Flow of fracturing foams in vertical, horizontal and inclined pipes

Abstract

Foams are complex mixtures of a gas and a liquid, with the latter being the continuous phase. The rheological properties of foams are strongly influenced by parameters like temperature, absolute pressure, foam quality, texture, foam-channel wall effects, liquid phase properties, and type and concentration of surfactant. The high solids carrying capacity, the minimum amount of fluid placed in the formation, and the excellent fluid recovery after treatment are some of the advantages that foam fluids present when used during fracturing operations. This thesis is a study of foam flow in pipes, the pressure calculations, the study of rheological properties and their evaluation. The objectives of this research are to: 1. Compare various rheological models representing foams. 2. Develop an algorithm that finds the rheological parameters for the different models at different pressures in the pipe. 3. Provide an engineer with a method that predicts pressure at one end, if pressure at the other end is known, given the rheological parameters of the fluid, the diameter of the pipe and the inlet stream properties. 4. Provide a spreadsheet program for different fluid models that calculates pressures in an inclined, vertical or horizontal pipe. 5. Validate the programs. General curve fitting techniques are used to fit different models: namely, power law, Bingham plastic and Herschel Bulkley models to shear stress vs. shear rate data. The trend of the power law and Bingham plastic rheological parameters with respect to quality is observed. A method to estimate the rheological parameters at different pressures along the pipe using regression methods is developed. Spreadsheet programs for power law Bingham plastic and volume equalized power law model have been developed, which calculate pressures in inclined, horizontal and vertical pipes. The methods for the power law and Bingham plastic fluids are iterative methods. The volume equalized power law program adopts the volume equalized principle, which uses mechanical energy balance with frictional losses calculated from a rheological model. The mechanical energy balance is integrated to obtain a non-linear equation containing the unknown pressure.