Targeting for Energy Integration of Multiple Fired Heaters

James Varghese and Santanu Bandyopadhyay*

Energy Systems Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India

Energy integration of a fired heater with the background process helps in targeting fuel requirement and theair preheat temperature prior to its detailed design. Existing integration procedures are applicable only forprocesses with a single fired heater. However, in certain processes, multiple fired heaters are required tosatisfy the total hot utility demand. In this paper, a methodology is proposed to target the minimum numberof fired heaters. To synthesize an energy integrated heat recovery network that incorporates a single firedheater, a cold stream should enter the fired heater at the pinch temperature, and the heat capacity of the coldstream should be within a permissible range. For processes with multiple fired heaters, the duties of differentfired heaters may be varied to simplify the design of the overall heat exchanger network. Entry conditions forcold process streams to the fired heaters are also established, to satisfy the overall energy target. In certaincases, the fuel requirement and air preheat temperature for every fired heater may have to be re-estimated toset achievable targets.

1. Introduction

Energy requirements and capital investment are two importantfactors that affect the conceptual design of a process. Techniquesof process integration, such as pinch analysis, help in targetingenergy and capital requirements prior to the detailed design ofprocess equipments and associated heat recovery networks. Firedheaters supply heat that is required by cold process streams atelevated temperature. Fired heaters are process equipment thatis both capital- and energy-intensive. Primary objective of thispaper is to develop an energy integration procedure, based onthe principles of process integration, for integrating fired heaterswith the background process.

Process furnaces, which are also known as fired heaters,supply heat to cold process streams at elevated temperaturedirectly by burning fuel. In many applications, such as combinedcrude and vacuum distillation units in refineries, multiple firedheaters are required to meet the total hot utility requirement. Insuch applications, it is important to estimate the minimumnumber of fired heaters required to supply the heat demand.Due to the fact that fired heaters are capital-intensive equipment,estimation of the minimum number of fired heaters is importantto estimate the total capital investment.

Linnhoff and de Leur1 had proposed an iterative procedurefor fired heater integration by matching the process grandcomposite curve (GCC) against the linear (in temperature-heatduty diagram) flue gas line. A graphical method for integratinga fired heater has been proposed by Hall and Linnhoff,2 basedon the concept of the utility GCC. The proposed graphicalmethodology avoids the iteration procedure that is otherwiserequired for the integration of a fired heater with air preheating.The procedure essentially minimizes the operating costs. A two-zone model of a fired heater has been proposed by Stehlik etal.3 for the integration of the fired heater system. Algorithmshave been suggested to optimize the air preheat temperatureand the stack temperature by considering the fuel and capitalcosts associated with the convection section only. The optimiza-tion of the air preheating system has been presented for retrofitcases by Jegla et al.4 Varghese and Bandyopadhyay5 haveproposed an analytical procedure, as well as an algorithmic

procedure, for integration of a fired heater with the backgroundprocess. Based on the analytical procedure proposed by Vargh-ese and Bandyopadhyay,5 the fuel requirement and air preheattemperature can be targeted for an integrated fired heater priorto the detailed design of the entire heat recovery network. Thismethodology is briefly discussed in the following section.

In this paper, a methodology is proposed to target theminimum number of fired heaters. Prediction of the performanceand appropriate integration of the fired heaters are necessaryfor the overall optimization of the entire plant. To translatetargets into reality, it is important to develop an appropriatemethodology to design, analyze, and synthesize heat recoverynetworks along with multiple fired heaters. The heat exchangernetwork of the background process may be synthesized usingtools of process integration. It may be essential to have acomplex heat exchanger network to meet the targets of fuelrequirements and appropriate air preheat temperature. Existingnetwork-evolution principles cannot be applied to such networksdirectly, because a fired heater is a connected utility. Perfor-mance of an integrated fired heater is dependent on the totalheat requirement, as well as the availability of process heat forair preheating. Any modification of the heat recovery networkmay influence the performance of an integrated fired heaterthrough hot utility requirements, the pinch temperature, and theprocess heat available for air preheating. Different network-evolution schemes with associated energy penalties are analyzedand discussed in detail. For example, simplified heat exchangernetworks with once-through fired heaters result in an increasein fuel requirements and, hence, a reduction in efficiency.Simplifications during the evolution of networks from a GCC-based structure may result in increasing the duty of fired heaters.However, this may reduce the number of heaters.

2. Fired Heater Targets

In this section, the procedure for targeting and energyintegration of fired heaters is reviewed briefly.5,6 The processGCC is matched against the utility GCC, which consists of fluegas and air preheating, as shown in Figure 1. The two-zonemodel, also known as the stirred reactor model for a fired heater,is used for energy integration of a fired heater.

The stirred reactor model is reported to predict, with asignificant degree of accuracy, the overall heat-transfer perfor-

* To whom correspondence should be addressed. Tel.:+91-22-25767894. Fax: +91-22-25726875. E-mail address: santanu@me.iitb.ac.in.

