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Simulation of an agitated thin film evaporator for concentrating orange juice using AspenPlusTM
Journal of Food Engineering 47 (2001) 247±253
www.elsevier.com/locate/jfoodeng
Simulation of an agitated thin ®lm evaporator for concentrating orange juice using AspenPlusTM Nongluk Chawankul a, Supaporn Chuaprasert a, Peter Douglas b,*, Wilai Luewisutthichat a a
Department of Chemical Engineering, King Mongkut's University of Technology, Bangkok 10140, Thailand b Department of Chemical Engineering, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada Received 7 January 2000; accepted 24 July 2000
Abstract The focus of this research is on the concentration of orange juice in agitated thin ®lm evaporators (ATFE). The AspenPlusä simulation program was used to develop a model of the ATFE. A rigorous heat exchanger model, Heatx followed by the rigorous 2phase ¯ash model, Flash2, was used to simulate the dominant eects of the ATFE. The thermo-physical properties of orange juice are not available in the AspenPlusä databank. They were, therefore, determined experimentally and modelled as functions of temperature and solid content. Heat transfer coecients were predicted using correlations and measured from process measurements. Experimental and simulation results are presented. The AspenPlusä simulation model using experimentally determined thermo-physical properties of orange juice compares well with the experimental data from the ATFE pilot plant. Process measurements were reconciled using the optimisation features of AspenPlusTM . Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Simulation; AspenPlus; Agitated thin ®lm evaporator; Orange juice
1. Introduction Simulation is used as a tool to analyse plant design and operating conditions. Simulation packages such as AspenPlusTM have built-in process models, thus oering a convenient and time saving means of examining an entire chemical process, Aspen Technology (1993). Most process simulation applications are found in the chemical process industries and there are few applications in the food industry. Evaporators are widely used in the food industry as concentrators and separators. In particular, agitated thin ®lm evaporators (ATFE) which have short residence times and relatively high heat transfer coecients, are best used for concentrating foods that are heat sensitive and cannot tolerate high temperatures for more than a few seconds. Chuaprasert, Douglas, & Nguyen (1999) used AspenPlusTM to simulate and perform data reconciliation of experimental measurements of a lab scale ATFE for concentrating sugar syrup. The focus of this paper is on the concentration of tangerine orange juice in an ATFE. Experiments were performed on two dierent ATFE systems. *
Corresponding author. Tel.: +1-519-888-4567 ext. 2913; fax: +1519-746-4979. E-mail address: [email protected] (P. Douglas).
One, a lab scale system used by Chuaprasert et al. (1999) and the other, a pilot plant scale capable of handling larger ¯ow rates. A generalised heat transfer coecient model was developed and applied to all the data. The process was simulated using the AspenPlusTM simulation model developed by Chuaprasert et al. (1999). The model consisted of a rigorous heat exchange model (Heatx) followed by a rigorous 2-phase ¯ash (Flash2). The heat exchanger model was used to simulate the evaporator and required the heat transfer area, A, and the overall heat transfer coecient, U. The output stream from the heat exchanger, a 2-phase stream consisting of concentrated orange juice and water vapour, was fed to the 2-phase ¯ash unit operating at the same pressure. The ¯ash unit then separated the water vapour from the concentrated orange juice liquid.
2. ATFE A schematic diagram of the ATFE systems in the Department of Chemical Engineering at King Mongkut's University of Technology, Thonburi, KMUTT, is shown in Fig. 1. Both the lab scale system and the pilot plant system have the same con®guration, the only difference being that the pilot plant system can handle
0260-8774/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 0 ) 0 0 1 2 2 - 9
248
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
Nomenclature A B Cp D De Fr Ff Fp Fs Fv g hp hs k kw K mavg N Nu
2
overall heat transfer area (m ) concentration (Brix) speci®c heat capacity (kJ/kg °C) diameter of cylinder (m) equivalent diameter (m) Froude number ¯ow rate of feed stream (kg/h) ¯ow rate of product stream (kg/h) ¯ow rate of steam (kg/h) ¯ow rate of vapour stream (kg/h) gravity (m/s2 ) heat transfer coecient of liquid steam (kw/m2 °C) heat transfer coecient of steam (kw/m2 °C) thermal conductivity (w/m °C) thermal conductivity of wall (kw/m °C) condensation number average mass ¯ow rate (kg/s) speed of agitator (rpm) Nusselt number
Ps Pr Re S T Tf Tp Tv Tsteam Tw U V Xf Xp rw k q g
pressure of steam (kPa) Prandtl number Reynold number total solid content (% w/v) temperature (°C) feed temperature (°C) temperature of orange juice product (°C) temperature of vapour (°C) steam temperature wall temperature (°C) overall heat transfer coecient (kw/m2 °C) vapour ¯ow rate (kg/h) mass concentration of orange juice in feed stream (% wet basis) mass concentration of orange juice in product stream (% wet basis) wall thickness (m) latent heat of evaporation (kJ/kg) density (kg/m3 ) viscosity (cP)
Fig. 1. Schematic diagram of ATFE systems.
