Accepted Manuscript Title: Temperature difference control and pressure-compensated temperature difference control for four-product extended Petlyuk dividing-wall columns Authors: Xing Qian, Kejin Huang, Shengkun Jia, Haisheng Chen, Yang Yuan, Liang Zhang, Shaofeng Wang PII: DOI: Reference:
S0263-8762(19)30169-8 https://doi.org/10.1016/j.cherd.2019.04.014 CHERD 3610
To appear in: Received date: Revised date: Accepted date:
28 November 2018 17 March 2019 8 April 2019
Please cite this article as: Qian X, Huang K, Jia S, Chen H, Yuan Y, Zhang L, Wang S, Temperature difference control and pressure-compensated temperature difference control for four-product extended Petlyuk dividing-wall columns, Chemical Engineering Research and Design (2019), https://doi.org/10.1016/j.cherd.2019.04.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Temperature difference control and pressure-compensated temperature difference control for four-product extended Petlyuk dividing-wall columns
Xing Qiana, Kejin Huanga*, Shengkun Jiab*, Haisheng Chena, Yang Yuana, Liang Zhanga, and
College of Information Science and Technology,
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a
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Shaofeng Wanga
Beijing University of Chemical Technology, Beijing 100029, P. R. China b
School of Chemical Engineering and Technology, Collaborative Innovation Center
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of Chemical Science and Engineering (Tianjin), Chemical Engineering Research Center,
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State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300350, P. R. China
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* Corresponding author at: College of Information Science and Technology, Beijing University of Chemical Technology, North Third Ring Road 15, Chaoyang District, Beijing 100029, China. (Kejin Huang) Email:
[email protected]. * Corresponding author at: School of Chemical Engineering and Technology, Tianjin University, Beiyangyuan Campus, Yaguan Road 135, Jinnan District, Tianjin 300350, China. (Shengkun Jia) Email:
[email protected].
Highlights
The four-product extended Petlyuk dividing-wall column (FPEP-DWC) is studied.
The FPEP-DWC is able to reduce energy consumption by about 50%.
Temperature difference control (TDC) is proposed to improve the controllability.
Pressure-compensated TDC (PCTDC) is proposed to compensate the pressure variations.
The TDC and PCTDC with only temperature sensors are first proposed for the FPEP-DWC.
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ABSTRACT
The four-product extended Petlyuk dividing-wall column (FPEP-DWC) saves 50% more energy than traditional distillation sequences. However, the complex structure of FPEP-DWC results in strong interactions between different control loops and highly nonlinear behaviors. For the control of the FPEP-DWC, the temperature control (TC) scheme fails to handle the disturbances inserted into the process and none of the existing control schemes can, to the best of our knowledge, avoid the
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use of a composition controller (which is not recommended in industrial processes). The proposed TC scheme in the current work is also unable to handle the disturbances. Therefore, a kind of temperature difference control (TDC) scheme is investigated for the FPEP-DWC to improve its controllability and operability. A pressure-compensated temperature difference control (PCTDC) is also studied for the FPEP-DWC to compensate the pressure variations. To provide an illustrative example of the FPEP-DWC fractionating, a mixture containing methanol, ethanol, 1-propanol, and n-butanol
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was used to verify the feasibility of the TDC and PCTDC schemes while a wide range of feed disturbances are confronted. The outcomes show that the dynamic performances of the FPEP-DWC are substantially enhanced in most cases by using
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the proposed TDC and PCTDC schemes, which are conducive to the industrialization of the FPEP-DWC.
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Keywords: Four-product dividing-wall columns; Extended Petlyuk column; TC; TDC; PCTDC
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Introduction
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Distillation is a mature but energy intensive separation process in the chemical industry. The dividing wall column
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(DWC) provides a promising method to reduce energy consumption and capital investment compared with the traditional distillation process (Jansen et al., 2016; Kiss, 2014). However, the complex structure of DWC results in strong interactions
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between the different control loops and highly nonlinear behavior. To solve with this problem, many scholars have conducted research on different three-product Petlyuk DWC (TPP-DWC) configurations. Mutalib and Smith ((Mutalib and Smith, 1998) studied degrees of freedom for the TPP-DWC. They reported that the TPP-DWC has two more degrees of
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freedom (the liquid split ratio and the vapor split ratio) than the traditional distillation column, which can be used as
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manipulated variables in contrast to the conventional distillation column. However, while the liquid split can be easily varied, it is impractical to manipulate the vapor split. Ling and Luyben (Ling and Luyben, 2009, 2010) proposed a
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composition control (CC) scheme and temperature control (TC) scheme for the TPP-DWC. They pointed out that arranging a composition control loop to retain the heaviest component in the distillate of the prefractionator may achieve minimum energy expense when the feed flow rate or feed composition disturbances were inserted. Dwivedi et al. (Dwivedi et al., 2013b) proposed four types of impurity CC schemes. The former two CC schemes manipulate vapor split, while the latter two can handle disturbances without employing the vapor split.
