Targeting for Energy Integration of Multiple Fired ... - ACS Publications

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

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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 the air preheat temperature prior to its detailed design. Existing integration procedures are applicable only for processes with a single fired heater. However, in certain processes, multiple fired heaters are required to satisfy the total hot utility demand. In this paper, a methodology is proposed to target the minimum number of fired heaters. To synthesize an energy integrated heat recovery network that incorporates a single fired heater, a cold stream should enter the fired heater at the pinch temperature, and the heat capacity of the cold stream should be within a permissible range. For processes with multiple fired heaters, the duties of different fired heaters may be varied to simplify the design of the overall heat exchanger network. Entry conditions for cold process streams to the fired heaters are also established, to satisfy the overall energy target. In certain cases, the fuel requirement and air preheat temperature for every fired heater may have to be re-estimated to set achievable targets. 1. Introduction Energy requirements and capital investment are two important factors that affect the conceptual design of a process. Techniques of process integration, such as pinch analysis, help in targeting energy and capital requirements prior to the detailed design of process equipments and associated heat recovery networks. Fired heaters supply heat that is required by cold process streams at elevated temperature. Fired heaters are process equipment that is both capital- and energy-intensive. Primary objective of this paper is to develop an energy integration procedure, based on the principles of process integration, for integrating fired heaters with the background process. Process furnaces, which are also known as fired heaters, supply heat to cold process streams at elevated temperature directly by burning fuel. In many applications, such as combined crude and vacuum distillation units in refineries, multiple fired heaters are required to meet the total hot utility requirement. In such applications, it is important to estimate the minimum number 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 important to estimate the total capital investment. Linnhoff and de Leur1 had proposed an iterative procedure for fired heater integration by matching the process grand composite curve (GCC) against the linear (in temperature-heat duty diagram) flue gas line. A graphical method for integrating a fired heater has been proposed by Hall and Linnhoff,2 based on the concept of the utility GCC. The proposed graphical methodology avoids the iteration procedure that is otherwise required for the integration of a fired heater with air preheating. The procedure essentially minimizes the operating costs. A twozone model of a fired heater has been proposed by Stehlik et al.3 for the integration of the fired heater system. Algorithms have been suggested to optimize the air preheat temperature and the stack temperature by considering the fuel and capital costs associated with the convection section only. The optimization of the air preheating system has been presented for retrofit cases by Jegla et al.4 Varghese and Bandyopadhyay5 have proposed an analytical procedure, as well as an algorithmic * To whom correspondence should be addressed. Tel.: +91-2225767894. Fax: +91-22-25726875. E-mail address: santanu@ me.iitb.ac.in.

procedure, for integration of a fired heater with the background process. Based on the analytical procedure proposed by Varghese and Bandyopadhyay,5 the fuel requirement and air preheat temperature can be targeted for an integrated fired heater prior to the detailed design of the entire heat recovery network. This methodology is briefly discussed in the following section. In this paper, a methodology is proposed to target the minimum number of fired heaters. Prediction of the performance and appropriate integration of the fired heaters are necessary for the overall optimization of the entire plant. To translate targets into reality, it is important to develop an appropriate methodology to design, analyze, and synthesize heat recovery networks along with multiple fired heaters. The heat exchanger network of the background process may be synthesized using tools of process integration. It may be essential to have a complex heat exchanger network to meet the targets of fuel requirements and appropriate air preheat temperature. Existing network-evolution principles cannot be applied to such networks directly, because a fired heater is a connected utility. Performance of an integrated fired heater is dependent on the total heat requirement, as well as the availability of process heat for air preheating. Any modification of the heat recovery network may influence the performance of an integrated fired heater through hot utility requirements, the pinch temperature, and the process heat available for air preheating. Different networkevolution schemes with associated energy penalties are analyzed and discussed in detail. For example, simplified heat exchanger networks with once-through fired heaters result in an increase in fuel requirements and, hence, a reduction in efficiency. Simplifications during the evolution of networks from a GCCbased 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 energy integration of fired heaters is reviewed briefly.5,6 The process GCC is matched against the utility GCC, which consists of flue gas and air preheating, as shown in Figure 1. The two-zone model, 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 a significant degree of accuracy, the overall heat-transfer perfor-

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

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

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

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

mance for a wide range of furnaces burning different fuels and having various configurations of the radiation chamber.7 The radiation chamber is modeled using three elements: a radiating gas medium at a uniform effective temperature Teff, a tube surface that acts as a heat sink at a mean metal temperature T1, and the radiatively adiabatic refractory surface. Neglecting radiation losses through openings, the net rate of combined radiation and convective heat transfer from the combustion gases to the process fluid can be expressed as

