A Mathematical Solution to Consider Geomechanics in SAGD Process

Abstract Steam Assisted Gravity Drainage (SAGD) process is a steam drive technique which is predominantly used for Alberta's unconventional reservoirs. Butler was the first researcher who proposed this technique and developed a theory to predict SAGD's performance and production. Although his theory is fast enough in terms of calculation speed for primary estimation of SAGD projects, it over-estimates the production and does not consider geomechanics. Many studies have proven now that geomechanics is inevitably a part of physics in this process. In this study, a classical theory of geotechnical engineering is employed to support the geomechanical part of a coupled simulator. Butler theory is also modified using model of slices to be a more realistic drainage model as a flow simulator. Combining these two models is able to solve fully coupled analytical analysis which has been presented in this paper. The solver is a fast and realistic proxy and can be used in any fast history matching and handling real-time data in future SAGD fields. Introduction Analytical solution has been always a favorable tool for engineers. They use it as a fast calculator for primary estimations and to handle the major problems of an engineering project. For SAGD, Butler and his colleagues1 proposed the first analytical solution that was able to predict oil production rate based on simple assumptions. The model, which is usually known as Butler theory, was firstly used as a tool to approve SAGD concept and showed the capability of such a technique in thermal oil extraction. Although the theory developed later by Butler and his team from time to time to consider more aspects of SAGD, the foundation of the theory in which geomechanics has been ignored didn't change. Other than Butler, more researchers such as Reis2, Akin3, Liang4, and Nukhaev et al.5have worked on different techniques and have proposed their models, but they do follow the same approach as Butler did. By other words, none of the models consider geomechanics as an important aspect of SAGD physics. Analytical solutions are not only helpful when there is no accurate method available, but they can also be a powerful tool when numerical-based models are time consuming. In future digital fields that real-time data flows into engineers' computers, data processing and history matching with numerical methods (i.e. using numerical-based solvers and simulators) is almost impossible. Hence, any other technique such as a robust analytical model would be a good local replacement. In the next sections a mathematical methodology has been developed to improve the current models and to make a geomechanical coupling analysis possible in an analytical theme. Based on Butler and Reis theory, a drainage model that is called in this paper as the model of slices is presented. To consider geomechanics, limit equilibrium analysis method has been adopted from geotechnical engineering. These two models together with a coupling technique are able to solve a SAGD problem fast, reasonably robust and physics-based. The proposed models are then validated with some laboratory and numerical data.

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