Module 06 Lecture 41: Integration of Heat Pump...

Integration of Heat Pump Module‐06 Lectrure‐41

Module‐06 Lecture‐41: Integration of Heat Pump

Key words: Heat Pump, Heat Engine, temperature lift, COP, PER, MVR, TVR, Heat

Transformer, Reverse Brayton‐cycle, It is known fact that heat flows naturally from a higher to a lower temperature. However, heat pumps, are able to force the heat flow in the other direction, using a relatively small amount of high quality drive energy (electricity, fuel, or high‐temperature waste heat). Thus, heat pumps can transfer heat from natural heat sources, such as from the air, ground, water or from heat sources such as industrial or domestic waste, to an industrial application or building. Heat pumps can also be used for cooling purposes also. For such a situation, heat is transferred in the opposite direction i.e. from the application that needs to be cooled to surroundings at a higher temperature where heat is rejected. In short, the objective of a refrigerator is to remove heat from the cold medium whereas, the objective of a heat pump is to supply heat to a warm medium. The Fig.41.1 distinguishes the functions of heat pump and refrigerator.

W = required input W = required input

Fig. 41.1 Difference between (a) Refrigerator and (b) Heat

Warm

environment,T1

Refrige

‐rator

Refrigerated

space (cold),T2

Q1

Q2= desired out put

Heat Pump

Q2

Q1 = desired output

Cold environ‐

ment, T2

(a) Refrigerator (b) Heat Pump

T1


Heat pumps offer unique way to provide heating and cooling in an energy‐efficient way in many applications, as they can use renewable heat sources around it. By investing a little extra energy, a heat pump can raise the temperature of available heat energy from the surroundings to the level needed for process applications. Heat pumps can also use waste heat sources of industrial processes, cooling equipment or ventilation air extracted from buildings to convert it into useful heat. A typical electrical heat pump will just need 100 kWh of power( for lifting the heat of 200kWh) to turn 200 kWh of freely available environmental or waste heat into 300 kWh of useful heat. Many industrial heat pumps can achieve even higher performance, and lift 100 kWh amount of heat with only 3‐10 kWh of electricity. Because heat pumps consume less drive energy than conventional heating systems, it is an a key technology for reducing gas emissions, such as carbon dioxide (CO2), sulphur dioxide (SO2) and nitrogen oxides (NOx). Industrial heat pumps are mainly used for, space heating; heating and cooling of process streams; water heating for washing, sanitation and cleaning; steam production; drying/dehumidification; evaporation; distillation and concentration. When heat pumps are used in drying, evaporation and distillation processes, heat is recycled within the process.

Through this unique ability, heat pumps can radically improve the energy efficiency and environmental value of any heating system that is driven by primary energy resources such as fuel or power. The following six facts should be considered when any heat supply system is designed[1]:

1. Direct combustion to produce heat is never the most efficient use of fuel as it creates pollution

2. Heat pumps are more efficient because they use renewable energy in the form of low‐temperature heat;

3. If the fuel used by conventional boilers were redirected to supply power for electric heat pumps, about 35‐50% less fuel would be needed, resulting in 35‐50% less emissions;

4. Around 50% savings are made when electric heat pumps are driven by CHP (combined heat and power or cogeneration) systems;

5. Whether fossil fuels, nuclear energy, or renewable power is used to generate electricity, electric heat pumps make far better use of these resources than do resistance heaters;

6. The fuel consumption, and consequently the emissions rate, of an absorption or gas‐engine heat pump is about 35‐50% less than that of a conventional boiler.

Heat Pump

In order to transport heat from a heat source to a heat sink, heat pumps need external energy. Theoretically, the total heat delivered by the heat pump is equal to the heat extracted from the heat source, plus the amount of drive energy supplied to it. It is simply a heat engine running in reverse direction, as shown in Fig.41.2 and the actual heat pump is shown schematically in Fig.41.3. It accepts heat Q2 from the sink at T2 ( at lower temperature), rejects heat Q1 into the source which is at a higher temperature , T1 in doing so it consumes work W.


