Thermoeconomic optimization of cascade refrigeration system using computational intelligence techniques

Abstract

This study presents the thermoeconomic optimization of LiBr-H₂O, LiCl-H₂O, (CaCl₂-LiBr-LiNO₃)-H₂O with R290, R123, R1234yf, and R1234ze in the compression-absorption cascade refrigeration system. The detailed thermodynamics and economic analysis have been presented. Nonlinear objective function formulated based on the concept of energy, exergy, economic, and environmental performance is minimized by using five recent computational intelligence techniques. Optimum cascade, evaporator, absorber, generator, condenser, and overlap temperatures and the effectiveness of the solution heat exchanger have been reported for the cascade refrigeration system. The effect of decision variables on the coefficient of performance, total exergy destruction, total heat exchanger area, and the total annual cost of cascade refrigeration system has also been reported within their upper and lower bounds for all absorbent-refrigerant-refrigerant combinations. Among all the studied algorithms, the coyote optimization algorithm reports the minimum total annual cost for all considered absorbent-refrigerant-refrigerant combinations. The minimum and maximum total annual costs are reported as 13,164.76 $ year⁻¹ and 15,406.65 $ year⁻¹ for (CaCl₂-LiBr-LiNO₃)-H₂O-R290 and LiBr-H₂O-R1234yf, respectively.

Appendices

Appendix

Thermo-physical properties of absorbent-refrigerant (VARC) working pairs (LiBr-H₂O, LiCl-H₂O, and (CaCl₂-LiBr-LiNO₃)-H₂O) used in this study are calculated using the following equations.

LiBr-H₂O

The concentration, enthalpy, and specific heat of LiBr solution are calculated as follows [57]:

$$X_{6} = \frac{{49.04 + 1.125\,\,T_{6} - T_{5} }}{{134.65 + 0.47\,\,T_{6} }}$$

(A.1)

$$X_{9} = \frac{{49.04 + 1.125\,\,T_{12} - T_{13} }}{{134.65 + 0.47\,\,T_{12} }}$$

(A.2)

where X₆ and X₉ (in %) are the concentrations of LiBr in weak solution and strong solution, respectively. Enthalpy and specific heat for the streams consisting of LiBr-H₂O (streams: 6–11 in Fig. 1) are given as [58]:

$$H_{\text{i}} = \left( {a_{0} + a_{1} X_{\text{i}} } \right)\,\,T_{\text i} + \,\,0.5\left( {b_{0} + b_{1} X_{\text{i}} } \right)\,\,T_{\text{i}}^{2} + \,\,\left( {d_{0} + d_{1} X_{\text{i}} + d_{2} X_{\text{i}}^{2} + d_{3} X_{\text{i}}^{3} } \right)$$

(A.3)

$$C_{{\text p}_{\text{i}}} = a_0 + a_1 X_{\text{i}} + \left( {b_0 + b_1 X_{\text{i}} } \right)T_{\text{i}}$$

(A.4)

Constant values used in Eqs. A.3–A.4 are given in Table 6.

Table 6 Constants for LiBr-H₂O/ LiCl-H₂O/CaCl₂ –LiBr-LiNO₃-H₂O thermo-physical properties calculation

LiCl-H₂O

The concentration and specific heat capacity of LiCl-H₂O are calculated as follows [59, 60]:

$$X = \left( {A_{1} + A_{2} T_{\text{s}} } \right) + \left( {B_{1} + B_{2} T_{\text{s}} } \right) \cdot T_{\text{R}}$$

(A.5)

In Eq. (A.5), the temperature is in °C, concentration is in %, and the constant values are given in Table 6.

$$\theta_{\text{i}} = \left( {\frac{{T_{\text{i}} }}{228}} \right) - 1$$

(A.6)

$$C_{{{\text p}_{\text{i}} ,\,{\text{water}}}} = A_{1} + B_{1} \theta_{\text{i}}^{0.02} + C_{1} \theta_{\text{i}}^{0.04} + D_{1} \theta_{\text{i}}^{0.06} + E_{1} \theta_{\text{i}}^{1.8} + F_{1} \theta_{\text{i}}^{8}$$

