STOCHASTIC HOMOGENISATION OF FLUID FLOWS IN HETEROGENEOUS POROUS MEDIA

摘要

We present here a general methodology for using homogenisation technique, based on a stochastically stationary description of heterogeneities in porous media, to provide an overall pressure drop/flow rate relation valid at scales larger than those of the correlation lengths for heterogeneity. A dual formulation arises depending on whether flow rate or pressure gradient are treated as the independent variable. The homogenisation technique combines perturbation of the local variables with stochastic linearisation of the fluctuation equations. Closure problems are solved by means of spectral Stieltjes-Fourier decomposition under the statistical stationarity assumption. We then require the dual formulation to be consistent in form. The methodology is illustrated on generalized Newtonian single phase flow.