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Computational Study on Binary Distillation of Heat-Driven Distillation System Min-Chih Chen, Kenji Takeshita,* and Masaru Ishida Chemical Resources Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan
A heat-driven distillation (HDD) system, in which each rectifying stage is divided into an evaporator and a condenser, was proposed for improving both the separation performance and the energy-saving effect. In this system, the mass transfer can be controlled by the internal flows of vapor and liquid, which are generated by the supply of heat to the evaporator and the release of heat from the condenser, respectively. Binary distillation of methanol and ethanol by a HDD system with 12 sets of evaporators and condensers was computed. The separation performance was improved by increasing the internal flow rates. When the internal flow rates were increased 5 times (from 1 to 5 mol/s), the overall separation factor of methanol at the appropriate recycle ratio was increased ∼22 times. Then, the energy consumption was also increased in proportion to the increase in the internal flow rates; however, it was reduced drastically by introducing the internal heat-exchange processes, in which heat generated by the isentropic compression of the vapor phase in the condensers is utilized for the vaporization of liquid in the evaporators. The pressures of the condensers were adjusted under the condition that total exergy loss was minimized. Then, the heat supplied to the evaporators was close to zero. The energy consumption is only the compression work of the condensers and is evaluated as ∼10% of the heat supplied to the reboiler of a conventional distillation system with the same separation factor, under the conditions that the internal flow rates and the heat transfer area of internal heat exchangers are 2 mol/s and 5 m2, respectively. A large energy-saving effect is expected for the HDD system. 1. Introduction Distillation is a key separation technology that is applied widely to oil refining, the pharmaceutical industry, the food industry, etc.; however, much energy is consumed in the industrial distillation systems, whose energy consumption corresponds to ∼3% of that of the world.1 Therefore, the energy saving of distillation systems is useful for the suppression of CO2 release and is indispensable as a solution of serious environmental problems such as global warming. Many energy-saving technologies have been developed since the 1940s,2-4 for example, the divided-wall column (DWC) proposed by Wright and Elizabeth,5-7 the ideal heat-integrated distillation column (HIDic) by Takamatsu and coworkers,8-10 the multi-effect batch distillation system by Hasebe et al.11 and Skogestad and Wittgens,12 and the diabatic distillation column by Rivero and coworkers.13,14 By introducing these technologies, the energy saving of distillation system will be attained successfully. Especially, the application of the HIDic process is valid for saving energy, and the energy consumption is reduced to∼60% of that of a conventional distillation column.10 Although these previous technologies are useful, further energy saving may be requested in the future. Then, the substantial improvement of mass and heat transfer mechanisms in distillation systems will be required for complying with such a request. * To whom correspondence should be addressed. Tel.: 81-45-924-5255. Fax: 81-45-924-5253. E-mail: takeshit@ res.titech.ac.jp.
In this study, we propose a new distillation system, which is constituted by the combination of many evaporators and condensers, as shown in Figure 1. The mass and heat transfer processes are quite different from those for the conventional distillation system. In the conventional distillation system (Figure 2a), the mass and heat transfer occurs by the vapor-liquid contact in each rectifying stage and these transport rates are affected strongly by the mechanical structure of the rectifying stage. On the other hand, in the proposed system (Figure 2b), a rectifying stage is divided into an evaporator and a condenser. Then, the mass and heat transfer are carried out by the internal flows between the evaporator and the condenser. Note that these internal flow rates can be controlled by the supply of external heat to the evaporators and the release of heat from the condensers and that the separation performance can be controlled by adjusting these internal flows. Moreover, when the internal heat-exchange process between the evaporator and the condenser with the same number is introduced and heat generated by the compression of vapor flows in the condensers is transferred to the evaporators, (Figure 6), the heat supplied to the evaporators may be suppressed; a large energysaving effect is expected. The proposed system is classified as a thermally controlled (diabatic) distillation system and is named “heat-driven distillation (HDD) system” from its unique features. In this paper, a mathematical model of the HDD system was developed, and the binary distillation of methanol and ethanol using a HDD system with 12 sets of evaporators and condensers was calculated. Further-
10.1021/ie0500624 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/01/2005
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Figure 1. Flow sheet of heat-driven distillation (HDD) system.
