Energy-Saving Mechanism in Heat Transfer ... - ACS Publications

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Energy-Saving Mechanism in Heat Transfer Optimization of Dividing Wall Column Fang Jing, Hu Yuqi, and Li Chunli* School of Chemical Engineering and Technology, Hebei University of Technology, Tianjin 300130, P. R. China ABSTRACT: Currently most of the dividing wall column (DWC) designs are based on a Petlyuk Column in which the heat transfer process across the dividing wall is ignored. This paper proposes a heat transfer model of DWC, in which additional virtual intermediate heat exchangers are introduced between the prefractionator and the main column, and thus the heat transfer process among the virtual intermediate heat exchangers will produce the thermal-coupled effect. This effect can be explored by fixing the beneficial heat transfer region and a corresponding algorithm of heat transfer. Compared with the designs based on a Petlyuk Column, this DWC model can further reduce the exergy loss and energy consumption. Besides, the optimal operating zone is enlarged, and the influence of liquid and vapor split ratio fluctuation on the minimum energy consumption of DWC is lowered. This model provides a guidance for the energy-saving design of DWC.

1. INTRODUCTION The distillation column is one of the most widely used unit operations. However, it is also a high energy consuming operation which accounts for about 40% of the whole energy used in the chemical industry.1 In order to save energy, one should first investigate the qualities of different energies in the column by applying the second law of thermodynamics. The high energy consumption in the processes of distillation may essentially result from the degradation of energy quality, which may be further traced to the following processes that feature the irreversibility: for one, the pressure drop of flowing fluid; for another, the mass transfer among the streams with nonequilibrium phase concentrations or mixing of the streams with different compositions; and also, the heat transfer among the streams with different temperatures.2 At each stage of the distillation column, driving forces (pressure difference, composition difference, and temperature difference) promote the processes of mixing, diffusion, and mass transfer as well as heat transfer between in-streams and out-streams and thus result in the increase of mole fraction for light key component in vapor phase and heavy key component in liquid phase of out-streams; and the existence of driving forces in distillation column indicates the irreversibility of these concerned processes.3 When these irreversible processes happen, the energy quality will change. The extent of changes on energy quality will have a direct impact on the loss of the energy transferred between in-streams and out-streams and even on the exergy loss, which is used as a quantifiable scale to evaluate the changes of energy quality in mass transfer, heat transfer, and other processes in distillation as well as an indicator of the irreversible degree of the concerned processes at each stage or even in the whole column. At stage n of a distillation column, the equation of enthalpy balance describing the change from state 1 (the state of instreams) to state 2 (the state of out-streams) is Hn1 + Q n1 = Hn2 + Q n2

Sn1 +

Tn1

≤ Sn2 +

Q n2 Tn2

(2)

In eq 2, only if the state is reversible, the equality holds; but, in practice, the driving forces will lead to the increment of entropy. Exergy is defined as the maximum amount of work output of a stream when it reaches equilibrium under specific conditions with the environment at T0 and p0,4 as manifested in eq 3: EX = H − T0S

(3)

It is known from above that the exergy of a stream is a function of its enthalpy and entropy. Since both enthalpy and entropy are functions of state, the exergy of a stream is also a state function, determined by initial and final states instead of process. If mass transfer occurs at stage n for streams from state 1 to state 2, the change of exergy can be measured by the following equation: ΔEX = (Hn1 − Hn2) − T0(Sn1 − Sn2)

(4)

In eq 4, the energy change in transfer is caused by the change in compositions and the irreversibility of mass transfer, and when heat transfer occurs, eq 5 can replace eq 4 to calculate the change of exergy: ⎛Q 1 Q 2⎞ ΔEX = (Q n1 − Q n2) − T0⎜⎜ 1n − 2n ⎟⎟ Tn ⎠ ⎝ Tn

(5)

As in eq 4, it is the irreversibility of heat transfer which happened in eq 5 that leads to the change of energy in transfer. Thus, when both mass transfer and heat transfer occur, the exergy can be obtained by combining eq 4 with eq 5. This may come to the conclusion that the irreversibility is the Received: Revised: Accepted: Published:

(1)

and the entropy equation is © 2013 American Chemical Society

Q n1

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April 12, 2013 October 21, 2013 December 2, 2013 December 2, 2013 dx.doi.org/10.1021/ie4011639 | Ind. Eng. Chem. Res. 2013, 52, 18345−18355

