Internally heat integrated batch distillation: Vapor recompression and nonlinear control

Internally heat integrated batch distillation: Vapor recompression and nonlinear control

Accepted Manuscript Internally heat integrated batch distillation: Vapor recompression and nonlinear control Sudip Banerjee, Amiya K. Jana PII: DOI: R...

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Accepted Manuscript Internally heat integrated batch distillation: Vapor recompression and nonlinear control Sudip Banerjee, Amiya K. Jana PII: DOI: Reference:

S1383-5866(17)31200-5 http://dx.doi.org/10.1016/j.seppur.2017.08.003 SEPPUR 13945

To appear in:

Separation and Purification Technology

Received Date: Revised Date: Accepted Date:

14 April 2017 24 July 2017 1 August 2017

Please cite this article as: S. Banerjee, A.K. Jana, Internally heat integrated batch distillation: Vapor recompression and nonlinear control, Separation and Purification Technology (2017), doi: http://dx.doi.org/10.1016/j.seppur. 2017.08.003

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Internally heat integrated batch distillation: vapor recompression and nonlinear control Sudip Banerjee and Amiya K. Jana Energy and Process Engineering Laboratory, Department of Chemical Engineering, Indian Institute of Technology − Kharagpur, India−721302

Abstract

This work proposes a vapor-recompressed heat integration scheme in batch distillation column and its nonlinear control. For this, first a thermal coupling is made to form a heat integrated batch distillation column (HIBDC). To further improve energetic and economic potential, a mechanical heat pump system is introduced in the HIBDC, which gives rise to the vapor-recompressed HIBDC (VRHIBDC). For a ternary hydrocarbon system, this VRHIBDC exhibits superiority in the aspects of energy savings and economic performance over the HIBDC with respect to the conventional batch distillation column (CBDC). Aiming to achieve a constant product composition and to collect higher amount of distillate from the VRHIBDC column, an extended generic model controller (EGMC) is formulated. To obtain the state information required for this model-based controller simulation, two nonlinear observers, namely high gain observer (HGO) and extended Kalman filter (EKF), are devised and then coupled with the EGMC, yielding the EGMC-HGO and EGMC-EKF, respectively. To avoid the design complexity and computational load, both the observers are designed based on only the component mole balance equation around the reflux drum. The open-loop performance of the EKF shows its superiority over the HGO for the same example system. Subsequently, the comparative closed-loop performance is evaluated between the EGMC-HGO and EGMCEKF with respect to a traditional proportional-integral (PI) controller. It is investigated that the EGMC-EKF shows the best result followed by EGMC-HGO.

Keywords: Internal heat integration; vapor recompression; multicomponent batch distillation; energy savings; economics; nonlinear control



Corresponding author: Tel. +91 3222 283918, Fax: +91 3222 282250. E-mail address: [email protected].iitkgp.ernet.in (A. K. Jana).

1

1. Introduction Energy integration has emerged as a promising approach to save energy1 as well as to reduce emission level of the greenhouse gases.2 There are various means of integration, starting from innovating the new energy efficient technology to the retrofitting of an external thermal arrangement in the existing unit. Distillation is one such old separation unit, where there lies immense scope of exploring the feasibility of energy integration.3 The motivation behind choosing this separator lies in its extensive use of thermal energy in an inefficient way. There are typically two types of heat integration scheme developed for distillation column, namely internal4 and external heat integration.5 The former approach includes an internally heat integrated distillation column (HiDiC)6 and divided-wall column (DWC),7 whereas the later one includes the vapor recompression technique,8-10 in which, the top vapor is compressed before utilizing it in bottom liquid reboiling. This compression is done to extract the latent heat of that vapor so that the energy requirement in the reboiler supplied from the external source gets reduced. Johri et al.11 have first configured this vapor recompression (VRC) scheme for batch distillation column. Jana and his coworkers12 have further evaluated this configuration13 with hybridizing it with a batch tower surrounded by a jacketed reboiler. This apart, there are a couple of studies14-16 reported to improve the performance of the VRC heat pump. Very recently, an internally heat integrated batch distillation column (HIBDC) is proposed17 and this work introduces vapor recompression in it to form the vapor recompressed HIBDC (VRHIBDC). Being non-stationary and nonlinear in nature, it is really difficult to control such energy integrated batch distillation column. There are a few communications available that deal with the nonlinear control of the heat integrated column operated in continuous mode.18,19 Interestingly, it is rare to have control structures20-23 for the heat integrated batch column. However, till now, there is no control system developed for the HIBDC and thus the present work has been undertaken. In this contribution, vapor recompression is introduced in the HIBDC. Simulating a ternary system, the proposed VRHIBDC is shown to be superior over the HIBDC scheme with respect to its conventional scheme in the aspects of energy savings and cost. Further, with the aim of achieving a constant product purity of the VRHIBDC, an extended generic model controller (EGMC) is formulated. This nonlinear controller is coupled separately with two nonlinear state observers, namely high gain observer (HGO)24 and extended Kalman filter (EKF),25 forming the EGMC-HGO and EGMC-EKF, respectively. The purpose of using a 2

state observer is to estimate the unmeasured states required for controller simulation. A comparative closed-loop control study is performed based on the performance criteria, namely constant composition control of the product. It should be stressed that unlike the conventional form of HGO and EKF, they are formulated here with a single modelling equation that is obtained by making a component balance around the condenser. This leads to reduce the degree of complexity and computational error at the expense of modelling uncertainty. With this, both the hybrid control systems are evaluated with reference to a conventional proportional integral (PI) controller. 2. Developing vapor-recompressed heat integrated batch distillation column This section presents the progressive development of the proposed vapor-recompressed heat integrated batch distillation column (VRHIBDC). 2.1. Conventional batch distillation column (CBDC) The conventional batch distillation column (CBDC) is first loaded with a fresh feed mixture. Introducing heat to the reboiler, it is allowed to run at total reflux until the steady state is reached. The time required to attain the steady state from the beginning of batch operation is termed as the start-up period. Subsequently, the product withdrawal begins in partial reflux mode. The time required to collect the product is called the production period. The combination of these two phases (start-up and production phase) leads to the total batch time. It should be noted that one is free to withdraw the product as soon as it meets the desired purity. 2.2. Heat integrated batch distillation column (HIBDC) For the sake of internal heat integration, the CBDC column is divided into two parts (as shown in Fig. 1), namely top and bottom section. A section consisting of a couple of bottom trays and the reboiler is termed as the bottom section, whereas the top section comprises of rest of the trays along with the overhead condenser. The HIBDC column is developed with a compressor at the top of the bottom section and it is used to compress the top vapor before feeding it at the bottom tray of the top section. This clearly increases the temperature of the top section thereby creating a driving force in between the two sections. With the intention of exchanging heat between these two diabatic sections, a couple of intermediate heat exchangers are installed. For pressure recovery, the liquid coming out from the bottom of the top section is flashed back to the top of the bottom section through a throttling valve. 3

