Generalizability of empirical correlations for predicting higher heating values of biomass

Figures & data

Figure 1. Data distributions of a) woody biomass feedstocks (137 data) and b) herbaceous and agricultural biomass feedstocks (254 data) with proximate analysis, ultimate analysis, and experimental HHV. “db” represents dry basis.

Table 1. Biomass types and categorized collected for the generalizability of the developed equations to predict the HHV.

Biomass types	Details
Woody biomass – Softwood and Hardwood (137 data)	Softwood stems
	Softwood bark
	Softwood residues
	Softwood leaves
	Softwood seed/fruit
	Hardwood stems
	Hardwood bark
	Hardwood twigs
	Hardwood leaves
	Hardwood residues
	Hardwood seed/fruit/berry
Herbaceous and agricultural biomass (254 data)	Herbaceous and agricultural grasses
	Herbaceous and agricultural stalks/stems/shrubs
	Herbaceous and agricultural fibres
	Herbaceous and agricultural shells/husks/processing residues
	Herbaceous and agricultural seeds/fruits/grains
	Herbaceous and agricultural leaf

Table 2. Empirical correlations for the prediction of biomass HHV using UA data.

Equation Number	Developed empirical correlations for HHV prediction (HHV, kJ/g)	Reference
Eq. 1	$0.4373\ast \mathit{C}-1.6701$	Channiwala and Parikh (2002), Sheng and Azevedo (2005)
Eq. 2	$0.4373\ast \mathit{C}-0.3059$	Channiwala and Parikh (2002)
Eq. 3	$\left(491.2\ast \mathit{C}-911.4\ast \mathit{H}+117.7\ast \mathit{O}\right)/1000$	Thipkhunthod et al. (2005)
Eq. 4	$\left(425.9\ast \mathit{C}-69.8\ast \mathit{H}+181.7\ast \mathit{O}-2277\right)/1000$	Thipkhunthod et al. (2005)
Eq. 5	$\left(414.8\ast \mathit{C}-184.1\ast \mathit{H}+178.9\ast \mathit{O}-2159.5\right)/1000$	Thipkhunthod et al. (2005)
Eq. 6	$0.3259\ast \mathit{C}+3.4597$	Sheng and Azevedo (2005), Yin (2011)
Eq. 7	$0.34\ast \mathit{C}+1.4\ast \mathit{H}-0.16\ast \mathit{O}$	Zanzi, Sjöström, and Björnbom (2002)
Eq. 8	$\left(416.638\ast \mathit{C}-570.017\ast \mathit{H}+259.031\ast \mathit{O}+598.955\ast \mathit{N}+5829.078\right)/1000$	Kathiravale et al. (2003)
Eq. 9	$0.301\ast \mathit{C}+0.525\ast \mathit{H}+0.064\ast \mathit{O}-0.763$	Channiwala and Parikh (2002), Sheng and Azevedo (2005)
Eq. 10	$\left(3.55\ast C^2-232\ast \mathit{C}-2230\ast \mathit{H}+51.2\ast \mathit{C}\ast \mathit{H}+131\ast \mathit{N}+20600\right)/1000$	Friedl et al. (2005), Yin (2011)
Eq. 11	$\left(5.22\ast C^2-319\ast \mathit{C}-1647\ast \mathit{H}+38.6\ast \mathit{C}\ast \mathit{H}+133\ast \mathit{N}+21028\right)/1000$	Friedl et al. (2005)
Eq. 12	$\left(1.87\ast C^2-144\ast \mathit{C}-2820\ast \mathit{H}+68.3\ast \mathit{C}\ast \mathit{H}+129\ast \mathit{N}+20147\right)/1000$	Friedl et al. (2005)
Eq. 13	$4.18\ast \left(103.34\ast \mathit{C}-73\right)/1000$	Demirbas (2004)
Eq. 14	$\left(33.5\ast \mathit{C}+142.3\ast \mathit{H}-15.4\ast \mathit{O}-14.5\ast \mathit{N}\right)/100$	Demirbaş (1997), Demirbas et al. (1997), Sheng and Azevedo (2005), Thipkhunthod et al. (2005)
Eq. 15	$\left(33.5\ast \mathit{C}+142.3\ast \mathit{H}-15.4\ast \mathit{O}\right)/100$	Demirbas et al. (1997)
Eq 16	$0.2949\ast \mathit{C}+0.825\ast \mathit{H}$	Yin (2011)
Eq. 17	$-5.29+0.493\ast \mathit{C}+5.052/\mathit{H}$	Callejón-Ferre et al. (2011)
Eq 18	$5.736+0.006\ast C^2$	Callejón-Ferre et al. (2011)
Eq. 19	$-3.393+0.507\ast \mathit{C}-0.341\ast \mathit{H}+0.067\ast \mathit{N}$	Callejón-Ferre et al. (2011)
Eq 20	$-2.907+0.491\ast \mathit{C}-0.261\ast \mathit{H}$	Callejón-Ferre et al. (2011)
Eq. 21	$-3.147+0.468\ast \mathit{C}$	Callejón-Ferre et al. (2011)

