Predicting oil recovery using percolation

One particular practical problem in oil recovery is to predict the time to breakthrough of a fluid injected in one well and the subsequent decay in th e production rate of oil at another well. Because we only have a stochastic view of the distribution of rock properties we need to predict the uncerta inty in the breakthrough time and post-breakthrough behaviour in order to c alculate the economic risk. In this paper we use percolation theory to pred ict (i) the distribution of the chemical path (shortest path) between two p oints (representing well pairs) at a given Euclidean separation and present a scaling hypothesis for this distribution which is confirmed by numerical simulation, (ii) the distribution of breakthrough times which can be calcu lated algebraically rather than by very time consuming direct numerical sim ulation of large numbers of realisalions. (C) 1999 Elsevier Science B.V. Al l rights reserved.