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Reducing consumption by cascading energy inputs according to temperature level
Applied Energy8 (1981) 79-85
Technical Note
Reducing Consumption by Cascading Energy Inputs According to Temperature Level
SUMMARY The conventional first law energy balance accounts for all energy inputs to a system in terms of eventual energy rejection to the environment. The second law analysis examines the thermodynamic grade of energy presented to each station within the system. A simple model is analysed to demonstrate the energy savings possible by cascading energy flows according to second law principles.
NOMENCLATURE A, B,C, D o r E
T
Processes undertaken at temperatures TA, Ta, Tc, To or TE, respectively. Heat flow (W). Absolute temperature (K).
X
Heat exergy { = ( ~ - )
0
Q}, W.
Exergetic potential. Efficiency of a process (0 < r/< 1). SuJfixes A, B,C, D o r E
Appropriate to the processes A, B, C, D, or E of the cascaded system. c With reference to a Carnot (i.e. ideal) thermodynamic cycle. co Overall (i.e. for the combined cycle). o Of the environment. 79 Applied Energy 0306-2619/81/0008-0079/$02-50© AppliedSciencePublishersLtd, England, 1981 Printed in Great Britain
80
P . W . O'CALLAGHAN, S. D. PROBERT ENERGY FLOW SYSTEMS
As every engineer knows, the first law of thermodynamics is that 'the energy contained within a closed system is conserved'. Thus energy engineers aim to conserve the quantity and quality (or grade) of the available energy and so reduce running costs. Fuels are used in buildings to energise: electrical appliances (e.g. TV sets, lights and refrigerators), cookers, water heaters and space heaters. In general, the quality of energy required for each of these activities is greater the higher the activity appears in this listing. Furthermore, we know from experience that the heat wasted by each activity may be profitably employed without the expenditure of further energy, as an input for an activity below (but not above) it in the listing. It is relatively easy to reduce energy expenditures for low-grade purposes by employing such 'wild' heat. Unfortunately, the proper design of industrial, commercial and domestic systems to achieve exact matching of the energy--that would otherwise be wasted--with the required energy inputs for lower grade activities remains esoteric. Thus this Note presents the thermodynamic concept which should help when making such design decisions for applications in a petrochemical refinery: there the rises in the ratio of costs of energy to equipment have risen dramatically during the last seven years. The conventional energy 'balance', based on the first law of thermodynamics, accounts for the energy inputs which initially serve a useful purpose, degrade and are eventually rejected to the environment, and the other, more direct, wastages to the environment. A pictorial form of this energy analysis is the well known 'Sankey' energy-flow diagram (an example of which is given in Fig. 1). This facilitates understanding what happens to the energy but does not provide any indication of the relative usefulness of the energy losses to the environment. Consequently, it is difficult, without further information, to decide the order of priorities for each programme of remedial measures to reduce fuel consumption. To appreciate the more refined technique for energy management, which is advocated in this Note, consider a simplified abstraction from reality. A set of steady-state, industrial processes requires power inputs to be supplied as shown by Scheme 1 in Table 1. The total power demand for all the processes, if undertaken independently, is 11,000 kW. However, this traditional approach is wasteful! For each process, energy is lost to the environment by heat transmission through the containing walls or via rejected fluids, yet some of these wild energy wastages may be profitably employed elsewhere. Usually, the essential requirement is to maintain process temperatures invariant rather than the energy throughputs constant. Thus the use of improved insulation and heat reclamation are normally feasible in order to reduce the rates of energy flow whilst still maintaining the required process temperatures. To put numbers on the theoretical 'bones' let us assume that insulation levels are doubled and, further, that 50 per cent of the reduced, resulting heat losses are recovered. (In practice the exact percentage savings for each process
REDUCING CONSUMPTION BY CASCADING ENERGY INPUTS
81
PURCHASES
~~.
REFRIGERATION POWER
BOILERPLANT LOSSES
TRANSMISSION LOSSES
LIGHTING
SPACEHEATING LOAO
'~
PROCESS
HEATINGLOAD
Fig. 1.
Simple energy account for a small factory.