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

Q1 ) gσ(Teff4 - T14) + hAc(Teff - T1)

where K accounts for the geometric complexities of the radiation chamber, multiple reflections from different surfaces, and reradiation from the refractory. Depending on the application, the average radiation section heat flux is generally specified during the design of a fired heater. A high value for the average radiation chamber heat flux calls for a lesser amount of tube surface area and, hence, produces a smaller and more-compact heater with lower investment cost. However, the refractory, the tubes, and its supports are exposed to higher temperature, because of the high average radiation chamber heat flux. It generally reduces the service life of the fired heater and increases the maintenance cost of the fired heater. Furthermore, it increases the potential for coke deposition and product degradation.8

(1)

where σ is the Stefan-Boltzmann constant, h the overall convective heat-transfer coefficient between the gas and heat sink (tube bank), and Ac the surface area of the tube bank; g representing the total transfer factor for radiation from the gas to the heat sink. If a cold fluid enter the radiation chamber at Tr;in and leaves at Tr;out, the mean tube metal temperature (also known as the skin temperature) may be estimated as 42 K higher than the mean fluid temperature.8

T1 )

Tr,in + Tr,out + 42 2

(2)

q)

Q1 gσ(Teff4 - T14) ) + h(Teff - T1) Ac Ac ) Kσ(Teff4 - T14) + h(Teff - T1)

(3)

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5633 Table 1. Values of Radiation Factor, Convective Heat Transfer Factor, and Degree of Stirring for Different Types of Fired Heatersa Value description radiation factor, K convective heat-transfer factor, h degree of stirring, d a

horizontal

vertical

0.237 0.0165 1.03

0.233 0.0263 1.03

From ref 6.

Fuel (with lower calorific value of F) is burned with the preheated combustion air at a temperature Ta in the combustion chamber. In the combustion chamber, there are several energy losses (setting loss, dissociation loss, etc.). These losses may be combined as a single loss factor of R (typically, R is taken to be 1%-3%) multiplied by the heat input in the fired heater through the combustion of the fuel. Therefore, the effective calorific value of the fuel may be expressed as

Feff ) (1 - R)F The adiabatic flame temperature (TFT) can be determined using the overall energy balance of the combustion chamber.

TFT )

maca(Ta - T0) + mfFeff cgmg

(4)

The mass flow rates of the air and flue gas, and that of the fuel, are related through the stoichiometric air-fuel ratio (S) and the fraction of excess air (E) provided for complete combustion of the fuel. Typical excess air requirements are 10% for gaseous fuels, 15%-20% for liquid fuels, and 20% or more for pulverized solid fuels. Based on the stoichiometric air-fuel ratio and the fraction of excess air, the adiabatic flame temperature (eq 4) can be simplified as follows:

TFT ) T0 +

Ca(Ta - T0) + Feff Cg

(5)

where

Ca ) cpa S(1 + E)

(6)

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

(7)

and

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

Tbw ) dTeff - (d - 1)TFT

(8)

The degree of stirring is greater than unity for imperfect stirring; the case of perfect stirring is represented by d ) 1. Numerical values of K, h, and d are dependent on numerous design variables (the type of fired heater, the size and layout of the radiant tubes, the composition and type of fuel, the interception factor of radiation heat transfer to the tubes, the emissivity of different surfaces, etc.). During the energy targeting and conceptual design stage, detailed design parameters of a fired heater are not defined. Therefore, exact values of K, h, and d are not known a priori. However,

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

approximate values of these parameters have been estimated for different operating scenarios.5 These approximate values are reported in Table 1 and are utilized in this paper for energy targeting.

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Figure 4. Targeting number of fired heaters.

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

Heat duties in the radiation and convection sections of the fired heater (Qr and Qc, respectively) may be estimated using the relationships

Qr ) Cgmf (TFT - Tbw)

(9)

Qc ) Cgmf (Tbw - Tgout)

(10)

and

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

Qfr )

TFT - Tbw TFT - Tgout

(11)

Using the aforementioned model, the heat-transfer performance of the fired heater may be estimated and utilized during network synthesis and evolution. Ambient air is initially heated to an intermediate temperature Ti, using process heat, and then it is further heated to a final temperature of Ta, using the flue gas. Flue gas leaves the fired heater convection section after supplying the required heat at a temperature Tgout and leaves to the stack at temperature Ts after preheating the combustion air.

