- Email: [email protected]
Simultaneous prediction of coal rank parameters based on ultimate analysis using regression and artificial neural network
International Journal of Coal Geology 83 (2010) 31–34
Contents lists available at ScienceDirect
International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Simultaneous prediction of coal rank parameters based on ultimate analysis using regression and artificial neural network S. Chehreh Chelgani a,⁎, Sh. Mesroghli b, James C. Hower c a b c
Surface Science Western, University of Western Ontario, London, Ont., Canada N6A 5B7 Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Poonak, Hesarak Tehran, Iran Center for Applied Energy Research, University of Kentucky, 2540 Research Park Drive, Lexington, KY 40511, USA
a r t i c l e
i n f o
Article history: Received 20 October 2009 Received in revised form 22 March 2010 Accepted 25 March 2010 Available online 31 March 2010 Keywords: Vitrinite maximum reflectance Gross calorific value Regression Artificial neural network
a b s t r a c t Results from ultimate analysis, proximate and petrographic analyses of a wide range of Kentucky coal samples were used to predict coal rank parameters (vitrinite maximum reflectance (Rmax) and gross calorific value (GCV)) using multivariable regression and artificial neural network (ANN) methods. Volatile matter, carbon, total sulfur, hydrogen and oxygen were used to predict both Rmax and GCV by regression and ANN. Multivariable regression equations to predict Rmax and GCV showed R2 = 0.77 and 0.69, respectively. Results from the ANN method with a 2–5–4–2 arrangement that simultaneously predicts GCV and Rmax showed R2 values of 0.84 and 0.90, respectively, for an independent test data set. The artificial neural network method can be appropriately used to predict Rmax and GCV when regression results do not have high accuracy. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Coal quality is a function of three fundamental, independent factors: coal rank, organic composition (including, but not restricted to, macerals), and inorganic components, which include minerals and organically associated elements. Commonly used coal rank parameters such as vitrinite reflectance, calorific value, volatile matter, and carbon content are variably influenced by all three fundamental properties. Vitrinite is the most common maceral group in most US coal. Consequently, it is the properties of vitrinite and the variation of those properties with rank that define the properties of a coal (Hower and Eble, 1996). Vitrinite reflectance values increase with rank, and measurements are typically independent of petrographic composition and mineral matter content (Davis, 1978; Gabzdyl, 1985; Taylor et al., 1998; Komorek, 2002). Reflectance is sometimes diminished where liptinites content is elevated (Raymond and Muchison, 1991; Hutton and Cook, 1980) and has also been shown to vary with the lithology of surrounding rock (Goodarzi et al., 1988). The standard test method for the measurement of vitrinite reflectance (ASTM D 2798-09a, 2009) covers the analysis of both the mean maximum reflectance and the mean random reflectance measured in oil for coals ranging in rank from lignite to anthracite (Speight, 2005). Volatile matter decreases as rank increases during coalification. Consequently, vitrinite reflectance and volatile matter have an inverse relationship (Grieve, 1992; Quick and Tabet, 2003).
⁎ Corresponding author. Tel.: +1 519 702 9356. E-mail address: [email protected] (S.C. Chelgani). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.03.004
Ultimate analysis results for whole-coal samples, especially in the high volatile bituminous stage of coalification, depend heavily on both maceral composition and the extent of coalification (Gurba and Ward, 2000). Nonetheless, carbon content generally increases during coalification whereas the hydrogen content decreases (Grieve, 1992). The carbon and hydrogen content of whole-coal samples may be a useful alternative to vitrinite reflectance as rank indicators for maturation studies (Gurba and Ward, 2000; Diessel and Gammidge, 1998; Grieve, 1992). Therefore, it is not surprising that relationships between vitrinite reflectance and the carbon and hydrogen content of coal have been observed (Smith and Smith, 2007; George et al., 1994; Burnham and Sweeney, 1989). Indeed, many investigators have found good correlations among coal rank parameters (Broadbent and Shaw, 1955; McCartney and Teichmüller, 1972; George et al., 1994, Grummel and Davis, 1933; Mott and Spooner, 1940, Given et al., 1986; IGT, 1978). Another measure of coal rank is the calorific value (Hower and Eble, 1996). Moreover, the calorific value is an essential measure of the quality coal burned at power plants; proximate and less commonly ultimate analyses are also used to evaluate the quality of thermal coal. The calorific value is usually expressed as the higher heating value or gross calorific value (GCV) (Patel et al., 2007). Estimation of GCV from the elemental composition of fuel is one of the basic steps in performance modeling and calculations on combustion systems (Channiwala and Parikh, 2002). Over the last 10 years, artificial neural networks (ANNs) and, particularly, feed-forward artificial neural networks (FANNs), have been extensively studied within process models, and their use in industry has been rapidly growing (Ungar et al., 1996). Artificial
32
S.C. Chelgani et al. / International Journal of Coal Geology 83 (2010) 31–34
Table 1 Description of data used in this study for 1018 Kentucky coal samples. Variables—dry ash free base
Minimum (%)
Maximum (%)
Mean
Std. deviation
Oxygen (%) Hydrogen (%) Carbon (%) Total sulfur (%) Volatile matter (%) GCV (MJ/kg) Rmax
0.43 3.56 72.28 0.35 27.72 26.43 0.39
