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Process alternatives for methyl acetate conversion using reactive
distillation. 1. Hydrolysis
Yu-Der Lin, Jun-Hong Chen, Jian-Kai Cheng, Hsiao-Ping Huang, Cheng-Ching Yu
∗Department of Chemical Engineering, National Taiwan University, Taipei 106-17, Taiwan
Received 27 March 2007; received in revised form 20 September 2007; accepted 5 November 2007 Available online 13 November 2007
Abstract
In a polyvinyl alcohol (PVA) plant, reaction stoichiometry indicates that equal molar of methyl acetate is generated for every mole of PVA produced. This work explores an alternative to convert methyl acetate back to acetic acid (raw materials of PVA plant), methyl acetate (MeAc) hydrolysis. The design and control of methyl acetate hydrolysis using reactive distillation is studied. Because of the small chemical equilibrium constant (∼ 0.013) and unfavorable boiling point ranking (MeAc being the lightest boiler), the reactive distillation exhibits the following characteristics: (1) total reflux operation and (2) excess reactant (water) design. The proposed flowsheet consists of one reactive distillation column with a reactive reflux drum, two separation columns, and one water-rich recycle stream. A systematic design procedure is used to generate the flowsheet based on the total annual cost (TAC). Two dominate design variables are: recycle flow rate (for the degree of excess in water) and the overhead impurity level of acetic acid in the product column (to avoid tangent pinch). Finally, the operability of the hydrolysis plant is evaluated. A plantwide control structure is developed followed by process identification and controller tuning. The results show that reasonable control performance can be achieved using simple temperature control for feed flow and feed composition disturbances. 䉷 2007 Elsevier Ltd. All rights reserved.
Keywords: Reactive distillation; Methyl acetate; Hydrolysis; Process design; Process control
1. Introduction
Large amount of methyl acetate (MeAc) is produced as by-product in the by-production of polyvinyl alcohol (PVA), around 1.68 times of the PVA product by weight. One approach is to hydrolyze MeAc back to acetic acid (HAc) and methanol (MeOH), raw materials for the PVA plant. The conventional hydrolysis process consists of a reactor and four distillation columns (Fuchigami, 1990). The hydrolysis reaction is carried out in a fixed bed reactor catalyzed by ion exchange resin. Because of the small equilibrium constant, (Keq∼ 0.04), the
one-pass conversion is relatively low and it results in large recycle flows. This subsequently leads to high energy demand for the conventional process. It is not likely to enhance the conversion or to reduce energy consumption by changing the molar feed ratio of H2O/MeAc (FRH2O/MeAc).
∗Corresponding author. Tel.: +886 2 3366 3037; fax: +886 2 2362 3040. E-mail address:[email protected](C.-C. Yu).
0009-2509/$ - see front matter䉷2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2007.11.009
Reactive distillation is an attractive alternative for reac-tion/separation processes and it gives clear advantages for systems with small equilibrium constant (Kaymak and Luyben, 2004). The number of papers in this field has grown rapidly in recent years for process design (Doherty and Buzad, 1992;
Okasinski and Doherty, 1998), steady-state behavior
descrip-tion (Barbosa and Doherty, 1988;Al-Arfaj and Luyben, 2000a,
b; Chen et al., 2000; Tang et al., 2005), and dynamics and
control (Sneesby et al., 1999;Al-Arfaj and Luyben, 2000a, b;
Luyben et al., 2004; Hung et al., 2006). For process systems
studied, related papers and patents in hydrolysis are much less than that of esterification reactions (Sundmacher and Kienle,
2003).Fuchigami (1990) proposes a reactive distillation
con-figuration with total reflux on the top with bottoms product withdrawal for the hydrolysis process. The catalyst consists of ion exchange resin and polyethylene powder. With a feed ratio greater than 8, i.e., FRH2O/MeAc= FH2O/FMeAc= 8.2, a near
complete conversion (∼ 99%) can be achieved. Also note that the reactive zone is placed in the mid-section of the column.
X = 98.4%,Fuchigami (1990) X = 50.0%,Han et al. (1997) X = 57.7%,Pöpken et al. (2001) X = 99.8%,Lee (2002)
X = 99.9%,Kim and Roh (1998) X = 72.0%,Wang et al. (2001) X = 73.9%,Hoyme and Holcomb (2003)
the hydrolysis using reactive distillation, but azeotrope feed of MeAc/MeOH is considered. Almost complete conversion, ∼99.9%, can be obtained with much higher water to methanol feed ratio, FRH2O/MeAc= 15. Using the same total reflux
con-figuration, Xiao et al. (2001)investigated the effect of three operating variables, feed ratio of H2O to MeAc (FRH2O/MeAc),
recycle flow rate, and catalyst holdup, to the overall conversion. They also concluded that near 100% conversion of MeAc can be achieved by increasing the feed ratio. In an experimental work,Han et al. (1997)add a pre-reactor to the reactive distil-lation configuration with sieve-type tray installed in the reac-tive zone. However, products are withdrawn from both top and bottoms of the column, a one-feed-two-product RD column. With a feed ratio of unity, the overall conversion, including the pre-reactor and RD column, is only 50%.Wang et al. (2001), fol-lowing the configuration ofHan et al. (1997), change the operat-ing condition by increasoperat-ing the molar feed ratio of H2O/MeAc
and the reflux ratio. The conversion of the limiting reactant, (MeAc), is improved, from 50% to 72%.Lee (2002)proposes a configuration which is similar to a distillation column plus a side-reactor. The reflux drum of the distillation column is re-placed by a fix bed reactor while the column is operated with total reflux. With an excess of water, almost complete conver-sion of MeAc (∼ 99.8%) can be obtained and trace amount of MeAc is detected in the column base. Different ion exchange catalysts and feed compositions were also tested inLee (2002).
