ExPAND Methodology

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An Extended Pinch Analysis and Design procedure utilizingpressure based exergy for subambient cooling

Audun Aspelund *, David Olsson Berstad, Truls Gundersen

The Norwegian University of Science and Technology, NTNU, Department of Energy and Process Engineering, NO-7491 Trondheim, Norway

Received 21 December 2006; accepted 23 April 2007Available online 10 May 2007

Abstract

A new methodology for process synthesis extending traditional Pinch Analysis with exergy calculations is described. The methodologyshows great potential for minimizing energy requirements (total shaft work) in subambient processes. This is achieved by optimizingcompression and expansion work for the process streams together with the work needed to create necessary cooling utilities. The pro-cedure, referred to as Extended Pinch Analysis and Design (ExPAnD), is illustrated by two examples, first in a simple example on how toutilize pressure based exergy in a cold stream for subambient cooling of a hot stream, then in the main example describing the use of thedesign methodology to develop a novel process for liquefaction of natural gas to LNG. 2007 Elsevier Ltd. All rights reserved.

Keywords: Process design; Heat recovery; Pressure recovery; Pinch; Exergy; Temperature

1. Introduction

Pinch Analysis has reached a very high level of indus-trial application over the years and has been successfullyapplied to improve heat recovery, to design better heatand power systems and to address utility systems. An over-view with references to original research is given in the textbook of Smith [1]. In addition, there have been a number ofexpansions of the Heat Pinch principle; examples includeMass Pinch [2], Water Pinch [3], Hydrogen Pinch [4], Oxy-gen Pinch [5], etc. The major limitation with the heat pinchmethodology is that only temperature is used as a quality

parameter of a stream, thus neglecting pressure andcomposition.The advantage of Exergy Analysis [6] is the inherent

capability of including all stream properties (temperature,pressure and composition); however, a limitation is itsfocus on the equipment units, rather than the flowsheetlevel. In addition, there is no strong link between exergy

and cost; in fact, there is often a conflict between reducingexergy losses and reducing cost. Nevertheless, Ananthar-aman et al. [7] tried to combine pinch and Exergy Analysisin drawing so-called energy level Composite Curves. Thenew energy level parameter was proposed by Feng andZhu [8].

In reverse Rankine refrigeration processes and heatpumping processes, the temperature is closely related toboth pressure and power, since compression and expansion(valve) will change the boiling and condensation tempera-tures in order to be able to transfer heat from a cold sourceto a hot sink. For refrigeration processes without phase

change, as the reversed Brayton cycle, both compressorsand expanders are utilized to provide refrigeration. Theserefrigeration or heat pumping processes may be performedby using the process streams as working fluids, in whichcase the term open cycle is used. In all cases, the requiredenergy (shaft work) and resulting refrigeration duty aredetermined by the hot and cold temperature levels, whichdictates the required pressure increase or decrease andthereby the need for shaft work.

Large savings can be obtained by integrating the hotand cold streams with the refrigeration processes (whether

1359-4311/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2007.04.017

* Corresponding author. Tel.: +47 951 83 925.E-mail address: [email protected] (A. Aspelund).

www.elsevier.com/locate/apthermeng

Applied Thermal Engineering 27 (2007) 26332649
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they are open or closed cycle) in the best possible way.Therefore, it would be very convenient to have pinch anal-ysis tools which include the effect of pressure. The ExPAnDmethodology will combine the targeting for minimumexternal heating and cooling (Pinch Analysis) with the min-imization of irreversibilities (Exergy Analysis) in an

attempt to guide the system design towards minimum totalannual cost, possibly including the use of numerical optimi-zation (Mathematical Programming) as an outer loop.

The decomposition of the design process has often beenillustrated by the onion diagram [9] in Fig. 1, indicating thelevels of process design as well as the natural sequence ofdecisions. The most common version of the onion diagramstarts with the reactor system (R), followed by the separa-tion system (S), then the heat recovery system (H) andfinally the utility system (U). In its first version, however,Linnhoff et al. [9] had included compressors and expanders(C&E) inside the heat recovery system. This is interestingand highly relevant to the present paper, since expanders

and compressors play a significant role in the proposedmethodology.

Important feedback or iteration loops exist, however,when designing subsystems corresponding to the differentlayers of the onion diagram. One of these iterations isrelated to the interaction between setting the pressure ofseparation equipment such as distillation columns andevaporators, and the design of the heat recovery system.By changing the pressure levels of such separators, the cor-responding temperature levels of important (large duty)heat sources and heat sinks will change, and this may havea significant impact on the scope for direct heat integration

or heat pumping.In subambient processes, this relation between pressure

and temperature is even more important. When a pressur-ized stream is expanded, the pressure is reduced and thetemperature decreased giving the stream a larger coolingduty while at the same time producing shaft work. In thisway at least some of the original pressure based exergy isconverted into temperature based exergy. Thus, pressureshould be included in the stream data definition in the sameway as temperature. This calls for an updated problem def-inition suitable for the Extended Pinch Analysis andDesign (ExPAnD) methodology. With particular focus onsubambient processes, the expanded problem definition isas follows (notice that the streams themselves may actas utilities, possibly by the use of expansion andcompression):

Given a set of process streams with a supply state (tem-

perature, pressure and the resulting phase) and a target

state, as well as utilities for external heating and cooling;

design a system of heat exchangers, expanders and com-

pressors in such a way that the irreversibilities are

minimized.

It should be emphasized that this problem definition is sig-nificantly more complex than in standard PA. First, the is-

sue of soft target temperatures is now expanded to also

include soft target pressures. Second, the thermodynamicprocess from the initial to the final condition is not speci-fied, and the change in temperature and pressure may fol-low a large set of different routes. Third, the distinctionbetween process streams and utilities as well as betweenhot and cold streams is no longer obvious; in fact streamsmay change identity. Some processes streams act like utili-ties and a cold process stream or utility may temporarilychange to a hot stream and vice versa. Fourth, stream

properties such as phase can be changed by manipulatingthe pressure. As an example, pumping a liquid at bubblepoint prior to heating avoids a large horizontal part ofthe Composite Curves that may be responsible for signifi-cant exergy losses. Furthermore, such an increase in pres-sure will increase the vaporization temperature anddecrease the latent heat of vaporization.

An Exergy Analysis of the hot and cold streams enteringand leaving the process will show if it is theoretically pos-sible to design a process without utilities (power, externalheating and cooling). Furthermore, the minimum exergyefficiency for the process to be self-supported i.e. without

utilities can be calculated. If the calculated exergy efficiencybased on inlet and outlet streams is above 100%, it simplymeans that the process is not self-supported, and that exter-nal utilities must be provided. In this case, the minimumrequired shaft work can be found.

In many cryogenic applications, some of the heatexchangers are of the multi-stream type, which enables sev-eral streams with different entering and leaving tempera-tures to be joined in one heat exchanger. In fact, theconcept of Composite Curves was used in these industrieslong before Pinch Analysis was established. The CompositeCurves show the ideal process and are drawn in a coun-ter-current fashion to indicate optimal use of temperaturedriving forces. When establishing a network of two-streamexchangers, however, considerable use of stream splitting isrequired to approach minimum total heat transfer area.Multistream exchangers have the great advantage thatstreams can enter and exit at the thermodynamically cor-rect place. Hence, the splitting of streams normally donein heat exchanger network design is not required. As a con-sequence, the current methodology only considers totalheat transfer area and does not consider each stream match(or exchanger) in detail.

