Dynamic vapor recompression in a reactive batch rectifier: Analysis and nonlinear control

Energy 115 (2016) 60e66

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Dynamic vapor recompression in a reactive batch rectifier: Analysis and nonlinear control Sudip Banerjee, Amiya K. Jana* Energy and Process Engineering Laboratory, Department of Chemical Engineering, Indian Institute of Technology, Kharagpur 721302, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 October 2015 Received in revised form 22 May 2016 Accepted 22 August 2016

This work proposes a dynamic vapor recompressed batch reactive rectifier (VRBRR) for the butyl acetate system that operates with a dynamic compression ratio (CR). In this configuration, along with the CR, we manipulate either the overhead vapor inflow rate to the compressor or the external heat input to the reboiler for the purpose of coupling the thermal arrangement with the existing batch tower. To improve the product purity and the amount of distillate collection of the dynamic VRBRR, we further formulate a nonlinear extended generic model controller (EGMC) that requires state information for its simulation. For this, we develop a closed-loop high gain observer (HGO) for estimating a limited number of states, exclusively required for the EGMC. This results in a significant structural mismatch that is taken care of by the hybrid EGMC-HGO system. For the representative butyl acetate system, it is investigated that the proposed nonlinear controller outperforms a traditional PI controller in regulating the dynamic VRBRR. © 2016 Published by Elsevier Ltd.

Keywords: Vapor recompression Dynamic compression ratio Batch reactive rectifier Energy savings Economics Nonlinear control

1. Introduction The dependency on fossil fuels of the modern human civilization has been increasing enormously with the gradual progress of industrial revolution. Apart from the severe concern of its consistent availability owing to its increasing demand [1,2], indiscriminate burning of fossil fuels releases CO2, which is one of the principal greenhouse gases (GHG) responsible for global warming and its adverse effects [3]. As a preventive measure, we show our interest to improve the thermal efficiency of industrial processes. In this regard, process intensification route is a viable alternative in order to obtain ultimate cheaper and sustainable technologies, by utilizing every possible source of waste heat. As an essential unit operation [4], distillation/rectification always attracts researchers as a major area of energy intensification. The existing schemes of energy integration can be categorized into two classes namely, internal and external heat integration. Popular examples of the internal and external heat integrated schemes are the heat integrated distillation column (HIDiC) [5] and vapor recompression column (VRC) [6], respectively. The first research work was published in the area of energy

* Corresponding author. E-mail address: [email protected] (A.K. Jana). http://dx.doi.org/10.1016/j.energy.2016.08.077 0360-5442/© 2016 Published by Elsevier Ltd.

intensification in 1960s [7]. It showed its superiority to enhance the energy performance of the system, and thus emerged as a popular thermal integration approach. On the other hand, Takamatsu et al. [8] first proposed a thermally coupled batch distillation configuration where we observe the incorporation of a jacketed reboiler surrounding the rectifying tower. Jana and Maiti [9] subsequently evaluated the advantage of this novel scheme over its conventional counterpart, in terms of energy efficiency and cost. Jana and his co-workers [10,11] proposed “variable speed” VRC scheme, and applied on energy efficient unsteady state batch distillation operation. This variable speed mechanism is further illustrated on a ternary batch distillation column having side withdrawals [12] and also on a batch distillation column containing a feed drum in between its rectifying and stripping section [13]. Apart from the feasibility analysis, Babu and Jana [14] in their recent communication used a closed-loop gain scheduled PI (GSPI) control structure on the variable speed vapor recompressed batch distillation column to achieve relatively high purity top product at a constant composition. Being nonstationary and nonideal in nature, heat integration in batch distillation and thereby its control is really a challenging task and to the best of our knowledge possibly no nonlinear model-based control scheme is available so far in the open literature showing its applicability on vapor recompressed column. It is with this intention the present work has been undertaken.

