coordination of process integration and exergoeconomic methodology for analysis and optimization of...

Transaction B: Mechanical EngineeringVol. 16, No. 4, pp. 301{312c Sharif University of Technology, August 2009

Coordination of Process Integration andExergoeconomic Methodology for Analysisand Optimization of a Pulp and Paper Mill

M. Fani1, A.A. Mozafari1;� and B. Farhanieh1

Abstract. By simultaneously applying pinch technology and the exergoeconomic method to a complexprocess system, bene�cial and energy-e�cient measures are identi�ed. The \three-link-model" exergoeco-nomic methodology optimizes the design and operability of a system. In this work, contrary to traditionalexergoeconomic methods, a reversed method is used. The approach proposed for the optimization ofsuch a complex system is to iteratively optimize subsystems. Since the reversed exergoeconomic methodis used, assumptions considered by Tsatsaronis (based on four assumptions for calculating the cost-optimal exergetic e�ciency and relative cost di�erence) are not applicable and new assumptions are to beconsidered. Unlike traditional exergoeconomic methods, the product exergetic speci�c cost is considered tobe known and the objective will be to maximize the exergetic cost of the fuel. Heat ows costs are calculatedwith the assistance of a Pinch analysis. The strength of the combination of a Pinch analysis and theexergoeconomic method is elucidated in a case study applied to the Mazandaran wood and paper industry.Replacement of the pressure valve and Direct Cyclone Contact Evaporation (DCCE) is proposed, while byselection of the optimum decision variable and applying Pinch technology simultaneously, the recoverableblack liquor could be increased by 7% and energy consumption decreased by 12%.

Keywords: Pinch technology; Exergoeconomic methodology; Process system; Optimization; Pulp andpaper.

INTRODUCTION

The pulp and paper industry is under increasing pres-sure to reduce its impact on the environment and itsenergy consumption. When modeling a system, it isvery important to know where to introduce the systemboundaries. Di�erent results may be obtained, basedon the boundaries chosen.

Pinch technology is a method to improve HeatExchanger Networks (HEN), only improving the struc-ture of a HEN under speci�c conditions. One keyto good energy e�ciency is the exchange of heat inthe most e�ective way between components within thesystem, thereby cutting the need for additional heatingor cooling [1]. The application of process integrationtools and methods in the pulp and paper industry datesback to the 1990's when Pinch analyses of pulp and

1. Department of Mechanical Engineering, Sharif University ofTechnology, Tehran, P.O. Box 11155-9567, Iran.

*. Corresponding author. E-mail: [email protected]

Received 23 July 2007; received in revised form 21 May 2008;accepted 24 November 2008

paper mills were �rst made. It was not until the late1990's and early 2000's that process integration becamemore widely used as a tool for energy analysis andretro�t application in the pulp and paper industry [2].

Noel generalized the use of a Pinch analysis inpulp and paper mills in 1995 by applying the Pinchanalysis to steam, water and liquor streams and, also,direct heat exchangers for the retro�tting of existingheat changer networks [3,4].

In 1999, Lombardo et al. [5] practiced Pinchand exergy analysis on a Kraft pulp and paper millretro�tting. However, only indirect heat exchangerswere considered and the exergy analysis was applied toeach unit individually. The Department of Heat andPower Technology at Chalmers University of Technol-ogy in Sweden is a pioneer in the retro�tting of thepulp and paper industry and also in application of thePinch analysis to pulp and paper mills [6-10].

Paris et al. have applied MILP (Mixed IntegerLinear Programming) and Pinch technology to a pulpand paper mill and energy and exergy recovery oppor-tunities have been examined to improve integration of

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302 M. Fani, A.A. Mozafari and B. Farhanieh

the utility system. The MILP optimization targetingmethod has been applied to identify the best energyconversion options and to optimize production of com-bined heat and power [11].

