Western Canada has large reserves of heavy crude oil and bitumen. The Steam Assisted Gravity Drainage (SAGD) process, which couples a steam-based in-situ recovery method to horizontal well technology, has emerged as an economic and efficient way to produce the shallow heavy oil reservoirs in Western Canada. Numerical reservoir simulation allows the ideal way of predicting reservoir performance under a SAGD process. However, prior to the prediction phase, integration of production data into the reservoir model by means of history matching is the key stage in the numerical simulation workflow. Therefore, research and developments on efficient history matching techniques is encouraged.
In this paper an automated technique to assist in the history-matching phase of a numerical flow simulation study for a SAGD process is implemented. The developed technique is based on a global optimization method known as Simultaneous Perturbation Stochastic Approximation (SPSA). This technique is easy to implement, robust with respect to non-optimal solutions, can be easily parallel zed and has shown an excellent performance for the solution of complex optimization problems in different fields of science and engineering. The reservoir parameters are estimated at reservoir scale by solving an inverse problem. At each iteration, selected reservoir parameters are adjusted. Then, a commercial thermal reservoir simulator is used to evaluate the impact of these new parameters on the field production data. Finally, after comparing the simulated production curves to the field data, a decision is made to keep or reject the altered parameters tested.
A Matlab code coupled with a reservoir simulator is implemented to use the SPSA technique to study the optimization of a SAGD process. A synthetic case that considers average reservoir and fluid properties present in Alberta heavy oil reservoirs is presented to highlight the advantages and disadvantages of the technique.
The Simultaneous Perturbation Stochastic Approximation (SPSA) methodology[1] has been implemented in optimization problems in a variety of fields with excellent performance. This paper mainly features production data integration into reservoir modeling for Steam Assisted Gravity Drainage (SAGD) processes by automatic history matching with SPSA. Essentially, automatic history matching problems turn out to be an optimization process, which can be translated into finding the minimum of an objective function. As one of the most important aspects related to the overall efficiency of an optimization methodology, the efficient determination of the gradient of the objective function cannot be omitted. For some cases, it is easy to obtain the gradient of the objective function and the application of ‘gradient-based’ methods for the solution of the optimization problem is usually the natural choice in these circumstances. However, for majority of practical problems, it is time-consuming and expensive to estimate the gradient of the objective function. The notion of ‘gradient-free’ ethods is introduced to overcome this problem. As a method in this category SPSA provides a powerful technique for automatic history matching. In this work, the objective function related to a synthetic SAGD case is defined for automatic history matching. The SPSA algorithm is implemented to improve the efficiency of the iterative procedure during the minimization phase.
