Minimum Total Annual Cost Research Articles

An innovative quick-decision strategy for evaluating the applicability of extractive distillation process with a preconcentration column in separating high-concentration organic waste liquid

In the face of the high energy consumption challenge in separating high-concentration organic waste liquid through extractive distillation (ED), the concept of preconcentration provides a new strategic direction. Therefore, it has become crucial to determine the suitability of the ED process with a preconcentration column for processing such complex mixture. Taking this into consideration, the study proposes an innovative quick-decision method that utilizes thermodynamic analysis of ternary phase diagram to determine the ratio of theoretical product flowrate at the bottom of the preconcentration column to the feed flowrate, which serves as the basis for deciding whether to choose the ED process with a preconcentration column for handling such separation tasks. Three azeotropic systems with different thermodynamic characteristics are chosen as case studies: cyclohexane/ethyl acetate/ethanol (Case 1), ethyl acetate/ethanol/water (Case 2), and n-hexane/ethyl acetate/acetonitrile (Case 3). The task of separating the above three systems is accomplished through the application of both three-column extractive distillation configuration (TCED), and four-column extractive distillation configuration (FCED). The objective functions for multi-objective optimization of all separation configurations include the minimum total annual cost (TAC), the minimum entropy generation and the minimum CO2 emissions. The research findings indicate that when the ratio of theoretical product flowrate at the bottom of the preconcentration column to the feed flowrate is not less than 0.56, or when there is a significant concentration difference among the components in the feed stream, the FCED configuration exhibits clear advantages over the TCED configuration in terms of economic, environmental, and thermodynamic aspects.

Evaluation of dimethyl carbonate production process from CO2 by rigorous simulation and detailed optimization

AbstractThe CO2‐derived dimethyl carbonate (DMC) synthesis process becomes greatly attentive but suffers high energy consumption in DMC distillation process. In this work, the DMC‐MeOH azeotropes separation process by pressure swing distillation and extractive distillation was compared, and key operating parameters, including the total number of trays and the feeding position of the mixture liquid, were optimized with the minimum total annual cost (TAC) as the objective function. On the basis of this optimization, economic evaluation of different distillation processes was conducted, and it was found that extractive distillation was more economical than pressure swing distillation. The application of the dividing‐wall distillation process upgraded by extractive distillation can significantly reduce the minimum annual total cost by 37.4% and 10.7% compared to the original pressure swing distillation and extractive distillation process, respectively. The optimization of relevant heat exchange network based on pinch technology resulted in energy consumption reduction by 27.2% and 25.9% for its hot and cold utilities, respectively. Carbon life cycle assessment (LCA) on the DMC distillation process revealed over 50% of energy as well as carbon emissions from steam consumption, whose reduction can significantly minimize CO2 emissions, energy consumption, and ultimate cost. © 2024 Society of Chemical Industry and John Wiley & Sons, Ltd.

Optimal design of a combined Power-Heating-Oxygen system for plateau hotel buildings

The Qinghai–Tibet Plateau of China is a region of low atmospheric pressure and oxygen deficiency, with a high heating demand in the winter; therefore, plateau hotel buildings have a demand for comprehensive power-heating-oxygen loads. Solar energy resources are particularly abundant in plateau areas, where a combined multi-energy system based on solar energy can be designed to meet the demand of plateau hotel buildings for multiple loads. However, currently, there is a relative lack of methods for the optimal design and performance evaluation of combined power-heating-oxygen (CPHO) systems. Thus, this study proposes a CPHO system model for plateau hotels, and provides two operation strategies, i.e., power priority and oxygen priority. Taking the minimum total annual cost of the combined system as the optimization objective, an optimized CPHO system model for plateau hotels has been proposed, followed by a case study of a hotel in Qilian County, Qinghai Province. Results showed that: 1) Compared with the conventional combined power-heating (CCPH) system, the CPHO system saw reductions of 0.8% and 1.3% in its total annual cost under the operation strategies of power priority and oxygen priority, respectively. 2) The energy self-consumption (SC) rates of the CCPH system and CPHO system under the operation strategies of power priority and oxygen priority were 84.8%, 64.2%, and 89.8%, respectively; with power self-sufficiency (PSS) rates of 8.3%, 49.9%, and 29.5%, and oxygen self-sufficiency (OSS) rates of 0.0%, 3.2%, and 4.7%, respectively. 3) The total annual cost of the CPHO system was affected slightly by the cost of photovoltaics (PVs) and energy storage devices, and significantly by the price of oxygen. When the price of oxygen was 8 yuan per normal cubic meter(Nm3) or above, the CPHO system was economically efficient under the operation strategy of oxygen priority. When the price of oxygen was 10yuan/Nm3 or above, the system was economically efficient under both operation strategies.

