Investigation of a Stochastic Optimization Method for Automatic History Matching of SAGD Processes
Authors: Jia X. , Cunha L.B. , Deutsch C.V. 
Published: March 2010

Abstract
Western Canada has large reserves of heavy crude oil and bitumen. The Steam-Assisted Gravity Drainage (SAGD) process that couples a steam-based in situ recovery method with horizontal well technology, has emerged as an economic and efficient way to produce the shallow heavy oil reservoirs in Western Canada. Numerical reservoir simulation is used to predict reservoir performance. 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. Research and development of efficient history matching techniques for the SAGD process is important.
An automated technique to assist in the history matching phase of the SAGD process is implemented and tested. 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 parallelized 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. This research is preliminary. Although the results are not ready for commercial implementation, the ideas and results presented here should prove interesting and fuel development in this important subject area.
A Matlab(1)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.

Introduction
The Simultaneous Perturbation Stochastic Approximation (SPSA) methodology(2) has been implemented in optimization problems in a variety of fields with excellent performance. This paper considers production data integration in reservoir modelling for Steam-Assisted Gravity Drainage (SAGD) processes by automatic history matching with SPSA.
Automatic history matching problems are optimization problems that must find the minimum of an objective function. The efficient determination of the gradient of the objective function is one of the most important aspects of the overall efficiency of an optimization methodology. 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 the natural choice in these circumstances. However, for many practical problems, it is time-consuming and expensive or simply impossible to estimate the gradient of the objective function. The notion of 'gradient-free' methods 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.