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Determining parameters of heat exchangers for heat recovery in a Cu–Cl thermochemical hydrogen production cycle
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
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Determining parameters of heat exchangers for heat recovery in a CueCl thermochemical hydrogen production cycle M. Rabbani*, I. Dincer, G.F. Naterer, M. Aydin Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe Street North, Oshawa, ON L1H 7K4, Canada
article info
abstract
Article history:
A heat exchanger is a device built for efficient heat transfer from one medium to another.
Received 2 March 2012
Shell and tube heat exchangers are separated wall heat exchangers and are commonly
Received in revised form
used in the nuclear and process industry. The CuCl cycle is used to thermally crack water
17 April 2012
in to H2 and O2. The present study presents the heat exchanger thermal design using
Accepted 1 May 2012
analysis of variance for heat recovery from oxygen at 500 C, coming from the molten salt
Available online 12 June 2012
reactor. Polynomial regressions in terms of the amount of chlorine in the oxygen, the mass flow rate on the tube side, and the shell’s outlet temperature are estimated for various
Keywords:
exchanger parameters and the results are compared with the bell Delaware method. Based
Heat exchanger
on energy and exergy analysis, this study also discusses the best possible path for the
CueCl cycle
recovered heat from oxygen. Optimal heat exchanger parameters are estimated by Design-
Hydrogen production
Expert Stat-Ease for most effective heat recovery.
Shell and tube
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
ANOVA
1.
Introduction
Heat exchangers transfer heat from a hot fluid to cold fluid with or without direct contact between the fluids. Different types of heat exchangers are used depending upon the application. Heat exchangers are also used to recover waste heat. Shell and tube heat exchangers are a modified form of double pipe heat exchanger. Shell and tube heat exchangers are the most widely used heat exchangers in industry [1]. Based on their large number of applications, the Tubular Manufacturer Exchanger Association (TEMA) has categorized shell and tube heat exchangers based on the front head, shell body and rear head. Shell and tube heat exchangers are widely used as heat recovery heat exchangers [2]. Researchers have examined various aspects of shell and tube heat exchangers for heat recovery. For example Desai and Bannur [3] used
a shell and tube heat exchanger to recover heat from a twin cylinder engine. Teke et al. [4] has defined a new nondimensional number (E ) for heat exchangers used in heat recovery applications as a function of thermal, geometric and economic parameters. The authors also considered flow arrangements (i.e. parallel flow, cross flow, mixed and unmixed streams). A non-dimensional number (E ) was used to find the maximum effectiveness of a heat exchanger. Teke et al. [4] also showed that the maximum effectiveness of a heat exchanger is proportional to the net heat recovered by the heat exchanger. The best heat exchanger for any specific application is the one which gives the highest value of effectiveness. Morcos [1] examined the overall heat transfer coefficient, heat exchanger effectiveness in terms of tube geometry, and the Reynolds number effects on heat exchange. Butcher [5]
* Corresponding author. Tel.: þ1 9057218668, þ1 703 829 2273. E-mail addresses: [email protected] (M. Rabbani), [email protected] (I. Dincer), [email protected] (G.F. Naterer), [email protected] (M. Aydin). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2012.05.004
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Nomenclature B Bc Ds Dotl Dctl do df Fc Fw ft fs Gs hs hi Jcombined JB JC JL JR JS L _s m _t m mc1 mO 2 mT MO2 Mc1 nt nb nc1 nO2
Baffle spacing, m Baffle Cut Shell diameter, m Outer tube limit diameter, m Central tube limit diameter, m Tube outer diameter, m degree of freedom Fraction of tube in cross flow between tips Fraction of tubes in one baffle window Friction factor tube side Friction factor shell side Mass flux shell side, kg/sm Heat transfer coefficient shell side, W/K m Inside heat transfer coefficient, W/K m2 Correction factor for baffle flow Correction factor for bundle by pass effect in baffle flow Correction factor for window effect in baffle flow Correction factor for baffle leakage area in baffle flow Correction factor for laminar flow in baffle flow Correction factor for unequal baffle spacing in baffle flow Length of heat exchanger, m Mass flow rate shell side, kg/s Mass flow rate tube side, kg/s Mass of chlorine, kg Mass of oxygen, kg Total mass of gas, kg Molar mass of oxygen, kg/kmol Molar mass of chlorine, kg/kmol Number of tubes Number of baffles Number of moles of chlorine Number of moles of oxygen
performed a first and second law analysis for a heat recovery power generation system using the second law. His results show that the second law performance of the system is sensitive to gas composition [5]. Shi et al. [6] discussed the performance of compact heat exchangers for latent heat recovery from exhaust flue gases. Their results showed that the Colburn factor and the friction factor of humid air are larger than that of dry air. They also developed a correlation of the convective heat transfer coefficient and the Colburn factor for fin and tube heat exchangers for heat recovery applications. Kim et al. [7] discussed the optimal number of passes for a given multi-channel heat exchanger. They observed the JF factor by changing the inlet diameter and number of passes. Their results showed that by increasing the inlet diameter for a fixed number of passes, the rate of heat transfer increases while pressure drop decreases e which ultimately improves the performance of the heat exchanger. Their results also showed that by increasing the number of passes, it increases the rate of heat transfer but also increases the pressure drop. Li et al. [8] used a mass transfer technique to determine the
DPS PT DPt PCL PO2 Q Ret Res Sm Stb Ssb Sb Sw T1 T2 T3 T4 Twall U VCL VO2 yc1 yO2
Shell side pressure drop, Pa Tube pitch square arrangement, m Pressure drop tube side, Pa Pressure of chlorine gas, Pa Pressure of oxygen gas, pa Heat transfer, W Reynolds number tube side Reynolds number shell side Cross flow area, m2 Tube to baffle leakage area, m2 Shell to baffle leakage area, m2 Bundle by pass flow area, m2 Window flow area, m2 Shell inlet temperature, K Shell outlet temperature, K Tube inlet temperature, K Tube outlet temperature, K Wall temperature, K Overall heat transfer coefficient, W/m K Volume of chlorine gas, m3 Volume of oxygen gas, m3 Mass fraction of chlorine Mass fraction of oxygen
Greek letters Tube to baffle clearance, m dtb Shell to baffle clearance, m dsb Central tube limit angle, rad qctl Baffle window angle, rad qds ˛ Effectiveness of heat exchanger Acronyms ANOVA Analysis of variance df Degree of freedom NTU Number of transfer units MM Mean Square Value PR Polynomial Regression
shell side heat transfer coefficient with different baffle shapes. Compared to a single segmented baffle disc, the doughnut baffle has shown higher heat exchanger effectiveness [8]. Wang et al. [9] used helical baffles in a multi shell, pass shell, and tube heat exchanger to improve the heat transfer performance. They compared their results with segmented baffles by using CFD analysis. For a given mass flow rate, the pressure drop and average rate of heat transfer is lower for a multi shell, pass shell, and tube heat exchanger with helical baffle as compared to a segmented baffle. Li et al. [10] also determined the local heat transfer on the outer surface of the tubes using a mass transfer technique with a staggered tube arrangement in a shell and tube heat exchanger. Garica et al. [11] developed a simplified model of a shell and tube heat exchanger when it operates as a condenser or evaporator. The model determines the outlet conditions of the heat exchanger in a refrigeration cycle without having any geometrical details [11]. Kapale et al. [12] studied the pressure drop on the shell side for a liquid flow in the shell and tube heat exchanger. Their model incorporates the pressure drop in nozzles and pressure drop between baffles [12]. Ozden et al.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
Fig. 1 e CoppereChlorine cycle for hydrogen production.
[13] performed a CFD analysis of the shell side in a shell and tube heat exchanger. They investigated the effect of baffle spacing, baffle cut and shell diameter on the shell side heat transfer coefficient and shell side pressure drop. They compared the results with the Bell Delaware and Kern methods. Their results showed that the Kern method underpredicts the heat transfer coefficient and the pressure drop, while the CFD analysis was in good agreement with the Bell Delaware method [13]. Different methods and technologies presently exist for producing hydrogen. However, the majority is based on reformation of fossil fuels and thus releases CO2 to the atmosphere [14,15]. Thermochemical water splitting cycles are cleaner and has to potential to be coupled with different types of energy sources (such as solar or nuclear energy). The main industrial process of producing H2 currently is the steam methane reforming [16,17]. A key challenge of producing H2 is a sustainable method of producing hydrogen with reduced impact on the environment. Thermochemical water splitting is a primary candidate for economical, sustainable and largescale production of hydrogen in industrial capacities. This paper examines the copperechlorine (CueCl) cycle of thermochemical hydrogen production, particularly internal heat recovery and handling molten CuCl within the cycle. The
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copper chlorine (CueCl) cycle is a thermochemical water splitting cycle which has been invented by Atomic Energy of Canada Limited (AECL) as the potential candidate for producing hydrogen with reduced environmental effect as compared to steam reforming. It has the advantages of lower operating temperatures (530 C) and potentially lower cost materials, when compared to other thermochemical cycles under development [18]. A team of universities led by UOIT collaborating with Argonne National Laboratory (AECL) in order to develop an integrated lab-scale CueCl cycle for hydrogen production [19]. The CueCl cycle involves three chemical reactions and one electrochemical process. Wang et al. [5] and Naterer et al. [20] have discussed the heat required by each of the steps involved in the CueCl cycle. Jaber et al. [21] has reported that the CueCl cycle’s efficiency is highly dependent on the effectiveness of internal heat recovery. Fig. 1 shows a schematic of the CueCl cycle and how a network of proposed heat exchangers can be integrated within the cycle to recover heat from molten CuCl exiting the molten salt reactor. This paper aims to design, develop and analyze a shell and tube heat exchanger based on statistically based model. It utilizesthe maximum available waste heat of the CueCl cycle in order to reduce the heat input. The paper finds the heat exchanger parameters as a function of mass flow rate in the tube side, and percentage of Cl2 in the oxygen. It also finds the shell’s outlet temperature and compares the results with existing methods. The paper also performs an optimization to find the optimal operating parameters which increase the heat exchanger effectiveness and reduce the pressure drop on the tube and shell sides. The analysis will use an energy and exergy analysis to find the optimal path and utilization of heat recovery.