Exergoeconomics combine exergy analysis andeconomic principles to provide the system designerwith information not available through conventionalenergy analysis and economic evaluations, but crucialto the design and operation of a cost-e�ective system.A general methodology for this kind of analysis waspresented by Tsatsaronis in 1985 [12] which was latercalled the exergoeconomic accounting technique [13].In recent years, a di�erent direction of developmentsin exergoeconomics has been taken and presentedby Tsatsaronis et al. [14-18], Valero et al. [19-22],Fragopoulos [23] and Spakovsky [24]. Tsatsaronisintroduces an iterative exergoeconomic optimizationprocedure based on exergoeconomic variables (relativecost di�erence, exergoeconomic factor and exergetice�ciency) and minimization of the product cost of eachsystem; components are treated in thermoeconomic iso-lation. In the case of pulp and paper making processes,the problem, due to the high number of simultaneousproducts, is more complex compared to cogenerationsystems producing only heat and power. Few studieshave proceeded to systems which produce productsother than heat and power [25-28]. No studies haveapplied exergoeconomics to pulp and paper processes(energy use and recovery processes).

APPLYING REVERSED EXERGYCOSTING METHOD TO RECOVERY LINK

Exergy improvement potential is a measure for deter-mining system performance, showing how much andhow easy the system could be improved for optimiza-tion purposes [26].

Pot = Irr(1� ") + Efl; (1)

where:

Irr =X

EF �XEP ; (2)

" =EntpEnts

=EPEF

; (3)

Efl =X

Erejected to the environment: (4)

It is formed by three contributions: Absolute potential(Irr), relative potential (1 � ") and environmentalpotential (Efl). The relative potential (1�") is a mea-sure showing the system potential for improvement;if the e�ectiveness is very low, the relative potentialapproaches its maximum value, so in principle thesystem could be improved from inside itself. In order

to optimize a system, it is necessary to preferably ap-proach the blocks with the higher exergy improvementpotential.

Exergoeconomic traditional sequential costingmethods deal with energy systems; systems whichconvert one certain type of energy into another. Con-versely, process systems produce certain products fromcertain raw materials.

Decomposition strategies have been proposed toreduce the complexity of complete systems. A `three-link-model' energy/mass structure for process systemsis proposed by Zhang et al. [25]; a rigorous quantitativemathematical energy/mass model which is suitablefor any process system. This study is based on a`reversed costing' strategy for computing recoverableenergy/mass costs in recovery subsystems.

This model makes it possible to divide whole sys-tems into main subsystems and recovery subsystems,optimizing each subsystem separately and improvingthe total system towards an optimum state. The`energy/mass recovery' link recovers raw materialsneeded for main subsystems in addition to energy.

In many systems, production costs are beingreduced by the recovery of whole or parts of rejectedstreams. With the development of technology andchanges in economical conditions and environmentconstraints, it has become possible to recover rejectedenergy/mass more and more e�ectively. The cost ofrecoverable exergy depends on the extent of recovery.Therefore, only the reversed exergy costing principle isavailable. The money balance equation for the recoverylink is as follows [25]:X

j

cOjEOj +Xi

cDjEDj +Xj

ZRj

=Xi

cEjEEj +Xi

cRiERi: (5)

The exergy-mass-economic model for the recovery linkis shown in Figure 1.

Equation 5 di�ers from a conventional moneybalance. In this equation, the unknown term, cOjis not at the right side of the equation, but at theleft side. First, the quantity of the recycled exergy,ERi, and the recovered export exergy, EEi, as wellas their costs, cRi and cEj , respectively, should bedetermined.

`Reversed costing' means that the cost of therecoverable exergy EO depends on the cost of therecovery driving exergy ED and the exergies recoveredfrom the energy-recovery subsystem, ER and EE .Factor cD will be calculated from the energy-conversionlink by using a sequential costing method.

The next step is determination of cE and cR. Twomethods are suggested for calculating cE :

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Analysis and Optimization of a Pulp and Paper Mill 303

Figure 1. Recovery link exergy-mass-economic model.

1. If cE is the speci�c cost of power, its cost is thesame as the market cost of the same ow;

2. If cE is the speci�c cost of heat, it can be calculatedwith the assistance of a Pinch analysis. cR is thesame as the market price of the same material.

