Pulverized coal pellets, which may be approximated as carbon spheres of radius ro= 1 mm, are burned in a pure oxygen atmosphere at 1450 K and 1 atm. Oxygen is transferred to the particle surface by diffusion, whereit is consumed in the reaction C + O2CO2. The reaction rate is first order and of the form NO2’’= -k1CO2 (ro), where k1= 0.1 m/s. Neglecting changes in ro, determine the steady-state O2molar consumption rate in kmol/s. At 1450 K, the binary diffusioncoefficient for O2inCO2is 1.71 x 10-4m2/s.

Explanation:

SO; If we assume that:

P should be the diffusion of oxygen towards the surface ; &

Q should be the  diffusion of carbondioxide away from the surface.

Then  the total molar flux of oxygen is illustrated by :

where;

r is the radial distance from the center of the carbon particle.

Since ;

; we have:

The system is not steady state and the molar flux is not independent of r because the area of mass transfer is not a constant term.

Therefore,  using quasi steady state assumption, the mass transfer rate   is assumed to be independent of r at any instant of time.

       = constant

The oxygen concentration at the surface of the coal particle will be calculated from the reaction at the surface.

The mole fraction of oxygen at a location far from pellet is 1.

Thus, separating the variables and integrating result into  the following:

The mole of oxygen arrived at the carbon surface is equal to the mole of oxygen consumed by the chemical reaction.

Obtaining the total gas concentration from the ideal gas law; we have the following:

where;

R=

The steady state molar consumption rate is: