By Jan Dirk Jansen
The introductory a part of the direction, i.e. the structures description of movement via porous media, varieties the subject of this short monograph. the most target is to provide the vintage reservoir simulation equations in a notation that allows using techniques from the systems-and-control literature. even if the idea is proscribed to the rather easy scenario of horizontal two-phase (oil-water) move, it covers a number of normal points of porous-media flow.
The first bankruptcy provides a short assessment of the fundamental equations to symbolize single-phase and two-phase move. It discusses the governing partial-differential equations, their actual interpretation, spatial discretization with finite adjustments, and the therapy of wells. It includes recognized concept and is essentially intended to shape a foundation for the following bankruptcy the place the equations might be reformulated by way of systems-and-control notation.
The moment bankruptcy develops representations in state-space notation of the porous-media movement 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) approach, enter, output and direct-throughput matrices. different subject matters comprise generalized state-space representations, linearization, removal of prescribed pressures, the tracing of circulation strains, carry tables, computational elements, and the derivation of an strength stability for porous-media flow.
The 3rd bankruptcy first treats the analytical resolution of linear platforms of standard differential equations for single-phase circulation. subsequent it strikes directly to the numerical answer of the two-phase stream equations, protecting numerous elements like implicit, particular or combined (IMPES) time discretizations and linked balance matters, Newton-Raphson new release, streamline simulation, computerized time-stepping, and different computational features. The bankruptcy concludes with easy numerical examples to demonstrate those and different points reminiscent of mobility results, well-constraint switching, time-stepping information, and system-energy accounting.
The contents of this short might be of price to scholars and researchers drawn to the appliance of systems-and-control strategies to grease and gasoline reservoir simulation and different functions of subsurface stream simulation resembling CO2 garage, geothermal power, or groundwater remediation.
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A Systems Description of Flow Through Porous Media (SpringerBriefs in Earth Sciences) by Jan Dirk Jansen