These principles connect the energy use subsys-tem to the energy/mass recovery subsystem and have agreat in uence on the optimization results. The cost ofthe irreversible, e�uent and total exergy losses of eachunit and their exergoeconomic improvement potentialis then calculated with the following expressions:

Cirr;U = Irr �ctte;U ; (6)

Cefl;U = Efl �ctte;U ; (7)

PotecU = Cirr;U (1� ") + Cefl;U ; (8)

where:

�ctte;U =PINi=1EUiciEtte;U

: (9)

CALCULATING HEAT FLOW COST

For calculating cE by Pinch technology, �rst energy-use link warm and cold streams are identi�ed frommass and energy balance process simulations. The heatcarrying streams are listed. Composite curves have tobe drawn; minimum hot and cold utility requirementscan be evaluated from composite curves and networkcapital cost has also to be calculated. In the nextstep, all warm and cold streams plus the \recoveredstream" from the recovery link (the cost of which hasto be calculated) are identi�ed. Minimum hot and coldutility requirements and network capital cost will againbe evaluated. The speci�c cost of a recovered stream

is evaluated as follows:

cE =(Qmin;1 �Qmin;2)� ceD

EE

� (network capital cost2 � network capital cost1)EE

:(10)

COORDINATION OF EXERGOECONOMICMETHOD AND PINCH TECHNOLOGY

Bengtsson et al. have proposed a structure for combin-ing Pinch technology and the MIND method [6]. Theproposed procedure for combining Pinch technologyand the MIND method is iterative. In this study, asimilar structure is proposed for combining Pinch tech-nology and the exergoeconomic method (see Figure 2).

The iterative procedure may be accomplished byusing the exergoeconomic analysis to determine aninvestment opportunity for di�erent alternatives.

OPTIMIZATION OF SYSTEM

The objective of this study is to minimize the total costof mass and energy consumption, exergy destructionand the investment equipment for the whole system.Apart from investment and maintenance costs, thesystem's essential costs consist of electricity, steamand raw material costs. Therefore, the goal is toreduce their consumption. Exergoeconomic and Pinchmethodology is applied for optimization, where Pinchanalysis is applied to the whole system. In thisstudy, since the energy/mass recovery subsystem is themost energy consuming subsystem, exergoeconomicsare applied only to this subsystem. According to thereversed costing strategy proposed by Zhang et al. [25],the goal is to get the maximum cost of the recoverablemass, EO, at the minimum driving exergy, ED. Theobjective function of exergoeconomic optimization is:

max cO=(PicEjEEj+

PicRiERi�P

icDjEDj�P

jZRj)P

JEOj

:(11)

Figure 2. Procedure for combined method.

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cO is the coordinating variable of the energy-use linkand mass/energy recovery link. Mass/energy recoverylink optimization is done under the boundary con-straint, EO, which produces the optimization resultsof ED and the new value of cO. Iteratively, anoptimization of the whole system and forward recoverylink will be done. The feasible coordinating rules are:

(cOj)k+1 = (cOj)k; (12)

(EOj)k+1 = (EOj)k: (13)

The convergence judgment rules are:

j(cOj)k+1 � (cOj)kj � ": (14)

Because of system complexity and the unavailabilityof input data and functions required, especially forblack liquor, mathematical techniques cannot be usedfor optimization.

The usual approach to the optimization of sucha complex system is to iteratively optimize subsys-tems. An alternative to this approach is an it-erative exergoeconomic optimization technique pro-posed by Tsatsaronis, which consisting of sevensteps [13].

Among the most important parameters in suchan optimization are cost-optimal values for exergetice�ciency and the relative cost di�erence. Tsatsa-ronis [13] has proposed an approach, based on fourassumptions, for calculating the cost-optimal exergetice�ciency and relative cost di�erence for a componentisolated from the remaining system components. Inthis study, since a reversed exergoeconomic methodis used, the assumptions considered by Tsatsaronisare no longer valid and new assumptions have to beconsidered. These assumptions are as follows:

1. The exergy ow rate of fuel, _EF , and the unitcost of product, cP , remain constant for the kthcomponent:

_EF;k = constant; (15)

and:

cP;k = constatnt: (16)

2. Every system component investment cost increaseswith its capacity and exergetic e�ciency. The totalcapital investment of the kth component can berepresented by:

TCIk = Bk�

"k1� "k

�nk_EmkF;k; (17)

where:

"k =EP;kEF;k

:

Parameter Bk and exponents nk and mk are con-stant. These parameters are calculated by use of apurchased-equipment cost and least square method.

