By Jan Dirk Jansen
The introductory a part of the path, i.e. the platforms description of circulate via porous media, types the subject of this short monograph. the most aim is to offer the vintage reservoir simulation equations in a notation that allows using suggestions from the systems-and-control literature. even though the speculation is restricted to the fairly easy scenario of horizontal two-phase (oil-water) movement, it covers a number of standard features of porous-media flow.
The first bankruptcy provides a quick assessment of the fundamental equations to symbolize single-phase and two-phase circulation. It discusses the governing partial-differential equations, their actual interpretation, spatial discretization with finite changes, and the therapy of wells. It comprises recognized idea and is essentially intended to shape a foundation for the subsequent bankruptcy the place the equations may be reformulated by way of systems-and-control notation.
The moment bankruptcy develops representations in state-space notation of the porous-media circulate equations. The systematic use of matrix partitioning to explain the different sorts of inputs ends up in an outline when it comes to nonlinear ordinary-differential and algebraic equations with (state-dependent) procedure, enter, output and direct-throughput matrices. different themes contain generalized state-space representations, linearization, removing of prescribed pressures, the tracing of circulation traces, carry tables, computational elements, and the derivation of an strength stability for porous-media flow.
The 3rd bankruptcy first treats the analytical answer of linear structures of standard differential equations for single-phase movement. subsequent it strikes directly to the numerical resolution of the two-phase movement equations, masking numerous facets like implicit, particular or combined (IMPES) time discretizations and linked balance concerns, Newton-Raphson new release, streamline simulation, automated time-stepping, and different computational facets. The bankruptcy concludes with uncomplicated numerical examples to demonstrate those and different facets similar to mobility results, well-constraint switching, time-stepping information, and system-energy accounting.
The contents of this short may be of worth to scholars and researchers drawn to the applying of systems-and-control ideas to grease and fuel reservoir simulation and different purposes of subsurface movement simulation similar to CO2 garage, geothermal power, or groundwater remediation.
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Extra info for A Systems Description of Flow Through Porous Media (SpringerBriefs in Earth Sciences)
A Systems Description of Flow Through Porous Media (SpringerBriefs in Earth Sciences) by Jan Dirk Jansen