## Self Assessment Quiz

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

Q9.2.1. Calculate time required for complete consumption of particle and relative resistance of ash layer diffusion.

Q9.2.2. Repeat for 0.05 mm particle.
Data: density solid 4.13 g/mL  = 0.0425 mol/L, ks = 2 cm/s, De in ZnO layer 0.08 sq.cm/s.

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 ?

Q9.4. A solid feed of 20% 1 mm particle, 30 % 2 mm particle , 50% 4 mm particle is passed through a rotary kiln where it reacts with a gas to form a non friable product. Find the residence time needed for 71 % conversion and 100 % conversion given that reaction control applies and that time for complete consumption of 2 mm particle is 5 min.

9.5. A fluidized bed is planned for continuous conversion of solid reactant  B to solid product R
To find the mean residence time of solids in this flow reactor following data are obtained on a batch fluidized unit. Solids were removed and analyzed. Results are:

 Particle size 4 mm 12 mm Temperature 550C 590C Time for 50% conversion 15 min 2 hr

What is the residence time required to achieve 98 % conversion if flow reactor is operated at 550°C with 2 mm particle ?
Ignore gas film resistance.

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 CAO. 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 KP.

Q9.7.1.
Set up the balance equations and show that gas conversion can be given as Where α = 3ЄRg/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 Kp = 5
XA (desired) = 0.8 Xe
FA0 = 3.6 kmol/hr = 0.7 = 1
CA0 = 0.2 kmol/cum

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 Kp = 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: ks = 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 ?