Computers them. Engng Vol. 20. No. 617, pp. 711-715. 1996

Pergamon 0098-135q95)00204-9

Copyright 0 1996 Elsevier Scicncc Ltd Printed in Great Britain. All rights reserved

OC98-1354196 $15.00+0.00

PRESSURE EXCHANGERS IN PINCH TECHNOLOGY

M. HOMSAK and P. GLAvrCt Department of Chemical Engineering, University of Maribor, P.O. Box 224, 62000 Maribor,

Slovenia

(Received 7 April 1995; received for publication 1 I May 1995)

Abstract-The role of pressure is not taken into account when using composite curves on a temperature/ enthalpy flow rate (T/Z) diagram to predict minimum utility requirement in a chemical process. Usually, pressure effects are neglected by assuming small pressure drops through the process. However, sometimes, the energy analysis should be applied to a part of the process involving large pressure changes, e.g. an expander coupled directly to a compressor. In such a case, enthalpy changes indicate neither the quality nor the energy flow direction between the streams exchanging energy. The problem of high pressure exchangers in pinch technology is now solved by a combination of exergy analysis in a temperature vs power availability (T/PJ diagram in addition to the usual approach in the pinch technology.

1. INTRODUCTION

The role of pressure is not known enough in normal presentation of composite curves (CCs) in the temperature/enthelpy flow rate (T/Z) diagrams. Because of that we have taken more attention to processes with pressure changes. This paper intro- duces an exergy analysis to be used in combination with the pinch analysis for problems involving high pressure exchangers. By using an evaporative pro- cess proposed by Himsworth and Cooper (1993) an exergy analysis was carried out.

Such an analysis allows more detailed and usable understanding of exergy quality, quantity and exergy flow direction which are not mastered in the TIZ diagram. Energy-important units, for instance heat exchanger networks (HENS), heat engines, separators, reactors, heat pumps, compressors and expanders are presented by different authors in the well-known T/Z diagrams. For HENS, composite curves (CCs) or grand composite curve (GCC) sim- ultaneously present heat exchange, heat sources like steam and heat sinks like cooling water. Pinch tech- nique is a usable method for process analysis and synthesis where heat exchange between process and utility streams plays an important role. If the gas mixture is being compressed, the gas becomes warmer. In the T/Z diagram this can presented as a cold stream. But the increased pressure is not to be seen although it may be utilized later. It can be calculated only by using boiling/condensing temper- ature.

Pressure-active process units like compressors or expanders have not been accounted for on a single

t To whom all correspondence should be addressed.

T/Z diagram. There are at least three reasons to present large pressure changes on the diagram:

1. Both temperature and pressure have an important influence on thermodynamic analy- sis of the process.

2. Enthalpy changes do not tell enough about the quality, quantity and flow direction of energy between the two process streams.

3. The true cost of the energy for a process depends on both the quantity and the quality of energy used.

Thermodynamic exergy or availability is the meas- ure of the work that exists in an energy stream. We shall use the expresSion “exergy”, E,, for a state variable and a power availability, P,, for a flow variable.

2. BASIC THEORY

Equation (1) for process flow analysis is useful and simple (Sussman, 1980):

EF-(AH,,,-TeAL,) (1) Exergy, E,, is always measured with respect to a

rest state in a standard environment (e) at 25°C and 1 bar. In a compressor, work is supplied to the gas so that enthalpy, H, temperature, T, and pressure, p, all change for both real and ideal gases (Linnhoff and Carpenter, 1981). This is expressed in the fol- lowing equations (24) with a change in enthalpy, AH, entropy, AS, and exergy, AE,, from an initial state (1) to a final state (2) in a general form (Smith and Van Ness, 1987):

AH=C,(T,-T,)+H,R-Hf (2)

AS=C,ln(Tz/T,)-Rln(p2/p,)+S?-Sk (3)

711

712 M. HOMSAK and P. GLAVIC

A.&-z) = AH - I;;(AS)

HRI(RTl= - T .’ I

’ (aZ/aT),dplp 0

(4)

(5)

S%=_- T I

’ (aZ/aT),dplp - ’ (Z- 1) dplp 0 0

(6)

Thus, AH and AS are calculated from the corres- ponding ideal-gas and residual properties by single addition. HR and SR are expressed by equations (5) and (6). Compressibility factor (Z) is by definition: Z=pVIRT, values of Z and of (aZlalT)r are calcu- lated directly from experimental pVT data.

