Comparison of Mathematical Models to Simulate Aeration of Wheat Stored in Brazil

J. agric. Engng Res. (1996) 64, 119 – 130

Comparison of Mathematical Models to Simulate Aeration of Wheat Stored in Brazil R. Sinicio;* W. E. Muir† * Centro Nacional de Treinamento em Armazenagem, Campus da UFV, 36570-000 Vic¸ osa, MG, Brazil † Department of Biosystems Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 5V6 (Receiy ed 20 May 1994; accepted in rey ised form 4 January 1996)

Equilibrium and non-equilibrium heat and mass balance models are compared to simulate aeration of stored wheat under tropical and subtropical climates using both linear and non-linear airflow distributions. The approach used was to compare deviations in predicted grain deterioration instead of deviations in grain moisture content and temperature. The results produced by the equilibrium and non-equilibrium models were significantly different (P 5 0?05) when simulating aeration of wheat stored for 1 yr in Curitiba, Brazil because the deviations in grain deterioration were equal to or greater than the uncertainty in predicting deterioration (Ú30%) for most test conditions. The non-equilibrium model appears more appropriate than the equilibrium model for simulating aeration of stored wheat because it is based on experimental thin-layer drying and wetting equations and equilibrium moisture content equations for desorption and adsorption. In addition, the equilibrium model over-predicts wheat moisture content and temperature, causing an over-prediction of grain deterioration. It is concluded that a more accurate deterioration model is needed to increase the uncertainty in predicting wheat deterioration for simulated aeration of stored wheat.

DASTE

K, K9 L L9 M Md

Me M0 Mw MR N, N9 p p 1 to p 4 q 1 to q 4

÷ 1996 Silsoe Research Institute

r1 to r6 RH s1 to s6 t T Tc Te V θ max

Notation A, B, C ASTE

ASTE eq ASTEneq

parameters in the equilibrium moisture content equations allowable storage time elapsed predicted by the deterioration model, decimal ASTE predicted by the equilibrium model, decimal ASTE predicted by the nonequilibrium model, decimal

0021-8634 / 96 / 060119 1 12 $18.00 / 0

119

deviation between ASTE predicted by the equilibrium and non-equilibrium models in the comparison of models, % parameters in the thin-layer equations latent heat of vaporization or condensation of water in wheat kJ kg21 latent heat of vaporization or condensation of free water, kJ kg21 grain moisture content, decimal, d.b. initial moisture content minus the equilibrium moisture content of the grain, decimal, d.b. equilibrium moisture content, decimal, d.b. initial moisture content, decimal, d.b. grain moisture content, %, w.b. moisture ratio, decimal parameters in the thin-layer equations statistical level of significance, decimal parameters in the equilibrium moisture content equations parameters in the equilibrium moisture content equations parameters in the thin-layer equations air relative humidity, decimal parameters in the thin-layer equations time, min temperature, K temperature, 8C equilibrium temperature, 8C air velocity, m s21 Maximum allowed storage times before seed germination drops by 5% or visible mould appears in the deterioration model, d ÷ 1996 Silsoe Research Institute

120

R. SINICIO ; W. E. MUIR

1. Introduction

A common problem during grain aeration in humid climates is wetting of grain around aeration ducts,1,2 but the problem is worse in warm-humid regions because the grain deterioration rate is accelerated by high grain temperatures. Thus, a reliable mathematical model is needed to predict accurately grain (wheat) moisture content, temperature, and deterioration, particularly for the grain close to the aeration ducts where large gradients in air velocity and distribution exist. To determine the appropriate airflow rates and fan control strategies for aeration of stored grain in a geographical region it is necessary to use a mathematical model to predict grain moisture content, temperature, and deterioration as a function of time, weather data and type of storage structure.3 Grain deterioration, which depends mainly on grain moisture content, temperature, and storage time, is the major variable used when making decisions on selecting and optimizing aeration systems. Therefore, grain deterioration is the most important variable to be predicted. At present it is not possible to calculate the exact quality parameters such as milling and baking quality, germination, and fat acidity values as a function of grain storage conditions. Deterioration predicted by empirical mathematical models give, however, an indication of quality changes and trends of spoilage of stored wheat under aeration.4 Heat and mass balance models are used to predict grain moisture content and temperature during ventilation of grain bulks.5,6 They are based on heat and mass balances for a thin-layer of grain in which it is assumed that air conditions are constant over a short time interval. These models can be classified as either equilibrium or non-equilibrium models. For each time interval, equilibrium models assume equilibrium of temperature and humidity between air and grain in each layer while non-equilibrium mathematical models assume only temperature equilibrium.7 Equilibrium models use equilibrium moisture content (EMC) equations to calculate the changes in grain moisture content during each time interval.6 Non-equilibrium mathematical models use thin-layer drying and wetting equations to describe the rate of change in grain moisture content for a single layer of grain kernels as a function of air conditions.5 Thinlayer equations and their use in mathematical models to simulate heat and mass transfer in deep-beds of grain have been presented by several authors.7–9

