one-dimensional simulation of co-current, dairy spray drying systems
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One-dimensional simulation of co-current, dairy spraydrying systems - pros and cons
Kamlesh Patel, Xiao Dong Chen, Romain Jeantet, Pierre Schuck
To cite this version:Kamlesh Patel, Xiao Dong Chen, Romain Jeantet, Pierre Schuck. One-dimensional simulation ofco-current, dairy spray drying systems - pros and cons. Dairy Science & Technology, EDP sci-ences/Springer, 2010, 90 (2-3), <10.1051/dst/2009059>. <hal-00895757>
Review
One-dimensional simulation of co-current,dairy spray drying systems – pros and cons
Kamlesh PATEL1, Xiao Dong CHEN1*, Romain JEANTET2,3, Pierre SCHUCK2,3
1 Biotechnology and Food Engineering Group, Department of Chemical Engineering,Monash University, Clayton Campus, Victoria 3800, Australia
2 INRA, UMR1253, F-35042 Rennes, France3 AGROCAMPUS OUEST, UMR1253, F-35042 Rennes, France
Received 15 June 2009 – Revised 12 November 2009 – Accepted 18 December 2009
Published online 9 February 2010
Abstract – One-dimensional (1-D) simulation is a useful technique for the evaluation of dryeroperating parameters and product properties before conducting real spray drying trials. The mainadvantage of a 1-D simulation tool is its ability to perform fast calculations with significantsimplicity. Mathematical models can be formulated using heat, mass and momentum balances at thedroplet level to estimate time-dependent gas and droplet parameters. One of the purposes of thispaper is to summarize key mathematical models that may be used to perform 1-D simulation forspray drying processes, predict essential product-drying gas parameters, assess the accuracy ofprediction using pilot-scale spray drying data and perhaps most importantly address the mainbenefits and limitations of the 1-D simulation technique in relation to industrial spray dryingoperations. The results of a recent international collaborative study on the development of spraydrying process optimization software for skim milk manufacture are presented as an example of theapplication of 1-D simulation in milk processing.
spray drying / one-dimensional simulation / modeling / drying kinetics / dairy product /droplet drying
摘要 – 乳粉顺流喷雾干燥系统一维模拟的利弊分析○ 一维模拟是在进行实际喷雾干燥之前用来评价干燥器操作参数和产品特性的一种技术方法○ 一维模拟最大的优点是可以用简单的方法进行快速计算○ 根据液滴的热、质量和动力平衡的数学方程来估算时间-气体的关系以及液滴的参数○ 本文概述了一些重要的、实用的一维模拟的数学模型，这些模型可以用来预测喷雾干燥过程，预测产品干燥的气体参数，评定中试级喷雾干燥预测数据的准确性;以及着重分析了一维模拟技术在喷雾干燥工业生产中的利与弊○ 最近国际上合作开发出的用于脱脂乳喷雾干燥生产工艺参数优化的软件就是一维模拟技术在乳品加工中最好的应用实例○
喷雾干燥 / 一维模拟 / 模型 / 干燥动力学 / 乳制品 / 液滴干燥
Résumé – Simulation monodimensionnelle de systèmes de séchage par atomisation deproduits laitiers en co-courant – avantages et inconvénients. La simulationmonodimensionnelle(1-D) est une technique utile pour évaluer les paramètres de séchage et les propriétés des produitsavant de conduire les essais de séchage en réel. Le principal avantage de l’outil de simulation 1-D estsa capacité à réaliser des calculs rapidement et avec une grande simplicité. Les modèles mathémat-iques peuvent être formulés avec les équilibres de chaleur, de masse et de quantité de mouvement
*Corresponding author (通讯作者): [email protected]
Dairy Sci. Technol. 90 (2010) 181–210© INRA, EDP Sciences, 2010DOI: 10.1051/dst/2009059
Available online at:www.dairy-journal.org
Article published by EDP Sciences
à l’échelle de la gouttelette pour estimer les paramètres de vapeur et de gouttelette qui varient au coursdu temps. Un des objectifs de cet article est de présenter de façon synthétique les modèles mathé-matiques clés qui peuvent être utilisés pour réaliser une simulation 1-D, prédire les paramètres devapeur essentiels pour le séchage du produit, évaluer la précision de la prédiction en utilisant lesdonnées du séchage par atomisation obtenues à l’échelle pilote, et enfin d’aborder les principauxbénéfices et limites de la technique de simulation 1-D en relation avec les opérations de séchage paratomisation industrielles. Les résultats d’une récente étude réalisée en collaboration internationale surle développement d’un logiciel d’optimisation du procédé de séchage par atomisation pour laproduction de poudre de lait écrémé sont présentés pour illustrer l’application de la simulation 1-D.
séchage par atomisation / simulation mono-dimensionnelle / modélisation / cinétique deséchage / produit laitier / séchage d’une gouttelette
1. INTRODUCTION
In the current environment of economicalcrisis and strict climate policies, industries inalmost all sectors are striving to improve pro-cess efficiencies or to adopt new technologiesso that energy and water consumption, man-ufacturing cost and carbon emission can beminimized. This is particularly evident inthe dairy and food processing industries.Replacing or modifying conventional tech-niques by newer cost effective technologiesmay not be straightforward because one hasto carefully study the requirement of addi-tional capital costs, the availability ofresources and personnel, the influence onproduct quality and the risk of “using it firsttime”. It is a challenge to all dairy manufac-turing researchers to develop innovativeapproaches for reducing processing costsand energy consumption during drying oper-ations while maintaining top product qualityin such a way that a minimum additionalinvestment (time, money and resources) isneeded.
Spray drying is a relatively high energy-intensive operation because the water (orsolvent) is removed mainly using thermalenergy. The energy needed to remove akilogram of water during single or multi-stage spray drying is usually 10–20 timeshigher than the energy required duringmulti-pass evaporation to remove the sameamount of water [9, 80]. Furthermore, alllarge-scale spray drying industries currentlyrely on fossil fuels to provide the energy
needed for water removal. Keeping the strictclimate policies in mind, there is a need torecover the energy from exhaust streamsand look for alternative “green” energyresources.
Apart from energy reduction and/orrecovery during spray drying operations,product quality improvement, new productdevelopment and minimizing other potentialproblems such as wall deposition and sticki-ness are major concerns for dairy powdermanufacturers. To understand how chemicaland process engineers can address theseissues, it is important to understand the rela-tionship between product quality, processparameters and equipment design. Whenthe physical principles of modeling aredefined, simulation can be a useful techniqueto mathematically characterize various dry-ing phenomena occurring during spray dry-ing and establish relationships between keyprocess and quality parameters. Reviewingthe current set of drying/feed parametersand tuning these parameters based on a morereliable optimization technique may be help-ful in dealingwith several critical issueswith-out the need for new equipments or majorchanges to process design.
Simulation is essentially an approxima-tion technique or tool that canprovidepredic-tions and trends of process and productparameters with acceptable accuracies. Sim-ulation techniques are increasingly becomingpopular in the software development com-munity to optimize spray drying processesand predict product properties before
182 K. Patel et al.
conducting real spray drying trials. As a pre-caution it should be noted that simulation isnot a unique “remedy” to all operationalproblems. The predictive power and the reli-ability of simulation techniques largelydepend on the appropriateness of the mathe-matical models used and how well they arevalidated. A programmer should be awareof the extent of details required from simula-tion tools because this information is directlylinkedwith the complexity of simulation pro-grams and the time, resources and skillsrequired. Different scales of mathematicalanalysis and a variety of process calculationtools can be employed depending on the typeof information required from a simulation.
Simulation may be helpful to processengineers in following ways:
d Traditionally, optimization and genera-tion of new process parameters and dry-ing kinetic data were realized usingexperimental trials that were expensiveand eventually risky. Simulation cangreatly reduce the experimental trialsrequired to study various drying phe-nomena and the associated trends uponchanging process parameters. Dryingprocesses can be pretested in this wayusing a set of appropriate mathematicalmodels. Simulation thus helps in mini-mizing product testing time, resources,hazards, energy consumption and wast-age. This can be considered a significantadvantage.
d Simulation can also provide earlyinsights for equipment design and newprocesses development as well as forscale-up, scale-down, process and qual-ity control and risk management duringspray drying.
d Simulation permits the development of aprocess-product integrated approach thathelps in studying process and productparameters together. Thus, it can behelpful in estimating energy consump-tion, process efficiencies, productioncosts and product quality sensitivity
to the changes in process and feedparameters.
d Simulation can be of a great benefit fortraining and education purposes at pro-duction sites, academic institutes andR&D centers.