5631Ind. Eng. Chem. Res.2007,46, 5631-5644

10.1021/ie061619y CCC: $37.00 © 2007 American Chemical SocietyPublished on Web 07/14/2007

mance for a wide range of furnaces burning different fuels andhaving various configurations of the radiation chamber.7 Theradiation chamber is modeled using three elements: a radiatinggas medium at a uniform effective temperatureTeff, a tubesurface that acts as a heat sink at a mean metal temperatureT1,and the radiatively adiabatic refractory surface. Neglectingradiation losses through openings, the net rate of combinedradiation and convective heat transfer from the combustion gasesto the process fluid can be expressed as

where σ is the Stefan-Boltzmann constant,h the overallconvective heat-transfer coefficient between the gas and heatsink (tube bank), andAc the surface area of the tube bank;grepresenting the total transfer factor for radiation from the gasto the heat sink. If a cold fluid enter the radiation chamber atTr;in and leaves atTr;out, the mean tube metal temperature (alsoknown as the skin temperature) may be estimated as 42 K higherthan the mean fluid temperature.8

Defining the average radiation chamber heat flux, based onthe convective heat-transfer area of the heat sink, eq 1 may berearranged as follows:

whereK accounts for the geometric complexities of the radiationchamber, multiple reflections from different surfaces, and re-radiation from the refractory. Depending on the application, theaverage radiation section heat flux is generally specified duringthe design of a fired heater. A high value for the averageradiation chamber heat flux calls for a lesser amount of tubesurface area and, hence, produces a smaller and more-compactheater with lower investment cost. However, the refractory, thetubes, and its supports are exposed to higher temperature,because of the high average radiation chamber heat flux. Itgenerally reduces the service life of the fired heater and increasesthe maintenance cost of the fired heater. Furthermore, itincreases the potential for coke deposition and product degrada-tion.8

Figure 1. Matching the utility GCC against the process GCC to target the appropriate air preheat temperature and the minimum fuel fired for an energy-integrated fired heater.

Figure 2. Flow chart for fired heater integration with air preheating, using process heat and flue gas heat.

Q1 ) gσ(Teff4 - T1

4) + hAc(Teff - T1) (1)

T1 )Tr,in + Tr,out

2+ 42 (2)

q )Q1

Ac)

gσ(Teff4 - T1

4)

Ac+ h(Teff - T1)

) Kσ(Teff4 - T1

4) + h(Teff - T1) (3)

5632 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

Fuel (with lower calorific value ofF) is burned with thepreheated combustion air at a temperatureTa in the combustionchamber. In the combustion chamber, there are several energylosses (setting loss, dissociation loss, etc.). These losses maybe combined as a single loss factor ofR (typically, R is takento be 1%-3%) multiplied by the heat input in the fired heaterthrough the combustion of the fuel. Therefore, the effectivecalorific value of the fuel may be expressed as

The adiabatic flame temperature (TFT) can be determined usingthe overall energy balance of the combustion chamber.

The mass flow rates of the air and flue gas, and thatof the fuel, are related through the stoichiometric air-fuelratio (S) and the fraction of excess air (E) provided for completecombustion of the fuel. Typical excess air requirements are10% for gaseous fuels, 15%-20% for liquid fuels, and 20%or more for pulverized solid fuels. Based on the stoichio-metric air-fuel ratio and the fraction of excess air, theadiabatic flame temperature (eq 4) can be simplified asfollows:

where

and

Imperfect stirring within the radiation chamber results in areduction in the temperature of the flue gas leaving the radiationchamber.7 The bridge wall temperature (Tbw) can be estimatedbased on the mean effective temperature of the radiating gas(Teff), the adiabatic flame temperature (TFT), and the degree ofstirring (d):

The degree of stirring is greater than unity for imperfect stirring;the case of perfect stirring is represented byd ) 1. Numericalvalues of K, h, and d are dependent on numerous designvariables (the type of fired heater, the size and layout ofthe radiant tubes, the composition and type of fuel, theinterception factor of radiation heat transfer to the tubes,the emissivity of different surfaces, etc.). During the energytargeting and conceptual design stage, detailed design para-meters of a fired heater are not defined. Therefore, exactvalues of K, h, and d are not known a priori. However,

approximate values of these parameters have been estimatedfor different operating scenarios.5 These approximate values arereported in Table 1 and are utilized in this paper for energytargeting.

Table 1. Values of Radiation Factor, Convective Heat TransferFactor, and Degree of Stirring for Different Types of Fired Heatersa

Value

description horizontal vertical

radiation factor,K 0.237 0.233convective heat-transfer factor,h 0.0165 0.0263degree of stirring,d 1.03 1.03

a From ref 6.

Feff ) (1 - R)F

TFT )maca(Ta - T0) + mfFeff

cgmg(4)

TFT ) T0 +Ca(Ta - T0) + Feff

Cg(5)

Ca ) cpa S(1 + E) (6)

Cg ) cpg[1 + S(1 + E)] (7)

Tbw ) dTeff - (d - 1)TFT (8)

Figure 3. Representing process stream through fired heater inthe temperature-heat duty diagram: (a) process stream line intersectingthe process GCC, (b) process stream line intersecting the utility GCC, and(c) process stream line contained between the process GCC and the utilityGCC.

Ind. Eng. Chem. Res., Vol. 46, No. 17, 20075633

Heat duties in the radiation and convection sections of thefired heater (Qr andQc, respectively) may be estimated usingthe relationships

and

Therefore, radiation duty, as a fraction of the total heat dutyrequired, can be expressed as

Using the aforementioned model, the heat-transfer performanceof the fired heater may be estimated and utilized during networksynthesis and evolution.

Ambient air is initially heated to an intermediate temperatureTi, using process heat, and then it is further heated to a finaltemperature ofTa, using the flue gas. Flue gas leaves the firedheater convection section after supplying the required heat at atemperatureTgout and leaves to the stack at temperatureTs afterpreheating the combustion air.

