No abstract

This paper is an investigation of the correlation model for transport of nonreactive solutes in media with random porosity and permeability. The method of perturbation is used to obtain a second‐order approximate, nonlocal (integrodifferential) equation for mean concentration. An approximate method of localization is used to convert to with the same order of approximation differential equations of transport. Exact averaged equations for one‐dimensional transport are examined, and the question of the consistency and asymptotic behavior for approximate averaged equations is discussed. A detailed investigation of transport in a stratified system has been carried out. The second moment of concentration is examined, the variance of the concentration is computed, and cross‐correlation moments are obtained for fields of porosity and velocity, including solute concentration.

No abstract

It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods-for example, the convergence behavior and the accuracy of truncated perturbation series-are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for threedimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem.

No abstract