Reactive distillation configuration for the production of ethyl acrylate

Esters of acrylic acid have many industrial applications, but existing industrial processes are not economical. Ethyl acrylate, a precursor to polymers and other chemicals is one of them. The existing method of production of ethyl acrylate by esterification of acrylic acid with ethanol using a homogeneous catalyst and reactor-distillation combination has limitation in terms of product purity, corrosion and existence of possible side reactions. The present work proposes a novel reactive distillation (RD) column configuration for ethyl acrylate production, with 99.99 % acrylic acid conversion and 99.99 % ethyl acrylate purity with no effluent stream. The proposed configuration is analyzed using Aspen Plus steady-state simulation software. Sequential iterative sensitivity analysis is performed to obtain all structural and operating parameters leading to a minimum Total Annual Cost (TAC). The result shows that, there is 10.8 % improvement in the purity of aqueous stream using RD configuration compared to existing method and the overall TAC of the process at desired conditions is 87.77 × 103 $/year.

Design and optimization for the separation of xylene isomers with a novel double extractants-based extractive distillation

Xylene is a crucial chemical raw material, serving as a synthetic monomer and solvent extensively employed in coating, medicine, rubber and other industries. It contains of three isomers: o-xylene (OX), m-xylene (MX), and p-xylene (PX), their separation is considered a worldwide challenge due to their extremely close boiling points. A novel extractive distillation based on double extractants is first proposed to separate these isomers in this paper, while it was considered impractical to separate these isomers by distillation technology alone in the past. Through the analysis of residual curve and extractant screening, two potential solvents, i.e., N-Methylpyrrolidone (NMP) and Tetramethylene sulfone (Sul) were used as extractants, and then the separation sequences were designed and optimized. The extractive distillation processes were optimized by sequential iterative method according to the minimum total annual cost (TAC), and the best separation sequence and process parameters were determined. For comparison, it was found that the optimized double extractant-based extractive distillation (DEED) process has the best economic performance with TAC of 5.72×106$, and the energy consumption was greatly reduced by 41.2% compared to the single extractant-based extractive distillation (SEED). This article provides a new perspective on energy-efficient distillation technology for industrial xylene separation and purification production.

Investigation of side-stream extractive distillation for separating multi-azeotropes mixture based on multi-objective optimization

In this study, a conventional triple-column extractive distillation process and three side-stream extractive distillation processes are investigated for separating a ternary mixture of n-hexane/ethyl acetate/acetonitrile. A multi-objective genetic optimization method is applied to optimize the four processes with the minimum total annual cost (TAC) and entropy production as two objective functions. The results indicate that the three side-stream extractive distillation processes can effectively reduce the remixing phenomenon, achieving a reduction in energy consumption. In addition, the three side-stream extractive distillation processes exhibit better economic advantages and significantly decrease entropy production compared to the conventional triple-column extractive distillation process. Among the processes, the single side-stream extractive distillation process presents the optimal performance considering economy, energy-efficient and entropy production. Specifically, it can reduce 6.17% of TAC, 7.85% of energy consumption and 15.54% of entropy production in comparison to the conventional triple-column extractive distillation process, respectively.

Mechanism analysis and energy-saving intensified exploration of green mixed solvents extractive distillation to separate ether-containing azeotropes

