n Short Communication 419

Ckmometrics and Intelligent Laboratory Systems, 14 (1992) 419-422 Elsevier Science ~blishers B.V., Amsterdam

A drying model for hygroscopic porous material

Kari Hillebrand * , Markku Kallio and Pertti Frilander

~o~b~t~n and peril E~~nee~g gyrator, Te~hn~al Research Centre of Fade, P.0. Box 221, SF-401 01 Jyuiiskylii (Finland]

(Received 20 June 1991; accepted 1 October 1991)

Abstract

Hillebrand, K, Kallio, M., and Frilander, P., 1992. A drying model for hygroscopic porous material. Chemornetricf and Intelligent Laboratory Systems, 14: 419-422.

A drying model was developed to simulate the drying of hygroscopic porous material in a soil-residue-atmosphere system. An experimental plan for controlling the five climate condition variables and four material variables in 35 different experiments was set up. The results obtained were analyzed by multivariate modelling software. The calculations were made with partial least squares regression. Besides the initial moisture content and the residue loading rate, other variables in the drying model are: solar radiation, air temperature, relative humidity, average wind speed, average particle size of the residue, and the number of times the residue is turned. The predicted drying times calculated from the model are in good agreement with the experimental results.

INTRODUCIION

The drying of moist porous solids involves si- multaneous heat and mass transfer in a multi- phase system. Several theoretical models have been proposed in the study of drying processes D-31, many of the approaches being limited to very specific applications. There has been consid- erable interest in describing the dynamic aspects of mass and energy transfer under various envi- ronmental conditions through one or more parts of the soil-plant (residue&atmosphere system [4]. The drying of fuel peat is especially difficult due to the inhomogeneous nature of the material, the coupling of the surface residue (layer of peat) to the soil-atmosphere system and the large number of independent factors influencing the drying rate. The transport of moisture in peat is caused by a variety of mechanisms, each of which

is prevalent under different conditions. The local moisture content, the temperature and the hygro- scopic properties of the material influence the contribution of each mechanism and conse- quently affect the drying rate. The drying of peat has been studied by Antonov et al. [5] and JPrvinen 161. In the drying model developed by Antonov and co-workers [S], the weather condi- tions are grouped into one single variable, evapo- ration, which clearly restricts the study of the effect of different variables on drying.

Numerical solutions require a large amount of precise information about the phenomenon of drying peat, which is often unknown. A more reliable procedure is therefore to simulate natu- ral conditions, both weather and field conditions, in a special drying chamber. Our objective is to develop a drying model for fuel peat including explicitly all the weather and field variables in the

0169-7439/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

420 Chemometrics and Intelligent Laboratory Systems n

experimental design and multivariate data analy- sis. In this way, the effect of different variables on the drying behaviour can be determined sepa- rately.

EXPERIMENTAL METHOD

The drying experiments were performed in a special drying chamber under constant climatic conditions. The parameters of the drying process were measured by a microcomputer, and mois- ture samples of the drying layer were taken at certain time intervals. The surface residue was a thin layer of milled peat (Carex, H7-H8 von Post) with a uniform horizontal distribution and the residue loading rate was 2-5 kg/m2 (20-40 mm thick).

A minimum-correlated stochastic plan (not or- thogonal) was drawn up for controlling the five climate condition variables and four material variables in 35 different experiments. A three- level design was used for seven variables and a two-level design was used for the remaining two variables. The correlation coefficients between the factors (partial least squares (PLS) model) are shown in Table 1. The effect of the different drying factors was used to form the basis for a statistical model for the drying time of the residue from the initial moisture content of 3-4 kg/kg (7580%) to the final moisture content of 0.67 kg/kg (40%).

RESULTS AND DISCUSSION

The drying experiments were carried out in a Altogether, 35 different drying experiments weather and field condition simulator, allowing were performed, of which four experiments were the effect of field factors, weather factors and duplicated and two were extreme point experi- peat factors on the drying of peat to be studied. ments. Ten variables were measured, one Y (time) The simulation apparatus consisted of a solid and nine X variables. The drying results were peat block with a certain ground water level, a analyzed by principal component analysis (PCA) layer of milled peat (Carex, H7-H8 von Post) on and PIS 17-91. Before the PI_8 analysis the data the block and a drying chamber with variable were scaled to unit variance (autoscaling) and climatic conditions. The following conditions mean-centered. In the score plot of the first and could be changed: solar radiation, air tempera- second principal components the objects were ture and humidity, wind speed, and ground water spread evenly, without any clear groups. The level and temperature. The simulator was con- dominant variables for the position of the score trolled by a microcomputer and all the informa- points were the residue loading rate and solar tion concerning drying and other environmental radiation, especially for greater residue loading conditions were logged by the computer. rates. Two other important variables were the

TABLE 1

Correlation coefficients between the different factors

UO

P d 50

R RH T, V, k

UO

(kg/kg)

1.00

-0.05 0.06 0.01

-0.12 0.00

-0.11 -0.19

Pkg/m?

- 0.05 1.00 0.21 0.00 0.32 0.00

-0.11 0.12

4, R (mm) (W/m*)

0.06 0.01 0.21 0.00 1.00 - 0.06

- 0.06 1.00

0.18 0.07 -0.18 0.01 -0.11 0.14 -0.12 0.04

-0.12 0.32 0.18 0.07 1.00 0.04 0.04

-0.05

T, V, (“Cl (m/s)

0.00 -0.11 0.00 -0.11

-0.18 -0.11 0.01 0.14 0.04 0.04 1.00 0.24 0.24 1.00

- 0.01 0.22

k

-0.19 0.12

-0.12 0.04

- 0.05 - 0.01

0.22 1.00

n Short Communication 421

initial moisture content and the particle size d,, (Fig. 1). The use of these four variables gave a drying model which is simpler and almost as accurate as the model using all the measured variables.