Table 3. Empirical correlations for the prediction of biomass HHV using combined PA and UA data.

Equation Number	Developed empirical correlations for HHV prediction (HHV, kJ/g)	Reference
Eq 22	$-1.3675+0.3137\ast \mathit{C}+0.7009\ast \mathit{H}+0.0318\ast \left(100-\mathit{C}-\mathit{H}-\mathit{Ash}\right)$	Sheng and Azevedo (2005)
Eq. 23	$23.668-7.032\ast \mathit{H}-0.002\ast \mathit{As}{h}^2+0.005\ast C^2+0.771\ast H^2+0.019\ast N^2$	Callejón-Ferre et al. (2011)
Eq 24	$4.622+7.912\ast H^{-1}-0.001\ast \mathit{As}{h}^2+0.006\ast C^2+0.018\ast N^2$	Callejón-Ferre et al. (2011)
Eq. 25	$9.756-309.454\ast \mathit{V}{M}^{-1}+6.164\ast H^{-1}+0.006\ast C^2$	Callejón-Ferre et al. (2011)
Eq 26	$-0.417-0.012\ast \mathit{VM}-0.035\ast \left(\mathit{Ash}+\mathit{C}\right)+0.518\ast \left(\mathit{C}+\mathit{N}\right)-0.393\ast \left(\mathit{H}+\mathit{N}\right)$	Callejón-Ferre et al. (2011)
Eq. 27	$-1.642-0.024\ast \mathit{Ash}\ast 0.475\ast \left(\mathit{C}+\mathit{N}\right)-0.376\ast \left(\mathit{H}+\mathit{N}\right)$	Callejón-Ferre et al. (2011)
Eq 28	$-0.465-0.0342\ast \mathit{Ash}-0.019\ast \mathit{VM}+0.483\ast \mathit{C}-0.388\ast \mathit{H}+0.124\ast \mathit{N}$	Callejón-Ferre et al. (2011)
Eq. 29	$-1.563-0.0251\ast \mathit{Ash}+0.475\ast \mathit{C}-0.385\ast \mathit{H}+0.102\ast \mathit{N}$	Callejón-Ferre et al. (2011)

Table 4. Empirical correlations for the prediction of biomass HHV using PA data.