TABLE 1 DEMAND SCHEDULES
(For simplicity of calculation the environment is assumed to be at 300 K)
Process
A B C D E
Demand
Scheme 1
temperature
power
Scheme 2 power
(K)
demand (kW')
demand (kW)
1000 800 600 400 350
1000 1500 2500 2000 4000 °
250 375 625 500 1000
° For space heating.
would be decided by optimising the total cost---capital investment plus running cost --over the proposed lifetime of the system.) This would reduce each process energy demand to 25 per cent of its initial value, resulting in the revised schedule shown in the final column of Table 1 with a net energy demand of 2750 kW. EXERGY CONSERVATION
So far the quality ofenergy (or power) has not been considered, and so the concept of exergetic potential is now introduced. Exergy is a measure of the ability of energy to
82
P. W. O'CALLAGHAN, S. D. PROBERT
perform useful work. The heat exergy of a thermal current, 0 , emerging from a system at an absolute temperature T in an environment at T O is:
Here Xis the power derived from a Carnot heat engine operating between an energy source at temperature T and a sink at To and 7 is the exergetic potential which indicates the grade of energy required at each stage of the process.l Redirecting energy that would otherwise be wasted through a system according to demand temperatures is referred to as 'cascading'. The processes described in Table 1 might be connected in sequence as described in Fig. 2 and Table 2, thereby reducing the overall input power demand still further to only 1000 kW.
kW 1000 K /~[k,~ 50 ,~250 800 K
kW
/fm "~.125 kWn" 1 375 kW
ooo K ~ " ~ _2so .w,,I \
500kW \ ~.oo K
()~
f'
125kW
/ '500kW/ I
350 K
~k,,,..~ --
ooo
300 K I OURCE OF ENERGY ~--~AMBIENT TEMPERATURE --
~
---
" kW
ENERGY
INPUT
CASCADE
LINE
BY- PASS ROUTE
ENVIRONMENT
Fig. 2.
An example of a cascaded process.
R E D U C I N G C O N S U M P T I O N BY C A S C A D I N G E N E R G Y I N P U T S
83
TABLE 2 THE EXERGETIC POTENTIAL AND EXERGY FOR EACH PROCESS STAGE OF THE SYSTEM SHOWN IN FIG. 2
Stage
A B C D E Total
Exergetic potential,
Exergy input X
External energy
0.7 0.625 0.5 0.25 0-14
175 78.1 125 0 52-5 430.6
250 125 250 0 375 1000
(k~
Q(k~
Although 1000 kW of power is still required, this represents only 430 kW ofexergy (see Table 2). Assuming that all the energy is supplied at 1000K (? = 0-7), the introduction of an exergy convertor I (such as a gas-fired heat-pump) operating between 1000 K and 300 K and having an overall exergetic conversion efficiency (see Fig. 3 and Table 3) of 50 per cent can reduce the primary energy supplied to the
W ~-T-~-~o)kw
Fig. 3. Schematicrepresentationof an exergyconvertor showing relative amounts of energy passing through the system. 350 K temperature level to 153 kW. An analysis of Table 3 shows that the use of a similar convertor to transduce exergy from 1000 K to any of the higher stations in the energy flow chain would result in a net loss in efficiency. So, using the convertor for the 350 K demand only, the resulting overall input demand becomes merely 778 kW (see Fig. 4). The total amount of energy saved is thus 92 per cent of the original load ! Still further power reductions may be achieved by directing any energy fluxes, after satisfying their prime purposes, via exergy convertors (e.g. heat pumps) and by employing the benefits of exergy conservation at intermediate levels (e.g. between
84
P. W. O'CALLAGHAN, S. D. PROBERT TABLE 3 OVERALL COMB1NED CYCLE EFFICIENCY FOR THE EXERGY TRANSDUCER S H O W N lN FIG. 3 #7o
T(K)
r/<,o
50
60
70
80
90
100
800 600 350
1.12 1.40 4.90
0.56 0.70 2.45"
0.67 0.84 2.94
0.78 0.98 3.43
0.90 1,12 3,90
1.01 1.76 4.41
1.12 1.40 4.90
t/o = Thermodynamic efficiency. " System adopted in the present analysis.
>1000 K 250 kW 1000 K ( 250 kW 800 K ~ = 1 2 5
kW
53 kW
375 kW 600 K ~ ) , , ~
2S0 kW
[
Z
-\
O kW \
/" ,, "~
300 K - Fig. 4.
1125 kW
'~=0.7
I
b
~
A cascaded process incorporating an exergy convertor.
REDUCING CONSUMPTION BY CASCADING ENERGY INPUTS
85
processes C and E). For the present analysis, a steady-state example has been chosen. However, the incorporation of thermal stores would allow intermittent and transient systems to be considered.
REFERENCES 1. M. HUSSEIN, R. J. WOOD, P. W. O'CALLAGHAN and S. D. PROBERT, Elticiencies of exergy transductions, Applied Energy, 6(5), 1980 pp. 371-84.
