A mathematical prediction of corn sorption isotherm was developed for three-parameter EMC correlation such as Modified-Henderson, Modified-Chung-Pfost, Modified-Oswin, and Modified-Halsey. Moisture sorption experimental data were determined using a dynamic method at temperature 30 oC, 40 oC and water activity range from 0.07 to 0.75. The vapor pressure regulation of air surrounding the grains was adjusted by varying sulfuric acid solution. Non-linear regression algorithms such as Simplex and/or Rosenbrock algorithm were used to fit the measured data to the EMC relations. The generalized correlation coefficient (R2) and the mean relative deviation were in the range of 0.90-0.99 and 2 % - 8 % respectively, in which comparison between predicted and experimental sorption isotherms. From the parameters of correlation, it is possible to get the best equations among them to represent equilibrium moisture content of corn grains. The Modified-Henderson and Modified-Oswin equations give the best model for predicting the adsorption and desorption EMC of corn grain for given range of temperature and water activity

Istadi, I.

Sitompul, J.P

Sumardiono, S.

English

Diponegoro University Institutional Repository

Published in: Proceedings Institut Teknologi Bandung, Lembaga Penelitian ITB, Volume 32, No. 1, pp. 411-417       NON-LINEAR PARAMETER ESTIMATION OF EMC/ERH CORRELATIONS FOR GRAIN-TYPE PRODUCTS  J.P. Sitompul, Istadi (*) , and S. Sumardiono Dept. of Chemical Engineering, Institute of Technology Bandung,  Jl. Ganesha 10, Bandung, 40132, Indonesia E-mail: johnner@termo.pauir.itb.ac.id ABSTRACT A mathematical prediction of corn sorption isotherm was developed for three-parameter EMC correlation such as Modified-Henderson, Modified-Chung-Pfost, Modified-Oswin, and Modified-Halsey. Moisture sorption experimental data were determined using a dynamic method at temperature 30 oC, 40 oC and water activity range from 0.07 to 0.75. The vapor pressure regulation of air surrounding the grains was adjusted by varying sulfuric acid solution. Non-linear regression algorithms such as Simplex and/or Rosenbrock algorithm were used to fit the measured data to the EMC relations. The generalized correlation coefficient (R2) and the mean relative deviation were in the range of 0.90-0.99 and 2 % - 8 % respectively, in which comparison between predicted and experimental sorption isotherms. From the parameters of correlation, it is possible to get the best equations among them to represent equilibrium moisture content of corn grains. The Modified-Henderson and Modified-Oswin equations give the best model for predicting the adsorption and desorption EMC of corn grain for given range of temperature and water activity.  NOTATION A,B,C parameters used in EMC relations  Aw water activity or relative humidity decimal R2 correlation coefficient  T absolute temperature K X* equilibrium moisture content % iX̂  calculated data  iX  mean value of experimental data  Xi experimental data  n number of experimental data                                                   (*) Permanent address: Dept. of Chemical Engineering, Diponegoro University, Jl. Prof. Sudarto, Semarang, Indonesia, 50239 1. INTRODUCTION Grain products, such as corn, paddy rice, coffee beans, etc., are widely cultivated grains in the world. The most of grain products are harvested at high moisture content. Hence, it requires immediate treatment to prevent quality along decreasing during storage. Drying is the most widely practiced preservation method for grains in the post-harvesting technology. With drying processing, the moisture content of grains is lowered to a level at which there is no danger of the growth of undesirable microorganisms. The minimum moisture content to which corn can be dried under certain conditions is given by the equilibrium moisture content (EMC) [Istadi et al. (1999)]. The concept of equilibrium relative humidity (ERH) is often used as it measures the availability of water to microorganisms and hence gives an indication of the biological activity within corn grain. The relationship between EMC and ERH are described by the EMC/ERH sorption isotherm equations [Sitompul et al. (2000)]. In an extensive study conducted by Sun and Woods (1998) on comparing a number of commonly used EMC/ERH equations for the corn grains. It is found that the Modified-Oswin and Modified-Chung-Pfost equations are identified as the most appropriate equations for describing EMC/ERH sorption isotherms of shelled-corn based on the ability to describe the nineteen individual data sub-sets. The analysis of sorption isotherm of corn grain had been conducted by Sitompul et al. (2000) and Papadakis et al. (1993) for the two- and three-parameter of EMC correlation. However, the two-parameter EMC correlation (Papadakis and Henderson model) can not provide better fitting to experimental data of corn grain, comparing with three-parameter EMC relations (Halsey and Iglesias-Chirife equations). The aims of this study is to analyze four sorption isotherm equations (Modified-Henderson, Modified-Chung-Pfost, Modified-Oswin, and Modified-Halsey), through non-linear regression of experimental data, and to find the best model representing the equilibrium moisture content of corn grains. The sorption isotherm data of corn grain were determined experimentally by the dynamic method at temperature of 30oC and 40oC [Sitompul et al. (2000), Makower et al. (1943), Molnar (1995)].   