Metzger and Muir10 used the equilibrium model of Thompson6 to simulate forced-convection in stored wheat. They found that equilibrium was not a good assumption for airflow rates as high as 9?0 l s21 m23 while this assumption gave relatively accurate moisture content predictions for airflow rates of 1?9 l s21 m23. Sanderson et al.4 evaluated the model of Metzger and Muir10 to simulate near-ambient drying of wheat using airflow rates from 0?8 to 23 l s21 m23. The original model of Thompson6 used for the simulation had been modified to include a 5% offset in the equilibrium relative humidity during moisture adsorption to account for hysteresis. The predicted drying rates were slower than those measured when wheat initial moisture content was 25% w.b. It was concluded, however, that this model is sufficiently accurate to predict airflow rates required to cool and dry stored wheat. The object of this paper is to compare the results produced by equilibrium and non-equilibrium mathematical models for simulating aeration of stored wheat under tropical and subtropical climates using both linear and non-linear airflow distributions. The results of this research will be useful for selecting a reliable mathematical model to determine the minimum airflow rates and fan control methods to preserve the quality of aerated wheat stored in large horizontal stores, that have inside aeration ducts which generate a non-linear airflow distribution.

2. Procedures

2.1. Heat and mass transfer under forced cony ection The mathematical model of Metzger and Muir10 was compared with the non-equilibrium mathematical model developed by Thompson et al.5 The drying model of Thompson et al.5 was modified to include the EMC desorption [Eqn (1)] and adsorption [Eqn (2)] equations and thin-layer drying [Eqns (3), (4) and (5)] and wetting [Eqns (3), (6) and (7)] equations developed for wheat by Sinicio et al.11

Fln 2(RHA )G

(1/B )

Me 5

(1)

where: A 5 p1 e ( p2T ) and B 5 p3 T p4 . Me 5 equilibrium moisture content, decimal, d.b.; T 5 air temperature,

121

AERATION OF WHEAT STORED IN BRAZIL

K; RH 5 air relative humidity, decimal; p 1 5 0?4209 3 1029; p 2 5 0?05434; p 3 5 0?8254 3 1010; p 4 5 23?856; and Me 5

H2q 1 ln F(T 1 q2)Cln (RH)GJ 2

(2)

1

where: C 5 q 3 1 q 4 . ln (M0); M0 5 initial moisture content, decimal, d.b.; q 1 5 20?25; q 2 5 2239?9; q 3 5 1134; q 4 5 307?6 MR 5

(M 2 Me) 5 exp (2Kt N ) (M0 2 Me)

(3)

where: MR 5 moisture ratio, decimal; M 5 moisture content, decimal, d.b.; t 5 time, min; K , N 5 grain dependent coefficients for drying (K 9 and N 9 for wetting). K 5 r1 exp (r2 T )Md(r3RH

r4)

N 5 r5 M r06

(4) (5)

where: Md 5 M0 2 Me, decimal, d.b.; r1 5 0?6348 3 1026; r2 5 0?03733; r3 5 0?1824; r4 5 20?6724; r5 5 1?13; r6 5 0?3225 K 9 5 s1 exp (s2 T )V [s3 exp (s4M0)]

(6)

N 9 5 s5 RH s6

(7)

where: V 5 air velocity, m s21; s1 5 0?8072 3 1029; s2 5 0?05516; s 3 5 0?1844; s4 5 2?849; s5 5 0?8599; s6 5 0?2806. The standard errors for the EMC desorption and adsorption equations are 0?19 and 0?39% w.b., respectively. These standard errors were determined for the experimental data sets (43 for drying and 88 for wetting) obtained by Sinicio et al.11 The EMC equations determined by Sinicio et al.11 [Eqns (1) and (2)] do not give true EMC but asymptotic values which give the best fit of the semi-empirical equations [Eqns (3) to (7)] to the drying and wetting experimental data. The standard errors for the thin-layer drying and wetting equations are 0?12 and 0?24% w.b., respectively. These standard errors were determined for the experimental points (452 for drying and 951 for wetting) obtained by Sinicio et al.11 Equilibrium temperature (Te) of the wheat and air was calculated by a heat balance between air and grain before calculating the moisture exchange using the equations presented by Thompson et al.5 Equilibrium relative humidity (ERH) of the air was calculated using the moisture content of the air and Te. Equilibrium moisture contents for desorption and adsorption by wheat were calculated using Te and ERH of the air. Drying was assumed when desorption

EMC was lower than the grain moisture content. Wetting was assumed when adsorption EMC was higher than the grain moisture content. No moisture exchange was assumed when neither drying nor wetting was possible. The equilibrium model of Metzger and Muir,10 however, was used when ERH of the air was equal to or higher than 95% due to the limitations of the EMC equations to predict above this limit and to predict vapour condensation although this event normally does not occur during aeration. The net heat of desorption and adsorption, that is, the amount by which the latent heat of vaporization or condensation, respectively, differs from that of free water, were calculated using the following equations for the latent heat of vaporization equation [Eqn (8)] and latent heat of condensation equations [Eqns (9) and (10)] L 5 1 1 3?23 exp (220?25 M ) L9 L 5 1 1 39?34 exp (243?63 M ) L9 L 51 L9

M , 0?2048

M > 0?2048

(8) (9)