When exergy, E,, normally expressed in Jlmol is multiplied by molar flow rate, qn, power availability, P,, is obtained [equation (7)]. The same is true for molar enthalpy difference, AH, which multiplied by molar flow rate in continuous processes yields enthalpy flow rate difference, AZ [equation (S)]:

P,=q,Ex (7)

AI=q.AH (8)

Power availability values of inlet and outlet compressor/expander streams can be calculated by the following set of equations (9-12):

P,, = s.]C,(L - 7.1) - TeALI (9 P,2 = - q.[Cp(Te - T2) - TALeI WI

AL, = C, WJTd -R Wp,lpJ (11) ASZP..= c,ln(T,IT2)-Rln(p,lp2) (12)

If a material moves through a continuous process from an initial state (1) to a final state (2) that is not the environmental rest state, then it experiences a change, AP,, in power availability for the com- pressor [equation (13)]:

AP+z) = Pa - P,, (13)

By using equations (l-13) all properties (AH, AS, AE, and AP,) of the expander and the compressor can be calculated.

Then, second law efficiencies (v) of energy transfer between two process units are determined. We will consider two kinds of efficiency: overall and extractive. Such efficiencies are ratios of power availability outputs to inputs across a process or process unit and are indices of approaches to rever- sible operations. Extractive second law efficiencies are defined as:

17 (extractive) = Z 1 P, ](cold side)/2 1 P, 1 (hot side)

(14)

The efficiency is meaningful in heat exchanger analysis and other applications where the ratio of

b dPx(lo8s)-A(in-B(aut)

u e l+ -,

. . . I I . I- .

vA(out)

t

PxncW

Fig. 1. Power availability levels in T/P, diagram.

availability gains to losses is a more sensitive index of equipment performance than is the ratio of total availability outputs to inputs. Extractive efficiencies are generally smaller than overall efficiencies.

The overall power availability efficiency is- the ratio of power availability outputs to its inputs:

r7(overall) = ]ZP,(output)lZP,(input)) (15)

3. POWER AVAILABILITY

The pinch analysis was supplemented by extended grand composite curves (EGCCs) (HomSak and GlaviE, 1991) where inappropriately placed energors were treated separately using utility composite curves (UCCs). It combines two types of curves, the GCC and UCCs, presented in T/(Z+ Ar) diagrams. EGCCs show integration possibilities resulting from heat transfer between hot and cold process and utility streams. UCCs show the temperature level between different process units with utility stream. Without consideration of the pressure changes a deceptive presentation about direction of energy flow between two pressure exchangers is obtained. In such cases exergy analysis is recommended. The new procedure with the power availability is an additional instrument to the conventional TII dia- gram and it is presented in Fig. 1 as a graphic visualization. Levels of the power availability in TIP, diagram can be presented. In general, when two pressure exchangers were choosen for the power availability presentation in T/P, diagram, all the data needed should be calculated from equations (9) to (15). Circles at the end of dashed lines (A and

r Pressure exchangers in pinch technology

I’ ./i /

Expander Final condeser

I I

713

Bottom product

Fig. 2. Evaporative process flowsheet with two pressure exchangers (an expander and a compressor).

B) represent the initial points A(in) and B(in) or the final state points A(out) and B(out) of the power availability. The hot and the cold sides differences of those lines express losses of the power availability, AP(losses). The highest power availability has the point A(in), which means that the pressure exchanger (line A) has a higher level of power availability than the other (line B). This procedure will be illustrated in the next section.

4. EXAMPLE AND RESULTS

To demonstrate this problem a simple process was used. An expander coupled directly to a com- pressor, a ‘supercharger’, can be used in an evapor- ative process (Himsworth and Cooper, 1993) which is shown in Fig. 2. The stream bulk properties for the thermodynamic analysis are presented in Table 1.

Power availability analysis of the expander and the compressor has been carried out and is pre- sented in Fig:3. The expander as an energy donor is a pressure source (exergy source) with a tempera- ture range between 81 and 38°C and the pressure

Table 1. Stream data for the thermodynamic analysis

Process unit Compressor Expander

Supply temp., “C 15.1 80.7 Target temp., “C 100.7 38 Supply pressure. bar 0.8 1.82 Target pressure, bar 2.0 0.37. Heat capacity Rowrate, kW/K 1.63 0.95 Enthalpy flowrate. kW 40.7 40.7

range betwen 1.8 and 0.3 bar absolute. The com- pressor as an energy acceptor is a heat sink (exergy sink) with a temperature range between 76 and 101°C. Its pressure range is between 0.8 and 2.0 bar. Process units like compressors or expanders have been so far treated as a process background. In our case the inappropriately placed compressor and expander are presented in Fig. 4 as UCCs. The compressor stream has a higher temperature level than the expander stream but power is flowing from the expander to the compressor.

40.7 kW of enthalpy tlow rate is exchanged between the expand& and the compressor streams.

POWER AVAILABILITY

I 1 T(in)-80.7°C T(m)-38°C p(in)-1.82bar p(ou+0,32bar

EXPANDER

AP,=26SkW -

COMPRESSOR

T(in)-75.7’C p(k)-0.8bw

T(our)-100.70C p(ou+Z.Obmr PJour)-22.4kW

Fig. 3. Exergy analysis and power availability losses between two process unit.