2.
Heat exchanger model
In the early 1950s, Kern [22] presented heat exchanger designs in the book entitled “Process Heat Transfer”. Also, an industrial project performed at the University of Delaware and Dr. Bell presented a report in 1963 involving the “Bell Delaware Method”. This method takes into account different losses that occur in baffle flow [23]. This section analyzes a heat exchanger design for its application to a thermochemical
Fig. 2 e Shell and tube heat exchanger for heat recovery from molten salt reactor.
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CueCl cycle of hydrogen production. In the CueCl cycle (see Fig. 1), oxygen with a maximum 10% of Cl2 by volume exits from the molten salt reactor and exits at 500 C. Similarly, HCl exits the fluidized bed at 400 C (see Fig. 1). The thermal energy of both oxygen and HCl can be recovered using heat exchangers and then be used to heat the water. This will reduce the external heat input. The amount of chlorine in oxygen affects the design of the heat exchanger and it is treated as an input variable. The mass flow rate of oxygen
Table 1 e Heat exchanger parameters. Tube side fluid Shell side fluid dtb (m) dsb (m) Ds (m) Dotl (m) Dctl (m) Sm (m2) qctl Fc Stb (m2) qds Ssb (m2) Sb (m2) Fw Sw (m2) Gs (kg/m2 s) Res hs (W/m2 s) Jcombined Nc Ncw
DPs (Pa) L (m) PT (m) B (m) Bc nb LMTD ( C) Ret U (W/m2 s) hi (W/m2 s) ft fs Q (W) DPt (Pa) T1 (K) T2 (K) T3 (K) T4 (K) Twall (K) do (m) nt 3
NTU _ s ðkg=secÞ m _ t ðkg=secÞ m % Volume Cl2
10% Cl2 þ 90O2 H2 O Tube to baffle clearance Shell to baffle clearance Shell diameter Outer tube limit diameter Central Tube limit diameter Cross flow area Central Tube limit angle Fraction of tubes in cross flow between tips Tube to baffle leakage area Baffle window area Shell to baffle leakage area Bundle by pass flow area Fraction of tube in one baffle window Window flow area Mass flux shell side Reynolds number shell side Heat Transfer coefficient shell side Correction factor for baffle area Number of tube rows crossed in flow between two baffle tips Effective number of tube rows crossed in flow through one baffle window Shell side pressure drop Length of heat exchanger Tube pitch e square arrangement Baffle spacing Baffle cut Number of baffles Log mean temperature difference Reynolds Number tube side Overall heat transfer coefficient Inside heat transfer coefficient Friction factor tube side Friction factor shell side Heat Transfer Pressure drop tube side Shell inlet temperature Shell outlet temperature Tube inlet temperature Tube outlet temperature Wall temperature Tube outer diameter Number of tubes Effectiveness of heat exchanger Number of transfer units Mass flow rate shell side Mass flow tube side Amount of chlorine in oxygen (% by volume)
0.0003 0.0016 0.4953 0.4613 0.4359 0.0119 94.04 0.7951 0.0031 106.3 0.0001 0.0033 0.1025 0.010 114.8 6014 1989 0.5105 9.36
Table 2 e ANOVA for tube length. Source
SS
Df
MS
F-value
p-value Prob > F
Model A B C AB AC BC A2 B2 C2 ABC A2 B A2 C AB2 AC2 B2 C BC2 A3 B3 C3 Residual Cor total
12.95461 0.784669 0.014527 0.066603 0.00236 0.008643 9.26E-06 0.376801 9.52E-07 0.001312 1.56E-05 2.01E-05 0.000377 1.44E-05 1.93E-06 2.09E-05 9.52E-08 0.018252 3.33E-07 8E-07 0.002655 12.95727
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 130 149
0.681822 0.784669 0.014527 0.066603 0.00236 0.008643 9.26E-06 0.376801 9.52E-07 0.001312 1.56E-05 2.01E-05 0.000377 1.44E-05 1.93E-06 2.09E-05 9.52E-08 0.018252 3.33E-07 8E-07 2.04E-05
33,387.15 38,423.34 711.3444 3261.41 115.5716 423.2197 0.4533 18,451.03 0.046636 64.25478 0.761795 0.985181 18.48376 0.705366 0.094437 1.023322 0.004664 893.7561 0.016323 0.039174
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.502 <0.0001 0.8294 <0.0001 0.3844 0.3228 <0.0001 0.4025 0.7591 0.3136 0.9457 <0.0001 0.8985 0.8434
exiting the molten salt reactor is dependent on the amount of hydrogen production. The shell and tube heat exchanger is designed to recover heat from oxygen exitingfrom the molten salt reactor. Hot gas flows on the tube side and cold fluid (water) flows on the shell side. The amount of chlorine in oxygen, outlet water temperature (water temperature after heating) and mass flow rate of oxygen were treated as input variables. The Tubular
2.496
260 3.06 0.0318 0.0978 0.2 31 144.1 18,405 84.28 105.6 0.0327 0.0677 426,968 12,104 293 368 773 323 330.7 0.0254 144 0.966 3.907 1.36 1.25 10
Table 3 e ANOVA for U. Source
SS
df
MS
F-value
p-value Prob > F
Model A B C AB AC BC A2 B2 C2 ABC A2 B A2 C AB2 AC2 B2 C BC2 A3 B3 C3 Residual Cor total
107,530 7618.64 2.115741 756.364 3.827211 1296.805 0.385665 196.7595 0.006404 161.4967 0.052553 0.011147 2.737134 0.00144 24.35201 0.000389 0.008176 4.372961 3E-06 2.631509 0.665948 107530.7
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 130 149
5659.475 7618.64 2.115741 756.364 3.827211 1296.805 0.385665 196.7595 0.006404 161.4967 0.052553 0.011147 2.737134 0.00144 24.35201 0.000389 0.008176 4.372961 3E-06 2.631509 0.005123
1,104,788 1,487,237 413.0146 147,650.1 747.111 253,149.7 75.28579 38,409.49 1.25009 31,525.83 10.25893 2.176037 534.3168 0.281196 4753.763 0.075869 1.596058 853.6472 0.000586 513.6978
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.2656 <0.0001 0.0017 0.1426 <0.0001 0.5968 <0.0001 0.7834 0.2087 <0.0001 0.9807 <0.0001
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0.5
Table 4 e ANOVA for DPShell. Source
SS
Df
MS
F-value
p-value Prob > F
Model A B C AB AC BC A2 B2 C2 ABC A2B A2C AB2 ACþ B2C BC2 A3 B3 C3 Residual Cor total
4980.729 393.192 4.417821 9.0018 13.93227 28.68037 0.276538 1.740797 0.164217 3.442788 0.043638 0.005863 0.016758 0.033755 0.799263 0.002992 0.018339 0.024017 8.02E-06 0.050065 0.50407 4981.233
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 130 149
262.1436 393.192 4.417821 9.0018 13.93227 28.68037 0.276538 1.740797 0.164217 3.442788 0.043638 0.005863 0.016758 0.033755 0.799263 0.002992 0.018339 0.024017 8.02E-06 0.050065 0.003877
67,607.07 101,404.6 1139.36 2321.572 3593.145 7396.692 71.3195 448.953 42.35164 887.8982 11.25423 1.51209 4.321851 8.705327 206.1306 0.771763 4.729721 6.194061 0.002069 12.91179
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 0.0010 0.2210 0.0396 0.0038 < 0.0001 0.3813 0.0315 0.0141 0.9638 0.0005
0.4
0.952
0.904
0.664
0.76
0.616
0.568
0.3 0.712
0.2 0.808
0.1
0 0
0.856
0.02
0.04
0.06
0.08
0.1
vcl
Fig. 3 e Percent volume of chlorine vs. mass fraction of oxygen and chlorine.
Exchanger Manufacturer Association (TEMA) standards have been followed as follows. A type A stationary head, E type shell and P-type floating head were chosen. A shell with a 19 1/2‘ diameterand1’ tube outside diameter and a square pitch of 1.250 were chosen. There is one tube pass and based on TEMA tube count tables, the total number of tubes was 144 [23]. The Bell Delaware method is used initially used for the heat exchanger parameter calculations. The results from the Bell method are varied by a factorial design and analyzed using ANOVA and regressions of the heat exchanger parameters
(e.g. required length, pressure drop on shell side and overall heat transfer coefficient) are calculated as a function of input parameters (e.g. shell outlet temperature, mass flow rate of oxygen and amount of chlorine in oxygen). Steady state, steady flow conditions and a constant tube wall temperature were assumed. Fig. 2 shows the schematic of the designed heat exchanger. The maximum possible amount of chlorine (undesired byproduct in oxygen reactor) is 10% by volume. In order to determine the thermophysical properties for the mixture of gasses (Cl2 þ O2), their mass fractions were calculated. Ideal gas equations for chlorine and oxygen are: PCL VCL ¼ ncl RT
(1a)
PO2 VO2 ¼ nO2 RT
(1b)
Table 5 e Coefficient of regression. Coefficients a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19
hs (W/m2 K)1.18
Length (m)
U (W/m2 K)
DPShell (Pa)0.5
48,6637.9 15,7587.5 3963.02 263,410 735.3 79,778.5 1352.7 4025.6 10.77554 309,162.9 148.6 6.53 1608.4 0.9 81,395.06 1.75 681.04 388.96 0.01 363,568
39.5074 6.86 0.36 92.83 0.046 0.95 0.53 1.09 0.001 1.5 0.006 0 0.4 0 0.3 0 0.006 0.42 0 2.78
177.7056 246.45 1.34 568.41 0.58 546.67 2.52 34.36 0.003 1570.3 0.37 0.02 37.82 0.0006 1142.2 0.003 1.7 6.44 0 5037.96
308.4056 456.7 2.4 1252.2 2.24 172.98 6.6 7.35 0.006 1046.43 0.33 0.01 2.96 0.003 206.9 0.01 2.6 0.48 0 694.9
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Fig. 4 e Comparison between polynomial regression and Bell Delaware- shell heat transfer coefficient (W/m2 K).
