Optimal determination of rheological parameters for herschel-bulkley drilling fluids using genetic algorithms (GAs)

The rheological properties of a drilling fluid directly affect flow characteristics and hydraulic performance. Drilling fluids containing bentonite mixtures exhibit non-Newtonian rheological behavior which can be described with a high degree of accuracy by the three-parameter Herschel-Bulkley (HB) model. To determine the HB parameters, standard statistical techniques, such as the non-linear regression (NL) method are routinely used. However, sometimes they provide non physically acceptable solutions which could produce wrong values of the significant hydraulic parameters which affect drilling operations. To obtain more accurate results, the Golden Section (GS) method was subsequently developed by Kelessidis et al. (2006). In this work a different technique was developed using the Genetic Algorithms (GAs) to provide an easy-to-use tool in order to determine the three parameters of the Herschel-Bulkley model more accurately. To evaluate the accuracy of the GAs method, experimental viscometric data sets of drilling fluids were taken from the literature and the results were compared with the ones obtained by using the NL and GS techniques. The results show that the GAs and the GS methods provide similar results with very high correlation coefficients and small sum of square errors for most of the samples exhibiting negative yield stress values by the NL technique, while giving similar to the NL technique for the samples that were predicted with positive yield stress. However, in some cases, the GAs method gives better and more realistic results than the GS method.