Forced convective drying of willow chips

Biomass and Bioenergy 19 (2000) 259–270

Forced convective drying of willow chips J.K. Giglera; ∗ , W.K.P. van Loonb , M.M. Vissersb , G.P.A. Bota; b a Institute

b Department

of Agricultural and Environmental Engineering, Wageningen, The Netherlands of Agricultural, Environmental and Systems Technology, Wageningen University, Bomenweg 4, 6703 HD Wageningen, The Netherlands

Received 1 September 1999; received in revised form 8 June 2000; accepted 9 June 2000

Abstract The forced convective drying process of willow chips was described with a deep bed drying model. The model was validated experimentally for bed moisture content, air temperature and relative humidity, and adequately described ambient air drying of a 1 m deep willow chip bed. At the top layers of the chip bed, the model overestimated the drying rate due to vapour condensation which was not incorporated into the model. However, the drying model was an appropriate tool to gain insight into the forced convective drying process of willow chips. The drying costs of willow chips using farm facilities for storage and drying of potatoes were assessed, based on average monthly weather data. March to September was the most suitable period for drying due to favourable ambient weather conditions. In this period, energy costs for drying from a moisture content of 1–0:18 kg (water) kg−1 (DM), which corresponds to 50% (wet base) to 15%, ranged from 12 to 25 c 2000 Elsevier EURO t−1 (DM), or from 28 to 59 EURO t −1 (DM) when investment costs were partly accommodated. Science Ltd. All rights reserved. Keywords: Forced convective drying; Deep bed PDE model; Willow chips; Costs

1. Introduction Replacing fossil fuels by biomass reduces CO2 emissions. In this perspective, short rotation coppice willow (Salix viminalis) gains increasing interest as a biomass fuel. Besides, growing willow can be an additional source of income for farmers. At harvest, the moisture content of willow is approximately 1 kg (water) kg−1 (DM) which corresponds to 50% (wet base). If willow is harvested as chips which is ∗

Corresponding author. Present address: Massey University, Institute of Technology and Engineering, Private Bag 11 222, Palmerston North, New Zealand. Tel.: +64-6-350-4357; fax: +64-6-350-5640. E-mail address: [email protected] (J.K. Gigler).

a common harvest technique, drying can be advantageous because: • a lower moisture content enables long term bulk storage of willow chips with low microbial activity, and thus low dry matter losses, and reduced health risks [1–3]; • a lower moisture content increases conversion eciency of willow into electricity and reduces gaseous emissions [4,5]. To reduce the moisture content of willow chips, farm facilities for potato storage and drying could be used during periods that these facilities are not used for potatoes. These facilities have a large capacity, are easily accessible, and equipment for handling and

c 2000 Elsevier Science Ltd. All rights reserved. 0961-9534/00/$ - see front matter PII: S 0 9 6 1 - 9 5 3 4 ( 0 0 ) 0 0 0 3 7 - 4

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Nomenclature a ath A cpa ; cv ; cw ; cwo C Ct;L Da De ; D0 DM h hv H k L M t Ta Two v V x; X     a a;i ; a;b wo Asp = 1− L Dp = 6V A e m = CC−C 0 −Ce U = Asp

empirical diusion exponent, dimensionless thermal diusivity, m2 s−1 area, m2 speci c heat capacity of air, water vapour, water and wood, respectively, J kg−1 K −1 water concentration in the chip, kg m−3 water concentration at the surface of the wood chip, kg m−3 diusivity of water in air, m2 s−1 eective and initial diusivity of water in wood, respectively, m2 s−1 dry matter height of the chip bed, m heat of desorption of water, J kg−1 water concentration of air, kg (water) kg−1 (dry air) mass transfer coecient, m s−1 diusion distance (half the smallest chip dimension), m average moisture content of wood, kg (water) kg−1 (DM) time, s air temperature, K wood temperature, K air velocity, m s−1 volume, m3 space coordinates in a single willow chip and in a chip bed, respectively, m heat transfer coecient, W m−2 K −1 bed porosity, dimensionless thermal conductivity, W m−1 K −1 dynamic viscosity, kg m−1 s−1 air density, kg m−3 water concentration of air at the wood surface and in the bulk, respectively, kg m−3 wood density, kg (DM) m−3 speci c surface area, m−1 equivalent particle diameter, m moisture concentration, dimensionless bed heat transfer coecient, W m−3 K −1