Table 1 summarizes different process configuration with
con-versions reported.Hoyme and Holcomb (2003)carry out the hydrolysis reaction in a high-pressure (10 atm) reactive distilla-tion column. They observed that the methanol dehydradistilla-tion side reaction is significant, under such a high reaction temperature as a result of high operating pressure and, the overhead product is dimethyl ether, instead of methanol. For reaction kinetics, literature review shows that much of the research focuses on the esterification reaction and much less is found for the hydrolysis
reaction. Nevertheless, two groups, Song et al. (1998) and
Pöpken et al. (2000), have studied the MeAc esterification and
hydrolysis reaction catalyzed by Amberlyst 15 ion exchange resin with various initial reactant compositions. Pilot plant test of hydrolysis reaction was carried out in a RD column by
Pöpken et al. (2001). Based on the experimental data and
sim-ulation results, the authors concluded that the adsorption-based kinetic model is more reliable than the pseudo-homogeneous one for hydrolysis reaction.
At the process design level, literature survey shows four pos-sible configurations for MeAc hydrolysis (Table 1). However, the competitiveness of these four flowsheets inTable 1 is not clear and, yet, is an improved design possible? The objective of this work is to find a process configuration for MeAc hydroly-sis using a mixed MeAc and MeOH feed with the composition MeAc/MeOH (60/40) close to the binary azeotrope. Next, the control aspect of the RD process will be explored. This paper is organized as follows. Section 2 explores process charac-teristic which includes reaction kinetics and phase equilibria. Conceptual design and systematic design procedure are studied in Section 3. The dynamics and control of the plantwide RD system is examined in Section 4 followed by the conclusion.
2. Reaction kinetics and phase equilibrium 2.1. Reaction kinetics
The hydrolysis of methyl acetate is a reversible reaction with the following expression:
MeAc+ H2O ↔ HAc + MeOH. (1)
The reaction kinetics is given in Pöpken et al. (2000) with Amberlyst 15 ion exchange resin as catalyst. The
adsorption-based model can be written as R = mcat× kfaMeAcaH2O− kra HAcaMeOH (aMeAc+ aH2O+ a HAc+ aMeOH) 2, ai= Kiai Mi , KMeAc= 4.15, KH2O= 5.24, KHAc= 3.15, KMeOH= 5.64, kf = 6.127 × 105exp −63 730 RT , kr= 8.498 × 106exp −60 470 RT . (2)
The overall reaction rateR has the unit of kilomole per sec-ond (kmol/s) and ai is the activity, mcatis the catalyst weight in
kilograms, Ki is the adsorption equilibrium constant, Mi is the molecular weight of component i. The parameters kf and krare forward and reverse rate constants with units of kmol/kgcat/s
and the activation energy in kilojoule per mole with tempera-ture in Kelvin. An important characteristic in MeAc hydroly-sis is extremely low equilibrium constant. This model gives an equilibrium constant of 0.013 (i.e., Keq=0.013) at 50◦C which
is far below unity. Notice that water has a stronger uptake into the catalyst than methyl acetate as can be seen from the values
of Ki/Mi. If we make water as the excess reactant, the
mo-lar ratio of H2O/MeAc at the surface of the catalyst should be
greater than that in the bulk. Thus, the adsorption-based kinet-ics model is more appropriate than the pseudo-homogeneous one. At each reactive section (i.e., reactive tray and reactive re-flux drum), we assume the catalyst occupies half of the holdup volume. A bulk catalyst density of 770 kg/m3is used to con-vert into a volume-based rate equation for Aspen Plus reaction setup.
2.2. Phase equilibrium
For the reactive distillation modeling, it is essential to capture the nonideal vapor–liquid equilibrium (VLE), especially for good prediction of azeotropes and liquid–liquid (LL) envelops whenever two-liquid zone exists. The UNIQUAC (Abrams and
Prausnitz, 1975) model is used for VLE calculation in the
qua-ternary system and model parameters are taken from byPöpken
et al. (2000). We also take the vapor phase dimerization (for
acetic acid) into account using Hayden–O’Conell second virial coefficient (Hayden and O’Connell, 1975) model and the model parameters are Aspen Plus built-in values.
The phase behavior gives two distinct features. The first is the existence of binary azeotropes: (1) methyl acetate and methanol form a minimum-boiling azeotrope with the compo-sition of 65.9 mol% methyl acetate at 53.7◦C, and (2) methyl acetate and water forms minimum-boiling azeotrope with the composition of 89.0 mol% at 56.4◦C. Both are predicted at at-mospheric pressure. Thus, the order of the normal boiling point temperature for pure components and azeotropes is:
HAc > H2O > MeOH > MeAc > MeAc/H2O > MeAc/MeOH
118◦C 100◦C 64.5◦C 57.5◦C 56.4◦C 53.6◦C 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 X (H2O) HAc/H2O X-Ydiagram Y (H 2 O)
Fig. 1. Vapor–liquid equilibrium of acetic acid (HAc) and water (H2O) system
and the tangent pinch indicated by the dashed line.
