sYoartm

latos woproponhe niry

d simulation within processocess sfor exabehavil proculationmak

en et aween

Rigorous process simulators such as Aspen Plus/Aspen Dynam-

ulators can directly provide steady state models, dynamic models,and performance analysis (e.g., Luyben, 2002).

Modeling and simulation of processes involving chemical reac-tants or products are well developed where sufcient physicalproperty data and prediction models are available (Dnnebierand Klatt, 2000; Han and Chung, 2001). Their application to food

processing has lagged behind due to the diversity of food process-ing, the great variety of food products, and the complex physical,chemical and biological structure of foods, which are mostly solid,

and VMGSim) were developed principally for the applications inre are a few rareions.roSimPlus sal gas and

phase activity coefcient models. No validation of the milk cnents thermo physical properties was presented. Halder(2011) and Abakarov and Nuez (2012) presented software examplesfor food engineering applications but these are lacking the mostimportant process simulator capability unit operation modules.

The use of a commercial process simulator for food process stud-ies is appropriate due to advantages derived from the availability oflarge number of simulation modules, both for unit operations andinformation management, and the ease with which it can simulatea process. A process simulator requires food components in its

Corresponding author. Tel.: +64 9 923 5606; fax: +64 9 373 7463.E-mail addresses: tajammal.munir@auckland.ac.nz (M.T. Munir), b.young@

Journal of Food Engineering 121 (2014) 8793

Contents lists availab

od

lsauckland.ac.nz (B.R. Young).ics, HYSYS and VMGSim have increasingly been used in recentyears for modeling and simulation tasks in many processes fromdifferent industries (Ruiz et al., 2010; Daz et al., 2011; Peterset al., 2011; Zhao et al., 2011; Munir et al., 2012a,b). Process sim-

the eld of chemical engineering. However, thesoftware examples for food engineering applicat

Bon (2005) and Bon et al. (2010) presented a Ption ow sheet for milk pasteurisation using ide0260-8774/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.jfoodeng.2013.07.033imula-liquidompo-et al.real-life operation, process simulators can provide reliable infor-mation on process operation due to the existence of comprehen-sive thermodynamic packages, vast component libraries andadvanced computational methods (West et al., 2008; Garcaet al., 2010).

2010). These difculties and complexities involved in food materi-als are the main reasons for the absence of food components in thecomponent libraries of commercial process simulators. This limitsgeneral process simulator applicability to the food industries.

Most commercial process simulators (e.g. Aspen Plus, HYSYS1. Introduction

The use of process modeling anengineering is well recognized as prtools for model based calculations They help to predict certain processat low cost without putting the reaoperation) at risk. Modeling and simrole in critical process decision(Rodrigues and Minceva, 2005; Thei(generally expected) differences betimulators are powerfulmple in process design.ours accurately enoughess (equipment or unitplay a very important

ing and optimizationl., 2011). Despite someprocess simulation and

semi-solid or in some cases liquid, e.g. liquid milk. Most food mate-rials also have highly complex compositions and their propertieschange irreversibly during the process (Wang and Hirai, 2011;Trystram, 2012). The complexities involved in the prediction offood material properties also bring an added difculty to predicttheir behaviour as a function of the operating conditions, i.e. T, P.These food material properties cause more difculties when mod-eling processes involving food reactants or products (Bon et al.,Development of hypothetical componentusing a commercial process simulator

Y. Zhang, Muhammad Tajammal Munir, W. Yu, B.R.Industrial Information & Control Centre (I2C2), Chemical and Materials Engineering Dep

a r t i c l e i n f o

Article history:Received 17 December 2012Received in revised form 24 May 2013Accepted 19 July 2013Available online 17 August 2013

Keywords:Process simulationMilk processingHypothetical components

a b s t r a c t

Commercial process simuprocessing. The aim of thicessing using commerciallibrary, a hypothetical comand functions to estimate tnow be extended to the da

Journal of Fo

journal homepage: www.efor milk process simulation

ung ent, The University of Auckland, New Zealand

rs do not contain all the components required for simulation of milkrk was to create credible hypothetical components to simulate milk pro-cess simulators. To create milk components in the simulator componentent database was built in a commercial process simulator with the valuesecessary physical properties of the milk. As a result process simulation canindustry.

