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Optimum design of cooling water systems for energy and water conservation
chemical engineering research and design 8 7 ( 2 0 0 9 ) 200–209
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Optimum design of cooling water systems for energy and water conservation M.H. Panjeshahi a,∗ , A. Ataei b , M. Gharaie c , R. Parand c a b c
Department of Chemical Engineering, Tehran University, P.O. Box 11155-4563, Tehran, Iran Department of Energy and Environment, Science and Research Campus, Azad University, P.O. Box 14515-775, Tehran, Iran Department of Mechanical Engineering, K.N. Toosi University of Technology, P.O. Box 1999143344, Tehran, Iran
a b s t r a c t Re-circulating cooling water systems (RCWSs) are widely used to reject waste process heat to the environment, conserve fresh water and reduce thermal pollution relative to once-through systems. Research on RCWS has mostly focused on individual components, cooling tower and heat-exchanger network. Kim and Smith [Kim, J.K. and Smith, R., 2001, Cooling water system design, Chem Eng Sci, 56(12): 3641–3658] developed a grass-root design method of RCWS (KSD). In this paper, the KSD method is expanded and a comprehensive simulation model of RCWS is developed accounting for interaction between cooling tower and heat-exchanger network. Regarding this model, a modern grass-root design method of RCWS, we call it Advanced Pinch Design (APD), based on combined pinch technology and mathematical programming is developed for minimum cost achievement. Having considered cycle water quality through introducing ozone treatment technology, APD methodology is further improved. This technique that we call Enhanced Cooling Water System Design (ECWSD), as the APD supplementary methodology, is provided water and energy conservation, minimum cost and environmental impacts. Related coding in MATLAB version 7.1 is developed for the illustrative example to get optimal values in RCWS design method computations. Finally the results of the introduced grass-root design methodologies, APD and ECWSD, are compared with KSD. Crown Copyright © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. All rights reserved. Keywords: Re-circulating cooling water system; Cooling tower; Pinch technology; Mathematical programming; Ozone treatment; Water-energy conservation
1.
Introduction
Re-circulating cooling water systems (RCWSs) are by far the most common industrial waste process heat rejection systems to the environment. RCWS provides conservational opportunity for water and energy and pollution reduction relative to once-through systems because of water re-use possibility. Previous related works, have been paid attention to issues of cooling water systems individually (Castro et al., 2000; Heikkila and Milosavljevic, 2001), water re-use and waste water minimization (Mann and Liu, 1999), numerical analysis of heat and mass transfer inside a reversibly used water cooling tower (Deng and Tan, 2003) and other operational aspects of cooling tower. Little consideration has been
placed to the interaction between cooling tower and heatexchanger network. To RCWS design, the effect of any possible changes of the system components on the cooling performance should be predicted properly. Therefore, the directly interacted cycle components should be considered simultaneously. Pinch technology as the most common design tools is helped. This technology is based on targeting before design and exploits conceptual understanding. Kim and Smith (2001) represented a grass-root design methodology of RCWS. Kim and Smith Design (KSD) method allowed the existing interactions within the cooling water system to be considered. In the KSD method, the maximum water re-use profile (minimum water flow rate) is participated in the design of the network configuration. Moreover, fix approach
∗
Corresponding author. Tel.: +98 21 88804272; fax: +98 21 88807687. E-mail addresses: [email protected] (M.H. Panjeshahi), [email protected] (A. Ataei), [email protected] (M. Gharaie), [email protected] (R. Parand). Received 15 October 2007; Accepted 6 August 2008 0263-8762/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. All rights reserved.
doi:10.1016/j.cherd.2008.08.004
chemical engineering research and design 8 7 ( 2 0 0 9 ) 200–209
Nomenclature a1 , b, c constant value of mass transfer coefficient A approach (◦ C) A0 , B0 , C0 constant value of vapor pressure APD advanced pinch design B blow-down (t/h) CP water heat capacity (MJ/t ◦ C) air heat capacity (MJ/t ◦ C) Cpa CC capital cost (k$/yr) dA differential of cooling tower area (m2 ) D drift loss (t/h) E evaporation loss (t/h) ECWSD enhanced cooling water system design Fair air flow rate (t/h) cooling system inlet water flow rate (t/h) Fin l cooling tower inlet water flow rate lower limit Fin (t/h) u Fin cooling tower inlet water flow rate upper limit (t/h) F1 outlet water flow rate of cooling tower (t/h) inlet water flow rate to cooling tower (t/h) F2 h pumping head (m) ha air enthalpy (kJ/t) convective heat transfer coefficient (kW/m2 ◦ C) hd hw water enthalpy (kJ/t) mass transfer coefficient of air (m/s) KG KSD Kim & Smith design ma air flow rate at control volume water flow rate at control volume mw M make-up (t/h) Mi initial make-up (t/h) OC operation cost (k$/yr) P total pressure (bar) PP pumping power (hp) Ps vapor pressure (bar) Q overall enthalpy (MJ/t) QACT actual heat removal (MJ) Qc enthalpy associated with convective transfer (MJ/t) QHEN overall network heat duty (MJ) enthalpy associated with mass transfer (MJ/t) Qm Qmax maximum heat removal (MJ) heat load at pinch point (MJ) QiPinch R range (◦ C) TC total cost (k$/yr) Ta air temperature (◦ C) Tamb ambient temperature (◦ C) THENmin minimum network temperature (◦ C) Tin cooling tower inlet water temperature (◦ C) minimum temperature approach of network Tmin (◦ C) TMA minimum approach (◦ C) minimum temperature with respect to Tmin of TMN the network (◦ C) TMR temperature of max. water re-use at network (◦ C) temperature at which no re-use at network (◦ C) TNR cooling tower outlet water temperature (◦ C) Tout TTL temperature limitation (◦ C) Tw water temperature (◦ C) wet bulb temperature (◦ C) TWB
TiPinch Vi wair wga(WBT) win wout wsat(WBT) XB Xm Z
201
temperature at pinch point (◦ C) water volume (m3 ) air humidity ratio (kgw/kga) air humidity at wet bulb temperature (kgw/kga) inlet air humidity (kgw/kga) interface humidity ratio (kgw/kga) saturated humidity at wet bulb temperature (kgw/kga) concentration in blow-down concentration in make-up cooling tower height (m)
Greek letters P pump efficiency C cycle of concentration initial cycle of concentration Ci Cii new cycle of concentration water density (kg/m3 ) water
value is considered in design procedure. However the minimum cooling water flow rate through the fix approach value does not necessarily ensure optimum value and the minimum cost of the cooling system. In the present paper, the grass-root design methodology introduced by Kim and Smith (2001) (KSD) is expanded. The pinch technology in water system design is improved through principle concepts to make opportunities for energy saving. A new systematic approach for the optimum design of cooling water systems, Advanced Pinch Design (APD) method, is developed. The presented grass-root design method allowed interaction between the cooling tower performance and heat-exchanger network configuration to be considered simultaneously. Also, the influence of any probable changes of RCWS components on the whole cooling cycle is taken into consideration. To achieve the above objectives, the cooling tower and the cooling water network are studied separately. Furthermore, a model of cooling water systems is developed to examine the cooling performance and efficiency to re-circulation flow rate and return temperature. Finally, the design of the overall cooling water system is developed by investigating the interactions and process constraints. The APD methodology allowed optimal heat-exchanger network, accessible water and energy conservation to be achieved. Having considered cycle water quality by introducing ozone treatment technology, APD is further improved. This grassroot design technique, we call it Enhanced Cooling Water System Design (ECWSD), as the supplementary methodology of APD, is accomplished maximum water and energy conservation, minimum cost and environmental impacts.
2. Cooling tower and heat-exchanger network interaction Conventional cooling water network design utilizes parallel configuration (Fig. 1) (Kim and Smith, 2001). In parallel configuration, fresh cooling water is supplied to individual heat-exchanger directly. The hot cooling water returns the cooling tower afterward. Mixing water from individual heat-exchanger decreases inlet water temperature and increases inlet water flow rate of
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Fig. 1 – Parallel configuration of cooling water network. cooling tower. It is noted that high flow rate and low temperature of inlet cooling water leads to poor cooling performance because it decreases the driving force (Smith, 2005). Furthermore, parallel arrangement, as the traditional design configuration cannot support when dealing with various processes. In addition, all cooling duties do not require cooling water at cooling water supply temperature. This allows changing configuration from parallel to series arrangement. Series arrangements provides water re-use opportunity that not only leads to water conservation, but also makes water with higher temperature and lower flow rate affordable for return; result in minimum cost achievement.
