Mass transfer theory

https://doi.org/10.1039/C7RA01352C

“At a particular point of an absorber column, mass transfer occurs because of a chemical potential gradient between gas and liquid phases. The mass transfer ends when equilibrium is reached. In other words, when the net mass transfer becomes zero.⁴⁶ Nevertheless, the question is at what rate can the mass be transferred? This problem can be associated with the mass transfer coefficient.⁴⁷ The mass transfer coefficient is an important parameter in designing absorber columns.^11,14 Knowledge of this parameter can help a designer accurately calculate the height of an absorber column. In an absorber packed column in a post-combustion CO₂ capture plant, the removal efficiency of CO₂ absorption by amine solutions can be determined by the gas–liquid contact degree, physicochemical properties and hydrodynamics of the absorber column, amine reactivity degree and operating parameters related to the gas and amine solution.¹⁷ Chemical absorption of CO₂ into an amine solution can be described by the two-film theory.⁴⁸ This theory proposes that there are two thin films near the gas and liquid phase interfaces, which separate them from the liquid and gas bulk phases. This theory assumes that bulk phases are in equilibrium and all resistances of mass and heat transfer exist in the two films.⁴⁸ In most cases, when CO₂ moves from the gas to the liquid phase, a chemical reaction between CO₂ and the amine solution can take place in the liquid film or liquid bulk.⁴⁹ According to Fig. 1 and based on the two-film theory, the reaction between CO₂ and the amine solution can be characterized as infinitely fast rate or very slow rate.⁴⁸ Depending on the relative values of the reaction rate constants, mass transfer coefficients of gas and liquid phases, concentration ratio of reactants and CO₂ equilibrium solubility, reactions occur in a narrow zone within the film or through the film and bulk of the liquid. The two-film theory is prevalently used in rate-based models.^49–55 A significant number of them consider that the reaction takes place within the liquid film, when the reaction is assumed to be infinitely fast (i.e., CO₂ absorption into the MEA solution).

3.1. Determination of K_GCO2a_V in an absorption packed column

At steady-state conditions, the absorbed mass flux of CO₂ (N_CO2) across the gas–liquid interface can be represented in terms of K_G and the difference between the CO₂ partial pressure in the gas bulk (Py_CO2) and the CO₂ partial pressure at the gas–liquid interface , as shown in eqn (1).^56,57(1)

It is obvious from eqn (1) that N_CO2 is greatest when  approaches zero and Py_CO2 is at a maximum value. In the same way, N_CO2 is zero when Py_CO2 is equal to .The significance of K_G can be seen from eqn (1)—for a given driving force, a greater K_G can give greater N_CO2 into the amine solution.⁵⁸ Since the driving force of mass transfer occurs at a small distance from the film, the concentration in the interface and, subsequently, K_G are difficult to measure in an absorption packed column because of the variations in the interfacial area with varying gas and liquid flow rates.⁵⁹ Therefore, it is more convenient and useful to express N_CO2 based on the unit volume of the absorption packed column rather than the interfacial area unit, as follows:⁵⁹(2)

In eqn (2), N_CO2a_V can be obtained from K_GCO2a_V and the difference between Py_CO2 and the CO₂ partial pressure in the gas phase in equilibrium with the CO₂ concentration in the liquid bulk . To calculate N_CO2a_V, the mass balance according to the rate-based model, considering a small differential height of packing (dZ) of the absorption packed column (Fig. 2), can be written as follow:⁵⁹(3)

By substituting eqn (3) into eqn (2), K_GCO2a_V can be determined using eqn (4):(4)

Most researchers have used eqn (4) to determine K_GCO2a_V from experiments on absorption packed columns.^{32,33,58–61} In eqn (4), the gas flow rate (G) and cross-section area of the column (A) as well as the packed column pressure (P) are known, and only two terms—the driving force and the derivative of the CO₂ molar ratio—have to be determined. The term  in eqn (4) can be obtained from the equilibrium solubility data of CO₂ into the amine solution. Often,  is assumed to be zero due to a fast reaction between CO₂ and the amine solution.^{14,32,49,58,60–65} The derivative of the CO₂ molar ratio  can be determined by measuring the CO₂ concentration (molar fraction) profile in the gas phase along the height of the absorber packed column. By converting molar fraction values to molar ratio values of CO₂, the term  is calculated by plotting Y_CO2 against the packing height of the absorber column (Z), as shown in Fig. 3.⁵⁹

When the CO₂ concentration is measured at the inlet and outlet of an absorber packed column, the average values of K_GCO2a_V can be obtained from eqn (5) suggested by Dey and Aroonwilas.⁶⁶(5)

The advantage of using directly K_GCO2a_V when simulating the CO₂ absorption process is avoiding the need to calculate the enhancement factor and individual mass transfer coefficients in liquid and gas phases. The correlations between individual mass transfer coefficients are dependent on dimensionless numbers such as the Remolds and Schmidt numbers, as well as some hydrodynamic properties of the absorber column; mostly however, they were not developed to use in specific systems (i.e., amine system and packing type). In our previous work,⁵¹ we have applied mass transfer correlations from literature, which were not developed for amine systems, in the simulation of CO₂ absorption in amine solutions. We have performed sensitivity analyses of individual mass transfer coefficients and kinetics constants of the CO₂ reaction in amine solutions (the kinetic constant is used for calculating the enhancement factor). We concluded that two mass transfer correlations had the best prediction for an absorber column profiles compared with other applied mass transfer correlations from the literature. Therefore, when K_GCO2a_V is used directly in modeling CO₂ absorption into amine solutions, there is no need to evaluate the sensitivity of the absorber model.

“