Stochastic optimization of cyclic steam stimulation in heavy oil reservoirs

Cyclic Steam Injection (CSS) has been used in the industry to increase the recovery factor and production rate from heavy oil reservoirs. CSS is multi-cycled steam recovery process with three stages and five operational parameters (injection rate and its duration, soak time, production rate and its duration in each cycle. Determining the optimal values of the operational variables in each cycle, for the existing reservoir conditions is challenging. The difficulty stems from the fact that these parameters cause significant changes in reservoir fluid flow, reservoir behavior and recovery performance during the project duration. Ability to effectively determine the best values of these parameters is expected to increase the recovery efficiency and the profitability of the project. In practice, the parameters of cyclic steam stimulation are often determined by running limited sensitivity studies on some or all the parameters. Such sensitivity studies are however very limited in scope and cannot explore the entire domain of interest. A more efficient method to estimate the optimal parameters of the CSS is to perform automatic optimization using an effective stochastic optimization algorithm. In this work, we propose the use of stochastic optimization to estimate the parameters of CSS. Three different CSS models were developed with three well types (vertical, horizontal and inclined wells). The operational parameters are extremely interdependent in CSS which has mulitiple drive mechanisms. The need for global search is imperative to find the best operating parameters in each cycle. Covariance Matrix adaption Evolution Strategy (CMA-ES) was used to optimize the operational parameters. The project net present value (NPV) was used as the objective function in the optimization process. Results showed that the NPV can be increased significantly when all the operational variables of CSS are optimized. This signifies the importance of simultaneous optimization of soak time, cycle length and rates. The results also showed that the vertical well model gave a higher NPV than the other two well models. The horizontal well model gave the lowest NPV.