Format And Type Fonts CCHHEEMMIICCAALL EENNGGIINNEEEERRIINNGG TTRRAANNSSAACCTTIIOONNSS VOL. 39, 2014 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong Copyright © 2014, AIDIC Servizi S.r.l., ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439141 Please cite this article as: Liu Y., Yang J., Cheng Z., Wang J., Wang Q., 2014, Cost benefits analysis for waste heat utilization in sinter cooling bed, Chemical Engineering Transactions, 39, 841-846 DOI:10.3303/CET1439141 841 Cost Benefits Analysis for Waste Heat Utilization in Sinter Cooling Bed Yan Liu, Jian Yang, Zhilong Cheng, Jin Wang, Qiuwang Wang* Key Laboratory of Thermal-fluid Science and Engineering, MOE, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P. R. China wangqw@mail.xjtu.edu.cn Based on numerical simulation work in sinter cooling bed of our previous work, AEG (annual energy gain) is obtained on energy and exergy analysis under WHCU (waste heat cascade utilization). In the present paper, a method that integrates economics and energy analysis of a sinter cooling bed is proposed. Firstly, the symbolic regression is employed to find an accurate correlation between operational parameters and AEG. In order to improve the performance of GPLAB (genetic programming toolbox) of MATLAB environment, the symbolic regression is modified by adding new function modules into GPLAB. Then, the cost model is established to evaluate effects of operational parameters on EAOC (equivalent annual operational cost). Finally, the CBR (cost benefits ratio) is calculated to assess the comprehensive performance of the sinter cooling bed. Furthermore, for the purpose of optimising CBR, the method of Genetic Algorithm (GA) is adopted. The studied cases show that, it is an effective way to obtain optimal sets of operational parameters in a sinter cooling bed within the range of operating conditions. The optimisation results show that, the CBR based on the first law and second law of thermodynamics could be reduced by 18.4 % and 29.8 % when the optimal sets of parameters are employed. 1. Introduction Iron and steel industry in China is a major one of the industries with high consumption of energy, accounting for about 15.2 % of the national total energy in 2006 (Guo and Fu, 2010). According to Caputo et al. (1996), the sinter cooling bed is widely employed in sintering process and pelletizing process for cooling high temperature sinters and pellets. A sinter cooling bed of Anshan Steel including trollys and hoods could be seen in Figure 1. Several related studies have been prevailed on heat transfer and WHU (waste heat utilization) in the sinter cooling bed. Zhang et al. (2013) investigated the influence of multi-layer feeding on WHU by optimising parameters with the mixed orthogonal experimental method. Liu et al. (2013a) numerically examined the gas flow field and sinter temperature field for different distributions of sinter porosity which was highly dependent on the arrangement and orientation of sinter within the sinter cooling bed. Economic analyses of process industry have also been studied and some meaningful conclusions have been drawn. Caputo and Pelagagge (2001) established a mathematical model based on total cost minimization of the sinter cooling bed. The results showed when an optimised design is adopted, the expected savings could range 10 % to 25 % of total cost. Ahamed et al. (2012) focused on improvement of the energy, exergy and recovery efficiencies of a grate cooling system through the optimisation of its operational parameters such as masses of cooling air and clinker, cooling air temperature, and grate speed. Nakano (2011) developed a differential equation that described sintering cost from basic relationships between relevant operational variables/parameters and to discuss the cost-minimum state and the direction for cost-minimum operation by applying the equation. In order to study effects of different operating parameters on WHCU in the sinter cooling