Clayton Copula as an Alternative Perspective of Multi-Reaction Model

Dhaundiyal, Alok; Singh, Sukhwinder; Hanon, Muammel M.; Schrempf, Norbert

doi:10.2478/rtuect-2018-0006

Cited by 4 publications

(5 citation statements)

References 33 publications

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“…In this manner, due to inertial effect, the biomass will collapse and allow the fresh intake of feedstock. The qualitative aspect of biomass conversion will be materialised once the biomass gets eaten away effectively with time and temperature [27]- [29]. The sudden reduction in the shear strain rate at surface of biomass is due to the reduction of pressure as the temperature of the centre of biomass reaches the furnace temperature.…”

Section: Resultsmentioning

confidence: 99%

Mathematical Modelling of Volatile Gas Using Lattice Boltzmann Method

Dhaundiyal

Singh

2020

Environmental and Climate Technologies

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This study investigates the behaviour of pyrolysis gas, generated by the thermal decomposing of biomass, in a pilot size reactor. The discreet mathematical model, Lattice Boltzmann, has adopted for mathematical simulation of flow of pyrolysis gas across a porous bed of biomass. The effect of permeability, pressure gradient, voidage of bed, density, temperature, and the dynamic viscosity on the mass flow rate of gas is examined by simulating the gas flow across the fixed bed of hardwood. The Darcy equation is used to estimate the flow rate of gas across the fixed bed of hardwood chips. The temperature in the reactor varies from 32 °C to 600 °C. The reactor has an external diameter of 220 mm and the vertical height of 320 mm. Rockwool insulation is used to prevent heat loss across the reactor. The external heating element of 2 kWe was provided to trigger the pyrolysis reaction. The properties of the system have been recorded by the pressure and temperature sensors, which are retrofitted along the periphery of the reactor. The temperature sensors are located at 80 mm apart from each other; whereas the pressure sensor, placed at the bottom circumference of the reactor. The effect of input parameters on the flow properties of gas is also examined to add up the qualitative assessment of the system to biomass pyrolysis. The polytropic equation of gas is found to be PV2.051 = C, whereas the compressibility of gas varies from 0.0025–0.042 m2·N–1.

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Section: Resultsmentioning

confidence: 99%

Mathematical Modelling of Volatile Gas Using Lattice Boltzmann Method

Dhaundiyal

Singh

2020

Environmental and Climate Technologies

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“…dT has no exact solution and it can be approximated by various proposed numerical or asymptotic methods, [32][33][34][35][36][37][38][39] but the most commonly used method for isoconversional models has been proposed by Doyle. [40] The solution of Equation ( 9) using Doyle's approximation (Equation ( 10)) [40] provides the FWO method, [5,6] which can be written as Equation (11):…”

Section: Methods Of Kinetic Analysismentioning

confidence: 99%

“…The temperature integral

((), I ((), \frac{E_{α}}{italicRT}) = \int_{T_{0}}^{T_{f}} e^{- \frac{E}{RT}} italicdT)

has no exact solution and it can be approximated by various proposed numerical or asymptotic methods, [ 32–39 ] but the most commonly used method for isoconversional models has been proposed by Doyle. [ 40 ]…”

Section: Methodsmentioning

confidence: 99%

The effect of torrefaction on the thermo‐kinetics of thermally processed black pine

2020

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This paper investigates the kinetic behaviour of thermal decomposition of pretreated pine needles. The model-free methods of Flynn-Wall-Ozawa (FWO), Kissinger-Akahira-Sunose (KAS), and Kissinger, are used to determine the kinetic parameters of the processed pine needles. For a comparative analysis, the kinetic characteristic of the pre-treated pine needles is equated to the thermal decomposition of the raw pine needles. For torrefaction of the raw substrate, some changes related to the design have been made to the furnace. The raw material has been thermally pre-treated at a temperature of 523 K for 5 minutes. The volumetric rate of nitrogen during the torrefaction process is 42 L Á min −1 , while the purge flow rate of nitrogen gas is 0.2 L Á min −1 for the thermogravimetric analysis. The temperature range for the thermal degradation of the torrefied pine needles is 308 K-873 K. The activation energies determined by the FWO and the KAS methods are 157.08 kJ Á mol −1 and 160.54 kJ Á mol −1 , respectively, whereas it is 137 kJ Á mol −1 by the Kissinger method. The activation energy computed by the FWO and the KAS schemes for the raw material is found to be 1.3% less than that of the processed pine needles. The aromaticity of the thermally processed pine needles is increased by 13.61%. Thermal immunity or stability due to the increasing fraction of lignin causes the activation energy and frequency factor of the pre-treated pine needles to slightly elevate. The redistribution of the pyrolysis stages has been observed for the torrefied pine needle sample, the temperature scale at a constant heating rate increases slightly by 0.34% during the char formation.

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“…The relationship between physical and thermal characteristics of wood and their influence on the decomposition process has been highlighted by the analogous scheme. However, the various modelling scheme pivoting around the kinetic aspect of the pyrolysis are summarised in the literature [1][2][3][4][5][6]. It is assumed that the fixed bed behaves like a porous wooden slab whose length sinks with time as a shrinking radius of the particle during combustion [7].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Pyrolysis of Hardwood (Acacia)

Dhaundiyal¹,

Singh²,

Bacskai³

2020

Preprint

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This paper emphasises on the analogous modelling of hardwood (Acacia) pyrolysis. The effect of physical characteristics of hardwood chips on the pyrolysis is examined through the conservation of solid mass fraction of biomass. The chip size of G30 and G50 are used in the pyrolysis reactor. In the analogous situation, the fixed bed is assumed to be a wooden slab with a porosity equivalent to the voidage of bed. The bulk density, the length of the bed and the porosity are some of the physical attributes of a fixed bed used to determine the variation of solid mass of the hardwood across the fixed bed. The four-temperature sensors separated from each other by 80 mm are used to determine the temperature along the length of the pyrolysis unit. The heating element of 2 kWe is used to initiate the pyrolysis of biomass. The experiments are conducted in three different stages. The ONORM standard chips, G30 and G50, and the combination of them are separately pyrolysis to determine the validity of a model for different sizes of chips. The proposed model is also used to establish the relationship between the kinetics of pyrolysis and decomposition of the hardwood.

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Clayton Copula as an Alternative Perspective of Multi-Reaction Model

Cited by 4 publications

References 33 publications

Mathematical Modelling of Volatile Gas Using Lattice Boltzmann Method

Mathematical Modelling of Volatile Gas Using Lattice Boltzmann Method

The effect of torrefaction on the thermo‐kinetics of thermally processed black pine

Mathematical Modelling of Pyrolysis of Hardwood (Acacia)

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