 Nu =  p 1− c Pr = pa

Nusselt number, dimensionless Prandtl number, dimensionless

Re =

Reynolds number, dimensionless

D

va Dp (1−) s2 R2adj = 1 − smod 2 data

2 2 fraction of variance accounted for, with sdata the data variance and smod the model variance, dimensionless

drying of potatoes can be used for chips. Using farm facilities for willow chip drying can be economically interesting: multiple use of facilities and equipment means that the xed costs can be shared by dierent

products, which can increase the overall pro tability for the farmer [6]. However, it is not known to which extent the ventilation equipment for potatoes is suited for willow chip drying. To evaluate the use of farm

J.K. Gigler et al. / Biomass and Bioenergy 19 (2000) 259–270

facilities for potatoes and the associated costs, drying and pressure drop characteristics of willow chips and average fan characteristics should be combined. The drying process of a product can be predicted with appropriate drying models given product mass, product drying characteristics and drying air conditions. During a drying process, two periods can be distinguished [7]. In the rst so-called constant drying rate period, mainly external water attached to the product is removed. In the second so-called falling drying rate period, internal diusion of water to the surface of the product takes place. To describe the drying process in a product bed, dierent types of models exist [8–12]. Of these models, partial dierential equation models (PDE models) have a good physical basis. Nellist [13] described the drying process of willow chips with a PDE model, but the water balance of chips was described with an empirical relation (Page’s equation). Nellist validated the deep bed model experimentally at dierent constant air temperatures, for chip bed temperature and moisture content. The disadvantage of an empirical drying equation is that many drying experiments at dierent air conditions are necessary to describe the drying characteristics at dierent external conditions. If the water balance is based on physical parameters, e.g. a diusion model, the effect of dierent external conditions can more easily be accommodated [14]. The main objectives of the current study are: 1. to provide a deep bed drying model for willow chips suited for varying drying air conditions which is calibrated with experimental data; 2. to assess the technical possibilities and the associated costs of drying willow chips with farm facilities for potatoes.

2. Theory 2.1. Deep bed drying model For deep bed drying, PDE models have been described extensively for grain [8,9,15 –18]. A PDE model contains four coupled balance equations describing water and energy balances of both product and drying air. Moisture and temperature gradients in product and air are accounted for. The main assump-

261

tions of the deep bed models were summarised by Sun et al. [18]. For willow chips a detailed explanation of a deep bed drying PDE model is given hereafter. For drying air, the simpli ed mass or water balance is based on the assumption that water, evaporated by the wood [left-hand part of Eq. (1)], is taken up by the drying air (right-hand part): @H @M = −wo : (1) @X @t The simpli ed energy balance of the drying air describes the change of the enthalpy of the air [left-hand part of Eq. (2)] which is equal to the heat necessary to increase the temperature of evaporated water from wood to air temperature, and the heat transfer from air to wood: @Ta va (cpa + cv H ) @X va

@M − U (Ta − Two ): (2) @t The energy balance of the wood describes the change of the enthalpy of the wood which is equal to the heat needed for evaporation of water and the heat transfer from the air to the wood: @Two @M = wo hv + U (Ta − Two ): wo (cwo + cw M ) @t @t (3) =wo cv (Ta − Two )

In our approach, @M=@t represents the water transferred from the chip surface to the drying air. This water has to diuse from the interior of the chip to the surface, which can be described by a diusion model for a plane sheet [14,19]:   @ @C @C = De : (4) @t @x @x The average moisture concentration of a willow chip is equal to wo M . One initial and two boundary conditions are necessary to fully describe the internal diusion process of a chip. The initial condition describes that the initial moisture concentration of a willow chip is homogeneous. The rst boundary condition describes symmetry around the centre of the chip which means that water diuses from the centre of the material to the outside (shortest way) without passing through the centre. The second boundary condition describes the mass transfer of moisture to the air: the diusive ux at the edge (x = ±L) of a willow chip is

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equal to the dierence in air moisture concentration at the surface of the wood a; i and in the drying air a; b , multiplied by the mass transfer coecient k: @Ct; L = k(a; i − a; b ): (5) @x All possible contributions to internal moisture transfer are lumped into one eective diusivity De for the willow chip. The eective diusivity is described with a simple algebraic function of the dimensionless moisture concentration m [20,21]:

t ¿ 0;

x = ± L;