much higher ¯ow rates. The speci®cations of the evaporator are the same in each case and are as follows: Material Height Diameter Heat transfer area Agitator blades
stainless steel (0.0034 m) 4.5 m 0.108 m 0.251 m2 4 Luwa ®xed clearance (smooth or meshed)
The dual system was used to test the model on two dierent-sized systems as a test for generality. The ATFE systems were operated under vacuum conditions to reduce the boiling point of the orange juice. The dilute orange juice feed solution was pumped from the Feed Tank; the ¯ow rate was controlled by adjusting valve V1. The solution ¯ows through a ¯owmeter and enters the ATFE and is distributed over the inner circumference of the heated ATFE cylinder. A thin liquid ®lm is formed
by the rotating wipers and the liquid ¯ows downwards under gravity. The liquid is concentrated by steam that enters the outer shell of evaporator. The concentrated liquid ¯ows into tank R1 and leaves the system via valve V5. The vapour formed during the process is condensed in the Condenser and ¯ows to the tank R2 and leaves the system via valve V7. A vacuum pump is used to create a vacuum in the ATFE system, valve V6 is used to control the vacuum pressure in the ATFE system. 3. AspenplusTM simulation of the ATFE process An AspenPlusTM model of the ATFE process was developed using a rigorous heat exchanger model, Heatx followed by a rigorous 2-phase ¯ash model, Flash2 as shown in Fig. 2, Chuaprasert et al. (1999). The feed to the Heatx block represents the dilute orange juice±water
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
249
Fig. 2. AspenPlusTM simulation ¯owsheet of the evaporation process.
feed to the process. Steam enters the Heatx and leaves as condensate. The product from the Heatx block is a 2phase mixture of water vapour and concentrated orange juice±water liquid; this stream does not exist in the real process. The Flash2 model is used to separate the concentrated orange juice from the water vapour. The products from the Flash2 represent the two products from the real process. The pressure in the Flash2 unit was assumed to be the same as in the Heatx unit and adiabatic operation was assumed. Adiabatic operation is a reasonable assumption since the feed to Flash2 is a 2phase mixture of water vapour and concentrated juice and the purpose of the Flash2 is merely to separate the two phases.
These thermo-physical property equations were used to determine the value of overall heat transfer coecient, U, using the models developed by Sae Tae (1999) as follows: 0:0112 0:02 NuDe 0:00538 Re0:285 Pr0:539 K 1:643 ; De 1 FrDe
where
m_ avg gavg De 5:492 q2avg B
% total dissolved solids; density;
S 1:294B 3:2167;
viscosity;
FrDe
N 2 D2 ; De g
9
Pr
Cp;avg gavg g ; kavg
10
K
L ; Cp;avg Tw ÿ Tf;avg
11
1
Tw Tsteam ÿ
2
U0
3
NuDe
g 3:269 ÿ 2:4592S 17:0113S 2
specific heat capacity;
Cp ÿ5
3:8325 ÿ 5:423 10 T 0:01027 ÿ 3:0486S 2 ÿ 0:68486S;
4
thermal conductivity; k 0:54689 ÿ 6:886 10ÿ6 T 2 0:00206T ÿ 0:15732S 2 ÿ 0:2776S:
1 1 hs
rkww
Q_ evap ; A U0
12
;
13
hp D e ; kavg
1 1 1 rw : U hs hp k w
2
5
7 8
q 1:001 0:348S ÿ 0:002S ÿ 2:947
ÿ 0:0673T 3:8 10ÿ4 T 2 ;
;
8 m_ avg ; De gavg g B
2
10ÿ7 T 2 ;
#0:25
ReDe
4. Physical property equations of orange juice The thermo-physical properties of tangerine orange juice were developed as a function of temperature and total dissolved solids over the temperature range of 32± 80°C and dissolved solids range 5±40% w/v by Boonsriudomsuk (1999). The correlations are as follows:
"
6
14 15
Eqs. (6)±(15) were developed based on the ATFE pilot plant data operating over the following range of operating conditions: feed ¯ow rate 60±120 kg/h, steam pressure 1±2 bar and agitator speeds of 0±1000 rpm and using a sugar-syrup solution, Sae Tae (1999). In our experiments we used tangerine orange juice and
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N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
operated both the pilot plant and lab scale ATFE under the following conditions: · rotational speed of the agitator 200±800 rpm; · concentration of feed 3±10 Brix; · feed ¯ow rate: lab scale (batches 1±8) 13±21 kg/h, pilot scale (batches 9±13) 60±117 kg/h; · absolute pressure of steam 1±2 bar. 5. Results and discussion 5.1. Predicted heat transfer coecients Eqs. (1)±(5) were used to determine the physical properties of the orange juice and then the overall heat transfer coecient, U, was predicted from Eqs. (6)±(15). The predicted U-value was then used in the AspenPlusTM Heatx model. Although we expect the general form of the heat transfer coecient model, Eq. (6), to remain the same for orange juice it is expected that the coecients in Eq. (6) will be dierent for orange juice. A new model is currently under development. Figs. 3±5 show the comparison between the predicted and measured values of product ¯ow rate, vapour ¯ow rate and product concentration, respectively. From Fig. 3, we can see that the simulation and experimental product ¯ow rate results compare well. In batches 1±8 (lab scale evaporator), the agreement is very good,