Equation (1a) and (b) in term of mass fraction can be co-related as: VCL ycl MO2 PO2 ¼ VO2 yO2 Mcl PCL
(2)
Based on the mass fractions of chlorine and oxygen, the thermophysical properties on the tube side were determined as: Cptube ¼ ycl Cpcl þ yO2 CpO2
(3)
ktube ¼ ycl kcl þ yO2 kO2
(4)
mtube ¼ ycl mcl þ yO2 mO2
(5)
Based on TEMA recommendations, a 1-1 shell and tube heat exchanger was designed. Design parameters of the heat
exchanger are shown in Table 1. Hohm et al. [24] presented the viscosity of chlorine gas as a function of temperature. This was used to find the effects of temperature on pure oxygen and a mixture of oxygen with 10% chlorine. Other thermophysical properties were obtained from Engineering Equation Solver (EES). The overall heat transfer coefficient is determined as: 11 do 2ln B do 1C di C U¼B @ht di þ do þ kwall þ hs A 0
(6)
where the heat transfer coefficient for baffle flow (i.e. on shell side) is given by [15]
Fig. 5 e Comparison between polynomial regression and Bell Delaware- overall heat transfer coefficient (W/m2 K).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
hs ¼ hideal JC JL JB JR JS
(7)
The correction factors were presented in past studies in both graphical form [25] and in terms of the following correlations [23]. The correction factor for the bundle by pass effect is pffiffiffiffiffiffiffiffiffi sb 1 3 2rss JB ¼ exp CJ sm
(8)
The correction factor for unequal baffle spacing is Js ¼
ðnb 1Þ þ ðBin =BÞ1n1 þðBout =BÞ1n1
ðnb 1Þ þ ðBin =BÞ þ ðBout =BÞ
The correction factor for baffle leakage area is
(9)
JL ¼ 0:44ð1 rs Þ þ ð1 0:44ð1 rs ÞÞexpð2:2r1 Þ
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(10)
The correction factor for laminar flow is given by JR ¼ ð10=Nct Þ0:18
(11)
For Reynolds number Re > 100 JR ¼ 1. The correction factor for the effect of the baffle window flow is Jc ¼ 0:55 þ 0:72Fc
(12)
Similarly, the inside (tube) heat transfer coefficient can be calculated based on the following empirical relation:
Fig. 6 e (a): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 0% on overall heat transfer coefficient (W/m K)). (b): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 10% on overall heat transfer coefficient (W/m K).
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ht ¼ 0:023Re0:8 Pr0:3
(13)
Thus, by using equations (7)e(13) in equation (6), the overall heat transfer coefficient can be determined. The length of the shell and tube heat exchanger can be estimated by a heat balance between the fluids and it can be calculated as: m$ cp DTtube m$shell cpshell DTshell L ¼ tube tube ¼ UTCMTD pdo nt UTCMTD pdo nt
(14)
Due to the variation of the outlet temperature on the shell side and the variation in mass flow rate on the tube side, the length of the heat exchanger varies. The pressure drop in the shell is divided into three components [9]. It is the summation of pressure drop in the baffle window, central baffle spacing and pressure drop in the shell nozzle. DPShell ¼ DPcentralbafflespacing þ DPbafflewindow þ DPShellNozzle
(15)
Using the statistical model (ANOVA) and least square method, the same heat transfer coefficient will be calculated, as well as the length of the heat exchanger and shell side pressure drop as a function of mass flow in the tube side, percent of Cl2 in oxygen and the shell’s outside temperature.
3.
Method of analysis of variance (ANOVA)
ANOVA is a statistical method used to find the statistical significance of factors [26]. It consists of four main components: the sum of squares (SS), degrees of freedom (df), mean square value (MM) and the F-value. The total sum of squares for the model is defined as a sum of the squared deviation from the mean due to the effect of the individual term or the interaction between two terms and the sum of the squared deviation [27]. SSTotal ¼ SSModelterms þ SSResidual
(16)
The degrees of freedom in ANOVA are defined as the minimum number of values required to specify all data points
in a sample. N data points require N number of degrees of freedom. If the mean of the data is known and there are N data points, then the degrees of freedom is N 1 [27]. The total df for a given model is defined as df total ¼ df ModelTerms þ df Residual
(17)
The mean square value is the ratio of the sum of squares to the degrees of freedom. Mathematically it can be expressed as [28] MM ¼
SS df
(18)
Like SS and df, it is also determined for both the error and model term. The F Value for model terms is a test for comparing the variance related with that term with the residual variance. It is the ratio between the mean square value for the term and mean square value for error [19]. FTerm ¼
MMterm SSterm =df term ¼ MMresidual SSresidual =df residual
(19)
For a larger F-value for the term, the term is more effective in the model. The p-Value is the probability value for the term that is associated with the F Value for this term. It is the probability of having an F Value of this size if the term does not have an effect on the response. In general, based on a 95% confidence level, a term that has a probability value less than 0.05 would be considered a significant effect. A probability value greater than 0.10 is generally regarded as insignificant [28,29].
4. Statistical model and regressions for heat exchanger Using the statistical model, different exchanger parameters (i.e. heat transfer coefficients, length, pressure drop, etc.) will be determined as a function of the desired input parameters
Fig. 7 e Comparison between polynomial regression and Bell Delaware for length (m).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
(shell’s outlet temperature, mass flow of the tube and the amount of chlorine in oxygen stream). Models for the heat transfer coefficients, length and pressure drop on the shell side will be given below. A cubic ANOVA model with an exponential factor on the Þ has been applied to find the heat transfer coefficient ðh1:18 s effect of variation of the shell’s outlet temperature and mass flow of the tube side on the shell side heat transfer coefficient. There is only a 0.01% probability that a “Model F-Value” of this large value could occur due to noise. Values of “Prob > F” less than 0.05 indicate model terms are significant. In this case, A, B, C, AB, AC, BC, A2, B2, C2, ABC, A2B, A2C, AB2, AC2, B2C, BC2, A3, and C3 are significant model terms. The regression for the shell side heat transfer coefficient as a function of the shell’s
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external temperature, mass flow of the tube and the amount of chlorine in oxygen have also been evaluated and regression coefficients are shown in Table 5 (Table 4).
¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 h1:18 s þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (20) The Cubic ANOVA model has been applied for the overall heat transfer coefficient. ANOVA for the overall heat transfer coefficient is shown in Table 3. The Model F-value of 1,104,787.89 implies the model is significant. There is only
Fig. 8 e (a): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at CL2 [ 0% on heat exchanger required length. (b): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 10% on heat exchanger required length.
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a 0.01% probability that a "Model F-Value" of this large value could occur due to noise. Values of “Prob > F” less than 0.05 indicate model terms are significant. In this case, A, B, C, AB, AC, BC, A2, C2, ABC, A2C, AC2, A3, C3 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. The regression for the overall heat transfer coefficient as a function of the shell’s outside temperature, mass flow of the tube and the amount of chlorine in oxygen have also been evaluated. Regression coefficients are shown in Table 5. U ¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (21) A Cubic model is used for length. Table 2 shows the ANOVA model for the length of the heat exchanger. The length Model F-value of 26,369.97 implies the model is statistically significant. There is only a 0.01% probability that such a large "Model F-Value" could occur due to noise. Values of “Prob > F” less than 0.0500 indicate model terms are significant. In this case, A, B, C, AB, AC, A2, C2, A2C, A3, and A4 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. The regression for length as a function of the shell’s outlet temperature, mass flow of the tube and the amount of chlorine in oxygen have also been evaluated. Table 5 shows the length coefficients for the calculated regression.
Length ¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (22) A cubic ANOVA model with a square root transformation pffiffiffiffiffiffiffiffiffiffiffiffiffi ð DPshell Þ has been applied to find the effect of variation of the
shell’s outlet temperature and mass flow of the tube side on the pressure drop of the shell side. The Model F-value of 67,607.07 implies the model is significant. There is only a 0.01% probability that such a large "Model F-Value" could occur due to noise. Values of “Prob > F” less than 0.0500 indicate model terms are significant. In this case, A, B, C, AB, AC, BC, A2, B2, C2, ABC, A2C, AB2, AC2, BC2, A3, and C3 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. The regression for the pressure drop on the shell’s side as a function of the shell’s outside temperature, mass flow of the tube and the amount of chlorine in oxygen are been evaluated. Regression coefficients for tube side pressure drop are shown in Table 5. pffiffiffiffiffiffiffiffiffiffiffiffiffi DPshell ¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (23) where A represents mass flow on the tube side, B represents the shell’s exit temperature and C represents the amount of chlorine in oxygen in Eqs.(21)e(23).
5.
