SPE10, Capillary Pressure, and Streamlines

The supposedly realistic waterflood of a highly heterogeneous undersaturated oil reservoir in SPE10 Model 2 is frequently used, and is the only reproducible example we are aware of that has been used, to substantiate the applicability and improved efficiency of Streamline models for recovery prediction in multiphase displacement processes (search the web for "streamline spe10").  Although the problem was specified with zero capillary pressure, realistic capillary forces are high in low permeability regions, cause counter-current imbibition transverse to the streamlines, and have a large first-order effect on recovery (for proof see The Importance of Capillary Pressure Inclusion and Accuracy).  When using realistic capillary forces, the SPE10 case shows that the basic streamline model formulation (representing incompressible immiscible multiphase flow on a single set of streamlines) is too simplistic and that it is inadequate for use in highly heterogeneous displacement processes, in which phases travel along their own, and in some regions countercurrent, sets of streamlines..  This observation invalidates large numbers of claims and conclusions in the literature, and some entire papers.  These capillary(/gravity)-induced transverse convective mechanisms have long been well understood, and they are the same mechanisms that generally strongly affect or determine recovery in dual porosity and dual permeability systems.  While the engineer should always use the simplest and most efficient tool and description that is sufficient to solve the problem, determination of sufficiency requires that no known basic physical process or mechanism should ever be ignored without first verifying that doing so has no significant affect on the answers.  Cinar et al, (SPEJ, June 2006) give an excellent review of research on capillary and gravity crossflow effects along with an experimental and numerical analysis.  They also present a streamline method that accounts for capillary crossflow, and compare against a finite difference model.  The authors concluded that for systems with high capillary forces, accuracy of the finite difference model is superior.  Relative efficiencies of the models were not reported, but it is likely that the errors and inefficiencies due to the approximate operator splitting methods used in streamline models to incorporate multiphase and compositional effects (because the basic formulation fails to explicitly account for them), the associated requirements for pressure and streamline updates, and mapping errors between 3D grids and streamlines and between sets of streamlines at update times more than eliminate any advantage in efficiency.  Since the strongly coupled and strongly non-linear effects of viscous, capillary, and gravity forces and phase behavior determine transport and the changes in variables over a Newton iteration or timestep, the effects of these forces cannot be considered or determined independently of each other without sacrificing significant accuracy due to seldom-mentioned "splitting error".  Extreme levels of complexity are needed in streamline models to obtain approximate and likely inadequate representations of the necessary physics in displacement processes that finite difference models represent clearly, simply, accurately, and we believe most efficiently in most real cases.  Streamline models should be used in multiphase processes only after their assumptions, approximations, and speed advantage have been found to be valid by comparison with a rigorous finite difference model.

Use the simplest and most efficient tools that are sufficient