Yield-power law model more accurately predicts mud rheology. Oil Gas J
ABSTRACT The yield-power law rheological model can calculate yield point much more accurately than that calculated by the Bingham plastic model. The yield-power law (Herschel-Bulkley) model offers many advantages over the Bingham plastic and power law models because it more accurately characterizes mud behavior across the entire shear rate range. The yield-power law model has not found widespread use in the oil field because of the lack of simple analytical solutions for viscometric and hydraulics calculations. These concerns are no longer pertinent, however, because of the rapid spread of personal computers in the field and recent developments in using this model. The paper describes yield stress, the Bingham plastic model, the power law model, the yield-power law model, calculation method, model comparison, mixed metal hydroxide drilling fluids, mud hydraulics, and results from applying the model to these drilling muds.
- "These fluids can be characterized as YPL. YPL fluid model better describes the fluid at low and high shear rates than the Bingham Plastic or Power Law models (Bern et al. 2007; Friedheim and Conn 1996; Hemphill et al, 1993). Yield stress of the drilling fluid suspends the cuttings and shear thinning ability enables lower pressure losses at the high flow rates. "
[Show abstract] [Hide abstract]
- "This equation reduces to the more commonly-known rheological models under certain conditions, like the Bingham plastic model when the flow behavior index and the power law (PL) model when . The true yield stress can be approximated using measurements from field viscometers (Zamora and Power, 2002; Power and Zamora, 2003; American Petroleum Institute, 2009; Kelessidis et al., 2008) or using non-linear regression and numerical techniques (Hemphill et al., 1993; Khataniar et al., 1994). Non-linear curve fitting to viscometer data may provide the best fitting with the highest correlation coefficient, , and the least mean square error. "
ABSTRACT: 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.Korea-Australia rheology journal 09/2012; 24(3). DOI:10.1007/s13367-012-0020-3 · 0.63 Impact Factor
[Show abstract] [Hide abstract]
- "The nonlinear three parameters model proposed by Herschel and Bulkley (1926) has not been used widely until very recently although it has been shown to fit much better rheological data of aqueous clay slurries and of drilling fluids (Fordham et al., 1991; Hemphil et al., 1993; Maglione and Ferrario, 1996; Kelessidis et al., 2005, 2007). Reasons for the non-frequent use were not only the complexity in derivation of the model's three parameters (Nguyen and Boger, 1987; Hemphil et al., 1993) but also the fact that analytical solutions for laminar or turbulent flow in annuli are not possible, requiring either graphical or trial-anderror solutions (Govier and Aziz, 1972; Hanks, 1979; Fordham et al., 1991). The on-line use, however, of personal computers enabled Maglione et al. (1999, 2000), Bailey and Peden (2000) and Becker et al. (2003) to utilize Herschel–Bulkley * Author to whom correspondence may be addressed. "
ABSTRACT: An integrated approach is presented for the flow of Herschel–Bulkley fluids in a concentric annulus, modelled as a slot, covering the full range of flow types, laminar, transitional, and turbulent flows. Prior analytical solutions for laminar flow are utilized. Turbulent flow solutions are developed using the Metzner–Reed Reynolds number after determining the local power law parameters as functions of flow geometry and the Herschel–Bulkley rheological parameters. The friction factor is estimated by modifying the pipe flow equation. Transitional flow is solved introducing transitional Reynolds numbers which are functions of the local power law index. Thus, an integrated, complete and consistent set, combining analytical, semi-analytical and empirical equations, is provided which describe fully the flow of Herschel–Bulkley fluids in concentric annuli, modelled as a slot. The comparison with experimental and simulator data from various sources shows very good agreement over the entire range of flow types. On présente une méthode intégrée pour l'écoulement des fluides d'Herschel–Bulkley dans un espace annulaire concentrique représenté par une fente, couvrant la gamme complète des types d'écoulement, à savoir laminaire, en transition et turbulent. Des solutions analytiques antérieures sont utilisées pour l'écoulement laminaire. Des solutions d'écoulement turbulent sont élaborées à l'aide du nombre de Reynolds de Metzner–Reed après avoir déterminé les paramètres de loi de puissance locaux en fonction de la géométrie de l'écoulement et des paramètres rhéologiques d'Herschel–Bulkley. Le facteur de friction est estimé en modifiant l'équation d'écoulement dans un tube. L'écoulement en transition est résolu en introduisant les nombres de Reynolds exprimés en fonction de l'indice de loi de puissance local. Ainsi, un ensemble intégré, complet et consistant, combinant des équations analytiques, semi-analytiques et empiriques, est fourni, qui décrit entièrement l'écoulement des fluides d'Herschel–Bulkley dans des espaces annulaires concentriques représentés par des fentes. La comparaison avec les données expérimentales et les données de simulateurs de diverses sources montre un très bon accord pour la gamme complète des types d'écoulement.The Canadian Journal of Chemical Engineering 08/2008; 86(4):676 - 683. DOI:10.1002/cjce.20074 · 1.31 Impact Factor