The heat pump is a heat lift. Eq.41.1 can be written based on First Law of Thermodynamics:

… 41.1 As per the second law of thermodynamics, Eq.41.2 can be written:

… 41.2

It is usual to define overall efficiencies for real heat engines and heat pumps, according to:

… (41.3)

with < c for heat engines, and > c for heat pumps. Eq.41.3 can be rewritten for heat pumps as:

… . 41.4

where COPp is the so‐called “coefficient of performance” based on heat output Q1 from a heat pump or vapour recompression system, and COPr is the coefficient for a refrigeration

Condenser, T1

Q1

Evaporator, T2

Q2

W

Compressor

Throttle Valve

Fig.41.3 Closed cycle heat pump

T1 > T2

HeatEngine

Heat, Q1

Heat, Q2

(Source) Temperature, T1

Temperature, T2 (sink)

T1 > T2

Work, W

Fig.41.2 Thermodynamic concept behind heat pump


system based on heat absorbed(Q2) from the process. From Equations (41.1), (41.2), (41.3) and (41.4), one can write:

… 41.4

1… 41.5

1

… 41.6

Hence, the heat pump as a low temperature lift (T2 → T1 ) gives a high COPHp and a large amount of upgraded heat per unit power. However, lower values of T2 reduce COPR, so refrigeration systems need more power per unit for upgraded heat as the absolute temperature falls. With the above understanding, one can start analyzing the CHP problems. Heat pump cycles Theoretically, heat pumping can be achieved by many more thermodynamic cycles and processes. These include Stirling and Vuilleumier cycles, single‐phase cycles (e.g. with air, CO2 or noble gases), solid‐vapour sorption systems, hybrid systems (notably combining the vapour compression and absorption cycle) and electromagnetic and acoustic processes. Some of these are entering the market or have reached technical maturity, and could become significant in the future. Almost all heat pumps fall on two categories, i.e. either based on a vapour compression, or on an absorption cycle. Heat pumps are used for two purposes; either as a refrigeration system to carryout cooling below‐ambient temperature, or as a heat recovery system to pump heat backwards across the pinch. However, the equipment used in both cases is similar. Industrial heat pumps can be divided into six principal types: 1. Closed‐cycle heat pumps (most refrigeration cycles): A great majority of heat pumps

work according to this principle. A volatile liquid, known as the working fluid or refrigerant, circulates through the components of this cycle. The main components in such a heat pump system are the compressor, the expansion valve and two heat exchangers referred to as evaporator and condenser. The components are connected to form a closed circuit. It takes in heat and evaporates in the evaporator, is compressed and then condensed to give out heat at a higher temperature at condenser, and returned to the evaporator via a expansion valve which cools the refrigerant to evaporator temperature.


2. Mechanical vapour recompression (MVR): Categorized as open or semi‐open heat pumps. In a open systems, vapour from an industrial process is compressed by a compressor( driven by electricity or a plant turbine) to a higher pressure (thus a higher temperature) and condensed in the same process giving off heat. In semi‐open systems, heat from the recompressed vapour is transferred to the process via a heat exchanger. Because one or two heat exchangers are eliminated (evaporator and/or condenser) and the temperature lift is generally small, the performance of MVR systems is high, with typical coefficients of performance (COPs) of 10 to 30.

Current MVR systems work with heat‐source temperatures from 70‐80C, and deliver heat between 110 and 150C, in some cases up to 200C. Water is the most common 'working fluid' (i.e. recompressed process vapour), although other process vapours are also used, notably in the petro‐ chemical industry.

3. Thermal vapour recompression (TVR): High‐pressure steam is passed into a venturi‐type thermocompressor, and mixed with lower‐pressure steam to give a larger flow at an intermediate temperature and pressure. This also includes ejectors, mainly used for drawing a vacuum.

