Deriving the shape factor of a fractured rock matrix
Fluid flow from a fractured rock matrix was investigated for accurately predicting oil recovery from fractured reservoirs. To relate the oil rate with rock geometry and average rock matrix pressure, a shape factor is used in the mathematical model of fractured reservoirs. The shape factor in the transfer function was derived by solving the three-dimensional diffusivity equation of a rock matrix block under unsteady-state production, in contrast to the quasi-steady-state condition assumed by most previous studies denoted in the literature. The diffusivity equation in the x, y, and z coordinate was solved in four cases by assuming different boundary conditions of (1) constant fracture pressure; (2) constant flow rate; (3) constant fracture pressure followed by linearly declining fracture pressure; and (4) linearly declining fracture pressure followed by constant fracture pressure. Shape factor values are high at the initial depletion stage under an unsteady-state condition. When the fracture pressure is constant, the shape factor converges to {pi}{sup 2}/L{sup 2}, 2{pi}{sup 2}/L{sup 2}, and 3{pi}{sup 2}/L{sup 2} for one-, two-, and three-dimensional rock matrix, respectively, at the dimensionless time ({tau}) of about 0.1. When the flow rate between the rock matrix and the fracture is constant, the fracture pressure varies with location on the rock surface. Based on the average fracture pressure, the shape factor decreases with production time until a {tau} value of 0.1 is reached. The boundary conditions of constant fracture pressure followed by a constant decline in fracture pressure are equivalent to the condition of a constant fracture pressure followed by a period of constant flow rate.
- Research Organization:
- National Inst. for Petroleum and Energy Research, Bartlesville, OK (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FC22-83FE60149
- OSTI ID:
- 10192737
- Report Number(s):
- NIPER-696; ON: DE93000170; BR: 35AA15000/35AA20000
- Resource Relation:
- Other Information: PBD: Sep 1993
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
FRACTURED RESERVOIRS
FLUID FLOW
MATHEMATICAL MODELS
ROCKS
GEOLOGIC FRACTURES
SHAPE
PRODUCTION
FORECASTING
THREE-DIMENSIONAL CALCULATIONS
BOUNDARY CONDITIONS
GEOMETRY
RESERVOIR ENGINEERING
FLOW RATE
020300
990200
DRILLING AND PRODUCTION
MATHEMATICS AND COMPUTERS