3.
Mathematical modeling of RCWS
To examine the interactions within the cooling system, RCWS modeling is developed. The model is included of the system components. In the presented model, counter-flow wet cooling tower with mechanical air draft is assumed. The model is to predict the conditions of the exit water and the air from the tower for given design and operating conditions. The energy and mass balances on the system are given by (Fig. 2) (Castro et al., 2000):
for the control volume is given by (Kröger, 2004):
ma (1 + w) + mw +
(1)
F0 T0 = (F1 − B)T1 + MTM
(2)
The overall heat load of the cooling water network is written as (3)
dmw dw dz =ma 1 + w + dz + mw dz dz
dw = KG (wout − wair ) dz
(5)
That KG is the mass transfer coefficient of air. Several experimental measurements on heat and mass transfer coefficient in cooling towers have been done and for air–water systems. The result is represented as a function of air and water flow rate (Coulson and Richardson, 1996): KG = a1 mba mcw
(6)
where wair is the humidity ratio of air and wout is the humidity ratio of interface.
wair =
Ps P − Ps
(7)
E wout − win
win = −
(8)
CPa [T − TWB ] + wsat(WBT) wga(WBT) amb
(9)
where wga(T) is defined as (Mann and Liu, 1999): wga(T) = 2501.3 + 1.82T
Consider an elementary control volume in the fill or packing of a counter-flow wet cooling tower (Fig. 3), a mass balance
(4)
Humidity ratio change along the cooling tower height is given by
wout = 0.622
F0 = F1 − B + M
QHEN = F2 CP (T2 − T0 )
Fig. 3 – Cooling towe control volume.
(10)
It is assumed that the air leaves the tower at the saturated condition. The saturated pressure as per the Antoine equation is given by (Smith, 2005): ln Ps = A0 −
B0 T + C0
(11)
Coefficients for above equation are presented as following (Kim and Smith, 2001): For 0 ◦ C < T < 57 ◦ C, A = 23.7093, B = 4111, C = 237.7An energy balance on control volume is written as
ma ha + mw +
Fig. 2 – Cooling system model.
= ma ha +
dmw dTw dz CP Tw + dz dz dz
dha dz + mw CP Tw dz
(12)
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Table 1 – Verification of cooling tower model 1
2
3
4
Experimental data Air flow rate (t/h) Water flow rate (t/h) Water inlet temperature (◦ C) Water outlet temperature (◦ C) Make-up flow rate (t/h) Blow-down flow rate (t/h)
2.41 0.72 36.70 19.80 0.042 0.0263
2.361 1.08 32 20.40 0.050 0.0207
2.39 1.43 29.30 20.70 0.040 0.0250
2.368 1.782 27.90 20.80 0.047 0.0197
Model output data Dry air flow rate (t/h) Blow-down rate (t/h) Make-up rate (t/h) Evaporation rate (t/h) Pumping power (kW) Heat rejection (mm W) Exit air temperature (◦ C) Water outlet temperature (◦ C) Effectiveness (%) Make-up error (%) Blow-down error (%) Temperature error (%)
2.48 0.0224 0.045 0.0224 0.0284 0.0143 17.59 19.81 63 0.06 0.15 0.05
2.40 0.0225 0.045 0.0225 0.0426 0.0140 18.00 20.44 52 −0.10 −0.08 0.19
2.42 0.0222 0.045 0.0222 0.0565 0.0125 17.83 20.66 30 0.11 0.11 −0.19
2.37 0.0225 0.045 0.2258 0.0703 0.0116 18.15 20.82 26 −0.04 −0.12 0.09
The bold values signify the model output data.
By neglecting second order terms of Eq. (12): mw CP
dTw dmw dha + CP Tw = ma dz dz dz
(13)
By substituting above equations: dTw ma = dz mw
1 dh a CP dz
− Tw
dw dz
(14)
The total enthalpy transfer at the air–water interface consists of an enthalpy transfer associated with the mass transfer due to the difference in vapor concentration and the heat transfer due to the difference in temperature (Kröger, 2004): dQ = dQm + dQC
(15)
The enthalpy transfer associated with the mass transfer is expressed by dQm = hw
dmw dz = hw hd (hw − w)dA dz
(16)
The convective transfer of sensible heat at the interface is given by dQC = hd (Tw − Ta )dA
(17)
The cooling tower water outlet temperature, flow rate and evaporation are all function of tower air flow rate, wet bulb temperature and inlet water temperature. The effect of each parameter, temperature difference along cooling tower (R) and flow rate (Fin ), should be extensively examined to achieve the optimum point. The result of the cooling tower modeling illustrated that decreasing the flow rate of cooling tower has a more significant effect on the effectiveness than decreasing the inlet temperature. To verify the proposed model, the simulation results are compared with the experimental data, which are obtained through a pilot plant cooling tower (Table 1). The results demonstrates that when cooling water inlet conditions are high temperature and low flow rate, the cooling tower effectiveness increases which means more heat removal of cooling tower. Verification result shows that the cooling tower model, which will be used for the design of cooling water system, is accurate enough to evaluate the cooling tower performance and predict the effectiveness of cooling tower.
4.
Optimum design of cooling water system
Traditional network design is parallel configuration. The best optimal design of the RCWS is based on providing water re-use opportunity. The optimum cooling water system through APD
Water temperature along the cooling tower height is expressed as dTw ma 1 dha = dz mw CP dz
(18)
The cooling tower effectiveness (e) is defined as the ratio of actual heat removal to the maximum achievable heat removal. High effectiveness of cooling tower represents efficient cooling performance and high heat removal. Effectiveness is given as below expression: e=
Qact Qmax
(19)
Fig. 4 – Effect of water flow rate on cooling cost.
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Fig. 5 – Cooling water composite curve and targeting for maximum re-use. method is carried out in three stages. The first step is to define the feasible region from the cooling composite curve taking into consideration the system constraints. The second step is to explore the feasible region to target the cooling water supply line. The final stage is to design the cooling water network for target conditions with pinch migration concept through water main synthesis method. The APD is based on a superior algorithm derived from combination of pinch analysis and mathematical programming. The minimum cost is obtained from the presented grass-root design procedure.
4.1.
Objective function
In grass-root design targeting the objective is to minimize total annual cost (Prasad, 2004). The total cost of cooling tower includes operation and capital cost (Kim et al., 2001). Capital cost of cooling tower is: CC = 746.749(Fin )
0.79
0.57
(R)
(A)
−0.9924
+ (0.022TWB + 0.39)
2.447
(20) where Fin is the cooling tower water flow rate, A is the cooling tower approach value, R is the cooling tower range and TWB is the wet bulb temperature. Operating cost of cooling tower :
4.2.
To establish the model constraints, first cooling water composite curve should be drawn. Cooling water streams depends on heat load and temperatures are graphed and all the cold streams are then summed up to figure out the composite curve. Fig. 5 shows the procedure for composite curve graph and targeting for maximum re-use of water flow rate. The cooling water supply line is shown for maximum re-use of water, which means the possible series configuration of heatexchangers (Smith, 2005). In conventional cooling water system design, the objective is to minimize the water flow rate. However, minimum flow rate does not necessarily guarantee the optimality. The point where the target supply line touches the composite curve creates a pinch point. It is noted that the interpretation of the pinch does not imply zero driving force of heat transfer, but minimum driving force. Fig. 6, illustrates the schematic of model constraints and the feasible region for targeting the water supply of a re-circulating cooling system. The cooling water network performance can be changed within a feasible region. As shown in Fig. 6, the feasible area is a region, limited with the minimum water flow rate (maximum water re-use profile) and maximum water flow rate (no re-use profile). The air flow rate is expressed as (Deng and Tan, 2003):
pumping cost + fan cost + make-up cost + chemical treatment cost + blow-down treatment cost; OC = 2.4094 × 10−3 (PP) + 44(Fair ) + 110(Fin ) + 2275.132(M) + 1138(B)
(21)
where PP is the pumping power, Fair is the tower air flow rate, M is the make-up flow rate and B is the blow-down flow rate. Finally, the objective function is defined as total annual cost. The optimization problem can be stated as follow: Min TC = CC + OC
Model constraints
Fair =
E wout − win
where inlet and outlet humidity ratio are both function of temperature. win = f (TWB , Tamb )
(22)
The operating cost and the capital cost of the cooling tower have different effects on the overall cost of cooling. Therefore, the problem becomes an optimization problem to search for the optimal cooling tower. In other words, by increasing water flow rate in cooling water system, the capital cost decreases and the operational cost increases. Fig. 4 shows the effect of water flow rate on the cooling tower cost.
