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Research Paper: PHdPostharvest Technology

Mathematical modelling of heat and moisture transfer ofwheat stored in plastic bags (silobags)

A. Gastona,*, R. Abaloneb, R.E. Bartosikc, J.C. Rodrıguezc

aCIC de la UNR, Fac. de Cs. Exactas, Ingenierıa y Agrimensura, UNR, Av. Pellegrini 250, 2000 Rosario, ArgentinabFac. de Cs. Exactas, Ingenierıa y Agrimensura, UNR, IFIR (CONICET/UNR), Av. Pellegrini 250, 2000 Rosario, ArgentinacNational Institute of Agricultural Technologies (INTA), Ruta 226 km 73.5, 7620 Balcarce, Argentina

a r t i c l e i n f o

Article history:

Received 29 October 2008

Received in revised form

1 May 2009

Accepted 16 June 2009

Published online 18 July 2009

* Corresponding author.E-mail address: analiag@fceia.unr.edu.ar

1537-5110/$ – see front matter ª 2009 IAgrE.doi:10.1016/j.biosystemseng.2009.06.012

A bidimensional finite element model that predicts temperature distribution and moisture

migration of wheat stored in silobags due to seasonal variation of climatic conditions is

described. The model includes grain respiration and calculates carbon dioxide and oxygen

concentrations during storage as well as the associated dry matter loss.

The model validation was carried out by comparing predicted with measured temperature

and moisture content (MC) data. The temperature standard errors of the model validation

were 1.94 �C at the bottom, 1.35 �C in the middle and 1.20 �C at the top layer. The model

predicted moisture increase in the top grain layer during storage ranging from 1.0 to 1.5%

w.b., while the measured increase ranged from 0.4 to 0.8% w.b.

Predicted average CO2 and O2 concentrations were compared with measured data. For dry

wheat (12.5% w.b.), after 100 days of storage, differences in concentrations were 1.8 and

0.6% points for CO2 and O2, respectively. For wet wheat (16.4% w.b.), the model predicted

the total consumption of O2 after five days while the observed O2 data never dropped below

5%. The difference between the measured and predicted CO2 concentration for the fifth day

was 1.1%. For the range of MCs considered in this work, the change in CO2 concentration

during storage was satisfactorily predicted by use of White et al. (1982) estimation of CO2

production rate, but prediction of O2 concentration was poor for wet grain.

ª 2009 IAgrE. Published by Elsevier Ltd. All rights reserved.

1. Introduction concentrations. This modified atmosphere inhibits the biotic

In Argentina, of a total grain production of 90 m tonnes in

2007, around 25 m were stored in ‘‘silobags’’, a new on-farm

storage system used for storing grains and seeds directly in

the field. This technique, originally used for grain silage,

consists of storing dry grain in hermetically sealed plastic

bags. The respiration process of the biological agents in the

grain ecosystem (grain, insects, mites and microorganisms)

increases carbon dioxide (CO2) and reduces oxygen (O2)

(A. Gaston).Published by Elsevier Ltd

activity, promoting a suitable environment for grain

conservation.

Because of its economic implications and productivity

advantages (grain identity preservation, variety segregation,

farm logistics, etc.) the silobag system has gained rapid

adoption in Argentina. However, storing grains in plastic bags

without proper care with regard to site selection and prepa-

ration, filling methodology, grain MC, storage temperature

and maintenance of the hermeticity of the bag could result in

. All rights reserved.

Nomenclature

a1, a2, a3, a4, a5 parameters of the rate of CO2 production

equation, dimensionless, �C�1, s�1, s�2,

dimensionless, respectively

x, y Cartesian coordinates, m

c specific heat capacity of grain bulk, J kg�1 K�1

CH, KH, N parameters of the modified Henderson equation,�C, �C�1, dimensionless, respectively

Dv water vapour diffusivity in air, m2 s�1

Def effective diffusivity of water vapour in

intergranular air, m2 s�1

dm mean rate of dry matter consumed by aerobic

respiration, in mg [dry matter] kg�1 [dry matter] in

24 h

DML cumulative mean dry matter loss at time t, mg [dry

matter] kg�1 [dry matter]

G incident solar radiation on the silobag surface,

W m�2

hc convective heat transfer coefficient, W m�2 K�1

k thermal conductivity, W m�1 K�1

L silobag characteristic length, m

Lg latent heat of vaporization of moisture in the

grain, J kg�1

M grain moisture content, % w.b.

MCO2 molecular weight of carbon dioxide, 44 g mol�1

mCO2 mass of carbon dioxide, mg [CO2] kg�1 [dry matter]

n normal direction

Nu Nusselt number ( f: forced convection; n: natural

convection)

ps saturation pressure of water vapour, Pa

pv partial pressure of water vapour, Pa

pat atmospheric pressure, 1 at or 101 325 Pa

qH heat released in respiration, 10.738 J mg�1 [CO2]

qw water vapour produced in respiration,

4.09� 10�5 kg [H2O] mg�1 [CO2]

Rv water vapour gas constant, 461.52 J kg�1 K�1

R gas constant, 8.314 J mol�1 K�1

t time, s

Tc temperature, �C

T absolute temperature, K

Ti daily or annual soil temperature parameters, �C,

i¼ 1, 2

V bed of grain volume, m3

W grain moisture content, d.b.

YCO2 rate of carbon dioxide production, mg [CO2] kg�1

[dry matter] in 24 h

YO2 rate of oxygen consumption, mg [O2] kg�1 [dry

matter] in 24 h

YH2O rate of water vapour production, mg [H2O] kg�1

[dry matter] in 24 h

XCO2 carbon dioxide concentration, % V/V

XO2 oxygen concentration, % V/V

a silobag surface absorptivity

3 porosity

4 daily or annual phase angle

G domain boundary

h change in the partial pressure due to change in the

moisture content at constant temperature, Pa

r density, kg m�3

rbs dry bulk density, kg [dry matter] m�3

s Stefan–Boltzmann’s constant,

5.6697� 10�8 W m�2 K�4

s tortuosity factor

u change in the partial pressure due to change in the

temperature at constant moisture content, Pa K�1

U domain

x emissivity

j daily or annual angular frequency, s�1

Subscripts

a intergranular air

amb ambient

b bulk grain

g grain

0 initial

sky sky

soil soil

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 5 73

substantial grain quality loss during storage time (dry matter

loss (DML), germination loss and mould damage among

others).

