Determining the best type of heat exchangers for heat recovery PDF

Preview

Summary

Applied Thermal Engineering 30 (2010) 577–583 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng Determining the best type of heat exchangers for heat recovery _ Ismail Teke, Özden Ag˘ra, Sß. Özgür Atayılmaz, Hakan Demir * Depar...

Description

Applied Thermal Engineering 30 (2010) 577–583

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Determining the best type of heat exchangers for heat recovery _ Ismail Teke, Özden Ag˘ra, Sß. Özgür Atayılmaz, Hakan Demir * Department of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey

a r t i c l e

i n f o

Article history: Received 19 June 2009 Accepted 31 October 2009 Available online 10 November 2009 Keywords: Effectiveness NTU Heat exchangers Economical optimization Heat recovery

a b s t r a c t It is a common problem to choose the most appropriate heat exchanger configuration for heat recovery. In this study, a new model has been developed for determining the area and type of the most appropriate waste heat recovery heat exchanger for maximum net gain. A non-dimensional E number has been defined based on known technical and economic parameters such as the life-time, unit area cost of the heat exchanger, lower heating value of the fuel, overall heat transfer coefficient of heat exchanger, boiler efficiency, operation time per year, heat exchanger effectiveness, ratio of heat capacities, annual variation of the temperature of fluids supplied to the heat exchanger and present worth factor. The non-dimensional E numbers has been demonstrated in graphical forms as a function of NTU and ratio of heat capacities and corresponding heat exchanger area giving maximum net gain can easily be obtained from these graphs. The best heat exchanger type and its area can be determined comparing net gains or effectiveness of heat exchangers at NTUmax. Application of the new method has been given with a case study as a sample calculation. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Energy demand is increasing as a consequence of population growth and economical development. On the other hand, fossil fuels meeting a great portion of the energy demand are very scarce and their availability is decreasing year by year. Today, energy efficiency is a hot topic which covers almost all appliances employed in industry, infrastructure and household appliances, etc. Developing and designing energy efficient systems are one of the main interest area of engineering. Approximately 26% of industrial energy is wasted as hot gas or fluid in many countries. It can be significantly reduced by employing simple heat recovery systems. Heat recovery does not only help to save energy but also decreases the environmental impact of energy generation systems simply by reducing the amount of CO2 released to the environment. An economical implementation of a heat recovery system on existing facilities requires a feasible and sustainable amount of waste heat. Amount of heat that recovered is highly dependent on fluid properties, particularly temperature and flow rate. The size of the heat recovery system, thus the cost of this system, is strongly associated with heat recovery potential and fluid temperature. Regarding these facts, a thermo-economical feasibility analysis should be conducted prior to installing heat recovery systems. This kind of analysis would reveal the most economical heat exchanger type among alternatives and thus guarantee the highest rate of heat recovery at a minimum cost. * Corresponding author. Tel.: +90 212 383 28 20; fax: +90 212 261 66 59. E-mail address: [email protected] (H. Demir). 1359-4311/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2009.10.021

In the literature, relevant studies on heat exchanger networks [1–14] can be easily found. But these previous studies are not directly related to the basic idea of the present study. In this study, a new model has been developed to determine the heat exchanger type, area and net gain of the most appropriate heat exchanger to be used in waste recovery systems and further to compare the results reciprocally. In this model, a non-dimensional E number has been defined based on technical and economical parameters. The relation giving general E number can be used for all heat exchangers regardless of the heat exchanger type. On the other hand, it has been determined that the value of E obtained by this method is equal to the derivative of effectiveness of the heat exchangers. In order to obtain the E value, the effectiveness has been derived as regards to NTU for all heat exchanger types. Then the non-dimensional E number has been demonstrated in graphical form as a function of NTU and ratio of heat capacities. The NTU value that gives maximum net gain and correspondingly the heat exchanger area can easily be derived by using non-dimensional E number calculated based on technical and economical parameters and the graphics or relations together. The calculated E value is employed in all heat exchanger graphs to find out the heat transfer area that gives maximum net gain. The best heat exchanger is chosen according to maximum net gain. Then the net profit concerning the best heat exchanger has separately been calculated. The net profit is calculated by subtracting the investment cost from the saving obtained. While calculating the saving to be yielded by thermal recovery, the present worth factor is employed. This expression is generally calculated as a function of interest rate and inflation. However, interest rate and inflation values are actually