(23)
Fig. 6 – Temperature feasible region.
(24)
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Table 2 – Hot process stream data Thot,in (◦ C)
Condition Conventional Max-re-use KSD APD
wout = f
Tcold,out (◦ C)
40.46 50 45 49
CP (kW/◦ C)
30 20 30 25.2
T + T out in
286.67 100 200 126
Evaporation rate is a function of water flow rate and temperature difference of cooling tower (Kim et al., 2001). E = 0.00153(Fin )(R)
e (%)
246.89 86.12 172.24 108.51
41 85 50 70
Feasibility constraints to avoid pinch crossing;
(25)
2
F (t/h)
Tout + R
QiPinch Q
≤ TiPinch
(33)
Feasibility constraints on the cooling water flow rate;
(26)
l u Fin ≤ Fin ≤ Fin
Heat load of cooling system: QHEN = Fin CP (Tin − Tout )
(27)
Range definition: R = Tin − Tout
(28)
Approach definition:
l and Fu are the upper and lower limit of the water where Fin in flow rate which are expressed at water temperature feasibility area that are obtained from the total heat rejection of cooling tower. Note that the amount of heat absorbed by the heatexchanger network is rejected through the cooling tower. Pumping power is a function of water flow rate.
PP =
A = Tout − TWB
(29)
The cooling water system cannot operate beyond a specific return cooling water temperature because the hot return cooling water temperature might cause fouling problems, corrosion or problems with the cooling tower packing. Therefore, it is common practice to introduce temperature constraints for return cooling water to the tower. Feasibility constraints on the inlet and outlet temperature of cooling tower: TNR ≤ Tin ≤ Min{TMR , TTL }
(34)
Fin hwater P
(35)
where h is the pumping head, water is the water density and P is the pump efficiency. Blow-down and make-up as a function of evaporation rate are carried out as B=
E C − 1
M=E
(36)
C C − 1
(37)
(30)
The water outlet temperature from the cooling tower varies between the minimum approach value considering wet bulb temperature and minimum temperature of water stream at heat-exchanger network: (TWB + TMA ) ≤ Tout ≤ TMN
The optimum performance parameters are achieved through applying the introduced optimization model taking into consideration the minimum cost achievement. An illustrative example is applied to develop the APD technique for cooling water network. The computations of the optimization model are done in MATLAB version 7.1.
(31)
4.3. where TMN is the minimum temperature of heat exchange network with respect to Tmin of the network and TMA is the minimum cooling tower approach. TMN = THENmin − Tmin
(32)
It is noted that to define the upper inlet temperature boundary, minimum value between TMR and TTL (temperature limitation), that is dictated by the tower packing type, is determined. It is emphasized that the optimum water supply conditions do not violate the cooling tower temperature limitations.
Illustrative example I—advanced pinch design
The cooling water system in example I has four heat exchangers using cooling water as cooling medium for hot process streams. The temperature, flow rate and cooling duty of hot process streams are given in Table 2. The following data are used for the example I. Wet bulb temperature: 15 ◦ C; ambient temperature: 25 ◦ C; minimum approach: 5 ◦ C; pump efficiency: 60%; pumping head: 10.67 m; cycle of concentration: 2; operating hours: 8600 h/yr; interest rate: 15%; payback period: 3 yr; minimum temperature difference (Tmin ): 10 ◦ C; temperature limitation: 57 ◦ C.
Table 3 – Performance parameters of conventional, KSD and APD methods Heat exchanger 1 2 3 4
Thot,in (◦ C) 50 45 55 65
Thot,out (◦ C) 40 40 50 55
CP (kW/◦ C) 100 100 200 50
Q (kW) 1000 500 1000 500
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Table 4 – Cost comparisons of various designs in (k$/yr) Design method Conventional KSD APD
OC
CC
TC
65.90 53.66 44.07
6.54 6.04 8.03
72.44 59.70 52.10
Fig. 8 – Cooling water main method for cooling water network design.
Fig. 7 – Pinch migration. The optimization results are given in Table 3. Optimization results are indicated that the optimum water supply flow rate is 108.51 t/h. The cooling water enters the tower with temperature of 49 ◦ C and leaves the tower with temperature of 25.2 ◦ C. The evaporation is constant because the heat rejection is constant. Therefore, the make-up and blow-down for KSD and APD methodologies are constant as per Eqs. (36) and (37). Table 4 shows the cost comparison of various design methods. The optimization results show that the operational cost including fan cost, pumping cost, make-up water cost, water chemical and blow-down treatment cost is 44.07 k$/yr and capital cost for cooling tower is 8.03 k$/yr which makes total cost of 52.10 k$/yr achievable. If the cooling water supply line does not correspond with minimum flow rate (either because of system interactions or temperature constraints), then a pinch point is not created with the limiting cooling water composite curve. Therefore, the cooling water composite curve needs to be modified to make a pinch point with the desired cooling water supplyline in the feasible region. Therefore, the cooling water network problem would be changed into a problem with a pinch (Smith, 2005). Pinch migration is introduced here to convert problems without a pinch into those with a pinch with the desired supply line. Fig. 7 shows the pinch migration of cooling water composite curve. Optimal heat-exchanger arrangement is then achieved through an advanced synthesis algorithm using water pinch technology (Smith, 2005). The synthesis algorithm by set-
ting up the water mains at water supply temperature, pinch points temperatures and exit temperature (Fig. 8) was used for developing an optimal heat-exchangers network configuration (Fig. 9) (Mann and Liu, 1999). This synthesis algorithm was based on composite curve decomposition and water main method. The water main method of Kuo and Smith (1997) for the design of water re-use networks can be extended to the design of cooling water networks. The original method identified water re-use opportunities for problems in which re-use was constrained by concentration limits. This method was carried out in four steps. The first step was to generate a grid diagram with cooling water mains and plot the cooling water using operations as shown in Fig. 8. The second stage was to connect the operations with cooling water mains. The third stage was to merge operations that cross mains. The final stage was to remove intermediate (pinch) cooling water mains. Following the method allows the design of the cooling water network to achieve the target predicted by the supply line. Details of the procedure are given by Kuo and Smith (1997) and are readily adapted from the concentration constraints in the original paper to the temperature constraints that are a feature of the cooling water network design problem. In order to achieve an optimum water supply line in the feasible region, using a limiting profile, which is defined from either Pinch point or cooling tower temperature limitation, was considered as the guide that represents the boundary between feasible and infeasible operation. The optimum design construction and optimum heat-exchanger configuration were then accomplished considering the maximum water re-use profile and water pinch synthesis (Fig. 9). The KSD configuration is presented in Fig. 10. As shown in Fig. 9, optimum configuration achieved through APD methodology is provided more series arrangement opportunity in comparison with KSD method (Fig. 10).
Fig. 9 – Optimum heat-exchanger configuration of APD method.
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ble methods for the use of make-up water. Magnetic and electro-magnetic, electrostatic, electrolysis, ozonation and hydrodynamic cavitations are some of these non-chemical treatments.
5.2.
Ozone water treatment
Fig. 10 – Heat-exchanger configuration of KSD. The conventional design (parallel configuration) does not make opportunity for water re-use. Therefore, parallel configuration cannot provide water conservation. The APD methodology is then improved through a procedure to maximize water and energy conservation. A new design method, ECWSD, is developed. In other words, the APD method is then improved taking into consideration the environmental features.