3. Annual levelized operating and maintenance costsattributed to the kth component are considered as:

ZOMk = k(TCIk) + !k� _EF;k +Rk: (18)

The coe�cient k for such a system is considered as0.1; !k is a constant that accounts for the variableoperating and maintenance costs associated withthe kth component and denotes the O & M costper unit of the product exergy; � is the averageannual time of plant operation at the nominal load;and Rk includes all the remaining operating andmaintenance costs that are independent of the totalcapital investment and the exergy of the product.The last two terms on the right side (!k� _EF;k andRk) may be neglected since they are small comparedwith the remaining term.

4. This study tries to optimize an established system,ZCIk = 0, by which Equations 19 to 21 are obtained:

Zk = ZCIk + ZOM

k = ZOMk

= k(TCIk) + !k� _EP;k +Rk: (19)

Thus, cost rate will be obtained as:

_Zk = k�

(TCIk) + !k _EF;k +Rk�: (20)

By use of Equation 20:

_Zk = kBk�

�"k

1� "k�nk

_EmkF;k

+ !k _EF;k +Rk�: (21)

The objective function to be maximized expressesthe cost per exergy unit of product for the kth compo-nent. Accordingly:

Maximize cF;k =cP;k _EP;k � _Zk

_EF;k: (22)

So:

Maximize cF;k = cP;k"k � kBk�E1�mk

F;k

�"k

1� "k�nk

+ !k +Rk� _EF;k

:(23)

During each iteration of optimization parameters�; k; �; !k and Rk remain constant. "k is the onlyvariable in this equation.

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The maximum cost per exergy unit of fuel isobtained by di�erentiating the above equation andsetting the derivative to zero:

dcF;kd"k

= 0: (24)

Finally, Equation 25 is achieved, which has to be solvedby numerical methods (contrary to direct exergoeco-nomic methods) for "OPT

k :

kBknk� _E1�mk

F;k cP;k=

(1� "OPTk )nk+1

("OPTk )nk�1 : (25)

Another useful and important variable for optimizationis the relative cost di�erence:

rk =cP;k � cF;k

cF;k; (26)

or:

rk =cP;k _EP;k � cF;k _EP;k

cF;k _EP;k: (27)

Equations 28 and 29 are used for eliminating _EP;k:

_EP;k = _EF;k + _ED;k + _EL;k; (28)

cP;k _EP;k = cF _EF;k + _Zk: (29)

So:

cP;k _EF;k = cF;k _EF;k + cP;k _EL;k + cP;k _ED;k + _Z:(30)

Finally, the following relation is achieved:

rOPTk =

1cP;k _EF;k

cP;k( _ED;k+ _EL;k)+ _ZOPT � 1: (31)

Tsatsaronis' priority for optimization of components inthe iterative exergoeconomic optimization technique is( _Zk + CD;k) [13]. The optimization proposed in thisstudy speci�es its priority based on exergoeconomicand exergetic improvement potentials. Componentswith small exergoeconomic improvement potential, butacceptable exergetic improvement potential, have tobe replaced. Components with high exergoeconomicand exergetic improvement potential are the best com-ponents for improvement and modi�cation. Compo-nents which have very low exergoeconomic improve-ment potential are not worth any capital investment.Components with low exergoeconomic and exergeticimprovement potential and high exergetic e�ciency areconsidered optimum.

CASE STUDY

Mill Description

The paper mill under consideration is an Iranian pulpand paper mill with a capacity of 600 tons/day. Thismill is a Chemical Thermal Mechanical Pulp (CTMP)integrated mill. The e�uent that is to be evaporated isfrom the CMTP plant, amounting to 137.9 tons/h, witha Dry Solid (DS) content of 5%, which is evaporatedto a �nal content of 63% DS before incineration in therecovery boiler.

