chl471

MOISTURE OIL AND ENERGY TRANSPORT DURINGDEEP-FAT FRYING OF FOOD MATERIALS

H NI and A K DATTADepartment of Agricultural and Biological Engineering Cornell University USA

Amultiphase porous media model has been developed to predict the moisture migrationoil uptake and energy transport in a food material such as a semi-dry potato duringdeep-fat frying The model predictions are validated using experimental data from

the literature Spatial moisture pro les show two distinctive regions (dry or crust region nearthe surface and wet region in most of the core) with a sharp interface which can be referred toas the evaporation front Spatial temperature pro les show two distinctive regions mdash higher butconstant temperature gradient region near the surface and lower temperature gradient region inthe core In the crust region vapour diffusional ux is comparable with vapour convective uxIn the more moist core region capillary ux of liquid water is comparable to the convective ux of liquid water Therefore all three modes of transport mdash diffusional capillarity andpressure driven (Darcy) ow are found to be important Sensitivity of the nal productmoisture and temperature to changes in oil temperature initial moisture content of the samplethickness of the sample and the surface heat and mass transfer coef cients are discussed

Keywords multiphase ow heat and mass transfer porous media deep-fat fryingDarcy ow

INTRODUCTION

Deep-fat frying is a widely used and industrially importantfood process The fried food develops a crispy porousstructure in addition to avour and other chemical changesthat is desired by the consumer During deep-fat fryingthe food is immersed into the oil at a high temperature(180 2 190degC) that leads to intensive vapourization of thewater in the food and transport out through the surface Aswater moves out part of the pore spaces are taken up bythe frying oil moving into the material The oil picked upby the food during the frying process has increasinglybecome a public health concern and there is a strongdesire to reduce the oil content A better understandingof the transport processes and their relationship to variousparameters should provide ways to optimize the fryingprocess thus controlling oil pickup for example

A mathematical description of frying at different levelsof complexity has been reported The simplest descriptioncan be empirical curve ts of experimental data12 A largenumber of models have been based on simple diffusion ofenergy and mass with various approximations to accountfor evaporation and sometimes ignoring evaporationaltogether For example only the diffusion of energy andmoisture was considered without evaporation in the worksof Rice and Gamble3 and Dincer and Yildiz4 Dagerskog5

calculated temperatures using only the diffusion term inthe energy equation and did not acount for the latent heatof evaporation The evaporation interface was tracked bysimply knowing the location where temperature exceeded100degC from the solution to the energy equation The amountof evaporation was calculated by following the rate ofmovement of the interface This is obviously a simple

description of a complex process Ateba and Mittal6

considered separate diffusion equations for energy moist-ure and oil phases without any evaporation term in theenergy or the moisture transport equation They includedonly surface evaporation as a boundary condition for theenergy equation and equated the rate of surface evaporationto the rate of diffusive moisture loss at the surface Thusevaporation was excluded from the inside even thoughtemperatures inside reached higher than 100degC Moreiraet al7 on the other hand used the same approach (ieevaporation included only at the surface and no internalevaporation) but considered only diffusion of energy andmoisture They provided no transport model for the oilphase Ikedalia et al8 treated evaporation as spatiallyuniform throughout the material and included it as a sinkterm in the energy equation The transient rate of moistureloss was obtained from experimental data They did notconsider transport of moisture or oil phases in their model

Farkas et al910 provided a more detailed model of tem-perature and moisture transport in deep-fat frying Theyprovided separate equations for two regions mdash crust andthe core with a moving boundary They were perhaps the rst ones to consider pressure-driven ow although theyrestricted such ow only in the crust region and only forthe vapour phase They ignored any diffusional ow in thecrust region They also ignored pressure driven ow ofliquid or vapour in the core region Such non-conside rationof uxes in various regions reduced mathematical compli-cations but their possible signi cance was not discussedTheir model did not include the oil phase A transport modelthat includes oil phase was reported by Chen and Moreira11 They did not include the vapour phase separately andtherefore the pressure driven mode of transport which is

194

0960 ndash308599$1000+000copy Institution of Chemical Engineers

Trans IChemE Vol 77 Part C September 1999

important and different from diffusion was absent (seediscussions below) Several oil absorption or uptake studiesthat do not include transport modelling have been reportedThese include experimentally measured oil uptake1213 andhow capillarity causes the surface oil to migrate inside duringcooling14 A statistical description of oil distribution in thefried product based on percolation theory was also reported15

Deep-fat frying is an intensive heat transfer process thatis expected to produce signi cant internal evaporation andpressure generation that are spatially-varying and are func-tions of the porous structure of the material At high ratesof internal evaporation signi cant pressure driven owscan be present for all phases and throughout the materialPressure driven ow is also a fundamentally differentmode of transport that cannot be lumped into an effectivediffusivity in a meaningful way ie without making thelsquodiffusivityrsquo completely empirical as was done in somestudies31611 In fact the constant diffusivity data that wasobtained by tting the experimental curves in Chen andMoreira11 has strong discrepancies between their modeland experimental moisture pro les particularly at higheroil temperature when pressure driven ows are likely to bemore important Also since oil water vapour and air willbe occupying the same pore space their amounts are notindependent of each other as has been used by most pre-vious studies Thus an acute need exists for a model thatwould consider all these factors simultaneously to providea comprehensive mechanistic understanding of transportphenomena in deep-fat frying which is the objective of thisstudy It appears that a multiphase porous media model ofthe type developed by Ni et al17 and applied to microwaveheating where signi cant pressure driven ows can bepresent is a type of model that can be developed to studydeep-fat frying Here all transport mechanisms (iemolecular diffusion capillary and pressure driven ow)and all the phases (ie oil water vapour air) keep theirindividual identity In addition to providing a comprehen-sive description such a model can give insight into therelative magnitudes of various transport mechanisms Thespeci c objectives of this study are to

1) Develop a multiphase porous media model for transportof energy liquid water vapour air and liquid oil duringdeep-fat frying2) Calculate the spatial and transient pro les of themoisture oil uptake temperature and pressure3) Compare the magnitudes of capillary and convectiveliquid uxes in the core region and diffusive and convec-tive uxes of vapour in the crust region4) Perform sensitivity analysis to nd the effect of oil tem-perature initial moisture content sample thickness andheat and mass transfer coef cients on temperature moistureloss and crust thickness