Industrial & Engineering Chemistry Research

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fundamental cause of the degradation of energy quality, and the loss of the energy transferred among streams is an apparent phenomenon of the degradation of energy quality. The change of the exergy (or called exergy loss) is the direct expression of the energy transfer loss. When the concerned processes are reversible, the exergy loss will be decreased to the minimum, but an infinite number of stages will be needed, which cannot be realized in practice. From eqs 1−5, the exergy equation is derived for streams at stage n of a distillation column EX n1 + EXQ1 1 ≥ EX n2 + EXQ2 2 n

(6)

n

and from eq 6, the exergy loss can be obtained by EX n1 − 2Loss = (EX n1 − EX n2) + (EXQ1 1 − EXQ2 2) n

n

(7)

Replacing the change values of exergy in eq 7 with those in eq 4 and eq 5, the result can be obtained as EX n1 − 2Loss = [(Hn1 − Hn2) − T0(Sn1 − Sn2)] ⎡ ⎛ ⎛ T ⎞ T ⎞⎤ + ⎢Q n1⎜1 − 01 ⎟ − Q n2⎜1 − 02 ⎟⎥ ⎢⎣ ⎝ Tn ⎠ Tn ⎠⎥⎦ ⎝

Figure 1. Fully thermally coupled distillation columns (Petlyuk Column). (8)

Assuming the heat loss from state 1 to state 2 at stage n is zero, which is to say Q1n = Q2n = Q, eq 8 can be simplified as EX n1 − 2Loss = T0(Sn2 − Sn1) −

T0 Tn1

Q+

T0 Tn2

Q (9)

Equation 9 can be equally rearranged into EX n1 − 2Loss = T0(ΔSsystem + ΔSenvironment )

(10)

According to eq 9 and eq 10, it is clear that even if the heat loss is zero, or rather, the total heat recovery is achieved, the increase of exergy loss and the degradation of energy quality occur as long as the processes involve mixing, diffusion, and mass transfer as well as heat transfer among streams with different compositions or temperatures, whether or not the phenomena in these processes occur simultaneously or individually. It also proves that using the first law of thermodynamics to recover the heat or reduce the energy loss in transfer in a distillation column is not appropriate. If the irreversible degrees of concerned processes are increased at all stages, the following results can be achieved: 1) the operating line of the column moves away from the vapor−liquid equilibrium line, indicating the increase of energy consumption; 2) the exergy loss of the whole column increases. So the increase of energy consumption is manifested in the increase of exergy loss of the whole column and the specific increase at some stages (or all the stages) and vice versa. Consequently, the key to reducing energy consumption of a distillation column is to reduce the exergy loss under the premise of not changing the purity of products. The fully thermally coupled distillation column (also called a Petlyuk Column, Figure 1), a typical representative device that applies the second law of thermodynamics to reduce energy consumption of the distillation system, can save 30% of energy when compared with the conventional sequences devices.5 Richard O. Wright et al.6 further improved this column by installing the prefractionator and the main column of a Petlyuk Column in a single shell and separating them with a dividing wall, so was the embryo of dividing wall column (DWC, Figure 2) established. Gerd Kaibel7 pioneered the industrial DWC

Figure 2. Dividing wall column (DWC).

implementation within BASF. DWC not only inherits the advantages of a Petlyuk Column [1) saving energy consumption and 2) avoiding the remixing of side product and the irreversibility that the remixing may bring about]8 but also saves the equipment investment by about 30%, compared with that of the Petlyuk Column. After that, different models of DWC including the shortcut design model9 and the rigorous dynamic model10 were developed; but in these models, the heat transfer process across the dividing wall (namely the location between the prefractionator and the middle section of the main column) is not taken into account. However, the influencing factors including the above process will make a discrepancy between the model operating point and the real one11 and thus will bring more difficulties to optimization and control of DWC.12,13 So it is not accurate to use the model without the heat transfer process across the dividing wall to analyze the operation parameters and predict the dynamic behavior of DWC.14−20 The effect of the heat transfer across the wall on the energy consumption was investigated by F. Lestak et al.,21 and they identified whether the heat transfer process had a beneficial or a nonbeneficial effect corresponding to different regions of the 18346

