Application of the Conjugate Gradients Method in the Simulation of Relative Permeability Properties of Porous Media

ABSTRACT

A model that is after the determination of the relative permeability characteristics of porous media is presented. It is part of a general model that deals with the simulation of capillary phenomena and immiscible fluid flow behaviour in porous media. The relative permeability characteristics in a water wet porous medium are simulated with the use of three-dimensional (3-D) network models of pore structure with pore body and pore throat size distributions. The major assumption involved is that a cubic network of pore bodies connected by pore throats with pore body and pore throat size distribution respectively, is a realistic representation of the pore structure of a porous medium. The physical laws that apply in real media are simulated in the network analysis, and the computed results are compared with experimental findings. A new algorithm was developed that leads to the solution of a large set of linear equations, with a sparse and positive definite coefficient matrix. Results obtained with the application of the Preconditioned Conjugate Gradients method and numerical aspects of the simulation are presented and discussed. Comparison of this method with other available numerical methods is also made. It is concluded that the Preconditioned Conjugate Gradients method is advantageous for large networks with regards to time of solution, convergence, and accuracy. The validity of the algorithm is tested against other methods in the literature.

A full version of this paper is available on Taylor & Francis Online.