2. EQUILIBRIUM MOISTURE CONTENT CORRELATIONS In air-drying system, when air is brought in contact with a wet-food material, equilibrium between the air and food material is eventually reached. The moisture content of grains at this stage is called the equilibrium moisture content (EMC) and the corresponding vapor pressure of surrounding air at the same temperature is called the equilibrium vapor pressure. The ratio of the equilibrium vapor pressure to the saturation vapor pressure is so called as the equilibrium relative humidity (ERH) or water activity [Sokhansanj et al. (1995), Marinos-Kouris et al. (1995)]. The equilibrium moisture content-equilibrium relative humidity (EMC/ERH) relationships are necessary to optimize drying and storing of food products, especially for grain products. The sorption data may be used for the proper choice of the end-point of drying process. Sorption isotherm vary drastically from one food product to another, depending on whether the product is being wetted - adsorption - or dried - desorption [Mujumdar et al. (1995)]. No single equation has been found to predict accurately the sorption isotherm of all types of foods in the entire range of water activity; consequently, many correlation have been reported to represent sorption isotherms [Parry (1985)]. A large number of theoretical, empirical or semi-empirical correlations have been proposed in the literature to estimate the equilibrium moisture of biological materials. The theoretical correlation are developed based on sorption kinetics theories such as that of Langmuir and BET. In many cases, the theoretical models can not predict the equilibrium moisture for grains in a wide range of temperature and water activity. Further, the empirical or semi-empirical models were used to increase the accuracy of the predicted values of interest. The most important correlation proposed available in the literature are given in Table 1. In these correlation, X* is the equilibrium moisture content for grains, while Aw and T is the water activity of air and the solid temperature respectively. Note that A, B, and C are the involved parameters of the correlation. Table 1. Equilibrium moisture content models [Barrozo et al. (1996), Stencl et al. (1998)] No. Name  Equation  Reference 1 Modified Henderson ( )B/1w)CT(AA1ln*X ⎟⎟⎠⎞⎜⎜⎝⎛+−−=              [Thompson et al. (1968)] 2 Modified Chung-Pfost ⎟⎠⎞⎜⎝⎛−+−=AAln  )TC(ln  B1*X w      [Chung and Pfost (1967)] 3 Modified Oswin CwwA-1A T) BA(*X ⎟⎟⎠⎞⎜⎜⎝⎛+=       [Stencl et al. (1998)] 4 Modified  Halsey  CwAln -)T B(A exp*X ⎟⎟⎠⎞⎜⎜⎝⎛ +=        [Stencl et al. (1998)]  Basically, the correlation (1) is the modification of Henderson equation (1952) based on sorption model of Gibbs in order to appropriate for grains [Thompson et al. (1968)]. The correlation (2) was introduced by Chung and Pfost (1967) based on potential theory and in a simplified equation of state. The correlation (3) is based on mathematical series expansion for sigmoidaly curve. The correlation (4) is the empirical modifications of the Halsey equation (1948), that are based on the theoretical model of BET.   3. MATERIAL AND METHODS  The materials used in this experimental study were shelled-corn grain and sulfuric acid solution. The technique used to obtain the equilibrium moisture content data was based on the dynamic method with the use of sulfuric acid solutions to provide a constant relative humidity. A series of different sulfuric acid solution was used, such that the relative humidity was between 7 % and 75 % [Wilson (1921)]. The EMC experiments were conducted in a temperature controlled at 30 oC and 40 oC [Sitompul et al. (2000)]. The dry matter content was then determined by drying the sample in an oven until constant weight. The moisture content at any time was calculated from the sample weight obtained [Molnar (1995)]. The equilibrium conditions were considered to be reached, when three-subsequent measurements of the sample weight give identical results. The moisture content of the material was determined by the time the equilibrium condition was reached.  