Distribution-free estimation of f(E) in the distributed activation energy model based on matrix singular value decomposition method

  • Hongxia Wang
  • Hui LiuEmail author
Original Paper


The distribution activation energy model (DAEM) is commonly used for characterizing pyrolysis kinetics of different types of thermally active materials such as coal, biomass, charcoal, polymer, and solid waste. In this work, a new distribution-free method for estimating the activation energy distribution function f(E) in DAEM is developed by establishing a physical and mathematical analogy between DAEM and the integral equation in adsorption. A parameter sensibility analysis of the present method and algorithms for calculating f(E) at different Gaussian distribution parameter, heating rates and pre-exponential factors shows that the present method gives f(E) that leads to predictions of conversion in good agreement with the test data, and applicable to pyrolysis analysis of thermally active solid materials.


DAEM Parameter estimation Biomass pyrolysis Matrix singular value decomposition (SVD) 



We are grateful for the financial support from the National Basic Research Program of China (no. 2011CB201300).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Ali I, Bahaitham H, Naebulharam R (2017) A comprehensive kinetics study of coconut shell waste pyrolysis. Bioresour Technol 235:1–11. CrossRefGoogle Scholar
  2. Alonso MZ, Tran K-Q, Wang L, Skreiberg Ø (2017) A kinetic study on simultaneously boosting the mass and fixed-carbon yield of charcoal production via atmospheric carbonization. Energy Procedia 120:333–340. CrossRefGoogle Scholar
  3. Bhavanam A, Sastry RC (2015) Kinetic study of solid waste pyrolysis using distributed activation energy model. Bioresour Technol 178:126–131. CrossRefGoogle Scholar
  4. Burnham AK, Braun RL (1999) Global kinetic analysis of complex materials. Energy Fuels 13:1–22. CrossRefGoogle Scholar
  5. Burnham AK, Weese RK, Weeks BL (2004) A distributed activation energy model of thermodynamically inhibited nucleation and growth reactions and its application to the β–δ phase transition of HMX. J Phys Chem B 108:19432–19441. CrossRefGoogle Scholar
  6. Burra KG, Gupta AK (2018) Kinetics of synergistic effects in co-pyrolysis of biomass with plastic wastes. Appl Energy 220:408–418. CrossRefGoogle Scholar
  7. Cai JM, Jin C, Yang SY, Chen Y (2011a) Logistic distributed activation energy model—part 1: derivation and numerical parametric study. Bioresour Technol 102:1556–1561. CrossRefGoogle Scholar
  8. Cai JM, Yang SY, Li T (2011b) Logistic distributed activation energy model—part 2: application to cellulose pyrolysis. Bioresour Technol 102:3642–3644. CrossRefGoogle Scholar
  9. Cai JM, Wu WX, Liu RH (2014) An overview of distributed activation energy model and its application in the pyrolysis of lignocellulosic biomass. Renew Sustain Energy Rev 36:236–246. CrossRefGoogle Scholar
  10. Chen XX, Huang YH (2005) A SVD-based approach of suppressing transient interference in high-frequency radar. J Electron Inf Technol 27(12):1879–1882Google Scholar
  11. Chen XY, Liu L, Zhang LY, Zhao Y, Zhang Z, Xie X, Qiu PH, Chen G, Pei JT (2018) Thermogravimetric analysis and kinetics of the co-pyrolysis of coal blends with corn stalks. Thermochim Acta 659:59–65. CrossRefGoogle Scholar
  12. Dawood A, Miura K (2001) Pyrolysis kinetics of γ-irradiated polypropylene. Polym Degrad Stab 73:347–354. CrossRefGoogle Scholar
  13. De Caprariis B, Santarelli ML, Scarsella M, Herce C, Verdone N, Filippis PD (2015) Kinetic analysis of biomass pyrolysis using a double distributed activation energy model. J Therm Anal Calorim 121:1403–1410. CrossRefGoogle Scholar
  14. Ding LP, Yuan YX, Farooq S, Bhatia SK (2005) A heterogeneous model for gas transport in carbon molecular sieves. Langmuir 21:674–681. CrossRefGoogle Scholar
  15. Du ZY, Sarofim AF, Longwell JP (1990) Activation energy distribution in temperature-programmed desorption: modeling and application to the soot oxygen system. Energy Fuels 4:296–302. CrossRefGoogle Scholar
  16. Fang S, Yu Z, Ma X, Lin Y, Chen L, Liao Y (2018) Analysis of catalytic pyrolysis of municipal solid waste and paper sludge using TG-FTIR, Py-GC/MS and DAEM (distributed activation energy model). Energy 143:517–532. CrossRefGoogle Scholar
  17. Fiori L, Valbusa M, Lorenzi D, Fambri L (2012) Modeling of the devolatilization kinetics during pyrolysis of grape residues. Bioresour Technol 103:389–397. CrossRefGoogle Scholar
  18. Golub GH, Reinsch C (1970) Singular value decomposition and least squares solutions. Numer Math 14(5):403–420. CrossRefGoogle Scholar
  19. House WA, Jaycock MJ (1974) A study of the surface heterogeneity of an anatase sample. J Colloid Interface Sci 1:50–58. CrossRefGoogle Scholar
