Computer Simulation of Hydraulic Fracturing in Shales-Influences on Primary Migration Ismail Ozkaya, Kuwait U.

Summary

Hydraulic tension fractures in a shale layer during sedimentation are simulated by use of computer tech­niques. The depth at which fractures form is directly pro­portional to the hydraulic conductivity and tensile strength, and inversely proportional to the rate of sedimentation and thickness of the shale layer. Hydraulic fractures may form at depths of oil generation to facilitate primary migration. This paper describes an at­tempt to simulate the process of hydraulic fracturing dur­ing burial and compaction of a shale layer by use of an elementary model. One objective is to investigate the role of various factors in hydraulic tension fracturing of shales in a tectonically relaxed area. Another objective is to see whether hydraulic fractures form at depths of oil generation.

Introduction

Hydraulic fracturing of rocks was first investigated by Hubbert and Willis, I and subsequently by other investigators. 2-1O The role played by hydraulic fractur­ing in the process of primary migration has attracted the attention of several authors. II ,12 Existing computer simulation experiments of oil generation and migra­tion,13,14 however, do not deal with hydraulic fracturing.

Simulation Model A horizontal shale layer of thickness h, bounded by porous and permeable sand layers, is taken as the basis of the simulation model. The shale is buried progressive­ly at a constant rate of sedimentation. Sands retain hydropressures during sedimentation, whereas shales generally develop abnormal fluid pressures because of compaction and low permeability values. 15 Pore fluids tend to flow from the abnormally pressured shale ver­tically upward and downward into the hydropressured envelope. The general differential equation governing such a vertical fluid flow from shale is 16

(Ch IS)(d2tfJldD2)=dtfJldt . .................. (1)

Solution of this equation with appropriate boundary con­ditions gives the value of potential and hence pressure in time across the shale layer.

In areas that are tectonically relaxed, the principal

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Copyright 1984 Society 01 Petroleum Engineers 01 AIME

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stress, 0' VI' is vertical and given by 17

O'VI=PbgD . .............................. (2)

The effective vertical stress, 0' Ve' is 18,19

O'Ve =O'VI-(l-a)pp' ....................... (3)

In such a case, the least stress is horizontal. If no lateral strain is assumed to exist, and if the effect of temperature is neglected, the least horizontal effective stress, 0' He' is related to effective vertical stress, 0' Ve' by 1,3,7,9

O'He =["/(l-")]O'Ve' ....................... (4)

Hydraulic fracture generation and propagation require an elaborate mathematical treatment taking into account stress-intensity factor, fracture length, height, rate of fluid flow in and out of the fracture, factors controlling such rates, effect of temperature and fracture geometry on tensile strength, etc. 5-8

In the present model, a simple criterion is used. Frac­tures propagate if

Pj>O'He +(I-a)pp +FI . .................... (5)

Maximum fluid pressure, Pmax' occurs around the center in compacting shales. When Pmax satisfies Eq. 5, then a fracture is initiated at the point where pore pressure is maximum. The fracture is oriented vertically since the least effective stress is horizontal and principal stress is vertical. Hence, a fracture extends from a high-pore­pressure zone into a low-pore-pressure and low­permeability zone. It is assumed that the rate of fluid flow into the fracture at the origin is high enough to keep P j at P max and to ensure propagation of the crack toward the edge of the shale layer.

Parameters The parameters and corresponding values used in this simulation experiment are listed in Table 1. Some of these parameters vary with depth and temperature. 2()..22 Nevertheless, constant values are used in a single simulation run to keep the model basic. The variation of parameters such as P \II and P b with temperature and depth has only a negligible effect on the final results. 16 Both hydraulic conductivity, C h' and storage coeffi­cient, S, decrease with depth of burial, while the ratio

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TOp 1000. a.- O.CIIXI.J ",1, If-a25 ... ." "-17'5.104

". s -O.~ .-1 700

~VVWVv

"'0... 0 DEPTH OF BUR,Al. 0

Fig. 1-Spikes represent pulsating fractures extending .upward from the center of the shale.

TABLE 1-LlST OF PARAMETERS

P W ' g/cm 3

Pb' g/cm 3

I-' a <I> S(1/m) h, m C h , m/a

R, mm/a

1.0 2.3

0.25 0.05

0.5 0.02 1000

0.0003 0.0005

0.001 50.0

100.0 175.0

0.1 0.25

0.5

ChiS remains nearly constant. 20 Poisson's ratio, /-t, also varies with depth. A commonly quoted average is used. I ,9 Tensile strength, F t , decreases with temperature. The values chosen are representative often­sile strength of shales at elevated temperatures. 22 Biot's constant, a, which is the ratio of bulk to grain com­pressibility, decreases with decreasing effective stress. 19

Quoted values range between 0.0 and 0.05. The max­imum value is used.