14.74 6.79 88.6 14.54 54.95 36.92 1.17
8.01 5.43 82.25 2.59 40.94 34.36 0.79
1.78 0.27 2.69 2.34 4.12 1.08 0.17
neural network (ANN) is an empirical modeling tool that is analogous to the behavior of biological neural structures (Yao et al., 2005). Neural networks are powerful tools, which are able to infer highly complex relationships between input and output data (Haykin, 1999). In the present work, the maximum vitrinite reflectance and gross calorific value are estimated according to ultimate analysis parameters that are expressed on a dry ash free basis. To our knowledge, this is the first time that ANN analysis has been used to simultaneously predict both Rmax and GCV from the results of the ultimate analysis. 2. Experimental data A robust mathematical model requires comprehensive data that include a wide variety of coal types. Such a model will be capable predicting both Rmax and GCV with a high degree of accuracy. Data used in study are from the University of Kentucky Center for Applied Energy Research. A total of 1018 Kentucky coal samples were used. Analytical data for these coals are described in Table 1. 3. Methods and results 3.1. Multivariable regression
equation is derived from a sequence of multiple linear regression equations, in a stepwise manner. At each step of the sequence, one variable is added to the regression equation. The variable added is the one that makes the greatest reduction in the error sum of squares of the sample data. Equivalently, it is the variable that, when added, provides the greatest increase in the F value. Variables not having a significant correlation with the dependent variable are those whose addition does not increase the F value; these variables are not featured in the regression equation. By a least square mathematical method, the correlation coefficients of hydrogen (H), oxygen (O), total sulfur (S), carbon (C), and volatile matter (V) with Rmax, were determined to be −0.52, − 0.72, − 0.61, +0.87, and −0.64, respectively. Where all of these parameters were used to predict Rmax, the stepwise regression resulted in the following equation: 2
Rmax = 9:096−0:129C + 0:001C −0:03O−0:021V
ð1Þ
2
−0:081LnðSÞ−0:738H + 0:077H :
The equation has an R2 value of 0.77 and the difference between the measured and predicted Rmax values for 1012 coal samples is illustrated in Fig. 1. 3.1.2. Multivariable correlation of GCV with ultimate analysis A multivariable equation that uses coal carbon, hydrogen and oxygen, volatile matter, and total sulfur to predict GCV was also found using the stepwise regression method. Inter-item correlation between carbon, hydrogen, oxygen, volatile matter, and total sulfur and gross calorific value was 0.94, 0.52, −0.90, −0.42, and −0.48, respectively. These results indicate that a positive relationship exists for hydrogen, and carbon with GCV whereas oxygen, total sulfur, volatile mater have a negative relationship with GCV. Using a stepwise regression, the best-correlated multivariable equations to predict GCV was found to be:
3.1.1. Multivariable correlation of Rmax with ultimate analysis In this study, a multivariable equation that uses coal carbon, hydrogen and oxygen, volatile matter and total sulfur to predict Rmax was determined by using a stepwise regression method. The stepwise regression method is commonly used to make predictions from several independent variables in a way that examines the power of the different independent variables to predict the dependent measure (Freed et al., 1991). For multiple independent variables, the regression
The equation has an R2 value of 0.69 and the difference between the measured and predicted GCV is illustrated for 1012 coal samples in Fig. 2.
Fig. 1. Distribution of the difference between measured Rmax values and estimated Rmax values obtained from multivariate regression Eq. (1).
Fig. 2. Distribution of the difference between measured GCV values and estimated GCV values obtained from multivariable regression Eq. (2).
GCV ðMJ=kgÞ = 64:62−0:262C−0:579O−0:46 S:
ð2Þ
S.C. Chelgani et al. / International Journal of Coal Geology 83 (2010) 31–34
33
Fig. 3. The architecture of FANN with ultimate analysis input.
3.2. Artificial neural network Among the existing numerous neural networks (NNs) paradigms, feed-forward artificial neural networks (FANNs) are the most popular due to their flexibility in structure, good representational capabilities, and large number of available training algorithms (Leondes, 1998; Lippmann, 1987; Sarkar, 1995). This type of network consists of three layers of nodes namely: an input layer, hidden layers, and an output layer. Feed-forward neural networks usually have one or more hidden layers, which enable the network to model non-linear and complex functions. In this study, feed-forward artificial neural network (FANN) was used to estimate both Rmax and GCV. Using the experimental data, FANNs have been applied to many aspects of coal processing (Cilek, 2002; Jorjani et al., 2007, 2008, 2009; Chehreh Chelgani et al., 2008). Experimental data records for 1018 coal samples were used in the present study; 700 of these records were used to train the FANN and 318 records were used to test its reliability. According to Eqs. (1) and (2), the selected variables were determined to be the appropriate variables for the prediction of Rmax and GCV. Therefore, these variables were used as inputs to the FANN. The 2–5–4–2 FANN model (Fig. 3) adequately recognized the effects of different parameters on the coal rank, and usefully predicted both Rmax and GCV, simultaneously. Neural network training can be made more efficient if certain preprocessing steps (normalizing processes) are performed on the network inputs and targets. Before training, it is often useful to scale the inputs and targets so that they always fall within a specified range.
