# Model-Based Cost Optimization of Double-Effect Water-Lithium Bromide Absorption Refrigeration Systems

^{1}

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## Abstract

**:**

_{2}O-LiBr absorption refrigeration system considering the total cost as minimization criterion, for a wide range of cooling capacity values. As a model result, the sizes of the process units and the corresponding operating conditions are obtained simultaneously. In this paper, the effectiveness factor of each proposed heat exchanger is considered as a model optimization variable which allows (if beneficial, according to the objective function to be minimized) its deletion from the optimal solution, therefore, helping us to determine the optimal configuration. Several optimization cases considering different target levels of cooling capacity are solved. Among the major results, it was observed that the total cost is considerably reduced when the solution heat exchanger operating at low temperature is deleted compared to the configuration that includes it. Also, it was found that the effect of removing this heat exchanger is comparatively more significant with increasing cooling capacity levels. A reduction of 9.8% in the total cost was obtained for a cooling capacity of 16 kW (11,537.2 $·year

^{−1}vs. 12,794.5 $·year

^{−1}), while a reduction of 12% was obtained for a cooling capacity of 100 kW (31,338.1 $·year

^{−1}vs. 35,613.9 $·year

^{−1}). The optimization mathematical model presented in this work assists in selecting the optimal process configuration, as well as determining the optimal process unit sizes and operating conditions of refrigeration systems.

## 1. Introduction

_{2}O-LiBr) ARSs is that they are activated by low-level energy sources [1] (such as geothermal or solar energies) or low-grade waste heat rejected from various processes, as opposed to through the use of electric energy. On the other hand, compared to other working pairs, such as ammonia-water (NH

_{3}-H

_{2}O), a LiBr solution has no ozone-depleting potential or global warming effect reported in literature, in line with the Montreal, Kyoto, and Paris Accords.

_{2}O-LiBr ARSs based on energy [2,3,4], exergy [4,5,6], exergo-economic [7,8], or cost [5,9] studies. Other authors have addressed such limitations by investigating other process configurations instead, including advanced configurations of multi-effect systems [10]. Among them, the double-effect schemes have comparatively received more interest, and are, in fact, the most frequently applied in industry [11,12]. Many studies on the double-effect H

_{2}O-LiBr ARS were conducted by performing energy analyses [13,14,15], exergy analyses [15,16], and exergo-economic analyses [1,17,18]. A special feature of the double-effect ARS is its capability of running in series, parallel, and reverse parallel flow schemes according to the working solution flow through the heat exchangers and generators [11,12,13,19].

_{2}O-LiBr absorption chiller with multiple heat sources. The integrated generation system included a HTG, a low-temperature generator (LTG), and a waste heat recovery generator (WHRG). The optimization problem consisted of the minimization of the total generation volume and the maximization of the total generation rate. It was found that the WHRG is dominant for reducing the total volume, and the HTG is dominant for improving the total generation rate.

_{2}O-LiBr absorption chillers. The aim of the control strategy was to keep the cold water flow at a desired temperature (11 °C). To this end, a dynamic model consisting of differential algebraic equations (DAE) was first developed and then reformulated into a set of algebraic equations by discretizing the state and control variables using orthogonal collocation on finite elements, by dividing the time horizon into finite elements. The resulting model was implemented in the General Algebraic Modeling System (GAMS) and solved with the Interior Point OPTimization (IPOPT) solver [31]. Both step and sinusoidal perturbations of the hot water inlet temperature were studied. The results obtained are promising because, through the implementation of the optimal control strategy, the COP was significantly improved, thus reducing the operational cost and maintaining the cold water outlet temperature at the desired level.

_{2}O-LiBr absorption refrigeration system, which is the main contribution of this paper.

## 2. Process Description

## 3. Mathematical Model

#### Optimization Problem: Total Annual Cost (TAC) Minimization

_{k}) of a process unit k is given by Equation (4).

^{−1}) and cooling water (in t·year

^{−1}), respectively. The unitary cost of vapor (C

_{HU}) is 2.0 $·t

^{−1}and for cooling water (C

_{CU}) it is 0.0195 $·t

^{−1}[5].

_{EVAP}) is the target design specification; it is a model parameter i.e., a known and fixed value in each optimization run. In this optimization study, Q

_{EVAP}is parametrically varied from 16 kW to 100 kW. The optimization result provides the optimal distribution of annCAPEX and OPEX, the optimal sizes of the process units, and optimal operating conditions (stream pressure, temperature, concentration, and flow rate).