S. Banerjee, A.K. Jana / Energy 115 (2016) 60e66

Here, we designed a nonlinear model-based extended generic model controller (EGMC) [15,16] based on differential geometry theory. This EGMC controller serves as a bridge between classical GMC [17] and generalized GMC [18]. The nonlinear EGMC controller so developed requires information about specific internal states of the process that are inevitably required for its simulation, and hence, we develop the reduced order nonlinear high gain observer (HGO) unlike EKF [19], ELO [20], etc. By continuous updating state information required for controller simulation, this nonlinear high gain observer (HGO) is capable of reducing the effect of structural discrepancy that generally arises due to the use of reduced order process model while developing a model-based controller. As per our present contribution is concerned, we focus our attention primarily on the implementation of the vapor recompressed batch reactive rectifier (VRBRR) scheme involved in the production and separation of butyl acetate (BuAc) as distillate. This work is an extension of the investigation conducted by Jana and Maiti [9] on the present BuAc system based on operating compression ratio (CR) at static mode. Aiming to achieve constant product purity and more amount of distillate collection, the closedloop performance of the energy efficient dynamic VRBRR column is evaluated. For this purpose, the model-based EGMC controller is developed and subsequently coupled with a nonlinear modelbased high gain observer (HGO) that serves as a state estimator solely required for the controller simulation. The closed-loop dynamic VRBRR under HGO-based EGMC control scheme proves its superiority over a traditional PI controller regarding energetic and economic aspect, product purity, as well as amount of distillate collection. 2. Process modelling The mathematical model of the vapor recompressed batch reactive rectifier (VRBRR) can be classified into two segments, namely modelling of the tray tower and modelling of the compressor. In general, we consider the following assumptions for model development: perfect mixing and equilibrium on all stages, vapor hold-up is negligible compared to liquid hold-up which varies in each tray, the energy dynamics of the column are fast, chemical reactions are confined to reactive zone and take place only in the liquid phase, constant Murphree plate efficiency based on the vapor-phase (¼75%) is considered, the compressor installed between the overhead vapor and bottom reboiler is isentropic, and difference in temperature between the compressed overhead vapor and reboiler is at least 20  C. Modelling of the tray tower is elaborately discussed by Jana and Maiti [9], so in this paper we only concentrate on the modelling of the compressor. 2.1. Modelling of the compressor The compressor duty of the VRBRR can be represented by the following mathematical equation [21]:

QComp ¼

i m1 VnT C mRTnT h ðCRÞ m  1 m1

(1)

In the above equation, QComp depicts the compressor duty, VnT C the flow rate of the compressed overhead vapor, TnT the corresponding temperature and R the universal gas constant. The CR represents the compression ratio and it can be represented by:

CR ¼

PnT C ¼ PnT



 TnT C m=ðm1Þ TnT

(2)

61

The polytropic coefficient m is a function of temperature and it can be calculated from the following equation: NC X 1 yi ¼ m  1 i¼1 mi  1

(3)

Here, PnT and PnT C are the pressure of overhead vapor and compressed vapor that correspond to TnT and TnT C , respectively. 3. Development of VRBRR The prime objective in developing the vapor recompressed column is the optimal utilization of available internal source of energy with the aim of reducing the capital as well as operating costs. Fig. 1 depicts the requisite transformation from conventional to vapor recompressed column. 3.1. Categorizing VRBRR based on mode of operating CR The gradual development of the VRBRR scheme based on static and dynamic CR is discussed in the following subsection and accordingly, names of the corresponding VRBRR are given as static VRBRR and dynamic VRBRR. 3.1.1. Static VRBRR As the name suggests, static VRBRR refers to the operation of the rectifier at static (fixed speed) CR mode. The difference in temperature (DTC) between the compressed vapor ðTnT C Þ and the reboiler liquid (TB) serves as the thermal driving force, and this is essential for latent heat transfer from the former to the latter stream. It is true that because of the transient nature of the batch processing, both the overhead vapor temperature ðTnT Þ as well as the reboiler liquid temperature (TB) vary with time. As stated, apart from constant reboiler heat duty (QR) to operate the VRBRR at static CR mode, the necessary condition which must be satisfied is DTC  20  C [9]. 3.1.2. Dynamic VRBRR Dynamic VRBRR comes into the picture when we wish to operate the compressor at a controlled CR. It is done with the aim to avoid unnecessary overheating of the overhead vapor prior to its thermal interaction with the reboiler liquid. To achieve this, the important criterion, which needs to be fulfilled apart from constant reboiler energy demand (QR) is DTC ¼ 20  C. Accordingly, the following equation can be used which is the extended form of Eq. (2)