2. SIMULATION OF SPRAYDRYING
A significant extent of research has beenconducted to mathematically characterizevarious phenomena occurring during spraydrying. Unfortunately a unique theoreticalapproach to characterize drying phenomena(e.g. drying kinetics, particle trajectories,and gas-flow pattern) and to design associ-ated equipments does not exist [59]. Oneof the reasons for this is the complexity ofthe spray drying process, which includesmany aspects of transport phenomena, fluidmechanics, heat and mass transfer, reactionengineering, particle engineering as well asmaterial science [15]. Mathematical analy-sis and simulation can become very com-plex when all these drying principles areconsidered together. Based on the complex-ity of mathematical analysis, simulationapproaches may be classified as follows.
2.1. “Zero”-dimensional (course-scale) simulation approach
In this approach, the spray dryer is essen-tially considered as a “black box”. Dryingprocesses are simulated using overall heatand mass balance equations to predict gastemperature, gas humidity and productmoisture content at the inlet or outlet of dry-ers [10]. Drying chambers are mostly trea-ted as well-mixed reactors [30, 95, 110].Calculations for heat and mass balancesover spay dryers and fluidized-bed dryersare usually done separately. The dryingkinetics model is mostly not incorporatedfor this course-scale simulation approach.
1-D Simulation of spray drying – pros & cons 183
This approach can provide “first-draft”information regarding gas and productconditions at the inlet and outlet of the dry-ing chambers by simply using a scientificcalculator or an Excel spreadsheet. Recently,Langrish [47] illustrated how this course-scale approach can be used to estimate aproduct’s sticky-point temperature at theoutlet of the spray dryer in order to predictstickiness behavior of the powder.
2.2. “1-D” (finer-scale) simulationapproach
In the 1-D simulation approach, mass,heat and momentum balances are performedat an individual droplet level by followingdrying time or dryer height [72, 73]. Dryingkinetics is incorporated in this approachwhich allows predicting drying-rate profilesand identifying fast and slow drying-rateperiods. It is usually considered that hotgas and droplets are moving in parallelwithin the drying chambers [70]. This sim-ulation approach is widely used to modelproduct characteristics during spray dryingwhere tall-form spray dryers were used[72, 109, 110, 112]. A major advantage ofthe 1-D approach is the capability to evalu-ate the “average” behavior (temperature,moisture concentration and velocity pro-files) of the powder and hot gas followingdrying time or dryer height integration.These profiles can assist in predicting vari-ous thermo-physical properties and qualityparameters of the product throughout drying[73]. A relatively simple Excel spreadsheetis usually sufficient to build effective 1-Dspray drying simulation software.
2.3. “2-D” and “3-D” (finest-scale)simulation approaches
Zero-D and 1-D simulation approachescannot effectively reveal information ongas-flow patterns, time-dependent particletrajectories, atomizer performance, agglom-eration, wall deposition and gas-particles
residence time data. Such information is cru-cial for scale-up, scale-down and equipmentdesign, and can be obtained using 2-D and3-D simulation approaches. In these multi-scale simulation approaches, the basic pro-cesses happening in the dryer are discretelyclassified with respect to space and time toapply the associated physical and chemicalprinciples on individual droplets.Drying-rateprofiles of these droplets can be predictedusing appropriate drying kinetics models.Simple and effective lumped-parametermodels (which do not provide internal tem-perature-moisture profiles within the drop-lets) are usually desired for 2-D and 3-Dsimulations due to their simplicity and speedduring computation. Several publicationshave comprehensively reported how 2-Dand 3-D simulation approaches using variousCFD packages (e.g. Fluent and CFX) can behelpful to predict agglomeration behaviorduring spray drying [33, 49, 97], evaluateparticle trajectories [11], design new dryingchamber configurations and assess atomizerperformance [11, 36–38] as well as to studygas distribution within drying chambers[11, 28, 33, 34, 45, 50, 53, 68, 93, 101,111]. The accuracy of prediction by finer-scale approaches mainly depends on theselection of mass-heat-momentum conserva-tion equations, the accuracy of turbulencemodels, the appropriateness of numericalmethods used for solving equations and thequality of grid generation and algorithmdevelopment [28, 47, 50]. Recently, Langrish[47] outlined important advantages and cur-rent challenges of 2-D and 3-D simulationapproaches. In spite of their ability to providefine details of drying processes, the use of2-D and 3-D simulation approaches is notcommon in industrial control rooms (espe-cially dairy and food processing industries)due to the high cost of computational pack-age licenses, long simulation time (usuallya few hours to several weeks or even monthsfor large-scale spray dryers) and the require-ment for programming experience andskilled personnel. CFD simulation of spray
184 K. Patel et al.
drying processes is now becoming morepopular and industrially feasible due to theavailability of fast computation machinesand new powerful CFD packages [38].
In this paper, themain focus is on how the1-D simulation approach can be helpful inoptimizing industrial spray drying opera-tions, the components that may be requiredto build an effective simulation tool and theimportant pros and cons of this 1-Dapproach.
3. ONE-DIMENSIONALSIMULATION
The 1-D simulation approach has previ-ously been used to model spray drying oper-ations due to its ability to predict a product’smoisture, temperature and velocity profilesthroughout drying [30, 31, 48, 66, 70, 72,73, 109, 112]. Three main components toformulate the 1-D simulation tool formodeling spray drying processes are (1)drying kinetics data from laboratory-scaleexperiments and drying kinetics model,(2) a set of appropriate mathematical equa-tions, and (3) a process calculation tool(e.g. Excel and MATLAB).
3.1. Drying kinetics
Drying kinetics is a key element in pre-dicting a material’s drying behavior andproduct quality. Drying kinetics modelsallow for predicting fast and slow dryingperiods in the drying chamber. Due toincreased resistances to heat-mass transferduring drying, the drying rate significantlyslows down during the later drying periodand will affect the overall drying time.Measurement of drying kinetics from labo-ratory-scale experiments and fitting ofmeasured data with an appropriate dryingkinetics model are important steps to per-form mathematical modeling and simula-tion. The appropriateness of a dryingkinetics model and the accuracy of labora-tory drying kinetics data will have a direct
influence on the accuracy of prediction by1-D simulation tools.
3.1.1. Drying kinetics measurement
Asimple approach for predicting thequal-ity of dried powders is to understand (andaccuratelymodel)what a single droplet/parti-cle actually experiences during its flight inthe drying chambers regarding its tempera-ture and moisture content, and how a singledroplet/particle may respond to thesechanges [18]. Several laboratory-based tech-niques havebeen described in the literature tomeasure drying kinetics data for use in devel-oping a drying kinetics model for spray dry-ing. Four commonly used techniques are:
1. Suspended droplet drying: Suspendeddroplet drying is the most commontechnique used to obtain drying kinet-ics data [2, 3, 17, 27, 55, 99]. Thistechnique is also used to study volatileretention [62] and morphology changes[5] during spray drying. In this method,small (1–3 mm), single droplets aresuspended in a small drying chamberusing a thin glass filament or similarmeans. Droplets are dried using hotair of constant temperature, velocityand humidity. Changes in the droplet’sweight, temperature and diameter arerecorded through independent experi-ments in order to determine a character-istic behavior of materials under dryingconditions. This technique is populardue to its simplicity and also becauseboth spray drying processes and sus-pended droplet drying techniques dealwith spherical droplets.
2. Thin-layer drying: In this technique,materials are dried in a thin-layer (orslab) form in order to record changesin the sample’s temperature, weightand thickness [6, 19, 20, 24, 58]. Theeffective area for heat-mass transfer isassumed to be constant when estimatingdrying flux. Experimental data are used
1-D Simulation of spray drying – pros & cons 185
to determine drying kinetics parametersor characteristic behavior of materialswhich can be used tomodel spray dryingprocesses.
