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## Revista mexicana de ciencias geológicas

*versión On-line* ISSN 2007-2902

#### Resumen

GOMEZ-ARIAS, Efraín; ANDAVERDE, Jorge; SANTOYO, Edgar y URQUIZA, Gustavo. **Determination of the viscosity and its uncertainty in drilling fluids used for geothermal well completion**: **application in the Los Humeros field, Puebla, Mexico**.* Rev. mex. cienc. geol* [online]. 2009, vol.26, n.2, pp.516-529.
ISSN 2007-2902.

Drilling the hard-rock found in and around geothermal systems for the completion of wells is widely recognized as a difficult and costly task. Drilling fluids of high viscosity (also called muds) are required for the well drilling operations. These fluids must be analyzed for the evaluation of their rheological properties, which are crucial for transporting geological formation cuttings to the surface, among other important applications. The goal of the present work was to develop a new rheological-statistical methodology to calculate dynamic viscosities of drilling fluids using 813 rheological data sets (*i.e.*, shear stress and shear rate measurements). The methodology involved the selection and computer programming of nine rheological-regression models (Bingham Plastic, Power Law, Robertson-Stiff, Casson, Herschel-Bulkley, Sisko, Quadratic, Modified Robertson-Stiff, and Modified Sisko) for finding out the "best fit" line or curve through the experimental data. "Studentized" residuals were calculated and later used for the data fitting evaluation through the application of thirteen univariate discordant tests of single-outlier types. The rheological-statistical analysis of the data sets showed that the most efficient discordant tests were the N14 (skewness), N15 (kurtosis), and N1 (Grubbs). It was also found that the Herschel-Bulkley equation provided the best regression model which enabled to estimate dynamic viscosities of drilling fluids at shear rates ranging from 100 to 1100 s^{-1}. Drilling fluid viscosities and their uncertainties were estimated using "normalized" rheological data sets. These viscosities together with some physical properties of rocks were finally used for calculating the critical velocities of drilling fluids required to transport the formation cuttings in some wells (of different lithologies) drilled in Los Humeros geothermal field. Details of all the application results obtained in this survey are outlined.

**Palabras llave
:
**rheology; non-Newtonian fluids; discordant outliers; linear regression; polynomial regression; univariate discordant tests; studentized residuals.