Spreadsheet Solutions for Rheological Properties and Viscoplastic Fluid Flow in Circular Pipes and in Parallel-plates

The rheological properties of cement slurries (including fresh concrete and high concentration paste for filling etc.) are complicated, therefore they are approximated by the Bingham plastic model. In recent years, the application of Herschel-Bulkley model is recommended for drilling mud. The rheological coefficients of these models are obtained by using measurement results of the rotational viscometer or experimental results of the flow in a circular pipe, and the pressure loss in pipe flows is obtained from these rheological coefficients. Therefor it is essential to properly select the model in order to design the slurry transportation. In the field of well drilling, the flow in a concentric annulus with a relatively large pipe diameter ratio is approximated by the flow in a parallel-plate, so it is also necessary to consider the flow in a parallel-plate. In this study, first, a method to determine the rheological coefficients by the least squares method from measurement results of the rotational viscometer using the function provided in a spreadsheet is shown and a method to quantitatively select the rheological model using Akaike's information criterion is also shown. Next, after the exact solutions of flows in a circular pipe and in a parallel-plate is summarized, an approximate expression of wall shear stress is derived and the error analysis is performed, and its effectiveness is confirmed by using past experimental data. In addition, a method of calculating the rheological coefficients by the least squares method from measurement results of flows in a circular pipe and in a parallel-plate using spreadsheet is shown and this method is practiced by using the experimental data of the flow in pipes.