2-Methoxyethanol is an important solvent with wide application prospects. Recovering 2-Methoxyethanol from wastewater has significant environmental and economic benefits. In this work, quantum chemistry methods are used to calculate the surface electrostatic potential, mutual penetration analysis, and reduced density gradient-independent gradient model of solvents and azeotrope. From the perspective of the mechanism of action, suitable extractants are selected. With the minimum total annual cost as the goal, the splendid process parameters and the excellent ratio of mixed solvents (30 % 1-ethyl-3-methylimidazole acetate + 70 % N, N-dimethyl acetamide) are acquired. Moreover, two reinforcing processes for energy saving and consumption reduction are also researched. All processes are appraised from three aspects: economy, environment and exergy. The results show that the total annual cost and gas emission of mixed solvent extraction distillation are reduced by 26.79 % and 35.45 %, respectively, compared with the process with NMP as an entrainer. Compared with the process with [EMIM][AC] as an entrainer, the total annual cost and gas emissions are reduced by 44.99 % and 25.04 %, respectively. Relative to mixed solvent, the total annual cost and gas emissions of the heat pump combined with mixed solvent extractive distillation technology decreased by 6.77 % and 21.78 % respectively, while that of the heat integration process decreased via 9.93 % and 12.30 % respectively. From the point of view of environmental sustainability, the process effect combined with the heat pump is better, and from the point of view of economic benefits, the heat integration process has better performance. This study reveals the intrinsic relationship between the structure of mixed solvents and explores the intensification of the process, which provides a theoretical basis for the industrial separation of 2-Methoxyethanol/water azeotrope.

Evaluation and control of energy‐efficient processes for separating epichlorohydrin‐oriented quaternary system

AbstractBACKGROUNDThe direct epoxidation of allyl chloride is a clean and efficient synthesis method for producing epichlorohydrin (ECH), which is a crucial organic intermediate widely used in the fields of renewable energy and aerospace. However, the presence of multiple azeotropes in the synthesized product using this method complicates the separation process and results in high energy consumption. To efficiently separate high‐purity ECH, this paper investigates and analyzes three separation schemes based on phase‐equilibrium analysis: hybrid extractive distillation (HED), pressure swing distillation (PSD) and three‐column batch distillation (TCBD).RESULTSThe operating parameters of the three separation processes are optimized by the sequential iterative optimization method such that the minimum total annual cost can reach $493 491 yr−1. The thermal integration method is used for process energy‐saving optimization, and the total annual cost can be further reduced by 6.9%. In addition, a comprehensive evaluation based on economic, energy, environmental and exergy analysis is conducted, and reveals that the TCBD process with thermal integration is optimal. A control structure is designed for the TCBD process to enhance its robustness such that the purity of ECH remains above 99.9 mol% under ±10% disturbances in feed flowrate and composition.CONCLUSIONSCompared with the HED and PSD processes, the TCBD process has better economic and environmental benefits, and its control structure can effectively resist disturbances. It is reasonable to believe that the TCBD process can be an excellent solution for the industrial production of ECH. © 2024 Society of Chemical Industry (SCI).

Energy-saving exploration of separation for EG/1,2-BDO binary azeotrope based on energy, environmental and economic analysis

In the synthesis of ethylene glycol (EG) from syngas, the inevitable by-product, 1,2-butanediol (1,2-BDO), is generated. Additionally, EG and 1,2-BDO form minimum boiling homoazeotrope, which is a challenge for conventional distillation method. To address this, four processes, extractive distillation process (EDP), extractive distillation with heat integration process (HI-EDP), side-stream extractive distillation process (SSEDP), and extractive dividing wall column process (EDWCP), are used for the separation of EG/1,2-BDO binary system. Firstly, a combination of VLE analysis and COSMO-SAC model analysis was employed to select appropriate entrainers (eugenol). Subsequently, interaction region indicator (IRI) was utilized to reveal the extractive distillation mechanism at the molecular level, demonstrating the feasibility of eugenol as an entrainer for separating EG/1,2-BDO mixture. Next, simulations of the EDP, HI-EDP, SSEDP, and EDWCP processes were conducted through Aspen Plus V11. The optimal process parameters for each flowsheet were determined by the minimum Total Annual Cost (TAC). Furthermore, the process performance was evaluated from economic, energy, and environmental aspects. The EDWCP process demonstrates superior performance compared to the EDP process, with reductions of 16.79% in TAC, 17.6% in TOC, and 14.8% in TCC. Additionally, emissions of acidic gases of decreased by 19.78%, while thermal efficiency improved by 32.91%. EDWCP process represent enormous potential in the field of energy efficiency, economy and environment.

Optimal Sizing and Life-cycle Cost Modelling of Hydraulic Capsule Pipelines

Estimation of the total cost is essential for the planning and the designing of pipelines in a cost-effective way. As a result, the total cost modelling could go beyond the established objectives of least-cost design and optimization. This study incorporates a design methodology for pipelines transporting spherical capsules, which have variant sizes and densities. A methodology has been developed to determine the optimal size and lifetime of pipelines transporting solid–liquid mixtures (Capsule Flow). The methodology includes a model for the prediction of various life-cycle costs. The methodology provides a closed form solution to predict the optimal pipe diameter corresponding to the least total cost. Such solutions are obtained for different life-cycle costs, of which the one associated with minimum annual total cost provides the lifetime. The developed methodology has been used to obtain the optimal diameter of a pipeline for a practical case. The study reveals the interrelationship between the optimal pipe diameter and the corresponding minimum total cost.

