Computer Aided Design and Analysis of Regenerators for Heat

Article pubs.acs.org/IECR

Computer Aided Design and Analysis of Regenerators for Heat Recovery Systems C. M. Narayanan* and Tamanash Pramanick Department of Chemical Engineering, National Institute of Technology, Durgapur 713209, India ABSTRACT: In many high temperature applications or energy intensive processes, energy utilization becomes inadequate and significant energy losses do occur due to faulty design, faulty maintenance, faulty operation, and lack of efficient energy recovery. This work deals with design and analysis of regenerative heat exchangers that employ refractory checker work and that are popularly recommended for use in industrial practices to improve the efficiency of energy recovery. Development of multiparameter software has been attempted to establish the relationship between the design and systems parameters and to predict reliably the useful heat wasted due to heat exchanger nonideality. In regenerators of this kind, both forced convection and radiation heat transfer occur. The developed software package discusses estimation of heat transfer (to cooling fluid such as air) by both of these mechanisms. The tortuous nature of flow geometry has been adequately taken care of. Radiation heat transfer has been estimated based on well-developed databases, including an additional database developed in this work (for the computation of spectral overlap correction factor). Attempts have also been made to compare the performance data predicted by the developed computer aided design package with industrial data compiled from power plants, steel plants, and others.

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INTRODUCTION Energy conservation is the talk of the day. Conservation of energy includes optimum utilization of energy and minimization of energy losses in process industries. Energy loss occurs due to (a) faulty design, (b) faulty maintenance, and (c) faulty operation. In many high temperature applications or energy intensive processes, energy utilization becomes inadequate and significant energy losses do occur due to lack of efficient energy recovery. Industrial waste heat refers to energy that is generated in industrial processes without being put to practical use. Sources of waste heat include hot combustion gases discharged to the atmosphere, heated products exiting industrial processes, and heat transfer form hot equipment surfaces. The exact quantity of industrial waste heat is poorly quantified, but various studies have estimated that as much as 20−50% of industrial energy consumption is ultimately discharged as waste heat. While some waste heat losses from industrial processes are inevitable, facilities can reduce these losses by improving equipment efficiency or installing waste heat recovery technologies. A waste heat recovery system or waste heat recovery unit (WHRU) is an energy recovery heat exchanger that recovers heat from hot streams with potential high energy content, such as hot flue gases from combustion units or steam from cooling towers or wastewater from different cooling processes such as cooling of hot steel. Waste heat found in the exhaust gases from various processes can be used to preheat the incoming gas. Capture and reuse of waste heat is an emission-free substitute to expensive fuel or electricity. Technologies are available for transferring waste heat to a productive end use. Commercial heat recovery systems popularly employed for recovering energy from high temperature fluid streams may be broadly classified into three categories: (a) recuperators; (b) waste heat boilers; (c) regenerators. © 2014 American Chemical Society

Recuperators are nothing but the conventional heat exchangers that are being used to implement the process of heat exchange between two fluids that are at different temperatures and separated by a solid wall. Here both fluids pass simultaneously over the two surfaces of the separating wall. Waste heat boilers are ordinarily water tube boilers in which the hot exhaust gases from gas turbines, incinerators, and so on pass over a number of parallel tubes containing water. The water is vaporized in the tubes and collected in a steam drum from where it is drawn out for use as process steam. The tubes may be finned in order to increase the effective heat transfer area on the gas side. A regenerator is a type of heat exchanger where both fluids pass alternately over the same solid surface and is used to improve the energy efficiency in high temperature processes. According to construction, the regenerators may be classified as (1) a static or fixed matrix regenerator or (2) rotary regenerators. In a fixed matrix regenerator, a single fluid stream has cyclical or reversible flow. In rotary regenerators, the matrix rotates continuously through two counterflowing streams of fluid. In this way the two streams are mostly separated, but the seals are generally not perfect. Only one stream flows through each section of the matrix at a time. However, over the course of a rotation, both streams eventually flow through all sections of the matrix in succession. Regenerators are normally operated in pairs (two or more regenerators are used in parallel) because of the normal Special Issue: Energy System Modeling and Optimization Conference 2013 Received: Revised: Accepted: Published: 19814

March 22, 2014 June 6, 2014 June 11, 2014 June 11, 2014 dx.doi.org/10.1021/ie501213s | Ind. Eng. Chem. Res. 2014, 53, 19814−19844

Industrial & Engineering Chemistry Research

Article

beds. It is based on an analytical solutions derived using Laplace transformations and explicitly accounts for temperature gradients, transient gas temperatures, and heat sources in gas and bed. Based on the predictions of the model, the design of a packed bed regenerator has been optimized. Erk and Duduković7 report heat recovery and storage in tower regenerators packed with phase change material. Such phase change regenerators (PCRs) could be used in many applications, ranging from storage of solar energy for domestic heating to providing a source of high temperature blast gas in the metallurgical industries. Rü hlich and Quack8 have investigated the effect of shape and arrangement of refractory matrix on the efficiency of the regenerative heat exchanger, with the help of computational fluid dynamics (CFD). As the main influencing parameter, the velocity changes within the matrix due to changes in the free flow area and the aspect ratio of the single elements have been determined. The optimum geometry proposed consists of slim elements in flow direction in a staggered overlapping arrangement. In the present work, performance analysis and computer aided design of regenerators that utilize a fixed/static matrix of refractory checker work has been attempted. This study could, therefore, be the first of its kind to propose a full-fledged CAD (software package) for the design and analysis of regenerative heat exchanger of this category.

requirement for a continuous stream of preheated air. During one part of the cycle, the hot combustion gases flow through one of the regenerators and heat up the refractory bricks, while the combustion air flows through and cools down the refractory bricks in a second regenerator. Both the exhaust gases and the combustion air directly contact the bricks in the regenerators, although not both at the same time since each is in a different regenerator at any given time. After a sufficient amount of time (usually from 5 to 30 min), the cycle is reversed so that the cooler bricks in the second regenerator are then preheated, while the hot bricks in the first regenerator exchange their heat with the incoming combustion air. A flow reversal valve is used to change the flow from one gas to another in each regenerator. This is called swing operation. Advantages of regenerators over recuperating heat exchangers are that they have much higher surface area for a given volume. Hence, a regenerator usually has a smaller volume and is lower in weight than an equivalent recuperator, making it more economical in terms of materials and manufacturing. The matrix surfaces of regenerators also have some degree of self-cleaning characteristics, reducing fluid-side fouling and corrosion. Regenerators are thus ideal for gas−gas heat exchange applications requiring effectiveness exceeding 85%. One of the problems associated with regenerating heat exchangers is that there will always be a small leakage between the two gases since an unavoidable carryover of a small fraction of one fluid stream trapped in the flow passages under the radial seal is pushed out by the other fluid stream just after the periodic flow switching. But, in those applications where these regenerative heat exchangers are used to preheat air using heat from the exhaust gases, the impact of this mixing of fluids is generally not significant. In spite of their excellent application as efficient heat recovery systems in process industries, comprehensive process analysis and computer aided design of these regenerators or regenerative heat exchangers have been little attempted by researchers in the past. Apart from a fairly elaborate survey on the design characteristics of regenerators reported by Schack1 and a short survey by Kern,2 little work is reported thereafter in the literature on the design and analysis of these systems/ equipment. A method of computation of thermal efficiency of regenerators with periodic operations has been presented by Lai and Duduković.3 They have presented two approaches for modeling of periodic operation of regenerators and calculation of their thermal efficiency. The first uses an approximate representation of the impulse response expressed in terms of its variance and the principle of superposition. The second consists of n-staged compartments in series. However, their analysis involves simplifications and does not effectively consider the contribution of radiation heat transfer in regenerators of this kind. Falk4 has presented a numerical procedure for estimating the performance of rotary regenerative heat exchangers. Though a quasi-steady state approach has been employed; this model also involves simplifying assumptions and has neglected heat transfer by radiation between the gases and the porous matrix as compared to convective heat transfer. Zunft et al.5 have discussed a design study for regenerator-type heat storage in solar power plants. Design solutions based on packed beds have been looked at and their specific technical risks highlighted. Nijdam6 in his thesis has presented a new model for the prediction of temperature and concentration profiles in packed