bed, we numerically examined WHCU based on the first and second law of thermodynamics (Liu et al., 2013b). In the study, a two-dimensional unsteady mathematical model was established to describe three-dimensional steady transport process and WHU in a sinter cooling bed. The Brinkman-Forchheimer extended Darcy 842 model and the LTNE (local thermal non-equilibrium) model were employed to describe flow and heat transfer in the sinter cooling Figure 1: A sinter cooling bed of Anshan Steel (a) Trolly, (b) Hoods bed. Based on above discussion, cost (economics analysis) and benefits (energy analysis) of the process industry have been studied independently. According to authors’ knowledge, few researches have been conducted on the combining of the cost and benefits of the sinter cooling process. Therefore, in the present work, following the study of Liu et al. (2013b), a method that integrates economics and energy analysis of a sinter cooling bed is proposed. Firstly, the symbolic regression is employed to find an accurate correlation between operational parameters and AEG. Then, the cost model is established to evaluate effects of operational parameters on EAOC (equivalent annual operational cost). Finally, the CBR (cost benefits ratio) is calculated to assess the comprehensive performance in the sinter cooling bed. Furthermore, for the purpose of optimising CBR, the method of Genetic Algorithm (GA) is also adopted. 2. Construction of the cost benefits model 2.1 Energy model of the sinter cooling bed The sinter cooling process has been examined in our previous work (Liu et al., 2013b). Temperature of cooling air, quantity and quality of waste heat have been obtained. AEG in each sector of the sinter cooling bed could be expressed as follows: f Sector Sector egy op m m AEG Q t  (1) x Sector Sector exy op m m AEG E t  (2) where f Sector m Q is quantity of waste heat per unit time of sector m; Sector egy m AEG is AEG based on the first law of thermodynamics in sector m; x Sector m E is quality of waste heat per unit time of sector m; Sector exy m AEG is AEG based on the second law of thermodynamics in sector m. top is operational time of sinter cooling bed per year. AEG of the sinter cooling bed could be expressed as follows: 4 Sector egy egy 1 m m AEG AEG    (3) 4 Sector exy exy =1 m m AEG AEG  (4) where AEGegy is AEG based on the first law of thermodynamics; AEGexy is AEG based on the second law of thermodynamics. 2.2 Cost model of the sinter cooling bed A typical sinter cooling process including top view and cross-sectional view could be seen in Figure 2. Construction of the Cost model is mainly based on Figure 2(b). According to Fudholi et al. (2013), EAOC (equivalent annual operating cost) of the sinter cooling bed could be determined by FCI (fixed capital investment) and AC (annual cost) which could be expressed as follows: 843 Cooling Air Exhaust Air Sinter Layer D isch arg in g Feeding Blowers Trolley h b W Blower Cooling air H a Figure 2: A typical sinter cooling process (a) Top view, (b) Cross-sectional view =EAOC CRF FCI AC  (5) where CRF is capital recovery factor. According to Turton et al. (2009), the definition of the CRF could be expressed as follows: (1+ ) = (1 ) 1 N N i i CRF i  (6) where i is lending rates and N is lifetime of the sinter cooling bed. According to different application, the sinter cooling bed could be divided into several parts containing trollys, moving bed, blowers, hoods, feeding and discharging devices (Caputo and Pelagagge, 2001). Based on the division, FCI could be expressed as follows: b bl t h f & d FCI FCI FCI FCI FCI FCI       (7) where FCIb is FCI of sinter cooling bed; FCIbl is FCI of blowers; FCIt is FCI of trollys; FCIh is FCI of hoods; FCIf&d is FCI of feeding and discharging devices. AC could be expressed as follows (Caputo and Pelagagge, 2001): m&l bl t f & d = + +AC AC AC AC AC (8) where ACm&l is AC of maintenance and labor; ACbl is AC of blowers; ACt is AC of trollys; ACf&d is AC of feeding and discharging devices. 