−De

De = D0 ma ;

(6)

where D0 and a are tted parameters. The heat transfer coecient  can be calculated with an empirical relation for Nu = f(Re; Pr) for a packed bed [22]: Nu = (0:5Re0:5 + 0:2Re0:67 )Pr 0:33 :

(7)

The mass transfer coecient k can be calculated from the heat transfer coecient according to [7]:  0:67 ath  = a cpa : (8) k Da The sorption isotherm which describes the relation between the water activity aw (which corresponds to the relative humidity) and the equilibrium moisture content is described with a Modi ed–Halsey equation [23]: aw = exp(ÿ1 M ÿ2 )

for M ¿ 0:

(9) ◦

At constant air temperature (Ta = 20 C); ÿ1 and ÿ2 are −0:017 and −1:6794, respectively. The drying model of a deep bed of willow chips is represented by Eqs. (1) – (9). 2.2. Pressure drop characteristics During forced drying, the air pressure drop over a product bed determines the volume ow of air through the bed for a given fan [24]. For reasons of simplicity, an empirical relation can be used for the pressure drop:
P = hk1 v k2 ;

(10)

where k1 and k2 are tted parameters which depend on the size and shape of the willow chips. The tted parameters can be determined from experimental data. Gustafsson [25], Kofman and Spinelli [26] and Nellist [13] derived values of the tted parameters of Eq. (10) for wood chips. In the size range 10–25 mm,

the average values of the tted parameters are k1 = 1; 755 and k2 = 1:67. When the characteristics of drying and pressure drop in the product, and the drying air conditions are known, for a given fan the drying time can be determined, as explained in Section 3. 3. Materials and methods 3.1. Willow material For the thin layer and deep bed drying experiments, dierent batches of chips were produced from 4 year old willow stems (Salix viminalis) with a mobile chipper (Schliesing 660ZX). The particle size distribution of the chips was determined by sieving [27]. In total seven batches of 5 kg each were sieved for 2 min. Chip dimensions were measured with a calliper-square for 50 chips taken at random from the two predominant sieving fractions. The moisture content was de◦ termined by drying at 105 C for 72 h [28]. Chip size, diusion distance (de ned as half the smallest chip dimension) and particle size distribution of the thin layer and deep bed drying experiments were in the same order of magnitude (Table 1), but on average, the chips of the thin layer drying experiments were slightly larger. Of both chips sizes, more than 80% of the total mass was within the size class 0.5 –2 cm. The values of the tted parameters of Eq. (6) were determined as D0 = (3:0 ± 1:0) × 10−10 m2 s−1 and a = 0:3 ± 0:1 [14]. 3.2. Drying equipment Thin layer drying experiments: The drying equipment consisted of a series of baskets with perforated bottoms. From below, drying air with constant rel◦ ative humidity (60%) and temperature (20 C) was blown through the baskets which were lled with willow chips. The super cial air velocity varied between 0.1 and 0:2 m s−1 . The baskets were weighed continuously on load sensors which sampled automatically at pre-set times [14]. Four baskets contained a chip layer of 1 cm and four baskets contained a layer of 8 cm. The drying curves of the 1 and 8 cm layers were determined by taking the average of four repetitions. Deep bed drying experiment: The deep bed drying equipment consisted of four commonly used potato

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Table 1 Characteristics of the willow chips Characteristics (10−3 m)

Length Width (10−3 m) Height (10−3 m) Diusion distance L (10−3 m) Equivalent particle diameter Dp ; (10−3 m) Initial moisture content, kg (water) kg−1 (DM) Particle size distributiona a

Thin layer

Deep bed

17:1 ± 2:3 11:0 ± 3:8 5:1 ± 1:8 2:6 ± 0:9 8.7 0:78 ± 0:03 ¿ 80%

13:3 ± 7:1 8:8 ± 4:2 4:5 ± 2:2 2:3 ± 1:1 7.3 0:75 ± 0:02 ¿ 80%

% of total weight in the range 0.5 –2.0 cm.