(A.7)

$$f_{1} \left( T \right) = a_{1} \,\theta_{\text i}^{0.02} + \,\,b_{1} \,\theta_{\text i}^{0.04} + \,\,c_{1} \,\theta_{\text i}^{0.06}$$

(A.8)

$$f_{2} (\xi ) = \left\{ \begin{gathered} d_{1} X_{\text{i}} + e_{1} X_{\text{i}}^{2} + f_{1} X_{i}^{3} \,\,\,\,\,\,\,\,if\,X_{\text{i}} \le 0.31 \hfill \\ g_{1} + h_{1} X_{\text{i}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,X_{\text{i}} \,\, > \,\,0.31 \hfill \\ \end{gathered} \right.$$

(A.9)

$${C}_{\text{p}_{\text{i}} ,\text{LiCl} } = {C}_{{\text{p}}_{\text{i} ,{\text{water}}} } ( {1\, - \,{f}_{1} (T)\,\,{f}_{2} (\xi)\,})$$

(A.10)

where T is in K; ζ is the mass fraction of the absorbent in the solution. The parameters used in Eqs. A.7–A.9 are listed in Table 7.

Table 7 Constants for LiCl-H₂O specific heat capacity Eqs. (A.7-A.9) [60]

Enthalpy equation for LiCl-H₂O is given by Chaudhari and Patil [61] for the concentration range of 0–50% of LiCl.

$$\begin{gathered} A = A_{1} \, + \,A_{2} \,X_{\text{i}} \, + A_{3} \,X_{\text{i}}^{2} + A_{4} \,X_{\text{i}}^{3} \, + A_{5} X_{\text{i}}^{4} \hfill \\ B = \,\,B_{1} \, + \,B_{2} \,X_{\text{i}} \, + B_{3} \,X_{\text{i}}^{2} + B_{4} \,X_{\text{i}}^{3} \, + B_{5} X_{\text{i}}^{4} \hfill \\ C = \,C_{1} \, + \,C_{2} \,X_{\text{i}} \, + C_{3} \,X_{\text{i}}^{2} + C_{4} \,X_{\text{i}}^{3} \, + C_{5} X_{\text{i}}^{4} \hfill \\ \end{gathered}$$

(A.11)

$$H_{\text{i,LiCl}} = A\, + \,B\,T_{\text{i}} \,\, + C\,T_{\text{i}}^{2}$$

(A.12)

where T is in °C and X is in %. The coefficient values of Eqs. A.11 and A.12 are given in Table 6.

CaCl₂-LiBr-LiNO₃/H₂O

Thermo-physical property expressions for specific heat capacity, vapour pressure, specific enthalpy are obtained from the literature [14]. The equation for vapour pressure is given as

$$\log \,\,P = \sum\limits_{\text{i} = 0}^{2} {\left[ {A_{\text{i}} + {{B_{\text{i}} } \mathord{\left/ {\vphantom {{B_{\text{i}} } {\left( {T - C_{\text{i}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {T - C_{\text{i}} } \right)}}} \right]} \left( {100w} \right)^{\text i}$$

(A.13)

The coefficient values of Eq. A.13 are given in Table 6. The specific heat capacity and enthalpy of the combination are given in Eqs. A.14 and A.15:

$$C_{\text p} = \sum\limits_{\text{i} = 0}^{2} {\left[ {\left( {A_{\text{i}} + B_{\text i} T + C_{\text{i}} T^{2} } \right)w^{\text{i}} } \right]}$$

(A.14)

$$H = \sum\limits_{\text{i} = 0}^{2} {\left[ {\left( {A_{\text{i}} + B_{\text{i}} w + C_{\text{i}} w^{2} } \right)T^{\text{i}} } \right]}$$

(A.15)

where P is in kPa, T is in °C, and w is in %. The coefficient values of Eqs. A.13–A.15 are mentioned in Table 6.

See Table 6, 7 and 8

Table 8 Parameters used in the current study

See Figs. 9

Fig. 9

Effect of operational parameters for LiCl-H₂O-R290

and 10

Fig. 10

Effect of operational parameters for CaCl₂-LiBr-LiNO₃-H₂O-R290