Internal heat sources (respiration of the biotic components

of the grain mass) as well as external sources (solar radiation,

seasonal variation of weather conditions) can modify the

temperature of stored grain, altering the local equilibrium

between the grain and its surrounding environment.

Temperature gradients within the grain mass promote

moisture migration from warm to cold regions and this

redistribution may create spots with conditions suitable for

grain deterioration (Khankari et al., 1994; Navarro et al., 2002).

Unlike storing grain in bins, in which it is possible to aerate

the grain to reduce temperature and condition MC to increase

storability, and even to transfer the grain to another bin if

a major problem is detected, none of these practices are

possible when grain is stored in the silobags. Thus, initial

grain conditions (MC, percentage of damaged grain, etc.),

management practices (proper site selection and preparation,

etc.) and weather characteristics during storage (ambient air

temperature, sun radiation, etc.) determine the allowable

grain storage time (Bartosik et al., 2008a, b; Rodrıguez et al.,

2008; Cardoso et al., 2008). Therefore, understanding how

different combinations of initial grain condition, manage-

ment practices and weather pattern affect grain storability in

the silobags is critical for farmers and the grain industry in

Argentina.

Numerical simulation models based on transport princi-

ples are useful and inexpensive tools to predict the potential

spoilage of stored grain, in comparison to the high cost and

time consuming operation of continuous temperature moni-

toring and grain probing for MC and quality. Sampling the

silobags for MC and grain quality is fairly easy to implement

(although it is a labour-intensive operation), but the damage to

the plastic cover affects the hermeticity and the proper

storage conditions of the system.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 574

Numerical models have been developed for conventional

storage systems and applied to analyze the heat and mass

transfer process in different grains, such as wheat (Alagu-

sundaram et al., 1990; Abbouda et al.; 1992a, b; Chang et al.,

1993, 1994; Singh et al., 1993; Khankari et al., 1994, 1995a, b;

Jayas et al., 1994; Jia et al., 2000a, b; Jiang et al., 2005); sorghum

(Jimenez-Islas et al., 2004); rice (Abe and Basunia, 1996; Iguaz

et al., 2004a, b) and corn (Andrade et al., 2002) among others.

With reference to dry grain storage in silobags, most of the

published work relates to experimental studies. The National

Institute of Agricultural Technologies (INTA) of Argentina, at

the Experimental Stations (EEA) located at Balcarce and

Manfredi developed a set of field tests. At EEA Balcarce, the

effect of grain MC and storage time on the quality of different

grains (wheat, corn, sunflower and soybean) stored in plastic

bags was investigated (Rodrıguez et al., 2001, 2002, 2004). In

these studies, several tests were performed to determine

changes in grain quality during storage: test weight, germi-

nation test, composition, oil acidity for soybean and

sunflower, and baking quality for wheat. The main results of

these studies were summarized by Bartosik et al. (2008a, b) and

indicated that the grain temperature in the sealed plastic bags

followed the pattern of the ambient temperature throughout

the year. The average MC did not significantly change during

the experiments for both dry and wet silobags. In general, no

MC stratification was observed except for wet sunflower,

where the top layer MC increased from 16.4 to 20.8% after 150

days of storage. When the grain was stored at the commercial

MC level (which, in general, represents the safe storage MC),

no significant decrease in the quality parameters was

observed during 150 days of storage. In contrast, when grain

was stored above the safe MC, a decrease in some quality

parameters was observed. Measurement of gas composition

in the interstitial air showed an increase in the carbon dioxide

(CO2) and a decrease in the oxygen (O2) levels concentration

towards the end of the storage time, especially in those bags

with wetter grain. The modification of the contained atmo-

sphere in the trial bags suggested that a reasonable standard

of gas-tightness was achieved. In these field tests, the effect of

the modified atmosphere on insect activity was also investi-

gated. Bags made of fine plastic mesh containing grain and

weevils were placed in the silobags and insect mortality was

determinated. In all cases, complete mortality was observed

during storage. Other complementary field studies in silobags

were carried out by Casini (2006) and Clemente et al. (2003) at

EEA Manfredi.

Recently, Darby and Caddick (2007) published a compre-

hensive analysis and field evaluation of silobag technology

under typical Australian conditions. As in the studies carried

out by INTA, the same pattern for temperature change of the

silobags was found, but moisture accumulation was detected

in the peripheral layer of the silobags. In contrast with INTA

studies, they reported difficulties in achieving effective levels

of gas-tightness in the pilot-scale tests as well as in the farm

level (full scale) trials.

Since silobags were locally adapted to store dry grain in

Argentina a few years ago (originally they were used for

ensilage of wet grain), no references have been found in the

international literature regarding the simulation of heat and

mass transfer for this storage system.

A comprehensive model of heat and moisture transfer for

silobags deals with the respiration of biological agents that

modifies the gas composition in the interstitial air of silobags.

All the chemical components involved in the respiration

process must be accounted for: water vapour, carbon dioxide,

oxygen and non-reacting elements in the intergranular spaces

(Thorpe, 2002). The problem is described by momentum,

mass, and energy components that must balance out with

those of the grain substrate. Inclusion of moisture and

temperature-dependent properties as well as realistic

boundary conditions in the model definition means that the

partial differential equations are nonlinear and must be

solved by numerical methods.

Among the published models for non-aeration periods,

only a few have considered the heat released and water

vapour produced by respiration in the energy and mass

balances. Singh et al. (1993) included these sources in a model,

applying the correlations developed by Thompson (1972) for

corn, and predicted the DML during the storage period. A

similar study was carried out by Jimenez-Islas et al. (2004) for

sorghum, in which the heat of respiration was modelled by

correlation of data extracted from Mohsenin (1980). Montross

et al. (2002a) presented a model for corn that accounts for

periods with and without aeration but neglects respiration in

the balances. However, the DML was estimated from

Thompson (1972) and Steele et al. (1969) correlations, using the

average daily grain temperature and MC predicted by the

model. None of these authors compared numerically pre-

dicted DMLs with experimental results.

The correlations to account for DML available in the liter-

ature for corn (Steele et al., 1969; Thompson, 1972), wheat

(White et al., 1982) or soybean (Rukunudin et al., 2004) were

developed under aerobic conditions. Silobags are waterproof

and have a certain degree of gas-tightness (O2 and CO2).

