FRAGMENTATION AND COALESCENCE IN SIMULATIONS OF MIGRATION IN A ONE-DIMENSIONAL RANDOM MEDIUM

A simple one-dimensional model of fluid migration through a disordered medium is presented. The model is based on invasion percolation and i s motivated by two-phase flow experiments in porous media. A uniform p ressure gradient g drives fluid clusters through a random medium. The clusters may both coalesce and fragment during migration. The leading fragment advances stepwise. The pressure gradient g is increased conti nuously. The evolution of the system is characterized by stagnation pe riods. Simulation results are described and analyzed using probability theory. The fragment length distribution is characterized by a crosso ver length s(g) similar to g(-1/2) and the length of the leading frag ment scales as s(p)(g) similar to g(-1). The mean fragment length is f ound to scale with the initial cluster length s(o) and g as [s] = s(o) (1/2)f(gs(o)(3/4)).