Fig. 5. Distribution of the difference between the measured GCV and estimated GCV obtained from the artificial neural network.
In this section of work, all inputs and outputs data were scaled so that they fall in the range [− 1, 1] using the following equation: Pn =
2ðP− minP Þ −1 ðmaxP− min P Þ
ð5Þ
where Pn is the normalized parameter, P is the actual parameter, min P is a minimum of the actual parameters, and max p is a maximum of the actual parameters (Demuth and Beale, 2002). The training process was stopped after 1000 epochs. In each epoch, the entire training set is presented to the network, case by case; and errors are calculated and used to adjust the weights in the network using sigmoid transfer function. This method is based on the BP (back propagation) error algorithm, an iterative supervised learning technique. A set of training examples is considered, and for each the desired output of the MLP (multilayer perceptron) is known. The network learns the trends contained in the data set and correlates the inputs and the outputs by finding the optimum set of weights that minimizes the differences between the predicted and actual output values. For each iteration, an error between the predicted value and the actual value is propagated backward from the output layer towards the input through the hidden layers until the error is within an acceptable limit (Statsoft, 1998). The correlation coefficients (R2) for the testing set on the dependent variables (Rmax and GCV) were 0.90 and 0.84, respectively. The distribution of difference between estimated Rmax and GCV from described ANN procedures and actual values is shown in Figs. 4 and 5. 4. Conclusions • Regression Eqs. (1) and (2) show the relation of Rmax and GCV with carbon, hydrogen and oxygen, volatile matter, and total sulfur for 1018 coal samples. Correlation coefficients (R2 values) for these regression equations to predict Rmax and GCV were 0.77 and 0.69, respectively. • Using the same experimental data, the FANN model (2–5–4–2) was able to predict both GCV and Rmax with R2 values of 0.84 and 0.90, respectively. Notably, the ANN procedure used in this study conveniently predicted both Rmax and GCV, simultaneously. • Compared to the stepwise regression method, the artificial neural network provided a more accurate estimate of Rmax and GCV. Acknowledgement
Fig. 4. Distribution of the difference between measured Rmax values and estimated Rmax values obtained from the artificial neural network.
The first author would like to thank Zinat alsadat Taba Tabaee.
34
S.C. Chelgani et al. / International Journal of Coal Geology 83 (2010) 31–34
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.coal.2010.03.004. References ASTM D 2798-09a, 2009. Standard Test Method for Microscopical Determination of Vitrinite Reflectance of Coal. ASTM International. Broadbent, S.R., Shaw, A.J., 1955. Reflectance of coal. Fuel 4, 385–403. Burnham, A.K., Sweeney, J.J., 1989. A chemical kinetic model of vitrinite maturation and reflectance. Geochim. Cosmochim. Acta 53, 2649–2657. Channiwala, S.A., Parikh, P.P., 2002. A unified correlation for estimating HHV of solid, liquid and gaseous fuels. Fuel 81, 1051–1063. Chehreh Chelgani, S., Hower, J.C., Jorjani, E., Mesroghli, Sh., Bagherieh, A.H., 2008. Prediction of coal grindability based on petrography, proximate and ultimate analysis with multiple regression and artificial neural network models. Fuel Process. Technol. 89, 13–20. Cilek, E.C., 2002. Application of neural networks to predict locked cycle flotation test results. Miner. Eng. 15, 1095. Davis, A., 1978. The reflectance of coal. In: Karr, C. (Ed.), Analytical Methods for Coal and Coal Products, vol. 1. Academic Press, New York, pp. 27–81. Demuth, H., Beale, M., 2002. Neural Network Toolbox for use with MATLAB. User's Guide Handbook, version 4, 154. Diessel, C.F.K., Gammidge, L., 1998. Isometamorphic variations in the reflectance and fluorescence of vitrinite — a key to depositional environment. Int. J. Coal Geol. 36, 167–222. Freed, M.N., Ryan, J.M., Hess, R.K., 1991. Handbook of statistical procedures and their computer applications to education and the behavioral science. American council on education and Macmillan Publishing Company, New York. p. 397. Grummel, E.S., Davis, I.A., 1933. A new method of calculating the calorific value of a fuel from Its Ultimate Analysis. Fuel 12, 199–203. Gabzdyl, W., 1985. Zeszyty Naukawe Politechniki Slakiej. Polish, Ważniejsze publikacje. 132, 31–42. George, S.C., Smith, J.W., Jardine, D.R., 1994. Vitrinite suppression in coal due to marine transgression: case study of the organic geochemistry of the Greta seam, Sydney Basin. APEA J. 34, 241–255. Given, P.H., Weldon, D., Zoeller, J.H., 1986. Calculation of calorific values of coals from ultimate analyses: theoretical basis and geochemical implications. Fuel 65, 849–854. Goodarzi, F., Gentzis, T., Feinstein, S., Snowdon, L., 1988. Effect of maceral subtypes and mineral matrix on measured reflectance of subbituminous coals and dispersed organic matter. Int. J. Coal Geol. 10, 383–398. Grieve, D.A., 1992. Relationship between coal quality parameters in British Columbia coals. Geol. Fieldwork 397–404. Gurba, W.L., Ward, R.C., 2000. Elemental composition of coal macerals in relation to vitrinite reflectance, Gunnedah Basin, Australia, as determined by electron microprobe analysis. Int. J. Coal Geol. 44, 127–147. Haykin, S., 1999. Neural Networks, a Comprehensive Foundation, USA, 2nd ed. Prentice Hall, USA.