DEVELOPMENT OF THE MULTIPHASEPOROUS MEDIA TRANSPORT MODEL FOR

DEEP-FAT FRYINGAssumptions

The mathematical formulation of the problem consider-ing the energy and mass balance of the phases aredeveloped following the work of Ni et al17 with the oilphase added to the system A schematic diagram of the

model system is shown in Figure 1 The major assumptionsof this model include

1) The solid liquid and gas phases are continuous2) Local thermal equilibrium exists between the phases3) Water vapour pressure is a function of water saturationand temperature oil vapour is not considered in the presentmodel4) Liquid water transport results from convective owdue to the gradient in total gas pressure and from capillary ow due to the gradient of capillary force which is a strongfunction of moisture content Oil transport is assumedresulting from capillary ow due to the gradient of capillaryforce which is a strong function of oil content5) Vapour and air transport are driven by convective owdue to the gradient in total gas pressure and diffusiondue to the concentration gradient6) The contribution of convection to energy transport canbe ignored as shown by Ni et al177) Geometry does not change during frying and overallshrinkage is ignored An equivalent porosity is de nedas the fraction of the total volume occupied by the liquidwater oil water vapour and air This equivalent porosityis assumed constant during the frying process and is usedto calculate the concentration of each phase mdash liquid wateroil gas (water vapour and air) Effect of structure changeduring frying manifests as changed gas porosity and relatedtransport properties For example loss of water increasesgas porosity and therefore the intrinsic permeability8) Moisture removal from the surface consists of twopartsmdash vapour diffuses to the boundary and is convectedaway from the surface area occupied by the gas fractionon the boundary Liquid water evaporates at the boundaryand is convected away from the surface area occupied bythe liquid fraction on the boundary For a high moisturefood or when signi cant water is pushed to the surface frominside due to pressure driven ow surface evaporationof liquid dominates For a drier surface vapor diffusiondominates9) Oil transport is driven by convective ow and capillary ow10) Oil saturation at the boundary is assumed constant

195MOISTURE OIL AND ENERGY TRANSPORT DURING DEEP-FAT FRYING OF FOOD MATERIALS


Energyvaporconvected away

0 127 x (cm)

Potatoslab

Symmetry(impermeablesurface)

Oil

Constantoil saturationat surface

Figure 1 Schematic diagram of the 1D system

Governing Equations

Equivalent porosity of an elemental volume DV is de nedas

w =DVw + DVo + DVg

DV(1)

Equivalent saturation values for the various componentsare de ned as

Sw =DVw

w DV(2)

So = DVo

w DV(3)

Sg =DVg

w DV(4)

where

Sw + So + Sg = 1 (5)

Mass concentration values of the components are de nedas

cv = pvMvSgw

RT(6)

ca = paMaSgw

RT(7)

cw = rww Sw (8)

co = row So (9)

Flux values of the components are de ned as

regnv = 2 rvk p

g

mg$ P 2

C2g

rgMaMv Deff g $ xv (10)

regna = 2 rak p

g

mg$ P 2

C 2g

rgMaMvDeff g $ xa (11)

regnw = 2 rwk p

w

mw$ P 2 Dwrww $ Sw (12)

regno = 2 rok p

o

mo$ P 2 Dorow $ So (13)

where P = pa + pv is total gas pressure and x = pP is themolar fraction The conservation equations for watervapour liquid water air oil and energy in the porousmedium are written respectively as

shy cv

shy t+ $ (regnv) = dI (14)

shy cw

shy t+ $ (regnw) = 2 dI (15)

shy ca

shy t+ $ (regna) = 0 (16)

shy co

shy t+ $ (regno) = 0 (17)

( rcp)effshy Tshy t

= $ (keff $ T) 2 l dI (18)

where

( rcp)eff = w (Sgrgcpg + Swrwcpw + Sorocpo)

+ (1 2 w )rscps (19)

keff = w Sgkg + Swkw + Soko( ) + (1 2 w )ks (20)

Equations (14)ndash(18) make the complete set of governingequations with four unknowns Sw So T and P Theseequations are developed in 1D for the model system shownin Figure 1

Boundary and Initial Conditions

The initial conditions are given by

Sw = Swi (21)

So = 0 (22)

T = Ti (23)

P = Pamb (24)

The boundary conditions at the frying surface (x = 0) aregiven by

nv + nw = w (Sg + Sw)pv Mv

RT2 rv0( ) hmv (25)

So = So1 (26)

P = Pamb (27)

q = h T 2 Tamb( ) + lnw (28)

Mass transport on the frying surface can be very com-plicated Equation (25) simply assumes the vapour to beconvected away by the surrounding oil Although it islikely that the vapour can be expelled by the internalpressure its numerical implementation is problematicFarkas et al9 considered that there is almost no resistancefor vapour to leave the surface and considered the pressuredriven ux on the boundary mdash however the boundarycondition they used by specifying vapour pressure is notconvincing Instead a large mass transfer coef cient hmv isused here to represent the lower resistance to mass transferfor the vapour In equation (28) lnw represents heat ux dueto the latent heat of surface evaporation This termis relatively large when the surface is wet and becomesinsigni cant as the surface gets dry

Equation (26) is a very simple assumption for oilboundary In fact the volume fraction near the surfaceoccupied by the oil may not be a constant It could dependon whether there is bubbling because the bubble can pushout the oil from the surface In this study it is assumedthat the oil saturation on the surface is constant with atime-averaged value of 035 Further work is certainlyneeded to re ne the boundary condition for oil at thefrying surface

At the centre of the slab symmetry boundary conditionsare used

nv = 0 (29)

nw = 0 (30)

no = 0 (31)

q = 0 (32)

Input Parameters

Input parameters are shown in Table 1 Some of theparameters are discussed here and further details are in Niet al17 The vapour pressure was considered as a functionof both temperature and water saturation of the material

196 NI and DATTA


and data from Ratti et al23 was used

lnpv

ps(T )= 2 00267M 2 1656

+ 00107e 2 1287MM1513 ln ps(T ) (33)

where ps(T ) and M are the vapour pressure of pure water attemperature T and the moisture content of the materialrespectively Capillary diffusivity values are assumed to bedependent on saturation only as given by

Dw = 103 10 2 8 exp( 2 28 + 20M ) (34)

for water Details of the formulation of water capillarydiffusivity is given in Ni24 Since there is no literature dataavailable for oil capillary diffusivity as a function of oil

saturation same form of dependence as given by equation(34) is used in this work for oil

The total permeability for gas (kpg) and water (kp

w) arecalculated by using two different intrinsic permeabilitiesk p

gi and kpwi for gas and water respectively as

k pg = kp

gikpgr

k pw = kp

wikpwr

(35)