CR ¼

PnT C ¼ PnT



   TnT C m=ðm1Þ DTC þ TB m=ðm1Þ ¼ TnT TnT

(4)

The necessary adaptation of the CR value at each and every time step is made with the help of the above equation. In the dynamic VRBRR scheme, apart from adjusting the CR, either the vapor inlet to the compressor or the external source responsible for supplying heat to the bottom reboiler needs to manipulate simultaneously. The mechanism is described below. 3.2. Mechanism for variable manipulation As per the availability of heat with the compressed vapor (QCV) compared to the reboiler energy demand (QR), we can categorically divide it into three schemes [Scheme 1 (when QCV < QR), Scheme 2 (when QCV > QR) and Scheme 3 (when QCV ¼ QR)]. This strategy of variable adjustment for the VRBRR is applicable equally to its static as well as the dynamic mode of operation to ensure the optimal use

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Fig. 1. A scheme showing requisite transformation from conventional column to vapor recompressed column: (A) CBRR, and (B) VRBRR [Here, L1 denotes the flow rate of a liquid stream leaving 1st tray, VB the vapor boil-up rate, VnT the overhead vapor rate and n the distillation tray].

of internal heat source. 4. A case study: multicomponent reactive system 4.1. Process description and reaction kinetics

we hereby employ the UNIQUAC model and nonlinear version of Francis weir formula, respectively. Following is a heterogeneously catalyzed liquid phase esterification reaction, which produces n-butyl acetate (component 3) as the main product along with the water (component 4) from reactants acetic acid (component 1) and n-butanol (component 2).

For the implementation of the proposed VRBRR scheme, we hereby choose conventional batch reactive rectifier (CBRR) pro-

ducing butyl acetate as distillate. The basic configuration of the CBRR consists of 16 stages (counting from bottom to top) excluding reboiler and total condenser. It has a diameter of 0.586 m. The CBRR can be divided into two distinct zones, namely reactive section (the reboiler and 1st tray) and rectifying section (2nd tray to 16th tray). The rectifier operates at a total pressure of 1 atm having a stage pressure drop of 0.3 kPa. It is worth to mention that for the computation of liquid phase activity coefficient and tray hydraulics,

As per this rectification process, the BuAc composition becomes richer in the still with the gradual removal of the water from the top of the column. The process is continued until the composition of BuAc attains 0.947 at the distillate with corresponding reboiler composition of 0.961. The thermodynamic data concerning the enthalpy calculation, the phase equilibrium, and the Antoine equation are available elsewhere [9]. The required kinetic data for the PH model are

S. Banerjee, A.K. Jana / Energy 115 (2016) 60e66 Table 1 Component compositions in reflux drum and reboiler of the batch reactive column. Component

HAc BuOH BuAc H2O

Reflux drum composition

Reboiler composition

At steady state

At the end

At steady state

At the end

0.00423 0.00233 1.26E-04 0.99332

0.04639 0.00342 0.94798 0.00221

0.14607 0.14636 0.39676 0.31081

0.01981 1.0E-05 0.961 0.01918

6 u¼4

21 1

Lg1 Lf

«

h1

Lg1 Lf2m 1 hn

/ /

21 1

Lgm Lf

h1

Lgm Lf2m 1 hm

31 7 5

Z

2 6 6 6 4

K11 e1 þ K12 Z Km1 em þ Km2

design equation of this controller. For more details, one may consult Banerjee et al. [16]. Consider the following nonlinear multi-input/multi-output (MIMO) system in its state space form as