## 4. Results and Discussion

^{−2}·°C

^{−1}for the evaporator, 1.0 kW·m

^{−2}·°C

^{−1}for the absorber, 2.50 kW·m

^{−2}·°C

^{−1}for the condenser, 1.50 kW·m

^{−2}·°C

^{−1}for the generators, and 1.0 kW·m

^{−2}·°C

^{−1}for the solution heat exchangers.

- –
- High temperature generator (HTG): saturated steam at 160 °C.
- –
- Absorber (ABS) and condenser (COND): cooling water at 20 °C.
- –
- Evaporator (EVAP): Inlet and outlet chilled water temperatures: 13.0 °C and 10.0 °C, respectively; evaporator working temperature: 4.0 °C.

^{−1}and 100 kg·s

^{−1}for flow rates, and 75% and 100% for the effectiveness factors of the solution heat exchangers.

^{−1}to 35,613.9 $·year

^{−1}, from 12,013.6 $·year

^{−1}to 30,644.4 $·year

^{−1}, and from 780.8 $·year

^{−1}to 4969.5 $·year

^{−1}).

^{−1}(352.6 $·year

^{−1}vs. 428.2 $·year

^{−1}) is observed for a cooling capacity of 16 kW and a difference of 371.7 $·year

^{−1}(2298.9 $·year

^{−1}vs. 2670.6 $·year

^{−1}) for a cooling capacity of 100 kW.

_{1}) and strong solutions (X

_{4}and X

_{13}leaving the LTG and HTG, respectively; and X

_{15}entering the ABS), with increasing cooling capacity levels. It can be seen that that the concentration values increase with the increase of the cooling capacity, but keep similar ratios between the concentration values in the different streams.

_{LTSHE}and η

_{HTSHE}of the solution heat exchangers LTSHE and HTSHE, respectively, are considered as (free) model variables, i.e., decision variables, as opposed to other published studies, which consider these factors as (fixed) model parameters instead, usually in the range between 65% and 90%, thus always forcing their presence in the process configuration. In this work, by allowing the heat exchanger effectiveness factor to take any value, the presence or absence of the solution heat exchangers is a result of the optimization problem. First, all the solved optimization problems considered the same lower bound for η

_{LTSHE}and η

_{HTSHE}of 75%. The results deserve detailed discussion because they may indicate changes in the process configuration, such as the removal of one or even both solution heat exchangers in order to obtain improved solutions, in terms of total annual costs, compared to the current optimal solutions. The optimal η

_{LTSHE}and η

_{HTSHE}values remain constant at the imposed lower bound (75%) throughout the range of cooling capacity values.

_{LTSHE}and η

_{HTSE}of 75%, in order to see how these bounds affect the current optimal solutions for the same range of cooling capacity values. The obtained optimization results are presented in the forthcoming discussions.

#### Influence of the Solution Heat Exchangers on the Optimal Solutions

_{LTSHE}and η

_{HTSHE}obtained by considering a lower bound of 1%, which, in practical terms, is virtually zero. (Note that, in this case, a ‘very small’ numerical value is imposed as the lower bound, instead of zero, to prevent numerical problems that may lead to model convergence failure). As seen in Figure 7, the obtained optimal values for η

_{LTSHE}result in the lower bound of η

_{LTSHE}, thus indicating that the LTSHE is removed from the configuration for all the specified cooling capacity values. However, the optimal η

_{HTSHE}values increase logarithmically, from 49.8% to 66.9%, with increasing cooling capacity levels in the examined range. This indicates that the heat integration between the weak and strong solutions leads to cost-effective solutions only when such integration takes place in the high-temperature region of the process through HTSHE (since LTSHE in the low-temperature region is not selected in any case).

^{−1}vs. 12,794.5 M$·year

^{−1}, and 10,684.3 M$·year

^{−1}vs. 12,013.6 M$·year

^{−1}, respectively). However, the OPEX in Conf. 2 is 9.2% higher than in Conf. 1 (852.9 M$·year

^{−1}vs. 780.8 M$·year

^{−1}). For a cooling capacity of 100 kW, Table 4 shows that the TAC and annCAPEX values obtained for Conf. 2 are, respectively, 12% and 15.1% lower than the values obtained for Conf. 1 (31,338.1 M$·year

^{−1}vs. 35,613.9 M$·year

^{−1}, and 26,001.7 M$·year

^{−1}vs. 30,644.4 M$·year

^{−1}, respectively). While the OPEX for Conf. 2 is 7.4% higher than for Conf. 1 (5336.4 M$·year

^{−1}vs. 4969.5 M$·year

^{−1}, respectively).

