Pyrolysis model

Step 4 of the thermal treatment process (see Fig. 2) involves desorption, pyrolysis, and char formation. Much Hterature exists on the pyrolysis of coal (qv) and on different pyrolysis models for coal. These models are useful starting points for describing pyrolysis in kilns. For example, the devolatilization of coal is frequently modeled as competing chemical reactions (24). Another approach for modeling devolatilization uses a set of independent, first-order parallel reactions represented by a Gaussian distribution of activation energies (25). 

A model for coal fluidity based on a macromolecular network pyrolysis model has been developed (33). In that model, bond breaking is described as a first-order reaction having a range of activation energies. A variety of lattices have also been used to describe the bonding in coal. In turn these stmctures... 

Miller, R. S. and Bellan, J. (1997) A generalized biomass pyrolysis model based on superimposed cellulose, hemicellulose and lignin kinetics. Comb. Sci. and Techn., 126, 97-137. 

Paules I.V., G. E. and Meixell Jr., M. D., "A Fundamental Free Radical Kinetic Pyrolysis Model for On-Line Closed-Loop Plant-Wide Optimization of Olefins Plants", Paper Presented at CIMPRO 94, New Brunswick, NJ (April 1994). 

The Arrhenius expression (Equation 19.1) using the activation energy and pre-exponential factor derived from TGA measurements of a PA6 sample in N2 was incorporated in a standard ID pyrolysis model described in Section 19.6. The thermal properties used in the model are the ones from the ignition tests (Section 19.4.2.2) as described in Section 19.6 in conjunction with the MDSC experiments (Section 19.3.2.2). Figures 19.25a-c show the predicted surface temperature histories for... 

Solid Fuels Heat Transfer Limited Pyrolysis Models.565... 

Solid Fuels Finite-Rate (Kinetically Limited) Pyrolysis Models.566... 

With empirical pyrolysis models, a material s burning rate is zero until its surface is heated to its ignition temperature (Tig), at which time ignition occurs. After ignition, the mass loss rate of a fuel element is estimated from the net heat flux to the fuel s surface (q"a) divided by the effective heat of gasification (A7/g) ... 

Empirical approaches are useful when macroscale HRR measurements are available but little or no information is available regarding the thermophysical properties, kinetic parameters, and heats of reaction that would be necessary to apply a more comprehensive pyrolysis model. Although these modeling approaches are crude in comparison with some of the more refined solid-phase treatments, one advantage is that all required input parameters can be obtained from widely used bench-scale fire tests using well-established data reduction techniques. As greater levels of complexity are added, establishing the required input parameters (or material properties ) for different materials becomes an onerous task. 

Temperature profiles can be determined from the transient heat conduction equation or, in integral models, by assuming some functional form of the temperature profile a priori. With the former, numerical solution of partial differential equations is required. With the latter, the problem is reduced to a set of coupled ordinary differential equations, but numerical solution is still required. The following equations embody a simple heat transfer limited pyrolysis model for a noncharring polymer that is opaque to thermal radiation and has a density that does not depend on temperature. For simplicity, surface regression (which gives rise to convective terms) is not explicitly included. 

The basic assumption inherent to heat transfer limited pyrolysis models is that heat transfer rates, rather than decomposition kinetics, control the pyrolysis rate. Consequently, thermal decomposition kinetics do not come into play, other than indirectly through specification of Tp. This approximation is often justified on the basis of high activation energies typical of condensed-phase pyrolysis reactions, i.e., the reaction rate is very small below Tj, but then increases rapidly with temperature in the vicinity of Tp owing to the Arrhenius nature, and the high activation energy, of the pyrolysis reaction. 

The FDS5 pyrolysis model is used here to qualitatively illustrate the complexity associated with material property estimation. Each condensed-phase species (i.e., virgin wood, char, ash, etc.) must be characterized in terms of its bulk density, thermal properties (thermal conductivity and specific heat capacity, both of which are usually temperature-dependent), emissivity, and in-depth radiation absorption coefficient. Similarly, each condensed-phase reaction must be quantified through specification of its kinetic triplet (preexponential factor, activation energy, reaction order), heat of reaction, and the reactant/product species. For a simple charring material with temperature-invariant thermal properties that degrades by a single-step first order reaction, this amounts to -11 parameters that must be specified (two kinetic parameters, one heat of reaction, two thermal conductivities, two specific heat capacities, two emissivities, and two in-depth radiation absorption coefficients). 