however, in batches 9±13 (pilot plant evaporator), the simulated product ¯ow rates are somewhat higher than the experimental results. If one compares the dierence between experimental and simulated results on a percentage basis then the high ¯ow rate results are also in very good agreement. Fig. 4 shows the vapour ¯ow rate results. Again there is good agreement in batches 1±8 (lab scale) and some larger discrepancies in batches 9±13 where we ®nd that the simulated vapour ¯ow rates are lower than the experimental vapour ¯ow rates. It is worthwhile to note that all the experimental results were measured independently and therefore may exhibit some mass balance errors when compared with the feed ¯ow rate and the liquid ¯ow rate. Fig. 5 presents the experimental and simulated product concentrations using heat transfer coecients predicted using Eqs. (6)±(15). The results are in reasonable agreement for batches 1, 8 and 11±13, however, in batches 5, 6 and 7 we ®nd large discrepancies between the simulation and experimental results where the predicted product concentrations are very high. These three experiments were run at the lowest feed ¯ow rates (13± 16 kg/h); in this range we had diculty in maintaining the ¯ow rates and small absolute errors in the ¯ow rates will lead to large errors in concentration. In addition because the ¯ow rate was so low the orange juice residence time in the ATFE was high and scalding of the orange juice on the heat transfer surface of the ATFE occurred. As a result the measured concentration of orange juice in the liquid product was abnormally low; it should have been much higher due to the high heat transfer rates and large residence time. 5.2. Measured heat transfer coecients
Fig. 3. Product ¯ow rates using predicted heat transfer coecients.
Fig. 4. Condensate ¯ow rates using predicted heat transfer coecients.
Fig. 5. Product concentrations using predicted heat transfer coecients.
The heat transfer coecient model, (Eqs. (6)±(15)), was developed using the pilot plant ATFE only and with sugar syrup. Discrepancies in the model when applied to orange juice and dierent sizes of evaporators may lead to errors in the predicted U-values. Therefore the eective heat transfer coecient was measured by direct measurement of process variables and using Eq. (16), where the reference temperature was assumed to be Tp . U
Ff Cp Tp ÿ Tf V k : ADTlm
16
The eective heat transfer coecient combines all heat transfer factors including any heat loss from the process and any fouling factors. Therefore one should expect to see an improvement in the ®t between the simulation results and the experiments. Figs. 6±8 show the comparison between the experimental and simulation results when the eective heat transfer coecient was used in the Heatx model. Figs. 6 and 7 show the product and condensate ¯ow rates; the simulated ¯ow rates were
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
Fig. 6. Product ¯ow rates using the eective heat transfer coecients.
Fig. 7. Condensate ¯ow rates using eective heat transfer coecients.
Fig. 8. Product concentrations using eective heat transfer coecient.
calculated using AspenPlusTM using the eective heat transfer coecients determined from Eq. (16). The agreement between the experiments (m) and the simulations (n) is better than in Figs. 3 and 4 because the eective overall heat transfer coecient was used and modelling errors were reduced. Fig. 8 shows an improvement in the product compositions ®t between the simulation and experimental results in batches 1±4 and 8±13. However, in batches 5, 6 and 7 a large discrepancy still exists, in fact the gap between the experimental results (m) and the simulation results (n) has widened when the eective heat transfer coecient was used. This is because the eective heat transfer coecient was greater than that predicted by the model and so our predicted concentrations will increase when compared to those in Fig. 5. As mentioned above the ¯ow rates used in batches 5, 6, and 7 were extremely low and hard to control. It was felt that these low ¯ow rates led to scalding of orange juice on the heat transfer surface of the ATFE resulting in lower than actual orange juice concentrations.