Hower, J.C., Eble, C.F., 1996. Coal quality — coal utilization link often ‘understated’ in discussions. Natl. Coal Lead. 30 (5), 12. Hutton, A.C., Cook, A.C., 1980. Influence of alginite on the reflectance of vitrinite from Joadja, NSW, and some other coals and oil shales containing alginite. Fuel 59, 711–714. IGT,, 1978. Coal Conversion Systems Technical Data Book. DOE contract Ex 76-C-012286. NTIS, Springfield,VA. Jorjani, E., Chehreh Chelgani, S., Mesroghli, Sh., 2007. Prediction of microbial desulfurization of coal using artificial neural networks. Miner. Eng. 20, 1285–1292. Jorjani, E., Chehreh Chelgani, S., Mesroghli, Sh., 2008. Application of artificial neural networks to predict chemical desulfurization of Tabas coal. Fuel 87, 2727–2734. Jorjani, E., Asadollahi Poorali, H., Sam, A., Chehreh Chelgani, S., Mesroghli, Sh., Shayestehfar, M.R., 2009. Prediction of coal response to froth flotation based on coal analysis using regression and artificial neural network. Miner. Eng. 22, 970–976. Komorek, J., 2002. Letter to Editor, Discussion: Relationship between the maximum and random reflectance of vitrinite for coal from the Upper Silesian Coal Basin (Poland). Fuel 81, 969–971. Leondes, C.T., 1998. Neural Network Systems Techniques and Applications: Algorithms and Architectures. Academic Press, New York. Lippmann, R., 1987. An introduction to computing with neural nets. IEEE ASSP Mag. 4 (2), 4–22. McCartney, J.T., Teichmüller, M., 1972. Classification of coals according to degree of coalification by reflectance of the vitrinite component. Fuel 51, 64–68. Mott, R.A., Spooner, C.E., 1940. The calorific value of carbon in coal: Dulong relationship. Fuel 5, 226–251. Patel, S.U., Kumar, B.J., Badhe, Y.P., Sharma, B.K., Saha, S., Subhasish, B., Chaudhury, A., Tambe, S.S., Kulkarni, B.D., 2007. Estimation of gross calorific value of coals using artificial neural networks. Fuel 86, 334–344. Quick, J.C., Tabet, D.E., 2003. Suppressed vitrinite reflectance in the Ferron coalbed gas fairway, central Utah: possible influence of overpressure. Int. J. Coal Geol. 56, 49–67. Raymond, A.C., Muchison, D.G., 1991. Influence of exinitic macerals on the reflectance of vitrinite in Carboniferous sediments of the Midland Valley of Scotland. Fuel 70 (2), 155–161. Sarkar, D., 1995. Methods to speed up error back-propagation learning algorithm, ACM Comput. Surveys 27, 519–542. Smith, J.R., Smith, J.W., 2007. A relationship between the carbon and hydrogen content of coals and their vitrinite reflectance. Int. J. Coal Geol. 70, 79–86. Speight, G.J., 2005. Handbook of Coal Analysis. Wiley-Interscience, Chichester, West Sussex, England. p. 122. StatSoft, Inc, 1998. Manual of STATISTICA Neural Networks Software. StatSoft, Inc., Tulsa, OK. Taylor, G.H., Teichmüller, M., Davis, A., Diessel, C.F.K., Littke, R., Robert, P., 1998. Organic Petrology. Gebrüber Borntraeger, Berlin. p. 704. Ungar, L.H., Hartman, E.J., Keeler, J.D., Martin, G.D., 1996. Process modelling and control using neural networks. Am. Inst. Chem. Eng. Symp. Ser. 92, 57–66. Yao, H.M., Vuthaluru, H.B., Tade, M.O., Djukanovic, D., 2005. Artificial neural networkbased prediction of hydrogen content of coal in power station boilers. Fuel 84, 1535–1542.