2.3. Vapor-recompressed heat integrated batch distillation column (VRHIBDC) In the HIBDC, there is a scope of having the overhead vapor of top section (heat source) at higher temperature than the liquid of bottom section (heat sink). If not, the temperature difference between the heat source and sink is not so significant, and one can use a compressor to maintain a desired thermal driving force (i.e., here 20 K) under the VRC scheme. The introduction of VRC in the HIBDC yields the VRHIBDC, which is depicted in Fig. 2. The thermal driving force depends on the intensity of compression made in the HIBDC column. Based on this existing driving force, one needs to choose whether the VRHIBDC would be arranged with one or two compressors. Accordingly, the following two schemes are formulated: Scheme 1: Under this scheme, it is proposed to use a single and same compressor in both the HIBDC and VRHIBDC columns. The target is fixed such that a single compressor of the HIBDC should attain a desired thermal driving force (i.e., 20 K) between the said overhead vapor and reboiler liquid of the VRHIBDC scheme. It clearly indicates the requirement of a reasonably large CR but avoiding the necessity of second compressor. Scheme 2: This scheme accompanies two compressors, one for the HIBDC and second one for the vapor recompression. Installation of a second compressor is suggested for the purpose of maintaining a thermal driving force of 20 K between the overhead vapor of top section and reboiler content of bottom section. By this way, one can choose a reasonably low CR for each of the compressors. More importantly, unlike the single compressor-based VRHIBDC, this dual compression scheme does not require to operate the top section at so high pressure. 3. Mathematical modelling of the process To perform the process modelling, the column is divided into three parts, namely tray tower, compressor and intermediate heat exchanger. Following assumptions26 are considered for the development of the model: A1 Perfect mixing and equilibrium on all stages A2. Vapor holdup is negligible compared to liquid holdup, which varies in each tray A3. Fast energy dynamics

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3.1. Tray modelling Fig. 3 depicts a sample nth tray and associated streams. The governing equations are as follows: Total mole balance dmn  Ln 1  Vn 1  Fn  ( Ln  SnL )  (Vn  SnV ) dt

(1)

Component (i) mole balance d (mn xn, i ) dt

 Ln 1xn 1, i  Vn 1 yn 1, i  Fn zn, i  ( Ln  SnL ) xn, i  (Vn  SnV ) yn, i

(2)

Energy balance d (mn H nL )  Ln 1H nL1  Vn 1H nV1  Fn H nF  ( Ln  SnL ) H nL  (Vn  SnV ) H nV  Qn dt

(3)

Equilibrium

yn, i  kn, i xn, i

(4)

Summation NC

x i 1

n, i

NC

y i 1

n, i

1

(5)

1

(6)

In the above modelling equations, F stands for the feed flow rate, H L the enthalpy of the liquid stream, H V the enthalpy of the vapor stream, k i the vapor-liquid equilibrium coefficient for the i th component and m the molar liquid holdup. The symbol N C represents the number of associated components. Here, Qn indicates the amount of heat loss from n th L V tray, and it is assumed to be negligible (i.e., Qn  0 ). S and S indicate the side streams of

liquid and vapor, respectively, and xi and yi the liquid and vapor phase mole fraction, 5

respectively. The composition of the feed component is represented by zi . Since, this is a batch distillation column, the feed flow rate (F ) and bottom product flow rate are taken to be zero. In the above equations, L and V represent the flow rates of liquid and vapor streams, respectively. 3.2. Modelling of compressor Let us first represent the compression ratio (CR ) , which is an important parameter for the evaluation of compressor duty27, as:

CR 

PnoC PniC

 Tn C  o  Tn C  i

   

 /(  1)

(7)

In the above expression, PniC and TniC represent the pressure and temperature of the vapor entering into the compressor, respectively. The pressure and temperature of the compressed vapor are denoted as PnoC and TnoC , respectively. The symbol  represents the polytropic coefficient, and the following equation is used for its calculation27 NC y 1  i   1 i1 i  1

(8)

Following represents the compressor duty (QComp ) 27  1  VnoC RTniC   QComp  (CR )  1   1  

(9)

In the above equation, VnoC denotes the molar flow rate of the compressed vapor and R the universal gas constant. 3.3. Modelling of intermediate heat exchangers Following gives the modelling equations of the internal heat exchangers installed to exchange heat in between two diabatic sections of the distillation column: N

QI   QI ,n

(10)

n 1

6

with

QI ,n  U n An T n

(11)

For a nth tray, QI represents the total amount of heat exchanged through internal heat exchangers, N the total number of heat exchangers, U the overall heat transfer coefficient, A the area of heat transfer and T the thermal driving force. For the said nth tray, following correlations are used:17 Bottom section

Vn 

QI , n

(12)

(i 1 yi i ) n NC

Top section

Ln 

QI , n

(13)

(i 1 xi i )n NC

Here,  denotes the molar latent heat of vaporization. 4. Energetic and economic performance This section presents two performance indicators, namely energy savings and total annual cost (TAC), and both are briefly presented below. 4.1. Energy savings The following equation17 is used to calculate the total energy supplied to a batch distillation column from external sources ( QCons ):

QCons  QR  f QComp

(14)

In the above, QR denotes the reboiler duty and QComp the compressor duty that is zero for CBDC. The multiplication factor f possesses a value of 3 as suggested by Iwakabe et al.28 This is because 3 kW of thermal energy is assumed for producing 1 kW of electrical power.

