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 Gp embedded onto P. In this paper we restrict ourselves to the two-dimensional case, formulate conditions on Gp and show that under natural conditions on P there exists exactly one Gp. In our approach Gp is a union of circuits. Thus, the mapping PGp 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 Gp. Moreover, all approximations of Gp are strong deformation retracts of P. Our concept is a dual one, i.e., the dual of Gp 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) Gp agree well with pore-scale simulations on P.
ASJC Scopus subject areas
- Water Science and Technology
- Geotechnical Engineering and Engineering Geology
- Ocean Engineering
- Mechanical Engineering