# Mathematical Modeling of the Differential Sticking Coefficient of Clay Drilling Fluids

Document Type : Research Paper

Authors

1 Mechanical Engineering Academic Unit, Petroleum Engineering, Federal University of Campina Grande, Brazil

2 PPG-CEMat, Center of Science and Technology, Federal University of Campina Grande, Brazil

Abstract

The main objective of this work is to propose a mathematical model for the differential sticking coefficient of clayey drilling fluids with a lubricant as an additive and evaluate the influence of differential pressure and lubricant content on filter cake thickness and permeability. Tests were carried out on fluids composed of water and 4.86% of active bentonite clay prepared in Hamilton Beach agitators at a high rotation speed (17000 rpm) for 20 minutes. After a 24-hour time-out in a closed container, lubricants were added to the fluids at different levels. To obtain the differential sticking coefficient (DSC), and the filter cake, a differential sticking tester by Fann with a spherical torque plate was used, and the filter cake thickness was determined in an extensometer. The setting time, differential pressure, and lubricant content were defined as the input variables (independent variables) to the DSC mathematical model. The differential pressure and lubricant rate were the independent variables to the mathematical model of filter cake thickness (FCT) and permeability (K), which varied according to a factorial planning, was known as a second order model. The experimental data regression was performed utilizing Statistic software, version 7.0. The results clearly showed that it was possible to obtain a statistically meaningful and predictive mathematical model for DSC. It was also observed that the increase in the lubricant content was responsible for a DSC value reduction due to the fact that the lubricant was a dispersing agent reducing the filtrate volume and the filter cake thickness, and thereby decreasing the sticking risk due to differential pressure. Finally, from the analysis of point values and response surfaces for FCT and K, it was possible to observe tendencies that made clear that the differential pressure and lubricant content influenced filter cake properties.

Keywords

#### References

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