A theory section is included prior to an illustratingexample of how to utilize pressure based exergy in a cold

stream for subambient cooling of a hot stream. Then the

R S

C

&

E

H U

R Reactor SystemS Separation SystemC&E Compression & ExpansionH Heat Exchanger NetworkU Utility System

Fig. 1. Illustration of the natural sequence in process design.

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ExPAnD methodology is described together with somegeneral heuristics, followed by an application in a casestudy describing the design development of a novel processfor liquefaction of natural gas to LNG.

2. Theoretical background

2.1. Exergy degeneration associated with heat transfer

across finite temperature differences

There is degeneration of exergy (irreversibilities) associ-ated with any heat transfer process operating across finitetemperature differences. As there is an upper practical limiton heat transfer area (not to mention the cost impact) ofheat exchangers, finite temperature differences must beallowed to ensure sufficient driving forces for heat transfer.

For an infinitesimal amount of heat dQ extracted from ahot stream at temperature TH, the inherent change inexergy is given by Eq. (1). Correspondingly, if heat is sup-plied to a cold stream at temperature TC, the cold streamexergy change is given by Eq. (2). It should be noted thatthe normal sign convention in thermodynamics is notapplied, thus the infinitesimal amount of heat dQ isregarded as a positive entity for both hot (Eq. (1)) and coldstreams (Eq. (2)).

dEH 1 T0

TH

dQ 1

dEC 1 T0

TC

dQ 2

The total irreversibility (and net exergy loss) associatedwith heat transfer between two streams can be expressedby Eq. (3). The Carnot factor is given by Eq. (4).

I

ZQ0

dEH dEC

ZQ0

gc;H gc;CdQ 3

gc 1 T0

T4

For subambient processes, irreversibility increases bothwith increasing temperature difference and decreasing tem-perature level. As a result, the irreversibility rate associatedwith a heat transfer process below ambient is considerablylarger than a similar process above ambient. As described

later, by using the ideal gas model and combining Eqs.(1)(4), the temperature term of the thermomechanical ex-ergy in a cold stream (Eq. (15)) and the irreversibilities dueto a finite and constant temperature difference in a heat ex-changer (Eq. (17)) can be derived.

2.2. Shaft power for cooling utilities

The refrigeration process (RP) in Fig. 2 withdraws heatat rate QC from a cold thermal energy reservoir (TER) attemperature TC and delivers a heat flow QH to a hotTER at TH. The RP consumes power at a rate W. A Coef-

ficient of Performance (COP, defined by Eq. (5)) is the

commonly used efficiency measure for RPs. The theoreti-cally maximum COP for the process is obtained when itoperates reversibly and adiabatically (Eq. (6)).

COP QCW

5

COPth;max 1TH=TC 1

6

For a process operating with the ambient temperature ashot TER, i.e. TH = T0 = 15 C (or 288 K), the maximumCOP is plotted in Fig. 3 as function of cold temperatureTC, at which the cooling duty is delivered. Since refrigera-tion processes have lower performance than the theoreti-cally maximum COP, correlations must be developed tofind approximate figures for power input, given coolingduty QC and temperature level TC. In other words, theCOPth,max must be scaled with a coefficient f 2 h0, 1i asindicated in Eq. (7). The power needed to provide coolingby the refrigeration process is then given by Eq. (8).

COP f COPth;max f

T0=TC 17

WQC

COP

QC T0=TC 1

f8

The factor, f, relating theoretical and practical COP valuesis approximately 0.4 for most refrigeration processes. FromFig. 3, it can be observed that COP ! 1 as T! T0. Thismeans that an infinite amount of cooling can be provided ifthe cooling temperature equals T0, which is intuitively

RP

QH

QC

W

Hot TER, TH

Cold TER, TC

Fig. 2. A refrigeration process.

0.001

0.01

0.1

1

10

100

1000

15 -35 -85 -135 -185 -235

T [C]

COPth,max

Fig. 3. COP as a function of temperature.

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understood as e.g. seawater cooling has no exergy input,except a small amount of water pump power.

2.3. Temperature and pressure based exergy in

low-temperature expanders

The total exergy of a stream or system can be dividedinto individual exergy contributions as indicated inFig. 4. This paper will focus on the thermo-mechanicalexergy, which is the sum of pressure and temperature basedexergy.

Using the 1st and 2nd laws of thermodynamics, thethermo-mechanical exergy can be derived [6]:

etm h h0 T0s s0 9

The chemical and mechanical exergies are not includedin the exergy efficiency calculations. Chemical exergy isnot included since the processes studied here do not includechemical reactions, mixing and separation, and mechanical

exergy is assumed to be negligible. Hence, exergy conver-sion efficiency (wconversion) can be defined as the sum ofthe useful thermo-mechanical exergy of the outlet streamsand the power generated from the process, divided by thesum of the total thermo-mechanical exergy of the inletstreams and the power required. Including chemical exergy,which often is much larger than thermo-mechanical exergy,would make all efficiencies large (approach 100%) andthereby dilute the effects of irreversibilities.

wconversion e

tmuseful;outlet wgenerated

etminlet winlet

10

For a stream whose thermodynamic state is described bytemperature Tand pressure P, its temperature based exergy(e(T)) is defined as the maximum obtainable work when thestream is brought from its current temperature T to ambi-ent temperature T0 at constant pressure P. The pressurebased exergy (e(P)) is then equal to the thermo-mechanicalexergy that is left in the stream, when the stream is broughtfrom initial pressure P to ambient pressure P0 at constanttemperature T0. Hence, the two exergy components thatconstitute thermo-mechanical exergy are given by Eqs.(11) and (12):

eT hT;P hT0;P T0sT;P sT0;P 11

eP hT0;P hT0;P0 T0sT0;P sT0;P0 12

If ideal gas with constant heat capacity Cp is assumed, theexpressions for temperature and pressure based exergybecome:

eT Cp T T0 1 lnT

T0

!13

eP

T0R lnP

P0 k 1

k CpT0 lnP

P0 14

The thermo-mechanical exergy change in a cold stream atsubambient temperatures to be heated from supply temper-ature (TC, s) to target temperature (TC, t) at constant pres-sure is:

D _EC _mCpC TC;t TC;s T0 lnTC;t

TC;s

!15

The minimum exergy _EC;min necessary to cool a hotstream by heat transfer at constant DT is given by Eq.(16). The irreversibility caused by heat transfer at finiteand constant temperature difference DT between the hot

and cold stream is given by Eq. (17). In fact, heat transferat constant DT means that the heat capacity flowrates ofthe hot and cold streams are equal; _mCpH _mCpC _mCp. An alternative formulation of Eq. (17) including

irreversibilities due to pressure drop in heat exchangers isshown in Eq. (18).

_EC;min D _EC D _ETHDT

_mCp TH;s TH;t T0 lnTH;s DT

TH;t DT

!16

_IDT D _EH _EC;min

_mCpT0 ln

TH;t

TH;s TH;s DT

TH;t DT !

17

_IDT;DP _mT0 Cp lnTH;s

q

Cp

TH;s

TH;s DT

TH;s q

Cp DT

" #(

R lnPC;s

PC;t

R ln

PH;s

PH;t

)18

Fig. 5 shows the temperatureentropy diagram fornitrogen with isobar curves for atmospheric pressure(1 bar) and 50 bar. At 1 bar there is no pressure basedexergy, hence the area (A) between the 1 bar isobar andthe ambient temperature is the total exergy. By increasing

the pressure of liquid nitrogen, there is a substantial changefrom temperature to pressure based exergy. The tempera-

Exergy

Mechanical Thermal

PotentialKinetic Thermo-mechanical Chemical

Temperature-based

Pressure-based

Fig. 4. Exergy components.