_{1}to m

_{6}, and m

_{11}to m

_{15}) obtained for Conf. 2 are comparatively lower than the values obtained for Conf. 1 (by around 30–45% depending on the particular stream considered). For 16 kW, m

_{1}decreases from 0.085 kg·s

^{−1}to 0.058 kg·s

^{−1}(a 32% decrease) and m

_{2}from 0.045 kg·s

^{−1}to 0.032 kg·s

^{−1}(a 29% decrease). However, the weak solution concentration X

_{1}remains virtually unchanged for 16 kW and changes by only 2.6% for 100 kW. However, the (absolute) values are different; they are 53.7% for 16 kW and 56.2% for 100 kW, in Conf. 2.

_{15}and temperature T

_{15}of stream #15 reached the values of 65.401% and 53.893 °C, respectively, which were obtained from the model constraint that describes the crystallization line. In fact, the inequality constraints that prevent crystallization became active, thus indicating that Conf. 2 operates in a region closer to the crystallization line than Conf. 1.

^{−2}$·t

^{−1}of cooling water and 84 $·t

^{−1}of steam, respectively. These numerical values are reported by Khan et al. [40] and Union Gas Limited [41], respectively. In addition, the influence of the global heat transfer coefficient values on the optimal solutions was studied. The optimization results showed that the optimal process configuration and the trends of the process variables do not vary with respect to the solutions discussed above when changes in the parameters were introduced.

## 5. Conclusions

_{2}O-LiBr ARS through the minimization of the total annual cost for a wide range of cooling capacity values. To this end, the existing trade-offs between process configuration, sizes of the process units, and operating conditions were optimized by employing a nonlinear mathematical model, which was implemented in GAMS. Interestingly, the effectiveness factors of the solution heat exchangers, which were treated as optimization variables instead of fixed parameters, allowed us to obtain a new process configuration. The low-temperature heat exchanger is removed from the configuration throughout the examined range of cooling capacity levels, keeping only the high-temperature solution heat exchanger, indicating that the heat integration between the weak and strong LiBr solutions takes place entirely at the high-temperature zone of the process. The importance in terms of the effectiveness factor of the high-temperature solution heat exchanger increases with increasing cooling capacity levels; the sizes and operating conditions of the other process units accommodate accordingly, in order to meet the problem specifications with the minimal total annual cost. However, the improved configuration operates in a region closer to the crystallization line than the original configuration.

## Supplementary Materials

_{2}O-LiBr ARS; Table S1: Parameter values for estimating process unit investment Z