6. Data reconciliation Process measurements generally do not satisfy material and energy balance constraints due to random or
251
possibly gross errors in the measuring device readings. Data reconciliation is a method of adjusting random errors in the measurements in a weighted least-squares sense in order to satisfy the process constraints. Steadystate simulators equipped with optimisation routines can be used to perform data reconciliation and parameter estimation. Readers are urged to consult Tjoa and Biegler (1991) and Picollo and Douglas (1996) for a review of data reconciliation and the use of AspenPlusTM for performing nonlinear data reconciliation of complex processes. Chuaprasert et al. (1999) presented an application of data reconciliation of an ATFE for concentrating sugar syrup using AspenPlusTM . The general nonlinear data reconciliation problem can be written as the following constrained weighted least squares problem: choose x: T
to minimise x ÿ y Q x ÿ y
17
such that h x 0 and g x P 0; where x is the vector of reconciled variables, y the vector of measured variables and Q is the weighting matrix, usually the inverse of the variance of the measured variables; h(x) are the set of equality constraints representing the model and g(x) are the set of inequality constraints present in the process. All measured variables are subjected to random error and should be considered in the formulation of the objective function. In addition, the heat transfer coecient, which was calculated from measurements, should be included. The measured, and/or calculated variables therefore include: · feed ¯ow rate, Ff ; · feed concentration of orange juice, Xf ; · feed temperature, Tf ; · steam ¯ow rate, Fs ; · steam pressure, Ps ; · product ¯ow rate, Fp ; · product concentration, Xp ; · product temperature, Tp ; · vapour ¯ow rate, Fv ; · vapour temperature, Tv ; · overall heat transfer coecient, U. It was decided not to include the overall heat transfer area, A, in the list of variables subjected to random error since it was measured only once and the eect of an error in its measurement would be compensated for in the overall heat transfer coecient. The overall objective function is a sum of the squares of the variable mismatches divided by their variances and multiplied by a factor denoting the importance and/ or con®dence we have in the accuracy of the particular variable measurement. The factor becomes larger as the variable becomes more important to match closely or its value is known more accurately. It was felt, for example, that the orange juice feed concentration was known to a high degree of accuracy i.e. the standard deviation
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N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
of the orange juice concentration is small compared to the standard deviation of other variables. Therefore we set the weighting factor for orange juice feed concentration to be a high value, 50, relative to the other weighting factors to force the optimiser to adjust other process variables rather than the orange juice feed concentrations. There was not enough information to calculate the standard deviations therefore it was decided to ignore standard deviations and use only weighting factors. The objective function was therefore written as OF 1 feed flow rate ÿ Ff
®t was obtained from the data reconciliation. One can think of the reconciled values (d) as improved experimental values that are both close to the actual experimental values (m) and also satisfy all the mass and energy balance constraints. Once the data have been reconciled to satisfy the heat and material balances, we can use these adjusted data for further studies. For example, the operation of the evaporator may now be studied to determine the eect of alternate operating procedures to improve production or reduce energy consumption.
2
50 feed concentration of orange juice ÿ Xf 2 1 steam flow rate ÿ Fs
2
1 product flow rate ÿ Fp 2 1 product concentration of orange juice ÿ Xp 2 2
1 vapour flow rate ÿ Fv :
18
One cannot directly manipulate all decision variables in AspenPlusTM . For example, in our case one cannot directly manipulate the product ¯ow rate and product concentration. Therefore manipulated variables that will indirectly adjust or manipulate these variables must be selected. Four manipulated variables were chosen to minimise the objective function, Eq. (18): · ¯ow rate of water in feed, · steam ¯ow rate, · heat transfer coecient, · ¯ow rate of orange juice component in feed. The adjustment of ¯ow rate of the orange juice component in the feed and the ¯ow rate of the water in the feed has the combined aect of adjusting the total feed ¯ow rate and composition of the feed simultaneously. The steam ¯ow rate was adjusted to try and match the evaporator temperature and product concentration. The overall heat transfer coecient was adjusted to try and match the concentration of orange juice in the product stream. Therefore, solution to the problem using AspenPlusTM can be written as choose
¯ow rate of water in the feed ¯ow rate of orange juice component in the feed steam ¯ow rate heat transfer coecient to minimise Eq. (18) such that h(x) 0
7. Results of data reconciliation The reconciliation results are presented in Figs. 6±8. The results indicate that the reconciled values (d) match the measured values (m) quite well. From the results in Figs. 6±8 one can clearly see that an improvement in the
8. Conclusions 1. A steady-state simulation model of an ATFE for concentrating tangerine orange juice was developed using AspenPlusTM . 2. The simulation results show good agreement with the experimental results when using overall heat transfer coecients predicted from an independent correlation and better agreement when using eective heat transfer coecients calculated from experimental process measurements. 3. Low and dicult to control feed ¯ow rates lead to large errors in the prediction of the product concentrations due to scalding of the orange juice on the heat transfer surface of the ATFE. 4. The steady-state AspenPlusTM simulation model combined with a built-in optimisation routine was used to reconcile the experimental data gathered from the evaporator. After data reconciliation a signi®cant improvement in the ®t of the measured data was observed. On average the ®t between measured values and the process model was increased by about 60%.
Acknowledgements The authors are very appreciative of research funding from The National Science and Technology Development Agency of Thailand (NSTDA) which enabled this research to be undertaken.
References Aspen Technology. (1993). AspenplusTM users manual. AspenTech Ltd, Cambridge MA, USA. Boonsriudomsuk, et al. S. (1998). Thermophysical Properties of Orange Juice. Bachelor Thesis, Department of Chemical Engineering, King Mongkut's University of Technology Thonburi, Bangkok, Thailand, (in Thai). Chuaprasert, S., Douglas, P. L., & Nguyen, M. (1999). Data reconciliation of an agitated thin ®lm evaporator using AspenPlusTM . Journal of Food Engineering, 39, 261±267.
