A continuous stirred tank heater simulation model with applications
Nina F.Thornhill
a,*
,Sachin C.Patwardhan b ,Sirish L.Shah
c
a
Centre for Process Systems Engineering,Department of Chemical Engineering,Imperial College London,London SW72AZ,UK
b
Department of Chemical Engineering,I.I.T.Bombay,Powai,Mumbai 400076,India
c
Department of Chemical and Materials Engineering,University of Alberta,Edmonton,Canada T6G 2G6
Received 18December 2006;received in revised form 2July 2007;accepted 11July 2007
Abstract
This article presents a first principles simulation of a continuous stirred tank heater pilot plant at the University of Alberta.The model has heat and volumetric balances,and a very realistic feature is that instrument,actuator and process non-linearities have been carefully measured,for instance to take account of the volume occupied by heating coils in the tank.Experimental data from step testing and recordings of real disturbances are presented.The model in Simulink and the experimental data are available electronically,and some suggestions are given for their application in education,system identification,fault detection and diagnosis.Ó2007Elsevier Ltd.All rights reserved.
Keywords:Benchmark simulation;Disturbance;Experimental validation;First-principles model;Hybrid model;Performance analysis;System identifi-cation
1.Introduction
Process simulations are of value to university teachers and academic researchers because they allow comparisons and demonstrations of the merits of different approaches in areas such as control design,system identification and fault diagnosis.
This paper has an educational purpose.It describes a simulation of an experimental continuous stirred tank hea-ter (CSTH)pilot plant.Volumetric and heat balance equa-tions are presented along with algebraic equations derived from experimental data for calibration of sensors and actu-ators and unknown quantities such heat transfer through the heating coils.Many of these relationships have non-lin-earities,and hard constraints such as the tank being full are also captured.A valuable feature is that the model uses measured,not simulated,noise and disturbances and there-fore provides a realistic platform for data-driven identifica-tion and fault detection.Code and data for the simulation presented in this article are available from the CSTH sim-ulation website [38].The model has been implemented in the Simulink simulation platform with a view to easy acces-sibility by students and researchers.
The next section of the paper reviews benchmark models from the process systems literature and places the CSTH model in context.Section 3presents the pilot plant,rele-vant equations and the calibrations.Section 4describes implementation of the model in the Simulink simulation platform.Section 5presents experimental data for model validation while Section 6shows the time trends of process and measurement disturbances captured from the experi-mental plant.All of these data sets are available at the CSTH web site.The model is then explored mathematically to give a linearized state-space representation at the operat-ing point and also an input–output transfer function
matrix representation.Finally,Section 8suggests some applications for the simulation and presents a challenge in the form of a system identification problem.
0959-1524/$-see front matter Ó2007Elsevier Ltd.All rights reserved.doi:10.1016/j.jprocont.2007.07.006
*
Corresponding author.Tel.:+4402075946622;fax:+4402075946606.
E-mail address:n.thornhill@imperial.ac.uk (N.F.Thornhill).
reaction to a book or an article
www.elsevier/locate/jprocont
Journal of Process Control xxx (2007)
xxx–xxx
2.Background and context
2.1.Introduction
Process simulations in the public domain have been used in education and academic research for many years to compare the performance and applicability of methods for control,identification and diagnosis.Broadly speak-ing,the simulations fall into two categories:(i)models in which the dynamics are captured throughfirst princi-ples,and(ii)linear models presented as transfer func-tions or in state-space form.Also available are detailed models for individual components of a process such as control valves and rotating machinery.Commercial train-ing simulators are a further important category of pro-cess simulation.The following sections review the literature and place the CSTH simulation in the context of other work.
2.2.First principles models
A very widely used model is the classic continuous stir-red tank reactor simulation with Van de Vusse reaction kinetics[39].It appears in text books[26,10]and has been used for demonstration of control schemes and fault diag-nosis.The reaction equations are non-linear because they include the bilinear products offlow rates,composition and temperature as well as the temperature dependence of reaction
rate[26].Other authors have made realistic additions such as the dynamics of a reactor with a cooling jacket[31,32].
