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Process Systems Engineering

Dynamic Performance Optimization of a Pilot-scale Reactive Distillation Process by Economics Optimizing Control Daniel Hasskerl, Clemens Lindscheid, Sankaranarayanan Subramanian, Steven Markert, Andrzej Gorak, and Sebastian Engell Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01815 • Publication Date (Web): 19 Jul 2018 Downloaded from http://pubs.acs.org on July 22, 2018

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Industrial & Engineering Chemistry Research

Dynamic Performance Optimization of a Pilot-scale Reactive Distillation Process by Economics Optimizing Control* Daniel Haßkerl*+, Clemens Lindscheid+, Sankaranarayanan Subramanian+, Steven Markert+, Andrzej Górak#, Sebastian Engell+ + Process Dynamics and Operations Group, TU Dortmund, Emil-Figge-Str. 70, 44227 Dortmund # Laboratory of Fluid Separations, TU Dortmund, Emil-Figge-Str. 70, 44227 Dortmund Abstract— The most prominent example of process intensification by process integration is reactive distillation (RD) which can realize a high reactant conversion and a high purity of the target product in equilibrium-limited reaction systems. Reactive distillation is mostly used for single reactions, but realizations for multiple-reaction systems leading to more than one target product can also be found. In multi-purpose chemical processes, the target product of a multiple-reaction system can be switched during the production. When combining fluid separation and multiplereaction systems, e.g. in a RD column, it is challenging to find operating conditions that lead to the most profitable operation of the process. Economics optimizing control where an economic objective is employed in a modelpredictive control framework has the potential to drive the process to the economic optimum during operation based upon a process model and online measurements. However, so far only few applications of such Advanced Process Control (APC) concepts to reactive distillation processes have been realized and these do not concern multiplereaction systems. In this contribution, we describe the application of economics optimizing control to a multi-product RD process. The selected case study is a homogeneously-catalyzed two-step transesterification reaction that is performed in a RD column in pilot-plant scale. Keywords: Economic performance optimization, economics optimizing control, multi-purpose chemical processes, reactive distillation, transesterification I. INTRODUCTION Process intensification by process integration is a promising approach to improve chemical and biochemical production processes by merging reaction and separation techniques in innovative processing units [1–3]. By combining chemical reaction and component separation simultaneously and in the same place of the apparatus, more efficient processing units can be realized that save a significant amount of investment and operating costs compared to classical process designs [4]. An overview from an industrial point of view of the importance of process intensification was given in [5] and excellent reviews are available for integrated reactive-separation processes, see [6, 7]. In [8] it is concluded that reactive distillation is the integrated reactive-separation process that is most widespread in the chemical industry. The chemical reactions that are realized in industrial reactive distillation processes are mostly esterification, etherification and hydrodesulphurization reactions. In 2007, it was reported that more than 150 reactive distillation processes are in operation worldwide [9]. For an excellent overview over important reactions for which reactive distillation processes have successfully been used, the reader is referred to [10, 11]. Experimental studies on reactive distillation processes have been published mostly by university laboratories. The majority of these studies cover laboratory-scale experiments for simple equilibrium-limited chemical reactions with few reactants and products. Such studies usually focus on the improvement of the conversion of the reactants while the selectivity towards a product is of minor importance. Chemical processes that implement multiple-reaction systems with more than one target product are more difficult to realize, especially if one of the reaction products should be produced with high selectivity (for an overview, see [12]). Several studies discuss operating experimental laboratory-scale plants manually or using simple controllers, but an open question is how to operate such complex multiple-input multiple-output processes with nonlinear behavior economically * The research leading to these results was funded by ERC Advanced Investigator Grant MOBOCON (FP7/2012−2017) under the grant agreement no 291458. Corresponding author: Daniel Haßkerl, Emil-Figge-Str. 70, 44227 Dortmund, Tel.: +49/231/755-3419, E-mail:{Daniel.Hasskerl, Clemens.Lindscheid, Sankaranarayanan.Subramanian, Steven.Markert, Andrzej.Gorak, Sebastian.Engell}@tu-dortmund.de

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efficiently. The investigations of control of reactive distillation processes started with linear control, e.g. two-point PI(D) controllers proposed in [13], and linear control strategies [14, 15] where step-response models were identified for linear model predictive control. Noticeable results for advanced control strategies concerned gain-scheduling control [16] and the systematic design of multivariable PI(D) controllers to operate a semi-batch reactive distillation column [17]. Early model predictive control approaches using a plant model in the form of a neural net were not entirely successful [18]. A discussion of control techniques for reactive distillation can be found in [11] and a critical review was presented in [19]. One method to overcome the difficulty of finding suitable operation points for the operation of multi-purpose RD processes is economics optimizing control, where Nonlinear Model Predictive Control (NMPC) is used with an economic or economically motivated cost function. In NMPC, a dynamic model of the process is used to repeatedly optimize the future behavior of the process according to a cost function which is evaluated over a finite prediction horizon. By adjusting the cost function (or the constraints) online, it is possible to switch the production of the RD column from one target product to the other, thus also optimizing the transient behavior during the product changeover. In the field of NMPC for RD processes, [20, 21] studied the application of economics optimizing NMPC to the example of the esterification of acidic acid and compared different control objectives in simulation studies. It was demonstrated that a complex rigorous process model can be used for NMPC and that economics optimizing control for RD processes is promising. However, an application to a real plant was not targeted. In this work, the realization of economics optimizing control at a pilot-plant RD process with two target products is reported. The implementation is based on the Python/C++ based software tool do-mpc [22], which utilizes efficient algorithms that drastically reduce the computation times of NMPC applications. The software consists of three main modules: A process simulator for performing simulation studies, a state estimator, and the NMPC algorithm. do-mpc was extended in this work with respect to the requirements for practical applications, such as real-time capability and communication interfaces. On this basis, the application of economics optimizing control to a real RD process utilizing a high-order first-principles nonlinear dynamic model could be realized. The chemical system under consideration in this paper is the homogeneously catalyzed two-step transesterification of dimethyl carbonate (DMC) with ethanol (EtOH) to form the intermediate product ethyl methyl carbonate (EMC) and the final product diethyl carbonate (DEC) in a pilot-scale reactive distillation (RD) process. The product changeover from DEC to EMC and vice versa was proven to be feasible in earlier experimental investigations using manual control (see [12]). The pilot-scale process is equipped with an online concentration measurement device based on near-infrared spectroscopy that was calibrated for the product streams (see [23]). Different state estimation techniques were investigated for this case study using a simplified model [24]. Furthermore, simulation studies for the set-up of the NMPC in general with respect to the choice of the underlying cost function were investigated in [25]. This paper provides a comprehensive description of the results that were obtained by bringing the hardware and software components together and realizing economics optimizing control at the real column from a process technology viewpoint. We not only show how the control algorithm improves the performance of the RD process but also that a transient product changeover can be realized with economics optimizing control. The paper is structured as follows: In section II we present the chemical process and the process model which is required for the NMPC controller which is described in section III. Short descriptions of the optimizing controller (section IV) and of the software framework (section IV.E) are presented next. The experimental results are presented and discussed in section V. Conclusions are drawn in section VI.