(10)

where: L 5 latent heat of vaporization or condensation of water in wheat, kJ kg21 and L9 5 latent heat of vaporization or condensation of free water, kJ kg21. The latent heat of vaporization and condensation equations were determined based on the EMC adsorption and desorption equations presented by Sinicio et al.11 using the method presented by Cenkowski et al.12 For both equilibrium and non-equilibrium models the bulk density was calculated as a function of grain moisture content13 for each grain layer during the ventilation period. The air – vapour relationships are given by ASAE.14

2.2 . Grain deterioration model The mathematical model of grain deterioration presented by Fraser and Muir15 [Eqn (11)] was used to predict the allowable safe storage time for wheat as a function of grain moisture content and temperature

θ max 5 10(a 1bMw1cTc)

(11)

where: θ max 5 Maximum allowed storage times before seed germination drops by 5% or visible mould appears, d; Mw 5 grain moisture content, % (w.b.);

122

R. SINICIO ; W. E. MUIR

Tc 5 grain temperature, 8C; a 5 6?2347 b 5 20?21175 c 5 20?05267 for 12 < Mw < 19% w.b. and a 5 4?1286 b 5 20?09972 c 5 20?05762 for 19 < Mw < 24% w.b. This model [Eqn (11)] predicts maximum storage times for wheat before germination drops by 5% or visible mould appears. A numerical procedure to calculate the allowable storage time elapsed for each time interval was used by Sanderson et al.4 In that procedure, the deterioration model was used to calculate the allowable storage time at each time interval based on the predicted temperature and moisture content of each spatial element. The proportion of allowable storage time elapsed during the time interval is the length of the time interval divided by the allowable storage time. These decimal fractions for all preceding time increments were added to obtain an estimate of the total proportion of allowable storage time elapsed (ASTE ).

2.3. Selection of weather data The selection of tropical and subtropical regions for this study was based mainly on the availability of weather data from Brazil and on the wheat storage capacities of Brazilian regions. A weather database from 1961 to 1970 for four Brazilian state capitals (Cuiaba´ , Mato Grosso State; Curitiba, Parana´ State; Goiaˆ nia, Goia´ s State; and Porto Alegre, Rio Grande do Sul State;) consisting of hourly data of dry-bulb and wet-bulb air temperatures and barometric pressures was used for the simulations (Table 1). Parana´ State has 37% of the total Brazilian bulk storage capacity16 and 62% of the total Brazilian wheat production requiring bulk storage.17 Weather data from Curitiba therefore were used for most of the simulations because of these facts. Cuiaba´ and Goiaˆ nia are classified as tropical climates and Curitiba and Porto Alegre are classified as

subtropical climates. The locations Cuiaba´ , Goiaˆ nia, and Porto Alegre were included to determine the effects of climatic conditions.

2.4. Year of simulation and total grain depth The weather conditions that prevailed in the median year (1966) and the worst year (1969) for grain storage from 1961 to 1970 for Curitiba were selected on the basis of the maximum allowable storage time elasped (ASTE ) simulated for any grain layer when ventilating the stored wheat from 0600 to 1200 hrs each day. The maximum ASTE for each year was determined by simulating aeration of stored wheat for 10 yr of weather data using the equilibrium model, 13% w.b. initial grain moisture content, 308C initial grain temperature, 1 l s21 m23 airflow rate, 18C fan temperature rise, and 5?6 m grain depth. The aeration period from 0600 to 1200 h was chosen because it gave less grain deterioration compared with 1200 to 1800 h, 1800 to 2400 h, or 0000 to 0600 h. This agrees with results presented by Sinicio et al.18 for the Brazilian city of Sorocaba, Sa˜ o Paulo State. The same ventilation period and initial moisture content and temperature of the grain were used in the comparison of models. The grain depth was divided into 20 layers: the first grain layers from the bottom were 5, 10, 15, 20 and 25 cm thick and the remaining 15 layers were 32 cm thick. Variable grain layer thicknesses were used in an attempt to detect accurately grain deterioration in the first layers from the bottom, where the ventilation air enters the grain, without the need to increase excessively the total number of layers. The grain layer thicknesses were determined according to the minimum amount of spoiled grain required to be detected in the grain bulk. It was important, however, to keep the total number

Table 1 Average weather conditions calculated for Cuiaba´ , Curitiba, Goiaˆ nia and Porto Alegre, Brazil from 1961 to 1970* Location

Temperature , 8C

Relatiy e humidity , %

Barometric pressure , kPa

South latitude

W. Gr. latitude †

Altitude , m

Cuiaba´ ‡ Curitiba Goiaˆ nia§ Porto Alegre

26?5 16?5 22?4 19?4

69?4 85?8 75?4 80?4

99?0 91?4 93?0 101?5

158339 258269 168419 308019

568079 498169 498179 518139

151 924 729 47

* † ‡ §

Original weather data was obtained from Instituto de Aerona´ utica e Espac¸ o, Brazil. W. Gr. 5 West of Greenwich. Year period: 1963 – 1970. Year period: 1961 – 1967.

AERATION OF WHEAT STORED IN BRAZIL

of grain layers as small as possible because the computer execution time increased proportionally to this number. In all the simulations to determine the median and worst years the maximum grain deterioration occurred in the first layer from the bottom. Also the deterioration in the bottom 1 m was always greater than the average grain deterioration for the whole bulk. Therefore the grain depth for the comparison of models was reduced to 1 m for the linear airflow distribution. The equilibrium model of Metzger and Muir10 was used for determining the median and worst years.

