Fast Predicting of Water Injection Breakthrough Time by Percolation Theory

Abstract

One particular practical problem in oil recovery is to predict the time to breakthrough of an injected fluid in one well and the subsequent decay in the production rate of oil in another. Because we only have a stochastic view of the distribution of rock properties, we need to predict the uncertainty in the breakthrough time and post-breakthrough behavior in order to calculate the economic risk. In this paper, we apply scaling laws from percolation theory to predict the distribution of breakthrough times that can be calculated algebraically rather than directly via very time-consuming numerical simulation of large number of realizations. The main contribution is to show that percolation theory, when applied to a realistic model, can be used to obtain the same results as calculated in a more conventional way but significantly more quickly. Specially, when the parameters of scaling law optimized, we found that a previously proposed scaling form for the breakthrough time distribution when applied to a real oil field is in good agreement with more time consuming simulation results. Consequently, these methods can be used in practical engineering circumstances to aid decision making for real field problems.