1194
Energy & Fuels 2004, 18, 1194-1198
Cumulative Exergy Analysis of Heat Exchanger Production and Heat Exchange Processes Xiao Feng,* Guohui Zhong, Ping Zhu, and Zhaolin Gu Department of Chemical Engineering, State Key Laboratory of Multi-Phase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China Received October 9, 2003. Revised Manuscript Received April 12, 2004
In this paper, on the basis of cumulative exergy consumption theory, the cumulative exergy contribution of equipment in processes is emphasized. In this way, the theory can not only analyze the process energy performance, but also optimize both the process parameters and the size of equipment at the same time. Heat exchangers are extensively used in process industries. In this paper, heat exchangers are treated as products. By investigating and calculating the energy consumption in the production process of heat exchangers, the cumulative exergy consumption of heat exchangers is obtained. Finally, based on the cumulative exergy of heat exchangers, heat exchange processes can be optimized to minimize the total cumulative exergy consumption.
Introduction The requirement for sustainable development of human society makes people seriously research the reasonable utilization of energy and natural resources and search for process systems with optimal resource utilization. According to life cycle assessment (LCA),1 both the energy and nonenergetic materials consumption in a process are very important. Szargut and Morris2-4 presented the concepts of cumulative exergy consumption. The cumulative exergy consumption of a product is the sum of the exergy of natural resources consumed in all links of the technological network that starts with these resources and leads to the product under consideration.4 In this way, cumulative exergy consumption can integrally involve raw materials, energy, equipment, and products. However, when the cumulative exergy consumption method was used to analyze processes, only the energy, raw materials, and products associated with the processes are considered: the cumulative exergy contribution of the equipment is omitted.2 Therefore, the cumulative exergy consumption method can only evaluate the thermodynamic perfection with different raw materials and production routes for the same product: it cannot optimize the process parameters (for example, the driving forces of the processes) that have a great effect on energy performance. It is well-known that the exergy consumption of a process is directly related to the driving force of the * Author to whom correspondence should be addressed. Fax: +8629-83237910. E-mail address:
[email protected]. (1) Azapagic, A. Life Cycle Assessment and Its Application to Process Selection, Design and Optimization. Chem Eng J. 1999, 73 (1), 1-21. (2) Szargut, J.; Morris, D. R. Cumulative Exergy Consumption and Cumulative Degree of Perfection of Chemical Process. Int. J. Energy Res. 1987, 11 (2), 245-261. (3) Szargut, J. Analysis of Cumulative Exergy Consumption. Int. J. Energy Res. 1987, 11 (4), 541-547. (4) Szargut, J.; Morris, D. R. Cumulative Exergy Loss Associated with the Production of Lead Metal. Int. J. Energy Res. 1990, 14 (6), 605-616.
process. The greater the driving force, the greater the exergy consumption but, conversely, the smaller the size of the equipment involved in the process. The equipment also consumes materials and exergy during its production. If the cumulative exergy consumptions of energy, raw materials, and products in the process, as well as the cumulative exergy contribution of the equipment, are taken into consideration, the process can be optimized to obtain the optimal driving force and the optimal equipment size. To optimize a process based on cumulative exergy, the cumulative exergy contribution of equipment should be known. However, until now, no such research has been conducted. In this paper, based on the cumulative exergy consumption method, the consumption of energy and nonenergy materials, as well as the contribution of cumulative exergy of equipment in the process, is taken into account. In this way, the method can not only analyze the process energy performance, but also optimize both the process parameters and the equipment size at the same time. This paper focuses on the analysis of the cumulative exergy consumption of heat exchanger production. Heat exchangers are widely used in process industries, and the shell-and-tube heat exchangers account for 80%90% of the total production of heat exchangers.5 Determination of the cumulative exergy of shell-and-tube heat exchangers is the important first step to determine the cumulative exergy consumption of the equipment. Based on the cumulative exergy consumption of heat exchanger production, heat exchange processes can then be optimized to minimize the total cumulative exergy consumption. The Method of Cumulative Exergy Analysis The cumulative exergy consumption of a product is the sum of the exergy of the natural resources consumed in all links of (5) Qian, S. W. Design of Shell-and-Tube Heat Exchanger (in Chin.); South China University of Technology Press: Guangzhou, China, 1990.