Based on the utility pinch at (Hj, Tj), the intermediate air preheat temperature Ti may be calculated as6

HUCg[CgTs - Ca∆Tga] ∆C[Cg(HUTjn + HjTs) - Hj(Feff + T0∆C) Ti ) (12) HUCaCg - HjCa∆C where ∆C ) Cg - Ca, and ∆Tga ) Tgout - Ta. The actual temperature of the flue gas may be expressed as6

Tjn ) Tj + 0.5∆Tp + ∆Tadl

(13)

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

Ta ) Ti +

Cg(Tp,n - Ts) Hp Ca mfCa

(14)

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5635

Tih )

Figure 6. For utility pinch, above the process pinch, the heat capacity of the portion of the cold stream passes through the fired heater becomes unique. Table 2. Process Stream Data for Example 1 stream

heat capacity, Mc (kW/K)

Tin (K)

Tout (K)

H1 H2 C3 C4

4 4 4 2

600 450 300 350

350 300 700 450

It may be noted that, as the process pinch temperature increases, the intermediate air preheat temperature decreases and thereby increases the fuel requirement (or decreases the fired heater efficiency). The maximum possible intermediate temperature may not be realizable if there is an additional utility pinch formed below the process pinch. This may happen in two possible ways, as shown in Figure 1. First, there may be a temperature violation due to intersection of the process GCC and the utility GCC. Second, there may not be enough process heat available to preheat the combustion air to its maximum possible intermediate temperature. In case the air preheating using the process heat below the pinch is limited by a utility pinch at the point (Hk, Tk), the intermediate temperature is revised from Ti to Tit. The revised heat balance of air preheater gives6

Hk ) mfCa(Tit - Tkn)

(15)

where Tkn is the actual temperature of the air:

Tkn ) Tk - 0.5∆Tp - ∆Tadl

(16)

Thus, the intermediate temperature can be expressed as

Tit )

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

(17)

The minimum among all the calculated intermediate temperatures Tit and Ti is chosen as the revised intermediated temperature Tit. In the special case of no formation of any utility pinch, Tit will be equal to Ti. Similarly, if there is a restriction on the availability of process heat for heating the combustion air, the intermediate temperature must be further revised. For restricted process heat availability below the pinch, the intermediate temperature is calculated using the following relation:6

QhuCaT0 + Hk(Feff - Cg(Ts - T0) - CaT0) Ca(HU - Hk)

(18)

The maximum among all the calculated intermediated temperatures is denoted as Tih. The minimum of Tit and Tih determines the final revised intermediate temperature Ti up to which combustion air may be preheated using process heat below the pinch. If the revised intermediate temperature, up to which combustion air may be preheated, is below the ambient temperature, the ambient temperature is taken as the intermediate temperature (no process heating possible). Combining the energy balance for the air preheater, the process hot utility requirement, and the expression for the adiabatic flame temperature, the mass flow rate of the fuel required to meet the process heat duty (HU) can be expressed as

mf )

HU Feff - Cg(Ts - T0) + Ca(Ti - T0)

(19)

The flow chart for the energy integration of a fired heater with the background process is shown in Figure 2. Note that the amount of fuel fired is dependent on the excess air and the limiting stack temperature, and it is independent of the air preheat temperature. The limiting stack temperature is governed by the acid dew point of the flue gas. Based on the sulfur content of the fuel, the limiting stack temperature is usually fixed at the design stage. Similarly, the amount of excess air required for 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 temperature are recommended to reduce the fuel requirement, and, hence, to increase the efficiency of the fired heater. The fired heater efficiency is defined as the ratio of the useful thermal energy supplied to meet the hot utility requirement of the process to the input energy of the fuel fired:

η)

HU F × mf

(20)

3. Targeting Number of Fired Heaters During synthesis of the heat recovery network involving fired heaters, it is important to translate the target set based on the GCC profile matching to an achievable reality. To control the terminal temperature (or coil outlet temperature from the fired heater) of a process stream, fuel fired in the heater can be varied. As there is only one manipulated variable, there can only be one control variable. Therefore, every fired heater can have only one process stream in the radiation section. The terminal temperature of this stream can be controlled by controlling fuel fired in the radiation section. It may be noted that this does not imply that the convection section of a fired heater must have only one cold stream. Typically, it is preferred to have only one process stream in the convection section. In case of an oilfired unit, steam may be produced in the convection section for atomization. This does not affect the performance of the fired heater significantly, because the atomizing steam requirement is proportional to the fuel that is fired. However, for simplicity, it is assumed that only one process stream can be heated in a fired heater. Based on this assumption, it is possible to target the minimum number of fired heaters required. The cold process stream, which exchanges heat with the fired heater, can also be represented on a temperature-heat duty diagram. As the heat capacity (Mc) flow rate is generally