3. Droplet drying using acoustic levita-tion: In this method, single dropletsare suspended using strong acousticfields in an acoustic levitator. Changesin the droplet’s temperature and diame-ter are measured using infrared thermaldevices and digital camera/recorders,respectively [32, 42, 51, 85, 86, 92,103, 105–108]. Moisture content pro-files are estimated either from diameterprofiles or often using a hygrometer tomeasure the outlet air humidity fromthe closed levitator. The role of internalwater circulation within acousticallysuspended droplets and the effects ofacoustic fields on internal water diffu-sion and total evaporation have notyet been clearly described. Recently,GEA Niro developed a simulation tool(DRYNETICS™) by combining dropletdrying data obtained from acoustic lev-itation experiments and a CFD packagein order to assist in optimizing spraydryer performance.
4. Desorption method: Drying by desorp-tion is another simple method tomeasure water availability or dryingbehavior of materials [87, 88]. Liquidmaterial is dried in the form of a thindisk using a small plastic cup that isplaced in a closed container filled withzeolite (or other adsorbents) particles.This container is placed in the ovenwhere liquid concentrates are dried ataround 45 °C that is believed to be anapproximate wet-bulb temperature forwater evaporation in real spray dryers[87]. The relative humidity profile inthe container is continuously recordedusing a sensor that is usually placedvery close to the surface of liquid sam-ples in the container. From the relativehumidity profiles, moisture contentprofiles of the liquid samples can be
evaluated. Recently, Schuck et al. [87]developed and licensed a spray dryingsimulation software (SD2P®) by com-bining the relative humidity profilesobtained by the desorption methodand the overall heat-mass balances(using a “black box” approach) in orderto optimize drying conditions for large-scale spray dryers.
3.1.2. Drying kinetics approaches
Once drying kinetics data are measuredfrom laboratory-based experiments, thesemeasured data are correlated with an appro-priate drying kinetics approach to formulatea model and predict a time-dependent “aver-age” drying flux. The appropriateness andaccuracy of the drying kinetics model willaffect the accuracy of prediction for a prod-uct’s behavior, quality parameters and sticki-ness data [17, 73, 76]. In the literature,several drying kinetics approaches have beenproposed for the modeling of spray dryingprocesses. Each approach is formulatedbased on various simplifications and has itsown advantages and drawbacks. The easeof usage, appropriateness and accuracyshould be considered for selecting a rightapproach for particular applications. Fourmain types of drying kinetics approacheshave been commonly used in the literature:
1. Reaction engineering approach (REA)2. Characteristic drying curves (CDC)
approach3. Internal moisture diffusion-based
approaches4. Receding interface (or moving bound-
ary) approaches.
The CDC and REA are lumped-parame-ter approaches and predict “average” behav-ior of products under drying conditions. TheCDC and REA have been widely used inthe literature to model droplet dryingprocesses as well as large-scale spray dryingprocesses, because both these approaches
186 K. Patel et al.
are fairly simple to use and hold physicalmeanings of the drying process. The REAhas been reported to be more accurate byvarious studies [17, 73]. Patel and Chen[73] effectively used the REA and CDCapproaches to predict and compare productquality parameters during spray dryingusing a spreadsheet-based 1-D simulationtool. The REA and CDC approaches havealso been successfully incorporated intoCFD simulations to study spray drying phe-nomena [35, 41, 100, 102]. Recently, Jinand Chen [41] used the REA in CFD mod-eling to simulate an industrial-scale spraydryer for studying gas-flow patterns, particletrajectories, gas-particles residence timedata and temperature and moisture contentprofiles of powders. They found the REAto be effective and simple to use becauseit does not require the modeling for constantand falling drying-rate periods separatelyunlike the CDC approach.
Diffusion-based [1, 2, 25–27, 44, 60, 61,83] and receding interface-based [22, 23,46, 63, 64, 84] drying kinetics approachesdeal with spatial moisture and/or tempera-ture distribution within droplets, and maybe useful to predict surface morphology.The latter drying kinetics approachesrequire solving a set of partial differ-ential equations using appropriate numericalmethods; therefore, further complexity isinvolved when these models are incorpo-rated into simulation tools. Moreover, acareful measurement of moisture diffusivityfrom laboratory-scale experiments isrequired to use these diffusion-based andreceding interface-based drying kineticsapproaches [16, 52, 81, 113]. Evaluatingand modeling the moisture diffusivitythrough laboratory-scale experiments is dif-ficult and time-consuming [4, 14, 52, 81].
An example is provided in this study toshow how the REA model can be usedin conjunction with laboratory-scale andpilot-scale experimental data to develop a1-D simulation tool for predicting the dry-ing behavior of skim milk.
3.1.3. REA
The REA is a relatively new approach,first introduced by Chen and Xie [20] andmodified by Chen and Lin [17] based oncareful experimentation on the drying ofmilk droplets. The REA has successfullybeen used to conduct dryer-wide simula-tions for large-scale spray dryers [73–75].In these studies, the REA appeared to besimple, effective and sensitive to the major-ity of the drying parameters. In the originalmodel proposed by Chen and Lin [17], theeffect of initial moisture content was nottaken into account while evaluating theliquid concentrate’s relative activationenergy, an important parameter of theREA. In other words, a single “fingerprint”was used to model liquid concentrates of allinitial moisture concentrations. This led tothe overestimation of the relative activationenergy profiles (or underestimation of dry-ing flux profiles) for liquid materials oflow initial moisture concentrations.Recently, Patel et al. [79] modified theapproach by considering the effect of initialmoisture contents which provided an indi-vidual relative activation energy profile forliquid concentrates of each initial moisturecontent. This modified REA model wasfound more accurate when simulating thedrying of sugar droplets in the work of Patelet al. [79].
In the case study provided in this paper,the modified REAwas incorporated into the1-D simulation tool to deliver the predic-tions of important feed/gas profiles. Whenusing the REA, the rate of water evapora-tion or drying flux can be estimated usingthe following equation [17, 79]:
� dmw
dt¼ �ms
d�Xdt
¼ hmAp qv;sat exp � �Ev
RgT p
� �� qv;b
� �;
ð1Þ
1-D Simulation of spray drying – pros & cons 187
where mw (kg) and ms (kg) are the weightsof water and solids in the droplet,�X (kg·kg−1, dry basis) is the droplet’s aver-age moisture content, ρv,sat (kg·m
−3) is thesaturated vapor concentration correspond-ing to average droplet temperature (Tp),ρv,b (kg·m−3) is the vapor concentrationof bulk drying gas, hm (m·s−1) is theaverage mass-transfer coefficient, Ap (m2)is the droplet’s surface area and ΔEv
(J·kg−1) is the apparent activation energy.The first term on the right-hand side of
equation (1) (ρv,sat terms) is the zero-orderdrying “reaction” that is the activation pro-cess. The second term on the right (ρv,bterms) is the first-order wetting “reaction”.Thus, the rate of moisture removal was seenas a competitive process between dryingand wetting reactions. The apparentactivation energy parameter (ΔEv) was nor-malized using an “equilibrium” or “maxi-mum” activation energy (ΔEv,b) to definea new dimensionless parameter called“relative activation energy” (ΔEv/ΔEv,b)[71, 79].
An exponential term in equation (1) iswater activity at the droplet’s surface and itwas correlated with the droplet’s averagemoisture content [17, 20]. A similar dryingkinetics approach was adopted by Bernardet al. [7] who correlated the surface wateractivity with the droplet’s average moisturecontent using anOswin-type empirical equa-tion unlike the REA’s relative activationenergy function. The relative activationenergy was in fact viewed as a difficulty inremoving water from the product [79].When the droplet surface is saturated withfree water (i.e. �X is high), the relative activa-tion energy and hence the difficulty inremoving the free moisture is expected tobe very small (close to zero). The relativeactivation energy gradually increases whenthe droplet’s moisture content is reducedduring drying. At the zero free moisture con-tent (i.e. �X ¼ X b), ΔEv/ΔEv,b is expected tobe unity.