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Figure 1. Schematic view of the reactive distillation process for the two-step transesterification reaction that is considered in this work with its degrees of freedom. II. PROCESS DESCRIPTION The homogeneously catalyzed transesterification of DMC with EtOH in a homogenously catalyzed reactive distillation process was investigated previously in [12] and [26]. Sodium ethoxide catalyzes the synthesis of ethyl methyl carbonate (EMC) and of diethyl carbonate (DEC) from the reactants DMC and EtOH in two consecutive equilibrium-limited reaction steps, see Fig. 1. The use of a reactive distillation column for the chemical conversion was shown to have several advantages over the classical approach of using a chemical reactor and a distillation column separately [26]. On the one hand, a single apparatus can be used to produce both products with a high selectivity. The appearance of the binary azeotropes when considering the reaction step and the separation step separately can be overcome by shifting the chemical equilibrium. Using the intensified process, the energy demand is reduced by the exploitation of synergies. On the other hand, the operation of a reactive distillation process is more demanding, especially when several components should be produced in one unit. Due to the complexity of the process also the dynamic Figure 2. Left: Top-down view of the pilot-scale reactive mathematical models required for the NMPC are of distillation column hosted in the facilities of the Laboratory of large size and of high complexity. Fluid Separations at TU Dortmund. Right, top: two students In the process considered here, the solubility of the taking samples at the condenser. Right, bottom: Intensive homogeneous catalyst in the liquid mixture is cooler and immersion probe for the NIR located at the limited [26]. Because the catalyst sodium ethoxide has a condenser. negligible vapor pressure and is diluted in the reactant EtOH, a single liquid distributor was selected to realize the feed to the column. The homogeneously catalyzed transesterification reaction takes place below the feed position in the stripping section. Due to their high boiling points, the products (EMC and DEC) are obtained in bottom product stream. Fig. 1 shows the reactive distillation processes schematically with the four degrees of freedom that define the operating conditions.


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A. Experimental Setup The pilot-scale reactive distillation column for the experimental work (see photos in Fig. 2) is made of glass and has a diameter of 50 mm. The column possesses six structured packing sections of Sulzer BXTM with an overall packing height of 5.4 m and can be operated at or below ambient pressure. Compared to the experimental setup reported in [12], some modifications were made. The natural circulation reboiler was replaced by a direct evaporator (Normag AG) with a maximum volume of 2.2 l and a total heat duty of 3 kW in order to reduce the time needed for the start-up and for the shutdown procedures. The bottom stream and the stream leaving the condenser were equipped with injection probes for nearinfrared spectroscopy (ABB/ Thermo Fischer Inc.) for the measurement of the compositions of the product streams. The column is automated using a Siemens PCS7 control system. For the data exchange between the control system and the optimizing control software, an OPC DA (Open Platform Communications for Data Access) server is used. The P&ID of the process is depicted in Fig. 3. The raw material is fed to the column at a packing height of 2.0 m using three pumps, one for the flowrate of DMC, one for the EtOH feed flow rate and one for the catalyst which is diluted in EtOH. The overall feed flow rate is kept at a constant value of 4 [kg/h] as given in [12], i.e. if the feed flow rate of DMC is changed, the flow rate of EtOH is adapted. The process has four degrees of freedom that can be used to define the operation of the plant, the feed flowrate of DMC (FeedDMC), the ratio between the flow rate of the catalyst that is dissolved in the EtOH feed relative to the overall feed flow rate (xcat), the reflux ratio (RR) and the distillate-to-feed-ratio (DF). Because of large delays that result from the distance between the heat supply located in the bottom and the flowmeter measuring the flow rate of the distillate stream, the distillate-to-feed ratio is not an actuated variable but at steady state it assumes a certain value that results from the feed flowrate, the reflux ratio and the boil-up rate. The control system of the pilot-plant manipulates the reboiler heat duty so as to realize an overall vapor flow rate at the top of the column. By this low-level control loop, a desired value of DF can be achieved. The loop is fast enough to neglect its dynamics in the overall process model. The remaining parameters such as the columns pressure measured at the condenser outlet to the vacuum pump, the temperature set-points of the feed and reflux thermostats as well as the overall feed flowrate were fixed to the values given in [12].


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Figure 3. P&ID of the RD process (Adapted from [26]).


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All materials that are used during the experiments were of analytical grade. Ethanol (Köster & Bömcke GmbH & Co KG) and dimethyl carbonate (Novasol N.V/ S.A.) had a purity higher than 96.0%. The catalyst sodium ethoxide (VWR chemicals, CAS: 141-52-6) was diluted in ethanol (mass fraction w=20%) and for the experiments, its concentration was further reduced to the desired feed concentration. Acetonitrile (eluent for gas chromatography) was purchased from VWR chemicals (99.9% purity). B. Analytical methods As the knowledge of the concentration profiles and of the compositions of the bottom and distillate streams is of major importance for the direct optimizing control of the RD process, the analytical methods that are used to determine their values online and offline are described here. For online measurements, a near-infrared spectrometer was employed while the concentration profile of the column was measured by analyzing samples that were taken using a gas chromatograph. a) Application of near-infrared spectroscopy At the investigated pilot-scale RD column, the online data of the composition of the product streams is collected by a near-infrared spectrometer which is connected to two injections probes (see Q611 and Q711 in Fig. 3). The infrared light is transmitted from a FTPA 2000 Spectrometer to the injection probe through optical fibers (3 m and 8 m length) and the NIR spectra are obtained at 16 cm-1 resolution. Due to the overlapping character of the combinatory and the overtone vibrations of NIR spectra, computer-aided tools to analyze the data are needed. For the calibration of the sensor, the Partial LeastSquares (PLS) method was employed for which all components of the reaction system that affect the spectrum are investigated separately (the catalyst and the influence of the operating temperature were neglected). During the calibration, all data points in a certain wavenumber region (in contrast to [23], we used the region 5725 cm-1 to 6000 cm-1 in the experimental work at the column because we observed that the measurements were more error prone when the sensors were installed at the product streams compared to [23], where pure chemicals in glass vessels were used) were analyzed regarding the significant and the secondary PLS-factors in order to draw conclusions on the impact of each of the properties on the − ̂ , where is the measured measurement. The predicted residual error sum of squares ( = ∑ concentration and ̂ is the predicted concentration of component ∈ {, , , , } of = 5 components) value for all the factors was used for choosing the number of significant PLS-factors. The number of factors at which the gradient of the PRESS plot for each component became negligible is displayed in Tab. 1. Larger numbers of PLSfactors did not improve the prediction accuracy. Table 1: Number of factors for each component at which the gradients of the PRESS values became negligible. Bottom Component MeOH EtOH DMC EMC DEC

