Separation of an AcetoneâMethanol Mixture by ... - ACS Publications

Ind. Eng. Chem. Res. 2010, 49, 3785–3793

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Separation of an Acetone-Methanol Mixture by Pressure-Swing Batch Distillation in a Double-Column System with and without Thermal Integration Gabor Modla* and Peter Lang Department of Building SerVices and Process Engineering, Budapest UniVersity of Technology and Economics, Muegyetem rkp. 3-5, H-1521 Budapest, Hungary

Pressure-swing batch distillation in a double-column system is suggested for the separation of an acetone-methanol pressure-sensitive azeotropic mixture. The studied column configuration is the doublecolumn batch stripper in open mode. We investigated this separation by rigorous simulation using a professional dynamic flow-sheet simulator. The influence of the most important operational parameters is studied. The energy demand of the separation is converted to carbon dioxide emission. The two columns can be thermally integrated to save energy. The effectiveness of thermal coupling is also investigated at different pressure gaps. 1. Introduction Pressure-swing distillation (PSD) is an efficient method for the separation of pressure-sensitive azeotropic mixtures. Many mixtures form an azeotrope whose position can be shifted substantially by changing the system pressure, that is, a pressuresensitiVe azeotrope. (At some pressures, the azeotrope may even disappear.) This effect can be exploited to separate azeotropic mixtures without the application of a separating agent by the so-called pressure-swing distillation. PSD in a continuous system was studied by several authors.1-8 Luyben7 compared the continuous extractive distillation and PSD for the separation of the mixture acetone-methanol. Steady-state designs and control structures are also developed for the two methods when the columns are heat-integrated. Acetone and methanol are widely used as solvents and reagents in the pharmaceutical and fine industries. An acetonemethanol mixture forms a minimum-boiling-point pressuresensitive azeotrope, so it can be separated by PSD. An alternative separation method for an acetone-methanol mixture is the homogeneous extractiVe distillation, when a third component (entrainer) is added to the mixture to help the separation. The extractive distillation of this mixture was investigated in a batch system by among others Lang et al.,9 Lelkes et al.,10 Milani,11 Hilal et al.,12 Lang et al.,13 Kotai et al.,14 and Yao et al.15 and in a continuous system by Laroche at al.,16 Langston et al.,17 Luyben,8 and Gil et al.18 Batch distillation (BD) has always been an important part of seasonal, uncertain, or low-capacity and high-purity chemical production. It is a process of key importance in the pharmaceutical and several other industries and in the regeneration of waste solvent mixtures. Phimister and Seider19 investigated the separation of a minimum azeotrope (tetrahydrofuran-water) by semicontinuous PSD. The semicontinuous configurations involve just one distillation column, which is adjusted from low to high pressure in a cyclic campaign. They also investigated the control and other practical aspects of these configurations, and their performances were compared with that of a continuous system as well. Wasylkiewicz et al.20 developed an algorithm that allows variation of the compositions of azeotropes with pressure * To whom correspondence should be addressed. E-mail: mgabor-bp@ freemail.hu.

to be tracked and all new azeotropes that appear within a specified pressure range to be found. To our knowledge, Repke et al.21 were the first who investigated experimentally the application of PSD in a batch. They studied the separation of a minimum-boiling-point homoazeotropic mixture (acetonitrile-water) by PSD in a batch rectifier and in a stripper (operated in an open mode) with pilotplant experiments and rigorous simulations. Modla and Lang22 studied the feasibility of pressure-swing BD (PSBD) of binary mixtures (forming minimum or maximum azeotropes) in different column configurations assuming maximal separation. They suggested two novel configurations containing two rectifying (double-column batch rectifier, DCBR) or two stripping sections (double-column batch stripper, DCBS). They made rigorous simulation calculations for the different column configurations as well. The different configurations were compared for a given set of operational parameters. The best results were obtained with the two new double-column configurations. For separating minimum azeotropes, they suggested the application of DCBS or batch stripper and for maximum azeotropes DCBR or batch rectifier. Modla et al.23 studied the feasibility of the PSBD separation of ternary homoazeotropic mixtures in different single- and double-column configurations. In that paper, the separation of the most frequent types of ternary mixtures was investigated. Kopasz et al.24 presented a simple scheme for control of the product compositions (the temperatures of bottoms product are controlled, and their flow rates are manipulated) for DCBS separating a minimum-boiling-point azeotropic mixture by PSBD. The goals of this paper are as follows: (i) to suggest PSBD by a double-column system operated in an open mode for the separation of a minimum-boiling-point pressure-sensitive azeotropic mixture acetone-methanol, (ii) to investigate the separation by rigorous simulation, (iii) to study the influence of the most important operational parameters (e.g., liquid division ratio, pressure gap between the two columns, etc.), (iv) to study different operation policies when the charge composition is located outside the region between the two azeotropic compositions, (v) to study the performance of the thermal integration, and (vi) to find the values of operational parameters providing the minimal carbon dioxide (CO2) emission. For the simulation, we used the dynamic simulator of CHEMCAD 6.0 (module CC-DCOLUMN, Chemstations25).

