Summary A practical mathematical model based on experimental data is presented for calculation of rheological properties of N2 and CO2 foam stimulation fluids. The laminar flow model is a yield pseudoplastic type, with viscosity dependent on foam quality, pseudoplastic type, with viscosity dependent on foam quality, yield point, base liquid consistency index (K'), and flow behavior index (n'). Turbulent foam flow data were analyzed with API RP39 procedures but were modified to include variable density effects procedures but were modified to include variable density effects of foam fluids. Water-based foam apparent viscosities compare closely to Mitchell's Bingham plastic model at high shear rates. The yield pseudoplastic model also includes viscous effects of gelling agents and measurement at much lower shear rates. Comparison of predicted pipe friction was made to actual field wellhead pressures with good agreement. Introduction Foams are being used in a number of petroleum industry applications that exploit their high viscosity and low liquid content. Some of the earliest applications for foam dealt with its use as a displacing agent in porous media and as a drilling fluid. Following these early applications, foam was introduced as a wellbore circulating fluid for cleanout and workover applications. In the mid-1970's, N2-based foams became popular for both hydraulic fracturing and fracture acidizing stimulation treatments. In the late 1970's and early 1980's, foamed cementing became a viable service, as did foamed gravel packing. Most recently, CO2 foams have been found to exhibit their usefulness in hydraulic fracturing stimulation. Regardless of why they are applied, these compressible foams are structured, two-phase fluids that are formed when a large internal phase volume (typically 55 to 95%) is dispersed as small discrete entities through a continuous liquid phase. Under typical formation temperatures of 90F [32.2C] encountered in stimulation work, the internal phases N2 or CO2 exist as a gas and hence are properly termed foams in their end-use application. In this properly termed foams in their end-use application. In this paper, we consider the formations of such fluids at typical paper, we consider the formations of such fluids at typical surface conditions of 75F [23.9C] and 900 psi [6205. kPa] where N2 is a gas but CO2 is a liquid. A liquid/liquid two-phase structured fluid is classically called an emulsion. The end-use application of the two-phase fluid, however, normally is above the critical temperature of CO2 where only a gas can exist, so we have chosen to consider the fluids together as foams. Evidence is presented later to show the similarity of two-phase structured fluids independent of the state of the internal phase. The liquid phase typically contains a surfactant and/or other stabilizers to minimize phase separation (or bubble coalescence). These dispersions of an internal phase within a liquid can be treated as homogeneous fluids, provided bubble size is small in comparison to flow geometry dimensions. Volume percent of the internal phase within a foam is its quality. The degree of internal phase dispersion is its texture. At a fixed quality, foams are commonly referred to as either fine or coarse textured. Fine texture denotes a high level of dispersion characterized by many small bubbles with a narrow size distribution and a high specific surface area, and coarse texture denotes larger bubbles with a broad size distribution and a lower specific surface area.