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253 Piccolo, M., & Douglas, P. L. (1996). Data reconciliation using AspenPlusTM . Developments in Chemical Engineering & Mineral Processing, 4(3/4), 157±182. Sae Tae, A. (1999). Heat transfer coecients in an agitated thin ®lm evaporator for concentrating sugar syrup. Masters Thesis, Depart-
253
ment of Chemical Engineering, King Mongkut's University of Technology Thonburi, Bangkok, Thailand, (in Thai). Tjoa, I. B., & Biegler, L. T. (1991). Simultaneous strategies for data reconciliation and gross error detection of nonlinear systems. Computers and Chemical Engineering, 15(10), 679±690.
www.elsevier.com/locate/jfoodeng
Simulation of an agitated thin ®lm evaporator for concentrating orange juice using AspenPlusTM Nongluk Chawankul a, Supaporn Chuaprasert a, Peter Douglas b,*, Wilai Luewisutthichat a a
Department of Chemical Engineering, King Mongkut's University of Technology, Bangkok 10140, Thailand b Department of Chemical Engineering, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada Received 7 January 2000; accepted 24 July 2000
Abstract The focus of this research is on the concentration of orange juice in agitated thin ®lm evaporators (ATFE). The AspenPlusä simulation program was used to develop a model of the ATFE. A rigorous heat exchanger model, Heatx followed by the rigorous 2phase ¯ash model, Flash2, was used to simulate the dominant eects of the ATFE. The thermo-physical properties of orange juice are not available in the AspenPlusä databank. They were, therefore, determined experimentally and modelled as functions of temperature and solid content. Heat transfer coecients were predicted using correlations and measured from process measurements. Experimental and simulation results are presented. The AspenPlusä simulation model using experimentally determined thermo-physical properties of orange juice compares well with the experimental data from the ATFE pilot plant. Process measurements were reconciled using the optimisation features of AspenPlusTM . Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Simulation; AspenPlus; Agitated thin ®lm evaporator; Orange juice
1. Introduction Simulation is used as a tool to analyse plant design and operating conditions. Simulation packages such as AspenPlusTM have built-in process models, thus oering a convenient and time saving means of examining an entire chemical process, Aspen Technology (1993). Most process simulation applications are found in the chemical process industries and there are few applications in the food industry. Evaporators are widely used in the food industry as concentrators and separators. In particular, agitated thin ®lm evaporators (ATFE) which have short residence times and relatively high heat transfer coecients, are best used for concentrating foods that are heat sensitive and cannot tolerate high temperatures for more than a few seconds. Chuaprasert, Douglas, & Nguyen (1999) used AspenPlusTM to simulate and perform data reconciliation of experimental measurements of a lab scale ATFE for concentrating sugar syrup. The focus of this paper is on the concentration of tangerine orange juice in an ATFE. Experiments were performed on two dierent ATFE systems. *
Corresponding author. Tel.: +1-519-888-4567 ext. 2913; fax: +1519-746-4979. E-mail address: [email protected] (P. Douglas).
One, a lab scale system used by Chuaprasert et al. (1999) and the other, a pilot plant scale capable of handling larger ¯ow rates. A generalised heat transfer coecient model was developed and applied to all the data. The process was simulated using the AspenPlusTM simulation model developed by Chuaprasert et al. (1999). The model consisted of a rigorous heat exchange model (Heatx) followed by a rigorous 2-phase ¯ash (Flash2). The heat exchanger model was used to simulate the evaporator and required the heat transfer area, A, and the overall heat transfer coecient, U. The output stream from the heat exchanger, a 2-phase stream consisting of concentrated orange juice and water vapour, was fed to the 2-phase ¯ash unit operating at the same pressure. The ¯ash unit then separated the water vapour from the concentrated orange juice liquid.
2. ATFE A schematic diagram of the ATFE systems in the Department of Chemical Engineering at King Mongkut's University of Technology, Thonburi, KMUTT, is shown in Fig. 1. Both the lab scale system and the pilot plant system have the same con®guration, the only difference being that the pilot plant system can handle
0260-8774/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 0 ) 0 0 1 2 2 - 9
248
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
Nomenclature A B Cp D De Fr Ff Fp Fs Fv g hp hs k kw K mavg N Nu
2
overall heat transfer area (m ) concentration (Brix) speci®c heat capacity (kJ/kg °C) diameter of cylinder (m) equivalent diameter (m) Froude number ¯ow rate of feed stream (kg/h) ¯ow rate of product stream (kg/h) ¯ow rate of steam (kg/h) ¯ow rate of vapour stream (kg/h) gravity (m/s2 ) heat transfer coecient of liquid steam (kw/m2 °C) heat transfer coecient of steam (kw/m2 °C) thermal conductivity (w/m °C) thermal conductivity of wall (kw/m °C) condensation number average mass ¯ow rate (kg/s) speed of agitator (rpm) Nusselt number
Ps Pr Re S T Tf Tp Tv Tsteam Tw U V Xf Xp rw k q g
pressure of steam (kPa) Prandtl number Reynold number total solid content (% w/v) temperature (°C) feed temperature (°C) temperature of orange juice product (°C) temperature of vapour (°C) steam temperature wall temperature (°C) overall heat transfer coecient (kw/m2 °C) vapour ¯ow rate (kg/h) mass concentration of orange juice in feed stream (% wet basis) mass concentration of orange juice in product stream (% wet basis) wall thickness (m) latent heat of evaporation (kJ/kg) density (kg/m3 ) viscosity (cP)
Fig. 1. Schematic diagram of ATFE systems.
