Dynamics and control of benzene hydrogenation via reactive distillation

Journal of Process Control 24 (2014) 113–124

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Dynamics and control of benzene hydrogenation via reactive distillation Vishal Mahindrakar a , Juergen Hahn a,b,∗ a b

Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States

a r t i c l e

i n f o

Article history: Received 14 October 2013 Received in revised form 3 January 2014 Accepted 7 January 2014 Available online 28 February 2014 Keywords: Reactive distillation Packed column Dynamic modeling Feedback control Feedforward control

a b s t r a c t This work develops a dynamic, first principles-based model of a reactive distillation column used for benzene hydrogenation of a reformate stream and investigates different control structures for this process. The model is used initially to develop and evaluate a feedback control strategy which provides good regulatory performance for small disturbances, however, it tends to be sluggish for significant disturbances in the feed composition. In order to address this point, adding a feedforward controller to the feedback structure has also been investigated. However, the feedforward controller can only be implemented if composition measurements of the feed are taken. As online composition measurements are expensive in practice, several different scenarios have been investigated where samples of the feed are taken and subsequently analyzed in a lab, as represented by measurement time delays. Simulation results show that adding feedforward control to the feedback scheme can be very beneficial for this process, however, this is only the case if the composition disturbance measurements do not involve a significant time delay. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Automotive emissions are a significant contributor to poor air quality [1]. As such, specifications for automobile fuels obtained from petroleum have received increasing levels of attention from the Environmental Protection Agency (EPA). Benzene is one of the compounds that is regulated as it is a carcinogen and the EPA requires all refiners to limit the amount of benzene in gasoline to 0.62 vol% [2]. While benzene in the gasoline pool results from a variety of sources, the main contributor is the reformer unit resulting in significant amounts of benzene present in reformate streams. As the reformate stream is used to boost octane rating, there are economic objectives that have to be taken into account while complying with environmental regulations. One option to remove benzene is to hydrogenate in the presence of a catalyst. However, a problem arises as the catalyst used for the reaction is not exclusively selective for benzene, and toluene, which is present in the reformate stream in considerable quantities, will also be hydrogenated. Toluene hydrogenation is undesirable as

∗ Corresponding author at: Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, NY 12180, United States. Tel.: +1 518 276 2138; fax: +1 518 276 3035. E-mail address: [email protected] (J. Hahn). 0959-1524/$ – see front matter © 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jprocont.2014.01.005

toluene has a high octane rating (RON) and should be retained in the final product. Benzene (100 RON) + 2H2 → cyclohexane (83 RON)

(1)

Toluene (120 RON) + 3H2 → methylcyclohexane (75 RON)

(2)

In order to avoid problems related to the selectivity of the catalyst, the reformate stream is split into light and heavy components in the conventional process (Fig. 1a). As benzene is a reasonably light component of this mixture, it is mostly concentrated in the distillate, and accordingly, is hydrogenated before being sent to the gasoline pool. The downside of this process is that a high capital investment is needed. Reactive distillation (Fig. 1b) offers an alternative route for solving this problem. By combining reaction with separation it is possible to selectively react one component in a specified region of the column while suppressing unwanted reactions of other components. Furthermore, additional savings can be achieved as the heat of reaction can directly be used for separation of the mixture. While reactive distillation (RD) can have significant advantages over traditional designs, there are also challenges that need to be considered. The simultaneous presence of reaction and separation phenomena can result in complex dynamic behavior. Combining reaction and separation into a single vessel results in fewer manipulated variables, thus increasing interactions between control loops [3]. RD columns have been observed to be very sensitive to changes in feed concentration. This is a crucial aspect

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Notation a A CA dp ds D Ea F hi Hlj Hvj HETP k K KA KH L M Mlj Mvj N P P0,j Pj Q R Rgas Rev rxn s T0 Tj V u x y y* z

geometric surface area of packing per unit volume (m2 m−3 ) cross sectional area of column concentration (mol m−3 ) packing particle diameter (m) column diameter (m) distillate flow rate (mol s−1 ) reaction activation energy (J mol−1 ) feed flow rate (mol s−1 ) total liquid holdup based on empty column (m3 m−3 ) molar enthalpy of liquid stream on stage j (J mol−1 ) molar enthalpy of vapor stream on stage j (J mol−1 ) height equivalent to a theoretical stage (m) reaction rate constant (mol s−1 kg−1 ) wall factor reaction adsorption coefficient (m3 mol−1) reaction adsorption coefficient (m3 mol−1 ) liquid flow rate (mol s−1 ) mass holdup (kg) liquid molar holdup on stage j (mol) vapor molar holdup on stage j (mol) number of stages pressure (Pa) dry column pressure drop across stage j (Pa) irrigated column pressure drop across stage j (Pa) external heat energy input (J) reflux ratio gas constant (J mol−1 K−1 ) vapor Reynolds number reaction rate (mol s−1 kg−1 ) Laplace variable reaction reference temperature (K) temperature on stage j (K) vapor flow rate (mol s−1 ) specific liquid load (m s−1 ) liquid mole fraction vapor mole fraction equilibrium vapor mole fraction feed mole fraction

Greek letters ε packing void fraction lj,i liquid fugacity coefficient of component i on stage j vapor fugacity coefficient of component i on stage j vj,i cat    c

catalyst density (kg m−3 ) Murphree efficiency relative gain relative gain array transfer function time constant (s) controller design parameter (s) transfer function time delay (s) resistance coefficient

Subscripts i component index j stage index

for benzene hydrogenation as the concentration of some of the main components in the feed can vary by 50% or more due to disturbances upstream from the column [4]. The importance of addressing these disturbances is increased by the fact that changes

in the feed happen on a daily basis and a column operating under a feedback control can take several hours to return to an acceptable steady states. This paper investigates these points by developing a detailed dynamic model, studying the dynamic behavior in simulations, and developing a control scheme. Furthermore, the possibility of implementing a feedforward control scheme, in addition to a feedback one, is investigated where it is taken into account that feed composition measurements may involve time delays if the measurements are taken as samples analyzed in a lab. The outline of this paper is as follows. A literature review is presented in the following subsection and Section 2 presents preliminary information. A detailed description of the model and control structure is presented in Section 3. Section 4 discusses column responses to a series of commonly occurring disturbances. Conclusions are given in Section 5. 1.1. Literature review Reactive distillation has received a lot of attention as part of process intensification efforts in the last couple of decades. Employing reactive distillation can result in energy savings as the heat of reaction is directly used for separation of the mixture. Harmsen [3] has reviewed commercial applications of reactive distillation. Reactive distillation systems have been shown to reduce variable cost, capital expenditure and energy requirements by 20% or more for some processes [3]. Also, since the heat of reaction is used for evaporation in a column, increased reaction rates can results in increased evaporation rates without significant changes of the temperature. Thus, reactive distillation columns have been found to be less susceptible to runway behavior than conventional reactors [3]. Reactive distillation models have been surveyed extensively by Taylor and Krishna [5] and several articles describing dynamic models, and control structures [6–9] are available. A variety of different applications of reactive distillation in refineries have been reported, such as processes involving ethers (MTBE, ETBE, and TAME [10]). Sneesby et al. [11–13] have developed dynamic models for ETBE and MTBE, and also made general recommendations for control system design. Different control strategies for MTBE reactive distillation columns were highlighted by Bartlett and Wahnschafft [14]. A number of authors have also explored the dynamics and control for reactive distillation of TAME [15–18]. However, despite these extensive efforts on reactive distillation in general, no papers on benzene hydrogenation via reactive distillation can be found in the open literature. This situation is especially peculiar as benzene hydrogenation is an important step in a refinery and several RD columns used for benzene hydrogenation are in operation in refineries throughout the world. 2. Preliminaries This section reviews preliminary information needed for the remainder of the paper. Section 2.1 reviews existing modeling approaches for reactive distillation columns, some of which will be used in this work. Existing control strategies for reactive distillation columns are discussed in Section 2.2.1 and Section 2.2.3 reviews the principles of feedforward control which will also be used. 2.1. Packed column modeling Reactive distillation can be viewed as an extension of conventional packed columns, where some of the packing includes a catalyst to facilitate a reaction taking place. A number of papers have discussed modeling of conventional packed columns. The key methods used for packed columns are equilibrium (EQ) stage modeling and non-equilibrium stage modeling (NEQ). In EQ stage