4. Absorption refrigeration cycles: These refrigeration cycles take waste heat above ambient and extract some below ambient heat from the process and rejects all heat at a medium temperature close to ambient. These are not widely used in industrial applications. Current systems with water/lithium bromide as working pair achieve an output temperature of 100ºC and a temperature lift of 65ºC. The COP typically ranges from 1.2 to 1.4. The new generation of advanced absorption heat pump systems will have higher output temperatures (up to 260ºC) and higher temperature lifts.

5. Heat transformers : These have the same main components and working principle as absorption heat pumps. With a heat transformer waste heat can be upgraded, virtually without the use of external drive energy. Waste heat of a medium temperature (i.e. between the demand level and the environmental level) is supplied to the evaporator and generator. Useful heat of a higher temperature is given off in the absorber. All current systems use water and lithium bromide as working pair. These heat transformers can

achieve a delivery temperatures up to 150C, typically with a lift of 50C. COPs under these conditions range from 0.45 to 0.48. In short, heat transformers take in waste heat, upgrade some of it to a useful temperature and cool the rest, thus acting as “heat splitters”.They are in effect a reversed absorption refrigeration cycle working entirely above‐ambient temperature. . 6. Reverse Brayton‐cycle heat pumps: It recovers solvents from gases in many

industrial processes. Solvent loaded air is compressed, and then expanded. The air cools through the expansion, and the solvents condense and are recovered. Further, expansion takes place in a turbine, which drives the compressor.

A simple closed‐cycle heat pump is illustrated in Figs.41.3 & 41.4 with T‐S diagram. In this heat pump moderate amount of electrical or mechanical power is used to upgrade a larger amount of heat. An absorption heat pump is shown in Fig.41.5. Absorption heat pumps are thermally driven, meaning that rather than mechanical energy, heat is used to drive the cycle. Absorption heat pumps for space conditioning are often gas‐fired, while


industrial installations are usually driven by high‐pressure steam or waste heat. Absorption systems make use of the ability of liquids or salts to absorb the vapour of the working fluid. The most common working pairs for absorption systems are:

water (working fluid) and lithium bromide (absorbent); and ammonia (working fluid) and water (absorbent).

In absorption systems, compression of the working fluid is achieved thermally in a solution circuit which consists of an absorber, a solution pump, a generator and then an expansion valve as shown in Fig.35.4, expands the working fluid to create low temperature to absorb heat. The low‐pressure vapour from the evaporator is absorbed in the absorbent in an absorber. This process generates heat. The solution is pumped to high pressure and then enters the generator, where the working fluid is boiled off with an external heat supply at a high temperature. The working fluid (vapour) is condensed in the condenser while the absorbent is returned to the absorber via the expansion valve.

Here, it is the “work potential” of above‐ambient heat (usually steam) which causes the heat pumping without actually converting heat into shaft power. These systems are not preferred due to their high capital costs (two columns required, one of them a high‐pressure column) and heavy heat demand.

Liquid+Vapor 1

2

3

4

5

Superheated vapor

Saturated liquid

Saturated Vapor

Isobars

LiquidVapor Liquid + Vapor

Specific entropy, S

Temperature, T

Evap

orator

Conden

ser

SuperheatedVapor

Valve

Compressor

Liquid+Vapor Liquid

Hot air

Vapor(Cold)

Expansion

Hotterair

Cold air

Fig.41.4 Single stage (a)vapor compression refrigeration cycle(b) T‐S diagram

2 1

3

4 5

1‐2 Compression of vapor2‐3 Vapor superheat removed in condenser 3‐4 Vapor converted to liquid in condenser 4‐5 Liquid flashed into Liquid+Vapor across expansion valve 5‐1 Liquid+vapor converted to all vapor in evaporator


Performance of Heat pump

The heat delivered by a heat pump is theoretically the sum of the heat extracted from the heat source and the energy needed to drive the cycle. The steady-state performance of an electric compression heat pump at a given set of temperature conditions is referred to as the coefficient of performance (COP). It is defined as the ratio of heat delivered by the heat pump and the electricity supplied to the compressor.

For engine and thermally driven heat pumps the performance is indicated by the primary energy ratio (PER). The energy supplied is then the higher heating value (HHV) of the fuel supplied. For electrically driven heat pumps a PER can also be defined, by multiplying the COP with the power generation efficiency.