Results and discussion
Fig. 3 shows the contours of the mass fraction of oxygen and chlorine at different volume flow rates of chlorine. The X-axis represents the volume fraction of chlorine, while the Y-axis represents the mass fraction of oxygen and the contours represent the mass fraction of chlorine. Results of Eq. (20) were compared with those evaluated using the Bell Delaware method (i.e. Eq. (7)) and shown in Fig. 4. A solid block curve shows the prediction of the Bell Delaware method and the solid line represents predictions of the statistical model. The model agrees well with the Bell Delaware method. Fig. 5
Fig. 9 e Comparison between polynomial regression and Bell Delaware for pressure drop on shell side (Pa1/2).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
shows the overall heat transfer coefficient predicted by the Bell method and Eq. (21). Square blocks represent the value of the overall heat transfer coefficient using the Bell method and the solid line represents the value of the overall heat transfer coefficient based on Eq. (20) (R2U ¼ 1 between statistical model prediction and Bell method). Fig. 6(a) and (b) shows the interaction between the mass flow rate in the tube and outlet temperature, as well as their mutual effect on the overall heat transfer coefficient at different percent volumes of chlorine. Results show that increasing the percent volume of chlorine will reduce the required overall heat transfer coefficient. Fig. 7 shows the predicted length by the Bell method and Eq. (22). Square blocks represent the value of length using the Bell method and the solid line represents the value of length calculated by Eq. (22). Fig. 8(a) and (b) shows the interaction
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between outlet water temperature (recovered from oxygen), mass flow rate on the tube side (oxygen), and their mutual effects on heat exchanger length at different percent volumes of chlorine. Results show that with an increase in the amount of chlorine, the required heat exchanger length also increases. This occurs since the thermal conductivity of chlorine is less than oxygen. Fig. 9 shows the pressure drop across the tube side predicted by the Bell method and Eq. (23). Square blocks represent the value of the pressure drop on the tube side using the Bell method and the solid line represents the value of the pressure drop on the tube side calculated by Eq. (20). Here R2DP;shell ¼ 0:9999 between the statistical model prediction and Bell method. Fig. 10(a) and (b) shows the total pressure drop across the shell side at different percent volumes of chlorine.
Fig. 10 e (a): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 0% on pressure drop on shell side (Pa). (b): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 10% on pressure drop on shell side (Pa).
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The amount of chlorine does not directly affect the pressure drop across the shell. However, the amount of chlorine does affect the required amount of the shell side flow rate. Fig. 10 shows that a high flow rate is required with a high percentage of chlorine. These high flow rates are actually responsible for the pressure drop across the shell. Based on the above analysis, optimization was performed using Design-Expert Stat-Ease (version 7.1.6) in order to find the optimal operating conditions. Stat-Ease uses a method developed by Derringer and Suich. The details of this method are not the objective of the present study and can be found in literature [29,30]. The aims of the optimization are to minimize length, minimize pressure drops on both the shell and tube side and to maximize heat transfer. The desirability
characterizes how close the target is from the sample. Its value varies from 0 to 1, where 0 is not desirable and 1 is highly desirable. Fig. 11(a) and (b) show the optimal processing conditions at different percentages of chlorine in oxygen. At 0%, chlorine’s best flow rate which satisfies the above mentioned criteria on the tube side is 0.87 kg/sec, and the shell side outlet temperature is 356 K. But with an increase in the amount of chlorine, the optimized tube side’s flow rate increasesto 1.04 kg/sec. Table 6 shows the optimal heat exchange parameters at different concentrations of chlorine. The objective is to reduce the amount of external heat input to the CueCl cycle and to maximize the usage of process heat internally (Q3) Two different fluids were considered to recover heat from HCl gas (Q2). A schematic of the layout is
Fig. 11 e (a): Optimal processing conditions at Cl2 [ 0%. (b): Optimal processing conditions at Cl2 [ 10%.
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Table 6 e Optimized parameters at different % of Cl2. _s m (kg/sec) 0.87 0.94 0.98 1.00 1.02 1.04 1.04 1.05 1.05 1.04 1.04
T4 (K) 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00
_s %Cl2 Length U hs ht m (kg/sec) (W/K m2) (W/K m2) (W/K m2) (m) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
2.53676 2.59361 2.63463 2.66909 2.69996 2.72843 2.75477 2.77913 2.80134 2.82139 2.84019
1.46748 1.52112 1.53284 1.52774 1.51382 1.49437 1.4704 1.44282 1.41202 1.37889 1.3466
90.2392 91.5813 90.8164 89.2605 87.3431 85.2455 83.0332 80.7533 78.4214 76.0667 73.8061
2040.69 2095.91 2107.13 2100.74 2085.3 2064.41 2039.3 2010.93 1979.62 1946.08 1913.18
113.262 114.883 113.852 111.83 109.359 106.668 103.837 100.927 97.9558 94.9589 92.0817
DPtube (Pa)
DPShell (Pa)
Q (W)
3
Desirability
26,414.8 20,541.6 164,453 13,835.1 12,191.9 11,149.8 10,454.7 9927.6 9423.53 8831.92 8097.44
253.049 277.8 286.05 287.119 284.33 279.184 272.27 264.073 254.834 244.94 235.554
387,188 401,529 404,384 402,625 398,515 393,016 386,471 379,142 371,127 362,618 354,354
0.897611 0.913938 0.922863 0.928707 0.932783 0.935649 0.937543 0.938644 0.939047 0.938887 0.938541
0.661502 0.672718 0.673561 0.669199 0.66195 0.652933 0.642768 0.631862 0.620532 0.609049 0.597644
Fig. 12 e Heat flow path e Option 1.
Fig. 13 e Heat flow path e Option 2.
shown in Fig. 12. Water as a heat recovery fluid was used to extract heat from HCl gas. Heat exchange from oxygen to water and HCl gas to water was performed in a mixer. This mixer acted as a preheating unit, where the temperature of water can be raised up to 90 C. External heat input for this _ H2 O ¼ 3 kg=s. system is Qexternal ¼ 8487 kW at m Fig. 13 shows the layout of the design. Air was used as a heat recovery media from HCl gas. A thermodynamics _ Air ¼ 1 kg=s. This analysis shows that Qexternal ¼ 8516 kW at m requires more external heat input at lower flow rates and
involves a more complex system configuration. Based on this analysis, Option 1 is preferred because it requires less external heat input at a high flow rate of water.
6.
Conclusions
The CueCl cycle has been identified as a promising cycle for thermochemical hydrogen production that can be coupled with various heat sources. In order to increase the efficiency of
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the cycle optimal heat exchanger parameters has been presented. Heat has been recovered from oxygen using a shell and tube heat exchanger in the CueCl cycle of hydrogen production. Water was used as a heat recovery fluid. TEMA standards and the Bell Delaware method were used for designing the heat exchanger. Different exchanger parameters are estimated in terms of the amount of chlorine in the oxygen, the mass flow rate on the tube side, and the shell’s outlet and the results are compared with the bell Delaware method. Optimizations of the parameters have been performed to determine the optimal conditions, which can maximize the heat exchanger’s effectiveness. Two different fluids were considered to find, the optimal path of heat recovery. Based on the thermodynamics analysis, less external heat is required when using water as a heat recovery from HCl gas.
references
[1] Morcos H. Performance of shell -and-dimpled tube heat exchangers for waste heat recovery. Heat Recovery Systems and CHP 1988;8(4):299e308. [2] Akyurt M, Lamfon NJ, Najjar YSH, Habeebullah MH, Alp TY. Modeling of waste heat recovery by looped water-in-steel heat pipes. International Journal of Heat and Fluid Flow August 1995;16(4):263e71. [3] Desai AD, Bannur PV. Design, fabrication and testing of heat recovery system from diesel engine exhaust. Journal of the Institution of Engineers (India) 2001;82:111e8. _ Ag ¨ , Atayılmaz S‚O ¨ , Demir H. Determining the best ra O [4] Teke I, type of heat exchangers for heat recovery. Applied Thermal Engineering May 2010;30(6e7):577e83. [5] Butcher CJ, Reddy BV. Second law analysis of a waste heat recovery based power generation system. International Journal of Heat and Mass Transfer June 2007;50(11e12): 2355e63. [6] Shi X, Che D, Agnew B, Gao J. An investigation of the performance of compact heat exchanger for latent heat recovery from exhaust flue gases. International Journal of Heat and Mass Transfer 15 January 2011;54(1e3):606e15. [7] Kim MS, Lee KS, Song S. Effects of pass arrangement and optimization of design parameters on the thermal performance of a multi-pass heat exchanger. International Journal of Heatand Fluid Flow February 2008;29(1):352e63. [8] Li H, Kottke V. Analysis of local shell side heat and mass transfer in the shell-and- tube heat exchanger with disc-anddoughnut baffles. International Journal of Heat and Mass Transfer September 1999;42(18):3509e21. [9] Wang Q, Chen Q, Chen G, Zeng M. Numerical investigation on combined multiple shell-pass shell-and-tube heat exchanger with continuous helical baffles. International Journal of Heat and Mass Transfer February 2009;52(5e6):1214e22. [10] Li H, Kottke V. Visualization and determination of local heat transfer coefficients in shell-and- tube heat exchanger for staggered tube arrangement by mass transfer measurements. Experimental Thermal and Fluid Science July 1998;17(3):210e6. [11] Vera-Garcı´a F, Garcı´a-Cascales JR, Gonza´lvez-Macia´ J, Cabello R, Llopis R, Sanchez D, et al. A simplified model for shell-and- tube heat exchanger: practical application. Applied Thermal Engineering July 2010;30(10):1231e41.