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115

Fig. 1. Schematics of (a) conventional reaction/separation process and (b) reactive distillation.

models, the vapor and liquid phase are assumed to be in equilibrium. NEQ stage models use rate-based equations to describe the mass transfer occurring in conventional distillation columns. NEQ stage models are generally based on the use of rigorous Maxwell–Stefan equations for estimating heat and mass transfer rates across the interface. Many papers have presented EQ models [6,8,12,13,19–21] and NEQ models [16,17,20–22] for reactive distillation. Most of the NEQ models developed for reactive distillation are generally steady state models [20–22]. However, Peng et al. [23] have compared the results of dynamic NEQ and EQ model, and concluded that the results are similar for their case. Contrary to this, Baur [17] pointed out that the responses from the models may differ quantitatively and the dynamics are influenced by column specifications. NEQ models are generally more challenging to simulate [17,23] and require thermodynamic properties for the calculation of mass transfer coefficients and interfacial areas. The dynamic behavior of a distillation column is strongly influenced by fluid hydraulics in the column. This is even more so in reactive distillation columns, as liquid hold-ups, and liquid residence times are important for determining the conversion and selectivity of the reactive distillation column. Very few dynamic models consider both liquid and vapor holdup in the columns. The vapor holdups are generally neglected because of the low density of vapor in comparison to liquid. Also, considering vapor holdups leads to additional computational difficulties in the model. As such, most dynamic models consider only dynamic liquid hold up or in some cases a constant liquid holdup [23]. However, Choe and Luyben [24] suggest that vapor holdup should be considered for dynamic models of columns operating at pressures greater than 5–10 atm. Equations governing the vapor and liquid flows, and hold-ups in a packed column have been discussed by many papers: Bemer and Kalis [25] have given equations for liquid holdup and pressure drops in irrigated columns while Mackowiak [26] has extensively reviewed methods for determining vapor flow in packed columns.

multi-loop control system [27]. A major concern with multi-loop control is the presence of process interactions, i.e., each manipulated variable may affect multiple controlled variables, however, these interactions are not taken into account for the control structure design. Multi-loop control systems may not provide satisfactory control in some scenarios and multivariable control strategies, such as model predictive control and decoupling control can provide better control. However, multi-loop control is the most widely used control strategy for distillation columns because of its simplicity, both in terms of maintenance and controller tuning. As no work has been done on modeling and control of benzene hydrogenation via reactive distillation, this work focuses on traditional control strategies and advanced control will be investigated in the future. The commonly used control structures for reactive distillation are similar to those of conventional distillation columns. Skogestad and co-workers [28–30] have discussed the selection of controlled and manipulated variables. Most distillation columns generally use either a 4 × 4 control or a 5 × 5 control structure. These configurations refer to the number of manipulated variables and the number of controlled variables used. Eq. (3) presents the set of manipulated variables u and controlled variables y that are used in 5 × 5 systems in no particular order of correlation; see Fig. 2 for an illustration of the variables. Columns having a 4 × 4 control system frequently

2.2. Control structure 2.2.1. Feedback control Reactive distillation columns are systems with multiple inputs and multiple outputs (MIMO). One approach to deal with MIMO systems is to treat the control problem as separate individual loops, i.e., assume that each manipulated variable affects only one particular controlled variable and design a controller for each loop separately. This type of control structure is also referred to as a

Fig. 2. Conventional distillation column.

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do not use the pressure at the top of column, P1 , as a controlled variable [30].

⎛

L1

⎞

⎜ ⎟ ⎜ VN , QN ⎟ ⎜ ⎟ ⎟ u=⎜ ⎜ D ⎟ ⎜ L ⎟ ⎝ N ⎠ V2 , QD

⎛x ⎞ 1 ⎜x ⎟ ⎜ N ⎟ ⎜ ⎟ ⎟ y=⎜ ⎜ M1 ⎟ ⎜ ⎟ ⎝ MN ⎠

(3)

P1

2.2.2. Relative gain array An important general problem for a multi-loop control structure is to pair the controlled variables and the manipulated variables. Incorrect pairing may result in poor control performance and interactions among controlled variables. One way to determine the pairing is Bristol’s relative gain array (RGA) [42]. Bristol developed the RGA as a systematic approach to measure the process interactions and recommend an effective pairing of manipulated and controlled variables. The relative gain between a controlled variable yi and manipulated variable uj is defined as follows [27]: (∂yi /∂uj )u (∂yi /∂uj )y

=

open-loop gain closed-loop gain

⎡

11

⎢ ⎢ 21 =⎢ ⎢. ⎣ ..

The 5 × 5 system shown in Fig. 2 is generally used for columns with a total condenser. For these columns, the pressure is typically controlled by manipulating the condenser heat removal as the condenser temperature and the column pressure are directly linked for a total condenser. Partial condensers are used when there are very light components in the column feed that would require a high column pressure or a low condenser temperature. In a column with a partial condenser, vapor is removed from the condenser as a vapor stream. The pressure of the column is strongly influenced by the outlet vapor stream flow rate. Luyben [31] and Hori and Skogestad [32] have discussed control structures for columns with partial condensers. Sloley [33] has extensively reviewed control strategies that can be used for columns based on the type of condenser. Recycle loops in chemical plants are known to significantly alter the control and dynamics of process networks [34–36]. Recycle streams increase the overall time constants, thus “slowing down” its overall response [34]. Designing a control structure for process networks with recycle can be challenging because recycle streams can induce a time scale separation, where the dynamics of the process evolves at a fast time scale, and the dynamics of the overall process with recycle at a slower time scale [37]. Dynamical analysis and control of such process networks with recycle have received considerable attention [37]. One of the first design procedures was proposed by Buckley [38] and has been widely used in industry for many years [39]. The first step is to design a control structure that handles the inventory of the entire process (liquid levels and gas pressures). This “hydraulic” structure provides smooth flow rate changes. Fast-acting proportional-only level controllers provide the most simple and most effective way to achieve this flow smoothing [39]. The second step is to close the “product quality” loops. These loops typically use slower proportional–integral controllers to hold product streams as close to the specification as possible. Larsson and Skogestad [40] and Luyben et al. [41] have discussed plant-wide controller design procedures for a large number of measurements and control loops. When applied to a smaller single unit scale, they mirror the steps that have been mentioned above.

ij 

The relative gains are arranged to form the matrix

(4)

n1

⎤

12

···

1n

22

···

2n ⎥

.. .

