Critical COP for an economically feasible industrial heat-pump application

Pergamon PII:

Applied Thermal Engineering Vol. 17, No. I. pp. 93-101, 1997 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-431 l/97 $15.00 + 0.00 S1359-4311(96)00010-5

CRITICAL COP FOR AN ECONOMICALLY FEASIBLE INDUSTRIAL HEAT-PUMP APPLICATION Xiao TDepartment

Feng*t

of Chemical Engineering, $.Chalmers University

and Thore

Xi’an Jiaotong of Technology,

Berntssont

University, Xi’an 710049, P. R. China; 412 96 Gothenburg Sweden

and

(Received 19 January 1996) Abstract-In this paper, the expression for critical COP is derived for an economically feasible industrial heat-pump application. It is a function of the price ratio between input energy and heating, the price ratio between equipment and energy, and the payback period. Using this critical COP, a preliminary assessment can be made of whether an industrial heat-pump application is worth discussing further. The influences of various economic factors on the critical COP for different types of heat pumps are also discussed. Copyright 0 1996 Elsevier Science Ltd. Keywords-Heat

pump,

coefficient

of performance.

NOMENCLATURE A B COP E N P P’ = 3600P PBP : Y Z

specific investment cost ($/kW heat output) annual working hours (h/year) coefficient of performance heat-pump input energy (kW) input power of electrically driven heat pump (kW) energy price (%/kJ) energy price ($/kW.h) payback period (years) heat (kW) saving in utility cost from use of heat pump ($/year) total investment cost ($) heat pump input energy cost ($/year)

Greek leiters Y = PIIPH I = A/PH’

price ratio price ratio

between between

input energy and heat equipment and energy (h)

Subscripts

C E G H I WH

critical electricity generator heat, heating input waste heat

INTRODUCTION In industrial applications, using a heat pump to upgrade waste heat can possibly result in substantial reductions in energy use. However, the number of heat pumps in industry is still very low. In addition to the reasons mentioned before [l], one other important reason is suspicion about a heat pump’s economic benefit. For the decision on investment, cost-effectiveness is of prime importance. The state of the art of industrial heat-pump technology has a limited application scope. Table 1 gives some technical characteristics and investment costs which are based on information collected from existing plants in the large-scale range, approximately 5 MW heat output [14]. *Author

to whom correspondence

should

be addressed. 93

94

Xiao Feng and T. Berntsson Table Delivery temperature,

System Electric compression R22 Rl2, R500 RI14 Mechanical vapour recompression Thermal vapour recompression Absorption Heat transformer

I.

Heat acceptance temperature. C

‘C

2&80 3&95 4&130 >I00 60-150 3&92 8C-150

Temperature lift ‘C <60 r60 <60 <50 <40 <45 t50

- 2lNo -20-65 IO-96 ~80 45-l 20 5-42 58-l IO

Typical COP

Investment $/kW ls/kW heat output

3-5 3-5 2-1 5-20 I.1 1.3 0.45-0.5

20&240 23&270 31&360 130-190 90-140 225-350 45&700

The investment costs vary with temperature lift and delivery temperature. For mechanical and thermal vapour-recompression heat pumps, they also depend on the cycle type (closed, semi-open or open). As we know, heat pumping will reduce the temperature driving force in the process heat-exchanger network, so the heat-interchanger area will increase. This factor varies from plant to plant. The investment costs in Table 1 considered this part of the cost on a reasonable basis. So the investment cost in Table 1 covered the cost of the heat source and heat sink equipment, control system, electrical transformer, the increased heat-exchanger area, etc. When an industrial heat-pump application is known to be technically feasible, how can one rapidly determine whether it is economically feasible? Some work has been done [5-71, but these studies either just qualitatively mentioned the ecomomic requirements (low electricity/heat price ratio, high annual working hours, etc.) [5], or solely considered the operation cost for compression heat pumps, so that the critical COP has the form [6, 71 COP, = PE/P, .

(1)

Practically all industries today make their investment decision based on payback period (PBP) calculations, and usually the acceptable PBP is somewhat short, while the investment cost for heat pumps is relatively high. In this case, the investment cost for heat pumps is one of the most crucial parameters besides energy cost. In this paper, a new critical COP is derived to determine rapidly whether an industrial heat pump is economically feasible. This criterion considers not only operation cost, but also investment cost and desired payback period. THE EXPRESSION

FOR CRITICAL

COP

The straight payback period, i.e. not including tax and depreciation,

is defined as

PBP = Y&S - Z) .

(2)

The total investment cost, Y, can be simply given as Y=AxQ,.

(3)

The saving in utility cost, considering only hot utility for simplicity, is S = 3600 x B x QH x PH

(4)

and the heat pump energy input cost can be expressed as Z = 3600 x B x E x P, .