Contents lists available at ScienceDirect
International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Simultaneous prediction of coal rank parameters based on ultimate analysis using regression and artificial neural network S. Chehreh Chelgani a,⁎, Sh. Mesroghli b, James C. Hower c a b c
Surface Science Western, University of Western Ontario, London, Ont., Canada N6A 5B7 Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Poonak, Hesarak Tehran, Iran Center for Applied Energy Research, University of Kentucky, 2540 Research Park Drive, Lexington, KY 40511, USA
a r t i c l e
i n f o
Article history: Received 20 October 2009 Received in revised form 22 March 2010 Accepted 25 March 2010 Available online 31 March 2010 Keywords: Vitrinite maximum reflectance Gross calorific value Regression Artificial neural network
a b s t r a c t Results from ultimate analysis, proximate and petrographic analyses of a wide range of Kentucky coal samples were used to predict coal rank parameters (vitrinite maximum reflectance (Rmax) and gross calorific value (GCV)) using multivariable regression and artificial neural network (ANN) methods. Volatile matter, carbon, total sulfur, hydrogen and oxygen were used to predict both Rmax and GCV by regression and ANN. Multivariable regression equations to predict Rmax and GCV showed R2 = 0.77 and 0.69, respectively. Results from the ANN method with a 2–5–4–2 arrangement that simultaneously predicts GCV and Rmax showed R2 values of 0.84 and 0.90, respectively, for an independent test data set. The artificial neural network method can be appropriately used to predict Rmax and GCV when regression results do not have high accuracy. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Coal quality is a function of three fundamental, independent factors: coal rank, organic composition (including, but not restricted to, macerals), and inorganic components, which include minerals and organically associated elements. Commonly used coal rank parameters such as vitrinite reflectance, calorific value, volatile matter, and carbon content are variably influenced by all three fundamental properties. Vitrinite is the most common maceral group in most US coal. Consequently, it is the properties of vitrinite and the variation of those properties with rank that define the properties of a coal (Hower and Eble, 1996). Vitrinite reflectance values increase with rank, and measurements are typically independent of petrographic composition and mineral matter content (Davis, 1978; Gabzdyl, 1985; Taylor et al., 1998; Komorek, 2002). Reflectance is sometimes diminished where liptinites content is elevated (Raymond and Muchison, 1991; Hutton and Cook, 1980) and has also been shown to vary with the lithology of surrounding rock (Goodarzi et al., 1988). The standard test method for the measurement of vitrinite reflectance (ASTM D 2798-09a, 2009) covers the analysis of both the mean maximum reflectance and the mean random reflectance measured in oil for coals ranging in rank from lignite to anthracite (Speight, 2005). Volatile matter decreases as rank increases during coalification. Consequently, vitrinite reflectance and volatile matter have an inverse relationship (Grieve, 1992; Quick and Tabet, 2003).
⁎ Corresponding author. Tel.: +1 519 702 9356. E-mail address: [email protected] (S.C. Chelgani). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.03.004
Ultimate analysis results for whole-coal samples, especially in the high volatile bituminous stage of coalification, depend heavily on both maceral composition and the extent of coalification (Gurba and Ward, 2000). Nonetheless, carbon content generally increases during coalification whereas the hydrogen content decreases (Grieve, 1992). The carbon and hydrogen content of whole-coal samples may be a useful alternative to vitrinite reflectance as rank indicators for maturation studies (Gurba and Ward, 2000; Diessel and Gammidge, 1998; Grieve, 1992). Therefore, it is not surprising that relationships between vitrinite reflectance and the carbon and hydrogen content of coal have been observed (Smith and Smith, 2007; George et al., 1994; Burnham and Sweeney, 1989). Indeed, many investigators have found good correlations among coal rank parameters (Broadbent and Shaw, 1955; McCartney and Teichmüller, 1972; George et al., 1994, Grummel and Davis, 1933; Mott and Spooner, 1940, Given et al., 1986; IGT, 1978). Another measure of coal rank is the calorific value (Hower and Eble, 1996). Moreover, the calorific value is an essential measure of the quality coal burned at power plants; proximate and less commonly ultimate analyses are also used to evaluate the quality of thermal coal. The calorific value is usually expressed as the higher heating value or gross calorific value (GCV) (Patel et al., 2007). Estimation of GCV from the elemental composition of fuel is one of the basic steps in performance modeling and calculations on combustion systems (Channiwala and Parikh, 2002). Over the last 10 years, artificial neural networks (ANNs) and, particularly, feed-forward artificial neural networks (FANNs), have been extensively studied within process models, and their use in industry has been rapidly growing (Ungar et al., 1996). Artificial
32
S.C. Chelgani et al. / International Journal of Coal Geology 83 (2010) 31–34
Table 1 Description of data used in this study for 1018 Kentucky coal samples. Variables—dry ash free base
Minimum (%)
Maximum (%)
Mean
Std. deviation
Oxygen (%) Hydrogen (%) Carbon (%) Total sulfur (%) Volatile matter (%) GCV (MJ/kg) Rmax
0.43 3.56 72.28 0.35 27.72 26.43 0.39
14.74 6.79 88.6 14.54 54.95 36.92 1.17
8.01 5.43 82.25 2.59 40.94 34.36 0.79
1.78 0.27 2.69 2.34 4.12 1.08 0.17