10.1021/ie9019352  2010 American Chemical Society Published on Web 03/23/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 Table 2. Comparison of Calculated and Measured Azeotrope Data calculated mixture

measured

P [bar] xAZ [%] TAZ [°C] xAZ [%] TAZ [°C]

acetone (A)- 1.0132 methanol (B) 4.058 7.826

78.1

55.32

78.5

55.20

54.5

99.12

54.0

99.65

41.9

123.85

41.8

124.55

ref Tochigi et al.26 Wilsak et al.27 Wilsak et al.27

1.) Notice that Figure 1 shows an unusual behavior in the purecomponent boiling points. At low pressure, acetone is the lowerboiling component; however, at high pressure, methanol has a lower boiling point. In Table 2, the calculated and measured azeotrope data are compared at different pressures. We can state that the agreement between the measured and calculated data is acceptable. Figure 2 gives the boiling points of the pure components as a function of the pressure. The mixture has a Bancroft point28 near 5 bar, where the two curves intersect (the boiling point of the two components are equal). 3. Rigorous Simulation Results

Figure 1. VLE diagrams of the mixture: (A) y-x equilibrium diagram; (B) boiling-point envelopes (T-x,y). Table 1. Calculated Data of the Azeotropes mixture

P [bar]

xAZ[%]

TAZ [°C]

TBP,A [°C]

TBP,B [°C]

acetone (A)methanol (B)

1.01

78

55.2

56.0

64.4

67 60 55 50 47 44 41 39 37

75.5 88.7 98.6 106.7 113.5 119.4 124.7 129.5 142.9

77.5 91.8 102.7 111.7 119.5 126.2 132.3 137.9 142.9

82.8 94.9 103.9 111.4 117.7 123.2 128.2 132.6 136.7

2 3 4 5 6 7 8 9 10

The following simplifying assumptions are applied: (i) theoretical trays, (ii) constant volumetric liquid holdup on the trays, and (iii) negligible vapor holdup. The model equations to be solved are well-known: (a) nonlinear differential equations (material balances and heat balances); (b) algebraic equations (VLE relationships, summation equations, holdup, and physical property models). For describing phase equilibria, the UNIQUAC model is applied. For solution of the above equations, the dynamic simulator of CHEMCAD 6.0 (program CC-DCOLUMN) is applied. Column sections are modeled by the module DYNAMIC COLUMN and the common vessel and product tanks by DYNAMIC VESSEL, respectively. Besides these units, the flow sheet still contains HEAT EXCHANGERs (condensers), MIXERs, DIVIDERs (stream splitters), PUMPs, VALVEs, CONTROLLERs, and CONTROL VALVEs. 3.1. Column Configuration. The DCBS in an open mode (DCBS-Open; Figure 3) is suitable for separation of the minimum-boiling-point pressure-sensitive binary azeotropic mixtures.22 At the start of distillation, plates of the columns are wet (they are filled with charge composition liquid at its boiling point at a given pressure). At the beginning of the process, the common vessel is filled with charge (Ucch). The charge composition (xch) is between the two azeotropic compositions (xRAZ, xβAZ) at the two pressures, or it is necessary to apply a preliminary step.

2. Vapor-Liquid Equilibrium (VLE) Data of Mixture Acetone-Methanol The mixture acetone-methanol forming a minimum azeotrope is a frequent waste in the pharmaceutical industry. This mixture cannot be separated into pure components by conventional rectification, but a special distillation method (e.g., PSD) must be applied. For two different pressures (1.01 and 10 bar), the calculated VLE diagrams and azeotropic data of the mixture acetonemethanol are shown in Figure 1 and Table 1, respectively. The large shift in the azeotropic composition from 78 to 37 mol % acetone indicates that a pressure-swing separation should be feasible. For the VLE calculation, the Uniquac model was used. (The Uniquac and Antoine parameters can be found in Appendix

Figure 2. Variation of the boiling points with the pressure

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Figure 3. Scheme of a DCBS-Open without thermal integration.

