I am solving the IMPES equation for the reservoir simulation. I wanted to know the criteria for stability of the equation.
IMPES method has two source of stability limitations: primary variables and transmissibility.
During IMPES method, capillary pressure term is treated explicitly which cause stability issue depending on the Pc-curve's magnitude. Fluid comprerssibility changes the stability limit. Nevertheless, it is common to consider the stability limit under the incompressible assumption for practical purposes.
Besides, explicit treatment of transmissibility term leads to strong non-linearity. The well known stability limit due to this is that flood front can only advance one grid block per iteration. Otherwise, the total throughput of any grid block per iteration must be less that its pore volume.
Ref: Aziz, K., and Settari, A. 1979, Petroleum Reservoir Simulation. London, UK: Applied Science Publisher
it should be is inversely proportional to the gridcell pore-volumes, because implicit-pressure–explicit-saturation (IMPES Method) is having bounded specific CFL region.
I AM NOT SO EXPERT IN THIS FEILD SO I WOULD LIKE YOU TO READ THIS TEXT WHICH MAY HELP YOU
IMPES method has two source of stability limitations: primary variables and transmissibility.
During IMPES method, capillary pressure term is treated explicitly which cause stability issue depending on the Pc-curve's magnitude. Fluid comprerssibility changes the stability limit. Nevertheless, it is common to consider the stability limit under the incompressible assumption for practical purposes.
Besides, explicit treatment of transmissibility term leads to strong non-linearity. The well known stability limit due to this is that flood front can only advance one grid block per iteration. Otherwise, the total throughput of any grid block per iteration must be less that its pore volume.
Ref: Aziz, K., and Settari, A. 1979, Petroleum Reservoir Simulation. London, UK: Applied Science Publisher
maybe you can couple the methods from J. Kou (2004) and Cruz (2014) to deal this issue. i'm doing this now.
- Badges
- Science topic
- Similar topics
- Engineering
- Petroleum Engineering