Extractive distillation of tetrahydrofuran–ethanol azeotropic mixture with ionic liquid as extractant

AbstractBACKGROUNDThe tetrahydrofuran–ethanol azeotrope cannot be separated by common distillation, but can be effectively separated by extractive distillation. Extractive distillation can be simulated by Aspen Plus software. The minimum annual cost of the process can be calculated to assess ionic liquid separation ability. The interaction energy can be used to explain the separation mechanism.RESULTSThe non‐random two‐liquid model parameters of ternary mixtures for tetrahydrofuran and ethanol containing tributylmethylammonium acetate or 1‐octyl‐3‐methylimidazolium acetate were obtained. Thermodynamic property databases of tributylmethylammonium acetate, 1‐hexyl‐2,3‐dimethylimidazolium acetate and 1‐octyl‐3‐methylimidazolium acetate were established. Based on the thermodynamic model parameters and properties, the sequential iterative method was used to determine the best operating conditions and minimum total annual cost the of extractive distillation process. The interaction energy was calculated to explain the separation mechanism.CONCLUSIONSThe separation performance of tributylmethylammonium acetate is better than that of 1‐hexyl‐2,3‐dimethylimidazolium acetate or 1‐octyl‐3‐methylimidazolium acetate. The selection and design of the ionic liquids can be conducted in terms of the interaction energy. © 2023 Society of Chemical Industry (SCI).

Study of Key Parameters and Uncertainties Based on Integrated Energy Systems Coupled with Renewable Energy Sources

The extensive research and application of integrated energy systems (IES) coupled with renewable energy sources have played a pivotal role in alleviating the problems of fossil energy shortage and promoting sustainability to a certain extent. However, the uncertainty of photovoltaic (PV) and wind power in IES increases the difficulty of maintaining stable system operation, posing a challenge to long-term sustainability. In addition, the capacity configuration of each device in IES and the operation strategy under different conditions will also significantly impact the operation cost and expected results of the system, influencing its overall sustainability. To address the above problems, this paper establishes an optimization model based on linear programming to optimize the equipment capacity and operation strategy of IES coupled with PV and wind power with the minimum total annual cost as the objective function, thereby promoting economic sustainability. Moreover, an integrated assessment framework, including economic, energy efficiency, and environmental aspects, is constructed to provide a comprehensive assessment of the operation of IES, ensuring a holistic view of sustainability. Finally, taking the IES of an industrial park in Xi’an, China, as the specific case, sensitivity analysis is used to explore the impact of a variety of critical parameters on the equipment capacity and operating strategy. Additionally, the Monte Carlo method is used to explore the impact of source-load uncertainty on the performance of the IES. The results show that the facilitating or constraining relationship between renewable energy access and the cascading utilization of combined heat and power generation (CHP) energy depends on the relative magnitude of the user load thermoelectric ratio to the prime mover thermoelectric ratio. To cope with the negative impact of source-load uncertainty on the stable operation of the IES, the capacities of the electric chiller and absorption chiller should be increased by 4.0% and 5.8%, respectively. It is worth noting that the increase in the penetration rate of renewable energy has not changed the system’s dependence on the grid.

Thermoeconomic and environmental analyses based single objective optimization of subcooled compression-absorption cascaded refrigeration system using evolutionary techniques