_{k}.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Garousi Farshi, L.; Mahmoudi, S.M.S.; Rosen, M.A.; Yari, M.; Amidpour, M. Exergoeconomic analysis of double effect absorption refrigeration systems. Energy Convers. Manag.
**2013**, 65, 13–25. [Google Scholar] [CrossRef] - Mazzei, M.S.; Mussati, M.C.; Mussati, S.F. NLP model-based optimal design of LiBr–H
_{2}O absorption refrigeration systems. Int. J. Refrig.**2014**, 38, 58–70. [Google Scholar] [CrossRef] - Kaynakli, O.; Kilic, M. Theoretical study on the effect of operating conditions on performance of absorption refrigeration system. Energy Convers. Manag.
**2007**, 48, 599–607. [Google Scholar] [CrossRef] - Avanessian, T.; Ameri, M. Energy, exergy, and economic analysis of single and double effect LiBr–H
_{2}O absorption chillers. Energy Build.**2014**, 73, 26–36. [Google Scholar] [CrossRef] - Mussati, S.F.; Gernaey, K.V.; Morosuk, T.; Mussati, M.C. NLP modeling for the optimization of LiBr-H
_{2}O absorption refrigeration systems with exergy loss rate, heat transfer area, and cost as single objective functions. Energy Convers. Manag.**2016**, 127, 526–544. [Google Scholar] [CrossRef] - Talbi, M.M.; Agnew, B. Exergy analysis: An absorption refrigerator using lithium bromide and water as the working fluids. Appl. Therm. Eng.
**2000**, 20, 619–630. [Google Scholar] [CrossRef] - Misra, R.D.; Sahoo, P.K.; Sahoo, S.; Gupta, A. Thermoeconomic optimization of a single effect water/LiBr vapour absorption refrigeration system. Int. J. Refrig.
**2003**, 26, 158–169. [Google Scholar] [CrossRef] - Kızılkan, Ö.; Şencan, A.; Kalogirou, S.A. Thermoeconomic optimization of a LiBr absorption refrigeration system. Chem. Eng. Process. Process Intensif.
**2007**, 46, 1376–1384. [Google Scholar] [CrossRef] - Rubio-Maya, C.; Pacheco-Ibarra, J.J.; Belman-Flores, J.M.; Galván-González, S.R.; Mendoza-Covarrubias, C. NLP model of a LiBr–H
_{2}O absorption refrigeration system for the minimization of the annual operating cost. Appl. Therm. Eng.**2012**, 37, 10–18. [Google Scholar] [CrossRef] - Srikhirin, P.; Aphornratana, S.; Chungpaibulpatana, S. A review of absorption refrigeration technologies. Renew. Sustain. Energy Rev.
**2001**, 5, 343–372. [Google Scholar] [CrossRef] - Garousi, F.; Seyed, M.; Rosen, M.A.; Yari, M. A comparative study of the performance characteristics of double-effect absorption refrigeration systems. Int. J. Energy Res.
**2012**, 36, 182–192. [Google Scholar] [CrossRef] - Garousi Farshi, L.; Seyed Mahmoudi, S.M.; Rosen, M.A. Analysis of crystallization risk in double effect absorption refrigeration systems. Appl. Therm. Eng.
**2011**, 31, 1712–1717. [Google Scholar] [CrossRef] - Arun, M.B.; Maiya, M.P.; Murthy, S.S. Performance comparison of double-effect parallel-flow and series flow water–lithium bromide absorption systems. Appl. Therm. Eng.
**2001**, 21, 1273–1279. [Google Scholar] [CrossRef] - Kaushik, S.C.; Arora, A. Energy and exergy analysis of single effect and series flow double effect water–lithium bromide absorption refrigeration systems. Int. J. Refrig.
**2009**, 32, 1247–1258. [Google Scholar] [CrossRef] - Kaynakli, O.; Saka, K.; Kaynakli, F. Energy and exergy analysis of a double effect absorption refrigeration system based on different heat sources. Energy Convers. Manag.
**2015**, 106, 21–30. [Google Scholar] [CrossRef] - Talukdar, K.; Gogoi, T.K. Exergy analysis of a combined vapor power cycle and boiler flue gas driven double effect water–LiBr absorption refrigeration system. Energy Convers. Manag.
**2016**, 108, 468–477. [Google Scholar] [CrossRef] - Misra, R.D.; Sahoo, P.K.; Gupta, A. Thermoeconomic evaluation and optimization of a double-effect H
_{2}O/LiBr vapour-absorption refrigeration system. Int. J. Refrig.**2005**, 28, 331–343. [Google Scholar] [CrossRef] - Bereche, R.P.; Palomino, R.G.; Nebra, S.A. Thermoeconomic analysis of a single and double-effect LiBr/H
_{2}O absorption refrigeration system. Int. J. Thermodyn.**2009**, 12, 89–96. [Google Scholar] - Gebreslassie, B.H.; Medrano, M.; Boer, D. Exergy analysis of multi-effect water–LiBr absorption systems: From half to triple effect. Renew. Energy
