Design and Control of Reactive Distillation System for Esterification of

Article pubs.acs.org/IECR

Design and Control of Reactive Distillation System for Esterification of Levulinic Acid and n‑Butanol Yao-Hsien Chung,† Tzu-Hsuan Peng,† Hao-Yeh Lee,‡ Cheng-Liang Chen,*,† and I-Lung Chien† †

Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan

‡

ABSTRACT: This work presents the conceptual process design and the associated control strategies for the manufacture of nbutyl levulinate, which can be a suitable fuel additive, because of its high octane number, high oxygen content, and low water solubility. A reactive distillation column is used to avoid problems of separation and equilibrium reaction in the conventional esterification process. Both the thermodynamic properties and the kinetic data are compiled from open literatures. Sensitivities of several key design variables, including the feed ratio of raw materials and operating pressure of the reactive distillation column, to the economic manufacturing of n-butyl levulinate are investigated. The optimal steady-state design is found through total annual cost analysis, using iterative optimization procedure. Two feasible control structures are presented for this reactive distillation process. A series of simulations shows that both of the control strategies can reject throughput disturbances quite well, but can only achieve ordinary control performance for handling the feed composition disturbances.

1. INTRODUCTION In recent years, pollution resulting from the storage and transportation of petrochemical products has raised many concerns. Methyl tert-butyl ether (MTBE), for example, is considered to be a probable carcinogen in the United States. Because of its high water solubility, MTBE is deemed a contaminant of groundwater in many places.1 Therefore, finding a substitute for MTBE becomes one of the important research topics. Among researchers dealing with the substitutes of MTBE, Fagan et al.2 compares the basic physical properties of levulinic esters and MTBE. Table 1 summarizes their main results. Therein, n-butyl levulinate (LABE) has a high potential to be a promising fuel additive, because of its high octane number, high oxygen content, large affinity for organic components, and low water solubility. Thus, LABE would be a relief for the groundwater pollution if LABE substitutes for MTBE. Also, two of the raw materials used to produce LABElevulinic acid (LA) and n-butanol (n-BuOH)can be produced from the biorenewable processes, which makes LABE more economically competitive. LA can be produced from the hydrolysis of lignocelluloses, which yields hextose and pentose. Hextose can then be converted, first to hydroxymethylfurfural (HMF) and further to LA. Pentose can be converted first to furfural and then to LA.3 The cost to produce LA is ∼0.2 USD/kg.4 [Note: USD = U.S. dollars.] Recently, BioMetics developed a process to produce LA at 50−70% yields from cellulosic feedstocks.5 nButanol can be produced from the integrated acetone−butanol− ethanol (ABE) fermentation process.6 Hextose and pentose from the biomass can be converted to pyruvate, which is fermented to produce butanol. Vacuum fermentation has been proved to recover more butanol in an integrated ABE fermentation process.7 There are two steps in the traditional synthesis of levulinic esters. LA is first dehydrated to Angelica lactone and then reacts with alcohol to generate levulinate.8 However, the complexity © 2015 American Chemical Society

and high costs are two main disadvantages of this two-step reaction process. Therefore, the one-step reaction, in which LA reacts directly with alcohol to form levulinate, is a better alternative. Reaction kinetics of LA and n-BuOH esterification has been studied by some researchers. Bart et al.9 used sulfuric acid as catalyst for the reaction. Yadav10 used a more environmentally friendly heterogeneous solid-acid catalyst (Novozym 435) for this esterification reaction. However, the kinetics of heterogeneous catalyzed reaction can only be applied in a temperature range of 40−60 °C. The operating temperature of this reactive distillation is outside of this limited range. For this reason, the homogeneous catalyst sulfuric acid is chosen in this study. The esterification step in the conventional processes has an equilibrium limitation, which leads to high operating costs, because of the separation of unreacted reactants and products. One can use the reactive distillation (RD) configuration to overcome such an equilibrium limitation. The RD configuration is a combination of the reactor and the separation system that can increase the conversion with lower energy consumption. In recent years, an increasing number of researchers have investigated characteristics of the RD. Malone and Doherty11 concluded several significant opportunities for research and development including the experiments, phase equilibrium, catalysis, equipment design, and the conceptual design for RD processes. Luyben and Yu12 showed 1105 related publications and 814 U.S. patents between 1971 and 2007. Luyben and Yu12 also highlighted 236 reaction systems that can be designed with RD configurations. Also, Sharma and Mahajani13 summarized more than 100 important industrial reactions. All of these surveys prove the importance of RD in the industry. Received: Revised: Accepted: Published: 3341