10.1021/ef034068m CCC: $27.50 © 2004 American Chemical Society Published on Web 06/09/2004
Cumulative Exergy Analysis of Heat Exchangers
Energy & Fuels, Vol. 18, No. 4, 2004 1195
the technological network leading from these resources to the product under consideration.4 For materials, the exergy of the material in its natural state (for example, the coal or iron ore) is taken as the calculated benchmark. For a specified material or energy in the process under consideration, the cumulative exergy of the material or energy is the sum of the benchmark exergy and the exergy introduced into it during series technologies until it becomes the matter in the process. The cumulative exergy of equipment is calculated by the same method as a general product from the raw materials to the final product (the equipment). Therefore, the cumulative exergy of any item in the studied system, including raw material, energy, equipment, the intermediate product and the final product, etc., can be expressed as in eq 1.
Ei )
∑Ex
+
∑Ex
+
MN,is
s
)
M,im
m
∑Ex
EN,is
s
∑Ex e
E,ie
+
∑Ex
dN,is
s
+
∑Ex
di
(1)
d
where Ei is the cumulative exergy of item i in the system and Ex is the exergy. The subscript M denotes the raw material, the subscript N means the natural state, the subscript E denotes the energy, and the subscript d means the equipment. The subscript s indicates that the parameter is that for the sth item. The benchmark of the cumulative exergy of all materials, energy, and equipment is the exergy of the natural substances in the environment. The exergy of the natural substances is determined by the conventional exergy method. For example, the cumulative exergy of a heat exchanger is composed of the cumulative exergy of materials (for instance, steel), the cumulative exergy of energy (mainly electricity), and the contribution of the cumulative exergy of all types of equipment used to produce the heat exchanger. In this way, the energy content of the raw materials, energy, equipment, and products can be addressed uniformly, using the cumulative exergy concept. Next, the cumulative exergy consumption of shell-and-tube heat exchangers, which are widely used in process industries, is determined based on careful investigation.
Production Process of the Heat Exchanger and the System Boundary The selection of system boundaries is very important in the cumulative exergy analysis. After the boundary has been decided, the cumulative exergy flowing into and out of the system will be determined and the cumulative exergy of the product will be calculated. There are two types of system boundaries: (1) The boundary consists of the substances in the environment. The extraction, transportation, and storage of fuels and raw materials and the usage of equipment and intermediate products should be included. (2) The boundary is the studied system. The input and output of the cumulative exergy of all materials, energy, and equipment should be included. The system boundary in this paper is the second type, as shown in Figure 1. In the production process of heat exchangers, the consumed energy is electricity and the equipment used is comprised of machining tools. The main parts and equipment used are listed in Table 1.
Figure 1. Analysis system for the production of a shell-andtube heat exchanger.
Cumulative Exergy Consumption of Heat Exchanger Production Cumulative Exergy of Consumed Energy. In the production of shell-and-tube heat exchangers, only electricity is used. The quantity of electricity in each step of the production is the power of the equipment used multiplied by the operation time of the equipment in the step. The electricity consumed in each step of the heat exchanger (BEM800-1.0-58-3.5/38-1/1) is shown in the second column of Table 1. Table 1 shows that the total electricity consumption is 5646.71 MJ in the production of the BEM800-1.0-583.5/38-1/1 heat exchanger. The exergy in electricity is 100%; namely, the quantity of electricity is equal to the quantity of exergy. Therefore, the cumulative exergy of consumed electricity is calculated by
ExE RE
EE )
(2)
where EE is the cumulative exergy of electricity, ExE the exergy of electricity, and RE the ratio of the quantity of exergy of electricity and the cumulative exergy of electricity. The RE value of the electricity is 0.24.1 Thus, the cumulative exergy of electricity consumption in the production of the shell-and-tube heat exchanger is calculated as
EE )
5646.71 MJ ) 23 527.95 MJ ≈ 23.53 GJ 0.24
Cumulative Exergy of Materials. The cumulative exergy of materials is calculated by
Em ) ME0(1 + F)
(3)
where Em is the cumulative exergy of materials, M the mass of the heat exchanger, E0 the unit cumulative exergy of the materials used, and F the discard coefficient of materials in the production process. The material of the investigated heat exchanger is ordinary low-carbon steel, and the related constants are as follows: M ) 3330 kg, E0 ) 0.0521 GJ/kg,2 and F ) 0.005. Thus, the cumulative exergy of the materials of the investigated heat exchanger is
Em ) 3330 kg × 0.0521 GJ/kg × (1 + 0.005) ) 174.36 GJ Cumulative Exergy of Equipment. The contribution of the equipment to the cumulative exergy of the heat exchanger is calculated using eq 4:
() ti
∑i Edi ) ∑i ξi T
i
(Edoi - EdTi)
(4)
1196 Energy & Fuels, Vol. 18, No. 4, 2004
Feng et al.