The final drying model (PLS model) was con- structed using eight X variables. Ground water level ( -0.3 and -0.6 m) was rejected. All 35 experiments were used to construct the model. Because the drying process is a nonlinear phe- nomenon, a power model was made. The drying model formula, with the variabIe limits for which it is vafid, is

t = e5.88

u 1.58~ 1.32~ 02.5 0

R0.88T0.24d~~2:‘ij0.053k0.19 a a

1

0.5

0

(1)

where t = residue drying time, h; U. = initial moisture content, 1.6-3.1 kg/kg; P = residue loading rate, 2.0-5.0 kg (dry solids)/m2; ZVI = relative humidity, 40-75%; R = solar radiation, 3~-7~ W/m*; T, = air temperature, 15-25°C; d,, = average particle size, 7-15 mm; U, = average wind speed, l-3 m/s; and k = number of turn- ings, 1 or 2.

The drying model was constructed by PLS using two factors and validated using cross-valida- tion. The third principal component will explain very minor additions to the unexplained part of the experimental data. Several other models were constructed, but the best results were achieved by the model given by Eqn. 1. When the measured and predicted drying times are compared, R* is 94% for the 35 experiments. When the residuals

INITIAL &ISTlJRE CONTENT

WIND SPEED*

PARTiCLE SIZE

0 0.5 1

Fig. 1. Loading plot between X and Y variables. The data are standardized to unit variance and mean-centered. The most important variables are initial moisture content, residue loading rate, solar radiation and average particle siz.e d,.

422 Chemometrics and Intelligent Laboratory Systems 8

2 25 3 3.3 4 I.5 5

RESIDUE LOADING RATE, kg (dr.Enn?

Fig. 2. Drying time as a function of residue loading rate at different solar radiation values. The curves have been calcu- lated using Eqn. 1 with the other variables constant (initial moisture content, 3.0 kg/kg; relative humidity, 50%; air tem- perature, 20°C; average particle size, d,,, 8 mm; wind speed, 2 m/s; number of turnings, 2). Solar radiation: (0) 300, (II) 500, (*I 700 W/m2.

are examined, the biggest errors are found to be for long drying times, which means that the vari- ance is not constant. On the other hand, the group of experiments with long drying times was small.

The model can be used to study the effect of different variables on the drying time of the milled peat layer. According to the model, the most important variables for the drying rate are the specific loading rate, the initial moisture content of the peat, solar radiation and the average parti- cle size. Doubling the specific loading rate or the initial moisture content wifl increase the drying time of the layer by about 2.5 and 3.0 times, respectively. Doubling the solar radiation will de- crease the drying time in half. As an example, the predicted drying time as a function of residue loading rate at different solar radiation values is plotted in Fig. 2.

CONCLUSION

The use of the experimental design and PCA and PLS provides a powerful tool for studying the drying of complex material. The method is both effective in predicting drying behaviour and also useful in exploring the impacts of important vari- ables on the drying process. Besides this, using the experimental design we have been able to reduce the number of required experiments re- markably.

The agreement between the e~erimental re- sults and the model was very satisfactory and one can readily use the model for predicting the dry- ing of peat in practice in various field and weather ~nditions.

REFERENCES

1 M. Fortes and M.R. Okos, Drying theories; their bases and limitations as applied to food and grains, in A.S. Mujumdar (Editor), Aduances in Drying, Vol. 1, Hemisphere, Wash- ington, DC, 1980, pp. 119-154.

2 J.L. Rossen and K. Hayakawa, Simultaneous heat and moisture transfer in dehydrated food: a review of theoreti- cal models, American Institute of Chemical Engineers Sym- posium Series, 73 (1977) 71-81.

3 P. Chen and D.C.T. Pei, A mathemati~l mode1 of drying processes, International Journal of Heat and Mass Transfer, 32 (1989) 297-310.

4 K.L. Bristow, G.S. Campbell, R.I. Papendick and L.F. El- liott, Simulation of heat and moisture transfer through a surface residue-soil system, Ag~cuItura~ and Forest Meteo- rology, 36 (1986) 193-214.

5 V.A. Antonov, L.M. Malkov and N.I. Gamajunov, Tehnologija Poleuoi &ski Torfa, Moskow, Nedra, 1981.

6 T.T. Jarvinen, The simulation of open sun peat drying and bog phenomena on a laboratory scale, in V.A. Dodd and P.M. Grace (Editors), Agricultural Engineering. Proceedings of tke 11th international Congress, Dublin, September 4-S, l989, Vol. I, Balkema, Rotterdam, 1989, pp. 13-16.

7 H. Martens and T. Nms, Multioa~te Cal~ration, Wiley, Chichester, 1989.

8 S. Wold, Principal component analysis, Ckemometrics and intelligent Laboratory Systems, 2 (1987) 37-52.

9 S. Wold, C. Albano, W.J. Dunn III, U. Edlund, K. Es- bensen, P. Geladi, S. Hellberg, E. Johansson, W. Lindberg and M. SjBstriim, Multivariate data analysis in chemistry, in B.R. Kowalski (Editor), Chemometrics: Matke~tics and Stat&ics in Chemistry, NATO Advanced Study Institute Series C 138, Reidel, Dordrecht, 1984, pp. 17-96.