2013 Elsevier Ltd. All rights reserved.

le at ScienceDirect

Engineering

evier .com/ locate / j foodeng

(b) Protein: Caseins are the proteins commonly found inmammalian milk, making up to 80% of the total proteinsin milk while whey proteins make up the rest 20%. Dueto the unavailability of public domain literature on thephysical properties of whey proteins, and consideringtheir relatively minor weight percentage in the total pro-teins, the protein of milk is simplied to be casein(Assumption 2). The average molecular weight of caseinwas set to 23,000 kg/kg mole, and the density of caseinwas set to be 1250 kg/m3 (Karlsson et al., 2005; Choi

Table 1Quantit

Prod

WhoConc

m

d Engineerincomponent library due to fact that food components are mandatoryfor food process modeling and simulation. In this work, importantfood components for modeling milk were built as hypotheticalcomponents for milk process studies.

One important industrial food process is the milk processingprocess, which involves the handling of uids, i.e. milk. For exam-ple, milk (whole or concentrated) is one of the main raw materialsin milk pasteurization processes, milk powder, and cheese plants.To develop a milk process simulation, based on a commercial pro-cess simulator, the milk as a collection of hypothetical componentsneeds to be developed. For that purpose, data on the properties(mostly physical properties) of milk (Ruiz et al., 2010; Bisig,2011; Sindhu and Arora, 2011) is used to predict actual milkbehaviour and properties.

In this work VMGSim was selected as the commercial processsimulator for its simulation capabilities, its ability to incorporatecustomized calculations using the spread sheet tool, user friendlyinterface and its most recent and updated thermodynamics fromTRC/NIST for the prediction of thermodynamic data (i.e. heatcapacity and thermal conductivity) required for the hypotheticalcomponents simulation. It is one of the latest commercial processsimulators mainly conceived for the chemical and petrochemicalindustries (Daz et al., 2011; Satyro et al., 2011; Munir et al.,2012a,b) and developed by Virtual Materials Group Inc. (VMG)(Virtual Materials Group Inc., 2012). It is extensively used to designa new process, troubleshoot an existing process unit or optimizeoperations in a process (Saber and Shaw, 2008; Jiang et al., 2011;Satyro et al., 2011; Motahhari et al., 2012). In addition to oil andgas, and chemical purposes, it has also been used for biofuel pro-cess applications (Lee et al., 2011).

The aim of this work was to develop hypothetical componentsbased on the process simulator to simulate actual milk. For thispurpose the data on the properties of milk needed to develophypothetical components were obtained from literature (Bylund,1995; Bon et al., 2010), and the VMGThermo thermodynamic data-base in the simulator. This would allow the simulation of milk as acollection of new components (hypothetical components) in thesimulator, needed to simulate milk processing, and to predict milkprocess behaviour closely enough to its real-life operation.

This manuscript is organized as follows. After this general intro-duction, the materials andmethods used in this work are explainedand discussed in Section 2. In Section 3 results are discussed. Final-ly in Section 4 results are summarized, limitations are discussed,and conclusions are made.

2. Materials and methods

2.1. Raw material (milk): composition and properties

The typical whole (13 wt.% total solids) and concentrated(50 wt.% total solids) milk compositions considered in this workare shown in Table 1 (Bylund, 1995; Bon et al., 2010). A materialstream was built in the simulator in order to develop a pseudomilk mixture having hypothetical components (represented by asuperscripted asterisk, ). Depending on the component informa-tion contained in the simulator (e.g. palmitic acid, n hexadeca-noic acid, oleic acid, sodium chloride (NaCl) and potassiumchloride (KCl) are already present in the simulator component li-brary) component library, each component of the milk composition(fat, proteins, lactose and minerals) was further classied into sim-pler components as shown in Table 2 and Fig. 1. The total solidcomponents include fat, proteins, lactose and minerals.