Equation Number	Developed empirical correlations for HHV prediction (HHV, kJ/g)	Reference
Eq. 30	$\left(255.75\ast \mathit{VM}+283.88\ast \mathit{FC}-2386.38\right)/1000$	Thipkhunthod et al. (2005)
Eq. 31	$\left(259.83\ast \left(\mathit{VM}+\mathit{FC}\right)-2454.76\right)/1000$	Thipkhunthod et al. (2005)
Eq. 32	$19.914-0.2324\ast \mathit{Ash}$	Sheng and Azevedo (2005)
Eq. 33	$-3.0368+0.2218\ast \mathit{VM}+0.2691\ast \mathit{FC}$	Sheng and Azevedo (2005)
Eq. 34	$4.183\ast {10}^{-3}\ast \left(8000+\mathit{VM}\ast \left(70-1.65\ast \mathit{VM}\right)\right)$	Majumder et al. (2008)
Eq. 35	$0.3536\ast \mathit{FC}+0.1559\ast \mathit{VM}-0.0078\ast \mathit{Ash}$	Ahmaruzzaman (2008), Majumder et al. (2008), Sheng and Azevedo (2005), Yin (2011)
E. 36	$\left(356.047\ast \mathit{VM}-118.035\ast \mathit{FC}-5600.613\right)/1000$	Kathiravale et al. (2003)
Eq. 37	$\left(356.248\ast \mathit{VM}-6998.497\right)/1000$	Kathiravale et al. (2003)
Eq. 38	$-10.81408+0.3133\ast \left(\mathit{VM}+\mathit{FC}\right)$	Ahmaruzzaman (2008), Cordero et al. (2001), Jiménez and González (1991), Majumder et al. (2008), Parikh, Channiwala, and Ghosal (2005)
Eq. 39	$0.312\ast \mathit{FC}+0.1534\ast \mathit{VM}$	Ahmaruzzaman (2008), Demirbaş (1997), Sheng and Azevedo (2005), Thipkhunthod et al. (2005)
Eq. 40	$0.196\ast \mathit{FC}+14.119$	Demirbaş (1997), Majumder et al. (2008), Parikh, Channiwala, and Ghosal (2005), Thipkhunthod et al. (2005)
Eq. 41	$0.3543\ast \mathit{FC}+0.1708\ast \mathit{VM}$	Ahmaruzzaman (2008), Cordero et al. (2001), Majumder et al. (2008), Parikh, Channiwala, and Ghosal (2005), Thipkhunthod et al. (2005)
Eq. 42	$0.1905\ast \mathit{VM}+0.2521\ast \mathit{FC}$	Yin (2011)
Eq. 43	$-2.057-0.092\ast \mathit{Ash}+0.279\ast \mathit{VM}$	Callejón-Ferre et al. (2011)
Eq. 44	$-13.173+0.416\ast \mathit{VM}$	Callejón-Ferre et al. (2011)
Eq. 45	$20.086-0261\ast \mathit{Ash}$	Callejón-Ferre et al. (2011)

Figure 2. The HHV prediction results of mixed biomass feedstocks (391 data in total) using the empirical correlations based on ultimate analysis data (eqs. (1)-(21)).

Table 5. Statistical analysis for the prediction of HHV of mixed biomass feedstocks using empirical correlations (eqs. (1)-(21)) based on ultimate analysis.

Equation	MAE	STDEV*	RMSE	MAPE (%)	R^2
Eq-1	0.530	0.40	0.665	2.887	0.821
Eq. 2	1.465	0.65	1.604	8.004	0.821.
Eq. 3	3.995	1.00	4.118	21.865	0.602
Eq. 4	6.539	1.03	6.618	35.765	0.549
Eq. 5	5.334	1.03	5.433	29.241	0.535
Eq. 6	0.517	0.42	0.663	2.849	0.821
Eq. 7	1.453	0.96	1.738	7.969	0.734
Eq. 8	15.110	1.34	15.169	82.532	0.279
Eq. 9	0.801	0.64	1.024	4.525	0.723
Eq. 10	0.490	0.41	0.636	2.693	0.818
Eq. 11	0.491	0.41	0.637	2.699	0.817
Eq. 12	1.244	0.61	1.383	6.808	0.826
Eq. 13	1.253	0.62	1.397	6.860	0.821
Eq. 14	1.402	0.94	1.685	7.697	0.739
Eq. 15	1.307	0.92	1.597	7.166	0.732
Eq. 16	0.548	0.47	0.724	3.038	0.768
Eq. 17	0.590	0.47	0.752	3.213	0.810
Eq. 18	0.714	0.54	0.893	3.842	0.818
Eq. 19	0.670	0.56	0.875	3.650	0.792
Eq. 20	0.611	0.50	0.789	3.324	0.799
Eq. 21	0.553	0.43	0.698	3.013	0.821

*STDEV of MAE. MAE, STDEV, MMAPE.

Table 6. Statistical analysis for the prediction of HHV of mixed biomass feedstocks using empirical correlations (eqs. (22)-(29)) based on both proximate and ultimate analyses.

