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Copyright 2000, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2000 SPE Rocky Mountain Regional/LowPermeability Reservoirs Symposium held in Denver, CO, 1215 March 2000.

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AbstractThe modified Mayerhofer method has been proposed for

estimating permeability from the pressure falloff data in

moderate and high permeability reservoirs before hydraulic

fracture closure following a diagnostic fracture injection test.

Applying the modified Mayerhofer method in low

permeability sands, however, requires understanding of the

closure mechanism, which is identified with G-function

derivative analysis of the before-closure pressure falloff data.

This paper demonstrates how G-function derivative analysis

and the modified Mayerhofer method are used in conjunction

to estimate reservoir permeability in low permeability

reservoirs.

Numerous applications of G-function derivative analysis

have shown the characteristic closure mechanismsnormal,

pressure-dependent leakoff from fissure opening, fracture-

height recession, fracture-tip extension, and changing

complianceall result in distinctive specialized plots using

the modified Mayerhofer method. When the two methods are

used in conjunction, G-function derivative analysis provides a

means for identifying the falloff data that can be used to

estimate permeability and fracture-face resistance withoutviolating the assumptions of the modified Mayerhofer method.

Field cases are included to demonstrate that reasonable

estimates of reservoir permeability in low permeability

reservoirs often can be obtained from the before-closure

pressure falloff following a diagnostic fracture injection test.

IntroductionValk and Economides

1 published the modified Mayerhofer

method for estimating permeability in moderate and high

permeability reservoirs from the before-closure pressure

falloff data following a diagnostic fracture injection test. The

modified Mayerhofer method is based on the technique

proposed by Mayerhofer, et al.,2

and differs from conventionapressure decline analysis in that the problem is formulated in

terms of permeability and fracture face resistance as opposed

to leakoff coefficient and spurt loss.

Before-closure pressure falloff analysis techniques are

beneficial for low permeability reservoirs since the shut-in

time requirements are substantially lower than the time

required for after-closure pressure falloff analysis.

Nolte, Maniere, and Owens,3 however, have noted tha

fracture extension and fracture recession during closure limi

the applicability of before-closure pressure falloff analysis

techniques. Nolte, et al.,3suggest that after-closure analysis of

pseudolinear and pseudoradial flow regimes are superior

methods for estimating reservoir parameters, but in lowpermeability reservoirs, the time required to achieve

pseudolinear and pseudoradial flow following a fracture

injection test can be excessive.

G-function derivative analysis was recently proposed for

identifying the leakoff mechanismnormal, pressure-

dependent leakoff from fissure opening, fracture-heigh

recession, fracture-tip extension, and changing compliance

from the pressure falloff following a diagnostic injection test

G-function derivative analysis also provides a method for

identifying the falloff data that can be used to estimate

permeability and fracture-face resistance without violating

assumptions of the modified Mayerhofer method.

The objective of this paper is to demonstrate how

G-function derivative analysis and the modified Mayerhofer

method are used in conjunction to estimate permeability in

low-permeability reservoirs. Additionally, field cases are

included to demonstrate that reasonable estimates of reservoir

permeability can often be obtained from the before-closure

pressure falloff data in low permeability reservoirs.

SPE 60291

Adapting High Permeability Leakoff Analysis to Low Permeability Sands for EstimatingReservoir Engineering ParametersDavid P. Craig and Michael J. Eberhard, Halliburton Energy Services, Inc.Robert D. Barree, Marathon Oil Company


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2 D. P. CRAIG, M. J. EBERHARD, AND R. D. BARREE SPE 60291

G-Function Derivative AnalysisRecently, Barree and Mukherjee

4 presented G-function

derivative analysis for identifying the leakoff mechanism

following a diagnostic fracture injection test. G-function

derivative analysis requires a graph of bottomhole pressure,

the derivative of pressure (dP/dG), and the superposition

derivative (GdP/dG) versus the G-function. The leakoff typeis identified using the characteristic shape of the derivative

and superposition derivative curves. Fig. 1 contains the

G-function derivative graphs for the four common leakoff

types observed in low permeability hard rock sandstones.

