An improved viscosity equation is proposed for shear-thinning polymer solutions, using a kinetic approach to model the rate of formation and loss of interactive bonding during shear flow. The bonds are caused by temporary polymer entanglements in polymer solutions, and by coordination bonding in metal ion cross-linked gels. The equation characterises the viscosity of shear-thinning fluids over a wide range of shear rates, from the zero shear region through to infinite shear viscosity.

The equation has been used to characterize fluid data from a wide range of fluids. Recent work indicates that a range of polymer solutions, polymer-based drilling fluids and frac-gels do not have a measurable yield stress, and that the equations which use extrapolated values of yield stress can be significantly in error. The new equation is compared with the Carreau and Cross equations, using the correlation procedure of Churchill and Usagi. It gives a significantly better fit to the data (by up to 50%) over a wide range of shear rates. The improved equation can be used for evaluating the fluid viscosity during the flow of polymeric fluids, in a range of oilfield applications including drilling, completion, stimulation and improved recovery (IOR) processes.

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