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MATHEMATICAL MODELING AND SOFTWARE DEVELOPMENT The regenerator under consideration is the fixed matrix or static matrix type. There are two prominent modes of heat transfer in regenerators of this kind, such as forced convection heat transfer and radiation heat transfer. Since the regenerator is composed of refractory checker work, the gas flow through the regenerator is highly tortuous in nature. Accordingly, an accurate estimation of forced convection heat transfer coefficient (h H or hC) becomes difficult. One of the experimental correlations reported by Schack1 has been observed to predict a reliable design value of forced convection heat transfer coefficient for the type of flow encountered in regenerators of this kind. This correlation has been used for the development of the present CAD package and is reproduced below. Note that it is a dimensional correlation: h = 0.263 VT (av)/De

(1)

where V = average velocity of gases through the channels measured at 0 °C and 1 atm, m/s

T(av) = average temperature of gases, K De = equivalent diameter of channels, m

If bricks are laid in a double-checkered grid to give channels measuring (a × b × c), then De = 4RH = 4[(flow area)/(wetted perimeter)]

19815

= 4[(ab)/2(a + b)]

(2)

= 2(ab)/(a + b)

(3)

dx.doi.org/10.1021/ie501213s | Ind. Eng. Chem. Res. 2014, 53, 19814−19844


Article

Table 1. [Database-1], Estimation of Emissivity of Carbon Dioxide (εC) from Equtaion 16a (pcL), m Pa

T, K

c0

c1

c2

463.27

391.33−805.22 805.22−1766.61 1766.61−2777.44 373.0−692.72 692.72−1730.22 1730.22−2499.66 2499.66−2777.44 303.83−653.83 653.83−1834.11 1834.11−2477.44 277.44−612.16 612.16−1599.66 1599.66−2777.44 277.44−478.83 478.83−1599.66 1599.66−2777.44 277.44−653.83 653.83−1599.66 1599.66−2777.44

−2.9473 −3.4418 −2.3122 −2.6492 −3.4001 −4.2391 −0.0011 −2.3214 −3.4911 −3.1074 −1.7012 −3.3681 −1.7071 −3.3033 −3.9248 −2.9230 −1.6605 −3.2615 −1.6498

−0.0013 0.0007 −0.0007 −0.0020 0.0008 0.0010 −1.88 −0.0029 0.0012 0.5993 × 10−4 −0.0044 0.0015 −0.0008 −0.0018 0.0006 −0.0008 −0.0021 0.0015 −0.0008

−0.118 × 10−5 −0.5894 × 10−6 −0.9338 × 10−7 0.1541 × 10−5 −0.6286 × 10−6 −0.4818 × 10−6

617.70

926.559

1235.41

1853.11

2470.824

a

Source: Reference

10

0.2834 −0.7546 −0.2233 0.4317 −0.8650 −0.2688 0.1671 −0.6148 −0.9294 0.4121 −0.8688 −0.2092

× × × × × × × × × × × ×

10−5 10−6 10−6 10−5 10−6 10−7 10−5 10−6 10−7 10−5 10−6 10−7

(only selected values reproduced).

For the hot fluid (flue gases), the total effective heat transfer coefficient is

If a = b (as is the case in many checker works), De = a

(4)

h TH = hH + hr

Radiation heat transfer between hot gases and the checker work is estimated based on a heat transfer coefficient which is defined as1,9 hr = (σF )[(εGT 4) − (αGTB 4)]/(T − TB)

And for cold fluid (air),

h TC = hC + hr

(5)

(9)

STEP-2: To start the trials, the following relationship is set.

where

h TH = h TC

F = emissivity correction factor, dimensionless = (1 + εB)/2.0

(8)

(10)

STEP-3: We first consider end-1 of the regenerator where the hot flue gases enter at temperature T1 (during the hot cycle) and air leaves at temperature t2 (during the cooling cycle). Now, the value of TB1 can be computed from1,9

(6)

εB = average emissivity of refractory bricks (assumed constant within the range of temperature handled)

TB1 = [(θHTh 1 TH) + (θCt 2h TC)]/[(θHh TH) + (θCh TC)]

σ = Stefan−Boltzmann’s constant

(11)

= 5.67 × 10−8 W/(m 2 K)

where

εG = average emissivity of gases, dimensionless

θH = duration of heating cycle, s

αG = mean absorptivity of gases, dimensionless

θC = duration of cooling cycle, s

TB = mean surface temperature of refractory bricks, K

h TH = total heat transfer coefficient for flue gases, W/(m 2 K)

T = gas temperature depending on the mode of

h TC = total heat transfer coefficient for air, W/(m 2 K)

operation, K

In the same way, the average temperature of the refractory checker work at end-2 (namely, TB2) is computed from the above eq 11 itself, after replacing T1 by T2 and t2 by t1. To note that, at end-2, hot gases leave at temperature T2 (during the hot cycle) and air enters at temperature t1 (during the cooling cycle) . On substituting hTH = hTC, the preceding equation reduces to

Now, the surface temperature of refractory bricks (TB) is not known at the outset. Therefore, a trial and error procedure is required for the estimation of the radiation heat transfer coefficient. This procedure is summarized as follows. STEP-1: The total effective heat transfer coefficient (hT) is defined as h T = h + hr

TB1 = [(θHT1) + (θCt 2)]/(θH + θC)

(7)

The value hT is calculated separately at both ends of the regenerator (at the hot end as well as at the cold end).