The assumptions considered in this work and the further classi-

88 Y. Zhang et al. / Journal of Foocation of each component of the milk composition (fat, proteins,lactose and minerals) into simplercomponents are given asfollows:2.1.1. AssumptionsThe following assumptions were adopted after the following

considerations:

(a) Fat: Milk fat is usually considered as a mix of triglycerideesters, which are composed of various fatty-acids and glyc-erol. As each glycerol can bind three fatty-acids and theyare not necessarily the same kind, the number of differentglycerides is extremely large. As a result, fats are usuallycharacterized by fatty-acids. (Bylund, 1995) In this researchwe used fatty-acids instead of fatty-esters in simulating milkdue to the following considerations. The composition of fatty esters is extremely complex,

none of which can be found in the literature or the VMG-Sim or other commercial process simulator thermody-namic databases.

Another compound in the VMGSim database named TRI-GLY(C18)3 (C54H105O6) and belonging to the oil familywas attempted to be used to represent the total amountof fat. However, the approach resulted in signicant dif-ferences in density (1223 kg/m3 vs. 1022 kg/m3), heatcapacity (1055 kJ/kmol K vs. 79 kJ/kmol K), thermal con-ductivity (0.23 W/m K vs. 0.55 W/m K) and viscosity(0.123 Pa s vs. 0.00203 Pa s) for the nal pseudo milk.

Fatty acids are the closest match to milk fat and usingthese fatty acids, the pseudo milk showed a close matchof the main physical properties to actual milk.

The main drawback is that the chemical properties ofesters and acids are very different. However since thisresearch only focuses on the physical properties, the dif-ferences in chemical properties can be ignored, whichneed to be considered in fouling reactions and cheesemaking.

The main component of milk fatty acid is palmitic acid (2529 wt.%) and oleic acid (3040 wt.%), which can both be found inthe simulator component list. Other minor fatty acids include bu-tyric acid, myristic acid, stearic acid, and so on. For the simplica-tion purpose and their similar weight percentage in total fatty acidcontents, the fraction of each of these two fats was set to half(50 wt.% palmitic acid and 50 wt.% oleic acid) and all other typesof fat components were ignored (Assumption 1).ative milk composition (% in mass) (Bylund, 1995; Bon et al., 2010).

uct Water Fat Proteins Lactose Minerals Totalsolids

le milk 87.0 4.0 3.4 4.8 0.8 13.0entratedilk

50.0 16.0 13.0 18.0 3.0 50.0

g 121 (2014) 8793et al., 2011). A hypothetical component was created inthe simulator based on these attributes to simulateproteins.

2.2. Prselecti

Befmilk mand daexplai

Thecompoand oavailacompo(Lactotheticthe in(NBP)prope

Themody

non-polar nature of some of the compounds.

Fig.

d En(c) Minerals: The mineral fraction in milk, which is a smallfraction of milk (0.8 wt.%), contains cations (calcium,magnesium, sodium and potassium) and anions (inor-ganic phosphate, citrate and chloride) (Bylund, 1995;Gaucheron, 2005). Due to the unavailability of calciumsalts in the VMGSim thermodynamic database, the min-erals in raw milk were specied as 50% NaCl and 50% KClfor simplicitys sake (Assumption 3). They can both befound in the simulator component list.

(d) Viscosity: Since oleic acid, palmitic acid, NaCl and KClcan be found in the component list in VMGSim, theirviscosity value cannot be manually changed. Also, thelactose as a hypothetical compound in VMGSim is con-sidered to have a high solubility in water, so it shouldhardly affect the total liquid viscosity. Due to the insolu-bility of proteins and the availability of changing theirviscosity value in VMGSim, they were selected as themain contributor of pseudo milk viscosity (Assump-tion 4).

