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A Systems Description of Flow Through Porous MediaSystem Models

A Systems Description of Flow Through Porous Media: System Models [This chapter develops representations in state-space notation of the porous-media flow equations derived in Chap. 1. For single-phase flow, the states are grid-block pressures, and for two-phase flow they are grid-block pressures and saturations. The inputs are typically bottom-hole pressures or total well flow rates, the outputs are typically bottom-hole pressures in those wells were the flow rates were prescribed, and phase rates in those wells were the bottom-hole pressures were prescribed. The use of matrix partitioning to describe the different types of inputs leads to a description in terms of nonlinear ordinary-differential and algebraic equations with (state-dependent) system, input, output and direct-throughput matrices. Other topics include generalized state-space representations, linearization, elimination of prescribed pressures, the tracing of stream lines, lift tables, computational aspects, and the derivation of an energy balance for porous-media flow.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Systems Description of Flow Through Porous MediaSystem Models

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Publisher
Springer International Publishing
Copyright
© The Author(s) 2013
ISBN
978-3-319-00259-0
Pages
39 –78
DOI
10.1007/978-3-319-00260-6_2
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter develops representations in state-space notation of the porous-media flow equations derived in Chap. 1. For single-phase flow, the states are grid-block pressures, and for two-phase flow they are grid-block pressures and saturations. The inputs are typically bottom-hole pressures or total well flow rates, the outputs are typically bottom-hole pressures in those wells were the flow rates were prescribed, and phase rates in those wells were the bottom-hole pressures were prescribed. The use of matrix partitioning to describe the different types of inputs leads to a description in terms of nonlinear ordinary-differential and algebraic equations with (state-dependent) system, input, output and direct-throughput matrices. Other topics include generalized state-space representations, linearization, elimination of prescribed pressures, the tracing of stream lines, lift tables, computational aspects, and the derivation of an energy balance for porous-media flow.]

Published: May 24, 2013

Keywords: Injection Well; Water Flow Rate; Reservoir Model; Reservoir Simulation; Grid Block

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