Normal leakoff behavior occurs when fracture area is

constant during shut-in and leakoff is through a homogeneous

rock matrix. With G-function derivative analysis, normal

leakoff is indicated by a constant derivative, and when the

superposition derivative lies on a straight line through the

origin. Fracture closure is identified when the superposition

derivative data deviate downward from the straight line.

Pressure-dependent leakoff from dilated fractures/fissures

is indicated by a characteristic hump in the superposition

derivative that lies above an extrapolated straight line throughthe normal leakoff data. The fissure opening pressure is

indentified at the end of the hump when the superposition

derivative data meet the extrapolated straight line. A period of

normal leakoff behavior is generally observed before fracture

closure is identified when the superposition derivative data

deviate downward from the extrapolated straight line.

Fracture-height recession during shut-in is indicated by

G-function derivative analysis when the superposition

derivative data fall below a straight line extrapolated through

the normal leakoff data. Fracture height recession is also

indicated by a concave down pressure curve and an increasing

pressure derivative. As previously noted, hydraulic fracture

closure is identified when the superposition derivative datadeviate downward from the straight line.

Fracture-tip extension, which occurs when a fracture

continues to grow after injection is stopped, is indicated when

the superposition derivative data lie along a straight line that

extrapolates above the origin.

The objective of the G-function derivative analysis is to

identify the leakoff type and fracture closure stress. In most

cases, the superposition derivative provides a definitive

indication of hydraulic fracture closure when the data deviate

downward from an extrapolated straight line through the

period of normal leakoff.

Modified Mayerhofer Permeability AnalysisModified Mayerhofer permeability analysis is a method

proposed by Valk and Economides1 for analyzing the

pressure falloff following a diagnostic fracture injection test,

but the Mayerhofer method differs significantly from

conventional leakoff analysis. Instead of formulating the

leakoff model in conventional terms, i.e., leakoff coefficient

and spurt loss, the Mayerhofer, et al.2model is formulated in

terms of fracture-face resistance and reservoir permeability.

As a result, the modified Mayerhofer method can be used to

determine fracture-face resistance from, for example, a filter

cake and the permeability to the reservoir fluid.

The original method of Mayerhofer, et al.2 uses an

estimate of permeability and fracture-face resistance from a

specialized plot and requires a history match of pressure drop

(

P) and pressure derivative [d(

P)/dln(

t)] versus timeduring the shut-in period. The history match algorithm

requires varying permeability, fracture face resistance, and

fracture area until the pressure decline and pressure derivative

can be satisfactorily simulated.

The modified Mayerhofer method is different in tha

fracture geometry is assumed; e.g., confined height or radia

and fracture extent (area) is determined from Nolte-

Shlyapobersky analysis of the pressure falloff data.1 As a

result, a history match of the pressure falloff is not required to

determine fracture area, and the estimated permeability and

fracture face resistance are representative, provided the

fracture dimensions are realistic.

The justification for using Nolte-Shlyapobersky analysis

and 2D fracture geometry is based on fracture imaging

experiments in low-permeability sands. The experiments have

demonstrated that small volume, low rate water injections are

typically confined to the sand body or perforated interval.5

Application of the modified Mayerhofer method to the

pressure falloff data results in a specialized plot. From the

specialized plot, fracture-face damage is proportional to the

intercept of a straight line through the data (fracture-face

damage increases as the intercept increases), and permeability

is proportional to the reciprocal of the slope.

Key assumptions for application of modified Mayerhofer

analysis include the following.

Homogeneous reservoir

Constant fracture area during closure Constant permeable area during closure

Constant compliance during closureValk and Economides

1 note that the method of

Mayerhofer, et al. is sensitive to deviations from its

assumptions. Thus, a means of identifying reservoi

heterogeniety, changing fracture area, or variable fracture

compliance would be beneficial when attempting modified

Mayerhofer analysis.