Top No of significant factors 10 8 8 9 8

Component MeOH EtOH DMC EMC DEC

No of significant factors 6 6 7 7 -

For the background spectra and for each sample, in total 64 scans were taken. The quality of the predicted composition was checked twice a week using a GC reference probe. When it was noticed that the quality decreased, new background spectra were taken. For the PLS method, the software Grams AI and Grams IQ from ABB as well as the software IQ-Predict from Thermo Fisher Scientific Inc. (Version 9.1) was used. The NIR was calibrated for steady-state conditions in the condenser and in the evaporator. The steady-state data published in the supporting information to [26] were used to prepare the calibrating samples. Because the high boiling component DEC is not assumed to appear in the distillate stream, its concentration in this stream was considered to be negligible. The accuracy of the NIR devices was checked by using the gas chromatograph for selected samples with concentrations which were not used for the calibration. b) Gas chromatography A gas chromatograph (Shimadzu GC-14A) equipped with a flame-ionization detector and an Innopeg FFPA capillary column (0.32 [mm] diameter, 25 [m] length and a film thickness of 0.5 [µm]) was employed for the offline analysis of the samples that were taken during the experiments as well as for the validation and verification of the resolution of the measured composition by NIR. Helium was used as carrier gas (gas velocity 22.0 [cm s-1]). The retention times of the components were obtained at a temperature of 373.15 [K] for 2.7 [min] with a temperature ramp of 20 [K min-1] to 403.15 [K] (retention times of the individual components: MeOH: 2.59 [min], EtOH: 2.71 [min], DMC: 3.14 [min], EMC: 3.55 [min], DEC: 4.02 [min]). Due to its physical characteristics (similar retention time, shifted peak), acetonitrile has


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proven to be a suitable choice for the internal standard and the mass fractions of all components were calculated by evaluating the resulting chromatogram with single-component calibration curves. Each sample was cooled down and analyzed within 2h for a comparison with the NIR data. C. Experimental procedure Because optimal start-up procedures are not in the focus of this work, a procedure similar to the one proposed in [12] was used. First, the liquid distributors and the reboiler were filled with ethanol. Because of the use of a direct evaporator that can dry out and lead to a safety risk, the column feeding with raw material (FeedEtOH = 3.5 kg/h and FeedDMC = 0.5 kg/h) and the evaporator are started at the same time. When vapor originating from the reboiler appears at the top, the column is operated at total reflux and after the steady state has been reached, i.e. the bottom flowrate matched the feed flowrate and the concentrations at the columns top reached steady-state conditions, the operating conditions are adjusted to the desired operating point (DF: 0.35 and RR: 2.0). The same start-up procedure was followed for each experiment so that the conditions after the start-up procedure was finished were the identical. A steady state is assumed to be reached if over a time period of ten minutes: •

The temperature profiles are constant (+/- 0.5 [K])

•

The NIR composition is constant (+/- 0.01 [mol/mol] of all components)

•

The overall mass balance of the RD column is fulfilled.

After the manually performed start-up has been finished, the optimizing controller is started, performing adjustments of the inputs online according to a specified production target of either EMC or DEC at a certain concentration. During each experiment, samples of the product streams and of each liquid distributor (except the feed liquid distributor) were taken every 60 minutes, cooled with dried ice and analyzed offline using the gas chromatograph. If the production of the desired product was achieved and the overall process reached steady state at the first operating conditions for approximately one hour, the product changeover was initiated. When the desired steady-state operating conditions at the second operating conditions were reached and all required samples and column profiles were obtained, the shutdown procedure was initiated. III. PROCESS MODEL A. General modeling approach Reactive distillation processes are difficult to model because a multicomponent reaction system has to be considered along with its multi-phase, possibly non-ideal thermodynamic behavior. Therefore the mathematical models that describe the RD process have to capture the dynamic and steady-state behavior of the hydrodynamics of the column, the mass and heat transfer resistances, the reaction kinetics and reaction equilibria along with the vapor-liquid equilibria [12]. Various approaches to model RD processes were extensively reviewed in [2, 12, 27, 28] and the literature therein leading to several models that differ in their complexity by which they describe the hydrodynamics, the chemical reactions and the mass transfer in the multi-phase system [12, 29]. B. Description of the process model for the two-step transesterification process In [12], detailed mathematical models of different complexity of the process considered here were developed using the MESH (Material, Equilibrium, Summation, Enthalpy or Heat balance) equations which were originally implemented in the equation-oriented simulation environment Aspen Custom Modeler® (ACM) (see [30] and [12]). From the set of models presented in [12], the EQ-Kin (equilibrium-stage model using reaction kinetics) model was selected as it can sufficiently well represent the steady state of the column as well as the dynamical behavior [30]. The model-based control algorithm is implemented in the Python programming language (see section IV), therefore the process model also had to be implemented in Python and the thermodynamic models had to be coded in Python as well. Similar to [30], we use the ideal gas law to describe the vapor phase and an activity-based approach to describe the nonideal behavior of the liquid phase. The activity ! relates to the molar fraction " of each component i∊{MeOH, EtOH, DMC; EMC, DEC} by ! = $ ∙ " , where the activity coefficients $ result from the UNIQUAC model. After a minor correction after consultation with the author of [30] (swap of the binary interaction parameters for DMC and DEC, compare [30] and [12]), we used the UNIQUAC parameters presented in [12]. The model equations that define the equilibrium stage model are described below. A schematic visualization of the structure of the model is presented in Fig. 4.