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There are very few industrialized four-product DWCs (FP-DWCs) and relatively little research has been conducted on FP-DWC configurations. Kaibel DWC is the simplest FP-DWC as it contains only one vertical dividing wall in the distillation column. Dwivedi et al. (Dwivedi et al., 2012a; Dwivedi et al., 2012b) experimentally verified an active vapor split control structure for Kaibel DWC for the first time. Qian et al. (Qian et al., 2016) proposed different control schemes
very good. This may be due to fewer interactions between the less complicated control loops.
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(including TC, CC, and composition and temperature cascade control) for Kaibel DWC and results show that the TC is
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The FPEP-DWC, which contains three vertical dividing walls in the distillation column as sketched in Fig. 1, saves 50% more energy than traditional distillation sequences (Dejanovic et al., 2011). The FPEP-DWC saves much more energy than the other four-product and three-product dividing-wall columns. The major obstruction for the industrialization of the
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FPEP-DWC is the fear of dynamic problems due to its inherently strong interactions and highly nonlinear behaviors.
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However, very few studies have been done on the FPEP-DWC. Dwivedi et al. (Dwivedi et al., 2013a) proposed four kinds
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of control schemes for the FPEP-DWC. A pure TC scheme, a pure CC scheme, a pure CC scheme with a max-selector, and
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a composition and temperature cascade control scheme with a max-selector were developed. The first two control schemes
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cannot achieve the objective of disturbance rejection, while the latter two control schemes can achieve this because of the light impurity composition controls in the side streams of the control schemes. However, composition controllers, which are not recommended in real industrial processes because of their unreliability, high cost, and long dead time, were needed
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in the control schemes proposed by Dwivedi et al. (Dwivedi et al., 2013a). Therefore, it is worth developing a novel control scheme containing only temperature controllers for the FPEP-DWC.
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In the current work, we propose three kinds of control schemes: TC, temperature difference control (TDC), and pressure-compensated temperature difference control (PCTDC) schemes. The dynamic performances were evaluated for a
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wide range of feed disturbances. In the last two sections, the results are discussed and conclusions are drawn. This paper considers alternative single-loop PI control structures for the FPEP-DWC. Both pressure-compensated temperatures and temperature differentials are explored to achieve novel and effective control structures for the FPEP-DWC for the first time. All the control structures use only temperature controllers and are therefore particularly interesting from an industrial point of view.
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1.
Process description The FPEP-DWC and its thermally coupled equivalent configuration studied in this work are sketched in Fig. 1. The
FPEP-DWC was established for separating a mixture containing methanol (A), ethanol (B), 1-propanol (C), and n-butanol (D). The system was also adopted in our previous research for the simpler Kaibel DWC (Qian et al., 2016)—the property
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method is NRTL. The NRTL model can describe VLE and LLE of strongly nonideal solutions. Aspen Physical Property System databanks offer many binary parameters for VLE and LLE from literature and from regression of experimental
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data. The binary interaction parameters are defined for all subsystems in this case. The specifications for the four products were set at 99 mol%. The steady state design was performed with Aspen Plus, and the dynamic simulations were done with Aspen Plus Dynamics. For the design of the FPEP-DWC, both operating variables (continuous variables) and structural
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variables (discrete variables) should be specified. The structural variables are adopted from the work of Dwivedi et al.
