Puigjaner L. (ed.) Syngas from Waste

Подождите немного. Документ загружается.

unattainable if the shell and tube exchanger is selected. The problem can be

observed if we take a closer look at the temperature distribution of counter-ﬂow

and the shell and tube heat exchangers (Fig. 7).

In counter-ﬂow heat exchangers, the outlet temperature of the cold stream can

be higher (Fig. 7a) because of the transfer area’s geometry. When U-tubes are

used, the ﬂow arrangement combines the counter and co-current ﬂows. The

temperature distribution becomes infeasible when a shell and tube exchanger is

selected and T

out

T

out

(Fig. 7b). To overcome this problem, an additional con-

straint has to be speciﬁed for the shell and tube with U-tubes exchangers (l = 4):

i;kþ1

 T

j;k

þ DT

ð1 y

i;j;k;4

ÞDT

min

i 2 H; j 2 C; k 2 KðÞð19Þ

Note that this constraint is a complicated one, since it tends to increase tem-

perature differences in the shell and tube exchangers causing some additional loss

of temperature potential for heat-recovery. This loss can be signiﬁcant, especially

when streams are deﬁned within wide ranges between inlet and outlet tempera-

tures. On the other hand, ﬁxed plate shell and tube HE exhibit counter-ﬂow

arrangement, so its temperature distribution should disobey the above constraint.

This means that by using a ﬁxed plate shell and tube exchanger we may efﬁciently

recover a considerable fraction of otherwise lost temperature potentials. However,

at higher pressure, this type of HE is considerably more expensive than shell and

tube with U-tubes (see Table 6). Thus, there is a trade-off between the potential

losses and the selection of different types of exchangers.

5.3 Disjunctive Modelling of Operating Limitations

for Selected Exchanger Types

The selection of exchanger types depends on the operating temperatures and

pressures of the involved streams (Table 5). As stream pressures are ﬁxed, they

can be taken into account in a pre-screening procedure before optimization.

However, all stage temperatures are optimization variables and, therefore, affect

the selection of exchanger types. The temperature ranges of the comprised

exchanger types have been modelled as scalar products between the vector for

binary variable regards exchanger types and the vector for lower and upper tem-

perature operating limits:

Fig. 7 Temperature

arrangement in a counter-

ﬂow HE and b shell and tube

HE with U-tubes

218 Z. Kravanja et al.

i;k



l2L

i;j;k;l

þ T

1 

l2L

i;j;k;l

i;k



l2L

i;j;k;l

þ T

1 

l2L

i;j;k;l

;

; 8i 2 H; j 2 C; k 2 K ð20Þ

j;k



l2L

i;j;k;l

þ T

1 

l2L

i;j;k;l

j;k



l2L

i;j;k;l

þ T

1 

l2L

i;j;k;l

;

; 8i 2 H; j 2 C; k 2 K ð21Þ

If an exchanger type in a match is selected then the last terms in the upper

constraints become zero and stage temperatures are enforced within the corre-

sponding operating limits; otherwise the constraints are redundant.

Logical constraints for utilities:

• Selection of hot and cold utilities, respectively:

hu;j

Q

 y

hu;j

; 8hu 2 HU; 8j 2 C ð22Þ

cu;i

Q

 y

cu;i

; 8hu 2 CU; 8i 2 H ð23Þ

Table 6 Cost data

Exchanger type Design pressure

(bar)

Fixed charge

coefﬁcient (k€)

Area cost

coefﬁcient

(k€ m

-2

)

Double pipe 0.01–125 46.0 2.742

Plate and frame 0.01–125 129.8 0.347

Fixed plate shell and tube 0.01–10 121.4 0.193

Fixed plate shell and tube 10–25 105.6 0.304

Fixed plate shell and tube 25–125 174.4 0.919

Shell and tube with U-tubes 0.01–125 100.9 0.272

Utility heat exchangers 0.01–125 105.6 0.304

Utilities Cost (€ kWh

-1

)

High-pressure steam 0.04

Cooling water 0.01

Refrigeration 0.08

Electricity 0.08

Other data

Expected project’s lifetime, a 15

Interest rate (%) 10

Yearly working fraction (h annum

-1

) 8,000

Process Integration: HEN Synthesis, Exergy Opportunities 219

• Positive temperature differences:

hu;j

 T

 T

out



þ DT

hu;j

1  y

hu;j



hu;j

 T

out

 T

j;1



þ DT

hu;j

1  y

hu;j



;