_ ¼ f ðx; d; zÞ þ gðx; d; zÞ:uðtÞ xðtÞ

(5)

xðtÞ2
available in literature [22]. Reflux drum and reboiler compositions during steady state and at the end of the operation are detailed in Table 1. For the static version of the VRBRR, we adopt the CR values for the start-up and production phase as 1.938 and 3.129, respectively [9]. As far as the dynamic VRBRR is concerned, the CR is manipulated using Eq. (4). Moreover, the optimal QR value is 879.21 kW, and the amount of available internal heat source is insufficient to fulfill the demand of the optimal QR value (Scheme 1). So some additional heat must be supplied by the external heat source as the makeup energy (QME) in order to continue the batch processing at

2

63

Here, the state vector the manipulated vector u2
yi

ð2 1Þ þ ai2i yi i þ ……… þ ai2 y_i þ ai1 yi Z     sp sp yi  yi dt ¼ Ki1 yi  yi þ Ki2

Here, sp stands for the set point, and ai2i ; …………ai1 ; Ki1 and Ki2 are tuning parameters of the controller. The final form of EGMC controller can be derived as [16]:

o n e1 dt  L2f 1 h1 þ a121 L2f 1 1 h1 þ / þ a11 L0f h1 «

n em dt  L2f m hm þ am2m Lf2m 1 hm þ / þ am1 L0f hm

constant QR. From this discussion, it is clear that the heat of the entire vapor which is coming out from the top of the column is being utilized as a potential internal heat source nullifying the requirement of the overhead condenser. In this context, it is worth to mention that as per the simulation study the amount of liquid gets vaporized after throttling is less than 5%, so there is no need to install any overhead condenser. 5. Proposing control strategy for the VRBRR The purity of the top product during the open-loop production phase decreases gradually over the period. Normally, the final product purity becomes lower than the steady state purity. To achieve the constant composition of water (xD;H2 O ), which is the lightest top product, we devise the following nonlinear modelbased control scheme. Furthermore, the reflux drum level is maintained by manipulating distillate flow rate, and for this purpose, a conventional PI controller is incorporated. 5.1. High gain observer-based extended generic model control The model-based control scheme represented in this section includes extended generic model controller (EGMC) and a nonlinear observer, namely high gain observer (HGO). Firstly, we develop the EGMC controller with the help of differential geometry theory. Any processes irrespective of their relative orders can be brought under this nonlinear controller. 5.1.1. Extended GMC For the design of EGMC controller, it is required to have some concept of the theory of differential geometry that is provided in the book by Isidori [23]. We at this moment provide only the final

(6)

3 7 7 o7 5

(7)

In the above equation L stands for the Lie derivative operator [23]. It is important to mention here that the relative order 2i is the smallest order of derivative of y that explicitly depends on the vector u. From Eq. (7), it is clear that the final form of EGMC controller consists of the product of two terms. The first term represents the inverse of the characteristic matrix (m  m), which is non-singular in nature. Based on the formulation discussed above, the final form of the EGMC controller equation for dynamic VRBRR column is derived as

0 VnT ynT ;j þ dj rn þ amD xD;j  mD @K1 e þ K2 R¼

xD;j

Z

t

1 edt A

0

D

(8)

In the above equation, rn and dj denote reaction rate and stoichiometric coefficient, respectively. Here, e is the error of the controller, and it can be expressed as e ¼ xDsp ;j  xD;j , where xD,j and xDsp ;j are the distillate compositions of component j, and set point value of xD,j, respectively. a, K1 and K2 are tunable parameters of the EGMC1 controller. mD is the molar hold-up of the reflux drum and D the distillate rate. Here, we assume that xD,j is a measured quantity. From Eq. (8), it is clear that for the sake of closed-loop controller simulation at each and every time step, we should have the knowledge about the component vapor flow rate (VnT ynT ;j ) leaving from the top tray. Since, this component vapor flow rate can't be measured directly, so there is a need to estimate it by the use of a state estimator and provide that value to

1 Tuning parameters are selected as,K1 ¼ 110.21,K2 ¼  278 based on ISE criteria.

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S. Banerjee, A.K. Jana / Energy 115 (2016) 60e66

the controller.