The COP or PER of a heat pump is closely related to the temperature lift, i.e. the difference between the temperature of the heat source and the output temperature of the heat pump. The COP of an ideal heat pump is determined solely by the condensation temperature and the temperature lift (condensation - evaporation temperature). Fig.41.6 shows the COP for an ideal heat pump as a function of temperature lift, where the temperature of the heat source is 0°C. Also shown is the range of actual COPs for various types and sizes of real heat pumps at different temperature lifts.

.


The ratio of the actual COP of a heat pump and the ideal COP is defined as the Carnot-efficiency. The Carnot-efficiency varies from 0.30 to 0.5 for small electric heat pumps and 0.5 to 0.7 for large, very efficient electric heat pump systems. An indication of achievable COP/PERs for different heat pump types at evaporation 0°C and condensing temperature 50°C is shown in Table 41.1

Table 41.1 COP/PER range for heat pumps with different drive engines

Heat Pump types(s) COP PER

Electric ( compression) 2.5-5.0

Engine(compression) 0.8-2.0

Thermal(Absorption) 1.0-1.8

Table 41.2 Technical Characteristics of heat pumps[3]

System Delivery

Temp.,C Heat acceptance

temp.,C Temperature

Lift,C Typical COP

Electric Compression

R22 20‐80 ‐20‐40 < 60 3‐5

R12, R500 30‐95 ‐20‐ 65 <60 3‐5

Fig.41.6 Coefficient of performance as a function of condensation temperature for different heat pumps


R114 40‐130 10‐96 < 60 2‐4

Mechanical Vapor comp. >100 >80 < 50 5‐20

Thermal vapor comp. 60‐150 45‐120 < 40 1.1

Absorption 30‐92 5‐42 < 45 1.3

Heat Transformer 80‐150 58‐110 < 50 0.45‐0.5

The choice between heat pump systems also depends on the working temperatures and on the relative heat loads below and above the pinch. Absorbed and released heat loads for different heat pumps When matching heat pumps against the process ( Process GCC), it should be remembered that the amount of load on either the process source side or the process sink side can limit the total energy saving, since placement across the pinch is the correct placement of Heat Pump. For closed‐cycle heat pumps and MVR, the heat loads below the pinch are similar but the heat released above the pinch is slightly greater, due to the energy put in by the power drive. However, for TVR, the driver steam flow is much more than the vapour sucked in, and thus, the waste heat recovered is far less than the heat released above the pinch. The opposite applies for heat transformers, where less than 50% of the waste heat is usually upgraded. The shape of the GCC therefore suggests which system will be most suitable. Fig.41.7 shows the different types of heat pumps fitted to their ideal GCCs.

Matching GCC for

thermo vapor

compression(TVR)

Heat in Q2

Heat out Q1

Driver steam,H

H, kW

Shifted Temp., TC

pinch

Matching GCC for

closed cycle heat

pump and MVR

Heat in Q2

Heat out Q1

Drive power, W

H, kW

Shifted Temp., TC

pinch

(a) (b)

(c)

Fig.41.7 Matching GCC for (a) closed cycle heat pump and MVR (b) TVR and (c) Heat transformer

Matching GCC for

Heat Transformer

Heat in Q2

Heat out Q1

H, kW

Shifted Temp., TC

pinch

Heat out W


Economics of Heat Pump Whether a heat pump is feasible, as far as thermodynamics and cost is concerned, depends on the temperature lift for which it has to be designed as well as cost of heat and power which changes very often. The power requirement is determined by the Carnot efficiency, as given in Eq.41.7.