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Figure 4. Structure of the reactive distillation process model; the packing sections are modelled by equilibrium-stage models that implement reaction kinetics (EQ-Kin, see [12]). The EQ-Kin model incorporates equations for all sections of the process, the packing section, the liquid distributor, the reboiler and the condenser (see Fig. 4). Each packing section is discretized into equilibrium stages using the height of an equivalent theoretical stage (HETS). Following [12], the HETS value is considered to be constant at 0.2 [m] for a Sulzer BXTM packing. The mass balance equations at stage j of the liquid phase for the equilibrium-stage models read as ./

; 1

&" ,' ∙ ()*),' = + ",, , ∙ -,, 0 " ,'1 ∙ 2'1 − " ,' ∙ 2' 0 4 ,'5 ∙ 6'5 − 4 ,' ∙ 6' 0 + + 7,,8 ∙ 98,' ∙ :' , & ,

8 ,

(1)

= 1, … , − 1, > = 1, … , ' . Here, @ is the number of the available feed flowrates at stage j. There are two reactions (8 = 2) and five components

that are considered in the balance equations (with number of components = 5). The activity-based reaction rates at stage j of nj stages are taken from [12] 9B = "C),' DE,B "F G

−H,B

9B = "C),' DE,B "F S

2 I>

J G!KLM,' !N)OP,' −

−H,B U S!NLM,' !N)OP,' − I'T

!NLM,' !LQOP,'

RC,B I> !KNM,' !LQOP,' 2

RC,B I'T

J,

> = 1, … , '

U,

> = 1, … , ' .

(2)

using the corrected correlations for the activity based reaction equilibrium constants (> = 1, … , ' ) V WRC,B I> X = 2

234.61

I>2

V WRC,B I> X = 2

0 4.29 ] 10

−112.70

I2>

−4

− 0.54.

,

(3)

The corresponding phase equilibrium can be computed from the extended Raoult’s law `TN 4 ,' = R ,' ∙ " ,' , I'` = I'T = I'Qa , (4) = 1, … , − 1, > = 1, … , > , where the vapor-liquid equilibrium constant for each component i∊{MeOH, EtOH, DMC, EMC, DEC} of stage j,

`TN R ,' =

eh b/W",> ,cdeX∙fg/,d Wcde X

id

is based upon the UNIQUAC model to compute the activity coefficients $ and upon the model

T` for the pure components vapor pressure FE ,' using the current pressure at stage j, ' . The overall mass balance is maintained using the summation equations for the liquid and for the vapor phase molar fractions

+ " ,' = + 4 ,' = 1,

> = 1, … , ' .

(5)

The summation condition for the liquid molar concentration was transformed into a representation that can be implemented as a set of differential equations by constraining its time derivative, i.e. 0= ∑=1 &",> . Furthermore, it is 8


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assumed that the total molar holdup of each equilibrium stage changes instantly and thus can be determined by the algebraic relation (neglecting the molar holdup of the vapor phase) ()*),' = j' W" ,' , I2> X ∙ k' ,

> = 1, … , ' .

(6)

The volumetric holdups k' of each liquid distributor, of the condenser and of the reboiler are presented in Tab. S2 (see supporting information). The relative volumetric holdup of the equilibrium stage model of the packing section and the corresponding pressure drop is determined by the correlations that were published in [31]. The mathematical formulation of the model of the reactive distillation column using the MESH equations results in a set of 186 differential and 288 algebraic equations. In contrast to [24] and [25], we use a dynamic model of the reactive distillation process i.e. we consider the rate of change of the liquid phase molar fraction of each component at each equilibrium stage and of the molar holdup of the evaporator. A library of correlations for the thermophysical properties (see Tab. S3 in the supporting information), the UNIQUAC model, models for the relative volumetric hold-up and the pressure drop for each element of the packing section according to [32] complete the model equations. Further assumptions are: • The liquid holdup of the evaporator is constant by using a proportional controller that manipulates the bottom molar flowrate • The evaporator is modeled as a partial evaporator in which the phase equilibrium between liquid and vapor is assumed. This assumption is justified by the instrumentation of the pilot plant in which an electrical heater with a heat supply of 3 [kW] is submerged into a relatively small liquid holdup of the evaporator • The column is insulated properly so that the heat losses to the environment can be neglected • The liquid holdup of the condenser is ideally controlled by a proportional controller that manipulates the molar reflux flowrate • Each liquid distributor can be represented by an equilibrium stage model • The holdup of each liquid distributor is constant and their values are given in Tab. S2, see supporting information • The liquid distributor at which the feeds enter the column is not ideally mixed (see [12] for further information) • The catalyst that enters the column is instantly diluted • The flow rate of catalyst that is fed to the column is considered relative to the overall feed flow rate. C. Process-related performance indicators To characterize the process performance from a chemical engineering point of view, suitable indicators are introduced next. For reactive distillation processes that implement only a single reaction, the conversion of the reactants is an important performance indicator which is computed by relating the molar flowrates of both feeds (F) to the distillate (D) and bottom (B) product streams. For multi-purpose reactors that realize more than one reaction, the selectivity towards the products is of importance. Therefore, the conversion of the reactants = {, } as well as the selectivity towards both products = {, } based on the limiting component DMC assuming pure feeds are considered: m K, 0 m n, , = {, } m o,KLM 0 m o,N)OP m K, 0 m n, = , = {, }. m o,KLM − m K,KLM − m n,KLM

l = 1 − ,KLM

(7) (8)

D. Mathematical model Throughout this paper, the nonlinear model of the reactive distillation process that was presented above is used which can be represented as a discrete-time semi-explicit index-1 differential-algebraic system of equations (DAE) of the form pq5 = rpq , sq , tq , u ,

0 = vpq , sq , tq , u ,

(9)

wq = xpq , sq , tq ,

where pq ∈ ℝz and sq ∈ ℝ{ refer to the differential and algebraic states, wq ∈ ℝ| represents the measurements and tq ∈ ℝ} the control input at each sampling instant D. r: ℝz ] ℝ{ ] ℝ} ] ℝ → ℝz and v: ℝz ] ℝ{ ] ℝ} ] ℝ → ℝ{ denote the differential and algebraic functions that are continuously differentiable and x: ℝz ] ℝ{ ] ℝ| → ℝ| is the measurement function. u ∈ ℝ denotes the vector of the parameters. From all measurements that are available at the pilot-scale column, those that are displayed in Tab. 2 are used for control purposes. 9



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Table 2: Measurements at the RD column. Name