G-function derivative analysis provides a means for

identifying heterogeneous (fractured/fissured) reservoirs

changes in fracture area during shut-in, or variable fracture

compliance during shut-in. G-function derivative analysis

therefore, is recommended for identifying when theassumptions implicit in the Mayerhofer, et al. method are

violated during pressure falloff.

Combining G-Function Derivative and ModifiedMayerhofer AnalysisThe leakoff types or closure mechanisms identified from

G-function derivative analysis all result in distinctive

specialized Mayerhofer plots. As described by Valk and


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ADAPTING HIGH-PERMEABILITY LEAKOFF ANALYSIS TO LOW-PERMEABILITYSPE 60291 SANDS FOR ESTIMATING RESERVOIR ENGINEERING PARAMETERS 3

Economides1, the data on a specialized Mayerhofer graph

should lie along a straight line with an intercept greater than or

equal to zero and with a positive slope. When the pressure-

falloff data deviate from the assumptions of the Mayerhofer

method, the data do not fall along a straight line.

The following examples illustrate the effects of normal

leakoff, pressure-dependent leakoff, fracture-height recession,and fracture-tip extension on the specialized Mayerhofer plot.

After analyzing more than 1,500 diagnostic fracture injection

tests, no examples of changing compliance during shut-in have

been observed in hard rock low permeability sandstones.

The recommended analysis procedure for the modified

Mayerhofer method and G-function derivative analysis can be

found in Refs. 1 and 4, respectively. All diagnostic fracture

injection tests shown used KCl treated water (1% to 4% KCl

depending on the formation), and as a result, no fracture face

damage is indicated in any of the specialized Mayerhofer plots

(damage intercept 0).

Normal Leakoff

The G-function derivative analysis for an example of normal

leakoff is shown in Fig. 2 with the specialized Mayerhofer

plot shown in Fig. 3. During normal leakoff, the fracture area

is constant, and the reservoir rock appears homogeneous. The

superposition derivative (GdP/dG), therefore, is linear until

fracture closure, and the pressure-falloff data in the specialized

Mayerhofer plot lie along a straight line.

Field Case. The normal leakoff field case is from a well in

southwest Wyoming that produces gas from a single sandstone

perforated between 12,729- and 12,738-ft (16-ft gross

thickness). The diagnostic fracture injection test consisted of

2,500-gal of 2% KCl water pumped at 6.20-bpm, and

hydraulic fracture closure was observed after 5.60 minutes of

shut-in. Fig. 4contains the G-function derivative analysis anddemonstrates that the superposition derivative is linear until

closure. A very early period of pressure-dependent leakoff

might be interpreted from the derivative and superposition

derivative, but the majority (80%) of the pressure decline

represents normal leakoff behavior.

Fig. 5 contains the specialized Mayerhofer plot and

demonstrates that the falloff data lie on a straight line with an

intercept at the origin. The permeability estimate is calculated

from the slope of the straight line and the fracture half-length,

which is calculated from Nolte-Shylapobersky analysis

assuming GDK fracture geometry. The estimated fracture

half-length is 116 ft; the estimated permeability is 0.227 md;

and the pore pressure, which was determined from after-closure analysis, is 8,850 psi.

The sandstone was subsequently fracture stimulated with

115,000-lb, intermediate-strength proppant, and a history

match of pressure with a fully 3D fracture model6 suggested

approximately 420-ft of conductive fracture half-length.

Fig. 6contains a comparison of observed gas production

and simulated gas production using results of the diagnostic

fracture injection test and the hydraulic fracture model. The

flowing bottomhole pressure input into the reservoir simulator

was calculated based on reported surface pressure and gas

rates. Fig. 6 shows excellent agreement between simulated

and observed gas production rates and cumulative production.

Since normal leakoff was observed, the permeability

estimate from the modified Mayerhofer method should be

reasonable, provided the fracture dimensions from the

injection test were correct. The simulation results shown inFig. 6validate the permeability estimates for this example o

normal leakoff.

