A Numerical Investigation of Micellar Flooding
Authors: Limon J.T. , Thomas G.W. , Zetik D.F. 
Published: March 2010

Abstract
This work deals with a two-dimensional mathematical model of the micellar flooding process. It includes up to six components: oil, water, surfactant, polymer, and monovalent and divalent cations in two immiscible phases. We also incorporate the effects of adsorption, dispersion, inaccessible' pore volume, cation exchange and mass transfer between phases.
The differential equations are solved by finite differences. Numerical dispersion is reduced by using two-point upstream weighting of concentration and saturation. Results from one-dimensional experiments indicate the model can be applied to displacements characterized by moderate dispersion levels. To approximate the time level, a procedure similar "to the IMPES technique is applied.
The mechanism of oil mobilization by the micellar fluid is simulated by changing the relative permeabilities as the residual oil" saturation is reduced. The capillary-number concept is employed to correlate residual oil saturation with interfacial tension.
Experimental data for a one-dimensional system were reproduced by the model with reasonable accuracy. Model performance was further analyzed by studying the effects of grid orientation, dispersion level and time-step size. It is concluded that cartesian grids can have a pronounced effect on the computed results, depending on their orientation. From a practical standpoint, time-step size limitations to guarantee tability are not so restrictive as to prevent one-dimensional; or small pilot-type, two-dimensional areal simulations.

Introduction
Micellar flooding is one of several enhanced recovery methods for recovering oil left after a waterflood. It involves injection of a micellar fluid into a reservoir to mobilize the oil by reducing the capillary forces that trap it in the pores. It has been demonstrated, in both laboratory and field tests, that residual oil saturation can be further reduced beyond waterflood values by this technique (1–8).
Some of the more important considerations of the process are phase behaviour, adsorption, cation exchange, capillary number and dispersion effects. A few mathematical models of the process have been developed which include some of these concepts (9–14). Most of these models have been made for the purpose of translating laboratory results. However, they generally are not suitable for predicting field-scale tests due to various simplifying assumptions made in their development. Furthermore, they are mostly limited to one-dimensional flow*.
For field-scale applications, two-dimensional geometry must be considered. Also, capillary and gravitational forces cannot be overlooked. Similarly, the dispersive transport of the miscible components should be included.
In this study, a two-dimensional, two-phase micellar flooding simulator is presented. The model includes up to six components-oil, water, surfactant, polymer, sodium and calcium. The flow of the two immiscible phases is governed by Darcy's Law, and hydrodynamic dispersion is permitted between the components within a phase. Phase behaviour is accounted for by allowing the oil, water and surfacant to partition between phases. Ion exchange, adsorption, inaccessible pore volume and capillary number are incorporated.
The results obtained with the simulator are compared with published data. A history match with a laboratory test was executed, and the effects of relative permeability and phase behaviour were analyzed.