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ture based exergy is found as area B between the 50 bar iso-bar and the ambient temperature. Thus, the pressure basedexergy equals the area between the isobars extending toambient temperature. For ideal gas, however, enthalpy is

only a function of temperature. As a result, Eq. (12) canbe simplified since the enthalpy terms cancel, and the pres-sure based exergy is given by e(P) = T0(s(T0, P0) s(T0, P)).This is indicated in Fig. 5 by area (C) which is a rectanglebetween ambient temperature and 0 K and between theentropy values for ambient temperature and 1 bar andambient temperature and 50 bar.

The entropy change and temperature increase, as well asthe work required (exergy input) by pumping liquid nitro-gen from 1 to 50 bar are small, hence the temperaturebased exergy for 1 bar liquid nitrogen (area A) is very closeto the sum of the temperature based exergy (area B) and

the pressure based exergy (area C) for liquid nitrogen at50 bar.

A subambient expander while producing power alsoincreases the temperature based exergy at the cost of pres-sure based exergy. The fundamental difference betweenhigh temperature expansions for power production andlow temperature expansions is the profile of the tempera-ture based exergy component. Whereas this componentdecreases and is converted to power in above ambientexpansions, it increases at the cost of pressure based exergyin a subambient expander. This also implies that the powerproduced per unit of pressure decrease is smaller for lowtemperature expanders than the power generated by tur-bines operating above T0. This is intuitively understood,as the pressure based exergy is apportioned to both powerand temperature based exergy in subambient expansions.Although the generation of low temperature based exergyis the main purpose, the power output is regarded as a use-ful by-product from the process. Actually, the conversionbetween the three exergy components work, pressure basedand temperature based exergy is the core of the methodol-ogy under development.

The flowsheet for an expansion process with corre-sponding exergy components is shown in Fig. 6. For anisentropic expansion with inlet state T1 = 15 C and

P1 = 10 bar, the change in each exergy component, or the

exergy conversion profile, is plotted as function of outletpressure P2 in Fig. 7. Ideal gas with constant heat capacity(Cp) and isentropic expansion is assumed, hence no irrever-sibilities occur. Fig. 8 illustrates the exergy conversion pro-file for an isentropic efficiency of 80%, which is a commonfigure for low temperature expanders (cryoexpanders), andwhere 26% of the inlet exergy is degenerated.

2.4. A very simple example

An illustrative example of how to utilize pressure basedexergy in a cold stream for subambient cooling of a hotstream is presented in this section. A fixed hot stream (spec-ified Ts and Tt with constant pressure) is to be integratedwith a gaseous cold stream which can be expanded from4 to 1 bar. Both streams exchange heat below ambient

-250

-150

-50

50

25 75 125

s [kJ/(kmoleK)]

T[C]

A

B

C

50 bar1 bar

Fig. 5. Temperature/entropy diagram for nitrogen streams at 1 and50 bar.

e1(T)

, e1(P)

e2(T)

, e2(P)

Wi

Fig. 6. Temperature and pressure based exergy in expansion processes.

0

0.2

0.4

0.6

0.8

1

Expander Outlet pressure [bar]

Relativeexergy

e(T) e(P) w i

910 8 7 6 4 3 2 1

Fig. 7. Exergy components as a function of outlet pressure for an idealexpander.

0

0.2

0.4

0.6

0.8

1

Expander Outlet pressure [bar]

Relativeexergy

910 8 7 6 4 3 2 1

e(T) e(P) w i

Fig. 8. Exergy components as a function of outlet pressure for an

expander with 80% efficiency.

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(T0 = 15 C). The hot stream with a heat capacity flow rate _mCp of 3 kW/K is to be cooled from 10 C to 85 Cgiving a total duty of 225 kW. The cold stream with an_mCp of 2 kW/K is to be heated from 55 C to 10 C, giv-

ing a total duty of 130 kW. Hence, the cold stream neitherhave a low enough temperature, nor a large enough cooling

duty to cool the hot stream. The PA CCs and the PA GCCfor a minimum temperature difference of 10 C are shownin Figs. 9 and 10, respectively. The GCC shows that theminimum hot and cold utility, QH and QC, are 60 kWand 155 kW, respectively. As the hot stream is fixed, theminimum heating of 60 kW cannot be avoided. However,the cold stream can be expanded to lower pressure, therebytransforming pressure based exergy to temperature basedexergy and work. As a result, additional cooling isprovided.

An Exergy Analysis using the simplified formulas in theprevious section is performed. The hot stream pressure isconstant; hence the total exergy change of 65 kW is pure

temperature based exergy. With a minimum approach tem-perature of 10 C, the inevitable irreversibility related tocooling of the hot stream (Eq. (17)) is 14 kW. The coldstream change in temperature based exergy is only20 kW, which is considerably less than the sum of 65 kWand 14 kW. Further, the _mCp for the cold stream is lessthan the _mCp for the hot stream. However, the cold streampressure based exergy assuming ideal gas and k= 1.4 is228 kW, giving a total exergy change (reduction) of248 kW. Since the total exergy released by the cold stream

is larger than the exergy needed to cool down the hotstream including the inevitable irreversibilities, it should,in theory, be possible to develop an ideal process whichdoes not require external cooling utility.

In the remaining part of the example, some possibilitiesfor utilizing pressure based exergy for cooling and the

implications of these actions are discussed. Isentropicexpansion of a gas will decrease the gas temperature andproduce shaft work. By increasing the number of expand-ers and heat exchanges, see Fig. 11, the cold stream CCcan be designed to be as close as possible to the hot streamCC, thereby reducing the irreversibilities.

Figs. 12 and 13 show the Expanded Composite Curves(ECCs) and Expanded Grand Composite Curve (EGCC)for the two streams when the cold stream is expanded to

-100

-80

-60

-40

-20

0

20

40

0 50 100 150 200

Q (kW)

T(C)

Fig. 10. PA Grand Composite Curve.

W1

EX-1

TC1-1,s

TH,sTH,t

TC1-1,t

TC1-2,s

W2EX-2

TC1-2,t

TC1-3,s TC1-3,t

Fig. 11. System with heat exchanger and expanders.

-100

-80

-60

-40

-20

0

20

0 50 100 150 200 250 300

Q (kW)

T(C)

Fig. 9. PA Composite Curves.

-140

-120

-100

-80

-60

-40

-20

020

0 50 100 150 200 250 300

Q (kW)

T(C)

Fig. 12. Expanded Composite Curves.

-140

-120

-100

-80

-60

-40

-20

0

20

40

0 20 40 60 80

Q (kW)

T(C)

Fig. 13. Expanded Grand Composite Curve.

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its target pressure of 1 bar prior to heat exchange(TC11,t = TC11,s). Complete expansion of the cold streamprior to heating will give the lowest possible supply temper-ature. Also note that the _mCp for the cold CC is constantand equal to its original value. As can bee seen from theEGCC, the required heating is still 60 kW. The required

cooling, however, is reduced from 155 to 12.5 kW. Further-more, 143 kW of work is produced in the ideal expansionmachine. The new cold stream supply temperature(TC12,s) is as low as 126 C, which is much lower thanthe required temperature of 95 C. Therefore, the drivingforces between the hot and cold CCs are considerably lar-ger than needed, resulting in unnecessary exergy losses.