Pressure-dependent Leakoff

Fig. 7 contains the G-function derivative analysis for a

diagnostic fracture injection test that exhibits pressure-

dependent leakoff. Pressure-dependent leakoff is indicated by

the large hump in the superposition derivative that lies

above a line through the normal leakoff data prior to hydraulic

fracture closure.

Pressure-dependent leakoff is the result o

fractures/fissures that were dilated by the injection test. As the

pressure declines during the falloff, the fractures/fissures

constrict until closure at the fissure opening pressure. Theresult of the dilation/constriction sequence is variable leakoff

during closure, and can be an indication of a heterogeneous

dual-porosity reservoir.

Ehlig-Economides, Fan, and Economides7 extended the

theoretical development of the Mayerhofer method to

naturally fractured reservoirs and found that application of the

Mayerhofer method in dual-porosity reservoirs will provide an

estimate of kfb (the product of bulk permeability of the

natural fracture system and fracture storativity ratio)

Unfortunately, dual-porosity behavior results in a non-linear

specialized Mayerhofer plot.

Fig. 8 contains the specialized Mayerhofer plot for the

pressure falloff data shown in Fig. 7. Fig. 8demonstrates thathe data are non-linear and sweep across the plot. As a

result, kfb varies from 0.010-md with a line through the

early-time data, and 0.002-md with a line through the late-time

data. In other words, the specialized Mayerhofer plot suggests

permeability is decreasing with time during fracture closure

which is consistent with a dilated fracture systems

constricting during closure.

Ehlig-Economides, et al.7 also note that reasonable

estimates of kfband fracture face resistance are possible if a

portion of the specialized plot is straight. The straight portion

of the data correspond to the normal leakoff data from the

G-function derivative analysis; thus, the G-function plot can

be used to locate the straight line on the specializedMayerhofer plot. For example, the straight line through the

late-time data in Fig. 8 (kfb = 0.002-md), represent the

normal leakoff data shown in Fig. 7between fissure opening

and fracture closure pressure.

Field Case. The pressure-dependent leakoff field case is

from a well producing dry gas from a single sandstone

perforated between 5,819 and 5,855 ft (35-ft gross thickness)

The diagnostic fracture-injection test consisted of 1,092-gal o


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2% KCl water pumped at 5.30-bpm. Hydraulic fracture

closure was observed after only 1.50 minutes of shut-in, which

qualitatively suggests relatively high permeability. Fig. 9

contains the G-function derivative analysis and shows a period

of pressure-dependent leakoff during the first half of the

before-closure data. As the pressure declines below the fissure

opening pressure (3,294-psi), the superposition derivative islinear until hydraulic fracture closure at 3,246-psi.

Since hydraulic fracture closure occurred rapidly, only a

few data points are plotted on the specialized Mayerhofer plot

shown in Fig. 10. The effects of pressure-dependent leakoff

are subtle compared to Fig. 8, but some curvature is evident,

and the correct straight line is drawn through the normal

leakoff data identified with Fig. 9.

The fracture half-length calculated from Nolte-

Shylapobersky analysis assuming GDK fracture geometry is

92-ft, and pore pressure is 2,380-psi from after-closure

analysis. Assuming a homogeneous reservoir, the

permeability estimated from the modified Mayerhofer method

is 0.0062-md.

The sandstone was subsequently fracture stimulated, and ahistory match of pressure with a fully 3D fracture model

6

suggested approximately 362-ft of conductive (1,000 md-ft)

fracture half-length.

Fig. 11 contains two comparisons of observed gas

production and simulated gas production using results of the

diagnostic fracture injection test and the hydraulic fracture

model. As previously noted, the flowing bottomhole pressure

input into the reservoir simulator was calculated from the

reported surface pressure and gas rates. Fig. 11 shows very

poor agreement between observed gas production rates and

simulated production rates assuming a single porosity

0.0062-md reservoir. If, however, a dual porosity reservoir is

modeled assuming kfb = 0.0062-md, a very good match isobtained with kfb= 0.826-md and = 0.0075 (= 9.210

-7).