February 18, 2014 March 13, 2015 March 17, 2015 March 17, 2015 DOI: 10.1021/ie500660h Ind. Eng. Chem. Res. 2015, 54, 3341−3354

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Industrial & Engineering Chemistry Research Table 1. Comparison of Levulinic Esters and MTBE

Dilution Ratio in Organic Compounds

methyl levulinate ethyl levulinate n-propyl levulinate isopropyl levulinate n-butyl levulinate isobutyl levulinate sec-butyl levulinate MTBE TAME a

molecular formula

molecular weight

boiling point (°C)

O2 content (wt %)

content in oxygenated gasolinea (wt %)

blending octane numberb

C6H10O3

130.1

196.0

37

5.4

106.5

C7H12O3

144.2

205.8

33

6.6

C8H14O3

158.2

221.2

30

C8H14O3

158.2

209.3

C9H16O3

172.2

C9H16O3

water solubility data

toluene

butyl alcohol

2.4

2.35

107.5

completely miscible 12.5 vol %

2.85

3.25

6.6

105

2.8 vol %

3

3.85

30

6.6

105

5.9 vol %

2.8

5.05

237.8

28

7.2

102.5

0.93 vol %

3.15

6.4

172.2

230.9

28

7.2

102.5

1.2 vol %

2.95

6

C9H16O3

172.2

225.8

28

7.2

102.5

1.6 vol %

2.75

5.55

C5H12O C6H14O

88.5 102.2

55.1 86.3

11 16

14.9 16.8

109 105

4.3 wt % 1.4 wt %

immiscible

immiscible

2.7 wt % O2 requirement. bOctane number = (RON + MON)/2.

Recently, Harwardt et al.19 proposed a superstructure-based mixed-integer nonlinear programming (MINLP) formulation for systematic design of the LABE production process. The reactive distillation column is rigorously modeled tray-by-tray with adequate thermodynamic behavior and chemical reactions. This study shows the feasibility of rigorous column optimization for reactive distillation. The approach of Harwardt et al. used for optimization of the process follows a mathematical optimization method, and the results can be considered to be the global optimum. Also, it can solve the problem more efficiently and systematically. However, in order to achieve convergence in the optimization, good initialization strategy is required due to highly nonlinear behavior of the thermodynamic model and the kinetic equations. The formulation of phase separation and the application of engineering heuristics will be challenging to the researchers. Furthermore, the designers are not easy to involve in the decision-making since the optimization is carried out by the computer.20 Therefore, most research concerning the conceptual design of reactive distillation process is still based on commercial simulators such as Aspen Plus for steady-state design and Aspen Plus Dynamics for control structures design. This research centers on the design and control of the LABE process with a RDC, including the steady-state design, process optimization, and control structure design. Most heavy-esters RD studies in the literature belong to the Ip process, where two products, ester and water, are the heaviest and lightest components in this quaternary system, respectively, and, therefore, the separation is easy. However, the LABE process belongs to Type IIIP. The reactant LA is the heaviest component, leading to low conversion of LA, since LA will go down in the column quickly. Therefore, one of the contributions of this study is to establish the RD design for Type IIIP process. Commercial simulators Aspen Plus and Aspen Plus Dynamics are used for simulation. The simulation-based approach for optimal design of the LABE production process emphasizes the involvement of designers’ domain knowledge and engineering tradeoff. Control strategies will also be investigated to test the capability of rejecting major operating disturbances such as the throughput changes and the composition disturbances.

Table 2. Classification for Process Types18 reaction

A + B ⇔ C + Da

Type I

IP IR

LK + HK ⇔ LLK + HHK LLK + HHK ⇔ LK + HK

Type II

IIP IIR

HK + HHK ⇔ LLK + LK LLK + LK ⇔ HK + HHK

Type III

IIIP IIIR

LK + HHK ⇔ LLK + HK LLK + HK ⇔ LK + HHK

a

Legend: LK, light key; LLK, lighter than light key; HK, heavy key; and HHK, heavier than heavy key.

