opm-simulators/doc/handbook/ModelDescriptions/2p2cdecoupledtransportmodel.tex
Andreas Lauser 0c1a15c2de handbook: cleanups, update the tutorial for the fully implicit models
- there are no LaTeX files with capital letters anymore
- there are no more "dangling" references
2012-10-16 18:16:19 +02:00

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1.3 KiB
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The transport step is described by the finite volume model for the solution of the transport equation for compositional two-\/phase flow. \[ \frac{\partial C^\kappa}{\partial t} = - \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{alpha} \bf{v}_{\alpha}\right) + q^{\kappa}, \] where $ \bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) $. $ p_{\alpha} $ denotes the phase pressure, $ \bf{K} $ the absolute permeability, $ \lambda_{\alpha} $ the phase mobility, $ \rho_{\alpha} $ the phase density and $ \bf{g} $ the gravity constant and $ C^{\kappa} $ the total \hyperlink{a00070}{Component} concentration. The whole flux contribution for each cell is subdivided into a storage term, a flux term and a source term. Corresponding functions ({\ttfamily \hyperlink{a00145_a13998fc22be58456c4bf8e3f4b12d89c}{get\-Flux()}} and {\ttfamily \hyperlink{a00145_a40fc97d83d3d15cdd29574d3a38fdafb}{get\-Flux\-On\-Boundary()}}) are provided, internal sources are directly treated.