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dividing wall by using the method of column grand composite curve (CGCC).22,23 However, the effect of the amount of heat transfer on energy consumption was studied by the sensitivity analysis of U·A (U: heat transfer coefficient; A: heat transfer area). In other words, the minimum energy consumption of DWC was determined by optimizing U·A, while the heat transfer algorithm aimed to achieve the lowest energy consumption was not given. In 2007, B. Suphanit et al.24 used the method of minimum driving force profile (MDFP) to analyze the heat transfer process across the dividing wall, and the amount of heat transferred across the dividing wall was largely reduced by the application of MDFP when compared with that by using the method of CGCC. Filipe Soares Pinto et al.25 pointed out that the amount of heat transfer induced by MDFP can be reduced by an amount that accounts for 20−30% of that analyzed by CGCC; but this research did not explore that once the process of heat transfer is introduced across the dividing wall, what impact it will have on the optimal operating zone in DWC. This issue, which plays a key role in directing the actual operation of DWC, is one of the works based on the new method for analyzing the heat transfer process and its corresponding algorithm in this paper. This approach is simpler and has more extensive application for other thermally coupled columns than CGCC and MDFP. Here, the intermediate heat exchanger will be briefly discussed before describing the application of this new method.

that the most efficient way to reduce energy consumption is to decrease the maximum exergy loss at a certain stage. By choosing the position where the minimum exergy loss appears (namely the feed stage in case (a)) as a demarcation point, the intermediate-condenser is installed above the point where the maximum exergy loss appears, and, likewise, the intermediatereboiler is installed below the point; but for the convenience of analysis, only the intermediate-reboiler is introduced in case (b) and case (c). As shown in Figure 3b, when an intermediatereboiler is installed at the stage with the maximum exergy loss (the 24th stage), the operating line for the stripping section is closer to the vapor−liquid equilibrium line, which indicates that the driving forces and the irreversible degree decrease. While the operating line for the rectifying section is further away from the vapor−liquid equilibrium line, following the rule in the operating calculation that the number of the stages in a column cannot be changed. The operating line for the rectifying section is declined with the same slope due to the fixed reflux ratio, which leads to the decrease of purity of distillate and bottom products. The products with the same purity can be retained by increasing the reflux ratio (including internal reflux ratio Ri, known as the falling liquid flow rate in a column, and external reflux ratio R, a regulated parameter, known as the refluxing liquid flow rate in a column) without changing the number of stages, when an intermediate-reboiler is installed as shown in Figure 3c. Compared with case (a), case (c) shows that the energy consumption decreases with increasing of R in Table 1, which conflicts with the theory that energy consumption of a distillation column is proportional to R. This conflict stems from the installation of the intermediate-reboiler, which makes Ri increase but the required R decreases. Compared with R in case (b), R in case (c) should be modified to a higher level to retain the same purity of products as in case (a) where no intermediate-reboiler is installed; but the rise of energy consumption resulted from the increase of R is much smaller in degree than the reduction of energy consumption caused by the increase of Ri. To make full use of this advantage in DWC, a detailed theoretical analysis and an algorithm will be proposed in this new method.

2. INTERMEDIATE HEAT EXCHANGERS To improve the precision of the DWC model, the heat transfer process between the prefractionator and the main column of DWC will be replaced by the process among the virtual intermediate heat exchangers in the new method, which can be regarded as real intermediate heat exchangers in their functions of energy-saving, but distinguished from the latter ones by assuming they themselves consume no energy. This section will start the research on real intermediate heat exchangers. By analyzing the examples of separating the binary systems of n-butane and n-pentane via three different conditions (the details are summarized in Table 1), we can illustrate the position where the intermediate heat exchanger should be installed and explore its energy-saving mechanism and its impact on the distillation system. In case (a), as shown in Figure 3a, where no intermediate heat exchanger is installed, the minimum value of exergy loss appears at the feed stage (the 14th stage), and higher values appear at the stages above and below the feed one. It is obvious

3. THE THERMAL-COUPLED EFFECT OF HEAT TRANSFER MODEL OF DWC The four columns model (Figure 4) is the basic model of DWC. In this section, it is introduced by a case of separating nhexane, n-heptane, and 1-octane. The thermodynamic model used in the calculations is NRTL. This four columns model is preferred to a Petlyuk Column model considering that the former owns the prefractionator and the middle section of main column (side-draw section) with the same number of stages on corresponding positions. The technical parameters and the parameters of four columns model are summarized respectively in Table 2 and Table 3. 3.1. Beneficial Heat Transfer Region for the ThermalCoupled Effect. The advantages of intermediate heat exchangers in a distillation system are obvious as discussed in Section 2, but the intermediate heat exchangers require heat sinks or heat sources at low quality from the outside. In DWC, when the heat transfer process across the dividing wall is transformed to the process among the virtual intermediate heat exchangers, the heat sinks or the heat sources needed by the virtual intermediate heat exchangers from one part of the