(e) Lactose: The component list of the simulator does notinclude lactose, thus another hypothetical componentwas created with these attributes: molecular weight

Lactose*

1. Composition of milk in the simulator ( = hypothetical components).Table 2Composition of milk in the simulator (pseudo milk mixture).

Product Water Fat

Palmitic acid Oleic acid

Whole milk 87.0 2.0 2.0Concentrated milk 50.0 8.0 8.0

Milk Water

Fat

Minerals

Proteins*

Mixture of Milk components

Components already available

in library

Pseudo components

Palmitic acid

Oleic acid

NaCl

KCl

Y. Zhang et al. / Journal of Foo(342.3), normal boiling point (668.9 C), density(1525 kg/m3) (Herrington, 1934; Zadow, 1984), andother properties estimated from these parameters andthe selected thermodynamic package.

ocess simulation: Components and thermodynamic modelons

ore setting up and solving the simulation cases, the pseudoixture was simulated using the assumptions, compositiontabases (databases from literature and the simulator library)ned in Section 2.1.simulator library contained information for the followingnents required for milk simulation: water, fat (palmitic acidleic acid), and minerals (NaCl and KCl). Components notble in the library were specied using the Hypotheticalund manager tool. Proteins (Proteins) and Lactosese) were specied in this manner. Specication of a hypo-al component (Proteins and Lactose in this study) requiresput of a number of properties such as normal boiling point, density, and molecular weight, as well as the criticalrties of the substance.accuracy of a process simulationmainly dependson the ther-

namic model used. Hence, selection of the thermodynamicThe APR model was selected because it can handle polar com-pounds (e.g. water), has the largest applicability range of operatingconditions (T and P), has the largest binary interaction parameterdatabase, an extended set of interaction parameters for the pro-cesses have strong temperature dependency, and has volumetranslation to get accurate liquid phase density estimation(Mhlbauer and Raal, 1995; Daz et al., 2011).

Bon et al. (2010) simulated the milk pasteurization process andselected the IDEAL thermodynamic model in the process simulator(ProSimPlus) in order to compute uid (i.e. milk) properties.However, no validation work was reported on. The IDEAL thermo-dynamic model in ProSimPlus is based on the GammaPhiapproach. APR in VMGSim is preferred because it is a more detaileddescription and is based on a better understanding of the complexdynamics underground the phase behaviour than IDEAL thermody-namic model. APR is preferred over IDEAL thermodynamic modelbecause it estimates more accurate interaction coefcients, specialhandling of water, and provides accurate volume translation cor-rection for phase densities (ProSimPlus, 2008; Bon et al., 2010;Jaworski and Zakrzewska, 2011).

3. Results and discussion

3.1. Simulation results and discussion

After selecting the components and the thermodynamic model,the raw milk stream was simulated. Input data information (tem-perature, pressure, ow and composition) of the raw milk streamwas specied to simulate the milk stream. The simulated milkstream and the calculated physical properties (i.e. density, heatcapacity, thermal conductivity, and viscosity) using equations builtinto the simulator database and property package are shown inTable 3.model is the crucial step in process simulation. The selection of aproperty model (thermodynamic model) is based on the followingfactors; type ofmixture, type ofmolecules, operating conditions, re-quiredproperties, level of accuracy required, and availability of data.

Owing to the presence of both hydrocarbon-based compounds(fat, proteins) and polar compounds such as water (87 wt.% inwhole milk and 50 wt.% in concentrated milk) in the process, theAdvanced PengRobinson (APR) equation of state model was ini-tially selected for use as the property package for the simulation.Other polar/activity based property packages (e.g. the Wilsonactivity package) were also tried but they gave poor results show-ing large differences in properties estimation, possibly due to the

Proteins Lactose Minerals Total solids

NaCl KCl

3.4 4.8 0.4 0.4 13.013.0 18.0 1.5 1.5 50.0

gineering 121 (2014) 8793 89The behaviour of the simulated milk (whole and concentratedmilk) stream was compared to the real milk literature data. Thecomparison of the main physical properties (i.e. density, heatcapacity, thermal conductivity, and viscosity) between the simu-lated milk and literature data is shown in Table 3.