Based on the utility pinch at (Hj, Tj), the intermediate airpreheat temperatureTi may be calculated as6

where ∆C ) Cg - Ca, and ∆Tga ) Tgout - Ta. The actualtemperature of the flue gas may be expressed as6

The utility pinch point is not known a priori; therefore,the intermediate air preheat temperature is calculatedfor every vertex on the process GCC. The minimum ofall the calculated temperatures defines the actual utility pinch(HP, TP), as well as the maximum possible intermediateair preheat temperatureTi. From the energy balance of theutility pinch, the final air preheat temperature may be expressedas

Figure 4. Targeting number of fired heaters.

Figure 5. Possible options for satisfying energy targets for processes with single fired heater.

Qr ) Cgmf (TFT - Tbw) (9)

Qc ) Cgmf (Tbw - Tgout) (10)

Qfr )TFT - Tbw

TFT - Tgout(11)

Ti )

HUCg[CgTs - Ca∆Tga] -∆C[Cg(HUTjn + HjTs) - Hj(Feff + T0∆C)

HUCaCg - HjCa∆C(12)

Tjn ) Tj + 0.5∆Tp + ∆Tadl (13)

Ta ) Ti +Cg(Tp,n - Ts)

Ca-

Hp

mfCa(14)

5634 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

It may be noted that, as the process pinch temperature increases,the intermediate air preheat temperature decreases and therebyincreases the fuel requirement (or decreases the fired heaterefficiency).

The maximum possible intermediate temperature may not berealizable if there is an additional utility pinch formed belowthe process pinch. This may happen in two possible ways, asshown in Figure 1. First, there may be a temperature violationdue to intersection of the process GCC and the utility GCC.Second, there may not be enough process heat available topreheat the combustion air to its maximum possible intermediatetemperature.

In case the air preheating using the process heat below thepinch is limited by a utility pinch at the point (Hk, Tk), theintermediate temperature is revised fromTi to Tit. The revisedheat balance of air preheater gives6

whereTkn is the actual temperature of the air:

Thus, the intermediate temperature can be expressed as

The minimum among all the calculated intermediate tempera-turesTit andTi is chosen as the revised intermediated temper-atureTit. In the special case of no formation of any utility pinch,Tit will be equal toTi.

Similarly, if there is a restriction on the availability of processheat for heating the combustion air, the intermediate temperaturemust be further revised. For restricted process heat availabilitybelow the pinch, the intermediate temperature is calculated usingthe following relation:6

The maximum among all the calculated intermediated temper-atures is denoted asTih. The minimum ofTit andTih determinesthe final revised intermediate temperatureTi up to whichcombustion air may be preheated using process heat below thepinch. If the revised intermediate temperature, up to whichcombustion air may be preheated, is below the ambienttemperature, the ambient temperature is taken as the intermediatetemperature (no process heating possible).

Combining the energy balance for the air preheater, theprocess hot utility requirement, and the expression for theadiabatic flame temperature, the mass flow rate of the fuelrequired to meet the process heat duty (HU) can be expressedas

The flow chart for the energy integration of a fired heaterwith the background process is shown in Figure 2. Note thatthe amount of fuel fired is dependent on the excess air and thelimiting stack temperature, and it is independent of the airpreheat temperature. The limiting stack temperature is governedby the acid dew point of the flue gas. Based on the sulfur contentof the fuel, the limiting stack temperature is usually fixed atthe design stage. Similarly, the amount of excess air requiredfor complete combustion is also fixed at the design stage(depending on the combustion characteristic of the fuel).However, a lowest possible excess air and stack temperatureare recommended to reduce the fuel requirement, and, hence,to increase the efficiency of the fired heater. The fired heaterefficiency is defined as the ratio of the useful thermal energysupplied to meet the hot utility requirement of the process tothe input energy of the fuel fired:

3. Targeting Number of Fired Heaters

During synthesis of the heat recovery network involving firedheaters, it is important to translate the target set based on theGCC profile matching to an achievable reality. To control theterminal temperature (or coil outlet temperature from the firedheater) of a process stream, fuel fired in the heater can be varied.As there is only one manipulated variable, there can only beone control variable. Therefore, every fired heater can have onlyone process stream in the radiation section. The terminaltemperature of this stream can be controlled by controlling fuelfired in the radiation section. It may be noted that this does notimply that the convection section of a fired heater must haveonly one cold stream. Typically, it is preferred to have onlyone process stream in the convection section. In case of an oil-fired unit, steam may be produced in the convection sectionfor atomization. This does not affect the performance of thefired heater significantly, because the atomizing steam require-ment is proportional to the fuel that is fired. However, forsimplicity, it is assumed that only one process stream can beheated in a fired heater. Based on this assumption, it is possibleto target the minimum number of fired heaters required.

The cold process stream, which exchanges heat with the firedheater, can also be represented on a temperature-heat dutydiagram. As the heat capacity (Mc) flow rate is generally

Figure 6. For utility pinch, above the process pinch, the heat capacity ofthe portion of the cold stream passes through the fired heater becomesunique.

Table 2. Process Stream Data for Example 1

streamheat capacity,Mc (kW/K) Tin (K) Tout (K)

H1 4 600 350H2 4 450 300C3 4 300 700C4 2 350 450

Hk ) mfCa(Tit - Tkn) (15)

Tkn ) Tk - 0.5∆Tp - ∆Tadl (16)

Tit )Hk[Feff - Cg(Ts - T0) - CaT0] + HUCaTkn

Ca(HU - Hk)(17)

Tih )QhuCaT0 + Hk(Feff - Cg(Ts - T0) - CaT0)

Ca(HU - Hk)(18)

mf ) HUFeff - Cg(Ts - T0) + Ca(Ti - T0)

(19)

η ) HUF × mf

(20)

Ind. Eng. Chem. Res., Vol. 46, No. 17, 20075635

assumed to be constant for a process stream, it is representedby a straight line on the temperature-heat duty diagram. It maybe noted that the temperature in the temperature-heat dutydiagram is shifted according to the minimum approach tem-perature difference. For any cold process stream, the stream linetypically starts from its target temperature and then it continuesup to its supply temperature. In the case of multiple fired heaters,streams passing through different fired heaters may be combinedto represent a composite stream line on the temperature-heatduty diagram. There are three cases to consider: the streamline cuts the process GCC, the stream line cuts the utility GCC,and the stream line is contained in the space between the processGCC and the utility GCC.

