An Updated Fractional Flow Model of Low Salinity Water Flooding with Respect to the Impact of Salt Diffusion

Abstract

Low Salinity Water Flooding (LSWF) is an emergent technology developed to increase oil recovery. Many laboratory tests of LSWF have been carried out since the 1990's, but modelling at the reservoir scale is less well reported. Various descriptions of the functional relationship between salt concentration and relative permeability have been presented in the literature, as have the differences in the effective salinity range over which salt content takes effect. This paper focuses on these properties and their impact on the fractional flow of LSWF. We present observations that help characterise the flow behaviour in a more general form, simplifying the interpretation of results. We explain how numerical or physical diffusion of salt affects the velocity of the waterflood front, and how this can be predicted from fractional flow analysis. We have considered various linear and non-linear shapes of the function relating salinity to relative permeability and different effective salinity ranges using a numerical simulator applied at the reservoir scale. The results are compared to fractional flow theory in which both salt and water movement is assumed to be shock-like in nature. We observe that diffusion of the salt front is an important process that affects the fractional flow behaviour depending on the effective salinity range. The simulator solution matches the analytical predictions from fractional flow analysis under the condition that the mid-point of the effective salinity range is at the mid-point between the formation and injected salt concentrations. However, an effective behaviour similar to adsorption/desorption occurs when these mid-point concentrations are not coincidental. The outcome is that the fronts representing high and low salinity water travel with altered velocities and at different saturations. We find that we can predict this behaviour from the input data alone as an augmented form of the fractional flow theory including the concept of retardation or acceleration as occurs for adsorption and desorption for other injectants. We use the analytical solution to the advection-diffusion equation and find that the changes in behaviour depends on the Peclet number. The result of our work is that we have produced an updated form of the fractional flow model of LSWF, to include the impact of salt front diffusion on the movement of fluids. A new factor is introduced, similar to adsorption in polymer flooding. We have developed a new mathematical formula, empirically, to estimate the magnitude of this factor. The new form can be used to modify the effects that numerical or physical diffusion have on the breakthrough times of high and low salinity water fronts during LSFW. This will improve predictive ability and also reduce the requirement for full simulation.