ABSTRACT This article analyses a subcooled compression-absorption cascaded refrigeration system (SCRS) in comparison with a standalone compression-absorption cascaded refrigeration system (CRS) based on thermoeconomic optimization. Three different absorbent solution/solution mixture-refrigerant combinations have been tested as working pairs in vapor absorption refrigeration system (VARS), whereas four environmentally friendly refrigerants have been utilized in vapor compression refrigeration system (VCRS). The total annual cost of the system is formulated using energy, exergy, and economic performance of the system and is minimized for optimal operational parameters by implementing five recent evolutionary optimization techniques. The effect of compression subcooling on various operational parameters of the cascaded system is reported. Amid all absorbent solution/solution mixture-refrigerant-refrigerant combinations, R290 combined with (CaCl2-LiBr-LiNO3)-H2O provides the minimum total annual cost of 13,164.8 US$ yr−1 and 15,401.9 US$ yr−1 for CRS and SCRS, respectively. Sanitized Teaching Learning Based Optimization (sTLBO) and Coyote Optimization Algorithm (COA) obtain the optimal total annual cost for most VARS-VCRS absorbent solution/solution mixture-refrigerant-refrigerant combinations. Though the coefficient of performance (COP) of an optimal SCRS is about 250% higher than its optimal CRS, higher compressor work results in a higher penalty cost for the optimal SCRS, which is almost 190% higher than the optimal CRS. A quick convergence is observed for sTLBO and COA.

An efficient optimization strategy for vapor compression–absorption-based cascaded refrigeration system using various evolutionary techniques

ABSTRACT A novel optimization strategy for a compression-absorption cascaded refrigeration system (CACRS) consisting of a single effect vapor absorption system (VARS) and vapor compression system (VCRS), which employs several absorbent solution-refrigerant-refrigerant pairs to consider the combination of absorbent solution-refrigerant in VARS and refrigerants in VCRS as an optimization variable, is successfully implemented using various evolutionary optimization techniques. This article analyzes three different absorbent solution-refrigerant in the VARS with eleven different refrigerants in the VCRS. A nonlinear objective function is formulated based on exergy and environmental analysis, which is minimized using 10 different evolutionary optimization techniques. The proposed novel strategy reduces the complexity of using optimization techniques to select the best optimum absorbent-refrigerant-refrigerant pair. Differential evolution with multi-population-based ensemble of mutation strategies determined the minimum total annual cost as 13,137.78 US$/year for (CaCl2-LiBr-LiNO3-)-H2O-R152a. Lower condenser temperature and higher temperature difference in the cascade-condenser resulted in a minimum value for the total annual cost.

Process design and comprehensive 3E analysis of low carbon diol production with and without heat integration

As an important chemical intermediate, the synthesis process of 1,4-butanediol is still energy-intensive and seriously polluting the environment. It is necessary to study its high efficiency and energy saving. The two step synthesis process of 1,4-butanediol: (1) ethynylation of formaldehyde reaction and separation, (2) hydrogenation of 1,4-butynediol reaction and separation are simulated. A sequential iterative optimization method is used to optimize the whole process of 1,4-butanediol production to obtain the best parameters which achieve the minimum annual total cost. In order to further explore the energy-saving process, the heat integration technology is introduced on the basis of the common process, and the annual total cost of the process is reduced by 28.30%. In addition, the exergy efficiency and environmental impact of common process and heat integration process are compared. The results showed that the exergy efficiency of the heat integration process is increased by 6.67% and the CO2, SO2 and NOX emission is reduced by 32.48%, 32.48% and 62.01% compared with the common process. Through the comprehensive analysis of the economy, exergy and environment of synthesis processes, it has important reference significance for the synthesis of 1,4-butanediol in industry.

Configuration Optimization of Hydrogen-Based Multi-Microgrid Systems under Electricity Market Trading and Different Hydrogen Production Strategies

Hydrogen-based multi-microgrid systems (HBMMSs) are beneficial for energy saving and emission reductions. However, the optimal sizing of HBMMSs lacks a practical configuration optimization model and a reasonable solution method. To address these problems, we designed a novel structure of HBMMSs that combines conventional energy, renewable energy, and a hydrogen energy subsystem. Then, we established a bi-level multi-objective capacity optimization model while considering electricity market trading and different hydrogen production strategies. The objective of the inner model, which is the minimum annual operation cost, and the three objectives of the outer model, which are the minimum total annual cost (TAC); the annual carbon emission (ACE); and the maximum self-sufficiency rate (SSR), are researched simultaneously. To solve the above optimization model, a two-stage solution method, which considers the conflicts between objectives and the objectivity of objective weights, is proposed. Finally, a case study is performed. The results show that when green hydrogen production strategies are adopted, the three objectives of the best configuration optimization scheme are USD 404.987 million, 1.106 million tons, and 0.486, respectively.