; 8hu 2 HU; 8j 2 C ð24Þ

cu;i

 T

i;Nþ1

 T

out



þ DT

cu;i

1  y

cu;i



cu;1

 T

out

 T



þ DT

cu;i

1  y

cu;i



;

; 8cu 2 CU; 8i 2 H ð25Þ

Generation of steam:

As in the previous section, we have to deﬁne variable heat capacity ﬂowrates

for hot steam producing steam-condensing i 2 C

and cold steam-producing

streams j 2 C

proportional to a steam mass production ﬂowrate q

, whilst the

heat capacity ﬂowrates of process streams i 2 H

and j 2 H

are ﬁxed. Thus,

the same constraints as the presented in Sect. 4.1 are applied (Eqs. 3, 4 and 5).

Objective function:

The objective function of the extended model deﬁnes the annual proﬁt of heat-

recovery network and steam/power generation and comprises the following terms:

• Income from selling electricity, Eq. 26a

• Cost for utility consumption, Eq. 26b

• Annualized investment for coolers and heaters, Eq. 26c, and

• Annualized investment for heat exchangers of different types, Eq. 26d

Profit ¼ c



s2S

spec

ð26aÞ

c



hu2HU

j2C

hu;j

 c



cu2CU

i2H

cu;i

ð26bÞ

f



i2H

cu2CU

fix

 y

cu;i

þ c

var



cu;i

D

cu;i

Ft

f



j2C

hu2HU

fix

 y

hu;j

þ c

var



hu;j

D

hu;j

Ft

ð26cÞ

f



i2H

j2C

k2K

l2L

fix

 y

i;j;k;l

þ c

var



i;j;k;l

i;j

 D

i;j;k

 Ft

ð26dÞ

where f

is an annualized factor depending on the given project’s lifetime, and the

selected interest rate. In order to avoid the numerical difﬁculties of using the above

logarithmic mean temperature differences when DT

= DT

, the temperature

driving forces are speciﬁed by Chen’s approximation [10]:

220 Z. Kravanja et al.

cu;i

¼ DT

cu;i

 DT

cu;i



cu;i

þ DT

cu;i

!"#

ð1=3Þ

ð27Þ

hu;j

¼ DT

hu;j

 DT

hu;h



hu;j

þ DT

hu;j

!"#

ð1=3Þ

i;j;k

¼ DT

i;j;k

 DT

i;j;kþ1



i;j;k

þ DT

i;j;kþ1



ð1=3Þ

Note that Ft denotes the correction factor for the temperature driving forces

within different exchanger types. It is equal to one for counter-ﬂow and is less than

one (0.8–0.95) for exchanger types with combination of counter and co-current

ﬂows as is the case with shell and tube HE with U-tubes.

5.4 Computational Feature of the Model

It should be noted that, in order to preserve the linearity of the constraints, all the non-

linear cost terms are presented in the objective function. However, the consideration

of different exchanger types drastically increases the combinatorics, size and, hence,

the computation effort needed to solve the problem. Problems, such as IGCC with 20

hot and 20 cold streams easily have 2,000 or more binary variables and ten thousands

of continuous variables and constraints. Efﬁcient strategies have to be applied in

order to decrease the computational burden and to ﬁnd a good solution:

• Pre-screening of alternatives for some exchanger operating limitations can be

done ahead of the optimization. The space for discrete decisions can thus be

drastically reduced.

• In many cases, an outer-approximation/equality-relaxation (OA/ER) algorithm

applied to solve this MINLP problem may not converge, since the sequence of

major iteration produces infeasible NLP subproblems. The problem is very time

consuming especially when MILP master problems take long CPU times for the

needed integrality gap. In such a case integer infeasible path optimization [8]

can be applied, thus preventing the OA/ER algorithm from obtaining infeasible

NLPs. Considerably faster convergence of the algorithm can thus be achieved.