As noted by Ehlig-Economides, et al.,7the storativity ratio,

, cannot be determined from a diagnostic fracture injection

test; thus, an additional well test is required to accurately

predict production. A diagnostic injection remains valuable,

however, by providing the opportunity to identify fractured

reservoirs with G-function derivative analysis and the ability

to determine the product kfbwith Mayerhofer analysis.

Fracture-Tip Extension

Fracture-tip extension after shut-in is the result of extremely

low leakoff. Physically, fracture-tip extension occurs when

the energy from the injection test cannot be released throughleakoff and is dissipated through fracture growth. Fracture-tip

extension typically occurs in very low permeability reservoirs

and has been shown to correlate with poor production.8,9

Fig. 12 contains the G-function derivative analysis, and

Fig. 13 contains the specialized Mayerhofer plot for a zone

exhibiting fracture-tip extension after shut-in. Similar to the

pressure-dependent leakoff example, the data on the

specialized Mayerhofer plot are non-linear and sweep across

the graph. Using only the specialized Mayerhofer plot, it

would be virtually impossible to distinquish between pressure-

dependent leakoff and fracture-tip extension after shut-in

Both leakoff mechanisms can result in large pressure drops

but the pressure falloff mechanisms are obviously very

different. For example, the pressure falloff in a fractured zone

is the result of dilated high permeability fractures while the

pressure falloff during fracture-tip extension results fromcontinued fracture growth.

Since the fracture continues to grow after shut-in, the

assumption of constant fracture area during closure is violated

and the permeability will be overestimated using the modified

Mayerhofer method. Fig. 13 contains two estimates of

permeability using the early-time data (kr,M= 0.009-md) and

the late-time data (kr,M = 0.0019-md). As the shut-in time

increases, the leakoff rate and the calculated permeability

appear to decrease until fracture closure. Although the late

time data during fracture-tip extension is recommended for

estimating permeability from the specialized plot, permeability

will still be overestimated since the fracture continues to grow

during closure.

Field Case. The case history demonstrating fracture-tipextension is actually a complex example that shows an early

period of pressure-dependent leakoff and tip extension. Since

the majority of the leakoff appears to be tip extension, the

estimated permeability should be overestimated by the

modified Mayerhofer method.

The pressure-dependent leakoff, fracture-tip extension

field case is from a well in southwest Wyoming producing dry

gas from a single sandstone perforated between 12,634- and

12,646-ft (18-ft gross thickness). The diagnostic fracture

injection test consisted of 930-gal of 2% KCl water pumped at

3.30 bpm, and hydraulic fracture closure was observed after

40.70 minutes of shut-in. Fig. 14 contains the G-function

derivative analysis and shows a very early period of pressuredependent leakoff followed by a long period of fracture-tip

extension.

Fig. 15 contains the specialized Mayerhofer plot and

demonstrates that the falloff data are scattered. Several line

could be drawn through the data, but the straight line shown

was drawn through the points corresponding to the late time

fracture-tip extension data on the G-function derivative graph

The fracture half-length is calculated from Nolte-

Shylapobersky analysis assuming GDK fracture geometry is

87-ft and the assumed pore pressure is 8,850 psi based on the

pressure in an offset well. Assuming that the fracture half

length calculated from Nolte-Shlyapobersky analysis is

correct, the permeability estimated from the modifiedMayerhofer method is 0.008 md.

The sandstone was subsequently fracture stimulated with

95,000-lb intermediate strength proppant, and a history match

of pressure with a fully 3D fracture model6 suggested

approximately 382-ft of conductive (1,000 md-ft) fracture

half-length.Fig. 16contains a comparison of observed gas production

and simulated gas production using results from the diagnostic

fracture injection test, the hydraulic fracture model, and the


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flowing bottomhole pressure calculated from reported surface

pressure and production rates. Please note that the observed

data points during the gas metering error were thought by

the well operator to be 500 Mscf/D too high.