more, the introduction of internal heat-exchange processes was considered for the reduction of energy consumption, and the effects of the introduction of internal heat exchange on the separation performance and the energy consumption were evaluated. From these results, the superiority of the HDD system over the conventional distillation system was discussed. 2. Numerical Calculation of Distillation Behavior of HDD System 2.1. Establishment of Mathematical Model. A mathematical model to calculate the mass and heat balance in the HDD system was established in this study. As shown in Figure 1, the HDD system consists of evaporators and condensers. These devices are connected by vapor flow (Vj), liquid flow (Lj), and internal flows of vapor and liquid (REj and RCj ). Feed flows of vapor and liquid (FVj and FLj ) are considered for all evaporators and condensers. Product flows, distillate (D) and bottom (B), are drawn out from the top condenser and the bottom evaporator, respectively. The mass and heat balance equations used in the mathematical model are described in Appendix A. For the calculation of mass balance, both the overall flow
balance and the component balance were considered. For the calculation of heat balance, the enthalpy changes of vapor and liquid by convection, the heat supplied to each evaporator (QEj ), and the heat released from each condenser (QCj ) were considered. When the internal heat exchange proposed for the reduction of energy consumption was considered (see Figure 6), the heat transferred from the condenser to the evaporator (Q j) was added in the heat balance equations. The calculation procedure of the mathematical model is as follows. The concentrations of components in the evaporators and the condensers are calculated from the mass balance equations, eqs A1-A12 in Appendix A. Next, the temperatures in the evaporators and the condensers are evaluated by the boiling point calculation. From these results, the heat balance equations, eqs A13-A18 in Appendix A, are calculated and the appropriate flow rates of vapor and liquid are determined. These steps are repeated until both the mass balance and the heat balance are satisfied for all evaporators and condensers. 2.2. Evaluation of Exergy Losses of HDD System. Exergy loss (EXL) is very useful as a thermodynamic measure to evaluate the energy efficiency and productivity in a chemical process. In this study, total exergy loss of the HDD system was calculated. The calculation procedure of total exergy loss of the HDD system is shown in Appendix B. We considered several exergy losses caused by the temperature changes of vapor and liquid flows introduced to the evaporators and the E C and EXLT,j ), the mixing of compocondensers (EXLT,j E nents in the evaporators and the condensers (EXLm,j C and EXLm,j), and the supply of heat to the evaporators E and the release of heat from the condensers (EXLQ,j C 15-17 and EXLQ,j). If necessary, the exergy loss for the EX ) was internal heat exchange shown in Figure 6 (EXLQ,j further considered. Total exergy loss (TEXL) was given as the sum of these exergy losses. 2.3. Calculation Conditions. The binary distillation of methanol (i ) 1) and ethanol (i ) 2) was calculated for a HDD system with 12 sets of evaporators and condensers. An equimolar mixture of methanol and ethanol was used as a feed solution. Half of the feed solution was vaporized by an external evaporator (q ) 0.5), and the feed flows of vapor and liquid were fed to the sixth evaporator and the sixth condenser, respectively. The feed rates of vapor and liquid were given as 0.5 mol/s. The flow rates of distillate, D, and bottom, B, were also given as 0.5 mol/s. The operating pressure of the evaporator, PEj , was kept constant at 1.01 × 105 Pa (1 atm) and that of the condenser, PCj , was increased freely by the compressors when the internal heat exchange shown in Figure 6 was considered. The activ-
Figure 2. Comparison of rectifying stages between the HDD system and the conventional one.
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Figure 4. Comparison of concentration profiles of methanol and ethanol between the HDD system and the conventional one. Both the recycle ratio of the HDD system (RC) and the reflux ratio of the conventional distillation system (R) were kept at 4.1. The E ) RCj ) internal flow rates of the HDD system were given as Rj-1 5 mol/s (2 e j e 12).
RC (dRC1/D). The RC value, which is similar to the reflux ratio (R) of the conventional distillation system, is an important parameter for the operation of the HDD E and RCj (2 e system. Then, the internal flow rates, Rj-1 j e 12), are changed in the range of 1-5 mol/s. The overall separation factor increased with increasing internal flow rates and was maximized by selecting the optimum recycle ratio. The relation between the Sov value and the optimum recycle ratio is summarized in Table 1. Note that the Sov value is enhanced 22× with increasing the internal flow rates from 1 to 5 mol/s. These results indicate that the increase in the internal flow rates is valid for improving the separation performance. The dotted line represents the relation between the overall separation factor and the reflux ratio for the conventional distillation system. The overall separation factor of the conventional distillation system increased gradually with increasing reflux ratio. This tendency is quite different from that of the HDD system. As shown in Table 1, for the conventional system, the high reflux ratio over 50 is required to attain the overall separation factor of 500. On the other hand, for the HDD E ) RCj ) 3 mol/s (2 e j e 12), the overall system at Rj-1 separation factor of 500 was attained easily at the low recycle ratio (RC) of 3.4. Figure 4 shows the comparison
Figure 3. Relation between the overall separation factor of methanol, Sov, and the recycle ratio, RC. The internal flow rates, E Rj-1 and RCj (2 e j e 12), were changed in the range of 1-5 mol/s. The dotted line represents the relation between Sov and the reflux ratio, R, for the conventional distillation system.