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The following equation provides the estimation of percent energy savings for both the HIBDC and VRHIBDC: CBDC HIBDC / VRHIBDC QCons  QCons % Energy savings   100 CBDC QCons

(15)

4.2. Total annual cost The overall performance of the two columns (HIBDC and VRHIBDC) is proposed to evaluate in terms of the total annual cost (TAC), which comes from the summation of yearly operating cost (OC) and capital investment (CI) per payback period (PP). It is represented as:

TAC  OC 

CI PP

(16)

Based on the formulas given in Table 1,27 the capital investment is to be calculated for the batch distillation column, which includes the column shell and trays, heat exchanger, condenser, reboiler, and compressor. The operating and utility costs are assumed identical28 for a year with about 8000 operating hours. A bhp (= hp/0.8) and 60% motor efficiency27 are taken into consideration while calculating the operating cost of the compressor. The utilities used are cooling water, electricity and low-pressure (LP) steam having unit costs15 of $0.06/t, $0.084/kW.h and $17/t, respectively. Here, a payback period of 3 years is adopted. 5. Nonlinear control scheme In this section, the nonlinear control scheme is devised for the vapor-recompressed heat integrated batch distillation column (VRHIBDC) to achieve constant purity of the products. This control scheme comprises of the extended generic model controller (EGMC) and a state observer. Here, the two state observers are used, namely high gain observer (HGO) and extended Kalman filter (EKF). Based on their coupling with the EGMC, they form the EGMC-HGO and EGMC-EKF, respectively. Following subsections provide the design equations of the EGMC controller followed by state observers. 5.1. Extended generic model controller (EGMC) The design equation of the EGMC controller has the following form:29

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L g1L1f 1h1    u       m 1 L g1L f hn



L gmL1f 1h1

   L gmLfm 1hm

1

        





 K11e1  K12 e1dt  L1f h1  1 L1f 1h1      11L0f h1  1            1  K m1em  K m 2  em dt  L fm hm   m m L fm hm       m1L0f hm



       

(17)



for the following nonlinear multi-input/multi-output (MIMO) system:

x (t )  f ( x, d ,  )  g ( x, d ,  ) u (t ) y(t )  h( x)

(18)

having a reference trajectory represented as: yi( i )   i i yi( i 1)  ........   2 i yi  1i yi  K1i ( yisp  yi )  K2 i  ( ysp i  yi )dt

(19)

Here, sp stands for the set point, and  i i ,............1i , K1i and K 2 i are tuning parameters of the controller. The state vector x(t )  n , the manipulated vector u  m , the output vector m y  m with h   , the process parameter vector   q and the disturbance vector d   .

l

There are three nonlinear functions involved, namely f (), g () and h() . In Eq. (17), L stands for the Lie derivative operator.30 It is important to mention here that the relative order  i is the smallest order of the derivative of y that explicitly depends on the vector u . For more details of the EGMC controller, one may consult the work of Banerjee et al.29 5.2. State observer To obtain the unmeasured state information needed for the EGMC controller simulation, one can use a state observer. Following subsections briefly highlight the two nonlinear state observers, namely high gain observer (HGO) and extended Kalman filter (EKF). 9

5.2.1. High gain observer (HGO) Farza et al.24 have proposed the high gain observer for the following nonlinear MIMO system:

x (t )  F ( x, d ) x  G( x, u, d )   (t )

(20)

y  Cx The HGO is derived to track the states as: xˆ  F ( xˆ, d ) xˆ  G( xˆ, u, d )     ( xˆ, d ) 1 S 1 C T C ( xˆ  x)    Corrector Predictor

(21)

The term   1 S 1 CT C is the gain of the observer. The purpose of this variable gain is to provide a dynamic correction of the residual (difference between the measured output and its predicted value). 5.2.2. Extended Kalman filter (EKF) The nonlinear EKF25 consists of a set of mathematical equations that form a predictorcorrector type observer. Based on the available measurements and predictions of a given model, the EKF provides an approximate optimal estimation value of the state vector. On the basis of the estimates of states at the present time step, let t k , the model predicts the future state vector

x(t k 1 / t k )  xk 1 / k at the time step t k 1 . Thereafter, it gets updated as

x(tk 1 / tk 1 ) ( xk 1/ k 1 ) at the time step t k 1 by using the updating algorithm. Following successive steps are adopted here to represent the EKF:25 Considering the following state-space representation of the model

x  f ( x, d , t )  w z  h ( x, t )  v

(22)

x(0)  ( x0 , P0 ), w(t )  (0, Q), v(t )  (0, R) where, z is the vector of the measured values, h the vector of the observations as predicted by the model from the state value xˆ . The first equation in Eq. (18) is represented by Eq. (22), in which, d includes the input variables, disturbances and imprecisely known parameters. In

10

Eq. (22), w and v represent the zero-mean white noise processes, and assuming these are uncorrelated with x(0) and each other. The initial condition is given by P(0)  P0 , xˆ (0)  x0 and

f ( x, d , t ) represents the

mathematical model. The predicted value of the state at tk 1 , x(tk 1 / tk )  xk 1/ k is obtained from the integration of the above equation from t k to t k 1 . Equation for state estimate update can be given as:

xˆ  f ( xˆ, d , t )  K [ z  h( xˆ )]

(23)

and K the gain matrix given by:

K  PH T ( xˆ, t ) R 1

(24)

In the above equation, H is the linearized observation matrix and R the covariance matrix of the measurement errors. The H can be represented in the following form

H ( xˆ, t ) 

hi ( xˆ, t ) x

(25)

Finally, the updated value of the error covariance matrix can be obtained from the following equation: P  f x P  Pf xT  Q  KRK T

where,

(26)

f x indicates the Jacobian of the predictor model and Q the model error covariance

matrix. One can have a quick idea about the operation of the EKF from Fig. 4. 6. Example A ternary hydrocarbon system is simulated to illustrate the proposed schemes. It consists of cyclohexane, n-heptane and toluene having boiling points of 353.74, 371.42 and 383.6 K, respectively. Being the most volatile component, the cyclohexane comes out first as distillate from the top of the column. Following subsections involve the development of the HIBDC and the proposed VRHIBDC column starting from its conventional counterpart for the present system.