.. .

.. .

n2

···

nn

⎥ ⎥ ⎥ ⎦

(5)

Controlled and manipulated variables are paired such that the corresponding relative gains are positive and as close to one as possible. While the above definition of RGA may seem difficult to estimate directly for real systems, the RGA can be determined from an open-loop gain matrix. The procedure for computing the RGA from an open-loop gain matrix, K, is given by H = (K −1 )

T

=K ⊗H

(6) (7)

where ⊗ denotes the Schur product (element by element multiplication) [27]. The controllers used for feedback control loops are generally controllers of PID-type, where PI controllers are the most commonly used ones. Luyben [31] has pointed out that flow controllers that regulate the inventory of a column, e.g., the distillate and bottom flow, should be proportional-only controller as the inventory in the column is sufficiently large to overcome the effect of offsets that may occur due to the use of proportional-only controllers. 2.2.3. Feedforward control Feedback control does not take corrective action until after deviations in the controlled variables occur. As the effects of feed disturbances will only be detected after a while, this lack of predictive control can limit the overall column performance, especially if the column includes large time constants or time delays. One option is to also include feedforward control in addition to feedback control in a control structure. Feedforward control systems measure the disturbance variables and take corrective action before upsets of the controlled variables can be recorded. The main disadvantage of feedforward control is that the disturbance variable must be measured online which is not always feasible, physically or for economic reasons. The basic idea for feedforward controller is to measure the disturbance affecting the system and compute a change of the manipulated variable such that the effect of the disturbance on the controlled variable is canceled by the change of the manipulated variable [44]. Feedforward controller designs are thus based on process models. A feedforward controller transfer function Gf for a system can be given by [27] Gf = −

Gd Gp Gmf

(8)

where Gd is the disturbance transfer function, Gp is the process transfer function, and Gmf is the disturbance sensor/transmitter transfer function. Sometimes modifications to the control law shown in Eq. (8) need to be made to ensure that the resulting controller is realizable [27]. Often, the dynamics between a process and a disturbance are neglected and a simple static feedforward controller may be designed if the responses are satisfactory. A static feedforward controller is given by the ratio of gains of disturbance, process, and measurement transfer functions [44] Gf = −

Kd Kp Kmf

(9)

where Kd , Kp , and Kmf are gains of the disturbance, process, and measurement transfer functions.

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124 Table 1 Feed composition for the RD column. Component n-Butane n-Pentane 2,3-Dimethylpentane 3-Methylpentane n-Hexane Benzene Cyclohexane 3-Methylhexane 2,4-Dimethylpentane n-Heptane Toluene m-Xylene Cumene Hydrogen Methylcyclohexane

Mole fraction C4 H10 C5 H12 C7 H16 C6 H14 C6 H14 C6 H6 C6 H12 C7 H16 C7 H16 C7 H16 C7 H8 C8 H10 C9 H12 H2 C7 H14

0.0126 0.0961 0.0116 0.0587 0.0350 0.0826 0.0000 0.0233 0.0234 0.0098 0.2814 0.2063 0.1594 0.0000 0.0000

Feedforward control depends on the accuracy of the disturbance measurement and on the accuracy of the model describing the process. As some inaccuracies cannot be avoided, feedforward control by itself would often result in an offset. As a consequence, feedforward control is commonly combined with feedback control in practice [43]. 3. RD column design and control 3.1. Development of dynamic model The RD column used in this benzene hydrogenation study is a packed column with a throughput of 200,000 lb/h. The reformate stream enters the column as feed which is processed into benzene-free lights and heavy stream. The feed stream has 15 components that need to be modeled and the feed composition is given in Table 1. The column has 70 theoretical stages which includes a partial condenser and a reboiler. The column stages have been numbered from top to bottom in this investigation. The first stage is the reflux drum and the last stage is the reboiler drum. The column model has 10 catalyst stages at the top, i.e., stage 2–stage 11. The feed to the column is added at stage 30. The reformate stream has a nominal benzene concentration of 6.0 vol% which is common in refineries [4]. It is expected that the feed benzene concentration may be as high as 11.0 vol% [4]. Hydrogen to the column is fed at stage 29 along with the unreacted hydrogen that is recycled from the partial condenser. The column is required to meet EPA specification of 0.62 vol% maximum benzene concentration at the outlet during regular operation. Note that the outlet benzene concentration throughout this investigation refers to the total volume percentage (vol%) taken over all the liquid streams (both distillate and bottom) exiting the unit. The RD column is a packed column where a section of the column is filled with catalyst. Industrial data regarding the packing details and type of catalyst used are unavailable as these are usually kept a trade secret. Also, no publications on reactive distillation for benzene hydrogenation are available in the open literature. Thus, in the absence of any sort of information regarding the packing, a standard packing size (25 mm pall rings) and catalyst size has been used in this work. The packing has been treated as equivalent to theoretical trays and a height equivalent to theoretical packing (HETP) of 0.45 m has been used throughout the column. The diameter of the column has been determined by assuming that the vapor velocity reaches a maximum of 80% of the flooding limit [26]. Based on the vapor flow estimated in the column, the diameter of the column was estimated to be 2.8 m. Two different modeling methods are commonly used for each stage of a column:

117

equilibrium-based (EQ) stages and non-equilibrium-based (NEQ) stages. NEQ models include more detail, but some of the model parameters are usually not well known and it is unclear if NEQ models provide a more accurate description than EQ-based models. As such an equilibrium-based modeling approached is used in this work. Reaction kinetics for the catalyst section have been taken from Toppinen et al.’s [45] work on hydrogenation of benzene and other alkyl benzenes. Benzene hydrogenation columns operate at a relatively high pressure of 8 atm, and hence variable vapor holdups have been taken into account. Also, the feed stream has 15 components that need to be modeled, and some of these components are bound to have low concentrations in some stages of column. If a dynamic model considers no vapor hydraulics, then the vapor flow rates are also dependent on the molar balances. This creates a problem for the initialization of the model, as the stark differences in the concentration of individual components may lead to inaccurate estimation of flow rates. In the presence of vapor hydraulics, the vapor flow rates are governed by the hydraulics facilitating initialization of the model. Equations governing liq´ uid and vapor hydraulics have been adopted from Mackowiak’s compilation [26] on packed bed fluid dynamics. The reflux drum and the reboiler drum have been sized to have a residence time for the liquid of approximately 5 min when the vessels are 50% full, based on the total amount of liquid entering or leaving the vessels. Not all of the hydrogen fed to the column will react due to disturbances in the feed composition. However, hydrogen is an expensive resource and thus, almost all the unreacted hydrogen is recycled as vapor outlet stream of the partial condenser. A recycle ratio of 0.99 has been used for the column. The equations of the model as well as the nomenclature can be found in Appendix A.

