Rheologica Acta

, Volume 57, Issue 11, pp 693–704 | Cite as

Rheological studies and optimization of Herschel–Bulkley parameters of an environmentally friendly drilling fluid using genetic algorithm

  • Hocine OuaerEmail author
  • Mourad Gareche
  • Reza Rooki
Original Contribution


The Herschel–Bulkley rheological parameters of an environmentally friendly drilling fluid formulated based on an Algerian bentonite and two polymers—hydroxyethyl cellulose and polyethylene glycol—have been optimized using a genetic algorithm. The effect of hydroxyethyl cellulose, temperature, pH and sodium chloride (NaCl) on the three-parameter Herschel-Bulkley model was also studied. The genetic algorithm technique provided improved rheological parameter characterization compared to the nonlinear regression, especially in the case of drilling fluids formulated with sodium chloride making it a better choice. Furthermore, the oscillatory test offered more reliable yield stress values. The rheological parameters were found to be very sensitive to different conditions. Yield stress and consistency index increased with increasing the hydroxyethyl cellulose concentration, reaching maximum at a temperature of 65 °C and decreased with decreasing pH and also when adding sodium chloride to the drilling fluid. The flow index changed inversely to yield stress and consistency index. The physical origins of these changes in rheological parameters were discussed and correlation between variation in rheological parameters and bentonite suspension properties were concluded. Based on these results, it is recommended to use the proposed formulation of drilling fluid at high temperature and when the formation of alkaline pH is encountered due to the gelation mechanism and to select the optimum concentration of NaCl to avoid degradation of the rheological parameters.

Graphical abstract


Drilling fluid Herschel–Bulkley Genetic algorithm Bentonite Hydroxyethyl cellulose Polyethylene glycol 



carboxymethyl cellulose






genetic algorithm


hydroxyethyl cellulose




nonlinear regression


polyethylene glycol


power law


particle swarm optimization


sample 1–18


X-ray fluorescence


consistency index (


number of data points


flow index


correlation coefficient


sum of square errors (Pa2)


temperature (°C)

\( \dot{\gamma} \)

shear rate (s−1)


shear stress (Pa)


yield stress (Pa)


measured shear stress (Pa)

\( {\widehat{\tau}}_i \)

predicted shear stress

\( {\overline{\widehat{\tau}}}_a \)

mean predicted shear stress



The authors wish to extend special thanks to Mr. Perry Mureau for his help.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire Génie Physique des Hydrocarbures, Faculté des Hydrocarbures et de la ChimieUniversité M’Hamed Bougara de BoumerdesBoumerdèsAlgeria
  2. 2.Birjand University of TechnologyBirjandIran

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