The pilot-plant has 20 variables that are measured electronically. These include seven temperatures, five pressures, four flows and four liquid levels. Their positions on the plant are indicated in Figure 2- 1 0 and are as follows:
Industrial Evaporation and Falling-Film Evaporators 35
Temperatures
- The temperature of the liquid is measured at base of each effect, at the outlet of each preheater and in the evaporator feed and outlet streams.Pressures
-The pressures are measured in the shell side of each effect and preheater.Flows
- The flowrates for the liquid streams are measured between each effect and at the inlet and outlet of the evaporator. They are positioned such a way that, if recirculation is used, they then measure the recirculated flows around each effect.Levels
- The height of the liquid in the feed tank and at the base of each effect is measured.No transducers are present for on-line measurement of concentration or density.
The actuators include four centrifugal pumps and a pneumatic steam valve. If recirculation is used four additional pneumatic control valves are available. The pumps are controlled via variable speed drives. All the transducers and actuators are wired into a Fisher & Paykel Programmable State Controller (PSC) Series 2. This is akin to a Programmable Logic Controller (PLC) but allows the programmer to use a state
machine programming language instead of ladder logic. The PSC performs all the low
level control functions; signal input and output, error handling and analogue-to-digital and digital-to-analogue conversion.
The PSC also communicates with a desktop computer VIa a serial link for the supervisory control function. The software package FixDMACS (ver.5.0) is used to carry out the Supervisory Control and Data Acquisition (SCADA) tasks. This allows the plant information to be displayed to an operator. It also performs the tasks of alarm monitoring, data storage and historical trending.
Proportional-Integral (PI) control has been used to regulate the concentrate levels in each effect. This ensures that the pumps are protected and that there is a constant mass of liquid in the plant. The effect pumps are used to control the levels in the straight through configuration, if recirculation is used the control valves are manipulated instead. The controller gains have been determined through a computer simulation of the level systems. PID control is also implemented on the steam valve in order to regulate the steam pressure into the plant. The measurement of the steam pressure in the first effect shell is taken as the controlled variable. The control loops have proven to be vital in helping to settle the plant during start-up. These control loops are realised within the PSC rather than in the SCADA software in order to optimise the response time.
The PSC is the robust element in the system, it alone runs the plant. If the computer crashes for some reason the evaporator will continue to operate and control will be
36 Neural Network Modelling of a Falling-film Evaporator for MPC
maintained by the PSC although the data storage tasks of the SCADA package will cease. Figure 2- 1 3 illustrates the information flow for the evaporator control system.
Evaporator Control signals Sensor measurements Human interface SCADA PSC program
,
Supervisory Plant information control actions Low-level control AID and D/AFigure 2-1 3 : Evaporator control system
2.5 References
[ 1 ] Brennan, J.G., Butters, J.R., Cowell, N.D. & Lilley, A.E
.
V.Food
Engineering Operations,
3rd Edition, Elsevier Applied Science, London, 1 990, p. 367.[2] Kroschwitz, J.I & Howe-Grant, M. (Eds.),
Kirk-Othmer Encyclopedia of
Chemical Technology,
4th Edition, vol. 9, John Wiley & Sons, New York, USA, 1 994, p. 960.[3] Hahn, G., Evaporator Design. In:
Concentration and Drying of Foods,
MacCarthy, D. (Ed.), Elsevier Applied Science, London, 1 986, pp. 1 1 3 - 1 3 1 . [4] Hall, C.W., Farrall, A.W. & Rippen, A.L. (Eds.),Encyclopedia of Food
Engineering,
2nd Edition, AVI Publishing Co., Westport, Connecticut, USA. 1 986, p. 348.[5] Perry, R.H., Green, D.W. & Maloney, J.O. (Eds.),
Perry 's Chemical
Engineers ' Handbook,
6th Edition, MCGraw-Hill B ook Co. , New York, USA, 1 984, P 1 1 -34.Industrial Evaporation and Falling-Film Evaporators 37
[6] Quaak, P., van Wijck M.P.C.M. & van Haren, J.J., Comparison of process
identification and physical modelling for falling-film evaporators.