5.5 Results and Discussion

In the IGCC problem we dealt with 16 hot and 13 cold process streams, and 3 hot

and 9 cold steam-producing streams (Tables 3 and 4), for which we assume

that the power is generated in a cascade of HP, MP and LP turbines operating at

Process Integration: HEN Synthesis, Exergy Opportunities 221

122, 32 and 5 bar, respectively. Note that the present cost data are given in

Table 6. When applying the above MINLP model for simultaneous heat-recovery

and steam/power generation network synthesis, optimal trade-offs between elec-

tricity income and utility cost plus investment can be obtained over different

lifetime periods and the prediction of future utility and electricity prices. Table 7

Table 7 Sensitivity analysis results

Electricity/utility cost factor 1 1 1 1 1.5 2 3

Estimated lifetime (annum) 5 10 15 30 30 30 30

HPS production (tons h

-1

) 378 384 398 401 405 409 409

LPS production (tons h

-1

) 0004000

Recovered enthalpy ﬂowrate HPS (MW) 332 338 350 353 356 360 360

Recovered enthalpy ﬂowrate LPS (MW) 0 0 0 3 0 0 0

Power HPS (MW) 101 103 107 108 107 110 110

Power LPS (MW) 0 0 0 1 0 0 0

Cold utility load (MW) 304 302 298 296 296 295 295

Annualized HEN investment (M€ annum

-1

) 17.7 15.2 10.2 10.2 11.6 13.1 18.0

HEN investment (M€) 67.2 93.2 101.7 100.5 109.7 123.1 161.0

Fig. 8 Heat exchanger

network for actual prices of

utilities and energy

222 Z. Kravanja et al.

shows the amount of generated steam and power, cold utility consumption,

annualized and total investment for IGCC HEN. From Table 7 it can be seen how,

at lower energy prices and shorter depreciation periods, the generation of power

decreases, when higher values are obtained for the actual HRAT. Note that a

similar trend was observed in the previous section, where it was seen that by

increasing HRAT the generation of power was reduced and the consumption of

cold utility increased. In all cases, complex heat-recovery networks are obtained.

The network, where actual prices for utilities and electricity, and a 15 year

depreciation period are considered, is shown in Fig. 8. It can be seen that about

35 MW of energy is wasted: 2/3 heat content of HCLEAN1-HCOOL,  of

HE2-COOLER and complete heat from the REGEN-COND condenser, whilst

350 MW of heat is recovered for the production of 398.1 tons h

-1

HPS and

107 MW power. HEN comprises 39 HE units, 4 coolers at ambient temperature

and 5 refrigeration units at very low temperatures and no heater. Due to integra-

tion, more than half (28.2 MW) of a very low temperature cooling requirement

could be saved. This solution yields 68.5 M€ annum

-1

of electricity income,

36 M€ annum

-1

cooling cost and 13.4 M€ annum

-1

annualized investment for

HEN, giving 19.1 M€ annum

-1

of annual proﬁt before tax.

Fig. 9 Heat exchanger

network for double the utility

and energy prices

Process Integration: HEN Synthesis, Exergy Opportunities 223

Since prices for energy in general, and utilities and electricity in particular, are

expected to increase faster in the future relative to other prices, we also, as

mentioned, performed synthesis for higher prices. HEN obtained when considering

double the utility and energy prices and doubled the project’s lifetime (30 years) is

shown in Fig. 9.

A quick analysis showed that about 7 MW of heat is additionally recovered by

steam production enabling 2.9 MW more of power generation. Also, integration

at very low temperatures saves an additional 2.0 MW of the refrigeration load.

It can again be seen that this solution is in accordance with the observation about a

trade-off between HRAT, and heat-recovery and power generation efﬁciency.

It also should be noted that, on average, one half of those HE units selected are

those with counter-ﬂow arrangements (one quarter double-pipe and one quarter

ﬁxed plate shell and tube exchangers) and one half is shell and tube exchangers

with U-tubes providing a combined co-current and counter-ﬂow arrangement.

Since ﬁxed plate exchangers are signiﬁcantly more expensive than U-tube

exchangers, they are selected at those positions in HEN where a higher efﬁciency

is required for heat recovery, thus enabling optimal steam and power generation

with a better exergy exploitation of the process.

6 Conclusions

This chapter has described a three-step approach for the synthesis of heat-recovery

and steam/energy generation network. Firstly, we start with a thermodynamic

analysis of a studied process ﬂowsheet. Detailed data extraction and acquisition

should be performed in order to thoroughly undertake the pinch analysis.

The results from the pinch analysis indicate possible heat-recovery and exergy

opportunities, which can be elaborated in more details over the next two mathe-

matical programming steps, where in the ﬁrst next step a simple, yet effective,

maximization of steam/power generation can be performed, with respect to tem-

perature potential losses within a heat-recovery network. A detailed synthesis of the

network is then performed in the last step where appropriate trade-offs are obtained

between the income from power generation and utility costs plus investment.