Measured state

Condenser

Liquid composition

Packing height 5.5m

Liquid Distributor 1

Vapor temperature

5.4m


Vapor temperature

4.2m


Vapor temperature

3.0m

Feed Liquid Distributor

Vapor temperature

2.0m


Vapor temperature

1.0m


Vapor temperature

0.5m


Vapor temperature

0.0m

Reboiler

Liquid temperature, Liquid holdup, Liquid composition

Below the packing

IV. PROBLEM DESCRIPTION AND REALIZATION OF THE CONTROLLER A. Direct optimizing control on a finite horizon The advantages of economics optimizing control on a finite horizon, which is a variant of the nonlinear model predictive control approach using an economically motivated control objective, were pointed out in several contributions (see e.g. [33] and the literature therein). With the increase of the computational power, the advances in optimization techniques and the standardization of communication interfaces, economics optimizing control based upon rigorous nonlinear models has become practically applicable [34]. Major achievements that significantly reduce the computational burden are the simultaneous approach to optimal control and automatic differentiation methods which are supported by related software implementations. These methods can be employed to optimize the operation of large and complex chemical processes described by high-fidelity models because they reduce the computation time of the solution significantly. B. Optimization problem To describe the dynamic optimal control problem in general, a discrete-time representation of the dynamic process model is utilized [35]. We can write the dynamic optimal control problem that is based on a Lagrangian-type cost function with the associated stage cost ∙ , t∙ for equal prediction and control horizons of length q as 1

∙ , t∙ = + 2q5 , tq t∙ , ∙ qE

subject to:

(10)

q5 = rq , tq , u ∀D∈{ 0, … , q − 1}

0 = vq , tq , u ∀D∈ { 0, … , q − 1}

0 ≤ q , tq ∀D∈ { 0, … , q − 1},

where p ∊ ℝ are model parameters and tq are piecewise constant inputs for q steps. The elements of the augmented state vector q = [pq , sq ] ∈ ℝ5 are NLP variables and the discretized differential and algebraic equations F(·): ℝz ] ℝ{ ] ℝ} ] ℝ → ℝz and G(·): ℝz ] ℝ{ ] ℝ} ] ℝ → ℝ{ and q , tq represent the equality and inequality constraint functions. The solution to the stated problem gives the optimal state and input trajectory of which only the inputs of the first control interval are applied. C. Control objective The control objective for economics optimizing control is to maximize the revenues minus the costs, i.e. max = − ∑ , where *) is the number of contributions to the operational costs. In many chemical processes especially in processes that implement separation steps, the product can only be sold if a certain purity is reached. This inherently imposes a switching-type objective that leads to a hybrid problem which is known for being difficult to solve. To overcome the issue, the purity requirement was included as a constraint in the optimal control problem. This and other process related constraints (see below) were implemented such that a violation of the constraints is possible, but the violation is penalized (regularization by soft constraint, in short Regx). This way, a trade-off between economic optimality and satisfaction of the constraints is implemented. To penalize large input fluctuations, additional regularization terms (Regu for input regularization) are added so that the final control objective reads as

;¢£,}

;¢£,z

'

'

max = − + − + ,' ∙ ¡ ,' − + ¤' ∙ ¡¥,' ,

(11) 10


Page 11 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research where Qu and ¤j are the corresponding weights. D. Implementation details The NMPC algorithm used in this work is a modified version of the algorithm used in the software package do-mpc [22, 36] which is implemented in the Python/C++ programming language. The software has interfaces to the automatic differentiation tool CasADi [37, 38] and the interior-point optimizer Ipopt [39]. do-mpc relies on the orthogonal collation method and provides the user with an out-of-the-box implementation for NMPC problems. The algorithm uses a symbolic representation of the nonlinear process model which improves the convergence of the solvers by providing exact computations of derivatives by automatic differentiation. The resulting speed-up of the solution methods enables the solution of the resulting large dynamic optimal control problems in real-time. Automatic differentiation also is used to speed up the state estimation algorithm. In our study, we use the fixed-structure multi-rate Extended Kalman Filter that was adapted to differential-algebraic equations, see [24, 40] and [41]. The EKF reconstructs the state of the column from the available measurements using the same RD model that is used in the optimizing controller. Due to using near-infrared spectroscopy, two sampling frequencies have to be considered and the fixed-structure multi-rate algorithm was found to be the best choice. Furthermore, it was proven to work well in practice, see [41]. E. Resulting software architecture The overall structure of the software and the communication interfaces that were realized to operate the plant by economics optimizing NMPC are shown in Fig. 5. Four different modules can be run in parallel on a separate PC that is connected to the process control system of the pilot plant. OPC servers are used for the internal communication and for the communication with the process control system.

Figure 5. Local network and connection of the modules of the control framework for the RD example. Several issues had to be resolved before applying economics optimizing control to such a large-scale case study. (1) A suitable basic automation is needed where no manual adjustments during the operation are necessary and all adjustments can be carried out by the NMPC algorithm. The automation must be implemented in such a way that the inputs provided by the NMPC controller can be used as inputs to the process, e.g., if the controller computes a value of a flow rate but the process is controlled by setting a valve position, a PI(D) controller for the flow rate must be realized in the basic automation. (2) The optimizing controller is executed every ten minutes. During the startup, rapid changes of inputs, e.g. of the boilup rate, are not possible because of the internal delays. Therefore the input changes were restricted to a certain step size, i.e. ‖∆t‖ ≤ ∆t¨C¥ . (3) The optimization variables of the optimization problem that represent the inputs are initialized using the actual inputs of the process. This is important if a plant operator has to apply changes to the operating condition e.g. to meet safety regulations. (4) In case the optimizer fails for five consecutive steps, all states are initialized with the most recent estimates and the controller is re-initialized with the current inputs. (5) There exists a temperature minimum azeotrope between the reactants EtOH and DMC (see [12]) at the column, which can be observed after the startup procedure described above. However, in the initial concentration profile of the 11



estimator a constant concentration is considered. Therefore, the DAE-EKF is executed first and after convergence to the process measurements (after about 30 seconds) the NMPC is started. V. RESULTS At the pilot-scale process, seven experiments with optimizing control, E1-E7 (see Tab. 3) were performed, including four experiments for the production of DEC first followed by the production of EMC (E1-E4), one experiment for the production of EMC first and followed by the production of DEC (E5) and two experiments for the production of EMC only (E6) and DEC only (E7) with higher purity specifications. Table 3: Economics optimizing control experiments at the pilot-scale RD process. First production period Experimental set Product

Second production period

Required purity [mol/mol]

Product

Required purity [mol/mol]

