This report extends the theory of the minimum pressure gradient (∇p)min for flowing foams in porous media to include the effects of gas compressibility. The compressibility of the gas phase raises (∇p)min because, in compressible foams, lamellac tend to lodge in pore throats, where capillary resistance to flow is greatest. The effect of compressibility depends on bubble size, gas compressibility, pore-throat geometry, compressibility of adjacent trapped-gas bubbles, capillary pressure pc, and bubble-train length, i.e., the number of consecutive bubbles between slugs of liquid. With reasonable parameter estimates, theory predicts that medium-textured steam foams (bubbles 400 μm in diameter in bulk) have (∇p)min of 1.2 MPa/m (55 psi/ft). For nearly, incompressible CO2 foams, the compressibility effect depends strongly on capillary pressure and (∇p)min is reduced by lower gas-liquid surface tension. Theory predicts (∇p)min = 125 and 20-40 kPa/m (6 and 1-2 psi/ft) for medium-textured CO2 foams at low and high capillary pressure, respectively. Finer textured CO2 foams have a still higher (∇p)min. Clearly, limited foam coalescence is essential for deep foam penetration away from the wellbore in an oil reservoir. Modified for the effect of compressibility, this theory of (∇p)min fits the beadpack data of Falls et al. © 1990.