2.5. Uncertainties in predicting grain moisture content , temperature , and grain deterioration The uncertainty (at 95% confidence level) in the measurement of grain moisture contents19 was assumed to be Ú0?20% w.b. and it was assumed to be Ú0?58C in the measurement of intergranular air temperatures using thermocouples.20,21 The uncertainty in the prediction of ASTE was determined by conducting an error analysis22 of the deterioration model developed by Fraser and Muir15 [Eqn (11)]. The uncertainties in measuring grain moisture content and temperature were used to determine the uncertainty in predicting ASTE . The uncertainties in determining the coefficients a , b and c of the deterioration model [Eqn (11)] were calculated based on the standard deviation for the coefficients calculated by the linear regression of the deterioration data. A 95% confidence level was used for all variables and coefficients. The uncertainty in predicting ASTE using the deterioration model of Fraser and Muir15 as a function of the uncertainties in measuring grain moisture content and temperature was Ú12%. The uncertainty in predicting ASTE when the uncertainties in esTable 2 Uncertainties (%) in the prediction of allowable storage time elapsed for wheat determined at 95% confidence level based on an error analysis of the deterioration model of Frazer and Muir15

Moisture content , % , w.b. 11 13 15 17

Temperature , 8C ——————————— 5 15 25 Ú32 Ú34 Ú36 Ú38

Ú33 Ú35 Ú37 Ú39

Ú35 Ú36 Ú38 Ú41

123

timating the model coefficients were included was much higher and depended on the grain moisture content and temperature (Table 2). Therefore, the absolute uncertainty in predicting ASTE when comparing the equilibrium and non-equilibrium models was assumed to be 30% which was less than the estimated minimum absolute uncertainty (Table 2). Thus, any absolute deviations in predicted ASTE that were less than 30% was not considered significant at the 95% confidence level in the comparison of models. Grain deterioration depends on many variables such as moisture content, temperature, time, mechanical damage, grain type and variety, grain history and type and amount of initial contamination by microflora. Therefore, such a high uncertainty in predicting ASTE for wheat can be expected. The deterioration model of Fraser and Muir15 however, is the only one developed for wheat. Sanderson et al.4 speculate that this deterioration model has a high factor of safety because it predicts spoilage (ASTE 5 1?0) before measured seed-quality decreases excessively. Because of this, Sanderson et al.4 advise the use of an ASTE of 1?5 to indicate unacceptable deterioration. Also, according to these authors, the deterioration model predicts deterioration trends which compare favourably with trends in seed germination and fat acidity values.

2.6. Comparison of equilibrium and non -equilibrium models

The grain deterioration (ASTE ), calculated as a function of moisture contents and temperatures predicted by the equilibrium and non-equilibrium mathematical models for each grain layer, was compared at the end of each month for 12 month of storage starting on 1 December for various sets of input conditions. Most simulations with linear airflow were run using a total grain depth of 1 m to simulate the grain conditions in the bottom of a bin with a fully perforated floor. The grain depth for the non-linear airflow case was set at 6 m (actual grain depths vary from 15 to 30 m) because the main concern was to simulate the grain deterioration in the region close to the aeration ducts of large horizontal grain storages. The airflow rates used for linear airflow (5?6 and 27?8 l s21 m23), however, were approximately the same as those used for non-linear airflow (5?5 and 27?3 l s21 m23). The grain layer thickness used for both linear and non-linear airflow distributions was determined by dividing the total grain depth (1 m for linear

124

R. SINICIO ; W. E. MUIR

airflow and 6 m for non-linear airflow) into 20 layers of equal thicknesses. Comparisons of grain moisture contents and temperatures were not necessary in the comparison of models because ASTE is a function of these variables and storage time. The deviation in ASTE between equilibrium and non-equilibrium models for each grain layer at any time was calculated as

S

DASTE 5 100 1 2

ASTEneq ASTEeq

D

(12)

where: DASTE 5 deviation of ASTE predicted by equilibrium and non-equilibrium models, %; ASTE neq 5 ASTE predicted by the non-equilibrium model, decimal and ASTEeq 5 ASTE predicted by the equilibrium model, decimal. ASTEeq was placed as denominator [Eqn (14)] because the equilibrium model

is already validated4,10 for near-ambient ventilation of stored wheat.

2.7 . Input data The recommended moisture for storing wheat in Brazil is 13% w.b.23 The standard starting date for storage was set at 1 December because the wheat harvest in Brazil normally occurs during November, December, and January.24 A 1 h time interval was used to simulate forced convection in the simulations. Standard conditions with linear airflow distribution were selected to be 1 l s21 m23 for a grain depth of 5?6 m and 5?5 bin diameter (100 t of wheat at 13% moisture content) resulting in an airflow of 0?0056 m3 s21 m22 (Table 3). The air velocity gradient