(12)

STEP-4: X is set as 19816



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Table 2. [Database-2], Estimation of Emissivity of Water Vapor (εW ′ ) from Equation 18 (pwL), m Pa

T, K

b0

b1

b2

216.197

277.444−555.222 555.222−975.45 303.899−765.659 765.659−1181.64 303.899−555.222 555.222−1252.501 303.899−625.368 625.368−1388.556 303.899−555.222 555.222−1110.778 1110.778−1530.28 303.889−833 833−1944.111 303.899−833 833−2083 303.899−695.514 695.514−2221.889 303.899−695.514 695.514−1388.556 1388.556−2221.889

−3.020 −3.196 −2.905 −2.86 −2.777 −3.349 −2.587 −3.1377 −2.3646 −2.7256 −0.0017 −2.173 −2.215 −2.083 −2.1523 −1.868 −2.221 −1.864 −2.069 −1.806

−0.0028 −0.002 −0.0022 −0.0018 −0.0021 −0.4483 × 10−3 −0.0023 −0.0006 −0.0025 −0.0019 −2.3037 −0.0018 −0.0014 −0.0018 −0.0013 −0.0022 −0.0009 −0.0018 −0.0010 −0.0012

−0.140769 × 10−5

308.853 370.624 463.279 617.706

1080.986 1235.412 1544.265 1853.118

Source: Reference

10

0.5331 × 10−6 0.5629 × 10−6 0.9418 × 10−6 −0.9357 × 10−7 0.71222 × 10−6 −0.4824 × 10−7

ln εC = c0 + c1T + c 2T 2

(13)

STEP-5: The average emissivity of gases (εg) is estimated as1,9,10 ′ C W )](1 − CSO) εG = [εC + (εW

(17)

where T is in kelvin and the values of correlation constants c0, c1, and c2 depend on the magnitude (pcL) product and the operating temperature range. Values of these constants have been listed in the form of a standard table10 (Table 1) and this constitutes database-1. Emissivity of water vapor (ε′W) is a function of temperature and (pwL), where pw is the partial pressure of water vapor and L is the mean beam length. Thus,

(14)

εC = emissivity of carbon dioxide, dimensionless εW = emissivity of water vapor (uncorrected), dimensionless C W = Beer’s law correction factor for water vapor, dimensionless

′ = f (pW L , T ) εW

CSO = spectral overlap correction factor, dimensionless

(18)

ε′W is also estimated from the family of plots available in the literature.9,10 In these plots, ε′W has been plotted against T at different values of (pwL) product. These graphical data have also been converted into an analytical correlation of the following form by Narayanan and Bhattacharya:10

The gas emissivity (εg) depends on the gas composition. Flue gases contain carbon dioxide, water vapor, nitrogen, and oxygen. Diatomic gases such as nitrogen and oxygen have very poor emissivities, and they shall contribute very little to the radiation heat transfer. Thus, the gas emissivity is predominantly controlled by the carbon dioxide and water vapor contents of the flue gases. If air is assumed to contain only water vapor other than nitrogen and oxygen, then emissivity of air shall depend on its water vapor content (humidity) only. Emissivity of carbon dioxide (εC) is a function of temperature and the product (pcL), where pc is the partial pressure of carbon dioxide in the gases and L is the mean beam length. Thus,

′ = b0 + b1T + b2T 2 ln εW

(19)

where T is in Kelvin and the values of correlation constants b0, b1, and b2 can be retrieved from the standard tables10 (see Table 2) which constitutes database-2. The correlations discussed above for the estimation of εC and ε′W are based on Beer’s law. Though Beer’s law is obeyed by carbon dioxide reasonably well, this is not true in the case of water vapor. Therefore, the value of εW ′ obtained from the preceding correlation (eq 19) is to be multiplied by a correction factor (CW) to get the actual emissivity of water vapor. CW) is computed from10

(15)

The mean beam length may be assumed equal to the equivalent diameter (De) of the flow channels with allowable error. Thus, L = De

0.8572 × 10−6 −0.6312 × 10−6 0.97902 × 10−6 −0.4734 × 10−6 0.10711 × 10−5 −0.1075 × 10−6

(only selected values reproduced).

X = TB1

εC = f (pc L , T )

0.6151 × 10−6

C W = d0 + [d1(P + pw )/2] + [d 2[(P + pw )/2]2 ]

(16)

(20)

The values of correlation constants d0, d1, and d2 are also listed in a standard table10 (see Table 3), which constitutes database3. When carbon dioxide and water vapor are present together, the total emissivity of the mixture will not be equal to (in fact, will be less than) the sum of the emissivities of the two gases. This is due to the fact that the two gases have common

Emissivity of carbon dioxide (εC) is computed from the standard plots available in the literature.2,3 In these plots, emissivity of carbon dioxide (εC) has been plotted against absolute temperature (T) at different values of (pcL) product. Thus, we get a family of plots. The graphical data of these plots have been fitted into a correlation of the following form by Narayanan and Bhattacharya:10 19817



Article

Table 3. [Database-3], Estimation of Beer’s Law Correction Factor (CW) from Equation 20a

a

(pwL), m atm

d0

d1

d2

3.048 1.524 0.762 0.3048 0.1524 0.0762 0.015 24

0.692 66 0.5772 0.4735 0.3680 0.3201 0.2824 0.1309

0.726 98 1.0164 1.2787 1.500 1.5757 1.6359 2.0143

−0.214 47 −0.3321 −0.4309 −0.4813 −0.4376 −0.3938 −0.5607

Table 4. [Database-4], Estimation of Spectral Overlap Correction Factor (CSO) from Equation 23 (pc + pw)L, Pa m 3089.0

7722.5

Source: Reference 10. 15445.0

wavelengths of absorption and, as a result, each gas becomes somewhat opaque to the other. A correction factor CSO, called spectral overlap correction factor, is, therefore, required to be introduced to take care of this effect. The value of CSO depends on two parameters such as Xp and Xm, where X p = (pc L + pw L)

(21)

X m = [xc/(xc + x w )]

(22)

23167.5

30890.0

xc and xw = mole fraction of carbon dioxide and that of water vapor, respectively, in the gas stream. Standard plots of CSO versus Xm at different values of Xp are available in the literature.9,10 These graphical data have been fitted into analytical correlations through nonlinear regression analysis and elaborate curve fitting procedure. It is observed that the data fit into a correlation of the following form (with R2 = 0.985): CSO/% = a0X m(a1 − X m)/(a 2 + X m)

46335.0

61780.0

′ C W(T /TB)0.45 ]) = ([εC(T /TB)0.65 ] + [εW

(24) (25)

αC = absorptivity of carbon dioxide = [εC(T /TB)

]

(27)

1/U (ideal) = [1/(h THθH)] + [1/(h TCθC)]

(30)

(31)

Computation of actual overall heat transfer coefficient at end-1 (U1) involves again an iterative procedure. This is outlined as follows. (i) The parameter Ψ1 is computed as follows:

(28)

(Refer to refs 1 and 9 regarding αW.) In the preceding equation also, ε′W the is emissivity of water vapor evaluated at T = TB from eq 19. Here also, the correlation constants (b0, b1, and b2) are to be evaluated at

(pw L) = (pw L)(TB/T )

−0.1076 3.0000 −1.5508 −1.2733 −0.2068 0.7337 −5.9256 −1.0818 0.2232 0.8737 −2.3633 −1.0542 0.1352 0.0857 −3.8354 −1.0315 0.0683 0.2032 −3.3717 −1.0335 0.0544 0.3302 2.5290 −1.0257 0.0157 0.1873 −24.2642 −1.0329

STEP-9: If DT is greater than 1.0, computations are repeated from STEP-4. The value of TB1 is thus finalized by trial. The overall ideal heat transfer coefficient per cycle at end-1 is now obtained as

(26)