The intrinsic permeability values in the very wet stage andthe very dry stage are different as shown in Table 1 Therelative permeabilities k p

gr and k pwr are given by Bear21

k pgr = 1 2 11Sw Sw lt 111

k pgr = 0 Sw gt 111

(36)

k pwr = Sw 2 Sir

1 2 Sir( )3

Sw gt Sir

k pwr = 0 Sw lt Sir

(37)

where Sir is the irreducible liquid saturation Equations (35)to (37) are shown graphed in Figure 2 using the kp

gi kpwi and

Sir values from Table 1 At high water content the totalgas permeability decays linearly to zero The total liquidpermeability is high at high liquid saturation but not aslarge as the total gas permeability at very low liquidsaturation This is the effect of the change in structure (moregas pores) In reality the intrinsic permeability changescontinuously from the very wet stage to the very dry stageIn the absence of such data the curves in Figure 2 are areasonable description of the effect of structural changeson permeability Data on permeability values for oil are alsounavailable The intrinsic permeability of oil is treated thesame as that for water The relative permeability of oil isalso assumed to vary in the same manner as water andequation (37) is used for oil with Sw replaced by So

Numerical Method

The above ve governing equations are transformed intofour equations with four variables (Sw So T and P) A nitedifference method is used with centre difference in spaceand fully implicit in time A non-uniform grid is used tosolve a slab with a half thickness of 127 cm The minimumgrid size (001 cm) is near the surface and the maximum



Table 1 Input parameters used in the simulations

Parameter Value Source

cpw (J kg 2 1 K 2 1) 4180Dw (m2 s2 1) Eqn 34 Ni17

Deff g (m2 s 2 1) 263 10 2 5 Mills18

h (W m 2 2 K 2 1) 250 Miller19

hmv (m s 2 1) 0015 This workks (W m 2 1 K 2 1) 021 Choi and Okos20

kw (W m 2 1 K 2 1) 065 Choi and Okos20

kg (W m 2 1 K 2 1) 0026 Choi and Okos20

ko (W m 2 1 K 2 1) 017 Choi and Okos20

k pgi (m2) 10 3 10 2 14 Ni24

kpwi (m2) 53 10 2 14 Ni24

kpoi (m2) 53 10 2 14 Ni24

Swi 05 This workSo1 035 This workSir 008 Bear21

Tamb (degC) 180 This workTi (degC) 20 This workro (kg m 2 3) 920 Choi and Okos20

rv (kg m 2 3) 0 Ni24

rw (kg m 2 3) 1000l (J kg 2 1) 24353 106

w 088 Ni24

mo (Pas) 00317 Steffe et al22

mg (Pas) 183 10 2 5

mw (Pas) 54683 10 2 4

10

8

6

4

2

0

Per

mea

bilit

y (1

0-14 m

2)

100806040200Liquid saturation Sw

Gas (kp)

Liquid (kpw or ko )

or So

p

g

Figure 2 Permeabilities of liquid and gas phases calculated from intrinsic and relative permeabilities plotted vs saturation

grid size (01 cm) near the centre Detailed numericalprocedures are given in Ni24

MODEL VALIDATION

The model predictions are compared with literatureexperimental data9 for a 1D slab of potato tissue withhalf thickness of 127 cm oil temperature of 180degC heattransfer coef cient between the oil and the fried surface hof 250 W m 2 2 K 2 1 and mass transfer coef cient hmv of0028 m s 2 1 The higher value of mass transfer coef cientis chosen to represent minimum surface transport resist-ance to vapor as was true for Farkas et al9

Figure 3 shows that the predicted temperatures comparewell with experimental data in all four locations Thetemperature increases slowly inside due to the low heatpenetration while the temperature near the surface risesfast The region where the curve becomes at signi es thepresence of strong evaporation Temperatures eventuallyapproach the oil bath temperature The moisture content andcrust thickness in Figure 4 shows that the calculated trendsare the same as those in the experimental data Thedifference in the magnitude for the crust thickness data isprobably due to the speci c temperature chosen to de ne thecrust In this model the crust is de ned as the region overwhich the temperature exceeds 100degC (moisture content isalready quite low here) Experimentally crust thicknesscannot be de ned the same way and discrepancies betweenmeasured and calculated crust thickness is inevitable

RESULTS AND DISCUSSION

Spatial and temporal pro les of temperature pressuremoisture oil saturation and oil uptake during deep-fatfrying of a slab of potato are discussed here Relativemagnitudes of the rates of moisture transport by pressurediffusional and capillary modes are compared Sensitivitiesof the frying process to changes in oil temperature initialmoisture content and slab thickness are also included here

Spatial Pro les of Temperature Moisture Oiland Pressure

Temperature pro les in Figure 4 show two distinctiveregions with very different temperature gradients As there

is less evaporation in the crust layer the linear temperaturepro les are almost the same as for a pseudo-steady stateheat conduction process Temperature is somewhat uni-form in the core region primarily due to the presence of theevaporation zone that acts as a sink for the incoming energyfrom the surface The temperature pro le is qualitativelysimilar to conventional drying as in the work of Nasrallahet al25

The evaporation temperature is about 90degC and is some-what lower than experimental data of Farkas et al9 whichis about 100degC The reason might be due to higher masstransfer coef cient (hmv = 0028 ms 2 1) used in the modelUsing a smaller value of hmv = 0015ms 2 1 increases theevaporation temperature to 93degC As discussed earlier alarge mass transfer coef cient is used here to representthe small resistance to surface mass transfer used by otherauthors However based on the decrease in the evaporationtemperature it appears that the no resistance assumptionfor the vapour to leave the boundary is questionable Another reason for the lower evaporation temperaturemight be the lower surface heat transfer coef cient(250 W m 2 2 K 2 1) used here Although the exact value isnot known it can be as much as twice this value duringthe intense bubbling period79 The effect of changes in heatand mass transfer coef cients is shown under sensitivityanalysis

Under intensive frying conditions water saturation Swnear the surface reduces rapidly as shown in Figure 5However water saturation in the wet region insidedecreases slowly due to a drastically reduced water capillarydiffusivity of 10 2 9 m2 s 2 1 in the very dry region near thesurface from a value of 10 2 7 m2 s 2 1 in the wet region (seeequation (34)) Initially the dry layer thickness increasesrapidly However it slows down as the crust becomesthicker and its low thermal conductivity reduces the rate

198 NI and DATTA


160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

1086420Frying time (min)

Surface 005 cm

042 cm

085 cm 127 cm

Prediction Experiment of

Farkas et al (1996)

Figure 3 Model prediction of temperatures compared with the experi-mental data of Farkas et al410 at various distances from the surface Thesurface temperature (predicted only) is shown to indicate its sensitivityto the location

020

015

010

005

000

Cru

st th

ickn

ess

(cm

)



Farkas et al (1996)

