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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 61, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-51-8; ISSN 2283-9216 

A Computer Model of the Evaporator and Its Sensors 

Yury Chursin*, Evgeny Efremov, Alexandr Gozhimov, Oksana Kabrysheva, Daniil 

Barkov 

National Research Tomsk Polytechnic University, 30, Lenin ave., 634050, Tomsk, Russian Federation 

yurychursin@mail.ru 

For the implementation of a closed nuclear fuel cycle it is necessary to carry out a series of experimental studies 

to justify the choice of technology. The operation of the radiochemical plant is impossible without high-quality 

automatic control systems. In the technologies of spent nuclear fuel reprocessing, the method of continuous 

evaporation is often used for a solution conditioning. Therefore, the effective continuous technological process 

will depend on the operation of the evaporation equipment. Its essential difference from similar devices is a 

small size. In this paper, the method of mathematic simulation is applied for the investigation of one-effect 

evaporator with an external heating chamber. Adequacy was tested using the experimental data obtained at the 

laboratory evaporation unit. The results proved that the studied subject is a Multiple Input Multiple Output 

(MIMO) plant, nonlinear over separate control channels and not self-balancing. 

1. Introduction 

Evaporation is conditioning of liquid waste and concentration of the desired products. Evaporation and 

specifically evaporators are used in different technological processes. For example, modelling, identification and 

control of evaporation presses was described by Lissane et al. (1999). The method of evaporation is often 

applied for conditioning solutions in spent fuel reprocessing technologies. The effective continuous operation of 

the technological process will depend on the operation of the evaporation equipment. Its essential difference 

from similar devices is a small size due to a relatively small-scale production for safety assurance. Existing 

models of evaporators mostly used for processes without high safety requirements of spent nuclear fuel 

production such as digestate thickening in biogas plants (Vondra et al., 2016) and sugar concentration in ethanol 

production (Prado et al., 2015). Such devices are MIMO plants, nonlinear over separate control channels and 

they are not self-balancing. To study various automated control system (ACS) using a one-effect evaporator 

with an external heating chamber for evaporation of uranyl nitrates solution (see Figure 1), it is necessary to 

create a mathematical model describing the dynamic relationships between key process variables. At the same 

time, according to a general engineering rule, for the synthesis of ACS 10 % accuracy is quite acceptable, due 

to the approximate formulas for analytical calculations of the controller parameters (Sovetov and Yakovlev, 

1998). Another system allowing 20 % accuracy was presented in Scarpa et al. (2015) article. 

2. Mathematical model  

The block diagram of evaporator is shown in Figure 1, where Qr, Qp, Qf – the volume flow of reflux, the 

evaporated uranium re-extract and feed solution of uranium re-extract, m3/h; T, Tr, Tf, Ts – the temperature of 

reflux, solution in the unit, feed solution of uranium re-extract and heating steam, оС; ρ, ρV, ρr, ρf – the density 

of the solution in the unit, secondary steam, reflux, feed solution of uranium re-extract, kg/m3; Wk, Ws, WV – the 

mass flow of the condensate, heating and secondary steam, kg/h; Ps, PV – the pressure of the heating and 

secondary steam, kPa; i, is, if, ir, iv, ip – the enthalpy of the solution in the unit, the heating steam, the feed 

solution, reflux, secondary steam and the evaporated uranium re-extract, J/kg; C, Cf – the concentration of the 

evaporated uranium re-extract and the feed solution of uranium re-extract, kg/m3. 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1761237

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Chursin Y., Efremov E., Gozhimov A., Kabrysheva O., Barkov D., 2017, A computer model of the evaporator and its 
sensors, Chemical Engineering Transactions, 61, 1435-1440  DOI:10.3303/CET1761237  

1435



 

Figure 1: Evaporator scheme showing input and output variables 

A mathematical model of uranium re-extract evaporation should represent the following: 

1) Time history of the solution level in the unit according to the flow of feed solution of uranium re-extract, 

evaporated uranium re-extract, reflux and heating steam flow; 

2) Time history of concentration/ density of evaporated solution, depending on the flow rate and the 

concentration/ density of the feed solution and the reflux, flow of the evaporated uranium re-extract and heating 

steam; 

3) Time history of the solution temperature in the unit depending on the temperature of feed solution, reflux, 

heating steam and its pressure. 

The model should take into account mutual influence of the controlled parameters, mentioned above. 

Mathematical formulation for analytical models of chemical units is based on generation of equations for mass 

and heat balance of the system. Equations for an evaporator similar to the one presented in this article are used 

in the model by Kozin et al. (2016). Chursin et al. (2016) presented a model of separation process with 

formulation for concentration.  

Mathematical formulation had to be simplified due to the lack of data on the thermodynamic properties of the 

evaporated product, physical and thermodynamic parameters of the heating and juice steam, as well as the 

necessary data for the description of the heat lost to the environment etc. 

