Download PDF by Jan Dirk Jansen: A Systems Description of Flow Through Porous Media

By Jan Dirk Jansen

this article kinds a part of fabric taught in the course of a direction in complex reservoir simulation at Delft collage of expertise over the last 10 years. The contents have additionally been provided at numerous brief classes for commercial and educational researchers attracted to history wisdom had to practice study within the zone of closed-loop reservoir administration, often referred to as clever fields, regarding e.g. model-based construction optimization, facts assimilation (or heritage matching), version aid, or upscaling innovations. each one of those themes has connections to system-theoretical concepts.
The introductory a part of the direction, i.e. the structures description of stream via porous media, varieties the subject of this short monograph. the most target is to offer the vintage reservoir simulation equations in a notation that enables using innovations from the systems-and-control literature. even supposing the idea is restricted to the fairly easy scenario of horizontal two-phase (oil-water) movement, it covers a number of usual elements of porous-media flow.
The first bankruptcy supplies a short assessment of the elemental equations to symbolize single-phase and two-phase stream. It discusses the governing partial-differential equations, their actual interpretation, spatial discretization with finite adjustments, and the remedy of wells. It includes famous concept and is essentially intended to shape a foundation for the subsequent bankruptcy the place the equations should be reformulated when it comes to systems-and-control notation.
The moment bankruptcy develops representations in state-space notation of the porous-media move 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 issues comprise generalized state-space representations, linearization, removing of prescribed pressures, the tracing of move traces, elevate tables, computational facets, and the derivation of an power stability for porous-media flow.
The 3rd bankruptcy first treats the analytical answer of linear platforms of standard differential equations for single-phase stream. subsequent it strikes directly to the numerical resolution of the two-phase move equations, protecting a variety of facets like implicit, specific or combined (IMPES) time discretizations and linked balance concerns, Newton-Raphson generation, streamline simulation, automated time-stepping, and different computational points. The bankruptcy concludes with basic numerical examples to demonstrate those and different elements resembling mobility results, well-constraint switching, time-stepping records, and system-energy accounting.
The contents of this short can be of price to scholars and researchers drawn to the appliance of systems-and-control ideas to grease and gasoline reservoir simulation and different purposes of subsurface move simulation akin to 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

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