Exergy analysis and thermodynamic accounting of utilities

Energy Vol. 13, No. 2, pp. 177-182, 1988 Printed in Great Britain. All rights reserved

EXERGY

0360-5442/88 $3.00+ 0.00 Copyright @ 1988 Pergamon Journals Ltd

ANALYSIS AND THERMODYNAMIC ACCOUNTING OF UTILITIES ENRIQUE ROTSTEIN? (UNS-CONICET),

(8000) Bahia Blanca, Argentina

(Received 6 March 1987)

Abstract-The exergy balance is a powerful tool for analysis of the energy status in a process installation. Proper incorporation of utilities is a significant issue. The approach of considering the contrtbution of utilities as heat exchanged reversibly via Carnot cycles is compared with that of handling utility streams in the same manner as process streams. The second approach is more realistic and flexible. Two applications illustrate this point.

INTRODUCTION

Exergy analysis has become accepted as a valid tool in evaluating energy utilization in the process industries.’ In most industries, utilities are a significant fraction of the operating cost and an important issue in energy conservation.* These include steam at several pressure levels, electricity, cooling water, process water, fuel of different qualities, etc. These utilities may play a significant role in process energy balance.“,4 It is open to discussion which is the best way to incorporate them in the exergy balance. Gou~,~ in one of the first papers dealing with exergy, referred to the case in which the system exchanges heat with sources at different temperatures, suggesting that all heat exchanges must be assumed to occur either among bodies at the same temperature or through reversible Carnot cycles. As a result, the differential exergy change in a reversible process, where heat from several sources and work are exchanged, is dB = dW + 2 [l - (TJZJ] This approach has been considered

de;.

(1)

by several authors.“.“’

THE

EXERGY

BALANCE

The exergy balance for an open system is dBldt = c w&, + W, - To&,, 4

(2)

where the q = 1, 2, . . , n identify all process stream ports and the summation includes the sign convention that inputs to the system are positive and outputs are negative. The system exergy is B = KY\ + poVsys - 7),Ssy~

(3)

and the q-stream specific exergy is fiq = fiq - Tosq.

UTILITY

(4)

ACCOUNTING;

One possible approach to account for utilities in the exergy analysis is to write-the energy and entropy balances for an open system, singling out electrical power in a term W, and tying t Present address: The Pillsburg Company, Pillsburg Center, Minneapolis, MN 55402, U.S.A 177

178

ENRIQUEROTSTEIN

thermal utilities to heat sources or sinks at T with which the system exchanges heat, with the following restrictions suggested by Gouy?

d (Usys + poV,ys)ldt= 2

Wqfiq + 2 Oi+ %, i

4

d Ss,,/dt = C

WqSq

+

(Qi/l;-)

+

fi3.

i

4

Multiplying Eq. (6) by T,, substracting (4), it follows that

C

(5)

it from Eq. (5), and taking into account Eqs. (3) and

dBldt = c wqBq + c [l - (T,/ZJ]Q q

+ l8$ - To&,

i

where the terms (1 - T,/TJ(& account for heating and cooling utilities. These terms have the physical meaning of reversible work corresponding to a Carnot cycle associated with heat sources at To and T, Qi being the heat exchanged with the system. This fact implies that the heat sources be uniform, have a heat capacity such that the exchange of Qi only results in infinitesimal temperature changes and the physical properties allow the assumption of reversibility. Equations (5) through (7) represent a thermodynamically valid approach since, if the balance equations are written for the surroundings and they are added to the system equations, the results verify the properties of an isolated system, i.e. dU,,,ldt = 0,

(8)

dS,,,ldt = d,,

(9)

and dB Jdt = - To&

(10)

Thus, energy is conserved, entropy cannot decrease and exergy cannot increase. There is an alternative manner of accounting for utilities in the exergy balance. We consider m process stream ports and j = m + 1, m + 2, . . . , n utility stream ports. In this k=1,2,..., case, Eq. (2) may be written as dBldt = 2 wkBk + c wjfij + vtr, - ToIt,. k