**2010**, 35, 1773–1782. [Google Scholar] [CrossRef] - Mussati, S.F.; Aguirre, P.A.; Scenna, N.J. Novel Configuration for a Multistage Flash-Mixer Desalination System. Ind. Eng. Chem. Res.
**2003**, 42, 4828–4839. [Google Scholar] [CrossRef] - Alasino, N.; Mussati, M.C.; Scenna, N.J.; Aguirre, P. Wastewater treatment plant synthesis and design: Combined biological nitrogen and phosphorus removal. Ind. Eng. Chem. Res.
**2010**, 49, 8601–8612. [Google Scholar] [CrossRef] - Oliva, D.G.; Francesconi, J.A.; Mussati, M.C.; Aguirre, P.A. Energy efficiency analysis of an integrated glycerin processor for PEM fuel cells: Comparison with an ethanol-based system. Int. J. Hydrogen Energy
**2010**, 35, 709–724. [Google Scholar] [CrossRef] - Oliva, D.G.; Francesconi, J.A.; Mussati, M.C.; Aguirre, P.A. Modeling, synthesis and optimization of heat exchanger networks. Application to fuel processing systems for PEM fuel cells. Int. J. Hydrogen Energy
**2011**, 36, 9098–9114. [Google Scholar] [CrossRef] - Arias, A.M.; Mussati, M.C.; Mores, P.L.; Scenna, N.J.; Caballero, J.A.; Mussati, S.F. Optimization of multi-stage membrane systems for CO
_{2}capture from flue gas. Int. J. Greenh. Gas Control**2016**, 53, 371–390. [Google Scholar] [CrossRef] - Manassaldi, J.I.; Arias, A.M.; Scenna, N.J.; Mussati, M.C.; Mussati, S.F. A discrete and continuous mathematical model for the optimal synthesis and design of dual pressure heat recovery steam generators coupled to two steam turbines. Energy
**2016**, 103, 807–823. [Google Scholar] [CrossRef] - Gebreslassie, B.H.; Guillén-Gosálbez, G.; Jiménez, L.; Boer, D. Design of environmentally conscious absorption cooling systems via multi-objective optimization and life cycle assessment. Appl. Energy
**2009**, 86, 1712–1722. [Google Scholar] [CrossRef] - Chahartaghi, M.; Golmohammadi, H.; Shojaei, A. Performance analysis and optimization of new double effect lithium bromide–water absorption chiller with series and parallel flows. Int. J. Refrig.
**2019**, 97, 73–87. [Google Scholar] [CrossRef] - Lee, S.; Lee, J.; Lee, H.; Chung, J.; Kang, Y. Optimal design of generators for H
_{2}O/LiBr absorption chiller with multi-heat sources. Energy**2019**, 167, 47–59. [Google Scholar] [CrossRef] - Sabbagh, A.; Gómez, J. Optimal control of single stage LiBr/water absorption chiller. Int. J. Refrig.
**2018**, 1–9. [Google Scholar] [CrossRef] - Lubis, A.; Jeong, J.; Giannetti, N.; Yamaguchi, S.; Saito, K.; Yabase, H.; Alhamid, M.I.; Nasruddin. Operation performance enhancement of single-double-effect absorption chiller. Appl. Energy
**2018**, 219, 299–311. [Google Scholar] [CrossRef] - Kawajir, Y.; Laird, C.; Wachter, A. Introduction to Ipopt: A Tutorial for Downloading, Installing, and Using Ipopt, 2087 ed. 2012. Available online: https://projects.coin-or.org/Ipopt (accessed on 23 November 2018).
- Mussati, S.F.; Cignitti, S.; Mansouri, S.S.; Gernaey, K.V.; Morosuk, T.; Mussati, M.C. Configuration optimization of series flow double-effect water-lithium bromide absorption refrigeration systems by cost minimization. Energy Convers. Manag.
**2018**, 158, 359–372. [Google Scholar] [CrossRef] - Udugama, I.A.; Mansouri, S.S.; Mitic, A.; Flores-Alsina, X.; Gernaey, K.V. Perspectives on Resource Recovery from Bio-Based Production Processes: From Concept to Implementation. Processes
**2017**, 5, 48. [Google Scholar] [CrossRef] - Mansouri, S.S.; Udugama, I.A.; Cignitti, S.; Mitic, A.; Flores-Alsina, X.; Gernaey, K.V. Resource recovery from bio-based production processes: A future necessity? Curr. Opin. Chem. Eng.
**2017**, 18, 1–9. [Google Scholar] [CrossRef] - Dincer, I. Refrigeration Systems and Applications; Wiley: Hoboken, NJ, USA, 2003; ISBN 978-0-471-62351-9. [Google Scholar]
- American Society of Heating, Refrigerating and Air-Conditioning Engineers. 1989 ASHRAE Handbook: Fundamentals; ASHRAE: Atlanta, GA, USA, 1989; ISBN 978-0-910110-57-0. [Google Scholar]
- Gilani, S.I.-u.-H.; Ahmed, M.S.M.S. Solution crystallization detection for double-effect LiBr-H
_{2}O steam absorption chiller. Energy Procedia**2015**, 75, 1522–1528. [Google Scholar] [CrossRef] - GAMS Development Corporation. General Algebraic Modeling System (GAMS) Release 23.6.5; GAMS Development Corporation: Washington, DC, USA, 2010. [Google Scholar]
- Drud, A. CONOPT 3 Solver Manual; ARKI Consulting and Development A/S: Bagsvaerd, Denmark, 2012. [Google Scholar]
- Khan, M.; Tahan, S.; El-Achkar, M.; Jamus, S. The study of operating an air conditioning system using Maisotsenko-Cycle. Mater. Sci. Eng.
**2018**, 323, 1–7. [Google Scholar] [CrossRef] - Union Gas Limited. Calculating the True Cost of Steam. Available online: http://members.questline.com/Article.aspx?articleID=18180&accountID=1863&nl=13848 (accessed on 23 November 2018).