LABE is a heavy ester, which is a type of chemical whose synthesis via the RD configuration has been investigated in recent research. Tang et al.14 proposed a configuration that combines a reactive distillation column (RDC) and a decanter for n-butyl and n-amyl acetate processes. Hung et al.15 showed the design and control of an amyl acetate process using the RD configuration to investigate the effect of different concentrations in the acetic acid feed. Arpornwichanop et al.16 studied the direct utilization of dilute acetic acid to produce the n-butyl acetate through esterification in an RDC. Niesbach et al.17 applied the concept of RD to production of n-butyl acrylate using nonequilibrium model with validation of experimental data. Tung and Yu18 studied the effect of relative volatility rankings on the design of quaternary reactive distillation processes. All possible rankings can be classified into six categories, according to relative volatilities of the reactants and the products as shown in Table 2. From Table 2, a distinct group with reactants or products having the middle volatility ranking is classified as Type I. The Type II group has relative volatilities of the two reactants and the two products adjacent to each other. The relative volatility ranking is arranged in an alternating manner for the reactants and the products for Type III group. The subscript, R or P, depending on the lighter-than-light key component denotes reactant or product, respectively. Table 2 provides a framework to study the reactive distillation processes. Therein, the LABE process can be classified as Type IIIP. 3342

DOI: 10.1021/ie500660h Ind. Eng. Chem. Res. 2015, 54, 3341−3354

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Industrial & Engineering Chemistry Research Table 3. NRTL Binary Parameters

a

component j

water

watera

LABE

LA

LA

water

component i

n-BuOH

n-BuOH

n-BuOH

n-BuOH

LABE

LABE

LA

source temp. unit Aij Aji Bij Bji Cij

ASPEN- VLE °C −2.0405 13.1102 763.8692 −3338.9536 0.3

ASPEN- LLE °C 204.2348 90.5263 −9291.7021 −4983.1548 0.2

UNIFAC °C 0 0 497.8222 −126.3424 0.3

UNIFAC °C 0 0 393.5913 −38.3496 0.3

UNIFAC °C 0 0 195.7617 −12.9595 0.3

UNIFAC °C 0 0 143.5528 1778.0108 0.3

UNIFAC °C 0 0 −261.3185 1030.1259 0.3

water

n-BuOH−water LLE binary parameters are used only in the decanter.

2. KINETICS AND THERMODYNAMICS 2.1. Kinetic Data. The esterification reaction of levulinic acid and n-butanol uses sulfuric acid as the catalyst, which is a Table 4. Boiling Point Ranking at 1 bar component n-BuOH/watera n-BuOH/watera (experimental data) LABE/watera water n-BuOH LABE LA H2SO4 a

temperature (°C)

composition (mole basis)

92.63 92.7

(0.2471, 0.7529) (0.247, 0.753)

99.98 100.02 117.68 237.80 256.98 274.80

(0.0061, 0.9939) 1 1 1 1 1

Figure 2. LABE−LA Txy diagram at 1 bar.

Heterogeneous azeotrope.

with

homogeneous reaction in liquid phase. A rate expression has been developed by Bart et al.9

⎛ −E ⎞ ⎛ − 54 275 ⎞ ⎟ k f (m 6 kmol−2 s−1) = A f exp⎜ f ⎟ = 280 687 exp⎜ ⎝ RT ⎠ ⎝ RT ⎠

C5H8O3 (LA) + C4 H10O (n‐BuOH) ⇋ C9H16O3 (LABE) + H 2O (water)

⎛ −E ⎞ ⎛ − 48 431 ⎞ ⎟ k b (m 6 kmol−2 s−1) = A b exp⎜ b ⎟ = 15 312 exp⎜ ⎝ RT ⎠ ⎝ RT ⎠

(1)

R (kmol s−1) = C H2SO4[k f C LACn‐BuOH − k bC LABECwater]

where Ci (kmol m−3) is component concentration; Ef and Eb (kJ kmol−1) are the forward and backward activation energy,

(2)

Figure 1. Water−n-butanol phase equilibrium diagram at 1 bar. 3343


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Industrial & Engineering Chemistry Research

Figure 3. Flowsheet of base case (neat design).

3. STEADY-STATE DESIGN Two important approaches can be considered for the operation of reactive distillation (RD) processes: the neat design and the

respectively; T (Kelvin) is the absolute temperature, and R is the universal gas constant (R = 8.314 kJ kmol−1 K−1). 2.2. Thermodynamic Data. The nonrandom two liquid (NRTL) thermodynamic model is used to predict the phase equilibriums of this system, including nonideal vapor−liquid equilibrium (VLE) and vapor liquid−liquid equilibrium (VLLE). However, LABE is a non-databank component in Aspen Plus. Hence, physical properties of LABE are needed to create a new component in Aspen Plus. The following LABE properties are reported in the literature and are used in this study: the boiling point is 237.8 °C at 1 bar; the specific gravity is 0.9735 at 25 °C; and the vapor−temperature relationship of LABE is provided by Cowley et al.,21 as shown in eq 3. log(P(mm Hg)) = 27.0531 − 5.97 log(T (K)) −