Fig. 16 shows the observed rates are slightly lower than

the simulated producing rates, which indicates that the

permeability may be overestimated by the modifiedMayerhofer analysis. Overall, however, the permeability

obtained from the before-closure data provides a reasonable

estimate of the productivity of the sand.

Fracture Height Recession

Fracture height recession occurs when the fracture grows into

high-stress, relatively impermeable layer(s) adjacent to the

permeable layer. During the shut-in, the fracture begins to

close in the impermeable layer(s) first, followed by closure in

the permeable layer. Fig. 17 contains the G-function

derivative analysis, and Fig. 18 contains the specialized

Mayerhofer plot for an example that exhibits fracture height

recession during shut-in.

Fig. 17 shows a very short period of normal leakoffbehavior followed by a period of fracture height recession and

finally another period of normal leakoff. Initially, the leakoff

rate is constant but relatively low because the leakoff in the

entire fracture volume is only through the permeable layer. As

the fracture closes in the impermeable layers during height

recession, the leakoff rate increases (shown by increasing

derivative). Finally, the total fracture area approaches the

permeable fracture area, and the leakoff rate is constant at a

rate higher than the initial period of normal leakoff.

The effects on the specialized Mayerhofer plot are shown

in Fig. 18. From the early-time data that correspond to the

first period of normal leakoff behavior, the permeability

estimate is 0.0007 md, and from the late-time data thatcorrespond to the second period of normal leakoff behavior,

the permeability estimate is 0.0017 md. Since the fracture

area is decreasing during closure, the constant fracture area

assumption of the modified Mayerhofer is violated, thus both

permeability estimates may be erroneous.

DiscussionUnderstanding the closure mechanism cannot be overstated

when using before-closure pressure falloff analysis for

determining permeability. In low permeability hard rock

sandstones, normal leakoff behavior is seldom observed. In a

recent paper by Craig, et al.9 normal leakoff behavior was

observed in only 17 of 190 (8.9%) diagnostic fractureinjection tests in Piceance Basin Mesaverde sandstones. The

most common leakoff types were pressure-dependent leakoff

(50.5%) and fracture-tip extension (34.7%).

Although normal leakoff behavior is uncommon in low

permeability sandstones, reservoir simulation results from this

paper and Craig, et al.9 show very good production history

matches are possible using the permeability derived from

before-closure pressure-decline analysis. It is important,

however, to recognize that permeability can be under- or

overestimated depending on the closure mechanism observed

For example, permeability is overestimated with fracture-tip

extension after shut-in.

Generalizations about sands exhibiting pressure-dependen

leakoff are not possible. In some cases, observed production

can exceed simulated production if a single porosity reservoir

is modeled. In the pressure-dependent leakoff field case, foexample, the single porosity simulation underestimated

production by 72 MMscf during the first 233 days of

production. In other cases, the simulated production from

sands with pressure-dependent leakoff is accurate.

Although a diagnostic injection test can determine the

product kfb, additional testing is required to specify theinterporosity flow coefficient and fracture storativity for

accurate simulation. Unfortunately, additional pressure

transient testing is economically impractical in most low-

permeability wells, thus the correct permeability wil

seldom be determined prior to stimulation and sustained

production.

Conclusions1. G-function derivative analysis is recommended for

identifying when assumptions implicit in the modified

Mayerhofer method are violated during the pressure

falloff following a diagnostic fracture injection test.

2. The straight line on the specialized Mayerhofer ploshould be drawn through the normal leakoff data

identified with G-function derivative analysis.

3. Pressure-dependent leakoff may identify aheterogeneous dual-porosity reservoir, but productivity

will be underestimated if kfb is determined with theMayerhofer method, and the fracture storativity ratio

, is less than one.4. Permeability will be overestimated using the modified

Mayerhofer method when fracture-tip extension is

indicated by G-function derivative analysis.

AcknowledgmentsThe authors wish to thank Halliburton Energy Services and

Marathon Oil Company for permission to publish this paper.