4. RESULTS AND DISCUSSION The experimental values of the equilibrium moisture contents corresponding to shelled-corn at 30 oC and 40 oC are presented in Fig.1 and Fig.2 for the range of water activity of 0.07-0.75, and they are best-fitted with the respective correlation. Generally, the curves have a sigmoid shape form. Equilibrium moisture content was found to increase with decrease in temperature at constant water activity. The increase in temperature causes an increase for desorped water and a decrease for adsorbed water, if Aw is kept constant. Similar trends for many food materials have been reported in the literature [McMinn et al. (1997), Sun (1998)]. The estimated constants of the Modified-Henderson, Modified-Chung-Pfost, Modified-Oswin, and Modified-Halsey and the corresponding correlation coefficient (R2) together with percentage mean relative deviation are given in Table 2 and Table 3.   The non-linear regression method was used in order to estimate the best model parameters, i.e. Simplex method in the form of the algorithm of SIMPLEX subroutine [Sitompul et al. (2000)]. The objective function to be minimized is given by Eq.(1) below, which is an important error parameter during the non-linear curve fitting process. The correlation coefficient (R2) measures the fitting ability of a model to a data set. The higher of R2 value represents the better of fitting ability of an equation. However, the correlation coefficient only gives the fitting ability of a correlation, but it can not provide a correct visualization of the goodness-of-fit of the equation to the experimental data. For this reason, percentage of mean relative deviation given by Eq.(3) is used to measure the goodness-of-fit of the correlation. It represents the mean departure of the measured data from the predicted data. Further, the consistency of parameters is also important when the correlation applied to different temperatures. Table 2. Regression results of parameters of Desorption isotherm correlation Estimated parameter value Name Temp. (oC) A B C  (R2)  Mean Rel. Deviation (%) 30 2.4259x10-5 1.8247 24.468 0.9952 3.18 Modified Henderson 40 2.6075x10-5 1.8497 23.299 0.9984 1.78 30 15008 0.19493 2300.4 0.9605 8.54 Modified  Chung-Pfost 40 15005 0.2108 2300.2 0.9681 7.34 30 -2.195x10-2 3.6319x10-2 0.43591 0.9797 5.68 Modified  Oswin 40 -4.8942x10-2 3.2404x10-2 0.43021 0.9866 4.79 30 -1.5147 1.2671x10-2 0.77337 0.9755 7.99 Modified Halsey 40 1.6999 3.7274x10-3 0.68901 0.9433 10.41  Table 3. Regression results of parameters of Adsorption isotherm correlation  Estimated parameter value Name Temp. (oC) A B C  (R2)  Mean Rel. Deviation (%) 30 5.2293x10-5 1.6675 23.665 0.9912 2.84 Modified Henderson 40 6.2134x10-5 1.6361 26.238 0.9869 4.81 30 10003 0.18563 2500.6 0.9906 4.31 Modified  Chung-Pfost 40 10004 0.20626 2500.7 0.98 7.08 30 1.7559 2.31x10-2 0.47982 0.9975 2.94 Modified  Oswin 40 1.6233 2.0565x10-2 0.48798 0.9986 1.87 30 -1.5147 1.2671x10-2 0.77337 0.9755 7.99 Modified Halsey 40 -2.7899 1.6416x10-2 0.73534 0.9887 5.49    Modified Halsey051015200 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 30 CX* Calc. Of Desorption at 30 CX* Exp. of  Adsorption at 30 CX* Calc. Of Adsorption at 30 CModified Henderson051015200 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 30 CX* Calc. Of Desorption at 30 CX* Exp. of  Adsorption at 30 CX* Calc. Of Adsorption at 30 C   (a)      (b) Modified Chung-Pfost051015200 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 30 CX* Calc. Of Desorption at 30 CX* Exp. of  Adsorption at 30 CX* Calc. Of Adsorption at 30 CModified Oswin051015200 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 30 CX* Calc. Of Desorption at 30 CX* Exp. of  Adsorption at 30 CX* Calc. Of Adsorption at 30 C   (c)      (d) Fig.1. The comparison between the predicted isotherm and the experimental data at 30 oC  Modified Halsey0246810121416180 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 40 CX* Calc. Of Desorption at 40 CX* Exp. of  Adsorption at 40 CX* Calc. Of Adsorption at 40 CModified Henderson0246810121416180 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 40 CX* Calc. Of Desorption at 40 CX* Exp. of  Adsorption at 40 CX* Calc. Of Adsorption at 40 C   (a)      (b) Modified Chung-Pfost02468101214160 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 40 CX* Calc. Of Desorption at 40 CX* Exp. of  Adsorption at 40 CX* Calc. Of Adsorption at 40 CModified Oswin0246810121416180 0.2 0.4 0.6 0.8Aw  (decimal)X* (% db)X* Exp. of Desorption at 40 CX* Calc. Of Desorption at 40 CX* Exp. of  Adsorption at 40 CX* Calc. Of Adsorption at 40 C   (c)      (d) Fig.2. The comparison between the predicted isotherm and the experimental data at 40 oC   Objective function :  ∑= ⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛ −=n1i2iiiXXX̂n1  FO   (1) Correlation coefficient :  ( )( )∑∑==−−−= n1i2iin1i2ii2XXX̂X1R  (2) Mean relative deviation (%):  ∑= ⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛ −=n1i iiiXXX̂ n100  .Dev %  (3) The correlation coefficient was found very high in most cases (R2>0.9) that calculated by Eq.