It should be noted that since the continuous uid (water) prop-erties in the simulator are slightly different from actual waterproperties, the milk properties were rescaled accordingly tocompare with literature data. Nevertheless, both re-scaled andun-scaled data are presented in Table 3. All the tests in Table 3were performed at 1 bar and 25 C.

a.

isco

d EnFrom Table 3 it can be observed that the raw milk liquid den-sity, heat capacity and thermal conductivity showed very little dif-ference between the literature and simulated values. Consideringthe small differences in the raw milk density, heat capacity andthermal conductivity between literature and simulated data, theseproperties were not further considered and compared for concen-trated milk. However, density, heat capacity and thermal conduc-tivity can vary to some extent with varying total solids in milk.

The liquid milk viscosity showed around a 1719% differencebetween the simulation results and literature data as shown inTable 3. As a result the liquid milk viscosity was further consideredto compare simulation and literature viscosity data for raw andconcentrated milks. The milk viscosity was therefore furtheroptimized by regressing literature viscosity data using the ModelRegression option in the simulator.

Model regression was used to estimate the parameters requiredto calculate the viscosity of the hypothetical components. The sim-ulators model regression tool uses an optimizer to manipulate theregressed variables and minimizes the total error of a model basedon the input data.

In this work, model regression was used to modify the viscosityof the milk mixture stream. The viscosity of the raw milk mixturestream was modied by manipulating the adjustable viscosityparameters (A, B, C, and D in Eq. (1)) of the hypothetical compo-nents. Eq. (1) can be used to regress the viscosity of any hypothet-ical component and represents the inuence of temperature on theviscosity of milk (viscositytemperature correlation). This is al-ready in place in the thermo physical property database. Howeverit does not consider the effect of total solids on the viscosity of milk(limitation of Eq. (1)).

lnl A B=T CT DT2 1

where l is the viscosity (Pa s), T the Temperature (K), A, B, C, and Dis the adjustable viscosity parameters.However the viscosity of milk

Table 3Comparison of the physical properties between simulated raw milk and literature dat

Physical properties RML RMV Difference (%)

q (kg/m3) 1030 1019 1.0Cp (kJ/kmol K) 3930 3860 2.0k (W/m K) 0.53 0.557 5.0l (cp) 1.296 1.05 19.0

where RML = Mean value of a given property of raw milk from literature.RMV = Mean value of a given property of raw milk from the simulator.WL = Mean value of a given property of water from literature.WV = Mean value of a given property of water from the simulator.RMVR = Mean value of a given property of raw milk (rescaled).Physical properties = density (q), heat capacity (Cp), thermal conductivity (k), and v

90 Y. Zhang et al. / Journal of Foois inuenced by the total solid content along with temperature(Bakshi and Smith, 1984; McCarthy, 2002). Eq. (1) represents onlythe inuence of temperature on the viscosity of milk. To re-calibrateand to consider the combined effect of temperature and total solidson milk viscosity, a Fernndez-Martn (1972) and Minim et al.(2002) type viscosity model was employed as shown in Eq. (2). It in-ter-relates viscosity, temperature and concentration (total solids). Itprovides a theoretical viscosity value to compare with the simulatorviscosity results based on Eq. (1).

logg A0 A1t A2t2 B0 B1t B2t2

s

C0 C1t C2t2

s2 2

where s is the total solids content (% in mass), Ai, Bi and Ci aredimensionless coefcients calculated by the least squares method,and are given in (Fernndez-Martn, 1972).D in Eq. (1).3.2. Simulation results validation

Simulation results validation was conducted to determine theimpact of different independent variables on a particular depen-dent variable and the differences were identied between the liter-ature and the simulated data under a given set of assumptions.Considering the small differences in the raw milk density, heatcapacity and thermal conductivity shown between simulationand literature, these properties were not further compared withactual milk data. Only the milk viscosity (which showed arounda 1719% difference between simulation and literature) wasfurther compared with measured milk viscosity data.