• super cial velocity of the air (hot wire anemometer Schmidt SS20.011), approximately 10 cm above the top chip layer. Before and after drying, samples were taken to determine the average initial and nal moisture content. The moisture content as a function of time was calculated from the weight loss during drying. The drying experiment started at March 20, 1998 at 3 PM. 3.3. Mathematical solutions of the drying equations Fig. 1. Side view of the large-scale drying equipment.

boxes with dimensions 1:05 × 1:35 × 1 m3 (l × w × h) which had closed side walls and perforated bottoms. The bottom of each box had an open pallet-like construction which enabled a draught of drying air through several boxes in a row simultaneously (see Fig. 1). The boxes were put on a rectangular metal frame which was supported by four load sensors with a range of 1000 kg (HBM, 10 kN). The boxes were lled with willow chips and ambient air was forced through by a fan. The following data were recorded every 600 s (data logging unit Datataker DT500): • total weight of the boxes (load sensor); • temperature (PT100 sensor) and relative humidity (rotronic sensor) of incoming ambient drying air; • temperature and relative humidity (rotronic sensor) of the air in the box closest to the incoming air at a height of 0:2; 0:4; 0:6; 0:8 and 1 m; • mean temperature at the centre of all boxes (thermocouples);

The diusion equation was solved numerically by discretisation with the nite dierence method of Crank–Nicolson [19]. The deep bed drying model was solved with an Euler forward nite dierence method [19]. The product bed was assumed to be divided into several thin layers. The outlet conditions of one layer were used as the inlet conditions of the layer above. Each layer was assumed to be uniform in moisture content and temperature [8]. Drying models were programmed in MATLAB [29]. The input parameters of the models were temperature, relative humidity and velocity of the drying air and the material characteristics (diusivity, chip dimensions, initial bed moisture content and temperature). Output parameters were moisture content and temperature of the chip layers, and temperature and relative humidity of the drying air. The deep bed drying model was calibrated on the experimental data by the following tted parameters: • air velocity v in the bed because only the super cial velocity of the air was measured;

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• bed heat transfer coecient U = Asp :  was approximated with a Nu relation which generally has an accuracy of ±25%; Asp was calculated assuming that all chips in the bed fully contributed to the speci c surface area, but in reality Asp will be smaller due to mutual overlap [22,30]; • chip size L, to comply with the range of the measured average chip size. The 1 cm chip layer was used to calibrate the deep bed model on the experimental data. The following procedure was adopted: 1. By varying air velocity v and the bed heat transfer coecient Asp , the deep bed drying model was calibrated on the experimental data during the constant drying rate period to t the slope of the drying curve. External conditions limit the drying process in the constant drying rate period. The fraction of variance accounted for, R2adj , was determined for dierent combinations of v and Asp . 2. With v and Asp xed, chip thickness L was used to calibrate the drying model on the experimental data during the falling drying rate period. In this period, the material characteristics limit the drying process. Step 1 and 2 were repeated with the new tted value for L until the optimal combination of all parameters was found. For the 8 cm chip bed the values of chip thickness L and Asp from the t procedure for a 1 cm bed were used. Only air velocity v was varied to t the model on the experimental drying data because the measured velocity of the air in the drying equipment varied between 0.1 and 0:2 m s−1 . The nal values of the tted parameters for the model simulations were selected by estimating the median from the values matching the criterion R2adj ¿ 0:995: This criterion was used to limit the range of valid tted parameters because these were not very sensitive to small changes. 3.4. Drying with farm facilities Agricultural facilities for potato storage and drying dier between countries. In this paper, calculations are presented for the typical situation in the Netherlands where the average potato store is for 800 t or