W=Q1

COPP=Q1

… 41.7

Typically, ηmech is 0.5 and so, for a temperature lift of 30°C (from ambient temperature (300 K)), W is about one‐fifth of Q1. Since power typically costs 3–4 times as much as heat energy, the cost savings from upgrading 20 kW of heat are only equivalent to the supply cost of about 4 kW, without even adjusting fixed cost of the equipment to handle 20 kW. At higher temperature lifts, the economic advantage of heat pumping can vanish altogether. In some countries only MVR systems have regularly yielded cost‐effective projects; the temperature lift is usually low, there is no separate evaporator with its associated pressure drop, and the equipment is simpler and cheaper. TVR has sometimes been economic due to its low capital cost even for the low ratio of recovered heat to steam supplied has been acceptable. Integration of two GCCs Two GCCs can be combined graphically, by taking the GCC of the first process(process‐1) and a mirror image ( around vertical axis) of the GCC of the second process(process‐2). The mirror image of the second GCC is then placed to the GCC of first process and sliding the first GCC it horizontally till it touches the mirror image of the second GCC. The horizontal distance between the two GCCs ( GCC of first and mirror image GCC of second) is the GCC of the combined set, and the pinch temperature is the point where the two curves just touch. This should be noted that this point need not be the pinch of either of the two processes. The Fig 41.8 shows the above process of creation of combined GCC from two GCCs. This method can be used to fit any set of processes together and is particularly powerful.

(a) Combined GCC

Fig.41.8 Mirror image method

T

H(b) Two GCC

T

H(c) Mirror image method

T

H

GCC process‐1

GCC process‐2

GCC process‐1

Mirror image

GCC process‐2

Combined GCC

of process 1+2


Grand composite curve of a Heat Pump Fig.41.3 shows a closed cycle heat pump. The GCC of the heat pump is shown in Fig.41.8(a) and its mirror image is shown in Fig.41.8(b). The shape of the curve is governed by the laws of thermodynamics, which show that for a reversible heat pump operating between evaporating and condensing temperatures T2 K and T1 K the following relationships hold:

… . 41.8

The COPHP(actual) = Q1/W = T1/(T1‐T2) as reported in Eq.41.4. Where lies between 0.5 to 0.7. The area, ”A” of the triangle formed by the condenser heat line and the temperature lift( T1‐T2) can be given as:

A = Q1(T1‐T2) = WT1 ….(41.9) This provides an alternative method to find work from graph. Using the mirror image technique as discussed above, the matching of the GCC of heat pump to that of process is relatively simple and it illustrated in Fig.41.10. Here it is assumed that the temperature difference between the stream and the heat pump fluid is the same as the temperature adjustment of the stream. The mirror image heat pump curve is shown being fitted to the process GCC, and the combined GCC ( Fig.41.10(b))

T

H

T1

T2Q2

Q1

(a) Mirror Image

Fig.41.9 Grand composite curve of heat pump

T

H

T1

T2

Q2(evaporator)

Q1(condenser)

(b) Heat Pump GCC


which is referred to as the remaining problem grand composite curve, is also shown in figure. It is interesting to note that the process GCC has been bracketed by two pinches at the condensing and evaporating temperatures of the mirrir image of the Heat Pump GCC. However, the shape of the GCC curve remains same above and below the temperature range involving the heat pump. The areas created between the pinch and the evaporating and condensing temperatures theoretically offers a chance to generate work by transferring heat from the higher temperature hot stream to the lower temperature cold stream through a heat engine. Though, such a heat engine appears to be impractical, it nevertheless shows that the heat pump has consumed more work than it is necessary in doing its task. This quantity of work can be reduced by the use of multiple heat pumps in horizontal cascade, as illustrated in Fig 41.11

Fig.41.11 Multi stage heat pump and its deployment on GCC

Condensers

Evaporators

Cold streams

Hot streams

(a) Multi Stage Heat Pumps(MSHP)