In theory, if one consumes all the light reactant (MeAc), the lightest pure component, toward the top of a single reactive distillation column, relatively pure light product (MeOH) can be obtained (Tung and Yu, 2007). However, the light product (MeOH) is a saddle MeAc–MeOH–H2O ternary residue curve
map (RCM) diagram (Tang et al., 2005). With a low equilib-rium constant (Keq ∼ 0.013), it is not likely to obtain high
purity MeOH product under the “neat” operation. Thus, total reflux design (e.g.,Fuchigami, 1990) with upper section reac-tive zone seems to be a reasonable choice, especially one of the reactants being the lightest pure component. Moreover, the removal of the light product (MeOH), heavy product (HAc), and excess reactant (H2O) from the bottoms of the column is
also relatively easy. The second feature in the VLE is related to the downstream separation columns.Fig. 1shows the binary VLE diagram for water–acetic acid system. It shows a tangent pinch point existing near the pure water end. This implies that a near complete removal of acetic acid from water will require excessive large reflux ratio, high reboiler duty. In terms of pro-cess design, this means recycling a certain portion of the heavy product (HAc) back to the RD may be acceptable as far as the energy consumption is concerned. Thus, the purity level of acetic acid at the top of acetic acid dehydration column should be investigated in the design of entire plant.
3. Steady state design 3.1. Process flowsheet
Reaction kinetics and phase equilibria reveal that, for a near complete conversion of methyl acetate, the reactive distillation systems possess the following characteristics. First, the “neat” design is not favorable because of the small equilibrium con-stant, i.e., (Keq ∼ 0.013). Second, from reaction perspective,
Fig. 2. Process flowsheet of MeAc hydrolysis system and design parameters indicated in italics.
we should make water as the excess reactant as explained ear-lier based on the adsorption-based kinetics. This implies that we make the heavy reactant (H2O) in excess. Third, from phase
equilibrium perspective, it is favorable to withdraw the products as well as excess reactant from the bottoms of the reactive dis-tillation column for the ease of separation (avoid azeotropes). Thus, a total reflux operation with product withdrawal from the bottoms of reactive column is, indeed, a good candidate for this hydrolysis reaction. It is also clear that the reactive zone should be placed at where the reactant is most abundant, up-per section of the column. Because the reflux drum has a large holdup with significant amount of MeAc (limiting reactant), it is made reactive by placing catalyst inside. Therefore, we have a reactive distillation column under total reflux operation with reactive zone placed at the upper section of the column, includ-ing a reactive reflux drum, as shown inFig. 2. For the subse-quent separation for the ternary mixture, the indirect sequence is adapted here. Therefore, the entire process consists of one reactive distillation column, two distillation columns with one recycle stream. The hydrolysis reaction takes place in the RD column with total reflux operation. There are three feeds into the RD column: fresh water feed (50 kmol/h), water-rich recy-cle stream from bottom of the 3rd column (methanol product column), and the fresh feed with a composition close to the binary azeotrope, i.e., 60 mol% methyl acetate and 40 mol% methanol, and a flow rate of 83.33 kmol/h. The two feeds, rich in water, are fed into the reflux drum. The third feed stream is the light reactant (MeAc) which is fed to the lower section of the RD column.
The following design specifications are made for the reactive distillation column. Five minutes residence time is assumed for the reactive reflux drum and half of the holdup volume is packed with catalyst. For reactive trays, we assume that the cat-alyst occupies half of the tray holdup volume. The tray holdup is determined by the column diameter which is sized using the Tray Sizing Utility in Aspen Plus by assuming a weir height of 10 cm. The conversion of methyl acetate is set to 98.7% by adjusting the reboiler duty. The bottoms product of the RD column is fed into acetic dehydration column, namely the 2nd column, with the product, 99 mol% acetic acid, taken from the bottoms. The overhead product, mostly methanol and water, of the 2nd column enters the recycle column, namely the 3rd
9 10 11 12 840 842 844 846 848 850 NRxn = 17 NRxn = 18 NRxn = 19 TAC [$1000/year] 4 5 6 7 8 841 842 843 844 900 901 902 903 904 NFH2O = 29 NFH2O = 30 TAC [$1000/year] NS [-] NFMeAc [-]
Fig. 3. Effects of design variables on TAC in the reactive column with per-turbation from nominal steady state (FR= 240 kmol/h and xD2,HAC= 0.13): (A) number of reactive trays and number of trays in the stripping section and (B) feed tray locations.
column, for further purification. High-purity methanol, 99 mol%, is withdrawn from the column top and water-rich bottoms flow is recycled back to the reflux drum of the RD column. The impurity level, methanol at the bottoms of the 3rd column, is set to 0.1 mol% for the recycle stream.
3.2. Design procedure
Once the conceptual design is completed and specifications are given, we can proceed with the preliminary design. The objective is to minimize total annual cost (TAC) by adjusting the design parameters, e.g., tray numbers in each section, feed location in the column, etc. The TAC is defined as (Douglas,
1988):
TAC= operatingcost + capital cost
11 12 13 14 15 16 640 660 680 700 720 NT2 = 14 NT2 = 15 NT2 = 16 TAC [$1000/year] 9 10 11 12 13 408 410 412 414 416 418 NT3 = 26 NT3 = 27 NT3 = 28 TAC [$1000/year] NF3 [-] NF2 [-]
Fig. 4. Effects of total number of trays and feed tray location on TAC with perturbation from nominal steady state (FR=240 kmol/h and xD2,HAC=0.13 for: (A) 2nd column, (B) 3rd column.
Here, a payback of 3 years is used. The operating cost includes the costs of steam, cooling water, and catalysts. The capital cost comprises the costs of the column, trays, and heat exchangers. Cost models and corresponding values are given in Appendix A and a catalyst life of 3 months is assumed.