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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 stream entering the fired heater in Example 1.

assumed to be constant for a process stream, it is represented by a straight line on the temperature-heat duty diagram. It may be noted that the temperature in the temperature-heat duty diagram is shifted according to the minimum approach temperature difference. For any cold process stream, the stream line typically starts from its target temperature and then it continues up to its supply temperature. In the case of multiple fired heaters, streams passing through different fired heaters may be combined to represent a composite stream line on the temperature-heat duty diagram. There are three cases to consider: the stream line cuts the process GCC, the stream line cuts the utility GCC, and the stream line is contained in the space between the process GCC and the utility GCC. Case (i): The Process Stream Line Intersects the Process GCC. As the stream line intersects the process GCC (Figure 3a), it has two consequences: an increase in the hot utility requirement and a shift of the pinch location. Because the stream does not have enough heat capacity (Mc), the total heat requirement at the required temperature cannot be met. The maximum distance between the process GCC and the stream line signifies the additional hot utility requirement (∆HU). The pinch point shifts to a location in the process GCC that determines 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 increase in pinch temperature. Therefore, this is not a desirable option.

To eliminate the energy penalty, multiple streams should be chosen such that the combined composite line should be entirely above the process GCC. Case (ii): The Process Stream Line Intersects the Utility GCC. In the case where the stream line or the stream composite line intersects the utility GCC (see Figure 3b), the targeted process heat requirement can be satisfied. In this case, the original utility GCC must be modified to avoid a temperature violation. The intersection of the stream line with the temperature axis defines a utility pinch point (see Figure 3b). This results in a decrease in the efficiency of the fired heater. Fired heater targets must be revised, with respect to the new utility pinch formed by the composite stream line. Case (iii): The Process Stream Line is Contained between the Utility GCC and the Process GCC. If the stream line or the stream composite line is contained between the utility GCC and the process GCC (see Figure 3c), the overall energy target can be satisfied. However, this may result in a complex network that involves multiple entries of the process stream into the fired heater. Based on the aforementioned observation, it is possible to target the minimum number of fired heaters required. 3.1. Algorithm for Targeting the Minimum Number of Fired Heaters. Previous discussion helps in setting the target for the minimum number of fired heaters required to satisfy the minimum hot utility requirement. It may be concluded that the stream line or the composite stream line should not intersect the process GCC. The minimum number of process streams required to produce a composite line that intersects the temperature axis at or above the process pinch and does not intersects the process GCC, represents the minimum number of fired heaters required. A simple procedure is suggested to target the minimum number of fired heater requirement. The proposed procedure may be stated as follows: (1) Start from the highest temperature terminal point of the process GCC. This ensures that the total heat requirement can be satisfied. (2) Among all the cold process streams that are present at the terminal point, choose one with the maximum heat capacity flow rate (Mc). Because the slope of a line on a temperature heat duty diagram is inversely proportional to the Mc of the stream, the resultant stream line will have the lowest possible


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

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

slope. This enhances the possibility that the stream line may lie above the process GCC. (3) Draw the stream line on the temperature-heat duty diagram. (4) Check whether the stream line intersects with the process GCC above the process pinch. (5) If the process stream line intersects the process GCC, then this 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 maximum Mc from a set of cold streams whose terminal temperature is above the intersection point. (6) Draw the composite stream line and check whether it intersects the process GCC. (7) Repeat this procedure until a composite stream line is identified that does not intersect the process GCC and intersects the temperature axis at or above the process pinch. (8) The number of cold streams required to produce such a composite stream line represents the minimum number of fired heaters required. The aforementioned procedure ensures that the composite stream line should be able to absorb the total heat requirement of the process. The procedure for targeting the minimum number of fired heaters is illustrated in Figure 4. In Figure 4, three

Table 3. Process Stream Data for Example 2 stream

heat capacity, Mc (kW/K)

Tin (K)

Tout (K)

H1 H2 C3 C4

12 4 10 8

650 550 450 300

350 300 620 700

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

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illustrated in Figure 6, the cold stream should also pass through the utility pinch point. In such a case, the heat capacity flow rate of the split portion of the cold stream becomes unique. At the utility pinch point, the heat capacity of the cold stream could be obtained as