1230 m3 of potatoes at a storage height of 3.5 m. In potato stores, usually axial fans are installed which have reasonable plane fan characteristics (slowly decreasing pressure drop at higher air ows). Ventilation equipment is usually designed for an air ow of 100 m3 (air) m−3 (product) h−1 at a pressure drop of 150 Pa with an average capacity of approximately 25000 m3 (air) h−1 per fan. Generally, the pressure drop of the air distribution equipment is 100 Pa [31,32]. For many agricultural and wood products, as a rule of thumb a moisture content below 15 –20% (wet base) or 0.18– 0.25 kg (water) kg−1 (DM) is regarded as safe for long-term storage without the risk of microbial degradation [25]. Here, for willow, it was assumed that the initial moisture content (at harvest) is 1.0 kg (water) kg−1 (DM) and the target moisture content after drying is 0.18 kg (water) kg−1 (DM). It was assumed that drying air leaves the chip bed always fully saturated. The following methodology was adopted to calculate the costs of forced convective drying of willow chips: 1. given the Dutch average monthly ambient RH and air temperature, the amount of water the air can take up to reach full saturation at wet bulb temperature was calculated for each month [33]; 2. from characteristics of an average fan (type: DLM10), the pressure drop in potatoes at dierent air ows was determined [34]; 3. for several combinations of pressure drop and air ow for potatoes, the maximum height at which willow chips can be stored in a potato store and the associated quantity of chips were determined; the pressure drop of the chips was calculated with Eq. (10); 4. for dierent chip quantities, the total volume of air necessary to evaporate all water and the consecutive drying time were calculated; 5. costs of farm facilities were determined and the share made speci cally for willow was calculated [6]; 6. from the pressure drop and the total amount of air needed, fan energy consumption was determined [25]; 7. facility and energy costs were added to determine the total costs necessary for dierent chip bed heights in dierent months [6].

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265

Table 2 Fraction variance accounted for by dierent combinations of the tted parameters Asp and v for the 1 cm willow chip bed (bold: combinations according to selection criterion R2adj ¿ 0:995; underlined: combination selected for model simulation) Asp (W m−3 K −1 )

v (m s−1 )

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30

— — — — — — — — — — — 0.802 0.827 0.852

— — — — — — 0.954 0.968 0.978 0.985 0.989 0.993 0.995 0.996

— — — 0.970 0.985 0.992 0.996 0.998 0.998 0.998 0.998 0.998 0.997 0.997

— — 0.984 0.994 0.998 0.998 0.998 0.997 0.997 0.996 0.995 0.994 0.994 0.993

0.933 0.983 0.996 0.998 0.998 0.997 0.996 0.995 0.994 0.993 0.993 0.992 — —

0.964 0.993 0.998 0.998 0.997 0.996 0.994 0.993 0.993 0.992 — — — —

0.980 0.997 0.998 0.997 0.996 0.994 0.993 — — — — — — —

0.988 0.998 0.998 0.996 0.995 0.994 — — — — — — — —

0.992 0.998 0.997 0.996 0.994 — — — — — — — — —

Table 3 Fraction variance accounted for by tted parameters L for the 1 cm willow chip bed (bold: combinations according to selection criterion R2adj ¿ 0:995; underlined: combination selected for model simulation)

Table 4 Fraction variance accounted for by tted parameter v for the 8 cm willow chip bed (bold: combinations according to selection criterion R2adj ¿ 0:995; underlined: combination selected for model simulation)

Fitted parameter L (×10−3 m)

R2adj

Fitted parameter v (m s−1 )

R2adj

2.5 2.6 2.7 2.8 2.9 3.0 3.1

0.985 0.993 0.998 0.998 0.996 0.989 0.979

0.14 0.15 0.16 0.17 0.18 0.19 0.20

0.982 0.993 0.998 0.999 0.998 0.994 0.989

4. Results and discussion 4.1. Drying experiments Thin layer drying experiments: The tted values of the 1 cm chip bed which were selected from Tables 2 and 3 for model simulation were (con dence intervals given for completeness): v = 0:12 ± 0:04 m s−1 , (Asp ) tted = 0:5 ± 0:3 × (Asp )calc and L = (2:8 ± 0:1) × 10−3 m. The tted value of Asp was 50% of the calculated value. This dierence was due to the low accuracy of the Nu number (±25%), and the fact that relations for Nu numbers for packed beds are signi cantly lower for shapes like cubes

compared to spherical objects [22]. Furthermore, the eective speci c surface area in the chip bed is considerably reduced due to mutual overlap [22,30]. The tted value of diusion distance L was within the range presented in Table 1. For the 8 cm chip layer, the tted value for the super cial velocity of the air was v = 0:17 m s−1 (±0:01; Table 4) which is about the same as the tted values for the 1 cm chip bed. Fig. 2 shows that a good t was achieved between the simulated and experimental drying curves. Deep bed drying experiment: The total quantity of willow chips in this experiment was 1440 kg. It was assumed that during drying only moisture was lost and that the total quantity of dry matter remained

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Fig. 2. Simulated (—) versus experimental drying curves for willow chips for a chip bed of 1 cm (•) and 8 cm (4).

