A practical method for determining the rheology of drilling fluid

Abstract A new mathematical model for analyzing the rheology of a drilling fluid was developed based on a nonlinear function fit of measured data of shear stress and shear rate of the drilling mud used during the drilling process of petroleum and geothermal wells. This mathematical model was obtained from a rational polynomial model proposed for determining of the viscosity behavior. We proposed an analytical approximation to allow a simple fit that approximately describes the rheology of a drilling mud obtaining squared correlation coefficients greater than 0.9995 for the fitted series. The logarithmic function and rational functions obtained describe the shear stress and viscosity behavior, respectively. The fitting process was automated using a simple Wolfram language script. The result is a simple, accurate and practical method to describe the rheology of a drilling mud. This model was compared against most used models, applied to a set of 87 experimental data series, had a good agreement in 81% of the analyzed series and being the best choice in 48.3% of all cases. The method has the advantages of using the Wolfram script with common measurements made during a drilling process and can be applied in either the petroleum or geothermal industries to analyze the drilling mud rheology.