Mc ) Ti +

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

the first stream intersects the GCC, the next-largest heat capacity stream is added at that point to complete the procedure. Thus, in this case, also two fired heaters are required to supply the total heat requirement. 4. Network Synthesis with a Single Fired Heater When the stream line for a single cold stream passes above the process GCC and the stream is present at the process pinch, only one fired heater is sufficient to satisfy the required heat duty. It is possible to have a simplified once-through condition for the fired heater. In the once-through case, the process stream enters the fired heater convection section and leaves the fired heater radiation section at the required temperature. This is preferred in industry, because of the simplicity and controllability of the associated heat exchanger network. If the stream line intersects the utility GCC and causes a utility pinch above the process pinch, the efficiency of the fired heater reduces. However, the increased fuel consumption in the fired heater increases the temperature difference between the process stream and the flue gas in the convection section. This may result in a reduced capital investment for the fired heater. This implies that capital-energy tradeoffs are required to choose between different network schemes. In Figure 5, it has been illustrated that the process stream line meets the temperature axis and it forms a utility pinch. For such a case, the fired heater targets must be reset accordingly. To meet the energy target, the stream line should be such that it is confined entirely between the process GCC and the utility GCC and intersects both of them at the process pinch. This calls for reduced mass flow rate for the process stream at the fired heater entry. Therefore, the process stream is split into two components: one portion of the stream enters the fired heater (see Figure 5), and the other portion of the cold process stream exchanges heat with hot process streams and re-enters the fired heater after completing the required process-to-process heat recovery. However, there are limits on the heat capacity of the split portion that enters the fired heater. The maximum heat capacity flow rate (Mcmax) is dependent on the process GCC, whereas its minimum value (Mcmin) is dependent on the utility GCC. As long as the heat capacity flow rate of the fraction of the cold process stream that enters the fired heater is within the minimum and the maximum range, the energy target can be satisfied (see Figure 5). It may be noted that the change in the heat capacity of the split portion affects the mixing temperature Tmix. If there is a utility pinch between the utility GCC and the process GCC above the process pinch, as

[Cg(Tjn - Ts) - Ta]mfCa Tjn - Tp

(21)

If there is no cold stream that meets this requirement, one of the cold streams may be split to put in the fired heater. Example 1. Applicability of the proposed methodology is illustrated through the following example. Process stream data for this example are given in Table 2. The fuel used has a net heating value of 41 000 kJ/kg. The stoichiometric air fuel ratio is 15, and the minimum excess air recommended is 10% for complete combustion. The ambient temperature is assumed to be 300 K. The average specific heats of air and flue gas are assumed to be 1.005 and 1.148 kJ/(kg K), respectively. The limiting temperature corresponds to the sulfur dew point of the flue gas is assumed to be 433 K. A minimum approach temperature difference of 30 K is specified for process-toprocess heat recovery heat exchangers. An additional temperature potential (∆Tadl) of 20 K between the flue gas and the cold process stream is included. This implies that the minimum approach temperature between the cold process stream and the flue gas is 50 K. The temperature potential between the preheat air 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 on the cold side. The inlet temperature of the hot process stream H2 holds the pinch. Process GCC for this example is shown in Figure 7. It may be concluded that a single fired heater is sufficient for this example. Different possible options for integrating the fired heater are highlighted in Figure 8. The range of heat capacity of the split stream through fired heater is determined to be between 0.31 (corresponds to the heat capacity of the flue gas) and 0.4 (obtained from the process GCC), as shown in Figure 8. A heat recovery network with a heat capacity of the split stream of 0.4 is shown in Figure 9. Along with the heat recovery network, the mean effective temperature, bridgewall temperature, and the radiation duty fraction are also highlighted in Figure 9. The mixing temperature after process heat recovery is 570 K, with the initial split of Mc ) 0.4 receiving 60 kW of heat from the fired heater and the combined stream receiving the remaining 520 kW from the fired heater. If the heat capacity of the split fraction is changed to 0.31, the mixing temperature decreases to 566.34 K and the heat received by the split fraction in fired heater is reduced to 45.37 kW (not shown for brevity). The combined stream receives the remaining 534.63 kW heat from the fired heater. Note that both of these networks have the same heater efficiency and heat loads. However, the heat capacities of the cold process stream entering the fired heater are different. If the entry stream heat capacity is increased to 4 (no stream split for process heat recovery), it will result in a once-through case. In this case, the process stream enters the fired heater at 555 K and leaves at 700 K. However, the efficiency of the fired heater was reduced, from 93.7% to 92.5%. It may be noted that the efficiency of the fired heater has increased because of utilization of the process heat below the process pinch for preheating the combustion air. The heat capacity of the split fraction influences the exit temperature of the fraction from the fired heater and through


