Bibliography - I. Goumiri

1. Goumiri, I., Jean Hervé Prévost, and M. Preisig, 2011: The effect of capillary pressure on the saturation equation of two-phase flow in porous media. International Journal for Numerical and Analytical Methods in Geomechanics, John Wiley & Sons, Ltd., doi:10.1002/nag.1022
   [ Abstract ]

   A complete and accurate simulation of two-phase flow in porous media requires knowledge of all the controlling physics (and values of physical parameters) that play a relevant role and an understanding of the effects of each one on the solution. Of particular concern here is the effect of capillary pressure and the length scale over which it is relevant. The goal of this paper is to provide guidance onto when to include the effects of capillary pressure in the model, and onto what are the resulting length scale restrictions if those effects are to be included.

2. Goumiri, I., and Jean Hervé Prévost, 2010: Cell to Node Projections: An Assessment of Error. International Journal for Numerical and Analytical Methods in Geomechanics, doi:10.1002/nag.927 1-10
   [ Abstract ]

   Reservoir simulators typically use cell-centered finite volume schemes and do not model directly the coupling of the flow processes with the geomechanics. Coupling of geomechanics with fluid flow can be important in many cases, but introducing fully coupled geomechanical effects in those simulators is not a trivial issue, because the geomechanics is better done by using the Galerkin vertex-centered finite element methods by which the solid displacements are computed at the vertices of the cells. This creates difficulties in interfacing cell variables with nodal variables. Uncoupled or loosely coupled models are used by many researchers/practitioners by which a reservoir model is coupled to a geomechanical model by staggering in-time flow and deformation via a sophisticated interface that repeatedly calls first flow and then mechanics. The method therefore requires projection of the reservoir cell variables onto the nodes of the geomechanics Galerkin finite element mesh. In this note, we attempt to quantify the errors associated with cell to node projection operations. For that purpose, we use a simple model of the pressure equation for a heterogeneous medium in one dimension. We are able to derive the exact analytical solution for this problem for both nodal and cell pressures. This allows us to compute the errors due to projection analytically, function of meshing refinement and permeability field variations. We compute upper and lower bounds for the errors, and analyze their magnitude for a variety of cases. We conclude that, in general, cell to node projection operations lead to substantial errors.

Direct link to page: http://cmi.princeton.edu/bibliography/results.php?author=4607