5. Environmental improvement of RCWS design 5.1.
Water quality
In RCWS, the quality of the cooling water and make-up needs to be considered not only for achieving better optimal values, but also for reducing the negative environmental impacts. In a cooling system, eventually, the minerals reach a cycle of concentration that will cause loss of efficiency due to scale formation or damage due to excessive corrosion. To conserve water and treatment chemicals, it is desirable to allow the dissolved minerals to reach a maximum cycle of concentration. The cycle of concentration (C ) is defined as the concentration ratio of a soluble component in the blow-down to that in the make-up stream (Heikkila and Milosavljevic, 2001). C =
XB M = XM B+D
(38)
The concentration of contaminants should be managed to control biological growth, corrosion and scale build-up. The maximum cycle of concentration will depend on the quality of make-up water (Parker, 1998). Chemical, physical and biological treatment processes are used to improve the make-up water quality to solve the problems related to cooling water treatment such as scale formation, corrosion and bacterial growth. Of all the methods, non-chemical treatment methods could be considered as safe and environmentally responsi-
Ozone (O3 ) has been recognized for nearly a century for its powerful ability to disinfect water. Cooling tower water must be treated to limit the growth of mineral and microbial deposits that can reduce the heat transfer efficiency of the cooling tower. The conditions in cooling towers can promote the growth of Legionella, which can exist in low concentrations in most water supply systems. By integrating ozone treatment, the levels of bacterial and mineral substances in the waters discharged through blow-down decreases (Gharaie, 2007). Fig. 11 shows a cooling tower integrated ozone water treatment unit (Parker, 1998). Integration of ozone water treatment with the RCWS increases the cycle of concentration, which decreases the concentration of insoluble components in circulating water (Viera et al., 2000). It reduces the blow-down dramatically that, in turn is environmentally constructive. Cooling water systems can be considered as energy conservation resources opportunities (Alsheyab and Munoz, 2007). For maximizing water and energy conservation, ozone treatment should be integrated in to the cooling tower. This also manages drastic environmental friendly implications. The effect of ozone treatment integration on cooling system and ECWSD method is studied through the illustrative example II.
5.3. Illustrative example—enhanced cooling water system design The hot process stream data are as given in Table 2. The design data are the same as given in example I. It is noted that integrating ozone treatment increases cycle of concentration up to 15. Theoretically, as per below equation, we predict 46% water saving in cooling system. V = Mi
Ci − Cii Ci (Cii − 1)
(39)
To achieve optimum performance parameters of cooling system, cooling tower total annual cost function is solved for minimum value. To attain optimum performance parameters
Fig. 11 – Ozone treatment of cooling tower water.
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Table 5 – Performance parameters of various design methods Condition Conventional KSD APD ECWSD
Thot,in (◦ C)
Tcold,out (◦ C)
40.46 45 49 48.35
30 30 25.2 28.22
CP (kW/◦ C) 286.67 200 126 149
F (t/h)
e (%)
246.89 172.24 108.51 128.32
41 50 70 60
Fig. 12 – Optimum heat-exchanger configuration of ECWSD.
Table 6 – Cost comparison of various design methods in (k$/yr) Design method Conventional KSD APD ECWSD
OC
CC
TC
65.90 53.66 44.07 20.20
6.54 6.04 8.03 19.55
72.44 59.70 52.10 39.75
through the cooling water supply line, feasible region is explored for minimum cost. The objective total cost function of the integrated cooling system is included of operational and capital cost. Cost function is expressed as: Operating cost of ECWSD
Fig. 13 – Cost comparison of variouse design methods.
Ozone capital cost = 24.43(Fin ) + 104
(40)
mum total cost achievable in comparison to the other design methods. Table 7 shows water and energy saving in various design methods, KSD, APD and ECWSD. As shown in Table 7, APD and ECWSD methods are resulted in 22% and 17% energy saving relative to KSD method, respectively. The amount of makeup water saved through ECWSD is 46% that is the same as predicted through Eq. (39) theoretically. By integrating ozone treatment into the cooling water system, the capital cost increases. On the other hand the operational cost decreases. The cost analysis shows that the aggregated total cost is accomplished the minimum value (Fig. 13).
Ozone electricity cost = 1.169(Fin )
(41)
6.
= fan cost + pumping cost + blow-down treatment cost + make-up water cost + ozone water treatment cost Capital cost of ECWSD = cooling tower cost + ozone water treatment capital cost Ozone treatment operational cost is consisted of ozone electricity cost $/yr and conversion factor. Capital cost of ozone water treatment is a function of water flow rate:
Table 5 shows optimum performance parameters, water flow rate and temperature, of cooling water system that are achieved through the ECWSD method. Fig. 12 shows the optimal heat-exchanger network configuration that is achieved through the advanced synthesis algorithm and water main concepts. The cost comparison of various design methodologies are presented in Table 6. It reveals that the ECWSD made mini-
Discussion and conclusions
Conventional design of RCWS is often carried out in parallel configuration. This loses opportunity for water re-use. However, re-use of cooling water between different cooling duties enables cooling water networks to be designed with series arrangements. This allows better cooling tower performance and increased cooling tower capacity. In this study a mathematical model of cooling systems has been developed to predict the tower performance and to provide design
Table 7 – Make-up, blow-down water and energy saving of various design methods Design method KSD APD ECWSD
Make-up (t/h) 7.90 7.90 4.23
Blow-down (t/h) 3.95 3.95 0.28
Energy (kW) 13 10.05 10.63
Make-up saving (%) – – 46
Blow-down saving (%) – – 93
Energy saving (%) – 22 17
chemical engineering research and design 8 7 ( 2 0 0 9 ) 200–209
guidelines for RCWS design. The optimum design of RCWS with possible series arrangement is achieved through a new grass-root design methodology, APD. The design is carried out with any target temperature by improving the concepts of pinch technology in water systems and applying mathematical programming. The interactions within the cooling system are considered in the presented design method, APD, simultaneously. Furthermore, having considered the water quality, the ADP method is improved to increase water and energy conservation opportunity. This new method, ECWSD, provides water and energy conservation, reduces negative environmental impacts and achieves the minimum cost. Results on the presented illustrative example show that the design total cost achieved through APD is 52.10 k$/yr. The ECWSD makes total cost of 39.75 k$/yr achievable relative to the KSD total cost of 59.70 and 72.44 k$/yr for conventional design. Relative programming in MATLAB version 7.1 has been developed to get the optimization results. The results have indicated that a four stream illustrative case caused 46 percent of make-up saving, 93 percent of blow-down water saving and 17 percent of energy conservation relative to the KSD method. Therefore, applying ECWSD methodology to industrial large-scale problems can provide greater water and energy conservational opportunity.
References Alsheyab, M.A.T. and Munoz, A.H., 2007, Optimization of ozone production for water and waste water treatment. Desalination, 217(1): 1–7. Castro, M.M., Pinto, J.M. and Song, T.W., 2000, Operational cost minimization in cooling water system. Braz J Chem Eng, 17(4): 4–7.
209
Coulson, J.M. and Richardson, J.F., (1996). Chemical Engineering: Fluid Flow, Heat Transfer and Mass Transfer (5th ed.). (Pergamon Press, Oxford). Deng, S. and Tan, K., 2003, A numerical analysis of heat and mass transfer inside a reversibly used water cooling tower. Build Environ, 38(1): 91–97. Gharaie M., 2007, Performance modeling and optimization of wet cooling tower parameters to minimize the exergy loss, MSc Thesis, K.N. Toosi University of Technology. Heikkila, P. and Milosavljevic, N., 2001, A comprehensive approach to cooling tower design. Appl Therm Eng, 21(9): 899–915. Kim, J.K. and Smith, R., 2001, Cooling water system design. Chem Eng Sci, 56(12): 3641–3658. Kim, K., Savulescu, L. and Smith, R., 2001, Design of cooling systems for effluent temperature reduction. Chem Eng Sci, 56(5): 1811–1830. Kröger, D.G., (2004). Air-cooled Heat Exchangers and Cooling Towers: Mass Transfer and Evaporative Cooling. (Penn Well Corporation, OK, USA), pp. 223–328 Kuo, W.J. and Smith, R., 1997, Effluent treatment system design. Chem Eng Sci, 52(23): 4273–4290. MATLAB software, version 7.1. Mann, J. and Liu, Y.A., (1999). Industrial Water Reuse and Waste Water Minimization. (McGraw-Hill, New York, USA). Parker, S.A., 1998, Ozone Treatment for Cooling Tower, The U.S. Department of Energy, Fed Tech Alert J, New York. Prasad, M., 2004, Economic up gradation and optimal use of multi-cell cross flow evaporative water cooling tower through modular performance. Appl Therm Eng, 24(4): 579–593. Smith, R., (2005). Chemical Process Design. (John Wiley & Sons, England), pp. 513–526 Viera, M.R., Guiamet, P.S., de Melle, M.F.L. and Videla, H.A., 2000, Use of dissolved ozone for controlling planktonic and sessile bacteria in industrial cooling systems. Int Biodeter Biodeg, 44(4): 201–207.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Optimum design of cooling water systems for energy and water conservation M.H. Panjeshahi a,∗ , A. Ataei b , M. Gharaie c , R. Parand c a b c
Department of Chemical Engineering, Tehran University, P.O. Box 11155-4563, Tehran, Iran Department of Energy and Environment, Science and Research Campus, Azad University, P.O. Box 14515-775, Tehran, Iran Department of Mechanical Engineering, K.N. Toosi University of Technology, P.O. Box 1999143344, Tehran, Iran
a b s t r a c t Re-circulating cooling water systems (RCWSs) are widely used to reject waste process heat to the environment, conserve fresh water and reduce thermal pollution relative to once-through systems. Research on RCWS has mostly focused on individual components, cooling tower and heat-exchanger network. Kim and Smith [Kim, J.K. and Smith, R., 2001, Cooling water system design, Chem Eng Sci, 56(12): 3641–3658] developed a grass-root design method of RCWS (KSD). In this paper, the KSD method is expanded and a comprehensive simulation model of RCWS is developed accounting for interaction between cooling tower and heat-exchanger network. Regarding this model, a modern grass-root design method of RCWS, we call it Advanced Pinch Design (APD), based on combined pinch technology and mathematical programming is developed for minimum cost achievement. Having considered cycle water quality through introducing ozone treatment technology, APD methodology is further improved. This technique that we call Enhanced Cooling Water System Design (ECWSD), as the APD supplementary methodology, is provided water and energy conservation, minimum cost and environmental impacts. Related coding in MATLAB version 7.1 is developed for the illustrative example to get optimal values in RCWS design method computations. Finally the results of the introduced grass-root design methodologies, APD and ECWSD, are compared with KSD. Crown Copyright © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. All rights reserved. Keywords: Re-circulating cooling water system; Cooling tower; Pinch technology; Mathematical programming; Ozone treatment; Water-energy conservation
1.
