Comparison of Two Mathematical Models for 3D Groundwater Flow: Block-Centered Heads and Edge-Based Stream Functions |
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Authors: | G A Mohammed W Zijl O Batelaan F De Smedt |
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Institution: | (1) Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Brussels, Belgium;(2) Department of Earth and Environmental Sciences, Katholieke Universiteit Leuven, Leuven, Belgium |
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Abstract: | Traditionally, groundwater flow models, as well as oil reservoir models, are based on the block-centered finite difference
method. Well-known models based on this approach are MODFLOW (groundwater) and ECLIPSE (oil and gas). Such models are well
proven and robust; their underlying principles are well understood by hydrologists and petroleum reservoir engineers. Nevertheless,
the desire to improve the block-centered finite difference paradigm has always been alive, for instance, to be able to apply
deformed grid blocks, or to model anisotropy that is not aligned along the coordinate axes. This article introduces the edge-based
stream function as a potential alternative to the paradigmatic model, not only to mitigate the above mentioned limitations,
but especially for its promise to inverse modeling. Computer programs have been developed for the discrete analog equations
of the stream function method and the conventional method. The two methods are tested by using synthetic forward modeling
problems of uniform and radial flow. The theoretical formulation and the numerical results show that the two methods are algebraically
equivalent and yield the same flux output. However, for rectangular grid blocks and anisotropy aligned along the coordinate
axes, the block-centered method is shown to be computationally more efficient than the edge-based stream function method.
The major advantage of the stream function method is that it is linear in the resistivities, proving it an ideal candidate
for direct inverse modeling. Moreover, any arbitrary specification of stream functions yields a solution that satisfies the
mass balance. |
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Keywords: | Discrete analogs Block-centered method 3D stream function Edge-based vector potential |
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