Table 1. Energy Consumption and Cumulative Exergy Contribution of the Equipment of Heat Exchanger (BEM800-1.0-58-3.5/38-1/1) Cumulative Exergy Contribution of Equipment (MJ) main parts of the heat exchanger
electricity (MJ)
up and down tubesheet tube φ219 × 6 φ32 × 3 shell baffle shell flange shell joint shell assembly flange cover tube flange φ219 × 6 φ32 × 3 final assembly sum
923.54
drilling machine 50# 80#
233.28 60.66 958.82 682.74 412.52 161.6 298.19 12.96
48.49 68.18
15.15 1.2
0.91
2.4 1.2
0.91
88.85
∑i ξi∑i Cdi
En
arc welder
plate blender
flaw detector
24.09
4.18 2.09 15.47
30.3
84.05
528.77 12.96 1360.7 5646.7
C
vertical lathe
185.6
0.68 0.68 1.79 0.34 0.34 0.34 0.85
8.04
2.09 8.36
30.3 200.8
where Edi is the contribution of cumulative exergy of equipment used to make part i; ξi is the coefficient when considering equipment transportation, installation, maintenance, and so on; ti is the operation time of the equipment while making part i; Ti is the operation life of the equipment used to make part i; Edoi is the original cumulative exergy of the equipment; and EdTi is the remaining cumulative exergy of the equipment at the end of its operation life. Equation 4 shows that the cumulative exergy of the equipment is linearly apportioned in its operation life. It is an approximate apportionment method and is widely used. Because the cumulative exergy of the equipment used in the production process is unknown, the ratio of the cumulative exergy of each item of equipment to the cumulative exergy of the heat exchanger is assumed to be equal to the ratio of the cost of equipment to the actual cost of the heat exchanger (Cdi/C). The assumption does not affect the calculation result, which will be discussed later. In the calculation process, an iteration method is adopted, because the cumulative exergy of the heat exchanger is also unknown. First, the cumulative exergy of raw materials and energy is taken as the initial value of the cumulative exergy of the heat exchanger. The cumulative exergy then is calculated based on the initial value by adding the cumulative exergy contribution of the equipment. The initial value is replaced by the current value and the cumulative exergy of the heat exchanger is iterated repeatedly. When the difference between the current value and the former one is less than a certain small value, the calculation is terminated. The iteration method may be expressed as follows:
En+1 ) Eo +
general lathe
(5)
where n is the number of iterations. The related constants are ∑i ξi ) 3.5,6 ∑iCdi ) 301.14 yuan, and C ) 110 000 yuan. (6) Douglas, J. M. Conceptual Design of Chemical Processes; McGrawHill: New York, 1988.
1.82
177.3
4.09 8.91
32.13
6.27 38.46
First, the cumulative exergy contribution of the equipment used in the production is not considered; the cumulative exergy of the heat exchanger then is
Eo ) EE + Em ) 23.53 GJ + 174.36 GJ ) 197.89 GJ The equipment then is considered: E1 ) 199.786 GJ and E2 ) 199.804 GJ. The relative error of the two calculation results is
E2 - E1 199.804 GJ - 199.786 GJ ) ) 0.009% E1 199.786 GJ The error is certainly within the limits of standard engineering precision. The cumulative exergy contribution of each item of equipment is given in Table 1. Cumulative Exergy of Shell-and-Tube Heat Exchanger. From the aforementioned calculation, the cumulative exergy of the investigated heat exchanger is 199.804 GJ. In the total cumulative exergy, the cumulative exergy of the raw material accounts for 87.27%; the energy accounts for 11.78%, and the equipment used only amounts to 0.95% of the total exergy. Therefore, in the production process of heat exchangers, the cumulative exergy contribution of the equipment can be neglected, because it only accounts for a very small portion. The ratio of cumulative exergy of energy consumption is relatively low. In this case, the material of the investigated heat exchanger is ordinary low-carbon steel. If better materials are used, the ratio of the cumulative exergy of energy and equipment to the total value will be decreased further. Therefore, in the production process of heat exchangers, the cumulative exergy of materials is the major component of the total value. As a result, when using heat exchangers, compact heat exchangers should be considered as long as they meet the performance demands. In this way, the cumulative exergy of heat exchangers can be decreased, so that energy and resources can be saved. By investigating more production processes of heat exchangers, the general expression of the cumulative exergy for heat exchangers can be expressed as
E)
∑i ξi[(a + bMc) + E0M(1 + F)]
(6)
Cumulative Exergy Analysis of Heat Exchangers
Energy & Fuels, Vol. 18, No. 4, 2004 1197