Introduction
Re-circulating cooling water systems (RCWSs) are by far the most common industrial waste process heat rejection systems to the environment. RCWS provides conservational opportunity for water and energy and pollution reduction relative to once-through systems because of water re-use possibility. Previous related works, have been paid attention to issues of cooling water systems individually (Castro et al., 2000; Heikkila and Milosavljevic, 2001), water re-use and waste water minimization (Mann and Liu, 1999), numerical analysis of heat and mass transfer inside a reversibly used water cooling tower (Deng and Tan, 2003) and other operational aspects of cooling tower. Little consideration has been
placed to the interaction between cooling tower and heatexchanger network. To RCWS design, the effect of any possible changes of the system components on the cooling performance should be predicted properly. Therefore, the directly interacted cycle components should be considered simultaneously. Pinch technology as the most common design tools is helped. This technology is based on targeting before design and exploits conceptual understanding. Kim and Smith (2001) represented a grass-root design methodology of RCWS. Kim and Smith Design (KSD) method allowed the existing interactions within the cooling water system to be considered. In the KSD method, the maximum water re-use profile (minimum water flow rate) is participated in the design of the network configuration. Moreover, fix approach
∗
Corresponding author. Tel.: +98 21 88804272; fax: +98 21 88807687. E-mail addresses: [email protected] (M.H. Panjeshahi), [email protected] (A. Ataei), [email protected] (M. Gharaie), [email protected] (R. Parand). Received 15 October 2007; Accepted 6 August 2008 0263-8762/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. All rights reserved.
doi:10.1016/j.cherd.2008.08.004
chemical engineering research and design 8 7 ( 2 0 0 9 ) 200–209
Nomenclature a1 , b, c constant value of mass transfer coefficient A approach (◦ C) A0 , B0 , C0 constant value of vapor pressure APD advanced pinch design B blow-down (t/h) CP water heat capacity (MJ/t ◦ C) air heat capacity (MJ/t ◦ C) Cpa CC capital cost (k$/yr) dA differential of cooling tower area (m2 ) D drift loss (t/h) E evaporation loss (t/h) ECWSD enhanced cooling water system design Fair air flow rate (t/h) cooling system inlet water flow rate (t/h) Fin l cooling tower inlet water flow rate lower limit Fin (t/h) u Fin cooling tower inlet water flow rate upper limit (t/h) F1 outlet water flow rate of cooling tower (t/h) inlet water flow rate to cooling tower (t/h) F2 h pumping head (m) ha air enthalpy (kJ/t) convective heat transfer coefficient (kW/m2 ◦ C) hd hw water enthalpy (kJ/t) mass transfer coefficient of air (m/s) KG KSD Kim & Smith design ma air flow rate at control volume water flow rate at control volume mw M make-up (t/h) Mi initial make-up (t/h) OC operation cost (k$/yr) P total pressure (bar) PP pumping power (hp) Ps vapor pressure (bar) Q overall enthalpy (MJ/t) QACT actual heat removal (MJ) Qc enthalpy associated with convective transfer (MJ/t) QHEN overall network heat duty (MJ) enthalpy associated with mass transfer (MJ/t) Qm Qmax maximum heat removal (MJ) heat load at pinch point (MJ) QiPinch R range (◦ C) TC total cost (k$/yr) Ta air temperature (◦ C) Tamb ambient temperature (◦ C) THENmin minimum network temperature (◦ C) Tin cooling tower inlet water temperature (◦ C) minimum temperature approach of network Tmin (◦ C) TMA minimum approach (◦ C) minimum temperature with respect to Tmin of TMN the network (◦ C) TMR temperature of max. water re-use at network (◦ C) temperature at which no re-use at network (◦ C) TNR cooling tower outlet water temperature (◦ C) Tout TTL temperature limitation (◦ C) Tw water temperature (◦ C) wet bulb temperature (◦ C) TWB
TiPinch Vi wair wga(WBT) win wout wsat(WBT) XB Xm Z
201
temperature at pinch point (◦ C) water volume (m3 ) air humidity ratio (kgw/kga) air humidity at wet bulb temperature (kgw/kga) inlet air humidity (kgw/kga) interface humidity ratio (kgw/kga) saturated humidity at wet bulb temperature (kgw/kga) concentration in blow-down concentration in make-up cooling tower height (m)
Greek letters P pump efficiency C cycle of concentration initial cycle of concentration Ci Cii new cycle of concentration water density (kg/m3 ) water
value is considered in design procedure. However the minimum cooling water flow rate through the fix approach value does not necessarily ensure optimum value and the minimum cost of the cooling system. In the present paper, the grass-root design methodology introduced by Kim and Smith (2001) (KSD) is expanded. The pinch technology in water system design is improved through principle concepts to make opportunities for energy saving. A new systematic approach for the optimum design of cooling water systems, Advanced Pinch Design (APD) method, is developed. The presented grass-root design method allowed interaction between the cooling tower performance and heat-exchanger network configuration to be considered simultaneously. Also, the influence of any probable changes of RCWS components on the whole cooling cycle is taken into consideration. To achieve the above objectives, the cooling tower and the cooling water network are studied separately. Furthermore, a model of cooling water systems is developed to examine the cooling performance and efficiency to re-circulation flow rate and return temperature. Finally, the design of the overall cooling water system is developed by investigating the interactions and process constraints. The APD methodology allowed optimal heat-exchanger network, accessible water and energy conservation to be achieved. Having considered cycle water quality by introducing ozone treatment technology, APD is further improved. This grassroot design technique, we call it Enhanced Cooling Water System Design (ECWSD), as the supplementary methodology of APD, is accomplished maximum water and energy conservation, minimum cost and environmental impacts.
2. Cooling tower and heat-exchanger network interaction Conventional cooling water network design utilizes parallel configuration (Fig. 1) (Kim and Smith, 2001). In parallel configuration, fresh cooling water is supplied to individual heat-exchanger directly. The hot cooling water returns the cooling tower afterward. Mixing water from individual heat-exchanger decreases inlet water temperature and increases inlet water flow rate of
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Fig. 1 – Parallel configuration of cooling water network. cooling tower. It is noted that high flow rate and low temperature of inlet cooling water leads to poor cooling performance because it decreases the driving force (Smith, 2005). Furthermore, parallel arrangement, as the traditional design configuration cannot support when dealing with various processes. In addition, all cooling duties do not require cooling water at cooling water supply temperature. This allows changing configuration from parallel to series arrangement. Series arrangements provides water re-use opportunity that not only leads to water conservation, but also makes water with higher temperature and lower flow rate affordable for return; result in minimum cost achievement.