In the flowsheet, obvious design parameters are shown in italics in Fig. 2. They are: the number of reactive and strip-ping trays (Nrxn and NS), water and acetate feed tray location
(NFH2O and NFMeAc) of the RD column, the total number of
trays and feed tray location of the 2nd column (NT 2and NF2)
and the 3rd column (NT 3 and NF3). In addition to tray
num-bers and feed locations in each columns, there are two impor-tant design variables (Yi and Luyben, 1997): recycle flow rate (FR) and the overhead acetic acid impurity in the 2nd column (XD2,HAc) as mentioned earlier. The former means the degree of excess water into the RD column. An increase in FR fa-vors the hydrolysis reaction at the expense of a higher recycle
200 220 240 260 280 700 800 900 1000 1100 1200 1900 1910 1920 1930 1940
TAC of Hydrolysis System TAC of Separation Columns TAC of RD Column
TAC ($1000/year)
FR (Kmol/hr)
Fig. 5. Effects of recycle flow rate (FR) on TAC of the entire plant, RD column, and distillation columns with perturbation from nominal steady-state
(xD2,HAC= 0.13). 700 800 900 1000 1100 1900 1910 1920 1930 1940 1950 1960 TAC ($1000/year)
TAC of Hydrolysis System TAC of Separation Columns TAC of RD Column
XD2,HAc
0.05 0.07 0.09 0.11 0.13 0.15
Fig. 6. Effects of the overhead acetic acid impurity of the 2nd column
(XD2,HAc) on TAC.
cost (energy for subsequent separation). The latter comes from the tangent pinch behavior between acetic acid and water. A higher product recovery, a small XD2,HAc value in the second column, prevents the product recycled back to the RD column, but a much larger energy consumption is needed as a result of the tangent pinch. Thus, a tradeoff between the reaction (RD cost) and separation (cost of 2nd column) should be made and XD2,HAcis also an important design variable.
We have identified 10 design variables above, and a system-atic design procedure is devised for the flowsheet generation
(Chiang et al., 2002; Tang et al., 2005). All the simulations are
carried out in Aspen Plus using the RADFRAC module with FORTRAN subroutines for the activity-based reaction kinet-ics. Given the production rate and product specifications, the
Fig. 7. Optimized process flowsheet “indirect” separation sequence for the hydrolysis system.
Table 2
Steady-state operating parameters and total annual cost (TAC) for MeAc hydrolysis process
Column RD column 2nd column 3rd column
Total no. of trays 29 15 27
No. of trays in reactive section (Nrxn) 18
No. of trays in stripping section (NS) 11 14 11
Reactive trays 12–29
Acetate feed tray (NFMeAc) 6
Water feed tray (NFH2O) 30
Feed tray 14 11
Catalyst in reflux drum (m3) 3.03
Catalyst in each tray/sum (m3) 0.11/1.98
Acetate/water feed flow rate (kmol/h) 83.33/50 Recycle flowrate (kmol/h) (FR) 240
Top product flow rate (kmol/h) 323.50 83.50
XD
m.f. of acid 0.108 0.130 0.000
m.f. of alcohol 0.106 0.256 0.990
m.f. of acetate 0.391 0.00198 0.00766
m.f. of water 0.395 0.612 0.00234
Bottom product flow rate (kmol/h) 373.33 49.83 240
XB m.f. of acid 0.245 0.990 0.175 m.f. of alcohol 0.222 3.922 × 10−7 0.00100 m.f. of acetate 0.00171 0.000 0.000 m.f. of water 0.531 0.010 0.824 Condenser duty (kW) −4036.42 −3862.52 −2010.94 Reboiler duty (kW) 4140.85 3779.98 2116.60 Column diameter (m) 1.75 1.80 1.05
Condenser heat transfer area (m2
) 500.34 199.28 215.43
Reboiler heat transfer area (m2
) 342.62 312.76 175.13
Damköhler number (Da) 3.68
TAC of RD column ($1000/year) 841.08 654.49 409.89
Total capital cost ($1000/year) 973.51
Column/trays/heat exchanger 328.37/57.26/587.88
Total operating cost ($1000/year) 931.95
Catalyst/energy 119.12/812.83
0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 0.0 0.2 0.4 0.6 0.8 1.0 HAc MeOH MeAc H2O Ri/Rtot Mole Fraction [-] Ri /R tot [-] NFMeAc NFH2O 0 5 10 15 20 25 30 50 60 70 80 90 100 Tempature [ °C ] Stage Number [-] NFH2O NFMeAc Stage Number [-]
Fig. 8. Composition and temperature profiles in the reactive column.
design steps are
(1) Guess a specification of acetic acid in distillate of 2nd column (e.g., XD2,HAc= 0.01).
(2) Guess the recycle flow rate (FR) (e.g., FR=100 kmol/h). (3) Guess a number of reactive trays (Nrxn).
(4) Guess a tray number in the stripping section (NS). (5) Guess the heavy reactant feed (NFH2O) and guess the light
reactant feed (NFMeAc).
(6) Change the heat input (QR) until the reaction conversion is achieved.
(7) Go back to (5) and change NSuntil the TAC is minimized. (8) Go back to (4) and vary Nrxnuntil the TAC is minimized.
(9) Go back to (3) and find the feed locations (NFH2O and
NFMeAc) until the TAC is minimized.
(10) Pick a total number of trays in the 2nd column (NT 2). (11) Guess a feed location in the 2nd column (NF2) and change
the reflux flow (R) and heat input (QR) until the product specification is met.
(12) Go back to (10) and change NF2until the TAC is
mini-mized.
(13) Go back to (9) and vary NT 2until the TAC is minimized. (14) Pick a total number of trays in the 3rd column (NT 3). (15) Guess a feed location in the 3rd column (NF3) and then
change the reflux flow (R) and heat input (QR) until the product specification is met.
(16) Go back to (14) and change NF3until the TAC is
mini-mized.
(17) Go back to (13) and vary NT 3until the TAC is minimized.
