A Theoretical Analysis of Water-flooding Networks

Abstract

The general problem of the simultaneous movement of water and oil in aconnected sand is of considerable practical interest from two points of view.First, there is the situation usually described as "edgewaterencroachment." Here the water in the sands contiguous to and flanking theoil sand begins to enter the latter as the oil is removed and the reservoirpressure declines. The physical questions involved concern an understanding ofthe mechanism of the advance of the water and its control, so as to aid the oilrecovery rather than to hinder it. In so far as the entry of the water into theoil sand means at least the partial replacement of the oil from the region ofthe encroachment by the advancing water, it is quite appropriate to considerthis type of situation as one of natural water-flooding. For the present discussion, however, we are primarily interested in the problemof artificial flooding. Here the water is deliberately injected into the oilsand with the intention of displacing the oil and removing it throughprearranged output wells. For the practical development of such a procedurerather large areas are included in the flooding program and the injection andoutput wells are arranged in regular patterns or networks, which are felt to bemost favorable for a high oil recovery. Although remarkable success has alreadybeen obtained in such flooding programs, especially in the Bradford field ofPennsylvania, essentially by the application of the lessons of practicalengineering experience, a more thorough physical analysis of the problemappeared to offer promise of leading to results of some interest andvalue. Another phase of the problem, which stimulated both the experimental andmathematical analysis, is that it is susceptible in large measure to empiricalfield tests. It is in itself but an example and illustration of the generaltheory of the flow of dead (gas-free) liquids through porous media, in whichthe authors have been interested for the last several years.