A combined approach towards the understanding of mass transfer in two-phase flow: The integration of numerical modelling with MRI

Lead Research Organisation: University of Cambridge
Department Name: Chemical Engineering and Biotechnology

Abstract

Many industrial processes require effective contact between two different liquids, or between a liquid and a gas. These processes include treatment of waste water and fermentation of alcoholic drinks. When these systems are stirred, the result is not a uniform mixture, but a very large number of small bubbles or droplets dispersed through the liquid. The droplets involved are not all the same, and have different sizes, velocities and chemical compositions. This makes it very difficult to accurately measure the important properties of the system. It is also very difficult to predict mathematically how such a system will behave.The proposed investigation has two main aims. The first is to make accurate experimental measurements of droplets within a liquid. The second is to use these measurements to develop mathematical models that can describe the system.Experimental Techniques:Droplets dispersed in a liquid undergo many different processes. Currents within the fluid can cause the droplets to follow convoluted paths. In the course of this flow through the liquid, they can join together to form large droplets, break up to form smaller ones, and their chemical composition can change through diffusion. Experimental measurement of all these processes is not an easy task: even simply visually tracing the path of a single droplet can be impossible if the liquids involved are not transparent.Magnetic Resonance Imaging (MRI) is a technique that involves tagging individual molecules by altering how they behave in a magnetic field. These molecules can then be accurately located in time and space, allowing us to determine the size, velocity and composition of moving droplets. MRI has never before been applied to a system such as this.Mathematical Modelling:The behaviour of large numbers of interacting droplets is described mathematically by using Population Balance Equations (PBEs). These equations can require vast computational power to solve, especially in complicated systems where the behaviour is dependent on many variables: size, shape, concentration profiles etc. Monte Carlo methods are a particular mathematical technique that allow us to solve these equations quickly and efficiently and predict (given the right model parameters) how the droplet-liquid system will behave.Combing Experiments and Models:The crucial aim of our research is to combine our experimental measurements and mathematical analysis. This will enable us to decide which factors have an important, noticeable effect on the system, and which can be ignored. Thus, prediction of the behaviour of complicated systems will be simplified and industrial processes will become more effective and efficient
 
Description Many industrial processes require effective contact between two different liquids, or between a liquid and a gas. These processes include treatment of waste water and fermentation of alcoholic drinks. When these systems are stirred, the result is not a uniform mixture, but a very large number of small bubbles or droplets dispersed through the liquid. The droplets involved generally have different sizes, velocities and chemical compositions. This makes it very difficult to accurately measure the important properties of the system and to predict mathematically how it will behave.

The project had two main aims, firstly, to make accurate experimental measurements of droplets within a liquid, and secondly to develop mathematical techniques that can describe such systems.

Experimental Techniques:

Droplets dispersed in a liquid undergo many different processes such as coalescence and breakage, and their chemical composition can change through diffusion. Experimental measurement of all these processes is not an easy task: even simply visually tracing the path of a single droplet can be impossible if the liquids involved are not transparent.

Magnetic Resonance Imaging (MRI) is a technique that involves tagging individual molecules by altering how they behave in a magnetic field. These molecules can then be accurately located in time and space, allowing us to determine the size, velocity and composition of moving droplets. MRI has never before been applied to such a system.

Mathematical Modelling:

The behaviour of large numbers of interacting droplets is described mathematically by using Population Balance Equations (PBEs). These equations can require vast computational power to solve, especially in complicated systems where the behaviour depends on many variables: size, shape, concentration profiles etc. Monte Carlo methods are a particular mathematical technique that allow us to solve these equations quickly and efficiently and predict (given the right model parameters) how the system will behave.

Combing Experiments and Models:

The crucial aim of our research was to combine our experimental measurements and mathematical analysis. This enables us to decide which factors have an important, noticeable effect on the system, and which can be ignored. Thus, prediction of the behaviour of complicated systems is simplified and industrial processes become more effective and efficient.

This project has seen significant advances and development in the use of ultra fast MRI techniques to study the structural and dynamic behaviour of both single bubbles and bubble swarms in multi-phase systems. Bubble size distributions were obtained but limited to gas voidages <10%. As a result of this MRRC have used this project, in part collaboration with Microsoft Research, to explore further advances in MR applications to multi-phase systems. New MRI protocols and k-space sampling strategies have been developed to capture quantitative information from non-steady state systems. In particular we have developed a new single shot GERVAIS technique that captures snapshot images of the internal velocity field of a rising droplet in a two-phase liquid system in less than 125ms. Furthermore, we have developed fast spin-echo imaging, along with data analysis, that allows us to track both the translational movement of a rising droplet and indeed follow how its shape changes, in the form of different bubble breathing modes, during its rising event, in addition to be able to continuously track liquid dynamics in a three phase system. Direct measurement of liquid-liquid mass transfer coefficients has also been demonstrated.

Bubble sizing in dynamic bubble swarms using data that has been acquired with non-linear sparse k-space sampling strategies combined with Bayesian Analysis been successfully applied. Significant challenges in both data acquisition, analysis and experimental set-up were overcome to achieve this goal.
Exploitation Route Some of the numerical techniques developed within this project can and have already been applied in industrial consultancy projects as well as academia.
Sectors Chemicals,Other
 
Description Some of the numerical techniques developed and published within this project have since been taken up by a spin-off company and applied in industrial consultancy projects.
First Year Of Impact 2010
Sector Chemicals,Energy,Environment
Impact Types Economic