The vapors leaving the tops of the two stripping sections (Figure 3) are condensed by free coolers and then the condensates are mixed in the top vessel operated at a lower pressure (PR). The composition of both top vapors is near the azeotropic one (xRAZ and xβAZ, respectively). The pressure of the vapor arriving from the high-pressure column is decreased with a valve before the condenser. The liquid leaving the vessel (L1total) is divided into two parts. The pressure of the reflux of the highpressure (Pβ) column must be increased with a booster pump (the reflux will be subcooled liquid). At the bottom of both columns, there is a divider (splitting the liquid stream flowing down from the column) and a total reboiler. For transport of the liquid, pumps are used, except for the top of the columns, where the condensates are transported by gravity (without pumps). The pipe loss and hydraulic height are simulated by valves. During the production step at the bottom of the columns, the products are continuously withdrawn (bottom flow rates WR and Wβ and specified product compositions xRspec and xβspec) into the product tanks. In the columns, the reboil ratios (RsR and Rsβ) are changed by PID controllers manipulating the bottom flow rates (WR and Wβ) in order to reach and keep the specified product compositions. The measured process variables are the compositions of the bottom flows. In this study in order to simplify the tuning of controllers, we considered the compositions of the bottom flows as measured process variables (and not a tray temperature near the bottom, which is the usual practice in the industry). The tuning of the PID controllers is done manually by taking into consideration the usual criteria (maximal overshoot, control time, and number of oscillations). The quality of control is determined by the evolution of the position of the two control valves (varying the bottom flow rate). The following criteria of quality of control are given concerning the two control valves: (i) maximal overshoot, 33%; (ii) maximum number of oscillations during the settling time (within an error band of (5%), 3. The PID controller parameters are found in Appendix 2. 3.2. Input Data. The initial charge contains 50 mol % acetone (xch,A ) 0.5). Column R produces methanol (product B), and column β produces acetone (product A). The specified purities are 98 mol %. The liquid holdup is 2 dm3/plate. The

Table 3. Electricity Emission Factor for Different Countries29 country

electricity emission factor [g of CO2/kWh]

Canada France Hungary Italy Japan Spain U.K.

223 83 437 525 417 443 475

number of theoretical stages (N) for each column section is determined in section 3.4. (The total condenser and total reboiler do not provide a theoretical stage.) In each case, the quantity of the charge in the common vessel is 2.6 m3 (Ucch ) 46.12 kmol). At the start, the columns are filled with boiling-point liquid at the operation pressure of the column. The total flow rate of liquid leaving the common vessel (L1total) is 6 m3/h (ca. 106.4 kmol/h). The whole process is finished when the amount of liquid in the common vessel decreases to 2% of the charge. The influence of the main operation parameters on the performance of the process is studied, and the values yielding the minimal specific overall CO2 emission are determined. 3.3. CO2 Emission Calculation. At the CO2 emission calculation, we suppose that the heating demand is supplied by a gas boiler. The CO2 emission factor of the gas boiler is 50.35 g of CO2/MJ. Moreover, we suppose that the cooling demand is supplied by a free cooler whose electric energy factor is 0.4 Wh/MJ. The electric energy demand (cooling and pumping) can be transformed to CO2 emission. The electricity emission factor depends on the country (Table 3). In this study, we calculated with a factor of 437 g of CO2/kWh. (This data set does not contain the electricity emission factor for the United States.) 3.4. Determination of the Number of Plates. The aim of this section is to determine the number of plates needed. For the first calculation, the number of theoretical stages (N) for each column section is 40 in order to be sure that the separation is feasible. Column R is always working at atmospheric pressure (PR ) 1.01 bar) and column β at different pressures (Pβ ) 10, 8, and 6 bar). After heatup, the columns are working near steady state, so the column profiles do not vary significantly. The column

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Figure 4. Column profiles: (A) column R at P ) 1.01 bar; (B) column β at 10 bar; (C) column β at 8 bar; (D) column β at 6 bar.