αW = absorptivity of water vapor ′ C W(T /TB)0.45 ] = [εW

a2

0.11003 4.69998 1.0049 1.0000 0.20692 3.8843 1.1550 1.0000 −2.2052 1.8889 1.1136 1.0000 −2.48 −1.6193 1.1794 1.0000 −1.1654 −22.8878 1.1953 1.0000 −1.1358 3.3284 1.40695 1.0000 −0.4475 9.1072 1.2938 1.0000

DT = Abs(X − TB1)

In the preceding equation, εC as emissivity of carbon dioxide evaluated at T = TB from eq 17. However, the correlation constants (c0, c1, and c2) are to be evaluated at (pc L) = (pc L)(TB/T )

a1

−4.0689 3.0345 −7.6837 −4.8602 −9.2699 2.5518 −58.7323 −5.1509 −2.7674 9.7636 −29.2019 −6.494 −2.4577 −3.2557 −56.1661 −6.9772 −4.4983 −0.3929 −51.5435 −8.0249 −5.0075 4.1759 47.3065 −8.5218 −9.2436 1.1864 −434.4779 −9.5973

After estimating hr using eq 5 and the forced convection heat transfer coefficient [hH for flue gases and hC for air] using eq 1, hTH and hTC are computed from eqs 8 and 9. STEP-7: The value of TB1 is now recalculated from eq 11, based on the previously computed values of hTH and hTC. STEP-8: The deviation is estimated as

where 0.65

a0

0.0−0.25 0.3−0.55 0.6−0.8 0.85−1.0 0.0−0.25 0.3−0.55 0.6−0.85 0.9−1.0 0.0−0.25 0.3−0.55 0.6−0.85 0.9−1.0 0.0−0.25 0.3−0.55 0.6−0.85 0.9−1.0 0.0−0.25 0.3−0.55 0.6−0.85 0.9−1.0 0.0−0.25 0.3−0.55 0.6−0.85 0.9−1.0 0.0−0.25 0.3−0.55 0.6−0.85 0.9−1.0

(23)

The values of correlation constants a0, a1, and a2 are also listed as a standard table (Table 4), which constitutes database-4. Mean absorptivity of gases (αG) is estimated as1,9 αG = (αC + αW )(1 − CSO)

range of X

Ψ1 = [ΔTC(1) + ΔTH(2)]/ΔT1

(32)

where ΔTC(1) = temperature change of cold fluid (air) at outlet (end‐1)

(29)

during one cycle (cold cycle), K

STEP-6: 19818



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(8) If DT is greater than 1.0, computations are repeated from step-3. Otherwise, the process proceeds to step-9. (9) The overall ideal heat transfer coefficient per cycle is estimated using eq 31. (10) The actual overall heat transfer coefficient at end-2 (U2) is computed as follows: (a) The parameter Ψ2 is computed as

ΔTH(2) = temperature change of hot fluid (flue gases) at outlet (end‐2) during one cycle (hot cycle), K

ΔT1 = temperature difference at end‐1, K = T1 − t 2

Since ΔTC(1) and ΔTH(2) are not known at the outset, as the first approximation, let Ψ1 = 0.5

Ψ2 = [ΔTC(1) + ΔTH(2)]/ΔT2

where

(34)

(ii) The dimensionless parameters α and β are computed as α = (h TH + h TC)θH/(CpBρB δ)

(35)

β = [1 − exp(−α)]/α

(36)

ΔT2 = temperature difference at end‐2, K = T2 − t1

(

)

Ψ2 = 0.5

(37)

ϕ = kB(θH + θC)/(CpBρB δ 2)

(38)

ηB = 0.98[1 − exp(− 2ϕ)]/tanh(8ϕ)

(39)

X=

−α

)

(51)

ϕ = (kBθHθC)/(CpBρB δ 2)

(52)

ηB = 0.98[1 − exp(− 2ϕ)]/tanh(8ϕ)

(53)

(e) The value of actual overall heat transfer coefficient at end-2 is then estimated as

(41)

All of the preceding calculations are to be repeated for end-2 also. The following summarizes the process. (1) hH for hot fluid (flue gases) and hC for cold fluid (air) are the same as those computed earlier using eq 1. (2) At end-2 of the regenerator, the cold fluid (air) enters at t1 (during the cooling cycle) and hot flue gases leave at T2 (during the hot cycle). Now, as the first approximation, TB2 is computed as

X=

(1 − e−α)[(1 − 2ηB) − [e−α(1 − e−α)(1 − ηB)]] 2ηB (54)

U2 = U2(ideal)[ξ /(1 + X )]

(55)

The overall heat transfer coefficient (U) of the regenerator is now obtained as U = U1 + U2/2

(42)

(56)

Once U has been estimated, the heat transfer area required is estimated as

(3) X is set as

A = (Q ′θ )/U ( −ΔT )ln

(43)

(4) εG is estimated using eq 14. εC and εW ′ ) are computed from the correlations 17 and 19 and using databases-1 and -2, after substituting T = T2. Values of CW and CSO shall remain the same as for end-1. αG is estimated from eq 24, after substituting T = T2 and TB = TB2. (5) hTH and hTC) at end-2 are now computed from eqs 8 and 9. (6) The value of TB2 is now recalculated as

(57)

where θ = cycle time, s. It has been assumed that θ = θH = θC

(58)

(ΔT )lm = log mean temperature difference (LMTD), K = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2)

(59)

ΔT1 = temperature difference at end‐1, K

TB2 = [(θHT2h TH) + (θCt1h TC)]/[(θHh TH) + (θCh TC)]

= T1 − t 2

(44)

(60)

ΔT2 = temperature difference at end‐2, K

(7) The deviation is estimated as DT = Abs(X − TB2)

(50)

(d) ηB of refractory bricks is computed as

(40)

X = TB2

β = [1 − exp(−α)]/α

(

2ηB

TB2 = [(θHT2) + (θCt1)]/(θH + θC)

(49)

⎡ ⎤ 1.05(1 − β) ⎥ ⎢ ξ = β + 9.52Ψ2⎢1.05(1 − β) − ⎥ 0.1 1+ α ⎦ ⎣

(1 − e )[(1 − 2ηB) − [e (1 − e )(1 − ηB)]]

U1 = U1(ideal)[ξ /(1 + X )]

α = (h TH + h TC)θH/(CpBρB δ)

(c) The dimensionless parameter ξ is computed as

(v) The value of the actual overall heat transfer coefficient at end-1 is then estimated as −α

(48)

(b) The dimensionless parameters α and β are computed as

(iv) The thermal utilization effectiveness (ηB) of refractory bricks is computed as

−α

(47)

As the first approximation, let

(iii) The dimensionless parameter ξ is computed as ⎡ ⎤ 1.05(1 − β) ⎥ ⎢ ξ = β + 9.52Ψ1⎢1.05(1 − β) − ⎥ 0.1 1+ α ⎦ ⎣

(46)

= T2 − t1

(45) 19819

(61)



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Figure 1. CAD flow sheet (summarized).

