| Abstract: | In the study of flow of a neutral admixture in a porous medium, it is most often assumed in the stochastic formulation that
the porosity is constant and a determinate quantity, and the velocity is a random function 1–4]. The velocity distribution
is usually regarded as known. Flow in a porous medium with random porosity has been studied to a far lesser extent. We note
5], which studies the averaged equations obtained within the framework of the correlation approximation. We consider the
model problem of one-dimensional motion of a fluid particle (position of the front for flow of a neutral admixture in a porous
medium) in a medium with random porosity. For a particular form of random porosity field, expressions are obtained for the
one- and two-point densities of the distribution of the position of the particle. A study is made of the dependences of the
first four moments and the correlation function of the position of the particle as functions of the time. It is shown that
for large values of the time the motion of the particle is asymptotically similar to Brownian motion. It is shown by means
of numerical modeling that the results obtained transfer to the case of an arbitrary random porosity field.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 59–65, November–December, 1986. |