Food
Control,
1 994, vol. 5, pp. 73-82.[7] Stapper, H.L., Control of an evaporator and spray drier using feedback and .ratio feedforward controllers.
New Zealand Journal of Dairy Science and
Technology,
1 979, vol. 1 4, pp. 241 -257.[8] Ricker, N.L., Sim, T. & Cheng, C.-M., Predictive control of a multi-effect evaporation system.
Proceedings of the American Control Conference,
1 986, Seattle, USA, pp. 3 55-359.[9] van Wijck, M.P.C.M., Quaak, P. & van Haren, J.J., Multivariable control of a four-effect falling-film evaporator.
Food Control,
1 994, vol. 5, pp. 83-89.[ 1 0] Bequette, B.W., Nonlinear control of chemical processes: a review.
Industrial
Engineering Chemistry Research,
1 99 1 , vol. 30, pp. 1 39 1 - 1 4 1 3 .39
3
Evaporator Analytical Model and
Simulation
O VER VIEW
This chapter presents a detailed explanation of the analytical model that has been formulated for the pilot-plant evaporator. After the theoretical discussion the model implementation within MA TLAB and SIMULINK is briefly described. The chapter then covers the important task of validating the model against the actual plant. Through the validation process some of the model parameters are adjusted in order to obtain reasonable model estimates when compared with the actual evaporator data. The chapter concludes with a discussion of the performance of the analytical simulation model in characterising the pilot-plant.
3.1 Model development
3.1 .1 Introduction
Before embarking on a task of model development one must first specify the purpose for which the model will be used. The purpose of the model influences the method of analysing the system and the complexity of the model.
The analytical evaporator model in this project is primarily to be used as a simulation tool for the development and testing of process control schemes. For this purpose the model is required to mimic the behaviour of the actual system in order to generate accurate estimates of the measurable outputs in response to the various input and disturbance signals. In this respect the model is not required to be overly complex and a dynamic lumped-parameter analysis is satisfactory. A systems approach is taken and therefore a distributed analysis of heat transfer, flow regimes and localised variations of
40 Neural Network Modelling of a Falling-film Evaporator for MPC
stream properties are not considered. The model is based on energy and mass balances through each part of the system. The analysis is simplified and hence a number of physical assumptions are required. These are outlined throughout the discussion of the model development. Once the system's basic characteristics have been described by the model, the model is tuned using a variety of coefficients and constants in order to quantitatively validate the model. The final model may not be the most accurate possible but, for the purpose of control system design, too much complexity can be a hindrance rather than adding to the model's performance.
3.1.2 Sub-system modelling approach
The basis for the approach used for the evaporator model development was taken from the work of Quaak and Gerritsen [ 1 ] . They developed a dynamic model for a multi effect evaporator and used a systems approach in which the process was divided into sub-systems for the purpose of analysis .
development of the model for the Production Technology evaporator pilot-plant was carried out by Illingworth [2] . He developed a dynamic model for the effects of the evaporator in the recirculating configuration (refer to §2.4. 1 ) and qualitatively verified it with some simple simulations. (The author aided in many of the plant trials to determine plant constants and operating characteristics for this model). A full three effect model for the recirculating system was not linked together however nor was any formal model validation carried out.
This recirculating model has since been developed further by the author so that the effect models are connected together. The recirculation model was then altered to model the evaporator in the feedforward configuration. New equations relating to the preheaters and venturi condenser have also been included. The development of the feedforward evaporator model is the subject of this chapter.
Illingworth's recirculating evaporator model followed the approach of Quaak and Gerritsen and included descriptions for the distribution plate, evaporation tube, product transport and energy systems for each effect. A similar analysis is used for the feedforward model with the addition of the temperature in the concentrate level as a state variable. This enables a direct comparison with the actual plant temperature measurements taken at the base of each effect.