E1 DEC

0.25

EMC

0.25

E2 Nominal NMPC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 25

E5

EMC

0.25

DEC

0.25

E6

EMC

0.40

-

-

E7

DEC

0.40

-

-

E3 E4

In the first part of this section, the quality of the NIR and of the GC measurements is discussed. The accuracy with which the composition of a given mixture can be determined using NIR instruments depends on the accuracy and reliability of the primary sensor and of the signal transmission. The aging process of the plastic cover of the optical fibers as well as the screw fittings that connect the sensor with the optical fibers and with the detector can lead to perturbations of the infrared light during transmission and to a reduced accuracy during the long-term use of the equipment. The manufacturer of the injection probes recommends to check the accuracy of the sensor regularly and to update the background spectra if the accuracy reduces significantly. The control experiments were designed to (i) demonstrate that both the intermediate and the final product can be produced economically optimally, (ii) show that the product changeover can be realized reproducibly and (iii) to show that different minimum purity requirements can be achieved by using the optimizing controller. The dynamic process behavior under optimizing control is discussed based on the raw data that was obtained from the NIR measurements. To evaluate the performance in terms of the selectivity towards the products and the conversion of the reactants, data reconciliation is employed. The procedure for data reconciliation is the same as in [12]. For all control experiments, problem (10, 11) as described in sections IV.B) and IV.C) was solved with the specifications given in Tab. 4. Table 4: Specification of the general control parameters that account for all controllers. Solver

Ipopt

Number of finite elements per sampling interval

Linear solver

MA27

Order of Lagrange polynomial

1

[Sampling time [min], prediction horizon]

[10, 5]

[PrEMC, PrDEC]

[21.29, 21.29]

Colocation methods

Chebychev 2nd order

[0.85, 0.15]

diag

[2.0, 4.0 ] 10 , 10.0, 15.0]

["q,KNM,n ,¨ , "q,NLM,n ,¨ ]

Cf for [FDMC, FEtOH, xcat, RR, DF]

[1.95, 1.78, 100.0, 4.25 ] 101¬ , 4.25 ] 101¬ ]

¬

[¤Q , ¤) ]

1

[0.4

or

0.25,

0.25]

12


Page 13 of 25

The constraint functions in Tab. 5 are used. Table 5: Specification of the constraint functions that are used for problem (10). Function Soft constraints *.) ®q , tq , ¯D , F °

Type

−@ ≤ WF ∙ W"q,KNM,n

,¨

− "q,KNM,n X 0 1 − F ∙ W"q,NLM,n

,¨

− "q,NLM,n X X − :,q ≤ 0

−@ ≤ S0.5 − W"q,LQOP,n 0 "q,N)OP,n XU − : ,q ≤ 0

0.02 ≤ -q ≤ 8.0 Hard constraint ®q , tq °

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.02 ≤ q ≤ 8.0 0.5 ≤ ±q ≤ 8.0

0.5 ≤ 6q ≤ 4.3

0.05 ≤ "LQOP,q ≤ 1.2

The constraint functions are divided into hard and soft constraints functions. While hard constraints functions define hard limits for the solution to the optimization problem, the soft constraints are added as a weighted quadratic contribution to the objective (11). The soft constraints are defined (i) to realize a desired minimum purity of the target product which can be chosen by setting F = {0,1} and (ii) defining a minimum alcohol-to-carbonate (ACR) ratio because if less alcohol is present, the catalyst will precipitate in the reboiler, see Fig. 6.

Figure 6. Catalyst precipitation at various molar alcohol-to-carbonate ratios XACR; overall volume in the flasks: 60 ml (left) and 55 ml (right), same amount of catalyst in each case. The hard constrains are set for ensuring minimum values for the reflux flowrate, -q , the bottom product and distillation flowrates ±q and q as well as for the overall vapor flowrate as a result of the boilup that can be realized at the pilotscale column, 6q . In addition, the liquid content of the component MeOH in the evaporator should be at least 5.0 [mol%].

13



Page 14 of 25

A. Reliability of the NIR during the control experiments

Figure 7. Molar fractions of the components measured by GC and NIR during experiment E1. Fig. 7 shows the molar fractions of the components in the liquid phase that were measured in the evaporator during experiment E1. It can be seen that the measurements that were obtained from the injection probe were mostly close to the values that were obtained by analyzing the samples offline with the gas chromatograph. While the concentration of DEC is measured with a high accuracy using the NIR device, the concentration measurement of EMC for values above 10.0 [mol%] is less accurate. The deviations that occurred when the concentration of EMC increases after 3h during experiment E1 are still within an acceptable range for control purposes. The results of the other experiments were similar. B. Production of DEC Fig. 8 shows the experimental raw data for experiment E1 with the optimizing controller, in which DEC is produced with a required purity of 0.25 [mol/mol]. It can be seen that the controller steers the process to the desired purity after about 1h which is indicated by a positive stage cost. After the start-up of the RD column, the optimizing controller was started (at time 0 sec). First the optimizing controller chooses conditions in which a significant amount of DMC and of the catalyst is added in order to satisfy the minimum purity requirement. After the required purity has been reached, the molar feed ratio of the reactants DMC and EtOH, is adjusted to a final value of 2.15 while the amount of catalyst in the overall feed flow rate is kept at the maximum value and the reflux ratio and the DF are kept almost constant. When the minimum purity has been reached, the soft constraint that penalizes the violation if the minimum purity constraint is deactivated and the revenue of the product is activated in the cost function. The controller then adjusts the operating conditions to realize a purity of 0.25 [mol/mol] for the component DEC in steady state by decreasing the amount of the more expensive reactant DMC and increasing the feed of the cheaper reactant EtOH. The value of the measured steady-state offset of the DEC purity in the bottom stream is 0.0167 [mol/mol] (NIR) and 0.0284 [mol/mol] (GC). A similar accuracy between steadystate NIR and GC values was observed for all other experiments except E6, which necessitated a production of EMC only. A minimum purity requirement of 0.4 [mol/mol] for DEC was set in experiment E7 (cf. Fig. 9). During this experiment, the amount of catalyst was at its maximum value whereas the other inputs were adjusted in order to reach the minimum purity of 0.4 [mol/mol]. The minimum purity was not reached throughout the experiment as measured by the NIR spectrometer due to the constraints on the ACR.

14


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Figure 8. Production of DEC during experiment E1; estimated concentrations (‘dashed lines’) and NIR measurements (‘squared’) marks. Left column: molar composition in the condenser (top) and in the reboiler (bottom), middle column: final estimated composition profile and NIR measurements (‘squared’) marks, the packing sections are indicated on the left hand side, right column: Profit plot (top) and operating conditions (bottom).



