Generation of two-dimensional pore networks for drainage simulations

The intuitive idea behind the notion of a pore network is that of representing a continous domain P, the pore space, by a finite graph G_p embedded onto P. In this paper we restrict ourselves to the two-dimensional case, formulate conditions on G_p and show that under natural conditions on P there exists exactly one G_p. In our approach G_p is a union of circuits. Thus, the mapping PG_p is continuous with respect to the Hausdorff distance-in contrast to the mapping of P onto its skeleton. We then interpret binary images of pore spaces as approximations of real pore spaces and present a parallel algorithm that takes a binary image of P and approximates G_p. Moreover, all approximations of G_p are strong deformation retracts of P. Our concept is a dual one, i.e., the dual of G_p represents the grain matrix. Thus, notions like formation of pore throats and pores by grains can be expressed formally. In the experimental part we show that drainage simulations on (approximations of) G_p agree well with pore-scale simulations on P.