In this work, the simulation of the physical properties of

densitrespecmodeequat

Cp 3

q 1

k 0:where

Theity mo(2002used tliterats:(a) Obtain whole milk viscosity data from VMGSim, from 1

to 70 C.(b) Obtain whole milk without protein data from VMGSim,

from 1 to 70 C.(c) Calculate the weighted natural logarithm difference of

the two sets of data.(d) Regress the data set obtained from step c with Eq. (1).(e) Fine-tune the adjustable viscosity parameters A, B, C, andThe Fernndez-Martn (1972) and Minim et al. (2002) viscositymodel (Eq. (2)) was used to t the viscosity results calculated in thesimulator using Eq. (1) as explained in Section 3.2.

Total solids content and temperature inuence the viscosity ofmilk (Bakshi and Smith, 1984; McCarthy, 2002). It is well knownthat of the solids components (fat, proteins, lactose and minerals),proteins are the main contributor to milk viscosity (Reddy andDatta, 1994; Bienvenue et al., 2003; Herceg and Lelas, 2005; Karls-son et al., 2005). Hence, in this work, protein was selected(assumption 4) as the main contributor (hypothetical compound)to milk viscosity and was the compound that the viscosity of whichwas actually re-calibrated. The re-calibration steps were asfollow

WL WV RMVR Rescaled difference (%)

998.2 996.2 1021 1.04188 4220 3830 3.00.58 0.607 0.532 0.40.91 0.89 1.074 17.0

sity (l).

gineering 121 (2014) 8793y, heat capacity, and thermal conductivity (q, Cp, and k,tively) were validated using the thermo-physical propertiesls available in Minim et al. (2002), shown as followingions.

744:48 1:15T 3:93E3T2; R2 0:982 3

042:01 0:37T 0:36E3T2; R2 0:993 4

49 2:23E3T 1:08E3T2; R2 0:991 5T is the Temperature (C), and R2 is the squared residuals.simulation of the milk viscosity was validated using viscos-dels available in Fernndez-Martn (1972) and Minim et al.), shown as Eq. (2). Measured milk viscosity data was alsoo see actual differences in milk viscosity data between theure, simulated and actual data.

Kessler (2002) also formulated a milk viscosity equation repre-senting the inuence of the temperature on the viscosity of milkwhich was stated to be valid for the temperature range 180 C,but was not used in this work because it only considers the effectof temperature on milk viscosity.

Eqs. (3)(5)represent simple linear polynomial relationshipsrelating the properties of milk (q, Cp, and k) to temperature (Minimet al., 2002). Minim et al. (2002) addressed the measurement ofthese properties (q, Cp, and k), developed empirical correlations(having R2P 0.98) for predicting these properties under differentprocess conditions, and concluded that water content in milk hasa large inuence on the properties while the total solids contenthas the least signicant inuence as stated in Minim et al.(2002), though not quantied.

3.3. Heat capacity, density and thermal conductivity results validation

From Table 3 it can be observed that the heat capacity (calcu-lated at 1 bar and 25 degrees) showed a small difference (13%) be-tween the literature and our simulated data. For the temperaturerange of 170 C, Eq. (3) from Minim et al. (2002) was employedfor the validation of heat capacity simulation results and to observethe differences between the literature model and the simulator re-sults as shown in Fig. 2(a).

Fig. 2(a) shows the plots of the literature and the simulatorderived values for whole milk heat capacity. At lower temperatures(130 C), the difference between the literature model and the sim-ulator heat capacity values is larger than at higher temperatures

From Table 3 it can be observed that the density and thermalconductivity (calculated at 1 bar and 25 degrees) showed smalldifferences (0.71.1%, and 0.35.1% respectively) between the lit-erature model and the simulator data. For a temperature range of170 C, Eqs. (4) and (5) available in Minim et al. (2002) wereemployed for the validation of the density and thermal conduc-tivity simulation results, and to observe the difference betweenthe literature model and simulator data as shown in Figs. 2(b)and (c).