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(Dwivedi et al., 2013a) as the system studied is the same. There were six degrees of freedom for the operating variables to
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achieve the minimum energy consumption. They were three liquid split ratios (R L1, RL2, and RL3) and three vapor split
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ratios (RV1, RV2, and RV3) in Fig. 2(a). The reflux ratio (RR), the distillate product stream rate (D), the first side product stream rate for the MDC (S1), and the second side product stream rate for the MDC (S2) are varied to maintain the four
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product purities. The optimization procedure of the FPEP-DWC is shown in Fig. 3. The liquid and vapor splits are varied sequentially to achieve the minimum reboiler duty (QR). The operating conditions for the FPEP-DWC are shown in Table 1 including the feed and product stages, flow rates
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and compositions for the prefraction column (PC), the intermediate distillation column (IDC), and the main distillation
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column (MDC). The detailed steady-state data for the FPEP-DWC is shown in Fig. 2(a). The temperature profile for the FPEP-DWC is shown in Fig. 2(b). The green dotted line indicates the PC, the red dashed line represents the IDC, and the
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black solid line means the MDC. The composition profiles for the FPEP-DWC are shown in Fig. 2(c). The locations of the composition profiles for the PC and IDC were arranged based on the composition profiles for the MDC to make the component splits apparent. The black solid line represents the lightest component A, the red dashed line signifies the lighter component B, the green dotted line indicates the heavier component C, and the blue dotted line indicates the heaviest component D. Component A fades away at the bottom of the PC, while component D disappears at the top of the PC.
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Component B falls to zero at the bottom of the IDC, while component C decreases to zero at the top of the IDC. Component C reaches zero at the bottom of the MDC, while component B descends to zero at the top of the MDC.
The FPEP-DWC has three sections: the PC performs a sharp A/D split, the upper part of the IDC carries out a sharp A/C split, and the lower part of the IDC implements a sharp B/D split. The upper part of the MDC executes a sharp A/B
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split, the middle part of the MDC fulfills a sharp B/C split, and the lower part of the MDC exhibits a sharp C/D split. As recommended, one stabilizing temperature control loop should be used for each component split (Skogestad, 2007). Since a
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temperature sensor is much faster and cheaper than a composition analyzer, temperature control is generally preferred over composition control in the chemical industry. In the current work, TC, TDC, and PCTDC are studied to promote the
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industrialization of FPEP-DWC.
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2.
Control schemes for FPEP-DWC The TC scheme is simple; however, it is unable to keep product purity within specs when feed disturbances are
inserted into the FPEP-DWC. For a binary system in a traditional distillation column at constant pressure, the temperature
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and the composition are uniquely related. However, these are not the case in a multicomponent distillation system. Yu and Luyben (Yu and Luyben, 1984) suggested the use of multiple sensitive temperatures in the multicomponent systems. As the
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FPEP-DWC separates four components, the TDC scheme is proposed for the FPEP-DWC to improve its controllability and operability. PCTDC is also proposed for the FPEP-DWC to compensate the pressure variations. The PCTDC scheme utilizes temperature sensors and pressure sensors. Compared with the dynamic performances using TC scheme, the
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dynamic performances using the TDC and PCTDC schemes have improved significantly. The proposed TDC and PCTDC
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schemes are much less complicated than the available composition and temperature cascade control schemes for the FPEP-
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DWC (Dwivedi et al., 2013a). Differential temperature control has been used for many years in traditional multicomponent
are effective for use in the chemical industry.
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distillation columns (Yu and Luyben, 1984). Therefore, the TDC scheme and PCTDC scheme proposed for the FPEP-DWC
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Proportional-integral (PI) controllers are utilized in the current work and proportional (P) controllers are employed to control liquid levels. The pressure control (PC) and level control (LC) are not illustrated in the figures of the control schemes. The manipulated variable for the top pressure control loop of the FPEP-DWC is the condenser heat duty, the
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manipulated variable for the sump level control loop is the bottom product flow rate, and the manipulated variable for the
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reflux drum level control loop is the reflux flow rate (as the reflux ratio = 7.243 > 3.0). The gains (KC) and integral times (TI) for PC and LC are taken from the literature (Luyben, 2013).
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With the pressure and level loops closed, ten degrees of freedom remains. The available manipulated variables (u) are as follows: 1.
Reboiler duty for the MDC (QR);
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Distillate product stream rate (D);
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Thermally coupled liquid reflux molar rate from the IDC to the PC (L1);
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Thermally coupled vapor boilup molar rate from the IDC to the PC (V1);
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Thermally coupled liquid reflux molar rate from the MDC to the IDC (L2);
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Thermally coupled vapor boilup molar rate from the MDC to the IDC (V2);
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Thermally coupled liquid side molar rate from the IDC to the MDC (L3);
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Thermally coupled vapor side molar rate from the MDC to the IDC (V3);
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First side product stream rate for the MDC (S1);
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10. Second side product stream rate for the MDC (S2).