Q ′ = rate of heat transfer, kJ/s

(E) If DT is greater than 1.0 kJ/s, computations are repeated from (C) with a lower/higher value of T2. Otherwise, we discontinue further trial, and T2 is finalized. Also,

The value of Q′, in fact, is computed at the very outset since it involves computation of he outlet temperature (T2) of hot fluid (flue gases) as well. It is to be noted that T2 is also not known at the outset, and accordingly, computation of Q′ also involves an iterative procedure. This is described in the following. (A) The specific heat of gases varies with absolute temperature as follows: Cp = a + bT + cT 2 + dT 3 + e/T

Q ′ = Q a′

We have to verify the values of Ψ1 and Ψ2 before proceeding further (since we assumed Ψ1 = Ψ2 = 0.5) . This is performed as follows: (1) The dimensionless parameters N1 and N2 are computed as follows:

(62)

where Cp is in kJ/(kmol K) and T is in K. The values of correlation constants (a, b, c, d, and e) differ from gas to gas and could be listed in the form of a standard table,10 which shall constitutes database-5. Integrating the preceding eq 62 between the limits t1 and t2,

∫t

t2

(67)

CC = (Q ′θC)/(T1 − t 2)

(68)

C H = (Q ′θH)/(T1 − t 2)

(69)

where CC and CH are in J/(cycle K)

(Cp dt ) = [a(t 2 − t1) + b(t 2 2 − t12)/2 + c(t 2 3 − t13)/3

γ1 = U1A1/[(1/C H) − (1/CC)]

(70)

γ2 = U2A 2 /[(1/C H) − (1/CC)]

(71)

1

+ d(t 2 4 − t14)/4 − e(1/t 2 − 1/t1)]

(63)

For the components considered in the present study such as nitrogen, oxygen, carbon dioxide, and water vapor, it is seen that c = d = 0. Accordingly, heat gained by air during the cooling cycle (Q′a) is estimated as Q a′ = [∑ niai(t 2 − t1) +

∑ nibi(t2

2

−

t12)/2

−

Since, for end-1, A1 = 0.0, γ1 = 0.0

For end-2, A2 = A and therefore

∑ niei(1/t2 − 1/t1)] (64)

(B) The outlet temperature of flue gases is determined by trial. Thus, a value of T2 is first assumed. (C) Heat lost by flue gases during the heating cycle (Qg′) is computed similarly from eq 64 as Q g′ = [Σniai(T1 − T2) +

∑ nibi(T12 − T2 2)/2 − ∑ niei(1/T1 − 1/T2)]

γ2 = U2A /[(1/C H) − (1/CC)]

(73)

γT = γ1 + γ2

(74)

N1 = γT[exp(−γ1)]/[1 − exp(−γT)]

(75)

N2 = γT[exp(−γ2)]/[1 − exp(−γT)]

(76)

(2) Computation of ΔTC(1) and ΔTH(2) are as follows:

(65)

(D) The deviation (DT) is estimated as DT = |Q g′ − Q a′|

(72)

(66) 19835

FB1 = (CpBρB ηBθHδ)

(77)

FB2 = (CpBρB ηBθCδ)

(78)



Article

ϵ1 = (Q ′N1)/[hCA(t 2 − t1)]

(79)

ϵ2 = (Q ′N2)/[hHA(T1 − T2)]

(80)

ΔTC(1) = [(2U1ΔT1)(θC/2)]/[FB1(1 + ϵ1)]

(81)

ΔTH(2) = [(2U2ΔT2)(θH/2)]/[FB2(1 + ϵ2)]

(82)

In the preceding equations, it has been assumed that each gas (hot gas/cold gas) attains its mean outlet temperature within 50% of the cycle time (θC/2 or θH/2). (3) The value of Ψ is computed as Ψ1 = [ΔTC(1) + ΔTH(2)]/ΔT1

(83)

Ψ2 = [ΔTC(1) + ΔTH(2)]/ΔT2

(84)

(4) It is checked whether Ψ1 and Ψ2 are close to 0.5. If not, the values of U1(actual) and U2(actual) are recomputed using the above computed values of Ψ1 and Ψ2. The thermal efficiency (η) of the regenerator is now estimated as η = [C H/C(min)](1 − f )/[1 − (C Hf /CC)]

Figure 2. Comparison of simulation results with real-life data from industries/pilot plants.

and the heat transfer analysis has been performed using the most updated correlations/computational technique. With a good degree of confidence, the developed CAD package could be, therefore, recommended for the efficient design of industrial heat recovery systems.

(85)

where C(min) = smaller of CC and CH f = exp[−UA[1 − (C H/CC)]/C H]

■

(86)

CC and CH are those defined earlier in eqs 68 and 69. The entire computational procedure is summarized in the CAD flow sheet shown in Figure 1.

RESULTS AND DISCUSSION The developed software package is executed many times to observe the dependence of regenerator efficiency and heat transfer area requirement of the regenerator on the process/ system parameters. The results are summarized as follows: 1. Dependence of Regenerator Efficiency and Heat Transfer Area Requirement on Inlet Temperature of Hot Gases (Heating Medium). The dependence of the heat transfer area requirement of the regenerator on the inlet temperature of hot gases is shown graphically in Figure 3. The following parameters are kept constant.

■

EXPERIMENTAL DATA COLLECTION AND SOFTWARE TESTING To analyze the accuracy and applicability of the CAD (software) package developed, real-life data were collected from process industries (integrated steel plants and thermal power plants) and also from pilot plant installations. All of them used air as the cold fluid (working fluid). Air was admitted at 25−30 °C and preheated to 600−700 °C. The hot gases (heating medium) were admitted at 800−1000 °C. The hot gas flow rate ranged from 1800 to 1900 kg/h and that of air from 1500 to 1600 kg/h. Air contained little carbon dioxide, while the carbon dioxide content of hot gases varied from 10 to 15% (by mole). The comparison between computed values of A (heat transfer area requirement of regenerator) and those of A employed in the industrial/pilot plant units is shown in Figure 2. The white circles stand for data collected from steel plants, dark circles are those from pilot plant installations, and the dark triangles represent data collected from thermal power plants. It can be seen that there is close agreement between computed values of A and real-life values of A in the case of pilot plant installations (maximum deviation = 10−12%) and fairly good agreement in the case of data collected from thermal power plants (maximum deviation = 15−18%). However, some of the data compiled from steel plants deviate from A (computed) by as much as 20−25%. This could very well be due to faulty operation of the regenerator. Large scale carbon deposition on the refractory checker work, significant fluctuations in hot gas flow rate/temperature, and inadequate monitoring of air outlet temperature could all lead to inefficient heat recovery and inferior performance of the regenerator. The overall observation, nevertheless, from Figure 2 is that the developed CAD package is reliable and reasonably accurate. Note that while developing the simulation model (software package), we have not incorporated any gross simplifications

inlet temperature of air: t1 = 288 K outlet temperature of air: t 2 = 1033 K

volumetric flow rate of air: Q C = 1415 m/h

(measured at 288 K and 1 atm)

volumetric flow rate of flue gases: Q H = 1530 m/h

(measured at 288 K and 1 atm)

duration of heating/cooling cycle: θH = θC = 4500 s

flue gases composition (% by mole): CO2 = 13.3%,

N2 = 66.3%,

O2 = 4.01%,

water vapor = 16.34%

It can be seen from the figure that the heat transfer area requirement of the regenerator is decreasing with an increase in the inlet temperature of flue gases. A higher temperature of heating medium (namely, the hot flue gases) increases the radiant heat transfer between the gases and the refractory checker work. This, in turn, enhances the checker work temperature (TB1), and the rate of heat transfer to cold fluid (air) is also augmented. Accordingly, for the same capacity 19836



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Figure 3. Dependence of the heat transfer area requirement of the regenerator on the inlet temperature of hot gases.