where, a, b, and c are constants that are determined by the type of heat exchanger. The cumulative exergy of each type of heat exchanger is observed to be a uniform function of its mass. Cumulative Exergy Optimization of the Heat Exchange Process To show how the concept of cumulative exergy is used to optimize a process, based on the cumulative exergy of heat exchangers, the heat exchange process is optimized as follows. Consider a water-water countercurrent heat exchange process. The following operating parameters are assumed. The volume flow of the cold water is 14.0 m3/ h. The incoming temperatures of the cold and hot water are fixed at 28 and 56 °C, respectively. The design requirement is that the cold water is heated to 43 °C. The heat losses and pressure decreases are ignored. The ambient temperature is 25 °C. The larger the temperature difference, the greater the consumption rate of the cumulative exergy of the hot stream; however, the smaller the heat exchange area, the smaller the depreciation rate of the cumulative exergy of equipment. According to cumulative exergy optimization, the optimal design of the heat exchange process should be conducted using an objective function that is based on the minimum annual cumulative exergy consumption rate of the cold stream. Annual Cumulative Exergy Consumption Rate of the Hot Stream. The hot stream in this system is assumed to come from a co-generation heat and power plant that has an exergetic efficiency of ηe, and the exergetic efficiency of the heat transport is set to ηt. Thus, the cumulative exergy of unit exergy in the hot stream (kh) may be expressed as
kh )
1 ηeηt
(7)
Therefore, the annual cumulative exergy consumption rate of the hot stream (Eh) is
Eh ) hrkh(Exin - Exout)
(8)
where Exin and Exout are the input and output exergy flow rates, respectively; hr is the annual operation time. Annual Cumulative Exergy Contribution of the Heat Exchanger. The weight of the heat exchanger (M) has the following relation with the heat transfer area, A:
M ) d + eAf
(9)
where d, e, and f are constants that are associated with the type and material of the heat exchanger. The annual cumulative exergy contribution of the heat exchanger can be obtained by
Ee )
E T
(10)
where T is the operation life of the heat exchanger and E can be calculated using eq 6. Results and Discussion From the aforementioned considerations, an expression is obtained for the cumulative exergy gained by the
Figure 2. Cumulative exergy consumption rate versus the logarithm of the mean temperature difference (LTMD). Curve 1 represents the total annual cumulative exergy consumption rate, curve 2 represents the annual cumulative exergy consumption rate of the hot stream, and curve 3 represents the annual cumulative exergy depreciation rate of the equipment.
cold stream, which must be minimized:
Ec ) Eh + Ee
(11)
where Eh and Ee are defined in eqs 8 and 10, respectively. The following operating parameters are assumed for the heat exchange process: a ) 12, b ) 4.8, c ) 0.8, d ) 482.35, e ) 40.39, f ) 1, T ) 3 years, ηe ) 0.50,7 ηt ) 0.75,7 and hr ) 7200 h/y. Figure 2 shows the cumulative exergy consumption rate of the cold stream versus the logarithm of the mean temperature difference (LTMD) of the heat exchanger. As illustrated in Figure 2, the almost-linear nature of the increase in the annual cumulative exergy consumption rate of the hot stream (curve 2) reflects the effect of increasing LTMD, and, at the same time, the annual cumulative exergy contribution of equipment (curve 3) descends drastically and then gradually. As a result, the total annual cumulative exergy consumption rate of the cold stream decreases drastically as LTMD increases initially, reaches a minimum, and then escalates. In correspondence to the minimum point are the optimal results where LTMD ) 5.4 °C, Ec ) 1.10 × 109 kJ/y, and A ) 37.7 m2. Herein, the optimum design of a heat exchange process can be achieved using the optimization technique described in this paper, from the standpoint of the conservation of natural resources. People usually take the conventional approach by considering the cost of heat exchangers and the energy cost for heat exchanger design at the same time. For the purpose of comparison, a cost optimization for the same heat exchange process is also performed. The objective of cost optimization is the annual total cost (CT), which can be expressed as follows:
CT )
dAe + hrCII T
(12)
where d and e are the cost constants of heat exchangers,
1198 Energy & Fuels, Vol. 18, No. 4, 2004
Feng et al.
Table 2. Comparison of Optimization Results
item
cumulative exergy optimization
LTMDa (°C) A (m2) objective
5.4 37.7 1.10 × 109 kJ/y
a
cost optimization first second third set set set 4.6 53.0 6754 $/y
3.7 66.4 8411 $/y
7.9 30.8 8591 $/y
Logarithm of the mean temperature difference.