Figs. 2(b) and (c) show the plots of the literature and the simu-lator based values for whole milk density and thermal conductiv-ity, respectively.

From Fig. 2(b) it can be observed that the whole milk density(for the temperature range of 170 C) showed a small difference(less than 2%) between literature and simulated data and it almostremains constant for the temperature range of 170 C. The resultsobserved in Fig. 2(b) are consistent with the milk density results inTable 1.

Fig. 2(c) shows the whole milk thermal conductivity (for thetemperature of range of 170 C). A small difference (less than0.4%) between literature model and simulator data is initially ob-served and it further decreases with increase in temperature forthe temperature range of 170 C. At 70 C the literature modeland simulator data of thermal conductivity match within 0.1%.

From the results shown in Fig. 2(a)(c) it is clear that the heatcapacity, density and thermal conductivity values, respectively, ofwhole milk calculated by the process simulator were in agreementwith the results of linear functions relating these thermo-physicalproperties (heat capacity, density and thermal conductivity) to the

1200

)

mpe

mpe

re (Mor th

iteraimul

(b)

Y. Zhang et al. / Journal of Food Engineering 121 (2014) 8793 910 10 20 30800

1000

Rho

(Kg/

m3

0 10 20 300.2

0.4

0.6

0.8

Te

k (W

/m.K

)

LiteratuSimulat

(c)(3170 C). From Fig. 2(a) it can be observed that the heat capacity(for temperature range 170 C) showed a small difference(1.32.6%) between the literature model and the simulator data.The results observed in Fig. 2(a) are consistent with the heat capac-ity results in Table 1.

0 10 20 30

3600

3800

4000

Cp

(KJ/

kgm

ole.

K)

Te

LS

(a)Tempe

Fig. 2. Plots of literature and simulator values for whole milk htemperature, water and total solid contents of milk, developed byMinim et al. (2002). Hypothetical components created in the sim-ulator can be used to predict milk heat capacity, density and ther-mal conductivity within 2.6%, 2%, and0.4%, respectively over thetemperature range of 170 C.

40 50 60 70

40 50 60 70

40 50 60 70

rature (C)

rature (C)

inim et al. (2002)) model based thermal conductivityermal conductivity

ture (Minim et al. (2002)) model based heat capacityator heat capacity

Literature (Minim et al. (2002)) model based densitySimulator densityrature (C)

eat capacity (a), density (b) and thermal conductivity (c).

3.4. Viscosity results validation

As the simulated liquid milk viscosity showed around a 1719%difference to literature as shown in Table 3, the simulator viscosityresults were compared with literature viscosity data for the wholeand concentrated milk. Measured milk viscosity data (for wholeand concentrated milk) was also used to observe actual differencesin milk viscosity data between the literature, simulated and mea-sured milk viscosity.

Fig. 3(a) and (b) represent the whole (13 wt.% total solids) andconcentrated (50 wt.% total solids) milk viscosities (for a tempera-ture range of 170 C), respectively, showing the validation of sim-ulated milk (whole and concentrated) viscosity with literaturemodel data and measured viscosity data. The Fernndez-Martn(1972) and Minim et al. (2002) viscosity model (Eq. (2)) was the lit-erature model based viscosity and Souzas (2011) work providedmeasured viscosity data. Actual milk viscosity data was only avail-able for the temperature range 2570 C. Souza (2011) robustlymeasured actual viscosity of milk on a pilot scale plant (Lin et al.,2009) over this temperature range.

Fig. 3(a) shows the plots of the differences between the litera-ture model, simulator, and measured values of whole milk viscos-ity. There is almost no difference between the literature model and

between the literature model, simulated and actual concentratedmilk viscosity data increased signicantly with a decrease intemperature.

