Inverse estimation of the sand concentration for sand-oil flow in a horizontal pipeline based on the Eulerian–Eulerian model

A method that predicts the sand concentration and volume fraction distribution of sand–oil flow in a horizontal pipeline was proposed based on the inverse heat transfer problem theory. The forward problem of the convective heat transfer process for the sand–oil flow was investigated using a computational fluid dynamics (CFD) simulation based on the Eulerian–Eulerian model. The inverse problem of sand concentration estimation was solved using the temperature distributions at different measurement locations. The sand volume fraction was controlled by an inverse problem algorithm and optimized by inputting the external experiment temperature. Experiments with different sand concentrations were carried out to verify the accuracy of the inverse problem approach. Due to the inherent error between the simulation results and the actual experimental measurements, appropriate modifications in the inverse procedure were made in the input information to ensure that the CFD calculation was more consistent with the actual concentration data. The relative error of the sand concentration estimations could be controlled within 6.0% when the modified measurements were considered the input information of the inverse problem. The volume fraction distributions were also investigated in this study. The important variables that can impact flow temperatures, such as flow velocities and sand diameters, were investigated, and the results showed the inverse method is feasible for estimating the sand concentration of sand–oil flow.