A Comparative Study of Hydraulic Models for Foam Drilling
Authors: Ozbayoglu M.E. , Kuru E. , Miska S. , Takach N. 
Published: March 2010

Abstract
Compared to conventional (incompressible) drilling fluids, relatively little is known about the hydraulic and rheological properties of foamed drilling fluids. The complex flow mechanisms involved in compressible drilling fluid circulation make determination of the optimum combination of liquid and gas injection rates very difficult. Modelling of foam rheology is the key issue in hydraulic design, in order to predict the bottom-hole pressure accurately, and to optimize the different controllable variables for effective cutting transport performance.
The University of Tulsa's low-pressure ambient temperature flow loop has been recently modified to accommodate foam flow. The flow loop permits foam flow through 0.0508 m (2 in.), 0.0762 m (3 in.), 0.1016 m (4 in.) diameter pipes, and a 0.2032 m (8 in.) by 0.1143 m (41/2 in.) annular section. Preliminary experiments have been conducted, in which pressure losses were measured for different foam qualities. Measured parameters were gas/liquid flow rates, pressure, differential pressure loss, and temperature.
Statistical analysis was carried out to see the degree of fit provided by Bingham plastic, power law, and yield power law models for the generalized foam flow curve data.
A comparative study was conducted to investigate the predictive ability of the available foam hydraulic models. Models presented by Beyer et al. (1972), Blauer et al. (1974), Reidenbach et al. (1986), Sanghani and Ikoku (1983), Gardiner et al. (1988) and Valko and Economides (1992) were used to estimate the frictional pressure losses during the flow of foam in horizontal pipes. Comparison of the model predictions with experimental pressure loss values show that model predictions of frictional pressure losses can be different from the actual values by 2 to 250 %.

Introduction
In the 1970s, high quality foams were developed into a viable fracturing stimulation tool for oil and gas wells(1). Since then, foam rheology has been the subject of numerous investigations, in an effort to design better proppant transport medium. Lord(2) presented one of the first comprehensive mathematical treatments of foam flow behaviour. He used the real gas law and mass balance considerations to develop an equation of state for foam with solids. Later, Spoerker et al.(3) modified Lord's solution and presented a new two-phase flow equation. They used a virial equation(4) instead of the real gas equation of state. They also solved the differential mechanical energy equation to obtain an explicit expresion for pressure loss prediction during foam flow. Reidenbach et al.(5) presented empirical correlations to calculate the rheological properties of N2 and CO2 foam fracturing fluids. Harris(6–9) conducted some excellent studies on the rheology and fluid loss properties of fracturing fluids. Harris and Reidenbach(10) also studied the effect of temperature on the rheology of foam fracturing fluids.
Foam has been used as a drilling fluid in many drilling operations, and the results from various field cases are well documented in the literature(11–23).