I._ Teke et al. / Applied Thermal Engineering 30 (2010) 577–583

578

Nomenclature A BYM Cp C E er f F g H Hu i _ m n NTUmax PT r Q_ T

heat transfer area of heat exchanger (m2) heat exchanger investment cost per unit area ($/m2) specific heat (J/kg °C) heat capacity (W/°C) dimensionless number real fuel price rate fuel price rate fuel cost ($/kg) inflation rate operation time per year (h) lower heating value of fuel (J/kg) interest rate mass flow rate (kg/s) heat exchanger life-time (years) NTU number giving the maximum net gain (–) money saved from waste energy for a year ($/year) real interest rate total heat transfer rate (W) temperature (oC, K)

not constant. In parallel to the variation of interest and inflation rate, the present worth factor and amount of saving will also change and it would not be possible to find only one best heat exchanger type and area. In this study, present worth factor expression has been restated after omitting the variation of inflation and interest rates. So, the effect of variation in inflation and interest rates over the calculations is prevented. The new developed present worth factor expression has been stated as a function of real change in fuel price and life-time. Application of the new method has been given with a case study as a sample calculation.

TPT U YM PWF

present worth of money saved from waste energy for (n) year ($) overall heat transfer coefficient (W/m2K) investment cost of heat exchanger ($) present worth factor

Greek letters effectiveness of the heat exchanger (–) boiler efficiency (%)

e g

Subscripts h hot fluid c cold fluid i inlet min minimum max maximum r ratio o outlet

NTU ¼

UA C min

ð4Þ

The effectiveness of a heat exchanger can be obtained as a function of NTU and heat capacities ratio (Cr):

e ¼ f ðNTU; CrÞ

ð5Þ

The effectiveness correlations for different types of heat exchangers are summarized in Table 1 [15,16,18]. If there is a phase change in heat exchangers effectiveness correlations became same

2. Theoretical analysis

e ¼ 1  expðNTUÞ

2.1. Fundamental concepts

2.2. Cost analysis of heat exchanger

The effectiveness (e) is the ratio of heat transfer rate to the maximum possible heat transfer rate when heat exchanger area goes to infinity;

In this section cost analysis of the heat exchanger, which is employed for waste heat recovery, has been performed and heat transfer area that yields maximum net saving has been determined.

Q_

e¼ _ Q max

ð1Þ

Heat capacity rates are obtained by multiplying the specific heat and mass flow rate of the fluids. The fluid having the higher heat capacity is designated Cmax and the lower fluid heat capacity as Cmin. If the cold fluid has the minimum heat capacity the effectiveness is

e¼

C max ðT h;i  T h;o Þ C min ðT c;o  T c;i Þ ¼ C min ðT h;i  T c;i Þ C min ðT h;i  T c;i Þ

ð2Þ

If there is a phase change in a heat exchanger, the heat capacity of the fluid changing phase becomes infinite and their ratio is zero. When both of the fluid heat capacities are equal, then effectiveness would be:

e¼

UA C min þ U  A

ð6Þ

2.2.1. Investment cost The investment cost could be expressed in terms of unit area cost of heat exchanger (BYM) and total heat transfer area (A)

YM ¼ BYM  A

ð7Þ

Heat transfer area A obtained from Eq. (4) can be inserted into Eq. (7). After this manipulation we receive Eq. (7) in the form;

YM ¼ BYM 

  C min  NTU U

ð8Þ

From Eq. (8) it can be seen clearly that all the terms are constant except (NTU) and these constants are designated by a new constant D.

YM ¼ D  NTU

ð9Þ

ð3Þ

NTU is a dimensionless parameter, related with the size of heat exchangers and is commonly used in heat exchanger analysis. NTU is expressed as

2.2.2. Amount of annual savings The temperatures of the waste heat fluid and the cold fluid, used in industrial plants may fluctuate over time. As shown in Eq. (10), it is essential to consider changes in hot and cold fluid temperatures in order to calculate the amount of heat recovery

I._ Teke et al. / Applied Thermal Engineering 30 (2010) 577–583

579

Table 1 Effectiveness and E number relations for heat exchangers. Type

E

e

Parallel flow

E ¼ exp½NTUð1 þ CrÞ

e¼

1exp ½NTUð1þCrÞ 1þCr

Counter flow

e¼ e¼

1exp ½NTUð1CrÞ 1þCr exp ½NTUð1CrÞ ; NTU Cr ¼ 1 1þNTU ;

Cr < 1

Cross flow Both fluid unmixed

e ¼ 1  exp ð1=CrÞNTU0:22 exp CrðNTUÞ0:78  1

h

n

n h ih o i 1 E ¼ eCr exp CrðNTUÞ0:78 0:22NTU0:78  0:78Cr  0:22ðNTUÞ0:78

Cross flow Cmin(unmixed), Cmax(mixed)