Figure 4. Dependence of regenerator efficiency on inlet temperature of hot flue gases.

Figure 5. Dependence of heat transfer area requirement of the regenerator on outlet temperature of air.

to note that an increase in inlet temperature of flue gases by

(same flow rate of air and same air inlet temperature), the heat transfer surface requirement of the regenerator decreases. No doubt, too high a temperature of flue gases shall not be practically feasible in many situations. However, it is interesting

100 °C brings down the heat transfer surface requirement of the regenerator by almost 50%. Consequently, it shall be most 19837



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Figure 6. Dependence of regenerator efficiency on outlet temperature of air.

Figure 7. Dependence of heat transfer area requirement of the regenerator on (A) the volumetric flow rate of air and (B) the mass flow rate of flue gases and air.

graphically at different values of inlet temperature of flue gases in Figure 4. In the case of a regenerator of given heat transfer surface (for example, A = 150 m2), the overall efficiency of heat recovery (η) increases with an increase in hot gas inlet temperature, as is seen from Figure 4. This agrees with the earlier observation that

desirable to maintain a high inlet gas temperature so as to accomplish more efficient heat recovery. Now, the software package is re-executed at a specific value of A (heat transfer area) such as A = 150 m2 (while keeping the values of other initial parameters the same as in the earlier case). Computed values of regenerator efficiency are plotted 19838



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Figure 8. Dependence of regenerator efficiency on (A) the volumetric flow rate of air and (B) the ratio of mass flow rate of flue gases and air.

turn, shall demand a larger heat transfer surface (when other influencing parameters such as the inlet temperature of hot gases, the flow rate of gases, and that of air are maintained the same). This is what is demonstrated in Figure 5. However, it can be seen from the plot that for 50 °C increases desired in air outlet temperature, the heat transfer surface requirement increases by only around 20% (by about 16−17 m2). This speaks for the overall cost effectiveness of the regenerator as a reliable heat recovery system even at higher heat duty (or higher heat exchange rate desired). Now, the software package is re-executed at a specific value of A (heat transfer area) such as A = 150 m2 (while keeping the values of other initial parameters the same as in the earlier case). Computed values of regenerator efficiency are plotted graphically at different outlet temperatures of air in Figure 6. If the heat transfer surface is fixed at a specified value (for example, 150 m2), then the efficiency of the regenerator shall be lower for maintaining a higher air outlet temperature (as is demonstrated in Figure 6). Figure 6 shows that the regenerator efficiency decreases with the increase in air outlet temperature (at specified values of hot gas flow rate, air flow rate, and hot gas inlet temperature). 3. Dependence of Regenerator Efficiency and Heat Transfer Area Requirement on Volumetric Flow Rate of Air and Mass Ratio of Flue Gases to Air. The dependence

a higher magnitude of hot gas inlet temperature enhances radiant heat transfer to bricks and, in turn, increases heat transfer from bricks to the cold fluid (air). This thus augments the overall thermal efficiency of the regenerator. It can be seen from the figure that regenerator efficiency increases sluggishly at low values of T1 (inlet temperature of flue gases). At higher values of T1, the increase of regenerator efficiency with increase in T1 is much sharper and close to linear. 2. Dependence of Regenerator Efficiency and Heat Transfer Area Requirement on Outlet Temperature of Air. Here, the outlet temperature of air is the variable, but all of the other parameters are fixed. Using the software package, the computed values of heat transfer area requirement of the regenerator are plotted graphically at different outlet temperatures of air in Figure 5. t1), T1), QC, QH, duration of heating/cooling cycle (θH = θC), and flue gases composition are maintained the same as before. It can be seen from the figure that the heat transfer area requirement is increasing sluggishly with the increase in the outlet temperature of air. The temperature to which the cold fluid (namely, air) is to be preheated is another system parameter and this decides the heat duty of the regenerator demanded. A high air outlet temperature corresponds to higher heat duty (larger heat load to be transferred to air), and this, in 19839



Article

Figure 9. Dependence of heat transfer area requirement of the regenerator on the carbon dioxide content of flue gases.

Figure 10. Dependence of heat transfer area requirement of the regenerator on water vapor content of flue gases.

of the heat transfer area requirement of the regenerator on the volumetric flow rate of air is illustrated graphically in Figure 7. Here also other process/system parameters such as t1, t2, T1, QH, θH = θC, and flue gases composition are maintained at the same values as in earlier cases. It can be seen from the figure that the heat transfer area requirement increases with the increase of the volumetric flow rate of air. The capacity of the regenerator is decided by the amount of air handled per hour (in other words, the amount of air preheated per hour within the specified temperature range). As the amount of air to be preheated increases, the heat transfer surface requirement of the regenerator also increases (as evidenced from Figure 7A). However, here also, it can be observed that when the air flow rate is increased by 100 m3/h, the heat transfer surface requirement increases only by around 15% (by around 17 m2). The regenerator may be therefore regarded as a cost-effective heat recovery system even at sufficiently large capacities. A better measure of the capacity of the regenerator is accomplished by observing the dependence of A on the gas to air volumetric/mass ratio (ratio of volumetric/mass flow rate of hot gases to that of air). An increase in this ratio brings down the heat transfer surface requirement of the regenerator as illustrated in Figure 7B). Nevertheless, the increase in the hot gas flow rate required for handling a larger amount of air per

hour is not substantially larger. For example, in the case of a 112 m2 regenerator, for increasing the air flow rate from 1465.0 to 1650 kg/h (volumetric flow rate increased from 1200 to 1300 m3/h), the hot gas flow rate is to be increased from 454 to 510 kg/h (volumetric flow rate to be increased from 1530 to 1720 m3/h) only. In other words, by increasing the gas flow rate by 60 kg/h (or volumetric flow rate by 190 m3/h), it is possible to increase the amount of air handled by190 kg/h (or by 150 m3/h), without altering the heat transfer surface of the regenerator. This once again illustrates the reliability of the regenerator toward high capacity operations/applications. Now, the software package is re-executed at a specific value of A (heat transfer area) such as A = 150 m2 (while keeping the values of other initial parameters the same as in the earlier case). Computed values of regenerator efficiency are plotted graphically at different volumetric flow rate of air in Figure 8. It can be seen from the Figure 8A that regenerator efficiency decreases with the increase in the volumetric flow rate of air. For any given regenerator of specified heat transfer surface (for example, A = 150 m2), the η decreases with any increase in air flow rate (when flue gas flow rate is kept fixed) and increases when the mass ratio (or volume ratio) of hot gases to air (heating fluid to cold fluid) is increased (see Figure 8B. The observation is in consonance with that discussed in the earlier paragraphs. 19840



Article

Figure 11. Dependence of regenerator efficiency on the carbon dioxide content of flue gases.

Figure 12. Dependence of regenerator efficiency on the water vapor content of flue gases.