Case (i): The Process Stream Line Intersects the ProcessGCC. As the stream line intersects the process GCC (Figure3a), it has two consequences: an increase in the hot utilityrequirement and a shift of the pinch location. Because the streamdoes not have enough heat capacity (Mc), the total heatrequirement at the required temperature cannot be met. Themaximum distance between the process GCC and the streamline signifies the additional hot utility requirement (∆HU). Thepinch point shifts to a location in the process GCC thatdetermines the additional hot utility requirement (see Figure 3a).This leads to an increase in utility demand and, consequently,a reduction in fired heater efficiency, because of the increasein pinch temperature. Therefore, this is not a desirable option.

To eliminate the energy penalty, multiple streams should bechosen such that the combined composite line should be entirelyabove the process GCC.

Case (ii): The Process Stream Line Intersects the UtilityGCC. In the case where the stream line or the stream compositeline intersects the utility GCC (see Figure 3b), the targetedprocess heat requirement can be satisfied. In this case, theoriginal utility GCC must be modified to avoid a temperatureviolation. The intersection of the stream line with the temper-ature axis defines a utility pinch point (see Figure 3b). Thisresults in a decrease in the efficiency of the fired heater. Firedheater targets must be revised, with respect to the new utilitypinch formed by the composite stream line.

Case (iii): The Process Stream Line is Contained betweenthe Utility GCC and the Process GCC.If the stream line orthe stream composite line is contained between the utility GCCand the process GCC (see Figure 3c), the overall energy targetcan be satisfied. However, this may result in a complex networkthat involves multiple entries of the process stream into the firedheater.

Based on the aforementioned observation, it is possible totarget the minimum number of fired heaters required.

3.1. Algorithm for Targeting the Minimum Number ofFired Heaters. Previous discussion helps in setting the targetfor the minimum number of fired heaters required to satisfythe minimum hot utility requirement. It may be concluded thatthe stream line or the composite stream line should not intersectthe process GCC. The minimum number of process streamsrequired to produce a composite line that intersects the tem-perature axis at or above the process pinch and does notintersects the process GCC, represents the minimum numberof fired heaters required. A simple procedure is suggested totarget the minimum number of fired heater requirement. Theproposed procedure may be stated as follows:

(1) Start from the highest temperature terminal point of theprocess GCC. This ensures that the total heat requirement canbe satisfied.

(2) Among all the cold process streams that are present atthe terminal point, choose one with the maximum heat capacityflow rate (Mc). Because the slope of a line on a temperatureheat duty diagram is inversely proportional to the Mc of thestream, the resultant stream line will have the lowest possible

Figure 7. Process GCC and targeting number of fired heaters for Example 1.

Figure 8. Possible range of heat capacity for the fraction of the cold streamentering the fired heater in Example 1.

5636 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

slope. This enhances the possibility that the stream line maylie above the process GCC.

(3) Draw the stream line on the temperature-heat dutydiagram.

(4) Check whether the stream line intersects with the processGCC above the process pinch.

(5) If the process stream line intersects the process GCC, thenthis stream alone cannot be considered. As discussed previously,this implies an energy penalty and shifting of the pinch location.In such a case, choose another cold stream with a maximumMc from a set of cold streams whose terminal temperature isabove the intersection point.

(6) Draw the composite stream line and check whether itintersects the process GCC.

(7) Repeat this procedure until a composite stream line isidentified that does not intersect the process GCC and intersectsthe temperature axis at or above the process pinch.

(8) The number of cold streams required to produce such acomposite stream line represents the minimum number of firedheaters required.

The aforementioned procedure ensures that the compositestream line should be able to absorb the total heat requirementof the process. The procedure for targeting the minimum numberof fired heaters is illustrated in Figure 4. In Figure 4, three

different cases are illustrated graphically: single fired heater issufficient, single fired heat is not sufficient as the supplytemperature of the cold stream is higher than the pinchtemperature, and single fired heat is not sufficient as the steamline intersects the process GCC. In Figure 4, case (i) demon-strates the targeting procedure for a process requiring only onefired heater. In this case, the stream present at the GCC terminalpoint is capable of receiving the total hot utility requirement.Case (ii) shows that more than one fired heater is required asthe largest heat capacity cold stream present at the terminal pointis not starting from the pinch, but at a temperature above pinchand it cannot absorb the entire heat requirement of the process.The cold stream with next-largest heat capacity is added to thefirst segment. The procedure is complete as the second streamintersects the temperature axis. Thus, two fired heaters arerequired to supply the total heat requirement. Case (iii)represents a case that requires more than one fired heater. As

Figure 9. Possible heat recovery network for Example 1; the heat capacity of the fraction of the cold stream entering the fired heater convection sectionis 0.4 kW/K.

Figure 10. Possible options for satisfying energy targets for processes with multiple fired heaters.

