TOWARDS REALISTIC FLOW MODELING - CREATION AND EVALUATION OF 2-DIMENSIONAL SIMULATED POROUS-MEDIA - AN IMAGE-ANALYSIS APPROACH

This work is part of an attempt to quantify the relationship between t he permeability tensor (K) and the micro-structure of natural porous m edia. A brief account is first provided of popular theories used to re late the micro-structure to K. Reasons for the lack of predictive powe r and restricted generality of current models are discussed. An altern ative is an empirically based implicit model wherein K is expressed as a consequence of a few ''pore-types'' arising from the dynamics of de positional processes. The analytical form of that implicit model arise s from evidence of universal association between pore-type and throat size in sandstones and carbonates. An explicit model, relying on the l ocal change of scale technique is then addressed. That explicit model allows, from knowledge of the three-dimensional micro-geometry to calc ulate K explicitly without having recourse to any constitutive assumpt ions. The predictive and general character of the explicit model is un derlined. The relevance of the change of scale technique is recalled t o be contingent on the availability of rock-like three-dimensional syn thetic media. A random stationary ergodic process is developed, that a llows us to generate three-dimensional synthetic media from a two-dime nsional autocorrelation function r(lambda(x), lambda(y)) and associate d probability density function epsilon(beta) measured on a single bina ry image. The focus of this work is to ensure the rock-like character of those synthetic media. This is done first through a direct approach : n two-dimensional synthetic media, derived from single set (epsilon( beta), r(lambda(x), lambda(y))) yield n permeability tensors K-i=1,n(i ) (calculated by the local change of scale) of the same order. This is a necessary condition to ensure that r(lambda(x), lambda(y)) and epsi lon(beta) carry all structural information relevant to K. The limits o f this direct approach, in terms of required Central Process Unit time and Memory is underlined, raising the need for an alternative. This i s done by comparing the pore-type content of a sandstone sample and n synthetic media derived from r(lambda(x), lambda(y)) and epsilon(beta) measured on that sandstone-sample. Achievement of a good match ensure s that the synthetic media comprise the fundamental structural level o f all natural sandstones, that is a domainal structure of well-packed clusters of grains bounded by loose-packed pores.