Nomenclaturekfb = bulk permeability of the natural fracture system, md

= fracture storativity ratio, dimensionless = interporosity flow coefficient, dimensionless

References1. Valk, P.P. and Economides, M.J.: Fluid-Leakoff

Delineation in High Permeability Fracturing, SPEProduction & Facilities(May 1999) 117-30.

2. Mayerhofer, M.J., Ehlig-Economides, C.A., and EconomidesM.J.: Pressure-Transient Analysis of Fracture-Calibration

Tests,JPT(March 1995) 229-234.


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3. Nolte, K.G., Maniere, J.L., and Owens, K.A.: After-ClosureAnalysis of Fracture Calibration Tests, paper SPE 38676

presented at the 1997 SPE Annual Technical Conference andExhibition held in San Antonio, TX, 5-8 October 1997.

4. Barree, R.D. and Mukherjee, H.: Determination of Pressure-dependent Leakoff and Its Effects on Fracture Geometry,

paper SPE 36424 presented at the 1996 Annual Technical

Conference and Exhibtion, Denver, 6-9 October 1996.5. Warpinski, N.R., et al.: An Interpretation of M-Site

Hydraulic Fracture Diagnostic Results, paper SPE 39950

presented at the 1998 SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium and Exhibition, Denver,CO, 5-8 April 1998.

6. Barree, R.D.: A Practical Numerical Simulator for ThreeDimensional Fracture Propagation in Heterogeneous Media,paper SPE 12273 presented at the 1983 SPE Symposium onReservoir Simulation, San Francisco, CA,15-18 November 1983.

7. Ehlig-Economides, C.A., Fan, Y., and Economides, M.J.Interpretation Model for Fracture Calibration Tests in

Naturally Fractured Reservoirs, paper SPE 28690 presentedat the 1994 SPE International Petroleum Conference &Exhibition of Mexico, Veracruz, Mexico10-13 October 1994.

8. Rollins, K. and Hyden, R.E.: Pressure-Dependent Leakoff in

FracturingField Examples from the Haynesville Sand,paper SPE 39953 presented at the 1998 SPE Rocky MountainRegional/Low Permeability Reservoirs Symposium, Denver

5-8 April 1998.9. Craig, D.P., et al.: Case History: Observations From

Diagnostic Injection Tests in Multiple Pay Sands of theMamm Creek Field, Piceance Basin, Colorado, pape

SPE 60321 presented at the 2000 SPE Rocky MountainRegional/Low Permeability Reservoirs Symposium, DenverColorado, 12-15 March 2000.

Figure 1. G-Function Derivative AnalysisLeakoff Mechanisms.

Normal Leakoff

1800

2650

3500

0 3 6

G-function

Pressure(psi)

0

500

1000

dP/dGo

rGdP/dG

Fracture Closure

Pressure

GdP/dG

dP/dG

Pressure Dependent Leakoff (Fissure Opening)

2700

3100

3500

0 2.5 5

G-function

Pressure(psi)

0

250

500

dP/dGo

rGdP/dG

Fissure Open ing Fracture Closure

Pressure

GdP/dG

dP/dG

Fracture Tip Extension

3200

3400

3600

0 1.75 3.5

G-function

Pressure(psi)

0

250

500

dP/dGo

rGdP/dG

Pressure

GdP/dG

dP/dG

Fracture Height Recession During Shut-in

3000

5000

7000

0 6 12

G-function

0

750

1500

Fracture Closure

Pressure

GdP/dG

dP/dG


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Figure 2. Normal Leakoff TypeG-Function

Derivative Analysis.

Normal Leakoff Type - Production History Match

0

2000

4000

6000

8000

0 50 100 150Producing Days

0

150

300

450

600

Simulator Results Actual Pr oduction

Simulated Cumulati ve Actua l Cumulati ve

Model Parameters

kg= .2266-mD

Pr= 8850-psi

Lf= 421-ft

Figure 6. Normal Leakoff TypeProduction History

Match.