Table 1. Comparison of Cases (a), (b), and (c)

feed composition (n-butane/n-pentane, mole fraction) feed flow rate/kmol·h−1 liquid mole fraction of feed pressure/kPa location of intermediate-reboiler heat load of intermediate-reboiler/kW R purity of n-butane in distillate (mol %) purity of n-pentane in bottom (mol %) energy consumption/kW

case (a)

case (b)

case (c)

0.5/0.5

0.5/0.5

0.5/0.5

100 0.4 101 ----1.385 98 98 362.776

100 0.4 101 24/25 95 1.385 97 97 267.139

100 0.4 101 24/25 95 1.387 98 98 267.814 18347



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Figure 3. Operating line profiles of the following: a. simple column; b. column in which an intermediate-reboiler is installed with constant reflux ratio; c. column in which an intermediate-reboiler is installed with variable reflux ratio.

Table 2. Technical Parameters parameters feed composition (n-hexane/n-heptane/ n-octane) feed flow rate liquid mole fraction of feed pressure purity of n-hexane in distillate purity of n-heptane in side product purity of n-octane in bottom product

value 0.2/0.6/0.2 (mole fraction) 100 kmol·h−1 0.42 101 kPa 95% (mol %) 95% (mol %) 95% (mol %)

column (the prefractionator or the middle section of main column) can be provided by the other virtual intermediate heat exchangers from the other part of the column; and the thermalcoupled effect between the prefractionator and the main column will be discussed as follows. As shown in Figure 5 and Figure 6, the exergy loss of streams at each stage in the four columns model can be worked out from eq 10. The public rectifying section and the public stripping section take a major proportion of exergy loss resulting from the increase of the irreversible degree that comes

Figure 4. Four columns model: 1public rectifying section; 2 prefractionator ; 3side-draw section; 4public stripping section.

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some virtual intermediate-reboilers below, as shown in Figure 7. The heat released from the virtual intermediate-condenser at a

Table 3. Parameters of Four Columns Model number of theoretical stages public rectifying section prefractionator side-draw section public stripping section location feed location in prefractionator side stream location in side-draw section

value 10 15 15 10 value 7 6

Figure 7. Schematic of the heat transfer model of DWC in which the virtual intermediate heat exchangers are introduced.

certain stage in the side-draw section is absorbed by the virtual intermediate-reboiler at its corresponding stage in the prefractionator, which leads to the thermal-coupled effect between the side-draw section and the prefractionator. So the beneficial heat transfer region is located in the range of stages where the virtual intermediate-condensers contained in the side-draw section correspond to the virtual intermediatereboilers contained in the prefractionator (the beneficial heat transfer region is the ninth−14th stages in the prefractionator or the side-draw section in this case). It was concluded that the thermal-coupled effect from the process of heat transfer among the virtual intermediate heat exchangers and that from the process of heat transfer between the prefractionator and the side-draw section both cause the declination of irreversibility of the mass and heat transfer processes to the same degree. A beneficial region for heat transfer may help reduce energy consumption. 3.2. Modeling Equations with the Thermal-Coupled Effect. Since owing the same thermal-coupled effect, the process of heat transfer across the dividing wall in the DWC model has the same amount of heat transfer as the process among the virtual intermediate heat exchangers in the heat transfer model of DWC. The installation of intermediate heat exchangers in the distillation column leads to the decrease of driving forces of the mass and heat transfer processes, and consequently the operation line is closer to the vapor−liquid equilibrium line. Therefore, the coincidence of the two lines indicates that one can simultaneously achieve the maximum heat load of the virtual intermediate heat exchangers, the infinitesimal driving forces of the mass and heat transfer processes, and the minimum energy consumption of the columns. With that, the amount of heat transferred between the prefractionator and the side-draw section can be calculated by following the heat load algorithm of the virtual intermediate heat exchangers. Equation A.7 is from the Appendix, in which the total heat load of the intermediate heat exchanges in the rectifying section of a distillation column (QR) is shown

Figure 5. Exergy loss profile of prefractionator.