3.2. Control structure 3.2.1. Selection and pairing of controlled and manipulated variables The set of controlled variables and manipulated variables need to be identified, in order to design a control structure. A degree of freedom analysis gives the following set of seven manipulated variables that can be used for control:

⎛

D

⎞

⎜ V1 ⎟ ⎜ ⎟ ⎜L ⎟ ⎜ N ⎟ ⎜ ⎟ ⎜ ⎟ u = ⎜ FH2 ⎟ ⎜ ⎟ ⎜ Q1 ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ QN ⎠

(10)

R

When compared with (3), Eq. (10) has two additional manipulated variables: the reflux drum vapor stream flow rate V1 , and the fresh hydrogen feed flow rate FH2 . This is due to the presence of very light gases such as hydrogen in the system which has a very low bubble point temperature. Condensing hydrogen is economically infeasible, which necessitates the need for a partial condenser with a liquid outlet stream and a vapor outlet stream. The first four manipulated variables of u are flow rates and hence, they are part of the control loops that regulate the inventory of the column. The influence of these variables on the

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corresponding controlled variables is straightforward and the pairing can be performed as follows:

(11) Even though the objective of an RD column is to maintain the purity and conversion of the product streams, RD control is based on temperature points instead of composition. This is because composition analyzers are expensive to purchase and have high maintenance costs [47]. They also introduce a delay in measurements if chromatographic methods are used. Temperature sensors are inexpensive, reliable and introduce small measurement lags. Based on a degrees of freedom analysis, three temperature points need to be selected for the remaining three manipulated variables. One of these control points should be somewhere above the feed and one should be somewhere below the feed. One temperature control point is selected at the top of the column to have a measurement related to the top product that is located above the reactive zone. Another of the temperature measurements is selected approximately halfway between the feed and the bottom of the column. Since the feed is at stage 30, a temperature measurement at stage 55 is a reasonable choice and has been found to be sensitive to changes in the manipulated variables. A third temperature control point needs to be fixed at some point within the column. Hori and Skogestad [46] and Luyben [47] have listed a number of criteria for selecting the tray at which a temperature sensor should be placed for column control. Conventional techniques are based, among others, on the slope of the temperature profile, sensitivity to changes in manipulated variables, SVD analysis, temperature invariance with changes in feed composition. However, the temperature profile in the reactive zone of the column may affect the outcomes of these techniques. Therefore a more general approach has been adopted here for selecting the temperature control tray. The following three criteria have been used: (i) Avoid trays near the feed tray: the temperature profile near the feed tray is generally influenced by the enthalpy of the feed to the column and may not be as sensitive to changes in the manipulated variable. (ii) Avoid trays near the top or the bottom of the column: since the distillate temperature and one temperature measurement below the feed have already been used as controlled variables, any temperature measurement near the top or bottom will be highly correlated with already selected measurements. (iii) Avoid the catalyst zone: reactions occurring in the catalyst zone are exothermic and this affects the temperature of the catalyst stages. A temperature control point should not be selected in this zone because the temperature is affected by reaction kinetics in addition to the regular dynamics due to separation. Based on these criteria the third temperature control point was chosen to be between the catalyst zone and the feed state. Stage 19 was considered to be a good temperature control point and showed significant sensitivity to step changes in the manipulated variables. Thus, T19 was chosen as the third controlled variable. The pairing of the remaining manipulated variables was done via RGA analysis. Step input changes were given to the manipulated variables of the model with some of the control loops open. Control loops corresponding to the controlled variables liquid distillate (D), reflux drum vapor flow (V1 ), bottom flow (LN ), and fresh hydrogen feed (FH2 ) are closed for determining the gain matrix. Simulated data obtained from this model involving partially open-loop

Fig. 3. Schematic of feedback and feedforward control structure for the RD column.

control was fitted to transfer functions which were estimated using the MATLAB system identification toolbox. Most of the responses were fitted to first order plus time delay (FOPTD) transfer functions. Some of the responses were fitted to second order transfer functions in order to obtain a better fit and some of these responses also included a lead term. Table 2 shows the computed transfer functions in response to step changes in the manipulated variables. Based on these transfer functions, the RGA was determined for the nominal operating conditions (feed benzene concentration = 6 vol%). The RGA was also computed for the RD column at the extreme operating conditions, i.e., when the feed benzene concentrations are 3 vol% and 11 vol%, since it is possible that the pairing may change at different operating conditions. These results have been presented in Table 3 and it can be seen that the pairing of the controlled and manipulated variables is unaffected by the investigated changes in operating conditions. Based on RGA computed at the three operating conditions and the discussion above, the pairing of manipulated and controlled variables results in the following:

(12) Fig. 3 gives a schematic of the control structure used for the column.

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Table 2 Open loop transfer functions. R

QN

T1

Q1 1.165 × 10−4 (1 + 6052.2 s)

−36.523(1 + 9632.8 s) 1 + 2(0.901)(3548.8) s + (3548.8 s)

2

1 + 2(0.815)(3850.5 s) + (3850.5 s)

T19

−15.972 1 + 4564.7 s

2.524 × 10−5 1 + 5817.4 s

T55

−10.502 1 + 3593.3 s

1.4123 × 10−5 (1 + 3081.3 s)(1 + 2259.4 s)

1.0684 × 10−4 1 + 1887.1 s

2

1.8704 × 10−5 (1 + 4555.3 s)(1 + 1834.3 s) 1.210 × 10−5 1 + 2(0.923)(3013.9) s + (3013.9 s)

2

Table 3 RGA for RD column at different feed benzene concentrations of (a) 6 vol%, (b) 3 vol%, and (c) 11 vol%. (a) Feed benzene concentration of 6 vol%

T1 T19 T55

(b) Feed benzene concentration of 3 vol%

(c) Feed benzene concentration of 11 vol%

R

QN

Q1

R

QN

Q1

R

QN

−0.643 −0.676 2.319

−0.157 7.322 −6.165

1.800 −5.646 4.846

−0.908 −0.214 2.122

−0.026 6.596 −5.570

1.933 −5.382 4.449

−0.518 −0.234 1.752

0.106 5.307 −4.413

3.2.2. Feedback controller design Both the reflux drum and reboiler drum need controllers to regulate the flows and maintain specified liquid levels in the vessels. The reflux drum also holds vapor which needs to be regulated such that the pressure of the column is maintained. Since the stream flow rates regulate the inventory of the column, P-only controllers have been used. These three proportional controllers were tuned via Ziegler Nichols tuning relations. A PI controller was used for maintaining the reflux drum outlet vapor flow rate V1 in order to avoid an offset in the column pressure at the top (P1 ). PI controllers were also used for the temperature point control loops. All the PI controllers were tuned using internal model control (IMC) tuning relations [41]. The transfer functions shown in Table 2 were used to compute the controller parameters for temperature control loops. A transfer function (13) was obtained for the fresh hydrogen feed (FH2 ) control loop by passing step change inputs to the model without the recycle stream. GPwithout recycle =