neural network (ANN) is an empirical modeling tool that is analogous to the behavior of biological neural structures (Yao et al., 2005). Neural networks are powerful tools, which are able to infer highly complex relationships between input and output data (Haykin, 1999). In the present work, the maximum vitrinite reflectance and gross calorific value are estimated according to ultimate analysis parameters that are expressed on a dry ash free basis. To our knowledge, this is the first time that ANN analysis has been used to simultaneously predict both Rmax and GCV from the results of the ultimate analysis. 2. Experimental data A robust mathematical model requires comprehensive data that include a wide variety of coal types. Such a model will be capable predicting both Rmax and GCV with a high degree of accuracy. Data used in study are from the University of Kentucky Center for Applied Energy Research. A total of 1018 Kentucky coal samples were used. Analytical data for these coals are described in Table 1. 3. Methods and results 3.1. Multivariable regression
equation is derived from a sequence of multiple linear regression equations, in a stepwise manner. At each step of the sequence, one variable is added to the regression equation. The variable added is the one that makes the greatest reduction in the error sum of squares of the sample data. Equivalently, it is the variable that, when added, provides the greatest increase in the F value. Variables not having a significant correlation with the dependent variable are those whose addition does not increase the F value; these variables are not featured in the regression equation. By a least square mathematical method, the correlation coefficients of hydrogen (H), oxygen (O), total sulfur (S), carbon (C), and volatile matter (V) with Rmax, were determined to be −0.52, − 0.72, − 0.61, +0.87, and −0.64, respectively. Where all of these parameters were used to predict Rmax, the stepwise regression resulted in the following equation: 2
Rmax = 9:096−0:129C + 0:001C −0:03O−0:021V
ð1Þ
2
−0:081LnðSÞ−0:738H + 0:077H :
The equation has an R2 value of 0.77 and the difference between the measured and predicted Rmax values for 1012 coal samples is illustrated in Fig. 1. 3.1.2. Multivariable correlation of GCV with ultimate analysis A multivariable equation that uses coal carbon, hydrogen and oxygen, volatile matter, and total sulfur to predict GCV was also found using the stepwise regression method. Inter-item correlation between carbon, hydrogen, oxygen, volatile matter, and total sulfur and gross calorific value was 0.94, 0.52, −0.90, −0.42, and −0.48, respectively. These results indicate that a positive relationship exists for hydrogen, and carbon with GCV whereas oxygen, total sulfur, volatile mater have a negative relationship with GCV. Using a stepwise regression, the best-correlated multivariable equations to predict GCV was found to be:
3.1.1. Multivariable correlation of Rmax with ultimate analysis In this study, a multivariable equation that uses coal carbon, hydrogen and oxygen, volatile matter and total sulfur to predict Rmax was determined by using a stepwise regression method. The stepwise regression method is commonly used to make predictions from several independent variables in a way that examines the power of the different independent variables to predict the dependent measure (Freed et al., 1991). For multiple independent variables, the regression
The equation has an R2 value of 0.69 and the difference between the measured and predicted GCV is illustrated for 1012 coal samples in Fig. 2.
Fig. 1. Distribution of the difference between measured Rmax values and estimated Rmax values obtained from multivariate regression Eq. (1).
Fig. 2. Distribution of the difference between measured GCV values and estimated GCV values obtained from multivariable regression Eq. (2).
GCV ðMJ=kgÞ = 64:62−0:262C−0:579O−0:46 S:
ð2Þ
S.C. Chelgani et al. / International Journal of Coal Geology 83 (2010) 31–34
33
Fig. 3. The architecture of FANN with ultimate analysis input.
3.2. Artificial neural network Among the existing numerous neural networks (NNs) paradigms, feed-forward artificial neural networks (FANNs) are the most popular due to their flexibility in structure, good representational capabilities, and large number of available training algorithms (Leondes, 1998; Lippmann, 1987; Sarkar, 1995). This type of network consists of three layers of nodes namely: an input layer, hidden layers, and an output layer. Feed-forward neural networks usually have one or more hidden layers, which enable the network to model non-linear and complex functions. In this study, feed-forward artificial neural network (FANN) was used to estimate both Rmax and GCV. Using the experimental data, FANNs have been applied to many aspects of coal processing (Cilek, 2002; Jorjani et al., 2007, 2008, 2009; Chehreh Chelgani et al., 2008). Experimental data records for 1018 coal samples were used in the present study; 700 of these records were used to train the FANN and 318 records were used to test its reliability. According to Eqs. (1) and (2), the selected variables were determined to be the appropriate variables for the prediction of Rmax and GCV. Therefore, these variables were used as inputs to the FANN. The 2–5–4–2 FANN model (Fig. 3) adequately recognized the effects of different parameters on the coal rank, and usefully predicted both Rmax and GCV, simultaneously. Neural network training can be made more efficient if certain preprocessing steps (normalizing processes) are performed on the network inputs and targets. Before training, it is often useful to scale the inputs and targets so that they always fall within a specified range.