Fig. 3. Measured relative humidity (top) and temperature (bottom) of the ambient air and in the 1 m chip bed at dierent heights (0.2–1 m). IN represents incoming air conditions.

constant. Fig. 3 (top) shows the relative humidity (RH) of the ambient air (IN) and the RH in the chip box at dierent heights (from 0.2 to 1 m) as a function of time (h). Because the RH indicated values larger than 100%, RH-data were corrected for measurement errors by subtracting the amount above 100% from the whole dataset for each RH sensor. The drying air left the chip bed fully saturated until the equilibrium moisture content (EMC) was (nearly) reached. The progression of the drying front through the chip bed can be clearly observed by a sharp drop of the RH to the ambient RH (for instance, Fig. 3 at ca 24 h, 0.2 m) which indicates that the part of the chip bed under the sensor was (nearly) at EMC. The willow chip bed reached its lowest moisture content after ca

124 h. The velocity of the drying front was not constant as indicated by the varying time pattern of the drying fronts as well as by the slope of the RH-curve when the drying front passes. This variation is due to variations of the ambient RH and temperature: at low RH (0.2 m) the drying front moved faster than at high RH (0.4 m). Between a height of 0.8 and 1 m, the drying front slowed down despite the low RH of the ambient air which was caused by vapour condensation in the top layers. Fig. 3 (bottom) shows the ambient air temperature and chip bed temperature at dierent heights in the chip box. The air temperature rises from wet bulb to ambient air temperature (indicated by circles) after the drying front has passed which is in accordance with the pattern of the RH graph. In Fig. 4 the day-night rhythm of the RH and temperature can also be observed. Fig. 4 (top) shows the measured and simulated average moisture content of the willow chip bed as a function of time. The simulated moisture content at 124 h, 0.10 kg (water) kg−1 (DM), was in accordance with the measured nal moisture content of 0:11 ± 0:01 kg (water) kg−1 (DM). The air velocity used for the simulations was 0:55 m s−1 which is plausible because the measured super cial air velocity was in the range of 0:3 m s−1 . The drying model adequately described the experimental drying curve except for the time interval 90 –120 h. In Fig. 4 (middle), the simulated and measured RH is shown. At a height of 0:2; 0:4; 0:6 and 0.8 m, the drying model successfully described the measured RH. Small dierences are probably due to inaccuracies with respect to the position of the RH-sensors in the chip bed. However, at 1 m the model predicted a much higher drying rate than the measured rate. Due to vapour condensation in the top chip layers, the drying rate was overestimated here because condensation was not incorporated into the model. Condensation can be explained as follows. The chip bed temperature followed the ambient air temperature but with some time delay. At ca 110 h, the temperature of the ambient ◦ air rose from 5 to 19 C. Because the temperature rise in the chip bed was slower, the drying air was cooled while going through the chip bed. In the top layers the drying air met the colder part of the bed which was the last part to be heated by the air and consequently condensation occurred. This phenomenon occurred especially around 110 h because then the temperature

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267

•

Fig. 4. Measured (4; ) and simulated (—) chip bed moisture content (top), relative humidity (middle) and temperature (bottom) of the ambient air at dierent heights (0.2–1 m) in the chip bed. IN represents incoming air conditions. ◦

dierence was large (14 C). However, even without incorporation of condensation into the drying model, the model predicted the drying process adequately. In Fig. 4 (bottom), the bold line represents the ambient air temperature. At 0.2 and 0.6 m, the simulated air temperature adequately describes the measured temperature. As discussed before, at 1 m there is no agreement between the simulations and measurements due to the fact that condensation was not incorporated into our drying model.

4.2. Possibilities of drying willow chips in a potato store The costs of drying willow chips in a potato store were time dependent (Fig. 5) because in dry months, the amount of air needed to evaporate a certain amount of water was smaller than in wet months. The storage height had little eect on drying costs: the drying time increased with storage height but the higher costs were largely compensated by a higher chip volume.

