Numerical method for interfacial heat transfer in an oil‐water displacement flow

Abstract

A numerical study of interfacial heat transfer is performed in an oil‐water displacement flow. The process of oil‐water displacement is one of the key technologies for the underwater tank in offshore oil exploitation. There is a need to investigate the interfacial heat transfer between oil and water as the wax precipitation and solidification of high pour point crude oil at low temperature will particularly affect the flow of oil. Before the numerical simulation is performed, it is necessary to find out the optimal numerical method. For the volume of fluid method, the property parameters in the temperature equation are mixture ones weighted by each fluid. When the unsteady term, convective term, and diffusion term are considered, there are three property parameters that are the coefficient of each term. For each coefficient, whether an algebraic scheme or a harmonic scheme could be used. When the three coefficients are considered together, there would be eight combinations of weighting form. A numerical method is developed by exploring an optimal combination of the weighting form. The results are demonstrated with an analytical solution. It is found that the combination of three harmonic schemes will significantly improve the error. The maximum and total error from this combination are reduced by 62% and 79% compared to the second‐best one and by 86% and 93% compared to the worst one. Meanwhile, the clock time only increases by 1.6% and 0.4%. The combinations of three harmonic schemes will result in the largest order of accuracy which is as large as 1.60. The harmonic scheme should be used for the property parameter of all the three terms in the vertical oil‐water flow.