[12] Kapale UC, Chand S. Modeling for shell-side pressure drop for liquid flow in shell-and-tube heat exchanger. International Journal of Heat and Mass Transfer February 2006;49(3e4):601e10. [13] Ozden E, Tari I. Shell side CFD analysis of a small shell andtube heat exchanger. Energy Conversion and Management May 2010;51(5):1004e14. [14] Leon A. Hydrogen technology: mobile and portable applications. 1st ed. Berlin: Springer; 2008. [15] Gupta RB. Hydrogen fuel: production, transport, and storage. 1st ed. Boca Raton: Taylor and Francis Group; 2008. [16] Rosen MA, Scott DS. Comparative efficiency assessment for a range of hydrogen production processes. International Journal of Hydrogen Energy 1998;23:653e9. [17] Simpson AP, Lutz AE. Exergy analysis of hydrogen production via steam methane reforming. International Journal of Hydrogen Energy 2007;32:4811e20. [18] Naterer GF, Daggupati VN, Marin G, Gabriel KS, Wang ZL. Thermochemical hydrogen production with a copperechlorine cycle, II: flashing and drying of aqueous cupric chloride. International Journal of Hydrogen Energy 2008;33:5451e9. [19] Rosen MA, Naterer GF, Sadhankar R, Suppiah S. Nuclearbased hydrogen production with thermochemical copperechlorine cycle and supercritical water reactor. Montreal: Canadian Hydrogen Association Workshop; October, 2006. [20] Naterer GF, Gabriel K, Wang ZL, Daggupati VN, Gravelsins R. Thermochemical hydrogen production with a copperechlorine cycle. I: oxygen released from copper oxychloride decomposition. International Journal of Hydrogen Energy 2008;33:5439e50. [21] Jaber O, Naterer GF, Dincer I. Heat recovery from molten CuCl in the CueCl cycle of hydrogen production. International Journal of Hydrogen Energy June 2010;35(12):6140e51. [22] Kern DQ. Process heat transfer. ISBN-10: 0070341907. [23] Serth RW. Process heat transfer: principles and applications; 2007. ISBN-10: 0123735882.Design Expert, State Ease, Version 7.1.6. [24] Hohm U, Zarkova L. Extending the approach of the temperature-dependent potential to the small alkanes CH4, C2H6, C3H8, n-C4H10, i-C4H10, n-C5H12, C(CH3)4, and chlorine, Cl2. Chemical Physics 8 March 2004;298(1e3):195e203. [25] Engineering data book III. Hojn R thome, Wolverine tube, Inc. [26] Burdick RK, Borror CM, Montgomery DC. Design and analysis of Gauge R&R studies: making decisions with confidence intervals in random and mixed Anova models (ASA-SIAM series on statistics and applied probability). Society for Industrial Applied Mathematics; 2005. ISBN-10/ASIN: 0898715881. [27] Doncaster CP, Davey AJH. Analysis of variance and covariance: how to choose and construct models for the life sciences. Cambridge University Press; 2007. ISBN-10/ASIN: 052186562X. [28] Quinn GP, Keough MJ. Experimental design and data analysis for biologists. Cambridge University Press; 2002. ISBN-13/ EAN: 9780521811286. [29] Derringer G, Suich R. Simultaneous optimization of several response variables. Journal of Quality Technology 1980;12(4): 214e9. [30] Wang J, He Z, Oh J, -Hyun S. Multi-response robust optimization using desirability function, advanced management of information for globalized enterprises, 2008. AMIGE 2008. In: IEEE symposium on, E-ISBN: 978-1-42442972-1; 22 December 2008.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Determining parameters of heat exchangers for heat recovery in a CueCl thermochemical hydrogen production cycle M. Rabbani*, I. Dincer, G.F. Naterer, M. Aydin Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe Street North, Oshawa, ON L1H 7K4, Canada
article info
abstract
Article history:
A heat exchanger is a device built for efficient heat transfer from one medium to another.
Received 2 March 2012
Shell and tube heat exchangers are separated wall heat exchangers and are commonly
Received in revised form
used in the nuclear and process industry. The CuCl cycle is used to thermally crack water
17 April 2012
in to H2 and O2. The present study presents the heat exchanger thermal design using
Accepted 1 May 2012
analysis of variance for heat recovery from oxygen at 500 C, coming from the molten salt
Available online 12 June 2012
reactor. Polynomial regressions in terms of the amount of chlorine in the oxygen, the mass flow rate on the tube side, and the shell’s outlet temperature are estimated for various
Keywords:
exchanger parameters and the results are compared with the bell Delaware method. Based
Heat exchanger
on energy and exergy analysis, this study also discusses the best possible path for the
CueCl cycle
recovered heat from oxygen. Optimal heat exchanger parameters are estimated by Design-
Hydrogen production
Expert Stat-Ease for most effective heat recovery.
Shell and tube
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
ANOVA
1.
Introduction
Heat exchangers transfer heat from a hot fluid to cold fluid with or without direct contact between the fluids. Different types of heat exchangers are used depending upon the application. Heat exchangers are also used to recover waste heat. Shell and tube heat exchangers are a modified form of double pipe heat exchanger. Shell and tube heat exchangers are the most widely used heat exchangers in industry [1]. Based on their large number of applications, the Tubular Manufacturer Exchanger Association (TEMA) has categorized shell and tube heat exchangers based on the front head, shell body and rear head. Shell and tube heat exchangers are widely used as heat recovery heat exchangers [2]. Researchers have examined various aspects of shell and tube heat exchangers for heat recovery. For example Desai and Bannur [3] used
a shell and tube heat exchanger to recover heat from a twin cylinder engine. Teke et al. [4] has defined a new nondimensional number (E ) for heat exchangers used in heat recovery applications as a function of thermal, geometric and economic parameters. The authors also considered flow arrangements (i.e. parallel flow, cross flow, mixed and unmixed streams). A non-dimensional number (E ) was used to find the maximum effectiveness of a heat exchanger. Teke et al. [4] also showed that the maximum effectiveness of a heat exchanger is proportional to the net heat recovered by the heat exchanger. The best heat exchanger for any specific application is the one which gives the highest value of effectiveness. Morcos [1] examined the overall heat transfer coefficient, heat exchanger effectiveness in terms of tube geometry, and the Reynolds number effects on heat exchange. Butcher [5]
* Corresponding author. Tel.: þ1 9057218668, þ1 703 829 2273. E-mail addresses: [email protected] (M. Rabbani), [email protected] (I. Dincer), [email protected] (G.F. Naterer), [email protected] (M. Aydin). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2012.05.004
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Nomenclature B Bc Ds Dotl Dctl do df Fc Fw ft fs Gs hs hi Jcombined JB JC JL JR JS L _s m _t m mc1 mO 2 mT MO2 Mc1 nt nb nc1 nO2
Baffle spacing, m Baffle Cut Shell diameter, m Outer tube limit diameter, m Central tube limit diameter, m Tube outer diameter, m degree of freedom Fraction of tube in cross flow between tips Fraction of tubes in one baffle window Friction factor tube side Friction factor shell side Mass flux shell side, kg/sm Heat transfer coefficient shell side, W/K m Inside heat transfer coefficient, W/K m2 Correction factor for baffle flow Correction factor for bundle by pass effect in baffle flow Correction factor for window effect in baffle flow Correction factor for baffle leakage area in baffle flow Correction factor for laminar flow in baffle flow Correction factor for unequal baffle spacing in baffle flow Length of heat exchanger, m Mass flow rate shell side, kg/s Mass flow rate tube side, kg/s Mass of chlorine, kg Mass of oxygen, kg Total mass of gas, kg Molar mass of oxygen, kg/kmol Molar mass of chlorine, kg/kmol Number of tubes Number of baffles Number of moles of chlorine Number of moles of oxygen
performed a first and second law analysis for a heat recovery power generation system using the second law. His results show that the second law performance of the system is sensitive to gas composition [5]. Shi et al. [6] discussed the performance of compact heat exchangers for latent heat recovery from exhaust flue gases. Their results showed that the Colburn factor and the friction factor of humid air are larger than that of dry air. They also developed a correlation of the convective heat transfer coefficient and the Colburn factor for fin and tube heat exchangers for heat recovery applications. Kim et al. [7] discussed the optimal number of passes for a given multi-channel heat exchanger. They observed the JF factor by changing the inlet diameter and number of passes. Their results showed that by increasing the inlet diameter for a fixed number of passes, the rate of heat transfer increases while pressure drop decreases e which ultimately improves the performance of the heat exchanger. Their results also showed that by increasing the number of passes, it increases the rate of heat transfer but also increases the pressure drop. Li et al. [8] used a mass transfer technique to determine the
DPS PT DPt PCL PO2 Q Ret Res Sm Stb Ssb Sb Sw T1 T2 T3 T4 Twall U VCL VO2 yc1 yO2
Shell side pressure drop, Pa Tube pitch square arrangement, m Pressure drop tube side, Pa Pressure of chlorine gas, Pa Pressure of oxygen gas, pa Heat transfer, W Reynolds number tube side Reynolds number shell side Cross flow area, m2 Tube to baffle leakage area, m2 Shell to baffle leakage area, m2 Bundle by pass flow area, m2 Window flow area, m2 Shell inlet temperature, K Shell outlet temperature, K Tube inlet temperature, K Tube outlet temperature, K Wall temperature, K Overall heat transfer coefficient, W/m K Volume of chlorine gas, m3 Volume of oxygen gas, m3 Mass fraction of chlorine Mass fraction of oxygen
Greek letters Tube to baffle clearance, m dtb Shell to baffle clearance, m dsb Central tube limit angle, rad qctl Baffle window angle, rad qds ˛ Effectiveness of heat exchanger Acronyms ANOVA Analysis of variance df Degree of freedom NTU Number of transfer units MM Mean Square Value PR Polynomial Regression
shell side heat transfer coefficient with different baffle shapes. Compared to a single segmented baffle disc, the doughnut baffle has shown higher heat exchanger effectiveness [8]. Wang et al. [9] used helical baffles in a multi shell, pass shell, and tube heat exchanger to improve the heat transfer performance. They compared their results with segmented baffles by using CFD analysis. For a given mass flow rate, the pressure drop and average rate of heat transfer is lower for a multi shell, pass shell, and tube heat exchanger with helical baffle as compared to a segmented baffle. Li et al. [10] also determined the local heat transfer on the outer surface of the tubes using a mass transfer technique with a staggered tube arrangement in a shell and tube heat exchanger. Garica et al. [11] developed a simplified model of a shell and tube heat exchanger when it operates as a condenser or evaporator. The model determines the outlet conditions of the heat exchanger in a refrigeration cycle without having any geometrical details [11]. Kapale et al. [12] studied the pressure drop on the shell side for a liquid flow in the shell and tube heat exchanger. Their model incorporates the pressure drop in nozzles and pressure drop between baffles [12]. Ozden et al.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
Fig. 1 e CoppereChlorine cycle for hydrogen production.