Typically, a fire growth model is evaluated by comparing its calculations (predictions) of large-scale behavior to experimental HRR measurements, thermocouple temperatures, or pyrolysis front position. The overall predictive capabilities of fire growth models depend on the pyrolysis model, treatment of gas-phase fluid mechanics, turbulence, combustion chemistry, and convective/radiative heat transfer. Unless simulations are truly blind, some model calibration (adjusting various input parameters to improve agreement between model calculations and experimental data) is usually inherent in published results, so model calculations may not truly be predictions. 

Lowndes et al. [91] used the commercial CFD model Fluent to simulate flame spread along a conveyor belt. Fluent, at the time this modeling was conducted, did not contain a conventional pyrolysis model in the sense that is normally implied in the fire literature. Instead, the authors adapted a discrete phase model, which is intended to simulate the combustion of pulverized coal. 

FIGURE 20.4 Comparison of measured and modeled HRR in room corner test on particle board. Model calculations are for total HRR calculated with heat transfer limited pyrolysis model. (Adapted from Yan, Z. and Holmstedt, G Fire Saf../., 27, 201, 1996.)... 

Lautenberger, C. and Fernandez-Pello, C. Pyrolysis modeling, thermal decomposition, and transport processes in combustible solids. In Faghri, M. and Sunden, B. (eds.). Transport Phenomena in Fires. Boston, MA WIT Press, 2008, pp. 209-259. 

Matala, A., Hostikka, S., and Mangs, J. Estimation of pyrolysis model parameters for solid materials using thermogravimetric data. Fire Safety Science—Proceedings of the Ninth International Symposium, Karlsruhe, Germany, 2008. 

Asphaltene and resid pyrolysis provide two relevant examples of global pyrolysis models. The pyrolysis of an isolated asphaltene feedstock typically yields the type of data summarized in Figure 2, a plot of the temporal variation of weight based product fractions as a function of time (7). This figure illustrates the exponential disappearance of asphaltene accompanied by the formation of coke, maltene and gas product fractions. Consideration of the initial slopes for the formation of coke, maltene and gas fractions led to the type of reaction network shown in Figure 3. Since resid and its reaction products can likewise be defined in terms of the solubility and volatility-based product groups asphaltene,... 

The mathematical models of the reacting polydispersed particles usually have stiff ordinary differential equations. Stiffness arises from the effect of particle sizes on the thermal transients of the particles and from the strong temperature dependence of the reactions like combustion and devolatilization. The computation time for the numerical solution using commercially available stiff ODE solvers may take excessive time for some systems. A model that uses K discrete size cuts and N gas-solid reactions will have K(N + 1) differential equations. As an alternative to the numerical solution of these equations an iterative finite difference method was developed and tested on the pyrolysis model of polydispersed coal particles in a transport reactor. The resulting 160 differential equations were solved in less than 30 seconds on a CDC Cyber 73. This is compared to more than 10 hours on the same machine using a commercially available stiff solver which is based on Gear s method. 

A commercial stiff ordinary differential equation solver subroutine, DVOGER, is available in the IMSL Library (3). This subroutine uses Gear s method for the solution of stiff ODE s with analytic or numerical Jacobians. The pyrolysis model was solved using DVOGER and the analytical Jacobians of Eqs. (14) and (15). For a residence time of 0.0511 in dimensionless time, defined as t/t where 9... 

TRANSFER MODELS PYROLYSIS MODELS FURNACE MODELS... 

In a previous publication (12,13) the development of pyrolysis models for gas and liquid feeds was discussed. In a more recent paper, Shu and Ross (14) described a generalized model for predicting the rate of thermal decomposition of naphthas. These models become key components of Braun s computational system. 

The present system is sufficiently general to incorporate any type of reaction network, from simple empirical models to detailed mechanistic ones. However, in the following discussion, pyrolysis models reported in our previous publications (12,13,14,16) will be employed. 

Shu, W. R., Ross, L. L., Pang, K. H., "A Naphtha Pyrolysis Model for Reactor Design11. Paper No 27d, the 85th National Meeting of AIChE, Philadelphia, June 1978. 

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