26

24

22

20

18

16

Moi

stur

e co

nten

t (d

b)



Farkas et al (1996)

Figure 4 Model prediction of total moisture loss and crust thicknesscompared with the experimental data of Farkas et al910

of heat transfer If the evaporation line can be de ned asthe location where the largest gradient of water saturationoccurs it is about 2 mm from the surface after 9 minutesof frying

Pressure reaches the maximum value near the evapora-tion front (see Figure 6) and it increases with frying timeas the front moves further away from the surface addingresistance to convective (Darcy) ow There is about 1 kPapressure increment up to 9 minutes and the effect of pressurewill be discussed in later sections

Pro les of oil saturation So (see Figure 6) is typical ofdiffusional (capillarity driven) transport in a semi-in nitemedia It seems that oil is not only absorbed in the crustlayer but can also penetrate to a distance twice the crustthickness This study for the rst time uses a mechanisticmodel that includes pressure driven ow and diffusion todescribe the oil saturation pro le

Temporal Pro les of Water Saturation and Pressure

As shown in Figure 7 it takes about 30 seconds for thesurface to get dry However it takes almost 2 minutesfor the location at 005 cm below the surface to get dryThis large time delay is also due to the larger capillarydiffusivity of water at high initial moisture in the coreregion

Initially the inside pressure is lower than the boundarypressure (see Figure 7) The internal pressure riseswith evaporation Near the surface (005 m) the pressureis built up quickly However after the pressure reaches themaximum it starts decreasing as the surface dries outWhile for the inside region the pressure keeps increasing



160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

12100806040200Location x (cm)

1 min 9 min

0 min

05

04

03

02

01Wat

er s

atur

atio

n S

w

12100806040200Location x (cm)

1 min

9 min

0 min

Figure 5 Spatial pro les of Sw and T in frying of a potato slab at times 1 35 7 9 minutes

035

030

025

020

015

010

005

000

Oil

sat

urat

ion

S o

12100806040200Location x (cm)

1 min

9 min

1010

1008

1006

1004

1002

1000Tota

l pre

ssur

e (0

1M

Pa)

12100806040200Location x (cm)

1 min

9 min

Figure 6 Spatial pro les of P and So in frying of a potato slab at times 1 35 7 9 minutes

Figure 7 Temporal pro les of Sw and P in frying of potato slab at times 13 5 7 9 minutes

within the calculated period due to high moisture Althoughthe pressure build-up is only 1 kPa its effect on the moisturetransport is still important (see later sections)

Total Oil Uptake With Time

The oil uptake is de ned as the ratio of the weight of oilintake to the weight of dry material Oil uptake with time(see Figure 8) shows that the rate of oil uptake is initiallyhigher and then slows down becoming linear with timeThe initial higher rate is due to a larger difference ofoil concentration between the surrounding oil and initialconcentration of oil in the food As the crust becomesthicker the oil uptake also increases proportionally After10 minutes the oil content reaches about 30 (db) asshown in Figure 8 The spatial distribution of oil follows adiffusion pro le in a semi-in nite media as discussedearlier

Vapour and Liquid Water Fluxes in the Crust andCore Region

Fluxes in the crust regionAs shown in Figure 9 the vapour diffuses from the

evaporation front to the surface and the vapour diffusional ux occurs only within the crust layer The maximum uxoccurs near the evaporation front and its magnitudedecreases with the frying time since the vapour concentra-tion decreases with moisture content The magnitude of the ux in Figure 9 is comparable with the maximum ux of8 g m 2 2 s 2 1 in the work of Farkas et al9

The vapour convective ux has the same trend as thediffusional ux as shown in Figure 9 The vapour is drivenby the pressure gradient from the evaporation front to thesurface The vapour convective ux also occurs only withinthe crust layer and its magnitudes are comparable to thosefor diffusional vapour ux Therefore the convection termcannot be discarded in describing the total vapour ux in thecrust layer

Fluxes in the core regionThe capillary diffusional ux of water in the core region

is towards the surface as shown in Figure 10 There is aregion of constant ux which starts from the evaporationfront and extends inside to about double the thickness ofthe crust In that region the water saturation is spatiallylinear and capillary diffusivity is relatively constant

200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)


Figure 8 Oil uptake of potato tissue in frying

20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)

0403020100Location x (cm)

1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min

Figure 9 Comparison of diffusive and convective uxes of vapour incrust layer during frying of potato slab at times 1 3 5 7 9 minutes

-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min

Figure 10 Comparison of diffusive (capillary) and convective uxes ofliquid water in frying of potato slab at times 1 3 5 7 9 minutes

In the core region water convective ux due to pressureis toward the centre The magnitude of the convective uxalthough smaller is comparable with capillary diffusional ux Therefore both the convective and the capillary diffu-sional mechanisms contribute to the total water uxin the core region Neither transport mechanism can beignored

Effect of Oil Temperature

The sensitivity analysis in this and the following sectionsdo not include the curves for oil content since the oiltransport into the material was relatively insensitive to theparameter changes in the range studied The effects of oiltemperature on the centre temperature of the slab moistureloss and crust thickness are shown in Figure 11 The centretemperature increases with the oil temperature but thisincrease is much lower than the increment of oil temperatureitself In addition to diffusional resistances of the solidparticularly the crust with low thermal conductivity this isalso caused by the internal evaporation limiting the heattransfer to the centre The moisture content decreases withthe oil temperature but only slightly The crust thicknessincreases with temperature and it is generally in the rangeof 1ndash15 mm at the end of 10 minutes of frying

The effect of increased oil temperature as predicted fromthis work is compared with the experimental data of Farkasat al9 in Table 2 The model predictions generally agreewith the experiment To make an absolute comparison more

accurate material properties and heat and mass transfercoef cients will be necessary for the mathematical model

Effect of Initial Moisture Content

The effects of initial moisture content on sampletemperature moisture loss and crust thickness are shownin Figure 12 The centre temperature decreases with initialmoisture content because increased evaporation in a highermoisture food reduces the energy ow to the centreMoisture loss increases signi cantly with initial moisturecontent because both surface evaporation and subsequentinternal evaporation are much higher for a high moisturefood The crust thickness increases signi cantly withdecreasing initial moisture content For an initial moisturecontent of 155 (db) the crust can form shortly after frying



25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160

Figure 11 Transient centre temperature moisture loss crust thicknessas affected by oil temperature

Table 2 Comparison of model prediction with experimental data forthe effect of oil temperature Two oil temperatures of 160 and 180degC areused The variable for comparison is de ned as the absolute magnitude

of (value(180) ndashvalue(160))value(160)3 100

Model prediction Experiment 410

Centre temperature 66 12Moisture loss 5 125Crust thickness 36 31

80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)

