The Study On Reduced Order Model Algorithm For Water Flooding Production Optimization Of Oil Reservoir

Oil Reservoir Numerical Simulation is the numerical calculations technology which is applied in the field of the oilfield development. During the process, we need to mesh the reservoir area which is so complex and discrete the mathematical model which is composed of seepage flow equation and boundary conditions. When the mathematical model is discreted, a huge linear algebra equation system will be generated. The solution process of this linear algebra equations system needs huge memory resources and computation times. When we solve the optimization problem with conventional injection gradient algorithm, the numerical reservoir simulation process requires iterative calculations. So it requires large amounts of calculation time to apply the numerical reservoir simulation technology directly in oilfield injection optimization and control. The main work about numerical reservoir simulation and optimal computation are as follows:First, the double correction and Multi-block correction technique is presented to calculate the reservoir pressure. A more advanced Multi-block correction technique to speed up convergence of numerical calculation of reservoir pressure is presented in this paper, which is based on the correction value to solve the algebraic equations. In this technique, the single block correction changed into multi-block correction. Depending on different boundary conditions and porosity which sits in the different blocks, the single block correction is changed into multi-block correction. The calculation for different test-eases indicates that in the same conditions the calculating convergence speed of Multi-block correction is faster than the single block correction.Second, the proper orthogonal decomposition(POD) is applied in the numerical simulation of the reservoir, and the water flooding lower order models are generated in two ways: POD-Galerkin method and direct interpolation transformation method. The main results are as follows:1) POD-Galerkin and direct interpolation transformation method were used to establish the one-dimensional water flooding lower order models. It was shown that the POD basis functions remained the optimal characteristics of "energy", even in coupling with variables of pressure, saturation, et.al in the oil reservoir, the reduced order models had a distinct advantage and demonstrated about dozens of times saving compared with the direct numerical solution.2) POD-direct interpolation transformation method were used to establish the two-dimensional water flooding lower order models. It was shown that when solving the problems of heterogeneity and anisotropy of reservoir rocks, the injection and production wells, the reduced order models based on POD basis functions got the more accurate results and demonstrated about dozens of time saving compared with the direct numerical solution. Moreover, with the increase of computational grid, the reduced order models had a more distinct advantage.Third, in the calculation of the optimal injection reservoir scheme, POD lower order model was generated, which is based on economic indicators injection(oil production) basis function. The performance of lower order model is demonstrated by the examples and is shown that the reduced order models can predict the oil output calculation error is less than 1%, and the computing time was significantly less than traditional solution reservoir injection optimal solution algorithm(conjugate gradient algorithm). So it be able to satisfy the requirements of fast calculation and oil production in real-time control.