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Forward and inverse modeling of near-well flow using discrete edge-based vector potentials

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Author: Zijl, W.
Type:article
Date:2007
Institution: TNO Bouw en Ondergrond
Source:Transport in Porous Media, 1, 67, 115-133
Identifier: 239878
Keywords: Geosciences · Discrete exterior calculus · Inverse modeling · Mass balance exactness · Near-well region · Stream function · Vector potential · Algebra · Inverse problems · Mathematical models · Mechanical permeability · Steady flow · Unsteady flow · Vectors · Discrete exterior calculus · Edge-based vector potential · Mass balance · Stream function · Transient flow · Flow of water · Algebra · Flow of water · Inverse problems · Mathematical models · Mechanical permeability · Steady flow · Unsteady flow · Vectors · forward modeling · permeability · steady flow · unsteady flow · vector

Abstract

Homogeneous effective permeabilities in the near-well region are generally obtained using analytical solutions for transient flow. In contrast, this paper focuses on heterogeneous permeability obtained from steady flow solutions, although extensions to unsteady flow are introduced too. Exterior calculus and its discretized form have been used as a guide to derive the system of algebraic equations. Edge-based vector potentials describing 3-D steady and unsteady flow without mass balance error stabilize the solution. After a physics-oriented introduction, relatively simple analytic examples of forward and inverse discrete modeling demonstrate the applicability. © Springer Science+Business Media B.V. 2006.