  20. Jaroniec M (1983) Physical adsorption on heterogeneous solids. Adv Colloid Interface Sci 18:149–225. CrossRefGoogle Scholar
  21. Jia CX, Chen JJ, Bai JR, Yang X, Song SB, Wang Q (2018) Kinetics of the pyrolysis of oil sands based upon thermogravimetric analysis. Thermochim Acta 666:66–74. CrossRefGoogle Scholar
  22. Kandasamy J, Gokalp I, Petrus S, Belandria V, Bostyn S (2018) Energy recovery analysis from sugar cane bagasse pyrolysis and gasification using thermogravimetry, mass spectrometry and kinetic models. J Anal Appl Pyrolysis 132:225–236. CrossRefGoogle Scholar
  23. Khonde RD, Chaursia AS (2016) Kinetics of tar reduction in two-stage gasifier using distributed activation energy model. Energy Source Part A 38:3132–3138. CrossRefGoogle Scholar
  24. Lakshmanan CC, White N (1994) A new distributed activation-energy model using Weibull distribution for the representation of complex kinetics. Energy Fuels 8:1158–1167. CrossRefGoogle Scholar
  25. Lin Y, Liao YF, Yu ZS, Fang SW, Ma XQ (2017) The investigation of co-combustion of sewage sludge and oil shale using thermogravimetric analysis. Thermochim Acta 653:71–78. CrossRefGoogle Scholar
  26. Lin Y, Chen Z, Dai M, Fang S, Liao Y, Yu Z, Ma X (2018) Co-pyrolysis kinetics of sewage sludge and bagasse using multiple normal distributed activation energy model (M-DAEM). Bioresour Technol 259:173–180. CrossRefGoogle Scholar
  27. Maaten B, Loo L, Konist A, Pihu T, Siirde A (2017) Investigation of the evolution of sulphur during the thermal degradation of different oil shales. J Anal Appl Pyrolysis 128:405–411. CrossRefGoogle Scholar
  28. Mersmann AB (1991) Fundamentals of adsorption. Engineering Foundation, New YorkGoogle Scholar
  29. Miura K (1995) A new and simple method to estimate f(E) and k 0(E) in the distributed activation energy model from three sets of experimental data [J]. Energy Fuels 9:302–307. CrossRefGoogle Scholar
  30. Miura K, Maki T (1998) A simple method for estimating f(E) and k 0(E) in the distributed activation energy model. Energy Fuels 12:864–869. CrossRefGoogle Scholar
  31. Ng Q-H, Chin BLF, Yusup S, Loy ACM, Chong KYY (2018) Modeling of the co-pyrolysis of rubber residual and HDPE waste using the distributed activation energy model (DAEM). Appl Therm Eng 138:336–345. CrossRefGoogle Scholar
  32. Niksa S, Lau C-W (1993) Global rates of devolatilization for various coal types. Combust Flame 94:293–307. CrossRefGoogle Scholar
  33. Paea S, McGuinness M (2018) Higher order approximations to coal pyrolysis distribution. J. Sust. Min. 2(17):76–86. CrossRefGoogle Scholar
  34. Rostami AA, Hajaligol MR, Wrenn SE (2004) A biomass pyrolysis sub-model for CFD applications. Fuel 83:1519–1525. CrossRefGoogle Scholar
  35. Sfakiotakis S, Vamvuka D (2015) Development of a modified independent parallel reactions kinetic model and comparison with the distributed activation energy model for the pyrolysis of a wide variety of biomass fuels. Bioresour Technol 197:434–442. CrossRefGoogle Scholar
  36. Song HJ, Liu GG, Wu JH (2016) Pyrolysis characteristics and kinetics of low rank coals by distributed activation energy model. Energy Convers Manag 126:1037–1046. CrossRefGoogle Scholar
  37. Sonobe T, Worasuwannarak N (2008) Kinetic analyses of biomass pyrolysis using the distributed activation energy model. Fuel 87:414–421. CrossRefGoogle Scholar
  38. Soria-Verdugo A, Garcia-Hernando N, Garcia-Gutierrez LM, Ruiz-Rivas U (2013) Analysis of biomass and sewage sludge devolatilization using the distributed activation energy model. Energy Convers Manag 65:239–244. CrossRefGoogle Scholar
  39. Ulloa C, Gordon AL, Garcia X (2004) Distribution of activation energy model applied to the rapid pyrolysis of coal blends. J Anal Appl Pyrolysis 71:465–483. CrossRefGoogle Scholar
  40. Vos CHW, Koopal LK (1985) Surface heterogeneity analysis by gas adsorption: improved calculation of the adsorption energy distribution function using a new algorithm named CAESAR. J Colloid Interface Sci 105(1):183–196. CrossRefGoogle Scholar
  41. Wang SR, Ru B, Lin HZ, Sun WX, Luo ZY (2015) Pyrolysis behaviors of four lignin polymers isolated from the same pine wood. Bioresour Technol 182:120–127. CrossRefGoogle Scholar
  42. Wang SR, Dai GX, Yang HP, Luo ZY (2017) Lignocellulosic biomass pyrolysis mechanism: a state-of-the-art review. Progress Energy Combust Sci 62:33–86. CrossRefGoogle Scholar

Copyright information

© Institute of Chemistry, Slovak Academy of Sciences 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Chemical Resource Engineering, Beijing Key Laboratory of Energy Environmental CatalysisBeijing University of Chemical TechnologyBeijingChina

Personalised recommendations