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Fig. 5. Energy costs (- - -) and total costs (—) of forced convective drying of willow chips in a potato store at dierent storage heights. The dashed window indicates the period which is focussed on.

From September until February (in some cases even for a longer period), a potato store is normally used for potatoes and, thus, not available for chip drying. However, this period is economically not interesting due to unfavourable drying air conditions (Fig. 5). The evaluation is focused on the period from March to September. Energy costs for fan electricity varied from 12 to 25 EURO t−1 (DM). The drying time varied from 21 to 100 days at a storage height of 1.1 m and more than 4 m, respectively. The energy consumption ranged from 348 kWh t−1 (DM) in March, and 250 kWh t −1 (DM) in April, to 193 kWh t −1 (DM) from May until August. Total costs, which include energy costs and investment costs for the share that facilities are used for chips, ranged from 28 to 59 EURO t−1 (DM). Energy costs were on average 44% of the total costs. The overall pro t of all activities determines the total farmer’s income so it seems more realistic to assign only energy costs to willow chips. Fig. 5 also shows that May to August was most pro table for drying but then, the period between harvest (November to March) and drying is at least 1 month which causes additional handling and intermediate storage problems, such as DM-losses and self heating. Thus, in reality drying costs will probably be close to costs in March which is 25 EURO t −1 (DM). The cost calculations were based on assumptions with respect to initial and target moisture content, technical possibilities, costs, weather conditions et cetera. However, a smaller chip size (¡ 10 mm) increases

the pressure drop and, thus, cause higher drying costs. A lower initial or higher target moisture content will decrease the drying costs. From October to March, drying times of up to 300 days were calculated because it was assumed that drying took place with the drying air conditions of one particular month. However, the period October to March was not focused on. For the other months, the error due to this assumption was small because drying air conditions do not vary as much as from October to March. The calculations attempt to indicate the order of magnitude of the drying costs. Handling costs for lling and emptying the potato store were not incorporated but they will increase the total drying costs. The calculations show that drying costs for willow chips using agricultural facilities can be considerable compared to, for example, harvest costs [12–14 EURO t−1 (DM)] and, thus, can become a considerable cost factor in the supply chain [14]. 5. Conclusions A PDE deep bed drying model was designed to describe forced convective drying of willow chips. The model was validated experimentally for bed moisture content, air temperature and relative humidity. It adequately described ambient air drying in a 1 m willow chip bed. Drying air left the chip bed constantly saturated until the chips were (nearly) at equilibrium

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moisture content. A sharp drying front was observed in the chip bed. At the top layers of the chip bed, the drying rate was overestimated due to vapour condensation which was not incorporated into the model. The energy costs of drying willow chips at farm facilities for potato storage and drying were time dependent and ranged from 12 to 25 EURO t−1 (DM). March to August was the most suitable period for drying due to favourable ambient weather conditions. Drying costs were hardly in uenced by storage height. If investment costs of the facilities were assigned to willow during use for willow, costs ranged from 28 to 59 EURO t −1 (DM). The costs of continuous forced convective drying of willow chips using farm facilities became a considerable factor in the total costs of the supply chain compared to, for example, harvest costs. The drying model is an appropriate tool to gain insight into the forced convective drying process of willow chips. However, the model showed that drying times for willow chips can be calculated with a simple approach, which assumes that drying air leaves the chip bed always fully saturated at wet bulb temperature. Acknowledgements The authors thank the Dutch Ministry of Agriculture, Nature Management and Fisheries for nancing this research (Research Programme 255, Energy from biomass), A. Saye (Wageningen University), Dr. I. Seres (Godollo University of Agricultural Sciences), C. Sonneveld (IMAG) and the personnel of the experimental farm ‘Oostwaardhoeve’ at Slootdorp, for their assistance with the experimental and modelling work. The valuable comments by Dr. W.J. Coumans (Eindhoven University of Technology), Dr. G. Meerdink (Wageningen University) and Dr. H. Breteler (IMAG) were highly appreciated. References [1] Gjolsjo S. Comparative studies on storage and drying of chips and chunks in Norway. In: Production, storage and utilization of wood fuels, Proceedings of IEA=BE Conference Task III, 6 –7 December, Uppsala, Sweden, vol. II. Swedish University of Agricultural Sciences, Garpenberg, Sweden, 1988. p. 47–71.

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