In Figs. 14 and 15, the cold stream (TC11,s) is heatedfrom 55 C to 37.5 C before it is expanded to 1 bar,and thereafter heated to its target temperature. Heatingthe cold stream before expansion will increase the new coldsupply temperature (TC12,s) and thus reduce the exergylosses in the heat exchanger. Furthermore, as discussed in

the theory section, expansion of a gas at higher tempera-ture provides more cooling and work. Notice that the coldECC has an _mCp of 4 kW/K between 55 and 37.5 C.As seen from the EGCC, the cold stream ECC providesjust enough cooling for the hot stream. Hence, QH andQC are 60 kW and 0 kW, respectively. Furthermore, thereare now two Pinch points, one at 10/20 C and one at45/55 C. The produced power in EX-1 is 154 kW. Alsonotice that the cold end supply temperature has increased

from 126 C to 115 C, thereby reducing the irreversi-bilities in the heat exchanger.

In Figs. 16 and 17, an additional expander and heatexchanger pass are added. The cold stream (TC11,s) isheated to 37.5 C and expanded to 2 bar and 80 C. Itis then heated to 66 C (TC12,t) and expanded to 1 bar

and 103 C, before it is heated to its target temperatureof 10 C. No utility cooling (QC) is required; however,the required utility heating (QH) has increased from 60 to64 kW. The produced work in EX-1 and EX-2 is 84.5and 74.5 kW, respectively, giving a total duty of 159 kW.The marginal increase in produced power can not be justi-fied in this case, since additional heating is required andthat the reduced driving forces in the heat exchange pro-cess will need substantially more heat transfer area. In con-clusion, the addition of one more expander and heatexchanger pass represents an uneconomic overkill in thiscase.

Based on the experiences in this very basic example,

some general conclusions can be made:

Pressure based exergy can effectively be transformed tocooling duty and work and may give a significant reduc-tion in the required utility cooling for subambientprocesses.

Expanding a cold stream at high temperature will gener-ate more work and cooling duty than at a lowertemperature.

-140

-120

-100

-80

-60

-40

-20

0

20

0 50 100 150 200 250 300

Q (kW)

T(C)


-140

-120

-100

-80

-60

-40

-20

0

20

40

0 20 40 60 80

Q (kW)

T(C)


-120

-100

-80

-60

-40

-20

0

20

0 50 100 150 200 250 300

Q (kW)

T(C)


-120

-100

-80

-60

-40

-20

0

20

40

0 20 40 60

Q (kW)

T

(C)




8/17

By heating the cold stream prior to expansion, morecooling duty will be produced and less irreversibilitymay occur in the heat exchanger, due to reduced drivingforces.

Additional expansion steps and heat exchange passesmay reduce the irreversibilities and create more cold

duty and work. If too much cold duty is produced, the heating require-

ment will increase and the driving forces will be reduced,however, some additional work can be generated.

3. The Extended Pinch Analysis and Design methodology for

subambient processes

A general methodology for how to manipulate processstreams using pressure to minimize irreversibilities in heattransfer processes is under development. Compared withtraditional Pinch Analysis (PA), the problem addressed

here is much more complex with a large number of alterna-tives for manipulation and integration of streams. The fol-lowing features of the process streams are important andadd complexity to the design of subambient processes:

In addition to temperature change, the streams may alsoundergo pressures change.

The phase of the streams (gas, dense, liquid, condensingor vaporizing) strongly affects the design decisions.

Cold process streams often act as cold utilities. Streams may temporarily change identity (hot to cold or

cold to hot) in the process to utilize local heat surplus or

deficit.

A set of heuristics are proposed for some special subam-bient situations. Also, a detailed design procedure is devel-oped for the favorable situation when Ps > Pt for a coldstream at subambient temperature and there is a need forcooling utility. The steps in the overall design procedureare:

Perform an Exergy Analysis and determine the totalexergy in the hot and cold streams in order to verify ifit is theoretically possible to create a process withoututilities (power, external heating and cooling). If this isnot the case (i.e. the calculated required exergy efficiencyis above 100%), the minimum required work that mustbe provided can be found.

If possible, establish an initial estimate for the inevitableirreversibilities given the minimum temperature differ-ences and equipment efficiencies.

Perform a basic PA (neglecting the pressure effects) anddevelop composite curves for the hot and cold streamsin order to identify the Pinch point and the minimumamount of hot and cold utilities, QH and QC.

Select an appropriate heuristic or design procedure inorder to find the most favorable way of manipulating

the pressure.

Develop the Expanded Pinch Curves after expansionand compression of the process streams.

Calculate the new exergy efficiency, compare the old andnew minimum utility values and evaluate the currentdesign through its new exergy efficiency value.

The design procedure is based on the use of heuristics,

thus it does not guarantee global optimality. The exergyanalysis will, however, indicate whether there is roomfor further improvements of the process. If this is thecase, one should explore other heuristics or design pro-cedures and see if this indeed will improve the design.

3.1. Design procedure for utilizing pressure based exergy

in a cold stream for cooling of a hot stream

One of the most favorable situations is when Ps > Pt fora cold stream at subambient temperature, and where tradi-tional PA indicates a need for cold utilities. The first step of

the ExPAnD methodology has thus been to develop adetailed procedure for how to utilize available pressurebased exergy. However, pressure based exergy can be uti-lized in several ways to meet different criteria. The follow-ing design guidelines or criteria for optimization have beenidentified:

(1) Maintain as high pressure as possible in the streams.(2) Match targeted enthalpy changes in order to avoid

auxiliary units.(3) Minimize heat exchanger area.(4) Maximize total power output.

(5) Maximize the overall exergetic efficiency.(6) Minimize total annual cost.

Some criteria can be obtained simultaneously, others arecontradictory. In the current stage of developing the designprocedure, criteria 1, 2 and 5 are used to set up the flowdiagram of the procedure (Fig. 18); however, the threeother criteria are obviously equally important.

The first criterion is similar to the well known keep hotstreams hot and cold streams cold in traditional PA. Also,the target pressure can often be regarded as a soft specifica-tion, again similar to some target temperatures. The secondcriterion reduces both operating cost and investment costby avoiding external heating or (more relevant in subambi-ent applications) external cooling.

Several simplifying assumptions similar to those of basicPA are made in the procedure. Pure counter current heatexchangers without pressure drop and a given global min-imum approach temperature (DTmin) are assumptionsmade for the heat exchanger network (HEN). The streamscan be manipulated similar to the illustrating exampleshown in Fig. 11. In addition, the cold stream can be com-pressed or expanded prior to the first heat exchanger pass.By comparing the cold end shifted temperatures( 0.5DTmin) and the heat capacity flowrates of the

streams, and evaluating the pressure of the cold stream, a



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procedure flow diagram for utilization of pressure basedexergy can be developed. A simplified version of the flowdiagram is shown in Fig. 18.

The first step (1) is to evaluate the modified hot and coldstream temperatures. The concept of modified tempera-tures (given the symbol T ) is well known in Pinch Analysissince it is used to establish the Grand Composite Curve. Inthat diagram, hot and cold streams can be drawn in onecurve after adjusting the temperatures by adding (coldstreams) or subtracting (hot streams) half ofDTmin. If theoriginal cold stream supply temperature is significantlycolder than the hot stream target temperature (1A), thecold stream can be compressed to reach the shifted hotstream target temperature in order to reduce exergy losses.The work used for compression may later be recovered byexpansion at a higher temperature while producing addi-tional cooling. As an opposite situation, if the cold streamsupply temperature is significantly higher than the hotstream target temperature (1C), the cold stream shouldbe expanded.