(5)

Substituting equations (3)-(5) into equation (2), we get PBP =

A x QH 3600 x B x (QH x PH - E x P,) = (@

3600 x B x&&j where COP = QH/E. Therefore, we can derive an expression for COP: PI

COP = ” -

A 3600 x B x PBP

Y =

1 ’-

B x PBP

’

(7)

Critical COP for industrial heat pump

95

Table 2. Coefficient of performance for various heat pumps Electric compression

COPC PBP,

R22

Rl2. R500

RI14

Mechanical vapour recompression

Thermal vapour recompression

Absorption

2.5-2.7

2‘62.8

3.G3.2

2.3-2.5

1.1-1.2

1.3-1.6

Heat transformer 2.3-3.7

where y = PI/PH, the price ratio between input energy and heat, and A = A/P”‘, the price ratio between equipment and energy. Equation (7) is the expression of critical COP for an economically feasible industrial heat pump. In a certain economic environment with a maximum PBP required by the user, we can use equation (7) to get COP,. If the COP of the heat pump considered is greater than COP,, the heat pump is worthy to be considered further; otherwise, the heat-pump project should be abandoned. The expression for COP, is a function of the price ratio between input energy and heating, the price ratio between equipment and energy, and the payback period. It quantitatively reflects the influnce of the relative cost between input energy and heating and between equipment and energy, and the user’s desired PBP on the economy of a heat-pump project. It covers every important design trade-off and is easy to calculate. When a heat pump project is under consideration, it can be used to assess whether a technically feasible heat-pump scheme may be economically feasible without much calculation. COP, FOR VARIOUS

HEAT PUMPS

Equation (7) is a generalized expression for every type of heat pump. Now, for different types of heat pumps, we will give specific expressions. For electric compression and mechanical vapour-recompression heat pumps, the expression is entirely the same as equation (7) because the input energy is electricity: Y = PEIPH . For absorption and thermal vapour-recompression heat, we have

(8)

heat pumps, because the input energy is also

y=l

(9)

10 9 -0 -7 -6 --

I, 8

?-

5-4 -3 -.

2 -1 -07 0.1

0.2

0.3

0.4

0.5

0.6

),

BxPBP Fig. 1. The generalized curve for COP,.

0.7

0.8

0.9

96

Xiao

Feng and T. Berntsson Absorption

2

3

4

5

6

7

a

9

10

PBP Fig. 2. The relationship

between

COPc and PBP for absorption

heat pumps.

and 1

COP = ’-

(10)

RI B x PBP

and for heat transformers, because the input energy is generally waste heat, if the waste heat has a cost PWH, the expression is the same as equation (7), just y=

(11)

PWHIPH .

However, if the cost for waste heat can be ignored, that is, y = 0, then we get from equation (7) that COP, is zero. This time we cannot use COPc but instead use PBPc to assess heat-pump projects. From equation (6) if P, = 0, we get PBP = l/B.

(12)

l-m

2.5

2

1.5 a

_._._._.-__._.-.-__.-.-._._.-

1.4

8 1

0.5

0 1

2

3

4

5

6

7

8

9

10

PBP Fig. 3. The relationship

between

COP,

and PBP for thermal

vapour-recompression

heat pumps.

Critical

COP for industrial

97

heat pump

10

“s 5

t

0 2

3

4

5

6

7

8

9

10

PBP Fig. 4. The relationship

between

COP,

and PBP for R22 electric compression $/kW.h.

heat pumps

at I’;l = 0.015

In a certain economic environment and with a given heat-pump device, there is a certain PBP, for the heat transformer. If this PBPc is shorter than the longest one required by the user, the heatpump project can be considered further. DISCUSSION In order to get a quantitative concept for economically feasible heat pump, we calculate the COP, of various heat pumps using typical economic values (A takes the value in Table 1 [2], B = 8000, y = 2, P;I= 0.024, PBP = 5, P,, = 0).The results are shown in Table 2. From equation (7), it can be seen that COP, is directly proportional to y. So using COP& as ordinate and 1/(B x PBP) (this parameter is the ratio of the investment cost per kW heat output

R22(P’s0.024)

8 6

6

7

8

9

10

PBP Fig. 5. The relationship

between

COP,

and PBP for R22 electric compression $/kW.h.

heat pumps

at PA = 0.024

Xiao Feng and T. Berntsson

98

RI 2(P’=O.O15)

18 16 14 12 g

10 6 6 4 2

3

4

5

6

7

8

9

10

PBP Fig. 6. The relationship

between

COP,

and PBP for R12 electric compression $/kW.h.

heat pumps

at P;, = 0.015

to the utility cost per kW heat output during the payback period) as abscissa, a generalized curve can be found, as shown in Fig. 1. When A/(B x PBP) > 0.6, COP& will increase rapidly. So we should avoid heat-pump design in this area. If B = 8000 and PBP = 5, A/(B x PBP) < 0.6 means I < 24000 (i.e. A < 360 for PH’= 0.015 [8], the typical heating cost in the United States and A < 576 for PH’= 0.024 [9], the typical heating cost in Sweden). In order to specifically study the influence of PBP on COPc, we draw the curves of COPc-PBP for different heat pumps. Figure 2 is for absorption heat pumps, Fig. 3 for thermal vapour recompression, Figs 4-9 for electric compression heat pumps and Figs 10 and 11 for mechanical vapour recompression. The bounds of the shaded areas in Figs 2-l 1 relate to the bounds on investment cost in Table 1.