Before simulating the spray drying pro-cess, it is essential to know the material’srelative activation energy profiles that corre-late relative activation energy with the prod-uct’s average moisture content (�X � X b)and thus allow estimating the average dry-ing flux as a function of drying time. Thisrelative activation energy profile wasconsidered as a characteristic behavior (orfingerprint) of individual materials. The rel-ative activation energy is mainly influencedby the composition of materials and the ini-tial moisture contents [79]. The relative acti-vation energy profiles for skim milkconcentrates of different initial moisturecontents are shown in Figure 1. For skimmilk having 20 and 30 wt% (all dry basis)initial solids contents, the relative activationenergy profiles were evaluated using weightloss and temperature data directly from theexperimental work and equations (1) and(2) [17, 77], while for 40 wt% and highersolid concentrations these profiles wereapproximated using a method shown byPatel et al. [79]. A comparison of these rel-ative activation energy curves in Figure 1provides an insight for using an appropriatefingerprint. Mathematical equations describ-ing the relative activation energy for 20, 30,40, and 50 wt% (all dry basis) skim milkdroplets are reported in Table I. The param-eter ΔEv,b can be calculated using the rela-tive humidity (ρv,b/ρv,sat) and temperature(Tb) of hot air
�Ev;b ¼ �RgT b lnqv;b
qv;sat
� �� ð2Þ
Mass-transfer coefficient (hm) in equa-tion (1) can be estimated using the follow-ing equations:
Sh ¼ hmdp
Dv¼ 2þ 0:6Re1=2Sc1=3; ð3Þ
188 K. Patel et al.
Re ¼ dp vp � vb�� ��qb
lb
; ð4Þ
Sc ¼ lb
qbDv; ð5Þ
where Sh is the Sherwood number, dp (m)is the droplet’s diameter, Dv (m
2·s−1) is theair-moisture diffusivity, Re is the Reynoldsnumber, Sc is the Schmidt number, ρb(kg·m−3) and μb (Pa·s) are the densityand viscosity of bulk gas, respectively,and vp and vb are the velocities of the drop-let and bulk gas, respectively. Correlationsto estimate various thermo-physical prop-erties are listed in Appendix I.
3.2. Mathematical equations
3.2.1. Heat balance
The temperature profile of a productcan be evaluated using the following
heat-transfer model:
dT p
dt¼ hApðT b � T pÞ þ�HLms
d�Xdt
mwCp;w þ msCp;s; ð6Þ
where h (W·m−2·K−1) is the convectiveheat-transfer coefficient, ΔHL (J·kg−1) isthe latent heat of vaporization, and Cp,w
and Cp,s (J·kg−1·K−1) are the specific heat
capacities of water and solids, respectively.The heat-transfer coefficient, h, can beestimated from the following Ranz-Marshall correlation:
Nu ¼ hdp
kb¼ 2þ 0:6Re1=2Pr1=3; ð7Þ
where Pr is the Prandtl number that can becalculated from
Pr ¼ Cp;blb
kb: ð8Þ
Temperature gradients across the dropletcan be assessed using a method proposed byPatel and Chen [77]. If the temperature
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
X–Xb, kg.kg–1
Rel
ativ
e ac
tivat
ion
ener
gy20 wt% skim milk30 wt% skim milkPoly. (50 wt% skim milk)Poly. (20 wt% skim milk)Poly. (60 wt% skim milk)Poly. (30 wt% skim milk)Poly. (40 wt% skim milk)Poly. (55 wt% skim milk)
Figure 1. Relative activation energy profiles to be used in the REA for the drying of skim milk of20, 30, 40, 50, 55 and 60 (all wt%, dry basis) initial solids contents.
1-D Simulation of spray drying – pros & cons 189
gradients are small or exist only for a shortdrying period, the assumption of uniformtemperature can be used when estimatingthe droplet’s average temperature profilesusing equation (6) [77, 78].
The temperature profile of hot gas can beevaluated using the following heat balance[71]:
Heat in ¼ Heat out þ Heat gained
by droplets � Heat gained
by gas through vapor
transfer þ Heat loss
_V qbH b ¼ _V qb H b þ dH bð Þ� �þ hApðT b � T pÞhdt� �
� dmw
dt�HL þ Cp;v T b � T p
� �hdt
� �þ UðpDedlÞðT b � T1Þ½ �;
ð9Þ
where _V (m3·s−1) is the volumetric gas-flowrate, Hb (J·kg
−1) is the enthalpy of gas, U(W·m−2·K−1) is the overall heat-transfercoefficient for heat loss,De (m) is the effec-tive dryer diameter (the arithmetic average
Table I. Relative activation energy correlations for the air drying of skim milk.
Milk solids (wt%) Relative activation energy correlations
20 �Ev
�Ev;b¼ �6:47438� 10�03ð�X � X bÞ5 þ 8:86858� 10�02ð�X � X bÞ4
� 0:471097ð�X � X bÞ3 þ 1:22317ð�X � X bÞ2� 1:62539ð�X � X bÞ þ 1:0092
30�Ev
�Ev;b¼ 3:0318� 10�02ð�X � X bÞ4 � 0:26637ð�X � X bÞ3
þ 0:85762ð�X � X bÞ2� 1:3635ð�X � X bÞ þ 0:99609
40 �Ev
�Ev;b¼ 0:99754� 1:28962ðX � X bÞ � 0:00958ðX � X bÞ2
þ 2:80140ðX � X bÞ3
� 4:66273ðX � X bÞ4 þ 3:26131ð�X � X bÞ5
� 0:84689ð�X � X bÞ6
50 �Ev
�Ev;b¼ 1:0063� 1:5828ðX � X bÞ þ 3:3561ðX � X bÞ2
� 9:389ðX � X bÞ3
þ 12:22ðX � X bÞ4 � 5:5924ðX � X bÞ5
190 K. Patel et al.
of inner and outer diameters) and T∞ (K) isthe room temperature. The enthalpy of hotair (Hb) can be estimated using [59]
H b ¼ Cp;bT b þ�HLY ; ð10Þ
where Cp,b (J·kg−1·K−1) and Y (kg·kg−1,dry basis) are the specific heat capacityand absolute humidity of hot air. The spe-cific heat of humid air can be estimatedusing the following equation:
Cp;b ¼ Cp;dry air þ YCp;v: ð11Þ
Using equations (9–11), the followingheat-balance model can be derived to evalu-ate the air temperature profiles within thedryer:
_V qbCp;bdT b
dl¼ h
vp
dmw
dt�HLf
�
þCp;v T b � T p
�� hAp T b � T p
�
� _V qb �HL þ Cp;vT b
dYdl
� UðpDeÞðT b � T1Þ�: ð12Þ
�
3.2.2. Mass balance
Similar to heat balance, the followingmass balance equation can be used to eval-uate the absolute gas humidity profile insidethe drying chamber:
dY
dl¼ � h
_V qbvp
dmw
dt; ð13Þ
where l (m) is the dryer’s axial height. Thewater evaporation rate dmw/dt can be cal-culated from equation (1).
3.2.3. Momentum balance
The axial velocity profile of droplets/par-ticles can be estimated using the followingmomentum balance equation:
dvpdt
¼ qp � qb
qp
!g � 0:75CDqb
dpvpðvp � vbÞ2
�" #;
ð14Þ
where CD is the drag coefficient. For0.5 < Re < 1000, CD can be estimatedfrom the following empirical correlation[21]:
CD ¼ 24
Re1þ 0:15Re0:687
: ð15Þ
It is often important to estimate the initialvelocity of the droplet to use as an inputparameter to the simulation tool. For a pres-sure nozzle, the initial droplet velocity canbe calculated by the following equation[59]:
vp;0 ¼ DC2 _V
2DObAC; ð16Þ
where DC (m) is the inlet channel (pipe)diameter (internal), AC (m2) is the channelsurface area, _V (m3·s−1) is the volumetric-flow rate of liquid concentrate, DO (m) isthe orifice diameter and b (m) is the liquidjet thickness at the orifice.
