A study of the diffusion coefficient term in counter current imbibition and its effect on production

Abstract

It is believed that most reservoirs have at least some degree of fractures and spontaneous imbibition is considered to be one of the most important recovery processes in fractured reservoirs. The imbibiton process can be described by a diffusion equation that combines Darcy's law and mass balance, which leads to an expression with a diffusion coefficient $D(S_w)$ that is dependant on water saturation. This diffusion coefficient make up a large part of the variables in the counter current imbibition process.

The diffusion equation is difficult to solve due to it being a non-linear equation and it is therefore of interest to see if it can be changed to a linear diffusion equation by assuming a constant D.

Simulations are done using the eclipse 100 simulator to try to replicate previously performed experiments on core plugs. These simulations are then used to explore the effect of the diffusion coefficient on oil recovery. As the diffusion coefficient is dependant on water it makes the imbibition formula difficult to solve and it is of interest to see how the oil recovery is dependant on the coefficient shape at different water saturations.

Simulation results show that for the diffusion coefficient shape and total area both affect the oil recovery rate and total oil recovery in a given time period.