3000 4000 5000 6000 7000 8000 9000 70 75 80 85 90 95 100 specification = 98.7% 4140 Conversion [%] Reboiler Duty[KW] 83.4 Bottom Product Steam Reboiler Separation Tower Reactor Water Feed Condenser NT = 29 Acetate Feed 6
Fig. 9. (A) The column with reactive reflux drum with 5.01 m3 catalyst loading and (B) the effect of reboiler duty (QR) on the conversion of MeAc (the red dashed line for nominal heat input and solid line for heat duty for desired conversion).
(18) Go back to (2) and change FRuntil the TAC is minimized. (19) Go back to (1) and find XD2,HAc until the TAC is
mini-mized.
These steps may seem excessive, but the procedure is set up in such a way (i.e., fixed specifications for all product streams) that the design of each column is decoupled. For example, steps (3)–(8), (9)–(12), and (13)–(16) are the design steps for the RD, the 2nd column, and the 3rd column, respectively, given a recycle flow rate and composition.
3.3. Results
For the RD column,Fig. 3 shows that the number of trays in the stripping section (NS) to the TAC is more sensitive than that of the number of reactive trays (Nrxn). The reason for that
is: almost∼ 70% of the total conversion occurs in the reactive reflux drum as a result of the large amount of catalyst and high reactant concentration. Subsequently, Nrxn has little effect on
the TAC. There are 18 reactive trays and 11 stripping trays in the RD column.Fig. 3also reveals that water should be intro-duced into the reactive reflux drum (denoted as 30th tray) and the light reactant (mixture MeAc/MeOH below the azeotropic
RD Column 14 11 LC Steam HAC MeOH 2nd Column 3rd Column set H2O 50 Kmol/hr set set set set se t MeAc 60 mol % MeOH 40 mol % 83.33 Kmol/hr Steam set TC TC TC FC FC FC FT FC X FT FT X FC FT LC FC FT PC FC FT LC LC FT FC X PC LC PC X FC FT LC TC 4 5 15 6 0 0 0
Fig. 10. Plantwide control of the hydrolysis plant.
composition) should be introduced into the stripping section (below the reactive zone in the 6th tray). This is also expected because the light reactant (MeAc) is lighter than MeOH and a certain degree of purification is helpful for the reactant compo-sition in the reactive zone. Note that the tray number is counted from the bottom-up.Fig. 4shows how the effects of total num-bers of trays and feed tray locations in the separation section (2nd and 3rd columns) to the TAC. Because of having large amount of water, the optimal feed tray is placed in the upper sec-tion of the column. The 2nd column has 15 trays with NF2=14.
The 3rd column has a total 27 trays with the feed introduced to the lower section of the column, i.e., NF3= 11. For the recycle
flow rate (FR),Fig. 5shows a minimum in TAC occurs when the recycle flow take the value of 240 kmol/h. The tradeoff comes from the RD cost and the separation column costs. The RD cost decreases as the recycle flow increases as the result of a higher reactant concentration, but the cost of subsequent separation also increases for a higher flow rate (Fig. 5). That implies the feed ratio (FRH2O/MeAc) is the dominant design variable and
the TAC minimum corresponds to FRH2O/MeAc= 4.95. Fig. 6
shows the overhead composition (impurity) of acetic acid of the distillate of 2nd column (XD2,HAc) has significant impact on the TAC. As shown inFig. 1, the tangent pinch point toward the pure water end makes the complete removal of HAc from the recycle stream difficult. Thus, we have a tradeoff between reactant composition (mixed with product HAc) and separation cost. As the XD2,HAcapproaches 0.13, the energy intensive sep-aration (tangent pinch) can be mitigated and, however, a further increase in the purity leads to a rapid increase in the TAC as a result of unfavorable reactant composition. In summary, for the plantwide design of the hydrolysis plant, two dominant de-sign variables are identified, FR and XD2,HAc. The optimized flowsheet can be obtained by carefully adjusting these design
parameters as shown inFig. 7.Table 2summarizes design pa-rameters and corresponding costs.
3.4. Discussion
Because of the small equilibrium constant, near complete conversion of the limiting reactant (MeAc) leads to a rela-tive large boilup-to-fresh feed (3.25 = 432/133) ratio. Fig. 8 shows the composition profile in the RD column and the ver-tical dashed line indicates the lower limit of the reactive zone with the feeds introduced on tray 6 and the reflux drum, re-spectively. The profiles in Fig. 8indicate that fairly large (∼ 40%) and constant reactant concentrations of both reactants, MeAc and H2O, throughout the reactive zone. This facilitates
the forward reaction for a system with small equilibrium con-stant. The reflux drum is packed with 3.03 m3 catalyst which results in∼ 70% of the total conversion (Ri/Rtot as indicated
by shaded area in Fig. 8). The rest of the catalyst holdup (on reactive trays) sums up to 1.98 m3(by volume) which accounts for the remaining 30% of the total conversion. A final note is that the introduction of the mixed MeAc/MeOH feed below the reactive zone indeed prevents the product MeOH from enter-ing the reactive zone as indicated by the profiles between the lower feed tray and bottoms of the reactive zone.
