Simulating Foam Processes at High and Low Foam Qualities

Abstract

Abstract Foams used for gas or acid diversion exhibit two flow regimes, depending on foam quality. Two foam simulators, one the most widely used commercial foam simulator and the other developed at our university, fit steady-state foam behaviour in both regimes. A simple procedure is described for fitting simulator parameters to a set of steady-state core flood data and examples are shown. Fitting model parameters to a single core flood data can err by fitting this datum to the wrong flow regime. Shear-thinning reported in the "low-quality regime" can increase foam injectivity in radial flow. Foams in low-quality regime fit the same correlation for overcoming gravity override previously derived for foam in the high-quality regime. The flow regime does greatly affect the effect of capillary crossflow on foam diversion between layers differing in permeability, however. Capillary crossflow harms diversion between adjacent layers, as found earlier, but the magnitude of the effect is much less for foam in the low-quality regime, and no single correlation matches all the results. Capillary crossflow can actually increase (by a small amount) diversion from adjacent layers differing somewhat in permeability to distant layers with much-different permeability. Introduction Foams find application in diversion of acid in well-stimulation treatments,1,2 diversion of gas in improved-oil-recovery processes,3,4 and diversion of treatment fluids in environmental remediation processes.5,6 These processes differ from foam drilling, fracturing, cementing and well cleanout processes in that foam flows through the porous medium itself. Foam exhibits at least two steady-state flow regimes as a function of foam quality ƒg (injected gas volume fraction), as illustrated in Fig. 1.7–10 At high foam qualities (upper left portion of figure), pressure gradient ?p is nearly independent of gas flow rate. This "high-quality" or "coalescence"11 regime is controlled by bubble coalescence at the "limiting capillary pressure" Pc*.12,13 In this regime, both capillary pressure Pc and water saturation Sw remain at Pc* and Sw* = Sw(Pc*), respectively, independent of gas and liquid flow rates. As a function of overall flow rate (at fixed back-pressure), behaviour can be shear-thinning, as shown in Fig. 1 (cf. also Ref. (12)), Newtonian,11,14 or even shear-thickening.10 In the "low-quality regime" (lower right portion of Fig. 1), ?p is nearly independent of liquid flow rate. It is thought that in this regime bubble size is fixed,8,10 but water saturation does change with flow rates. The low-quality regime is shear-thinning as a function of overall flow rate. The transition between regimes occurs at a foam quality ƒg*. These two foam-flow regimes are reported with both N2 and CO2 gas, with various surfactants, and in various porous media, including sand- and bead packs, relatively uniform Berea sandstone, strongly layered Antolini sandstone, and field cores.7–10 Fig. 2 shows an example from Alvarez et al.10 in Berea sandstone. Alvarez et al. made no attempt to smooth these data, to avoid possibly biasing the trend of the contours, but the vertical trend of the ?p contours in the high-qulaity regime and nearly horizontal trend in the low-quality regime and nearly horizontal trend in the low-quality regime are both evident in the figure. It is not yet clear whether the tow flow regimes apply to "weak" forms, with relatively small decreases in gas mobility; examples uncovered to date have show large reductions in mobility. The transition form quality ƒg* that separates low- and high-quality regimes depends on surfactant formulation and concentration, probably other compositional factors (gas type, ionic strength, etc.), and one permeability and possibly other properties of the porous medium.10 For instance, ƒg* increases as permeability increases. Fig. 3 shows how more-restricted studies of foam at fixed foam quality or fixed overall flow rate appear on a plot like Figs. 1 or 2.