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- W2897577499 abstract "Abstract The flow equations presented in Chapter 7 are generally nonlinear. Even if solved implicitly, the nonlinearity comes boundary conditions and wells, which invoke discontinuities. Solving nonlinear algebraic equations is limited to trivial ones. All other forms have to be linearized before they are amenable to solutions. Only recently, some progress has been made for solving flow equations in their nonlinear forms. These solutions are extremely cumbersome to obtain and often result in hitting spurious solutions. Fortunately, such rigorous treatment is not necessary for most practical applications, for which a priori linearization suffices. To obtain the pressure distribution in the reservoir, these equations are linearized to use linear equation solvers. In this chapter, we aim at obtaining the linearized flow equation for an arbitrary gridblock (or gridpoint). To achieve this objective, we identify the nonlinear terms in the flow equations, present methods of linearizing these terms in space and time, and subsequently present the linearized flow equation for single-phase flow problems. To simplify the presentation of concepts, we use the implicit formulation of the 1-D flow equation in the x-direction and use a block-centered grid in discretizing the reservoir. We first discuss the incompressible fluid flow equation that exhibits linearity, then the implicit formulation for the slightly compressible fluid flow equation that exhibits very weak nonlinearity, and finally the implicit formulation for the compressible fluid flow equation that exhibits a higher degree of nonlinearity. Although single-phase flow equations exhibit different degrees of nonlinearity, these equations are usually classified as having weak nonlinearities." @default.
- W2897577499 created "2018-10-26" @default.
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- W2897577499 date "2020-01-01" @default.
- W2897577499 modified "2023-09-25" @default.
- W2897577499 title "Linearization of flow equations" @default.
- W2897577499 doi "https://doi.org/10.1016/b978-0-12-819150-7.00008-6" @default.
- W2897577499 hasPublicationYear "2020" @default.
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