much higher ¯ow rates. The speci®cations of the evaporator are the same in each case and are as follows: Material Height Diameter Heat transfer area Agitator blades
stainless steel (0.0034 m) 4.5 m 0.108 m 0.251 m2 4 Luwa ®xed clearance (smooth or meshed)
The dual system was used to test the model on two dierent-sized systems as a test for generality. The ATFE systems were operated under vacuum conditions to reduce the boiling point of the orange juice. The dilute orange juice feed solution was pumped from the Feed Tank; the ¯ow rate was controlled by adjusting valve V1. The solution ¯ows through a ¯owmeter and enters the ATFE and is distributed over the inner circumference of the heated ATFE cylinder. A thin liquid ®lm is formed
by the rotating wipers and the liquid ¯ows downwards under gravity. The liquid is concentrated by steam that enters the outer shell of evaporator. The concentrated liquid ¯ows into tank R1 and leaves the system via valve V5. The vapour formed during the process is condensed in the Condenser and ¯ows to the tank R2 and leaves the system via valve V7. A vacuum pump is used to create a vacuum in the ATFE system, valve V6 is used to control the vacuum pressure in the ATFE system. 3. AspenplusTM simulation of the ATFE process An AspenPlusTM model of the ATFE process was developed using a rigorous heat exchanger model, Heatx followed by a rigorous 2-phase ¯ash model, Flash2 as shown in Fig. 2, Chuaprasert et al. (1999). The feed to the Heatx block represents the dilute orange juice±water
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
249
Fig. 2. AspenPlusTM simulation ¯owsheet of the evaporation process.
feed to the process. Steam enters the Heatx and leaves as condensate. The product from the Heatx block is a 2phase mixture of water vapour and concentrated orange juice±water liquid; this stream does not exist in the real process. The Flash2 model is used to separate the concentrated orange juice from the water vapour. The products from the Flash2 represent the two products from the real process. The pressure in the Flash2 unit was assumed to be the same as in the Heatx unit and adiabatic operation was assumed. Adiabatic operation is a reasonable assumption since the feed to Flash2 is a 2phase mixture of water vapour and concentrated juice and the purpose of the Flash2 is merely to separate the two phases.
These thermo-physical property equations were used to determine the value of overall heat transfer coecient, U, using the models developed by Sae Tae (1999) as follows: 0:0112 0:02 NuDe 0:00538 Re0:285 Pr0:539 K 1:643 ; De 1 FrDe
where
m_ avg gavg De 5:492 q2avg B
% total dissolved solids; density;
S 1:294B 3:2167;
viscosity;
FrDe
N 2 D2 ; De g
9
Pr
Cp;avg gavg g ; kavg
10
K
L ; Cp;avg Tw ÿ Tf;avg
11
1
Tw Tsteam ÿ
2
U0
3
NuDe
g 3:269 ÿ 2:4592S 17:0113S 2
specific heat capacity;
Cp ÿ5
3:8325 ÿ 5:423 10 T 0:01027 ÿ 3:0486S 2 ÿ 0:68486S;
4
thermal conductivity; k 0:54689 ÿ 6:886 10ÿ6 T 2 0:00206T ÿ 0:15732S 2 ÿ 0:2776S:
1 1 hs
rkww
Q_ evap ; A U0
12
;
13
hp D e ; kavg
1 1 1 rw : U hs hp k w
2
5
7 8
q 1:001 0:348S ÿ 0:002S ÿ 2:947
ÿ 0:0673T 3:8 10ÿ4 T 2 ;
;
8 m_ avg ; De gavg g B
2
10ÿ7 T 2 ;
#0:25
ReDe
4. Physical property equations of orange juice The thermo-physical properties of tangerine orange juice were developed as a function of temperature and total dissolved solids over the temperature range of 32± 80°C and dissolved solids range 5±40% w/v by Boonsriudomsuk (1999). The correlations are as follows:
"
6
14 15
Eqs. (6)±(15) were developed based on the ATFE pilot plant data operating over the following range of operating conditions: feed ¯ow rate 60±120 kg/h, steam pressure 1±2 bar and agitator speeds of 0±1000 rpm and using a sugar-syrup solution, Sae Tae (1999). In our experiments we used tangerine orange juice and
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N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
operated both the pilot plant and lab scale ATFE under the following conditions: · rotational speed of the agitator 200±800 rpm; · concentration of feed 3±10 Brix; · feed ¯ow rate: lab scale (batches 1±8) 13±21 kg/h, pilot scale (batches 9±13) 60±117 kg/h; · absolute pressure of steam 1±2 bar. 5. Results and discussion 5.1. Predicted heat transfer coecients Eqs. (1)±(5) were used to determine the physical properties of the orange juice and then the overall heat transfer coecient, U, was predicted from Eqs. (6)±(15). The predicted U-value was then used in the AspenPlusTM Heatx model. Although we expect the general form of the heat transfer coecient model, Eq. (6), to remain the same for orange juice it is expected that the coecients in Eq. (6) will be dierent for orange juice. A new model is currently under development. Figs. 3±5 show the comparison between the predicted and measured values of product ¯ow rate, vapour ¯ow rate and product concentration, respectively. From Fig. 3, we can see that the simulation and experimental product ¯ow rate results compare well. In batches 1±8 (lab scale evaporator), the agreement is very good,
however, in batches 9±13 (pilot plant evaporator), the simulated product ¯ow rates are somewhat higher than the experimental results. If one compares the dierence between experimental and simulated results on a percentage basis then the high ¯ow rate results are also in very good agreement. Fig. 4 shows the vapour ¯ow rate results. Again there is good agreement in batches 1±8 (lab scale) and some larger discrepancies in batches 9±13 where we ®nd that the simulated vapour ¯ow rates are lower than the experimental vapour ¯ow rates. It is worthwhile to note that all the experimental results were measured independently and therefore may exhibit some mass balance errors when compared with the feed ¯ow rate and the liquid ¯ow rate. Fig. 5 presents the experimental and simulated product concentrations using heat transfer coecients predicted using Eqs. (6)±(15). The results are in reasonable agreement for batches 1, 8 and 11±13, however, in batches 5, 6 and 7 we ®nd large discrepancies between the simulation and experimental results where the predicted product concentrations are very high. These three experiments were run at the lowest feed ¯ow rates (13± 16 kg/h); in this range we had diculty in maintaining the ¯ow rates and small absolute errors in the ¯ow rates will lead to large errors in concentration. In addition because the ¯ow rate was so low the orange juice residence time in the ATFE was high and scalding of the orange juice on the heat transfer surface of the ATFE occurred. As a result the measured concentration of orange juice in the liquid product was abnormally low; it should have been much higher due to the high heat transfer rates and large residence time. 5.2. Measured heat transfer coecients
Fig. 3. Product ¯ow rates using predicted heat transfer coecients.