Fig. 5. Distribution of the difference between the measured GCV and estimated GCV obtained from the artificial neural network.
In this section of work, all inputs and outputs data were scaled so that they fall in the range [− 1, 1] using the following equation: Pn =
2ðP− minP Þ −1 ðmaxP− min P Þ
ð5Þ
where Pn is the normalized parameter, P is the actual parameter, min P is a minimum of the actual parameters, and max p is a maximum of the actual parameters (Demuth and Beale, 2002). The training process was stopped after 1000 epochs. In each epoch, the entire training set is presented to the network, case by case; and errors are calculated and used to adjust the weights in the network using sigmoid transfer function. This method is based on the BP (back propagation) error algorithm, an iterative supervised learning technique. A set of training examples is considered, and for each the desired output of the MLP (multilayer perceptron) is known. The network learns the trends contained in the data set and correlates the inputs and the outputs by finding the optimum set of weights that minimizes the differences between the predicted and actual output values. For each iteration, an error between the predicted value and the actual value is propagated backward from the output layer towards the input through the hidden layers until the error is within an acceptable limit (Statsoft, 1998). The correlation coefficients (R2) for the testing set on the dependent variables (Rmax and GCV) were 0.90 and 0.84, respectively. The distribution of difference between estimated Rmax and GCV from described ANN procedures and actual values is shown in Figs. 4 and 5. 4. Conclusions • Regression Eqs. (1) and (2) show the relation of Rmax and GCV with carbon, hydrogen and oxygen, volatile matter, and total sulfur for 1018 coal samples. Correlation coefficients (R2 values) for these regression equations to predict Rmax and GCV were 0.77 and 0.69, respectively. • Using the same experimental data, the FANN model (2–5–4–2) was able to predict both GCV and Rmax with R2 values of 0.84 and 0.90, respectively. Notably, the ANN procedure used in this study conveniently predicted both Rmax and GCV, simultaneously. • Compared to the stepwise regression method, the artificial neural network provided a more accurate estimate of Rmax and GCV. Acknowledgement
Fig. 4. Distribution of the difference between measured Rmax values and estimated Rmax values obtained from the artificial neural network.
The first author would like to thank Zinat alsadat Taba Tabaee.
34
S.C. Chelgani et al. / International Journal of Coal Geology 83 (2010) 31–34
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.coal.2010.03.004. References ASTM D 2798-09a, 2009. Standard Test Method for Microscopical Determination of Vitrinite Reflectance of Coal. ASTM International. Broadbent, S.R., Shaw, A.J., 1955. Reflectance of coal. Fuel 4, 385–403. Burnham, A.K., Sweeney, J.J., 1989. A chemical kinetic model of vitrinite maturation and reflectance. Geochim. Cosmochim. Acta 53, 2649–2657. Channiwala, S.A., Parikh, P.P., 2002. A unified correlation for estimating HHV of solid, liquid and gaseous fuels. Fuel 81, 1051–1063. Chehreh Chelgani, S., Hower, J.C., Jorjani, E., Mesroghli, Sh., Bagherieh, A.H., 2008. Prediction of coal grindability based on petrography, proximate and ultimate analysis with multiple regression and artificial neural network models. Fuel Process. Technol. 89, 13–20. Cilek, E.C., 2002. Application of neural networks to predict locked cycle flotation test results. Miner. Eng. 15, 1095. Davis, A., 1978. The reflectance of coal. In: Karr, C. (Ed.), Analytical Methods for Coal and Coal Products, vol. 1. Academic Press, New York, pp. 27–81. Demuth, H., Beale, M., 2002. Neural Network Toolbox for use with MATLAB. User's Guide Handbook, version 4, 154. Diessel, C.F.K., Gammidge, L., 1998. Isometamorphic variations in the reflectance and fluorescence of vitrinite — a key to depositional environment. Int. J. Coal Geol. 36, 167–222. Freed, M.N., Ryan, J.M., Hess, R.K., 1991. Handbook of statistical procedures and their computer applications to education and the behavioral science. American council on education and Macmillan Publishing Company, New York. p. 397. Grummel, E.S., Davis, I.A., 1933. A new method of calculating the calorific value of a fuel from Its Ultimate Analysis. Fuel 12, 199–203. Gabzdyl, W., 1985. Zeszyty Naukawe Politechniki Slakiej. Polish, Ważniejsze publikacje. 132, 31–42. George, S.C., Smith, J.W., Jardine, D.R., 1994. Vitrinite suppression in coal due to marine transgression: case study of the organic geochemistry of the Greta seam, Sydney Basin. APEA J. 34, 241–255. Given, P.H., Weldon, D., Zoeller, J.H., 1986. Calculation of calorific values of coals from ultimate analyses: theoretical basis and geochemical implications. Fuel 65, 849–854. Goodarzi, F., Gentzis, T., Feinstein, S., Snowdon, L., 1988. Effect of maceral subtypes and mineral matrix on measured reflectance of subbituminous coals and dispersed organic matter. Int. J. Coal Geol. 10, 383–398. Grieve, D.A., 1992. Relationship between coal quality parameters in British Columbia coals. Geol. Fieldwork 397–404. Gurba, W.L., Ward, R.C., 2000. Elemental composition of coal macerals in relation to vitrinite reflectance, Gunnedah Basin, Australia, as determined by electron microprobe analysis. Int. J. Coal Geol. 44, 127–147. Haykin, S., 1999. Neural Networks, a Comprehensive Foundation, USA, 2nd ed. Prentice Hall, USA.