321 Heat Pumps 3

3

2

2 1

1

T

H (b) MSHP on process GCC

Fig.41.10 Addition of a heat pump to process GCC

(a) Mirror image method (b) Combined GCC

T T

H H

Mirror image GCC of heat pump

Process GCC


The restrictions on the size of heat pump take place when either the maximum temperature lift is reached or when the heat pump's mirror image GCC re‐intersects the process GCC as shown in Fig.41.12. If this intersection is with the end of the curve ( Fig.41.12(a)) then no further heat pumping is possible, as any further heating by the condenser prevents cooling of the high temperature streams, and any further cooling by the evaporator prevents heating of the low temperature streams. If the intersection of the heat pump GCC line is with some intermediate portion of the process GCC as in Fig41.12(b), then this point, D, becomes a new secondary pinch in the remaining problem. For further heat pumping a heat pump is required across both the primary and secondary pinch, Fig.41.13. For this to be economic the total temperature lift across both heat pumps must be less than 50 K. It is sometimes possible in such cases, if a unit operation is creating the secondary pinch, then operating parameters of the process can be so adjusted that the secondary pinch coincides with the primary pinch and thus one heat pump can be used for both pinches.

Maximum Economic Lift for a given Heat pump can be given as[ 7]:

. .

/ … 41.10

T T T

H H H

D

Fig.41.12 Re‐intersection of heat pump Fig.41.13 Two pinch heat pumping(a) (b)

Primary pinch

Secondary pinch


Where:

TA - temperature at which heat is accepted (K)

TD – temperature at which heat is delivered (K)

CHPE- cost of heat pump evaporator ($ energy-1)

CHPC – cost of heat pump condenser ($ energy-1)

CC – compressor cost ($ energy-1)

C1 – capital cost of the remaining process ($ energy-1)

CHI – heater cost ($ energy-1)

CCOI- cooler cost ($ energy-1)

HI - fraction of heater area that can be reused

COI - fraction of cooler area that can be reused

NT – thermodynamic efficiency

NM – mechanical efficiency

H – hours of operation per year (h yr-1)

P – payback period (yr-1)

QD – heat delivered by the heat pump (thermal energy time-1)

(MV)H – marginal value of the level of thermal energy saved by heat pumping ($ energy-1)

(MV)I – marginal value of the waste thermal energy used by the heat pump ($ energy-1)

(MC)D – marginal cost of the electricity or shaft power ($ energy-1)

The derivation of Eq.41.40 is hown in Appendix-“A”


Appendix-A

Derivation of Eq.41.10

HEAT TRANSFER AREA PENELTY DUE TO HEAT PUMPING

Fig.41.14 shows hot and cold composite curves for the process without placement of any heat pump. However,. Fig.41.15 shows the same process integrated with heat pump.

ACO

A1

A2

AH

Fig.41.14 Hot and cold composite curve before heat pump integration

Cold composite Hot composite

tem

per

atu

re

Heat duty

∆Tmin


When the heat pump is placed across the pinch, the hot and cold utility requirement decreases as it clearly seen from the Fig.41.15, but the total heat transfer area of the process consists of the heat exchange area that exchange heat from process to process, utility heater and utility cooler areas.

ACO’

A11 A12

A13

A21

A22

A23

AH’

tem

per

atur

e

heat duty

condenser of heat pump

evaporator of heat pump

Fig.41.15 ‐Hot and cold composite curve after heat pump

integration

W

Q1

Q2

Condenser temp.(T1)

Evaporator temp.(T2)


From Fig.41.15 it is clear that after the heat pump placement the hot and cold utility requirement decrease as:

ACO > ACO’

AH > AH’

For simple system with identical heat transfer coefficient, the minimum heat transfer area for ∆Tmin between the hot and cold composite curves is given by :

n

JJT AA

1

Where, n is total number of enthalpy intervals

from Fig.41.14 (before heat pump placement)

target heat exchange area – A1+A2

target heater area - AH

target cooler area - ACO

from Fig.41.15 i.e. after heat pump placement

target heat exchange area – A11+A12+A13+A21+A22+A23

target heater area – AH’

target cooler area – ACO’

from the above figures it is clear that –

AH’ < AH

ACO’ < ACO

And, due to the reduction in the temperature driving force

A11+A12+A13+A21+A22+A23 ≥ A1+A2

So the total increase in the heat exchange area is –

∆A = (A11+A12+A13+A21+A22+A23)-( A1+A2)