(11)

i

The difference with Eq. (7) is that the restriction with respect to sources at r is no longer necessary and two features appear which are more realistic in an industrial context. One is that utilities are not simple heat sources or sinks but, as they perform their role, they change, becoming streams with a different energy content. These streams can be used in eventual optimization tasks. Thus, it is useful to have them showing up in an explicit manner. The other feature is that, when a process is analyzed from an optimization standpoint, what stream is a utility stream becomes quite often a matter of decision for the analyst. Equation (11) is just as rigorous as Eq. (2) and, when added to the exergy balance of the surroundings, results in Eq. (10). The same happens with the corresponding energy and entropy balances. In summary, the exergy balance incorporating utilities in an explicit manner is made by using the following equation: k

the work interactions obtained from utilities can be accounted for either by means of Eq. (13), which follows from Eq. (7), or Eqs. (14) or Eq. (ll), viz., (13) bVu,i, = C j

WjSj.

(14)

Exergy analysis

179

The process analyst may select one expression. However, because Eq. (14) incorporates the utility streams explicitly, it is particularly useful for process analysis or synthesis. The following applications illustrate this point. APPLICATION

TO A SEPARATION

PROCESS

An analysis has been made of a steady-state propylene-propane separation process by using Eq. (7).5 There are two essential sections, namely, compression and separation (Fig. 1). The separation section is made up of two distillation columns in series, the bottom of the second being fed to the top of the first. The distillate leaves from the top of the second column and the bottom product from the bottom of the first. Table 1 provides the stream exergies and power input corresponding to the process. Table 2 indicates the itemized exergy balance for the compression section, using the two alternative approaches. In using Eq. (7), it is assumed that there is an infinite source of cooling water at To and the system is C. When Eq. (11) is used, the system is C + IC + AC and the resulting heating of cooling streams is explicitly recognized. As may be seen, both analyses agree because, for a reversible process, only an energy input of 1679 MJ/h is needed and the electricity consumption of 2179 MJ/h. Using Eq. (14) for non-electrical utilities, Eq. (11) shows that -370 MJ/h is exported via the heated cooling streams. As a result, the production of entropy predicted from Eq. (14) is considerably lower and more realistic than that found from Eq. (13). The same analysis was carried out for the distillation section and the results are shown in Table 3. For W,,i, obtained from Eq. (14), we show two values, namely, +6487MJ/h corresponding to energy input to the reboiler fluid and -194 MJ/h corresponding to energy leaving at the partial condenser. The same conclusions apply as before.

APPLICATION

TO TECHNOLOGY

SELECTION

Three alternative catalytic processes have been presented for the commercial manufacture of formaldehyde by oxidation and dehydrogenation of methanol: one involves the use of a silver catalyst, another is the silver-steam process, and the third involves a metallic oxide catalyst.” Table 4 shows the utility and raw material requirements for the competing processes per ton of 37% wt formaldehyde. The first and third technologies give a methanol-free product, while the second leads to a product containing 3% methanol. In this case, the exergy balance is a tool to

Fig. 1. The propane-propylene separator is shown: C = compression section; D = distillation section; AC = compressor aftercooler; IC = compressor intercooler; PC = partial condenser; R = reboiler.

ENRIQUE ROTSTEIN

180

Table 1. Stream exergies and power for the propane-propylene

stream

separator.

Property value B1

=

- 18,921 N/h

B2

=

- 17,242 MJ/h

B3

=

-

9,713 MJ/h

B4

=

-

7,042 W/h

5 - Cooling water, 32.2"C

B5

=

-

639 MJJ/h

6 - Water, 64°C

B6

=

-

5 MJ/h

7 - Cooling water, 32.2"C

B7

=

-

182 MJJ/h

8 - Water, 80°C

B8

=

157 MJ/h

9 - Cooling water, 32.2"C

Bg

=

- 10,152 MJ/h

1 - Propylene 59.99% mol.- Propane, 21.1"C, 101.3 kPA 2 - Propylene 59.99% mol.- Propane, 52.1"C, 2.027 MPa 3 - Propylene 99% mol., 46.7"C, 1.931 MPa 4 - Propane 95% mol., 57.7"C, 2.068 MPa

