A closed form and easy-to-use analytical model has been developed in this study for foam hydraulics. The analytical model fully couples the frictional and hydrostatic pressure components in vertical and inclined boreholes. The newly developed model together with screened rheological model was validated using bottom pressure data measured from two wells drilled with stable foams. The maximum difference between the model-predicted and measured bottom hole pressures is 9.2%. Theoretical analyses with the model indicate that injection GLR is a dominating factor affecting depth limit and ECD in stable foam drilling. In the practical range of GLR (1 to 20) and a gas injection rate limit of 2000 scfm, the maximum borehole depth is about 5000 ft where the lower limit of stable foam quality of 0.55 is reached. The new model was used in this study to generate depth limit and ECD curves that can be used for multi-gradient drilling on-shore and in deepwater development.

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