Optimal Injection Policies for Enhanced Oil Recovery: Part 2-Surfactant Flooding

Abstract

Abstract The optimal control theory of distributed-paranieter systems has been applied to the problem of determining the best injection policy of a surfactant slug for a tertiary oil recovery chemical flood. The optimization criterion is to maximize the amount of oil recovered while minimizing the chemical cost. A steepest-descent gradient method was used as the computational approach to the solution of this dynamic optimization problem. The performance of the algorithm was examined for the surfactant injection in a one-dimensional flooding problem. Two types of interfacial tension (IFT) behavior problem. Two types of interfacial tension (IFT) behavior were considered. These are a Type A system where the IFT is a monotonically decreasing function with solute concentration and a Type B system where a minimum IFT occurs at a nominal surfactant concentration. For a Type A system, the shape of the optimal in 'faction strategy was not unique, however, there is a unique optimum for the amount of surfactant needed. For a Type B system, the shape of the optimal injection as well as the amount injected was unique. Introduction Surfactant recovery systems are being investigated by the petroleum industry as a means of increasing the petroleum supply. Commercial application of any petroleum supply. Commercial application of any surfactant flooding process relies upon economic projections that indicate a decent return on investment. projections that indicate a decent return on investment. Previously. surfactant systems for tertiary oil recovery have been optimized by adjusting concentrations of individual components empirically. Salinity has been shown to be an important variable in surfactant system optimization. The particular choice of surfactant and cosurfactant has been studied by Salager et al. Multivariable optimization of surfactant systems based on minimizing the IFT has been studied by Vinatiere et al. As reported, such an optimization may or may not coincide with optimal oil recovery since low IFT is a necessary. but not a sufficient condition for achieving, high displacement efficiency. Chemical supply and cost are important parts of economic projections. Because of the high cost of chemicals, it is essential to optimize surfactant systems to provide the greatest oil recovery at the lowest cost. In this paper, an optimization surfactant is taken as the minimization of the chemical cost and maximization of the recovered oil. The goal is to determine the best way of injecting a surfactant slug into the reservoir formation. Mathematical Formulation of the Performance Index Performance Index We desire to obtain maximum oil recovery with a minimum amount of chemical surfactant injected. These objectives can he expressed in a quantitative form through the formulation of a cost functional. J', which is to be minimized, where J' equals the cost of surfactant injected minus the value of oil recovered. This descriptive statement of the cost functional must be translated into a mathematical form to use quantitative optimization techniques. The oil value can be formulated as (1) where C1 = cost of oil per unit volume ($251.6/m 3[$40/bbl]),= volumetric flow, rate of oil at the coreoutlet L = core length, and a = time. The chemical cost is expressed mathematically as (2) where C2 = chemical cost per unit weight ofsurfactant ($5.45 × 10–3/g [$2.47/lbm]), Cs( ) = surfactant concentration of the injectedfluid in weight fraction, P slug = slug density ( 1 g/cm 3 ). and Qw, ( ) = volumetric flow rate of water at thecore inlet. The objective functional is, therefore, (3) JPT P. 333