3D Simulation of Viscous Fingering and WAG Schemes

Abstract

Summary Water-alternating-gas (WAG) injection has been suggested as a way to reduce viscous-fingering. This paper presents 3D simulations to assess the combined effects of gravity segregation in the vertical plane and areal viscous fingering for miscible displacements with substantial viscous fingering and for WAG injection. The simulations illustrate variations in recovery with WAG ratio and viscous-to-gravity ratio. A procedure to recalibrate the Todd and Longstaff parameter for WAG schemes in which buoyancy forces have little effect is described. Use of this recalibration provided excellent agreement with results from detailed simulation. Where gravity is important, recalibration of the parameter is required; examples of recalibration coarse-grid calculations are presented. Introduction In a field-scale miscible flooding project viscous fingering is likely when the mobility ratio between oil and miscible gas is adverse. The more mobile gas fingers through the oil, leading to early solvent breakthrough. This reduces the rate of oil recovery and increases gas handling costs. Alternating injection of water and miscible gas in a WAG project has been suggested1 as a way to reduce the impact of viscous fingering. The water decreases the mobility of the gas in a zone (the WAG zone) where the two fluids flow together, and the gas mobilizes most of the oil. In theory, WAG injection can reduce dramatically the effects of viscous fingering and lead to significant increases in recovery for a given volume of solvent injected. Three-dimensional effects are most important when viscous and gravitational forces are significant.2 On a field scale, the flow around an injection well is radial (ignoring permeability variations or fractures), and (for most miscible injection strategies) the rate and the density contrast mean that gravitational effects are important somewhere in the flow. The grid sizes used in reservoir simulation are generally too coarse to represent the details of viscous fingering. Instead, empirical models3 are used to represent the average flow in the reservoir model. The choice of empirical model parameters, such as ? in the Todd and Longstaff model, can have a critical influence on field-scale predictions. Use of high-resolution simulation allows the choice of ? to be based on the correct representation of the detailed physics on scales smaller than the dimensions of the gridblocks in the field-scale model. Stone4 described previous studies of WAG efficiency based on segregated flow. Gorrell5 also investigated the effect of layering on the efficiency of tertiary WAG injection. The purpose of this paper is to quantify the effects of fingering and the improvement in recovery resulting from WAG and to describe ways of recalibrating empirical fingering models. 3D Simulation of Viscous Fingering Simulations were carried out with a 3D version of the high-resolution viscous fingering simulator that Christie and Bond6 described. Christie7 gave a full description of the original program. The assumptions and equations solved are summarized in the Appendix. The model has been validated by comparison with experiment.2,7,8 We chose to model 3D fingering flow in a volume with dimensions equivalent to several full-field gridblocks. This meant that flow was essentially linear, and variations in the relative importance of viscous and gravity forces were controlled by only the injection rate. A 60×30×30 grid was used; the grid size was limited by the amount of memory available on a Cray X-MP/24. The length/depth ratio of the model was 20:1; the length/width ratio was 2:1. The model had a thickness of 60 ft and a distance between wells of 1,200 ft. Table 1 gives the fluid properties used. The gas/oil mobility ratio is 30, and the water/oil mobility ratio at the shock front saturation is 1.65. A quarter-power mixing rule was used to determine the oil-phase viscosity. The solvent/water and oil/water relative permeabilities were the same. In the reservoir, viscous fingers will be triggered by variations in permeability. We used the same mechanisms to initiate fingers in the simulations. In these studies, we triggered fingers by using a log-normal uncorrelated permeability distribution with a variance of 5 %. Random variations in permeability ensure that fingers are triggered at the leading edge of an overriding tongue. 3D Simulations - No Shales. We used 3D simulation to investigate the recoveries obtained in a homogeneous, isotropic reservoir for three different displacements. The injection rate corresponded to an average reservoir flow rate of 1 ft/D. At this rate, both viscous and gravity forces are significant. Stalkup9 described a method for choosing the optimum WAG ratio from "matched velocity flooding" (in which water and solvent travel at the same speeds). Simulations7 have shown that the "matched-velocity" WAG ratio is optimum for flow in a 2D horizontal cross section. The matched-velocity WAG ratio is chosen by requiring that the water and solvent travel at the same speed in the reservoir. This leads to a zone of constant saturation and potentially to maximum stabilization of fingering. For the fluid properties used here, this matched-velocity WAG ratio was 0.5. The three cases selected consisted of a 100% miscible displacement and two secondary WAG displacements. To assess the effects of gravity and 3D flow on the recovery efficiency, one WAG displacement used the matched-velocity WAG ratio and the other used a WAG ratio of four. The simulations assumed simultaneous water and gas injection. Fig. 1 compares the recovery curves obtained from the 3D simulations of flow in the homogeneous reservoir model. The best recovery of the three simulations is obtained with a WAG ratio of four. The matched-velocity WAG ratio gives a better recovery at 1 PV injected (PVI) than the miscible flood, although breakthrough is earlier. After 1 PVI total, the amount of solvent injected is 1 PV for the miscible case, 0.66 PV for the matched-velocity WAG case, and only 0.2 PV for the case where the WAG ratio is four. The physical mechanisms determining the spread of recovery for these cases can be determined by examination of the concentration distributions for the matched-velocity WAG and miscible cases. In the WAG case, the water has indeed suppressed the viscous fingers. The water/solvent density contrast, however, is greater than the oil/solvent density contrast, and this higher density contrast has increased the gas override and hence reduced recovery. Recovery improves with respect to the miscible displacement at later times because the water continues to sweep out the reservoir after solvent breakthrough. p. 19–26 3D Simulations - No Shales. We used 3D simulation to investigate the recoveries obtained in a homogeneous, isotropic reservoir for three different displacements. The injection rate corresponded to an average reservoir flow rate of 1 ft/D. At this rate, both viscous and gravity forces are significant. Stalkup9 described a method for choosing the optimum WAG ratio from "matched velocity flooding" (in which water and solvent travel at the same speeds). Simulations7 have shown that the "matched-velocity" WAG ratio is optimum for flow in a 2D horizontal cross section. The matched-velocity WAG ratio is chosen by requiring that the water and solvent travel at the same speed in the reservoir. This leads to a zone of constant saturation and potentially to maximum stabilization of fingering. For the fluid properties used here, this matched-velocity WAG ratio was 0.5. The three cases selected consisted of a 100% miscible displacement and two secondary WAG displacements. To assess the effects of gravity and 3D flow on the recovery efficiency, one WAG displacement used the matched-velocity WAG ratio and the other used a WAG ratio of four. The simulations assumed simultaneous water and gas injection. Fig. 1 compares the recovery curves obtained from the 3D simulations of flow in the homogeneous reservoir model. The best recovery of the three simulations is obtained with a WAG ratio of four. The matched-velocity WAG ratio gives a better recovery at 1 PV injected (PVI) than the miscible flood, although breakthrough is earlier. After 1 PVI total, the amount of solvent injected is 1 PV for the miscible case, 0.66 PV for the matched-velocity WAG case, and only 0.2 PV for the case where the WAG ratio is four. The physical mechanisms determining the spread of recovery for these cases can be determined by examination of the concentration distributions for the matched-velocity WAG and miscible cases. In the WAG case, the water has indeed suppressed the viscous fingers. The water/solvent density contrast, however, is greater than the oil/solvent density contrast, and this higher density contrast has increased the gas override and hence reduced recovery. Recovery improves with respect to the miscible displacement at later times because the water continues to sweep out the reservoir after solvent breakthrough. p. 19–26