The estimated frictional pressure loss of fluid flow in a pipe is highly dependent on the rheological properties of the fluid. The applied curve fitting method of the viscosity curve will impact the accuracy of the modelled frictional pressure loss. This study evaluates a new approach for application of the power law model previously presented by Saasen and Ytrehus (2018), using dimensionless shear rates, allowing for simpler comparison between fluid characteristics.
The modelling approach is based on selecting an appropriate characteristic shear rate for the flow, replacing the consistency index. The curvature exponent is subsequently fitted to the shear rate region of interest. The applied test fluid is Poly-Anionic Cellulose (PAC) in aqueous solutions. Apparent viscosity measurements have been performed using a high precision rheometer (Anton Paar MCR 302) keeping the temperature constant at 20˚C.
A method for evaluating the accuracy of estimated frictional pressure loss when using the new model of Saasen and Ytrehus is presented. The uncertainty evaluation of the derived model coefficients is based on the estimated probability distribution of the apparent viscosity measurements and error in the model parameter estimation. This uncertainty is further propagated in the estimated frictional pressure loss for evaluation of total modelling accuracy. The new simplified model is more robust and reduces the need for iterative calculations. It has the advantages of simplifying digitalization of the drilling process, being easier and quicker to curve fit at the rig and making it easier to compare different fluids.
Considering the uncertainties related to the rheological properties of the fluid and the impact on the frictional pressure loss is highly applicable when evaluating non-Newtonian fluid flow in pipes. This increased understanding of the uncertainties related to the modelled frictional pressure is also essential information when automating the drilling process.