Equation	MAE	STDEV*	RMSE	MAPE (%)	R^2
Eq. 22	1.674	0.65	1.795	9.213	0.803
Eq. 23	1.815	1.19	2.167	9.759	0.672
Eq. 24	0.807	0.58	0.992	4.324	0.803
Eq. 25	1.360	0.80	1.574	7.277	0.808
Eq. 26	0.655	0.51	0.831	3.550	0.778
Eq. 27	0.677	0.59	0.898	3.687	0.787
Eq. 28	0.714	0.63	0.949	3.888	0.774
Eq. 29	0.670	0.59	0.891	3.651	0.784

*STDEV of MAE.

Table 7. Statistical analysis for the prediction of HHV of mixed biomass feedstocks using empirical correlations (eqs. (30)-(45)) based on proximate analysis.

Equation	MAE	STDEV*	RMSE	MAPE (%)	R^2
Eq. 30	3.673	1.35	3.913	20.236	0.326
Eq. 31	3.522	1.32	3.761	19.430	0.336
Eq. 32	0.961	0.83	1.272	5.278	0.321
Eq. 33	0.995	0.89	1.336	5.464	0.320
Eq. 34	5.514	3.67	6.622	29.591	0.089
Eq. 35	1.368	1.23	1.837	7.451	0.209
Eq. 36	2.420	1.97	3.119	13.253	0.034
Eq. 37	2.541	1.70	3.057	13.972	0.094
Eq. 38	1.153	1.00	1.526	6.366	0.336
Eq. 39	1.681	1.31	2.129	8.959	0.224
Eq. 40	1.664	1.13	2.009	8.892	0.063
Eq. 41	1.422	1.09	1.791	7.932	0.059
Eq. 42	1.094	0.87	1.400	6.111	0.062
Eq. 43	1.506	1.26	1.960	8.212	0.088
Eq. 44	1.879	1.66	2.503	10.223*	0.020
Eq. 45	0.998	0.88	1.332	5.487	0.082

*STDEV of MAE.

Table 8. Statistical analysis of the best two empirical correlations for the prediction of HHV of herbaceous and agricultural biomass feedstocks (254 data set) and woody biomass feedstocks (137 data set) using either ultimate analysis or combined ultimate-proximate analyses data.

Biomass Feedstocks	Equation	MAE	STDEV	RMSE	MAPE (%)	R^2
Herbaceous and Agricultural (254 data set)	Ultimate analysis
	Eq-10	0.501	0.43	0.661	2.806	0.811
	Eq-11	0.500	0.43	0.660	2.804	0.811
	Combined proximate-ultimate analysis
	Eq-26	0.684	0.55	0.877	3.763	0.760
	Eq-29	0.743	0.65	0.986	4.102	0.765
Woody biomass (137 data set)	Ultimate analysis
	Eq-10	0.469	0.35	0.587	2.482	0.805
	Eq-11	0.474	0.36	0.593	2.506	0.800
	Combined proximate-ultimate analysis
	Eq-26	0.541	0.43	0.690	2.839	0.799
	Eq-29	0.536	0.43	0.683	2.813	0.799

*STDEV of MAE. The statistical analysis for other empirical correlations is presented in the appendix (Table B1 and Table B2).

Figure 3. The HHV prediction results of mixed biomass feedstocks (391 data in total) using the empirical correlations based on combined proximate-ultimate analyses data (eqs. (22)-(29)).

Figure 4. The best four empirical correlations based on average confidence intervals to predict the HHV of mixed biomass feedstocks using proximate analysis data; a)Eq. (32), b) equation (33), c) equation (42), d)Equation (45).

Figure 5. The best two empirical correlations for the prediction of HHV of herbaceous and agricultural biomass feedstocks (254 data set) using ultimate analysis data a) equation (10) and b) equation (11) and combined ultimate-proximate analyses data; c) equation (26) and d) equation (29).

Figure 6. The best two empirical correlations for the prediction of HHV of woody biomass feedstocks (137 data set) using ultimate analysis data a) equation (10) and b) equation (11), and combine ultimate-proximate analyses data; c) equation (26) and d) equation (29).

Channiwala, S., and P. Parikh. 2002. A unified correlation for estimating HHV of solid, liquid and gaseous fuels. Fuel 81 (8):1051–63. doi:10.1016/S0016-2361(01)00131-4.