The analysis of each effect of the evaporator therefore consists of the following sub systems (Figure -3- 1 ) :
Evaporator Analytical Model and Simulation
Evaporation Tube
&
Evaporation Tube Energy Sul>-syst<:ms
Product Transport
Sui>-system
Figure -3-1 : Sub-system boundaries in an effect.
•
Distribution plate sub-system
4 1
This models the flow of liquid through the distribution plate and into the evaporation tube.
•
Evaporation tube sub-system
This models the mass transfer occurring in the evaporation tube which results in a flow of concentrated product and a flow of vapour.
•
Product transport sub-system
This models the flow of product from one effect to the following effect downstream. Involves the reservoir of liquid concentrate, the pipework connecting the effects and the distribution nozzle in the downstream effect. The temperature changes that occur through the product transport system are also modelled.
•
Evaporation tube energy sub-system
This models the heat flows involved in the evaporation of the product. It includes the heat into the evaporation tube and the condensation of the vapour in the downstream effect.
The above sub-systems relating to each effect are combined with equations relating to the following sub-systems:
•
Feed sub-system
This models the flow of product from the feed tank through the preheater tubes and into the first effect.
42 Neural Network Modelling of a Falling-film Evaporator for MPC
•
Preheater sub-system
This models the heat transfer in the two preheaters.
•
Venturi condenser sub-system
This models the suction pressure produced by the venturi condenser and the rise in cooling water temperature due to the condensate and vapour exhaust streams.
•
External steam input sub-system
This models the temperature of the external steam input which is regulated via a PID controller.
A block diagram representation of the evaporator model is depicted in Figure 3-2. This shows that how the energy sub-systems underlie the whole model and have a strong influence over the other sub-systems.
Effect I Effect 2 Effect 3
Energy Sub-systems
To
Figure 3-2 : Sub-system representation of the evaporator model
F or the feedforward model the equations relating to the distribution plate and evaporation tube system for the pilot-plant evaporator are equivalent to those developed by Illingworth. The equations for the product transport and feed systems have been altered from Illingworth's model to account for the feedforward flow configuration. Also a differential equation has been added to calculate the temperature of the liquid concentrate at the base of each effect. This enables a direct comparison with the actual plant temperature measurements taken at these points on the plant. The equations relating to the preheaters, the venturi condenser and the external steam input have been developed by the author. All the sub-systems have been linked together to fully define the feedforward evaporator system. Some of what Illingworth determined in terms of
Evaporator Analytical Model and Simulation 43
constants can be transferred directly to the feedforward model, however most constants have been re-calculated to account for the different flow configuration used.
The pilot-plant evaporator has yet to be operated with concentrated solutions nor can the product density be measured on-line. Therefore, as a result, concentration equations have not been implemented in the final model. Throughout the discussion of the sub systems however, equations relating to the concentration of the product stream are given for completeness. The fluid densities used in the equations can be assumed to be fimctions of the fluid temperature but, if concentrations are considered in the model, this also influences the density and the relationship between temperature, concentration and density must be determined.
Each sub-system in the evaporator will now be briefly discussed and their equations derived. The description of the variables are given during the discussion of the model and a glossary of the model variables and constants can be found in Appendix
I.
3.1.3 Distribution plate sub-system
The distribution plate is assumed to behave as a perfectly mixed tank with a variable level. A simplified diagram of the system is given in Figure
3-3. Figure 3-3 : Distribution plate
sub-system.
The flow through the distribution plate, Qd' can be determined using the following equation.
where Ld is the height of liquid above the plate, Ah is the area of the holes in the plate, g is the gravitational acceleration constant and Kh is a friction factor dependent on the dimensions of the holes.
(3. 1 )
The height of liquid above the plate i s a state variable and is given by the following differential equation.
dLAt) -
=
dt
where Qi is the flow into the distribution plate system of the effect and Ad is the area of the liquid surface.
44 Neural Network Modelling of a Falling-film Evaporator for MPC
The concentration (mass fraction of dry matter) of the flow through the distribution plate, W d, is given by a mass balance.
where Pi and Pd are the densities of the input and output flow respectively and Wi is the input concentration.