4089.1 T (K) (3)

The NRTL parameters (six pairs in total) for the related four components are given in Table 3. Note that there are two sets of NRTL parameters for the H2O/n-BuOH pair. The Aspen builtin LLE parameters are used in the simulation of a decanter, while Aspen built-in VLE parameters are used in other units. Other five sets of NRTL parameters are estimated by Aspen, using the UNIFAC group contribution method. The NRTL model predicts that there are two azeotropes. One is between water and n-butanol, and the other one is between LABE and water, as depicted in Table 4. Stockhardt et al.22 and Hill et al.23 provided the VLE and LLE experimental data of H2O/n-BuOH system. The comparison of the above experimental data and Aspen predicted phase equilibrium at 1 bar can be seen in Figure 1. There is a liquid−liquid separation between water and nBuOH system, as shown in Figure 1. The LABE−LA Txy diagram is given in Figure 2. It shows that there is a pinch point zone at high LABE purity. Therefore, the LABE−LA separation should be avoided, because of its large consumption of energy. In the proposed process design, LA is the limiting reactant that should be completely consumed.

Figure 4. Liquid composition of the RDC column.

excess design. Therein, all reactants are fed into reactive zone, according to the stoichiometric condition for the neat design. On the other hand, there is extra feed for one of the two reactants in the excess design. The excess ratio of the two reactants is an important design variable. Higher excess ratio would improve the conversion for the limited reactant in each stage of the reactive zone. In addition, it would also help to decrease the required stages of reactive zone in the RDC under the same LABE production rate. However, the energy consumption for recycling extra reactant is also higher. In contrast, a low excess ratio requires a larger number of stages in the RDC but lower energy consumption for recovery of residual reactant. Therefore, an inherent tradeoff exists. The neat and excess designs are studied and compared in the following. 3344


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Figure 5. Flowsheet of optimal excess design with an excess ratio of 6.

3.1. Neat Design. Figure 3 shows the base case of the neat design with a toichiometric feed ratio of n-BuOH and LA. The goal of the RDC is to reach 99.5% conversion of LA, so that there is no need to separate LA and LABE. Vapor from the top of the RDC, an azeotrope of n-BuOH/H2O, approaches to the lowest temperature of the system. The azeotrope composition can be separated into two liquid phases in a decanter, as shown in Figure 1. The organic phase liquid, consisting of mostly n-BuOH, is totally refluxed back to the column. The aqueous phase is sent to a flash tank to remove small amounts of n-BuOH contained in the water and to keep the mole fraction of water at 99.7%. The vapor out of the top of the flash tank, which contains some residual n-BuOH, is recycled back to the decanter after condensation. LA, along with sulfuric acid, is fed into the RDC on the 2nd stage and n-BuOH on the 63rd stage. Three assumptions are made to design the RDC:

sulfuric acid, which will remain in the water layer and a distillation column is required later to separate the sulfuric acid from water. 3.2. Excess Design. Since it is difficult to separate LA and LABE, LA is considered to be the limiting reactant in the excess design. We define the excess ratio of n-BuOH as described in eq 4: excess ratio =

number of moles of n‐BuOH fed into RDC number of moles of LA fed into RDC (4)

The optimal flowsheet of excess design is presented in Figure 5, for the purpose of comparison. The excess ratio is set at 6 for the production goal, so that 500 kmol/h unreacted n-BuOH can be obtained in the distillate and 99.5 kmol/h LABE can be obtained at the bottom. The total annual cost (TAC) analysis is used to find the optimal design. Equation 5 depicts the TAC, which consists of the annual operating cost (AOC) and the annualized total capital cost (TCC), with a payback period of 3 years. The calculation is based on Douglas,24 ignoring the costs of piping and pumps.

(1) The downcomer area occupies 10% tray area; (2) The liquid holdup is half-full of each tray; and (3) The weir height is 0.1016 m, and, as a result, liquid holdup is 0.081 m3. The temperature of the decanter is set at 40 °C. The RDC has 64 stages, including the reboiler, and is operated at a pressure of 3 bar. It requires hot oil (Dowtherm A) as the heat source, because of the high reboiler temperature. Notice that the reboiler duty (5181.44 kW) is adjusted to reach the design specification of LA conversion. Figure 4 is the liquid composition profiles in the RDC. The concentrations of two reactants are quite low near the bottom. The bottom stream contains the main products: 99.5 kmol/h LABE and 8.6 kmol/h sulfuric acid. The sulfuric acid will be separated from LABE and then be recycled back to the RDC. There are two approaches for the separation. First, an extra distillation column can be used to separate sulfuric acid from the mixture. However, both the components have very high boiling points, leading to high energy consumption in the distillation column. Second, the mixture can be sent to a water-washing unit. Since LABE is immiscible with water, it can be separated from