As a result, time history of the material, element and heat flows in the unit is described by the Eq(1), where A – 

cross sectional area of the evaporator, m2; cf – specific thermal capacity of the feed solution, kJ/(°C∙kg); ρw – 

water density, kg/m3 and the mass flow of secondary steam Wv is calculated by the Eq(2). 

         

v
f r p

w

v f f

w f

s s c f f f r r r v v ar

f f

dh W
Q Q Q

dt A

d
W Q ,

dt Ah

W i i Q i i Q i i W i i L T TdT

dt c Ah

1

1
1 1

  
     

 


    
         

     


           







  


 

 



 (1) 

Q c T Q cT Q i W i
W

i

f f f f p r r r s s

v

v

.
  


  

 (2) 

Enthalpy of heating steam, secondary steam, and dew is determined using the expression obtained by fitting 
the tabular data: 

 

 

 

i T T T T T

T
P

i T T

6 2 3

s,v sat sat sat s,v sat

sat

s

2 3

c s s

2.5 10 1813 0.417 0.11 2090

2147
273.2

10.76 lg( )

0.0051 1.5595 2467.1 10

          

 


      

 (3) 

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The developed approach and mathematical description of the evaporator as a controlled object was 

implemented as a computer model in the MATLAB/ Simulink package. 

Level and density of solution in evaporator are measured with two pressure differences (ΔP1, ΔP2) in three 

different points with use of differential pressure sensors (Gofman et al., 2012). These points are at different 

heights of evaporator. Pressure measurement of controlled environment is done with three capillary pipes filled 

with separation liquid (see Figure 2). 

 

Figure 2: Block diagram of density and level measurement 

The solution density ρ in separation chamber is calculated as follows: 

sep

P
H

g
2


     (4) 

where ρsep – density of separation liquid; ΔH – length between lowest points where pressure is measured, m; g 

– gravitational acceleration, m/s2. 

The solution level in evaporator is calculated as follows:  

P
L L

g
0

2


 


 (5) 

where L0 – constant, m. 

Linear pressure and density dependence was acquired experimentally. Experimentally obtained pressure and 

level dependences for different solution density is shown in Figure 3. 

 

 

Figure 3: Pressure and level dependences for different solution density 

For testing qualitative adequacy of the model, research results of the evaporators presented by other 

researchers were used (Taubman, 1970). One of the study subjects there was a two-stage vacuum evaporator 

"Edinstvo". 

D2 D1

level

Lρ 

capillaries

++ - -

pump

separation

liquid

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3. Simulation results 

Figure 4 shows the transition processes of the solution level in the second device of "Edinstvo" evaporator and 

in the developed model of uranium re-extract evaporator. The flow of the feed solution ΔSp = 1,700 kg/h to the 

unit was changed up to 62 %. 

As it is seen from the graphs, the behaviour of the level in both cases is identical, and the channel of the 

controlled object can be regarded as an astatic link. 

Figure 5 shows the transient responses of the concentration in the first device of "Edinstvo" evaporator and the 

appropriate transitional process in the developed computer model of the evaporator. The fluid flow from the unit 

ΔSp = -250 kg/h was changed up to 30 %. 

The above graphs show that transient responses of concentration obtained at the evaporator and the simulation 

results are qualitatively equal. In addition, this channel of the controlled object can be regarded as a first order 

aperiodic link. 

Figure 6 shows the transient responses of the temperature of the solution in the first device of "Edinstvo" 

evaporator and the appropriate transitional process in the developed computer model of the evaporator. The 

heating steam flow from the unit ΔSp = 480 kg/h was changed up to 17 %. 

The above graphs show that the transient responses of temperature, obtained at the evaporation unit and the 

simulation results are qualitatively equal.  

 
(a) Level (evaporator)                                    (b) Level (model) 

Figure 4: Transition process in the level 

 
(a) Concentration (evaporator)                      (b) Concentration (model) 

Figure 5: Transition process in concentration 

Model

0       50     100     150    200     250     300   t, s

h, m

1.5

1.6

1.55

1.5

1.45

simulation results

f 55 kg/h (62%)S 

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(a) Temperature (evaporator)                   (b) Temperature (model) 

Figure 6: Transition process in temperature 

Similarly to the transient responses of concentration, it can be seen that the object of the present channel can 

be regarded as a first order aperiodic link. Comparison of simulation results with the data presented by Kam et 

al., (2002) shows their qualitative agreement. 

The analysis of the given above transient responses shows that the time constant of the evaporators for 

concentration/ density is substantially higher than time constant for the level and temperature. This fact should 

be considered when developing ACS of an evaporation unit. 

Qualitative adequacy of the developed model was tested using the experimental data obtained at a laboratory 

evaporator at V.G. Khlopin Radium Institute, St. Petersburg, Russian Federation. 

