Hybrid Modeling for Estimating Solid Transport Critical Velocity and its Uncertainty

Abstract

The accurate prediction of critical velocity is crucial for multiphase flow applications where the critical velocity is defined as the minimum carrier fluid velocity that transports solid particles without any deposition in wellbores/pipelines. This work uses a parallel structure hybrid modeling approach that combines semi-mechanistic and data-driven models. Three semi-mechanistic models, namely the Mantz (Mantz, 1977), Oroskar and Turian (Oroskar and Turian, 1980), and the Tulsa (Najmi, 2015) models are used as the semi-mechanistic models, and the GPM (Gaussian Process Modeling) (Rasmussen and Williams, 2006) is used as the data-driven model. Using this parallel hybrid modeling structure, two different hybrid modeling frameworks are introduced, which are referred to as ‘Hybrid Modeling Framework I’ and the ‘Hybrid Modeling Framework II’. These frameworks adopt the same parallel hybrid modeling structure and provide prediction uncertainty and aim to make more accurate predictions of uncertainty compared to the semi-mechanistic models. In addition, Hybrid Modeling Framework II includes the development of a semi-mechanistic model selection process to decide which semi-mechanistic model is more appropriate to be used for a given operating condition. Results yield that hybrid models by these two hybrid modeling frameworks provide more accurate predictions of critical velocities compared to the semi-mechanistic models overall based on the root mean square error (RMSE) metric. Additionally, area metric (AM) is used for predictions made by two frameworks which enable us to compare both mean and the variance of the predictions and the measurements. The comparison of the RMSE and AM values for the hybrid models’ predictions produced by the two different hybrid modeling frameworks reveals that lower RMSE and AM values are obtained by the Hybrid Modeling Framework II compared to Hybrid Modeling Framework I. The semi-mechanistic model selection process embedded in Hybrid Modeling Framework II provides more accurate predictions of critical velocity by identifying the correct semi-mechanistic model and the corresponding hybrid model to use for a certain operating condition.