2.3 Cost benefits model of the sinter cooling bed Based on the construction of energy model and cost model of the sinter cooling bed, we can obtain AEG and EAOC independently. For the purpose of comprehensive consideration of energy and economics aspect, the conception of CBR (cost benefits ratio) is proposed in the sinter cooling bed. CBR based on the first law and second law of thermodynamic could be expressed as follows: egy egy = EAOC CBR AEG (9) exy exy = EAOC CBR AEG (10) where the unit of CBR is $/GJ. 3. Results and Discussion 3.1 WHU of the sinter cooling bed Based on the principle of WHCU, the sinter cooling bed is divided into power recovery zone and heat recovery zone. Waste heat from power recovery zone could be used to generate electricity and waste heat from heat recovery zone could be adopted to preheat the sintering feed. In the present work, we mainly concern about 844 11 1. 6 10 2. 6 11 8. 1 10 2. 4 12 3 94 .6 12 6. 7 37 .2 41 .1 33 .7 24 .2 47 .6 27 .7 47 .6 0 25 50 75 100 125 150 175 H 0. 95 mH 0. 65 m V 0. 02 1 m /s V 0. 01 4 m /s F f, in 60 0 kg /s F f, in 40 0 kg /s W a st e h e a t q u a n ti ty / G J ·h -1 Power recovery zone Heat recovery zone St an da rd C on di ti on s 36 .6 35 .2 35 .3 31 40 .4 27 .6 43 .2 5. 6 7. 7 4 2. 6 8. 3 3. 3 8. 5 0 10 20 30 40 50 H 0. 95 mH 0. 65 m V 0. 02 1 m /s V 0. 01 4 m /s F f, in 60 0 kg /s F f, in 40 0 kg /s E x e rg y o f W a s te h e a t / G J ·h -1 Power recovery zone Heat recovery zone S ta nd ar d C on di tio ns Figure 3: WHU of the sinter cooling bed (a) Based on the first law of thermodynamics, (b) Based on the second law of thermodynamics WHU in power recovery zone. Figure 3 illustrates WHU of the sinter cooling bed based on the first and second law of thermodynamics. As shown in Figure 3(a), WHU based on the first law of thermodynamics in power recovery zone increases with Ff, in, V and H. We can see from Figure 3(b) that WHU based on the second law of thermodynamics in power recovery zone increases with V and H. However, both increase and decrease of Ff, in lead to decrease of WHU based on the second law of thermodynamics. In short, influence of mass flow rate of cooling air should be examined further. For other operational parameters, increase of V and H could be adopted to increase WHU. For the purpose of the optimising of CBR, the correlation between operational parameters and AEG should be obtained. In present work, The symbolic regression method based on MATLAB environment is employed to find an accurate correlation between operational parameters and AEG. However, when the undetermined function contains constant term, symbolic regression results usually have complicated structure and it is difficult to use them for practical applications adopting the original genetic programming toolbox. In order to improve the performance of genetic programming toolbox GPLAB of MATLAB environment, four new function modules were added into GPLAB by Xu et al. (2012), including structure simplification module, constants optimisation module, expansion rate reduction module with “self-swap” genetic operator, small term search intensity enhancement module with “intro-new” genetic operator. It is proved that, the correlations based on the modified symbolic regression have higher predictive accuracy and are less sensitive to the disturbance variation of the arguments (Xu et al., 2012). In order to expand the sample capacity of experimental data, a orthogonal table is designed and more sample are added. Correlation obtained between AEG and operational parameters based on the modified genetic programming toolbox is as follows: 7 1 egy op f, in 8 44 . V AEG . t H F    (11) exy op f, in (3700 1.29 )AEG t V H F V         (12) The average deviation rate and the maximum deviation rate of Eq(11) are 1.04 % and 4.15 %. The average deviation rate and the maximum deviation rate of Eq(12) are 1.69 % and 5.92 %. The small deviations indicate that