Figure 5. Influence of the liquid ratio division on (A) the overall specific heating and electric energy consumption and (B) the overall specific CO2 emission.

profiles are investigated (Figure 4) when the process time is 100 min. Those plates are operating efficiently (separate the mixture) where the composition of the liquid is changing significantly, plate by plate. The other ones do not operate efficiently; they are in the pinch zone (the zone where there is almost no change in the composition of the liquid or vapor from plate to plate in a distillation column with a finite number of stages). It can be seen that the number of plates of both columns is overestimated. Figure 4a shows that for column R 20 plates would be enough. Parts b-d of Figure 5 show that for column β the number of plates (20-22) depends on the operation pressure (10-6 bar). On the basis of the above results, in the next section, the number of plates is 20 for column R and 25 for column β. 3.5. Influence of the Liquid Division Ratio. Column R is working at 1.01 bar (PR ) 1.01 bar) and column β at 10 bar (Pβ ) 10 bar). The influence of the liquid division ratio (φL )

Table 4. Influence of the Liquid Division Ratio: Detailed Results

ΦL

time [min]

heating energy [MJ/kmol]

electric energy [kWh/kmol]

CO2 emission [kg of CO2/kmol]

0.10 0.20 0.30 0.40 0.50 0.55 0.60 0.70 0.80 0.90

596.0 359.0 284.5 254.0 245.0 246.0 250.5 277.5 346.6 565.0

877.2 489.3 366.1 311.4 287.5 284.1 286.3 307.5 371.8 591.7

0.8277 0.4498 0.3231 0.2601 0.2237 0.2122 0.2040 0.1964 0.2071 0.2771

44.53 24.84 18.57 15.79 14.57 14.40 14.51 15.57 18.81 29.91

LR1 /Ltotal 1 ) on the performance of the process is studied. The liquid division ratio is varied in the region 0.1-0.9. The optimum value yielding the minimal overall specific CO2 emission (kg of CO2/kmol) is determined (Figure 5 and Table 4). Moreover, the minimum overall specific heating and electric energy consumptions and minimum process time are determined.


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Figure 6. Influence of the pressure gap (∆P) on (A) the overall specific heating and electric energy consumption and (B) the overall specific CO2 emission.

Figure 7. Evolution of the bottom stream compositions: (A) column R (PR ) 1.01 bar); (B) column β (Pβ ) 10 bar). Table 5. Detailed Results of the Influence of the Pressure Gap ∆P [bar]

xβAZ,A [mol/mol]

time [min]

heating energy [MJ/kmol]

9 8 7 6 5

0.37 0.39 0.41 0.44 0.47

246.0 260.5 278.5 302.0 333.5

284.1 299.5 318.6 343.04 376.7

electric energy [kWh/kmol]


0.2122 0.2139 0.2173 0.2240 0.2319

14.40 15.17 16.14 17.37 19.07

The results show that the minimum values are slightly different (highlighted values in Table 4). The best result (the minimal overall specific CO2 emission) is obtained at φL ) 0.55. It can be also seen that the specific electrical energy demand is much lower than the heating one (1 kWh ) 3.6 MJ); therefore, the value of the electricity emission factor has no significant influence on the CO2 emission. 3.6. Influence of the Pressure Gap between the Two Columns. Column R is always working at 1.01 bar, and the pressure of column β is varied. The liquid division ratio (φL) is 0.55. The influence of the pressure gap (∆P ) Pβ - PR) as an operational parameter on the performance of the process is studied. The optimum value yielding the minimal overall specific CO2 emission (kg of CO2/kmol) and process time are determined (Figures 6 and 7 and Tables 5 and 6).

Two different cases are investigated; at first the charge composition is located between the two azeotropic compositions, and then it is out of this interval. 3.6.1. Charge Composition between the Two Azeotropic Compositions. First those results are presented (Figure 6 and Table 5) when column β is working at a minimum of 6 bar because in these cases the charge composition (xch,A ) 0.5) is located between the two azeotropic compositions (xRAZ,A ) 0.78 and xβAZ,A varies with the operation pressure). The CO2 emission increases by 32% with a decrease in the pressure gap from 9 to 5 bar. Upon a decrease of the pressure gap, the process time also increases, which means that the capacity of the system decreases. Figures 7 and 8 present evolution of the bottom stream compositions. By comparison of Figures 7b and 8b, it is observed that the duration of the heatup period in column β rises (from 38 to 50 min) with a reduction of the operation pressure in Column β (from 10 to 6 bar). It must still be noted that upon an increase of the pressure gap the investment cost increases. 3.6.2. Charge Composition outside the Two Azeotropic Compositions. Those results are presented when column β is working at less than 6 bar. In these cases, the charge composition is out of the region between the two azeotropic compositions

