Pc. Water saturation is implied in BVH through the relation

Vbh = ¢ 0 - Sw), (25)

where Vbh = BVH or bulk volume hydrocarbon (Figure 7) (Heseldin, 1974).

This method is essentially a modification of the Aufricht and Koept (1957) method, which presents a mathematical procedure to derive a single capillary pressure relationship from which a saturation can be calculated for a given rock type at the appropriate sub- sea depth.

The rock type can be expressed as a continuously varying parameter such as porosity or permeability. The relationship can also be used as a basis for generating one or more representative capillary pressure curves for reservoir simulation.

Capillary pressure data from a number of cores are usually correlated or smoothed by plotting Sw vs. either porosity or permeability at constant Pc. There are three advantages in plotting (at constant Pc) BVH vs. porosity to establish a correlation. First, this emphasizes in-place hydrocarbon volume, which is the primary economic feature of interest. Second, by plotting BVH rather than the fractional pore volume (PV) of hydrocarbon (1 - Sw), the effect of possible erratic Sw values at low porosities is minimized. Third, by relating Pc data to porosity rather than permeability, results can easily be applied to well logs (Alger et al., 1989).

If the mathematical relation relationship between water saturation or Pc and porosity cannot be shown to be valid then this method cannot be used. W


SKELT AND HARRISON This method can map hydrocarbon saturation, Sh, and determine the Sw average at each grid node depending on the rock type and height above the free-water level, h and can be designed so that each term in the function can be related directly to a physical parameters.

Skelt's original method proposed using capillary pressure data to characterize the shape of the transition zone and then modified the coefficients to fit log data. In effect this is calibrating the Pc height transform while simultaneously finding the oil/water contact less the free-water level ( O W C - FWL offset).

This is done by using the following equation to determine the constants a, b, and c. The equation determines a single or layer-specific capillary pressure height (Pc(Hr)) vs. Sw curve from core capillary pressure data only in the form

Sh = 1 - Sw - a x exp(- b/(h + d)) c . (26)

The value of Pc is determined with an equivalent expression that replaces h with Pc. Depending on the context, a, b, c, and d are constants, or alternatively they may be simple functions of rock properties such as permeability or porosity. The effect on the function of altering each coefficient is as follows (Figure 8) (Skelt and Harrison, 1995):

a is the asymptotic hydrocarbon saturation,

1 - Sw(irr).

• b is a vertical scaling factor for the curve as a whole, which may be used to transform data between the laboratory pressure and height domains.

• c distorts the vertical axis to account for the saturations not following the simple form [a x exp(-b/h)]. Both b and c are related to the pore-throat size distribution.

• d applies a vertical displacement to the entire curve, and can be used to locate the free water level.

Two important considerations in the process of fitting data to a generic algorithm need to be addressed (Skelt and Harrison, 1995).

Although least-squares error minimization is popular, it is not necessarily the best method to use with data that are skewed and typically

peppered with outliers. Trying least-squares minimization has shown that the best approach seems to be fitting by minimizing absolute differences, which, although mathematically more difficult, is less affected by the non- Gaussian distribution of a typical data set. Weighting should be or should not be used depending on the purpose of the fit. The requirements for field-wide saturation mapping maybe different from those of localizing the hydrocarbon water contact.

The Skelt and Harrison method then uses well logs to derive the zonal average Sw data and mid-zone height (above each well's apparent Hr water contact) and "PhiCap" (~c,4P) (see Figures 9 and 10). This simple function of rock quality from porosity, called PhiCap, is determined from trial and error in an Excel macro solver. The macro solver changes PhiCap until Sw matches the original log Sw average as close as 10 -7.

Since we are trying to determine Sw average at each grid node, we need to map PhiCap, which at this step is renamed the rock quality index (RQI) to avoid confusion with log porosity, and determine Sw at each grid node from RQI and the mid-zone height by using the preceding equations. This pseudo-porosity method allows for characterization of the relationship between RQI and Sw. The example graphs for poor rock (5% to 15% porosity) and good rock (9% to 20% porosity) in Figures 9 and 10, respectively, illustrate this relationship using simple functions of rock properties such as porosity and capillary pressure data from HPMI.

CONCLUSIONS Three of these methods are similar, using mathematical fimctions of data sets to statistically derive correlations.

• Leverette 'J' function • Lambda functions • FOIL functions

Four other methods use porosity, permeability, or both to relate the various saturations, permeabilities, and pressures to one another.