Figure 12. Heat recovery network for Example 2.

the process heater. Thus, it influences the heat-transfer area requirement of the fired heater convection section and the process-to-process heat recovery heat exchangers involved with these fractions. It may be noted that it is possible to optimize the split fraction, considering the capital investment for the entire heat recovery network. 5. Network Synthesis with Multiple Fired Heaters Issues related to synthesizing heat recovery networks that involve multiple fired heaters are discussed in this section. If cold process streams that require fired heaters are present at the process pinch, the duties of individual fired heaters can be varied. However, the total duty of fired heaters remains constant. This is illustrated in Figure 10 with multiple fired heaters required to meet the total duty. The sum of the heat capacities entering fired heaters may be determined using the procedure described in the previous section. The minimum of the combined heat capacity is determined by the combined flue gas heat capacity, and the maximum of the combined heat capacity is found from the process GCC limit. To achieve the maximum efficiency for all fired heaters, streams should enter the fired heaters at the pinch temperature and the combined heat capacity should be limited within the identified range. Streams combine after completing the process-to-process heat recovery at the mixed temperature (Tmix) and re-enter the fired heater to complete the heat requirement. Consider a case where two fired heaters are required to meet the total hot utility requirement of HU. The cold streams are both present at the pinch, and they are split into Mc1,in and Mc2,in fractions passing through the fired heater. The combined heat capacities Mc1,in and Mc2,in are supposed to be between the minimum and the maximum. The sum of the duties of the fired heaters must match the total hot utility requirement targeted. Referring to Figure 10, consider that fired heater 1 supplies heat to stream C3 with

heat capacity Mc1 and fired heater 2 supplies heat to C4 with heat capacity Mc2. At the pinch, the Mc1,in fraction of C3 enters fired heater 1 and the Mc2,in fraction of C4 enters fired heater 2. The remaining portions of the cold streams, after completing the process-to-process heat recovery, combine with the corresponding fractions that received part of the heat from the respective fired heaters. Heat that is transferred by the fired heaters, at the mixing temperature Tmix can be obtained as

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

(22)

However, it may be noted that the combined Mc1,in + Mc2,in can be met by different combinations of the individual heat capacities Mc1,in and Mc2,in. The combined heat capacity Mc1,in + Mc2,in is limited within the minimum and maximum values previously identified. This range of heat capacities of the fractions Mc1,in and Mc2,in results in a permissible individual fired heater heat duty range, as is evident from eq 22. This gives flexibility to the design of the heat recovery network, along with the fired heaters. Economic considerations can be used further to optimize the duty split between different fired heaters. For a chosen combination of combined Mc1,in + Mc2,in, the individual entry values of Mc1,in and Mc2,in themselves possess a possible minimum and maximum range. The heat capacity Mc1,in is limited to a minimum for a chosen total Mc1,in + Mc2,in, as given by

Mc1,in,min )

HU1 TFT - (Tmix + ∆T)

(23)

where HU1 is the heat supplied to stream 1 between Tmix and its terminal temperature. The minimum heat capacity limit Mc2,in,min could be obtained in a similar method by replacing HU2 in the aforementioned equation. The maximum limit for Mc1,in is the difference of the maximum of the combined heat

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Table 4. Comparison of Different Network Options for Example 2 Network

Duty (kW)

Efficiency (%)

Mc1,in (kW/kg)

Mc2,in (kW/kg)

fired heater 1

fired heater 2

fired heater 1

fired heater 2

total fuel (kg/s)