The next step (2) is to compare the heat capacity flow-rates of the hot and cold streams. At this point, the newcold stream supply temperature TC11,s is at least DTminlower than the hot stream target temperature (TH1,t). Ifthe total heat capacity flowrate of the cold streams

(expanding the cold stream creates substreams that will

be added together) is larger or equal to that of the hotstream in the cold end region, i.e.

P_mCp

CP _mCp

H,

the CCs will diverge and consequently there will be nocrossover in the cold end region. Note that a cold streamcan be expanded (and heated) several times to increasethe total cold stream heat capacity flow rate. Each passof such a cold stream is denoted as a substream. If utilitiesare needed, these will occur at higher temperatures. Sincethe cold end is solved, a satisfactory solution is possiblyobtained (2A). It is of course possible that external heatingand/or cooling is required at higher temperatures, depend-ing on the total changes in enthalpy and the _mCp profiles ofthe streams. If P _mCp

C

decreases and/or _mCpHincreases with temperature, a crossover may occur, which

requires a cold utility in the temperature range of the cross-over. If the total hot stream enthalpy change is larger thanthat for the cold stream (even after full utilization of coldstream pressure based exergy), there will also be require-ments for external cooling. In the opposite case, there isa requirement for external heating.

If there still is pressure available in the cold stream, it ispossible to allow one more expansion in the process (3). IfP

_mCpC < _mCpH, at least one additional substream isneeded in the cold end to make the CCs diverge, i.e.

P _mCpC P _mCpH. Hence, an expansion is neededto make one more substream contribute. It may then,

(1)TC1,s vs. TH1,t

(1C)TC1,s > TH1,t

Pre-expansion

(1A)TC1,s < TH1,t

Pre-compression

(1B)TC1,s TH1,t

(2)mCp C vs. mCp H1

In cold end

(2A)mCp C >= mCp H1

(2B)mCp C < mCp H1

(2A)Cold end solved

(5)No expansions

available

(3)Expansions

available

(5)Cold end not

solved

(4)Pressure shift

(3)Add expander

Fig. 18. Procedure for cooling a hot stream by utilizing pressure based exergy in a cold stream.

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however, be favorable to shift some of the pressure drop inother expansions to the recently added expander (4). Thedefault value in the procedure is to distribute an equal pres-sure ratio over the expanders. However, by doing this, thepressure ratio across the other expanders is lowered, whichin turn means that the corresponding inlet temperatures

must be increased in order to obtain targeted outlettemperatures.If the number of expanders can not be increased, the

cold end can not be solved (5), and external cooling utilityis required. After solving the subproblem using Fig. 18, oneshould return to the ExPAnD methodology, draw the newECCs and perform new exergy calculations.

3.2. Some general heuristics

Based on the experiences from the theory section andthe small illustrative example, two basic heuristics can beestablished.

Heuristic 1: Available pressure (Ps > Pt) can be utilizedthrough expansion to reduce cold utility requirements withpower generation as an important by-product. Contrary,lack of pressure (Ps < Pt) requires power, however, this sit-uation may reduce hot utility requirements.

Heuristic 2: Temperature gap (DT> DTmin) between thehot and cold CCs, results in unnecessary irreversibilities.The pressure of the streams may be manipulated todecrease the irreversibilities, generate power and reducethe need for heating and cooling utilities. Streams withphase transitions are particularly suited for suchmanipulation.

3.3. Heuristics for streams with target pressure different from

the supply pressure

A well established result in pinch analysis is the decom-posing effect of the Pinch point which divides the heatrecovery system into two parts; a heat deficit region abovePinch and a heat surplus region below Pinch [10]. Thus, toachieve the energy target set by the composite curves, theremust be no (net) cross-Pinch heat transfer. Three basicrules have been derived:

Do not transfer heat from a hot process stream abovePinch to a cold process stream below Pinch.

Do not use external heating utilities below Pinch (wherethere is heat surplus).

Do not use external cooling utilities above Pinch (wherethere is heat deficit).

Any violation of either of these rules results in a doublepenalty in the sense that 1 kW of cross-Pinch heat transferincreases both QH and QC by 1 kW. From these basic rules,some heuristics that describe how the pressure can bemanipulated have been derived.

Heuristic 3: Compression of a vapor or dense phase

stream requires power and will add heat to the system.

Hence, from a PA point of view, compression should pref-erably be done above the Pinch point.

Note: Compression at high rather than low temperaturewill generate more heat at higher temperature; however,more work is required for the compression. From athermodynamic point of view, work is more valuable than

thermal energy down to approximately 129 C (thenCOPth,max becomes 1, see Fig. 3). It should be noted thatHeuristic 3 primarily refers to cases where a stream hasto be compressed. The rule is, however, also applicable toan open cycle heat pump, where a hot stream below Pinchis compressed to obtain a temperature above Pinch. Theactual amount of hot utility saved depends on compressorinlet temperature (outlet should be above Pinch) and pos-sible Pinch changes (compression will change the shapeof the CCs).

Heuristic 4: Expansion of a vapor or dense phase streamin an expander will provide cooling to the system, and atthe same time generate power. Hence, expansion should

preferably be done below Pinch. In subambient processes,a stream with a supply pressure higher than the target pres-sure should always be expanded in an expander (not avalve) if the stream is located below the pinch point.

Note: Expansion at low temperature will provide lesscooling and generate less work than at high temperatures;however, a colder outlet temperature can be achieved. Asfor Heuristic 3, the expansion process will modify the shapeof the CCs with possible Pinch changes as a result.

Heuristic 5: If expansion of a vapor or dense phasestream above Pinch is required, a valve should be used tominimize the increase in utility consumption, unless the

main purpose of the expansion is to produce work.

3.4. Heuristics for streams with target pressure equal

to the supply pressure

A stream with the same supply and target pressure canstill be manipulated in order to reduce the total irreversibil-ities. The stream can either be compressed before the heatexchange with subsequent re-expansion, or it can beexpanded before the heat exchange and then be re-com-pressed. There are two different situations where these pres-sure manipulations can have significance. First, it can beused to generate work and/or reduce hot utility consump-tion by reducing the driving forces between the hot andcold CCs. Second, it can be used to open up close and par-allel CCs (almost equal total heat capacity flowrate over arelatively large temperature region). It should be kept inmind; however, that compression and expansion of a gashave relatively large irreversibility losses compared to thelosses associated with heat exchange between two fluidswith a reasonable temperature difference. Furthermore, asboth a compressor and an expander are required, therewill be a substantial addition to the capital cost. Never-theless, there are a few applications where such manipula-

tions are done, e.g. as the bottoming cycle in cryogenic

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refrigeration cycles (reversed Brayton cycles) such as airseparation and peak shave natural gas liquefaction plants.

Work is in progress on a categorization and evaluationof the different possibilities for manipulating pressure inprocess design. In this paper, however, only one heuristicrule in this category is presented, as it is needed in the main

example.Heuristic 6: A hot gas or dense phase fluid that is com-pressed above the Pinch point, cooled to near Pinch pointtemperature and then expanded will decrease the need forboth cold and hot utilities. Additional work is, however,required.

Note: The net work generated in the expander will belower than the work consumed in the compressor for tworeasons; irreversibilities occur in the compressor and theexpander, and more work is generated or consumed athigher than lower temperatures even for an ideal expanderor compressor.

