MODELING OF GRAVITY EFFECTS IN STREAMLINE-BASED SIMULATION FOR THERMAL RECOVERY

Abstract

Gravity effects are more prominent in thermal recovery simulations due to larger density
difference between phases. Historically, the streamline method has been unable to
account for gravity effects. This is a result of assuming that the fluid path follows the
streamline path and therefore no communication among streamlines. However with gravity,
a fluid pathline is different from a fluid streamline. Each phase can move vertically as
a result of the gravity segregation effect in addition to the flow along streamline.
Gravity effects are accounted in the streamline method by an operator splitting technique.
The idea is to isolate the convective flow from diffusion due to gravity for separate
solutions. The convective part is calculated along the common streamline trajectories and
the diffusion part is determined by the direction of gravity. While this has been done successfully
for isothermal problems, it is still a challenge to obtain both accuracy and efficiency
for non-isothermal flow. This paper further examines the mixed streamline method
with an operator splitting technique for this class of problems. The pressure equation for
defining streamlines was derived by summing up the mass conservation equations. Then,
the mass and heat transport equations in terms of the streamline time-of-flight coordinate
were solved for each streamline. A gravity step will be followed by solving the segregation
equations over the dimensional grid. For simplification of modeling, heat was assumed to
transfer by convection only, of which direction is parallel with the flowing phases and the
influence of temperature in the simulation model is through changes in fluid viscosity only.
The proposed approach was tested through simulation of heavy oil recovery by means of
hot waterflooding. The results were verified with those of a commercial fully implicit thermal
simulator.