TAC = AOC +

TCC 3

(5)

Tables 5A and 5B shows the design results and TAC analysis of different designs. Although the capital cost of the RDC in excess design is lower than that in neat design, the TCC value is still higher, because of the additional product column. Utility cost is also higher, because of large energy consumption in the product column. Consequently, neat design is adopted in this study for subsequent optimization. 3.3. Optimization of Design Flowsheet. From the results of TAC analysis, it turns out that the capital and utility costs in the RDC play the most important role in the LABE production process. There are five flowsheet variables in the RDC: (1) the number of reactive stages (Nrxn), (2) the number of stages in the rectifying section (Nr), (3) the number of stages in the stripping section (Ns), (4) the LA feed stage (NA), and (5) the n-BuOH feed stage (NF). Here, we will make two additional assumptions. First, there is no stripping section in the RDC. The main function 3345


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Industrial & Engineering Chemistry Research Table 5. Comparison of Operating Conditions and TAC under Different Designs (A) Comparison of Operating Conditions under Different Designs RDC pressure (bar)

1

3

12

17

3

excess ratio

1

1

1

1

6

42464.76 1.58 5105.98 33.15 −3283.94 1.6 3.2 105

47277.95 1.51 5181.44 42.46 −2981.10 1.53 3.06 64

73772.81 1.7 6217.398 148.14 −2917.00 1.47 2.94 52

87885.43 1.85 6556.18 393.79 −2850.94 1.45 2.9 42

36724.22 1.75 5316.66 19.55 −2899.83 1.54 3.08 40

1 2

1 2

1 2

1 2

1 2

RDC bottom vapor flow (kg/h) diameter (m) reboiler duty (kW) reboiler area (m2) condenser duty (kW) decanter diameter (m) decanter length (m) stage number Flash Tank diameter (m) length (m) Product Column reboiler duty (kW) diameter (m) condenser duty (kW) reflux drum diameter (m) reflux drum length (m)

5548.81 2 −6406.62 2.8 5.6 (B) Comparison of TAC under Different Designs (Units: 106 USD)

RDC pressure (bar)

1

3

12

17

3

excess ratio

1

1

1

1

6

1.828 0.267 0.188 0.102 0.058

1.165 0.151 0.161 0.096 0.053

1.117 0.147 0.424 0.095 0.049

1.025 0.134 0.641 0.093 0.048

0.920 0.116 0.110 0.057 0.053

0.030 0.020

0.030 0.020

0.030 0.020

0.030 0.020

0.030 0.021

RDC column tray reboiler condenser decanter Flash Tank flash tank condenser Product Column column tray reboiler condenser total capital cost

2.493

1.674

1.881

1.992

0.550 0.063 0.167 0.036 2.124

annualized capital cost Dowtherm A cooling water electricity annual operating cost total annual cost

0.831 1.921 0.037 0.266 2.225 3.056

0.558 1.950 0.035 0.266 2.251 2.809

0.627 2.341 0.033 0.266 2.641 3.268

0.664 2.467 0.033 0.266 2.766 3.430

0.708 4.089 0.099 0.266 4.454 5.162

of stripping section is to separate LABE and n-BuOH, which is quite easy, because of the large difference between their boiling points, as shown in Table 4. In addition, reactants and catalyst are homogeneous so the assumption is reasonable. Second, stages below the feed stage of LA are assumed to be the reactive zone, because LA and sulfuric acid are well-mixed and then fed to the column. With these two assumptions, the remaining variables are Nrxn, Nr, and NF. An iterative optimization procedure is shown in Figure 6. The optimization is conducted through the steps below:

(3) Change the number of reactive stages (Nrxn) until the minimum TAC is found (4) Go back to step 2, change Nr until the minimum TAC is found (5) Go back to step 1, change NF until the minimum TAC is found The operating pressure of the RDC is another important variable for the process design. Generally, the VLE at high pressure has a narrow envelope in the XY diagram; hence, it is not favorable for separation,25 which will either increase the number of stages or the reboiler duty for separation. Furthermore, increasing the column pressure in the RDC will also increase the operating temperature. Higher temperature will lead to faster

(1) Guess the n-BuOH feed stage (NF) (2) Guess the number of stages in the rectifying section (Nr) 3346


