Numerical and dimensional investigation of two-phase countercurrent imbibition in porous media
KAUST DepartmentComputational Transport Phenomena Lab
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Environmental Science and Engineering Program
Physical Science and Engineering (PSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/562694
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AbstractIn this paper, we introduce a numerical solution of the problem of two-phase immiscible flow in porous media. In the first part of this work, we present the general conservation laws for multiphase flows in porous media as outlined in the literature for the sake of completion where we emphasize the difficulties associated with these equations in their primitive form and the fact that they are, generally, unclosed. The second part concerns the 1D computation for dimensional and non-dimensional cases and a theoretical analysis of the problem under consideration. A time-scale based on the characteristic velocity is used to transform the macroscopic governing equations into a non-dimensional form. The resulting dimensionless governing equations involved some important dimensionless physical parameters such as Bond number Bo, capillary number Ca and Darcy number Da. Numerical experiments on the Bond number effect is performed for two cases, gravity opposing and assisting. The theoretical analysis illustrates that common formulations of the time-scale forces the coefficient Da12Ca to be equal to one, while formulation of dimensionless time based on a characteristic velocity allows the capillary and Darcy numbers to appear in the dimensionless governing equation which leads to a wide range of scales and physical properties of fluids and rocks. The results indicate that the buoyancy effects due to gravity force take place depending on the location of the open boundary. © 2012 Elsevier B.V. All rights reserved.
SponsorsThe work was partially supported by the KAUST-UTAustin AEA project entitled "Simulation of Subsurface Geochemical Transport and Carbon Sequestration".