0.3 10 0.3 10 1.2

0.6 0.6 8 8 0.8

565.5 565.5 565.5 588.9 600

1134.5 1134.5 1134.5 1111.1 1100

94.3 93.3 94.3 93.32 94.3

94.3 94.3 93.34 93.32 94.3

0.04398 0.04413 0.04427 0.0444 0.04398

capacity (Mc1,in + Mc2,in) determined previously and the minimum heat capacity limit for Mc2,in,min. The upper limit of Mc2,in could also be calculated in a similar manner. Thus, the individual limits of the heat capacities for a sum of Mc1,in + Mc2,in could be determined using the aforementioned expressions. However, during network synthesis, certain fired heaters can be simplified to once-through cases with the appropriate choice of different heat capacities. The fired heater targets must be revised, based on the procedure described previously. For the cold process stream with an entry temperature higher than the process pinch temperature, the fired heater parameters must be re-targeted, corresponding to the shifted utility pinch location for this stream. As the pinch temperature increases, it is not possible to satisfy the original target established using the process GCC. Example 2. Example 2 has been considered to illustrate the flexibility of designing heat recovery networks with multiple fired heaters. Process stream data for example 2 are provided in Table 3. The pinch is located at 450 and 500 K, corresponding to a minimum approach temperature of 50 K (∆Tmin). The hot utility requirement is determined to be 1700 kW, with the cold utility requirement of 1400 kW. It is observed that a single fired heater is not sufficient to supply the entire hot utility requirement. The largest Mc of 8 kW/K line present at the terminal point is found to intersect the process GCC and therefore, another stream is added to make certain that the composite stream line does not intersect the process GCC. Thus, for this example, two fired heaters are required to supply the total hot utility requirement of 1700 kW. Three different options for supplying the required total hot utility requirement are illustrated in Figure 11. The minimum Mc value for the combined fractions of the cold streams to be admitted to the fired heaters is 0.9 kW/K, and the maximum possible value is 2 kW/K. Thus, the sum of the heat capacities of the fractions (Mc1,in and Mc2,in) at the entry points of the fired heaters must be within these limits. One of the permissible heat recovery networks for example 2 is shown in Figure 12. Mean effective temperatures, bridgewall temperatures, and radiation duty fractions for both of the fired 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 566.95 K. The fired heater duties are 565.5 kW and 1134.5 kW, respectively. This network could be simplified with one of the fired heaters modified to be a once-through heater. If the heat capacities of the cold stream fractions at the entry are changed to Mc1,in ) 0.8 kW/K and Mc2,in ) 1.2 kW/K, the mixing temperature changes to 575 K. The duties for the fired heaters would be changed to 600 and 1100 kW, respectively. The network structure remains the same, while the duties of the fired heater get modified. This range of duty gives flexibility to the designer during the network synthesis and evolution. Similarly, by changing the heat capacity of the cold stream fractions, different heat recovery networks may be generated.

% fuel change

remarks meets targets one once through one once through both once through meets targets

0.34 0.66 0.95

Table 5. Stream Data for Example 3 Temperature Enthalpy supply temperature (K)

target temperature (K)

375

Stream 1 600

600

Stream 2 323

308

Stream 3 437

413

Stream 4 773

768

Stream 5 580

493

Stream 6 332

353

Stream 7 396

332

Stream 8 442

495

Stream 9 340

358

Stream 10 398

753

Stream 11 773

temperature (K)

enthalpy (kW)

375 502 600

0 16.2 25.8

600 447 365 323

31.5 15.34 4.9 0

308 437

0 10.5

413 449 640 773

0 8.4 37.7 56.7

768 580

29.3 0

493 433 417 398 332

30.5 22.1 18.3 13.5 0

353 396

0 3.8

332 442

0 7.9

495 403 340

12.3 4.4 0

358 398

0 4.8

753 773

0 37.8

Table 4 summarizes a comparison of some of the different possible heat recovery networks. Example 3: Naphtha Reformer Example. The following example illustrates the importance of targeting the number of fired heaters during heat recovery network synthesis. The process data for this naphtha reformer example are given in Table 5.9 The flow sheet in Figure 13 shows that three fired heaters are used in the original problem to meet the total heat requirement of 54.0 kW, corresponding to a minimum approach temperature of 10 K. Existing heat recovery network of the problem is shown in Figure 14. The individual duties of fired


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

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

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

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

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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.

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

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


Figure 17. Heat recovery network for the naphtha reformer example, based on grassroots design. Table 6. Comparison of Integration Results for Example 3 parameter total heat duty (kW) number of fired heaters fired heater duties (kW) total fuel (kg/s) % fuel change with existing fired heater efficiencies (%)

existing (Figure 14)

revised (Figure 16)

grass root design (Figure 17)

54 3 37.77, 12.55, 3.72 1.42 × 10-3

54 2 37.77, 16.3 1.419 × 10-3 0.1 92.7, 93.5

54 2 37.77, 16.3 1.411 × 10-3 0.63 92.7, 95.3

92.7, 93.3, 94.3

results shows that only two fired heaters were required to supply the required total heat duty. Also, the efficiency of the fired heater could be improved by 0.6% from the base case. 6. Conclusions The procedure for energy-integration of a fired heater with the process grand composite curve (GCC) provides the fuel and air preheat targets prior to the detailed design of the equipment. For processes with multiple fired heaters, it is important to estimate the minimum number of fired heaters required to supply the total heat demand of the process. It has been observed that the composite stream line of the cold process streams receiving heat in the fired heaters, when represented in the temperatureheat duty diagram, must lie above the process GCC and intersects the temperature axis at or above the process pinch. Based on this observation, a procedure has been proposed to target the minimum number of fired heaters required to meet the heat duty prior to the synthesis of the heat recovery network.