Respiration rate is assumed to be reduced by decreasing O2

beyond a certain level. Thus, correlations depending on O2

and CO2 concentrations have yet to be developed to account

properly for respiration under the anaerobic conditions of

silobags.

Diffusion of carbon dioxide through grain bulks has been

addressed by several authors (Singh et al., 1983, 1984; Jayas

et al., 1988; Alagusundaram et al., 1991, 1996; Xu et al., 2002;

Shunmugam et al., 2003) to model the distribution of the

injected gas with the purpose of helping in the design of the

gas injection and maintenance systems and in the overall

management of controlled atmosphere (CA) storage

systems. In silobags, understanding the diffusion of the

carbon dioxide produced may play a key role. Measurement

of gas composition in the interstitial air has been used as an

indication of the biological activity of the grain mass in

conventional storage systems, and a tool for monitoring

grain storability (Ileleji et al., 2006). Later, Bartosik et al.

(2008b) implemented a procedure for monitoring biological

activity and storability based on carbon dioxide measure-

ment in the interstitial air of wheat and soybean stored in

silobags.

This work is the first part of a general study that aims to

develop a comprehensive model for the silobag storage

system, taking progressively into account all the aspects

mentioned above.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 5 75

The objectives of this phase of the study were to adapt the

heat and mass transfer model presented by Khankari et al.

(1994) and Montross et al. (2002a) for non-aeration periods by

incorporating suitable boundary conditions for the silobag

and using the correlation of White et al. (1982) to account for

respiration of wheat. Then the model was used to:

(1) validate the simulation model with experimentally

measured temperature and MC data,

(2) evaluate whether the available correlation for CO2

production in wheat developed by White et al. (1982) was

suitable for modelling respiration of the grain and micro-

flora in silobags by comparing the measured and predicted

CO2 and O2 concentrations.

2. Materials and method

2.1. Silobags

Silobags are 60 m long, 2.70 m diameter and 230–250 mm thick.

The bags are made with a three-layer plastic, black in the

inner side and white in the outer side with UV stabilizers. The

plastic layers are a mixture of high density (HDPE) and low

density polyethylene (LDPE). Permeability at 25 �C of HDPE to

O2 is 6.42� 10�13 m3 m d�1 m�2 Pa�1 and of LDPE is

1.92� 10�12 m3 m d�1 m�2 Pa�1. Permeability at 25 �C of HDPE

to CO2 is 1.87� 10�12 m3 m d�1 m�2 Pa�1 and of LDPE is

1.04� 10�11 m3 m d�1 m�2 Pa�1 (Osborn and Jenkins, 1992).

Approximately 200 tonnes of grains (wheat, corn and

soybean) can be held in the bag and usually farmers store their

grain for six to eight months. Fig. 1 shows a picture of the

silobag storage system.

2.2. Mathematical modelling

The following assumptions were considered to simplify the

mathematical model:

(1) The bed of grain is assumed to be a continuum where the

grain phase and intergranular air phase are evenly

distributed through the porous media.

(2) In a control volume, grain and intergranular air are in local

thermodynamic equilibrium.

(3) Heat and mass transfer in the longitudinal direction is

negligible compared to heat and mass transfer in the cross

section of the silobag. Thus, a planar 2D model is adopted.

Fig. 1 – Silobag sto

(4) The silobag is gas-tight (hermetic) to O2. A resistance series

model was applied to derive an effective permeability of

the plastic layer of 9.62� 10�13 m3 m d�1 m�2 Pa�1. For

a 230 mm thickness a low permeance to O2 of

4.15� 10�9 m3 d�1 m�2 Pa�1 at 25 �C was estimated.

(5) Convection transport is not considered.

(6) Grain bed shrinkage is negligible.

2.2.1. Heat and moisture content balanceStating the energy and moisture balances for the grain and air

phases in a control volume, the following single phase

coupled system is obtained:

cbrb

vTvt¼�

v

vx

�kb

vTvx

�þ v

vy

�kb

vTvy

��þ rbLg

vWg

vtþ rbsqHYCO2

in U1

(1)

rb

vWg

vt¼ v

vx

�Def

�h

vWg

vxþ u

vTvx

��þ v

vy

�Def

�h

vWg

vyþ u

vTvy

��þ rbsqwYCO2

in U1 (2)

where density rb in kg m�3, specific heat cb in J kg�1 K�1 and

thermal conductivity kb in W m�1 K�1, are bulk properties of

the porous medium defined by:

cbrb ¼ ð1� 3Þcgrg (3)

rb ¼ ð1� 3Þrg þ 3rayrbs

�1þWg0

�(4)

kb ¼ ð1� 3Þkg þ 3ka (5)

Def in m2 s�1 is the effective diffusivity of water vapour in the

intergranular air (Keey, 1975):

Def ¼Dv3

RVsT(6)

where Dv in m2 s�1 is the diffusivity of water vapour in air, 3 is

the bed porosity, s is the bed tortuosity and Rv in J kg�1 K�1 is

the water vapour gas constant.

Lg in J kg�1 is the latent heat of vaporization of moisture in

the grain (Giner, 1999):

Lg ¼ RT2

�vln pv

vT

�Wg

(7)

h in Pa is the change in the partial pressure due to change in

the MC at constant temperature, u in Pa K�1 is the change in

the partial pressure due to change in the temperature at

constant MC and pv in Pa is the equilibrium sorption isotherm

rage system.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 576

h ¼ vpvðWg;TcÞvWg

jT

(8)

u ¼ vpvðWg;TcÞvT

jWg

(9)

A detailed derivation of this system is presented in Abalone

et al. (2006). It was assumed that moisture diffusion by grain to

grain contact and accumulation of moisture in the inter-

granular air are negligible and that the air–vapour mixture

behaves as an ideal gas. Two source terms where considered

in Eq. (1). The first states that grains act as a sink/source of

moisture absorbing or releasing the latent heat of vapor-

ization/condensation and the second represents the heat

released by respiration of the ecosystem.

Eq. (2) states that in a control volume the change of MC over

time equals the net diffusion of water vapour through the void

spaces of the bed plus the water vapour produced by respi-

ration of the ecosystem.