V1 75.265 = FH2 1 + 678.4 s

(13)

An IMC controller was designed based on transfer function (13) which was determined for the distillation column without the recycle loop in accordance with design procedure described for plant-wide control [38–40]. Table 4 shows the controller tuning parameters that were derived and used for the control loops operating on the model. The values of c were chosen by adjusting the desired speed of the closed-loop response. The faster the desired response, the lower the value of c . As faster response can lead to larger overshoots, c needs to be chosen to achieve a tradeoff between speed of response and potential for overshoot. Chien and Fruehauf [48] have given the following general guideline to determine acceptable values of c for FOPTD systems, > c >

(14)

where is the time delay. The values of c chosen for the PI controlled loops are listed in Table 4.

benzene concentrations for a significant period of time. As such it was hypothesized that adding feedforward action to this structure will improve the performance. The off-spec concentration of benzene in the product stream can be reduced if the flow of hydrogen to the column is regulated according to the feed composition. Based on the disturbance variables, manipulated variables, and controlled variables, Gp and Gd from Eq. (8) are defined as follows: Gp =

V1 FH2

(15)

Gd =

V1 zC6 H6

(16)

These transfer functions were determined using the MATLAB system identification toolbox on simulated data for open-loop step responses: Gp =

99.39 1 + 3269.9 s

(17)

Gd =

−7.457 × 104 1 + 3580.2 s

(18)

In order to keep the process realistic, feedforward control with different levels of measurement delay mf : Gmf = e− mf s

(19)

were used for the measurement transfer function. Also, since the feedforward controller is represented by a lead-lag element, the controller transfer function was augmented with a filter with a time constant of 120 s in order to avoid large sudden changes in the manipulated variable. The resulting dynamic feedforward controller is given by Gf = 750.3

3.3. Feedforward controller Most conventional columns use feedback-only control [30]. As reactive distillation columns can be viewed as an extension of conventional columns, the first approach was to design a feedback-only control structure, appropriately tune the controllers, and observe the performance. However, as will be shown in Section 4, feed composition disturbances affect the column performance adversely, i.e., the product does not meet the specifications for

Q1 1.412 −4.073 3.661

1 + 3269.9 s 1 1 + 3580.2 s 1 + 120 s

(20)

If a static feedforward control law would be considered then this would result in Gf = 750.3

(21)

Fig. 3 shows the control structure used for the column along with the feedforward controller for controlling the fresh hydrogen feed.

120

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124

Table 4 Feedback controller settings. Manipulated variable

Controlled variable

Q1

T1

QN

T19

R

TN

FH2

V1

D LN V1

h1 hN P1

Kc 1.766 × 107 c 2.305 × 108 c 342.15 − c 9.013 c 3340 3830 −12.5

i (s)

c (s)

Type of controller and tuning method used

1887.1

110

PI (IMC)

5817.4

582

PI (IMC)

3593.3

610

PI (IMC)

678.4

128.7

PI (IMC)

– – –

– – –

P (Ziegler Nichols) P (Ziegler Nichols) P (Ziegler Nichols)

Table 5 Steady state results for inlet and outlet streams. Stream

Feed

Fresh hydrogen

Distillate

Bottom

Vent

Phase Temperature (K) Pressure (kPa abs) Total flow rate (mol s−1 )

Liquid 430.0 797.0 265.0

Vapor 430.0 797.0 65.9

Liquid 293.5 792.4 85.4

Liquid 495.5 801.0 180.0

Vapor 293.5 792.4 3.0

Component

Mole fraction

n-Butane n-Pentane 2,3-Dimethylpentane 3-Methylpentane n-Hexane Benzene Cyclohexane 3-Methylhexane 2,4-Dimethylpentane n-Heptane Toluene m-Xylene Cumene Hydrogen Methylcyclohexane

C4 H10 C5 H12 C7 H16 C6 H14 C6 H14 C6 H6 C6 H12 C7 H16 C7 H16 C7 H16 C7 H8 C8 H10 C9 H12 H2 C7 H14

Benzene conc. (vol%)

1.26E−02 9.61E−02 1.16E−02 5.87E−02 3.50E−02 8.26E−02 – 2.33E−02 2.34E−02 9.77E−03 2.81E−01 2.06E−01 1.59E−01 – –

– – – – – – – – – – – – – 1.00E+00 –

6.010

–

4. Investigation and comparison of different control schemes for the column 4.1. Steady state results The RD column model is assumed to initially operate at the same steady state for any of the comparisons of different control schemes made in this section. This steady state corresponds to nominal feed (composition and temperature) being fed to the column, where the benzene concentration is 6 vol%. Table 5 includes the steady state values of all feed and product streams. Fig. 4 depicts the profile of benzene and toluene concentration at steady state in the column. The objective of the RD column is to

Benzene molfraction Toluene molfraction

0.6

Mole fraction

0.5 0.4 0.3

Catalyst Zone

0.2 0.1 0

10

20

30 40 Stage number

50

Fig. 4. Profiles of benzene and toluene in RD column.

60

70

3.87E−02 2.97E−01 3.58E−02 1.82E−01 1.08E−01 1.09E−02 2.45E−01 1.54E−02 5.92E−02 6.48E−05 8.86E−07 5.20E−14 8.42E−18 7.10E−03 6.09E−06

1.85E−28 1.32E−17 2.59E−11 1.32E−09 9.37E−09 2.74E−05 6.26E−05 2.70E−02 6.27E−03 1.43E−02 4.14E−01 3.04E−01 2.35E−01 0.00E+00 1.88E−04 0.251 (combined)

1.31E−02 2.35E−02 1.32E−03 5.33E−03 2.56E−03 2.14E−04 4.19E−03 1.63E−04 8.34E−04 5.08E−07 4.84E−09 8.68E−17 8.09E−21 9.49E−01 5.04E−08 –

react as much benzene as possible while minimizing the amount of toluene entering the stage containing catalysts packing. It can be seen that the benzene mole fraction increases along the height of the column, until the reactive zone, where it decreases due to the reaction. Very little toluene is present in the catalyst zone of the RD column and as a result 99.8% of the toluene from the reformate stream is retained in the bottom stream. 4.2. Feedback controller results The rigorous model built in gPROMS was augmented with the control structure shown in Fig. 3. The controllers specified in Table 4 were used for investigation. The model combined with the controllers was subjected to changes in the inputs, representing step disturbances that occur after 1hr, to evaluate the performance of the control schemes. The set-points of all the controlled variables remain unchanged throughout this investigation resulting in a regulatory control problem. Fig. 5 depicts the benzene concentration in the product for the column under feedback-only control subjected to step changes in the temperature of ±5 K (Fig. 5(a)) and the feed flow rate of ±5% (Fig. 5(b)). The responses indicate that the effect of the disturbances on the product benzene concentration is not significant, i.e., only small changes can be seen in the benzene concentration and the concentration stays far below the allowable limit. One of most common disturbances for the benzene hydrogenation process is a change in the feed composition. The benzene concentration in the reformate stream can increase up to a value

