Conjugate thermal-hydrodynamic model for the study of heavy oil transport

In the present work, the thermal impact induced by the environment on the hydrodynamics of heavy oil transport in pipelines is analyzed. Here, the thermal dependence of the dynamic viscosity of heavy oils, in addition to the mechanical heating caused by viscous dissipation are taken into account; therefore, the mathematical models that represent the flow and temperature fields of the heavy oil have to be solved in a coupled manner. Moreover, given that the pipeline is protected by a thermal insulation (soil), the domain of study defines a conjugate system between the heavy oil, the pipeline and the soil, which indicates that before knowing the temperature in the fluid region, temperatures in the other two zones must be calculated. To define properly how thermal energy is transferred and generated during the crude oil transport, the analysis is carried out in dimensionless form, solving the conjugate mathematical model by using numerical approaches and simplified asymptotic approximations. The main results reveal that the transport of heavy oils is seriously affected by a small reduction in temperature, increasing substantially the dynamic viscosity and the flow rate is reduced significantly in comparison with the case of a full thermal insulation condition. Then, we can infer that when the losses of thermal energy and its effects on the hydrodynamics are controlled, an efficient transport process is obtained. Employing the asymptotic analysis, results show that such a condition can be achieved by two ways: the first one by improving the thermal insulation, and the second one by optimizing the ratio of the internal radius to the length of the pipeline or increasing the volumetric flow rate, which indicates that the conjugate phenomenon is a modified version of the Graetz-Nusselt problem.