To Determine Herschel-Bulkley Coefficients

Abstract

E&P Exchange This article presents a straightforward, accurate method for determining the three coefficients of the Herschel-Bulkley equation from six-speed Fannviscometer data. Within the past several years, the Herschel-Bulkley, oryield-power-law, equation has gained acceptance as a better descriptor of drilling-fluid viscosity than either the Bingham plastic or power-law equations. The Herschel-Bulkley equation has three coefficients. The drilling-fluid literature, however, does not seem to contain a good method for calculating these coefficients from the data points obtained from a Fannsix-speed VG meter. We present the following equations for making that calculation. Obviously, such a search can be automated by means of a computer search program. Table 1 and Fig. 1 illustrate results of such a calculation with some of the Ref. 1 Fann viscometer data. The Herschel-Bulkley coefficients in Table 1 were calculated with Eqs. 1 and2. The curves of Fig. 1 were then calculated with these coefficients. As can be seen, the curves go through data points very well. Where the data are notsmooth enough to be fit exactly with a three-coefficient curve, this calculation method results in a curve that has as many data points above as below the curve.