FLOW PHENOMENA IN ROCKS - FROM CONTINUUM MODELS TO FRACTALS, PERCOLATION, CELLULAR-AUTOMATA, AND SIMULATED ANNEALING

In this paper, theoretical and experimental approaches to flow, hydrod ynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically ho mogeneous and heterogeneous rocks are considered. The latter are chara cterized by large-scale spatial variations and correlations in their e ffective properties and include rocks that may be characterized by sev eral distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity those of the pores and of the fractures. First, the diagenetic processes that give rise to the p resent reservoir rocks are discussed and a few geometrical models of s uch processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topo logy, and pore surface roughness, and morphological properties of frac ture networks are discussed. lt is shown that fractal and percolation concepts play important roles in the characterization of rocks, from t he smallest length scale at the pore level to the largest length scale s at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to the se phenomena are compared. The first approach is based on the classica l equations of transport supplemented with constitutive equations desc ribing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the pheno mena at the smallest scale, a pore or fracture, and then employs large -scale simulation and modern concepts of the statistical physics of di sordered systems, such as scaling and universality, to obtain the macr oscopic properties of the system. The fundamental roles of the interco nnectivity of the rock and its wetting properties in dispersion and tw o-phase flows, and those of microscopic and macroscopic heterogeneitie s in miscible displacements are emphasized. Two important conceptual a dvances for modeling fractured rocks and studying flow phenomena in po rous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its st ructure. The second, simulated annealing, borrowed from optimization p rocesses and the statistical mechanics of spin glasses, is used for fi nding the optimum structure of a fractured reservoir that honors a lim ited amount of experimental data.