Fig. 4. Condensate ¯ow rates using predicted heat transfer coecients.
Fig. 5. Product concentrations using predicted heat transfer coecients.
The heat transfer coecient model, (Eqs. (6)±(15)), was developed using the pilot plant ATFE only and with sugar syrup. Discrepancies in the model when applied to orange juice and dierent sizes of evaporators may lead to errors in the predicted U-values. Therefore the eective heat transfer coecient was measured by direct measurement of process variables and using Eq. (16), where the reference temperature was assumed to be Tp . U
Ff Cp Tp ÿ Tf V k : ADTlm
16
The eective heat transfer coecient combines all heat transfer factors including any heat loss from the process and any fouling factors. Therefore one should expect to see an improvement in the ®t between the simulation results and the experiments. Figs. 6±8 show the comparison between the experimental and simulation results when the eective heat transfer coecient was used in the Heatx model. Figs. 6 and 7 show the product and condensate ¯ow rates; the simulated ¯ow rates were
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253
Fig. 6. Product ¯ow rates using the eective heat transfer coecients.
Fig. 7. Condensate ¯ow rates using eective heat transfer coecients.
Fig. 8. Product concentrations using eective heat transfer coecient.
calculated using AspenPlusTM using the eective heat transfer coecients determined from Eq. (16). The agreement between the experiments (m) and the simulations (n) is better than in Figs. 3 and 4 because the eective overall heat transfer coecient was used and modelling errors were reduced. Fig. 8 shows an improvement in the product compositions ®t between the simulation and experimental results in batches 1±4 and 8±13. However, in batches 5, 6 and 7 a large discrepancy still exists, in fact the gap between the experimental results (m) and the simulation results (n) has widened when the eective heat transfer coecient was used. This is because the eective heat transfer coecient was greater than that predicted by the model and so our predicted concentrations will increase when compared to those in Fig. 5. As mentioned above the ¯ow rates used in batches 5, 6, and 7 were extremely low and hard to control. It was felt that these low ¯ow rates led to scalding of orange juice on the heat transfer surface of the ATFE resulting in lower than actual orange juice concentrations.
6. Data reconciliation Process measurements generally do not satisfy material and energy balance constraints due to random or
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possibly gross errors in the measuring device readings. Data reconciliation is a method of adjusting random errors in the measurements in a weighted least-squares sense in order to satisfy the process constraints. Steadystate simulators equipped with optimisation routines can be used to perform data reconciliation and parameter estimation. Readers are urged to consult Tjoa and Biegler (1991) and Picollo and Douglas (1996) for a review of data reconciliation and the use of AspenPlusTM for performing nonlinear data reconciliation of complex processes. Chuaprasert et al. (1999) presented an application of data reconciliation of an ATFE for concentrating sugar syrup using AspenPlusTM . The general nonlinear data reconciliation problem can be written as the following constrained weighted least squares problem: choose x: T
to minimise x ÿ y Q x ÿ y
17
such that h x 0 and g x P 0; where x is the vector of reconciled variables, y the vector of measured variables and Q is the weighting matrix, usually the inverse of the variance of the measured variables; h(x) are the set of equality constraints representing the model and g(x) are the set of inequality constraints present in the process. All measured variables are subjected to random error and should be considered in the formulation of the objective function. In addition, the heat transfer coecient, which was calculated from measurements, should be included. The measured, and/or calculated variables therefore include: · feed ¯ow rate, Ff ; · feed concentration of orange juice, Xf ; · feed temperature, Tf ; · steam ¯ow rate, Fs ; · steam pressure, Ps ; · product ¯ow rate, Fp ; · product concentration, Xp ; · product temperature, Tp ; · vapour ¯ow rate, Fv ; · vapour temperature, Tv ; · overall heat transfer coecient, U. It was decided not to include the overall heat transfer area, A, in the list of variables subjected to random error since it was measured only once and the eect of an error in its measurement would be compensated for in the overall heat transfer coecient. The overall objective function is a sum of the squares of the variable mismatches divided by their variances and multiplied by a factor denoting the importance and/ or con®dence we have in the accuracy of the particular variable measurement. The factor becomes larger as the variable becomes more important to match closely or its value is known more accurately. It was felt, for example, that the orange juice feed concentration was known to a high degree of accuracy i.e. the standard deviation
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of the orange juice concentration is small compared to the standard deviation of other variables. Therefore we set the weighting factor for orange juice feed concentration to be a high value, 50, relative to the other weighting factors to force the optimiser to adjust other process variables rather than the orange juice feed concentrations. There was not enough information to calculate the standard deviations therefore it was decided to ignore standard deviations and use only weighting factors. The objective function was therefore written as OF 1 feed flow rate ÿ Ff
®t was obtained from the data reconciliation. One can think of the reconciled values (d) as improved experimental values that are both close to the actual experimental values (m) and also satisfy all the mass and energy balance constraints. Once the data have been reconciled to satisfy the heat and material balances, we can use these adjusted data for further studies. For example, the operation of the evaporator may now be studied to determine the eect of alternate operating procedures to improve production or reduce energy consumption.
