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• W1979979345 abstract "Abstract The front tracking method gives high quality solutions for problems with important discontinuities. The method has been applied to several model problems in reservoir simulation. Results are problems in reservoir simulation. Results are given for quarter 5-spot studies in an areal reservoir and the water coning problem in a vertical cylindrical section surrounding a production well. Both problems were treated as incompressible flow in the absence of capillary pressure. We have studied miscible and immiscible displacement for frontal mobility ratios of 1 and 5. Validation studies include mesh refinement, grid orientation and orthogonal coordinate changes. Introduction A large class of physical problems involves important discontinuities in physical quantities. Standard discretization methods (e.g. finite difference schemes) do not handle such discontinuities effectively. Front tracking on the other hand, is ideally suited to the computation and resolution of discontinuities. A successful scheme has been developed which combines the flexibility and efficiency of general purpose hydrodynamics methods with the accuracy of a special purpose calculation such as the method of characteristics. In this scheme there is no appreciable inefficiency due to front-tracking; front-tracking costs represent only a small fraction of the overall computation. This approach is currently being pursued by, the authors in problems of oil reservoirs, gas dynamics and fluid interface instabilities. In this paper we describe some of the results for oil reservoirs. The essential features of the front-tracking implementation are:The use of a one-dimensional time dependentgrid to track the position of oil-water(or other) discontinuity fronts in a 2-dimensional calculation.The use of an accurate analysis of non-linear wave modes and interactions to propagate saturation banks with their correct wave speed.The use of mesh alignment in the pressure equation, to obtain accurate velocities near a discontinuity front.The use of coherent, computationally efficient and user-oriented data structures for the storage and manipulation of interface data. The quarter 5-spot problem is a standard model problem used to test the capabilities of reservoir simulators. It describes an injector-producer pair in a hypothetical secondary recovery simulation, pair in a hypothetical secondary recovery simulation, where various symmetries and homogeneity assumptions allow only two wells in a planar reservoir to be studied. The reservoir is treated as a horizontal layer of uniform thickness and with vertical variation in reservoir quantities ignored. The injector and producer are located at diagonally opposite corners of a rectangle on which no-flow boundary conditions are imposed. In certain situations, for example with unit mobility ratio, an exact solution is available for this problem. The most interesting aspects of the 5-spot problem are the effects of mobility ratio and reservoir heterogeneity on the saturation profile and oil recovery. At high mobility ratios, fingering of the oil-water interface is observed both experimentally and numerically. The 5-spot problem is ideal for testing various features expected of a reservoir simulator, such as independence of results on the grid orientation. The quarter five-spot problem was solved with both diagonal and parallel grid orientations and also with grid lines taken from the exact solution of the mobility-ratio 1 case, i.e. as defined by Jacobi elliptic functions, or equivalently by conformal mapping. In this way convergence under mesh refinement and invariance under change of mesh orientation was demonstrated. In the unstable case (mobility-ratio greater than 1) the solution depends significantly on reservoir heterogeneity. These effects have been studied systematically. p. 41" @default.
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• W1979979345 date "1983-11-15" @default.
• W1979979345 modified "2023-09-29" @default.
• W1979979345 title "Front Tracking for Petroleum Reservoir Simulation" @default.
• W1979979345 doi "https://doi.org/10.2118/12238-ms" @default.
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