Aerobic respiration of the grain ecosystem consumes

oxygen and produces carbon dioxide, water vapour and heat

according to the following equation (complete combustion of

a typical carbohydrate):

C6H12O6 þ 6O2/6CO2 þ 6H2Oþ 2835 kJ=mol180 g þ 192 g/264 g þ 108 g þ 2835 kJ

(10)

Thus, if the rate of carbon dioxide released YCO2in

mg [CO2] kg�1 [dry matter] in 24 h is known, according to this

stoichiometric respiration equation, the heat released, water

vapour produced and O2 consumed can be calculated.

Heat released YResp in J kg�1 [dry matter] in 24 h is:

YResp ¼2835 kJ264 g

YCO2¼ qHYCO2

(11)

where qH is 10.738 J mg�1 [CO2].

Water vapour produced YH2O in mg [H2O] kg�1 [dry matter]

in 24 h is:

YH2O ¼108 g264 g

YCO2¼ qwYCO2

(12)

where qw is 4.09� 10�5 kg [H2O] mg�1 [CO2].

O2 consumed YO2 in mg [O2] kg�1 [dry matter] in 24 h is:

Fig. 2 – Schematic diagram of the calculation domain. Finite

YO2¼ 192 g

264 gYCO2

(13)

2.2.2. Initial and boundary conditionsFig. 2 shows the calculation domain and boundaries, which

represents a cross section of the silobag.

Initial and boundary conditions associated to Eq. (1) are:

Tðx; y; t ¼ 0Þ ¼ T0ðx; yÞ (14)

�kvTvn¼ hcðT� TambÞ � aGþ xs

�T4 � T4

sky

on G1 (15)

where the sky temperature Tsky is defined by Mills (1995):

sT4sky ¼ xskysT4

amb (16)

and the heat transfer coefficient hc in W m�2 K�1 is evaluated

according to Mills (1995):

hc ¼ka

L

�Nu7=2

f þNu7=2n

(17)

The solar radiation G in W m�2 on G1 was evaluated taking

into account 11 planes of incidence on the boundary (see

Fig. 2), and calculating the horizontal global solar irradiance

with Model C (Iqbal, 1983). Model C is a well documented

radiation model that evaluates solar radiation by considering

the mechanisms of transmittance, reflectance and absor-

bance of the atmosphere. A detail presentation is outside the

scope of the present work.

To account for the interaction between the soil and the

bottom layer of the silobag, the subdomain U2 was incorpo-

rated into the heat transfer model. It was assumed that the

initial and boundary temperature Tsoil in K on G3, is a known

relationship having the form (Carslaw and Jaeger, 1959):

T ¼ Tsoilðy; tÞ

¼ T1ðyÞ þ T2exp

� y

ffiffiffiffiffiffiffiffiffiffi2J

Dsoil

s !"cos

Ut� y

ffiffiffiffiffiffiffiffiffiffi2J

Dsoil

s� f

!#on G3

(18)

Initial and boundary conditions associated to Eq. (2) are as

follow:

element mesh (3290 elements in the silobag domain).

Table 1 – Input parameters of bed of wheat

Reference Property

Henderson equation parameters (Giner, 1999) KH ¼ 2:31� 10�5; CH ¼ 55:813; N ¼ 2:2857

CO2 produced in oxidation of hexose, mg [CO2] kg�1

[dry matter] in 24 h (White et al., 1982)

a1 ¼ �4:054; a2 ¼ 0:0406; a3 ¼ �0:0165;

a4 ¼ 0:0001; a5 ¼ 0:2389

Bulk density, kg m�3 (Giner, 1999) rb ¼ 824

Grain thermal conductivity, W m�1 K�1 (Giner, 1999) kg ¼ 0:14þ 0:68Wg

Grain specific heat, J kg�1 K�1 (Nellist, 1987) cg ¼ 1300þ 4187Wg

Porosity (Giner, 1999) 3 ¼ 0:38

Tortuosity (Keey, 1975) s ¼ 1:53

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 5 77

Wgðx; y; t ¼ 0Þ ¼W0ðx; yÞ (19)

vpv

vn¼ 00hDef

vWg

vn¼ �uDef

vTvn

on G1 þ G2 (20)

Eq. (20) implies the hermetic condition of the silobag to

moisture transfer.

2.2.3. Input model parameters for wheatIn this section, the model parameters Lg, h, u, and YCO2 and

bulk thermal properties will be defined for wheat.

The Modified Henderson equation was used to model the

equilibrium MC of wheat (Brooker et al., 1992):

pv ¼ ps

n1� exp

h� KHðCH þ TcÞ

�100Wg

�Nio

(21)

where ps in Pa is the saturation vapour pressure.

The latent heat of vaporization of moisture Lg in J kg�1 is

defined by:

Lg ¼ RT2

�vln ps

vT

�Wg

þKH

�100Wg

�Nexp

�� KH

�100Wg

�NðTþ CH � 273:15Þ

1� exp�� KH

�100Wg

�NðTþ CH � 273:15Þ

!(22)

The coefficients h and u take the form:

h ¼ psexph� KHðCH þ TcÞ

�100Wg

�Ni

h� KHðCH þ TcÞ

�100Wg

�N�1�100Wg

�ið23Þ

u ¼ pv

ps

dps

dTcþ ps

�KH

�100Wg

�N �

1� pv

ps

�(24)

Table 2 – Water vapour properties

Reference Property

Water vapour diffusivity in air,

m2 s�1 (Thorpe, 1981)

DV ¼ 9:1� 10�9ðTÞ2:5=ðTþ 245:18Þ

Saturation vapour pressure, Pa

(Giner et al., 1996)

ps ¼ expf54:12� ð6547:1=TÞ�4:230ln Tg

White et al. (1982) carried out numerous experiments on the

carbon dioxide release rates of cereal grain and established

robust models, expressed by the following generic equation,

where YCO2is in mg [CO2] kg�1 [dry matter] in 24 h, q in days is

the storage time, Tc in �C is grain temperature and M is MC in %

w.b.:

logYCO2¼ a1 þ a2Tc þ a3qþ a4q2 þ a5M (25)

Eq. (25) accounts for grain and microflora CO2 production. In

the present study, the contribution to CO2 production by

insect respiration is not included. No infestation was detected

during grain sampling of the silobags.

Parameters of Eqs. (21) and (25) are listed in Table 1 as well

as bulk density, porosity of the bed and thermal properties of

wheat grain. Bulk thermal properties were calculated

according to Eqs. (3)–(5). Water vapour properties are listed in

Table 2.