P. W. O'CALLAGHANand S. D. PROBERT,
School of Mechanical Engineering, Cranfield Institute of Technology, Bedford, MK43 OAL (Great Britain)
Technical Note
Reducing Consumption by Cascading Energy Inputs According to Temperature Level
SUMMARY The conventional first law energy balance accounts for all energy inputs to a system in terms of eventual energy rejection to the environment. The second law analysis examines the thermodynamic grade of energy presented to each station within the system. A simple model is analysed to demonstrate the energy savings possible by cascading energy flows according to second law principles.
NOMENCLATURE A, B,C, D o r E
T
Processes undertaken at temperatures TA, Ta, Tc, To or TE, respectively. Heat flow (W). Absolute temperature (K).
X
Heat exergy { = ( ~ - )
0
Q}, W.
Exergetic potential. Efficiency of a process (0 < r/< 1). SuJfixes A, B,C, D o r E
Appropriate to the processes A, B, C, D, or E of the cascaded system. c With reference to a Carnot (i.e. ideal) thermodynamic cycle. co Overall (i.e. for the combined cycle). o Of the environment. 79 Applied Energy 0306-2619/81/0008-0079/$02-50© AppliedSciencePublishersLtd, England, 1981 Printed in Great Britain
80
P . W . O'CALLAGHAN, S. D. PROBERT ENERGY FLOW SYSTEMS
As every engineer knows, the first law of thermodynamics is that 'the energy contained within a closed system is conserved'. Thus energy engineers aim to conserve the quantity and quality (or grade) of the available energy and so reduce running costs. Fuels are used in buildings to energise: electrical appliances (e.g. TV sets, lights and refrigerators), cookers, water heaters and space heaters. In general, the quality of energy required for each of these activities is greater the higher the activity appears in this listing. Furthermore, we know from experience that the heat wasted by each activity may be profitably employed without the expenditure of further energy, as an input for an activity below (but not above) it in the listing. It is relatively easy to reduce energy expenditures for low-grade purposes by employing such 'wild' heat. Unfortunately, the proper design of industrial, commercial and domestic systems to achieve exact matching of the energy--that would otherwise be wasted--with the required energy inputs for lower grade activities remains esoteric. Thus this Note presents the thermodynamic concept which should help when making such design decisions for applications in a petrochemical refinery: there the rises in the ratio of costs of energy to equipment have risen dramatically during the last seven years. The conventional energy 'balance', based on the first law of thermodynamics, accounts for the energy inputs which initially serve a useful purpose, degrade and are eventually rejected to the environment, and the other, more direct, wastages to the environment. A pictorial form of this energy analysis is the well known 'Sankey' energy-flow diagram (an example of which is given in Fig. 1). This facilitates understanding what happens to the energy but does not provide any indication of the relative usefulness of the energy losses to the environment. Consequently, it is difficult, without further information, to decide the order of priorities for each programme of remedial measures to reduce fuel consumption. To appreciate the more refined technique for energy management, which is advocated in this Note, consider a simplified abstraction from reality. A set of steady-state, industrial processes requires power inputs to be supplied as shown by Scheme 1 in Table 1. The total power demand for all the processes, if undertaken independently, is 11,000 kW. However, this traditional approach is wasteful! For each process, energy is lost to the environment by heat transmission through the containing walls or via rejected fluids, yet some of these wild energy wastages may be profitably employed elsewhere. Usually, the essential requirement is to maintain process temperatures invariant rather than the energy throughputs constant. Thus the use of improved insulation and heat reclamation are normally feasible in order to reduce the rates of energy flow whilst still maintaining the required process temperatures. To put numbers on the theoretical 'bones' let us assume that insulation levels are doubled and, further, that 50 per cent of the reduced, resulting heat losses are recovered. (In practice the exact percentage savings for each process
REDUCING CONSUMPTION BY CASCADING ENERGY INPUTS
81
PURCHASES
~~.
REFRIGERATION POWER
BOILERPLANT LOSSES
TRANSMISSION LOSSES
LIGHTING
SPACEHEATING LOAO
'~
PROCESS
HEATINGLOAD
Fig. 1.
Simple energy account for a small factory.