Figure 6. Exergy loss profile of side-draw section.

with the intense exchange of vapor and liquid streams. The minimum exergy loss appears at the ninth stage of the prefractionator and the 14th stage of the side-draw section. In order to reduce energy consumption of the columns without changing the purity of products, intermediate heat exchangers or any other heat transfer methods (here, virtual intermediate heat exchangers), if they can improve the energy quality, should be introduced to reduce the exergy loss of streams at each stage and especially to reduce the irreversibility that leads to the larger exergy loss in large scale. By choosing the stages where the minimum exergy loss locates in the prefractionator and in the side-draw section as the demarcation points, some virtual intermediate-condensers are supposedly to be installed above the demarcation point and

r

QR =

i=1

18349

⎛y

− xD ⎞ ⎟⎟ ⎝ yr + 1 − xr ⎠

∑ Q i = D(HrL − HrV )·⎜⎜

r+1



Article

ninth−14th stages) can be calculated by eq 15 (e is one of the stages in the side-draw section, and f is the stage in the prefractionator which corresponds to e):

and that in the stripping section (QS) is shown in eq A.10: ⎛x −x ⎞ s W ⎟ ⎟ y − ⎝ s + 1 xs ⎠

n

QS =

∑ Q i = W (HsL − HsV )·⎜⎜ i=s

ΔQ e → f =

While the operation line coincides with the vapor−liquid equilibrium line for each column of the heat transfer model of DWC, the total heat load of virtual intermediate heat exchanges in the rectifying section of each column (QR*) is as follows ⎛ y* − xD ⎞ Q R* = D(HrL − HrV ) ·⎜ ⎟ ⎝ y* − x* ⎠

de

−

dQ S * df

(15)

The amount of heat transferred from the side-draw section to the prefractionator in this case is as follows: 12.078 kW at the ninth stage, 20.135 kW at the 10th stage, 25.278 kW at the 11th stage, 28.559 kW at the 12th stage, 30.342 kW at the 13th stage, and 30.005 kW at the 14th stage, respectively. As shown in Figure 9, the differences in temperatures and driving forces of temperatures decrease after the heat calculated by eq 15 is transferred from the side-draw section to the prefractionator.

(11)

and that in the stripping section (QS*) is ⎛ x* − x W ⎞ Q S* = W (HsL − HsV ) ·⎜ ⎟ ⎝ y* − x* ⎠

dQ R *

(12)

Assuming that (H − H ) is constant at each stage (H − HV = ΔHR in the rectifying section and HL − HV = ΔHs in the stripping section), the heat load of virtual intermediate heat exchanger at each stage in the rectifying section of each column can be calculated by eq 13 L

dQ R * dr

V

L

⎡ dy * (x − x*) − (x − y*) ⎤ D D ⎥ ·⎜⎛ dx* ⎞⎟ = DΔHR ⎢ dx * 2 ⎢ ⎥ ⎝ dr ⎠ (y* − x*) ⎣ ⎦ (13)

and that in the stripping section can be calculated by eq 14: dQ S * ds

⎡ dy * (x* − x ) − (y* − x ) ⎤ W W ⎥ ⎛ dx * ⎞ ⎟ = W ΔHS⎢ dx * ·⎜ 2 ⎢ ⎥ ⎝ ds ⎠ ( y x ) * − * ⎣ ⎦ (14)

Figure 9. Comparison of the heat transfer process and the adiabatic process in temperature profiles.

Figure 8 shows the heat loads of virtual intermediate heat exchangers in the heat transfer model of DWC. In the enclosed region formed by the heat load curves of the side-draw section and that of the prefractionator, the heat loads in the side-draw section are less than that in the prefractionator, and the amount of heat transferred between the corresponding stages of the side-draw section and the prefractionator in that region (the

4. RESULTS AND DISCUSSION 4.1. Effect of Heat Transfer on Exergy Loss. As shown in Figure 10, the process of heat transferred from the side-draw section to the prefractionator in the heat transfer model of DWC affects the exergy loss of streams at each stage. The public rectifying section and the public stripping section, where much larger exergy loss appears when the adiabatic process between the side-draw section and the prefractionator is designed, show a significant reduction of exergy loss (as shown in Figure 10a and Figure 10d). Besides, we find that the exergy loss of the prefractionator decreases greatly (as shown in Figure 10b) while that of the side-draw section increases slightly (as shown in Figure 10c). This is because the heat loads of the sidedraw section are much smaller than that of the prefractionator, which is shown in Figure 8. Although the heat needed by the side-draw section is small, it still requires some heat from the outside. The approach we adopted is to transfer the heat from the side-draw section to the prefractionator and ignore the heat supporting the side-draw section from the outside. This new method will help realize the thermal-coupled effect between the side-draw section and the prefractionator. In summary, when the heat transfer process is introduced between the side-draw section and the prefractionator, the exergy loss of the three columns decreasees significantly although a minor increase of exergy loss in the side-draw section is observed, which leads to

