Local Transient Model of a Pilot Plant Distillation Response

Transcription

1 Volume 114 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Local Transient Model of a Pilot Plant Distillation Response Vinayambika S. Bhat 1, S. Shanmuga Priya 2, I. Thirunavukkarasu 3, and R. Russell Rhinehart 4 1,3 Department of ICE 2 Department of CE, MIT, Manipal, Karnataka, India. 3 School of Chemical Engineering, Oklahoma State University, Stillwater, OK *Corresponding author: it.arasu@manipal.edu Abstract A description of the mathematical model of a pilot plant binary distillation column so developed is hereby presented. The binary mixture is composed of isopropyl alcohol and water. The steady state behaviour of the distillation column is used to identify the transfer matrix model. The obtained transfer matrix model is in the form of First Order Plus Time Delay (FOPTD). The open loop experimental test is conducted to identify the linear model of the pilot plant distillation column using leapfrogging technique. This technique is used here, to obtain the minimum root-mean-square deviation between the experimental and modelled data. The experimentation is performed by introducing small step change in the reboiler electric heater power and the responses of the tray temperatures are recorded in the MATLAB environment. Similarly, step change in the reflux flow rate is introduced to record the tray temperatures. Key Words and Phrases: Binary Distillation Column, Reboiler heater electric power, Reflux flow control, Isopropyl alcohol- Water feed

2 Abbreviations FOPTD : First Order Plus Time Delay MIMO : Multiple Input Multiple Output L-V : Liquid-Vapour RTD : Resistance Thermometer DAC : Digital to Analog Converter PT : Potentiometer VBA : Visual Basic for Applications QFT : Quantitative Feedback Theory Nomenclatures T 3 : Temperature at Tray-3, near the bottom of the column in degree Celsius T 6 : Temperature at Tray-6, near the top of the column in degree Celsius F c : Feed composition in percentage F f : Feed flow rate in ml/min T c : Column temperature in degree Celsius u 1, u 2 : Manipulated variables y 1, y 2 : Controlled variables L : Reflux flow rate in rpm Q : Reboiler heater electric power in watts N : Number of data points K p : Process gain o C/% τ : Time constant in hours θ : Time delay in hours 1 Introduction The control of closed loop distillation column is an essential operation in most of the chemical processes which has high energy consumption. Also, it is one of the most important unit operations in the process of control engineering. It is a widely used technique to separate the mixtures from the chemical species in petroleum and chemical industries, natural gas processing and oil refining, etc. The separation process is based on the boiling point of the substances used for the separation. The principle of thermodynamic properties is used for the separation of the components from the mixture [1]. During the separation process, the more volatile components will tend towards the top of the column as vapour and the less volatile components will gravitate towards the bottom of the column as liquid. In the column, vapours and liquids are usually at their dew and bubble point, respectively [2]. The temperature at Tray-3 (T 3 ) near the bottom of the column will read higher temperature and temperature at Tray-6 (T 6 ) 2 278

3 near the top of the column will read lower temperature. The greatest difficulty in the distillation column control is due to the presence of nonlinear characteristics, Multiple Input Multiple Output (MIMO) configuration, and disturbances during operation [3, 4]. The disturbance in the column present may be due to the feed composition (F c ), feed flow rate (F f ), and column temperature (T c ). Also, there is a high degree of interaction between the input and output variables, which attract the researchers of various disciplines [5]. Modelling is the preliminary stepping stone towards the control of the distillation column, which in turn helps to understand its dynamic behavior [6]. Moreover, the degree of separation of the mixture in the column can be precisely predicted through reliable mathematical model [7, 8]. In addition, transfer matrix model is established using the Liquid-Vapour (L-V) configuration. The academic literature provides insights into different modelling, and simulation techniques for the setup under study. Further, a comprehensive model will optimize the utilization of available resource and thus minimizes the cost. The steady state experimental data is used to identify the process parameters that assisted to establish First Order Plus Time Delay (FOPTD) model. The objective of the current study is to attain the better process parameters such as process gain, time constant, and time delay (K p, τ, and θ) of the system under study. The Leapfrogging Optimizer Technique is utilized to optimize the process parameters (K p, τ, and θ) where data is gathered from open loop experimentation. In classical FOPTD model optimal parameters are derived by fitting the model to a few key points. But, in the present work least-square fit is used over the entire transient, to get more comprehensive fit. 2 Experimental Setup The distillation, a separation technique, is the inseparable part of the process industry for the refinement of the end products. Figure 1 illustrates the experimental setup. The present set up consists of 8 trays along with feed section, reboiler, column section, condenser, reflux drum to collect distillate and the bottom product collection tank. As shown in Figure 1, peristaltic pump is responsible for the feed to the distillation unit, as the unit operates continuously. Moreover, the setup made up of bubble cap trays, including the reboiler. Having two sections in the setup, rectifying section 3 279

