# Determination Mass Transfer Co-efficient

## Keywords

Mass transfer, industrial processes, mass transfer coefficient, driving force concentration, fluid mixtures, porous solid, flux, turbulence.

## Introduction

Mass transfer is the net movement of mass such as stream, phase, fraction, or component from one location to another. Many processes, including absorption, evaporation, drying, precipitation, membrane filtration, and distillation, involve mass transfer.

Different scientific disciplines use mass transfer for various processes and mechanisms. A common example of a mass transfer process is evaporation of water into the atmosphere from a pond. Mass transfer operations in industrial processes include chemical component separation in distillation columns, absorbers such as scrubbers or stripping, adsorbers such as activated carbon beds, and liquid-liquid extraction.

Mass transfer is frequently linked to other transport processes, such as in industrial cooling towers. In engineering, the mass transfer coefficient is a diffusion rate constant that relates the mass transfer rate, mass transfer area, and concentration change as driving force.

$$\mathrm{k_{c}=\frac{\dot{n}A}{A\Delta\:c_{A}}}$$

Where:

$\mathrm{k_{c}}$is the mass transfer coefficient [mol/(s·m2)/(mol/m3), or m/s]

$\mathrm{\dot{n}A}$is the mass transfer rate [mol/s]

A is the effective mass transfer area [m2]

$\mathrm{\Delta\:c_{A}}$is the driving force concentration difference [mol/m3].

This can be used to calculate the mass transfer between phases, immiscible and partially miscible fluid mixtures (or between a fluid and a porous solid). Quantifying mass transfer allows for design and manufacture of separation process equipment that can meet specified requirements, and estimate what will happen in real life situations like chemical spill etc.

## Significance of Mass Transfer Coefficient

A chemical potential driving force causes mass transfer across an interface or across a virtual surface in the bulk of a phase. This driving force is more commonly expressed in terms of species concentrations, or partial pressures in the case of gas phases. The rate of transfer of a given species per unit area normal to the surface, i.e., the species flux, depends on some of the physical properties of the system as well as the degree of Turbulence of the phases involved. In general, the relationship between the flux and these parameters is not easily developed from the fundamentals of mass transfer, so mass transfer coefficients that lump them all together have been defined as below.

Flux = coefficient (concentration difference)

In the case of species crossing an interface, there are several expressions for the flux based on different driving forces. The interfacial flux, can be expressed in the four following ways depending on the concentration driving force used:

$\mathrm{\dot{m}=\beta_{G}\lgroup\:p-p_{i}\rgroup=\beta_{L}\lgroup\:c_{i}-c\rgroup}$

$\mathrm{=\beta_{OG}\lgroup\:p-H_{c}\rgroup=\beta_{OL}\lgroup\:p/H-c\rgroup}$

where is the mass flux; β, the mass transfer coefficient; and the subscripts L and G indicate the gas and liquid phases. The first two equations define the single-phase gas and liquid mass transfer coefficients. Since the interfacial concentrations pi and ci are usually unknown, the overall mass transfer coefficients βOG and βOL defined by the two last equations, are more commonly used, in these equations H is the equilibrium distribution coefficient of the solute between the two phases at equilibrium. Since the interfacial flux must be the same irrespective of the driving force used to express it, the four numerical coefficients are different and have different units. This is also the case when dimensionless driving forces, such as molar or mass fractions, are used. The mass transfer coefficients depend on the diffusivity of the solute and the hydrodynamics of the phases. They can be calculated using expressions derived from fundamentals of mass transfer, in the case of laminar flow, or from empirical correlations.

## Highlights

• Mass transfer of CO2 into a H2O rich phase at high pressure in a capillary can be studied.
• A method for the determination of volumetric mass transfer coefficient can be presented.
• In mass transfer a thermodynamic model and Raman spectroscopy are coupled to obtain CO2 concentrations.
• The influence of flow rates on the volumetric mass transfer coefficient can be studied.
• The mass transfer coefficient varies along the length of the micro-capillary tube.

## Problems with Mass Transfer Coefficient

Mass transfer coefficients are frequently regarded as a difficult subject, not because the subject is inherently difficult, but because of different definitions and because of complexities for mass transfer from one solution into a second solution. These distinctions merit further discussion.

The complexities of definitions arise primarily because concentration can be expressed in so many different variables. In the above, we assumed that it is expressed in mass per volume or moles per volume. The complexities of definitions occur primarily because concentration can be expressed in so many different variables.

In the above, we have assumed that it is expressed in mass per volume or moles per volume. The concentration can also be expressed as a mole fraction, which in the liquid phase is commonly indicated by the symbol x1 and in the gas phase the symbol is expressed as y1. In gases, concentrations are expressed as partial pressures.

The second reason that mass transfer coefficients are considered difficult happens when mass transfer occurs from one fluid phase into another. This is a genuine source of difficulty, with frequent confusion. Consider extracting bromine from water into benzene to understand why this is difficult.

When we start, the bromine concentration in the water is higher than in the benzene. Water and benzene concentrations eventually equalize. Later, the concentration in the water will be much lower than that in the benzene. Even then, bromine can still diffuse from its low concentration in water into its much higher concentration in the benzene.

This happens because bromine is much more soluble in benzene than it is in water. It separates from water and into benzene. At equilibrium, the concentration in benzene divided by the concentration in water will be a constant much greater than one, and almost independent of the initial bromine concentration in the water.

In other words, the concentrations are not equal in the eventual equilibrium. Although free energies are equal, free energy is a much more difficult concept to grasp than concentration. The result of this chemistry is that the mass flux across an interface from one phase into the other is not directly proportional to the concentration difference between the two phases.

Instead, it is proportional to the concentration in one phase minus the concentration that would exist in the other phase if it were in equilibrium. In the example just given, this concentration difference is the value in water minus the value in hypothetical water in equilibrium with benzene. This concentration difference makes the study of mass transfer coefficients difficult.

## Conclusions

Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties, and flow regime (laminar or turbulent flow). Selection of the most applicable model is dependent on the materials and the system, or environment, being studied.

Updated on: 18-May-2023

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