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6.1. Conventional batch distillation column The CBDC consists of total twelve trays (excluding overhead condenser and bottom reboiler), counting from the bottom with a stage pressure drop of 0.003 atm. Detailed operating conditions and column specification are provided in Table 2. It should be pointed out that the liquid phase activity coefficient and tray hydraulics are calculated using the Hildebrand regular solution model and nonlinear Francis weir formula, respectively. Here, a Murphree plate efficiency of 90% is considered. The distillate flow rate during production period is maintained at 30 gmol/min. The amount of heat consumed (QCons ) to run this CBDC column is 1.57 108 kJ. As depicted in Fig. 5, the maximum purity achieved for cyclohexane and n-heptane are 99.3 and 84.01 mol%, respectively with the corresponding start-up period of 700.92 and 2565.06 min, and production period of 387.78 and 656.88 min. It should be noted that the maximum purity corresponds to the steady state condition that attains within a time period, called start-up period. On the other hand, the time period, during which the product is withdrawn, is called the production period. 6.2. Heat integrated batch distillation column To develop the HIBDC column, as stated, the CBDC column is divided into two sections, bottom and top section. Excluding the bottom reboiler, there are total six trays (counting from the bottom) present in the bottom section, whereas the top section consists of an equal number of trays along with the overhead condenser (shown in Fig. 1). The detail component compositions achieved in separating the example hydrocarbon mixture under the HIBDC are provided in Table 2. A parametric sensitivity analysis is conducted here to obtain the operating CR ( 2.5) on the basis of the minimum TAC as shown in Fig. 6. This CR leads to create a thermal driving force as evident from the tray temperature profile shown in Fig 7. Based on this simulation, it is justified to install total six internal heat exchangers in between the two diabatic sections that to be connected as: 1-7, 2-8, 3-9, 4-10, 5-11 and 6-12. Performing a sensitivity test, similarly we select the UA of 2510.4 kJ/s.K.stage with fixing CR at 2.5 as demonstrated in Fig. 8. For calculating heat transfer area (A) of the heat exchanger required in cost estimation, the U is adopted as 1.146 kJ/s.K.m2.stage [31]. With this, the composition dynamics of the HIBDC is produced in Fig. 5 in comparison with that of CBDC, showing a reasonably close profile. Table 2 reports the detailed 12

simulation results. The total heat consumed by this HIBDC is obtained as 1.06 108 kJ. This gives to an energy savings of 32.71%. Similarly, a detailed cost analysis is carried out in Table 3. It is evident that the HIBDC achieves a 26.14% savings in operating cost but the capital cost increases about 1.67 times. Overall, the heat integration provides a 3% savings in TAC with a payback period of 2.53 year. 6.3. Vapor-recompressed heat integrated batch distillation column Here, a vapor recompression system is devised to introduce in the HIBDC for the example ternary system. For this, Scheme 1 that suggests the use of same compressor for both the HIBDC and VRHIBDC is adopted. For the example system, attempt is made to ensure a thermal driving force of at least 20 K between the thermally coupled overhead vapor of the top section and reboiler liquid of the bottom section. With this, the amount of heat consumption

(QCons ) gets reduced to 3.88 107 kJ, securing a significant increase in energy savings (75.34%) as compared to HIBDC column (32.71%). As far as economic performance is concerned, the proposed VRHIBDC as shown in Table 3 outperforms the HIBDC in the aspects of operating cost (savings = 44.06%) and TAC (savings = 18.54%). As a consequence, this novel scheme provides the lowest payback time of 1.32 year. 7. Control schemes This section deals with the development of a nonlinear control system that to be evaluated for the sample ternary system with respect to a PI controller. It should be noted that the control objective is to maintain the distillate product ( xD ) with the adjustment of reflux rate ( RT ) .

7.1. Nonlinear control As stated, this nonlinear control scheme consists of the EGMC and a state observer, which are designed below. 7.1.1. Extended GMC Using the design equation of the EGMC controller (Eq. (17)), the controller equation for the VRHIBDC column is obtained for the ternary system as:

13

t   VnT ynT , i  mD xD , i  mD  K1e  K 2  edt  0  D RT  xD , i

(27)

Here, e is the error signal to the controller, and it can be expressed as e  xDsp, i  xD, i , where

xD , i and xDsp, i are the distillate compositions of component i ( i  1 for cyclohexane and i  2 for n-heptane) and its set point value, respectively.  , K1 and K 2 are the tunable parameters of the EGMC1 controller, mD the molar hold-up of the reflux drum and D the distillate rate. Here, xD , i is assumed as a measured quantity. It should be noted that here K i1 and K i 2 are replaced by K1 and K 2 . The derivation of controller Eq. (27) is shown in the Appendix. 7.1.2.

State observers

For closed-loop controller simulation, one needs the information of the component vapor flow rate ( VnT ynT ,i ) leaving the top tray (nT ) at each and every time step as evident from Eq. (27). For this, there is a need to estimate it by the use of a state observer and provide the estimated value to the controller. Following provides the development of the two state observers proposed to couple with the EGMC controller. 7.1.2.1. High gain observer The design equation of the predictor for the example VRHIBDC is given as:

 dxD , i 1  dt  m [VnT ynT , i  ( D  RT ) xD , i ]  D   d (VnT ynT , i ) 0  dt

(28)

Here, VnT ynT , i (where i  1, 2 ) and xD , i represent the augmented and true state, respectively. The final form of the HGO is represented as follows:

Tuning parameters are selected as   1.8E  10 , K1  10.00025 , K 2  7.0 E  5 based on the integral square error performance criterion. 1

14

 dxˆ D , i     D dt  ˆ    mD  d (VnT yˆ nT , i )   0    dt

1  xˆ  x   D , i   D , i   21     R  mD   ˆ m  T 2 m xˆ D ,i  xD ,i  D   VnT yˆ nT , i    2 D 0   0 

(29)

 21  It should be noted that  2  denotes the variable gain of the HGO with 1 and 2 selected 2 mD  as 20.0 and 1.2, respectively.