3.5. Heuristics for liquid streams and streams with phasechange

The temperatureenthalpy phase envelope for CO2 withisobars for 10 bar, 40 bar and 100 bar is shown in Fig. 19.Similarly, Fig. 20 shows a simplified phase envelope withisobars for a natural gas which consists of nitrogen, meth-ane, ethane, propane and butane. From a PA point of

view, the most important difference between pure andmulticomponent fluids is that phase change at constantpressure occurs at non-constant temperatures. It is alsoworth noticing that the Critical Point (CP) is shifted tothe left, which means that a two phase mixture may existabove the CP. Furthermore, a gas can be expanded into

as well as out of the phase envelope.Notice that expansion or compression of a liquid willgenerate or require much less power than in the gas phase.The temperature change for liquids subject to pressurechange is neglectable. This is the background for heuristics7 and 8.

Heuristic 7: A fluid with Ps < Pt should be compressed inliquid phase if possible to save compressor work.

Heuristic 8: In a liquid stream with Ps = Pt, a phasetransition is necessary for the CCs to be manipulated, sincethe effect of expansion/compression in the liquid phasealone is marginal.

Pumping a cold stream to be vaporized will increase the

vaporization temperature, and thereby reduce the tempera-ture difference between the CCs. The heat capacity flowrate _mCp will be close to constant as long as the fluid isin the subcooled region. Also, the latent heat of vaporiza-tion and the required heating will be reduced, meaning thatthe ability of the cold stream to act as a coolant is reduced.Hence, temperature based exergy is transformed to pres-sure based exergy both by reduced duty and increased tem-perature. By increasing the pressure above the CriticalPoint (CP), the _mCp is close to constant for the wholestream. As can be seen from Fig. 19, the required heatingis significantly reduced. The exergy losses are also consider-

ably reduced since the near constant temperature phasechange region occurring at lower pressures is avoided.Two heuristics can be derived from this discussion.

Heuristic 9: If a cold liquid stream to be vaporized doesnot create a Pinch point, it should be pumped to avoidvaporization at constant temperature, reduce the totalcooling duty and increase the pressure based exergy. Workand cooling duty should be recovered by expansion ofthe fluid in the vapor phase at a later stage (highertemperature).

Note: If a single component fluid is compressed higherthan the critical point (CP), the temperatureenthalpy pro-file will be close to linear.

Heuristic 10: Compression of a hot gas stream to be con-densed will increase the condensation temperature. Thelatent heat of vaporization will also be reduced. Hence,work is used to increase the driving forces and therebyreduce the heating requirements.

3.6. Main example

A novel energy and cost effective process for liquefactionof stranded natural gas (NG) was recently presented byAspelund at CryoPrague in 2006 [11]. In the process, natu-ral gas is liquefied to LNG by utilizing the cold exergy in

liquid carbon dioxide (LCO2) and liquid inert nitrogen

-60

-40

-20

0

20

40

60

80

0 5000 10000 15000 20000

Enthalpy [kJ/kmole]

Temperature[C]

Bubble P Dew P 10 bar 40 bar 100 bar

CP

Fig. 19. Phase envelope with isobars for CO2.

-160

-120

-80

-40

0

40

0 2000 4000 6000 8000 10000 12000 14000

Enthalpy [kJ/kmole]

Bubble P Dew P 5 bar 40 bar 100 bar

CP

Temperature[C]

Fig. 20. Phase envelope with isobars for NG.



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(LIN), which are used as cold carriers. LCO2 is used forcooling in the first part (hot end) of the LNG production.The low temperature LIN is used in the cold end. The pro-cess is self-supported with power and can operate with littlerotating equipment and without flammable refrigerants. In

the fully developed process, the natural gas is expandedin two stages. The CCs for the novel process are shownin Fig. 21 with a process flow diagram (PFD) in Fig. 22.

The novel LNG process was developed in parallel withthe ExPAnD methodology and the design route isexplained to show how useful this methodology can be inprocess design. The design basis stream data are found inTable 1 and equipment data are shown in Table 2. The cal-culations are performed with the commercially availablesimulator HYSYS, using the SRK equation of state. Notethat the amounts of LCO2 and LIN used in the main exam-ple are the minimum amounts of cold carriers in the fully

developed and integrated process. Hence, without properintegration and utilization of pressure based exergy, workand/or cold utilities will be required. Only one cold utilitylevel at constant temperature is used. The required powerfor producing the cold utility is calculated from Eq. (8),using a factor f= 0.4. There is no significant energy penalty

for the hot utility as seawater can be used.The first step in the ExPAnD methodology is to performan Exergy Analysis to determine the total exergy in the hotand cold streams. At the outset there is only one hotstream, the natural gas (NG) stream. NG at 60 bar is tobe transformed to liquefied natural gas (LNG) at164 C and 1 bar. The flowrate in this example is8.1 kg/s of NG, which corresponds to 0.25 Mt/y. Note thatthe target pressure and temperature are hard specificationsfor the NG stream. The pressure based exergy of NG at60 bar and ambient temperature is 4457 kW. The tempera-ture based exergy of LNG at atmospheric pressure and164 C is 7812 kW. The net exergy difference between

the NG at 60 bar and LNG at 1 bar is therefore 3355 kW.There are originally two cold streams, LCO2 and LIN.

The LCO2 at 5.5 bar and saturated liquid is to be com-pressed to 150 bar and heated to 20 C. The temperatureis a soft specification and can vary between 10 C and40 C. After heating and compression of the CO2, it isinjected to an oil field for enhanced oil recovery (EOR).The flowrate is 18.0 kg/s, an amount that corresponds to82% of the CO2 produced by combustion of the trans-ported LNG. Note that Ps < Pt, hence power is requiredfor compression. The pressure based exergy of CO2 at150 bar and 20 C is 3754 kW. The temperature and

-180

-130

-80

-30

20

0 2 4 6 8

Heat flow [MW]

Hot CC Cold CC

HX-101

HX-102

T

emperature[C]

Fig. 21. CCs of the novel LNG process.

K-100

P-102

NG-2

LIQ-EXP-101

NG-1

NG-3 NG-4

LIQ-EXP-102

NG-5

NG-6

NG-PURGE

LNG

P-101

N2-2

N2-5

N2-10

N2-11

N2-6

N2-3

EXP-101

EXP-102

N2-1

P-100

CO2-2

CO2-1

N2-9

K-101N2-8

CO2-3

N2-12

N2-4

N2-7

CO2-4

HX-101 HX-102

V-101

Fig. 22. PFD of the novel LNG process.

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pressure based exergies of LCO2 at 5.5 bar are 2196 kWand 1813 kW, respectively, giving a total exergy of4009 kW. The net exergy difference between LCO2 at5.5 bar and high pressure CO2 at 150 bar is only 255 kW.Thus, temperature based exergy in the LCO2 is to be trans-formed to pressure based exergy during the process.

The other cold carrier, LIN at 6 bar and 177 C, is to

be vaporized and emitted at close to atmospheric tempera-ture and pressure (soft constraints). A flow of 8 kg/s isneeded for the process to be self-supported with heating,cooling and power. Note that Ps > Pt for the nitrogenstream. The temperature and pressure based exergies ofLIN at 6 bar are 3800 and 1222 kW, respectively, givinga total exergy of 5022 kW. As the nitrogen is emitted tothe atmosphere at ambient conditions, the net exergychange is the same as the initial exergy, 5022 kW.

The total exergy of the inlet streams (NG, LCO2 andLIN) is 13,488 kW, whereas the useful exergy in the outletstreams (LNG and high pressure CO2) is 11,566 kW.Hence, a process with an exergy conversion efficiency of85.7% will enable the NG to be liquefied by CO2 andLIN without the need for power and/or cold utilities.

