Download PDF by Jan Dirk Jansen: A Systems Description of Flow Through Porous Media
By Jan Dirk Jansen
This textual content kinds a part of fabric taught in the course of a path in complicated reservoir simulation at Delft college of expertise over the last 10 years. The contents have additionally been offered at quite a few brief classes for commercial and educational researchers drawn to heritage wisdom had to practice study within the quarter of closed-loop reservoir administration, often referred to as shrewdpermanent fields, relating to e.g. model-based creation optimization, facts assimilation (or heritage matching), version relief, or upscaling concepts. every one of those subject matters has connections to system-theoretical concepts.
The introductory a part of the path, i.e. the structures description of move via porous media, types the subject of this short monograph. the most target is to give the vintage reservoir simulation equations in a notation that allows using innovations from the systems-and-control literature. even though the speculation is proscribed to the particularly easy state of affairs of horizontal two-phase (oil-water) circulation, it covers numerous ordinary facets of porous-media flow.
The first bankruptcy offers a quick 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 alterations, and the remedy of wells. It includes famous concept and is basically intended to shape a foundation for the subsequent bankruptcy the place the equations should be reformulated by way of systems-and-control notation.
The moment bankruptcy develops representations in state-space notation of the porous-media stream equations. The systematic use of matrix partitioning to explain the differing kinds of inputs results in an outline when it comes to nonlinear ordinary-differential and algebraic equations with (state-dependent) process, enter, output and direct-throughput matrices. different subject matters contain generalized state-space representations, linearization, removing of prescribed pressures, the tracing of circulation strains, carry tables, computational points, and the derivation of an strength stability for porous-media flow.
The 3rd bankruptcy first treats the analytical answer of linear platforms of normal differential equations for single-phase circulate. subsequent it strikes directly to the numerical resolution of the two-phase circulation equations, masking quite a few points like implicit, specific or combined (IMPES) time discretizations and linked balance concerns, Newton-Raphson generation, streamline simulation, computerized time-stepping, and different computational features. The bankruptcy concludes with basic numerical examples to demonstrate those and different elements equivalent to mobility results, well-constraint switching, time-stepping information, and system-energy accounting.
The contents of this short can be of worth to scholars and researchers drawn to the applying of systems-and-control suggestions to grease and gasoline reservoir simulation and different purposes of subsurface move simulation equivalent to CO2 garage, geothermal power, or groundwater remediation.
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Additional resources for A Systems Description of Flow Through Porous Media
The bottom-left and bottom-right figures display details of T and illustrate the side bands and the ‘holes’ in the tri-diagonals at every 21st row which are typical for a regular numbering scheme. In this case the 441 grid blocks have been numbered row-wise from top-left to bottom-right. e. not at an edge or at a corner, is connected to its Western and Eastern neighbors with numbers i - 1 and i ? 1 respectively, which results in the tri-diagonals, and to its Northern and Southern neighbors i - 21 and i ?
Pet Trans AIME 146:107–116 Chen Z, Huan G, Ma Y (2006) Computational methods for multiphase flows in porous media. SIAM, Philadelphia Ding Y, Lemonnier PA, Estebenet T, Magras J-F (2000) Control-volume method for simulation in the well vicinity for arbitrary well configurations. SPE J 5(1):118–125. 2118/62169-PA Ewing RE (1983) Problems arising in the modeling of processes for hydrocarbon recovery. In: Ewing RE (ed) The mathematics of reservoir simulation. SIAM, Philadelphia Fanchi JR (2006) Principles of applied reservoir simulation, 3rd edn.
An example of a finite-difference discretization as applied to porous-media flow has been worked out in Chap. 1. All of the discretization methods result in systems of ordinarydifferential equations (ODEs) which can typically be represented as 8 d ð 1 Þ > > ^e1 1 ; ¼ ^f1 ðt; 1 ; 2 ; . ; n ; w1 Þ; > > dt > > > > > d ð 2 Þ > > < ^e2 2 ; ¼ ^f2 ðt; 1 ; 2 ; . ; n ; w2 Þ; dt ð2:2Þ > .. > > > . > > > > > d ð Þ > n > : ^en n ; ¼ ^fn ðt; 1 ; 2 ; . ; n ; wn Þ; dt where the continuous dependent variable and the continuous source term w of Eq.
A Systems Description of Flow Through Porous Media by Jan Dirk Jansen