Figure 8. Heat load profiles of the virtual intermediate heat exchangers in the heat transfer model of DWC. 18350



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Figure 10. Exergy loss profiles under different processes of heat transfer: a: public rectifying section, b: prefractionator, c: side-draw section, d: public stripping section.

the general reduction of the total exergy loss as well as the irreversibility of the columns. 4.2. Effect of Heat Transfer on Energy Consumption. Figure 11 shows the changes of the energy consumption of the heat transfer model under different processes of heat transfer (in which the amount of heat transfer decreases by various percentage points from the calculation stated in Section 3.2). Some conclusions can be made as follows: the energy saving effect of the heat transfer process is better than that of the adiabatic process in the beneficial heat transfer region; the more the stages within the beneficial heat transfer region are involved in the heat transfer process, the less energy is consumed; the significant reduction of energy consumption can be achieved by increasing the amount of heat transferred from the side-draw section to the prefractionator. When the stages involved in the heat transfer process are just those that consist of the beneficial heat transfer region (the ninth−14th stages in this case), the energy consumption under process 1 is 15% less than that under the adiabatic process. Indeed, the energy saving effect of DWC will be below that of

process 1 because of the limitation of the temperatures differences and the heat transfer area between the side-draw section and the prefractionator; but it is clear that the introduction of heat transfer process between the side-draw section and the prefractionator will be another way to further reduce the energy consumption when the amount of heat transfer is increased. 4.3. Effect of Heat Transfer on Optimal Operating Zone. Figure 12 shows the effect of different combinations of the vapor split ratio (RV) and the liquid split ratio (RL) on the minimum energy consumption of the heat transfer model of DWC under different processes of heat transfer within the beneficial heat transfer region. The joining points of every dotted line with the curves of energy consumption take the same value of RV. There is a point, known as the optimal combining point of RL and RV where the minimum energy consumption appears, around which there is an area with gentle curves of energy consumption (fluctuating within 1% as defined) that constrains 18351



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Figure 11. Energy consumption profiles under different processes of heat transfer.

Figure 12. The effect of different combinations of RV and RL on the minimum energy consumption.

Figure 13. The relationship between RL and RV and RL and R.

flow rate of the vapor flowed from the public stripping section to the prefractionator. The RL-R curve indicates that with the increase of RL, there is an initial fall to a minimum value followed by a rise in R. This is because the process of heat transferred from the side-draw section to the prefractionator leads to the vaporization of the liquid streams in the latter and the condensation of the vapor streams in the former. As a result, more liquid flow is needed in the prefractionator for mass transfer with the increased vapor flow, and more vapor flow is required in the side-draw section with the increased liquid flow. Consequently, the internal reflux ratio (Ri) increases, while the external reflux ratio (R) decreases; but R cannot decrease so much to avoid a failure of the separation task. This is similar to the effect of intermediate heat exchangers

the optimal operating zone under a specific process of heat transfer. Figure 12 also indicates that the curves of energy consumption, with the increase of RL and RV, initially fall to the minimum value followed by steep rise; and the effect that RL and RV bring to the energy consumption can be explained by investigating the relevance of RL and RV as well as that of RL and R (the external reflux ratio). As shown in Figure 13, under process 1, the RL-RV curve shows that RV increases with the increase of RL. The growth of RL results in an increased flow rate for the liquid flowed from the public rectifying section to the prefractionator. To maintain the same separation effect in the prefractionator, RV should be enhanced by increasing the 18352



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under different processes of heat transfer provide guidance for the improvement and practical operation of DWC.

