Cell to node projections: An assessment of error

Reservoir simulators typically use cell centered finite volume schemes and do not model directly the coupling of the flow processes with the geomechanics. Introducing fully coupled geomechanical effects in those simulators creates difficulties in interfacing cell variables with nodal variables. Uncoupled or loosely coupled models are used by many researchers/practitioners. These methods require 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. After bounding and analyzing the magnitude of these errors, we conclude that, in general, cell to node projection operations lead to substantial errors.