Prediction of Recovery in Miscible Displacement in Porous Media Using the Dispersion Equation
Authors: Patel R.D. , Greenkorn R.A. 
Published: December 2007

Patel, R.D., Patel, R.D., Polytechnic Institute of Brooklyn, and Polytechnic Institute of Brooklyn, and Greenkorn, R.A., Member AIME, Purdue U. Purdue U. Copyright 1969, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 44th Annual Fall Meeting of the of the Society of Petroleum Engineers of AIME, to be held in Denver, Colo., Sept. 28-Oct. 1, 1969. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal, provided agreement to give proper credit is made.
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Abstract
The one-dimensional dispersion equation is used to predict the fractional recovery of displaced fluid as a function of PV of displacing fluid injected in miscible displacement in a porous pack. Two solutions are used corresponding to infinite and semi-infinite packs. packs. The Peclet number is found to characterize the shape of the recovery curve for both solutions. It is found that the predicted recovery using the solution for a semi-infinite medium corresponds more closely to the literature data. Data of several workers are analyzed and the corresponding Peclet numbers determined. An empirical graphical relationship is found between the Peclet number and the mobility ratio of the two fluids. This relationship could be used to estimate the Peclet number and hence the recovery curve for a particular miscible displacement. particular miscible displacement

Introduction
Miscible displacement is of interest as a secondary recovery process. The simplest such process consists of one fluid displacing another process consists of one fluid displacing another of different viscosity and has been studied extensively in laboratory models and in field tests. These studies have been conducted in a variety of geometries - in one-dimensional flow in tubular cores, two-dimensional flow in rectangular models simulating portions of a five-spot, and in the field under more complicated conditions of injection and production wells. The cores used in the model tests have been natural cores and unconsolidated packs of glass beads or sand. Both homogeneous packs of glass beads or sand. Both homogeneous and heterogeneous packs have been used. Other parameters studied include angle of dip, parameters studied include angle of dip, densities of the fluids, etc.
The most important finding is that recover of in-place fluid is low and breakthrough of the injected fluid occurs at a low value of PV fluid injected. Economic evaluation of such recovery processes requires a reliable method of predicting the recovery.
Previous authors cite the following factors as affecting the recovery:
mobility ratio, heterogeneity of the core, geometry of the model, density differences of the fluids [leading to gravity segregation] and angle of dip, etc. Of these, the effect of mobility ratio appears to be the most significant.
Several authors have proposed methods for predicting the recovery in such a miscible predicting the recovery in such a miscible displacement. These methods usually involve the fluid mechanics of fingering and usually invoke free parameters that are correlated with mobility ratio.