Evaporation of the e�uent means that the itis divided into two fractions, clean condensates andresidue with a high content of dry substance, containingboth organic and inorganic material. The residue canbe combusted in the recovery boiler and condensatescan be reused in the process, thereby increasing thee�ciency of the mill. The recovery link is shown inFigure 3.

The following assumptions have been consideredduring a simulation of the recovery link:

� System operates under steady state conditions.� Ideal-gas mixture principles are applied to air and

combustion products.� Combustion in the recovery boiler chamber and

conversion tower is complete.� Except for the recovery boiler, all components oper-

ate without heat loss.

Applying Pinch to Heat Exchanger Network

The main aim is to make a survey of the excess heatin the system, with unchanged live steam consumption,therefore some parts of the system are excluded. Theseparts are steam consumers such as paper machines,digesters and cold streams whose heat demands, dueto process conditions, have to be met with steam. Theheat supplied from incinerating the e�uent residue isneglected because the heating value is poor. Table 1summarizes the cold and hot streams chosen for theformation of cold and hot composite curves.

For streams containing �ber, water and/or liquor,cp, is calculated by use of the following relations:

cp = (0:005 + 1:092��Tin + Tout

2

��consistency=100 + (1� consistency)�4:178; (32)

where consistency is de�ned as [29]:

consistency =_m�ber

_m�ber + _mwater: (33)

After computing streams Tin; Tout; cp and _m, the hotand cold composite curves are drawn by specifying a

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Figure 3. Mill's recovery link.

Table 1. Summary of cold and hot streams.

Cold Streams Hot Streams

Inlet chipsBlack liquorWhite liquorFresh water E�uentProcess water Blow steamEvaporator inlet Evaporator condensateBoiler make up waterProcess pulp*

* Only pulps whose temperature has to increase considerably.

minimum temperature driving force for heat transferfrom hot to cold streams (�Tmin) of 25�C, selectedaccording to the process constraints and investmentcriteria of the mill. Figure 4 shows the Mazandaranmill's cold and hot composite curve.

APPLYING EXERGOECONOMIC METHODTO THE MILL

An exergetic and exergoeconomic system analysis isperformed to determine all mass, exergy, exergy de-struction, exergetic cost, exergy destruction cost, com-ponent investment cost ow rates, component exergetice�ciencies and system total cost.

Figure 4. Mill's cold and hot composite curve.

Selection of the independent variables for char-acterizing design options is very important. Allimportant variables that a�ect the performance andcost e�ectiveness of the system must be included.Independent variables whose values are amenable haveto be distinguished; only decision variables may bevaried. Decision variables for cogeneration systemshave been presented and introduced, but since thesystem under consideration is a process system, se-lection of its decision variables is not the same asenergy systems. Choosing decision variables is di�cult,especially because some variables a�ect the productcost without in uencing the e�ectiveness of the system�ne details, thus, variables of minor importance should

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not be included. Compounded methodology is usedfor the identi�cation of decision variables that a�ectthe cost and exergetic e�ciency of the system. Thismethodology combines recent available exergoeconomictechniques with new qualitative and quantitative crite-ria [30].

Table 2 shows decision variables and their limitsfor the system under consideration.

OPTIMIZATION

Tsatsaronis has proposed an iterative optimization pro-cedure for complex systems, consisting of the followingsteps [13]:

� For components, particularly the ones having arelatively high value of the sum ( _Zk + _CD;k), �"kand �rk, the calculation for one decision variablechanges, while other decision variables are keptconstant, where:

�"k ="k � "OPT

k"OPTk

� 100; (34)

�rk =rk � rOPT

krOPTk

� 100: (35)

� The e�ects of the decision variables are examinedon the objective function. If, in comparison withthe previous design, this value has been improved,it may be decided to proceed with another iteration.However, if the value of the objective function isnot better in the new design than in the previousone, some design changes may either be revised or aprevious step be repeated.

� Repetition of the above steps for the other decisionvariables.

Among design guidelines, some are very usefulwhen considering a recovery link. These are:

� Maximizing the use of cogeneration of power andprocess steam, this can be interpreted as the use ofa turbine instead of a pressure valve.