2.2.4. Carbon dioxide and oxygen concentrationEq. (25), which evaluates the rate of CO2 production, depends

on temperature, MC and storage time. Thus, to determine the

temperature and moisture change of the grain due to respi-

ration it is not necessary to couple the transport process of the

interstitial gases to Eqs. (1) and (2), since Eq. (25) does not

explicitly depend on local concentrations of CO2 and O2. In

a first approach, a lumped model was adopted to evaluate the

mean gas concentration in the silobag (Navarro et al., 1994),

based on the experimental evidence that no stratification of

gases was measured in the silobags as will be shown latter.

Hermetic conditions to gas transfer were assumed.

For each time step, the local CO2 production rate deter-

mined by Eq. (25) was averaged over the domain to obtain

a mean rate production.

YCO2ðtÞ ¼ 1

U

ZU

YCO2ðx; y; tÞdU (26)

The cumulative CO2 production at a given time mCO2in

mg [CO2] kg�1 [dry matter] was calculated by integration over

time:

mCO2ðtÞ ¼

Z t

0

YCO2ðt0Þdt0 (27)

Assuming an ideal gas behaviour for CO2 and O2, concen-

trations X in % V/V were determined by:

Table 3 – Input parameters of the thermal model

Reference Parameter

Sky emissivity (Mills, 1995) xsky ¼ 0:82

Silobag emissivity x ¼ 0:6

Silobag absorptivity a ¼ 0:26

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 578

XCO2¼�

mCO2

1000MCO2

rb

�RT3

100Pat

(28)

XO2¼ 21� XCO2

(29)

2.2.5. Dry matter lossAccording to the stoichiometric respiration equation (Eq. (10)),

the mean rate of dry matter consumed by aerobic respiration

dm in mg [dry matter] kg�1 [dry matter] in 24 h is:

dmðtÞ ¼180 g264 g

YCO2ðtÞ (30)

and the cumulative mean DML in mg [dry matter] kg�1 [dry

matter] matter at time t was calculated by integration over

time:

DMLðtÞ ¼Z t

0

dmðt0Þdt0 (31)

2.2.6. Numerical solutionThe PDE system was numerically solved by the finite element

method. Eqs. (1) and (2) with associated initial and boundary

conditions were built in COMSOL Multiphysics 3.4. Fig. 2 shows

the discretization of the silobag and part of the soil domain. A

refined mesh was generated at the boundaries were the

highest temperature and moisture gradients are expected to

occur. Quadratic Lagrangian elements and a fourth order

numerical quadrature were applied.

2.3. Experimental field tests

Two tests were carried out for wheat (Triticum aestivum,

‘‘ProINTA–Isla Verde’’ cultivar) on a farm (Estancia San Lor-

enzo de Zubiaurre S.A) close to Tandil (37.317 South, 59.150

West) in the south east of the Buenos Aires province,

Argentina (Rodrıguez et al., 2002). The objective was to inves-

tigate the effect of silobag storage conditions (temperature

and MC) on the evolution of grain quality parameters during

a storage period of 150 days. After harvest, one bag was filled

with wet wheat (16.4% w.b.; 19.62% d.b.) and the other with dry

wheat (12.5% w.b.; 14.28% d.b.). The ends of the silobags were

sealed to restore the hermetic condition, and the grain was

not disturbed until the end of the test. During the experi-

ments, several variables were monitored. Grain temperature

at three levels in the bags (top¼ 1.45 m; middle¼ 0.8 m;

bottom¼ 0.10 m; total height of the bag¼ 1.5 m) were recor-

ded every 10 min along with the ambient temperature (HOBO

temperature datalogger). The sensors were inserted in the

filled bag by means of a rod. Afterwards, the holes produced in

the plastic cover were sealed with a special sealant glue and

plastic tape to keep the system airtight. Carbon dioxide (CO2)

and oxygen (O2) concentrations were monitored during the

storage time using a gas analyzer (ABISSPRINT, Abiss, Viry

Chatillon, France).

The grain was sampled after 45, 80 and 150 days. Samples

were taken with a simple truck probe at three levels in three

locations along the length of the bag, with three replicates per

location. After each sampling date, the airtightness of the

silobag was restored by sealing the holes in the plastic cover.

Grain samples from each of the three sampling locations were

segregated by level (top, middle, bottom). Then, wheat from

each level at each sampling location was blended together for

a composite sample per level. MC (ASAE Standard method,

ASAE, 1984) and several quality analyses (germination, test

weight, damage test, composition, baking quality) were per-

formed on each of the sub-samples.

The effect of the modified atmosphere on insect activity

was also investigated. Bags made of fine plastic mesh con-

taining grain and weevils (Sitophilus oryzae (L.)) were placed in

a plastic pipe with holes to facilitate gas flow between the

interstitial air in the grain bulk and the inside of the pipe. The

pipes were 1.5 m long and were divided into three cages cor-

responding to top, middle and bottom sections of the silobag.

Each cage contained 50 live insects. Nine pipes were inserted

into each silobag, thus the number of insects per grain kilo-

gram represents a negligible infestation (1 insect/148 kg). In

the dry and wet silobags, no live insects were found in caged

samples after 45 days. In addition, no insect infestation was

detected in the grain mass during grain sampling of the silo-

bags. A detailed discussion of the results of these tests is

presented in Rodrıguez et al. (2002).

3. Results

3.1. Heat and mass transfer model validation

To validate the model, temperature and MC evolution were

simulated and the numerical results were compared with the

experimental data. The field test started on January 2nd, 2001.

The initial MCs were 12.5% w.b. (14.28% d.b.) and 16.4% w.b.

(19.62% d.b.). In these field tests, ambient temperature was

exceptionally high (middle of summer), so after harvest the

grain was directly loaded in the silobags at an initial temper-

ature of 43.5 �C.

The horizontal global solar irradiance was calculated for

the climatic conditions of Buenos Aires province with variable

cloudiness. It was assumed that the silobag had an N–S

orientation. With this value, the incident solar radiation was

determined for the 11 planes defined previously on the

boundary G1.

Ambient temperature and solar radiation have hourly and

daily fluctuations. Hourly weather data was used as input data

in the model validation. The dependence of the ambient

temperature on the time variable was modelled by linear

interpolation of measured data. The radiometric properties of

the plastic bag were experimentally determined for the solar

range (Integrating Sphere, Licor 1800 Spectroradiometer,

Lincoln Corp, Liconln Nebraska, USA) and are listed in Table 3.