ðNTUÞg e ¼ 1exp fCr½1exp Cr

E ¼ ð1  eCrÞ expðNTUÞ

Cross flow Cmax(unmixed), Cmin(mixed)

e ¼ 1  expfð1=CÞ½1  expðNTU  CrÞg

E ¼ ðe  1Þ expðCrNTUÞ

Shell and tube One shell pass (2, 4, . . . , tube passes)

e1 ¼ 2 1 þ Cr þ ð1 þ Cr2 Þ1=2

n Shell passes (2n, 4n, . . . , tube passes)

en ¼



h

1e1 Cr 1e1

n

E ¼ ð1  CrÞ2

h

i

1þexp NTUð1þCr2 Þ

1=2

1exp NTUð1þCr2 Þ

1=2

 

3600 Hu  g

Z

H

ðT h;i  T c;i Þdt

ð10Þ

0

Life-cycle cost analysis has been used to calculate the total energy savings. Life-time and present worth factor (PWF) are effective in this approach. PWF has been calculated in relation to the real interest rate and energy cost rate. Real interest rate (r) and energy cost rate (er) have been calculated by employing interest (i), fuel price rate (f) and inflation (g) rates. Then, PWF has been calculated as follows: If r – er

PWF ¼

1 r  er





1

 n  1 þ er 1þr

1 

n ih i1 1e1 Cr 1  Cr 1e1

accurately. The amount of saved money for a year using a heat exchanger:

PT ¼ e  C min  F

oi

ð11Þ

n PWF ¼ 1 þ er

E¼

ð12Þ

f g er ¼ 1þg

Inflation rate has been ignored in the formulation given in Eq. (11). Otherwise, PWF would be susceptible to interest and inflation rates due to the unsteady nature of these rates. PWF and thereby savings would change and the results would be erroneous. The present worth of saved money for n year would be;

3600 Hu  g

Z

H

ðT h;i  T c;i Þdt

ð13Þ

0

ð14Þ

All the terms except (e) are constant in Eq. (13). When these constants are designated by a new constant B, total saving is;

TPT ¼ B  e



n1

1e1 Cr 1e1

h

ð1CrÞ2

n

1e1 Cr 1e1

i2

Cr

dðTPTÞ dðYMÞ ¼ dðNTUÞ dðNTUÞ

ð16Þ

The derivates of TPT and YM are

dðTPTÞ de ¼B dðNTUÞ dNTU

and

dðYMÞ ¼D dðNTUÞ

ð17Þ

After equalizing the right hand side and rearranging these two derivates, a dimensionless equation is obtained;

E¼

de D ¼ dNTU B

ðconstant and dimensionlessÞ

ð18Þ

Dimensionless E number is a function of technical and economical parameters and can be written as follows:

E¼

D BYM  Hu  g ¼ R B U  F  PWF  3600 H ðT h;i  T c;i Þdt

ð19Þ

This equation is valid for all types of heat exchangers. At the same time E is a function of effectiveness,

ð15Þ

ð20Þ

BYM  Hu  g RH ðT h;i  T c;i Þdt 0

U  F  PWF  3600

ð21Þ

The NTUmax is obtained either from the given charts in Figs. 1–6 or the equation at Table 1. Using the calculated (or read) NTUmax value corresponds the heat exchanger area is determined from the following equation:

A¼ 2.2.3. Heat exchanger area giving maximum net gain Considering the YM and TPT as a function of NTU, the maximum difference between saving and investment cost is at such NTU value that the derivates of the mentioned functions according to (NTU) are equal [17].

de dNTU

E can also be obtained as a function of NTU for different types of heat exchangers but the right hand side of the Eq. (20) is dependent on the heat exchanger type. The E values have also been given charts as a function of Cr and NTU for different types of heat exchangers deriving the effectiveness relations in Figs. 1–6. In order to determine the area of a heat exchanger giving maximum net gain the initial step is to obtain heat capacities ratio and E value. Employing the following equation:

E¼

or

TPT ¼ PT  PWF

nE1

4ð1þCr2 Þ exp ½NTUð1þCr2 Þ1=2  ½1þCrþð1þCr2 Þ1=2 f1þexp ½NTUð1þCr2 Þ1=2 g

ð1e1 Þ2

E¼

TPT ¼ e  PWF  C min  F

1=2

E ¼ E1 ¼

0

If r = er

ig r¼ ; 1þg

exp ½NTUð1CrÞ ½1Cr exp ½NTUð1CrÞ2

NTUmax  C min U

ð22Þ

2.2.4. The best heat exchanger type giving the maximum net gain In order to determine the best effectiveness or maximum net gains of heat exchangers at NTUmax area compared. The heat ex-