TABLE 1 DEMAND SCHEDULES
(For simplicity of calculation the environment is assumed to be at 300 K)
Process
A B C D E
Demand
Scheme 1
temperature
power
Scheme 2 power
(K)
demand (kW')
demand (kW)
1000 800 600 400 350
1000 1500 2500 2000 4000 °
250 375 625 500 1000
° For space heating.
would be decided by optimising the total cost---capital investment plus running cost --over the proposed lifetime of the system.) This would reduce each process energy demand to 25 per cent of its initial value, resulting in the revised schedule shown in the final column of Table 1 with a net energy demand of 2750 kW. EXERGY CONSERVATION
So far the quality ofenergy (or power) has not been considered, and so the concept of exergetic potential is now introduced. Exergy is a measure of the ability of energy to
82
P. W. O'CALLAGHAN, S. D. PROBERT
perform useful work. The heat exergy of a thermal current, 0 , emerging from a system at an absolute temperature T in an environment at T O is:
Here Xis the power derived from a Carnot heat engine operating between an energy source at temperature T and a sink at To and 7 is the exergetic potential which indicates the grade of energy required at each stage of the process.l Redirecting energy that would otherwise be wasted through a system according to demand temperatures is referred to as 'cascading'. The processes described in Table 1 might be connected in sequence as described in Fig. 2 and Table 2, thereby reducing the overall input power demand still further to only 1000 kW.
kW 1000 K /~[k,~ 50 ,~250 800 K
kW
/fm "~.125 kWn" 1 375 kW
ooo K ~ " ~ _2so .w,,I \
500kW \ ~.oo K
()~
f'
125kW
/ '500kW/ I
350 K
~k,,,..~ --
ooo
300 K I OURCE OF ENERGY ~--~AMBIENT TEMPERATURE --
~
---
" kW
ENERGY
INPUT
CASCADE
LINE
BY- PASS ROUTE
ENVIRONMENT
Fig. 2.
An example of a cascaded process.
R E D U C I N G C O N S U M P T I O N BY C A S C A D I N G E N E R G Y I N P U T S
83
TABLE 2 THE EXERGETIC POTENTIAL AND EXERGY FOR EACH PROCESS STAGE OF THE SYSTEM SHOWN IN FIG. 2
Stage
A B C D E Total
Exergetic potential,
Exergy input X
External energy
0.7 0.625 0.5 0.25 0-14
175 78.1 125 0 52-5 430.6
250 125 250 0 375 1000
(k~
Q(k~
Although 1000 kW of power is still required, this represents only 430 kW ofexergy (see Table 2). Assuming that all the energy is supplied at 1000K (? = 0-7), the introduction of an exergy convertor I (such as a gas-fired heat-pump) operating between 1000 K and 300 K and having an overall exergetic conversion efficiency (see Fig. 3 and Table 3) of 50 per cent can reduce the primary energy supplied to the
W ~-T-~-~o)kw
Fig. 3. Schematicrepresentationof an exergyconvertor showing relative amounts of energy passing through the system. 350 K temperature level to 153 kW. An analysis of Table 3 shows that the use of a similar convertor to transduce exergy from 1000 K to any of the higher stations in the energy flow chain would result in a net loss in efficiency. So, using the convertor for the 350 K demand only, the resulting overall input demand becomes merely 778 kW (see Fig. 4). The total amount of energy saved is thus 92 per cent of the original load ! Still further power reductions may be achieved by directing any energy fluxes, after satisfying their prime purposes, via exergy convertors (e.g. heat pumps) and by employing the benefits of exergy conservation at intermediate levels (e.g. between
84
P. W. O'CALLAGHAN, S. D. PROBERT TABLE 3 OVERALL COMB1NED CYCLE EFFICIENCY FOR THE EXERGY TRANSDUCER S H O W N lN FIG. 3 #7o
T(K)
r/<,o
50
60
70
80
90
100
800 600 350
1.12 1.40 4.90
0.56 0.70 2.45"
0.67 0.84 2.94
0.78 0.98 3.43
0.90 1,12 3,90
1.01 1.76 4.41
1.12 1.40 4.90
t/o = Thermodynamic efficiency. " System adopted in the present analysis.
>1000 K 250 kW 1000 K ( 250 kW 800 K ~ = 1 2 5
kW
53 kW
375 kW 600 K ~ ) , , ~
2S0 kW
[
Z
-\
O kW \
/" ,, "~
300 K - Fig. 4.
1125 kW
'~=0.7
I
b
~
A cascaded process incorporating an exergy convertor.
REDUCING CONSUMPTION BY CASCADING ENERGY INPUTS
85
processes C and E). For the present analysis, a steady-state example has been chosen. However, the incorporation of thermal stores would allow intermittent and transient systems to be considered.
REFERENCES 1. M. HUSSEIN, R. J. WOOD, P. W. O'CALLAGHAN and S. D. PROBERT, Elticiencies of exergy transductions, Applied Energy, 6(5), 1980 pp. 371-84.
P. W. O'CALLAGHANand S. D. PROBERT,
School of Mechanical Engineering, Cranfield Institute of Technology, Bedford, MK43 OAL (Great Britain)