Hower, J.C., Eble, C.F., 1996. Coal quality — coal utilization link often ‘understated’ in discussions. Natl. Coal Lead. 30 (5), 12. Hutton, A.C., Cook, A.C., 1980. Influence of alginite on the reflectance of vitrinite from Joadja, NSW, and some other coals and oil shales containing alginite. Fuel 59, 711–714. IGT,, 1978. Coal Conversion Systems Technical Data Book. DOE contract Ex 76-C-012286. NTIS, Springfield,VA. Jorjani, E., Chehreh Chelgani, S., Mesroghli, Sh., 2007. Prediction of microbial desulfurization of coal using artificial neural networks. Miner. Eng. 20, 1285–1292. Jorjani, E., Chehreh Chelgani, S., Mesroghli, Sh., 2008. Application of artificial neural networks to predict chemical desulfurization of Tabas coal. Fuel 87, 2727–2734. Jorjani, E., Asadollahi Poorali, H., Sam, A., Chehreh Chelgani, S., Mesroghli, Sh., Shayestehfar, M.R., 2009. Prediction of coal response to froth flotation based on coal analysis using regression and artificial neural network. Miner. Eng. 22, 970–976. Komorek, J., 2002. Letter to Editor, Discussion: Relationship between the maximum and random reflectance of vitrinite for coal from the Upper Silesian Coal Basin (Poland). Fuel 81, 969–971. Leondes, C.T., 1998. Neural Network Systems Techniques and Applications: Algorithms and Architectures. Academic Press, New York. Lippmann, R., 1987. An introduction to computing with neural nets. IEEE ASSP Mag. 4 (2), 4–22. McCartney, J.T., Teichmüller, M., 1972. Classification of coals according to degree of coalification by reflectance of the vitrinite component. Fuel 51, 64–68. Mott, R.A., Spooner, C.E., 1940. The calorific value of carbon in coal: Dulong relationship. Fuel 5, 226–251. Patel, S.U., Kumar, B.J., Badhe, Y.P., Sharma, B.K., Saha, S., Subhasish, B., Chaudhury, A., Tambe, S.S., Kulkarni, B.D., 2007. Estimation of gross calorific value of coals using artificial neural networks. Fuel 86, 334–344. Quick, J.C., Tabet, D.E., 2003. Suppressed vitrinite reflectance in the Ferron coalbed gas fairway, central Utah: possible influence of overpressure. Int. J. Coal Geol. 56, 49–67. Raymond, A.C., Muchison, D.G., 1991. Influence of exinitic macerals on the reflectance of vitrinite in Carboniferous sediments of the Midland Valley of Scotland. Fuel 70 (2), 155–161. Sarkar, D., 1995. Methods to speed up error back-propagation learning algorithm, ACM Comput. Surveys 27, 519–542. Smith, J.R., Smith, J.W., 2007. A relationship between the carbon and hydrogen content of coals and their vitrinite reflectance. Int. J. Coal Geol. 70, 79–86. Speight, G.J., 2005. Handbook of Coal Analysis. Wiley-Interscience, Chichester, West Sussex, England. p. 122. StatSoft, Inc, 1998. Manual of STATISTICA Neural Networks Software. StatSoft, Inc., Tulsa, OK. Taylor, G.H., Teichmüller, M., Davis, A., Diessel, C.F.K., Littke, R., Robert, P., 1998. Organic Petrology. Gebrüber Borntraeger, Berlin. p. 704. Ungar, L.H., Hartman, E.J., Keeler, J.D., Martin, G.D., 1996. Process modelling and control using neural networks. Am. Inst. Chem. Eng. Symp. Ser. 92, 57–66. Yao, H.M., Vuthaluru, H.B., Tade, M.O., Djukanovic, D., 2005. Artificial neural networkbased prediction of hydrogen content of coal in power station boilers. Fuel 84, 1535–1542.