ABSTRACT
This chapter highlights some of the progresses achieved in the study of flow and transport in heterogeneous porous media using stochastic approaches. It reviews the state of the art techniques used for unconditional and conditional stochastic simulation models in porous formations. Stochastic techniques either analytical or numerical are available to solve these differential equations with stochastic parameters. There are several methods for the generation of stochastic fields. The chapter discusses ‘Multi-variate Method’ developed by Iman, ‘Nearest Neighbour Method’ developed by Whittle, ‘Turning Bands Method’ developed by Matheron. Spectral method is based on studying the spatial variation of the stochastic parameter in the continuum sense as a random field characterized by theoretical spatial covariance functions in real (space) domain or by spectral density functions in the frequency domain. An alternative solution method, the Green’s function approach, has also been used to analyze the stochastic partial differential equations of flow through porous media.
