Generalized Hydraulic Calculation Method Using Rational Polynomial Model

Abstract

Abstract Abstract: Current methods of hydraulic calculations for non-Newtonian fluids encountered in the oil fields necessitate, as a first step, determination of an appropriate fluid model, e.g., Bingham plastic or yield power law. The calculated parameters of the chosen fluid model are then plugged into the corresponding set of hydraulic formulas. In this study, a generalized hydraulic calculation technique has been developed and programmed that requires as input only the raw rheological data for the fluid and the values of the relevant hydraulic parameters. It is not necessary to incorporate in the program the many empirical models currently used to represent non-Newtonian fluid behavior and the associated logic to determine which model is appropriate for a given set of rheological data. The new hydraulic calculation technique is based on two important developments. First, a new and powerful rheological model, called Rational Polynomial (RP), has been developed. Using a variety of data from the literature, it is shown that the rational polynomial model is capable of accurately representing the rheogram of virtually any time-independent fluid. Second, a generalized hydraulic calculation procedure has been developed which is applicable to any time-independent non-Newtonian fluid. The Rabinowitsch-Mooney1 equation is integrated numerically utilizing the rational polynomial correlation. For laminar flow, this integration directly provides the solution for flow rate versus pressure drop. The integration also provides the parameters needed in the calculation of turbulent flow utilizing the generalized power law procedure developed by Metzner and Reed2. The predictions of the developed method have been compared with several sets of experimental hydraulic data from different sources, gathered from large-scale flow loops. The tested cases include laminar and turbulent flow of various drilling fluids in both pipe and annular geometry. The predictions of the rational polynomial and the generalized hydraulic calculation method are shown to be quite accurate and superior to those obtained by the currently available standard techniques.