Eq(11) and Eq(12) have high precision for the description of AEG. 3.2 Cost of the sinter cooling bed We investigate the effect of operational parameters and economic parameters on the cost of the sinter cooling bed. It can be seen from Figure 4(a), (b) and (c) that EAOC increases with the three operational parameters under the same bed length. For a certain operational condition, there is an optimal bed length for the minimum of EAOC. For very short beds the EAOC could be very large, which shouldn’t be adopted in industrial production. When the bed length is shorter than the optimal one, EAOC decreases as the bed length increases. When the bed length is greater than the optimal one, EAOC increases with the bed length. Figure 4(d) illustrates that EAOC decreases with N (lifetime of the sinter cooling bed). According to common sense of economics, i (lending rates) and N are corresponding with each other. Generally, a 845 larger N corresponding to a small i. In this perspective, continuous use of sinter cooling bed should be adopted. In other words, planning 0 20 40 60 80 100 120 140 160 180 200 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 E A O C (1 m il li o n U S D /y e a r) Bed length(m) F f, in =400 kg/s F f, in =500 kg/s F f, in =600 kg/s Operating condition V=0.018 m/s W=4 m H=0.8 m T s, in =550ºC 0 20 40 60 80 100 120 140 160 180 200 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 E A O C (1 m il li o n U S D /y e a r) Bed length(m) V=0.014 m/s V=0.018 m/s V=0.021 m/s Operating condition W=4 m H=0.8 m T s, in =550ºC F f, in =500 kg/s 0 20 40 60 80 100 120 140 160 180 200 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 E A O C (1 m il li o n U S D /y e a r) Bed length(m) H=0.65 m H=0.8 m H=0.95 m Operating condition V=0.018 m/s W=4 m T s, in =550ºC F f, in =500 kg/s 0 20 40 60 80 100 120 140 160 180 200 220 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 E A O C (1 m il li o n U S D /y e a r) Bed length(m) i=0.0615, N=3 i=0.0655, N=5 i=0.0655, N=20 Operating condition V=0.018 m/s W=4 m H=0.8 m F f, in =500 kg/s T s, in =550ºC Figure 4: Cost of the sinter cooling bed (a) Effects of Ff,in, (b) Effects of V, (c) Effects of H, (d) Effects of i and N and program demonstration are indeed important for reducing EAOC. Figure 4 illustrates that economic parameters have larger effects than operational parameters on the cost of sinter cooling bed. 3.3 Parameter optimisation based on CBR Before parameter optimisation, effects of operational parameters on CBR are investigated. CBR based on the first law and the second law of thermodynamics could be seen in Figure 5. From Figure 5 we can know that decrease of Ff, in, increase of V and H could be adopted to reduce CBR. In order to assess the comprehensive performance of WHU and economics in the sinter cooling bed, We employ the method of Genetic Algorithm (GA) based on MATLAB environment to optimise CBR. The objective function is CBR since we pursuit the minimum CBR. In the optimisation process, Ff, in, V and H range from 400 kg/s, 0.014 m/s and 0.65 m to 600 kg/s, 0.021 m/s and 0.95 m. According to Caputo et al. (1996), under the standard conditions, Ff, in, V and H are set to 500 kg/s, 0.018 m/s and 0.8 m. The optimisation results show that based on the first law of thermodynamics, the CBRegy could be reduced to 0.323 $/GJ when the parameters set of 412.9 kg/s, 0.021 m/s and 0.95 m is adopted for Ff, in, V and H, while CBRegy under the standard conditions is 0.396 $/GJ. The CBRegy could be reduced by 18.4 % when the optimal set of parameters is employed. Based on the second law of thermodynamics, the CBRexy could be reduced to 1.006 $/GJ when the parameters are set to be 400 kg/s, 0.021 m/s and 0.95 m for Ff, in, V and H, while CBRexy under the standard conditions is 1.434 $/GJ. The CBRexy could be reduced by 29.8 % when the optimal set of parameters is employed. 