Optimal Simulation and Mathematical Correlation of Mud Weight for Effective Wellbore Stability Management

Wellbore instability is a problem that affects drilling activities. It is therefore important to provide an optimal solution that prevents or reduces the occurrence of wellbore collapse and not compromise the integrity of the well. In this study, work was done to assess the impact of several parameters including tubing pressure, tubing fluid temperature, length of tubing, gas density, liquid density, tubing hold-up and total mass flow on mass fraction of tubing muds were considered. Data points for this investigation were obtained using OLGA multiphase simulator. The results of the simulation (including the trend and plot data) were exported to MATLAB to develop a mud weight model (correlation) using the MATLAB regress function. The correlation was also validated using statistical techniques such as the R square and Significance F values. Comparison of the trend plots of the actual data points from OLGA and the predicted data points was also done to further prove the reliability of the correlation. The correlation predictions agreed with the OLGA results excellently with a relative error of less than 0.001 %. This study revealed that the tubing mud weight is significantly impacted on by variables like tubing holdup, tubing gas density, tubing liquid densities and the total mass flow. Whereas the tubing pressure, fluid temperature, and the tubing length have insignificant effects on the tubing mud weight. From the trend plots of the variables, it was deduced that as the tubing pressure increased, the temperature and the mud weight also increased. While, the total mass and volumetric flows reduced with increased tubing pressure. The effect of input data uncertainties on the developed correlation were also tested by using 22 observation points to predict tubing mud weight and calculating the resulting residual values. Over 90% of the residual values were negative and the percentage difference in mud weight between the first and the last observation points was approximately 4%. Hence, the effect of input data uncertainties on the developed correlation is insignificant. This report will serve as a template for drilling engineers, assisting them with a simple, fast and reliable technique for determining optimum drilling parameters with a lesser engineering exertion and drilling experience.