Theory Research On Dynamic Real-Time Optimization Of Reservoir

The objective pursued by developers of reservoir is to exploit demonstrated reserves more efficiently and economically. One possible approach to tackle this problem is to produce oil in a dynamic real-time optimal state on the basis of existing production conditions. Reservoir is recognized as a complex dynamic system in this work. The optimal objective is to maximize net present value of production. Mathematical Model can be solved to determine real-time control settings and obtain optimal production schedule. Because dynamic real-time optimization of reservoir is a large-scale complicated optimization problem, efficient gradient-based algorithm is used to solve it. The control gradients are obtained by the maximum principle first and then optimal control settings of each control step can be determined by line search. But this process is so complicated. So in order to save computing time, an modified adjoint construction procedure combined with full implicit simulator is adopted, which greatly improve calculation efficiency under the premise of guaranteeing the accuracy of solution. After gradients are gained, calculation efficiency of simultaneous perturbation stochastic approximation(SPSA) algorithm is compared with that of steepest descent algorithm. The result of comparison shows that steepest descent algorithm is more efficient although SPSA is simple and easier to realize. Nonlinear constraints always exist in the process of dynamic real-time optimization of reservoir. This leads to production problem is quite difficult to solve because of so many constraints. Therefore, a projected gradient algorithm combined with maximum principle and log transform are proposed. It can get rapidly constrained gradient for the real-time optimal control settings while linear and nonlinear constraints are satisfied efficiently. This method of dynamic real-time optimization of reservoir discussed in this paper can not only calculate optimal production settings such as bottom hole pressure, injection rate and oil production rate etc but also be used to optimize well placement of reservoir. Based on the above theoretical study, two-dimensional and three-dimensional applied example of reservoir are analyzed. The results show real-time optimal production scheme are coincident with the demand of actual field and it will provide a strong theoretical basis and technical support for more scientific, valid and efficient development of reservoirs.