5.1.2. Development of state estimator We devise here a high gain observer (HGO) for the estimation of the unmeasured state solely required for the EGMC controller simulation. As stated, there is only one unmeasured state, namely partial vapor flow rate (VnT ynT ;j ), which is an augmented state. The values of all other states and parameters are known to us. Following the method proposed by Farza et al. [24], the nonlinear closed-loop observer for the following nonlinear MIMO model

_ ¼ Fðx; dÞx þ Gðx; u; dÞ þ εðtÞ xðtÞ y ¼ Cx

(9)

can be employed to compute the states as: 1 T b x ; dÞD1 x  xÞ x_ ¼ Fðb x ; dÞb x þ Gðb x ; u; dÞ  l Lþ ðb l S C Cðb |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

(10)

Corrector

Predictor

1 T In the above Eq. (10), the term l Lþ D1 l S C C is collectively known as the variable gain of the estimator. For more details, one may consult the work of Banerjee et al. [16]. From the design concept of high gain observer, the predictor can be represented by the following model:

8 h i > < x_D;j ¼ 1 Vn yn ;j  ðD þ RÞxD;j T T mD > :V y ¼0

(11)

nT nT ;j

In the above predictor model, VnT ynT ;j is the imprecisely known parameter (augmented state), and xD,j is the true state. Since, VnT ynT ;j is the extra state having no dynamics, the precise estimation of that state is no doubt a challenging task. By the high gain observer theory, we represent the variable gain for our present system as: 1 T l Lþ D1 l S C C¼



2l l2 mD

 (12)

The final form of the high gain observer [Eq. (10)] for the present BuAc dynamic VRBRR column is represented as follows:

"

b x_ D;j _b b_ V nT y nT ;j

#

2

3

"

D 1 b x D;j 6 7 ¼ 4 mD mD 5 b y nT ;j V nT b 0 0  

2l b  2 1 x D;j  xD;j l2 mD

#

2

3 xD;j  6 7 þ 4 mD 5½R

Fig. 2. Comparison between estimated and actual process output under a pulse change in reboiler heat input [Here, xD,4 denotes the distillate composition of component 4 (i.e., H2O) and VnT ynT ;4 the vapor flow rate of component 4 leaving topmost tray].

6.1. Estimator performance

It is important to mention at this point that we have considered two different values of l since the dynamics of xD,j and VnT ynT ;j are not same. The tuning parameter values l1 and l2 are selected as 11.53, and 3.0, respectively, using a trial and error approach.

In this open-loop test, we investigate the performance of the HGO in the presence of a large initialization error by introducing bn b values of b x D;j and V y nT ;j to zero, that creates a huge difference T from their nominal values. With this, the two consecutive step changes are introduced in the external heat input to the reboiler. The first step change is incorporated at time ¼ 10 h by increasing (10%) the heat input from 3.0  106 to 3.3  106 kW, and then decreasing it from 3.3  106 to 3.0  106 kW at time ¼ 13 h. The tracking performance of the HGO is depicted in Fig. 2. In spite of the presence of large initialization error, the performance of the estimator is quite satisfactory.

6. Simulation results

6.2. Comparative control performance

In this section, we investigate the closed-loop performance of the proposed HGO-based EGMC control scheme. To achieve this, first we analyze the open-loop performance of the estimator, which serves as an integral part of the proposed control scheme. Subsequently, we also present the closed-loop performance of the aforementioned control structure and compare it with a traditional PI controller.

In this section, we evaluate the performance of the proposed nonlinear EGMC controller by comparing it with a traditional PI2 controller. In the present case, the desired set point is fixed at 99.32 mol%, which is the steady state distillate composition. We

0 (13)

2

Tuning parameter values KC ¼ 10.89, tI ¼ 0.01 h.

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65

Table 2 Comparative performance of dynamic VRBRR under the same product composition and same amount of distillate collected.

Average product composition, mol% Start-up period, h Production period, h Batch time, h Total distillate collected, kmol

Average product composition, mol% Start-up period, h Production period, h Batch time, h Total distillate collected, kmol

Dynamic VRBRR

Dynamic VRBRR

(PI)

(HGO-based EGMC)

99.32 7.92 4.7 12.62 89.84

99.32 7.92 6.32 14.24 119.99

Dynamic VRBRR

Dynamic VRBRR

Dynamic VRBRR

(Open-loop)

(PI)

(HGO-based EGMC)

73.5

97.88

99.32

7.99 5.96 13.95 119.99

7.92 6.28 14.20 119.99

7.92 6.32 14.24 119.99

also employ a PI3 controller to control the reflux drum hold-up (mD).