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tray costs almost remain at the same level for various operating pressures, as shown in Table 5B. However, the cost of reboilers varies greatly with the operating pressure. The required reboiler heat-transfer area increases as the operating pressure increases, because of the smaller temperature difference between the process fluid and the heating medium in the reboiler. As a result, the total capital cost is higher with increased operating pressures. It is noted that the TCC is very high under the 1 bar scenario, since the RDC requires 105 stages. Although the utility cost is the lowest of all alternative designs, it is still not economical, because of its high capital cost. Therefore, 3 bar is selected as the optimal operating pressure in the RDC. The results of optimization at 3 bar are shown in Figure 7. There are Nrxn = 53 reactive stages, Nr = 1 rectifying stage, and nBuOH should be fed on the 52th stage. When Nrxn is less than 53, the LABE composition in the vapor product from the top of the RDC increases. Because of the poor ability of separation and insufficient generation of LABE, it is difficult to produce 99.5 kmol/h LABE from the bottom of the RDC. In contrast, when Nrxn is greater than 53 stages, one can obtain 99.5 kmol/h LABE, but the cost of the column increases. Note that the conversion cannot reach 99.5% when n-BuOH is fed above the 51th stage. Even with higher reboiler duty, it is still impossible to obtain the targeted product rate from the bottom, because higher reboiler duty pushes more LABE to leave the RDC from the top. When Nr increases, the capital cost will increase; and if there is no rectifying stage, a very small amount of LABE will leave from the top of RDC. Therefore, the optimal rectifying stage is one. Figure 8 shows the optimal design. The optimization algorithm mentioned above is based on the rigorous models built by Aspen Plus modules. It generally can be applied to other processes. The advantage is that designers can apply their domain knowledge to observe and explain the production phenomena. Sensitivity of design variables can be recorded and understood. However, the time needed for the optimization is heavily dependent on the case and the number of design variables. Also, it cannot be guaranteed that the global optimum point can be found. Instead, the result can only be claimed to be very close to the optimal design.

Figure 6. Iterative optimization procedure.

reaction rate, which will reduce the required stages in the reactive zone. The resulting high reboiler temperature may require hot oil or high pressure steam for heating. In this way, the utility cost also will increase. In contrast, a less-expensive heating source can be used in lower-pressure operation. However, there must be more reactive stages to reach the required conversion rate, which causes an increase in the total capital cost. Again, there is a tradeoff here. TAC analysis can be used to determine the optimal operating pressure. In this paper, the design of the RDC at pressures of 1, 3, 12, and 17 bar are investigated. The design results and the TAC analysis are given in Table 5. From the previous discussion, one might expect lower capital cost under higher operating pressures, such as 12 or 17 bar. However, the results of simulation are contradictory to what is expected. By following the optimization procedure, it is found that the reboiler duties increase with the same tendency as operating pressure from the TAC analysis. In fact, the reboiler duty will be influenced by not only operating pressure but also the total number of stages. Higher reboiler duty will vaporize more liquid, thus increasing the vapor flow rate and the column diameter. As shown in Table 5A, when the operating pressure increases from 3 bar to 12 bar, the vapor flow rate increases from 47 277 kg/h to 73 772 kg/h. Thus, the column diameter increases from 1.5 m to 1.7 m. In fact, the column and

4. PROCESS CONTROL This section investigates the control strategies for the LABE process. The purpose of the control strategies is to keep the conversion rate of LA at 99.5% and the mole fraction of water at the bottom of flash tank at 99.7%. The conversion rate of LA can be viewed as the ratio of the flow rate of LABE in the bottom of RDC divided by the LA feed flow rate. The control loops are organized into two hierarchies. The first one is inventory control, including level control and pressure control, for keeping material balance in the process. The second one is quality control, whose function is to maintain the desired product purity. Figure 9 shows two different control structures. Two feeds are flow-controlled and accompanied by a ratio controller. The RDC pressure is controlled by the condenser duty and its sump level is controlled by the bottom flow rate. Both levels of the organic and the aqueous phases in the decanter are maintained by regulating their respective output flow rates, and temperature is controlled by the coolant flow rate. In the flash tank, the pressure, temperature, and liquid level are maintained by changing the condenser duty, the flash tank heating duty, and the liquid outlet flow rate, respectively. 3347


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Figure 7. (A) Effect of Nrxn, (B) Nr, and (C) NF on TAC.

Figure 8. Flowsheet of optimal neat design.