 Web of Science ®Google Scholar

Sheng, C., and J. Azevedo. 2005. Estimating the higher heating value of biomass fuels from basic analysis data. Biomass and Bioenergy 28 (5):499–507. doi:10.1016/j.biombioe.2004.11.008.

 Web of Science ®Google Scholar

Thipkhunthod, P., V. Meeyoo, P. Rangsunvigit, B. Kitiyanan, K. Siemanond, and T. Rirksomboon. 2005. Predicting the heating value of sewage sludges in Thailand from proximate and ultimate analyses. Fuel 84 (7–8):849–57. doi:10.1016/j.fuel.2005.01.003.

 Web of Science ®Google Scholar

Yin, C.-Y. 2011. Prediction of higher heating values of biomass from proximate and ultimate analyses. Fuel 90 (3):1128–32. doi:10.1016/j.fuel.2010.11.031.

 Web of Science ®Google Scholar

Zanzi, R., K. Sjöström, and E. Björnbom. 2002. Rapid pyrolysis of agricultural residues at high temperature. Biomass and Bioenergy 23 (5):357–366. doi:10.1016/S0961-9534(02)00061-2.

 Web of Science ®Google Scholar

Kathiravale, S., M. N. M. Yunus, K. Sopian, A. H. Samsuddin, and R. A. Rahman. 2003. Modeling the heating value of municipal solid waste☆. Fuel 82(9):1119–25. doi:10.1016/S0016-2361(03)00009-7.

 Web of Science ®Google Scholar

Friedl, A., E. Padouvas, H. Rotter, and K. Varmuza. 2005. Prediction of heating values of biomass fuel from elemental composition. Analytica Chimica Acta 544 (1–2):191–98. doi:10.1016/j.aca.2005.01.041.

 Web of Science ®Google Scholar

Demirbas, A. 2004. Combustion characteristics of different biomass fuels. Progress in Energy and Combustion Science 30 (2):219–230. doi:10.1016/j.pecs.2003.10.004.

 Web of Science ®Google Scholar

Demirbaş, A. 1997. Calculation of higher heating values of biomass fuels. Fuel 76 (5):431–34. doi:10.1016/S0016-2361(97)85520-2.

 Web of Science ®Google Scholar

Demirbas, A., D. Gullu, A. Çaglar, and F. Akdeniz. 1997. Estimation of calorific values of fuels from lignocellulosics. Energy Sources 19 (8):765–70. doi:10.1080/00908319708908888.

 Web of Science ®Google Scholar

Callejón-Ferre, A., B. Velázquez-Martí, J. A. López-Martínez, and F. Manzano-Agugliaro. 2011. Greenhouse crop residues: Energy potential and models for the prediction of their higher heating value. Renewable and Sustainable Energy Reviews 15 (2):948–55. doi:10.1016/j.rser.2010.11.012.

 Web of Science ®Google Scholar

Majumder, A., R. Jain, P. Banerjee, and J. Barnwal. 2008. Development of a new proximate analysis based correlation to predict calorific value of coal. Fuel 87 (13–14):3077–81. doi:10.1016/j.fuel.2008.04.008.

 Web of Science ®Google Scholar

Ahmaruzzaman, M. 2008. Proximate analyses and predicting HHV of chars obtained from cocracking of petroleum vacuum residue with coal, plastics and biomass. Bioresource Technology 99 (11):5043–5050. doi:10.1016/j.biortech.2007.09.021.

 PubMed Web of Science ®Google Scholar

Cordero, T., F. Marquez, J. Rodriguez-Mirasol, and J. J. Rodriguez. 2001. Predicting heating values of lignocellulosics and carbonaceous materials from proximate analysis. Fuel 80 (11):1567–71. doi:10.1016/S0016-2361(01)00034-5.

 Web of Science ®Google Scholar

Jiménez, L., and F. González. 1991. Study of the physical and chemical properties of lignocellulosic residues with a view to the production of fuels. Fuel 70 (8):947–50. doi:10.1016/0016-2361(91)90049-G.

 Web of Science ®Google Scholar

Parikh, J., S. Channiwala, and G. Ghosal. 2005. A correlation for calculating HHV from proximate analysis of solid fuels. Fuel 84 (5):487–494. doi:10.1016/j.fuel.2004.10.010.

 Web of Science ®Google Scholar