Table 6. Influence of the Pressure Gap for Different Policies: Detailed Results policy 1 β

policy 2

policy 3

∆P [bar]

x AZ,A [mol/mol]

time [min]


time [min]


time [min]


3 2 1

0.55 0.60 0.67

432.5 536.0 813.5

24.17 29.42 43.65

455.5 576.0 864.0

25.53 31.79 46.91

455.5 604.0 967.0

25.53 33.51 52.74

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Figure 8. Evolution of the bottom stream compositions: (A) column R (PR ) 1.01 bar); (B) column β (Pβ ) 6 bar).

Figure 9. Evolution of the bottom stream compositions (policy 1): (A) column R (PR ) 1.01 bar); (B) column β (Pβ ) 3 bar).


(xRAZ and xβAZ), which means that a preliminary process step is necessary. For this preliminary step, three operation policies are possible. For column β, the process steps differ by the different operation policies. By each operation policy in column R, two steps are performed: 1. Heatup: the bottom composition does not reach its specified value, so there is no product withdrawal. 2. Production: when the bottom composition reaches its specified value, product (methanol) withdrawal is started and is continued until the end of the process. Policy 1. During the preliminary step, only column R is working and producing methanol (B) until the common vessel composition reaches the azeotropic one (xβAZ) at a given pressure. Figure 9 presents evolution of the bottom stream compositions for policy 1. For column β, different process steps can be observed:

1. Preliminary step: the bottom composition of column β cannot reach its specified value and, hence, column β is not operated. 2. Heatup: when the common vessel composition reaches the azeotropic one for Pβ, the heating of column β is started. 3. Production: when the bottom composition of column β reaches the specified value, product (acetone) withdrawal is started and is continued until the end of the process. Policy 2. During the preliminary step, both columns are working and producing methanol (B) until the common vessel composition reaches xβAZ at a given pressure. Figure 10 presents evolution of the bottom stream compositions for policy 2. For column β, different process steps can be observed: 1. Heatup: the bottom composition of column β cannot reach the specified value, so there is no product withdrawal.


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Figure 12. Influence of the pressure gap on the overall specific CO2 emission.

2. Preproduction step: the bottom composition of column β can reach the specified value for column R, so it can produce the same component as column R (methanol). 3. Intermediate step: the bottom composition of column β can reach the specified value neither for column R nor for column β, so there is no product withdrawal. 4. Production: when the bottom composition of column β reaches the specified value, product (acetone) withdrawal is started and is continued until the end of the process. Policy 3. During the preliminary step, both columns are working, but only column R is producing methanol (B). Column β is working at an infinite reboil ratio until the common vessel composition reaches xβAZ at a given pressure. Figure 11 presents evolution of the bottom stream compositions for policy 3. For column β, different process steps can be observed: 1. Heatup and preliminary step: the bottom composition of column β cannot reach the specified value, so there is no product withdrawal but column β is operated at an infinite reboil ratio. 2. Production: because the common vessel composition has already reached the azeotropic one for Pβ, the bottom composition of column β can reach the specified purity and the production of acetone can be started. Comparison of the Different Operation Policies. Figure 12 presents the influence of the pressure gap on the overall specific CO2 emission for different operation policies. The detailed results can be found in Table 6. We can conclude that upon an increase of the pressure gap the difference between operation policies decreases because the initial charge composition gets closer to the azeotropic one at the operation pressure of column β. From the point of view of industrial practice, the duration of the preliminary step is nearly the same for the different policies.

Figure 13. Scheme of a DCBS-Open with thermal integration.