I._ Teke et al. / Applied Thermal Engineering 30 (2010) 577–583

580

1 E=0.001 0.002 0.003

0.004 0.006

0.9

Effectiveness

0.01

0.02 0.8 0.04 Cr=1 0.06

Cr=0.75

0.08

0.7

Cr=0.5 0.1

Cr=0.25 Cr=0

0.6

NTU Fig. 1. Effectiveness and E number for counter-flow heat exchanger.

0 .1

5

2

0 .0

0 .0

1

1 0 08 06 04 0 .0 0 . 0 .0 0.0

0 .0

02 E =0.0

01

0.9 0.8

Effectiveness

0.7 0.6 0.5 0.4

Cr=0

0.3

Cr=0.25 Cr=0.5 Cr=0.75 Cr=1

0.2 0.1 0 0

1

2

3

4

5

6

7

8

NTU Fig. 2. Effectiveness and E number for parallel-flow heat exchanger.

1

1

E=0.002

0.9

0.004

0.8

0.04 0.02 0.06 0.08 0.1 Cr=0 Cr=0.25 Cr=0.5 Cr=0.75 Cr=1

0.6 0.4 0.2

0.01 0.008

0.006

Effectiveness

Effectiveness

0.8

0.1

2 1 08 06 004 0.0 5 .03 0.0 0.0 0.0 0.0 0. 0.0 0

02

E=

01 0.0

0.7 0.6 Cr=0 0.5 Cr=0.25 0.4 Cr=0.5 Cr=0.75

0.3 0.2

Cr=1

0.1

0 0

5

10

15

NTU

0 0

1

2

3

4

5

6

7

8

NTU Fig. 3. Effectiveness and E number for cross flow heat exchanger, both fluids unmixed.

Fig. 4. Effectiveness and E number for cross flow Cmax(mixed), Cmin(unmixed).

I._ Teke et al. / Applied Thermal Engineering 30 (2010) 577–583

0.7

0.0

02

E=

0 0.0

Table 2 Characteristic values for all types of heat exchangers used in sample calculations.

1

0. 01

0. 02

Effectiveness

0.8

0. 00 4

0. 00 8

1 0.9

0.6 Cr=0

0.5 0.4

Cr=0.25

0.3

Cr=0.5

0.2

Cr=0.75

0.1

Cr=1

0 0

2

4

6

8

10

12

14

NTU Fig. 5. Effectiveness and E number for cross flow heat exchanger Cmin(mixed), Cmax(unmixed).

1 E=0.1

E=0.001 0.002 0.004

Temperature of waste fluid Mass flow rate of waste fluid Mass flow rate of circulating fluid Heat exchanger cost per unit area (BYM) Lower calorific value of fuel (Hu) Boiler efficiency (g) Operation time per year (H) Life of heat exchanger (n) Overall heat transfer coefficient (U) Fuel price (F) Inflation-corrected rate of return Specific heat of cold and hot fluid (Cp) Interest rate (i) Inflation rate (g) Fuel price rate (f)

40 °C 3.8 kg/s 7.59 kg/s 350 $/m2 41  106 J/kg 0.85 8300 h 15 years 1200 W/m2K 0.5 $/kg 0.2 4186 J/kg °C 0.32 0.2 0.25

Temperature of circulating fresh water during the year as is shown 1000 h 10 °C 1500 h 14 °C 1800 h 17 °C 3000 h 20 °C 1000 h 25 °C

0.03

0.8

Effectiveness

0.01 0.02

581

Employing the calculated E and Cmin/Cmax values, NTUmax numbers giving the maximum net gains are determined from the given Figs. 1–6 or the equations in Table 1. Afterwards, heat exchanger areas giving maximum net gains and effectiveness at NTUmax are calculated from the following relations:

0.6 Cr=0 Cr=0.25 Cr=0.5 Cr=0.75 Cr=1

0.4

0.2

A¼

NTUmax  C min U

0 0

2

4

6

8

10

12

NTU Fig. 6. Effectiveness and E number for shell and tube heat exchanger one shell pass (2, 4, . . . , tube passes).

e ¼ f ðNTU; CrÞ Then, TPT and YM values and their difference are calculated as net gain.

Net gain ¼ TPT—YM changer type having th...