**Figure 1.**Schematic of the studied double-effect H

_{2}O-LiBr ARS. EV1, EV2, EV3 and EV4 represent expansion valves; EVAP evaporator, ABS absorber; PUMP1 and PUMP2 solution pumps; LTSHE and HTSHE low and high temperature solution heat exchangers, respectively; LTG and HTG low- and high-temperature generators; COND condenser; dash-dotted line (stream #16) refers to an energy stream associated to the refrigerant formed in HTG.

**Figure 4.**Optimal values for each process unit of (

**a**) heat transfer area; (

**b**) heat loads; (

**c**) driving force, versus the cooling capacity level.

**Figure 5.**Optimal distribution of the operating expenditures (OPEX) versus the cooling capacity level.

**Figure 6.**(

**a**) Optimal LiBr concentration values of weak solution (X

_{1}) and strong solutions (X

_{4}and X

_{13}leaving the LTG and HTG, respectively; and X

_{15}entering the ABS); (

**b**) Optimal ABS (low), LTG (medium) and, HTG (high) operating pressure values, versus the cooling capacity level.

**Figure 7.**Optimal effectiveness factors η of the low-temperature solution heat exchanger (LTSHE) and the high-temperature solution heat exchanger (HTSHE) versus the cooling capacity when their lower bounds η

_{LB}are relaxed.

**Figure 8.**(

**a**) Optimal total annual cost (TAC); (

**b**) Optimal annualized capital expenditures (annCAPEX); (

**c**) Optimal operating expenditures (OPEX) for configurations Conf. 1 and Conf. 2 as a function of the cooling capacity level.

**Figure 9.**(

**a**) Optimal cost values for steam requirements; (

**b**) Optimal cost values for cooling water requirements, as a function of the cooling capacity level.

**Figure 10.**Optimal annualized capital expenditure (annCAPEX) values for each process unit in configuration Conf. 2 as a function of the cooling capacity level.

**Table 1.**Optimal costs obtained for configurations Conf. 1 and Conf. 2 for a cooling capacity of 16 kW.

Cost Item | Conf. 1 | Conf. 2 | Deviation (%) |
---|---|---|---|

TAC (M$·year^{−1}) | 12,794.5 | 11,537.2 | −9.8 |

annCAPEX (M$·year^{−1}) | 12,013.6 | 10,684.3 | −11.1 |

CAPEX (M$) | 106,315.5 | 94,551.5 | −11.1 |

EVAP | 27,384.7 | 27,384.7 | 0 |

HTG | 29,794.7 | 29,470.8 | −1.1 |

LTG | 29,447.1 | 29,195.3 | −0.9 |

COND | 3701.9 | 3802.2 | +2.7 |

LTSHE | 7135.8 | 121.2 (*) | − |

HTSHE | 5997.4 | 1911.9 | −68.1 |

ABS | 2853.9 | 2665.6 | −6.6 |

OPEX (M$·year^{−1}) | 780.8 | 852.9 | +9.2 |

Steam | 352.6 | 405.0 | +14.9 |

Cooling water | 428.2 | 447.9 | +4.6 |

**Table 2.**Optimal values of heat transfer areas, heat loads, and driving forces obtained for configurations Conf. 1 and Conf. 2 for a cooling capacity of 16 kW.

Heat Load (kW) | Heat Transfer Area (m ^{2}) | Driving Force (°C) | ||||
---|---|---|---|---|---|---|

Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | |

EVAP | 16.000 | 16.000 | 1.443 | 1.443 | 7.393 | 7.393 |

HTG | 12.029 | 13.816 | 0.313 | 0.287 | 25.633 | 32.144 |

LTG | 9.056 | 10.030 | 0.285 | 0.265 | 20.525 | 24.462 |

COND1 | 0.223 | 0.202 | 0.004 | 0.004 | 23.486 | 21.981 |

COND2 | 7.302 | 6.409 | 0.220 | 0.235 | 13.674 | 11.251 |

LTSHE | 3.378 η = 75% | 0.047 η = 1.521 | 0.356 | 0.001 | 9.484 | 44.725 |

HTSHE | 7.375 η = 75% | 3.197 η = 49.767 | 0.278 | 0.054 | 26.544 | 58.918 |

ABS | 20.503 | 23.205 | 2.074 | 1.997 | 9.888 | 11.619 |

**Table 3.**Optimal values of operating conditions obtained for configurations Conf. 1 and Conf. 2 for a cooling capacity of 16 kW.