(as discussed in Section 2) on the internal reflux ratio, the external reflux ratio, and energy consumption of a distillation system. Thus, under a specific process of heat transfer, both RL and RV need to be adjusted to determine the necessary minimum R to accomplish the separation task at the lowest energy consumption. Comparison of the different processes of heat transfer, as shown in Table 4, gives a hint that the increase of amount of

■

Deduction of the Total Heat Load of Intermediate Heat Exchangers in a Distillation Column

The total heat load of the intermediate heat exchangers in the rectifying section (Σri=1Qi) and that in the stripping section n (Σi=s Qi) of a distillation column (Figure 14) can be obtained by the following:

Table 4. Optimal Operating Zone under Different Processes of Heat Transfer process

RL

RV

R

process 1 process 2 process 3 process 4 adiabatic process

[0.293,0.394] [0.297,0.385] [0.302,0.376] [0.308,0.365] [0.314,0.351]

[0.25,0.5] [0.28,0.5] [0.3,0.5] [0.35,0.5] [0.4,0.5]

[7.50,7.62] [7.85,7.93] [8.02,8.1] [8.25,8.32] [8.71,8.75]

APPENDIX

heat transferred from the side-draw section to the prefractionator helps expand the optimal operating zone. The maximum interval length of RL is 2.73 times higher than that under the adiabatic process, and the maximum interval length of RV is 2.5 times higher than the latter. Under these processes of heat transfer, the limited fluctuation of RL and RV will not induce significant change of the minimum energy consumption, which is favorable to RV since it is hard to regulate; but the fluctuation of RV must be confined to a certain range, or else, even with the operation of regulating RL, the optimal operating points for minimum energy consumption could possibly be missed, resulting in the decrease of operating stability. Under the different processes of heat transferred from the side-draw section to the prefractionator, RL and RV must be reregulated to find the optimal operating zone. For the convenience of experimental direction and real application, the various intervals of RL, RV, and R within the optimal operating zone are listed in Table 4.

Figure 14. A distillation column in which the intermediate heat exchangers are introduced.

The material balance of the whole column:

F=D+W FxF = DxD + WxW

(A.1)

The enthalpy balance of the whole column: n

∑ Q i + FHF = DHD + WHW i=1

Solving eq A.1 for D and W x − xw D= F F xD − xW x − xF W= D F xD − xW

5. CONCLUDING REMARKS Based on the analysis of the exergy loss of streams at different stages, the process of heat transfer among the virtual intermediate exchangers is introduced in the heat transfer model of DWC. The virtual intermediate exchangers are used to replace the heat transfer process between the side-draw section and the prefractionator. Particularly, the virtual intermediate exchangers are able to realize the thermal-coupled effect of the heat transfer process which can minimize the driving forces of mass and heat transfer as well as lower the irreversibility and energy consumption of the whole columns. The virtual intermediate exchangers are also used as an assisted tool to analyze the beneficial heat transfer region and the amount of heat transfer for the minimum energy consumption, providing a generalizable and systematic analysis of DWC featuring a heat transfer process across the dividing wall. Compared with a Petlyuk Column featuring an adiabatic process between the main column and the prefractionator, the heat transfer model of DWC with the process of heat transfer has less exergy loss, lower energy consumption, and more expanded optimal operating zone. The limited fluctuation of RL and RV will not lead to significant change of the minimum energy consumption, which is favorable to RV since it is hard to regulate. The operating intervals of the optimal RV, RL, and R

(A.2)

(A.3)

Solving eq A.2 for Σni=1Qi n

∑ Q i = DHD + WHW − FHF i=1

(A.4)

The material balance at the stage r (which requires 1 < r < f) in the rectifying section of the column Vr + 1 = Lr + D Vr + 1yr + 1 = Lr xr + DxD

(A.5)

and the enthalpy balance at the stage r r

∑ Q i + Vr+ 1HrV+ 1 = Lr HrL + DHD i=1

(A.6)

Replacing Vr+1 and Lr in eq A.6 with those in eq A.5 arrives at a result (simply suppose HVr = HVr+1) as 18353


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⎛y

r

∑ Q i = D(HrL − HrV )·⎜⎜ i=1

y* = equilibrium mole fraction for the light key component in vapor phase

r+1

(A.7)

Subscripts

D = distillate F = feed R = rectifying section S = stripping section W = bottom product e = the stage in the side-draw section of heat transfer model of DWC f = the stage in the prefractionator of heat transfer model of DWC n = the stage in the distillation column r = the stage in the rectifying section of distillation column s = the stage in the stripping section of distillation column

The material balance at the stage s (which requires f < s < n) in the stripping section of the column Ls = Vs + 1 + W Lsxs = Vs + 1ys + 1 + WxW

(A.8)

and the enthalpy balance at the stage s n

∑ Q i + LsHsL = Vs + 1HsV+ 1 + WHW i=s

(A.9)

Replacing Vs+1 and Ls in eq A.9 with those in eq A.8 arrives at a result (simply suppose HVs = HVs+1) as ⎛

n

∑ Qi = i=s

■

W (HsL

−

Superscripts

L = liquid phase V = vapor phase 1 = the state of in-streams 2 = the state of out-streams

⎞

x − xW ⎟⎟ HsV ) ·⎜⎜ s y ⎝ s + 1 − xs ⎠

(A.10)

Greek Letters

AUTHOR INFORMATION

■

Corresponding Author

*Phone: 86-022-60202246. Fax: 86-022-26564475. E-mail: [email protected].