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In the current study, the three thermally coupled vapor streams were not used as manipulated variables (i.e., the three vapor splits RV are fixed) in order to be more applicable for the industrialization of FPEP-DWC. Therefore, seven degrees of freedom were used as the manipulated variables. In this study, we used one TC/TDC loop for each component split.
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Therefore, the PC needs one TC/TDC loop due to a sharp A/D split. The IDC needs two TC/TDC loops because the upper
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part of the IDC performs a sharp A/C split and the lower part of the IDC performs a sharp B/D split. The MDC needs three
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TC/TDC/PTC loops because the upper part of the MDC performs a sharp A/B split, the middle part of the MDC performs a
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sharp B/C split, and the lower part of the MDC performs a sharp C/D split. There are six sharp splits in the FPEP-DWC. Therefore, at least six TC/TDC/PTC loops should be used to control of the FPEP-DWC. In the TC scheme, six TC loops
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are employed to ensure the six sharp splits.
Compared with the TC scheme proposed by Dwivedi et al. (Dwivedi et al., 2013a), we reduce four TC/TDC loops corresponding to three vapor splits and one reboiler heat duty as we use one TC/TDC loop for each component split. These
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not only decrease the installation and maintenance cost but also reduce excessive interactions between the different control
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loops. However, the TC scheme is unable to keep product purity within specs. The failure of TC may be due to sensitive temperatures that cannot effectively indicate the corresponding compositions. Therefore, all TC loops are replaced by TDC
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loops in the TDC scheme because the temperature difference is able to indicate the variance of compositions. The PCTDC scheme is proposed to reduce complexity and compensate the pressure variations. Because there are all sharp splits between adjacent components and nearly no other components exist in each part of the MDC, as sketched in Fig. 1, the sensitive temperatures are able to effectively indicate the corresponding compositions in the MDC. Therefore, TDC loops are employed in the PC and the IDC, while PTC loops are used in the MDC in the PCTDC scheme.
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It is important to decide which sensitive stages should be controlled. Sensitivity analysis is used for selecting sensitive temperatures. Singular value decomposition is used for choosing reference temperatures. Detailed principles for the determination of sensitive and reference stages in terms of SA and SVD techniques can be found in the literature (Ling and Luyben, 2010; Luan et al., 2013). Singular value decomposition for FPEP-DWC is shown in Fig. 4. In the figures, the stars indicate the stage temperatures that should be controlled by TC and the dashed lines show the differential temperatures that
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must be controlled through TDC. The controlled temperatures for TC scheme are [TP,4, TI,33, TI,68, TM,12, TM,111, TM,173], the controlled differential temperatures for TDC scheme are [TP,19-TP,4, TI,50-TI,33, TI,84-TI,68, TM,31-TM,12, TM,124-TM,111, TM,173-
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TM,154], and the controlled variables for PCTDC scheme are [TP,19-TP,4, TI,50-TI,33, TI,84-TI,68, PTM,12, PTM,111, PTM,173]. On the basis of the “pair close rule”, the corresponding manipulated variables are [L1, L2, L3, D, S1, S2], respectively. As the reboiler duty should increase as the feed rate increases, a feedforward controller (QR/F ratio controller) was introduced to
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be more adaptable when feed flow rate disturbances occur. The dead time in each temperature control loop was set to 1
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min. The proposed TC, TDC, and PCTDC schemes for the FPEP-DWC are shown in Fig. 5.
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Note that the pressure-compensated temperatures are the inputs of the controllers PTC4, PTC5, and PTC6 in the
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PCTDC scheme in Fig. 5(c). For example, the controller PTC6 ensures the sharp C/D component split. And it can be considered as two components (C and D) system in the lower part of the MDC. Therefore, there is a linear relationship
achieved as follows:
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between temperatures and pressures at a fixed composition. After regression data from 1.5atm to 2.5atm, the relationship is
T (K) = 15.984×P (atm) + 369.64
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Considering the initial state, the controlled pressure-compensated temperature (PT) is as follows:
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PT = 15.984×(P-P0) + T0
The other two controllers (PTC4 and PTC5) are similar to the controller PTC6. The PCTDC scheme is studied for the
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FPEP-DWC to compensate the pressure variations.