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124

a)

Feed temperature -5 K Feed temperature +5K

b) Benzene vol%

Benzene vol%

0.26 0.255 0.25

121

0.27

Feed flowrate +5% Feed flowrate -5%

0.26

0.25

0.24

0.245 0

5

Time (hours)

10

15

0

5

Time (hours)

10

15

Fig. 5. Responses to step changes in (a) feed temperature and (b) feed flow rate.

of 11 vol% [4]. In order to evaluate such a scenario, a step change was given to the feed benzene composition from 6 vol% to 11 vol% and the concentrations of all other components were reduced proportionally. The graphs in Fig. 6 labeled “feedback-only” show the responses of the outlet benzene concentration and of the other manipulated variables for a step change in the feed concentration. The steady state benzene concentration meets the specifications. However, it can be seen that the responses have significant overshoot and also a large settling time under a feedback-only control scheme. This situation presents a clear opportunity for feedforward control in order to minimize the effect of the disturbance on the controlled variable. 4.3. Comparison of feedback and feedforward/feedback control schemes The simulations shown in Fig. 6 for feedback-only control involve significant overshoot and as a result a considerable amount of product does not meet the EPA specifications of 0.62 vol% [2] for

the benzene concentration. Use of feedforward control can reduce the overshoot and settling time. All subfigures in Fig. 6 include a comparison of the responses of the column for feedback-only control and feedforward–feedback control to a step disturbance in the feed composition from 6 vol% to 11 vol% benzene. It can be clearly seen that there is significant improvement in the response time and the overshoot when feedforward control is added to the existing feedback control scheme. Additionally, the trajectories of all manipulated variables also remain within reasonable bounds for feedforward–feedback regulatory control. While Fig. 6 shows the positive impact that the addition of feedforward control can have on the process, the simulation assumed that concentration measurements are available instantaneously. This is not a very realistic assumption in practice unless an online analyzer is used. One commonly used alternative is that samples from streams are taken and then analyzed in a lab, i.e., measurements will only be available at discrete points in time and with a certain time delay. As such, it is important to know how much of an effect measurement time delay has on the performance of

Fig. 6. Responses of controlled and manipulated variables for step change in feed composition: (a) benzene concentration of the product, (b) fresh H2 feed – FH2 , (c) condenser duty – Q1 , (d) reboiler duty – QN , and (e) reflux ratio – R.

122

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124 Feedback-only FF-FB with continuous measurements FF-FB with sampling time of 15min FF-FB with sampling time of 30min FF-FB with sampling time of 45min FF-FB with sampling time of 60min

Benzene vol%

1

0.8 0.6

0.4

0.2 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (hours)

Fig. 7. Response to step change in feed composition for feedback-only control and feedforward–feedback control for five different sampling times (continuous, 15 min, 30 min, 45 min, 60 min).

the feedforward–feedback (FF–FB) control system. This case has been analyzed next. Fig. 7 shows a comparison of the responses for feedback-only control and combined feedforward–feedback control where the disturbance measurement transfer function Gmf uses several different time delays corresponding to the sampling times. As before, the step change disturbance occurs after an hour and the system is initially at steady state. It can be clearly seen that longer measurement time delays significantly degrade the advantages that the addition of feedforward control has on the performance. In order to quantify the performance of the responses shown in Fig. 7, a measure is defined to quantify the area between the curve and the EPA specification of 0.62 vol% [2]:



Dev =

∞

H(Bz vol% − 0.62) × (Bz vol% − 0.62) dt

(22)

0

where H is the Heaviside function defined as



H(x) =

0,

x < 0

1,

x≥0

(23)

Table 6 shows a comparison of the deviation value computed from Eq. (22) for different sampling times. Not surprisingly, it can be concluded that feedforward control reduces the upset condition, as measured by Eq. (22), for all investigated cases. Similarly, it is also not surprising that the best performance is achieved for the combined feedforward–feedback control structure that uses an online composition analyzer. However, the largest benzene concentration Table 6 Deviations, as measured by Eq. (22), for (a) dynamic feedforward controllers and (b) static feedforward controllers. (a) Control structure

Dev

% reduct.

Feedback-only FF–FB with continuous measurements FF–FB with sampling time of 15 min FF–FB with sampling time of 30 min FF–FB with sampling time of 45 min FF–FB with sampling time of 60 min

1074 423 559 756 874 917

61% 48% 30% 19% 15%

Dev

% reduct.

Max Bz vol% 0.85 0.66 0.76 0.97 1.02 0.94

(b) Control structure Feedback-only FF–FB with continuous measurements FF–FB with sampling time of 15 min FF–FB with sampling time of 30 min FF–FB with sampling time of 45 min FF–FB with sampling time of 60 min

1074 444 543 756 888 939

59% 49% 30% 17% 13%

Max Bz vol% 0.85 0.67 0.74 1.04 1.13 1.04

that is occurring at some point during the operation among all cases is not occurring for the feedback-only control scheme but instead for feedforward–feedback control with significant time delays. It can be clearly seen from Table 6 that the larger the time delay for the composition measurement, the less of a benefit in the overall reduction of the offspec product can be achieved. At the same time, the largest deviations from the target are occurring for long measurement time delays. It is beyond the scope of this study to evaluate these responses for different design specifications. However, in order to put the discussion of the performance for different measurement delays into a more general perspective, it should be pointed out that the dominant time constant of the systems is equal to 1.6 h. It can be concluded that the feedforward–feedback scheme is superior to feedback-only control for the case of continuous measurements or measurements with a time delay of up to 15 min, which corresponds to 15% of the dominant time constant. There is only a marginal benefit to the feedforward–feedback scheme if the time delay is 30 min, corresponding to 31% of the dominant time constant, and it is questionable if there are any benefits of including feedforward control if the measurement time delay is 45 min or more, corresponding to 46% of the dominant time constant. In addition to investigating a dynamic feedforward controller, a static feedforward controller has also been investigated. Table 6b shows a comparison of the deviation values computed using the static feedforward controller given by Eq. (21) instead of the dynamic feedforward controller from Eq. (20). The results are close to those obtained by using a dynamic feedforward controller. In fact, the graphs of the responses overlap with those depicted in Fig. 7 for dynamic feedforward control and as such no separate figure for the graphs is included. Thus, from an application point of view, a simple static feedforward controller could be used instead of a dynamic feedforward controller without significant loss of performance. One last point to consider is that this investigation focused on step disturbances as these are the most common disturbances for the scenario investigated in this work. As such, it was appropriate to model the measurements occurring from lab samples as continuous samples with a time delay instead of using discrete samples with time delays as the two will return identical results for step disturbances. However, it should be pointed out that if the benzene concentration disturbances would have had a different nature than a step, that it would have been required to use discrete sampling and time delays. This was not necessary for the cases investigated in this work, though. It was one of the goals of this investigation to determine the benefit of using a control scheme that combines feedforward and feedback control over a feedback-only control scheme. The simulation results indicate that a significant benefit only exists if upsets in the feed composition can be quickly detected. 5. Conclusions Benzene hydrogenation via reactive distillation is a process that has found significant use in the process industries. However, no models of this process can be found in the open literature. This paper addresses this point by developing a dynamic equilibrium-based model for a reactive distillation column used for the hydrogenation of benzene. Simulations were carried out to determine transfer functions between manipulated and controlled variables. Control loop pairing was performed using RGA analysis and the feedback controllers were tuned via IMC tuning (PI) and Ziegler Nichols tuning (P). a model-based feedforward controller was also designed to reduce upset conditions caused by disturbances. Simulations indicate that the column performance for feed temperature and feed flow rate disturbances remains acceptable for