ity coefficients of methanol and ethanol in the liquid phase, γij, which were required for the correction of Raoult’s law, were evaluated by Wilson’s equation. From the calculation results, the overall separation factor of methanol between the top condenser and the C C E /(1-y1,1 )]/[x1,12 / bottom evaporator, Sov, defined as [y1,1 E (1-x1,12)], was evaluated. The same calculation was carried out for a 12-stage conventional distillation system by a mathematical model based on the classical tridiagonal method.18 The separation performance and energy consumption for the HDD system were calculated and compared with those for the conventional distillation system. 3. Results and Discussion 3.1. Separation Performance of HDD System. Figure 3 shows the relationship between the overall separation factor of methanol, Sov, and the recycle ratio,
Table 1. Summary of Separation Performance, Heat Consumption, Compression Work, and Exergy Loss for HDD System and Conventional Distillation System
system
internal flow rates RCj , REj (mol/s)
optimum recycle ratio or reflux ratio RC or R
overall sep. fac. Sov
heat supplied to evaporators or reboiler (kJ/s)
heat released from condensers or top condenser (kJ/s)
heat-driven distillation
without internal heat exchange
1 2 3 4 5
2.3 3.0 3.4 3.8 4.1
63 236 517 908 1396
462 893 1320 1740 2170
483 913 1340 1760 2190
heat-driven distillation
with internal heat exchange
2a 2b 5a 5b
3.0 3.0 4.1 4.1
201 213 904 1084
∼0 ∼0 ∼0 ∼0
37 32 107 69
2.3 3.0 3.4 3.8 4.1 10 50 100
18 30 39 48 55 203 479 536
40 53 60 67 72 179 899 1800
42 55 62 69 75 181 901 1801
conventional distillation
compression work (kJ/s)
TEXL (kJ/s) 34 70 105 141 176
16 10 83 47
14 8 70 40 2.5 3.4 4.0 4.5 5 13 72 146
a In the case that the heat transfer area between each condenser and evaporator is given as A ) 5 m2. b In the case that the heat transfer area is increased to A ) 10 m2.
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Figure 5. Results of the exergy analysis for the HDD systems with and without the internal heat exchange.
of the concentration profiles of methanol and ethanol between the HDD system and the conventional one. Then, both the recycle ratio of the HDD system and the reflux ratio of conventional distillation system were kept at 4.1 and the internal flow rates of the HDD system E ) RCj ) 5 mol/s (2 e were given as 5 mol/s, namely Rj-1 j e 12). Note that the difference between the concentrations of methanol in the liquid flow outputted from the evaporators, Lj, and in the vapor flow outputted from the condensers, Vj, is larger than that between the concentrations of methanol in the liquid flow and in the vapor flow outputted from the rectifying stages of the conventional system. This is because the vapor that abundantly contains the light component (methanol) is transferred from the evaporator to the condenser and the liquid that abundantly contains the heavy component (ethanol) is transferred from the condenser to the evaporator by the internal flows, REj and RCj . As a result, the mass transfer is promoted by the internal flows, and the high separation factor that cannot be attained by the conventional distillation system is found for the HDD system with internal flow rates >3 mol/s, as shown in Figure 3. The energy consumption as well as the mass transfer should be considered for the evaluation of practicability of the HDD system. As shown in Table 1, the serious increase in the energy consumption was observed by increasing the internal flow rates. Under the conditions E ) RCj ) 5 mol/s (2 e j e 12) and RC ) 4.1, the that Rj-1 exergy loss for the HDD system was increased to ∼35× that for the conventional distillation system. Figure 5 shows the results of the exergy analysis of the HDD system. See the results of the HDD system without the internal heat exchange. The large exergy loss, which is E C and EXLQ,j , is caused by the supply observed for EXLQ,j of a large amount of heat from the heat source to the evaporators and the release of a large amount of heat from the condensers to the heat sink. The supply of external heat to the evaporators should be suppressed for the energy saving of the HDD system. 3.2. Energy-Saving Effect of HDD System with Internal Heat Exchange. The concept of the internal heat exchange is shown in Figure 6. As shown in this figure, the heat-exchange processes, in which heat obtained by the compression of vapor flows in the condensers is used for the vaporization of liquid in the
Figure 6. Schematic diagram of the HDD system with the internal heat-exchange process.