4. Dependence of Regenerator Efficiency and Heat Transfer Area Requirement on Composition of Hot Gases (Heating Medium). The heat transfer area requirement of the regenerator is computed at different values of carbon dioxide content of flue gases, and the data are illustrated graphically in Figure 9. The oxygen content and the water vapor content are kept constants at 4.01% and 16.34%, respectively. Carbon dioxide content changes and the nitrogen content also changes proportionally. t1, t2, T1), QC, QH, and θH = θC are maintained at the same values as in earlier cases. The dependence of the heat transfer area requirement of the regenerator on water vapor content of flue gases is illustrated graphically in Figure 10. The oxygen content and the carbon dioxide content are kept constant at 4.01% and 13.3%, respectively. Water vapor content changes and the nitrogen content also changes proportionally. t1, t2, T1, QC, QH, and θH = θC are maintained at the same values as in earlier cases. It can be seen from the figure that the heat transfer area requirement decreases with the increase in carbon dioxide content in the flue gases. As stated earlier, the radiant heat transfer from hot gases to the refractory checker work is controlled by the carbon dioxide content and water vapor content of the hot gases, since these are the only two constituents that possess substantially larger emissivity (other

constituents such as nitrogen and oxygen, being diatomic gases, possess very low emissivity). Consequently, as the mole fraction of carbon dioxide or that of water vapor in the hot gases increases, the radiant heat transfer to the checker work also increases. This brings down the heat transfer surface requirement of the regenerator for a given duty, as shown in Figures 9 and 10. However, since carbon dioxide has a larger emissivity than water vapor, the carbon dioxide content of the hot gases is relatively more controlling. For example, from Figure 9, it can be seen that as the mole fraction of carbon dioxide in the hot gases increases from 0.1 to 0.3, the heat transfer surface requirement of the regenerator decreases by about 15% (by around 22.0 m2), while a similar increase in water vapor content of hot gases brings down the heat transfer surface requirement by around 11% only (by about 18.0 m2), as can be seen from Figure 10). No doubt, when flue gases from a combustion furnace are being used as the heating medium, then too large a carbon dioxide content in these gases shall be undesirable. Carbon dioxide, being a green house gas, tends to create serious environmental concerns when these flue gases are ultimately exhausted to the atmosphere. Now, the software package is re-executed at a specific value of A (heat transfer area) such as A = 150 m2 (while keeping the values of other initial parameters same as in the earlier case). 19841



Article

Figure 13. Dependence of heat transfer area requirement of the regenerator on duration of heating/cooling cycle.

Figure 14. Dependence of regenerator efficiency on duration of heating/cooling cycle.

It can be seen from the figure that the heat transfer area requirement decreases with the increase the duration of the heating/cooling cycle. The heating/cooling cycle time (θH, θC) is another operating parameter that influences the regenerator performance. In most cases and for best results, the durations of both of these cycles are maintained equal (θH = θC). When the cycle time is increased, the overall heat transfer coefficient per cycle (U) also increases and this brings down the heat transfer surface requirement of the regenerator for performing a given duty. However, this decrease in A is observed to be not substantial. For example, when the cycle time is doubled from 60 to 120 min, the value of A decreases from 155 to 140 m2, a decrease by 15 m2 only (see Figure 13). Now, the software package is re-executed at a specific value of A such as A = 150 m2 (while keeping the values of other initial parameters the same as in the earlier case). Computed values of regenerator efficiency are plotted graphically at different durations of the heating/cooling cycle in Figure 14. Increase in cycle time does increase the thermal efficiency of the regenerator as shown in Figure 14, but this increase is also not substantial. For instance, when the cycle time is doubled (from 60 to 120 min), the efficiency of heat recovery increases only by 3% (from 65.38% to 68.68%).

Computed values of regenerator efficiency are plotted graphically at different carbon dioxide content of flue gases in Figure 11. For a regenerator of specified heat transfer surface at hand, a higher carbon dioxide content of hot gases corresponds to higher heat recovery. As can be seen from Figure 11, η of the regenerator increases from 64.6% to 74.5%, when the mole fraction of carbon dioxide in hot gases is increased from 0.1 to 0.3 (other process parameters being maintained constant). The same is the case with the water vapor content of hot gases, though the degree of augmentation in the thermal efficiency attained is relatively lower (see Figure 12). For example, when the water vapor content of hot gases is increased from 10% (by mole) to 30% (by mole), the overall thermal efficiency of the regenerator increases by only 6% (from 63.66% to 69.36%). 5. Dependence of Regenerator Efficiency and Heat Transfer Area Requirement on Duration of Heating/ Cooling Cycle. The dependence of the heat transfer area requirement of the regenerator on the duration of the heating/ cooling cycle is illustrated graphically in Figure 13. Here also other process/system parameters, such as t1, t2, T1, QH, and flue gases composition, are maintained at the same values as in earlier cases. 19842



Article

design/operation for attaining augmented and more efficient heat recovery. (8) The limitations of the present study are also to be kept in mind such as the study does not account for fouling of refractory checker work due to carbon deposition or deposition of metallic oxides. Contribution of conduction heat transfer has been neglected as compared to those from radiative and convective modes of heat transfer, since the thickness of refractory checker work is very small and has also been found to be true from real-life observations. Pressure drop computations have also not been included in the package, since the analysis has been focused on the thermal efficiency and heat transfer area requirement of the heat recovery system.

It can be, therefore, concluded that a large cycle time is unnecessary since it does not significantly improve the performance of the regenerator. In most industrial applications, therefore, θH = θC = 60−75 min shall be satisfactory.

■

CONCLUSION (1) Attempts have been made to perform computer aided analysis and simulation of the performance of regenerators that employ fixed matrixes of refractory checker work and that are widely used in process industries as heat recovery systems. (2) A versatile CAD (software) package has been developed that predicts all the design/operating parameters of regenerators of this kind with reliable accuracy. The applicability of the package has been verified by comparing the simulation results with real-life data collected from integrated steel plants, thermal power plants, and pilot plant installations. (3) The heat transfer area requirement of regenerators of this kind has been found to decrease with the increase in inlet temperature (T1) of hot gases (heating medium) but increases with the increase in outlet temperature (t2) of cold fluid (working fluid). The thermal efficiency of the exchanger increases with the increase in gas inlet temperature (T1) but decreases with the increase in outlet temperature (t2) of the working fluid desired. However, it is observed that the heat transfer requirement of the regenerator increases by only around 20% with a 50% increase desired in air (working fluid) outlet temperature. This illustrates that the operation of these regenerators is efficient and cost effective even when high heat duty (high rate of heat recovery) is demanded. (4) It has also been observed that the heat transfer surface requirement of the regenerator decreases and the thermal efficiency increases with the increase in volume/mass ratio of hot gases to air. Nevertheless, the increase in gas flow rate required to handle a larger volume of air (working fluid) per hour is not substantially large (Figures 7B and 8B), and this highlights the high reliability of regenerators of this kind even for operation at high capacities. (5) The higher the carbon dioxide content and water vapor content of the hot gases (heating medium), the higher is the thermal efficiency of the regenerator and the lower is its heat transfer surface requirement for performing a given duty. Here, the carbon dioxide content is found to be more controlling. In other words, the degree of enhancement in thermal efficiency of the regenerator attained is relatively larger with the increase in carbon dioxide content as compared to a similar increase in water vapor content of the heating medium (hot gases). (6) The ncrease in the duration of the heating cycle/cooling cycle (θH, θC) does increase the efficiency of the regenerator and bring down its heat transfer surface requirement (A). However, this decrease in A or increase in thermal efficiency has been found to be not substantial. Accordingly, it may be concluded that maintaining a large cycle time is unnecessary and θC = θH = not more than 60−75 min could be recommended for most industrial applications. The data collected from thermal power plants and pilot plant installations also substantiate this. (7) Since the CAD package has been developed without any undue simplifications and by using well-developed databases, this software may be recommended, with confidence, for the design and installation of heat recovery systems (regenerative heat exchangers) in process industries. The package may also be employed for analyzing the performance of existing regenerators and for proposing suitable modifications in its

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Web: www.profcmn.com. Notes

The authors declare no competing financial interest.