� Minimizing the mixing of streams with di�er-ent temperatures, DCCE (Direct Cyclone ContactEvaporation) can be replaced by an indirect heatexchanger.

� Minimizing the use of combustion or preheating thereactants and minimizing the use of excess air.

The use of these guidelines can reduce the totalnumber of iterations required.

In this study, exergoeconomic and exergetic im-provement potential are used instead of ( _Zk + _CD;K),specifying the order of component modi�cation. Fig-ures 5 and 6, respectively, show the exergetic andexergoeconomic improvement potential of the compo-nents and exergetic e�ciency at initial decision variablevalues.

These �gures give ideas about conditions whenencountering di�erent components. For example,the evaporator is optimum, however decision variablechanges can improve its function. DCCE and pressurevalve replacement is proposed, while the recovery boilerand conversion tower can be modi�ed. It should benoted that the conversion tower low e�ciency and

Figure 5. Exergetic and exergoeconomic improvementpotential of components at initial decision variable values.

Table 2. Decision variables of all components and their limit.

Component Input Variable ValueMinimum Maximum

Number of e�ect 4 6Backward-forward

Evaporator centralTsteam,in(�C) 90 400

_msteam,in (kg/s) 3 4.5

AFR 1 1.6Recovery boiler T uegas (�C) 250 1200

Tair,in (�C) 25 200Twater,in (�C) 25 200

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Figure 6. Exergetic e�ciency of components at initialdecision variable values.

exergetic and exergoeconomic improvement potentialare related to the combustion nature.

After de�ning component priorities, based onexergetic and exergoeconomic improvement potentials,the relative deviations of the actual values from the costoptimal values for the exergetic e�ciency and relativecost di�erences are calculated [13]. The design is modi-�ed to reduce the values of �"k and �rk. If con ictingdesign changes are suggested from the evaluation ofdi�erent components, the design changes with higherexergoeconomic improvement potential values prevail.

Subsequent �gures show the in uence of somedecision variables on di�erent components, �"k and�rk. For better perception, absolute values of �"k areused in theses �gures. It should be noted that somevariables have a great in uence on some componentslike �"k and/or �rk, but little or even no in uence onother components. Figure 7 shows an impression of therecovery boiler's ue gas temperature on the recoveryboiler, DCCE and conversion tower, �"k.

Since a pressure valve performance is not depen-dent upon decision variables under consideration, it isnot included in these �gures.

Since DCCE's delta exergetic e�ciency is notice-ably higher than other components, its replacement is

Figure 7. Recovery boiler's ue gas temperature in uenceon recovery boiler, DCCE and conversion tower, �"k.

suggested. Besides, an evaporator has the highest exer-getic e�ciency and the lowest improvement potential.Therefore, the selection of decision variable values isbased on the recovery boiler and conversion tower, �"kand �rk.

As seen in Figures 7 to 13, the recovery boiler andconversion tower optimum decision variable values areclose, leading to an easier selection of decision variables.Figures 12 and 13 show the relative cost di�erenceversus decision variables in some components. Thedecision variables, in uence on DCCE and the recoveryboiler's �"k is also shown in Figures 7 to 11.

It is deduced from Figure 7 that probably thebest ue gas temperature is at the point where therecovery boiler curve cuts the conversion tower curve.Based on professional research [31], the best ue gasoutlet temperature for recovery boilers in pulp andpaper mills is about the same. It should be notedthat delta exergetic e�ciency and the delta relative

Figure 8. Recovery boiler's fraction of stoichiometric airin the lower in uence on recovery boiler, DCCE andconversion tower, �"k.

Figure 9. Evaporator's inlet steam mass ow ratein uence on recovery boiler, DCCE and conversion tower,�"k.

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Figure 10. Evaporator's inlet steam temperaturein uence on recovery boiler, DCCE and conversion tower,�"k.

Figure 11. Recovery boiler's inlet air temperaturein uence on recovery boiler, DCCE and conversion tower,�"k.

cost di�erence minimum point is not necessarily theoptimum point. However, Figure 8 shows very smallchange in the recovery boiler, DCCE and conversiontower delta exergetic e�ciency. The proposed valuefor recovery boilers' LFA is about 1.2 to 1.4 [31]. This�gure indicates that optimization iteration is in verygood agreement with professional research.