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124

a feedback-only control scheme. However, the column has a significant settling time for disturbances in the feed composition. Feedforward control can reduce these upset conditions resulting from feed disturbances. However, it was shown that the use of a feedforward–feedback control scheme is only beneficial if the time delay associated with the feed composition measurement is small. In summary, this paper (1) presented the first detailed model of a reactive distillation column for the hydrogenation of benzene, (2) designed and evaluated a feedback control scheme for the column, and (3) investigated the benefit of using a feedforward/feedback control structure for different sampling times of the feed composition measurement.

123

∗ yj,i = yj+1,i (1 − ) + yj,i 

(A11)

Energy balance d(Mlj Hlj + Mvj Hvj ) dt

= Vj+1 Hj+1 + Lj−1 Hlj−1 − Lj Hlj − Vj Hvj − Hrxn,j (A12)

Flow rate and holdups Liquid Mj vollj = hj (HETP)A

(A13)

2/3

hj = 0.34a1/3 uj Acknowledgment

Vapor

The authors gratefully acknowledge partial financial support from the American Chemical Society - Petroleum Research Fund (Grant PRF# 50978-ND9).

Pj A(HETP)(ε − hj ) = Mvj Rgas Tj P0,j HETP

Appendix A. A.1. Model



Mass balance (A1)

Component balances d(Ml1 x1,i + Mv1 y1,i ) dt n 

x1,i = 1;

i=1

= V2 y2,i − L1 x1,i − V1 y1,i

∀i : 1 to n − 1 (A2) rxnj,Toluene = −

y1,i = 1

(A3)

(A4)

Energy balance

d(Ml1 Hl1 + Mv1 Hv1 ) dt

(A5)

= V2 H0 − (L1 + D)Hl1 − V1 Hv1

(A6)

d(MlN )

3

kj,2 KA2 KH2 CAj,2 CHj (3KA2 CAj,2 + (KH2 CHj )1/2 + 1) Ea Rgas



1 1 − Tj T0

3

(A20)

(A21)



(A22)

= LN−1 − LN − VN

n 

 n

= Vj+1 + Lj−1 − Vj − Lj + Ahj (HETP)cat

rxnj,i

(A7)

= Fj zj,i + Vj+1 yj+1,i − Lj−1 xj−1,i − Vj yj,i − Lj xj,i

∀i : 1 to n − 1

(A8)

n

yj,i = 1

(A9)

i=1

Vapor–liquid equilibrium and Murphree efficiency

∀i : 1 to n

∀i : 1 to n − 1

(A24)

(A25)

Energy balance dt

+ Ahj (HETP)cat rxnj,i



xN,i = 1

d(MlN HlN )

Component balances

dt

= LN−1 xN−1,i − LN xN,i − VN yN,i

i=1

i=1

d(Mlj xj,i + Mvj yj,i )

(A23)

Component balances dt

Mass balance

∗ xj,i lj,i = yj,i lj,i

(3KA1 CAj,1 + (KH1 CHj )1/2 + 1)

Reboiler

d(MlN xN,i )

Plate j

i=1



dt

Packed section

xj,i = 1;

(A18)

dp a

Mass balance

0 = V2 Hv2 − V1 H0 + Q1



−5

kj,1 KA1 KH1 CAj,1 CHj

ki,j = ki,0 exp −

∀i : 1 to n

x1,i l1,i = y1,i v1,i

n

2hj

(A19)

rxnj,Benzene = −

Vapor–liquid equilibrium

dt

(A17)

Reaction rate

i=1

d(Mlj + Mvj )

(A16)

Pj+1 = Pj + Pj = V2 − L1 − D − V1

dt

(A15)

(1 − ε) u2v v dp K ε3

Pj = P0,j 1 −

Condenser and reflux drum

n 

=

150 + 1.75 Rev

=

d(Ml1 + Mv1 )

(A14)

(A10)

= LN−1 HlN−1 − (LN + VN )HlN

VN HlN − VN HvN + QN = 0

(A26) (A27)

References [1] Mobile Source Air Toxics: Control of Hazardous Air Pollutants from Mobile Sources, United States Environmental Protection Agency, EPA420-R-05-901, 2005, November. [2] Control of Hazardous Air Pollutants from Mobile Sources: Final Rule to Reduce Mobile Source Air Toxics, United States Environmental Protection Agency, EPA420-F-07-017, 2007, February. [3] G.J. Harmsen, Reactive distillation: the front-runner of industrial process intensification: a full review of commercial applications, research, scale-up, design and operation, Chemical Engineering and Processing: Process Intensification 46 (9) (2007) 774–780.

