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 |