∆A can also be written as –

AHPE+AHPC+A1

Where-


AHPE – heat pump evaporator area

AHPC – heat pump condenser area

A1- change in the interchange area of the remainder of the process

Decrease in the heater area – AH-AH’

Decrease in cooler area – ACO – ACO’

If –

HI - fraction of heater area that can be reused

COI - fraction of cooler area that can be reused

So the net increase in the heat transfer area –

''1 COICOICOIHIHIHIHPCHPE AAAAAAA

So the net increase in the heat transfer area after the heat pump placement is basically the combination of heat pump evaporator area, heat pump condenser area, change in the interchange area of the remainder of the process and the decrease in the amount of hot and cold utility base on the fraction of heater and cooler area.


DERIVATION OF A GENERAL EQUATION FOR MAXIMUM ECONOMIC LIFT

Equation for the maximum economic lift is:

. .

/ … 41.10

PROOF - consider a heat pump operating in a temperature region bounded by the

temperature of a low and a high level utility (i.e. UHDAUI TTTT )with marginal values

(MV)I and (MV)H respectively.

Assuming the mechanical and thermodynamic efficiencies to be NM and NT , respectively, so –

D

A

MT

Da T

TNN

QW 1

(1)

TUH (MV)H

TD

QA

QD

(MV)I

WP

(MC)D

TUI

TA

Fig.41.16 Heat pump in a region bounded by two utility levels


D

A

T

DP T

TN

QW 1

Where;

Wa – actual work including the mechanical losses

WP – work that does not include the mechanical losses

QD – heat delivered by the heat pump

TA - temperature at which heat is accepted

TD – temperature at which heat is delivered

On rearranging the equation (2) -

D

ADPT T

TQWN 1

T

D

A

D

DT N

T

T

WQ

QN 1

D

DADPT T

TTQWN

D

DA

D

D

D

DT T

TT

WQ

QWQ

QN 1

T

D

A

A

DT N

T

T

Q

QN 1

Expression for AQ -

T

D

A

T

DA N

T

T

N

QQ 1

QA – heat accepted by the heat pump

(3)

(2)


Annual saving at H hours of operation per year for QD units of energy delivered per hour at TD (K) can be expressed as :

Annual saving = value of Uh saved – cost of driver power – value of UI saved

Where –

Uh – high level utility

UI – low level utility

Annual saving = HMCWMVQMVQ DaIAHD

(MV)H –it is the marginal value of the level of thermal energy saved by heat pumping and can be defined as the total cost avoided in reducing by one unit the amount of that level of thermal energy being provided under the operating conditions existing at a given point in time.

(MV)I – it is the marginal value of the waste thermal energy used by the heat pump, and it is positive if there is the demand of thermal energy outside the system

(MC)D –it is the marginal cost of the electricity or shaft power and can be defined as the total additional cost actually incurred in providing the next additional unit of electricity or shaft power under the operating conditions existing at a given point in time.

H – hours of operation per year

Put the value of QA and Wa-

HMT

D NMVNN

HQ

IMDIHMTIMDD

A

MT

D MVNMCMVMVNNMVNMCT

T

NN

HQ

DT

T

NN

HQN

T

T

N

HQMVHQ A

MT

DT

D

A

T

DHD 11

(4)

……(4)


If P is the payback period in years. So based on the total increase in the area, the annual capital expenditure can be given as –

PCCCCCC COICOIHIHICHPCHPE /][ 1

Where –

CHPE- cost of heat pump evaporator

CHPC – cost of heat pump condenser

CC – compressor cost

CHI – heater cost

CCOI- cooler cost

On equating equations of annual saving and annual capital expenditure, we can obtain the maximum economic lift –

PCCCCCC COICOIHIHICHPCHPE /][ 1

On rearranging the equation we get the equation for maximum economic lift –

. .

/

=

IMDIHMTIMDD

A

MT

D MVNMCMVMVNNMVNMCT

T

NN

HQ

(5)


Illustrative Example ( From Ref.7)

Fig.41.17 illustrates a heat pump operating on a site with two steam levels. It is desired to

find out the minimum economic temperature of heat reception, Tmin for the heat pump

under the following condition :

(a) LP steam can be exported from the process, i.e steam has a positive marginal value.