3.
Mathematical modeling of RCWS
To examine the interactions within the cooling system, RCWS modeling is developed. The model is included of the system components. In the presented model, counter-flow wet cooling tower with mechanical air draft is assumed. The model is to predict the conditions of the exit water and the air from the tower for given design and operating conditions. The energy and mass balances on the system are given by (Fig. 2) (Castro et al., 2000):
for the control volume is given by (Kröger, 2004):
ma (1 + w) + mw +
(1)
F0 T0 = (F1 − B)T1 + MTM
(2)
The overall heat load of the cooling water network is written as (3)
dmw dw dz =ma 1 + w + dz + mw dz dz
dw = KG (wout − wair ) dz
(5)
That KG is the mass transfer coefficient of air. Several experimental measurements on heat and mass transfer coefficient in cooling towers have been done and for air–water systems. The result is represented as a function of air and water flow rate (Coulson and Richardson, 1996): KG = a1 mba mcw
(6)
where wair is the humidity ratio of air and wout is the humidity ratio of interface.
wair =
Ps P − Ps
(7)
E wout − win
win = −
(8)
CPa [T − TWB ] + wsat(WBT) wga(WBT) amb
(9)
where wga(T) is defined as (Mann and Liu, 1999): wga(T) = 2501.3 + 1.82T
Consider an elementary control volume in the fill or packing of a counter-flow wet cooling tower (Fig. 3), a mass balance
(4)
Humidity ratio change along the cooling tower height is given by
wout = 0.622
F0 = F1 − B + M
QHEN = F2 CP (T2 − T0 )
Fig. 3 – Cooling towe control volume.
(10)
It is assumed that the air leaves the tower at the saturated condition. The saturated pressure as per the Antoine equation is given by (Smith, 2005): ln Ps = A0 −
B0 T + C0
(11)
Coefficients for above equation are presented as following (Kim and Smith, 2001): For 0 ◦ C < T < 57 ◦ C, A = 23.7093, B = 4111, C = 237.7An energy balance on control volume is written as
ma ha + mw +
Fig. 2 – Cooling system model.
= ma ha +
dmw dTw dz CP Tw + dz dz dz
dha dz + mw CP Tw dz
(12)
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Table 1 – Verification of cooling tower model 1
2
3
4
Experimental data Air flow rate (t/h) Water flow rate (t/h) Water inlet temperature (◦ C) Water outlet temperature (◦ C) Make-up flow rate (t/h) Blow-down flow rate (t/h)
2.41 0.72 36.70 19.80 0.042 0.0263
2.361 1.08 32 20.40 0.050 0.0207
2.39 1.43 29.30 20.70 0.040 0.0250
2.368 1.782 27.90 20.80 0.047 0.0197
Model output data Dry air flow rate (t/h) Blow-down rate (t/h) Make-up rate (t/h) Evaporation rate (t/h) Pumping power (kW) Heat rejection (mm W) Exit air temperature (◦ C) Water outlet temperature (◦ C) Effectiveness (%) Make-up error (%) Blow-down error (%) Temperature error (%)
2.48 0.0224 0.045 0.0224 0.0284 0.0143 17.59 19.81 63 0.06 0.15 0.05
2.40 0.0225 0.045 0.0225 0.0426 0.0140 18.00 20.44 52 −0.10 −0.08 0.19
2.42 0.0222 0.045 0.0222 0.0565 0.0125 17.83 20.66 30 0.11 0.11 −0.19
2.37 0.0225 0.045 0.2258 0.0703 0.0116 18.15 20.82 26 −0.04 −0.12 0.09
The bold values signify the model output data.
By neglecting second order terms of Eq. (12): mw CP
dTw dmw dha + CP Tw = ma dz dz dz
(13)
By substituting above equations: dTw ma = dz mw
1 dh a CP dz
− Tw
dw dz
(14)
The total enthalpy transfer at the air–water interface consists of an enthalpy transfer associated with the mass transfer due to the difference in vapor concentration and the heat transfer due to the difference in temperature (Kröger, 2004): dQ = dQm + dQC
(15)
The enthalpy transfer associated with the mass transfer is expressed by dQm = hw
dmw dz = hw hd (hw − w)dA dz
(16)
The convective transfer of sensible heat at the interface is given by dQC = hd (Tw − Ta )dA
(17)
The cooling tower water outlet temperature, flow rate and evaporation are all function of tower air flow rate, wet bulb temperature and inlet water temperature. The effect of each parameter, temperature difference along cooling tower (R) and flow rate (Fin ), should be extensively examined to achieve the optimum point. The result of the cooling tower modeling illustrated that decreasing the flow rate of cooling tower has a more significant effect on the effectiveness than decreasing the inlet temperature. To verify the proposed model, the simulation results are compared with the experimental data, which are obtained through a pilot plant cooling tower (Table 1). The results demonstrates that when cooling water inlet conditions are high temperature and low flow rate, the cooling tower effectiveness increases which means more heat removal of cooling tower. Verification result shows that the cooling tower model, which will be used for the design of cooling water system, is accurate enough to evaluate the cooling tower performance and predict the effectiveness of cooling tower.
4.
Optimum design of cooling water system
Traditional network design is parallel configuration. The best optimal design of the RCWS is based on providing water re-use opportunity. The optimum cooling water system through APD
Water temperature along the cooling tower height is expressed as dTw ma 1 dha = dz mw CP dz
(18)
The cooling tower effectiveness (e) is defined as the ratio of actual heat removal to the maximum achievable heat removal. High effectiveness of cooling tower represents efficient cooling performance and high heat removal. Effectiveness is given as below expression: e=
Qact Qmax
(19)
Fig. 4 – Effect of water flow rate on cooling cost.
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Fig. 5 – Cooling water composite curve and targeting for maximum re-use. method is carried out in three stages. The first step is to define the feasible region from the cooling composite curve taking into consideration the system constraints. The second step is to explore the feasible region to target the cooling water supply line. The final stage is to design the cooling water network for target conditions with pinch migration concept through water main synthesis method. The APD is based on a superior algorithm derived from combination of pinch analysis and mathematical programming. The minimum cost is obtained from the presented grass-root design procedure.
4.1.
Objective function
In grass-root design targeting the objective is to minimize total annual cost (Prasad, 2004). The total cost of cooling tower includes operation and capital cost (Kim et al., 2001). Capital cost of cooling tower is: CC = 746.749(Fin )
0.79
0.57
(R)
(A)
−0.9924
+ (0.022TWB + 0.39)
2.447
(20) where Fin is the cooling tower water flow rate, A is the cooling tower approach value, R is the cooling tower range and TWB is the wet bulb temperature. Operating cost of cooling tower :
4.2.
To establish the model constraints, first cooling water composite curve should be drawn. Cooling water streams depends on heat load and temperatures are graphed and all the cold streams are then summed up to figure out the composite curve. Fig. 5 shows the procedure for composite curve graph and targeting for maximum re-use of water flow rate. The cooling water supply line is shown for maximum re-use of water, which means the possible series configuration of heatexchangers (Smith, 2005). In conventional cooling water system design, the objective is to minimize the water flow rate. However, minimum flow rate does not necessarily guarantee the optimality. The point where the target supply line touches the composite curve creates a pinch point. It is noted that the interpretation of the pinch does not imply zero driving force of heat transfer, but minimum driving force. Fig. 6, illustrates the schematic of model constraints and the feasible region for targeting the water supply of a re-circulating cooling system. The cooling water network performance can be changed within a feasible region. As shown in Fig. 6, the feasible area is a region, limited with the minimum water flow rate (maximum water re-use profile) and maximum water flow rate (no re-use profile). The air flow rate is expressed as (Deng and Tan, 2003):
pumping cost + fan cost + make-up cost + chemical treatment cost + blow-down treatment cost; OC = 2.4094 × 10−3 (PP) + 44(Fair ) + 110(Fin ) + 2275.132(M) + 1138(B)
(21)
where PP is the pumping power, Fair is the tower air flow rate, M is the make-up flow rate and B is the blow-down flow rate. Finally, the objective function is defined as total annual cost. The optimization problem can be stated as follow: Min TC = CC + OC
Model constraints
Fair =
E wout − win
where inlet and outlet humidity ratio are both function of temperature. win = f (TWB , Tamb )
(22)
The operating cost and the capital cost of the cooling tower have different effects on the overall cost of cooling. Therefore, the problem becomes an optimization problem to search for the optimal cooling tower. In other words, by increasing water flow rate in cooling water system, the capital cost decreases and the operational cost increases. Fig. 4 shows the effect of water flow rate on the cooling tower cost.
