Calculation Method of Power Law and Herschel-Bulkley Model of Drilling Fluid Rheological Parameters Based on Gradient Descent

Abstract

The determination of drilling fluid rheological parameters plays an important role in the calculation of drilling circulation friction. The traditional method uses the least squares method to solve the problem. For the Power Law and Herschel-Bulkley models, by taking the logarithm to linearize of the equation, and then solved by linear regression. This method is not solved in the nonlinear space, it is not the optimal solution to the equation, is only the optimal solution in the linear space. In this paper, according to the characteristics of Power Law and Herschel-Bulkley rheological equations, the gradient descent method is used to calculate the local optimal solution of the rheological model. By selecting an appropriate initial value, the iterative algorithm can quickly and stably converge to the target solution range, and obtain accurate rheological parameters. This algorithm directly solves in nonlinear space, so the result is the optimal solution, and has higher precision than traditional methods. It is also proved by practical examples, the parameters of the Power Law and Herschel-Bulkley rheological models obtained by this method have higher precision. This method can be applied to the optimization selection of drilling fluid rheological models, and evaluation of drilling fluid property.

Copyright 2022, IFEDC Organizing Committee.

This paper was prepared for presentation at the 2022 International Field Exploration and Development Conference in **’an, China, 16–18 November 2022.

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