Abstract
This paper presents the analytical solutions in Laplace domain for two-dimensional nonsteady flow of slightly compressible liquid in porous media with double porosity by using the methods of integral transforms and variables separation. The effects of the ratio of storativities ω, interporosity flow parameter λ on the pressure behaviors for a vertically fractured well with infinite conductivity are investigated by using the method of numerical inversion. The new log-log diagnosis graph of the pressures is given and analysed.
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Abbreviations
- c :
-
compressibility, Pa−1
- s :
-
Laplace space variable
- h :
-
formation thickness, m
- t :
-
time, s
- k :
-
permeability, m2
- x, y, z :
-
coordinates
- p :
-
pressure, Pa
- μ :
-
viscosity, Pa·s
- p N :
-
initial pressure, Pa
- φ :
-
porosity
- Q :
-
flow rate, m3/s
- f :
-
related to fissures
- D :
-
dimensionless
- m :
-
related to matrix
- W :
-
wellbole
References
Gringarten, A. C. et al., Unsteady state pressure distributions created by a well with a single infinite conductivity vertical fracture,Soc. Pet. Eng. J., Aug. (1971), 317–364.
Houxze, O. P. et al., Pressure transient response of an infinite-conductivity vertical-porosity behavior,SPE Formation Evaluation, Sept. (1988), 510–518.
Stehfest, H., Numerical inversion of Laplace transforms,Communications of the ACM, Jan. (1974), 47–49.
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Dedicated to the Tenth Anniversary and One Hundred Numbers of AMM (III)
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Ci-qun, L. The transient two-dimensional flow through double porous media. Appl Math Mech 12, 265–270 (1991). https://doi.org/10.1007/BF02098056
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DOI: https://doi.org/10.1007/BF02098056