THE EVOLUTION OF FINITE LENGTH ELEMENTS IN UNLIMITED HETEROGENEOUS SYSTEMS

Abstract

The paper considers the collector conductivity in the pore volume of oil bearing rock. The mathematical model for this category of phenomena is the Cauchy problem as applied to the Smoluchowski evolution equation. The paper covers a novel phenomenon: the transformation of the conservation ratio into the dissipation ratio derived from the Smoluchowski equation solutions. The dissipation of an average length graph represents a set of connected pores with a positive probability in a system of connected line segments those lengths match the system size that ensures a macroscopic connectivity. The latter is important for modeling the transfer process in porous media under various physical effects leading to pore coalescence.