Fig. 3 compares the predicted and measured temperatures at

the three levels (top¼ 1.45 m; middle¼ 0.80 m; bottom¼ 0.10 m)

Fig. 3 – Comparison between measured (symbol) and

predicted temperatures (line) at three levels in the silobag

during the five months of storage (January–May 2001). B d,

top; 7 ., middle; 6 - - -, bottom; M0, initial MC 12.5% w.b.;

T0, initial temperature 43.5 8C.

Fig. 5 – Effect of incident solar radiation on top temperature

evolution during a sequence of sunny days (January 2001).

B, measured; - - -, predicted; d, ambient temperature; M0,

initial MC 12.5% w.b.; T0, initial temperature 43.5 8C.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 5 79

in the silobag filled with dry wheat (12.5% w.b.) during 150 days.

For the silobag with wet wheat (16.4% w.b.) computed temper-

atures were compared only in the first 50 days (Fig. 4). Middle

and bottom temperature records presented anomalies on the

15th day which could not be explained, and after 50 days

temperature sensor measurements were disrupted.

In the previous figure it is difficult to appreciate the

evolution of the top temperature for the whole storage period.

Fig. 5 is a magnification for the period from day 15 to day 30,

which shows how the top temperature followed ambient

temperature fluctuations.

Fig. 4 – Comparison between measured (symbol) and

predicted temperatures (line) at three levels in the silobag

during 50 days of storage (January–February 2001). B d,

top; 7 ., middle; 6 - - -, bottom; M0, initial MC 16.4% w.b.;

T0, initial temperature 43.5 8C.

Measured MC at the top, middle and bottom levels after 45,

80 and 150 days, is compared with the computed change of MC

in Figs. 6 and 7 for dry and wet wheat, respectively.

Measured values for dry wheat suggest that moisture tends

to accumulate towards the top but a random behaviour was

observed in the wet silobag. This may be a consequence of the

sampling procedure. Grain samples taken with the truck

probe were divided in three parts, each one collecting the

grain within a layer of about 0.5 m. The MC of the upper third,

middle and lower third were named top, middle and bottom

MC of the silobag, respectively.

After 150 days measured moisture stratification was about

0.4–0.8% w.b. and that predicted by the model was about 1.0

and 1.5% w.b., for dry and wet wheat, respectively. To some

extent, these differences may be explained by the fact that

Fig. 6 – Comparison between measured (symbol) and

predicted MCs (line) at three locations in the silobag during

the five months of storage (January–May 2001). ; -$-$-, top;

: ., middle; C - - -, bottom; d, mean; M0, initial MC 12.5%

w.b.; T0, initial temperature 43.5 8C.

Fig. 7 – Comparison between measured (symbol) and

predicted MCs (line) at three locations in the silobag during

the five months of storage (January–May 2001). ; -$-$-, top;

: ., middle; C - - -, bottom; d, mean; M0, initial MC 16.4%

w.b.; T0, initial temperature 43.5 8C.

Table 5 – Measured CO2 and O2 concentration (%) at threelocations in the silobag with dry wheat 12.5% w.b.

Dry wheat (12.5% w.b.)

Location 5 days 5 days 45 days 45 days 100 days 100 days

CO2 % O2 % CO2a % O2

a % CO2 % O2 %

Bottom 4.5 14.7 8.75 12.6 13.0 10.5

Middle 4.5 14.8 8.75 12.6 13.0 10.4

Top 4.3 14.7 8.65 12.5 13.0 10.2

Average 4.4 14.7 8.7 12.6 13.0 10.4

a Interpolated value.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 580

measured values were the result of a blending and averaging

procedure as described previously, while numerical results

are point values. Also, the analysis of the MC values of indi-

vidual samples at different locations in the same bag showed

a variability which was of the same order of magnitude as that

of the predicted moisture migration. This variability is typi-

cally found in large grain masses, like those in the silobags

(200 tonnes).

Predicted moisture gradients (not shown) in the silobag

developed within a top layer of about 0.15 m. A greater

number of sampling levels would have been necessary to

experimentally detect them. Additionally, a larger number of

sampling locations should be considered to account for the

typical variability of the MC values, but such an experimental

setup may be rather difficult to implement in a large scale test,

and also a large number of sampling sites would compromise

the hermeticity of the system.

The overall behaviour predicted by the model was an

increase in moisture MC in the peripheral grain layer and

a slight decrease at the middle of the bag. Recently, Darby and

Caddick (2007) reported this behaviour in a pilot-scale plant

test carried out with 20 tonnes of wheat stored at 11.4% w.b.

and 14.1% w.b. in silobags from February 2006 to May 2007 at

Table 4 – MRD and SE of the estimate SE betweenmeasured Tm and T predicted temperatures; ns samplesize

Location MRDa SEb, �C

Bottom 0.064 1.94

Middle 0.059 1.35

Top 0.170 1.20

a MRD ¼ 1=nsPns

i¼1 jðTim � TiÞj=Tim.

b SE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPns

i¼1ðTim � TiÞ2=ns

q

CSIRO Black Mountain, Canberra, Australia. Changes between

0.7 and 1.1% w.b. were recorded in the upper layer of the

silobags, which were of the same order of magnitude as those

predicted by the model.

The mean relative deviation (MRD) and standard error (SE)

were used to determine the model accuracy. High values of SE

and MRD indicate that a model fails to explain the variation in

the data. Values of MRD and SE are summarized in Table 4 and

show that the numerical model adequately predicted the heat

transfer and moisture migration in the bulk grain stored in

a silobag. Although MC measurements were few compared to

temperature measurements, the heat transfer model is

strongly coupled to the mass transfer model by source terms

and moisture dependent thermal properties. As discussed by

Iguaz et al. (2004b), global model validation was based mainly

on temperature data, and the error of present model is of the

same order as those reported by this and other authors

(Alagusundaram et al., 1990; Montross et al., 2002b).

3.2. CO2 and O2 concentrations model validation

Measured concentrations of CO2 and O2 are presented in

Tables 5 and 6, for dry and wet wheat, respectively. As

mentioned previously, these values suggested that for a given

time, stratification was negligible and the gas distribution was

almost uniform.

For dry wheat, O2 decreased to 14.7% after five days and to

13.0% after 100 days while CO2 increased to 4.4% and to 10.4%,

respectively. The respiratory quotient ranged from 0.69 to 1.3.

