Supplementary information files for "An artificial neural network model for the prediction of entrained droplet fraction in annular gas-liquid two-phase flow in vertical pipes"

Supplementary files for article "An artificial neural network model for the prediction of entrained droplet fraction in annular gas-liquid two-phase flow in vertical pipes"<br>The entrained droplet fraction (<i>e</i>) is an important quantity in annuar gas-liquid two-phase flows as it allows more precise calculation of the gas core density. This results in more accurate calculation of pressure drop in pipes involving such flows. Accurate pressure drop modelling which incorporates the entrained liquid fraction is crucial for the appropriate design of downstream oil and gas facilities and for predicting the inception of dry-out in heat transfer applications involving boiling two-phase flows. While experimentation and correlations from the experimental data are widely used for closure relationships in prediction models (such as the two-fluid model), this method has drawback of the prediction limited to the range of data and discontinuities when mechanistic models (embedded with these correlations) are solved. Furthermore, correlation with a large number of input variables is usually difficult as the prediction contains a large amount of scatter. Machine learning methods are known to overcome this under-fitting problem. This study proposes an artificial neural network (ANN) model for the entrained liquid fraction in annular gas-liquid flows. Using the superficial gas velocity (<i>u</i>_<em>s</em>_<em>g</em>), superficial liquid velocity (<i>u</i>_<em>s</em>_<em>l</em>), gas viscosity (<i>μ</i>_<em>g</em>), liquid viscosity (<i>μ</i>_<em>l</em>), gas density (<i>ρ</i>_<em>g</em>), liquid density (<i>ρ</i>_<em>l</em>), pipe diameter (D) and liquid surface tension (<i>σ</i>_<em>l</em>) as input variables, 6 neurons (chosen after a sensitivity analysis) were used to relate these to the output variable, <i>e</i>. The results show that the ANN model performed well exhibiting much less scatter than previous widely used correlations. Furthermore, it was demonstrated from a sensitivity analysis that <i>u</i>_<em>s</em>_<em>g</em> has the most impact on the ANN model when removed, and is the most significant variable. To varying degrees, other variables such as <i>u</i>_<em>s</em>_<em>l</em>and ρ_g were shown to have lesser effects on the accuracy of the ANN model. Based on the 1367 data points gathered, it was quantitatively shown that the new ANN model gave superior predictions of the entrained droplet fraction when compared to two previous correlations developed from even larger datasets.© The Authors CC BY 4.0

论文《垂直管道内环状气液两相流夹带液滴份额预测的人工神经网络模型》补充材料

夹带液滴份额（e）是环状气液两相流中的重要参数，可实现气芯密度的精确计算，进而更准确地求解含此类流动的管道内压降。纳入夹带液滴份额的精准压降建模，对于下游油气设施的合理设计，以及涉及沸腾两相流的传热应用中干涸起始点的预测均至关重要。

尽管实验及基于实验数据的关联式被广泛用于预测模型（如双流体模型（two-fluid model））的封闭关系，但此类方法存在缺陷：当求解嵌入此类关联式的机理模型时，预测结果仅能局限于训练数据的范围，且会出现不连续性。此外，当输入变量较多时，传统关联式往往难以建立有效映射，且预测结果存在较大离散性。机器学习方法则可有效解决此类欠拟合问题。

本研究针对环状气液两相流的夹带液滴份额，提出了人工神经网络（Artificial Neural Network, ANN）模型。本研究选取表观气速（u_sg）、表观液速（u_sl）、气相粘度（μ_g）、液相粘度（μ_l）、气相密度（ρ_g）、液相密度（ρ_l）、管道直径（D）以及液相表面张力（σ_l）作为输入变量，经敏感性分析后选用6个神经元构建输入与输出变量e之间的映射关系。

结果表明，所提人工神经网络模型表现优异，其预测结果的离散性远低于此前广泛使用的各类关联式。此外，敏感性分析结果显示，移除表观气速（u_sg）会对模型性能造成最大影响，因此该变量为最重要的输入参数。其余变量（如表观液速u_sl与气相密度ρ_g）则在不同程度上对模型精度的影响相对较小。

基于所收集的1367组数据，本研究定量证明，相较于此前基于更大数据集开发的两种关联式，本研究所提人工神经网络模型对夹带液滴份额的预测性能更优。© 作者 CC BY 4.0