With regard to quality control, temperature control is used instead of composition control. This is because most composition analyzers, such as the gas chromatographs, have large measurement delay, high capital cost, and maintenance

cost. Consequently, temperature control strategies will be discussed in the following sections. 4.1. Design of Control Loop. The conventional proportional−integral (PI) controllers are used for the flow, temper3348


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Figure 9. (A) Control structure 1 (single temperature control). (B) Control structure 2 (dual temperature control).

ature, and pressure control loops. Simple proportional (P) controllers are used for level control. Controller parameters are shown in Tables 6 and 7. Through sensitivity analysis, the measurement point of temperature in the RDC is found. Temperature controllers are tuned using the auto tune variation (ATV) method.26 ATV starts from relay-feedback method, which can help us get ultimate gain and ultimate period. Then,

Table 6. Controller Parameters of Inventory Control controlled variable

controller parameters

pressure level flow rate

Kc= 2, τi = 10 min Kc= 2 Kc= 0.5, τi = 0.3 min

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The result is shown in Figure 10C. Both stages 53 and 54 have the smallest temperature deviation; however, stage 53 is a better controlled variable. Two control structures are presented for subsequent study: (1) Control structure 1 (CS1): single-point temperature control, where the manipulating variable is feed ratio; and (2) Control structure 2 (CS2): dual-point temperature control, where the manipulating variables are reboiler duty and feed ratio. Two main disturbances, ±10% throughput and 3% or 5% water in n-butanol feed, are applied to investigate the disturbance rejection capabilities of both control strategies. There is no need to test the control structures with LA feed composition disturbances. In the production of LA, the byproducts are usually formic acid and fufural. Water will be removed in the earlier stage of the process.27 4.2. Single-Point Temperature Control (CS1). Figure 9A shows the structure of single-point temperature control. Based on the result of sensitivity test, the temperature of the 53rd tray is controlled by the feed ratio. In addition, reboiler duty is set to be proportional to the total feed flow rate with ratio control. A time lag of 100 min is added in the loop to prevent the reboiler duty from affecting the system too quickly. Tuning parameters are shown in Tables 6 and 7. Figure 11 shows the dynamic responses of temperature and water mole fraction under two different disturbances. It can be seen that the dynamic responses are relatively slow and oscillatory, which requires ∼17 h to reach steady state. The reason is that the reboiler duty is determined by total feed flow rate, which is affected by the feed ratio. The strong interaction between these variables makes the process slow. Under

Table 7. Controller Parameters of Quality Control CV RDC 53rd tray temperature RDC 5th tray temperature

RDC 63rd tray temperature reboiler duty

MV

controller type and parameters

Control Scheme CS1 feed ratio PI (Kc = 5.92, τi = 19.80 min) RDC reboiler PI (Kc = 20.39, τi = 19.80 min) duty Control Scheme CS2 feed ratio PI (Kc = 6, τi = 9 min) total feed flow rate

ratio control with 100 min lag

controller parameters are set using the Tyreus−Luyben turning relations. The sequential iterative tuning procedure is used to determine the final settings. Moreover, two first-order time lags are added to the temperature control loop to improve the realism of the simulation. There are two degrees of freedom in the control of RDC: the feed ratio and the reboiler duty. In order to simplify the control loop and to avoid complicated interaction, only one or two degrees of freedom will be used in each control structure. Openloop sensitivity test and close-loop sensitivity test are conducted to determine the controlled variables. Figures 10A and 10B show the profiles of stage temperature difference under reboiler duty (±0.1%) and feed ratio (±0.5%). The results indicate that temperature of stages 5 and 53 have the largest gain to the reboiler duty and the feed ratio, respectively. The concept of close-loop sensitivity analysis is that the conversion rate of LA is maintained at 99.5% by manipulating feed ratio under composition disturbances. The stage with minimum temperature difference is the most suitable position for temperature control.

Figure 10. (A) Reboiler duty open loop sensitivity test. (B) Feed ratio open loop sensitivity test. (C) Composition close loop sensitivity test. 3350


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Figure 11. (A) Dynamic response of CS1 under throughput disturbances. (B) Dynamic response of CS1 under composition disturbances. 3351


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Figure 12. (A) Dynamic responses of CS2 under throughput disturbances. (B) Dynamic responses of CS2 under composition disturbances. 3352


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Chemical Processes.24 A payback period of three years is used in the calculation.

