Char gasification modeling equations

A model Is presented for char gasification with simultaneous capture of sulfur In the ash minerals as CaS. This model encompasses the physicochemical rate processes In the boundary layer, In the porous char, and around the mineral matter. A description of the widening of the pores and the eventual collapse of the char structure Is Included. The modeling equations are solved analytically for two limiting cases. The results demonstrate that pore diffusion effects make It possible to capture sulfur as CaS In the pores of the char even when CaS formation Is not feasible at bulk gas conditions. The model predictions show good agreement with experimentally determined sulfur capture levels and reaction times necessary to complete gasification. 

The specific char surface area, Sc, the char porosity, e, and the effective diffusivities, De vary with char conversion and thus have to be determined from a model of the pore structure evolution Various models can be used for that purpose [10-12]. We chose to use Gavalas s random capillary model [12,13] to describe the widening of the pores and the eventual collapse of the char structure This model provides exact expressions for Sc, e, and De in terms of a local carbon conversion, q(r,t), which represents the length the pore surface has retreated at time t due to char gasification, i.e. the pore radius at the radial coordinate r and time t the initial pore radius + q(r,t). The conservation equation for this local carbon conversion takes the form ... 

A dynamic one-dimensional model of char gasification in a fixed-bed reactor has been developed. The model is based on conservation of mass and energy together with chemical equilibrium in the gas phase between H2O, H2, CO2, CO, using the water-gas shift reaction. Methane is assumed inactive in the char bed. The basic equations are ... 

The steady-state permeation model of in situ coal gasification is presented in an expanded formulation which includes the following reactions combustion, water-gas, water-gas shift, Boudouard, methanation and devolatilization. The model predicts that substantial quantities of unconsumed char will be left in the wake of the burn front under certain conditions, and this result is in qualitative agreement with postburn studies of the Hanna UCG tests. The problems encountered in the numerical solution of the system equations are discussed. 

Attempts have been made to predict gasification rates using mathematical models. This area has been briefly reviewed by Rafsanjani et al. (2002) who discuss the use of (what are termed) the grain model, the random pore model, the simple particle model and the volume reaction model. They report that differential mass conservation equations are required for the oxidant gas and char particle. These authors use a simplified mathematical model (the quantise method (QM)) for activation of coal chars when both diffusion and kinetic effects have to be considered. Results are compared with other methods when it is found that QM predictions of rate are more accurate than predictions by the random pore model and the simple particle model. 

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