Table 3 Comparison of equilibrium and non-equilibrium mathematical models, using linear airflow distribution, determined by the maximum and average absolute deviations of ASTE , to simulate aeration of stored wheat in Brazil after 1 yr of storage Dey iation of ASTE , % Test no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Variable Standard conditions* Airflow: 0?0111 m3 s21 m22 Airflow: 0?0278 m3 s21 m22 Fan temperature rise: 08C Fan temperature rise: 38C Ventilation time: 0400 to 1000 h Ventilation time: 0000 to 0600 h Ventilation time: 1200 to 1800 h Ventilation time: 1800 to 2400 h Grain layer thickness: 2?5 cm Grain layer thickness: 10 cm Grain layer thickness: 20 cm Grain layer thickness: 100 cm Grain depth: 4 m; grain layer thickness: 20 cm; and airflow: 0?0040 m3 s21 m22 Grain depth: 8 m; grain layer thickness: 20 cm; and airflow: 0?0080 m3 s21 m22 Initial grain moisture content: 12% w.b. Initial grain moisture content: 14% w.b. Initial grain temperature: 408C Offset in the equilibrium relative humidity in the equilibrium model: 5% Same as test no. 19 and ventilation time: 1200 to 1800 h Location: Porto Alegre Location: Cuiaba´ Location: Goiaˆ nia Worst year: 1969 Storage period: 1 November 1965 – 31 October 1966

Maximum

Ay erage

51 51 44 59 49 61 64 38 57 53 49 47 38 45 46 61 40 52 37 26 47 43 49 52 52

43 44 35 45 35 48 50 23 47 44 42 40 38 15 14 53 33 45 29 13 40 27 42 45 43

* Standard conditions were used as follow unless the variable specifies otherwise: location: Curitiba; ventilation time: 0600 to 1200 h; airflow: 0?0056 m3 s21 m22; fan temperature rise: 18C; total grain depth: 1 m; grain layer thickness: 5 cm; initial grain moisture content: 13% w.b.; initial grain temperature: 308C; storage period: 1 December 1965 – 30 November 1966; and offset in the equilibrium relative humidity was not simulated in the equilibrium model.

AERATION OF WHEAT STORED IN BRAZIL

Grain

125

were tested (0?2 and 1?0 m s21). The temperature rise of the air as it passed through the fan and ducting was set at 1, 3, or 58C because axial fans add about 1 to 38C and centrifugal fans (static pressures of 1?24 to 1?73 kPa) add about 3 to 58C due to heat of compression.25

6·0 m 35° 1·7 m 0·6 m Perforated floor Plenum

3. Results and discussion

Fig. 1. Scheme of storage used to simulate grain aeration using non-linear airflow distribution

Grain temperature, °C

Grain moisture content, %, w.b.

for the non-linear airflow case was determined assuming that the air velocity was inversely proportional to the distance from the bottom of the horizontal storage (rectangular shape in plan view) with a V-shaped bottom (Fig. 1 ). Two air velocities leaving the duct

18

16

14

30 25 20 15 10 6

Allowable storage time elapsed, decimal

The average execution time for the equilibrium model, using a IBM 370, model 3090 mainframe computer at the University of Manitoba, was about 0?13 s for the simulation of one grain layer for 100 h using a 1 h time interval. The non-equilibrium mathematical model was about 25% faster than the equilibrium model. Heat and mass balance models such as the non-equilibrium model are recommended for operational research studies because they are reasonably accurate and computationally efficient.26

3.2. Changes of moisture content , temperature and ASTE

12 35

5 4 3 2 1 0

3.1 . Execution time

0

100

200

300

400

Storage period, d

Fig. 2. Moisture content , temperature , and allowable storage time elapsed (ASTE) predicted by the non -equilibrium mathematical model for wheat stored for 365 d at Curitiba , Brazil and aerated with a linear airflow distribution. , , top ; . , bottom; h , ay erage

The moisture content, temperature, and allowable storage time elapsed (ASTE ) predicted by the nonequilibrium model for 1 yr of storage at standard conditions and using linear airflow (Fig. 2 ) were similar to those obtained for non-linear airflow (results not shown). The basic differences between the two airflow conditions, besides the airflow distribution, were the grain depth and airflow range. The ASTE at 12 month for the top and bottom layers and for the average of all layers were 1?6, 5?2 and 2?4 for linear airflow distribution compared with 1?7, 9?1 and 3?6 for non-linear airflow. The deterioration was higher for the non-linear airflow because the higher air velocity in the bottom layers brought in more moisture to these layers. For the selected standard aeration conditions for Brazil the simulation results indicated that the climate should be considered humid because wetting, drying, and hysteresis conditions were predicted for 70, 20 and 10% of the time, respectively. Hysteresis conditions indicated that the grain moisture content did not change for a specific grain layer and time interval. Also, the percentage of times that the equilibrium relative humidity of the air entering any grain layer

126

Allowable storage time elapsed, decimal

was equal to or greater than 95% was 0?8%. In other words, the search technique to find the final grain moisture content given by Thompson6 was used in only 0?8% of the moisture content calculations for all grain layers. In that search technique, three equations and three unknowns (final grain moisture content, air temperature, and humidity) are solved simultaneously. Therefore, for wetting conditions, the assumption of equilibrium used in the non-equilibrium model when the equilibrium relative humidity of the air entering any grain layer was equal to or greater than 95% did not affect the predictions of moisture content by the non-equilibrium model. The equilibrium, model compared with the nonequilibrium model, over-predicted grain deterioration (ASTE ) for 12 months of storage for various air conditions and for both linear and non-linear airflow distributions (Figs. 3 and 4 ). The over-prediction of spoilage was a result of the humid climate that was used for the simulations, that is, the over-prediction of wetting in the equilibrium model was not balanced out by an over-prediction of drying. Several other researchers have also found that equilibrium models over-predict the drying and wetting rates especially in the bottom layers.27–29 The use of equilibrium models to determine the best airflow rates and fan-control methods would increase the factor of safety on the results because it gives the more pessimistic result, but on the other side, this could result in increased capital and operating costs because of over sizing of the aeration fan. The levels of grain deterioration (ASTE ) dete