Figure 12 Transient centre temperature moisture loss and crust thicknessas affected by the initial water saturation

After 10 minutes of frying the crust thickness increasesto 26 mm which is almost twice the crust thickness for aninitial moisture content is 258 (db) as compared to onewith initial moisture of 155 Therefore controlling initialmoisture content can dramatically affect the crust thicknessof the nal product

Effect of Thickness

When the sample becomes very thin such as a potatochip (1ndash2 mm thick) the model prediction for moistureloss and surface temperature has some discrepancy com-pared to the experimental data This can be due to materialinhomogeneity when it becomes very thin Predicted moistureloss does not increase as fast as the experimental values duringthe initial 20 seconds and the predicted surface temperaturealso cannot increase as fast as the experimental values

The effect of thickness on the centre temperaturemoisture loss and crust thickness and oil uptake areshown in Figure 13 The centre temperature increasessigni cantly with decreasing thickness This is due to athinner sample having less moisture and a shorter dis-tance for heat ux to reach to the centre The surface ofa thinner sample can be quickly dried out which reducesthe surface evaporation and decreases the moisture lossCrust thickness increases with decreasing slice thickness

but the change is not signi cant Further work is neededto improve predictions for very thin materials In thiswork a comparatively larger thickness (half thicknessabout 1 cm) is used

Effect of Heat and Mass Transfer Coef cients

The effect of heat transfer coef cient on surface andcentre temperature and moisture loss are shown inFigure 14 Heat transfer coef cient has a much strongereffect on surface temperature than the centre temperatureAs heat transfer coef cient increases the heat ux fromthe oil to the food increases which leads to a higher surfacetemperature In addition surface temperature shows ashorter plateau before 2 minutes which means that surfaceevaporation is faster The centre temperature also increaseswith heat transfer coef cient although not appreciably

The effect of mass transfer coef cient on surfaceand centre temperature and moisture loss are shown inFigure 15 Increasing mass transfer coef cient causesmore surface evaporation initially therefore increasingmoisture loss and decreasing surface temperature duringsurface evaporation period within the rst 2 minutes Afterthat period the surface temperature increases above 100degCSince most of the moisture loss comes from internalevaporation at this stage increasing mass transfer coef -cient leads to increased moisture loss and a lower centretemperature

CONCLUSIONS

1) A multiphase porous media model has been developedto predict temperature moisture oil pickup and crustthickness during deep-fat frying The model considersthe transport of oil water vapour and air components

202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm

Figure 13 Transient centre temperature moisture loss and crust thicknessas affected by thickness

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200

Figure 14 Transient centre and surface temperature and moisture lossas affected by heat transfer coef cient

separately It is validated using available experimentaldata in the literature2) Pressures from internal evaporation produce signi cantconvective (Darcy) ow Diffusional and convective uxes of vapour are comparable in the outer (crust)region while capillary and convective uxes of liquid arecomparable in the core region Thus all three modes oftransportmdash diffusional convective and capillary areimportant3) Spatial temperature pro les show two distinct regions mdasha pseudo steady state region in the drier crust and atransient diffusion-like pro le in the interior becomingspatially uniform with time Spatial moisture pro les alsoshow two distinct regions mdash a drier region near the surfaceand a more wet region in most of the core A somewhatsharp interface which can be referred to as the evaporationfront is also seen4) Increasing oil temperature reducing initial moisturecontent and reducing thickness can increase the centretemperature moisture loss and crust thickness Increasingheat transfer coef cient increases surface temperaturesigni cantly more than the centre temperature Increasingmass transfer coef cient decreases centre temperature dueto increased internal evaporation and higher moisture loss

NOMENCLATUREcp speci c heat J kg 2 1 Kc mass concentration kg m 2 3 total volumeC molar density of gas mixture kmol m 2 3

Deff g effective gas diffusivity in moist materials m2 s 2 1

Dw capillary diffusivity m2 s2 1

h heat transfer coef cient W m 2 2 Khmv vapour transfer coef cient m s 2 1

dI volumetric evaporation kg m 2 3 s 2 1

k thermal conductivity W m 2 1 Kk p total permeability m2

k pwi k p

gi intrinsic permeability at very wet stage and at very dry stagerespectively m2

k pwr k p

gr liquid and gas relative permeability respectivelyM molecular weight kg kmol 2 1 moisture content (dry basis or db)n total ux kg m 2 2 sP p total pressure and partial pressure respectively PaR universal gas constant J kmol 2 1 KS saturationt timeT temperature KV volume m3

x molar fraction coordinate

Greek symbolsr intrinsic density kg m 2 3

l latent heat of vapourization J kg 2 1

w porositym dynamic viscosity Pa s

Subscriptsa airamb ambienteff effectiveg gas (vapour + air)i initialo oils solid matrix surfacev vapourw water

REFERENCES1 Baumann B and Escher F 1995 Mass and heat transfer during

deep-fat frying of potato slices mdash I Rate of drying and oil uptakeLebensm-Wiss u-Technol 28 395ndash 403

2 Kozempel M F and Tomasula P M and Craig Jr J C 1991Correlation of moisture and oil concentration in french fries Lebensm-Wiss u-Technol 24 445 ndash448

3 Rice P and Gamble M H 1989 Technical note modelingmoisture loss during potato slice frying Int J Food Sci amp Tech 24183 ndash187

4 Dincer I and Yildiz M 1996 Modeling of thermal and moisturediffusions in cylindrically shaped sausages during frying J Food Eng28 35 ndash43

5 Dagerskog M 1979 Pan frying of meat patties A study of heat andmass transfer Lebensm-Wiss u -Technol 12 217ndash 224

6 Ateba P and Mittal G S 1994 Modeling the deep-fat frying ofbeef meatballs Int J Food Sci Tech 29 429 ndash440

7 Moreira R Palau J and Sun X 1995 Simultaneous heat and masstransfer during the deep fat frying of tortilla chips J of Food Proc Eng18 307ndash 320

8 Ikediala J N Correia L R Fenton G A and Ben-Abdallah N1996 Finite element modeling of heat transfer in meat patties duringsingle-sided pan-frying J Food Sci 61(4) 796ndash 802

9 Farkas B E Singh R P and Rumsey T R 1996a Modeling heatand mass transfer in immersion frying Model development J FoodEng 29 211ndash 226

10 Farkas B E Singh R P and Rumsey T R 1996b Modeling heatand mass transfer in immersion frying Model solution and veri cationJ Food Eng 29 227 ndash248