3.2.4. Shrinkage model
Modeling of a drying process requires ashrinkage model to estimate the change inthe droplet’s diameter because the evapora-tion of water from the droplets makes themshrink. This shrinkage effect has a directinfluence on the physical quality of theend products [43, 75]. Different models such
1-D Simulation of spray drying – pros & cons 191
as a perfect (or ideal) shrinkage model, areceding interface model and empirical (lin-ear or non-linear) shrinkage models werereported in the literature to estimate the tran-sient change in the diameter during drying[46, 54, 82, 89, 91, 98, 104]. Recedinginterface models assume that the dropletsshrink only during the constant drying-rateperiod [46]. The formation of a solid crustduring the falling-rate period is likely torestrict a shrinkage behavior. The perfectshrinkage and empirical models havewidely been used in the literature becausethey are straightforward to incorporate into1-D simulation tools. Selection of a shrink-age model should be based on how wellthese models are validated for specific mate-rials under given drying conditions.
The perfect (ideal) shrinkage model,which is the simplest and possibly the mostfrequently used approach, assumes that thechange in droplet diameter is proportionalto the quantity of water removed from thedroplets during drying [70]. Empirical mod-els have also been used since they appear toprovide higher accuracy in many studies[54–56]. For instance, Lin and Chen [54]used the following linear empirical modelto estimate the change in diameter duringthe drying of skim milk droplets:
dp
dp;0¼ bþ 1� bð Þ
�XX 0
; ð17Þ
where parameter β is the empirical coeffi-cient that is reported to be 0.59 and 0.69for 20 and 30 wt% skim milk droplets[54]. Since the accurate values of β forthe drying of higher initial solids concen-trations skim milk are not yet reported,the ideal shrinkage model was used forsimulation runs in this study.
The initial “representative” droplet diam-eter (dp,0) in equation (17) can be estimatedusing the known atomizer parameters and
the corresponding correlations published inthe literature. For a pressure nozzle, the fol-lowing correlation has widely been used[59]:
D3;2 ¼ 286 0:0254 DO þ 0:17ð Þ
� exp39
vp;0� 0:00313
_VAC
� �;
ð18Þ
where D3/2 (m) is the Sauter meandiameter that can be used as the initial“representative” droplet diameter to con-duct simulation.
3.2.5. Equilibrium moisture isotherm
It is essential to estimate equilibriummoisture contents (Xb) when using theREA to simulate drying processes. For dif-ferent materials, different equilibrium mois-ture isotherms may be used to estimate Xb.The Guggenheim-Anderson-de Boer (GAB)model, which has been fitted at elevatedtemperatures (up to 90 °C) and over a widerange of relative humidity (up to 100%)conditions, can be used to calculate Xb ofskim milk droplets [57]:
X b ¼ CKm0awð1� KawÞ � ð1� Kaw þ CKawÞ ;
ð19Þ
where C, K and m0 are three parameters ofthe model and aw is the water activity.These parameters were presented for skimmilk using the following correlations [57]:
C ¼ C0 exp�H 1
RgT
� �; ð20Þ
K ¼ K0 exp�H 2
RgT
� �� ð21Þ
192 K. Patel et al.
Here, C0 and K0 are fitting parameters,ΔH1 and ΔH2 (J·mol−1) are the enthalpiesof water sorption, R (J·mol−1·K−1) is the uni-versal gas constant and T (K) is the absolutetemperature. Parameters m0, C0, K0, ΔH1
and ΔH2 for skim milk were reported tobe 0.06156, 0.001645, 5.71, 24 831 and−5118, respectively, by Lin et al. [55].
3.2.6. Product quality parameters
Density, glass-transition temperature andinsolubility index are a few parameters ofinterest from the quality point of view.The true density profile of a particle canbe estimated using the densities of solidsand water. Since the water content profileof the particle is known from the dryingkinetics model, the density profile can beestimated using mass fractions and densitiesof water and solids. Alternatively, the parti-cle density can be predicted using the fol-lowing equation:
qp ¼ qs
1þ �X1þ qs
qw�X� ð22Þ
Glass-transition temperature and insolu-bility index are frequently used now to opti-mize process conditions to ensure that theproduct is non-sticky and has a good solu-bility. The first “spray drying” stage hashowever a large influence on these productproperties, and it is advisable to know thembeforehand. The glass-transition tempera-ture (Tg) is a characteristic property of anamorphous component of materials andcan be related to the stickiness behavior ofpowders during processing and storage.The Gordon-Taylor equation that seems toaccount for the water content effect can beused to estimate Tg of the solids-water mix-ture containing single or multiple solutes[1–3, 12, 29, 90, 96]:
T g ¼ xsT g;s þ kgxwT g;w
xs þ kgxw; ð23Þ
where kg is the solid-water (binary) con-stant, Tg,s and Tg,w are the glass-transitiontemperatures of solids and water, and ωs
and ωw are the mass fractions of solidsand water, respectively. Tg of skim milksolids (3 wt% moisture, dry basis) andwater were reported to be 72 and −137 °C,respectively [13]. The parameter kg has tobe obtained from independent experiments[8]. It is often accepted that Tg profiles ofskim milk droplets may be approximatedby Tg of anhydrous lactose (101 °C) witha corresponding kg of 7.4 [47, 69].
Solubility or insolubility index is anotherimportant property of dairy/food powdersand usually considered as a post-dryingproperty [65]. This property is often usedby commercial milk powder manufacturersas a criterion to indicate the quality of milkpowders. The insolubility index is an indica-tor of the presence of insoluble materials inthe particle/powder and the ability of pow-der to dissolve in the solvent (water, milk,etc.) [9]. The rate of insoluble materialformation during drying mainly dependson the protein contents of feed, the dryingconditions and the temperature and moisturecontent profiles of the droplets. Straatsmaet al. [94] proposed a zero-order kineticmodel to determine the insolubility indexof skim milk powders assuming that theinsoluble material forms only when the par-ticle moisture content is between 10 and30 wt% (dry basis). The rate of insolublematerial formation (risi) was described byStraatsma et al. [94] using the followingempirical equation:
risi ¼ kisi exp�Eisi
Rg
1
T p� 1
T p;0
� �� �;
ð24Þ
where kisi and Eisi are the kinetic constantsat a reference temperature, and Tp and Tp,0are the product temperature (K) andreference temperature (K), respectively.
1-D Simulation of spray drying – pros & cons 193
Straatsma et al. [94] evaluated constantskisi = 0.054 mL·s−1 and Eisi = 2.7 × 105
J·mol−1 at T0 = 348 K for skim milk pow-ders. Since a qualitative model to show theeffect of the moisture on the rate of insol-uble material formation is not available todate, this idealistic kinetic model may pro-vide “indicative” trends within the limitedoperating range.
Other product quality parameters such asthe rate of deactivation of bioactive sub-stances (e.g. enzymes and vitamins) andtheir residual activity in the final productsmay also be estimated by incorporatingappropriate mathematical models into 1-Dsimulation tools.
4. DEVELOPMENTOF A SPREADSHEET-BASED1-D SIMULATION TOOL
In this example, a Microsoft Excelspreadsheet was used as a process calcula-tion tool to simultaneously solve all the for-mulated equations andbuild a 1-D simulationspray drying software. A first-order finitedifference method was used to solvemass-, heat- and momentum-transfer differ-ential equations by following time integra-tion. At each time step, a droplet travels asmall distance (dh) in the dryer, thus divid-ing the dryer into many dryer “slices”. Allthe droplets in each dryer slice were consid-ered to experience the identical conditions,thus having the same thermo-physical prop-erties. The total number of droplets θ insidethe dryer was estimated using the flowrate of concentrate and a representativedroplet diameter (i.e. total droplets persecond = total volumetric flow per second/volume of a single droplet).