(2). The Modified-Henderson model presents the highest R2 and the minimum of mean relative deviation for this data. Therefore, the Modified-Henderson equation gives the best fit to the experimental data at the temperature range of 30 oC - 40 oC. The Modified-Oswin equation gives also better fitting than the Modified-Chung-Pfost and Modified-Halsey equations, but gives less fitting than the Modified-Henderson equation. In the case of comparison of temperature 30 oC and 40 oC, it is found that parameters correlation of the Modified-Henderson and Modified-Oswin relatively having constant value compared with others. It is noted that these models can be used to predict sorption equilibrium moisture content at different temperature.  5. CONCLUSIONS An EMC experiment has been performed for shelled-corn by using dynamic method. The data obtained were used to determine the best model for predicting the adsorption and desorption EMC of corn grain for given levels of temperature and water activity. The equilibrium moisture content of corn grain decreases with an increase in temperature at constant relative humidity. The Modified-Henderson and Modified-Oswin equations are identified as the most appropriate equations for describing EMC/ERH sorption isotherms of shelled-corn based on the best ability to fit the equation on the set of experimental data. The Modified-Chung-Pfost and Modified Halsey equations have slightly better fitting ability than the Modified-Henderson and Modified-Oswin correlation. The non-linear regression based on Simplex and/or Rosenbrock algorithm is a good technique to fit non-linear correlation on the experimental data set. Therefore, the two correlations as describe above can be used to predict sorption isotherm of the shelled-corn grain and the other grain-type products.   ACKNOWLEDGMENTS  The authors are grateful for financial support of the RUT Grant through Indonesia Research Council. The second author also acknowledges the Dept. of Chemical Engineering, Diponegoro University for permission to study on leave in the Dept. of Chemical Engineering, Institute of Technology Bandung.      REFERENCES 1. Barrozo, M.A.S., D.J.M. Sartori, J.T. Freire, and J.A. Achcar, 1996, Discrimination of Equilibrium Moisture Equations for Soybean Using Nonlinearity Measures, Drying Technology, Vol. 14, No. 7&8, pp. 1779-1794. 2. Chung, D.S., and H.B. Pfost, 1967, Adsorption and Desorption of Water Vapour by Cereal Grains and Their Product. Part II, Trans. of The ASAE, Vol. 10, No. 4, pp. 549-551. 3. Halsey, G., 1948, Physical Adsorption on Non-Uniform Surface, J. of Chem. Phys., Vol. 16, No. 10, pp. 931-937. 4. Henderson, S.M., 1952, A Basic Concept of Equilibrium Moisture, Agric. Eng., Vol. 33, pp. 29-32. 5. Istadi, J.P. Sitompul, and S. Sasmojo, 1999, Deep-bed Drying of Corn Grain: Modelling and Simulation (in Indonesian), Prosiding Seminar Teknik Kimia Soehadi Reksowardojo 1999, ITB, Indonesia, pp. VI.47 - VI.54 6. Makower, B., and G.L. Dehority, 1943, Equilibrium Moisture Content of Dehydrated Vegetables, Ind. Eng. Chemistry, Vol. 35, No. 2, pp. 193-197 7. Marinos-Kouris, D., and Z.B. Maroulis, 1995, Transport Properties in The Drying of Solids, in Handbook of Industrial Drying, A.S. Mujumdar (ed.), Vol. 1, Marcel Dekker, Inc., New York, pp. 113-159. 8. McMinn, W.A.M., and T.R.A. Magee, 1997, Moisture Sorption Characteristics of Starch Materials, Drying Technology, Vol. 14, No. 5, pp. 1527-1551 9. Molnar, K., 1995, Experimental Techniques in Drying, in Handbook of Industrial Drying, A.S. Mujumdar (ed.), Vol. 1, Marcel Dekker, Inc., New York, pp. 41-79. 10. Mujumdar, A.S., and A.S. Menon, 1995, Drying of Solids: Principles, Classification, and Selection of Dryers, in Handbook of Industrial Drying, A.S. Mujumdar (ed.), Vol. 1, Marcel Dekker, Inc., New York, pp. 1-39. 11. Papadakis, S.E., R.E. Bahu, K.A. McKenzie, and I.C. Kemp, 1993, Measurement and Prediction of The Equilibrium Moisture Content for Drying, The 1993 Research Event, pp. 507-509. 12. Parry, J.L., 1985, Mathematical Modelling and Computer Simulation of Heat and Mass Transfer in Agricultural Grain Drying: A Review, J. Agric. Eng. Res., Vol. 32, pp. 1-29. 13. Sitompul, J.P., Istadi, and S. Sumardiono, 2000, Correlation and Prediction of Equilibrium Moisture Content (EMC) for Grain Agricultural Product (in Indonesian), Prosiding Seminar Nasional Teknologi Proses Kimia II, Universitas Indonesia, Indonesia, pp. VI.47 - VI.54. 14. Sokhansanj, S. and D.S. Jayas, 1995, Drying of Foodstuffs, in Handbook of Industrial Drying, A.S. Mujumdar (ed.), Vol. 1, Marcel Dekker, Inc., New York, pp. 589-625. 15. Stencl, J., J. Gotthardova, and P. Homola, 1998, Equilibrium Moisture Content of Dried Blood Flour in The Temperature Range of 20 - 50 oC, Drying Technology, Vol. 16, No. 8, pp. 1729-1739. 16. Sun, Da-Wen, 1998, Selection of EMC/ERH Isotherm Equations for Shelled Corn Based On Fitting to Available Data, Drying Technology, Vol. 16, No. 3-5, pp. 779-797. 17. Thompson, T.L., R.M. Peart, and G.H. Foster, 1968, Mathematical Simulation of Corn Drying - A New Model, Trans. of  The ASAE, Vol. 11, No. 4,  pp. 582-586. 18. Wilson, R.E., 1921, Humidity Control by Means of Sulfuric Acid Solutions with Critical Compilation of Vapor Pressure Data, J. of Industrial and Eng. Chemistry, Vol. 13, No. 4, pp. 326-331.  

