Precipitated wax content and yield stress of model wax-oil mixtures determined by arrest of flow during cooling at fixed stress

Abstract

To estimate yield stress and other rheological properties relevant to modeling of wax deposition in pipelines where flow is continuous, but stress varies across the pipe radius, model wax-oil mixtures are cooled at multiple cooling rates under constant shear stress until a temperature is reached, at which flow is arrested by gelation due to wax crystal formation. From these data, combined with a measurement of temperature-dependence of precipitated wax concentration by differential scanning calorimetry, an apparent yield stress σy, below which flow is arrested at each temperature, is related to the concentration of precipitated wax Cp and the cooling rate. Results are reported for multiple concentrations in oil of two independent wax mixtures: a many-component commercial wax mimicking the composition of field oil, and a simpler six-alkane mixture. These transient rheological data are fit to a pseudo “Herschel–Bulkley” constitutive equation from which it is found that the yield stresses obtained during flow under cooling are generally an order of magnitude, or more, lower than the yield stresses obtained in the previous work in flow at a comparable constant temperature after cooling in the absence of flow. We also find a strong decrease in the arrest temperature with a decreasing cooling rate, with no convergence even at the lowest cooling rate of 0.0625 °C min−1, indicating that under slower cooling, flow continues even under low stresses. The cooling-rate-dependent yield stress obtained in our study under constant stress provides a challenge to the recent models of gelation under flow stress and is of relevance to wax deposition in pipelines.