(23)
Fig. 6 – Temperature feasible region.
(24)
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Table 2 – Hot process stream data Thot,in (◦ C)
Condition Conventional Max-re-use KSD APD
wout = f
Tcold,out (◦ C)
40.46 50 45 49
CP (kW/◦ C)
30 20 30 25.2
T + T out in
286.67 100 200 126
Evaporation rate is a function of water flow rate and temperature difference of cooling tower (Kim et al., 2001). E = 0.00153(Fin )(R)
e (%)
246.89 86.12 172.24 108.51
41 85 50 70
Feasibility constraints to avoid pinch crossing;
(25)
2
F (t/h)
Tout + R
QiPinch Q
≤ TiPinch
(33)
Feasibility constraints on the cooling water flow rate;
(26)
l u Fin ≤ Fin ≤ Fin
Heat load of cooling system: QHEN = Fin CP (Tin − Tout )
(27)
Range definition: R = Tin − Tout
(28)
Approach definition:
l and Fu are the upper and lower limit of the water where Fin in flow rate which are expressed at water temperature feasibility area that are obtained from the total heat rejection of cooling tower. Note that the amount of heat absorbed by the heatexchanger network is rejected through the cooling tower. Pumping power is a function of water flow rate.
PP =
A = Tout − TWB
(29)
The cooling water system cannot operate beyond a specific return cooling water temperature because the hot return cooling water temperature might cause fouling problems, corrosion or problems with the cooling tower packing. Therefore, it is common practice to introduce temperature constraints for return cooling water to the tower. Feasibility constraints on the inlet and outlet temperature of cooling tower: TNR ≤ Tin ≤ Min{TMR , TTL }
(34)
Fin hwater P
(35)
where h is the pumping head, water is the water density and P is the pump efficiency. Blow-down and make-up as a function of evaporation rate are carried out as B=
E C − 1
M=E
(36)
C C − 1
(37)
(30)
The water outlet temperature from the cooling tower varies between the minimum approach value considering wet bulb temperature and minimum temperature of water stream at heat-exchanger network: (TWB + TMA ) ≤ Tout ≤ TMN
The optimum performance parameters are achieved through applying the introduced optimization model taking into consideration the minimum cost achievement. An illustrative example is applied to develop the APD technique for cooling water network. The computations of the optimization model are done in MATLAB version 7.1.
(31)
4.3. where TMN is the minimum temperature of heat exchange network with respect to Tmin of the network and TMA is the minimum cooling tower approach. TMN = THENmin − Tmin
(32)
It is noted that to define the upper inlet temperature boundary, minimum value between TMR and TTL (temperature limitation), that is dictated by the tower packing type, is determined. It is emphasized that the optimum water supply conditions do not violate the cooling tower temperature limitations.
Illustrative example I—advanced pinch design
The cooling water system in example I has four heat exchangers using cooling water as cooling medium for hot process streams. The temperature, flow rate and cooling duty of hot process streams are given in Table 2. The following data are used for the example I. Wet bulb temperature: 15 ◦ C; ambient temperature: 25 ◦ C; minimum approach: 5 ◦ C; pump efficiency: 60%; pumping head: 10.67 m; cycle of concentration: 2; operating hours: 8600 h/yr; interest rate: 15%; payback period: 3 yr; minimum temperature difference (Tmin ): 10 ◦ C; temperature limitation: 57 ◦ C.
Table 3 – Performance parameters of conventional, KSD and APD methods Heat exchanger 1 2 3 4
Thot,in (◦ C) 50 45 55 65
Thot,out (◦ C) 40 40 50 55
CP (kW/◦ C) 100 100 200 50
Q (kW) 1000 500 1000 500
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Table 4 – Cost comparisons of various designs in (k$/yr) Design method Conventional KSD APD
OC
CC
TC
65.90 53.66 44.07
6.54 6.04 8.03
72.44 59.70 52.10
Fig. 8 – Cooling water main method for cooling water network design.
Fig. 7 – Pinch migration. The optimization results are given in Table 3. Optimization results are indicated that the optimum water supply flow rate is 108.51 t/h. The cooling water enters the tower with temperature of 49 ◦ C and leaves the tower with temperature of 25.2 ◦ C. The evaporation is constant because the heat rejection is constant. Therefore, the make-up and blow-down for KSD and APD methodologies are constant as per Eqs. (36) and (37). Table 4 shows the cost comparison of various design methods. The optimization results show that the operational cost including fan cost, pumping cost, make-up water cost, water chemical and blow-down treatment cost is 44.07 k$/yr and capital cost for cooling tower is 8.03 k$/yr which makes total cost of 52.10 k$/yr achievable. If the cooling water supply line does not correspond with minimum flow rate (either because of system interactions or temperature constraints), then a pinch point is not created with the limiting cooling water composite curve. Therefore, the cooling water composite curve needs to be modified to make a pinch point with the desired cooling water supplyline in the feasible region. Therefore, the cooling water network problem would be changed into a problem with a pinch (Smith, 2005). Pinch migration is introduced here to convert problems without a pinch into those with a pinch with the desired supply line. Fig. 7 shows the pinch migration of cooling water composite curve. Optimal heat-exchanger arrangement is then achieved through an advanced synthesis algorithm using water pinch technology (Smith, 2005). The synthesis algorithm by set-
ting up the water mains at water supply temperature, pinch points temperatures and exit temperature (Fig. 8) was used for developing an optimal heat-exchangers network configuration (Fig. 9) (Mann and Liu, 1999). This synthesis algorithm was based on composite curve decomposition and water main method. The water main method of Kuo and Smith (1997) for the design of water re-use networks can be extended to the design of cooling water networks. The original method identified water re-use opportunities for problems in which re-use was constrained by concentration limits. This method was carried out in four steps. The first step was to generate a grid diagram with cooling water mains and plot the cooling water using operations as shown in Fig. 8. The second stage was to connect the operations with cooling water mains. The third stage was to merge operations that cross mains. The final stage was to remove intermediate (pinch) cooling water mains. Following the method allows the design of the cooling water network to achieve the target predicted by the supply line. Details of the procedure are given by Kuo and Smith (1997) and are readily adapted from the concentration constraints in the original paper to the temperature constraints that are a feature of the cooling water network design problem. In order to achieve an optimum water supply line in the feasible region, using a limiting profile, which is defined from either Pinch point or cooling tower temperature limitation, was considered as the guide that represents the boundary between feasible and infeasible operation. The optimum design construction and optimum heat-exchanger configuration were then accomplished considering the maximum water re-use profile and water pinch synthesis (Fig. 9). The KSD configuration is presented in Fig. 10. As shown in Fig. 9, optimum configuration achieved through APD methodology is provided more series arrangement opportunity in comparison with KSD method (Fig. 10).
Fig. 9 – Optimum heat-exchanger configuration of APD method.
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ble methods for the use of make-up water. Magnetic and electro-magnetic, electrostatic, electrolysis, ozonation and hydrodynamic cavitations are some of these non-chemical treatments.
5.2.
Ozone water treatment
Fig. 10 – Heat-exchanger configuration of KSD. The conventional design (parallel configuration) does not make opportunity for water re-use. Therefore, parallel configuration cannot provide water conservation. The APD methodology is then improved through a procedure to maximize water and energy conservation. A new design method, ECWSD, is developed. In other words, the APD method is then improved taking into consideration the environmental features.