10 8 6 4 2 0

0

1

2 3 4 5 Grain height above the floor, m

6

7

Fig. 4. Allowable storage time elapsed predicted by the equilibrium and non-equilibrium models as a function of grain height aboy e the floor for stored wheat aerated with air y elocities y arying from 0?018 m 3 s 22 m 22 at the top to 0?159 m 3 s 21 m 22 at the bottom for 365 d at Curitiba , Brazil . , , equilibrium at 18C fan temperature rise ; . , non equilibrium at 18C fan temperature rise; h , equilibrium at 58C fan temperature rise; j , non -equilibrium at 58C fan temperature rise

rmined in the comparison of models were above 1?5 for several cases indicating unacceptable deterioration. These high levels of grain deterioration indicated that ventilation from 0600 to 1200 h for 1 yr is not a good fan-control method. These high levels of grain deterioration, however, do not invalidate the results of the comparison of models because only the relative deviations between ASTE predicted by the models were compared. 3.3. Comparison of predictions of ASTE by the equilibrium and non -equilibrium models

10 8 6 4 2 0 0·0

Allowable storage time elapsed, decimal

R. SINICIO ; W. E. MUIR

0·2

0·4 0·6 0·8 Grain height above the floor, m

1·0

1·2

Fig. 3. Allowable storage time elapsed predicted by the equilibrium and non-equilibrium mathematical models as a function of grain height aboy e the floor for stored wheat aerated with a linear airflow distribution and 18C fan temperature rise for 365 d at Curitiba , Brazil. , , equilibrium at 0?0056 m 3 s 21 m 22 airflow; . , non -equilibrium at 0?0056 m 3 s 21 m 22 airflow; h , equilibrium at 0?0278 m 3 s 21 m 22 airflow: j , non -equilibrium at 0?0278 m 3 s 21 m 22 airflow

The comparison of equilibrium and nonequilibrium mathematical models (Tables 3 and 4) showed that the results produced by these models were significantly different when simulating aeration of stored wheat because the maximum absolute deviations of ASTE between the models were equal to or higher than 30% for all tests except for tests 20 (Table 3), and 29 and 30 (Table 4) where the maximum deviations of ASTE were 26, 29, and 22%, respectively. The comparison of mathematical models using non-linear airflow (Table 4) showed almost the same trend as shown for the linear airflow case. The deviations of ASTE , however, were less for the non-linear airflow because the air velocity range was much higher than that used for linear airflow. The deviations of ASTE between the equilibrium and non-equilibrium models changed over the years (Figs. 5 and 6 , and tests 33 and 34, Table 4) and were affected by different variables as follows.

127

AERATION OF WHEAT STORED IN BRAZIL

Table 4 Comparison of equilibrium and non-equilibrium mathematical models, using non-linear airflow distribution, determined by the maximum and average absolute deviations of ASTE to simulate aeration of stored wheat in Curitiba, Brazil after 1 yr of storage Test no. 26 27 28 29 30 31 32 33 34

Dey iation of ASTE , % ——————————————— Maximum Ay erage

Variable Standard conditions* Airflow: 0?091 – 0?796 m3 s21 m22 Fan temperature rise: 38C Fan temperature rise: 58C Ventilation time: 1200 to 1800 h Grain layer thickness: 60 cm Offset in the equilibrium r.h. in the equilibrium model: 5% Same as test no. 32 and storage period: 1 – 31 December 1965 Same as test no. 32 and storage period: 1 December 1965 to 31 October 1966

33 24 29 24 19 29 20 16 20

45 34 32 29 22 33 230 61 30

* Standard conditions as given in Table 3 except: airflow: 0?018 – 0?159 m3 s21 m22; total grain depth: 6 m; grain layer thickness: 30 cm.

Table 5 Effect of 5% offset in the equilibrium relative humidity in the equilibrium mathematical model, determined by the maximum and average absolute deviations of ASTE , to simulate aeration of stored wheat in Curitiba, Brazil after 1 yr of storage , using linear airflow distribution* Test Airflow , Fan temperature no. m 3 s 21 m 22 rise , 8C 35 36 37 38

0?0056 0?0056 0?0278 0?0278

1 3 1 3

Dey iation of ASTE , % ————————————– Maximum Ay erage 27 20 27 22

* Standard conditions as given in Table 3.

