This Is AuburnElectronic Theses and Dissertations

Development of Hybrid Model for Estimating Liquid Entrainment Fraction and Uncertainty: Integrating Machine Learning and First Principles




Deng, Yushi

Type of Degree

PhD Dissertation


Chemical Engineering

Restriction Status


Restriction Type

Auburn University Users

Date Available



In two-phase annular flow, a thin liquid film forms around the pipe as gas flows through the pipeline center. Some portion of the liquid is carried into the gas core. The liquid entrainment fraction, which is defined as the flow rate of the entrained liquid droplets relative to the overall liquid flow rate, is an essential parameter for accurately estimating pressure drop, flow rate, liquid holdup, and dry-out conditions in annular flow. Accurate estimates of these variables are essential for the design and operation of wet gas transmission pipelines, pipeline corrosion inhibition wellbore and flow line design, and downstream separation design and optimization. Numerous first-principle models exist for predicting liquid entrainment fraction in a two-phase flow. However, due to the intricate complexity of the entrainment phenomena, none of the models incorporates effects from all observations nor can they be extended across a wide range of operating conditions, which results in inaccurate estimation of the liquid entrainment fraction. Moreover, none of these models is developed with the capability of quantifying the entrainment fraction prediction uncertainty. In this dissertation, a hybrid modeling framework combines first-principle model and data-driven model is developed to estimate the liquid entrainment fraction with its uncertainty in two-phase flow. A database composed of 1,662 entrainment fraction experimental measurements is used for predicting the liquid entrainment fraction for three different flow orientations. The first-principle model predict the liquid entrainment fraction while the data-driven model predict the model discrepancy, which is defined as the difference between the experimental measurements and the first-principle model prediction. Different machine learning techniques and uncertainty quantification methodologies are applied to estimate entrainment fraction with its uncertainty within the hybrid model. To pick the best model, a novel metrics for evaluating the performance of machine learning model with stochastic output called uncertainty width is proposed to compare the model performance and best model is picked for each flow orientation. As a result, Bagging Gaussian Process Modeling (GPM) with estimated noise is identified as the best model with the best accuracy and uncertainty calibration. The hybrid model performance is enhanced using different methodologies. To extend the hybrid model’s applicability from laboratory to field scale, dimensional analysis (DA) is performed to obtain dimensionless numbers used as the updated inputs. To prune the irrelevant inputs, a novel Gaussian Process embedded feature selection approach called Derivative Decomposition Ratio (DDR) is proposed and its performance is compared with another feature selection approach derived from normalizing the sensitivity. To extend the hybrid model’s capability to assistant the development of mechanism, a partial derivative based framework delivering quantitative first-principle model refinement decisions is proposed in this study. The methodology developed in this dissertation can be applied to estimate the liquid entrainment fraction with its uncertainty for three flow orientations given operating conditions. The methodologies developed in this study, such as the feature selection method and the first-principle model refinement decisions, can also be used in other applications in addition to the liquid entrainment fraction. Those methodologies can be considered for any GPM feature selection and any mechanism refinement studies.