A Basic Concept of Equilibrium Moisture,

Adsorption and Desorption of Water Vapour by Cereal Grains and Their Product. Part II,

Correlation and Prediction of Equilibrium Moisture Content (EMC) for Grain Agricultural Product (in

Deep-bed Drying of Corn Grain: Modelling and Simulation (in Indonesian), Prosiding Seminar Teknik Kimia Soehadi Reksowardojo

Discrimination of Equilibrium Moisture Equations for Soybean Using Nonlinearity Measures,

Drying of Foodstuffs,

Equilibrium Moisture Content of Dehydrated Vegetables,

Equilibrium Moisture Content of Dried Blood Flour

Humidity Control by Means of Sulfuric Acid Solutions with Critical Compilation of Vapor Pressure Data,

Mathematical Modelling and Computer Simulation of Heat and Mass Transfer in Agricultural Grain Drying: A Review,

Measurement and Prediction of The Equilibrium Moisture Content for Drying, The

Physical Adsorption on Non-Uniform Surface,

Selection of EMC/ERH Isotherm Equations for Shelled Corn Based On Fitting to Available Data,

Transport Properties in The Drying of Solids,

NON-LINEAR PARAMETER ESTIMATION OF EMC/ERH CORRELATIONS FOR GRAIN-TYPE PRODUCTS

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NON-LINEAR PARAMETER ESTIMATION OF EMC/ERH CORRELATIONS FOR GRAIN-TYPE PRODUCTS

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