The total reflux configuration in Fig. 7 seems to be a vi-able choice to overcome systems with a small chemical equi-librium constant. However, it is also observed that most of the conversion occurs in the reactive reflux drum. The question then becomes: can we further simplify the process flowsheet by removing all the catalyst from reactive trays and putting them into the reflux drum? That is: we have a total of 5.01 m3 catalyst (3.03 + 1.98 = 5.01 m3) placed in the reflux drum while making the upper section of the RD column non-reactive
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 -0.50 -0.25 0.00 0.25 0.50 RD Column Reboiler Duty + 0.01% Reboiler Duty - 0.01% Δ T/| Δ QR 1 | [ %/% ] Stage Number [−] 0 2 4 6 8 10 12 14 16 -20 -10 0 10 20 2nd Column Reboiler Duty + 0.01% Reboiler Duty - 0.01% Δ T/| Δ QR 2 | [ %/% ] 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 -15 -10 -5 0 5 10 15 3rd Column Reflux Ratio + 0.01% Reflux Ratio - 0.01% Δ T/ Δ | RR 3 | [ %/% ] Stage Number [−] Stage Number [−]
Fig. 11. Sensitivities of trays temperature for±0.01% changes in the manip-ulated variable: (A) RD column, (B) 2nd column, and (C) 3rd column.
Fig. 9A. Using the same total number of tray, feed conditions,
and the same reboiler duty, the results show that the conversion drops to 83.4% as compared to 98.7% of the proposed one (in-dicated by the dashed line in Fig. 9B). Moreover, in order to achieve the desired conversion (98.7%), the reboiler should be doubled (solid line inFig. 9B). This clearly shows that, despite
having insignificant contribution to the total conversion, the re-active trays are essential for a near complete conversion of the limiting reactant. This is especially true of chemical systems with a small equilibrium constant.
The second question is: what will happen if pure methyl acetate is used instead of mixed MeAc/MeOH feed (60/40)? Certainly, this will require pre-processing of the azeotropic mix-ture using, for example, pressure swing to break the azeotrope. However, the purified MeAc reactive distillation system only gives a 12% reduction (from $1,905,468 to $1,681,250) in the TAC as compared to the mixed 60/40 mixed MeAc/MeOH feed. The reduction is almost equally distributed between the capi-tal cost and the operating cost. A noticeable difference in the process flowsheet is that the pure MeAc should be introduced into the reactive reflux drum, instead of tray 6 for the mixed MeAc/MeOH feed.
Before leaving this section, we would like to explore alterna-tive separation sequence on the design of this hydrolysis plant.
Fig. 7shows that we have an “indirect” separation sequence for
the mixture of methanol, water, and acetic acid. The “direct” separation is examined. The result shows that these two se-quences differ by less than 10% in TAC for the two distillation columns and the “indirect” sequence inFig. 7 is more favor-able in terms of capital as well as operating costs. Appendix B gives the optimized process flowsheet for the hydrolysis plant with direct separation sequence.
4. Process dynamics and control
Plantwide control of processes with reactive distillation col-umn and separation colcol-umns is less common as compared to the control of reactive distillation columns and plantwide control of reactor/separator (Luyben et al., 1998;Wu and Yu, 1996).
Al-Arfaj and Luyben (2004) develop control scheme for the
“pseudo-neat” TAME process (one RD with two columns) us-ing temperature control and effective control performance can be obtained. In this work, temperatures are used to infer the product composition as well as degree of conversion. As pointed out byAl-Arfaj and Luyben (2000a, b), two fresh feeds cannot be adjusted using simple ratio control. One of the feed should be under feedback control to maintain stoichiometric balance. Following these principles, a control structure is developed for the hydrolysis plant (Fig. 10).
(1) Control a tray temperature of reactive distillation by chang-ing the reboiler duty to meet the desired conversion. (2) Control a tray temperature of the 2nd column by adjusting
reboiler duty to maintain the product (HAc) purity and control a tray temperature of the 3rd column by changing the reflux ratio to maintain product (MeOH) purity. (3) Ratio the fresh feed of MeAc/MeOH mixture to the recycle
flow (FR). Note that this mixed MeAc/MeOH feed is the throughput manipulator.
(4) Maintain the 3rd column base inventory by adjusting the fresh water feed.
(5) Fix the reflux ratio in the 2nd column and maintain the boilup ratio in the 3rd column.
74.0 74.5 75.0 3600 4000 4400 113.6 114.0 114.4 114.8 3300 3600 3900 4200 79.8 80.0 80.2 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.44 0.49 0.54 T1,4 (˚c) QR 1 (KW) T2,5 (˚c ) QR 2 (KW) T3,15 (˚c ) Time (hr) RR 3
Fig. 12. Sequences of relay feedback tests for the hydrolysis plant.
(6) Control the top and bottoms holdups in the reactive distil-lation column by changing the reflux flow rate and bottoms flow rate, respectively.
(7) Control the top and bottom holdups of the 2nd column by manipulating the distillate flow rate and bottoms flow rate, respectively.
(8) Control the top holdup of the 3rd column by changing the distillate flow rate.