3.1.4 Evaporation tube sub-system
Figure 3-4 shows a generalised diagram of the evaporation tube sub-system. To model this system two simplifying assumptions are made.
i) The fall velocity of the liquid film is assumed to be constant and uniform. ii) The heat flow across the tube is
assumed to be unifonn. Ste3lll -+ q hell Condensate -+
Q.*w.
r
Vapour Liquid (3 .3)The first assumption can be considered reasonable since the velocity of the falling-film is predominantly due to gravity and an increase in flowrate
increases the film thickness. The Figure 3-4 : Evaporation tube sub-system. implication of this assumption is that there is a uniform residence time, 'fe' through the tube. This was confinned through tests which found times for the flow through the tube were approximately constant for a variety of flowrates (see section 3. 1 . 1 2)
The second assumption implies a linear decrease in product concentration down the tube length. In reality the heat transfer across the tube wall varies in a nonlinear fashion down the tube. Generally the heat transfer is better at the top of the tube since the flow is more turbulent and the condensate film on the vapour side of the wall is thin. Moving down the tube the resistance to heat transfer increases as the condensate film gets thicker and the falling-film becomes less turbulent. Another influence on the rate of heat transfer is the case when the incoming liquid may be cooler than the effect temperature and energy must be used up to heat the liquid before evaporation can take place.
Despite the nonlinear relationships the assumption of uniform heat flow allows a simple lumped analysis of the heat transfer in the tube. An allowance is made by using mean
Evaporator Analytical Model and Simulation 45 heat transfer coefficients not local coefficients in the heat flow equations. The coefficients have been derived assuming a lumped analysis. Additionally, with the small temperature differences occurring in the pilot-plant the assumption of unifonn heat transfer should not cause significant problems.
Since the residence time is assumed constant the mass of liquid out of the tube at time
t
is equal to the mass flow into the tube att
-Te
minus the amount of product vaporised during the residence time.where Qe is the volumetric product flow from the evaporation tube,
qshe//
is the heat supplied to the product andAe
is the product's latent heat of vaporisation.(3.4)
The integral tenn in equation (3.4) calculates the mass of liquid evaporated over the residence time. This integral can be replaced by My to give
(3.5)
My is the total mass of vapour produced in the evaporation tube during the previous
Te
seconds and is estimated byq shell (t - T e)
Ae(t - Te)
(3.6)The product concentration exiting the evaporation tube is calculated via a mass balance involving only pure delay;
(3.7)
3.1.5 Product transport sub-system
Product level and flowrate
The product transport system is concerned with the flow- of product from one effect to the next. The boundaries of the system are the top of the concentrate level in the upstream effect and the distribution nozzle in the following effect. Quaak and Gerritsen made the assumption that the concentrate level remains constant. However, for this model a differential equation with the height of the concentrate level, L, as the state variable was used;
46 Neural Network Modelling of a Falling-film Evaporator for MPC
dt
Al
where Qp is the flowrate out of the effect and AI is the area of the level surface.
(3.8)
AI is a function L since the geometry of the pipework changes over the operating range
of the level.
To calculate Qp an energy balance between points CD and
®
in Figure 3-5 is required. Using Bernoulli's equation one arrives at:where Pe and PI are the tube pressure of the upstream and downstream effects, Mp is the pressure increase across the pump,
MN is the pressure drop across the distribution nozzle of the next effect, M [ric is the pressure drop due to the friction in the pipe line,
hN is the height of the distribution nozzle, Pp is the discharge density, and
Ve and vp are the flow velocities at the input and discharge points.
CD
L
Figure 3-5: Product transport sub-system.
Evaporator Analytical Model and Simulation 47
The pressures
Pe
andPj
are taken to be the saturation pressures at temperatures Te andTtube inside the evaporation tubes.
The velocity terms are given by the volumetric flowrate divided by the cross-sectional area of the pipe at the particular point. The input velocity, Ve, is the velocity at the surface of the liquid level at the base of the effect and therefore is given by
(3 . 1 0)
The discharge velocity into the next effect is also calculated using Qp with the cross