(b) LP steam cannot be exported from the process, i.e the waste heat from the process

has no demand outside the system and has to be rejected to cooling water.

The data can be given as –

Table 41.3 – data for maximum economic lift calculation Electricity price $51.0 MWh-1

IP steam marginal value $17.0 MWh-1 heat absorbed LP steam marginal value $5.0 MWh-1 heat absorbed Cooling water cost $4.0 MWh-1 heat rejected Capital cost of compressor $400 kW-1 absorbed heat(installed) Capital cost of heat pump exchanger $60 kW-1 absorbed heat(installed) Capital cost of LP raising heat exchanger $30 kW-1 absorbed heat(installed) Capital cost of cooling water cooler $12 kW-1 rejected heat (installed) Hours of operation 8000 h yr-1

Simple payback period 2 yr-1

COP(practical) 0.6 COP(based on working medium temperature)

HP

LP STEAM

HP STEAM 473˚K

PROCESS SINK 463˚K

PROCESS SOURCE

10˚K

QD-WP

QD

WP

393˚K

Figure 41.17 – Maximum economic lift


Case(a) – data from the table 41.3

(MC)d = 51.0$MWh-1

(MV)h = 17.0$MWh-1

(MV)I = 5.0$MWh-1

NT = 0.6

NM = 1.0

H = 8000h yr-1

TD = 473K

C1 = 0

P = 2 yr

CHPE = CHPC = 60*103(QD/NT)[(TA/TD)-(1-NT)]

CCO = 30*103(QD/NT)[(TA/TD)-(1-NT)]

CC = 400*103(QD/NT)[1-(TA/TD)]

For a heat pump operating in a temperature region bounded by the temperatures of a low and a high level utility with marginal values (MV)I and (MV)h, the general equation for the maximum economic lift can be given as -

. .

/

By putting all the values in the above equation and taking = 1, we get –

TA = TMIN = 445.32K

Case(b) – cooling water cost = $4.0 MWh-1 heat rejected (MV)I = -4.0$MWh-1

capital cost of cooling water cooler = $12kW-1 rejected heat (installed), so-

CCO = 12*103(QD/NT)[(TA/TD)-(1-NT)]

So, by putting these values in the above equation we get

TA = TMIN = 417.68K


References 1. http://www.heatpumpcentre.org/en/aboutheatpumps/howheatpumpsachieveene

rgysavings/Sidor/default.aspx 2. Pongsid Srikhirin , Satha Aphornratana and Supachart Chungpaibulpatana, A

review of absorption refrigeration technologies, Renewable and Sustainable Energy Reviews, 5 (2001) 343–372

3. Xiao Feng and Thore Berntssont, Critical Cop For An Economically Feasible Industrial Heat‐Pump Application, Applied Thermal Engineering Vol. 17, No. I. pp. 93‐101, 1997

4. Robin Smith, “Chemical Process Design”, McGraw Hill, 1995. 5. B. Lynhoff et al., “Process Integration for the Efficient Use of Energy”, Institution of

Chemical Engineers, 1983. 6. R. BENSTEAD and F.W. SHARMAN, (1990), “HEAT PUMPS AND PINCH

TECHNOLOGY”, Heat Recovery Systems & CliP, 10, 4, 387‐398. 7. Saidas M. Ranade, (1988), “New insights on optimal integration of heat pumps in

industrial sites”, Heat Recovery Systems & ClIP Vol. 8, No. 3, 255‐263. 8. Chi‐I Tuan, Yi‐Lung Yeh, Chi‐Jen Chen, Ting‐Chien Chen, (2011) “Performance

assessment with Pinch technology and integrated heat pumps for vaporized concentration processing”, Journal of the Taiwan Institute of Chemical Engineers.

9. K.J. Chua *, S.K. Chou, W.M. Yang, “Advances in heat pump systems: A review”, Applied Energy 87 (2010) 3611–3624

Module 06 Lecture 41: Integration of Heat Pump...

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