The Tyreus-Luyben tuning method was employed in this study. First, the D loop in the top of the MDC was tuned as it affects all of the other process variables. Second, the S1, S2, L2, and L3 loops were tuned sequentially. Finally, the L1 loop in the top of the PC was tuned. The controller tuning parameters for TC, TDC, and PCTDC are shown in Table 2 (the units
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of the integral times are minutes).
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Results and discussions The performances were satisfying when the proposed TDC and PCTDC schemes were used. Comparison between the
TC, TDC, and PCTDC schemes when ±10% step disturbance in feed flow rate and ±10% step disturbance of feed
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compositions occur are shown in Figs. 6 and 7, respectively. The TC scheme is shown in dotted curves while the TDC and PCTDC schemes are illustrated in dashed and solid curves, respectively. On some occasions, the solid PCTDC curves in
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some figures overlap the dashed TDC curves because the controlled variables (differential temperatures) are the same in the prefractionator and the intermediate distillation column. The TC scheme is unable to keep product purity within specs. The second side product composition decreased to 97.7% using TC scheme when +10% step disturbance in feed flow rate
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disturbance occurs. The first side product composition settled down in about 10 hours using TC scheme when -10% step
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disturbance in feed flow rate disturbance occurs. In face of ±10% step disturbances in feed flow rate, the PCTDC scheme is
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the best among the three control schemes. As for ±10% step disturbances of feed compositions, the TDC scheme is the best
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among the three control schemes. Tables 3 and 4 show the steady-state and maximum deviations for the step changes in feed flow rates and feed compositions. Considering the number of the minimum values of the steady-state and maximum
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deviations, the dynamic performances using the TDC and PCTDC schemes are better than those using the TC scheme. The TDC scheme is better at keeping the purities of the top and bottom products while the PCTDC scheme is better at keeping the purities of the two side products.
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The second side product compositions using the TC scheme are the lowest among those using the three control
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schemes when +10% step disturbance of feed flow rate disturbance occurs. The failure of the TC scheme is due to the inherent strong interaction and the high degree of process nonlinearity which results in the complex dynamic behaviors of
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the FPEP-DWC. Compared with the TC scheme, the steady-state deviations and the peak deviations are suppressed substantially by employing the TDC and PCTDC schemes. The sensitive temperature cannot indicate the corresponding compositions appropriately, which results in the failure of TC. The temperature difference indicated the variance of compositions. Therefore, all TC loops were replaced by TDC loops in the TDC scheme. The PCTDC scheme was proposed to reduce complexity and compensate the pressure variations. In summary, the TDC and PCTDC schemes are better than
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the TC scheme.
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Conclusions With three pairs of thermally coupled liquid streams and vapor streams, the FPEP-DWC shows inherent strong
interactions and highly nonlinear behaviors. The complicated dynamic behaviors of the FPEP-DWC preclude the TC
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scheme from achieving tight product quality control. However, the dynamic performances of the FPEP-DWC are
substantially enhanced in most cases by using the proposed TDC and PCTDC schemes. In the proposed control schemes
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for the FPEP-DWC, only temperature controllers are used for product quality control to be conducive to the
industrialization of the FPEP-DWC. To make them be less complicated than the TC scheme described elsewhere in the literature, minimum allowable controllers are used in the proposed TC, TDC, and PCTDC schemes. We used one TC/TDC
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loop for each component split to reduce interactions between the different control loops. One TC/TDC loop is installed in
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the prefractionator to ensure the A/D sharp split and keep the impurity components leaving from the top and bottom of the
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first dividing wall. Two TC/TDC loops are arranged in the intermediate distillation column to guarantee the A/C sharp split
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and the B/D sharp split and keep the impurity components leaving from the top and bottom of the second and third dividing walls. Three TC/TDC/PCTDC loops are settled in the main distillation column to ensure three sharp splits (A/B, B/C and
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C/D splits). In our previous study (Qian et al., 2016), the TC scheme worked surprisingly well for the four-product Kaibel DWC because it produced sharp splits between adjacent components in each column section. In the FPEP-DWC, there is at least one distributing component between the light key component and the heavy key component in the prefractionator and
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the intermediate distillation column. Multiple components (distributing and key components) coexist in the prefractionator
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and the intermediate distillation column. Therefore, the sensitive temperature cannot effectively indicate the corresponding compositions. These reasons result in the failure of the TC scheme of the FPEP-DWC. The temperature difference is able
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to indicate the variance of the compositions. The pressure-compensated temperature is able to compensate the pressure variations. Therefore, the TDC and PCTDC schemes exhibit better performances than the TC scheme. We reduce four TC/TDC loops corresponding to three vapor splits and one reboiler heat duty as we use one TC/TDC loop for each component split. These not only decrease installation and maintenance cost but also reduce excessive interactions between the different control loops. To the best of our knowledge, there are no feasible control schemes without composition
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controllers to control the FPEP-DWC discussed in the literature. The proposed TDC and PCTDC schemes are feasible control schemes of the FPEP-DWC with pure temperature controllers employed for the first time. This is conducive to the industrialization of the FPEP-DWC.
