Water flooding optimization with adjoint model under control constraints

• Published in: Journal of hydrodynamics. Series B Vol. 26; no. 1; pp. 75 - 85
• Main Author: 张凯 张黎明 姚军 陈玉雪 路然然
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier Ltd 01.02.2014; Springer Singapore
• Subjects: adjoint model; Adjoints; Computer simulation; Computing time; constrained optimization; Engineering; Engineering Fluid Dynamics; fully implicit simulation; gradient projection; Hydrology/Water Resources; Mathematical analysis; Mathematical models; Numerical and Computational Physics; Oil fields; Optimization; Reservoirs; Simulation; water flooding optimization; 伴随模型; 共轭梯度方法; 实时优化; 控制约束; 水驱; 油田开发; 油藏数值模拟; 油藏模拟器; adjoint model; fully implicit simulation; water flooding optimization; constrained optimization; gradient projection
• ISSN: 1001-6058; 1878-0342
• DOI: 10.1016/S1001-6058(14)60009-3

The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conventional solving method of the maximum principle requires two solutions of time series: the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelerates the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.