throughput disturbance, the deviations of both steady-state conversion and water purity are negligible. In contrast, the deviation of conversion (0.01) is relatively large, under composition disturbances. The dual-point temperature is expected to enhance the control performance under composition disturbance. 4.3. Dual-Point Temperature Control (CS2). Figure 9B shows the dual-point temperature control. Based on the result of open-loop sensitivity test, the temperature at the 5th stage is controlled by the reboiler duty and the temperature of the 53rd stage is controlled by the feed ratio. Tuning parameters are shown in Tables 6 and 7. Figure 12 shows the dynamic responses under throughput and composition disturbances. The dynamic response is faster than that of CS1. Within 10 h after the disturbances occur, the process can reach steady state again. Both control structures have similar performances with disturbances tests. The performance is very good under throughput disturbances. However, the performance is acceptable for composition disturbances. Furthermore, it is found that the steady-state deviations of conversion are ∼0.01 under composition disturbances. The reason is that, when the system reaches the steady state again, the steady value of feeding nBuOH is less than that of LA. In these situations, n-BuOH becomes the limiting reactant, so the conversion rate of LA is lower. Adjustment of set points of both temperature controllers in the RDC may improve the control performances while dealing with composition disturbance. This is not included in this study.

A. Reboiler Heat Exchange Area (AR)

The reboiler heat exchange area (AR) is determined using the following relation: AR [ft2] =

QR UR ΔTR

where UR = 250 BTU/(h ft2) and ΔTR = 45 °F. B. Condenser Heat Exchange Area (AC)

The condenser heat exchange area (AC) can be calculated using the expression A C [ft2] =

QC UCΔTC

where UC = 250 BTU/(h ft2) and ΔTC is given by ΔTC =

120 − 90

(

ln

Tb − 90 Tb − 120

)

with Tb being the condenser operating temperature (in °F). C. Height of Columns (LC)

The column height (LC) is defined using the expression LC [ft] = 2.3 × (NT − 1) D. Cost of Columns

Column cost is given by the expression

5. CONCLUSION n-Butyl levulinate (LABE) is a suitable fuel additive, because of its high oxygen content, high octane number, and low water solubility, when compared with methyl tert-butyl ether (MTBE). A novel LABE production process with a reactive distillation column (RDC) is proposed in this paper to overcome the equilibrium limitation of esterification. The ultimate goal of this design is to convert 99.5% levulinic acid (LA) and keep the purity of byproduct (water) at 99.7%. The effect of several key design variables on the economic manufacturing of n-butyl levulinate are investigated, including feed ratio of reactants and operating pressure of the RDC. The results show that neat design is more economical than excess design, since the penalty of reactant recovery column in the excess design is quite heavy. The operating pressure of the RDC is suggested to be 3 bar. Low operating pressure causes high capital cost, while high operating pressure leads to both high operating and capital costs. Detailed optimal steady-state design is then found through total annual cost analysis. Finally, two control strategies are presented: singlepoint temperature control (CS1) and the dual-point temperature control (CS2). Controlled variables are found by open-loop tests as well as closed-loop tests. Two main disturbances are used to test the control performances, including throughput and feed composition changes. Simulation results show that CS2 performs faster than CS1 and both control structures can handle throughput disturbances quite well. However, the performance is ordinary for both control strategies for handling composition disturbances, while the steady-state deviations of conversion are slightly larger.

column cost [$] =

M&S × 101.9 × DC1.066LC 0.802 × (2.18 + 3.67) 280

where M&S = 1446.5 (2009, 4th quarter). E. Cost of Trays in Distillation Columns

The tray cost in distillation columns can be defined as tray cost [$] =

M&S × 4.7 × DC1.55 × LC × (1 + 1.8 + 1.7) 280

F. Cost of Heat Exchangers

The following expression is used to determine the heat exchanger cost: heat exchanger cost [$] =

M&S (AR 0.65 + A C 0.65) 280

G. Utility Cost

Utility costs include the following terms: Dowtherm A, $17/GJ; electricity, $17/GJ; and cooling water, $0.354/GJ.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +886-2-3366-3039. Fax: +886-2-2362-3040. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Garrett, P.; Moreau, M.; Lowry, J. A. MTBE as a Ground Water Contaminate. In Proceedings of the NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Ground WaterPrevention, Detection, and Restoration, Nov. 13−15, 1985, Houston, TX; National Water Well Association: Dublin, OH, 1986. (2) Fagan, P. J.; Korovessi, E.; Manzer, L. E.; Mehta, R.; Thomas, S. M. (Dupont) International Patent No. WO 03/085071 A1, 2003.

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APPENDIX: TOTAL ANNUAL COST CALCULATION Data used to determine the total annualized cost (TAC) have been taken from the 1988 publication, Conceptual Design of 3353


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