At the time of writing,more than150articles in the Science Citation index are using the Tennessee Eastman challenge problem[9].This simulation represents a com-plete process comprising a reactor and several separation columns and heat exchangers.The process presents signif-icant plant-wide multivariable control challenges and the authors also provided simulations of process faults.A baseline control system was reported by[24]and the sim-ulation has been widely used for demonstration of advanced control [23,30,22,20,40]),and for testing of fault detection and diagnosis schemes,both data driven and model-based[19,12,5,14–16,34].The ori-ginal code was written in Fortran,while[29]has made an implementation in Simulink available to other researchers.
Otherfirst principles models from the literature are:•The vinyl acetate process[4];
•The reactor/regenerator section of a Model IVfluid cat-alytic cracking unit[25];
•Emulsion polymerization with population and particle balance[11];
•The ALSTOM gasifier that produces gas from carbon-based feedstock[8,7];
•Non-linear distillation model[35].Matlab code is avail-able for this simulation[36].2.3.Linear dynamic models
The non-linear distillation model paper of[35]offered transfer function models linearized at different operating points as well as thefirst principles model.
Models expressed in the form of a transfer function matrix are helpful for demonstrating multivariable prob-lems where interactions are the key issue.Their clear cap-ture of these effects also gives them value for teaching purposes.For instance,[33]use the Wood–Berry two-by-two transfer function model of a pilot-scale distillation [42].The model relates plant inputs(reflux rate and steam flow rate)to outputs(top and bottom product composi-tions).It is expressed as transfer functions in the form of first order lags plus time delays(FOPTD).[21]used the Wood–Berry model to demonstrate performance monitor-ing of a model predictive controller.
The Shell challenge problem[28]is a transfer function representation of an industrial debutanizer.Again,each transfer function is afirst order lag with delay where some of the delays are very long,giving a considerable challenge for multivariable control.The paper by[3]concerned worst-case bounds and statistical uncertainty in the evalu-ation of the Relative Gain Array.It presented results
from several transfer function benchmark models including a simplified model for the Shell challenge problem and a three-by-three model for a pilot scale distillation column which originated with[27].
State-space benchmarks are used for the testing of model reduction algorithms in which the aim is to derive a smaller representation with many fewer states which has almost the same dynamic input–output behaviour as the original prob-lem.The SLICOT collection[37]created as part of the European Union’s BRITE-EURAM III NICONET pro-gramme gives some huge state-space models as challenges for this purpose and the Oberwolfach model reduction benchmark collection[18]has similar uses.
2.4.Hybrid and data-based models
An issue with the use of simulations for applications in fault diagnosis and robust control can be that noise and disturbances are difficult to model accurately.There is a tendency to model these asfiltered or integrated Gaussian random noise or as piecewise linear disturbances,but in many case such simple signals fail to capture real effects. For instance,time trends of instruments measuring the out-put of a non-linear system typically have a non-Gaussian distribution and a spectrum characterized by phase cou-pling.Real data captured from processes provide more realistic tests than simulated data.
[41]provided benchmark data for a non-linear dynamic model identification challenge problem.The dat
a are from a laboratory surge tank which generated non-linear input–output data for the comparison of non-linear modeling methods.A specific issue was that models should be robust to noise in the identification data.
2N.F.Thornhill et al./Journal of Process Control xxx(2007)xxx–xxx
The approach taken by[17]combined measurements from a real process with a simulated exothermic reaction. The process is a tank that behaves as if an exothermic reaction is taking place.There are no real reactants and instead the reaction is simulated.The reactant feed rate in the model is set to the measured cold water feed rate, while directly injected steam provides the heat released by the simulated reaction.The partially simulated reac-tor provides a platform for testing of control strategies under realistic conditions of process constrains,measure-ment noise,quanitized measurements and sampled data control.
