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Classical and Neural Network–Based Approach of Model Predictive Control for Binary Continuous Distillation Column

  • Amit Kumar Singh EMAIL logo , Barjeev Tyagi and Vishal Kumar
Published/Copyright: February 6, 2014
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Chemical Product and Process Modeling
From the journal Chemical Product and Process Modeling Volume 9 Issue 1

Abstract

The objective of present research work is to develop a neural network–based model predictive control scheme (NN-MPC) for distillation column. To fulfill this objective, an existing laboratory setup of continuous binary-type distillation column (BDC) is used. An equation-based model that uses the fundamental physical and chemical laws along with valid normal assumptions is validated for this experimental setup. Model predictive control (MPC) is one of the main process control techniques explored in the recent past for various chemical engineering applications; therefore, the conventional MPC scheme and the proposed NN-MPC scheme are applied on the equation-based model to control the methanol composition. In NN-MPC scheme, a three-layer feedforward neural network model has been developed and is used to predict the methanol composition over a prediction horizon using the MPC algorithm for searching the optimal control moves. The training data is acquired by the simulation of the equation-based model under the variation of manipulated variables in the defined range. Two cases have been considered, one is for set point tracking and another is for feed flow disturbance rejection. The performance of the control schemes is compared on the basis of performance parameters namely overshoot and settling time. NN-MPC and MPC schemes are also compared with conventional PID controller. The results show the improvement in settling time with NN-MPC scheme as compared to MPC and conventional PID controller for both the cases.

Keywords: model predictive control; neural network–based model predictive control; binary continuous distillation column

Acknowledgment

The authors wish to acknowledge the financial support of the Ministry of human resource and developments (MHRD), India under faculty initiation grant scheme with grant no. MHRD-03-29-801-108(FIG).

Appendix

Equation-based modeling

Dynamic simulation of distillation is characterized by stiff set of differential algebraic equations of material and efficiency equilibrium relationships. The dynamic model to be developed in this work is expected to meet the following objective: The model should be easy to use for the design of distillation column control schemes, online identification and optimization purposes.

To develop the equation-based model, the following information has been taken directly from the existing experimental setup of BDC:

  1. Liquid composition on each tray

  2. Liquid flow rates from each tray

  3. Temperature of each tray

  4. Condenser and reboiler duties

To simplify the model, the following assumptions have been considered [19]:

  1. The relative volatility α is constant throughout the column.

  2. The vapor–liquid equilibrium relationship can be expressed by

y=αx1+(α−1)x

where

  • α = Relative volatility

  • x = Composition of more volatile component in liquid, mole fraction,

  • y = Composition of more volatile component in vapor, mole fraction

  1. The overhead vapor is totally condensed in the condenser.

  2. The holdup of vapor is negligible throughout the system (i.e. the same immediate vapor response, dV1=dV2=⋯=dVN+1=dV), where N = total number of trays

  3. The molar flow rates of the vapor and liquid through the stripping and rectifying sections are constant:

    V1=V2=⋯=VN+1;
    L2=L3=⋯=LN+2

  4. Reboiler and condenser are also considered as a tray. Numbering of trays is done from the bottom, i.e. boiler is considered as a first tray and condenser is considered as a last tray. This means that if there is N number of trays then boiler is first tray and condenser is (N + 1)th tray.

Figure 21 Distillation column used in modeling
Figure 21

Distillation column used in modeling

Ist section

Component material balance equations

The constant molar holdup in reboiler has been considered, i.e. dMB/dt = 0, so by this

B=L1−VB

Component material balance around reboiler is given by

(4)MBdxB,jdt=L1x1,j−VByB,j−(L1−VB)xB,j

where

  • MB = Liquid molar hold up in reboiler, kmol,

  • L1 = Total liquid flow rate from tray-1 entering to reboiler, kmol/hr,

  • xB,j = Liquid fraction of component j in bottom product, % mole fractions,

  • VB = Total vapor flow rate leaving reboiler, kmol/hr,

  • yB,j = Vapor fraction of component j in bottom product, % mole fractions,

  • B = Total bottom product rate, kmol/hr,

The vapor fraction of component j from reboiler is given by

(5)yB,j=η1,jvk1,jxB,j

where

  • η1,jv = vaporization efficiency of component j in reboiler,

  • k1,j = Equilibrium constant of component j in reboiler

Total enthalpy balance equations

Total enthalpy balance equation for reboiler is given by

(6)MBdhBdt=L1h1−VBHB−(L1−VB)hB+QB

where

  • h1 = Total molar enthalpy of liquid entering from tray-1 to reboiler, kJ/kmol,

  • hB = Total molar enthalpy of liquid leaving reboiler, kJ/kmol,

  • HB = Total molar enthalpy of vapor leaving reboiler, kJ/kmol,

  • QB = Reboiler heat duty, kW

IInd section

In the second section, modeling for general ith tray is considered. Material balance and energy balance equations are obtained from this section.