7.1.2.2. Extended Kalman filter In the EKF, the gain matrix K corrects (with an additive term) the model-based state prediction according to the error between the actual measurement and the value predicted by the model. The performance of EKF is greatly dependent on the proper selection of the two parameters, namely process noise covariance (Q) and measurement noise covariance (R) . The following parameter values are selected for this EKF as: Q11  1.5 106 , Q12  0.0,

Q21  0.0, Q22  2.5 10 5 and R  0.6 . 7.2. Proportional Integral (PI) control To evaluate the performance of the EGMC controller, a traditional proportional-integral (PI) controller is designed aiming to achieve the constant product purity. The PI controller is expressed as: t   1  RT  RS  K C  e   edt   I 0 

(30)

where, RT and RS denote the reflux rate and its bias signal, respectively. K C and  I are the two tuning parameters and they are selected as 17.0 and 0.3 min, respectively. At this point, it should be highlighted that a PI controller is used to maintain the liquid holdup in the reflux drum with K D  1.2 and  D  500 min. 7.3. Control performance

15

This section first evaluates the open-loop performance of the two observers, namely HGO and EKF. Then a comparative closed-loop performance is presented between the EGMCHGO and EGMC-EKF with reference to the PI controller. 7.3.1. Performance of the observers In addition to estimating the augmented state vector, VnT ynT , i the observers estimate the true state xD , i . To investigate the comparative performance between the said observers, an initialization error is introduced in the following two studies with setting 0 to both VˆnT yˆ nT , i and xˆD , i , which denote the estimated values of VnT ynT , i and xD , i , respectively. At this point, it should be noted that i  1 is used for cyclohexane and i  2 for n-heptane throughout.

A pulse change in reboiler heat input In the next study, the two consecutive step changes are introduced in heat input to the reboiler. These are 33472 to 35480.32 kJ/min at time = 1000 min and then 35480.32 to 33472 kJ/min at time = 1500 min. As shown in Fig. 9, even though the performance of both the state observers is quite satisfactory, minute observation will bring in notice the superiority of the EKF compared to the HGO. 7.3.2. Performance of the control systems In the present study, the composition of the two distillate components (cyclohexane and nheptane) is to be controlled for the proposed VRHIBDC through the manipulation of reflux rate ( R ). For this, the first product (i.e., cyclohexane) withdrawal is started as it meets the desired product specification ( xD ,1 = 98.78%). As the product purity of the cyclohexane ( i  1 sp

) falls from the set point, the controller is switched off until the intermediate product (i.e., nheptane ( i  2 )) reaches the desired purity ( xD , 2 = 84.87%). During this period, the slop-cut is sp

collected in a separate tank. Constant purity control To evaluate the nonlinear control scheme, the proposed VRHIBDC is to be operated with a constant distillate composition. As stated, the first product enriched with cyclohexane is aimed to collect with 98.78 mol% purity, whereas the next product enriched with n-heptane is 16

set at 84.87 mol% purity. With this, we produce Fig. 10, comparing the EGMC-HGO, EGMC-EKF and PI controller. In this regard, Table 4 provides comparative simulated data. It is evident that the EGMC-EKF controller leads to provide maximum distillate production compared to the other two schemes. Here, one can observe a similar trend for both the EGMC controllers. Obviously, the EKF based EGMC controller shows the best performance followed by the EGMC-HGO and this is confirmed through the integral square error (ISE) documented in Table 5. 8. Conclusions This work proposes vapor recompression in a heat integrated batch distillation and its nonlinear control for maintaining constant distillate composition. For a ternary hydrocarbon system, it is investigated that the vapor recompressed heat integrated batch distillation column (VRHIBDC) secures a significant energy saving ( 75.34%) compared to its internal heat integrated counterpart (i.e., HIBDC) that shows an energy savings of 32.71% with respect to a conventional batch column. As a consequence, the proposed VRHIBDC provides a least payback time of 1.32 year. In the subsequent part, a nonlinear control system, consisting of the extended generic model controller (EGMC) and a state estimator, is synthesized for the vapor recompressed heat integrated batch distillation column. Here, two state observers, namely high gain observer (HGO) and extended Kalman filter (EKF), are formulated to estimate the unmeasured state based on a single equation that is derived by making component balance around the condenser-reflux drum system. This leads to make the estimator design simple but at the expense of modelling uncertainty. With this, the EKF shows a better tracking performance than the HGO. Finally, although a better closed-loop performance is delivered by the EGMCEKF than the EGMC-HGO, the EGMC controller shows its superiority over the conventional PI controller in constant composition control.

17

Appendix

Derivation of Eq. (27) The reference trajectory (Eq. (19)) can be expressed as:





yi i   i i yi i 1  ........   i 2 y i   i1 yi  K i1ei  K i 2  ei dt  0

(A1)

It is quite simple to find the relative order for the sample distillation as one (   1 ). Accordingly, the above equation reduces to the following form:





y i   i1 yi  K i1ei  K i 2  ei dt  0

(A2)

Here, yi  xD,i and thus,





x D,i   i1 xD,i  Ki1ei  Ki 2  ei dt  0

(A3)

A component balance equation around the reflux drum gives the following expression: d (mD xD ,i ) dt

 VnT ynT ,i  ( RT  D) xD ,i

(A4)

Since, mD is maintained constant by a level controller, Eq. (A4) yields,

mD

d ( xD,i )  VnT ynT ,i  ( RT  D) xD ,i dt



d ( xD ,i ) dt

 x D ,i 



VnT ynT ,i  ( RT  D) xD,i mD

VnT ynT ,i  ( RT  D) xD,i

(A5)

mD

Substituting Eq. (A5) into (A3) and rearranging, one obtains Eq. (27).