The second step in the ExPAnD methodology is toestablish an estimate for the inevitable irreversibilities.The total cooling duty required for liquefaction of NG is6.5 MW. The temperature difference is 179 C, which givesan average constant _mCp of 36.3 kW/K. Using Eq. (17) anda constant temperature difference of 5 C, the minimumirreversibility due to heat exchange is 308 kW, or 2.3%. Atemperature difference of 10 C and 20 C gives 4.7% and10.1% irreversibilities, respectively. Assuming that half ofthe irreversibilities are caused by pumping, compression

and expansion, a constant temperature difference of about

15 C is acceptable. This assumption will be checked oncethe design is completed.

The third step is to perform a traditional PA. Thismeans that (alternative A, Fig. 23) NG, CO2 and LINexchange heat at their initial pressures. CO2 is then com-pressed to 150 bar. After heat exchange, the subcooledand pressurized LNG is expanded to atmospheric pressureat bubble point conditions through an expander which gen-

erates 115 kW. Fig. 23 shows the hot and cold CCs for thestreams, where 4.2 MW of hot utility at 30 C is included inorder to heat the CO2 to 20 C. Notice that the CCs inFigs. 2328 are drawn with focus on heat balance ratherthan thermodynamic feasibility. As a result, Fig. 23 hasan infeasible crossover region between 100 C and50 C. To make this heat recovery system feasible, thereis a need for 2.3 MW of cooling at 100 C and an addi-tional 2.3 MW of hot utility. In addition, 6070 kW of

Table 1Design basis stream data

Stream Type Rate(kg/s)

Supplyphase

Targetphase

Ts (C) Tt (C) Ps (bar) Pt (bar) Supply exergy(kW)

Target exergy(kW)

Hot NG 8.1 Gas Liquid 15.0 164.0 60.0 1 4457 7812Cold 1 CO2 18.0 Liquid Dense 54.5 20.0 5.5 150 4009 3754Cold 2 N2 8.0 Liquid Gas 177.0 15.0 6.0 1 5022 0

Total cold CO2/N2 26.0 9031 3754

Table 2Equipment data

Compressors Polytropic eff. 82%Pumps Adiabatic eff. 85%Expanders Isentropic eff. 85%Liquid expanders Isentropic eff. 85%Heat exchangers T> 0 C 5 C(DTmin) 0 > T> 80 C 3 C

T< 80 C 2 CPressure drop 0.2 bar

Flash drums Efficiency 100%Mechanical to electrical Efficiency 97%

-200

-150

-100

-50

0

50

0 2 4 6 8 10 12

Duty [MW]

Temperature[C

]

Hot CC Cold CC

Fig. 23. Alternative A.

-200

-150

-100

-50

0

50

0 2 4 6 8

Duty [MW]

Temperature[C]

Hot CC Cold CC

Fig. 24. Alternative B.

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power is required for the CO2 compressor, giving a net pro-cess power requirement of 5955 kW. The resulting exergyefficiency for alternative A is only 49.7%.

The next step in the methodology is to select an appro-priate heuristic or design procedure in order to identify themost favorable way of manipulating the pressure. Noticing

that the liquid CO2 stream has a lower supply than targetpressure, heuristic 7 is selected.Heuristic 7: A fluid with Ps < Pt should be compressed in

liquid phase if possible to save compressor work.Accordingly, in alternative B (Fig. 24), the CO2 is

pumped to 65 bar prior to heat exchange to avoid vapori-zation of CO2. Gas phase compression is then avoided, andthe pump work is only 393 kW. As a result, the net powerconsumption is reduced from 5955 to 278 kW. When CO2is pumped to a much higher pressure in the liquid phase,the fluid will remain in liquid phase, and the tempera-tureenthalpy profile changes from a flat constant tem-perature boiling situation to a sliding (non-constant

temperature) profile. As a result, the need for hot utilityis significantly reduced. The expanded Composite Curves(ECCs) are shown in Fig. 24. To make this heat recoverysystem feasible, about 2.5 MW of external cooling isrequired at 100 C. From a heat balance point of view,there is a corresponding need for 2.5 MW of hot utility.The exergy efficiency for alternative B is 64.6%. By pump-ing the CO2 in liquid phase, significantly less work isrequired, the CO2 compressor can be removed, the needfor hot utility is reduced from 6.5 (4.2 + 2.3) to 2.5 MW,and the need for external cooling is slightly increased (from2.3 to 2.5 MW).

There is, however, still room for improvement of thedesign. From Fig. 24, it can be seen that the LIN vaporizesat a lower temperature than required for the subcooling ofthe LNG, hence there are large irreversibilities in the coldend of the CCs. Heuristic 9 is used to overcome this.

Heuristic 9: If a cold liquid stream to be vaporized doesnot create a Pinch point, it should be pumped to avoidvaporization at constant temperature, reduce the totalheating duty and increase the pressure based exergy. Workand cooling duty should be recovered by expansion of thefluid in the vapor phase at a later stage.

Based on this, the LIN stream is pumped to a pressureof 100 bar, which is above the CP for nitrogen. LIN is thenused for cooling of the NG before it is expanded andreleased to the environment. The temperatureenthalpyprofile of the LIN stream is now (Alternative C) muchmore favorable, as can be seen from the expanded compos-ite curves in Fig. 25.

Since much of the temperature based exergy in the LINis transformed to pressure based exergy, the ECCs are clo-ser, with a Pinch point at 160 C. The hot and cold utilityrequirements increase to 3.0 MW to make the heat recov-ery system feasible, and the cold utility needs to be suppliedat lower temperature. Net power requirements increasewith 128 kW to 406 kW due to the nitrogen pump. The

exergy efficiency of the process (alternative C) is 51.8%

-200

-150

-100

-50

0

50

0 2 4 6 8

Duty [MW]

Temperature[C]

Hot CC Cold CC

Fig. 25. Alternative C.

-200

-150

-100

-50

0

50

0 2 4 6 8

Duty [MW]

Tempe

rature[C]

Hot CC Cold CC

Fig. 26. Alternative D.

-200

-150

-100

-50

0

50

100

0 2 4 6 8

Duty [MW]

Temperature[

C]

Hot CC Cold CC

Fig. 27. Alternative E.

-200

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-100

-50

0

50

100

0 2 4 6 8

Duty [MW]

Temperature[C]

Hot CC Cold CC

Fig. 28. Alternative F.



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due to the extra cold utility needed. Even though the resultsat first sight seem to be poor, the pressure based exergy innitrogen can be used to provide both additional power andcold duty, as indicated by heuristic 4.

Heuristic 4: Expansion of a vapor or dense phase streamin an expander will provide cooling to the system, and at

the same time generate power. Hence, expansion shouldpreferably be done below Pinch. In subambient processes,a stream with a supply pressure higher than the target pres-sure should always be expanded in an expander (not avalve) if the stream is located below the Pinch point.

In alternative D, the nitrogen (after being pumped to100 bar) is heated to 40 C and then expanded to 8 barand 160 C. It is then reheated to 40 C and expandedonce more to 1.2 bar and 135 C. The new ECCs areshown in Fig. 26. The Procedure Flow Diagram inFig. 18 is used to determine the thermodynamically bestway of utilizing the pressure based exergy in the coldstream to cool a hot stream. The two expanders produce

approximately 1.4 MW (1409 kW) of power and 1.2 MWof additional cooling duty. Notice that the cold CC hasapproximately the same heat capacity flowrate as the hotCC, giving a close temperature approach and reduced irre-versibility in the cold end of the heat exchanger. The Pinchpoint is increased to 75 C, and there is a crossover regionbetween 75 C and 0 C. The required heating and cool-ing utility requirements (to make the process feasible) havechanged to 2.2 MW and 1.0 MW, respectively. The exergyefficiency for alternative D is significantly improved to84.3%.