5. Environmental improvement of RCWS design 5.1.
Water quality
In RCWS, the quality of the cooling water and make-up needs to be considered not only for achieving better optimal values, but also for reducing the negative environmental impacts. In a cooling system, eventually, the minerals reach a cycle of concentration that will cause loss of efficiency due to scale formation or damage due to excessive corrosion. To conserve water and treatment chemicals, it is desirable to allow the dissolved minerals to reach a maximum cycle of concentration. The cycle of concentration (C ) is defined as the concentration ratio of a soluble component in the blow-down to that in the make-up stream (Heikkila and Milosavljevic, 2001). C =
XB M = XM B+D
(38)
The concentration of contaminants should be managed to control biological growth, corrosion and scale build-up. The maximum cycle of concentration will depend on the quality of make-up water (Parker, 1998). Chemical, physical and biological treatment processes are used to improve the make-up water quality to solve the problems related to cooling water treatment such as scale formation, corrosion and bacterial growth. Of all the methods, non-chemical treatment methods could be considered as safe and environmentally responsi-
Ozone (O3 ) has been recognized for nearly a century for its powerful ability to disinfect water. Cooling tower water must be treated to limit the growth of mineral and microbial deposits that can reduce the heat transfer efficiency of the cooling tower. The conditions in cooling towers can promote the growth of Legionella, which can exist in low concentrations in most water supply systems. By integrating ozone treatment, the levels of bacterial and mineral substances in the waters discharged through blow-down decreases (Gharaie, 2007). Fig. 11 shows a cooling tower integrated ozone water treatment unit (Parker, 1998). Integration of ozone water treatment with the RCWS increases the cycle of concentration, which decreases the concentration of insoluble components in circulating water (Viera et al., 2000). It reduces the blow-down dramatically that, in turn is environmentally constructive. Cooling water systems can be considered as energy conservation resources opportunities (Alsheyab and Munoz, 2007). For maximizing water and energy conservation, ozone treatment should be integrated in to the cooling tower. This also manages drastic environmental friendly implications. The effect of ozone treatment integration on cooling system and ECWSD method is studied through the illustrative example II.
5.3. Illustrative example—enhanced cooling water system design The hot process stream data are as given in Table 2. The design data are the same as given in example I. It is noted that integrating ozone treatment increases cycle of concentration up to 15. Theoretically, as per below equation, we predict 46% water saving in cooling system. V = Mi
Ci − Cii Ci (Cii − 1)
(39)
To achieve optimum performance parameters of cooling system, cooling tower total annual cost function is solved for minimum value. To attain optimum performance parameters
Fig. 11 – Ozone treatment of cooling tower water.
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Table 5 – Performance parameters of various design methods Condition Conventional KSD APD ECWSD
Thot,in (◦ C)
Tcold,out (◦ C)
40.46 45 49 48.35
30 30 25.2 28.22
CP (kW/◦ C) 286.67 200 126 149
F (t/h)
e (%)
246.89 172.24 108.51 128.32
41 50 70 60
Fig. 12 – Optimum heat-exchanger configuration of ECWSD.
Table 6 – Cost comparison of various design methods in (k$/yr) Design method Conventional KSD APD ECWSD
OC
CC
TC
65.90 53.66 44.07 20.20
6.54 6.04 8.03 19.55
72.44 59.70 52.10 39.75
through the cooling water supply line, feasible region is explored for minimum cost. The objective total cost function of the integrated cooling system is included of operational and capital cost. Cost function is expressed as: Operating cost of ECWSD
Fig. 13 – Cost comparison of variouse design methods.
Ozone capital cost = 24.43(Fin ) + 104
(40)
mum total cost achievable in comparison to the other design methods. Table 7 shows water and energy saving in various design methods, KSD, APD and ECWSD. As shown in Table 7, APD and ECWSD methods are resulted in 22% and 17% energy saving relative to KSD method, respectively. The amount of makeup water saved through ECWSD is 46% that is the same as predicted through Eq. (39) theoretically. By integrating ozone treatment into the cooling water system, the capital cost increases. On the other hand the operational cost decreases. The cost analysis shows that the aggregated total cost is accomplished the minimum value (Fig. 13).
Ozone electricity cost = 1.169(Fin )
(41)
6.
= fan cost + pumping cost + blow-down treatment cost + make-up water cost + ozone water treatment cost Capital cost of ECWSD = cooling tower cost + ozone water treatment capital cost Ozone treatment operational cost is consisted of ozone electricity cost $/yr and conversion factor. Capital cost of ozone water treatment is a function of water flow rate:
Table 5 shows optimum performance parameters, water flow rate and temperature, of cooling water system that are achieved through the ECWSD method. Fig. 12 shows the optimal heat-exchanger network configuration that is achieved through the advanced synthesis algorithm and water main concepts. The cost comparison of various design methodologies are presented in Table 6. It reveals that the ECWSD made mini-
Discussion and conclusions
Conventional design of RCWS is often carried out in parallel configuration. This loses opportunity for water re-use. However, re-use of cooling water between different cooling duties enables cooling water networks to be designed with series arrangements. This allows better cooling tower performance and increased cooling tower capacity. In this study a mathematical model of cooling systems has been developed to predict the tower performance and to provide design
Table 7 – Make-up, blow-down water and energy saving of various design methods Design method KSD APD ECWSD
Make-up (t/h) 7.90 7.90 4.23
Blow-down (t/h) 3.95 3.95 0.28
Energy (kW) 13 10.05 10.63
Make-up saving (%) – – 46
Blow-down saving (%) – – 93
Energy saving (%) – 22 17
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guidelines for RCWS design. The optimum design of RCWS with possible series arrangement is achieved through a new grass-root design methodology, APD. The design is carried out with any target temperature by improving the concepts of pinch technology in water systems and applying mathematical programming. The interactions within the cooling system are considered in the presented design method, APD, simultaneously. Furthermore, having considered the water quality, the ADP method is improved to increase water and energy conservation opportunity. This new method, ECWSD, provides water and energy conservation, reduces negative environmental impacts and achieves the minimum cost. Results on the presented illustrative example show that the design total cost achieved through APD is 52.10 k$/yr. The ECWSD makes total cost of 39.75 k$/yr achievable relative to the KSD total cost of 59.70 and 72.44 k$/yr for conventional design. Relative programming in MATLAB version 7.1 has been developed to get the optimization results. The results have indicated that a four stream illustrative case caused 46 percent of make-up saving, 93 percent of blow-down water saving and 17 percent of energy conservation relative to the KSD method. Therefore, applying ECWSD methodology to industrial large-scale problems can provide greater water and energy conservational opportunity.
References Alsheyab, M.A.T. and Munoz, A.H., 2007, Optimization of ozone production for water and waste water treatment. Desalination, 217(1): 1–7. Castro, M.M., Pinto, J.M. and Song, T.W., 2000, Operational cost minimization in cooling water system. Braz J Chem Eng, 17(4): 4–7.
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Coulson, J.M. and Richardson, J.F., (1996). Chemical Engineering: Fluid Flow, Heat Transfer and Mass Transfer (5th ed.). (Pergamon Press, Oxford). Deng, S. and Tan, K., 2003, A numerical analysis of heat and mass transfer inside a reversibly used water cooling tower. Build Environ, 38(1): 91–97. Gharaie M., 2007, Performance modeling and optimization of wet cooling tower parameters to minimize the exergy loss, MSc Thesis, K.N. Toosi University of Technology. Heikkila, P. and Milosavljevic, N., 2001, A comprehensive approach to cooling tower design. Appl Therm Eng, 21(9): 899–915. Kim, J.K. and Smith, R., 2001, Cooling water system design. Chem Eng Sci, 56(12): 3641–3658. Kim, K., Savulescu, L. and Smith, R., 2001, Design of cooling systems for effluent temperature reduction. Chem Eng Sci, 56(5): 1811–1830. Kröger, D.G., (2004). Air-cooled Heat Exchangers and Cooling Towers: Mass Transfer and Evaporative Cooling. (Penn Well Corporation, OK, USA), pp. 223–328 Kuo, W.J. and Smith, R., 1997, Effluent treatment system design. Chem Eng Sci, 52(23): 4273–4290. MATLAB software, version 7.1. Mann, J. and Liu, Y.A., (1999). Industrial Water Reuse and Waste Water Minimization. (McGraw-Hill, New York, USA). Parker, S.A., 1998, Ozone Treatment for Cooling Tower, The U.S. Department of Energy, Fed Tech Alert J, New York. Prasad, M., 2004, Economic up gradation and optimal use of multi-cell cross flow evaporative water cooling tower through modular performance. Appl Therm Eng, 24(4): 579–593. Smith, R., (2005). Chemical Process Design. (John Wiley & Sons, England), pp. 513–526 Viera, M.R., Guiamet, P.S., de Melle, M.F.L. and Videla, H.A., 2000, Use of dissolved ozone for controlling planktonic and sessile bacteria in industrial cooling systems. Int Biodeter Biodeg, 44(4): 201–207.