[13] performed a CFD analysis of the shell side in a shell and tube heat exchanger. They investigated the effect of baffle spacing, baffle cut and shell diameter on the shell side heat transfer coefficient and shell side pressure drop. They compared the results with the Bell Delaware and Kern methods. Their results showed that the Kern method underpredicts the heat transfer coefficient and the pressure drop, while the CFD analysis was in good agreement with the Bell Delaware method [13]. Different methods and technologies presently exist for producing hydrogen. However, the majority is based on reformation of fossil fuels and thus releases CO2 to the atmosphere [14,15]. Thermochemical water splitting cycles are cleaner and has to potential to be coupled with different types of energy sources (such as solar or nuclear energy). The main industrial process of producing H2 currently is the steam methane reforming [16,17]. A key challenge of producing H2 is a sustainable method of producing hydrogen with reduced impact on the environment. Thermochemical water splitting is a primary candidate for economical, sustainable and largescale production of hydrogen in industrial capacities. This paper examines the copperechlorine (CueCl) cycle of thermochemical hydrogen production, particularly internal heat recovery and handling molten CuCl within the cycle. The
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copper chlorine (CueCl) cycle is a thermochemical water splitting cycle which has been invented by Atomic Energy of Canada Limited (AECL) as the potential candidate for producing hydrogen with reduced environmental effect as compared to steam reforming. It has the advantages of lower operating temperatures (530 C) and potentially lower cost materials, when compared to other thermochemical cycles under development [18]. A team of universities led by UOIT collaborating with Argonne National Laboratory (AECL) in order to develop an integrated lab-scale CueCl cycle for hydrogen production [19]. The CueCl cycle involves three chemical reactions and one electrochemical process. Wang et al. [5] and Naterer et al. [20] have discussed the heat required by each of the steps involved in the CueCl cycle. Jaber et al. [21] has reported that the CueCl cycle’s efficiency is highly dependent on the effectiveness of internal heat recovery. Fig. 1 shows a schematic of the CueCl cycle and how a network of proposed heat exchangers can be integrated within the cycle to recover heat from molten CuCl exiting the molten salt reactor. This paper aims to design, develop and analyze a shell and tube heat exchanger based on statistically based model. It utilizesthe maximum available waste heat of the CueCl cycle in order to reduce the heat input. The paper finds the heat exchanger parameters as a function of mass flow rate in the tube side, and percentage of Cl2 in the oxygen. It also finds the shell’s outlet temperature and compares the results with existing methods. The paper also performs an optimization to find the optimal operating parameters which increase the heat exchanger effectiveness and reduce the pressure drop on the tube and shell sides. The analysis will use an energy and exergy analysis to find the optimal path and utilization of heat recovery.
2.
Heat exchanger model
In the early 1950s, Kern [22] presented heat exchanger designs in the book entitled “Process Heat Transfer”. Also, an industrial project performed at the University of Delaware and Dr. Bell presented a report in 1963 involving the “Bell Delaware Method”. This method takes into account different losses that occur in baffle flow [23]. This section analyzes a heat exchanger design for its application to a thermochemical
Fig. 2 e Shell and tube heat exchanger for heat recovery from molten salt reactor.
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CueCl cycle of hydrogen production. In the CueCl cycle (see Fig. 1), oxygen with a maximum 10% of Cl2 by volume exits from the molten salt reactor and exits at 500 C. Similarly, HCl exits the fluidized bed at 400 C (see Fig. 1). The thermal energy of both oxygen and HCl can be recovered using heat exchangers and then be used to heat the water. This will reduce the external heat input. The amount of chlorine in oxygen affects the design of the heat exchanger and it is treated as an input variable. The mass flow rate of oxygen
Table 1 e Heat exchanger parameters. Tube side fluid Shell side fluid dtb (m) dsb (m) Ds (m) Dotl (m) Dctl (m) Sm (m2) qctl Fc Stb (m2) qds Ssb (m2) Sb (m2) Fw Sw (m2) Gs (kg/m2 s) Res hs (W/m2 s) Jcombined Nc Ncw
DPs (Pa) L (m) PT (m) B (m) Bc nb LMTD ( C) Ret U (W/m2 s) hi (W/m2 s) ft fs Q (W) DPt (Pa) T1 (K) T2 (K) T3 (K) T4 (K) Twall (K) do (m) nt 3
NTU _ s ðkg=secÞ m _ t ðkg=secÞ m % Volume Cl2
10% Cl2 þ 90O2 H2 O Tube to baffle clearance Shell to baffle clearance Shell diameter Outer tube limit diameter Central Tube limit diameter Cross flow area Central Tube limit angle Fraction of tubes in cross flow between tips Tube to baffle leakage area Baffle window area Shell to baffle leakage area Bundle by pass flow area Fraction of tube in one baffle window Window flow area Mass flux shell side Reynolds number shell side Heat Transfer coefficient shell side Correction factor for baffle area Number of tube rows crossed in flow between two baffle tips Effective number of tube rows crossed in flow through one baffle window Shell side pressure drop Length of heat exchanger Tube pitch e square arrangement Baffle spacing Baffle cut Number of baffles Log mean temperature difference Reynolds Number tube side Overall heat transfer coefficient Inside heat transfer coefficient Friction factor tube side Friction factor shell side Heat Transfer Pressure drop tube side Shell inlet temperature Shell outlet temperature Tube inlet temperature Tube outlet temperature Wall temperature Tube outer diameter Number of tubes Effectiveness of heat exchanger Number of transfer units Mass flow rate shell side Mass flow tube side Amount of chlorine in oxygen (% by volume)
0.0003 0.0016 0.4953 0.4613 0.4359 0.0119 94.04 0.7951 0.0031 106.3 0.0001 0.0033 0.1025 0.010 114.8 6014 1989 0.5105 9.36
Table 2 e ANOVA for tube length. Source
SS
Df
MS
F-value
p-value Prob > F
Model A B C AB AC BC A2 B2 C2 ABC A2 B A2 C AB2 AC2 B2 C BC2 A3 B3 C3 Residual Cor total
12.95461 0.784669 0.014527 0.066603 0.00236 0.008643 9.26E-06 0.376801 9.52E-07 0.001312 1.56E-05 2.01E-05 0.000377 1.44E-05 1.93E-06 2.09E-05 9.52E-08 0.018252 3.33E-07 8E-07 0.002655 12.95727
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 130 149
0.681822 0.784669 0.014527 0.066603 0.00236 0.008643 9.26E-06 0.376801 9.52E-07 0.001312 1.56E-05 2.01E-05 0.000377 1.44E-05 1.93E-06 2.09E-05 9.52E-08 0.018252 3.33E-07 8E-07 2.04E-05
33,387.15 38,423.34 711.3444 3261.41 115.5716 423.2197 0.4533 18,451.03 0.046636 64.25478 0.761795 0.985181 18.48376 0.705366 0.094437 1.023322 0.004664 893.7561 0.016323 0.039174
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.502 <0.0001 0.8294 <0.0001 0.3844 0.3228 <0.0001 0.4025 0.7591 0.3136 0.9457 <0.0001 0.8985 0.8434
exiting the molten salt reactor is dependent on the amount of hydrogen production. The shell and tube heat exchanger is designed to recover heat from oxygen exitingfrom the molten salt reactor. Hot gas flows on the tube side and cold fluid (water) flows on the shell side. The amount of chlorine in oxygen, outlet water temperature (water temperature after heating) and mass flow rate of oxygen were treated as input variables. The Tubular
2.496
260 3.06 0.0318 0.0978 0.2 31 144.1 18,405 84.28 105.6 0.0327 0.0677 426,968 12,104 293 368 773 323 330.7 0.0254 144 0.966 3.907 1.36 1.25 10
Table 3 e ANOVA for U. Source
SS
df
MS
F-value
p-value Prob > F
Model A B C AB AC BC A2 B2 C2 ABC A2 B A2 C AB2 AC2 B2 C BC2 A3 B3 C3 Residual Cor total
107,530 7618.64 2.115741 756.364 3.827211 1296.805 0.385665 196.7595 0.006404 161.4967 0.052553 0.011147 2.737134 0.00144 24.35201 0.000389 0.008176 4.372961 3E-06 2.631509 0.665948 107530.7
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 130 149
5659.475 7618.64 2.115741 756.364 3.827211 1296.805 0.385665 196.7595 0.006404 161.4967 0.052553 0.011147 2.737134 0.00144 24.35201 0.000389 0.008176 4.372961 3E-06 2.631509 0.005123
1,104,788 1,487,237 413.0146 147,650.1 747.111 253,149.7 75.28579 38,409.49 1.25009 31,525.83 10.25893 2.176037 534.3168 0.281196 4753.763 0.075869 1.596058 853.6472 0.000586 513.6978
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.2656 <0.0001 0.0017 0.1426 <0.0001 0.5968 <0.0001 0.7834 0.2087 <0.0001 0.9807 <0.0001
11025
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
0.5
Table 4 e ANOVA for DPShell. Source
SS
Df
MS
F-value
p-value Prob > F
Model A B C AB AC BC A2 B2 C2 ABC A2B A2C AB2 ACþ B2C BC2 A3 B3 C3 Residual Cor total
4980.729 393.192 4.417821 9.0018 13.93227 28.68037 0.276538 1.740797 0.164217 3.442788 0.043638 0.005863 0.016758 0.033755 0.799263 0.002992 0.018339 0.024017 8.02E-06 0.050065 0.50407 4981.233
19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 130 149
262.1436 393.192 4.417821 9.0018 13.93227 28.68037 0.276538 1.740797 0.164217 3.442788 0.043638 0.005863 0.016758 0.033755 0.799263 0.002992 0.018339 0.024017 8.02E-06 0.050065 0.003877
67,607.07 101,404.6 1139.36 2321.572 3593.145 7396.692 71.3195 448.953 42.35164 887.8982 11.25423 1.51209 4.321851 8.705327 206.1306 0.771763 4.729721 6.194061 0.002069 12.91179
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 0.0010 0.2210 0.0396 0.0038 < 0.0001 0.3813 0.0315 0.0141 0.9638 0.0005
0.4
0.952
0.904
0.664
0.76
0.616
0.568
0.3 0.712
0.2 0.808
0.1
0 0
0.856
0.02
0.04
0.06
0.08
0.1
vcl
Fig. 3 e Percent volume of chlorine vs. mass fraction of oxygen and chlorine.
