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.
Stable foams have been used as circulating fluids in drilling and workover operations since late 1960's. Successful applications have been well documented.1–10 Research work have been done on the behavior of stable foams.11–17 Recently, stable foams have been used for Underbalanced drilling (UBD) both in vertical18,19 and in inclined holes.20
Accurate prediction of shut-in and flowing bottom hole pressures is particularly important for foam drilling inclined holes where borehole integrity is a major concern. As foam is a compressible fluid, special care needs to be taken in hydraulics calculations. This is mainly because of:
inadequate foam rheology model, and
influence of frictional and hydrostatic pressure components through the pressure-dependent fluid density.
A number of rheology models have been developed for foam hydraulics calculations in the past three decades. These models include Beyer et al.,12 Blauer et al.,14 Sanghani,21 Reidenbach et al.,22 Valko-Economides,23 and Gardiner et al.24 Ozbayoglu et al.25 conducted a comparative study of these models. They also measured foam pressure drops across a 90 ft horizontal pipe. Based on the comparison of experimental data and results of the models, they concluded that there is no "best" model for predicting the pressure losses during foam flow in pipes under the experimental conditions. Models that may predict pressure losses closer to actual values in one case, may not be suitable for another condition. Their experimental data indicate that foam rheology can be better characterized by the Power Law model for 0.70 and 0.80 foam qualities, whereas the Bingham plastic model gives better fit for 0.90 foam quality.
Guo et al.26 presented a trial and error method to couple the frictional and hydrostatic pressure components through the pressure-dependent fluid density. Their technique gives results similar to that given by the computer models of Anderson8 and Okpobiri and Ikoku.20
Both steady state flow and transient flow simulators are available in drilling industry for foam drilling hydraulics calculations.8,11,13,20,27 Unfortunately, the results from these simulators are frequently conflicting28,29 due to assumptions that were made in mathematical formulations and rheological modeling.
In order to improve the accuracy of pressure prediction in foam drilling, we have developed a closed form equation to fully couple the frictional and hydrostatic pressure components in this study. 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 measured and model-calculated bottom hole pressures is 9.2%. The new model was used in this study to generate depth limit and ECD curves that can be used for multi-gradient drilling in deepwater development.