■

19843

NOMENCLATURE A = total heat transfer area of regenerator, m2 A1 = heat transfer area at end-1 of regenerator, m2 A2 = heat transfer area at end-2 of regenerator, m2 AC = area of each flow channels, m2 A(min) = minimum area for gas flow, m2 CC = parameter defined in eq 68, J/(cycle K) CH = parameter defined in eq 69, J/(cycle K) C(min) = smaller of CC and CH, J/(cycle K) Cp = specific heat of gases, J/(kmol K) CpB = specific heat of refractory bricks, J/(kg K) CW = Beer’s law correction factor CSO = spectral overlap correction factor De = equivalent diameter of channels, m f = parameter defined in eq 86 F = emissivity correction factor FB1 = parameter defined in eq 77, (J/cycle) s/(m2 K) FB2 = dimensional parameter defined in eq 78, (J/cycle) s/ (m2 K) h = forced convection heat transfer coefficient, W/(m2 K) hC = forced convection heat transfer coefficient for cold fluid (air), W/(m2 K) hH = forced convection heat transfer coefficient for hot fluid (hot gases), W/(m2 K) hTC = total heat transfer coefficient for cold fluid, W/(m2 K) hTH = total heat transfer coefficient for hot fluid, W/(m2 K) hr = radiation heat transfer coefficient, W/(m2 K) L = mean beam length, m n = molar flow rate, kmol/s NC = total number of channels N1 = parameter defined in eq 75 N2 = parameter defined in eq 76 P = total pressure, atm pc = partial pressure of carbon dioxide, atm pw = partial pressure of water vapor, atm Q′ = rate of heat transfer, J/s Qg = volumetric flow of hot gases at 25 °C and 1 atm, m3/s Qa′ = heat gained by the air during cooling cycle, J/s Q′g = heat lost by the hot gases during heating cycle, J/s R = universal gas constant, atm m3/(kmol K) RH = hydraulic radius of flow channels, m t1 = air inlet temperature, K dx.doi.org/10.1021/ie501213s | Ind. Eng. Chem. Res. 2014, 53, 19814−19844


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(3) Lai, S. M. ; Duduković, M. P. Periodic Operation of Heat Regenerators: A New Method for Calculation of Thermal Efficiency. Master’s Thesis, Sever Institute of Washington University: Saint Louis, MO, USA, August 1983. (4) Falk, C. Predicting Performance of Regenerative Heat Exchanger. Project Report, MVK160 Heat and Mass Transport; Lund University: Lund, Sweden, May 2009. (5) Zunft, S.; Hänel, M.; Krüger, M.; Dreißigacker, V. A Design Study for Regenerator-Type Heat Storage in Solar Tower PlantsResults and Conclusions of the HOTSPOT Project. Energy Procedia 2013, 49, 1088−1096. (6) Nijdam, J. L. Behaviour and Optimization of Packed Bed Regenerators. Ph.D. Thesis, Pioerscbrift Technische Universiteit Eindhoven: Eindhoven, The Netherlands, October 1995. (7) Erk, H. F. ; Duduković, M. P. Heat Regenerators with PhaseChange Materials. Ph.D. Thesis, Sever Institute of Washington University: Saint Louis, MO, USA, April 1990. (8) Rühlich, I. ; Quack, H. Investigations on Regenerative Heat Exchangers, Technical Report; Technische Universität Dresden: Dresden, Germany, 1990. (9) Perry, R. H. ; Green, D. W. Chemical Engineers’ Handbook; McGraw Hill: New York, 1997. (10) Narayanan, C. M. ; Bhattacharya, B. C. Unit Operations and Unit Processes, Vol. 1; CBS: New Delhi, India, 2006.

t2 = air outlet temperature, K t(av) = average temperature of air, K T1 = flue gases inlet temperature, K T2 = flue gases outlet temperature, K T(av) = average temperature of flue gases, K TB1 = mean surface temperature of refractory bricks at end-1, K TB2 = mean surface temperature of refractory bricks at end-2, K U = overall heat transfer coefficient of the regenerator, J/(m2 K cycle) U(ideal) = overall ideal heat transfer coefficient per cycle, J/ (m2 K cycle) U1 = overall heat transfer coefficient at end-1, J/(m2 K cycle) U2 = overall heat transfer coefficient at end-2, J/(m2 K cycle) V = average velocity of gas/gases through the channels measured at 0 °C and 1 atm, m/s V(max) = maximum velocity of gases through the regenerator, m/s xc = mole fraction of carbon dioxide in the gas stream xw = mole fraction of water vapor in the gas stream X = parameter defined in eq 40 Y = molal humidity of air, kmol of water vapor/(kmol of dry air) α = parameter defined in eq 35 αC = absorptivity of carbon dioxide αG = mean absorptivity of gases αW = absorptivity of water vapor β = parameter defined in eq 36 γ1 = parameter defined in eq 70 γ2 = parameter defined in eq 71 γT = parameter defined in eq 74 δ = thickness of the flow channels, m ΔT1 = temperature change at end-1, K ΔT2 = temperature change at end-2, K ΔTC(1) = temperature change of cold fluid (air) at outlet (end-1) during one cycle (cooling cycle), K/cycle ΔTH(2) = temperature change of hot fluid (flue gases) at the outlet (end-2) during one cycle (hot cycle), K/cycle (−ΔT)lm = log mean temperature difference (LMTD) of the regenerator, K ϵ1 = parameter defined in eq 79 ϵ2 = parameter defined in eq 80 εB = average emissivity of refractory bricks εC = average emissivity of carbon dioxide εG = average emissivity of gases εW ′ = emissivity of water vapor (uncorrected) εW = emissivity of water vapor (corrected) η = thermal efficiency of the regenerator ηB = thermal utilization effectiveness of refractory bricks θC = duration of cooling cycle, s θH = duration of heating cycle, s ξ = parameter defined in eq 37 ρB = density of the refractory bricks, kg/m3 σ = Stefan−Boltzmann constant, W/ (m2 K4) ϕ = parameter defined in eq 38, s ψ = parameter defined in eqs 32 and 46

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REFERENCES

(1) Schack, A. Industrial Heat Transfer; Chapman and Hall: London,

1965. (2) Kern, D. Q. Process Heat Transfer; McGraw Hill: New York, 1950. 19844


Computer Aided Design and Analysis of Regenerators for Heat

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