Pressure (kPa) | Temperature (°C) | Solution Conc. (kg LiBr kg ^{−1} sol.) × 100 | Mass Flow Rate (kg·s ^{−1}) | |||||
---|---|---|---|---|---|---|---|---|

Point | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 |

1 | 0.813 | 0.813 | 30.944 | 30.967 | 53.668 | 53.681 | 0.085 | 0.058 |

2 | 7.150 | 5.835 | 30.944 | 30.967 | 53.668 | 53.681 | 0.045 | 0.032 |

3 | 7.150 | 5.835 | 66.918 | 31.659 | 53.668 | 53.681 | 0.045 | 0.032 |

4 | 7.150 | 5.835 | 78.910 | 76.438 | 57.578 | 58.449 | 0.042 | 0.030 |

5 | 7.150 | 5.835 | 38.298 | 75.638 | 57.578 | 58.449 | 0.042 | 0.030 |

6 | 0.813 | 0.813 | 38.198 | 42.666 | 57.582 | 59.863 | 0.042 | 0.030 |

7 | 7.150 | 5.835 | 78.910 | 76.438 | − | − | 0.003 | 0.003 |

8 | 7.150 | 5.835 | 39.345 | 35.595 | − | − | 0.007 | 0.007 |

9 | 0.813 | 0.813 | 4.005 | 4.005 | − | − | 0.007 | 0.007 |

10 | 0.813 | 0.813 | 4.005 | 4.005 | − | − | 0.007 | 0.007 |

11 | 81.299 | 58.161 | 30.944 | 30.967 | 53.668 | 53.681 | 0.040 | 0.026 |

12 | 81.299 | 58.161 | 117.292 | 89.468 | 53.668 | 53.681 | 0.040 | 0.026 |

13 | 81.299 | 58.161 | 146.074 | 148.517 | 59.245 | 63.889 | 0.037 | 0.022 |

14 | 81.299 | 58.161 | 55.368 | 89.756 | 59.245 | 63.889 | 0.037 | 0.022 |

15 | 0.813 | 0.813 | 42.516 | 53.893 | 59.787 | 65.401 | 0.037 | 0.022 |

16 | 81.299 | 58.161 | 146.074 | 148.517 | − | − | 0.004 | 0.004 |

17 | 81.299 | 58.161 | 94.023 | 85.209 | − | − | 0.004 | 0.004 |

18 | 7.150 | 5.835 | 39.345 | 35.595 | − | − | 0.004 | 0.004 |

**Table 4.**Optimal cost values obtained for configurations Conf. 1 and Conf. 2 for a cooling capacity of 100 kW.

Cost Item | Conf. 1 | Conf. 2 | Deviation (%) |
---|---|---|---|

TAC (M$·year^{−1}) | 35,613.9 | 31,338.1 | −12.0 |

annCAPEX (M$·year^{−1}) | 30,644.4 | 26,001.7 | −15.1 |

CAPEX (M$) | 271,189.7 | 230,103.8 | −15.1 |

EVAP | 75,306.6 | 75,306.6 | 0 |

HTG | 48,532.7 | 45,984.3 | −5.3 |

LTG | 48,642.3 | 45,325.2 | −6.8 |

COND | 14,649.4 | 13,715.8 | −6.4 |

LTSHE | 28,054.3 | 514.0 (*) | − |

HTSHE | 23,875.4 | 13,062.0 | −45.3 |

ABS | 32,128.8 | 36,709.9 | +14.3 |

OPEX (M$·year^{−1}) | 4969.5 | 5336.4 | +7.4 |

Steam | 2298.9 | 2358.8 | +2.6 |

Cooling water | 2670.6 | 2977.6 | +11.5 |

**Table 5.**Optimal values of heat transfer areas, heat loads, and driving forces obtained for configurations Conf. 1 and Conf. 2 for a cooling capacity of 100 kW.