2.5.Equipment models
Published models are available for components and items of equipment.The DAMADICS simulation[2]pro-vides a benchmark challenge in identification of control valve faults.It comprises a Simulink model of a specific valve in a sugar refinery with properties such as friction together with data
from the refinery that capture normal running and several valve faults.[6]created an empirical model of a valve with parameters that specify deadband and the amount of stick-slip without the need for determin-ing friction forces,the mass of the moving parts or the spring constant.Its behaviour matched closely to that of afirst principles model.
Models for items of equipment such as motor drives, generators and turbines are well developed and commer-cially available in Simulink SimPower Systems from the Mathworks.The documentation gives an example of the use of a steam turbine model within an IEEE benchmark simulation[1]for a synchronous generator.
2.6.Models for teaching and training
Benchmark simulations have a role in teaching and sev-eral of those mentioned above feature in mainstream pro-cess control text books.
In the workplace,simulators are used to train process control operators especially in start-up and shut-down pro-cedures and dealing with emergencies.Such simulators are specific for the process for which they were designed and generally include constraints and detailed representations of instruments,valves and equipment such as pumps.The Honeywell Shadow Plant simulator[13]is an ex
ample of
a commercial training simulator.
2.7.Motivation for the CSTH simulation
The stirred tank heater model presented in this article is a hybrid simulation which uses measured data captured from a process to drive afirst principles model.The noise and dis-turbances signals therefore have more complex and more realistic characteristics than if they were created by a ran-dom number generator.There are also experimentally mea-sured data available for the purposes of identification.
It is a small model in comparison with many of those reviewed above,and there is no chemical reaction.It does, however have a complete characterization of all the sensors and valves and the heat exchanger.Its simplicity makes it primarily of value in a classroom setting,while the incorpo-ration of constraints and non-linearities and the use of real noise sequences provide a practical benchmark for control-ler design and data-driven identification and diagnosis.
3.Process description and model
3.1.The continuous stirred tank heater
The pilot plant in the Department of Chemical and Materials Engineering at the University of Alberta is a stir-red tank experimental rig in which hot and cold water are mixed,heated further using steam through a heating coil and drained from the tank through a long pipe.The config-uration is shown in Fig.1.The CSTH is well mixed and therefore the temperature in the tank is assumed the same as the outflow temperature.The tank has a circular cross section with a volume of8l and height of50cm.
3.2.Utilities and instrumentation
The utilities of the CSTH are shared services and there-fore subject to disturbances from other users.The cold and hot water(CW and HW)in the building are pressurised with a pump to60–80psi,and the hot water boiler is heated by the university campus steam supply.The steam to the plant comes from the same central campus source.
Control valves in the CSTH plant have pneumatic actu-ators using3–15psi compressed air supply,the seat and stem sets being chosen to suit the range of control.
Flow instruments are orifice plates with differential pres-sure transmitters giving a nominal4–20mA output.The level instrument is also a differential pressure measurement. Finally,the temperature instrument is a type J metal sheathed thermocouple inserted into the outflow pipe with a Swagelock T-
fitting.
N.F.Thornhill et al./Journal of Process Control xxx(2007)xxx–xxx3
3.3.Volumetric and heat balance
The dynamic volumetric and heat balances are shown in the following equation:
d VðxÞ
d t
¼f cwþf hwÀf outðxÞð1Þd H
d t
¼W stþh hw q hw f hwþh cw q cw f cwÀh out q out f outðxÞð2Þwhere x is the level;V the volume of water;f hw the hot waterflow into the tank;f cw the cold waterflow into the tank;f out the outflow from tank;H the total enthalpy in the tank;h hw the specific enthalpy of hot water feed;h cw the specific enthalpy of cold water feed;h out the specific en-thalpy of water leaving the tank;q cw the density of incom-ing cold water;q hw the density of incoming hot water;q out the density of water leaving the tank;and W st the heat in-flow from steam.
The temperatures of the hot and cold water feeds were set to50°C and24°C respectively in the base case simulation.
3.4.Related equations
The following algebraic equations also apply.
3.4.1.Specific enthalpy
In the well mixed case:
h out¼
H
V q out
ð3Þ
3.4.2.Level,x
The relationship between level and volume is not linear because of the volume occupied by heating coils in the lower half of the tank.The relationship between level and volume was measured experimentally,as discussed in Section3.5.