Table 6 – Measured CO2 and O2 concentration (%) at threelocations in the silobag with wet wheat 16.4% w.b.

Dry wheat (16.4% w.b.)

Location 5 days 5 days 45 days 45 days 100 days 100 days

CO2 % O2 % CO2a % O2

a % CO2 % O2 %

Bottom 19.5 5.3 21.25 5.35 23.0 5.2

Middle 18.5 5.6 20.75 5.65 23.0 5.7

Top 18.6 5.6 20.55 5.75 22.5 5.9

Average 18.9 5.5 20.9 5.55 22.8 5.6

a Interpolated value.

Fig. 8 – Comparison between mean measured (symbol) and

mean predicted O2 and CO2 concentrations (line) in the

silobag during the five months of storage (January–May

2001). :, d, O2; C, - - - , CO2; M0, initial MC 12.5% w.b.; T0,

initial temperature 43.5 8C.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 5 81

For wet wheat, because of the high respiration rate (43.5 �C

initial temperature and 16.4% w.b.), after five days O2

decreased to 5.5% while CO2 increased to 18.9%. Thereafter,

experimental data showed that O2 remained nearly constant

around 5.5% and, after 100 days, CO2 slightly increased to

22.8%. The respiratory quotient varied from 1.2 to 1.47.

Fig. 8 compares measured and predicted average concen-

tration values for dry wheat (12.5% w.b.). Good agreement was

obtained, with a difference of less than 10% after 100 days for

both gases (1.8 and 0.6 % concentration difference for CO2 and

O2, respectively).

Fig. 9 – Comparison between mean measured (symbol) and

mean predicted O2 and CO2 concentrations (line) in the

silobag during the five months of storage (January–May

2001). :, d, O2; C, - - -, CO2; M0, initial MC 16.4% w.b.; T0,

initial temperature 43.5 8C.

Fig. 9 compares measured and predicted average concen-

tration values for wet wheat. The model predicted that O2

decreased to 5.5% in 90 h (w4 days), and was almost consumed

in 130 h (w5.5 days). The difference between the average

observed and predicted values was of about 5% concentration

for O2. The predicted CO2 concentration after 5 days was 21%;

this was about 2% concentration higher than the observed

data (w19%). After 100 days, the CO2 concentration increased

above 21% (22.8%), and this could be the result of anaerobic

respiration inside the bag (White et al., 1982).

The measured and computed changes in gas concentration

found in this study were consistent with recently published

results at laboratory scale. Weinberg et al. (2008) presented in

vitro studies of the effect of various MCs on the quality of corn

in self-regulated atmospheres during hermetic conditions at

30 �C. Most of the O2 in the containers with 16% w.b. was

consumed after 120 h (5 days) decreasing to less than 2%. For

16% w.b. it appeared that respiration was aerobic since CO2

did not exceed 20%. Above 18% w.b., after a plateau in CO2

concentration, it increased above 21%, indicating that anaer-

obic respiration occurred. Bispo Dos Santos et al. (2008)

presented similar results, but O2 in the containers decreased

to 4–5% level.

The reported errors between measured and predicted

values may be expected when dealing with biological systems

in commercial scale tests. For the range of MCs considered in

this work (12.5–16.4% w.b.), the authors concluded that the

change in O2 and CO2 concentrations during storage was

satisfactorily predicted by use of White et al. (1982) correlation.

4. Discussion

4.1. Analysis of the temperature changeand moisture migration

Figs. 3 and 4 presented the temperatures at the three levels in

the silobag. The figures showed that, even for the wet grain, the

measured and predicted temperatures at the middle and

bottom of the silobag started to decrease from the beginning of

storage, as a result of heat exchange with the surroundings.

This behaviour is quite different from that of a conventional

bin, where the initial storage temperature at the core is not

influenced during long periods by the fluctuating ambient

conditions imposed on the boundary. This can be explained by

the ratio of transfer area/grain volume which is substantially

higher for a silobag (w1.43 m2 m�3 for a 200 tonnes silobag)

than for a regular bin of similar storage capacity (0.79 m2 m�3

for a bin 7 m diameter and 9 m height of 200 tonnes of capacity).

Fig. 5 illustrated the temperature fluctuations at the top

layer. In summer, during a sequence of sunny days, solar

radiation on the surface produced a difference between the

grain top layer and the ambient temperature as great as 10 �C,

while during a sequence of cloudy days (not shown) the

difference was reduced to about 2 �C. This effect tends to

decrease during the fall and winter. On winter nights, the top

temperature was lower than the ambient temperature (not

shown), due to radiation loss to the clear sky. The amplitude of

temperature oscillations was about 10 �C in summer,

decreasing to 5 �C in winter.

Fig. 10 – Distribution of predicted equilibrium relative

humidity in the silobag after 150 days of storage (May

2001). M0, initial MC 16.4% w.b.; T0, initial temperature

43.5 8C.

Fig. 11 – Comparison between the computed mean

temperature of the dry and wet stored grain during 150

days of storage (January–May 2001). Initial MC: d, 12.5%

w.b.; ., 16.4% w.b. (with heat of respiration during 150

days); - - -, 16.4% w.b. (with twofold heat of respiration

during 150 days) T0, initial temperature 43.5 8C.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 582

Figs. 6 and 7 showed the computed change of MC in the

silobag. The grain was stored at a high initial temperature

43.5 �C, but climatic conditions and soil influence where such

that the grain mass begun to cool down promoting moisture

migration mainly towards the surface and, to a lesser extent,

to the bottom.

Numerical results revealed that temperature and moisture

gradients were concentrated below the silobag surface within

a layer of 0.10–0.20 m thick. This means that roughly 25% of

the stored grain followed the hourly fluctuations of weather

climatic conditions and will be exposed to greater quality

losses and spoilage.

By use of the sorption isotherm, the model predicted the

equilibrium relative humidity, ERH. Safe storage condition

(ERH< 70%) holds from summer to winter for 12.5% w.b. initial

MC. For 16.4% w.b., interstitial ERH was always higher than

70%, and although wheat cools down during winter, the

temperature reduction was not enough to bring ERH to safe

levels (Fig. 10). Wet grain creates anaerobic of conditions, and

under these conditions, aerobic microflora are not active and

grain damage is prevented (Weinberg et al., 2008). But if the

silobag is not sufficiently gastight (leakage, structural

damage), the interstitial ERH level would be favourable to

support mould activity during storage of wet grain, causing

damage and reducing the safe storage time.