11 Chen Y and Moreira R G 1997 Modeling of a batch deep-fat fryingprocess for tortilla chips Trans IChemE Part C Food Bioprod Proc75(C3) 181ndash 190

12 Ufheil G and Escher F 1996 Dynamics of oil uptake during deep-fatfrying of potato slices Lebensm-Wiss u-Technol 29 640 ndash644

13 Moreira R G Sun X and Chen Y 1997 Factors affecting oil uptakein tortilla chips in deep-fat frying J Food Eng 31 485 ndash498

14 Moreira R G and Barrufet M A 1998 A new approach to describeoil absorption in fried foods a simulation study J Food Eng 35 1ndash22

15 Moreira R G and Barrufet M A 1995 Spatial distribution of oilafter deep-fat frying of tortilla chips from a stochastic model J FoodEng 27 279ndash 290

16 Ngadi M O and Correia L R 1995 Moisture diffusivity in chickendrum muscle during deep-fat frying Canadian Agric Eng 37(4)339 ndash344

17 Ni H Datta A K and Torrance K E 1998 Moisture transportin intensive microwave heating of biomaterials A multiphase porousmedia model accepted in Int J of Heat Mass Transfer



140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001

Figure 15 Transient centre and surface temperature and moisture lossas affected by mass transfer coef cient

18 Mills A F 1995 Basic Heat and Mass Transfer (Irwin ChicagoUSA)

19 Miller K S 1992 Physical and thermal properties of edible fryingoils MSc thesis (University of California Davis USA)

20 Choi Y and Okos M R 1986 Thermal properties of liquid foodsmdashA review in Physical and Chemical Properties of Liquid Foods OkosM R (ed) (ASAE St Joseph Michigan USA)

21 Bear J 1972 Dynamics of Fluids in Porous Media (AmericanElsevier New York)

22 Steffe J F Mohamed I O and Ford E W 1986 Rheologicalproperties of liquid foods data compilation in Physical and ChemicalProperties of Liquid Foods Okos M R (ed) (ASAE St JosephMichigan USA)

23 Ratti C Crapiste G H and Rotstein E 1989 A new water sorptionequilibrium expression for solid foods based on thermodynamicconsiderations J Food Science 54(3) 738 ndash747

24 Ni H 1997 Multiphase moisture transport in porous media underintensive microwave heating PhD Dissertation (Cornell UniversityUSA)

25 Nasrallah S B and Perre P 1988 Detailed study of a model ofheat and mass transfer during convective drying of porous media Int JHeat Mass Transfer 31(5) 957ndash 967

ADDRESSCorrespondence concerning this paper should be addressed to Professor

A K Datta Department of Agricultural and Biological EngineeringCornell University Riley-Robb Hall Ithaca NY 14853-5701 USA

The manuscript was received 6 July 1998 and accepted for publicationafter revision 4 March 1999

204 NI and DATTA


important and different from diffusion was absent (seediscussions below) Several oil absorption or uptake studiesthat do not include transport modelling have been reportedThese include experimentally measured oil uptake1213 andhow capillarity causes the surface oil to migrate inside duringcooling14 A statistical description of oil distribution in thefried product based on percolation theory was also reported15

Deep-fat frying is an intensive heat transfer process thatis expected to produce signi cant internal evaporation andpressure generation that are spatially-varying and are func-tions of the porous structure of the material At high ratesof internal evaporation signi cant pressure driven owscan be present for all phases and throughout the materialPressure driven ow is also a fundamentally differentmode of transport that cannot be lumped into an effectivediffusivity in a meaningful way ie without making thelsquodiffusivityrsquo completely empirical as was done in somestudies31611 In fact the constant diffusivity data that wasobtained by tting the experimental curves in Chen andMoreira11 has strong discrepancies between their modeland experimental moisture pro les particularly at higheroil temperature when pressure driven ows are likely to bemore important Also since oil water vapour and air willbe occupying the same pore space their amounts are notindependent of each other as has been used by most pre-vious studies Thus an acute need exists for a model thatwould consider all these factors simultaneously to providea comprehensive mechanistic understanding of transportphenomena in deep-fat frying which is the objective of thisstudy It appears that a multiphase porous media model ofthe type developed by Ni et al17 and applied to microwaveheating where signi cant pressure driven ows can bepresent is a type of model that can be developed to studydeep-fat frying Here all transport mechanisms (iemolecular diffusion capillary and pressure driven ow)and all the phases (ie oil water vapour air) keep theirindividual identity In addition to providing a comprehen-sive description such a model can give insight into therelative magnitudes of various transport mechanisms Thespeci c objectives of this study are to

1) Develop a multiphase porous media model for transportof energy liquid water vapour air and liquid oil duringdeep-fat frying2) Calculate the spatial and transient pro les of themoisture oil uptake temperature and pressure3) Compare the magnitudes of capillary and convectiveliquid uxes in the core region and diffusive and convec-tive uxes of vapour in the crust region4) Perform sensitivity analysis to nd the effect of oil tem-perature initial moisture content sample thickness andheat and mass transfer coef cients on temperature moistureloss and crust thickness

DEVELOPMENT OF THE MULTIPHASEPOROUS MEDIA TRANSPORT MODEL FOR

DEEP-FAT FRYINGAssumptions

The mathematical formulation of the problem consider-ing the energy and mass balance of the phases aredeveloped following the work of Ni et al17 with the oilphase added to the system A schematic diagram of the

model system is shown in Figure 1 The major assumptionsof this model include

1) The solid liquid and gas phases are continuous2) Local thermal equilibrium exists between the phases3) Water vapour pressure is a function of water saturationand temperature oil vapour is not considered in the presentmodel4) Liquid water transport results from convective owdue to the gradient in total gas pressure and from capillary ow due to the gradient of capillary force which is a strongfunction of moisture content Oil transport is assumedresulting from capillary ow due to the gradient of capillaryforce which is a strong function of oil content5) Vapour and air transport are driven by convective owdue to the gradient in total gas pressure and diffusiondue to the concentration gradient6) The contribution of convection to energy transport canbe ignored as shown by Ni et al177) Geometry does not change during frying and overallshrinkage is ignored An equivalent porosity is de nedas the fraction of the total volume occupied by the liquidwater oil water vapour and air This equivalent porosityis assumed constant during the frying process and is usedto calculate the concentration of each phase mdash liquid wateroil gas (water vapour and air) Effect of structure changeduring frying manifests as changed gas porosity and relatedtransport properties For example loss of water increasesgas porosity and therefore the intrinsic permeability8) Moisture removal from the surface consists of twopartsmdash vapour diffuses to the boundary and is convectedaway from the surface area occupied by the gas fractionon the boundary Liquid water evaporates at the boundaryand is convected away from the surface area occupied bythe liquid fraction on the boundary For a high moisturefood or when signi cant water is pushed to the surface frominside due to pressure driven ow surface evaporationof liquid dominates For a drier surface vapor diffusiondominates9) Oil transport is driven by convective ow and capillary ow10) Oil saturation at the boundary is assumed constant