Acknowledgements
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Financial support from the National Nature Science Foundation of China (21808007, 21878011, 21676011, and 21576014), Open Foundation of State Key Laboratory of Chemical Engineering (No. SKL-ChE-18B01), China
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Postdoctoral Science Foundation (No. 2017M620587), and Fundamental Research Funds for the Central Universities
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(ZY1837 and ZY1930) are gratefully acknowledged.
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References Dejanovic, I., Matijasevic, L., Halvorsen, I.J., Skogestad, S., Jansen, H., Kaibel, B., Olujic, Z., 2011. Designing fourproduct dividing wall columns for separation of a multicomponent aromatics mixture. Chem. Eng. Res. Des. 89, 11551167.
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Dwivedi, D., Halvorsen, I.J., Skogestad, S., 2013a. Control structure selection for four-product Petlyuk column. Chem. Eng. Pro. 67, 49-59.
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Dwivedi, D., Halvorsen, I.J., Skogestad, S., 2013b. Control structure selection for three-product Petlyuk (dividing-wall) column. Chem. Eng. Pro. 64, 57-67.
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Dwivedi, D., Strandberg, J.P., Halvorsen, I.J., Preisig, H.A., Skogestad, S., 2012a. Active vapor split control for dividing-
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wall columns. Ind. Eng. Chem. Res. 51, 15176-15183.
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Dwivedi, D., Strandberg, J.P., Halvorsen, I.J., Skogestad, S., 2012b. Steady state and dynamic operation of four-product
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dividing-wall (Kaibel) Columns: Experimental verification. Ind. Eng. Chem. Res. 51, 15696-15709.
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Jansen, H., Dejanovic, I., Rietfort, T., Olujic, Z., 2016. Dividing Wall Column as Energy Saving Retrofit Technology. Chem. Ing. Tech. 88, 200-207.
Kiss, A.A., 2014. Distillation technology-still young and full of breakthrough opportunities. J. Chem. Technol. Biot. 89,
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479-498.
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Ling, H., Luyben, W.L., 2009. New control structure for divided-wall columns. Ind. Eng. Chem. Res. 48, 6034-6049. Ling, H., Luyben, W.L., 2010. Temperature control of the BTX divided-wall column. Ind. Eng. Chem. Res. 49, 189-203.
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Luan, S., Huang, K., Wu, N., 2013. Operation of dividing-wall columns. 1. A simplified temperature difference control scheme. Ind. Eng. Chem. Res. 52, 2642-2660.
Luyben, W.L., 2013. Distillation design and control using Aspen simulation. John Wiley & Sons, New York. Mutalib, M.I.A., Smith, R., 1998. Operation and control of dividing wall distillation columns - Part 1: Degrees of freedom
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and dynamic simulation. Chem. Eng. Res. Des. 76, 308-318. Qian, X., Jia, S., Skogestad, S., Yuan, X., 2016. Control structure selection for four-product Kaibel column. Comput. Chem. Eng. 93, 372-381. Skogestad, S., 2007. The dos and don’ts of distillation column control. Chem. Eng. Res. Des. 85, 13-23. Yu, C.-C., Luyben, W.L., 1984. Use of multiple temperatures for the control of multicomponent distillation columns. Ind.
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Eng. Chem. Proc. Des. Dev. 23, 590-597.