4. Conclusions In the present paper, energy model and cost model of the sinter cooling bed are constructed independently, a method that integrates energy and economics analysis of the sinter cooling bed is put forward. Based on carefully analyses of CBR, the optimal operational parameters of the sinter cooling bed are obtained. The major findings are as follows: 1. Based on previous parametric study of WHCU of the sinter cooling bed (Liu et al., 2013b), we obtain correlations between AEG and operational parameters based on the modified GPLAB method. The correlations have simple structure and high predictive accuracy which would meet the requirements of engineering applications. 846 2. We examine effects of operational parameters and economics parameters on EAOC of the sinter cooling bed. For operational parameters aspect, the results shows that there are optimal bed length for different 0. 39 6 0. 39 4 0. 41 1 0. 43 8 0. 36 2 0. 45 0 0. 36 1 1. 43 4 1. 32 2 1. 58 6 1. 65 0 1. 26 7 1. 78 6 1. 21 7 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 C B R ( $ /G J ) CBR egy CBR exy St an da rd C on di ti on s F f, in 40 0 kg /s F f, in 60 0 kg /s V 0. 01 4 m /s V 0. 02 1 m /s H 0. 65 m H 0. 95 m Figure 5: CBR of the sinter cooling bed operational conditions and EAOC increases with the three operational parameters under the same bed length. For economics parameters aspect, planning and program demonstration are indeed important for reducing EAOC. 3. We employ the method of Genetic Algorithm (GA) to optimise CBR, which is proposed to assess the comprehensive performance of the sinter cooling bed. The results shows that it is an effective way to obtain optimal sets of operational parameters in a sinter cooling bed within the range of operational conditions. It is also shown that, the CBRegy and CBRexy could be reduced by 18.4 % and 29.8 % when an optimising sets of parameters are adopted. Acknowledgements We would like to acknowledge financial support for this work provided by the National Basic Research Program of China (973 Program, NO. 2012CB720402) and China National Funds for Distinguished Young Scientists (NO. 51025623). References Ahamed J.U., Madlool N.A., Saidur R., Shahinuddin M.I., Kamyar A., Masjuki H.H., 2012, Assessment of energy and exergy efficiencies of a grate clinker cooling system through the optimization of its operational parameters, Energy, 46, 664-674. Caputo A.C., Cardarelli G., Pelagagge P.M., 1996, Analysis of heat recovery in gas-solid moving beds using a simulation approach, Applied Thermal Engineering, 16, 89-99. Caputo A.C., Pelagagge P.M., 2001, Economic design criteria for cooling solid beds, Applied Thermal Engineering, 21, 1219-1930. Fudholi A., Sopian K., Ruslan M.H., Othman M.Y., 2013, Performance and cost benefits analysis of double-pass solar collector with and without fins, Energy Conversion and Management, 76, 8-19. Guo Z.C., Fu Z.X., 2010, Current situation of energy consumption and measures taken for energy saving in the iron and steel industry in China, Energy, 35, 4356-4360. Liu Y., Wang J., Yuan X., Yang J., Wang Q.W., 2013a, Numerical investigation of sinter cooling process in sinter cooler, AIP Conference Proceedings, 1547, 788-795. Liu Y., Yang J., Wang J., Cheng Z.L., Wang Q.W., 2013b, Energy and exergy analysis for waste heat cascade utilization in sinter cooling bed, Energy, doi.org/10.1016/j.energy.2013.11.086. Nakano M., 2011, A differential analysis for the cost minimum operation of iron ore sintering machines, ISIJ International, 51, 552-556. Turton R., Bailie R.C., Whiting W., Shaeiwitz J.A., Bhattacharyya D., 2009, Analysis, synthesis and design of chemical processes, Prentice Hall. New Jersey, USA. Xu J., Wang Q.W., Zeng M., 2012, Improvement of genetic programming symbolic regression and its application in heat exchangers, Journal of Engineering Thermophysics, 33, 1415-1418 (in Chinese). Zhang X.H., Chen Z., Zhang J.Y., Ding P.X., Zhou J.M., 2013, Simulation and optimization of waste heat recovery in sinter cooling process, Applied Thermal Engineering, 54, 7-15.