CI is the unit cost of exergy loss for heat exchange, and I is the exergy loss rate of heat exchange. Three sets of cost data are chosen from the literature. For the first set,8 d ) 72 $/m2, e ) 1, and CI ) $1.556 × 10-5 $/kJ; for the second set,9 d/T ) 13.40 $ m-2 a-1, e ) 1, and CI ) 2.22 × 10-5 $/kJ; for the third set,10 d ) 1800 yuan/m2, e ) 0.582, and CI ) 9.5 × 10-6 yuan/kJ. ($ denotes U.S. dollars.) The other conditions are the same as those under cumulative exergy analysis. The cost optimization results can be obtained using eq 12 (see Table 2). The optimization results show that the cost optimization is related to the economic environment, whereas the cumulative exergy optimization reflects the utilization of natural resources. Conclusions In this paper, the cumulative exergy contribution of equipment to processes is emphasized on the basis of cumulative exergy consumption theory. The presented method takes into account the consumption of both energy and nonenergy materials, as well as the cumulative exergy contribution of equipment used in the process. The method can simultaneously consider the cumulative exergy contents of raw materials, energy, equipment, and products. Thus, it is more satisfactory, because it can not only analyze the process energy performance, but also optimize both the process parameters and the size of equipment at the same time. In this paper, the cumulative exergy of a heat exchanger production process is studied by cumulative exergy analysis. The cumulative exergy includes the cumulative exergy of raw materials, the electricity consumption, and the contribution of the equipment used in the production process. Because the production of heat exchangers involves mainly machining processes, the energy consumption is relatively small. As a result, the cumulative exergy of raw materials is the major component of the total value. Because the equipment used is a durable installment, the cumulative exergy contribution of equipment is very small and, (7) Cornelissen, R. L.; Hirs, G. G. Thermodynamic Optimisation of a Heat Exchanger. Int. J. Heat Mass Transfer 1999, 42 (5), 951-960. (8) Aceves-Saborio, S.; Ranasinghe, J.; Reistad, G. M. An Extension to the Irreversibility Minimization Analysis Applied to Heat Exchangers. J. Heat Transfer 1989, 111 (1), 29-36. (9) Zubair, S. M.; Kadaba, P. V.; Evans, R. B. Second-Law-Based Thermoeconomic Optimization of Two-Phase Heat Exchangers. J. Heat Transfer 1987, 109 (2), 287-294. (10) Wang, J.; Zhang, H. Thermoeconomics in Power Engineering (in Chin.); Water Conservancy and Electricity Press: Beijing, 1995.
thus, can be neglected. Furthermore, based on the cumulative exergy consumption theory presented in this paper, a heat exchange process is optimized. This paper presents a guide for determining the cumulative exergy of other process equipment and establishes a basis for the cumulative exergy optimization of process systems. The optimization results reflect the utilization of natural resources, which is different from the cost optimization results. Acknowledgment. The financial support for this research, provided by the National Natural Science Foundation of China (under Grant No. 20176045) and the Major State Basic Research Development Program (under Grant No. G2000026307), is gratefully acknowledged. Notation A ) heat transfer area a, b, c ) constants determined by the type of heat exchanger C ) actual cost of the heat exchanger Cdi ) cost of equipment i CT ) annual total cost d, e, f ) constants associated with the type and material of heat exchanger Ec ) cumulative exergy gained by the cold stream Exin ) input exergy flow rate Exout ) output exergy flow rate Edi ) contribution of cumulative exergy of equipment used to make part i Edoi ) original cumulative exergy of equipment EdTi ) remaining cumulative exergy of equipment at the end of its operation life Ee ) annual cumulative exergy depreciation of the heat exchanger EE ) cumulative exergy of electricity Eh ) annual cumulative exergy consumption rate of hot stream Ei ) cumulative exergy of item i in the system Em ) cumulative exergy of materials E0 ) unit cumulative exergy of materials used Ex ) exergy ExE ) exergy of electricity hr ) annual operation time F ) discard coefficient of materials in the production process kh ) cumulative exergy of unit exergy in the hot stream M ) mass of the heat exchanger RE ) ratio of the quantity of exergy of electricity and the cumulative exergy of electricity T ) operation life of heat exchange process ti ) operation time of the equipment used to make part i Ti ) operation life of the equipment used to make part i ξi ) coefficient when considering equipment transportation, installation, maintenance, and so on ηe ) exergetic efficiency of cogeneration heat and power plant ηt ) exergetic efficiency of the heat transport Subscript D ) equipment E ) energy M ) raw material N ) natural state EF034068M