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(a) FPEP-DWC
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(b) Thermally coupled equivalent configuration
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Fig. 1. FPEP-DWC and its thermally coupled equivalent configuration
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(a) FPEP-DWC
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(b) Temperature profile
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(c) Composition profiles
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Fig. 2. FPEP-DWC and its steady-state behaviors: (a) FPEP-DWC, (b) temperature profile, and (c) composition profiles
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Start
Guess the initial design of the FPEP-DWC
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Adjust RL1 and RV1
Adjust RL3 and RV3
No
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Can QR be further reduced by adjusting RL3 and RV3?
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Adjust RL2 and RV2
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Can QR be further reduced by adjusting RL2 and RV2?
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No
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Can QR be further reduced by adjusting RL1 and RV1?
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Generate the optimum process design of the FPEP-DWC
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End
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Fig. 3. Optimization procedure of the FPEP-DWC
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(b) L2
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(a) L1
(d) D
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(c) L3
(e) S1
(f) S2
Fig. 4. Singular value decomposition for FPEP-DWC
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(a) TC scheme
(b) TDC scheme
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(c) PCTDC scheme Fig. 5. TC, TDC, and PCTDC schemes for the FPEP-DWC: (a) TC scheme, (b) TDC scheme, and (c) PCTDC scheme
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IP T SC R U N A M TE D EP CC A Fig. 6. Comparison between the TC, TDC, and PCTDC schemes when ±10% step disturbance in feed flow rate occur
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IP T SC R U N A M TE D EP CC A (a) Methanol disturbances
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IP T SC R U N A M TE D EP CC A (b) Ethanol disturbances
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IP T SC R U N A M TE D EP CC A (c) Propanol disturbances
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IP T SC R U N A M TE D EP CC A (d) Butanol disturbances Fig. 7. Comparison between the TC, TDC, and PCTDC schemes when ±10% step disturbance of feed compositions occur: (a) methanol, (b) ethanol, (c) propanol, and (d) butanol
25
Table 1. Operating conditions for the FPEP-DWC FPEP-DWC IDC
MDC
Total stages
60
120
180
Feed stage
30
30/90
30/90/150
Product stage
1/60
1/60/120
1/60/120/180
Pressure (atm)
1.408
1.204
1
D (kmol/h)
0.6809
1.6718
0.2523
S1 (kmol/h)
-
0.60
0.2476
S2 (kmol/h)
-
-
0.2477
B (kmol/h)
1.3991
1.6882
0.2524
Mole reflux ratio (RR)
-
-
7.243
Liquid split ratio (RL)
-
0.2128/0.5729
0.7958
Vapor split ratio (RV)
-
0.5821
0.6693/0.6485
QC (kW)
-
-
-20.359
QR (kW)