• Johnson method "pseudo-permeability" • Pseudo-porosity method (capillary porosity) • Guthrie polynomial method • Heseldin method and its derivatives

These methods will work for only one rock type at a time and will not work at all if there is no relation


between porosity, saturations, permeabilities, and pressures to one another. Only the Thomeer and Swanson method can reliably predict FWL in a reservoir if the sand is in a transition zone. It cannot be used in a reservoir model simulation because of mapping problems with Fg, Pd, and Shoo. Therefore using only one method will not provide an accurate initialization of the original fluid saturation distribution in a reservoir model simulation.

The Skelt and Harrison method that models the shape of the hyperbolic curve, can handle reservoirs with more than one rock type. These variations are best handled by building a non-linear formulation and optimization method, designed so that each term in the function can be related directly to a physical parameter. If the following are available--high-pressure mercury injection (HPMI) capillary data, well logs and their associated water level, and a good knowledge of the rock quality--then the Skelt and Harrison method in relation to the pseudo-porosity method for PhiCap can be used with confidence as seen in Figures 9 and 10.

ABOUT THE AUTHORS Nick A. Wiltgen received his BS degree in electrical engineering from Purdue University. He has worked for Schlumberger Well Services, Shell Oil Company, Amerada Hess, Sun/Oryx, ResTech, and Qatar General Petroleum Company. He is now with Schlumberger, College Station, Texas.

Jo~l Le Calvez received his BS degree in mathematics and physics from the Universit6 de Nice-Sophia Antipolis and MS in tectonophysics fi'om the Universit6 Pierre et Marie Curie. He received his PhD in geology from the University of Texas at Austin, where he also worked for the Applied Geodynamics Laboratory at the Bureau of Economic Geology. He is now with Schlumberger, College Station, Texas.

Keith Owen received his BS degree in petroleum engineering from Texas A&M University. He has seven years' experience in the industry with Schlumberger, including prior field assignments in the Rocky Mountains, San Joaquin Basin of California, and Gulf of Mexico. He is now with Schlumberger, College Station, Texas.

REFERENCES CITED Alger, R.P., Luffel, D i . , and Truman, R.B., 1989, New unified method of integrating core capillary pressure

data with well logs: SPE Formation Evaluation, pp. 145-152. Amyx, J.W., Bass, D.M., and Whiting, R.L., 1960, Petroleum Reservoir Engineering: McGraw-Hill Book Company, pp. 155-159, 542-544. Aufricht, W.R., and Koept, E.H., 1957, Interpretation of capillary pressure data from carbonate Reservoirs" Trans. AIME, pp. 402-405. Cuddy, S., Allinson, G., and Steele, R., 1993, A simple convincing model for calculating water saturations in southern North Sea gas fields: SPWLA 34 th Annual Logging Symposium, paper H. Guthrie, R.K., and Greenburger, M.H., 1955, The use of multiple correlation analyses for interpreting petroleum engineering data: presented at the Spring Meeting of the S.W. District Division of Production, New Orleans, LA. Hawkins, J., Luffel, D., and Harris, T., 1993, Capillary pressure model predicts distance to gas/water, oil/water contact: Oil & Gas Journal, pp. 39-43. Haynes, B., 1995, An evaluation of a method to predict unknown water levels in reservoirs and quantifying the uncertainty: SPE Production Operations Symposium, Oklahoma City, OK, pp. 225--~232. Heseldin, G.M., 1974, A method of averaging capillary pressure curves" SPWLA 15 th Annual Logging Symposium, paper I. Johnson, A., 1987, Permeability averaged capillary data: a supplement to log analysis in field studies: SPWLA 28 th Annual Logging Symposium, paper EE. Leverett, M.C., 1941, Capillary behavior in porous solids: Trans. AIME, 142, pp. 151-169. Pittman, E.D., 1992, Relationship of porosity and permeability to various parameters derived from mercury injection capillary pressure curves for sandstone: AAPG Bulletin, 76, No. 2. Skelt, C., and Harrison, B., 1995, An integrated approach to saturation height analysis: SPWLA 36 th Annual Logging Symposium, paper NNN. Smith, D., 1992, How to predict down-dip water level: World Oil, pp. 85-88. Swanson, B., 1981, A simple correlation between permeabilities and mercury capillary pressures: Journal of Petroleum Technology, pp. 2498-2504. Thomeer, J.H.M., 1960, Introduction of a pore geometrical factor defined by the capillary pressure curve:, Petroleum Transactions, AIME, 219, pp. 354- 358. Thomeer, J.H.M., 1983, Air permeability as a function of three pore network parameters: Journal of Petroleum Technology, pp. 809-814. W


instantaneous Sw J (sw) ~ot ff~ in

(sw) loo

J,Sw, ~ocosO ~ I~) °

Figure 1 - Levere t t ' J ' funct ion

log k I I I

• , - | ,.... , , . . . . . , . . , , . , .