3.4.3.Outflow
The manual outflow valve wasfixed at50%as a stan-dard operating condition.At thisfixed setting,the empiri-cal expression below was derived experimentally by seeking a square root relationship between the head of water in cm above the manual outflow valve and the measuredflow in m3sÀ1.
f out¼10À40:1013Â
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
55þx
ðÞ
p
þ0:0237
The expression has this particular form because the manual outflow valve is55cm below the bottom of the tank and the head of water therefore is55+x where x is the level in the tank in cm.
3.4.4.Thermodynamic properties
The relationships between specific enthalpy,density and temperature in liquid water were taken from steam tables and used for the conversions of h to T,T to h,and T to q in piecewise linear look-up tables.Specific enthalpies are referenced to0°C.3.4.5.Heat transfer from steam system
The heat transfer from the steam system depends on the steam valve setting.The relationship was det
ermined empirically from steady state running at different steam valve settings since the heat exchange area and heat trans-fer coefficient could not be measured.The heat balance when the CSTH is in a steady state running with a cold water inflow only is:
W st¼h out q out f outÀh cw q cw f cw
and f cw=f out in steady state.
The calculations for W st are in Table1.The steady state flow in these experiments was9.0410À5m3sÀ1,the incom-ing cold water temperature was24°C with h cw=100.6kJ kgÀ1and q cw=997.1kg mÀ3.
The results of the calculations are used in a piecewise-linear look-up table that determines the amount of steam heating for a given steam valve setting.The data in Table 1may be used in simulation under non-steady conditions given some assumptions:
(i)That the tank is well mixed so the temperature of the
outflow is the same as that in the tank.The assump-tion is reasonable,because stirrer provides a high liquid velocity across the heating coils and distributes heat quickly throughout the tank.
(ii)That the amount of heat transferred at a given steam valve setting is not dependent on the temperature of the water in the tank.The assumption is reasonable since most of the heat in the steam is its latent heat of2257kJ kgÀ1compared to,say,the difference of
62.7kJ kgÀ1between water at25°C and40°C. (iii)That all the steam condenses and that circumstances do not arise where steam goes to waste.This assump-tion is reasonable unless the level is very low so that the heating coils are significantly exposed.It was observed that the maximum achievable temperature at the standard operating conditions was65°C when the steam valve was fully open.The steam should condense fully under these conditions.
3.5.Sensor and valve calibration
The inputs to the CSTH are electronic signals in the range4–20mA that go to the steam and cold water valves. The outputs are measurements from the temperature,level Table1
Relationship between heat transfer rate and steam valve setting
Valve/mA T/°C h out/kJ kgÀ1q out/kg mÀ3W st/kJ sÀ1 424100.6997.10
7.530125.7995.2  2.24 931129.9994.8  2.61
1136.5152.8992.9  4.65 1448200.9988.78.89 1761255.3982.313.60 2065272.0980.215.04
4N.F.Thornhill et al./Journal of Process Control xxx(2007)xxx–xxx
and cold waterflow instruments,nominally in the range4–20mA.Calibration models were determined by measure-ment at several points in the range,and are represented in the model as piece-wise linear look-up tables.The level of detail presented in this section was found necessary to provide a highfidelity match between experimental obser-vations and the simulation.
3.5.1.Level and volume
Data for the calibration of level and volume are plotted in Fig.2a and b.The level instrument calibration converts the level in the tank to an instrument output on a4–20mA scale while the volume calibration gives a look-up table converting level in the tank to volume.The steam heating coils occupied a noticeable volume in the lower half of the tank and became fully covered when the level was 16.9cm.Therefore the volume versus level characteristic is not linear when the level is low.
3.5.2.Cold and hot waterflow calibration
Calibration of the cold and hot water valves is shown in Fig.2c and d in which the volumetricflow rate is
N.F.Thornhill et al./Journal of Process Control xxx(2007)xxx–xxx5

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