-
-
20.029
XD, A
0.4623
0.3162
0.9900
XD, B
0.5129
0.6838
0.0100
XD, C
0.0248
0.0000
XS1, A
-
0.0009
XS1, B
-
0.9666
XS1, C
-
0.0325
XS2, B
-
-
XS2, C
-
XS2, D
-
XB, B
0.3392
0.0021
0.0000
XB, C
0.4276
0.7511
0.0100
XB, D
0.2317
0.2468
0.9900
U
SC R
PC
N
0.0000
M
A
0.0007 0.9900 0.0093 0.0094
-
0.9900
-
0.0006
A
CC
EP
TE D
IP T
Parameter
26
Table 2. Tuning parameters
8.26
17.16
L2
5.43
15.84
L3
3.94
14.52
D
10.26
43.56
S1
2.24
30.36
S2
3.98
21.12
L1
0.697
14.52
L2
0.365
14.52
L3
0.228
15.84
D
0.933
38.28
S1
0.779
23.76
S2
0.816
18.48
L1
0.528
17.16
L2
0.373
14.52
L3
0.213
17.16
D
15.10
38.28
S1
2.08
30.36
S2
3.77
IP T
L1
19.80
A
CC
EP
TE D
M
A
PCTDC
TI (min)
SC R
TDC
KC
U
TC
Control loop
N
Schemes
27
Table 3 Steady-state composition deviations of the four products (⊿XDA,⊿XS1B,⊿XS2C,⊿XBD) Disturbance TC (%)
TDC (%)
PCTDC (%)
+10%A
(+0.0312, +0.1226, +0.0212, -0.0894) (+0.0085, -0.0065, +0.0127, -0.0091) (-0.1151, +0.2257, +0.041, +0.0299)
-10%A
(-0.0326, -0.1474, -0.0271, +0.0831) (-0.0085, -0.0366, -0.0232, +0.0111) (+0.1029, -0.4132, -0.0801, -0.0304)
+10%B
(+0.0387, -0.2169, +0.0399, +0.0288) (+0.0059, -0.1908, +0.0427, +0.0037) (+0.038, -0.1899, +0.0462, +0.0299)
-10%B
(-0.0418, +0.266, -0.1027, -0.028)
+10%C
(-0.1173, +0.0547, +0.0238, +0.0273) (-0.0189, +0.222, +0.0395, +0.0038) (+0.0367, -0.1509, -0.5253, 0.0346)
-10%C
(+0.1034, -0.0467, -0.117, -0.0267)
+10%D
(+0.0376, +0.041, -0.6837, +0.0359) (+0.0061, -0.1524, -0.4803, +0.0034) (+0.0324, -0.0059, +0.015, -0.0952)
-10%D
(-0.0399, -0.0601, +0.0438, -0.0296) (-0.0069, +0.1101, +0.0585, -0.0026) (-0.0334, -0.0366, -0.0281, +0.0875)
+10%F
(+0.0273, -0.4177, -1.313, -0.3397)
(-0.061, +0.0892, -0.1406, -0.0445)
-10%F
(-0.0115, -0.5489, +0.19, +0.2691)
(+0.0554, -0.2175, +0.1179, +0.0432) (+0.1076, +0.02, +0.1006, +0.0866)
(-0.0062, +0.2937, -0.0923, -0.0036) (-0.0407, +0.2942, -0.1001, -0.0304)
SC R
IP T
(+0.0217, -0.4148, -0.0741, -0.0034) (-0.0391, +0.1109, +0.0629, -0.0316)
A
CC
EP
TE D
M
A
N
U
(-0.0027, +0.0863, -0.1333, +0.018)
28
Table 4 Maximum composition deviations of the four products (⊿XDA,⊿XS1B,⊿XS2C,⊿XBD) Disturbance TC (%)
TDC (%)
PCTDC (%)
(+0.0312, +0.1226, +0.0313, -0.0914) (-0.0108, -0.1, +0.0226, +0.0458)
(-0.1151, +0.2674, +0.0702, +0.0488)
-10%A
(-0.0326, -0.1474, -0.0315, +0.0841)
(+0.009, +0.0843, -0.0232, -0.0503)
(+0.1029, -0.4511, -0.0911, -0.0556)
+10%B
(+0.0387, -0.2586, -0.1876, +0.0885) (-0.0232, -0.3363, -0.1553, +0.0714)
(+0.038, -0.3446, -0.2343, +0.1184)
-10%B
(-0.0418, +0.2763, +0.1283, -0.0963) (+0.0245, +0.3386, +0.1229, -0.0763) (-0.0407, +0.3491, +0.1651, -0.1357)
+10%C
(-0.1173, +0.215, -0.1215, +0.0921)
(+0.0415, +0.2657, +0.0748, +0.0349) (+0.0367, -0.1558, -0.5253, -0.1361)
-10%C
(+0.1034, -0.2697, -0.1292, -0.1233)
(-0.0398, -0.4481, -0.0941, -0.041)
(-0.0391, +0.1272, -0.1157, +0.0836)
+10%D
(+0.0376, -0.0443, -0.6837, -0.1005)
(-0.017, -0.1559, -0.4803, -0.1285)
(+0.0324, -0.0989, +0.0422, -0.0976)
-10%D
(-0.0399, -0.0601, -0.0681, +0.0711)
(+0.0155, +0.1249, -0.078, 0.0854)
(-0.0334, +0.0837, -0.0517, +0.0939)
+10%F
(+0.1156, -0.5686, -1.3176, -0.9961)
(-0.0662, +0.5451, -0.4634, -0.2427)
(-0.051, +0.5575, -0.6112, +0.2967)
-10%F
(-0.1123, -0.5489, +0.3135, -0.5585)
(+0.0626, -0.7033, +0.4373, -0.6324) (+0.1076, -0.328, -0.3103, +0.3281)
A
CC
EP
TE D
M
A
N
U
SC R
IP T
+10%A
29