Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model
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摘要: 考虑了二次梯度项的非线性双重介质模型．在模型中假设岩块和裂缝间的压力差作为初始未知量，在岩块中是拟先态的，从而避免了解联立方程组．利用广义Hankel变换求得了径向流动的解析解，由于解析解是无穷级数，无法得到具体的值．通过数值求解特征值问题，从而算得了窟体的压力值，并探讨了非线性参数和双重介质参数变化时压力的变化规律，给出了典型压力曲线图版，这些结果可用于实际的试井分析．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.
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Key words:
- nonlinear dual porosity /
- Hankel transform /
- analytical solution /
- pressure curve
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[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. -
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