Figure 7. Optimum pressure profiles of condensers in the HDD system with the internal heat exchange, which was operated at E the conditions of Rj-1 ) RCj ) 5 mol/s (2 e j e 12) and RC ) 4.1
evaporators, were introduced in the HDD system. The heat transfer in the HDD system with the internal heat exchange is estimated roughly as follow. For example, if the temperatures of the condensers are assumed to be 13 K higher than those of the evaporators (∆T ) 13 K), the heat transfer rate is evaluated as 195 kJ/s ()hA∆T) under the conditions that the heat transfer area (A) and the overall heat transfer coefficient (h) are 5 m2 and 3000 W m-2 K-1, respectively. Such a temperature difference can be attained easily by appropriately adjusting the pressures of the condensers in the range of 1.5-2 atm. Since the latent heat for the equimolar mixture of methanol and ethanol (feed solution) is evaluated as 38 kJ/mol, the high vaporization rate of 5 mol/s can be attained easily in the evaporators. This estimation indicates that the liquid in the evaporators can be vaporized sufficiently by the internal heat exchange. Under the condition of isentropic compression, the temperature changes of vapor in the condensers are represented generally as follows,
( )
Tout Pout ) (R/Cp) Tin Pin
(1)
where Tin and Pin denote the temperature and pressure of the vapor before compression and Tout and Pout
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E Figure 8. Heat balance of the HDD system under the conditions of Rj-1 ) RCj ) 2 mol/s (2 e j e 12) and RC ) 3.0. QEj , QCj , Qj and WCj denote the total heat supplied to the evaporators, the total heat released from the condensers, the total heat of the internal heat exchange, and the compression work, respectively.
represent those after compression. Therefore, the total work (W) required for the compression of the internal vapor flow, REj , is given as19 n
W)
∑ j)1
{ [( ) ]} REj
Cp TEj
C Pj+1
PEj
(R/Cp)
-1
(2)
The compression works of other vapor flows, Vj and FVj , are also evaluated in the same manner. From these relations, the appropriate pressures of the condensers were calculated under the condition that total exergy loss, TEXL, was minimized. Figure 7 shows the appropriate pressure profiles of the condensers. When each condenser is adjusted to the appropriate pressure, the external heat supplied to the evaporators is close to zero by the internal heat exchange from the condensers to the evaporators. When the heat transfer area, A, is increased from 5 to 10 m2, the pressures of the condensers are reduced. The design of a heat exchanger with a large heat transfer area is important for the practical use of the HDD system. Figure 8 shows the calculation results of the heat balance for the HDD systems with and without the internal heat exchange. The heat supplied to each evaporator (QEj ), that released from each condenser (QCj ), that transferred to each evaporator by the internal heat exchange (Qj), and the compression work (WCj ) were calculated. Then, the internal flow rates and the E ) RCj ) 2 mol/s (2 e j e recycle ratio were given as Rj-1 12) and 3.0, respectively. In the HDD system without the internal heat exchange (Figure 8a), it should be noted that a large amount of heat is supplied to the evaporators (total heat supply ) 893 kJ/s) and is released from the condensers (total heat release ) 913 kJ/s). On the other hand, in the HDD system with internal heat exchange (Figure 8 b), the heats supplied to the evaporators are reduced drastically by introducing the internal heat exchange, and the QEj values are close to zero. Then, total compression work is only 16 kJ/s. As shown in Table 1, total energy consumption is reduced drastically for the HDD system with the internal heat exchange and corresponds to ∼10% of the heat supplied to the reboiler of the conventional distillation system with the same separation factor. These results suggest that the HDD system with internal heat exchange is valuable as a new energy-saving distillation