Fig. 11 illustrates the computed mean temperature of the dry

stored grain. Wheat harvested in summer time, by early April

reached the safe storage temperature for preventing insect

development (below 17 �C) (Fields, 1992). This implies that the

silobags have a double effect on insect control. On the one hand,

the hermetic storage conditions would create a hostile envi-

ronment for insects that would prevent development, espe-

cially with wet grain (lack of O2 and/or toxic concentrations of

CO2). On the other hand, the low temperature reached during

winter time would also reduce insect ability to survive. An

additional advantage of the silobags with regard to insect

infestation is that the plastic cover acts as a physical barrier, so

if grain comes from the field free of insects, no further infes-

tation should occur during storage. Though the transfer area/

grain volume ratio is favourable for natural cooling during fall

and winter, with the advent of spring and summer the adverse

warming effect would take place. The rate at which tempera-

ture increases is strongly dependent on climate, so it would be

expected that storage conditions during spring would become

more risky at lower latitudes and in warmer areas.

In a conventional silo, any temperature increase detected

at the core by thermocouples is associated with local heating

due to respiration of the ecosystem and spoilage. Because of

the high ratio of transfer area/grain volume of the silobag, the

temperature change at the core results from the balance

between the heat released by respiration and heat transferred

to the environment, and thus, temperature monitoring is less

reliable to detect biological activity. This effect was tested by

numerical simulation.

In the previous section it was shown that in the case of wet

grain, respiration caused a quick depletion of O2 and after 5

days aerobic respiration was significantly reduced. If O2

ingress were allowed, because of lack of gas-tightness or

structural damage of the plastic bag, aerobic respiration could

be possible. However, the heat released could not compensate

for the heat losses to the environment and again, the

temperature of the silobag would continuously decreased.

Temperature change was computed including the heat

released by respiration during the whole storage period (150

days). Compared to dry wheat (Fig. 11), which has a low

respiration, the difference between mean temperatures was

at most 1.5 �C. By use of Eq. (11), the highest value of the heat

released by respiration for wet wheat (16.4% w.b.) was of about

4.5 W m�3, while for dry wheat (12.5% w.b.) of about

0.48 W m�3. A worst condition was tested by doubling the heat

released by wet wheat. In this case, the temperature at the

centre only increased about 3 �C at the beginning of storage

but after 15 days it started to decrease. These numerical

examples clearly showed that the temperature at the centre of

the silobag did not increase because of the heat released.

Besides, with the advent of the warm season, a temperature

rise at the core of a silobag would not necessarily mean bio-

logical activity. This suggests that, for certain combinations of

storage factors (temperature, MC, infestation pest, climatic

conditions), temperature monitoring in silobags may not be

Fig. 12 – Predicted mean DML in the silobag during the five

months of storage (January–May 2001). Initial MC: - - -,

12.5% w.b.; d, 16.4% w.b.; ., 16.4% w.b. (simulated with

heat of respiration during 150 days) T0, initial temperature

43.5 8C.

b i o s y s t e m s e n g i n e e r i n g 1 0 4 ( 2 0 0 9 ) 7 2 – 8 5 83

appropriate to detect biological activity (mould or insects) and

hence to predict grain storability.

The use of a simulation model to rapidly analyze numerous

situations and describe the critical limits of the different

factors is a very useful tool, in view of the complexity of the

grain bulk ecosystem prevailing under hermitic conditions as

was mentioned by Navarro et al. (1994).

Future work will couple momentum, heat and mass

balances to analyze the effect of natural convection on the

isotherm and moisture migration patterns as well as the

transfer process of CO2 and O2 through the interstitial air.

4.2. Dry matter loss estimation

DML was estimated by applying Eq. (31). White et al. (1982)

considered that a 0.1% DML is unacceptable for wheat, and if

stored wheat is to be used as seed the approximate limit for

safe storage is 0.04% DML.

Fig. 12 shows the evolution of the percentage mean DML

(%). For dry wheat, because of the low initial MC and the

temperature decrease over time (see Fig. 11) mean DML was

less than 0.01% after 150 days.

Fig. 13 – Distribution of computed DML after 150 days in the

silobag when heat of respiration is included during the

whole storage period (May 2001). M0, initial MC 16.4% w.b.;

T0, initial temperature 43.5 8C.

In the case of wet wheat, after five days, the model

predicted that O2 was consumed, and mean DML was 0.013%.

For comparison, DML computed for wet wheat if aerobic

respiration were allowed (numerical example of previous

section) was also plotted as a dashed line in Fig. 12. This curve

gives an estimation of the amount of DML when the silobag is

not gas-tight. In this case mean DML was about 0.075%,

exceeding safe limits for seed use but not high enough to reduce

grain commercial quality. The distribution of the local DML after

150 days is shown in Fig. 13. Even though there was a slight

increase in grain MC at the top and bottom layer over time, the

respiration rate slowed down as the temperature decreased at

the periphery, so the higher DML would be located at the core of

the silobag.

The development of a grain respiration correlation

depending on CO2 and O2 concentration, would improve

model predictions of gas concentrations and DML, especially

for grain with high initial MC.

5. Conclusions

In this work a bidimensional coupled heat and mass transfer

model was described to predict the temperature distribution

and moisture migration owing to seasonal variation of

climatic conditions of wheat stored in hermetic plastic bags

(silobag). The numerical solution was carried out applying the

finite element method.

Predicted values of temperature were compared with field

test data at three levels in the silobag. The model showed good

agreement with the experimental data with an average SEs of

1.94 �C at the bottom, 1.35 �C in the middle and 1.20 �C at the

top grain layer. MC change in time showed the same trend of

behaviour measured for dry wheat. Nevertheless, since the

heat transfer model is strongly coupled to the mass transfer

model, MC predictions were validated via the accordance with

temperature data.

CO2 and O2 concentrations in the silobag were predicted

applying White et al. (1982) correlation to model the rate of CO2

production (mg [CO2] kg�1 [dry matter] in 24 h). For the range,

12.5–16.4% w.b., good agreement between measured and

numerical values was obtained (less than 10% difference for

dry wheat experiment).

For most typical storage conditions, the model can esti-

mate with an acceptable degree of accuracy the O2 and CO2

concentration levels. It can assist in the design of a monitoring

protocol of these variables as a tool for predicting grain stor-

ability for the silobag system.

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