Table 3. Process Stream Data for Example 2

streamheat capacity,Mc (kW/K) Tin (K) Tout (K)

H1 12 650 350H2 4 550 300C3 10 450 620C4 8 300 700

Ind. Eng. Chem. Res., Vol. 46, No. 17, 20075637

the first stream intersects the GCC, the next-largest heat capacitystream is added at that point to complete the procedure. Thus,in this case, also two fired heaters are required to supply thetotal heat requirement.

4. Network Synthesis with a Single Fired Heater

When the stream line for a single cold stream passes abovethe process GCC and the stream is present at the process pinch,only one fired heater is sufficient to satisfy the required heatduty. It is possible to have a simplified once-through conditionfor the fired heater. In the once-through case, the process streamenters the fired heater convection section and leaves the firedheater radiation section at the required temperature. This ispreferred in industry, because of the simplicity and control-lability of the associated heat exchanger network. If the streamline intersects the utility GCC and causes a utility pinch abovethe process pinch, the efficiency of the fired heater reduces.However, the increased fuel consumption in the fired heaterincreases the temperature difference between the process streamand the flue gas in the convection section. This may result in areduced capital investment for the fired heater. This implies thatcapital-energy tradeoffs are required to choose between differentnetwork schemes. In Figure 5, it has been illustrated that theprocess stream line meets the temperature axis and it forms autility pinch. For such a case, the fired heater targets must bereset accordingly.

To meet the energy target, the stream line should be suchthat it is confined entirely between the process GCC and theutility GCC and intersects both of them at the process pinch.This calls for reduced mass flow rate for the process stream atthe fired heater entry. Therefore, the process stream is split intotwo components: one portion of the stream enters the firedheater (see Figure 5), and the other portion of the cold processstream exchanges heat with hot process streams and re-entersthe fired heater after completing the required process-to-processheat recovery. However, there are limits on the heat capacityof the split portion that enters the fired heater. The maximumheat capacity flow rate (Mcmax) is dependent on the processGCC, whereas its minimum value (Mcmin) is dependent on theutility GCC. As long as the heat capacity flow rate of the fractionof the cold process stream that enters the fired heater is withinthe minimum and the maximum range, the energy target canbe satisfied (see Figure 5). It may be noted that the change inthe heat capacity of the split portion affects the mixingtemperatureTmix. If there is a utility pinch between the utilityGCC and the process GCC above the process pinch, as

illustrated in Figure 6, the cold stream should also pass throughthe utility pinch point. In such a case, the heat capacity flowrate of the split portion of the cold stream becomes unique. Atthe utility pinch point, the heat capacity of the cold stream couldbe obtained as

If there is no cold stream that meets this requirement, one ofthe cold streams may be split to put in the fired heater.

Example 1.Applicability of the proposed methodology isillustrated through the following example. Process stream datafor this example are given in Table 2. The fuel used has a netheating value of 41 000 kJ/kg. The stoichiometric air fuel ratiois 15, and the minimum excess air recommended is 10% forcomplete combustion. The ambient temperature is assumed tobe 300 K. The average specific heats of air and flue gas areassumed to be 1.005 and 1.148 kJ/(kg K), respectively. Thelimiting temperature corresponds to the sulfur dew point of theflue gas is assumed to be 433 K. A minimum approachtemperature difference of 30 K is specified for process-to-process heat recovery heat exchangers. An additional temper-ature potential (∆Tadl) of 20 K between the flue gas and thecold process stream is included. This implies that the minimumapproach temperature between the cold process stream and theflue gas is 50 K. The temperature potential between the preheatair and the flue gas outlet is fixed at 70 K.

The hot utility requirement of 580 kW, corresponding to a∆Tp of 30 K, is obtained from the problem table algorithm.The pinch corresponds to 450 K on the hot side and 420 K onthe cold side. The inlet temperature of the hot process streamH2 holds the pinch. Process GCC for this example is shown inFigure 7. It may be concluded that a single fired heater issufficient for this example. Different possible options forintegrating the fired heater are highlighted in Figure 8. The rangeof heat capacity of the split stream through fired heater isdetermined to be between 0.31 (corresponds to the heat capacityof the flue gas) and 0.4 (obtained from the process GCC), asshown in Figure 8. A heat recovery network with a heat capacityof the split stream of 0.4 is shown in Figure 9. Along with theheat recovery network, the mean effective temperature, bridge-wall temperature, and the radiation duty fraction are alsohighlighted in Figure 9. The mixing temperature after processheat recovery is 570 K, with the initial split of Mc) 0.4receiving 60 kW of heat from the fired heater and the combinedstream receiving the remaining 520 kW from the fired heater.If the heat capacity of the split fraction is changed to 0.31, themixing temperature decreases to 566.34 K and the heat receivedby the split fraction in fired heater is reduced to 45.37 kW (notshown for brevity). The combined stream receives the remaining534.63 kW heat from the fired heater. Note that both of thesenetworks have the same heater efficiency and heat loads.However, the heat capacities of the cold process stream enteringthe fired heater are different. If the entry stream heat capacityis increased to 4 (no stream split for process heat recovery), itwill result in a once-through case. In this case, the process streamenters the fired heater at 555 K and leaves at 700 K. However,the efficiency of the fired heater was reduced, from 93.7% to92.5%. It may be noted that the efficiency of the fired heaterhas increased because of utilization of the process heat belowthe process pinch for preheating the combustion air.

The heat capacity of the split fraction influences the exittemperature of the fraction from the fired heater and through

Figure 11. Selected few possible options of distributions of duties amongtwo fired heaters in Example 2.