2
50 feed concentration of orange juice ÿ Xf 2 1 steam flow rate ÿ Fs
2
1 product flow rate ÿ Fp 2 1 product concentration of orange juice ÿ Xp 2 2
1 vapour flow rate ÿ Fv :
18
One cannot directly manipulate all decision variables in AspenPlusTM . For example, in our case one cannot directly manipulate the product ¯ow rate and product concentration. Therefore manipulated variables that will indirectly adjust or manipulate these variables must be selected. Four manipulated variables were chosen to minimise the objective function, Eq. (18): · ¯ow rate of water in feed, · steam ¯ow rate, · heat transfer coecient, · ¯ow rate of orange juice component in feed. The adjustment of ¯ow rate of the orange juice component in the feed and the ¯ow rate of the water in the feed has the combined aect of adjusting the total feed ¯ow rate and composition of the feed simultaneously. The steam ¯ow rate was adjusted to try and match the evaporator temperature and product concentration. The overall heat transfer coecient was adjusted to try and match the concentration of orange juice in the product stream. Therefore, solution to the problem using AspenPlusTM can be written as choose
¯ow rate of water in the feed ¯ow rate of orange juice component in the feed steam ¯ow rate heat transfer coecient to minimise Eq. (18) such that h(x) 0
7. Results of data reconciliation The reconciliation results are presented in Figs. 6±8. The results indicate that the reconciled values (d) match the measured values (m) quite well. From the results in Figs. 6±8 one can clearly see that an improvement in the
8. Conclusions 1. A steady-state simulation model of an ATFE for concentrating tangerine orange juice was developed using AspenPlusTM . 2. The simulation results show good agreement with the experimental results when using overall heat transfer coecients predicted from an independent correlation and better agreement when using eective heat transfer coecients calculated from experimental process measurements. 3. Low and dicult to control feed ¯ow rates lead to large errors in the prediction of the product concentrations due to scalding of the orange juice on the heat transfer surface of the ATFE. 4. The steady-state AspenPlusTM simulation model combined with a built-in optimisation routine was used to reconcile the experimental data gathered from the evaporator. After data reconciliation a signi®cant improvement in the ®t of the measured data was observed. On average the ®t between measured values and the process model was increased by about 60%.
Acknowledgements The authors are very appreciative of research funding from The National Science and Technology Development Agency of Thailand (NSTDA) which enabled this research to be undertaken.
References Aspen Technology. (1993). AspenplusTM users manual. AspenTech Ltd, Cambridge MA, USA. Boonsriudomsuk, et al. S. (1998). Thermophysical Properties of Orange Juice. Bachelor Thesis, Department of Chemical Engineering, King Mongkut's University of Technology Thonburi, Bangkok, Thailand, (in Thai). Chuaprasert, S., Douglas, P. L., & Nguyen, M. (1999). Data reconciliation of an agitated thin ®lm evaporator using AspenPlusTM . Journal of Food Engineering, 39, 261±267.
N. Chawankul et al. / Journal of Food Engineering 47 (2001) 247±253 Piccolo, M., & Douglas, P. L. (1996). Data reconciliation using AspenPlusTM . Developments in Chemical Engineering & Mineral Processing, 4(3/4), 157±182. Sae Tae, A. (1999). Heat transfer coecients in an agitated thin ®lm evaporator for concentrating sugar syrup. Masters Thesis, Depart-
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ment of Chemical Engineering, King Mongkut's University of Technology Thonburi, Bangkok, Thailand, (in Thai). Tjoa, I. B., & Biegler, L. T. (1991). Simultaneous strategies for data reconciliation and gross error detection of nonlinear systems. Computers and Chemical Engineering, 15(10), 679±690.