Mechanistic modelling of separating dispersions in pipes using model-based design of experiments techniques

This work presents a parametric study on a mechanistic model for separating liquid–liquid dispersions in pipes. The model considers drop-settling, drop-interface coalescence and drop-drop coalescence, predicting the evolution of four characteristic layers during separation. Parameter estimation, parametric sensitivity analysis (PSA), and model-based design of experiments (MBDoE) techniques are employed to acquire precise parameter estimates and propose optimal experimental conditions, thereby enhancing the accuracy of existing models. Experimental data from literature using oil-in-water dispersions are used for parameter estimation. PSA reveals regions of high sensitivity of the model outputs to uncertain parameters, which are corresponding to favourable sampling locations. Manipulating the mixture velocity, the dispersed phase fraction, and the layer heights at the inlet influences these sensitive regions. Clustered measurements around highly sensitive regions in the pipe enhance the information content they provide. MBDoE demonstrates that either of the A-, D-, or E-optimal experimental design criteria improves the expected parameter precision

A mechanistic model for the prediction of flow pattern transitions during separation of liquid-liquid pipe flows

A one-dimensional mechanistic model that predicts the flow pattern transitions during the separation of dispersed liquid-liquid flows in horizontal pipes was developed. The model is able to capture the evolution along the pipe of the four characteristic layers that develop from initially dispersed flows of either oil-in-water or water-in-oil at a range of mixture velocities: a pure water layer at the bottom, a settling (flotation/sedimentation) layer, a dense-packed zone, and a pure oil layer on the top. Coalescence correlations from literature were included in the model to predict the drop growth due to binary drop coalescence and the coalescence rate of drops with their corresponding interface. The model predictions on the evolution of the heights of the different layers were partly compared against available experimental data obtained in a pilot scale two-phase flow facility using tap water and oil (828 kg m−3, 5.5 mPa s) as test fluids. It was shown that the evolution of the four characteristic layers depends on the rates of drop settling and drop-interface coalescence. Oil-in-water dispersions separated faster than water-in-oil ones, while dispersions with smaller drop-sizes were more likely to exhibit depletion of the dense-packed zone