Heat Load (kW) | Heat Transfer Area (m ^{2}) | Driving Force (°C) | ||||
---|---|---|---|---|---|---|

Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | |

EVAP | 100.00 | 100.00 | 9.017 | 9.017 | 7.393 | 7.393 |

HTG | 78.424 | 80.466 | 2.295 | 1.988 | 22.781 | 26.979 |

LTG | 56.767 | 61.849 | 2.308 | 1.911 | 15.866 | 20.885 |

COND1 | 1.582 | 1.389 | 0.049 | 0.039 | 12.977 | 14.307 |

COND2 | 45.018 | 40.332 | 3.602 | 3.189 | 5.175 | 5.233 |

LTSHE | 20.039 (η = 75%) | 0.316 (η = 1.794%) | 2.518 | 0.008 | 7.960 | 38.000 |

HTSHE | 52.188 (η = 75%) | 29.361 (η = 66.910%) | 1.999 | 0.845 | 26.101 | 34.758 |

ABS | 131.825 | 138.745 | 7.842 | 8.438 | 16.809 | 16.442 |

**Table 6.**Optimal values of operating conditions obtained for configurations Conf. 1 and Conf. 2 for a cooling capacity of 100 kW.

Pressure (kPa) | Temperature (°C) | Solution Conc. (kg LiBr kg ^{−1} sol.) × 100 | Mass Flow Rate (kg·s ^{−1}) | |||||
---|---|---|---|---|---|---|---|---|

Point | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 | Conf. 1 | Conf. 2 |

1 | 0.813 | 0.813 | 38.569 | 35.667 | 57.774 | 56.253 | 0.667 | 0.416 |

2 | 4.575 | 4.146 | 38.569 | 35.667 | 57.774 | 56.253 | 0.349 | 0.223 |

3 | 4.575 | 4.146 | 67.385 | 36.162 | 57.774 | 56.253 | 0.349 | 0.223 |

4 | 4.575 | 4.146 | 76.991 | 74.414 | 61.017 | 60.766 | 0.330 | 0.207 |

5 | 4.575 | 4.146 | 45.083 | 73.914 | 61.017 | 60.766 | 0.330 | 0.207 |

6 | 0.813 | 0.813 | 44.983 | 46.760 | 61.021 | 61.902 | 0.330 | 0.207 |

7 | 4.575 | 4.146 | 76.991 | 74.414 | − | − | 0.019 | 0.017 |

8 | 4.575 | 4.146 | 31.244 | 29.525 | − | − | 0.042 | 0.042 |

9 | 0.813 | 0.813 | 4.005 | 4.005 | − | − | 0.042 | 0.042 |

10 | 0.813 | 0.813 | 4.005 | 4.005 | − | − | 0.042 | 0.042 |

11 | 66.147 | 51.122 | 38.569 | 35.667 | 57.774 | 56.253 | 0.318 | 0.193 |

12 | 66.147 | 51.122 | 120.781 | 110.365 | 57.774 | 56.253 | 0.318 | 0.193 |

13 | 66.147 | 51.122 | 148.185 | 147.306 | 62.407 | 64.801 | 0.294 | 0.167 |

14 | 66.147 | 51.122 | 63.409 | 68.330 | 62.407 | 64.801 | 0.294 | 0.167 |

15 | 0.813 | 0.813 | 49.006 | 53.893 | 63.008 | 65.401 | 0.294 | 0.167 |

16 | 66.147 | 51.122 | 148.185 | 147.306 | − | − | 0.024 | 0.025 |

17 | 66.147 | 51.122 | 88.538 | 81.941 | − | − | 0.024 | 0.025 |

18 | 4.575 | 4.146 | 31.244 | 29.525 | − | − | 0.024 | 0.025 |

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## Share and Cite

**MDPI and ACS Style**

Mussati, S.F.; Mansouri, S.S.; Gernaey, K.V.; Morosuk, T.; Mussati, M.C.
Model-Based Cost Optimization of Double-Effect Water-Lithium Bromide Absorption Refrigeration Systems. *Processes* **2019**, *7*, 50.
https://doi.org/10.3390/pr7010050

**AMA Style**

Mussati SF, Mansouri SS, Gernaey KV, Morosuk T, Mussati MC.
Model-Based Cost Optimization of Double-Effect Water-Lithium Bromide Absorption Refrigeration Systems. *Processes*. 2019; 7(1):50.
https://doi.org/10.3390/pr7010050

**Chicago/Turabian Style**

Mussati, Sergio F., Seyed Soheil Mansouri, Krist V. Gernaey, Tatiana Morosuk, and Miguel C. Mussati.
2019. "Model-Based Cost Optimization of Double-Effect Water-Lithium Bromide Absorption Refrigeration Systems" *Processes* 7, no. 1: 50.
https://doi.org/10.3390/pr7010050