On the basis of the results (Figure 12 and Table 6), we can conclude that policy 1 is the most efficient and the most economical. For a pressure gap of 1 bar by policy 1, savings of 7% against policy 2 and of 20% against policy 3 can be reached. It must still be noted that upon a decrease of the pressure gap the investment cost decreases because of lower requirements for the constructional materials. 3.7. Thermal Integration. The flow sheet of the original process, where there is no thermal integration, is presented in Figure 3. It shows independent reboilers and condensers (free coolers) for both columns. However, the boiling point of the azeotrope [top stream temperature of the high-pressure column β (133.9 °C at 10 bar)] is higher than the boiling point of the methanol product [bottom stream temperature of the lowpressure column R (near 64 °C at 1.01 bar)], so heat integration could be attractive in terms of energy consumption. In this paper, we study the case where the two columns are partially heatintegrated, which means that the economizer must be completed with an auxiliary reboiler (Figure 13). The economizer is used to recover energy from the top vapor of column β by (partial) vaporization of the reboil stream of column R. The operational parameter of the economizer is that the recycled top vapor from column β is subcooled to 80 °C. Figure 14 presents the influence of the pressure gap on the overall specific CO2 emission with and without thermal integration. The detailed results can be found in Table 7. The results show that 42% CO2 emission can be saved with thermal integration without variation of the process time. Moreover, the relative emission reduction is higher if the pressure gap is higher. Upon an increase of the pressure gap, the investment cost of the economizer decreases because the

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Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 P ) pressure, bar Rs ) reboil ratio SQtotal ) overall energy consumption, MJ T ) temperature, °C t ) time, h U ) liquid holdup, m3 W ) bottom flow rate, m3/h x ) liquid mole fraction y ) vapor mole fraction Greek Letter φ ) division

Figure 14. Influence of the pressure gap on the overall specific CO2 emission with and without thermal integration. Table 7. Detailed Results of the Thermal Integration time [min]


without with ∆P thermal thermal [bar] integration integration 9 7 5 3 2 1a a

246.0 279.0 334.0 432.5 536.0 813.5

246.0 279.0 334.0 432.5 536.0 813.5

without thermal integration

with thermal integration

relative CO2 emission reduction [%]

14.40 15.17 16.14 24.17 29.42 43.65

8.37 9.37 11.09 14.81 18.45 27.49

42 38 31 39 37 37

The recycled top vapor from column β is cooled to 70 °C.

logarithmic mean temperature difference increases (the temperature of the top vapor of column β rises). 4. Conclusion PSBD in a double-column system was suggested for the separation of a pressure-sensitive azeotropic mixture acetonemethanol. The column configuration studied was DCBS-Open. This separation was investigated by rigorous simulation by using a professional dynamic simulator [CC-DCOLUMN (CHEMCAD 6.0)]. The influence of the most important operational parameters (liquid division ratio and pressure gap between the two columns) was studied. The energy demand of the separation was converted to CO2 emission. Three different operation policies were studied for the case where the charge composition is located outside of the region between two azeotropic compositions. We concluded that policy 1 (during the preliminary process step, only the lowpressure column is working) is more efficient and more economical than policy 2 [during the preliminary step, both columns are working and producing the same product (methanol)] and policy 3 [during the preliminary step, both columns are working: column R is producing methanol (B), and column β is working at an infinite reboil ratio]. For a decrease of the pressure gap from 9 to 5 bar, the CO2 emission increased by 32% and the process time increased by 35% (which means the capacity of the system decreased). The two columns can be thermally integrated in order to save energy. The results indicate that CO2 emission can be reduced by 42% with thermal integration of the two columns.

Subscripts A ) component A AZ ) azeotrope B ) component B ch ) charge i, j ) components spec ) specified value L ) liquid LV ) liquid leaving the vessel V ) vapor W ) bottom flow 1, ..., N ) plate index Superscripts c ) common opt ) optimum R ) column index β ) column index

Appendix 1 The values of the parameters used for the phase equilibrium calculations are as follows. a. Antoine parameters: ln(p) ) A -

B T+C

where p is the vapor pressure (mmHg) and T the temperature (K). component acetone methanol

A

B

C

16.732 18.5100

2975.9 3593.4

-34.523 -35.225

b. UNIQUAC parameters for an acetone (A)-methanol (B) mixture: i

j

uij - ujj [cal/mol]

uji - uii [cal/mol]

A

B

434.944

-101.228

Appendix 2 The values of the PID parameters used for rigorous calculations are as follows: column R column β

PB [%]

TI [min]

TD [min]

setpoint [mol/mol]

80 50

2.5 10

0 1

0.98 methanol 0.98 acetone

Appendix

Acknowledgment

Notation BP ) bubble point, °C L ) liquid flow rate, m3/h N ) number of plates

This work was financially supported by the Hungarian Scientific Research Fund (OTKA; Grant K-82070) and by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences.


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ReceiVed for reView December 7, 2009 ReVised manuscript receiVed February 14, 2010 Accepted March 4, 2010 IE9019352

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