Energyvaporconvected away

0 127 x (cm)

Potatoslab

Symmetry(impermeablesurface)

Oil

Constantoil saturationat surface

Figure 1 Schematic diagram of the 1D system

Governing Equations


w =DVw + DVo + DVg

DV(1)


Sw =DVw

w DV(2)

So = DVo

w DV(3)

Sg =DVg

w DV(4)

where

Sw + So + Sg = 1 (5)


cv = pvMvSgw

RT(6)

ca = paMaSgw

RT(7)

cw = rww Sw (8)

co = row So (9)


regnv = 2 rvk p

g

mg$ P 2

C2g


regna = 2 rak p

g

mg$ P 2

C 2g


regnw = 2 rwk p

w


regno = 2 rok p

o



shy cv


shy cw

shy t+ $ (regnw) = 2 dI (15)

shy ca

shy t+ $ (regna) = 0 (16)

shy co

shy t+ $ (regno) = 0 (17)

( rcp)effshy Tshy t

= $ (keff $ T) 2 l dI (18)

where


+ (1 2 w )rscps (19)





Sw = Swi (21)

So = 0 (22)

T = Ti (23)

P = Pamb (24)



RT2 rv0( ) hmv (25)

So = So1 (26)

P = Pamb (27)

q = h T 2 Tamb( ) + lnw (28)




nv = 0 (29)

nw = 0 (30)

no = 0 (31)

q = 0 (32)

Input Parameters


196 NI and DATTA



lnpv

ps(T )= 2 00267M 2 1656

+ 00107e 2 1287MM1513 ln ps(T ) (33)


Dw = 103 10 2 8 exp( 2 28 + 20M ) (34)






k pg = kp

gikpgr

k pw = kp

wikpwr

(35)



k pgr = 1 2 11Sw Sw lt 111

k pgr = 0 Sw gt 111

(36)

k pwr = Sw 2 Sir

1 2 Sir( )3

Sw gt Sir

k pwr = 0 Sw lt Sir

(37)


gi kpwi and


Numerical Method







Deff g (m2 s 2 1) 263 10 2 5 Mills18

h (W m 2 2 K 2 1) 250 Miller19





k pgi (m2) 10 3 10 2 14 Ni24

kpwi (m2) 53 10 2 14 Ni24

kpoi (m2) 53 10 2 14 Ni24



rv (kg m 2 3) 0 Ni24

rw (kg m 2 3) 1000l (J kg 2 1) 24353 106

w 088 Ni24


mg (Pas) 183 10 2 5

mw (Pas) 54683 10 2 4

10

8

6

4

2

0

Per

mea

bilit

y (1

0-14 m

2)


Gas (kp)

Liquid (kpw or ko )

or So

p

g



MODEL VALIDATION










198 NI and DATTA


160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface 005 cm

042 cm

085 cm 127 cm


Farkas et al (1996)


020

015

010

005

000

Cru

st th

ickn

ess

(cm

)



Farkas et al (1996)

26

24

22

20

18

16

Moi

stur

e co

nten

t (d

b)



Farkas et al (1996)










160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

12100806040200Location x (cm)

1 min 9 min

0 min

05

04

03

02

01Wat

er s

atur

atio

n S

w

12100806040200Location x (cm)

1 min

9 min

0 min


035

030

025

020

015

010

005

000

Oil

sat

urat

ion

S o

12100806040200Location x (cm)

1 min

9 min

1010

1008

1006

1004

1002

1000Tota

l pre

ssur

e (0

1M

Pa)

12100806040200Location x (cm)

1 min

9 min












200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)



20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)


1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min


-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA


Governing Equations


w =DVw + DVo + DVg

DV(1)


Sw =DVw

w DV(2)

So = DVo

w DV(3)

Sg =DVg

w DV(4)

where

Sw + So + Sg = 1 (5)


cv = pvMvSgw

RT(6)

ca = paMaSgw

RT(7)

cw = rww Sw (8)

co = row So (9)


regnv = 2 rvk p

g

mg$ P 2

C2g


regna = 2 rak p

g

mg$ P 2

C 2g


regnw = 2 rwk p

w


regno = 2 rok p

o



shy cv


shy cw

shy t+ $ (regnw) = 2 dI (15)

shy ca

shy t+ $ (regna) = 0 (16)

shy co

shy t+ $ (regno) = 0 (17)

( rcp)effshy Tshy t

= $ (keff $ T) 2 l dI (18)

where


+ (1 2 w )rscps (19)





Sw = Swi (21)

So = 0 (22)

T = Ti (23)

P = Pamb (24)



RT2 rv0( ) hmv (25)

So = So1 (26)

P = Pamb (27)

q = h T 2 Tamb( ) + lnw (28)




nv = 0 (29)

nw = 0 (30)

no = 0 (31)

q = 0 (32)

Input Parameters


196 NI and DATTA



lnpv

ps(T )= 2 00267M 2 1656

+ 00107e 2 1287MM1513 ln ps(T ) (33)


Dw = 103 10 2 8 exp( 2 28 + 20M ) (34)






k pg = kp

gikpgr

k pw = kp

wikpwr

(35)



k pgr = 1 2 11Sw Sw lt 111

k pgr = 0 Sw gt 111

(36)

k pwr = Sw 2 Sir

1 2 Sir( )3

Sw gt Sir

k pwr = 0 Sw lt Sir

(37)


gi kpwi and


Numerical Method







Deff g (m2 s 2 1) 263 10 2 5 Mills18

h (W m 2 2 K 2 1) 250 Miller19





k pgi (m2) 10 3 10 2 14 Ni24

kpwi (m2) 53 10 2 14 Ni24

kpoi (m2) 53 10 2 14 Ni24



rv (kg m 2 3) 0 Ni24

rw (kg m 2 3) 1000l (J kg 2 1) 24353 106

w 088 Ni24


mg (Pas) 183 10 2 5

mw (Pas) 54683 10 2 4

10

8

6

4

2

0

Per

mea

bilit

y (1

0-14 m

2)


Gas (kp)

Liquid (kpw or ko )

or So

p

g



MODEL VALIDATION










198 NI and DATTA


160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface 005 cm

042 cm

085 cm 127 cm


Farkas et al (1996)


020

015

010

005

000

Cru

st th

ickn

ess

(cm

)