Mc ) Ti +[Cg(Tjn - Ts) - Ta]mfCa

Tjn - Tp(21)

5638 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

the process heater. Thus, it influences the heat-transfer arearequirement of the fired heater convection section and theprocess-to-process heat recovery heat exchangers involved withthese fractions. It may be noted that it is possible to optimizethe split fraction, considering the capital investment for the entireheat recovery network.

5. Network Synthesis with Multiple Fired Heaters

Issues related to synthesizing heat recovery networks thatinvolve multiple fired heaters are discussed in this section. Ifcold process streams that require fired heaters are present atthe process pinch, the duties of individual fired heaters can bevaried. However, the total duty of fired heaters remains constant.This is illustrated in Figure 10 with multiple fired heatersrequired to meet the total duty. The sum of the heat capacitiesentering fired heaters may be determined using the proceduredescribed in the previous section. The minimum of the combinedheat capacity is determined by the combined flue gas heatcapacity, and the maximum of the combined heat capacity isfound from the process GCC limit. To achieve the maximumefficiency for all fired heaters, streams should enter the firedheaters at the pinch temperature and the combined heat capacityshould be limited within the identified range.

Streams combine after completing the process-to-process heatrecovery at the mixed temperature (Tmix) and re-enter the firedheater to complete the heat requirement. Consider a case wheretwo fired heaters are required to meet the total hot utilityrequirement of HU. The cold streams are both present at thepinch, and they are split into Mc1,in and Mc2,in fractions passingthrough the fired heater. The combined heat capacities Mc1,in

and Mc2,in are supposed to be between the minimum and themaximum. The sum of the duties of the fired heaters must matchthe total hot utility requirement targeted. Referring to Figure10, consider that fired heater 1 supplies heat to stream C3 with

heat capacity Mc1 and fired heater 2 supplies heat to C4 withheat capacity Mc2. At the pinch, the Mc1,in fraction of C3 entersfired heater 1 and the Mc2,in fraction of C4 enters fired heater2. The remaining portions of the cold streams, after completingthe process-to-process heat recovery, combine with the corre-sponding fractions that received part of the heat from therespective fired heaters. Heat that is transferred by the firedheaters, at the mixing temperatureTmix can be obtained as

However, it may be noted that the combined Mc1,in + Mc2,in

can be met by different combinations of the individual heatcapacities Mc1,in and Mc2,in. The combined heat capacity Mc1,in

+ Mc2,in is limited within the minimum and maximum valuespreviously identified. This range of heat capacities of thefractions Mc1,in and Mc2,in results in a permissible individualfired heater heat duty range, as is evident from eq 22. This givesflexibility to the design of the heat recovery network, alongwith the fired heaters. Economic considerations can be usedfurther to optimize the duty split between different fired heaters.

For a chosen combination of combined Mc1,in + Mc2,in, theindividual entry values of Mc1,in and Mc2,in themselves possessa possible minimum and maximum range. The heat capacityMc1,in is limited to a minimum for a chosen total Mc1,in + Mc2,in,as given by

where HU1 is the heat supplied to stream 1 betweenTmix andits terminal temperature. The minimum heat capacity limitMc2,in,min could be obtained in a similar method by replacingHU2 in the aforementioned equation. The maximum limit forMc1,in is the difference of the maximum of the combined heat

Figure 12. Heat recovery network for Example 2.

HUmix ) (Mc1,in + Mc2,in)(Tmix - Tp) (22)

Mc1,in,min)HU1

TFT - (Tmix + ∆T)(23)

Ind. Eng. Chem. Res., Vol. 46, No. 17, 20075639

capacity (Mc1,in + Mc2,in) determined previously and theminimum heat capacity limit for Mc2,in,min. The upper limit ofMc2,in could also be calculated in a similar manner. Thus, theindividual limits of the heat capacities for a sum of Mc1,in +Mc2,in could be determined using the aforementioned expres-sions.

However, during network synthesis, certain fired heaters canbe simplified to once-through cases with the appropriate choiceof different heat capacities. The fired heater targets must berevised, based on the procedure described previously. For thecold process stream with an entry temperature higher than theprocess pinch temperature, the fired heater parameters must bere-targeted, corresponding to the shifted utility pinch locationfor this stream. As the pinch temperature increases, it is notpossible to satisfy the original target established using theprocess GCC.

Example 2.Example 2 has been considered to illustrate theflexibility of designing heat recovery networks with multiplefired heaters. Process stream data for example 2 are providedin Table 3. The pinch is located at 450 and 500 K, correspondingto a minimum approach temperature of 50 K (∆Tmin). The hotutility requirement is determined to be 1700 kW, with the coldutility requirement of 1400 kW. It is observed that a single firedheater is not sufficient to supply the entire hot utility require-ment. The largest Mc of 8 kW/K line present at the terminalpoint is found to intersect the process GCC and therefore,another stream is added to make certain that the compositestream line does not intersect the process GCC. Thus, for thisexample, two fired heaters are required to supply the total hotutility requirement of 1700 kW. Three different options forsupplying the required total hot utility requirement are illustratedin Figure 11. The minimum Mc value for the combined fractionsof the cold streams to be admitted to the fired heaters is 0.9kW/K, and the maximum possible value is 2 kW/K. Thus, thesum of the heat capacities of the fractions (Mc1,in and Mc2,in) atthe entry points of the fired heaters must be within these limits.

One of the permissible heat recovery networks for example2 is shown in Figure 12. Mean effective temperatures, bridge-wall temperatures, and radiation duty fractions for both of thefired heaters are also shown in Figure 12. The values of Mc1,in

and Mc2,in are chosen to be 0.3 kW/K and 0.6 kW/K,respectively, with a corresponding mixing temperature of 566.95K. The fired heater duties are 565.5 kW and 1134.5 kW,respectively. This network could be simplified with one of thefired heaters modified to be a once-through heater.

