Mathematical model of coal

Weiss, V., and Fett, F. N. Mathematical modelling of coal combustion in a circulating fluidized bed reactor, in Circulating Fluidized Bed Technology (P. Basu, ed.), p. 167. Pergamon Press, 1986. 

A Simple Model of Coal Pyrolysis. In this section, a simple mathematical model of coal pyrolysis is formulated to qualitatively describe the pyrolysis of coal in a fluidized bed. This model is based on the assump-... 

With the mathematical modeling of coal gas seepage, the discretizating of the gas by numeri-... 

Rafsanjani HH, Jamshidi E (2008) Kinetic study and mathematical modeling of coal char activation. Chem Eng J 140(1-3) 1-5... 

These precautions may not be entirely sufficient during dry periods. The spreading of water on haul roads and working floors is the principal operational practice aimed at minimizing airborne dust release. Mathematical models of dust release from opencast mine haul roads have recently been developed, which allow forward planning of water-spreading frequencies for summer and winter conditions in opencast coal mines in specific climatic settings (Thompson Visser 2002). Under the driest of... 

A.B. Hedley and E.W. Jackson. A Simplified Mathematical Model of a Pulverized Coal Flame Showing the Effect of Recirculation on Combustion Rate. J. Inst. Fuel, 39 208,1966. 

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. 

Weiss, V., Fett, F. N., Helmrich, H., and Janssen, K. Mathematical modelling of circulating fluidized bed reactors by reference to a solids decomposition reaction and coal combustion, Chem. Eng. Process, vol. 22, No. 2, pp. 79-90 (1987). 

Bliek A, Mathematical modelling of a cocurrent fixed bed coal gasifier (1984), Ph.D. thesis University of Twente... 

The National Science Foundation is sponsoring a study led by Dr. Richard Bartha of Rutgers University on the multisubstrate biodegradation kinetics of PAHs from creosote, coal tar, and diesel fuel. The relative biodegradabilities and substrate interactions of PAHs in sole and multi-substrate systems will be determined and related to dissolution kinetics processes governing bioavailability. An integrated mathematical model of the behavior of PAHs in NAPL-contaminated soils will be developed and validated. 

Lockwood, F. C., Mahmud, T., and Yehia, M. A. "Mathematical Modelling of Some Semi-Industrial Pulverized Coal Flames." The Eighth Annual International Pittsburgh Coal Conference, 41-46, 1991. 

The processes of thermal decomposition play an important role in various practical fields including metallurgy, mineral conversion processes, pyrogenic chemical technology, pyrolysis and thermal treatment of wood and coal, com-hustion of natural and synthetical fuels, coal carbonization, the prevention of grain spontaneous ignition, and so on. There is still a need for scientifically well-founded approaches to control the thermal decomposition of materials. Many studies focus attention on the chemical transformations and reactions in the pyrolized systems and on the creation of mathematical models of such processes as the major parts of the theory of chemical decomposition of complex substances. 

THE MATHEMATICAL MODEL OF SEEPAGE IN THE HIGH-PRESSURE WATER INJECTION COAL SEAM GENERAL INSTRUCTIONS... 

The process of coal seam water injection can be regarded as water flow at low speed in porous medium. Therefore, based on darcy s law, the seepage mathematical model of high-pressure water injection coal is solved (J. et al. 1983, R.E. 1984, Kong 2010). 

Dimensionless analysis in mathematical model of gas emission in coal particles... 

Once the mathematical model of gas emission in coal particle is set up, how to choose the specific conditions is vital for the solution. The conditions of coal samples with different particle size are varied greatly, even the physical parameters of the same coal sample under different pressures change a lot, and bringing all conditions into the model is almost impossible, so an effective method is needed to simplify the solution (Zhou Lin 1999). Actually the gas flow in coal particle has much in common, and the dimensionless method can combine several meaningful physical parameters to reflect the common (Zhang et al. 2001, Qin et al. 2009, Qin et al. 1998), which can not... 

According to Darcy law, the mathematical model of gas emission in the coal particle and its boundary conditions is established, by means of which the dimensionless pressure, the dimensionless time and the dimensionless radius are put forward to simphfy the model. 

Qin, Y.P. et al. 2012. Mathematical model of gas emission in coal particles and the numerical solution. Journal of China Coal Society 37(9) 1466-1471. 

ABSTRACT Analyzed the mechanism of the occurrence of time-varying diffusion coefficient in the process of diffusion in the pea coal on account of Pick diffusion, measured the relationship between time and the diffusion coefficient of Nantong coal samples, by the formula of seeking for the variant diffusion coefficient. Got the mathematical model of variant diffusion coefficient by analysis of the experimental data, derived the analytic solution of time varying diffusion equation. 

MATHEMATICAL MODEL OF GAS-SOLID COUPLING OF COAL CONTAINING GAS... 

Zhang, Z.R. Yuan, C.F. 1999. Study on mathematical model of coalbed gas geology used to prediction of mine gas emission. Journal of China Coal Society 24(4) 8. 

Korobeinikov, V.P., and Menshov, I.S., Mathematical Modeling of Blast Wave Propagation in Coal Mines, Book of Abstracts VIII Int. Col, on Gasdvnamics of Explosion and Reactive Systems. Minsk, USSR, 1981, p. 103. 

B. M. Visser. Mathematical Modeling of Swirling Pulverized Coal Flames. PhD Dissertation, IFRF, 1991. 

Table VI gives an example of the reaction pathways proposed by different investigators for the production of liquid fuel from coal It is apparent that as the mechanism becomes more and more complicated, so do the mathematical models of the reaction.

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

This contribution deals with some important aspects of coal structure evaluation using modified Gaussian models. Further clarification of the nature and functionality of the crosslinks is presented, including an analysis of refinements in the mathematical equations for the determination of Mc. Preliminary experimental data of relevance to this analysis are also presented and discussed. 

Experimental observations show that bituminous coals satisfy at least one important macroscopic characteristic of a cross-linked network they swell in numerous solvents without being dissolved by them even at high temperatures Cl, 6 9), unless thermal degradation or reaction occurs In the development of mathematical models to describe network behavior, crosslinks are assumed to be points (usually carbon atoms) or short bfudgeA (usually of molecular weight much smaller than Mc) whence three or more chains are initiated. 

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