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unilogo Universität Stuttgart
Institut für Wasser- und Umweltsystemmodellierung - IWS



"Comparison of mathematical and numerical models for twophase flow in porous media"

This thesis compares a fully coupled twophase flow formulation and two different kinds of fractional flow formulations. The fully coupled formulation is directly described by two mass balance equations - one equation for each phase. The governing equations of the fractional flow formulations are one saturation equation and one pressure equation. The pressure equation is formulated in terms of a global pressure where the saturation equation shows an advection diffusion form, as well as in terms of a phase pressure where the saturation equation is purely advective. Different numerical schemes are applied for the discretisation of the fully coupled formulation and the discretisation of the fractional flow formulations. The solution behaviour of the numerical models according to the mathematical formulations is investigated concerning accuracy and efficiency. Depending on the physical process, a superior scheme is tried to be determined which can be used for more complex applications. Therefore, different benchmark problems representing different flow characteristics are solved and the results are analysed. It can be shown that in case of a one dimensional problem the best results concerning the accuracy of the approximation can be achieved using the fractional flow approach and the global pressure fractional flow approach, respectively. This applies for advection dominated and diffusion dominated problems as well as for problems combining both processes. Differences concerning the efficiency can be found depending on the nonlinearity introduced by the constitutive relationships used for the relative permeabilities and the capillary pressure. Here, the fully coupled approach shows advantages with increasing nonlinearity. For the considered two dimensional problem the best results can be achieved using the fully coupled approach. The phase pressure fractional flow formulation is expected to combine the possibility to account well for different kinds of transport processes with the advantage of using a phase pressure as physically meaningful quantity. With the numerical schemes applied so far, this can not be approved.