Farkas et al (1996)

26

24

22

20

18

16

Moi

stur

e co

nten

t (d

b)



Farkas et al (1996)










160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

12100806040200Location x (cm)

1 min 9 min

0 min

05

04

03

02

01Wat

er s

atur

atio

n S

w

12100806040200Location x (cm)

1 min

9 min

0 min


035

030

025

020

015

010

005

000

Oil

sat

urat

ion

S o

12100806040200Location x (cm)

1 min

9 min

1010

1008

1006

1004

1002

1000Tota

l pre

ssur

e (0

1M

Pa)

12100806040200Location x (cm)

1 min

9 min












200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)



20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)


1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min


-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA



lnpv

ps(T )= 2 00267M 2 1656

+ 00107e 2 1287MM1513 ln ps(T ) (33)


Dw = 103 10 2 8 exp( 2 28 + 20M ) (34)






k pg = kp

gikpgr

k pw = kp

wikpwr

(35)



k pgr = 1 2 11Sw Sw lt 111

k pgr = 0 Sw gt 111

(36)

k pwr = Sw 2 Sir

1 2 Sir( )3

Sw gt Sir

k pwr = 0 Sw lt Sir

(37)


gi kpwi and


Numerical Method







Deff g (m2 s 2 1) 263 10 2 5 Mills18

h (W m 2 2 K 2 1) 250 Miller19





k pgi (m2) 10 3 10 2 14 Ni24

kpwi (m2) 53 10 2 14 Ni24

kpoi (m2) 53 10 2 14 Ni24



rv (kg m 2 3) 0 Ni24

rw (kg m 2 3) 1000l (J kg 2 1) 24353 106

w 088 Ni24


mg (Pas) 183 10 2 5

mw (Pas) 54683 10 2 4

10

8

6

4

2

0

Per

mea

bilit

y (1

0-14 m

2)


Gas (kp)

Liquid (kpw or ko )

or So

p

g



MODEL VALIDATION










198 NI and DATTA


160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface 005 cm

042 cm

085 cm 127 cm


Farkas et al (1996)


020

015

010

005

000

Cru

st th

ickn

ess

(cm

)



Farkas et al (1996)

26

24

22

20

18

16

Moi

stur

e co

nten

t (d

b)



Farkas et al (1996)










160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

12100806040200Location x (cm)

1 min 9 min

0 min

05

04

03

02

01Wat

er s

atur

atio

n S

w

12100806040200Location x (cm)

1 min

9 min

0 min


035

030

025

020

015

010

005

000

Oil

sat

urat

ion

S o

12100806040200Location x (cm)

1 min

9 min

1010

1008

1006

1004

1002

1000Tota

l pre

ssur

e (0

1M

Pa)

12100806040200Location x (cm)

1 min

9 min












200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)



20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)


1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min


-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA



MODEL VALIDATION










198 NI and DATTA


160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface 005 cm

042 cm

085 cm 127 cm


Farkas et al (1996)


020

015

010

005

000

Cru

st th

ickn

ess

(cm

)



Farkas et al (1996)

26

24

22

20

18

16

Moi

stur

e co

nten

t (d

b)



Farkas et al (1996)










160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

12100806040200Location x (cm)

1 min 9 min

0 min

05

04

03

02

01Wat

er s

atur

atio

n S

w

12100806040200Location x (cm)

1 min

9 min

0 min


035

030

025

020

015

010

005

000

Oil

sat

urat

ion

S o

12100806040200Location x (cm)

1 min

9 min

1010

1008

1006

1004

1002

1000Tota

l pre

ssur

e (0

1M

Pa)

12100806040200Location x (cm)

1 min

9 min












200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)



20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)


1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min


-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA










160

140

120

100

80

60

40

20

Tem

pera

ture

(degC

)

12100806040200Location x (cm)

1 min 9 min

0 min

05

04

03

02

01Wat

er s

atur

atio

n S

w

12100806040200Location x (cm)

1 min

9 min

0 min


035

030

025

020

015

010

005

000

Oil

sat

urat

ion

S o

12100806040200Location x (cm)

1 min

9 min

1010

1008

1006

1004

1002

1000Tota

l pre

ssur

e (0

1M

Pa)

12100806040200Location x (cm)

1 min

9 min












200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)



20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)


1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min


-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA











200 NI and DATTA


030

025

020

015

010

005

000

Oil

con

tent

(d

b)



20

15

10

05

00V

apor

con

vect

ive

flux

(g

m2 s)


1 min

9 min

6

4

2

0Vap

or d

iffu

sion

flu

x (g

m2 s)


1 min

9 min


-14

-12

-10

-08

-06

-04

-02

00

Wat

er c

onve

ctiv

e fl

ux (

gm

2 s)

12100806040200Location x (cm)

1 min

9 min

30

25

20

15

10

05

00

Wat

er c

apill

ary

flux

(g

m2 s)

12100806040200Location x (cm)

1 min

9 min











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA











25

24

23

22

21

20

Moi

stur

e co

nten

t (dr

y ba

se)


180degC 170 160

12

08

04

00

Cru

st th

ickn

ess

(mm

)


180degC 170 160

80

70

60

50

40

30

20Cen

ter

tem

pera

ture

(degC

)


180degC 170 160






80

70

60

50

40

30

20

Cen

ter

tem

pera

ture

(degC

)


M=258 (db) M=206 (db) M=155 (db)

25

20

15

10

05

00

Cru

st th

ickn

ess

(mm

)


M=258 (db) M=206 (db) M=155 (db)

06

05

04

03

02

01

00

Moi

stur

e lo

ss (

dry

base

)


M=258 (db) M=206 (db) M=155 (db)



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA



Effect of Thickness







CONCLUSIONS


202 NI and DATTA


14

12

10

08

06

04

02

00

Cru

st th

ickn

ess

(mm

)


95 mm 127 mm 140 mm

08

06

04

02

00

Moi

stur

e lo

ss (

dry

base

)


95 mm 127 mm 140 mm

100

80

60

40

20

Cen

ter

tem

pera

ture

( C

)


95 mm 127 mm 140 mm


25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


h=250 Wm2K

200

150

160

140

120

100

80

60

40

20

Tem

pera

ture

( C

)


Surface Center

h=250 Wm2K

200150

150

250 200









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA









k pwi k p


k pwr k p



























140

120

100

80

60

40

20

Tem

pera

ture

(degC

)


Surface Center

hmv = 002 ms

001

002

001

25

24

23

22

21

20

Moi

stur

e co

nten

t (d

b)


hmv = 002 ms

001













204 NI and DATTA













204 NI and DATTA


chl471

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