Figure 4. Normal Leakoff TypeG-Function


Normal Leakoff Type

Modified Mayerhofer, et. al. Technique; GdK Geometry

0

10

20

0.0E+00 3.0E-09 6.0E-09

X(n)

Y(n)

kr,M= 0.2266-md

Figure 5. Normal Leakoff TypeModified

Mayerhofer Analysis.

Figure 7. Pressure Dependent LeakoffG-Function


Normal Leakoff Type

1 Second G-function Derivative Analysis

7000

9000

11000

0 2.5 5

G-function

Pressure(psi)

0

500

1000

dP/dGo

rGdP/dG

Fracture Closure

Pressure

GdP/dG

dP/dG

Normal Leakoff

1800

2650

3500

0 3 6

G-function

0

500

1000

Fracture Closure

Pressure

GdP/dG

dP/dG

Normal Leakoff


0

15

30

0.0E+00 2.0E-09 4.0E-09

X(n)

kr,m= 0.050-md

Figure 3. Normal Leakoff TypeSpecialized

Mayerhofer Plot.

Pressure Dependent Leakoff

G-Function Plot

9000

10500

12000

0 9 18

G-function

0

500

1000

Fracture Closure

Pressure

GdP/dG

dP/dG

Fissure Opening


8/9




0

45

90

0.0E+00 1.3E-09 2.5E-09

X(n)

kr,M= 0.00212-md

kr,M= 0.01032-md

Figure 8. Pressure Dependent LeakoffModified



1 Second G-function Plot

8000

11000

14000

0 6 12

G-function

Pressure(psi)

0

1000

2000

dP/dGo

rGdP/dGFracture Closure

Pressure

GdP/dG

dP/dG

Figure 12. Fracture Tip ExtensionG-Function




0

15

30

0.0E+00 2.5E-09 5.0E-09

X(n)

Y(n

)

kr,M= 0.0019-md

kr,M= 0.0090-md

Figure 13. Fracture Tip ExtensionModified

Mayerhofer Method.


0

1000

2000

3000

0 125 250

Time (days)

Production (mcf)

Dual Porosity Simulation

Single Porosity Simulation

0.826 0.0075fbk md = =

0.0062k md=

Figure 11. Pressure Dependent LeakoffDual Porosity

Reservoir ExampleProduction.

Figure 9. Pressure Dependent LeakoffDual Porosity

Reservoir ExampleG-Function Derivative Analysis.

Pressure Dependent Leakoff-Dual Porosity Reservoir Example1 Second G-function Plot

2900

3200

3500

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2G-function

0

500

1000

Fracture Closure

Pressure

GdP/dG

dP/dG

Pressure Dependent Leakoff--Dual Porosity Reservoir


0

3

6

0.0E+00 3.0E-10 6.0E-10

X(n)

Figure 10. Pressure Dependent LeakoffDual

Porosity Reservoir ExampleSpecialized Mayerhofer

Plot.


9/9


Figure 17. Fracture Height RecessionG-Function

Derivative Analysis



0

10

20

0.0E+00 7.0E-10 1.4E-09

X(n)

kr,M = 0.00174-mdkr,M = 0.00068-md

Figure 18. Fracture Height RecessionModified




0

4000

8000

0 4 8

G-function

0

2000

4000

Fracture Closure

Pressure

GdP/dG

dP/dG



8000

10000

12000

0 6 12

G-function

0

500

1000

Fracture Closure

Figure 14. Pressure Dependent Leakoff-Fracture Tip

ExtensionG-Function Derivative Analysis.

Pressure Dependent Leakoff - Fracture Tip Extension


0

7

14

0.0E+00 7.0E-10 1.4E-09

X(n)

kr,M= 0.008-md


ExtensionModified Mayerhofer Analysis.


ExtensionProduction History Match.


0

1000

2000

0 45 90

Time (days)

Production (mcf)

Simulation (mcf)

Model Parameters

kg= 0.0076-md

PR= 8,850-psi

Lf= 382-ft

Gas Metering Error

g function spe 60291

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