The complete paper presents a new three-phase relative permeability model for use in chemical-flooding simulators. A model that has been widely used in chemical-flooding simulators for decades has numerical discontinuities that are not physical in nature and that can lead to oscillations in the numerical simulations. The proposed model is simpler, has fewer parameters, and requires fewer experimental data to determine the relative permeability parameters compared with the original model.

## Background

Two- and three-phase relative permeability measurements at low interfacial tension (IFT) have been published previously, and microemulsion relative permeability models have been proposed in the literature as well. But none of these can model the microemulsion phase across different phase-behavior environments, from oil-in-water, to the middle phase, to water-in-oil emulsions. Desirable features should include agreement between two- and three-phase microemulsion relative permeability and oil-recovery data, and relative simplicity for use in reservoir simulators with a minimum number of model parameters that can be estimated from experimental data in a straightforward way. Satisfying these requirements has turned out to be an extremely challenging task.

The objective of this study was to develop a simple, continuous two- and three-phase microemulsion relative permeability model with relatively few parameters that is practical for use in chemical-flooding simulators. Discontinuities in relative permeability cause numerical problems that can cause severe reductions in the size of the timesteps. Discontinuities also cause errors in the physical predictions of important phenomena such as phase trapping and surfactant retention. The need for a continuous model has been well-known, but it was a challenging task to develop a continuous model because of the complexity of three-phase microemulsion phase behavior.

The microemulsion properties vary gradually and continuously as the salinity increases. Other variables such as temperature and pressure also cause the microemulsion to gradually change properties. When the surfactant concentration is below the critical micellar concentration (CMC), no micelles form and no oil is solubilized to form a microemulsion. For surfactant concentrations below the CMC, IFT is high and the surfactant is soluble in water at low salinity and in oil at high salinity. For high-performance surfactants, the CMC is typically less than 0.1 wt%; thus, the surfactant concentration in the water or oil is well below the CMC. Such low concentrations are not very significant with respect to surfactant transport and usage. However, if the relative permeabilities of the microemulsion, water, and oil phases are modeled independently with different parameters, a discontinuity in the relative permeability occurs when the surfactant concentration either increases to values greater than the CMC or decreases to values below the CMC. Both of these changes will occur when a surfactant slug is injected and then displaced by either water or polymer drive.

## New Relative Permeability Model

The relative permeability is modeled using Corey-type functions assuming that the relative permeability of each phase is a function of its own saturation. This process is discussed in detail in the complete paper.

Fig. 3 of the complete paper shows the step-by-step procedure for calculating the two- and three-phase relative permeability values in the simulator. The smooth behavior of the relative permeability as water or polymer drive displaces a microemulsion and the surfactant concentration eventually decreases to below the CMC can be explained in part as follows. As the surfactant concentration decreases from above the CMC, the oil solubilized in a Type I microemulsion decreases faster than the surfactant concentration, the oil solubilization ratio decreases, the calculated IFT increases, and the trapping number approaches a low value corresponding to the waterflood value. Thus, the calculated relative permeability approaches the low trapping-number value for water.

In the traditional model, the residual microemulsion saturation, microemulsion endpoint relative permeability, and microemulsion Corey exponent were calculated by use of microemulsion parameters at low and high trapping numbers. This required the user to enter values for microemulsion parameters at both low and high trapping numbers for a total of six parameters that are not needed in the new model. Experimental data show that, at very high trapping number, the microemulsion residual saturation approaches zero and the microemulsion relative permeability endpoint and Corey exponent are both approximately unity, so these values are typically used as defaults in simulation studies. The same approach is adopted here, and this further reduces the number of model parameters to eight.

Coreflood experiments to test chemical solutions are typically performed with the following flooding sequence:

- The core is flooded with brine.
- Oil is injected at low trapping number to steady state, and the oil endpoint relative permeability is measured at residual water saturation.
- Brine is injected at low trapping number to steady state, and the water endpoint relative permeability is measured at residual oil saturation.
- Chemical solutions are then injected.

The second and third floods provide four parameters at low trapping number (high IFT). The unsteady-state pressure data measured during the waterflood can be used to estimate the water and oil exponents at low trapping number by history matching the results. The only remaining parameters are the oil and water trapping parameters, which are often known from previous capillary desaturation experiments, but which otherwise must be measured in a separate experiment on the same or a similar core. Thus, relative permeability experiments with microemulsion/oil, microemulsion/water, or microemulsion/oil/water phases are not required to estimate any of the parameters in the new model. It is still desirable to have such data, but, because they are rarely measured, it is a huge advantage to have a model that does not require them. Fortunately, the simulation results are not sensitive to the microemulsion relative permeability because it is nearly always close to a straight line because of the high trapping number. The model parameters can also be verified by comparisons between oil-recovery data and numerical simulations of those experiments.**Numerical-Simulation Test Cases.** The five simulation cases listed in **Table 1** were used as test cases. For the first four cases, a vertical coreflood was simulated using a 1×1×100 grid. The gridblock sizes are 0.109×0.109×0.00984 ft in the *x*-, *y*-, and *z*-direction, respectively. The porosity is 0.25, and the permeability is 200 md. The initial oil saturation is 0.4, which is equal to the residual oil saturation at low trapping number.

## Conclusions

Several numerical-simulation test cases, described in detail in the complete paper, illustrate the continuity of the new relative permeability model across the microemulsion phase-behavior boundaries. The development of a model without discontinuities was difficult because of the inherent complexity of two- and three-phase microemulsion/water/oil phase behavior and flow, especially near the CMC. Simulations using the new model showed excellent agreement with alkaline/surfactant/polymer (ASP) -coreflood data. Additional validation of the new model would be desirable, but, on the basis of the results presented in the complete paper, it appears to be an improvement over previous models used in chemical-flooding simulators.

This article, written by *JPT* Technology Editor Chris Carpenter, contains highlights of paper SPE 187369, “A New Three-Phase Microemulsion Relative Permeability Model for Chemical-Flooding Reservoir Simulators,” by **Hamid R. Lashgari, Gary A. Pope, Mohsen Tagavifar, Haishan Luo,** and **Kamy Sepehrnoori, **The University of Texas at Austin, and **Zhitao Li **and **Mojdeh Delshad,** Ultimate EOR Services, prepared for the 2017 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8–11 October. The paper has not been peer reviewed.