An Accurate Determination of the Shear Rate for High-Yield-Stress Drilling Fluids Using Concentric Cylinder Fann 35 Viscometer Data

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Summary Rheology is very important for drilling fluid because it directly influences the cutting transportability, hole cleaning ability, lubricity, and filtration loss behavior while drilling. Over the years, the concentric cylinder Fann® 35 viscometer (Houston, Texas, USA) has been used regularly to monitor the properties of drilling fluids because of its simplicity in operations. In the Fann 35 viscometer, the dial readings at different rotor rotations are converted into shear stress; in contrast, the rotor rotation is transformed into the equivalent shear rate using a priori assumed Newtonian behavior of the test drilling fluids. Because the real-life drilling fluids are mostly non-Newtonian with a finite yield stress, the applicability of the simple shear-rate equation, which is frequently used to monitor drilling-fluid rheology, is questionable. A fluid exhibiting sufficiently high yield stress and an unsheared plug flow region near the vicinity of the cup also complicates the estimation of the shear rate. Besides this, the inaccurate values of true yield stress may also result in a poor estimate of the shear rates at different rotor rotations. In the present study, a comprehensive mathematical model is developed to estimate the rheology of drilling fluids with high-yield stress accounting for the fundamentals of rheology using the Fann 35 viscometer data. A generalized difference equation and subsequent Taylor series expansions are used to obtain the accurate wall shear-rate equation for the high-yield-stress non-Newtonian drilling fluids. The true yield stress, an input parameter for the shear-rate prediction, is also accurately determined with the proposed yield-stress model based on the capillary-rise method using two different capillaries. Six different experimental fluids involving aqueous suspension of polyanionic cellulose (PAC; a salt-resistant filtration loss control agent), xanthan gum (XG; a viscosifying agent exhibiting the low shear rate viscosity), carboxymethyl cellulose (CMC; a fluid loss control additive), bentonite nanoclay (an additive for filtration and rheology control), and high-pressure and high-temperature synthetic drilling fluids based on American Petroleum Institute (API)-grade bentonite (BEN) and α-glycol functionalized fly ash (FNFA) were studied to validate the proposed yield stress and the shear-rate model. Finally, the shear rate, apparent viscosity, plastic viscosity, and Bingham yield point are predicted using the proposed models, and the results are compared with the existing shear-rate models.