From the results shown in Figs. 3(a) and (b) it is clear that theviscosity values of whole and concentrated milk, calculated by pro-cess simulation were in agreement with the results from literaturemodels and actual milk viscosity data over a temperature range of170 C for whole milk and 2070 C for concentrated milk. Theresults of milk viscosity for whole and concentrated milk wereused because total solids also inuence the viscosity of milk withtemperature. Hence, hypothetical components generated in simu-lations with viscosity re-calibrated can be used to predict milkviscosity.

4. Summary and conclusions

In this work, hypothetical components in a process simulatorwere developed for simulating pseudo milk. The properties re-quired to simulate milk in the process simulator were obtainedfrom the literature and the simulators database. The simulationresults of the physical properties (heat capacity, density, thermalconductivity and viscosity) were compared with literature models

pe

re (ed isc

re ed isc

92 Y. Zhang et al. / Journal of Food Engineering 121 (2014) 8793the simulator whole milk viscosity for a temperature range of170 C. The actual measured milk viscosity was closer to the liter-ature model and simulated viscosity at lower temperatures range.A small difference (less than 0.02%) between the literature model,simulated and actual whole milk viscosity data was observed forthe temperature range of 3070 C. A difference of 0.1% betweenthe literature, simulator and actual whole milk viscosity data wasobserved for the temperature range of 2530 C.

Fig. 3(b) shows the plots of the literature model, simulator, andactual values of concentrated milk viscosity. There is almost no dif-ference between the literature model and the simulator milk vis-cosity for a temperature range of 3570 C. The actual milkviscosity is also closer to the literature model and simulated vis-cosity for lower temperature ranges. A small difference (less than0.05%) between the literature model, simulator and actual concen-trated milk viscosity data was observed for a temperature range of2070 C. For the temperature range of 020 C the difference

0 10 20 300

200

400

600

800

Visc

osity

(cP)

0 10 20 300

2

4

6

Tem

Visc

osity

(cP)

LiteratuSimulatActual v

LiteratuSimulatActual v

(a)

(b)Tempe

Fig. 3. Plots of literature correlations, simulator results and measured d40 50 60 70

40 50 60 70rature (C)

(Minim et al. (2002)) model based viscosityviscosityosity data (Souza, 2011)and actual milk data. After this work, the simulation of milk as acollection of hypothetical components in a process simulator ispossible.

The simulation results of the physical properties (heat capacity,density, thermal conductivity and viscosity) were in agreementwith literature models and actual milk data. The hypothetical com-ponents created in this work can be used to represent the proper-ties of actual milk for the temperature range of 170 C for wholemilk (and 2070 C for concentrated milk). The liquid density,heat capacity, thermal conductivity and viscosity showed veryfew differences between literature models, simulated and actualmilk data over this temperature range.

In the present approach, fattyacids were used instead of fattyesters because simulation of esters caused signicant difcultiesand complexities. However, since fattyacids helped to matchthe physical properties of pseudo milk with actual milk to a fairlygood extent, and milk processing does not involve any signicant

Minim et al. (2002)) model based viscosityviscosityosity data (Souza, 2011)rature (C)

ata values for whole milk (a) and concentrated milk (b) viscosities.

chemical reactions of these components for design purposes, weconsider the drawback as minor.

The creation of a hypothetical component database in a processsimulator allowed it to be used as a tool for milk process simula-tion. Milk process simulation using a process simulator offers theuser the potential to analyse the process and to observe parame-ters of interest which are difcult to study in practice.

The creation of new databases and the extension of the already

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Y. Zhang et al. / Journal of Food Engineering 121 (2014) 8793 93existing components in component libraries to materials like milkand other liquid foods will expand the application of processsimulators.

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Development of hypothetical components for milk process simulation using a commercial process simulator1 Introduction2 Materials and methods2.1 Raw material (milk): composition and properties2.1.1 Assumptions

2.2 Process simulation: Components and thermodynamic model selections

3 Results and discussion3.1 Simulation results and discussion3.2 Simulation results validation3.3 Heat capacity, density and thermal conductivity results validation3.4 Viscosity results validation

4 Summary and conclusionsReferences