A Graphical Method for Calculating Linear Displacement With Mass Transfer and Continuously Changing Mobilities
Authors: Claridge E.L. , Bondor P.L. 
Published: December 2007

Abstract
In carbonated waterflooding, carbon dioxide transfers from the injected water to crude oil lagging behind the waterflood front. When the oil viscosity is high and the carbon dioxide saturation pressure is 1,000 psi or more, the oil-phase pressure is 1,000 psi or more, the oil-phase viscosity is reduced by a factor of 5 to 20 by the dissolved carbon dioxide. We present here an extension of Welge's graphical method of calculating immiscible displacements of oil by injected gas or water. This extension takes into account the effect of interphase mass transfer on the phase mobilities. Thus it is able to represent the carbonated water displacement process. Oil displacement efficiencies obtained by this method should be supplemented by corrections for areal and vertical sweep efficiency, if predictions of oil recovery under field conditions are desired.

Introduction
In considering possible supplemental recovery processes for given oil fields, it is helpful to processes for given oil fields, it is helpful to establish ranges of reservoir characteristics that are required or are particularly favorable for various processes. A good example of such a classification processes. A good example of such a classification was given recently by Geffen. These ranges often have regions of overlap for two or more processes. One of the overlap regions occurs for viscous oil reservoirs, which may be candidates for waterflooding, polymer-thickened waterflooding, carbonated waterflooding, or steam flooding. In particular, for mobility ratio M = 5 or more (M = particular, for mobility ratio M = 5 or more (M = k rw o/k ro w), polymer flooding or carbonated waterflooding may be more attractive than plain waterflooding. When the oil viscosity is very high (M = 100 or more), there is no effective substitute for thermal methods such as steam drive or in-situ combustion. However, steam drive is also attractive at lower mobility ratios, despite its higher cost compared with that of waterflooding, since it produces very low residual oil saturations in the produces very low residual oil saturations in the swept zone. Hence, all of these methods may be applicable between M = 5 and M = 100. When a given reservoir appears to be a candidate for more than one process, rapid methods for estimating the comparative profitability of these processes are useful. Relatively simple methods processes are useful. Relatively simple methods have long been available for estimating process performance of waterflooding. We give below a performance of waterflooding. We give below a simple graphical method of calculating linear displacement efficiency that is applicable to polymer flooding and to carbonated waterflooding, polymer flooding and to carbonated waterflooding, as well as to waterflooding, and thus enables comparison of these three processes. The same method may be used to calculate the course of immiscible displacements of oil by a condensing or a vaporizing gas drive, given be gas/oil relative permeability curves and phase viscosities, and data on the variation of the relative permeabilities and phase viscosities as hydrocarbon intermediates are transferred between phases. While the method is described below in phases. While the method is described below in terms of carbonated waterflooding, we believe that As mode of application to gas drive with mass transfers will become apparent. A typical starting point for a simplified oil recovery estimation method is calculation of the linear oil displacement efficiency inside the swept zone of an oil reservoir. For two-phase immiscible displacements, Leverett, Buckley and Leverett, and Welge gave the essential physical analyses and mathematical methods, for the limited case of one-dimensional flow in a homogeneous porous medium. Capillary pressure forces, gravity forces, and viscous drag forces were included in Leverett's original fractional flow equation, but capillary and gravity forces have usually been neglected in simple numerical or graphical solutions.
Our graphical method is a direct extension of this previous work, and is subject to the same limitations.
SPEJ
P. 609