Exchanger Manufacturer Association (TEMA) standards have been followed as follows. A type A stationary head, E type shell and P-type floating head were chosen. A shell with a 19 1/2‘ diameterand1’ tube outside diameter and a square pitch of 1.250 were chosen. There is one tube pass and based on TEMA tube count tables, the total number of tubes was 144 [23]. The Bell Delaware method is used initially used for the heat exchanger parameter calculations. The results from the Bell method are varied by a factorial design and analyzed using ANOVA and regressions of the heat exchanger parameters
(e.g. required length, pressure drop on shell side and overall heat transfer coefficient) are calculated as a function of input parameters (e.g. shell outlet temperature, mass flow rate of oxygen and amount of chlorine in oxygen). Steady state, steady flow conditions and a constant tube wall temperature were assumed. Fig. 2 shows the schematic of the designed heat exchanger. The maximum possible amount of chlorine (undesired byproduct in oxygen reactor) is 10% by volume. In order to determine the thermophysical properties for the mixture of gasses (Cl2 þ O2), their mass fractions were calculated. Ideal gas equations for chlorine and oxygen are: PCL VCL ¼ ncl RT
(1a)
PO2 VO2 ¼ nO2 RT
(1b)
Table 5 e Coefficient of regression. Coefficients a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19
hs (W/m2 K)1.18
Length (m)
U (W/m2 K)
DPShell (Pa)0.5
48,6637.9 15,7587.5 3963.02 263,410 735.3 79,778.5 1352.7 4025.6 10.77554 309,162.9 148.6 6.53 1608.4 0.9 81,395.06 1.75 681.04 388.96 0.01 363,568
39.5074 6.86 0.36 92.83 0.046 0.95 0.53 1.09 0.001 1.5 0.006 0 0.4 0 0.3 0 0.006 0.42 0 2.78
177.7056 246.45 1.34 568.41 0.58 546.67 2.52 34.36 0.003 1570.3 0.37 0.02 37.82 0.0006 1142.2 0.003 1.7 6.44 0 5037.96
308.4056 456.7 2.4 1252.2 2.24 172.98 6.6 7.35 0.006 1046.43 0.33 0.01 2.96 0.003 206.9 0.01 2.6 0.48 0 694.9
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Fig. 4 e Comparison between polynomial regression and Bell Delaware- shell heat transfer coefficient (W/m2 K).
Equation (1a) and (b) in term of mass fraction can be co-related as: VCL ycl MO2 PO2 ¼ VO2 yO2 Mcl PCL
(2)
Based on the mass fractions of chlorine and oxygen, the thermophysical properties on the tube side were determined as: Cptube ¼ ycl Cpcl þ yO2 CpO2
(3)
ktube ¼ ycl kcl þ yO2 kO2
(4)
mtube ¼ ycl mcl þ yO2 mO2
(5)
Based on TEMA recommendations, a 1-1 shell and tube heat exchanger was designed. Design parameters of the heat
exchanger are shown in Table 1. Hohm et al. [24] presented the viscosity of chlorine gas as a function of temperature. This was used to find the effects of temperature on pure oxygen and a mixture of oxygen with 10% chlorine. Other thermophysical properties were obtained from Engineering Equation Solver (EES). The overall heat transfer coefficient is determined as: 11 do 2ln B do 1C di C U¼B @ht di þ do þ kwall þ hs A 0
(6)
where the heat transfer coefficient for baffle flow (i.e. on shell side) is given by [15]
Fig. 5 e Comparison between polynomial regression and Bell Delaware- overall heat transfer coefficient (W/m2 K).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
hs ¼ hideal JC JL JB JR JS
(7)
The correction factors were presented in past studies in both graphical form [25] and in terms of the following correlations [23]. The correction factor for the bundle by pass effect is pffiffiffiffiffiffiffiffiffi sb 1 3 2rss JB ¼ exp CJ sm
(8)
The correction factor for unequal baffle spacing is Js ¼
ðnb 1Þ þ ðBin =BÞ1n1 þðBout =BÞ1n1
ðnb 1Þ þ ðBin =BÞ þ ðBout =BÞ
The correction factor for baffle leakage area is
(9)
JL ¼ 0:44ð1 rs Þ þ ð1 0:44ð1 rs ÞÞexpð2:2r1 Þ
11027
(10)
The correction factor for laminar flow is given by JR ¼ ð10=Nct Þ0:18
(11)
For Reynolds number Re > 100 JR ¼ 1. The correction factor for the effect of the baffle window flow is Jc ¼ 0:55 þ 0:72Fc
(12)
Similarly, the inside (tube) heat transfer coefficient can be calculated based on the following empirical relation:
Fig. 6 e (a): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 0% on overall heat transfer coefficient (W/m K)). (b): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 10% on overall heat transfer coefficient (W/m K).
11028
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
ht ¼ 0:023Re0:8 Pr0:3
(13)
Thus, by using equations (7)e(13) in equation (6), the overall heat transfer coefficient can be determined. The length of the shell and tube heat exchanger can be estimated by a heat balance between the fluids and it can be calculated as: m$ cp DTtube m$shell cpshell DTshell L ¼ tube tube ¼ UTCMTD pdo nt UTCMTD pdo nt
(14)
Due to the variation of the outlet temperature on the shell side and the variation in mass flow rate on the tube side, the length of the heat exchanger varies. The pressure drop in the shell is divided into three components [9]. It is the summation of pressure drop in the baffle window, central baffle spacing and pressure drop in the shell nozzle. DPShell ¼ DPcentralbafflespacing þ DPbafflewindow þ DPShellNozzle
(15)
Using the statistical model (ANOVA) and least square method, the same heat transfer coefficient will be calculated, as well as the length of the heat exchanger and shell side pressure drop as a function of mass flow in the tube side, percent of Cl2 in oxygen and the shell’s outside temperature.
3.
Method of analysis of variance (ANOVA)
ANOVA is a statistical method used to find the statistical significance of factors [26]. It consists of four main components: the sum of squares (SS), degrees of freedom (df), mean square value (MM) and the F-value. The total sum of squares for the model is defined as a sum of the squared deviation from the mean due to the effect of the individual term or the interaction between two terms and the sum of the squared deviation [27]. SSTotal ¼ SSModelterms þ SSResidual
(16)
The degrees of freedom in ANOVA are defined as the minimum number of values required to specify all data points
in a sample. N data points require N number of degrees of freedom. If the mean of the data is known and there are N data points, then the degrees of freedom is N 1 [27]. The total df for a given model is defined as df total ¼ df ModelTerms þ df Residual
(17)
The mean square value is the ratio of the sum of squares to the degrees of freedom. Mathematically it can be expressed as [28] MM ¼
SS df
(18)
Like SS and df, it is also determined for both the error and model term. The F Value for model terms is a test for comparing the variance related with that term with the residual variance. It is the ratio between the mean square value for the term and mean square value for error [19]. FTerm ¼
MMterm SSterm =df term ¼ MMresidual SSresidual =df residual
(19)
For a larger F-value for the term, the term is more effective in the model. The p-Value is the probability value for the term that is associated with the F Value for this term. It is the probability of having an F Value of this size if the term does not have an effect on the response. In general, based on a 95% confidence level, a term that has a probability value less than 0.05 would be considered a significant effect. A probability value greater than 0.10 is generally regarded as insignificant [28,29].
4. Statistical model and regressions for heat exchanger Using the statistical model, different exchanger parameters (i.e. heat transfer coefficients, length, pressure drop, etc.) will be determined as a function of the desired input parameters
Fig. 7 e Comparison between polynomial regression and Bell Delaware for length (m).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
(shell’s outlet temperature, mass flow of the tube and the amount of chlorine in oxygen stream). Models for the heat transfer coefficients, length and pressure drop on the shell side will be given below. A cubic ANOVA model with an exponential factor on the Þ has been applied to find the heat transfer coefficient ðh1:18 s effect of variation of the shell’s outlet temperature and mass flow of the tube side on the shell side heat transfer coefficient. There is only a 0.01% probability that a “Model F-Value” of this large value could occur due to noise. Values of “Prob > F” less than 0.05 indicate model terms are significant. In this case, A, B, C, AB, AC, BC, A2, B2, C2, ABC, A2B, A2C, AB2, AC2, B2C, BC2, A3, and C3 are significant model terms. The regression for the shell side heat transfer coefficient as a function of the shell’s
11029
external temperature, mass flow of the tube and the amount of chlorine in oxygen have also been evaluated and regression coefficients are shown in Table 5 (Table 4).
¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 h1:18 s þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (20) The Cubic ANOVA model has been applied for the overall heat transfer coefficient. ANOVA for the overall heat transfer coefficient is shown in Table 3. The Model F-value of 1,104,787.89 implies the model is significant. There is only
Fig. 8 e (a): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at CL2 [ 0% on heat exchanger required length. (b): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 10% on heat exchanger required length.