714 M. HOMSAK andP. GLAVIC

t _~ucc,~ i” “1 storm 1 _I

EGCCs-UCCs-GCC

40.7 I+ AllkW

Fig. 4. Extended grand composite curves with inappro- priately placed energors.

Notice that enthalpy is conserved in this process. There are no heat losses. Nevertheless, 56.1% of the availability is lost, because the heat is transferred across a large temperature interval. The overall efficiency, q(overall), of energy transfer between the compressor and the expander was 81.3% [equa- tion (15)]. The second efficiency, extractive efficiency, q(extractive), was smaller than the over- all efficiency by 43.9% [equation (14)]. Efficiences of energy transfer were calculated from equations (14)-(H). From the enthalpy point of view, we could make wrong conclusions about direction and quality of energy flow. In this case the pressure of the stream as the main quality parameter was not taken into account.

A new approach with the power availability (PJ which is a property and the temperature (7’) in TIP, diagram (dashed bold lines) is shown in Fig. 5. Power availability losses on both sides of the curves (33.5 kW + 0.4 kW = 33.9 kW) arise because of energy transfer between process units. In Fig. 5 it is clearly presented that the expander has the highest exergy level [circle PxlcexpJ in comparison with the compressor [circle PxZ(compJ or PxltmmpJ. Such an analysis gives us a more realistic presentation of energy flow direction between process units where the role of the pressure cannot be neglected.

The expander at the same temperature (point B in Fig. 5) has 60% higher power availability than the compressor (point A). The expander has the same power availability (18 kW) at 75°C as the com- pressor at 94°C (point C). The initial and final state

end of the dashed lines. In other words, initial state of the expander (P,,=22.8 kW) at 80.7”C .has a higher level of power availability than the final state_. of the compressor at 100.7”C (Pd= 22.4 kW). All the other P, levels (the compressor inlet and the . . expander outlet) are lower. The conclusion after such an approach is that energy flowed from the expander to the compressor with a power availabil- ity loss of 33.9 kW.

4. CONCLUSIONS

Pressure is an important process parameter. Power availability analysis is recommended for a fast visualization of a particular process unit exploit- ing high pressure change. Power availability analysis provides us with the right information about exergy levels and power availability between the com- pressor and the expander. In heat exchanger networks where pressure is not an important para- meter (the pressure loss is small) the proposed procedure is not necessary. But we cannot do with-= out it in processes including refrigerant systems, heat pumps, heat engines, compressors and expanders. In cases with small pressure drops energy flow direction becomes obvious when tem- peratures are determinated.

In our case the expander has higher power avail- ability level than the compressor and both pressure as well as temperature changes are important. The role of the pressure is hidden in an analysis carried out by the TII diagram. A combination of the usual

100

90

SO

70 u % b 60

50

40

30

A

-

-

-

1

A/‘,(lor+0.4kW

I I I I I __ __ _

-30 -20 -10 0 10 20

PJkW

Fig. 5. Compressor and expander power availabilities and . -.- of power availability are marked by circles at the temperature levels m Y’/pX diagram.

Pressure exchangers in pinch technology 715

pinch analysis And the new pdtier aiailability analy- sis enables a suitable approach when both tempera- ture and pressureare important for efficient under- standing of processes.

‘i .NOMENCLATLJRE

Cp= Molar heat capacity, Jl(mol . K) EXi = Molar exergy at state i, J/m01 H = Molar enthalpy, J/mol I = Enthalpy flow rate, W p = Pressure, bar

P, = Power availability, W q. = Amount flow rate, mol/s R = Universal gas constant, Jl(mo1.K) S= Molar entropy, Jl(mo1.K) T= Temperature, K Z = Compressibility factor, -

Subscripts e = Environment i = Process at state i v = Property at const. wlume p = Property at const. pressure I= Initial state 2 = Final state

Superscript

R = Residual property

Greek letters

r] = Efficiency (overall or extractive) a = Partial A = Difference X=Sum

REFERENCES

Himsworth J. R. and A. C. G. Cooper, Supercharged heat exchanger networks. Trtzns IChemE 71,203-211 (1993).

HomSak M. and P. GlaviE, Thermodynamic Analysis of Inappropriately Placed Energetic Units. Computer-Oriented Process Engineering (Edited by L. Puigjaner and A. Espuna), pp. 363-369. Elsevier, Amsterdam (1991).

Linnhoff B. and K. J. Carpenter, Energy Conservation by Exergy Analysh. The Quick and Simple Way, ICI Corporate Laboratory, Runcorn, Cheshire (1981).

Smith J. M. and H. C. Van Ness. Introduction to Chemical Engineering Thermodynamics.‘McGraw-Hill, New York (1987).

Sussman M. V., Availability (Exergy) Analysb. A Self Instruction Manual, Tufts University, Lexington (1980).