Abstract
The chromatographic movement of surfactant mixtures through porous media is examined to determine possible injection strategies for minimizing the amount of surfactant required in a tertiary oil recovery chemical flood. The model used does not consider the presence of oil but does account for mixed micelle formation. Expressions are derived that represent the surfactant required to expose an entire reservoir to an "effective oil recovery mixture." This effective mixture may be either one whose overall composition is within prescribed limits of the composition of the injected surfactant solution or it may be a mixture whose overall composition varies but which contains micelles of fixed composition. Mixtures considered contain cosolvents and one, two, or three surfactant components. Initial calculations neglect dispersion, but numerical calculations including dispersion leave the conclusion unchanged; within the limitations of the model, there are optimal strategies for the propagation of surfactant mixtures through porous media. The optimal injection strategy varies, depending on the nature of the surfactant solution injected into the porous medium. Conditions for and the location of the optimum are discussed. Conclusions based on observations about these systems then are extended to cover the injection of surfactant mixtures currently available commercially.
Introduction
Commercial application of surfactants for EOR now appears feasible. The principle at work in such processes is the lowering of interfacial tension (IFT) between the continuous flowing water and trapped residual oil droplets to allow the oil to be mobilized. Mixtures that effectively lower oil/water IFT are often blends of various surfactant types, isomers of the same surfactant, and/or cosurfactants in an electrolyte solution. The oil recovery efficiency of the injected mixture generally is quite sensitive to changes in mixture composition. Change of composition after injection into the reservoir may occur by one or a combination of mechanisms. For example, the mixture components may partition selectively into the various phases present in the reservoir.
The mechanism considered here is the chromatographic separation of the mixture into its components due to preferential adsorption of various components onto reservoir minerals-"the chromatographic problem." The recent reports of the Bell Creek Unit A micellar/polymer pilot showed 20% of the injected surfactant produced before any oil bank with negligible concomitant incremental tertiary oil production. Significantly, the surfactants produced were the lower-molecular-weight species. Though alternative mechanisms for this separation yet may be established, the hypothesis of chromatographic separation of the components in the mobile aqueous phase seems adequate. Not only did this produced surfactant not result in enhanced recovery, but since the injected solution was designed to give ultralow IFT's with the low-molecular-weight components in place, it seems likely that the oil recovery efficiency of the remaining surfactant also may have been impaired. These results emphasize the importance of understanding the mechanisms of surfactant chromatographic movement.
One means of combatting the chromatographic problem is to reduce the local adsorption of the mixture components-that is, modify the adsorption isotherms of the constituents. This may be done either by changing the reservoir minerals (e.g., by a caustic flood) or by modifying the structure of the surfactant molecules. A complementary approach is to examine the dynamics of the chromatographic movement of surfactant mixtures to identify injection strategies, if they exist, that minimize the total surfactant requirement. It is this question that is considered here.
The analysis considers an oil-free linear system and neglects many of the complex features that are encountered in an actual chemical flood. There are several reasons for ignoring these complicating factors. The coherence solutions apply to the systems considered here; whereas the only solutions that include the presence of oil employ numerical computations. An analytical solution is desirable; however, there is an additional more compelling argument that has been used to justify neglecting the presence of oil.
The chromatographic movement of a surfactant/ cosurfactant mixture through an oil-free core should demonstrate the qualitative features of the actual oil recovery process. While multiple flowing phases do arise in an actual flood, the released oil forms a bank ahead of the surfactant slug.
SPEJ
P. 545^
Optimal Control of Polymer Flooding Based on Maximum Principle