18

Nomenclature

Fn

feed input rate of a typical n th tray [mol/min]

f

a multiplication factor [dimensionless]

H nL

enthalpy of the liquid stream of a typical n th tray [kJ/mol]

H nV

enthalpy of the vapor stream of a typical n th tray [kJ/mol]

i

component [dimensionless]

kn , i

vapor-liquid equilibrium coefficient of i th component for a typical n th tray [dimensionless]

Ln

flow rate of liquid stream from a typical n th tray [mol/min]

mn

liquid holdup of a typical n th tray [mol]

nT

top most tray of the column [dimensionless]

NC

number of component [dimensionless]

PnT

pressure of the overhead vapor [atm]

PniC

pressure of the vapor before compression [atm]

PnoC

pressure of the compressed overhead vapor [atm]

QComp

the duty of electric compressor [kJ/min]

QCons

total energy supplied from the external source [kJ/min]

CBDC QCons

total energy supplied from the external source for CBDC [kJ/min]

HIBDC / VRHIBDC QCons

total energy supplied from the external source for HIBDC/VRHIBDC [kJ/min]

QR

reboiler heat duty [kJ/min]

QI

total heat exchanged through internal heat exchangers in between the two sections of the column [kJ/min]

RT

reflux rate [mol/min]

R

universal gas constant [kJ/mol K]

S nL

side stream withdrawn from the liquid coming out from a typical n th tray [mol/min]

S nV

side stream withdrawn from the vapor coming out from a typical n th tray 19

[mol/min]

TB

temperature of the reboiler liquid [K]

TnT

temperature of the overhead vapor coming out from the top most tray [K]

TnoC

temperature of the compressed overhead vapor [K]

T

thermal driving force between the two sections of the column [K]

UA

product of overall heat transfer coefficient with heat transfer area [kJ/min]

Vn

flow rate of vapor stream from a typical n th tray [mol/min]

VnT

overhead vapor coming out from the topmost tray [mol/min]

VniC

overhead vapor directed to the compressor [mol/min]

xi

liquid phase composition of component i [mol fraction]

yi

vapor phase composition of component i [mol fraction]

zi

feed composition of component i [mol fraction]

i

relative order of the process [dimensionless]



polytropic coefficient [dimensionless]



latent heat [kJ/mol]

n C

latent heat of the compressed vapor [kJ/mol]



payback period [year]

o

Abbreviations CBDC

conventional batch distillation column

CI

capital investment

CR

compression ratio

DWC

divided wall column

EGMC

extended generic model controller

EKF

extended Kalman filter

HiDiC

heat integrated distillation column

HIBDC

heat integrated batch distillation column

HGO

high gain observer

ISE

integral square error

MIMO

multi-input/multi-output

20

OC

operating cost

PI

proportional integral controller

PP

payback period

TAC

total annualized cost

VRC

vapor recompression

VRHIBDC

vapor-recompressed heat integrated batch distillation column

21

References [1] A. K. Jana, Bottom flashing with interreboiling action in a transient batch rectifier: economic feasibility, dynamics and control, Sep. Purif. Technol. 179 (2017) 320 – 327. [2] J. R. Alcántara-Avila, M. Kano, S. Hasebe, Multiobjective optimization for synthesizing compressor-aided distillation sequences with heat integration, Ind. Eng. Chem. Res. 51 (2012) 5911–5921. [3] S. Feng, X. Lyu, Q. Ye. H. Xia, R. Li, X. Suo, Performance enhancement of reactive dividing-wall column via vapor recompression heat pump, Ind. Eng. Chem. Res. 55 (2016) 11305-11314. [4] B. Kiran, A. K. Jana, A hybrid heat integration scheme for bioethanol separation through pressure-swing distillation route, Sep. Purif. Technol. 142 (2015) 307 – 315. [5] A. K. Jana, D. Maiti, Assessment of the implementation of vapor recompression technique in batch distillation, Sep. Purif. Technol. 107 (2013) 1-10. [6] A. A. Shenvi, D. M. Herron, R. Agrawal, Energy efficiency limitations of the conventional heat integrated distillation column (HIDiC) configuration for binary distillation, Ind. Eng. Chem. Res. 50 (2011) 119–130. [7] A. A. Kiss, R. M. Ignat, Innovative single step bioethanol dehydration in an extractive dividing-wall column, Sep. Purif. Technol. 98 (2012) 290 – 297. [8] K. J. Chua, S. K. Chou, W. M. Yang, Advances in heat pump systems: A review, Appl. Energy 87 (2010) 3611-3624. [9] D Bruinsma, S. Spoelstra, Heat pumps in distillation. In: Proc. Distillation and Absorption 2010, 12–15 September 2010, Eindhoven (NL), pp. 21–28. [10] G. Modla, P. Lang, Heat pump systems with mechanical compression for batch distillation, Energy 62 (2013) 403-417. [11] K. Johri, GUB Babu, A. K. Jana, Performance investigation of a variable speed vapor recompression reactive batch rectifier. AIChE J. 57 (2011): 3238-3242. [12] D. Maiti, A. K. Jana, A. N. Samanta, A novel heat integrated batch distillation scheme, Appl. Energy 88 (2011) 5221-5225. [13] T Takamatsu, A Tajiri, K Okawa, In: Proceedings of the chemical engineering conference of Japan, Nagoya (1998) 628–629. [14] M. A. Waheed, A. O. Oni, S. B. Adejuyigbe, B. A. Adewumi, D. A. Fadare, Performance enhancement of vapor recompression heat pump, Appl. Energy 114 (2014) 69-79.