The synthesis comprises a heat-recovery network and variable steam production at

different pressure-levels for power generation. Optimal arrangement, number,

loads, temperature driving forces and types of heat exchanger units, as well as

optimal mass ﬂowrates for the production of LPS, MPS and HPS are obtained

during this step. An optimal solution with current energy prices and 15 years of an

expected project’s lifetime yields 107 MW power productions, whilst the one with

double prices and doubled lifetime enables 3 MW more power, which indicates that

when considering future prices, and lifetime periods more realistically, additional

increase in the heat/energy-recovery efﬁciency can be achieved. Whilst applying

this three-step procedure we have also demonstrated how basic optimization

models can be adapted and customized for solving large-size industrial problems.

224 Z. Kravanja et al.

Finally, it should be noted that only complete heat-recovery network was

analyzed, together with steam and power generation at ﬁxed process streams and

ﬁxed levels of steam. In order to obtain a global solution the whole process,

including a gas turbine system with variable ﬂows and their temperatures has to be

optimized simultaneously, giving rise to an extensive optimization problem.

Serious research work would be needed to accomplish this task.

References

1. Duran MA, Grossmann IE (1986) Simultaneous optimization and heat integration of

chemical processes. AIChE J 32:123–138

2. Yee TF, Grossmann IE (1990) Optimization models for heat integration-II, heat exchanger

network synthesis. Comput Chem Eng 14:1165–1184

3. Pérez-Fortes M, Bojarski AD, Velo E, Nougués JM, Puigjaner L (2009) Conceptual model

and evaluation of generated power and emissions in an IGCC plant. Energy 34:1721–1732

4. Smith R (2005) Chemical process design and integration. John Wiley & Sons, Chichester,

West Sussex

5. Klemeš J, Friedler F, Bulatov I, Varbanov P (2010) Sustainability in the process industry:

integration and optimization. McGraw-Hill, Maidenherd, New York

6. Papoulias SA, Grossmann IE (1983) A structural optimization approach to process

synthesis—II, heat recovery networks. Comput Chem Eng 7:707–722

7. Biegler LT, Grossmann IE, Westerberg AW (1997) Systematic method of chemical

engineering. Prentice Hall PTR, New Jersey

8. Soršak A, Kravanja Z (2002) Simultaneous MINLP synthesis of heat exchanger networks

comprising different exchanger types. Comput Chem Eng 26:599–615

9. Hewitt GF, Shires GL, Bott TR (1994) Process heat transfer. CRC Press, Boca Raton, Florida

10. Chen JJJ (1987) Letter to the editors: comments on improvement on a replacement for the

logarithmic mean. Chem Engng Sci 42:2488–2489

Process Integration: HEN Synthesis, Exergy Opportunities 225

Global Clean Gas Process Synthesis

and Optimisation

Mar Pérez-Fortes and Aarón D. Bojarski

Abstract This chapter begins with an introduction to the different possible metrics

related to clean gas process synthesis and its subsequent usage. Latter, the different

techniques for tackling with multiple criteria are presented, emphasising the use of

multi-criteria decision analysis (MCDA) and multi-objective optimisation (MOO).

The different criteria elected here for optimisation are described and later used as

key performance indicators (KPI) for the proposed scenarios, in chapter

‘‘ Selection of Best Designs for Speciﬁc Applications’’. Finally, a case study related

to the operation of an IGCC plant considering coal–petcoke or natural gas as a fuel

is assessed applying the optimization concepts introduced here and taking into

account the operation considerations developed in this and in previous chapters.

Notation

ADP Abiotic depletion potentials

AHP Analytical hierarchy process

AoPs Areas of protection

AP Acidiﬁcation potentials

bc Base case

CBA Cost beneﬁt analysis

CCS Carbon capture and storage

CED Cumulative energy demand

CExD Cumulative exergy demand

CF Characterisation factor

COE Cost of energy

CSTR Continuous-stirred tank reactor

M. Pérez-Fortes (&)  A. D. Bojarski

Universitat Politècnica de Catalunya, ETSEIB,

Diagonal 647, 08028 Barcelona, Spain

e-mail: mar.perez-fortes@upc.edu

A. D. Bojarski

e-mail: aaron.david.bojarski@upc.edu

L. Puigjaner (ed.), Syngas from Waste, Green Energy and Technology,

DOI: 10.1007/978-0-85729-540-8_10,  Springer-Verlag London Limited 2011

227

Puigjaner L. (ed.) Syngas from Waste - Emerging Technologies

Подождите немного. Документ загружается.