technology. Finally, the exergy loss for the HDD system with the internal heat exchange was calculated. The E and results were shown in Figure 5. Both EXLQ,j C EXLQ,j are reduced drastically, and total exergy loss was reduced to ∼20% of that of the HDD system without the internal heat exchange. The large energy consumption of the HDD system can be suppressed by the introduction of the internal heat-exchange process. 4. Conclusions The increase in the internal flow rates is very effective for improving the separation performance of the HDD system. The overall separation factor of methanol at the optimum reflux ratio increases ∼22× with increasing internal flow rates from 1 to 5 mol/s. The mass transfer is promoted by the internal flows, and the high separation factor that cannot be attained by the conventional distillation system is observed for the HDD system with internal flow rates >3 mol/s. The energy consumption of the HDD system is increased in proportion to the internal flow rates and is much larger than that of the conventional distillation system. However, the energy consumption can be reduced drastically by the introduction of the internal heat-exchange process, in which the heat obtained by the compression of vapor flows in the condensers is used for the vaporization of liquid in the evaporators. The heat supplied to the evaporators, QEj , is close to zero by adjusting the pressures of condensers appropriately, and the energy consumption is only the compression work E of the condensers. Under the conditions of Rj-1 ) RCj ) 2 mol/s (2 e j e 12) and A ) 5 m2, the compression work is evaluated as 16 kJ/s and the energy consumption is reduced to ∼10% of the heat supplied to the reboiler of the conventional distillation system with the same separation factor. These results suggest that the HDD system is valuable as a new energy-saving distillation technology Appendix A. Mass and Heat Balance Equations Used in the Mathematical Model For the calculation of the mass and heat balances of the HDD system, the equilibrium between vapor and liquid are assumed for all evaporators and condensers. Therefore, both the overall flow balance and the mass
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balance for the ith component are described as the following algebraic equations; for the top condenser and evaporator (j ) 1),
FV1 + V2 ) D + RC1
(A1)
F C C CC FyV,1 i,1 + V2y i,2 ) Dyi,1 + Rxi i,1
(A2)
FL1 + RC1 + RC2 ) L1 + RE1
(A3)
F C E E C FL1 xi,1 + RC1 xi,1 + RC2 xi,2 ) L1 xi,1 + RE1 yi,1 (A4)
for the jth condenser and the jth evaporator (2 e j e n - 1), E ) Vj + RCj FVj + Vj+1 + Rj-1
(A5)
F C E E C C FVj yi,j + Vj+1 yi,j+1 + Rj-1 yi,j-1 ) Vj yi,j + RCj xi,j (A6) C ) Lj + REj FLj + Lj-1 + Rj+1
(A7)
F E C C E E FLj xi,j + Lj-1 xi,j-1 + Rj+1 xi,j+1 ) Lj xi,j + REj yi,j (A8)
and for the bottom condenser and evaporator (j ) n), E FVn + Rn-1 + REn ) Vn + RCn
tor, QEj , and the heat released from the condenser, QCj , are evaluated. If the heat exchange between the jth evaporator and the jth condenser is considered, the heat transfer rate, Qj ()hA(TCj - TEj )), which is shown in the parentheses of the heat balance equations, should be added in the heat balance equations, where h and A denote the heat transfer coefficient and the heat transfer area, respectively. Appendix B. Evaluation of Exergy Loss in the HDD System Exergy loss (EXL) is a thermodynamic measure to evaluate the energy efficiency and productivity of chemical process. For the HDD system, we consider several exergy losses. The exergy losses for the jth evaporator and the jth condenser, EXLEj and EXLCj , are represented as E E E EX EXLEj ) EXLT,j + EXLm,j + EXLQ,j + EXLQ,j C C C EXLCj ) EXLT,j + EXLm,j + EXLQ,j