Fig. 3. Comparative transient profile of the dynamic VRBRR under conventional PI and HGO-based EGMC controller: (A) constant composition control, and (B) reflux rate profile.

6.2.1. Performance under equal composition As shown in Fig. 3(A), to maintain the same product composition (99.32 mol%), the PI controller needs to operate up to 12.62 h, whereas the HGO-based EGMC is capable of maintaining the abovestated composition up to 14.24 h of the batch operation. In this connection, Fig. 3(B) depicts the corresponding manipulated variable profile. One can observe that with the gradual decrease of process gain after their aforementioned periods of time, both the controller exhibit similar type of trend in its manipulated variable by a sudden rise of its value, indicating that the water is almost disappeared in the column. This simulation experiment is further analyzed in Fig. 4 and Table 2 under equal composition control. Obviously, the closed-loop HGO-based EGMC controller is superior in terms of the amount collected as distillate (i.e., 119.99 kmol) over the PI controller that leads to collect a 34.5% less amount of distillate (i.e., 89.24 kmol). 6.2.2. Performance under equal amount of distillate collection Under this mode of operation, we compare the performance of both the controllers having an equal amount of distillate (119.99 kmol) collected after the batch time of about 14.24 h. It is interesting to observe that to obtain the higher amount of distillate collection, the average product purity under closed-loop conventional PI controller drastically decreases to 97.88 mol%, as shown in Fig. 4 and Table 2. On the other hand, the HGO-based EGMC is capable of proving its superiority by maintaining the constant product composition (99.32 mol%) throughout the entire batch operation yielding an equal amount of distillate collected. In this regard, one can note the ISE values as 6.06  106 and 4.48  108 for PI and HGO-based EGMC, respectively. 6.3. Improvement in energetic and economic performance Fig. 5 shows a detailed cost comparison of dynamic VRBRR between the PI and the HGO-based EGMC. For the case of HGO-based EGMC controller, the TAC, CI and OC [21] are $210636.2213, $433296.19 and $66204.158, respectively. For the conventional PI

Fig. 4. Product purity verses amount of distillate collected.

3

Tuning parameters obtained for reflux drum KD ¼ 0.007, tD ¼ 0.04 h.

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S. Banerjee, A.K. Jana / Energy 115 (2016) 60e66

Scientific and Industrial Research (CSIR), India, Grant No. 22(0509)/ 10/EMR-II.

References

Fig. 5. Comparative economic and energetic performance.

controller, the corresponding values are $221788.196, $444917.42 and $73482.39, respectively. It clearly indicates that the HGO-based EGMC overperforms the conventional PI controller with giving a comparatively less payback time (1.16 years for HGO-based EGMC and 1.27 years for PI) and more energy savings (73.758% for HGObased EGMC and 73.527% for PI). 7. Conclusions In this communication, we develop a nonlinear control scheme for a vapor recompressed batch reactive rectifier that produces nbutyl acetate. At first, for the proper utilization of internal heat source, apart from compression ratio, we additionally manipulate the auxiliary heat input to the still pot for the open-loop VRBRR. Then a high gain observer is developed to formulate the nonlinear EGMC control law for the dynamic VRBRR. Showing a satisfactory state estimation performance, the HGO-based EGMC controller is applied on the heat integrated batch column to show its superiority over the conventional PI controller in terms of purity and the amount of distillate collected. Further, the proposed VRBRR shows its ability to provide 73.527 and 73.758% energy savings, and a payback period of 1.27 and 1.16 years for its closed-loop configuration with PI and that with HGO-based EGMC, respectively. It is clear from the simulation results presented in this communication that the proposed HGO-based EGMC controller outperforms the conventional PI. Acknowledgement The authors acknowledge the grant awarded by the Council of

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