0 - Water, 38°C

B10 =

1 - Saturated steam, 104"~

-

6,836 MJ/h

Bll =

2 - Saturated liquid, 104°C

9,958 MJW/h

351 MJ/h

B12 =

over input to compressors

605 kW

ower input to pumps in distillation section

47 kW

Table 2. The compression section. h AB=-ZW Equation

q

B

9’

'ntil,

MJ,hq

MJ/h

(7)

1,679

0

(11)

1,679

- 370

To Rs’ MJ/h

W

e'

M.J/h

500

2,179

130

2,179

evaluate the energy performance of these processes with the scant information provided. The results are shown in Table 4. It may be seen that there is only a slight difference in W,, and, consequently, in T,R, between the two approaches. From the standpoint of total utilities, W”,i, and We, the silver-steam process is the best, followed by the metallic oxide process. The silver catalyst process is the worst, both in terms of utility consumption and production of entropy.

181

Exergy analysis Table 3. Distillation section.

AB=-Z~ q

Equation

q

B^ q

MJ/h

'uti.1

To Rs

MJ/h

MJ/h

we

MJ/h

(7)

487

6,523

6,204

168

(11)

487

h,487 - 194

5,974

168

The explicit use of utility-stream exergies provided by Eq. (14) enables the analyst to redefine the problem. It may be desirable to define the system so that, instead of considering steam, fuel becomes the utility under consideration. For this purpose it was assumed that methane is burnt in a boiler with 10% excess air and a 75% boiler efficiency. The result is given at the bottom of Table 4. It may be seen that the best selection, in terms of total utility consumption and production of entropy, is the metallic oxide process. The silver-steam

Table 4. Technology selection example (basis: 1 ton. 37% wt formaldehyde)

Utilities and

Steam at 6 at.,kgt Power,

raw materials

Silver-steam

Xetallic oxide

500

150

- 4011

90

54

43:

429

138

420

Silver

PrOCeSS

MJ

Methanol

(lOO%),kg

EXfI-gy change

AB, MJ

Eqs. (12)

W

and (13)

T

Eqs.

W

- 2,264

339

102

2,683

2,LZO

MJ

324

97

and (14)

To Rs, MJ

2,668

Eqs.

Wutil,

MJ

1,418

425

To Rs, MJ

3,762

2,743

(12)

(12) and

util' 0

R

MJ

- 2,254

s' MJ

util'

- 2,254

-

271 2,415

-

254 2,L2;

2,:+15

-

259

(14) with natural

gas

*Negative sign in this row indicates steam leaving as a byproduct.

2,427

182

ENRIQUE ROTSTEIN

technology is now second best and the least desirable is the silver catalyst process. Although it is not impossible to extend the use of Eq. (13) to this system configuration, this approach is relatively more involved. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

D. R. Morris and J. Szargutt, Energy 11, 733 (1986). F. C. Jelen, Cost and Optimization Engineering, McGraw-Hill, New York (1970). K. G. Denbigh, Chem. Engng Sci. 6, 1 (1956). E. Rotstein, Chem. Engng Sci. 39, 413 (1984). M. Gouy, J. Phys., 2e Se’rie, t. VIII, 501 (1889). N. De Nevers and J. D. Seader, Eighty-Sixth AIChE Natl. Meeting, Houston (April l-5, 1979). R. E. Fitamorris and R. S. H. Mah, AlChE J. 26, 265 (1980). P. Johnson and W. L. Conger, Fuel hoc. Technol. 5, 141 (1981). Anonymous, Hydrocarbon Proc. 56(11), 165 (1977).

NOMENCLATURE B= System exergy B= Exergy H= Enthalpy P= Pressure Q= Heat flow R= Production of entropy s= Entropy I = Time T= Temperature lJ= Internal energy v= Volume w= Mass flow rate w= Work

Subscripts e i

= Electrical = Thermal sources

= Utility port = Process stream ports excluding ports 0 = State of the surroundings q = Port s = Entropy sys = System U = Useful util = Utility i k

thermal

utility