The importance of targeting the number of fired heaters has been illustrated through examples. In cases where all streams are present at the process pinch, it is possible to meet the minimum energy targets by making some appropriate changes in the network design. On the other hand, if all the streams are not present at the process pinch, the minimum fuel target cannot be satisfied and new fuel targets must be re-estimated. For a feasible heat recovery network, the stream segment passing through the fired heater must be contained within the utility GCC and the process GCC. The entry conditions of the cold streams to the fired heater convection section should be within a certain range, as dictated by the flue gas heat capacity and the process GCC. Also, the cold process stream should enter the fired heater at the process pinch conditions, to satisfy the fuel target established based on the process GCC. The mass fraction of the cold stream entering the fired heater may be varied within a range. Variation in the flow rate (and, equivalently, the heat capacity) of the fraction entering the fired heater affects the capital cost of the fired heater

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convection section and the process-to-process heat exchangers involved with the cold process stream. It may be possible to perform a cost optimization to determine the optimum value for the fraction. Design and synthesis of the heat recovery network with multiple fired heaters can be addressed by utilizing the proposed methodology. Conventional techniques of network evolution cannot be applied directly to heat recovery networks with fired heaters. The optimal performance of an energy-integrated fired heater is dependent on both the above-pinch heat requirement and the below-pinch heat available. Optimum performance of an energy-integrated fired heater is dependent on the process heat recovered below the process pinch through preheating the combustion air and the heat requirement above the process pinch. In this sense, a fired heater is a connected utility. To address and evaluate different network evolutions, the proposed methodology can be applied. The same has been demonstrated through 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 stirring E ) excess air fraction F ) lower calorific value [kJ/kg] g ) overall radiation transfer factor from gas to sink GCC ) grand composite curve h ) heat-transfer coefficient [kWm-2K-1] H ) enthalpy [kJ] HU ) heat duty [kJ] K ) overall radiation coefficient m ) mass flow rate [kg/s] Mc ) heat capacity [kW/K] Q ) heat [kW] q ) heat flux [kW/m2] S ) stoichiometric air:fuel ratio T ) temperature [K] Greek Symbols R ) setting loss fraction in the radiation chamber ∆ ) difference σ ) Stefan-Boltzmann constant; σ ) 5.67 × 10-11 kW m-2 K-4 η ) efficiency Subscripts 0 ) ambient 1 ) heat sink a ) air

adl ) additional bw ) bridge wall c ) convection eff ) effective f ) fuel fr ) radiation fraction FT ) adiabatic flame condition g ) flue gas gout ) condition of gas after the convection section i ) intermediate ih ) intermediate based on enthalpy limitation in ) inlet it ) intermediate based on temperature limitation j ) temperature interval above pinch k ) temperature interval below pinch max ) maximum min ) minimum n ) transformed out ) outlet p ) pinch r ) radiation s ) stack Literature Cited (1) Linnhoff, B.; de Leur, J. Appropriate placement of furnaces in the integrated process. In Understanding Process Integration II; IChemE Symposium Series, No. 109 (EFCE Publication 65); Institution of Chemical Engineers: Washington, DC, 1988; p 1. (2) Hall, S. G.; Linnhoff, B. Targeting for furnace systems using pinch analysis. Ind. Eng. Chem. Res. 1994, 33, 3187. (3) Stehlik, P.; Zagermann, S.; Gangler, T. Furnace integration into processes justified by detailed calculation using a simple mathematical model. Chem. Eng. Process. 1995, 34, 9. (4) Jegla, Z.; Stehlik, P.; Kohoutek, J. Furnace integration in to process based on pinch analysis. In Proceedings of the 13th International Congress of 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, Indian Institute of Technology, Bombay, India, 2006. (7) Truelove, J. S. Furnaces and combustion chambers. In Heat Exchanger Design Handbook; Hewitt, G. F., Ed.; Begell House: New York, 2002. (8) Berman, H. L. Fired heaterssIII: How combustion conditions influence 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 Integration for the Efficient Use of Energy, Institution of Chemical Engineers (IChemE): Rugby, Warwickshire, U.K., 1982.

ReceiVed for reView December 16, 2006 ReVised manuscript receiVed May 15, 2007 Accepted May 31, 2007 IE061619Y

Targeting for Energy Integration of Multiple Fired ... - ACS Publications

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