Mass Transfer Equation & Film Mass Transfer Coefficients

In commercial absorption equipment, both the liquid and the gas are usually in turbulent flow and the film thickness is not easy to determine. Therefore instead of analysis of mass transfer using Fick's Law, it is more convenient to write the molar flux of A using mass transfer equation of the form below:

Molar Flux, NA = Mass Transfer Coefficient x Driving Force

At a point A (xAL, yAG), we can write the mass transfer equations for each of the phases:

where :

NA | molar flux of component A, mole/(area.time) |

ky | mass transfer coefficients in the gas phase |

( yAG - yAi ) | concentration driving force in the gas phase (mole fraction) |

kx | mass transfer coefficients in the liquid phase |

( xAi - xAL ) | concentration driving force in the liquid phase (mole fraction) |

The k-values above are also known as film mass transfer coefficients, and they are usually determined experimentally, or by correlations. Because there are many analogies between heat transfer and mass transfer, many correlations originally derived from heat transfer are used for the prediction of mass transfer coefficients.

[In fact, the mass transfer equation is obtained based on the analogy with the heat transfer equation q = Q/A = h (DT); where DT is the temperature difference driving force for heat flow. There are 2 mass transfer equations for 2 different mass transfer coefficients, one in the gas phase and another in the liquid phase; just like the case of a heat exchanger (e.g. double-pipe, or shell-and-tube) whereby there is a tube-side heat transfer coefficient and a shell-side heat transfer coefficient.

Similar definition can be made using overall mass transfer coefficients. Click here for more information.

Mass Transfer Dimensionless Groups and Correlations

The attached Table below (left) showed examples of similarity of dimensionless groups for heat and mass transfer; and the other Table (right) showed several correlations for mass transfer. Generally, the mass transfer correlations are more complex and difficult to use. In addition, they are very specific in applications and are limited to some simple situations.]

[ See also pp. 66-70, 72-77 in R.E. Treybal, "Mass Transfer Operations", 3rd Ed. for more discussion on analogies between heat and mass transfer, and see pp. 666-674 in McCabe et al, "Unit Operations for Chemical Engineering", 5th Ed. for examples of using various mass transfer correlations ]

In the above analysis of mass transfer across an interface, note that since the
interface concentrations varies throughout the gas absorption equipment (e.g.
a tray column). It is worthwhile highlighting that NA
depends on the conditions at the particular point in the column. In other words,
NA may vary throughout the entire length of the
column.