Figure 9 shows that the best value is proportionalto the black liquor mass ow rate. The results inFigure 10 are very acceptable, since the best evaporatorinlet temperature is 20 to 30 degrees above the inletstream, 90-100�C.

A slight change in the recovery boiler, DCCEand conversion tower delta exergetic e�ciency versusthe recovery boiler inlet air temperature is shown inFigure 11. However, from a graphical optimizationmethod (which it is not discussed in this paper) itcan be deduced that the best value for the inlettemperature is about 200�C.

Figure 12. Recovery boiler's ue gas temperaturein uence on DCCE's delta relative cost di�erence andrecovery boiler's inlet air temperature in uence onrecovery boiler's delta relative cost di�erence.

Figure 13. In uence of evaporator's inlet steam mass ow rate on recovery boiler delta relative cost di�erence.

This contradiction is due to the heat exchangernetwork and the impression of the inlet stream cost onthe objective function. This result coincides with theconsequences in Figure 12.

After choosing the best value in each iteration, theobjective function is calculated. If, in comparison withthe previous iteration, this value has been improved, itwill proceed to the next iteration, otherwise changesshould be revised and the iteration repeated. Asexplained before, the objective value is the value ofCfuel for the recovery link for which the black liquorcost has to be maximized.

In the next step, Pinch technology is applied tothe heat transfer network, and the design is optimumwhen the annual levelized costs associated with thenetwork are minimum and the recovery link objectivevalues are maximum. With 3 to 4 iterations, the designoptimum is achieved.

Figure 14 shows the objective value in someiterations.

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Figure 14. Variation of objective values with number ofiterations.

CONCULUSION

The present study shows that the existing design con-sumes 23% more energy than the gross root design. Byretro�tting the existing design, about 15% reductionin the energy consumption is possible. However, opti-mization of the heat exchanger network and recoverylink together will lead only to 12% reduction in energyconsumption. From components, exergetic e�ciency,exergetic improvement potential and exergoeconomicimprovement potential �gures, it is concluded thatDCCE and the pressure valve should be replaced bymore e�cient components. The best values for otherdecision variables are as indicated in Table 3. Thesevalues are achieved after 14 iterations. By applyingthese values, the mass ow rate of recoverable blackliquor increases by almost 7%.

ACKNOWLEDGMENT

The authors would like to gratefully acknowledge thesupport of the MWPI (Mazandaran Wood and PaperIndustry) engineering team for their valuable collabo-ration during the development of this research work.

Table 3. Optimized decision variables.

Component Input Variable Value

Number of e�ect 5Backward-forward Central

Evaporator centralTsteam,in (�C) 97

_msteam,in (kg/s) 4.15

AFR 1.2Recovery boiler T uegas (�C) 459

Tair,in (�C) 112Twater,in (�C) 73

NOMENCLATURE

B constantc exergy speci�c cost (US $/kW)C cost of a stream (US $)cp heat capacity (kJ/kgK)D exergy destruction (kW)e speci�c exergy (kW/kg)E exergy (kW)EFL e�uent exergy losses (kW)Irr irreversible exergy losses (kW)m constant_m mass ow rate (kg/s)n constantPot exergy improvement potential (kW)Potec exergoeconomic improvement potential

($/s)Qmin minimum hot and cold utility

requirement (kW)r relative cost di�erenceR remaining operating and maintenance

costs ($)T temperature (K) or (C)TCI total capital cost ($)Z equipment cost (US $/s)

Greek Symbols

coe�cient! constant� average annual operating time of plant

(s)" exergetic e�ciency

Subscripts

1 pinch analysis without stream fromrecovery link

2 pinch analysis with stream fromrecovery link

D recovery driving, destructedE recovered exportefl e�uent exergy lossesF fueli exergy formirr irreversible exergy lossesj unit numberJ rejectedk component and number of iterationsL losses

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ntp net producednts net suppliedO recoverableP productR recycledtte total inputU unit

Superscripts

CI capital investmentOM operating and maintenanceOPT optimum

REFERENCES

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