Component material balance equations

Component material balance equation for ith tray is given by

(7)d(Mixij)dt=Li+1xi+1,j−Lixij−Viyij+Vi−1yi−1,j+FixFij
yij is calculated as
(8)yij=ηij(yij*−yi−1,j)+yi−1,j

where

  • Mi = Molar liquid hold up on tray i, kmol

  • xij = Liquid fraction of component j, leaving the tray i, % mole fraction

  • Li = Total liquid flow rate leaving tray i, kmol/hr

  • Vi = Total vapor flow rate leaving tray i, kmol/hr

  • Fi = Total feed flow rate injected to tray i, kmol/hr

  • xFij = Liquid fraction of component j in feed on tray i, % mole fractions,

  • yij = vapor fraction of component j leaving the tray i, % mole fractions,

  • ηij = Murphree stage efficiency based on vapor phase of component j on tray i

  • yij* = Equilibrium vapor fraction of component j on tray i

  • Li = is an additional variable and it is related to Mi through

(9)Li=3.33lw[Mi/(AnetMDi)−hw]3,6002.204MDi

where

  • lw = Length of the weir, ft

  • Anet = Net area of the tray, ft2

  • hw = Height of the weir, ft

  • MDi = Average molar density of liquid on tray i, kmol/ft3

Total material balance equation for ith general tray is calculated as

(10)dMidt=Li+1−Li−Vi+Vi−1+Fi

where

  • Li+1 = Total liquid flow rate entering to tray i, kmol/hr,

  • Vi–1 = Total vapor flow rate entering to tray i, kmol/hr,

  • Fi = Total feed flow rate injected on tray i, kmol/hr

Enthalpy balance equation for general tray i

Enthalpy balance equation for general tray i is given as

(11)d(Mihi)dt=Li+1hi+1−Lihi−ViHi+Vi−1Hi−1+FihFi

where

  • hi = Total molar enthalpy of liquid leaving tray i, kJ/kmol,

  • Hi = Total molar enthalpy of vapor leaving tray i, kJ/kmol,

    Enthalpy on any tray are calculated by mixing rule as given by

    (12)hi=∑j=1NChlijxij
    (13)Hi=∑j=1NCHvijyij

    where

  • hlij = Pure component enthalpy of component j in liquid, kJ/kmol,

  • Hvij = Pure component enthalpy of component j in liquid, kJ/kmol

Next section, i.e. IIIrd section produces the modeling of condenser.

IIIrd section

Component material balance equations

Reflux drum level is considered constant. This means at any time D = VNT − R

Component material balance around condenser is given by

(14)MDdxD,jdt=VNTyNT,j−VNTxD,j

where

  • MD = Liquid molar hold up in the reflux drum, kmol,

  • D = Distillate flow rate, kmol/hr,

  • xD,j = Liquid fraction of component j in reflux drum, % mole fractions

  • yNT,j = Vapor fraction of component j leaving tray NT, % mole fractions,

  • R = Total liquid flow rate entering to the tray NT from reflux drum, kmol/hr,

  • VNT = Total vapor flow rate leaving the tray NT, kmol/hr,

Enthalpy balance equation

The enthalpy balance equation for liquid and vapor for condenser is

(15)MDdhDdt=VNTHNT−VNThD−Qc

where

  • hD = Total molar enthalpy of liquid leaving the reflux drum, kJ/kmol,

  • HNT = Total molar enthalpy of vapor leaving the last tray NT, kJ/kmol,

  • QC = Condenser duty, kW

Figure 22 Simulation algorithm
Figure 22

Simulation algorithm

All the above equations have been used to develop the model. The flow diagram of the simulation algorithm to develop the equation-based model of BDC is given in Figure A.2 to simulate open-loop BDC the environment of Matlab®/Simulink® has been used.

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Published Online: 2014-2-6
Published in Print: 2014-6-1

©2014 by Walter de Gruyter Berlin / Boston

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https://doi.org/10.1515/cppm-2013-0013
Keywords for this article
model predictive control; neural network–based model predictive control; binary continuous distillation column

Articles in the same Issue

  1. Frontmatter
  3. Application of Finite Element Method for Modeling of Multi-tube Fixed Bed Catalytic Reactors
  4. Using a Fractional Experimental Design for the Study of the Tensile Strength of a Film of Polyethylene Plastic Degradable
  5. CFD Modeling and Experimental Study of a Spray Dryer Performance
  6. Computational Antioxidant Capacity Simulation (CAOCS): A Novel Framework of Antioxidant Capacity Profiling
  7. WPC Soft: Prototype Simulation Software to Predict the Internal Changes During Hot Pressing of Wood Plastic Composites
  8. Genetic Algorithm Approach to Optimize Biodiesel Production by Ultrasonic System
  9. Classical and Neural Network–Based Approach of Model Predictive Control for Binary Continuous Distillation Column
  10. Modeling, Simulation, and Configuration Improvement of Horizontal Ammonia Synthesis Reactor
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