O Sw

At depth n --~ f ixed .. .Pc n

S w n = al~b + a 2 ¢ 2 + a 3 log(K) + a 4 ( log(K)) 2 + c

Figure 3 - Guthrie po lynomia l

100

.,I 10

\ \ '

\

1 10 100 Log Sw

At depth n ~ Pc n

Log (Swn) = aPc -b + ALog (K )

Figure 2 - Johnson "pseudo-permeab i l i ty"

logPc

~ Vbp~

........................ 4 ~ Pfl

IOgSNw

ka = 3.8068 * Fg-l'3334(Sboo / pd)2"O

[I 'a° 12'4112 Fg = In 5.21 ¢ /2.303

Pd = 937.8 / (ka 0"3406) ¢

Figure 4 - T homee r and Swanson m e t h o d

S P W L A 44 th Annual Logging Sympos ium, June 22-25, 2003

_

~;b- (%)...~25.6 '18.0 12.7 3.0 1000.

.,,..

' i i J ! / r ~ : - -4-_____

': . . . . ' . . . . . . . = I = , ~ _ ' : L ~ 1 o.1 o~a~ ==., sb o.1 i or.--= ~.0 At A': (--)K" 1 . 8 4 , 0.2O0 • . = o= . I , , ~ . a pc 9 .2

ALL e~mtem: rowe,,) A. oJm 2-! k=~. l~.~,~

| DETERMINATION AND NON-.-UI ~ IOUENESS OF THE (Sb/P¢) / PARAMETER

' ~o " ~ ' = ' , ~ ' =~ . . . . . i ' i

(~ * O - sw})

0 ~ Pcincreases/" / ~

(or togk)

E f f e c t o f A l t e r i n g "a' .

! i , i i

~.- I n c r e a s i n g

~'~, '~.~ \, ~,

B VH = Vbh = ~ (1- Sw)

Figure 5 - Thomeer and Swanson methods Figure 7 - Heseldin method and its derivatives

Function of G, Pd and Sb

-...2-' _ _ [ . . ~ _ m 2

-

0.3 O.4 0.8 O 6 O'7

0.9 - ~ / L 1 . o - - . , -

,o.o ,.o ~ . , , ~ . . . . . .

Figure 6 - Thomeer and Swanson methods

H y d r o c a r b o n Saturat ion

E f f e c t o f Al ter injg "d'

E f f e c t o f A l t e r i n g 'b" 1

i i "f + . . . . . . . ,o~'u '~

E f f e c t o f A l t e r i n g ' c '

ii ~ ', i ii ! i

Figure 8 - Skelt and Harrison method

W


P o o r R o c k ( 5 - 1 5 % P o r o s i t y )

450

400 [] 5%

350 - "~ - 6%

7 % • ~ - 300 -~ - 8%

=~ 250 9% 10%

.' 200 11%

~. 150 + - - 12% 13% /

100 D - - 14% /

l 50 15%

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sw (dec)

G o o d R o c k ( 9 - 20% Porosity)

450

[] 9 % 400 ~- - 10%

350 -'- 11%

x - - 1 2 % 300 = 13%

250 - - - - - 1 4 %

= 15% 200 - - o - - 1 6 %

" 150 ¢ 17% + - - 18%

100 = 19%

- - ~,- - 20%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sw (dec)

Figure 9 - Example of poor rock characterized from capillary pressure data from HPMI by Sw = 1- (aexp-(b(400-0.3PhiCapZ)/(Pc-0.3PhiCap2))^c)*(1-(0.0 lPhiCapa5))

Figure 10 - Example of good rock characterized from capillary pressure data from HPMI by Sw = 1- (aexp-(b(400-0.05PhiCap2)/(Pc-0.05PhiCap^-2))^c)(1-(0.0 lPhiCapls))

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