Numerical stability and precision are required when using simulations to predict Enhanced Oil Recovery processes and these can be difficult to achieve for Low Salinity Water Flooding (LSWF). In this paper we investigate the conditions that lead to numerical instabilities when simulating LSWF. We also examine how to achieve more precise simulation results by upscaling the flow behaviour in an effective manner.
An implicit finite difference numerical solver was used to simulate LSWF. The stability and precision of the numerical solution has been examined as a function of changing the grid size and time step. We used the Peclet number to characterise numerical dispersion with these changes. Time step length was compared with the Courant condition. We also investigated some of the nonlinear elements of the simulation model such as the differences between the concentrations of connate water salinity and the injected brine, effective salinity concentration range and the net mobility change on fluids through changing the salt concentration.
We observe that numerical solution of LSWF tends to be conditionally stable, with problems occurring as a function of the range of effective salinity concentration relative to the initial reservoir water and the injected brine concentrations. We observe that the Courant condition is necessary but not sufficient. By definition, the precision of the numerical solution decreased when increasing numerical dispersion but this also resulted in slowing down the low salinity water and increased the velocity of the formation water further reducing precision. These numerical problems mainly depend on fluid mobility as a function of salt concentration. We conclude that the total range and the mid-concentration of effective salinity affect the stability and precision of the numerical solution, respectively. In this work, we have developed two approaches that can be used to upscale simulations of LSWF and tackle the numerical instability problems. The first method is based on a mathematical form that gives the relationship between the fractional flow, effective salinity concentration and the Peclet number. The second method is that we have established an unconventional proxy method that can be used to imitiate pseudo relative permeabilities.
This work enables us for the first time to simulate LSWF by using a single table of pseudo relative permeability data, instead of two tables as traditionally done in previous studies. This removes the need for relative permeability interpolation during the simulation and will help engineers to more efficiently and accurately assess the potential for improving oil recovery using LSWF and optimise the value of the field development. We also avoid the numerical instabilities inherent in the traditional LSWF model.