Figure 9. Raw data for experiment E7. (‘dashed lines’) correspond to estimates, (‘circle’) marks correspond to NIR measurements and (‘squared’) marks correspond to GC or temperature measurements. Fig. 9 visualizes the concentration profiles for experiment E7 at every hour when the GC samples were taken. It can be seen that the estimated concentration and temperature profiles which are computed by the multi-rate EKF using the


Page 16 of 25

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process measurements and the NIR data are in good agreement with the analysis of the samples, which were taken manually during the experiment. C. Production of EMC From simulations (results not shown here), it was found that the production of EMC is more challenging than the production of DEC due to a small operating window and the conflict between the purity requirement and the ACR constraint. Fig. 10 shows the data obtained in experiment E5 (see Tab. 3) in which EMC was the target product. It can be seen that after a phase where the catalyst was added with the maximum flow rate, the flow rate of the catalyst was reduced and the reflux ratio was increased to favor the production of EMC. After around 3800 sec, the feed of DMC was reduced and the feed of EtOH was increased as much of the initially available EtOH has already reacted. To produce EMC which is obtained by an equimolar conversion of the reactants DMC and of EtOH, further DMC would be required but since significant concentrations of DMC and of EMC are already present in the evaporator, the process is operated close to the ACR constraint. In order not to violate the constraint, the feed flow rate of DMC was reduced instead. Additionally, during the experiment a slight clouding of the bottom stream could be observed due to the flocculation of the catalyst at these operating conditions. This effect caused a reduction in the effectiveness of the catalyst and affected the online measurement of the NIR which shows a reduced amount of EMC as compared to the GC reference measurement. Both effects are not represented in the process model, which led to a reaction of the amount of catalyst while the adjustments of the feeds of the reactants were constrained by the lower limit for the ACR. Thus, the profitable operating window for the production of EMC was reached very late. D. Product changeover Fig. 11 shows the data obtained in experiment E4 during the dynamic product changeover. First the production of DEC was established and at about two hours at which steady-state conditions were observed, a product changeover was initiated to establish the production of EMC with a required purity of 25%. The production of DEC was successfully realized and the transient changeover to the intermediate product EMC shows a significant increase of the molar fraction of EMC in the evaporator. The changeover to the production of EMC was caused by a significant increase of the feed flow rate of DMC. Furthermore, the DF was reduced when more EMC is present in the bottom stream while the other inputs were mostly kept constant. However, the desired purity of EMC could not be reached due to the clouding of the bottom stream.

17


Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 18 of 25

Figure 10. Production of EMC during experiment E5 (see Tab. 3); estimated concentrations (‘dashed lines’) and NIR measurements (‘squared’) marks. Left column: molar composition in the condenser (top) and in the reboiler (bottom), middle column: final estimated composition profile and NIR measurements (‘squared’) marks, the packing sections are indicated on the left hand side, right column: Profit plot (top) and operating conditions (bottom).


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Figure 11. Dynamic product changeover during experiment E4 indicated by the molar concentration of the valuable products (NIR raw data in (‘straight’) lines, GC measurements indicated by (‘square’) marks) in the evaporator (top); the operating conditions are shown in the middle and bottom plots. The product changeover was initiated at about two hours.



Page 20 of 25

E. Performance evaluation To show the effect of the controller on the process performance, the reconciled data for the steady states of the experiments are presented in Tab. S1, see supporting information. It can be seen that the production of DEC is accompanied by a higher amount of DMC in the overall feed and the DF is almost two times larger compared to the production of EMC, while the other two inputs are similar for both products. When producing DEC, the resulting bottom flowrate is mostly below a flowrate of 2.3 [kg/h], whereas for producing EMC, it is mostly above 3.0 [kg/h]. Due to the fact that the catalyst is fed at the upper limit during the experiments and the prices for EtOH, DMC and energy are low compared to the other contributions to the cost function such as the soft constraints, the revenue is mainly determined by the bottom product stream. Therefore the production of EMC at a concentration of 25.0 [mol%] is more profitable because a higher bottom flow rate can be realized. When a higher purity is required in E6 and E7, the bottom product stream must be reduced significantly leading to a reduced profitability of the process. This however is an artefact because the concentration of the product was not considered in the profit function. The performance of the process depends on several key performance indicators which have not been included in the control objective. The reactants should be converted in the best way and the selectivity towards the desired product should be as high as possible. It must however be noted that by using an economic objective in optimizing control, a compromise is made between the conversion of the reactants and the selectivity towards the products and the costs that are necessary to realize a certain selectivity or conversion. In Fig. 12, the average selectivity for EMC and for DEC (with respect to the converted DMC) and the conversion of both reactants are displayed (see their values per experiment in Tab. 6). It can be seen that the conversion of DMC is high at over 70% on the average compared to the conversion of EtOH. This can be explained by the fact that DMC is more expensive than EtOH. The fact that an equimolar conversion of EtOH and of DMC is required to produce EMC leads to a small operating window for the production of EMC. For the production of DEC, the RD process can be operated at a range of values for conversion. The selectivity towards the product DEC attains an average value of 66.29%. The selectivity towards EMC is lower with an average of 51.42%. When EMC is produced, DEC is produced by almost the same amount due to the reaction mechanism and the limitations caused by the necessary ACR. The production of EMC is more challenging because on the one hand the production is sensitive to small changes of the inputs and on the other hand the inputs affect both the reactions simultaneously and are not selective enough to favor one reaction strongly over the other one. Table 6: Tabulated performance of the nominal optimizing controller (process data calculated from reconciled GC concentrations).

Conversion of EtOH [%] Conversion of DMC [%] Selectivity of the products [%]

