Application of the Quemada Viscosity Model for Drilling Fluids

Abstract

A number of different models are used to describe the shear rate dependent viscosity of drilling fluids. Most, such as the Herschel-Bulkley model, have a purely empirical basis. The Quemada model, while still empirical, is based on physical principles. It is based on the notion that structural units develop in the fluid at low shear rates which are then partially broken down as the applied shear rate increases. In the current work, drilling fluid rheological data are fitted to the Herschel-Bulkley and the Quemada model. The development of the Quemada model and the calculation of each model parameter are presented. We show that the Quemada model better fits measurements over a wider range of shear rates than the Herschel-Bulkley model. We describe how to select the parameters of the Quemada model. Knowing the difficulty of obtaining a known shear rate for fluids with yield stresses, we discuss how this can affect the quality of the Quemada model fit. Furthermore, in principle, the Quemada model is not applicable in presence a non-zero yield stress. Therefore, we show how to handle the yield stress using a (very high) zero shear rate viscosity.

Calibration of Thixotropic and Viscoelastic Shear-Thinning Fluids Using Pipe Rheometer Measurements

“…With Equation ( 2), it is possible to obtain the shear rate at the wall from the volumetric flowrate and the pressure gradient, and since in steady-state conditions the shear stress at the wall is directly related to the pressure gradient (see Equation ( 1)), it is possible to obtain a flow curve, and, by utilizing the method described in [15], the steady-state Quemada model can be calibrated. The difficulty with this method is to estimate dln(Q) dln(τ w ) .…”

“…Then, the model of Equation ( 19) is used to estimate dln(Q) dln(τ w ) for each measurements, and therefore, a series of shear rate and shear stress values at the wall can be found using, respectively, Equations ( 2) and ( 1). This series of shear rates and stresses are finally used to determine the Quemada model parameters using the method described in [15].…”

“…Depending on the chosen rheological behavior, the flow curve points can be used to fit the rheological model parameters. Typically, this is done by solving a minimization problem of the form [15]:…”

“…There are several possible candidates for the rheological model, but amongst them, the model proposed by Quemada [10] is particularly interesting. This is, first, because it is derived from physical principles, and second, because it provides a very good fit to many different shear-thinning fluids such as drilling muds [15] or biological fluids like blood [16]. The Quemada rheological behavior is:…”

Influence of motile gyrotactic microorganisms over cylindrical geometry attached Cross fluid flow mathematical model

“…Some real‐life situations included time‐consuming procedures, pharmaceutical industries, oil exploration industries, designing devices, petroleum production, lubricant oil, and many biofuels as well as thousands of chemicals are more common evidence of its performance. Drilling fluids viscosity model applications was provided by Knutsen et al 33 Later, Shende et al, 34 Salahuddin et al, 35 and Mader et al 36 developed some more remarkable numerical facts and findings.…”