Procedure

Fluid flow from the shale layer into the sand envelope is simulated by a numerical timestep solution of Eq. l. Simulation is conducted in two steps with different boundary conditions. The initial stage represents deposi­tion of the shale layer itself. The main stage is the burial of the shale layer during sedimentation. The sediment load is increased by an amount proportional to the rate of deposition, R, at each step. Pore pressure, PP' across the shale is modified accordingly before the next iteration phase is entered. Porosity variation across the shale is computed by the modified form of Aty's equation 15 to determine thickness reduction of the shale with compac­tion. The maximum depth of burial is 10 000.0 m [32,808 ft]. Simulation of fluid flow is conducted without addition of new sediment beyond that stage. Hydraulic fractures are formed and propagated vertically upward and downward as long as Eq. 5 is satisfied.

MAY 1984

500

+ + I!!J()

~~+ .. .. + ..

*+ .. .. z.o 700 1000

DEPTH.O tm)

Fig. 2-Variation of depth of fracturing with tensile strength for different sedimentation rates and hydraulic conductivity values.

I I I \

l \ ~500+-~~--+-------+-------+-------4-------~ -! ot

I ~ZOO+---~--+-~ __ --+-------+-------+-------4

i 1000

HYDRAULIC CONDUCTIVITY. K (.10--' ",/,

Fig. 3-Plot of tensile strenth vs. hydraulic conductivity values at which fractures form.

When a propagating fracture reaches a sand boundary, hydraulic conductivity, C h, of the shale is increased to an arbitrary large value, 0.1 m/a [0.33 ft/yr]. Fractures are closed and original hydraulic conductivity values are resumed when Eq. 5 is no longer satisfied-i.e., when tensile strength is zero. Fractures are reopened when the fluid pressure builds up once again to satisfy Eq. 5. In the second and subsequent reopening of the fractures the tensile strength, F t, is set to zero.

Results

The simulation experiment shows that hydraulic tension fractures may form within a compacting shale layer dur­ing sedimentation when a suitable combination of hydraulic conductivity, C h' sedimentation rate, R, ten­sile strength, F t , and thickness, h, is attained (Fig. 1). Fractures extend upward from the center of the shale in most cases. Downward fractures rarely form. Fractures form only with a hydraulic conductivity value, C h, less than 0.0003 m/a [0.0001 ft/yr]. A plot of tensile strength, F t , vs. depth of fracturing, D, and hydraulic conductivity, C h (Figs. 2 and 3) shows that depth is directly proportional to hydraulic conductivity and ten­sile strength while it is inversely proportional to the rate of sedimentation, R, and thickness, h, of the shale layer.

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Discussion

The value of Biot's constant, a, must be greater than zero for hydraulic fracturing in the present model. This may not be justified in reality since Biot's constant, a, tends toward zero with decreasing porosity and increas­ing pore pressure. 19 The hydraulic conductivity, Ch ,

limit for fracture generation is very low. This results mainly from the approximation of the least horizontal ef­fective stress from effective vertical stress (Eq. 4). If the total horizontal stress is assumed proportional to the total vertical stress,23 then fractures form at much higher hydraulic conductivity values for the same sedimentation rates and tensile strength values, even when Biot's con­stant is set to zero.

The source of abnormal fluid pressure is compaction in this simulation experiment. It is possible that aquather­mal pressuring,24 osmosis,25 and clay dehydration 26,27

contribute to pore pressures within a shale during burial, enhancing the possibility of hydraulic fracturing at higher hydraulic conductivity and tensile strength values than those obtained in this simulation experiment.

Conclusions

The results presented should be viewed as having qualitative rather than quantitative significance because of the simplicity of the model. Nevertheless, it may be suggested that hydraulic fracturing is expected within the depth ranges of oil generation in source shales. Such fractures may close and reopen several times and may pump fluids out of the shale into the sand layers above. Such fluid pumping may greatly facilitate primary migration.

Nomenclature

a = Biot's constant

C h = hydraulic conductivity, m/a [ft/yr]

D = depth of burial of the shale layer, m [ft]

FI tensile strength, Pa [psi]

g = acceleration of gravity, cm/s 2 [in./sec 2]

h = thickness of shale layer, m [ft]

PI = fluid pressure within a fracture, Pa [psi]

Pmax = maximum pore pressure, Pa [psi]

P p = pore pressure, Pa [psi]

R = rate of sedimentation, mm/a [in./yr] S = storage coefficient, m -I [ft -I]

t = time, years

/l. Poisson's ratio

Pb = bulk rock density, g/cm3 [g/cu in.]

Pw = water density, g/cm 3 [g/cu in.]

cP = porosity, fraction

<I> = potential energy, J [kW -hr]

(J He = effective least horizontal stress, Pa [psi]

(J HI = total least horizontal stress, Pa [psi]

(J Ve = effective vertical stress, Pa [psi]

(JVI = total vertical stress, Pa [psi]

References

I. Hubbert, M.K. and Willis, D.G.: "Mechanics of Hydraulic Frac­turing," Trans., AIME (1957) 210, 157-67.

2. Secor, D.T.: "Role of Fluid Pressure in Jointing," Amer. J. Sci. (Oct. 1965) 263, 633-46.

3. Eaton, B.A.: "Fracture Gradient Prediction and Its Application in Oilfield Operations," J. Pet. Tech. (Oct. 1969) 1353-60: Trans., AIME,246.

