Application of dynamic optimization methods for foam floods in stratified reservoirs
Efficient recovery of oil from heavily stratified carbonate reservoirs can be very technically challenging, even when applying waterflood, gasflood, or WAG (water-alternating gas) processes. To date, relatively few field or pilot applications of foam flooding have been conducted due to an incomplete understanding of how foam will behave in the field. The reservoir of interest studied in this work is oil-wet and consists of a stratified upper high-permeability zone overlaying a lower low-permeability zone. This study seeks to assess the performance of the foam flooding process in oil recovery and develop an optimum field injection strategy based upon various objective functions. In the process, the impact of initial waterflooding and varying foam strength on the optimum project termination time, as well as the sensitivity of foam parameters on the optimum field injection strategy is investigated. Two main optimization techniques are tested: static optimization, where the injection parameters are set once at the beginning of the simulation, and dynamic optimization, where injection parameters are optimized in five-year intervals over the life of the well. The dynamic optimization was performed in two ways: a local dynamic optimization and an early-time weighted optimization. In general, the dynamic optimization outperformed the static optimization with respect to all objective functions. Over the course of the study, a variety of objective functions were utilized. The objective functions began with maximizing cumulative oil recovery and evolved to maximizing oil recovery while minimizing gas utilization ratio, and finally maximizing net present value (NPV). From the results, it was ultimately shown that the global dynamic optimization of NPV was the most useful way of obtaining a field injection strategy. The optimal process design parameters indicated that high volumes of surfactant as well as gas in the lower zone needed to be injected early in the life of the project to best maximize NPV. From the optimal termination time study, it was found that the optimal termination time for the project was around ten years. Varying extents of initial waterflooding and alteration of foam strength did not have an impact on the suggested termination time. From the foam strength sensitivity, it was found that among the factors (water saturation, oil saturation, surfactant concentration) considered, the maximum dry-out water saturation had the most profound impact on the NPV. Ultimately, this work develops the framework necessary to create a field injection strategy for foam flooding in the stratified oil-wet reservoir used in this study, but can be extended to other types of reservoirs.