The Excel spreadsheet was divided intothree main parts where specific calculationswere performed using a time interval of0.005 s. The first part of the spreadsheetdefines various inputs of spray drying pro-cesses. These inputs are absolute humidity,
flow rate and temperature of inlet gasstreams (i.e. main hot gas, cooling gas andgas with fines recycle) as well as tempera-ture, flow rate and solids concentrationof liquid feed, the dryer’s dimensions(diameter and height) and the representativediameter and velocity of the droplets. Thesecond part of this 1-D tool calculates allrequired thermo-physical, chemical, trans-port and equilibrium properties of vapor,water, dry air and liquid feed including heatcapacity, density, viscosity, thermal conduc-tivity, latent heat of vaporization, partialvapor pressure, saturated vapor pressureand drag coefficient. These properties weretime-dependent and varied along the axialdistance in the drying chamber. The thirdpart of the simulation tool handles withthe drying kinetics of liquid feed and calcu-lates a product’s physical properties such asdensity, moisture content, size, Tg, solubilityindex, water activity, equilibrium moisturecontent, heat- and mass-transfer coefficients,drying rate and the distance travelled by thedroplets at each time step.
Simulation for integrated fluid-bed dry-ing was also combined with first-stage dry-ing. Several important parameters after firstand second drying stages were predictedand compared with experimental measure-ments. Synchronization of first-stage dryingand fluid-bed drying of individual particlesis a challenge although it is possible to com-bine them by introducing several simplifica-tions. In this study, the fluid-bed dryer wastreated as a well-mixed reactor. The detailedkinetic profiles of the product in the fluid-bed dryer were not projected. Drying kinet-ics profiles are reported in this paper onlyfor first-stage drying in order to highlightthe pros and cons of the 1-D simulation tooldeveloped at the Clayton Campus ofMonash University in Australia.
A few assumptions were used duringsimulation. These assumptions are:
1. A spray dryer was treated as a plug-flow reactor having a co-current flow.
194 K. Patel et al.
2. The droplets were considered asspheres of a binary mixture (solidsand water).
3. All the droplets in a specific dryer“slice” have identical size, shape andproperties.
4. A perfect shrinkage model was consid-ered reasonable to estimate shrinkagebehavior.
5. The initial “representative” diameterand velocity can be estimated usingappropriate empirical correlationsavailable in the literature for individualatomizers [59].
5. SPRAY DRYING TRIALSON A PILOT-SCALEMULTI-STAGE DRYER
To compare predicted parameters andstudy their trends, spray drying trialswere performed at the Bionov pilot plant(Rennes, France). The evaporation capacityof this dryer was in the range of 70–100 kgwater per hour. An internal static fluid-beddryer and an external vibro fluid-bed dryerwere used for final drying and agglomera-tion of powders. In this plant, the exhaustair stream is drawn out from the ceiling ofthe drying chamber to a set of two cycloneswhere fine particles are collected andreturned to the top of the drying chamber.The diameter of the cylindrical chamberwas 2 m, while the total height of this dryerwas 3.9 m. Schematic layouts of this dryingplant are presented by Bimbenet et al. [10]and not repeated here. A single pressurenozzle was used to spray liquid concentratesof known initial solids contents. Requiredoperating and feed parameters were eitherrecorded from a control panel board in thecontrol room or measured directly fromthe plant wherever possible. The heat lossthrough the dryer surface was estimated tobe ~ 2.5% of the total heat input. This heatloss was taken into account when estimating
air temperature profiles. Three trials wereperformed using skim milk concentrates of20 and 40 wt% solids contents. Inlet feedand operating conditions for these three tri-als are presented in Table II.
“Mixed air” in Table II indicates the totalmixed air (hot air, cooling air around pres-sure nozzle and air coming in with fines)that is available to a spray of droplets nearatomization zone. Temperature of mixedair was not measured during the spray dry-ing trials but it was calculated using the rel-evant enthalpy of each air stream (excludingthe hot air stream entering through staticfluid-bed dryer). This means
ð _mHÞhot þ ð _mHÞcooling þ ð _mHÞfines ¼ ð _mHÞtotal;ð25Þ
where _m (kg·h−1) and H (kJ·kg−1) are themass-flow rate and enthalpy of individualair streams. As an example, Htotal of mixedair during skim milk trial 1 would be (seeTab. II for humidity, temperature and flowrate values)
ð1899� 224:91Þhot þ ð500� 27:66Þcoolingþ ð350� 27:66Þfines ¼ 2749� H total
) H total ¼ 164 kJ�kg�1:
Temperature of this mixed air withenthalpy of 164 kJ·kg−1 and absolutehumidity of 1 g·kg−1 was calculated to be160.4 °C. This mixed air temperature wasused in the 1-D tool as an initial airtemperature.
6. RESULTS AND DISCUSSION
Detailed profiles and trends of importantfeed and gas parameters are predicted inthis section using the 1-D simulation tool.
1-D Simulation of spray drying – pros & cons 195
Predictions of the 1-D tool are comparedwith experimental measurements and pre-dictions of SD2P® software wherever possi-ble. Figure 2a demonstrates the airtemperature profiles estimated using the1-D tool. The hot region within the dryercan be identified using these profiles. Over-all outlet air temperatures predicted by the1-D tool and SD2P® are presented inFigure 2b. To study the trend of predictionusing three drying trials, measured outletair temperatures are also reported inFigure 2b. Results indicate that the trendsof prediction using both the software weresimilar to the measured outlet air tempera-tures (see Fig. 2b). When compared withmeasured outlet air temperatures, the aver-age and maximum relative differenceswere estimated to be ~ 4.2% and 7.9% withthe 1-D tool, and 1.7% and 2.0% withSD2P®. Both predictive tools slightly over-estimated the outlet air temperatures.
Figure 3a presents the air humidity pro-files predicted by the 1-D tool. These airhumidity and temperature profiles may beused to avoid stickiness and wall deposition
issues. The trend of predictions using the1-D tool and SD2P® and the measured out-let air humidity are shown in Figure 3b. Itwas observed that the outlet air humiditywas somewhat overpredicted by the 1-Dtool and SD2P®. Average and maximumrelative errors in predictions by the 1-D toolwere 10.8% and 17.4%, respectively, whilethese errors for SD2P® were ~ 6.3% and9.7%, respectively. It was further observedthat the air humidity after first-stage dryingtends to be slightly higher than the outletair humidity.
Powder moisture content profiles duringthe first-stage drying are predicted usingthe 1-D tool and illustrated in Figure 4a.These profiles help in identifying the dryerzones where the majority of the water isremoved. Powder moisture contents afterboth first-stage and fluidized-bed drying(see Fig. 4b) are also estimated. The finalmoisture contents of the powder (i.e. afterexternal fluid-bed drying) were measuredand reported to be 0.044 kg·kg−1 (dry basis)for all three drying trials. Because theSD2P® software presumes the average
Table II. Inlet conditions for skim milk drying trials.
Feed/gas parameters Trial 1 Trial 2 Trial 3
Inlet gas conditionsHot air temperature (°C) 221 173 213Hot air flow rate (kg·h−1) 1899 1920 1890Cooling air temperature (°C) 25 25 25Cooling air flow rate (kg·h−1) 500 500 500Recirculated air temperature (°C) 25 25 25Recirculated air flow rate (kg·h−1) 350 350 350Mixed air temperature (°C) 160.4 127.6 153.1Mixed air flow rate (kg·h−1) 2750 2770 2740Inlet air humidity (g·kg−1, db) 1.0 1.0 1.0
Inlet skim milk conditionsTemperature (°C) 40 40 40Concentration (wt%, db) 40 40 20Flow rate (L·h−1) 95 61 73Density (kg·cm−3) 1100 1100 1050Pressure at nozzle (bar) 200 90 130
196 K. Patel et al.
moisture contents of the powder after thefirst drying stage and fluidized-bed drying,the predicted moisture contents by the 1-Dtool could not be compared with the predic-tions of SD2P®. It should be noted thatSD2P® used the final moisture content asan input parameter to the model while the1-D tool “predicts” the powder’s moisture
contents throughout drying, and thus allowsthe estimation of other moisture content-based product properties such as glass-tran-sition temperature, insolubility index andresidual activity of bioactive components.
Figure 4b shows that the powder’s mois-ture content was overpredicted for the sec-ond drying trial while it was underpredicted
0
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Air
tem
pera
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, OC
Dryer height, m
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ir te
mpe
ratu
re, O
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EXP
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Figure 2. (a) Air temperature profiles predicted by the 1-D simulation tool and (b) outlet airtemperatures from drying trials, 1-D simulation tool and SD2P® software.