This is a relatively simple control structure where the stoi-chiometric balance is maintained by adjusting the fresh water feed flow rate via column base level control as mentioned in step (4), avoid accumulation or depletion of water in the sys-tem. Also note that the reason the base level of the 3rd col-umn can be controlled using the fresh water feed is that, the total recycle rate is under flow control, i.e., the sum of bottoms flow and fresh feed is fixed. The next step is to achieve com-position control by identifying the temperature control trays in all three columns. The objective is to infer conversion in the RD column, the bottoms HAc composition in the 2nd column, and the overhead MeOH composition in the 3rd column. Sen-sitivity analyses are performed for±0.01% variations in the corresponding manipulated variables. Because of small pertur-bations, the temperature responses are quite linear as shown
Table 3
Tuning parameters of temperature control
CV MV Tuning parameter
T1,4 QR1 KC,1= 04.24,I,1= 10.32 (min) T2,5 QR2 KC,2= 14.62,I,2= 06.96 (min) T3,15 RR3 KC,3= 20.10,I,3= 12.00 (min)
inFig. 11. The temperature control points are tray 4, tray 5
and tray 15 for the RD column, 2nd column, and 3rd column, respectively. Performing dynamic simulation using Aspen Dy-namics, a third-order 0.5 min time lag is assumed for temper-ature measurement (Luyben et al., 1998). Liquid level is con-trolled using proportional-only controller. Proportional-integral controllers are used for flow, pressure, and temperature controls. Relay feedback tests (Shen and Yu, 1994) are performed on the temperature loops to find the ultimate gains (Ku) and ultimate period (Pu) of each temperature control loop followed by the Tyreus–Luyben settings (Luyben et al., 1998) and a simple ver-sion is: Kc= Ku/3 and I= 2Pu. The multifunctional nature of the reactive distillation complicates already very nonlinear natures of either reaction or separation, in addition to recycle structure of the process. To mitigate the interaction arisen from
0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0.81 0.82 0.83 0.84 0.98 0.99 1.00 0.000 0.001 0.002 0.003 0.004 240 300 360 420 480 72 74 76 78 0.98 0.99 1.00 2600 3400 4200 5000 5800 30 50 70 40 80 120 160 240 320 113 114 115 78 80 82 20 40 60 80 2600 3200 3800 4400 5000 1.3 1.5 1.7 60 80 100 Feed Flowrate + 20% Feed Flowrate - 20% XB 3 ,H 2 O XB 2 ,HAc XB1, MeAc B1 (kmol/hr) T1,4 (˚c) XD 3 ,MeOH Time (hr) Time (hr) Time (hr) QR 1 (KW) Time (hr) B2 (kmol/hr) D3 (kmol/hr) B3 (kmol/hr) T2,5 ( ˚c) T3,15 (˚c ) FH 2 O (kmol/hr) QR 2 (KW) RR 3 FMeAc (kmol/hr) 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0.80 0.82 0.84 0 2 4 6 8 10 12 14 0.9896 0.9898 0.9900 0.9902 0.9904 0.0010 0.0015 0.0020 0.0025 365 370 375 380 74.2 74.7 75.2 0.988 0.990 0.992 2600 3600 4600 5600 40 50 60 80 84 88 230 235 240 245 250 114.1 114.2 114.3 79.9 80.0 80.1 40 50 60 3600 3800 4000 1.0 1.5 2.0 75 80 85 90
MeAc Feed Composition 65% MeAc Feed Composition 55%
XB 3 ,H 2 O XB 2 ,HAc XB 1 ,MeAc B1 (kmol/hr) T1,4 (˚c ) XD3,MeOH Time (hr) Time (hr) Time (hr) QR 1 (KW) Time (hr) B2 (kmol/hr) D3 (kmol/hr) B3 (kmol/hr) T2,5 ( ˚c) T3,15 ( ˚c) FH 2 O (kmol/hr) QR 2 (KW) RR 3 FMeAc (kmol/hr)
to the RD column as shown inFig. 12. The sequential tuning procedure converges faster this way (Shen and Yu, 1994). Con-troller settings for all three loops are summarized inTable 3.
The plantwide control is tested for feed flow and compo-sition disturbances. Fig. 13A shows that fast and symmetric responses can be obtained for ±20% feed flow changes. The temperature control trays (T1,4, T2,5, and T3,15) and product
compositions (XB2,HAc and XD3,MeOH) settle in less than 5 h. The recycle flow to the fresh feed ratio loop calls for a large recycle flow as the production rate increases. This affects the base holdup in the 3rd column and subsequently leads to a large overshoot in the water feed flow rate initially (Fig. 13A). It can also be seen that with temperature control, steady-state errors exist for both product compositions, by a factor of 0.5% error for 20% production rate changes. Nonetheless, reasonable control performance can be obtained using simple temperature for production rate variations. On the contrary, the feed compo-sition disturbances are more difficult to handle. It takes almost twice the time span (∼ 10 h) to settle the transient responses. However, the steady-state offsets in the product composition are much smaller as compared to the flow disturbances. De-spite having relatively symmetric responses for temperatures, compositions (XB1,MeAc and XD3,MeOH) exhibit nonlinear behavior (Fig. 13B).
5. Conclusion
In this work, design and control of methyl acetate hydrolysis plant is explored. The low chemical equilibrium constant and unfavorable boiling point ranking of the reactant (MeAc is the lightest pure component) lead to a new process configuration which is an improved version of existing ones. Next, a system-atic design procedure is proposed to complete the preliminary design based on the total annual cost (TAC). Two dominate design variables are identified and they are: recycle flow rate (FR) and the overhead impurity of acetic acid (XD2,HAc) in the HAc dehydration column (i.e., the 2nd column in our nota-tion). Quantitative comparison is made between the proposed one and a literature example (the hybrid system ofLee, 2002) and the results show that 50% energy saving can be obtained in the reactive distillation column alone. Finally, the operability of the proposed process flowsheet is tested for feed flow and feed composition disturbances. The results show that reasonable control performance can be obtained using simple temperature control scheme.
Notation
ai activity coefficient for each component i
Da Damköhler number
Fd factor for design type
Fm factor for radiant tube material Fp factor for design pressure FR recycle flow rate
HAc acetic acid
kf forward rate constant
kr backward rate constant
Kc controller gain
Ki adsorption equilibrium constants for each com-ponent i
Keq equilibrium constant for the hydrolysis reaction
Ku ultimate gain
mcat catalyst weight
MeAc methyl acetate
MeOH methanol
Mi molecular weight of component i
Nrxn number of trays in the reactive section
NS number of trays in the stripping section NT 2 total number of trays in the 2nd column NT 3 total number of trays in the 3rd column NFH2O water feed location
NFMeAc acetate feed location
NF2 feed location in the 2nd column
NF3 feed location in the 3rd column
Pu ultimate frequency
QR reboiler duty
R reaction rate
Ri reaction on tray i
Rtot total reaction in the column
T reaction temperature
TAC total annual cost
XB liquid mole fraction in the bottom product XD liquid mole fraction in the distillate
XD2,HAc the overhead specification of acetic acid in the 2nd column
Greek letter
I integral time
Acknowledgments
We are grateful to the insightful comments made by the reviewers. The constructive comments made this a much improved paper. This work was supported by the Ministry of Economic Affairs and National Taiwan University.
