Extended Fractional-Flow Model of Low-Salinity Waterflooding Accounting for Dispersion and Effective Salinity Range

Abstract

Summary Low–salinity waterflooding (LSWF) is an emergent technology developed to increase oil recovery. Laboratory–scale testing of this process is common, but modeling at the production scale is less well–reported. Various descriptions of the functional relationship between salinity and relative permeability have been presented in the literature, with respect to the differences in the effective salinity range over which the mechanisms occur. In this paper, we focus on these properties and their impact on fractional flow of LSWF at the reservoir scale. We present numerical observations that characterize flow behavior accounting for dispersion. We analyzed linear and nonlinear functions relating salinity to relative permeability and various effective salinity ranges using a numerical simulator. We analyzed the effect of numerical and physical dispersion of salinity on the velocity of the waterflood fronts as an expansion of fractional–flow theory, which normally assumes shock–like behavior of water and concentration fronts. We observed that dispersion of the salinity profile affects the fractional–flow behavior depending on the effective salinity range. The simulator solution is equal to analytical predictions from fractional–flow analysis when the midpoint of the effective salinity range lies between the formation and injected salinities. However, retardation behavior similar to the effect of adsorption occurs when these midpoint concentrations are not coincidental. This alters the velocities of high– and low–salinity water fronts. We derived an extended form of the fractional–flow analysis to include the impact of salinity dispersion. A new factor quantifies a physical or numerical retardation that occurs. We can now modify the effects that dispersion has on the breakthrough times of high– and low–salinity water fronts during LSWF. This improves predictive ability and also reduces the requirement for full simulation.

Semi-Analytical Solution of Chemical Flooding in Heterogeneous Non-Communicating Layers with a Focus on Low Salinity Water Flooding

“…Then, we assumed that the dispersion terms could be represented via numerical dispersion by choosing an appropriate size of grid cell and time step. For a more detailed discussion, see Al-Ibadi et al (2019b). This has been discussed for some time in the literature (Jerauld et al 2008, discussed it in the context of LSWF).…”

“…The grid cell size in the x-direction was then modified for various coarse models to examine the effect of numerical dispersion, which can be used to mimic the physical dispersion that may be induced in a heterogeneous system, where both spread out the salinity front and the water saturation. The similarity between numerical and physical dispersion has been known for some time (Lantz 1971) and we have previously discussed using the former to represent the latter in some detail (Al-Ibadi et al 2019b). Two sets of relative permeability were then used, one set to simulate fluid flow behavior for high salinity formation water and another to simulate fluid flow after the salinity has been reduced.…”

“…We have presented evidence of this dispersion-induced retardation previously for LSWF simulations where salinity caused a change in wettability. (More details can be found in , 2019b.) The key to this effect is the range of chemical concentrations over which the wettability changes relative to the mixing zone created by dispersion.…”

“…In the case of numerical and physical retardation, D can be obtained (Al-Ibadi et al 2019b) from the input data as: where v ref is the velocity of the solute front for a reference case in which there is zero retardation;v Mid A is the velocity that the true concentration, C mid-eff d , would travel in an imaginary situation where C mid-eff d = 1 (in which case the wettability changes instantaneously). The advantage of this hypothetical condition is that we can obtain the solution analytically (for details, see Al-Ibadi et al 2019b). v C * and v F * are injected and formation water velocities, respectively, for the analytical solution with D = 0 in Eqs.…”

“…For instance, in models that simulate the alteration of wettability due to the injection of low salinity or engineered water, various mechanisms result in adsorption of active ions such as Ca 2+ and Mg 2+ (Lager et al 2006; Sharma and Mohanty 2018; Al-Shalabi and Sepehrnoori 2017) which slows down the front as a chemical retardation. Further, there is evidence that dispersion and diffusion can retard the active ion or salinity front as well (Al-Ibadi et al 2019d) causing the displacing fronts to be either accelerated or retarded as a function of the effective concentration range , 2019b. This creates a physical retardation.…”