Δ = change

REFERENCES

(1) Humphrey, J. L.; Seibert, A. F. New Horizons in distillation. Chem. Eng. 1992, 99, 86−98. (2) Shinskey, F. G. Distillation Column; McGraw Hill: New York, 1984. (3) Zemp, R. J.; de Faria, S. H. B.; de L. Oliveira Maia, M. Driving force distribution and exergy loss in the thermodynamic analysis of distillation columns. Comput. Chem. Eng. 1997, S523−S528. (4) Kotas, T. J. The exergy method of thermal plant analysis; Butterworths: London. 1985. (5) Petlyuk, F. B.; Platonov, V. M.; Slavinski, D. M. Thermodynamically optimal method for separating multicomponent mixtures. Ind. Chem. Eng. 1965, 5, 555−561. (6) Wright, R. O.; Elizabeth, N. J. Fractionation Apparatus. U.S. Patent 2471134. 1949. (7) Kaibel, G. Distillation column with vertical partitions. Chem. Eng. Technol. 1987, 10, 92−98. (8) Schultz, M. A.; Stewart, D. G.; Harris, J. M. Reduce costs with dividing-wall columns. Chem. Eng. Prog. 2002, 98, 64−71. (9) Triantafyllou, C.; Smith, R. The design and optimization of fully thermally coupled distillation columns. Chem. Eng. Res. Des. 1992, 70, 118−132. (10) Hernandez, S.; Jimenez, A. Design of energy-efficient Petlyuk systems. Comput. Chem. Eng. 1999, 23, 1005−1010. (11) Halvorsen, I. J.; Skogestad, S. Optimal operation of Petlyuk distillation: steady-state behavior. J. Process Control 1999, 9, 407−424. (12) Niggemann, G.; Hiller, C.; Fieg, G. Modeling and in-depth analysis of the start-up of dividing-wall columns. Chem. Eng. Sci. 2011, 66, 5268−5283. (13) Rewagad, R. R.; Kiss, A. A. Dynamic optimization of a dividingwall column using model predictive control. Chem. Eng. Sci. 2012, 68, 132−142. (14) Carlberg, N. A.; Westerberg, A. W. Temperature heat diagrams for complex columns. 2: Underwood’s method for side strippers and enrichers. Ind. Eng. Chem. Res. 1989, 28, 1379−1386. (15) Carlberg, N. A.; Westerberg, A. W. Temperature heat diagrams for complex columns. 3: Underwood’s method for the Petlyuk Configuration. Ind. Eng. Chem. Res. 1989, 28, 1386−1397. (16) Dunnebier, G.; Pantelides, C. C. Optimal design of thermally coupled distillation columns. Ind. Eng. Chem. Res. 1999, 38, 162−176. (17) Abdul Mutalib, M. I.; Smith, R. Operation and control of dividing wall distillation columns: part 1: degrees of freedom and dynamic simulation. Trans IChemE 1998, 76, 308−318.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to thank the Excellent Youth Foundation of Hebei University of Technology (2011004) and the National Natural Science Foundation of China (21306036) for the financial support.

■

NOMENCLATURE B = bottom product flow rate D = distillate flow rate EX = exergy EXQ = exergy of heat transfer process EX Loss = exergy loss F = feed flow rate H = enthalpy L = liquid flow rate Q = heat load; amount of heat transfer R = external reflux ratio Ri = internal reflux ratio RL = liquid split ratio (namely the ratio of the falling liquid flow in the prefractionator to that from the bottom of the public rectifying section) RV = vapor split ratio (namely the ratio of the rising vapor flow in the prefractionator to that from the top of the public stripping section) S = entropy T = temperature T0 = environment temperature V = vapor flow rate p0 = environment pressure x = mole fraction for the light key component in liquid phase x* = equilibrium mole fraction for the light key component in liquid phase y = mole fraction for the light key component in vapor phase 18354



Article

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