11030
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
a 0.01% probability that a "Model F-Value" of this large value could occur due to noise. Values of “Prob > F” less than 0.05 indicate model terms are significant. In this case, A, B, C, AB, AC, BC, A2, C2, ABC, A2C, AC2, A3, C3 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. The regression for the overall heat transfer coefficient as a function of the shell’s outside temperature, mass flow of the tube and the amount of chlorine in oxygen have also been evaluated. Regression coefficients are shown in Table 5. U ¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (21) A Cubic model is used for length. Table 2 shows the ANOVA model for the length of the heat exchanger. The length Model F-value of 26,369.97 implies the model is statistically significant. There is only a 0.01% probability that such a large "Model F-Value" could occur due to noise. Values of “Prob > F” less than 0.0500 indicate model terms are significant. In this case, A, B, C, AB, AC, A2, C2, A2C, A3, and A4 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. The regression for length as a function of the shell’s outlet temperature, mass flow of the tube and the amount of chlorine in oxygen have also been evaluated. Table 5 shows the length coefficients for the calculated regression.
Length ¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (22) A cubic ANOVA model with a square root transformation pffiffiffiffiffiffiffiffiffiffiffiffiffi ð DPshell Þ has been applied to find the effect of variation of the
shell’s outlet temperature and mass flow of the tube side on the pressure drop of the shell side. The Model F-value of 67,607.07 implies the model is significant. There is only a 0.01% probability that such a large "Model F-Value" could occur due to noise. Values of “Prob > F” less than 0.0500 indicate model terms are significant. In this case, A, B, C, AB, AC, BC, A2, B2, C2, ABC, A2C, AB2, AC2, BC2, A3, and C3 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. The regression for the pressure drop on the shell’s side as a function of the shell’s outside temperature, mass flow of the tube and the amount of chlorine in oxygen are been evaluated. Regression coefficients for tube side pressure drop are shown in Table 5. pffiffiffiffiffiffiffiffiffiffiffiffiffi DPshell ¼ a0 þ a1 A þ a2 B þ a3 C þ a4 AB þ a5 AC þ a6 BC þ a7 A2 þ a8 B2 þ a9 C2 þ a10 ABC þ a11 A2 B þ a12 A2 C þ a13 AB2 þ a14 AC2 þ a15 B2 C þ a16 C2 B þ a17 A3 þ a18 B3 þ a19 C3 (23) where A represents mass flow on the tube side, B represents the shell’s exit temperature and C represents the amount of chlorine in oxygen in Eqs.(21)e(23).
5.
Results and discussion
Fig. 3 shows the contours of the mass fraction of oxygen and chlorine at different volume flow rates of chlorine. The X-axis represents the volume fraction of chlorine, while the Y-axis represents the mass fraction of oxygen and the contours represent the mass fraction of chlorine. Results of Eq. (20) were compared with those evaluated using the Bell Delaware method (i.e. Eq. (7)) and shown in Fig. 4. A solid block curve shows the prediction of the Bell Delaware method and the solid line represents predictions of the statistical model. The model agrees well with the Bell Delaware method. Fig. 5
Fig. 9 e Comparison between polynomial regression and Bell Delaware for pressure drop on shell side (Pa1/2).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
shows the overall heat transfer coefficient predicted by the Bell method and Eq. (21). Square blocks represent the value of the overall heat transfer coefficient using the Bell method and the solid line represents the value of the overall heat transfer coefficient based on Eq. (20) (R2U ¼ 1 between statistical model prediction and Bell method). Fig. 6(a) and (b) shows the interaction between the mass flow rate in the tube and outlet temperature, as well as their mutual effect on the overall heat transfer coefficient at different percent volumes of chlorine. Results show that increasing the percent volume of chlorine will reduce the required overall heat transfer coefficient. Fig. 7 shows the predicted length by the Bell method and Eq. (22). Square blocks represent the value of length using the Bell method and the solid line represents the value of length calculated by Eq. (22). Fig. 8(a) and (b) shows the interaction
11031
between outlet water temperature (recovered from oxygen), mass flow rate on the tube side (oxygen), and their mutual effects on heat exchanger length at different percent volumes of chlorine. Results show that with an increase in the amount of chlorine, the required heat exchanger length also increases. This occurs since the thermal conductivity of chlorine is less than oxygen. Fig. 9 shows the pressure drop across the tube side predicted by the Bell method and Eq. (23). Square blocks represent the value of the pressure drop on the tube side using the Bell method and the solid line represents the value of the pressure drop on the tube side calculated by Eq. (20). Here R2DP;shell ¼ 0:9999 between the statistical model prediction and Bell method. Fig. 10(a) and (b) shows the total pressure drop across the shell side at different percent volumes of chlorine.
Fig. 10 e (a): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 0% on pressure drop on shell side (Pa). (b): Effect of mass flow tube side (kg/sec) and outlet water temperature (K) at Cl2 [ 10% on pressure drop on shell side (Pa).
11032
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
The amount of chlorine does not directly affect the pressure drop across the shell. However, the amount of chlorine does affect the required amount of the shell side flow rate. Fig. 10 shows that a high flow rate is required with a high percentage of chlorine. These high flow rates are actually responsible for the pressure drop across the shell. Based on the above analysis, optimization was performed using Design-Expert Stat-Ease (version 7.1.6) in order to find the optimal operating conditions. Stat-Ease uses a method developed by Derringer and Suich. The details of this method are not the objective of the present study and can be found in literature [29,30]. The aims of the optimization are to minimize length, minimize pressure drops on both the shell and tube side and to maximize heat transfer. The desirability
characterizes how close the target is from the sample. Its value varies from 0 to 1, where 0 is not desirable and 1 is highly desirable. Fig. 11(a) and (b) show the optimal processing conditions at different percentages of chlorine in oxygen. At 0%, chlorine’s best flow rate which satisfies the above mentioned criteria on the tube side is 0.87 kg/sec, and the shell side outlet temperature is 356 K. But with an increase in the amount of chlorine, the optimized tube side’s flow rate increasesto 1.04 kg/sec. Table 6 shows the optimal heat exchange parameters at different concentrations of chlorine. The objective is to reduce the amount of external heat input to the CueCl cycle and to maximize the usage of process heat internally (Q3) Two different fluids were considered to recover heat from HCl gas (Q2). A schematic of the layout is
Fig. 11 e (a): Optimal processing conditions at Cl2 [ 0%. (b): Optimal processing conditions at Cl2 [ 10%.
11033
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
Table 6 e Optimized parameters at different % of Cl2. _s m (kg/sec) 0.87 0.94 0.98 1.00 1.02 1.04 1.04 1.05 1.05 1.04 1.04
T4 (K) 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00 356.00
_s %Cl2 Length U hs ht m (kg/sec) (W/K m2) (W/K m2) (W/K m2) (m) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
2.53676 2.59361 2.63463 2.66909 2.69996 2.72843 2.75477 2.77913 2.80134 2.82139 2.84019
1.46748 1.52112 1.53284 1.52774 1.51382 1.49437 1.4704 1.44282 1.41202 1.37889 1.3466
90.2392 91.5813 90.8164 89.2605 87.3431 85.2455 83.0332 80.7533 78.4214 76.0667 73.8061
2040.69 2095.91 2107.13 2100.74 2085.3 2064.41 2039.3 2010.93 1979.62 1946.08 1913.18
113.262 114.883 113.852 111.83 109.359 106.668 103.837 100.927 97.9558 94.9589 92.0817
DPtube (Pa)
DPShell (Pa)
Q (W)
3
Desirability
26,414.8 20,541.6 164,453 13,835.1 12,191.9 11,149.8 10,454.7 9927.6 9423.53 8831.92 8097.44
253.049 277.8 286.05 287.119 284.33 279.184 272.27 264.073 254.834 244.94 235.554
387,188 401,529 404,384 402,625 398,515 393,016 386,471 379,142 371,127 362,618 354,354
0.897611 0.913938 0.922863 0.928707 0.932783 0.935649 0.937543 0.938644 0.939047 0.938887 0.938541
0.661502 0.672718 0.673561 0.669199 0.66195 0.652933 0.642768 0.631862 0.620532 0.609049 0.597644
Fig. 12 e Heat flow path e Option 1.
Fig. 13 e Heat flow path e Option 2.
shown in Fig. 12. Water as a heat recovery fluid was used to extract heat from HCl gas. Heat exchange from oxygen to water and HCl gas to water was performed in a mixer. This mixer acted as a preheating unit, where the temperature of water can be raised up to 90 C. External heat input for this _ H2 O ¼ 3 kg=s. system is Qexternal ¼ 8487 kW at m Fig. 13 shows the layout of the design. Air was used as a heat recovery media from HCl gas. A thermodynamics _ Air ¼ 1 kg=s. This analysis shows that Qexternal ¼ 8516 kW at m requires more external heat input at lower flow rates and
involves a more complex system configuration. Based on this analysis, Option 1 is preferred because it requires less external heat input at a high flow rate of water.
6.
Conclusions
The CueCl cycle has been identified as a promising cycle for thermochemical hydrogen production that can be coupled with various heat sources. In order to increase the efficiency of
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 1 0 2 1 e1 1 0 3 4
the cycle optimal heat exchanger parameters has been presented. Heat has been recovered from oxygen using a shell and tube heat exchanger in the CueCl cycle of hydrogen production. Water was used as a heat recovery fluid. TEMA standards and the Bell Delaware method were used for designing the heat exchanger. Different exchanger parameters are estimated in terms of the amount of chlorine in the oxygen, the mass flow rate on the tube side, and the shell’s outlet and the results are compared with the bell Delaware method. Optimizations of the parameters have been performed to determine the optimal conditions, which can maximize the heat exchanger’s effectiveness. Two different fluids were considered to find, the optimal path of heat recovery. Based on the thermodynamics analysis, less external heat is required when using water as a heat recovery from HCl gas.
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