Deformation of an interface between two fluids in a porous medium

The interface between 2 moving fluids in a porous medium will, in general, deform under the influence of gravity and drag forces. This paper deals with the displacement of oil by water in a homogeneous nonhorizontal oil stratum. The deformation of such an interface can be deduced by numerical procedures based upon exact methods. The use of these methods is limited, however, owing to the fact that in oil reservoirs the dip is usually smaller than 10-20$. In such cases, where the interface is initially horizontal, an approximative method is more useful. In this paper 2 approximate solutions are presented. The first one is obtained by using a simplified form of the dynamic interface condition. More complicated results are obtained by using the second approximation. In both methods, the form of the interface as a function of time is expressed in a parametric representation. Moreover, the amount of water that has passed a given cross section and the flow of water at this section are obtained as a function of time and the parameter used. Results of both methods are compared with each other and with those obtained by an exact method. Both approximations are found to be good inmore » those cases where the dip of the reservoir is not too high, but this is precisely when exact methods are impracticable.« less