4 (absorption, enriching) being situated at the top whereas stripping section (exhausting) at the bottom. The feed (isopropyl alcoholwater mixture) is the input to the setup. Two 3kW electrical heaters are used to heat the reboiler, connected at the lower side of the setup. The condenser (located at the top) collects the condensate, and the same is stored in the reflux drum. Thus, collected distillate is also utilized to control the temperature at the top of the column along with the reboiler heater current control. Further, peristaltic pump (mounted at the top of the column) pumps the reflux to the top of the column. Two outputs, namely top product (isopropyl rich stream), and distillate product (water rich stream) are produced by the setup. The RTDs (connected via DAC card through the temperature transmitter are used to record the temperature from T 3 to T 6 continuously. All the column tray temperatures are monitored by PT 100 temperature transmitter. Effective control of T 3 and T 6 are achieved by manipulating the reboiler electrical heater supply, and the reflux flow rate (top of the column). Further, control of the reboiler heat supply is accomplished through solid state relay whereas reflux flow rate is controlled by peristaltic pump. 3 Process Model The locally valid linear model is determined by open loop experimentation [9, 10]. This is achieved by introducing incremental changes in the reboiler heater power and reflux flow rate, and then recording the respective tray temperatures. Based on the control configuration strategy, following manipulated variable are assumed: u 1 = reflux flow rate L (% of the peristaltic pump in rpm); u 2 = reboiler power rate Q (% of heater power-in). These variables, in pair, are in turn represent the operating point of the column. T 3 -T 6 are controllable variables and can be recorded. These two control variable are sensitive to change in the manipulated variables and thus form the controlled variable outputs (y 1,y 2 ) )=(T 6,T 3 ) as per the control configuration strategy. The experimentation is initiated with a defined initial operating condition of (u 1,u 2 )=(25,60), and a step of Δu 1 =+15%. Figure 2 and 3 shows the corresponding experimental, and modelled response whereas Figure 4 and 5 illustrates the reponses at a step of Δu 2 =+25%

5 Fig. 1. Experimental setup of Distillation Column Fig. 2. Experimental and modelled response of T 3 to a step of +15% in the reflux at the operating point (u 1,u 2 )=(25,60) Fig. 3. Experimental and modelled response of T 6 to a step of +15% in the reflux at the operating point (u 1,u 2 )=(25,60) 5 281

6 Fig. 4. Experimental and modelled response of T 3 to a step of +25% in the reboiler electric power at the operating point (u 1,u 2 )=(25,60) Fig. 5. Experimental and modelled response of T 6 to a step of +25% in the reboiler electric power at the operating point (u 1,u 2 )=(25,60) 4 Modelling of Distillation Column Modelling in the distillation column is classified as fundamental modelling (established based on the physical properties of the system such as exergy, enthalpy, entropy, mass-energy etc), empirical modelling (established based on input-output real time data), and hybrid modelling/ grey box modelling (combination of earlier two modelling). Out of these three models process industries are extensively rely on empirical modelling. In this method model is identified upon the collection analysis of experimental data. Moreover, this methodology minimizes the root-mean-square deviation between model and data over the entire transient

7 5 Empirical FOPTD Model The current research adopts empirical modelling technique (black box modelling) to determine the model. In this model input-output relations are built on input-output data obtained through the open loop test. The responses are optimized through the Leapfrogging Optimization Technique which utilizes all N data points to fit the model whereas it rejects the noise and disturbances significantly [11]. The FOPTD model, using nonlinear regression, is developed using Visual Basic for Applications (VBA) excel sheet (for fitting the distillation column input-output data). Further, this also provides coefficient of the FOPTD model. Due to the robustness of Leapfrogging Optimization Technique to the surface features, it helps to identify global optimum value. This optimization uses a steady-state criterion for convergence. The best of 100 results from random initialization to ensure the global best model has been found [12]. The FOPTD model is represented as deviation variables as given in eq. (1) i.e, ' dy ( t) ' ' y ( t) K pu ( t ) dt (1) Where, ' '' y ( t) y ( t) ' '' u ( t) u ( t) y base u base t = user defined start point The initial condition is ( ) { Six model coefficients appear: K p, τ, θ, y initial, u base, and y base. However, since there is a steady state relationship between y and u, there are only five independent model coefficients, namely, K p, τ, θ, y initial, and y base. These influence makes the regression nonlinear. Finally, the model is established based on the best match between the model and the experimental plant output. The most commonly used plant transfer matrix model considered here is of the form as 7 283

