Abstract Foam is one of the most frequently used drilling fluids for underbalanced drilling operations. This paper introduces a more accurate model than the existing models for estimating the pressure drop of foam flowing through the drill bit. The major difference between the proposed and existing models is that the proposed model includes the effect of foam expansion and velocity change as a function of pressure. It has been observed that pressure drop increases significantly as the upstream pressure and foam average velocity increases. For the same flow conditions, pressure drop decreases as the foam quality increases, and as the upstream pressure increases, pressure drop also increases. These events cannot be detected by existing models. In some cases, the pressure drop at the bit can be 10 times greater than the pressure drop predicted by existing models. Introduction Foam has been used as a drilling fluid in many drilling operations; especially in underbalanced drilling applications. In a number of cases, drilling with foam has shown to provide significant benefits, including increased productivity (by reducing formation damage), increased drilling rate, reduced operational difficulties associated with drilling in low pressure reservoirs (e.g. lost-circulation and differentially stuck pipe) and improved formation evaluation while drilling. Foams consist of a continuous liquid phase, forming a stable cellular structure that surrounds and entraps a gas phase. Special chemicals, called surfactants, are used to capture the gas phase; at least for a desired period of time. Foams are considered to be dry or wet, depending on the gas content. Wet foams have spherical bubbles with large amounts of liquid between the bubbles. Dry foam bubbles are polyhedral in shape, with definite contact between the bubbles. In between these two extremes, geometrical figures having both curved and flat faces can exist. Foams are thermodynamically unstable systems because they always contain more than a minimal amount of gas solution interface(1). This interface represents surface free energy, the amount of which can be estimated from knowledge of the surface tension and the interfacial area of the foam. Wherever a foam membrane breaks and the liquid coalesces, there is a decrease in surface free energy. Thus, the decomposition of foam into its constituent phase is a spontaneous process. Since the solution phase is always denser than the gaseous phase, there is a strong tendency for the liquid to separate or drain from the main body of foam unless it is circulated or agitated in some way. Foams can have extremely high viscosity. In all instances, their viscosity is greater than either the liquid or the gas that they contain(2). At the same time, their densities are much lower than the density of water. They are stable at high temperatures and pressures. So, by using foam as a drilling fluid, its high viscosity allows efficient cuttings transport and its low density allows underbalanced conditions to be established; thereby minimizing formation damage. Foams are also preferred when water influx is a problem because they can handle large amounts of water.
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