Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model

TONG Deng-ke; ZHANG Hong-qing; WANG Rui-he

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(10): 1161-1167

TONG Deng-ke, ZHANG Hong-qing, WANG Rui-he. Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model[J]. Applied Mathematics and Mechanics, 2005, 26(10): 1161-1167.

Citation:

TONG Deng-ke, ZHANG Hong-qing, WANG Rui-he. Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model[J]. Applied Mathematics and Mechanics, 2005, 26(10): 1161-1167.

Citation:

TONG Deng-ke, ZHANG Hong-qing, WANG Rui-he. Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model[J]. Applied Mathematics and Mechanics, 2005, 26(10): 1161-1167.

PDF( 2221 KB)

Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model

1.
Department of Applied Mathematics, Petroleum University(East of China), Dongying, Shangdong 257061, P. R. China;

Received Date: 2003-04-28
Rev Recd Date: 2005-03-25
Publish Date: 2005-10-15

Abstract

Abstract

A nonlinear dual-porosity model considering a quadratic gradient term is presented. Assuming the pressure difference between matrix and fractures as a primary unknown, to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the blocks from the fractures was furnished with a quasi-steady-state flow in the blocks. Analytical solutions were obtained in a radial flow domain using generalized Hankel transform. The real value cannot begotten be cause the analytical solutions were infinite series. The real pressure value was obtained by numerical solving the eigen-value problem. The pressure law of the changes of nonlinear parameters and those of dual-porosity parameters was studied, and the plots of typical curves are given. All these result can be applied in well testanalysis.
- nonlinear dual porosity,
- Hankel transform,
- analytical solution,
- pressure curve

FullText(HTML)

References(7)

References

[1]	Odeh A S,Babu D K.Comprising of solutions for the nonlinear and linearized diffusion equations[J].SPE Reservoir Engineering,1998,3(4):1202—1206.
[2]	Finjord J,Aadony B S.Effects of quadratic gradient term in steady-state and quasi-steady-state solutions for reservoir pressure[J].SPE Formation Evaluation,1989,4(3):413—417.
[3]	Wang Y,Dusseault M B.The Effect of quadratic gradient terms on the borehole solution in poroelastic media[J].Water Resource Research,1991,27(12):3215—3223. doi: 10.1029/91WR01552
[4]	Chakrabarty C,Farouq Ali S M,Tortike W S.Analytical solutions for radial pressure distribution including the effects of the quadratic-gradient term[J].Water Resource Research,1993,29(4):1171—1177. doi: 10.1029/92WR02892
[5]	Bai M Q,Roegiers J C.A nonlinear dual-porosity model[J].Appl Math Modelling,1994,18(9)：602—610. doi: 10.1016/0307-904X(94)90318-2
[6]	Streltsova T D.Well Testing in Heterogeneous Formation[M].New York:John Wiley & Sons,1988.
[7]	Warren J E,Root P J.Behavior of naturally fractured reservoirs[J].Soc Pet Eng J,1963,228(3):245—255.