Α new void fraction correlation inferred from artificial neural networks for modeling two-phase flows in geothermal wells

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A new empirical void fraction correlation was developed using artificial neural network (ANN) techniques. The artificial networks were trained using the backpropagation algorithm and production data obtained from a worldwide database of geothermal wells. Wellhead pressure, steam quality, wellbore diameter, the fluid density and viscosity, and the dimensionless numbers Reynolds, Weber, and Froude were used as main input parameters. The target ANN output was defined by the optimized void fraction values (αopt), which were calculated from the numerical modeling of two-phase flow using GEOWELLS (a wellbore simulator). The Levenberg–Marquardt algorithm, the hyperbolic tangent sigmoid, and the linear activation functions were used for the development of the ANN model. The best ANN learning was achieved with an architecture of six neurons in the hidden layer, which made it possible to obtain a set of void fractions (αANN) with a good accuracy (R2=0.9722). These void fraction estimates were used to obtain the new correlation, which was later coupled into the simulator GEOWELLS for the prediction of pressure gradients in two-phase geothermal wells. The accuracy of the new correlation (αANN) was evaluated by a statistical comparison between simulated pressure gradients and measured field data. These simulation results were also compared with those data calculated by using Duns-Ros and Dix correlations, which were also programmed into GEOWELLS. Pressure gradients predicted with the new αANN correlation showed a better agreement with measured field data, which was also confirmed by the lower values of some statistical parameters (MPE, RMSE, and Theil's U). The statistical evaluation demonstrated the efficiency of the new correlation to predict void fractions and pressure gradients with a better accuracy, in comparison to the other existing correlations. These successful results suggest the use of the new correlation (αANN) for the analysis of two-phase flow mechanisms of geothermal wells.