If the heat capacities of the cold stream fractions at the entryare changed to Mc1,in ) 0.8 kW/K and Mc2,in ) 1.2 kW/K, themixing temperature changes to 575 K. The duties for the firedheaters would be changed to 600 and 1100 kW, respectively.The network structure remains the same, while the duties ofthe fired heater get modified. This range of duty gives flexibilityto the designer during the network synthesis and evolution.Similarly, by changing the heat capacity of the cold streamfractions, different heat recovery networks may be generated.

Table 4 summarizes a comparison of some of the differentpossible heat recovery networks.

Example 3: Naphtha Reformer Example.The followingexample illustrates the importance of targeting the number offired heaters during heat recovery network synthesis. Theprocess data for this naphtha reformer example are given inTable 5.9 The flow sheet in Figure 13 shows that three firedheaters are used in the original problem to meet the total heatrequirement of 54.0 kW, corresponding to a minimum approachtemperature of 10 K. Existing heat recovery network of theproblem is shown in Figure 14. The individual duties of fired

Table 4. Comparison of Different Network Options for Example 2

Network Duty (kW) Efficiency (%)

Mc1,in

(kW/kg)Mc2,in

(kW/kg)fired heater

1fired heater

2fired heater

1fired heater

2total fuel

(kg/s)% fuelchange remarks

0.3 0.6 565.5 1134.5 94.3 94.3 0.04398 meets targets10 0.6 565.5 1134.5 93.3 94.3 0.04413 0.34 one once through0.3 8 565.5 1134.5 94.3 93.34 0.04427 0.66 one once through

10 8 588.9 1111.1 93.32 93.32 0.0444 0.95 both once through1.2 0.8 600 1100 94.3 94.3 0.04398 meets targets

Table 5. Stream Data for Example 3

Temperature Enthalpy

supplytemperature (K)

targettemperature (K)

temperature(K)

enthalpy(kW)

Stream 1375 600 375 0

502 16.2600 25.8

Stream 2600 323 600 31.5

447 15.34365 4.9323 0

Stream 3308 437 308 0

437 10.5

Stream 4413 773 413 0

449 8.4640 37.7773 56.7

Stream 5768 580 768 29.3

580 0

Stream 6493 332 493 30.5

433 22.1417 18.3398 13.5332 0

Stream 7353 396 353 0

396 3.8

Stream 8332 442 332 0

442 7.9

Stream 9495 340 495 12.3

403 4.4340 0

Stream 10358 398 358 0

398 4.8

Stream 11753 773 753 0

773 37.8

5640 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

heaters are 3.72, 12.55, and 37.77 kW, respectively. The pinchis held by stream 4 at 413 K. All the existing fired heaters areonce-through types.

To determine the minimum number of fired heaters requiredto meet the hot utility requirement of 54.0 kW, the proposedprocedure is applied on the process GCC, as shown in Figure

Figure 13. Simplified process flow diagram of the naphtha reformer example.

Figure 14. Existing heat recovery network for the naphtha reformer example.

Ind. Eng. Chem. Res., Vol. 46, No. 17, 20075641

15. The stream with the largest Mc value (1.88 kW/K) isobserved to intersect the process GCC. Hence, the next-largeststream, with Mc) 0.143 kW/K, is added to it. The resultantcomposite stream line does not intersect the process GCC, andit is able to absorb the total heat duty requirement. Theindividual duties of the fired heaters are determined to be 37.77and 16.29 kW, respectively. The fired heater with a duty of37.77 kW supplies heat to cold stream 11, which is not presentat the process pinch (this stream starts from 753 K). This firedheater thus fails to meet the target obtained using the process

GCC. The revised heat recovery network with two fired heatersis shown in Figure 16. Fuel, air, and flue gas properties areassumed to be the same as those used for Example 1. Ambientair is assumed to be at a temperature of 303 K. The efficiencyof the fired heater is calculated to be 92.7% for the stream withMc ) 1.88 kW/K and 93.5% for the stream with Mc) 0.1433kW/K. A possible heat recovery network is synthesized byconsidering the problem as a grassroots problem, and thenetwork is shown in Figure 17. The results of different heatrecovery networks are compared in Table 6. The integration

Figure 15. Targeting number of fired heaters for the naphtha reformer example.

Figure 16. Revised heat recovery network with two fired heaters for the naphtha reformer example.

5642 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

results shows that only two fired heaters were required to supplythe required total heat duty. Also, the efficiency of the firedheater could be improved by 0.6% from the base case.

6. Conclusions

The procedure for energy-integration of a fired heater withthe process grand composite curve (GCC) provides the fuel andair preheat targets prior to the detailed design of the equipment.For processes with multiple fired heaters, it is important toestimate the minimum number of fired heaters required to supplythe total heat demand of the process. It has been observed thatthe composite stream line of the cold process streams receivingheat in the fired heaters, when represented in the temperature-heat duty diagram, must lie above the process GCC andintersects the temperature axis at or above the process pinch.Based on this observation, a procedure has been proposed totarget the minimum number of fired heaters required to meetthe heat duty prior to the synthesis of the heat recovery network.

The importance of targeting the number of fired heaters hasbeen illustrated through examples.