F yi,n
+
E Rn-1
E yi,n-1
+
REn
E yi,n
)
C Vn yi,n
+
(A20)
Total exergy loss (TEXL) is given as the sum of exergy losses for all evaporators and condensers
(A9) n
FVn
(A19)
RCn
C xi,n
(A10) FLn + Ln-1 ) B + REn
(A11)
E E F E FLn xi,n + Ln-1 xi,n-1 ) Bxi,n + REn yi,n
(A12)
On the other hand, the heat balance is described by the use of the enthalpies of vapor and liquid. For the top condenser and evaporator (j ) 1), C FV,1 hFV,1 + V2 hCV,2 ) DhCV,1 + RCi hL,1 + QC1 (+Q1) (A13) F C C FL1 hL,1 + RC1 hL,1 + RC2 hL,2 + QEi (+Q1) ) E + RE1 hEV,1 (A14) L1hL,1
for the jth condenser and the jth evaporator (2 e j e n - 1), F C E E + Vj+1 hV,j+1 + Rj-1 hV,j-1 ) FVj hV,j C C + RCj hV,j + QCj (+Qj) (A15) Vj hC,j F E C C + Lj-1hL,j-1 + Rj+1 hL,j+1 + QEj (+Qj) ) FLj hL,j E E + REj hV,j (A16) Lj hL,j
and for the bottom condenser and evaporator (j ) n) F E E E + Rn-1 hV,n-1 + REn hV,n ) FVn hV,n C C + RCn hL,n + QCn (+Qn) (A17) VnhV,n F E E E + Ln-1hL,n-1 + QEn (+Qn) ) BhL,n + REn hV,n FLn hL,n (A18)
From these equations, the heat supplied to the evapora-
TEXL )
∑ j)1
n
EXLEj +
EXLCj ∑ j)1
(A21)
E C E C E C Then, EXLT,j , EXLT,j , EXLm,j , EXLm,j , EXLQ,j , EXLQ,j , EX and EXLQ,j are calculated as follows. E C and EXLT,j . For the jth Evaluation of EXLT,j E evaporator, EXLT,j is represented as the sum of exergy C losses by the temperature changes of Lj-1, FLj , Rj+1 inputted in the jth evaporator.
E L FL RC ) EXLT,j + EXLT,j + EXLT,j EXLT,j
(A22)
Each term can be calculated according to the previous paper.15-17
[( ) ( [( ) ( [( ) ( T0
L L EXLT,j ) Qj-1 1-
FL ) QFL 1EXLT,j j
TEj
T0
TEj
RC RC ) Qj+1 1EXLT,j
T0
TEj
2T0
- 1-
- 1-
E Tj-1
2T0 E TFL j + Tj
- 1-
2T0 RC Tj+1
)] )] )]
+ TEj
+ TEj
(A23)
(A24)
(A25)
where T0 is the environment temperature ()298.15 K). L C , QFLj , and QRj+1 represent the heats required for Qj-1 the temperature changes of the inputted flows and are given by the enthalpy calculation of each flow. The expression in the parentheses of each equation represents the change of energy quality. C The exergy loss for the jth condenser, EXLT,j is given as the sum of exergy losses by the vapor flow from the (j+1)th condenser (Vj+1), the feed vapor flow (FVj ), and
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the internal vapor flow from the (j-1)th evaporator E ), (Rj-1 C V FV RE EXLT,j ) EXLT,j + EXLT,j + EXLT,j
(A26)
E . and can be calculated in the same manner as EXLT,j E C Evaluation of EXLm,j and EXLm,j. The exergy loss for the mixing of components in liquid phase of the jth evaporator is given as
m
E EXLm,j
) RT0
∑
i)1
(
E Lj-1 xi,j-1
ln
E xi,j-1
+
E xi,j
C Rj+1
FLj
RC xi,j+1
ln
F xi,j
ln
)
RC xi,j+1 E xi,j
F xi,j
+
E xi,j
(A27)
from the change of mixing enthalpy of the liquid phase. On the other hand, the exergy loss for the mixing of components in the vapor phase of the condenser is given similarly as C EXLm,j )
(
RT0 Vj+1 ln
C Pj+1
PCj
+ FVj ln
PFV j PCj
E + Rj-1 ln
)
RC Pj-1
PCj
(A28)
from the change of partial pressures of the components in the vapor phase. E C EX , EXLQ,j , and EXLQ,j . The Evaluation of EXLQ,j heat supplied to the jth evaporator and the heat released from the jth condenser are considered as the heat transfer from an external heat source to the jth evaporator and that from the jth condenser to a heat sink, respectively. Temperatures of the heat source and the heat sink are assumed as TEn + 10 and TC1 - 10, respectively. Thus, these exergy losses are given as
) ( )] [( )] [( ) (
E ) QEj 1 EXLQ,j
C ) QCj 1 EXLQ,j
T0
TEn T0
TCj
+ 10
- 1-
- 1-
T0
TEj
T0
TC1
- 10
(A29)
(A30)
When the internal heat exchange between the jth evaporator and the jth condenser is considered, the heat obtained by the compression of the jth condenser is transferred to the jth evaporator. Then, the exergy loss EX , is given as for the internal heat exchange, EXLQ,j
[( ) ( )]
EX ) Qj 1 EXLQ,j
T0
TCj
- 1-
T0