Next, looking at the hot CC (the cooling of NG); the

non-linear profile is caused by cooling close to the CP forNG. Since, however, surplus power is available from theexpansion of nitrogen; heuristic 10 can be applied toimprove the process further.

Heuristic 10: Compression of a hot gas stream to be con-densed will increase the condensation temperature. Thelatent heat of vaporization will also be reduced. Hence,work is used to increase the driving forces and reduce theheating requirements.

According to heuristic 10, the natural gas is compressedto a pressure of 100 bar, which is higher than the critical

point resulting in process alternative E in Fig. 27. SinceNG is a multicomponent fluid, condensation will take placeat sliding (non-constant) temperature for all pressures,however, increasing the pressure before cooling will makethe temperatureenthalpy diagram more linear. The resultis a better match with the cold CC. The compression of

NG from 60 to 100 bar requires 676 kW, giving a totalpower requirement of 1197 kW. The work provided fromexpansion of subcooled NG increases with 44 kW. Notethat there is still 371 kW power available. The correspond-ing ECCs for alternative E are shown in Fig. 27, indicatingthere is a Pinch region between 65 C and 40 C. Theneed for hot and cold utilities is 1.2 MW and 0.2 MW,respectively, and the exergy efficiency of the process is87.1%.

Noticing that there is still some work available and thatthere is a surplus of cooling duty in the process abovePinch, a compressor can be inserted in the nitrogen path.According to heuristic 6, this should be done above the

Pinch point at a temperature of 40 C.Heuristic 6: A gas or dense phase fluid that is com-

pressed above the Pinch point, cooled to near Pinch pointtemperature and then expanded will decrease the need forboth hot and cold utilities. Additional work is, however,required.

After the first expansion, nitrogen is compressed from7.8 to 16 bar. The compressed gas is then cooled to40 C and expanded to 1.2 bar and 154 C to generateadditional work and cooling duty at lower temperatures,thereby increasing the minimum internal temperatureapproach from 0.5 to 3 C in the region around 50 C.

This exactly evens out the power balance in the process,such that all generated power is utilized for compressionand pumping of the fluids. Moreover, there is no needfor either cold or hot utilities. The composite curves inFig. 28 show a very close temperature profile giving smallirreversibilities. The CO2 and nitrogen outlet temperatureis 17 C, which is within the limits of the soft constraints.The exergy efficiency for the process, referred to as alterna-tive F, is 85.7%. The small reduction in exergy efficiencyshows that it could have been more effective to utilizean external cooling cycle; however, by manipulating the

Table 3Energy and exergy balance for the alternative processes

Unit A B C D E F

Total duty HX MW 10.6 9.1 9.1 9.9 8.8 7.7Cold utility MW 2.3 2.5 3.0 1.0 0.2 0.0

@ 100 C @ 100 C @ 160 C @ 75 C @ 75 CHot utility MW 6.5 2.5 3.0 2.2 1.2 0.0

@ 15 C @ 15 C @ 15 C @ 15 C @ 15 CRequired power for compression kW 6070 393 521 521 1197 1720Generated power in expanders kW 115 115 115 1524 1568 1720Net process power kW (5955) (278) (406) 1003 371 0.0Required power, cold utility kW 3819 4151 11,600 1230 176 0.0Total power balance including util ities kW (9774) (4429) (12,006) (227) 195 0.0

Exergy efficiency % 49.7 64.6 51.8 84.3 87.1 85.7



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pressures it is possible to avoid the extra equipment andthereby reduce both investment cost and process complex-ity. A summary of the utility balance (external heating,cooling and power) as well as the exergy efficiencies forthe various alternatives are found in Table 3. In fact, thedesign referred to as alternative F is indeed the process

described in Fig. 22, with the exception that the heat recov-ery system has been split into two separate heat exchangerswith an additional liquid expander in the natural gasstream between the heat exchangers.

4. Discussion

The ExPAnD methodology combines pinch analysis andexergy analysis. Through the main example, the methodol-ogy has proven to be a powerful design tool. However, asthe pressure is allowed to change, there are considerablymore degrees of freedom and hence more decisions to bemade than in ordinary PA. Of course, the best process con-

figuration also needs to take into account other design fac-tors such as investment cost, safety, operability andavailability. Hence, at the current stage of development,it seems very difficult to develop a formal procedure notto mention a computer program that will automaticallydiscover optimal solutions. As a result, the ExPAnD meth-odology presented here relies heavily on a set of heuristicsand engineering insight of the designer. It is believed thatthe methodology will make it possible for the skilled engi-neer to use creativity in such a way that solutions will beidentified that would have been hard to find without usinga systematic approach as devised by ExPAnD.

At first sight, adding additional compressors andexpanders leads to a more complex process with higherinvestment cost. However, as shown in the main example,both hot and cold utilities are reduced and finally elimi-nated. Further, the power input is gradually reduced andthe final process configuration does not require anyimported power, as the temperature and pressure exergiesare fully utilized.

The main difficulty with the proposed methodology is toselect the order in which to use the heuristics and proce-dures. Starting with a wrong heuristic may force the pro-cess design in a direction where the most favorablemanipulations are not easily identified. Generally, thereshould always be an increase in the exergy efficiency aftereach modification. However, as demonstrated with alterna-tive C above, this is not always the case. Further, thereshould be a reduction in the driving forces between thehot and cold CCs. Some heuristics, such as 4 and 7 arestronger than the others and should be used at an earlystage. Finally, as the energy losses are largest at the lowesttemperatures, it makes sense to start in the cold end of theCCs.

The long term objective of our work is to develop a toolor methodology for analysis, design and optimization ofcomplex energy chains and processes that includes pressure

as an important design variable. The next step in the devel-

opment is to map the many complex situations for pressuremanipulations where Ps = Pt. Heuristics for processesabove ambient temperature should also be developed.The heuristics and procedures will be implemented in a toolbased on the HYSYS platform and Microsoft Excel. Thetool will combine Pinch (minimum external heating and

cooling), Exergy (minimum irreversibilities) and Optimiza-tion (minimum total cost).

5. Conclusions

The ExPAnD methodology is a promising tool fordeveloping energy intensive processes. The methodologyshows great potential for minimizing energy requirements(total shaft work) in subambient processes. This is achievedby optimizing the process streams compression and expan-sion work together with the work needed to generate nec-essary cooling utilities. Furthermore, the methodologycombines Pinch Analysis and Exergy Analysis in a trans-

parent way. Analytical expressions for pressure basedexergy and irreversibilities in a heat exchanger have beendeveloped. Also, several heuristics and a procedure forhow to utilize pressure based exergy in a cold stream forsubambient cooling of a hot stream have been developed.Finally, the ExPAnD methodology has been used in thedesign of a novel LNG process, where the exergy efficiencyis increased from 49.7% to 85.7% compared to using stan-dard pinch analysis. This improvement is achieved by tak-ing maximum advantage of pressure changes of thestreams.

The problem definition used in this paper is significantly

more complex than in standard pinch analysis. In additionto temperature and thermal energy, the methodology hasbeen expanded to consider pressure, phase and mechanicalenergy. As a result, the process to be designed consists ofheat exchangers, compressors and expanders. Thus, theunderstanding of the engineer is even more critical thanin standard pinch analysis.

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ExPAND Methodology