Analysis of Dynamic and Static Foam Behavior

Abstract

Summary An equation of state describing pressure, volume, and temperature interactions of compressible foam is presented. Also shown is how this equation of state, when used in a unique solution of the mechanical energy balance for compressible-fluid flow, permits prediction of static and dynamic foam properties. A fracturing-treatment case history is presented for illustration. Introduction Low-permeability gas reservoirs are noted for their retention of water-base stimulation fluids within the matrix following treatment. In addition to retaining treatment fluids, many low-permeability formations are underpressured and water sensitive, creating other possibilities for matrix damage from exposure to water-base treatments. Such conditions indicate the need for a stimulation fluid, other than a hydrocarbon, which has a low water content. Foam has fulfilled that need because, on a volume basis, it is composed of a larger percentage of gas than liquid. Typically, foams used for fracturing and fracture acidizing contain 65 to 80 vol% gaseous nitrogen. Several foam fracturing treatments have placed proppant using a liquid phase composed of a 50/50 mixture of water and methanol. Such treatments further limit matrix exposure to a possibly damaging water phase. Compressible fluids, as a class, normally are considered gases; gases are considered Newtonian fluids. If corrections are made for acceleration losses and provisions made for variable density, it is found that gases follow Newtonian-fluid laminar and turbulent flow relationships. Gas viscosity changes are small compared with density changes that occur with changes in pressure. Foam is composed of gas bubbles, which are dispersed uniformly throughout a continuous liquid phase, and can be treated as a homogeneous fluid with both variable density and viscosity. When considered such a homogeneous fluid, foam is probably the only known compressible non-Newtonian fluid. Theory This section presents a state-of-the-art report on equations of state and flow equations for foam. Very few references to an equation of state for foam appear in the literature. However, a number of available references provide methods of estimating dynamic foam behavior. Equation of State Ross proposed an equation of state for foam in the following form. (p ............(1) Eq. 1 offers little from an engineering viewpoint because it is difficult to determine values for such parameters as Pgf, and . However, this equation does provide considerable understanding of foam physical properties. For example, if Eq. 1 is rearranged to the form ...(2) we find that interfacial area per unit volume is determined uniquely by (1) the average excess pressure of gas within the foam above that of the surroundings and (2) liquid surface tension. In addition to this equation of state, Ross provides a guide to other foam behavior and to foam morphology. JPT P. 39^