Development of a deep neural network and empirical model for predicting local gas holdup profiles in bubble columns

Estimating local gas holdup profiles in bubble columns is key for their performance evaluation and optimization, as well as for design and scale-up tasks. Up to the current day, there are important limitations in the accuracy and range of applicability of the available models in literature. Two alternatives for the prediction of such local fields can be found in the application of empirical models and the development of deep neural networks (DNN). The main drawback preventing the application of these techniques in previous years was the availability of a large enough databank of local gas holdup experimental measurements. Advances over the last decades in measurement techniques have resulted enough data reported in literature to gather a significative databank for these models' development. A databank containing 1252 experimental points was gathered and used for the development of a quadratic model and a DNN with the rectified linear unit (ReLU) algorithm as the activation function and the adaptive moment estimation (ADAM) algorithm as the optimizer function. The quadratic model and the DNN allowed a highly accurate prediction of the local gas holdup profiles, exhibiting a MSE of 0.0013 and 0.0010, respectively, and an $R_{\text{adjusted}}^2=0.9361$ and $R_{\text{adjusted}}^2=0.9499$ for the quadratic model and the DNN, respectively. Furthermore, these developed models allowed for the estimation of the single and multi-feature effects of the operation conditions, geometrical characteristics, and physical properties of the fluids, over the local gas holdup profiles. The two developed models exhibited an enhanced predictive quality when compared with other models available in literature.