TEj
(A31)
Nomenclature A ) heat transfer area between evaporator and condenser, m2 B ) flow rate of bottom, mol/s Cp ) heat capacity of vapor, J/mol K D ) flow rate of distillate, mol/s EXLCj ) exergy loss in the jth condenser, kJ/s EXLEj ) exergy loss in the jth evaporator, kJ/s C ) exergy loss for mixing of vapor flows inputted in EXLm,j the jth condenser, kJ/s
E ) exergy loss for mixing of liquid flows inputted in EXLm,j the jth evaporator, kJ/s C EXLQ,j ) exergy loss for heat transfer from the jth condenser to the heat sink, kJ/s E ) exergy loss for heat transfer from heat source to EXLQ,j the jth evaporator, kJ/s EX EXLQ,j ) exergy loss for heat transfer by internal heat exchange, kJ/s C EXLT,j ) exergy loss for temperature changes of flows inputted in the jth condenser, kJ/s E EXLT,j ) exergy loss for temperature changes of flows inputted in the jth evaporator, kJ/s FL EXLT,j ) exergy loss for temperature change of liquid feed flow inputted in the jth evaporator, kJ/s L EXLT,j ) exergy loss for temperature change of liquid flow inputted in the jth evaporator, kJ/s RC EXLT,j ) exergy loss for temperature change of recycle flow inputted in the jth condenser, kJ/s FLj ) liquid feed to the jth evaporator, mol/s FVj ) vapor feed to the jth condenser, mol/s h ) overall heat transfer coefficient, W/m2‚K C hL,j ) enthalpy of liquid phase in the jth condenser, J/mol C ) enthalpy of vapor phase in the jth condenser, J/mol hV,j E hL,j ) enthalpy of liquid phase in the jth evaporator, J/mol E hV,j ) enthalpy of vapor phase in the jth evaporator, J/mol F hL,j ) enthalpy of liquid feed flow supplied to the jth evaporator, J/mol F hV,j ) enthalpy of vapor feed flow supplied to the jth condenser, J/mol KCi,j ) equilibrium ratio of i component in the jth condenser KEi,j ) equilibrium ratio of i component in the jth evaporator Lj ) liquid flow rate from the jth evaporator, mol/s m ) number of components (m ) 2) n ) number of stages, evaporators, or condensers (n ) 12) PCj ) pressure of the jth condenser, Pa PEj ) pressure of the jth evaporator, Pa Qj ) heat transferred from the jth condenser to the jth evaporator, kJ/s QCj ) heat released from the jth condenser to the heat sink, kJ/s QEj ) heat supplied from the heat source to the jth evaporator, kJ/s QLj ) heat transferred by liquid flow Lj, kJ/s QFLj ) heat transferred by liquid feed flow FLj , kJ/s QRCj ) heat transferred by internal liquid flow RCj , kJ/s R ) reflux ratio of conventional distillation system RC ) recycle ratio of HDD system ()RC1 /D ) R ) gas constant, J/mol‚K RCj ) internal liquid flow rate from the jth condenser to the (j-1)th evaporator, mol/s REj ) internal vapor flow rate from the (j-1)th evaporator to the jth condenser, mol/s Sov ) overall separation factor of methanol T ) temperature, K T0 ) environmental temperature ()298.15 K), K TCj ) temperature in the jth condenser, K TEj ) temperature in the jth evaporator, K TFLj ) temperature in the liquid feed flow supplied to the jth evaporator, K TRCj ) temperature in the internal liquid flow from the jth condenser, K TEXL ) total exergy loss, kJ/s
Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9163 Vj ) vapor flow rate from the jth condenser, mol/s WCj ) work required for the compression of vapor phase, J/s xCi,j ) mole fraction of i component in the liquid phase of the jth condenser xEi,j ) mole fraction of i component in the liquid phase of the jth evaporator yCi,j ) mole fraction of i component in the vapor phase of the jth condenser yEi,j ) mole fraction of i component in the vapor phase of the jth evaporator Subscripts i ) component (i ) 1 for methanol, i ) 2 for ethanol) j ) stage number Greeks γi,j ) activity coefficient
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Received for review January 17, 2005 Revised manuscript received August 6, 2005 Accepted August 16, 2005 IE0500624