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4. Pollard, D.D. and Holzhausen, C.: "On the Mechanical Interac­tion Between Fluid Filled Fracture and The Earth's Surface," Tec­tonophys. (Oct. 1969) 27-57.

5. Beach, A.: "Numerical Models of Hydraulic Fracturing and the Interpretation of Syntectonic Veins," J. Structural Geol. (1980) 4, No.4, 425-35.

6. Hagoort, J., Weathill, B.D., and Settari, A.: "Modeling the Prop­agation of Waterflood-Induced Hydraulic Fractures," Soc. Pet. Eng. J. (Aug. 1980) 293-303.

7. Daines, S.R.: "Prediction of Fracture Pressures for Wildcat Wells," J. Pet. Tech. (July 1982) 863-72.

8. van Eekelen, H.A.M.: "Hydraulic Fracture Geometry: Fracture Containment in Layered Formations," Soc. Pet. Eng. J. (June 1982) 341-49.

9. Watts, N.L.: "Microfractures in Chalks of Albuskjell Field, Norwegian Sector, North Sea: Possible Origin and Distribution," Bull., AAPG (1983) 201-34.

10. Pratts, M.: "Effect of Burial History on the Subsurface Horizontal Stresses of Formations Having Different Material Properties," Soc. Pet. Eng. J. (1981) 658-62.

II. Magara, K.: "Mechanism of Natural Fracturing in a Sedimentary Basin, Bull., AAPG (1981) 123-32.

12. Rouchet, J.: "Stress Fields, a Key to Oil Migration," Bull., AAPG (1975) 74-85.

13. Welte, D.H. and Yukler, M.A.: "Petroleum Origin and Ac­cumulation in Basin Evaluation-A Quantitative Model," Bull., AAPG (1981) 1387-96.

14. Namayama, K. and Von Sielen, D.C.: "Simulation Model for Petroleum Exploration," Bull., AAPG (1981) 1230-55.

15. Chapman, R.E.: "Clays with Abnormal Interstitial Fluid Pressures," Bull., AAPG (1972) 790-95.

16. Sharp, J.M. and Domenico, P.A.: "Energy Transport in Thick Sequence of Compacting Sediments," Bull., GSA (1976) 390-400.

17. Gretener, P.E.: "Pore Pressure Fundamentals, General Ramifica­tions, and Implications for Structural Geology (Revised)," AAPG Course Note Series No.4.

18. Fyfe, W.S., Price, N.J., and Thompson, A.B.: "Fluids in the Earth's Crust," Elsevier Scientific Publishing Co., New York Ci­ty (1978).

19. Nur, A. and Byerlee, J.D.: "An Exact Effective Stress Law for Elastic Deformation of Rock Units With Fluids," J. Geophys. Res. (Sept. 1971) 4, No. 26, 6414-19.

20. Bishop, R.S.: "Calculated Compaction States of Thick Abnor­mally Pressured Shales," Bull., AAPG (1979) 918-33.

21. Plumley, W.J.: "Abnormally High Fluid Pressure: Survey of Some Basic Principles," Bull., AAPG (1980) 414-30.

22. Closmann, P.J. and Bradley, W.B.: "The Effect of Temperature on Tensile and Compressive Strengths and Young's Modulus of Oil Shale," Soc. Pet. Eng. J. (Oct. 1979) 301-12.

23. Barr, W. and Currie, J.B.: "Origin of Fracture Porosity-Exam­ple From Altamont Field, Utah," Bull., AAPG (1982) 1231-47.

24. Barker, C.: "Aquathermal Pressuring; Role of Temperature in Development of Abnormal Pressure Zones," Bull., AAPG (1972) 2068-71.

25. Magara, K.: "Compaction, Ion Filtration and Osmosis in Shale and Their Significance in Primary Migration," Bull., AAPG (1974) 283-90.

26. Powers, M.C.: "Fluid Release Mechanisms in Compacting Marine Mudrock and Their Importance in Oil Exploration," Bull., AAPG (1967) 1240-54.

27. Burst, J.F.: "Diagenesis of Gulf Coast Clayey Sediments and Its Possible Relation to Petroleum Migration," Bull., AAPG (1969) 73-93.

SI Metric Conversion Factors cu in. x 1.638706 E+OI cm 3

ft x 3.048* E-Ol m in. X 2.54* E+OO cm psi x 6.894757 E+OO kPa

*Conversion factor is exact. JPT Original manuscript received in SOCiety of Petroleum Engineers oflice Nov. 17, 1982. Paper accepted for publication Aug. 2. 1983. Revised manuscript received Dec. 28, 1983. Paper (SPE 11455) first presented at the 1983 SPE Middle East Oil Technical Conference held in Manama, Bahrain, March 14-17.

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