124

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124

[4] Control of Hazardous Air Pollutants from Mobile Sources: 40 CFR Parts 59, 50, 85 and 86, Environmental Protection Agency, EPA-HQ-OAR-2005-0036, 2006, February. [5] R. Taylor, R. Krishna, Modelling reactive distillation, Chemical Engineering Science 55 (22) (2000) 5183–5229. [6] K. Alejski, F. Duprat, Dynamic simulation of the multicomponent reactive distillation, Chemical Engineering Science 51 (18) (1996) 4237–4252. [7] D.B. Kaymak, W.L. Luyben, Evaluation of a two-temperature control structure for a two-reactant/two-product type of reactive distillation column, Chemical Engineering Science 61 (13) (2006) 4432–4450. [8] M.C. Georgiadis, M. Schenk, E.N. Pistikopoulos, R. Gani, The interactions of design control and operability in reactive distillation systems, Computers & Chemical Engineering 26 (4) (2002) 735–746. [9] P. Kumar, N. Kaistha, Decentralized control of a kinetically controlled ideal reactive distillation column, Chemical Engineering Science 63 (1) (2008) 228–243. [10] G.R. Gildert, K. Rock, T. McGuirk, Advances in process technology through catalytic distillation, in: Proceeding of the International Symposium on Large Chemical Plants, Antwerpen, 1998, pp. 103–113. [11] M.G. Sneesby, M.O. Tade, T.N. Smith, Two-point control of a reactive distillation column for composition and conversion, Journal of Process Control 9 (1) (1999) 19–31. [12] M.G. Sneesby, M.O. Tade, T.N. Smith, Steady-state transitions in the reactive distillation of MTBE, Computers & Chemical Engineering 22 (7) (1998) 879–892. [13] M.G. Sneesby, M.O. Tade, R. Datta, T.N. Smith, ETBE synthesis via reactive distillation. 2. Dynamic simulation and control aspects, Industrial & Engineering Chemistry Research 36 (5) (1997) 1870–1881. [14] D.A. Bartlett, O.M. Wahnschafft, Dynamic simulation and control strategy evaluation for MTBE reactive distillation, in: Foundations of Computer-Aided Process Operation, AIChE Symposium Series, vol. 320, Snowbird, 1998, pp. 315–321. [15] N. Sharma, K. Singh, Model predictive control and neural network predictive control of TAME reactive distillation column, Chemical Engineering and Processing: Process Intensification 59 (2012) 9–21. [16] A.M. Katariya, R.S. Kamath, K.M. Moudgalya, S.M. Mahajani, Non-equilibrium stage modeling and non-linear dynamic effects in the synthesis of TAME by reactive distillation, Computers & Chemical Engineering 32 (10) (2008) 2243–2255. [17] R. Baur, R. Taylor, R. Krishna, Dynamic behaviour of reactive distillation columns described by a nonequilibrium stage model, Chemical Engineering Science 56 (6) (2001) 2085–2102. ´ ˛ [18] A. Kołodziej, M. Jaroszynski, W. Sałacki, W. Orlikowski, K. Fraczek, M. Klöker, A. Górak, Catalytic distillation for TAME synthesis with structured catalytic packings, Chemical Engineering Research and Design 82 (2) (2004) 175–184. [19] R. Jacobs, R. Krishna, Multiple solutions in reactive distillation for methyl tertbutyl ether synthesis, Industrial & Engineering Chemistry Research 32 (8) (1993) 1706–1709. [20] R. Baur, A.P. Higler, R. Taylor, R. Krishna, Comparison of equilibrium stage and nonequilibrium stage models for reactive distillation, Chemical Engineering Journal 76 (1) (2000) 33–47. [21] J. Peng, S. Lextrait, T.F. Edgar, R.B. Eldridge, A comparison of steady-state equilibrium and rate-based models for packed reactive distillation columns, Industrial & Engineering Chemistry Research 41 (11) (2002) 2735–2744. [22] A.P. Higler, R. Taylor, R. Krishna, Nonequilibrium modelling of reactive distillation: multiple steady states in MTBE synthesis, Chemical Engineering Science 54 (10) (1999) 1389–1395. [23] J. Peng, T.F. Edgar, R.B. Eldridge, Dynamic rate-based and equilibrium models for a packed reactive distillation column, Chemical Engineering Science 58 (12) (2003) 2671–2680. [24] Y.S. Choe, W.L. Luyben, Rigorous dynamic models of distillation columns, Industrial & Engineering Chemistry Research 26 (10) (1987) 2158–2161.

[25] G.G. Bemer, G.A.J. Kalis, A new method to predict hold-up and pressure drop in packed columns, Transactions of the Institution of Chemical Engineers 56 (1978) 200. [26] J. Mackowiak, Fluid Dynamics of Packed Columns: Principles of the Fluid Dynamic Design of Columns for Gas/Liquid and Liquid/Liquid Systems, Springer, New York, 2010. [27] D.E. Seborg, D.A. Mellichamp, T.F. Edgar, F.J. Doyle III, Process Dynamics and Control, Wiley, New York, 2010. [28] S. Skogestad, M. Morari, Control configuration selection for distillation columns, AIChE Journal 33 (10) (1987) 1620–1635. [29] S. Skogestad, P. Lundström, E.W. Jacobsen, Selecting the best distillation control configuration, AIChE Journal 36 (5) (1990) 753–764. [30] S. Skogestad, Dynamics and control of distillation columns – a critical survey, Modeling, Identification and Control 18 (3) (1997) 177–217. [31] W.L. Luyben, Alternative control structures for distillation columns with partial condensers, Industrial & Engineering Chemistry Research 43 (20) (2004) 6416–6429. [32] E.S. Hori, S. Skogestad, Control structure selection of a deethanizer column with partial condenser, in: Proceedings of European Congress of Chemical Engineering (ECCE-6), Copenhagen, 2007. [33] A.W. Sloley, Effectively control column pressure, Chemical Engineering Progress 97 (1) (2001) 38–48. [34] M.M. Denn, R. Lavie, Dynamics of plants with recycle, Chemical Engineering Journal 24 (1) (1982) 55–59. [35] N. Kapoor, T.J. McAvoy, T.E. Marlin, Effect of recycle structure on distillation tower time constants, AIChE Journal 32 (3) (1986) 411–418. [36] J. Morud, S. Skogestad, Effects of recycle on dynamics and control of chemical processing plants, Computers & Chemical Engineering 18 (1994) S529–S534. [37] A. Kumar, P. Daoutidis, Nonlinear dynamics and control of process systems with recycle, Journal of Process Control 12 (4) (2002) 475–484. [38] P.S. Buckley, Techniques of Process Control, Wiley, New York, 1964. [39] W.L. Luyben, Dynamics and control of recycle systems. 1. Simple open-loop and closed-loop systems, Industrial & Engineering Chemistry Research 32 (3) (1993) 466–475. [40] T. Larsson, S. Skogestad, Plantwide control – a review and a new design procedure, Modeling, Identification and Control 21 (4) (2000) 209–240. [41] M.L. Luyben, B.D. Tyreus, W.L. Luyben, Plantwide control design procedure, AIChE Journal 43 (12) (1997) 3161–3174. [42] E.H. Bristol, On a new measure of interactions for multivariable process control, IEEE Transactions on Automatic Control AC-II (1966) 133. [43] F.G. Shinskey, Process Control Systems: Application, Design and Tuning, McGraw-Hill, Inc., New York, 1990 (Chapter 7). [44] B.W. Bequette, Process Control: Modeling, Design, and Simulation, Prentice Hall Professional, New Jersey, 2003. [45] S. Toppinen, T.K. Rantakylä, T. Salmi, J. Aittamaa, Kinetics of the liquid-phase hydrogenation of benzene and some monosubstituted alkylbenzenes over a nickel catalyst, Industrial & Engineering Chemistry Research 35 (6) (1996) 1824–1833. [46] E.S. Hori, S. Skogestad, Selection of controlled variables: maximum gain rule and combination of measurements, Industrial & Engineering Chemistry Research 47 (23) (2008) 9465–9471. [47] W.L. Luyben, Evaluation of criteria for selecting temperature control trays in distillation columns, Journal of Process Control 16 (2) (2006) 115–134. [48] I.-L. Chien, P.S. Fruehauf, Consider IMC tuning to improve controller performance, Chemical Engineering Progress 86 (1990) 33–41.