Production DEC/EMC evaluated for GC

E1

E2

E3

E4

E5

E6

E7

DEC EMC DEC EMC DEC EMC

61.29 78.43 75.08 65.92 69.02 52.68

59.83 72.47 73.91 71.14 70.42 50.43

54.52 69.84 78.92 77.44 65.82 40.04

52.22 72.05 76.46 72.40 68.98 62.12

64.89 65.53 73.77 65.53 57.78 59.05

78.53 59.23 38.81

46.52 79.90 85.98 -


20

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Figure 12. Average conversion of the reactants and selectivity towards the products for the economics optimizing control experiments E1-E5; computed from reconciled GC data. F. Discussion of the results The optimizing control strategy was efficient and reliable when DEC is the desired product for which a purity of either 25% or 40% can be reached. It could be shown that the conversion of the more expensive feed DMC is high so that this reactant is exploited in the best possible way to achieve the maximum profit. It could further be shown that a higher purity is accompanied by lower bottom product flow rates to realize an enhanced selectivity towards the product DEC. These results are in accordance with the simulation-based optimization results shown in [42] where for the production of DEC it was shown that a high selectivity could be achieved and at the same time a reasonable conversion of the reactant DMC is possible. On the other side, if EMC is the desired product, the experiments showed that the production of EMC given the constraint that the amount of alcohols in the evaporator of the column is limited to 50.0 [mol%] is very challenging. This is in also in agreement with the results in [42] where it was also found that for a high selectivity towards the product EMC, the conversion of the reactant DMC is quite low. Furthermore, when producing EMC, large amounts of the other carbonates DMC and DEC are present in the evaporator which brings the process closer to the minimum alcohol-to-carbonate ratio. Measurement errors that are a result of the clouding of the bottom steam were observed and the effectiveness of the catalyst was reduced which led to the fact that the optimizing controller could achieve the desired purity of 25 [mol%] only temporarily. That a higher purity can be achieved in principle was demonstrated by experiment E7 in which the limitation of the alcohol-to-carbonate ratio was relaxed. In this experiment, the molar ACR assumed a value of 0.37 in the steady state, which is as an extreme operating point at which a significant catalyst clouding was observed which points to the technical limitations of this specific RD process. We could not reach a selectivity of 95% for each target product as in the numerical study presented in [42] because we had to respect the operational constraints. Also the control objective was plant economics, not selectivity. The reduced effectiveness of the catalyst was not included in the process model. The precipitation of the catalyst shifts the reaction equilibrium leading to a plant model mismatch. A reaction equilibrium that gives a reduced temperature is predicted, while in the real process, the equilibrium composition has a higher temperature. This is also indicated by the fact that compared to tabulated data using standardized tests for the determination of the constants, the reaction equilibrium constants


21


Page 22 of 25

published in [12] (see Tab. 4.9 in [12]) deviate by approx. -30% in the case of RC,Qa and +40% in the case of RC,Qa from experimental values. In addition, the regression model for the second reaction equilibrium constant has a fitness value R2 of only 0.336 (see Fig. 4.8 in [12]) and therefore it must be considered to be significantly uncertain. To overcome the issue of uncertain model parameters, robust multi-stage model predictive control [43] is a promising approach which will be considered in future work. VI. CONCLUSIONS In this article, we have studied the application of an advanced process control approach –economics optimizing control– to a real reactive distillation column with a coupled reaction scheme in pilot-plant scale. The chemical process considered is the transesterification of dimethyl carbonate with ethanol by which ethyl methyl carbonate and diethyl carbonate can be synthesized in a homogeneously catalyzed two-step chemical reaction. Economics optimizing control as a variant of the model predictive control technique has been employed to automate the column and to operate it using dynamic optimization in real-time. The operational goal was to realize a prescribed purity of the two products in this multi-purpose unit in the most economical manner by means of dynamically manipulating four operating parameters (degrees of freedom). Such an application had so far been studied in simulations studies only and this is to our knowledge the first application of an optimizing control scheme to a real RD plant. It could be shown that the method can be applied to such a complex chemical process in real-time by using a high-fidelity process model for the controller and for the soft sensor (EKF). The multi-rate EKF which was employed to reconstruct the systems state from the measurements of the process gave good results every 10 seconds while the dynamic optimization was executed at every ten minutes. By connecting the software tool to the pilot plant and executing it in real time, the production of DEC and of EMC as well as the transient product changeover could be realized in the most economical manner. The performance indicators that apply for such a process are the conversion of the reactants and the selectivity towards the products. Reconciled values were presented for various experiments. The conversion of the reactants was mostly above 65% considering the reconciled GC measurements and the selectivity towards the products was mostly above 60%. While the production of DEC at the specified purity using optimizing control was achieved without major problems, the production of EMC was more challenging because a significant clouding of the catalyst in the bottom product stream could be observed, which led to a diminished catalyst performance and to measurement errors. Despite these obstacles, the controller could steer the pilot-scale plant towards the limitations of the process for the production of both products. Further work will address the robustness of the controller where in particular multi-stage optimizing control [43] will be applied. ACKNOWLEDGEMENT The authors gratefully acknowledge inspiring discussions with Dr. Radoslav Paulen, now with the Institute of Information Engineering, Automation and Mathematics in Slovak University of Technology, Bratislava. We further acknowledge the support of Mr. Rüdiger Spitzer in the preparation of the experiments. SUPPORTING INFORMATION Additional material is made available as supporting information. This information is available free of charge via the Internet at http://pubs.acs.org/.

NOMENCLATURE Variables ai Gj h `TN R ,'

m

Lj m n nu nx

Activity of component i Vapor molar flowrate at stage j (mol s-1) Height (m) Vapor-liquid equilibrium constant of component i at stage j Liquid molar flowrate at stage j (mol s-1) Mass (kg) Mass flowrate (kg h-1) Mol (mol) Number of inputs Number of differential variables


22

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m


ny nz

Number of measurements Number of algebraic variables Molar flowrate (mol s-1) Number of samples Number of parameters Pressure (kPa) Reaction rate of component i (mol s-1) Temperature (K) Number of minor instant steps Sampling time (sec) Sampling time (sec) at slow sampling instances Sampling time (sec) at fast sampling instances Input to the system Mass fraction of component i in the liquid phase Molar fraction of component i in the liquid phase Differential state variable at time instance k Molar fraction of component i in the vapor phase Measured variable at time instance k Algebraic state variable at time instance k

N p P ri T Ts ts ts,s ts,f u wi xi xk yi yk zk Greek letters γ Activity coefficient of component i εj Reaction volume at stage j εk Slack variable at time instance k Stoichiometric coefficient of reaction rate νi Subscripts/Superscripts aug Augmented boil Boiling point eq Equilibrium exp Experiment fi Number of feed flowrates fixed Fixed structure F Major sampling instance in Inlet k Sampling instant L Liquid phase m Number of measured variables nc Number of components nr Number of reactions nv Number of parallelized instances nx Number of differential state variables nz Number of algebraic state variables p Number of input variables S Minor sampling instance sim Simulation V Vapor phase var Variable structure Abbreviations ACM Aspen Custom MeOH Methanol Modeler® ACR Alcohol-toMHE Moving carbonate ratio horizon estimator CAS Chemical MR Multi-rate abstract service number cat Catalyst NIR Nearinfrared D Distillate PF Particle filter DEC Diethyl RR Reflux


23


DF DMC

EKF EMC EtOH

GC

carbonate Distillate-tofeed ratio Dimethyl carbonate Extended Kalman filter Ethyl methyl carbonate Ethanol

RD RMSE

SR tot VLE

Page 24 of 25

Ratio Reactive distillation Root mean squared error Single-rate Total Vaporliquid equilibrium

Gas chromatography

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