Pollution trading as a mathematical game

A game theory approach is used to study a market-based pollution trading strategy among different point sources. Point sources discharge effluents to the same watershed and participate as rational entities with particular objectives, interacting with each other in a hierarchical organization. Each point source must implement technologies to sell credits to other sources or buy credits to compensate for non-compliance with environmental regulations. The objective function of the formulations proposed considers the minimization of total annual costs for each point source. The participants in the pollutant credit trading are related in a Nash Game by a mixed complementarity problem (MCP) and in a Stackelberg Game by a bilevel optimization problem (BLP). Both systems are solved using the disjunctive constraint method. Different scenarios of interaction among the participants are proposed in order to observe the behavior of each decision strategy. These models should generate more reliable results with respect to non-competitive approaches as the interaction of the participants is considered.

Reliable design optimization for industrial hybrid energy systems with uncertain sustainable energy

More and more attention has been paid to the industrial hybrid energy systems which comprise fossil energy and renewable energy for achieving carbon neutrality. Wherein, the uncertainty of renewable energy, fluctuation of energy requirement from process units, and failure rate of energy conversion devices have significant effects on the reliability of industrial hybrid energy systems and thus restrict the application and promotion. How to simultaneously address these issues for realizing the reliable design of industrial hybrid energy systems has been a matter of great concern and challenge. Hence, a systematic reliable design optimization method is presented in this study to tackle these challenges. In this study, the two-stage stochastic programming method is implemented to conduct the uncertain optimization in dealing with the uncertainty of renewable energy and fluctuation of energy requirement, while a mixed stand-by redundancy allocation problem is proposed for simultaneously enhancing the reliability and minimizing the number of stand-by devices. A multi-objective mixed integer non-linear programming framework using reliability and total annual cost as the dual objectives is then formulated and applied to a refinery site for the reliable design optimization of the industrial hybrid energy system. According to the solution results, compared to the minimum total annual cost scheme without stand-by redundancy, the maximum reliability of the industrial hybrid energy system can reach 0.9878 using the stand-by redundancy strategy. As a result, the reliability can be significantly enhanced by 44%, with only a 5% increment of the total annual cost. Moreover, a Pareto frontier under multi-objective optimization is constructed, and the optimization schemes at the Pareto frontier can realize the trade-off between reliability and the total annual cost of the industrial hybrid energy system. Subsequently, a reliability-gain index is proposed to further evaluate the trade-off schemes and thus guide the choice of appropriate design schemes.

Novel Reactive Distillation Process for Cyclohexyl Acetate Production: Design, Optimization, and Control.

A side-reactor column (SRC) configuration, comprising a vacuum column coupled with atmospheric side reactors, is proposed to overcome the thermodynamic restriction in the esterification of cyclohexene with acetic acid to produce cyclohexyl acetate. Meantime, this configuration can avoid the utilization of the high-pressure steam and provide enough zone for catalyst loading. In order to obtain the minimum total annual cost (TAC), the process is optimized by a mixed-integer nonlinear programming optimization method based on the improved bat algorithm. The results indicate that the optimized SRC configuration saves about 44.81% of the TAC compared to the reactive distillation process. Based on the optimized SRC process, dynamic control is carried out. The dual-point temperature and temperature-composition control structures are proposed to reject throughput and feed composition disturbances. The dynamic performances demonstrate that the temperature-composition control structure is better in maintaining product purity.

Optimization of radiator area of CHP-based district heating system based on energy cascade utilization

Based on energy cascade utilization, the relative radiator area ratio (RRAR) of combined heat and power (CHP)-based district heating (DH) system was optimized. An optimization model for obtaining the optimal RRAR and minimum annual total cost (ATC) was developed. A CHP-based DH system in Tianjin, China, was taken as a case study. The impact of RRAR on the extracted and exhaust heat was analyzed. Moreover, the impact of equipment lifetime, radiator price, electricity price and interest rate on the optimization results was analyzed through sensitivity analysis. Results confirm that the developed model can be used to obtain the optimal RRAR. With the increase of RRAR, the extracted and exhaust heat used in absorption heat pump (AHP) increases, whereas the extracted heat used in heat exchanger related to extracted heat (HEXT) decreases. Correspondingly, the increase of RRAR results in the decrease of the total extracted heat and increase of the total exhaust heat. Enormous economic, energetic and environmental benefits can be achieved through the utilization of the optimal RRAR. According to sensitivity analysis, the radiator price and electricity price have a larger impact on the optimal RRAR, while the impact of electricity price on the minimum ATC is the largest.