20 16 25 19

at 18C during the first 150 d of storage at 0?0056 m3 s21 m22, for linear airflow (Fig. 5 ). A similar pattern of changes for the maximum deviations of ASTE over the year was obtained for non-linear airflow when the fan temperature rise was increased from 1 to 58C (Fig. 6 ). These deviations, however, were greater for linear airflow compared with nonlinear airflow at 38C fan temperature rise. The grain under non-linear airflow showed a quicker response to climate changes because the airflow was much higher. The percentages of calculations predicting wetting,

80 Maximum deviation of ASTE, %

3.3.1. Airflow and fan temperature rise The maximum deviations of ASTE decreased when the airflow or fan temperature rise was increased for both linear (Fig. 5 ) and non-linear airflows (Fig. 6 ). These deviations decreased as the air velocity increased (tests 1, 2, and 3, Table 3 or 26 and 27, Table 4) because, as the air velocity increases, the grain moisture contents predicted by the non-equilibrium model approach the same equilibrium moisture contents that are calculated in the equilibrium model. The results produced by the equilibrium and nonequilibrium models were not significantly different for 58C fan temperature rise and ventilation time from 1200 to 1800 hrs because the differences in ASTE decreased as the airflow and the fan temperature rise were increased (tests 29 and 30, Table 4). The maximum deviations of ASTE at 38C fan temperature rise were much lower than the deviations

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Fig. 5. Maximum dey iations of allowable storage time elapsed predicted by the equilibrium and non-equilibrium mathematical models to simulate aeration of stored wheat with a linear airflow distribution at Curitiba , Brazil. , , 0?0056 m 3 s 21 m 22 airflow and 08C fan temperature rise; . , 0?0056 m 3 s 21 m 22 airflow and 18C fan temperature rise; h , 0?0056 m 3 s 21 m 22 airflow and 38C fan temperature rise; j , 0?0278 m 3 s 21 m 22 airflow and 18C fan temperature rise

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Maximum deviation of ASTE, %

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Storage time, d

Fig. 6. Maximum dey iations of allowable storage time elapsed predicted by the equilibrium and non-equilibrium mathematical models to simulate aeration of stored wheat with a non-linear airflow distribution at Curitiba , Brazil at 1 , 3 and 58C fan temperature rise. , , 18C; . , 38C; h , 58C

drying and hysteresis with non-linear airflow at standard conditions were about 66, 25 and 9%, respectively, while for a 58C fan temperature rise they were 48, 34 and 18%, respectively. Therefore, deviations in ASTE predicted by the models decreased significantly for test conditions where drying predominated (tests 8, 20, 22, 29 and 30, Tables 3 and 4). Other sets of conditions that promote drying had a similar effect as increased fan temperature rise. 3.3.2. Ventilation period Of the five 6 h ventilation periods throughout the day that were compared (tests 1 and 6 to 9, Table 3) for linear airflow the deviations in ASTE between the two models were all high except for the driest, warmest period of 1200 to 1800 h (test 8, Table 3). For example, the average absolute deviation in ASTE after 1 yr of storage was 23% for 1200 to 1800 h while for the other four time periods it varied between 43 and 50%. The maximum deviations of ASTE, however, were significant (greater than 30%) for all ventilation periods for linear airflow but not for non-linear airflow during the period 1200 to 1800 h (test 30, Table 4). 3.3.3. Grain layer thickness and grain depth For linear airflow, the deviations in ASTE decreased when the grain layer thickness was increased from 20 to 100 cm (tests 12 and 13, Table 3) while they decreased only slightly when the thickness was increased from 2?5 to 20 cm (tests 1, 10, 11, and 12, Table 3). For non-linear airflow, the deviations decreased slightly when the grain layer thickness was increased from 30 to 60 cm (tests 26 and 31, Table 4).

When the grain layer thickness was doubled the changes in the deviations of ASTE (tests 1 and 11, Table 3) were smaller than those for non-linear airflow (tests 26 and 31, Table 4). The average absolute deviations of ASTE changed significantly when the grain depth was increased to 4 or 8 m (tests 14 and 15, Table 3). These deviations decreased when the grain depth was increased because the number of times that wetting was calculated was significantly decreased. The changes in the deviations, however, were not significant between 4 and 8 m. The maximum and average deviations in ASTE decreased for tests 14 and 15 compared with test 1 because the grain layer thickness was increased and because these deviations were calculated only in the bottom 1 m for test 1 while they were calculated in the whole bin for tests 14 and 15 although a same airflow was used for all three tests (1 l s21 m23). 3.3 .4. Initial moisture content and temperature of the grain The deviations of ASTE decreased slightly when the initial grain moisture content was increased from 13 to 14% w.b. (tests 1 and 17, Table 3). The average ASTE predicted by the equilibrium model for 13 and 14% initial moisture contents were 4?3 and 4?6, respectively, while they were 2?4 and 3?0 when using the non-equilibrium model. The increased initial moisture content caused an increase in the drying calculations and a decrease in the wetting calculations which led to a decrease in the deviations of ASTE . For the same reason, the deviations of ASTE decreased when the initial moisture content was increased from 12 to 13% w.b. A change in the initial grain temperature from 30 to 408C did not affect the deviations of ASTE. 3.3 .5. Offset in the equilibrium relatiy e humidity A 5% offset in the equilibrium relative humidity in moisture adsorption in the equilibrium model decreased significantly the deviations of ASTE (tests 19, Table 3 and 32, Table 4) after 1 yr of storage for linear and non-linear airflow. Sanderson et al.4 found that a 5% offset in the equilibrium relative humidity was adequate for simulating the readsorption of water by wheat up to moisture content of 15% w.b. For readsorption to 17%, however, other modifications to the equilibrium model were needed. Therefore, it is reasonable that the non-equilibrium model is more accurate when predicting aeration of stored wheat than the equilibrium model. The models presented no significant differences for the ventilation period 1200 to 1800 h when the offset in the equilibrium relative humidity was included. Considering the results obtained by Schultz et al.30 and also considering the

