Statistical behavior of fingering in a displacement process in heterogeneous porous medium with capillary pressure

Abstract

The stabilization of fingers in a specific oil–water displacement process with capillary pressure has been statistically discussed for a given heterogeneous porous medium. The equation of motion has been solved by a perturbation method. It is shown that the perturbation solution does produce "stable" fingers in one special case corresponding to the investigated problem.

Similarity Solution of Non-Linear Boussinesq’s Equation Arising in Infiltration of Incompressible Fluid Flow

“…-α β= ,n>α n only. Equating the coefficients in front of the same power on both sides of (25), respecting (24) and using some elementary properties of Beta and Gamma functions, we obtain the following expression for the coefficient 1…”

“…Thus, assuming a possible solution to (25) with k0  in the form (26) one can easily verify that it exists for n = 2. The values of the constants and are simply obtained from their corresponding values for by inserting there n = 2.…”

“…Since a = 0 indicates k0  it is natural to try to find an exact solution of (25) for the case k0  again in the form (26). Thus, assuming a possible solution to (25) with k0  in the form (26) one can easily verify that it exists for n = 2.…”

“…Another exact solution of (11) has the form of a wave propagating along the X-axis with certain speed c and cannot be obtained from (25). To get this solution another similarity transformation of (13) has to be performed for k = 0 It reads a cT h=X U(ξ) , ξ= -1 X…”

Numerical Study of Instabilities in Porous Media Using Finite Difference Method

“…Instabilities occur due to the different viscosities of flowing fluids. Many authors like Scheidegrer , A.E [1,2,3], Verma [4], Coss [5], G. Hu, P.A. Zegeling [6], Singh T. [7], R.N.Borana, V.H.Pradhan, and M. N. Mehta [8], D.E.HillandJ.Y.…”