Q9.1. Calculate time needed to burn to completion particles of graphite R = 5 mm, density 2.2 g/mL, ks = 20 cm/s in 8 % oxygen stream and at reaction temperature 900°C. Assume film diffusion not important

Q9.2. Spherical particles of zinc blende (ZnS) of size R = 1 mm are roasted in an 8 % oxygen stream at 900°C and 1 atm. The stoichiometry of the reaction can be given as
2 ZnS +  3 O₂  =  2 ZnO  + 2 SO₂

Q9.3. A large stock pile of coal is burning. The surface is in flames. In a 24 hr period the linear rate of the pile as measured by its silhouette against horizon seems to decrease by about 5 %. Obtain expression for size of burning mass with time. When would the fire burn itself out ?

Q9.6. In a gaseous environment particles of B are converted to solid product as per A(g) + B (s) = R (g) + S (solid). Reaction proceeds according to shrinking core model under reaction control and time for complete conversion is 1 hr. A fluidized bed is to be designed to treat 1 ton/hr of solid to 90 percent conversion using stoichiometric quantity of A fed at C_AO. Find the weight of solid in the reactor if gas is assumed to be in mixed flow. Take into account variation of gas composition due to chemical reaction

Q9.7. A gas solid reaction A (g) + B(s) = C (g) + D(s) is bought about in a rotary kiln at normal pressure. The reaction follows the shrinking core model under gas diffusion control. Heat effects are negligible. The equilibrium is K_P.

Q9.7.1. Set up the balance equations and show that gas conversion can be given as

                                                                      
Where α = 3Є_Rg/R, β =  and  is the gas residence time

Q9.7.2. Determine solids conversion. Gas residence time, solid residence time is reactor volume for the following conditions.

Data:

Particle size R = 0.05m
Solids hold up  = 0.15 cum solid/cum reactor
Solid density  = 50 kmol/cum solid
Mass transfer coefficient kg = 0.01 m/sec
Equilibrium constant K_p = 5
X_A (desired) = 0.8 Xe
F_A0 = 3.6 kmol/hr
  = 0.7
  = 1
C_A0 = 0.2 kmol/cum

V = 0.9 cum,  = 2.66 hrs,  =17.8 sec, X_B = 0.76

Q9.9. Gasification of a batch of solid carbon particles using an initial charge of CO₂ isto be carried out in an isothermal enclosure . The reaction stoichiometry is given as  C + CO₂ = 2 CO. The reaction is carried out at 850°C and 1 atm pressure using pure CO₂. Equilibrium constant is K_p = 14.1 at 850°C with pressures in atmosphere.

This is case of shrinking particle with external diffusion as the controlling mechanism. Assume that kg R/D = 1 where D is diffusion coefficient and kg is external as transfer coefficient.
Set up model and obtain expression for variation of solid conversion with time. Estimate time required for 95 %  of equilibrium conversion; Initial charge 1 mol  carbon, 10 mol CO₂ ,  solid density 1 mol/mL R = 1 cm.

Q9.11 Iron ore of density 4.6 g/mL (MW 225) size R = 5 cm undergoes following reaction.
4 H₂ + Fe₃ O₄ = 4 H₂O + 3 Fe

Q9.11.1. Estimate time required fot 98 % conversion in hydrogen environment at 600 C and 1 atm pressure.
Data: k_s = 1.93 10**5 * exp( - 12000/RT ) , hydrogen diffusion coefficient in product layer 0.03 sqcm/s, film diffusion coefficient 10 cm/s

Q9.11.2. Using the results sketch a process for the smelting of iron oxide to produce sponge iron specifying the important design and operating decisions. What do you see are the potentials of this process in relation to blast furnace technology ?