22

[15] D. Maiti, A. K. Jana, A. N. Samanta, Intensified thermal integration in batch reactive distillation, Appl. Energy 103 (2013) 290-297. [16] G Modla, P. Lang, Vapour Compression for Batch Distillation: Comparison of Different Working Fluids, Ind. Eng. Chem. Res.54 (2015) 1081-1092. [17] A. K. Jana, A novel energy-efficient batch stripper: Thermodynamic feasibility, cost analysis and CO2 emissions, Appl. Therm. Eng. 84 (2015) 292-300. [18] Y. Fu, X. Liu, Nonlinear control based on wave model of high-purity heat integrated air separation column, Chemom. Intell Lab. Syst. 146 (2015) 1-9. [19] Y. Fu, X. Liu, Nonlinear dynamic behaviors and control based on simulation of highpurity heat integrated air separation column, ISA Trans. 55 (2015) 145-153. [20] A. K. Jana, An energy-efficient cost-effective transient batch rectifier with bottom flashing: process dynamics and control. AIChE J. 61 (2015) 3699 -3707. [21] G. U. B. Babu, A. K. Jana, Impact of vapor recompression in batch distillation on energy consumption, cost and CO2 emission: open-loop versus closed-loop operation Appl. Therm. Eng. 62 (2014) 365-374. [22] G. U. B. Babu, A. K. Jana, Reducing total annualized cost and CO2 emissions in batch distillation: dynamics and control AIChE J. 59 (2013) 2821-2832. [23] S. Banerjee, A. K. Jana, Dynamic vapor recompression in a reactive batch rectifier: analysis and nonlinear control. Energy 115 (2016) 60-66. [24] M. Farza, M. M’Saad, L. Rossignol, Observer design for a class of MIMO nonlinear systems, Automatica 40 (2004) 135–143. [25] A. K. Jana, A. N. Samanta, A hybrid feedback linearizing-Kalman filtering control algorithm for a distillation column, ISA Trans. 45 (2006) 87-98. [26] A. K. Jana, Chemical Process Modelling and Computer Simulation, second ed., PrenticeHall, New Delhi, 2011. [27] J. M. Douglas, Conceptual Design of Chemical Processes, McGraw-Hill, New York, 1988. [28] K. Iwakabe, M. Nakaiwa, K. Huang, T. Nakanishi, A. Røsjorde, T. Ohmori, A. Endo, T. Yamamoto, Energy saving in multicomponent separation using an internally heatintegrated distillation column (HIDiC), Appl. Therm. Eng. 26 (2006) 1362-1368. [29] S. Banerjee, A. K. Jana, High gain observer based extended generic model control with application to a reactive distillation column, J. Process Control 24 (2014) 235-248. [30] A. Isidori, Nonlinear Control Systems, 3rd ed., Springer Verlag, New York, 1995.

23

24

Figure Captions Fig. 1. Heat integrated batch distillation column (HIBDC). Fig. 2. Vapor-recompressed heat integrated batch distillation column (VRHIBDC) (Scheme 1). Fig. 3. An equilibrium n th stage. Fig. 4. Operation of the extended Kalman filter (EKF). Fig. 5. Comparative dynamics of CBDC and HIBDC column. Fig. 6. Selection of operating CR based on TAC and energy savings (%) at UA  41.76 kJ/min K stage. Fig. 7. Temperature profile of the HIBDC. Fig. 8. Selection of UA based on TAC and energy savings (%) at CR  2.5 . Fig. 9. Comparative observer performance under a pulse change in heat input to the reboiler with respect to (a) cyclohexane ( i  1 ) and (b) n-heptane ( i  2 ). Fig. 10. Comparative closed-loop performance.

25

Figures

Condenser

Compressor

Reflux drum Reflux Distillate HEX

6

12

HEX

5

11

4

HEX

4

10

3

HEX

3

9

2

HEX

2

8

1

HEX

1

7

6

5

Reboiler

Throttling valve

Steam

Fig. 1. Heat integrated batch distillation column (HIBDC).

26

Condenser

Compressor

Reflux drum Reflux Distillate HEX

6

12

HEX

5

11

4

HEX

4

10

3

HEX

3

9

6

5

2

HEX

2

8

1

HEX

1

7

Reboiler

Throttling valve

Throttling valve

Steam

Fig. 2. Vapor recompressed heat integrated batch distillation column (VRHIBDC) (Scheme 1).

27

Ln+1 xn+1,i

Vn yn,i

SnV , yn,i

Tray n (holdup= mn)

SnL , xn,i Ln

Vn 1

xn , i

yn 1,i

Fig. 3. An equilibrium n th stage.

28

Fn , zn,i

Time update (“Predict”)

Measurement update (“Correct”)

Step 1: System model and measurement model

Step 1: Update of estimate

Step 2: Computation of the Kalman gain Step 2: Initialization Step 3: Update of error covariance

Fig. 4. Operation of the extended Kalman filter (EKF).

29

1.2

xD, i (mol fract.)

1.0 0.8 0.6

CBDC cyclohexane n -heptane toluene HIBDC cyclohexane n -heptane toluene

0.4 0.2 0.0 0

1000

2000

3000

4000

3000

4000

xB, i (mol fract.)

Time (min)

1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

CBDC cyclohexane n -heptane toluene HIBDC cyclohexane n -heptane toluene

0

1000

2000

Time (min) Fig. 5. Comparative dynamics of CBDC and HIBDC column.

30

40

Energy savings (%)

35 30 25 20 15 10

5 0 1.7

1.9

2.1

2.3

2.5

2.7

2.9

CR 215000

210000

TAC ($/year)

205000 200000 195000 190000 185000 180000 175000 1.7

1.9

2.1

2.3 CR

2.5

2.7

2.9

Fig. 6. Selection of operating CR based on TAC and energy savings (%) at UA  41.76 kJ/min K stage.

31

Tray temperature (K)

425 420 415 410 405 400 395 390 385 380 375 370 365 360 355

HIBDC 1st tray 2nd tray 3rd tray 4th tray 5th tray 6th tray 7th tray 8th tray 9th tray 10th tray 11th tray 12th tray

0

1000

2000

3000

Time (min) Fig. 7. Temperature profile of the HIBDC.

32

4000

40

Energy savings (%)

35 30 25 20 15 10

5 0 8.3

16.7

25.1

33.5

41.8

50.2

UA (kJ/min.K.stage)

220000 215000 210000 TAC ($/year)

205000 200000 195000 190000 185000 180000 175000 170000 8.3

16.7

25.1

33.5

41.8

50.2

UA (kJ/min.K.stage)

Fig. 8. Selection of UA based on TAC and energy savings (%) at CR  2.5 .