8 shown in eq. (2). K p s y( e u( s 1 (2) Where, K p is the process gain, τ is the time constant and θ is the time delay. The step test is used to determine process parameters K p, τ, and θ. The step change is applied to the manipulated variable reboiler level and reflux, and a regression curve is obtained with respect to output response across T 6 and T 3 with time. In general, these model is represented as transfer matrix model. They relate to two manipulated variables and controlled variables. The process model can be written as shown in eq. (3). y( G( u( (3) i.e, y1( G y2( G ( ( G G ( u1( ( u2( Where, y1( T6 y2( T3, u1( L u2( Q G e s e s s s e s s e s 1 ( s 235 s Here, K p is the process gain measured in o C/%, τ is the time constant and θ is the time delay both are measured in hours. 6 Conclusions The article discusses the experimental setup used to investigate deeper into the pilot plant distillation column. The identified model is basically based on the Liquid-Vapour configuration. The tray temperature is recorded by conducting a open loop test having a small step change in the reboiler electric power and reflux flow. The Leapfrogging optimizer technique is adopted to analyze the model. Further, the least square fit, an iterative process, is used to 8 284

9 obtain local transient model over the entire transient. The distillation column is observed to achieve steady state status to develop the First Order Plus Time Delay (FOPTD) transfer matrix model. Future Work The possible direction of the future work is to simulate the control algorithm such as decoupler, Quantitative Feedback Theory (QFT), Predictive QFT for the identified model of the distillation column. Further, validation of the simulation results in real time. Acknowledgment Vinayambika S. Bhat would like to acknowledge the Mangalore Institute of Technology and Engineering (MITE), Moodabidri, for sponsoring her Ph.D. programme. References [1] O.A. Olafadehan, V.O. Adeniyi, L.T. Popoola, L. Salami, Mathematical modelling and simulation of multicomponent distillation column for acetone-chloroform-methanol system, Advanced Chemical Engineering Research 2(4) (2013), [2] J.D. Seader, E.J. Henley, D.K. Roper, Separation process principles, 3rd ed., New York: John Wiley and Sons, [3] V. Steffen, E.A. da Silva, Steady-state modeling of reactive distillation columns, Acta Scientiarum 34(1) (2012), [4] Majaaz, V.S. Bhat, I. Thirunavukkarasu, S.S. Priya, Centralized Controller Tuning for MIMO Process with Time delay, in 4 th International Conference on Renewable Energy Research and Application (ICRERA), IEEE Xplore, Palermo, Italy (2015), [5] H.S. Truong, I. Ismail, R. Razali, Fundamental modelling and simulation of binary continuous distillation column, in International Conference on Intelligent and Advanced Systems (ICIAS), Kuala Lumpur, Malaysia (2010), 1-5. [6] V.T. Minh, A.M.A. Rani, Modeling and control of distillation column in petroleum process, Mathematical Problems in 9 285

10 Engineering, 2009 (2009), [7] A.N. Garcia, J.C.Z. Loria, A.R. Marin, A.V.C. Quiroz, Simple multicomponent batch distillation procedure with a variable reflux policy, Brazilian Journal of Chemical Engineering, 31(2) (2014), [8] B. Wittgens, S. Skogestad, Evaluation of dynamic models of distillation columns with emphasis on the initial response, Modeling, Identification and Control 21(2) (2000), [9] P.A. Martin, D. Odloak, F. Kassab, Robust model predictive control of a pilot plant distillation column, Control Engineering Practice 21 (2013), [10] S. Ay, S. Karacan, Decoupling constrained model predictive control of multi-component packed distillation column, World Applied Sciences Journal, 13(3), (2011), [11] R.R. Rhinehart, M. Su, U. Manimegalai-Sridhar, Leapfrogging and synoptic leapfrogging: A new optimization approach, Computers and Chemical Engineering 40 (2012), [12] R.R. Rhinehart, Nonlinear regression modeling for engineering applications, Wiley, New York,

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