1-D Simulation of spray drying – pros & cons 197
for the third drying trial when using the 1-Dtool. Average powder moisture contentsafter first-stage drying should be in therange of 0.07–0.09 kg·kg−1 (dry basis)based on overall moisture balance calcula-tions. The error in prediction may be dueto the inclusion of various assumptions
(such as co-current axial flow, no droplet sizedistribution, spherical droplets, no agglomer-ation, no droplet-droplet or droplet-wallinteractions, no gas recirculation withinthe chamber and ignorance of fines nearthe atomization zone) and various approxi-mate models (such as ideal shrinkage,
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ir hu
mid
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. kg–1
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Figure 3. (a) Air humidity profiles predicted by the 1-D simulation tool and (b) outlet air humidityfrom drying trials, 1-D simulation tool and SD2P® software.
198 K. Patel et al.
empirical correlation for estimating thedroplet size and Ranz-Marshall correla-tions). It is expected to have a certain degreeof errors due to these approximations.
Variations in the feed/air parametersduring spray drying operations may alsointroduce errors in recording drying/gasparameters and hence during spray drying
simulation. For instance, a variation in thefeed-flow rate during the pilot-scale dry-ing trials was recorded to be ~ ± 3.0–8.0 L·h−1. A variation in the gas-flow rateduring drying was more noticeable. There-fore, it was often difficult to record accurategas and feed parameters to enter in thesimulation program. Other spray drying
0
1
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oist
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Trial no.
1-D Simulation (1st stage)1-D Simulation (2nd stage)Exp. (3rd stage)
1 2 3 4
1 2 3
(a)
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Figure 4. (a) Powder moisture content profiles predicted by the 1-D simulation tool and (b) outletpowder moisture contents from drying trials, 1-D simulation tool and SD2P® software.
1-D Simulation of spray drying – pros & cons 199
software products available in the marketwhich require inlet/outlet gas and feedparameters as inputs to the simulation toolmay also face this challenge.
During spray drying experiments, fineswere returned at the top of the drying cham-ber and mixed with fresh droplets. However,the return of fines was not considered duringheat and mass balances by the 1-D simula-tion software. In fact, fines returns couldbe as high as 60–80% of the total powderproduced after first-stage drying [40]. Sucha high fraction of fines may have a certaininfluence (not necessarily significant) on theoverall heat-mass balances and averagedrying flux of fresh droplets. The interactionsof fresh droplets with the fines near theatomization zone, their impact on the averagedrying flux and the modeling for thesedroplet phenomena have remained a chal-lenge. Nevertheless, the trend of productmoisture contents delivered by the 1-D simu-lation approach appeared to be correct, andthese trendsmaybeused to study thesensitiv-ity of various drying/feed parameters.
A higher accuracy may be achieved bytuning the empirical coefficients of severalmathematical models for specific productsor process conditions. Another way toimprove the accuracy of prediction may beto incorporate an adjustment parameter oran air-droplets mixing coefficient into themodel. However, it is not clear yet howand where to introduce adjustment parame-ters during spray drying simulations.
Particle velocity and gas velocity profilesare predicted by the 1-D tool and presentedin Figure 5. The initial “representative”axial droplet velocity was estimated to be~ 31.5, 29.5, and 35.4 m·s−1 for drying tri-als 1, 2, and 3. The inlet gas velocity wasapproximated around 6.0 m·s−1. The realdryer geometry was considered during sim-ulation. It was observed that both the parti-cle and gas velocities slightly went up at thebottom of the drying chamber due to theconical shape of the chamber. Particle resi-dence time during the first-stage drying,
assuming co-current parallel flow, was inthe range of 3.5–5.0 s for the reported dry-ing trials.
Figure 6a demonstrates glass-transitiontemperature (Tg) and product temperature(Tp) profiles. Tg for skim milk powder wasestimated using Tg of anhydrous lactose asdone by Langrish [47]. Tg values afterfirst-stage drying corresponding to the dry-ing trials 1, 2, and 3 (product moisture con-tents of 6.3, 16.6, and 2.4 wt%) were 64.2,−19.8, and 100.1 °C, respectively. Respec-tive Tp–Tg values after first-stage dryingwere approximately 20, 95, and −22 °C.These predictions show that the productmay be slightly sticky for trial 1, very stickyfor trial 2, and non-sticky for trial 3. Theerror of prediction in estimating theproduct’s moisture concentrations directlyreflected in the Tg predictions. Accurate Tgprofiles can be helpful in drawing safe dry-ing regime maps and taking decisions ontuning inlet/outlet gas temperature/humidityto produce non-sticky products with mini-mum wall deposition.
Insolubility index profiles are alsopredicted by the 1-D tool and reported inFigure 6b. One should be careful whenreading the insolubility index when predict-ing them using the model (equation 24)used in this study. The model assumed thatthe insoluble material forms only when theproduct moisture content was between 10and 30 wt%. Based on this assumption,the insolubility index for the drying trials1, 2 and 3 was ~ 1.09, 0.07, and 0.14 mL(at 10 wt% powder moisture). The effectof the product’s temperature profiles hasbeen reflected on the insolubility index.Experimental solubility data and SD2P®
predictions for this property are not avail-able. The insolubility index data duringfirst-stage drying may help in giving arough estimate on how much insolublematerial forms during the subsequent dryingstages and storage.
It was noticed during this case studythat the trends of prediction using the 1-D
200 K. Patel et al.
simulation tool were similar to experimentaldata recorded from the plant. The 1-D toolalso helped in observing the variations inproduct and gas properties upon changinginlet feed and air parameters. Despite intro-ducing several simplifications in this studyto make the 1-D tool simpler and faster,the correct trends of important product andgas properties were obtained. The absoluteerrors of prediction by the 1-D tool for thedrying trials conducted on the pilot-scaledryer were in the range of 3–17%. Theseerrors may be minimized by modifying heatand mass balances that closely resemble realspray drying trials, by tuning several empir-ical parameters and by introducing anadjustment coefficient in the model.
It should be noted that the input parame-ters to the 1-D simulation tool built for thisstudy and SD2P® software are quite differ-ent. SD2P® requires the outlet moisturecontent and outlet air temperature as inputparameters in order to calculate the inletair temperature for achieving the presumedmoisture content. The 1-D simulation tool
requires all the inlet conditions to the dryeras inputs to the simulation and predictsimportant parameters at the outlet of thedrying chamber. To achieve the desiredoutlet moisture content or outlet gas temper-ature with the 1-D tool, the input parametersshould be changed until the desired outletconditions are obtained. Nevertheless,both the 1-D simulation tool and SD2P®
software are quite useful to perform simula-tions for spray drying operations. Severalimportant pros and cons of the 1-D simula-tion approach are mentioned in the nextsection.
7. PROS AND CONS
7.1. Pros of 1-D simulation approach
d The first important advantage of a 1-Dsimulation tool with an Excel spread-sheet platform is that fast calculationscan be performed. Product and processparameters can be predicted and their
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Figure 5. Droplet and air velocity profiles predicted by the 1-D simulation tool.
1-D Simulation of spray drying – pros & cons 201
trends can be projected within a fewseconds unlike multi-dimensional simu-lation approaches that may requirehours, days or even weeks to evaluatevaluable information for industrial-scaledrying operations. Spreadsheet-based1-D software is becoming an indispen-sible tool for process and plant engi-
neers because of the ease of use andthe saving of time and resources.
d 1-D approach requires only a few inletfeed and gas parameters as inputs tothe simulation program.
d 1-D tool evaluates the product’s temper-ature and moisture content throughoutdrying which allow for predicting the
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(a)
(b)
Figure 6. (a) Glass-transition temperature (Tg) and product temperature profiles and (b) insolubilityindex profiles estimated by the 1-D simulation tool for the skim milk drying trials.