33

a

1.2 Process HGO EKF

xD, 1 (mol fract.)

1.0 0.8 0.6 0.4 0.2 0.0 500

1000 1500 2000 2500 3000 3500 4000

Time (min)

200 Process HGO EKF

VnTynT, 1 (gmol/min)

150

100

50

0 500

1000 1500 2000 2500 3000 3500 4000

Time (min)

34

b

1.0

xD, 2 (mol fract.)

0.8 0.6 0.4 Process HGO EKF

0.2 0.0 500

1000 1500 2000 2500 3000 3500 4000

Time (min)

250

VnTynT, 2 (gmol/min)

200 150 100 Process HGO EKF

50 0 500

1000 1500 2000 2500 3000 3500 4000

Time (min) Fig. 9. Comparative observer performance under a pulse change in heat input to the reboiler with respect to (a) cyclohexane ( i  1 ) and (b) n-heptane ( i  2 ).

35

xD, i (mol fract.)

1.00 0.98

0.98800

0.96

0.98795 0.98790

0.94

0.98785

0.92

0.98780

0.90

0.98775

0.88 0.86

Set pt. 1 PI EGMC-HGO EGMC-EKF Set pt. 2 PI EGMC-HGO EGMC-EKF

0.98770 0.98765 0.98760 600

800

1000

1200

1400

1600

1800

0.84 0.82 0.80 500

1000 1500 2000 2500 3000 3500 4000

Time (min)

400

Reflux rate (gmol/min)

350

PI EGMC-HGO EGMC-EKF

300 250 200 150 100 500

1000 1500 2000 2500 3000 3500 4000

Time (min) Fig. 10. Comparative closed-loop performance.

36

Table 1. Cost estimating formulas27



M &S  1.066 0.802 Column shell : ($)   101.9Dc Lc (cin  cmc p )  280 

where Dc is the column diameter (ft), Lc is the column height (ft), M & S  950 and the coefficients cin  2.18 , cm  3.67 and c p  1.0 . 

M &S  1.55 Column tray : ($)    4.7 Dc Lc (cs  ct  cm )  280 

where the coefficients cs  1 , ct  1.8 and cm  1.7 

M &S  0.65 Heat exchanger : ($)   101.3 A (cin  cm (ct  c p ))  280 

where A is the heat transfer area (ft 2), and the coefficients cin  2.29 , cm  3.75 ,

ct  1.35 and c p  0 . 

 M &S  0.82 Compressor : ($)    517.5(bhp ) (2.11  Fd )  280 

where Fd  1.0 . This expression is valid in the range of 30  bhp  10,000

37

Table 2. Comparative operating conditions, column specification and component compositions Items System

CBDC

HIBDC

cyclohexane/n-heptane/toluene

cyclohexane/n-heptane/toluene

Total no. of trays

12

12

Murphree efficiency, %

0.9

0.9

Feed composition, mol fract. Total feed charge, kmol

0.4/0.4/0.2

0.4/0.4/0.2

80 (reboiler) +12 (trays) ×1.25+5

80 (reboiler) +12 (trays) ×1.25+5

(reflux drum)

(reflux drum)

30.0

30.0

0.75

0.75

Distillate rate, gmol/min (production phase) Column diameter, m Composition

reflux drum

reboiler

reflux drum

reboiler

at steady at the state end

at steady at the state end

at steady state

at the end

at steady state

at the end

cyclohexane

0.99302

0.03405

0.33473

6.0E-5

0.98776

0.0070

0.3263

1.0E-5

n-heptane

0.00692

0.8401

0.44184

0.5065

0.0121

0.8487

0.4482

0.5026

toluene

6.0E-5

0.1227

0.22343

0.4934

1.4E-4

0.1475

0.2255

0.4974

38

Table 3. Comparative energetic and economic performance

Item

CBDC

HIBDC

VRHIBDC

Column Shell

78194.28

78194.28

78194.28

Column Tray

8344.05

8344.05

8344.05

Condenser

25053.61

6405.53

0

Reboiler

44905.64

36689.52

30570.09

Compressor

0

53004.96

53004.96

Internal heat exchangers

0

78257.65

78257.65

156497.58

260895.99

248371.03

Heating steam

145160.16

106374.31

80337.46

Cooling water

12788.09

2269.62

0

Electricity

0

8011.05

8011.05

Total OC

157948.25

116654.98

88348.51

TAC, $/yr

210114.11

203620.31

171138.85

TAC savings,%

3.0

18.54

Payback time, yr

2.53

1.32

Capital investment, $

Total CI Operating cost (OC), $/yr

39

Table 4. Comparative performance of the closed-loop VRHIBDC under the same product composition VRHIBDC

VRHIBDC

VRHIBDC

(PI)

(EGMC-HGO)

(EGMC-EKF)

Average product composition, mol%

98.78

98.78

98.78

Start-up period, min

701.94

701.94

701.94

Production period, min

966.3

995.64

1006.8

1668.24

1697.58

1708.74

8.52

8.74

8.83

Average product composition, mol%

84.87

84.87

84.87

Start-up period, min

672.9

643.56

632.4

Production period, min

1124.12

1240.5

1259.16

Batch time, min

3465.26

3581.64

3600.3

11.8

12.34

12.52

Cyclohexane:

Batch time, min Total distillate collected, kmol n-heptane:

Total distillate collected, kmol

40

Table 5. Integral square error (ISE) for performance comparison

sp

ISE value ( xD ,1 ) (Fig. 10) sp

ISE value ( xD , 2 ) (Fig. 10)

EGMC-EKF

EGMC-HGO

PI

4.139E-09

1.046E-08

4.63E-07

1.02E-12

9.85E-11

5.25E-07



41

Highlights ● Introducing vapor recompression in a heat integrated batch column ● Thermal coupling made with developing internal heat exchangers ● Estimator-based nonlinear controller formulated for composition control ● Energy savings and total annual cost used as performance indicators

42