AERATION OF WHEAT STORED IN BRAZIL

importance of accurately predicting wetting in the bottom of large horizontal grain storages in warm and humid climates, it is reasonable to assume that the non-equilibrium model is preferable to the equilibrium model in such conditions. The deviations of ASTE between the equilibrium model with and without a 5% offset in the equilibrium relative humidity were not significant for airflows of 0?0056 and 0?0278 m3 s21 m22 and fan temperatures rises of 1 and 38C (Table 5). These results show that a simple inclusion of an offset in the equilibrium relative humidity is not sufficient to generate a significant change in the equilibrium model. The over-prediction in ASTE , however, was greatly decreased when the offset in the equilibrium relative humidity was assumed. These results agree with those of Schultz et al.30 who stated that adsorption should be considered separately and hysteresis (no moisture exchange) must be included if the model is to accurately predict wetting. Schultz et al.30 also found that the equilibrium model over-predicted wetting while the non-equilibrium model over-predicted drying. 3.3.6. Geographical location , year of simulation , and storage period The average absolute deviation of ASTE for Cuiaba´ , which has the highest average temperature and lowest relative humidity (Table 1), where much lower than those for the other geographical locations (tests 1 and 21 to 23, Table 3). There were no significant differences among the maximum deviations of ASTE for the Brazilian locations. There was no significant difference in the deviations of ASTE simulated when comparing the median year and the worst year (tests 1 and 24, Table 3) or when the storage date was advanced 1 month.

equilibrium relative humidity in moisture adsorption calculated by the equilibrium model. The initial grain moisture content and temperature, year of simulation, or grain layer thickness less than 20 cm slightly affected the differences between the models. An error analysis of the deterioration model and results of the comparison of equilibrium and nonequilibrium models indicated that a more accurate model is needed to decrease the uncertainty in predicting wheat deterioration (Ú30%) for simulating wheat aeration. Acknowledgements We thank the Conselho Nacional de Pesquisa Cientı´fica e Tecnolo´ gica (National Scientific and Technological Research Council) of Brazil and the Natural Sciences and Engineering Research Council of Canada for their financial support. We also thank Colonel W. Gomes, Major J. Branda˜ o, and researcher J. S. Silva Filho, Instituto de Aerona´ utica e Espac¸ o (Aeronautics and Space Institute) of Brazil for providing Brazilian weather data.

References 1

2

3

4

5

4. Conclusions 6

The results produced by the equilibrium and nonequilibrium models were significantly different (P 5 0?05) when simulating aeration of wheat stored in Curitiba, Brazil for 1 yr for most test conditions. The differences in predicted grain deterioration were due to over-prediction of wetting rates by the equilibrium model especially in the bottom layers of grain near the air entrance. The differences between equilibrium and nonequilibrium models were affected by airflow rate, fan temperature rise, airflow distribution, grain layer thickness, grain depth, geographical location, ventilation time, and the assumption of a 5% offset in the

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Sinicio R; Muir W E; Jayas D S; Cenkowski S Thin-layer drying and wetting equations for wheat. Postharvest Biology and Technology 1995, 5: 261 – 275 Cenkowski S; Jayas D S; Hao D Latent heat of vaporization for selected foods and crops. Canadian Agricultural Engineering 1992, 34: 280 – 285 Nelson S O Moisture-dependent kernel-and bulk-density relationships for wheat and corn. Transactions of the ASAE 1980, 23: 139 – 143 ASAE Psychrometric data. ASAE Standard: ASAE D271.2 DEC92. In Agricultural Engineer’s Handbook. Pp. 48 – 55, St. Joseph, MI: American Society of Agricultural Engineers, 1993 Fraser B M; Muir W E Airflow requirements for drying grain with ambient air and solar heated air in Canada. Transactions of the ASAE 1981, 24: 208 – 210 CIBRAZEM Cadastro nacional de unidades armazenadoras. Companhia Brasileira de Armazenagem (Brazilian Storage Company), Brası´lia, DF, Brazil, 1985 FIBGE Levantamento sistema´ tico da produc¸ a˜ o agrı´cola. Brası´lia, Fundac¸ a˜ o Instituto Brasileiro de Geografia e Estatı´stica (Brazilian Institute of Geography and Statistics). Brası´lia, DF, Brazil, 1985 Sinicio R; Muir W E; Sanderson D B; Jayas D S Simulated fan control systems for aerated corn and wheat in Sorocaba, Brazil. Sciences des Aliments 1991, 11: 141 – 153 ASAE Moisture measurement—unground grain and seeds. ASAE Standard: ASAE S352.2 DEC92. In Agricultural Engineer’s Handbook. Pp. 449, St. Joseph, MI: American Society of Agricultural Engineers, 1993 Omega The 1986 temperature measurement and control handbook. Stamford, CT: Omega Engineering, 1986

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