Optimal Reservoir Production Scheduling By Using Reservoir Simulation

This paper addresses the optimization of field operations under a given set of technical and economic constraints and demonstrates that an optimal control procedure may be applied to any industrial oil and/or gas reservoir at reasonable cost and at acceptable accuracy level. Both primary and secondary recovery processes can be considered. The method proposed here is presented in two main sections. First, the modeling phase provides an approximately and locally linear model of the reservoir. A previously calibrated reservoir simulator model is used to perform a series of experiments. and a multiple variable regression analysis is used to fit the experimental data. The experimental design was one of the key issues in this work. Second, the optimization phase is performed with a linear programming algorithm. Nonlinear effects, such as performed with a linear programming algorithm. Nonlinear effects, such as those generated by the presence of gas, are approximated by several procedural iterations. procedural iterations. The application of this method to the case of a hypothetical reservoir demonstrates the validity of the optimal control procedure and shows convergence within an acceptable number of iterations. Introduction This investigation demonstrates the application of linear programming to a set of behavior equations derived from reservoir simulation results by use of a least-squares inversion procedure. The method is intended to optimize the production schedule of any reservoir for which the producer or injector well locations have already been fixed. The accuracy of this optimization procedure depends on many factors. the most important being the approximate procedure depends on many factors. the most important being the approximate linearization of the nonlinear system. Also important is reducing the required number of simulation runs until a satisfactory cost/accuracy compromise is obtained. It appears, that the reservoir engineer may contribute in reducing the experimental and calculation cost by properly selecting the series of simulation experiments. Simulator experiments, multivariable regression, least-squares inversion, the simplex algorithm. and validation are the major steps of this theoretical optimization procedure. The application of the process is demonstrated by working out a hypothetical practical example. The optimization of field operations has been explored by many authors, and many approaches have been suggested. Lee and Aronofsky established the first principles of this type of procedure by designing a time-discretized optimization process applied to a set of single-well reservoirs. Linear programming was used, and the objective function considered was the net profit. This first approach was improved by Aronofsky and Williams, who reduced the assumptions concerning the reservoir. Attra et al. refined the Lee and Aronofsky production model by introducing additional economic and technical factors, such as sales contract requirements or gas compressor limitations. For all these methods, the linear equations constituting the reservoir model were derived from material-balance considerations, and the reservoirs generally were assumed uniform and single-phase. SPEJ p. 717