202 K. Patel et al.
product’s quality parameters not only atthe dryer’s inlet and outlet but alsowithin the dryer chambers.
d Safe drying regime maps can be pre-pared to produce non-sticky products,to determine the extent of particle crys-tallinity required for product stabilityand to minimize wall deposition.
d 1-D simulation approach can be a greatmeans to track the consequences ofchanges in process and feed parameterson important product quality parame-ters, energy consumptions and processefficiencies. For instance, if the inletair humidity to the dryer is changingin a rainy season, it is fast and straight-forward to decide what changes shouldbe made to inlet air temperature or inletfeed-flow rates or other parameters tokeep the product’s moisture contentconsistent at the dryer outlet. Further-more, it can be quickly estimated whatinlet air temperatures should be usedfor any variation in the feed’s initial sol-ids concentrations. This information canbe presented using simple graphs ortables and provided to the plantoperators.
d Recently, Patel and Chen [76] demon-strated the ability of estimating surfaceproperties of particles throughout dryingusing the 1-D simulation tool and theREA. Previously, the surface propertiesof products were estimated using a dif-fusion-based drying kinetics approachor a receding interface approach thatrequired using much more complex pro-cess calculation tools such as MATLABand FlexPDE.
7.2. Cons of 1-D simulationapproach
d Several dryer geometries involve therecirculation of particles within the dry-ing chamber, the recirculation of humidair to the ceiling of the chamber and the
fines return to the dryer. At this stagethe 1-D approach does not account forthese phenomena and cannot predictgas distribution within the chamber,droplet/particle trajectories and gas-particles residence time data. 2-D and3-D simulation approaches may behelpful to handle these spray dryingphenomena in order to study these phe-nomena in more depth.
d The 1-D simulation approach does notconsider droplet-droplet interactionsand droplet-particle interactions in thedryer which are common phenomenafor real spray drying operations.
d Simulation of the drying of agglomer-ated particles is also a challenge forthe 1-D approach.
d The 1-D approach requires severalparameters from the laboratory-scaleexperiments prior to simulation if theyare not known. These parametersinclude drying kinetics parameters(e.g. relative activation energy), shrink-age parameters, equilibrium moistureisotherm parameters and quality param-eters (e.g. Tg of anhydrous solids). Anyerrors in obtaining experimental dataand validating associated mathematicalmodels may have a certain influenceon the accuracy of prediction by the1-D simulation approach.
8. CONCLUSION
The 1-D simulation approach offersvaluable information on operating parame-ters before production of powders. Moisturecontent and temperature-dependent productproperties can be predicted at any locationsin the dryer, thus giving an additionaladvantage over the “black box” approach.When a good understanding of the princi-ples of spray drying and the characteristicsof the particular plant in use is coupled withthe information obtained by the predictive
1-D Simulation of spray drying – pros & cons 203
tools, sensible decisions can be made toavoid potential problems and to improveproduct quality and process efficiencies.The user of 1-D simulation tools should,however, be aware of the accuracy of pre-diction when taking decisions based onthe trends/numbers provided by the 1-Dtools. From the customer’s point of view,simulation software should be easy to use,of low cost and be readily available in themarket. Predictive tools based on a 1-D sim-ulation approach can be constructed usingspreadsheet-based platforms like Excelwhich offer simplicity and cost-related ben-efits over other CFD- and MATLAB-basedprocess calculation tools.
Acknowledgments: The authors gratefullyacknowledge Dairy Innovation Australia Limited(Australia), the Geoffrey Gardiner Dairy Founda-tion (Australia), and l’Institut National de laRecherche Agronomique (France) for their finan-cial and other support for this research. Theauthors also thank Dr. Martin Palmer from DairyInnovation Australia Limited (Australia) for hisvaluable comments and suggestions on varioustechnical aspects of this paper.
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Appendix
CORRELATIONS USEDIN THE CALCULATIONS
RH b ¼qv;b
qv;sat
qv;b ¼P vMw
RgT b
P v ¼ P � YY þ Mw=Mbð Þ
qv;sat ¼P satMw
RgT�
208 K. Patel et al.
Vapor pressure at saturated conditions[67]
log P sat ¼ 7:94917� 1657:462
T þ 227:02;
where T is expressed in °C and Psat in Torr.Specific heat of air-vapor mixture
(J·kg−1·K−1) [39]
Cp;b ¼ 1:9327� 1010T 4 � 7:9999� 107T 3
þ 1:1407� 103T 2 � 0:4489T þ 1057:3;
where T is expressed in K and is suitablefor 295 K < T < 800 K, R2 = 0.9995.Specific heat of water-vapor mixture
(J·kg−1·K−1)
Cp;v ¼ 0:0167T 2 � 0:0261T þ 1866:4;
where T is expressed in °C.Viscosity of air (MPa·s) [39]
lb ¼ �0:00003T 2b þ 0:0687T b þ 0:885;
where T is expressed in K and suitable for250 K < Tb < 400 K, R2 = 0.9996.Density of air-vapor mixture (kg·m−3)
[80]
qb ¼353:12832
T b
1þ Y1þ 1:6Y
;
where Tb is expressed in K.Diffusivity of air-vapor mixture (m2·s−1)
[39]
Dv ¼ 1:963� 10�7T � 3:33307� 10�5;
where T is expressed in K and suitable for293 K < T < 373 K, R2 = 1.0.
Thermal conductivity of air-vapor mix-ture (W·m−1·K−1) [39]
kb ¼ 1:5207� 10�11T 3 � 4:8574� 10�8T 2
þ 1:0184� 10�4T � 0:00039333;
where T is expressed in K.
Nomenclature
Letters
aw water activity (–)A surface area (m2)AC cross-section area of atomizer
pipe (channel) (m2)b thickness of liquid jet at the
orifice (m)C GAB isotherm model parameter
(–)C0 GAB isotherm model constant
(–)CD drag coefficient (–)Cp specific heat capacity
(J·kg−1·K−1)dp diameter of droplet or particle
(m)D3/2 Sauter mean diameter (m)DC diameter of atomizer pipe
(channel) (m)De effective diameter of drying
chamber (m)DO orifice diameter (m)Dv air-vapor diffusion coefficient
(m2·s−1)Eisi kinetic constant from solubility
model (J·mol−1)ΔEv apparent activation energy
(J·mol−1)ΔEv,b equilibrium activation energy
(J·mol−1)g universal gravitational constant
(= 9.8 m·s−2)
1-D Simulation of spray drying – pros & cons 209
h convective heat-transfer coeffi-cient (W·m−2·K−1)
hm mass-transfer coefficient (m·s−1)H enthalpy (J·kg−1)ΔH1 enthalpy parameter from GAB
model (J·kg−1)ΔH2 enthalpy parameter from GAB
model (J·kg−1)ΔHL latent heat of vaporization
(J·kg−1)k thermal conductivity
(W·m−1·K−1)K GAB isotherm model parameter
(–)K0 GAB isotherm model constant
(–)kg constant from the Gordon-
Taylor modelkisi kinetic constant from solubility
model (mL·s−1)l axial distance in dryer (m)m mass (kg)mo monolayer moisture content
(kg·kg−1)_m mass-flow rate (kg·h−1)M molecular weight (g·mol−1)Nu Nusselt number (–)P pressure (kPa)Pr Prandtl number (–)risi rate of insoluble material forma-
tion (mL·s−1)Rg universal gas constant
(= 8.314 J·mol−1·K−1)RH relative humidity (%)Re Reynolds number (–)Sc Schmidt number (–)Sh Sherwood number (–)
t time (s)T temperature (K)Tg glass-transition temperature (K)T∞ room temperature (K)v velocity (m·s−1)_V volumetric-flow rate (m3·s−1)U overall heat-transfer coefficient
for heat loss (W·m−2K−1)�X average droplet moisture con-
tent (dry basis) (kg·kg−1)X0 initial moisture content (dry
basis) (kg·kg−1)Xb equilibrium moisture content
(dry basis) (kg·kg−1)Y air absolute humidity (dry basis)
(kg·kg−1)
Greek symbols
β shrinkage model constant (–)ω weight fraction (–)θ number of droplets/particles (–)μ viscosity (Pa·s)ρ density (kg·m−3)ρv vapor density (kg·m−3)
Subscripts
b bulk drying gasp particle, droplets solidssat saturated conditionsv vaporw water
210 K. Patel et al.