Power series analytical solution for 2D quasi-Laplace equation with piecewise constant conductivities

Abstract In this paper, the analytical solution for 2D quasi-Laplace equation with piecewise constant conductivities is provided. The analytical solution can be expressed as an infinite power series with a group of intrinsic non-integer power exponents around each singular point. Combined with the given boundary conditions, the coefficient of each term can be determined by numerical methods.

[1]  S. M. Farouq Ali,et al.  Determining Interblock Transmissibility in Reservoir Simulators , 1974 .

[2]  Benoit Noetinger,et al.  Calculation of Internodal Transmissivities in Finite Difference Models of Flow in Heterogeneous Porous Media , 1995 .

[3]  Peter R. King,et al.  Upscaling permeability: Error analysis for renormalization , 1996 .

[4]  Xiaohong Wang,et al.  Finite analytic numerical method for solving two‐dimensional quasi‐Laplace equation , 2014 .

[5]  Charles A. Appel,et al.  A note on computing finite difference interblock transmissivities , 1976 .

[6]  A. Dykhne Conductivity of a Two-dimensional Two-phase System , 1971 .

[7]  Zhifeng Liu,et al.  FINITE ANALYTIC METHOD FOR 2D FLUID FLOW IN POROUS MEDIA WITH PERMEABILITY IN TENSOR FORM , 2016 .

[8]  Joseph B. Keller,et al.  Effective conductivity of periodic composites composed of two very unequal conductors , 1987 .

[9]  Oystein Pettersen Finite-Difference Representation Of Permeabilities In Heterogeneous Models , 1983 .

[10]  Robert W. Zimmerman,et al.  Accuracy of the Renormalization Method for Computing Effective Conductivities of Heterogeneous Media , 2001 .

[11]  Zhi-Feng Liu,et al.  Finite analytic numerical method for two-dimensional fluid flow in heterogeneous porous media , 2013, J. Comput. Phys..

[12]  Xiaohong Wang,et al.  Finite analytic method for 2D steady fluid flows in heterogeneous porous media with unstructured grids , 2018 .

[13]  D. W. Peaceman Fundamentals of numerical reservoir simulation , 1977 .

[14]  P. King The use of renormalization for calculating effective permeability , 1989 .

[15]  Emmanuel Ledoux,et al.  Two Dimensional Stochastic Modelling of Flow in Non-Uniform Confined Aquifers. Correction of the Systematic Bias Introduced by Numerical Models when they are used Stochastically , 1990 .

[16]  R. Ababou,et al.  Three-dimensional flow in random porous media , 1988 .