Appendix A. TAC calculation
The evaluation of equipments follows the procedure of
Douglas (1988) and specific equations of Elliott and Luyben
(1996),Chiang et al. (2002), andTang et al. (2005). A payback
period of 3-year is assumed and a M&S index of 1108.1 (the year of 2002) is applied in the calculation. Materials of con-struction are stainless steel. The equipment is sized as follows:
(1) Reboiler heat transfer area (AR)
AR(ft2) = QR
UR· TR
where QR(Btu/h) is the reboiler duty, the overall heat-transfer coefficient URis assumed 250 Btu/(h∗ft2), and the temperature driving forceTR (F) in the reboiler depends on the steam.
(2) Condenser heat transfer area (AC)
AC(ft2) = QC
UC· TC
, (A.2)
where QC(Btu/h) is the condenser duty, the overall heat-transfer coefficient UC is assumed 150 Btu/(h ∗ ft2), and the log-mean temperature driving force TC (F) depends on the dew points and bubble points for a total condenser. (3) Column length (LC)
LC(ft) = 2.4NT, (A.3)
where NT is the total number of trays.
The capital and operating costs are calculated according to (1) Column cost Column cost [$] = M&S 280 (101.9D 1.066 C L0.802C (2.18 + FC)), (A.4) where FC= FmFp = 3.67. (2) Tray cost
Tray cost[$] = M&S
280 (4.7D
1.55
C LCFC), (A.5)
where FC= Fs+ Ft+ Fm= 1 + 1.8 + 1.7. (3) Heat exchanger cost
Heat exchanger cost [$] = M&S 280 (A
0.65(2.29 + F
C)), (A.6) where FC = (Fd + Fp)Fm = (1.35 + 0) × 3.75 for the reboiler and FC= (Fd+ Fp)Fm= (1 + 0) × 3.75 for the condenser.
(4) Steam cost
steam cost [$/year] = $2.28 1000 lb× QH 947.0 8150 h year
for RD column, (A.7)
steam cost [$/year] = $3.00 1000 lb× QH 905.5 8150 h year
for 2nd column, (A.8)
steam cost [$/year] = $2.45 1000 lb× QH 934.7 8150 h year
for 3rd column. (A.9)
(5) Cooling water cost Cooling water cost
$ year = $0.03 1000 gal 1 gal 8.34 lb QC 30 8150 h year . (A.10)
(6) Catalyst cost (assuming a catalyst life of 3 months) Catalyst cost [$] = catalyst loading [lb] × 3.5$
lb. (A.11)
Appendix B. Process flowsheet for the hydrolysis plant with the “direct” separation sequence
In the flowsheet, we use the same RD column and explore the effect of separation sequencing on the total annual cost. Thus, we have the same inlet and outlet streams for the “direct” separation sequence. The design parameters become: the total number of trays and feed tray location of the 2nd column (NT 2 & NF2) and the 3rd column (NT 3& NF3). Given the production
rate and product specifications, the design steps are
(1) Pick a total number of trays in the 2nd column (NT 2).
13 14 15 16 462 464 466 468 470 NT2 = 27 NT2 = 28 NT2 = 29 TAC ($1000/year) 13 14 15 16 17 683 685 687 689 691 693 NT3 = 18 NT3 = 19 NT3 = 20 TAC ($1000/year) NF2 [-] NF3 [-]
Fig. B1. Effects of total number of trays and feed tray location on TAC for the direct separation sequence with perturbation from nominal steady state for: (A) 2nd column, (B) 3rd column.
Fig. B2. Optimized process flowsheet with the “direct” separation sequence for the hydrolysis system.
Table B1
Comparison of TAC with “direct” and “indirect” separation sequences
Sequence Indirect Direct
NT 2 15 28
NF2 14 15
TAC2nd column($1000/year) 654.49 463.5
NT 3 27 19
NF3 11 15
TAC3rd column($1000/year) 409.9 684.6
TAC2nd column+ TAC3rd column 1064.4 1148.1
(2) Guess a feed location in the 2nd column (NF2) and change
the reflux flow (R) and heat input (QR) until the product specification is met.
(3) Go back to (2) and change NF2until the TAC is minimized.
(4) Go back to (1) and vary NT 2until the TAC is minimized. (5) Pick a total number of trays in the 3rd column (NT 3). (6) Guess a feed location in the 3rd column (NF3) and then
change the reflux flow (R) and heat input (QR) until the product specification is met.
(7) Go back to (6) and change NF3 until the TAC is
mini-mized.
(8) Go back to (5) and vary NT 3 until the TAC is mini-mized.
Fig. B1 shows how the effects of total number of trays
and feed tray locations in the separation section (2nd and 3rd columns) to the TAC. The 2nd column has 19 trays with NF2=
15. The 3rd column has a total 28 trays with the feed intro-duced to the middle section of the column, i.e., NF3= 15.
The optimized flowsheet can be obtained by adjusting these design parameters and the result is given inFig. B2.Table B1 summarizes design parameters and corresponding TAC for the distillation columns for these two, “indirect” and “direct”, sep-aration sequences.
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