Modeling Foams for Acid Diversion

Abstract

ABSTRACT Successful foam diversion in matrix acid treatments depends on foam mobility during foam injection and liquid (acid) mobility after foam injection. We present new coreflood data for both flow regimes. At fixed quality and high flow rates, we find that foam behaves as a shear-thinning fluid with power-law exponent of about 0.6. For qualities below about 80%, when gas and liquid flow rates are varied separately, pressure gradient is nearly independent of water flow rate, as reported by Osterloh and Jante (1992) for foam below a threshold foam quality. Upon liquid injection after foam, pressure gradient falls to a steady-state value that varies little with liquid flow rate. The transition to this steady-state pressure gradient is strongly affected by gas expansion as pressure falls, which makes extrapolation from laboratory coreflood to field application tricky. However, although some gas escapes during this transition period, the foam front does not advance; that is, this escaping gas moves as free gas, not foam. These findings are intermediate between the simple quasi-Newtonian model of Zhou and Rossen (1994) and the extremely shear-thinning behavior reported by Parlar et al. (1995) and Robert and Mack (1995). A simple new model accounts for many of the trends observed. This model assumes that foam mobility is controlled, not by foam coalescence and capillary pressure as for high-quality foams, but by trapping and mobilization of foam bubbles of fixed size. This model explains how foam mobility can be independent of liquid flow rate; why steady-state pressure gradient falls moderately during liquid injection following foam; and why this pressure gradient is relatively insensitive to liquid flow rate. Implications of the model for design of foam processes are discussed.