(166a) Hybrid Modeling for Critical Velocity Predictions for Solid Transport

Accurate critical velocity predictions in multiphase flows are crucial for solid transport where the critical velocity is the minimum velocity that the solids are transported without any deposition in wellbores/pipelines (Dabirian et al., 2016). The hybrid modeling approach, which is a combination of the first principal model and data-driven model, is one of the methods that can be used in predicting the critical velocity. This work adopts the parallel structure of a hybrid modeling approach for critical velocity and its uncertainty predictions (Sansana et al., 2021) (Deng et al., 2022) where the Oroskar and Turian (Oroskar & Turian, 1980), Mantz (Mantz, 1977) and Tulsa Models (Najmi, 2015) are used as the semi-mechanistic models and the Gaussian Process Modeling (GPM) (Rasmussen & Williams, 2006) is used as the data-driven model. Fig 1 represents the parallel structure of the hybrid modeling approach where 𝑦^𝑚 and 𝑦̂^𝑒 represents the predictions made by the semi-mechanistic model and hybrid model respectively. Also, the ẟ and ẟ̂ represents the discrepancy and discrepancy estimates by the data-driven model where the discrepancy is defined as the difference between the critical velocity measurements (𝑦^𝑒), and critical velocity predictions by the semi-mechanistic model (𝑦^𝑚). Additionally, 𝑋 terms represent the input data set which includes solid density and solid concentrations, fluid viscosity and densities, and hydraulic and particle diameters. The GPy is used as the Gaussian Process (GP) framework to train the GPM model for the estimation of model discrepancy where the method of k-fold cross-validation is used for training the model with four folds. This work discusses the hybrid modeling framework and analyzes the findings from three semi-mechanistic models and three hybrid models. Also, it compares the performance of these resulting models for different ranges of critical velocity measurements