In cases where all streams are present at the process pinch,it is possible to meet the minimum energy targets by makingsome appropriate changes in the network design. On the otherhand, if all the streams are not present at the process pinch, theminimum fuel target cannot be satisfied and new fuel targetsmust be re-estimated. For a feasible heat recovery network, thestream segment passing through the fired heater must becontained within the utility GCC and the process GCC. Theentry conditions of the cold streams to the fired heaterconvection section should be within a certain range, as dictatedby the flue gas heat capacity and the process GCC. Also, thecold process stream should enter the fired heater at the processpinch conditions, to satisfy the fuel target established based onthe process GCC. The mass fraction of the cold stream enteringthe fired heater may be varied within a range. Variation in theflow rate (and, equivalently, the heat capacity) of the fractionentering the fired heater affects the capital cost of the fired heater

Figure 17. Heat recovery network for the naphtha reformer example, based on grassroots design.

Table 6. Comparison of Integration Results for Example 3

parameter existing (Figure 14) revised (Figure 16) grass root design (Figure 17)

total heat duty (kW) 54 54 54number of fired heaters 3 2 2fired heater duties (kW) 37.77, 12.55, 3.72 37.77, 16.3 37.77, 16.3total fuel (kg/s) 1.42× 10-3 1.419× 10-3 1.411× 10-3

% fuel change with existing 0.1 0.63fired heater efficiencies (%) 92.7, 93.3, 94.3 92.7, 93.5 92.7, 95.3

Ind. Eng. Chem. Res., Vol. 46, No. 17, 20075643

convection section and the process-to-process heat exchangersinvolved with the cold process stream. It may be possible toperform a cost optimization to determine the optimum valuefor the fraction.

Design and synthesis of the heat recovery network withmultiple fired heaters can be addressed by utilizing the proposedmethodology. Conventional techniques of network evolutioncannot be applied directly to heat recovery networks with firedheaters. The optimal performance of an energy-integrated firedheater is dependent on both the above-pinch heat requirementand the below-pinch heat available. Optimum performance ofan energy-integrated fired heater is dependent on the processheat recovered below the process pinch through preheating thecombustion air and the heat requirement above the processpinch. In this sense, a fired heater is a connected utility. Toaddress and evaluate different network evolutions, the proposedmethodology can be applied. The same has been demonstratedthrough an illustrative example.

Nomenclature

A ) heat-transfer area [m2]C ) heat capacity per unit of fuel flow [kJ K-1 kg-1 (fuel)]c ) specific heat at constant pressure [kJ kg-1 K-1]d ) degree of stirringE ) excess air fractionF ) lower calorific value [kJ/kg]g ) overall radiation transfer factor from gas to sinkGCC ) grand composite curveh ) heat-transfer coefficient [kWm-2K-1]H ) enthalpy [kJ]HU ) heat duty [kJ]K ) overall radiation coefficientm ) mass flow rate [kg/s]Mc ) heat capacity [kW/K]Q ) heat [kW]q ) heat flux [kW/m2]S ) stoichiometric air:fuel ratioT ) temperature [K]

Greek Symbols

R ) setting loss fraction in the radiation chamber∆ ) differenceσ ) Stefan-Boltzmann constant;σ ) 5.67× 10-11 kW m-2

K-4

η ) efficiency

Subscripts

0 ) ambient1 ) heat sinka ) air

adl ) additionalbw ) bridge wallc ) convectioneff ) effectivef ) fuelfr ) radiation fractionFT ) adiabatic flame conditiong ) flue gasgout ) condition of gas after the convection sectioni ) intermediateih ) intermediate based on enthalpy limitationin ) inletit ) intermediate based on temperature limitationj ) temperature interval above pinchk ) temperature interval below pinchmax ) maximummin ) minimumn ) transformedout ) outletp ) pinchr ) radiations ) stack

Literature Cited

(1) Linnhoff, B.; de Leur, J. Appropriate placement of furnaces in theintegrated process. InUnderstanding Process Integration II; IChemESymposium Series, No. 109 (EFCE Publication 65); Institution of ChemicalEngineers: Washington, DC, 1988; p 1.

(2) Hall, S. G.; Linnhoff, B. Targeting for furnace systems using pinchanalysis.Ind. Eng. Chem. Res.1994, 33, 3187.

(3) Stehlik, P.; Zagermann, S.; Gangler, T. Furnace integration intoprocesses justified by detailed calculation using a simple mathematicalmodel.Chem. Eng. Process.1995, 34, 9.

(4) Jegla, Z.; Stehlik, P.; Kohoutek, J. Furnace integration in to processbased on pinch analysis. InProceedings of the 13th International Congressof Chemical and Process Engineering(CHISA’98), Prague, 1998; p 245.

(5) Varghese, J.; Bandyopadhyay, S. Energy integration of fired heater.In Proceedings of the International Mechanical Engineering Conference(IMEC2004), Kuwait, 2004; Book 2, 30.

(6) Varghese, J. Energy Integration of Fired Heaters, Ph.D. Thesis, IndianInstitute of Technology, Bombay, India, 2006.

(7) Truelove, J. S. Furnaces and combustion chambers. InHeatExchanger Design Handbook; Hewitt, G. F., Ed.; Begell House: New York,2002.

(8) Berman, H. L. Fired heaterssIII: How combustion conditionsinfluence design and operation.Chem. Eng.1978, (August), 129.

(9) Linnhoff, B.; Townsend, D. W.; Boland, D.; Hewitt, G. F.; Thomas,B. E. A.; Guy, A. R.; Marsland, R. H.User Guide on Process Integrationfor the Efficient Use of Energy, Institution of Chemical Engineers(IChemE): Rugby, Warwickshire, U.K., 1982.

ReceiVed for reView December 16, 2006ReVised manuscript receiVed May 15, 2007

AcceptedMay 31, 2007

IE061619Y

5644 Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007