R12(P’=O.O24)

18 7 16 14 12 a

10

S8 6 4 2 0 2

3

4

5

6

7

8

9

10

PBP Fig. 7. The relationship

between COPc and PBP for RI2 electric compression %/kW.h.

heat pumps

at P;I = 0.024

99

Critical COP for industrial heat pump

20

15

5 10

5

0

a

1 3

7

4

5

6

7

6

9

10

PBP Fig. 8. The relationship between COPc and PBP for RI 14 electric compression heat pumps at PA = 0.015 $/kW.h.

In all these figures, we assume B = 8000. If B is less than 8000, the associated PBP will increase the same proportion as B decreases from 8000. For absorption heat pumps used today, COP is a constant of approximately 1.3 [I]. So the dotted line at COP = 1.3 shows the limit for absorption heat pumps, as shown in Fig. 2. From Fig. 2 it can be seen that even with the highest heating cost of PH'= 0.024, absorption heat pumps can only be used at a PBP greater than 5 years. It implies that with current costs, absorption heat pumps can only be acceptable if a very long payback is tolerated. For thermal vapour-recompression heat pumps, although the typical value is 1.1, COP can at most reach 1.4. So we use a dotted line at COP = 1.4 to show the feasible range, as shown in Fig. 3. We can know from Fig. 3 that with the two kinds of heating cost, thermal vapour-recompression heat pumps can be accepted if the temperature lift is not too high.

R114(p’=O.O24)

6

6

PBP Fig. 9. The relationship between COP, and PBP for RI 14 electric compression heat pumps at PA = 0.024 $/kW.h.

Xiao Feng and T. Berntsson

100

MVR(P’=O.O15)

4 2

3

4

5

6

7

8

9

10

PBP

Fig. 10. The relationship between COPc and PBP for mechanical vapour-recompression P;c = 0.015 $/kW.h.

heat pumps at

For electric compression heat pumps, COPc will change greatly with y, as shown in Figs 4-9. So the higher the y, the lower the temperature lift should be to get a high COP. If y is greater than 3, COP of heat pumps must be higher than at least 5. If y is less than 3, there exists a good opportunity for application of electric compression heat pumps. Because a mechanical vapour-recompression heat pump normally has a very high COP (typically 5-20 and possibly even higher than 20), it will be of benefit even with a higher y, as shown in Figs 10 and 11. As for heat transformers, it is clear from equation (12) that the critical PBP is proportional to 1. CONCLUSION

1. In this paper, the expression of critical COP is derived for assessing whether an industrial heat pump is economically feasible. MVR(P’=0.024)

8

6

2

0 2

3

4

5

6

7

8

9

10

PBP

Fig. 1I. The relationship between COPc and PBP for mechanical vapour-recompression PA = 0.024 %/kW.h.

heat pumps at

Critical

COP for industrial

heat pump

101

2. Under present typical economic conditions, mechanical vapour recompression, thermal vapour recompression and heat transformers are generally of benefit; compression heat pumps should operate under low temperature lift so as to make the COP greater than at least 5, and absorption heat pumps are only economically feasible when the heating cost is very high and the payback period is sufficiently long. 3. The economic factors which have an important effect on critical COP are in turn: y, PBP and 1. REFERENCES of heat pumps in industrial processes. I 1th Infernational Congress of Chemical I. E. Wallin and T. Berntsson, Integration Engineering, Chemical Equipmenr Design and Automation, Praha, Czech Republic, 29 August-3 September (1993). in Heat Pump Technology 2. T. Berntsson, Future prospects for industrial heat pumps in Europe. Heat Pumps-Prospects and Marketing. Lewis Publishers, New York (1987). 3. H. L. Von Cube and F. Steimle, Hear Pump Technology. Butterworths, London (1981). 4. R. C. Niess and J. S. Gilbert, Future prospects for industrial heat pumps in North America. Heat Pumps-Prospects in Heat Pump Technology and Markering. Lewis Publishers, New York (1987). and M. Tomsic, Heat pumps in industry. Heat Recovery Sysfems & CHP 14(l) (1994). 5. F. Al-Mansour 6. Z. Fonyo and P. Mizsey, Economic applications of heat pumps in integrated distillation systems. Heat Recovery Systems & CHP 14(3) (1994). and S. Sakashita, Operating experience with industrial heat pump systems: economic advantages, 7. M. Wakabayashi Heat Pumps-Prospects in Heat Pump Technology and Marketing. Lewis obtained by several actual installations. Publishers, New York (1987). heat pump placement in industrial processes, Final Report, DOE/ID/12583-1, DE87 8. TENSA Services, Optimum 009626, March 1987. 9. P. Holmberg, K. M. Berntsson and T. Berntsson, Technico-economic aspects on heat transformers. Indo-British 1991. Workshop on Industrial Energy Conservation, Pune, India, 68 February