This unit is equipped with an automated control system, based on two control algorithms. The first algorithm is 

designed for evaporation mode with a required density. The level of the solution in the still is maintained constant 

by controlling the flow of feed solution. In the transient mode (to achieve the desired density) the solution in the 

still was not drained. In the continuous mode, the solution was drained in proportion to the average flow of the 

feed solution. The second algorithm provides required density of the solution at the output of the evaporation 

unit in a continuous mode. The desired density of the solution in the still was maintained by the flow of feed 

solution, while the level was maintained by draining the solution in the still. 

The following experiment was carried out at the laboratory evaporator. In the starting mode, after initial filling 

with the feed solution and beginning of the evaporation process control was maintained by the first algorithm in 

the transient mode. After reaching a required value of density ρ = 1,400 kg/m3, that is, tapering off to a steady-

state regime, control was maintained by the second algorithm. If the measured density of the solution in the still 

was greater than ρ, the maximum flow rate of feed solution was set. If it was less than that, the minimum flow 

rate was set. That is, the control was maintained according to the relay rules. After tapering off to a steady-state 

regime, transition process was recorded while set point of density was changed from ρ = 1,400 kg/m3 to ρ = 

1,500 kg/m3. 

A similar experiment was carried out on the developed computer model of the evaporation unit. The 

experimental data and simulation results are shown in Figure 7(a). 

Another experiment was carried out at the laboratory evaporator. After reaching a required density value of 

ρ = 1,315 kg/m3, it was decreased to ρ = 1,285 kg/m3. The results of the experiment are presented in Figure 7(b), 

Figure 8(a, b). 

 

 
(a) density 

 
(b) density (second experiment) 

Figure 7: Transition process in density for first (a) and second experiment (b) 

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(a) temperature (b) level 

Figure 8: Transition process in temperature (a) and level (b) 

4. Conclusion 

Implementation of a closed nuclear fuel cycle requires substantiation of spent nuclear fuel technology through 

studies at the experimental and pilot equipment. At the same time, the creation of an effective radiochemical 

production with regard to its high radioactive, nuclear and environmental hazards is impossible without the use 

of automatic control systems. Mathematical model is required to develop an ASC. Mathematical model of an 

evaporator presented in this article has the relative standard errors of simulation in the level, density and 

temperature of the solution being less than 9 %, 5 % and 7 %. That allows its application for the development 

of ACS of an evaporation unit. Described method of the solution density and level measuring in the unit showed 

its efficiency and can be used in process control system.  

Acknowledgments 

This work was funded as a part of the project 8.3079.2017/PCh of the Federal government-sponsored program 

«Science». 

References 

Chursin, Y.Y.A., Gozhimov, A.A.I., Liventsov, S.S.N., Shmidt, O.O.V., 2016, Mathematical model of separation 

of transplutonium and rare earth elements by ion-exchange chromatography method with complexation 

during elution, Chemical Engineering Transactions, 52, 199-204. 

Gofman, F.E., Gofman, R.D., Zilberman, B.J., Rjabkov, D.V., Andreeva, E.V., 2012, Laboratory stand 

evaporator with an automated control system, Chemical Technology,13-9, 565-570. 

Kam K.M., Saha, P., Tadé, M.O., Rangaiah, G.P., 2002. Models of an industrial evaporator system for education 

and research in process control, Developments in Chemical Engineering and Mineral Processing, 10 (1-2), 

105–127. 

Kozin K.A., Efremov E.V., Kabrysheva O.P., Grachev M.I., 2016. A computer model of the evaporator for the 

development of an automatic control system, IOP Conference Series: Materials Science and Engineering, 

142-1, art. 012043, Yurga, Russian Federation 

Lissane Elhaq, S., Giri, F., Unbehauen, H., 1999, Modelling, identification and control of sugar evaporation - 

theoretical design and experimental evaluation, Control Engineering Prectice, 7, 931-942. 

Prado C., Souza O., Sellin N., Marangoni C., 2015, Comparison between single and multi-effect evaporators for 

sugar concentration in ethanol production, Chemical Engineering Transactions, 43, 541-546.  

Scarpa F., Reverberi A., Tagliafico L.A., Fabiano B., 2015, An experimental approach for the dynamic 

investigation on solar assisted direct expansion heat pumps, Chemical Engineering Transactions, 43, 2485-

2490.  

Sovetov B.J., Yakovlev S.A., 1998. Modelling of Systems: Textbook for Universities, Visshaja shkola, Moscow, 

Russia, 344 ps. 

Taubman E. I., 1970. Calculation and simulation of evaporators, Chemistry, Moscow, Russia, 216 ps. 

Vondra M., Máša V., Bobák P., 2016, The potential for digestate thickening in biogas plants and evaluation of 

possible evaporation methods, Chemical Engineering Transactions, 52, 787-792. 

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