Rapid variations in the fluid velocity field influence pressure loss calculations. In this paper, we propose numerical methods for estimating pressure losses in a circular pipe when the flow rate oscillates. The method is described for Newtonian and two non-Newtonian rheological behaviors: the power law and the Quemada models. Also, as drilling fluids are usually thixotropic, i.e., their rheological behavior depends on the shear history, an expansion of the Quemada model is proposed to account for shear history effects.
A laboratory flow-loop has been assembled and measurements conducted with a non-thixotropic aqueous solution of Carbopol and a thixotropic potassium chloride solution of xanthan gum. The measurements were analyzed and compared with estimates made with the proposed models.
It is found that when applying a square wave oscillating flowrate to a non-thixotropic fluid, large surge and swab pressure spikes are generated. The same square wave signal does not produce pressure spikes when circulating a thixotropic fluid; on the contrary the acceleration and deceleration fronts are largely attenuated.
When applying a triangular or sinusoidal wave form to the flowrate while circulating a non-thixotropic fluid, the peak-to-peak pressure gradient gets progressively larger when the oscillation amplitude increases or the signal period reduces, compared to the expected value when estimating the pressure losses with the steady state approximation. However, under the same conditions, when circulating a thixotropic fluid, the peak-to-peak pressure gradients are lower than those estimated with the steady state approximation.