Factors Affecting Mass Transfer Rates in Water-Lean Solvents

Following this approach, CO₂ concentration in the vapor–liquid interface is constrained by the thermodynamical equilibrium dictated by Henry’s law for dilute components. In the liquid bulk, diffusion of CO₂ is followed by its reaction with amine molecules, forming carbamate and a protonated base according to Reactions R1 and R2. These reactions constitute the so-called zwitterion mechanism. (23) There is an ongoing debate in the literature regarding whether the zwitterion mechanism correctly represents the real phenomena behind the reaction between CO₂ and amines. (24) Regardless, the rate equations obtained by employing the zwitterion mechanism can be shown to give results consistent with those derived by consideration of the one-step termolecular mechanism. (25,26) Furthermore, the reasons for choosing the zwitterion mechanism in our approach will be evidenced briefly in Section 2.3.

(R1)

(R2)

One can consider reactions R1 and R2 to derive an expression for the reaction rate of CO₂. Typically, the strongest base in a solution will be the amine itself, and so this will be the preferable reactant, B, in reaction R2. Furthermore, the zwitterion is an unstable molecule, and its concentration can be approximated by zero at all times. This results in the reaction rate expression given by eq 1, where A is CO₂, B is an amine, C is a carbamate, and D is a protonated amine (notice that C_C = C_D, so that C_D will always be omitted in the following equations):

(1)

Equation 1 gives an expression for the irreversible reaction between CO₂ and the amine forming carbamate and a protonated amine. For more general uses, however, it is interesting to consider that the conversion might be bounded by chemical equilibrium. This can easily be taken into account by modifying eq 1 into eq 2.

(2)

The reaction rate expressions for amine and carbamate come directly from stoichiometric relationships, so that r_B = 2·r_A and r_C = – r_A. The penetration equation for an arbitrary component i is then given by eq 3, where r_i is the reaction rate of component i.

(3)

Substituting for A, B, and C results in eq 4a–c.

(4a)

(4b)

(4c)

The resolution of eq 4a–c requires two sets of boundary conditions, one for the interface and another for the liquid bulk, along with one set of initial conditions. The initial conditions are ordinarily given by setting the initial concentrations of all components before absorption homogeneously throughout the whole liquid solvent, as seen in the following equations:

(5a)

(5b)

(5c)

In the interface, one can assume that the concentration of CO₂ is in equilibrium with the partial pressure of CO₂ in the vapor phase by Henry’s law and that there is no vaporization either of the amine or of the products. This results in the following equations:

(6a)

(6b)

(6c)

In the liquid bulk, far from the interface at x = δ, all of the concentrations are the same as those before the absorption took place. This can be seen in the following equations:

(7a)

(7b)

(7c)

As one can see, with the aforementioned assumptions and approximations, the CO₂ mass transfer rates can be somewhat characterized by fixing two transport properties, two kinetic properties, and two thermodynamical properties. These are as follows.

• Transport properties: CO₂ diffusivity D_A and amine diffusivity D_B.

• Kinetic properties: kinetic rate constant k₂ and kinetic rate constant ratio k_b/k_–1.

• Thermodynamical properties: equilibrium coefficient K and Henry’s coefficient H_A.

These six parameters will be discussed further in the next sections. Before that, however, an explanation should be given about the equilibrium coefficient K. This property can be defined as by the following equation:

(8)

As mentioned previously, in this work, we are assuming that the only mechanisms through which CO₂ is absorbed are physical absorption and carbamate formation, i.e., no other CO₂-consuming reactions such as bicarbonate formation are taken into account. With this in mind, it is practical to discuss the equilibrium coefficient in terms of the loading α, which accounts for mols of CO₂ absorbed per moles of amine in solution. As a function of α, the concentrations of CO₂, amine, and carbamate are given, respectively, by eqs 9, 10, and 11.

(9)

(10)

(11)

Substituting eqs 9–11 in eq 8, one ends up with eq 12. This expression shows how to obtain the equilibrium coefficient K by employing α.

(12)