Heat Recovery in the Cross-Heat Exchanger

In a previous study, Lin and Rochelle (55) had performed a parametric optimization of the cross-heat exchanger in the context of CO₂ capture from which this analysis will draw heavily. As those authors pointed out, optimum operation of this unit is dependent on solvent properties such as heat capacity and viscosity. However, their findings were applied to the context of reducing capital and operational costs. Conversely, our analysis will be divided into two different scenarios, case C and case D.

• Case C: This scenario assumes that the CO₂ capture plant already exists, meaning that its capital costs are fixed. The existing capture plant has been designed for traditional solvents, so that the area available for heat transfer will be evaluated for T_X = 105 °C when using aqueous absorbents. Once this area is calculated, it will be kept constant while studying different organic diluents. As will be seen in this approach, T_X is typically lower than 105 °C, which translates into more sensible heat expenses in the reboiler.

• Case D: In this scenario, we consider that a new heat exchanger of a different area could be installed to deal with the heating of the rich amine up to T_X = 105 °C. This unit will be bigger than that used for warming up the aqueous solvent although calculation of how this impacts the capital costs of the CO₂ capture plant is beyond the scope of this study. Overall, the results of this analysis will be more optimistic than those of case C.

The amount of heat that can be transferred in the cross-heat exchanger is given by eq 31a−b.

(31a)

(31b)

In eq 31a, U_HX is the overall heat transfer coefficient, A_HX is the area available for heat exchange, and ΔT_lm is the log mean temperature difference between rich and lean streams. Equation 31b is also true, since the heat transferred in the unit is responsible for raising the temperature of the rich stream from T₀ up to T_X. This stream has a mass flow rate of q and a heat capacity of C_P. Equality between eqs 31a and 31b results in eq 32 for the exit temperature of the rich stream.

(32)

Following the approach of Lin and Rochelle, (55) one can consider this equipment to be a plate-and-frame-type exchanger (PHE), and the following derivations will be based both on that work and on Dhar’s. (56) Assuming a PHE with plate spacing D_HX, plate width W_HX, plate height H_HX, and number of plates N_HX, the mass flow rate of the rich solvent q can be calculated by eq 33. Meanwhile, eq 34 expresses the area available for heat transfer. With eqs 32–34, one can obtain eq 35.

(33)

(34)

(35)

Lin and Rochelle (55) have assumed that the resistance to heat transfer in the PHE plates is negligible. Furthermore, they propose that the convective heat transfer coefficients h of both rich and lean streams can be averaged. Following this approach, eq 36 suggests that the global heat transfer coefficient of the PHE is half the convective heat transfer coefficient evaluated at the average temperature between rich and lean amine streams.

(36)

Substitution of eq 36 into eq 35 yields eq 37.

(37)

The convective heat transfer coefficient h can be obtained using the three nondimensional numbers—Nusselt (Nu), Reynolds (Re), and Prandtl (Pr) (eqs 38–40)—and a suitable correlation, expressed generically in eq 41, where C_Nu, m, and n are empirical parameters. Notice that, in these equations, the characteristic length of the PHE is 2·D_HX or 2 times the spacing between plates.

(38)

(39)

(40)

(41)

With eqs 38–41, the convective heat transfer coefficient h can be approximated by eq 42. Finally, eq 43 shows how the exit rich solvent temperature T_X can be calculated. Notice in eq 43 that the first few terms of that expression are related either to the dimensions of the equipment (D_HX, L_HX) or to how one chooses to operate the process (u, ΔT_lm), whereas the solvent properties ρ, C_P, λ, and η appear in the end. As for the empirical parameters C_Nu, m, and n, a good overview of their values has been cataloged by Lin and Rochelle. (55) A common thread among the alternatives is that m and n are always numbers between 0 and 1 and m > n, meaning that T_X increases with λ and decreases with ρ, C_P, and η for a fixed process configuration and operational conditions.

(42)

(43)