A More Flexible Approach of Dynamic Local Grid Refinement for Reservoir Modeling

Abstract

This paper describes a new and more flexible approach of dynamic local grid refinement, which can also be used to subdivide the grid block fixedly in any desired parts of reservoir. The amount of fundamental blocks and subblocks can be minimized by using a step-by-step scheme of subdivision almost without any restriction. Moreover, it is shown that the specially developed system of ordering scheme and data managment of this method is very simple and effective. Especially in dynamic grid refinement, no inactive grid block is produced in the process of ordering, and just a little of additional running time is needed to execute this system in computer. This paper reports that the results produced by using the dynamic grid refinement is very close to those obtained with the conventional fine grid system, and the running time are much lower. Introduction It is known that the accuracy of the finite difference solution of the flow equations is affected significantly by the grid size. The finer grid system will lead to less truncation error and consequently result in more accurate solution and vice versa. Moreover, the refinement of grid system is also an effective method for decreasing the numerical dispersion in the displacement front. But the conventional fine grid system requires larger storage and computation time. Therefore, great interest has been paid to local grid refinement technique recently. In comparison with the conventional fine grid system, this technique can considerably reduce the amount of the grids and in turn saves the computation time and does not sacrifice the accuracy. There are two types of local grid refinement technique, fixed and dynamic. In general for problems with faults, pinchouts, fractures and the simulation of the vicinity of well bore, it is satisfactory to use the fixed local grid refinement method. On the other hand, dynamic local refinement is capable of tracking the movement of the displacement front. Especially for small slugs, usually occuring in EOR recovery processes, the dynamic method may be one of the better ways to describe their behavior precisely. The fixed refinement method have been studied by many authors. But less work involving the dynamic local refinement has been done because of its complexity. Z.E. Heinemann et al. have proposed the application of the dynamic local refinement in reservoir simulation, and discussed the subdivision of grid blocks, its discretization error and the ordering scheme of blocks. But in their methods there are a lot of restrictions in subdivision and many inactive grids may be produced by their grid ordering process. These restrictions in their method make it more difficult to be used and increase the storage requirement. It should be noted that to realize the dynamic local grid refinement in practice, a series of complicated problems have to be solved. Since the displacement front moves with time, the location for grid refinement, its block size, order, and the formulation of coefficient matrix are all time-dependent, and need to be treated accordingly. Therefore, it is necessary to design a whole set of sophisticated and flexible programs in order to solve these problems satisfactorily. P. 243^

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