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Unformatted text preview: ubject: Time to leach 95% of the sucrose from ground coffee particles with water at 25oC.
Given: Coffee particles of average diameter = 2 mm. Diffusivity of sucrose in the particles =
1.0 x 106 cm2/s.
Assumptions: Leaching is controlled by internal mass transfer in the particles. Particles are
6
− π2 Det
Eavg = 2 exp
(1)
spheres. If NFo > 0.10,
π
a2
Find: Time to leach 95% of the sucrose.
Analysis: a = particle radius = 1 mm = 0.1 cm.
Want Eavg = 1 – 0.95 = 0.05
Rearranging (1) and using cgs units, a2
6
0.12
6
t = 2 ln 2
ln
= 2,530 s = 42.2 min
=
2
2
−6
π De
π Eavg
3.14 ( 0.05 )
3.14 (1× 10 )
Check the Fourier number for mass transfer to see if (1) is valid.
−6
Det 1× 10 ( 2530 )
NFo = 2 =
= 0.25 which is > 0.10
a
0.12 Therefore, (1) is valid. Exercise 16.13
Subject: Effect of particle size on the leaching of CuO from copper ore by sulfuric acid in
Example 16.8, using the shrinkingcore model.
Given: Particles ranging in size from 0.5 mm to 50 mm (or 0.05 to 5.0 cm). Data from Example
16.8.
Assumptions: Applicability of the shrinkingcore model. CuO is uniformly distributed in the
particles. Pseudosteadystate assumption is valid.
Find: Effect of particle size on leaching time for 98% of the Cu.
Analysis: Equation (1634) is applied: ρB rs2
r
1− 3 c
t=
6 DebM BcAb
rs 2 r
+2 c
rs 3 (1) where, the leaching reaction is assumed to be that of Eq. (1) in Example 16.8.
Using cgs units and data from Example 16.8, the symbols are:
t = time in s
ρB = mass of CuO per volume of ore = 0.054 g/cm3
rs = radius of particle in cm
rc/rs = radius ratio corresponding to 2% of the particle volume = (0.02)1/3 = 0.271
De = effective diffusivity of the hydrogen ion of the H2SO4 = 0.6 x 106 cm2/s
b = stoichiometric coefficient of the solid reactant, CuO in Eq. (1) of Example 16.8 = 0.5
MB = molecular weight of CuO = 79.6
cAb = concentration of H+ in bulk fluid = 0.001 mol/cm3
Substituting these values into (1), gives:
t = 376,900rs2 [ 0.819]
(2)
Calculations for particle diameters of 0.05, 0.5, and 5 cm give the following results:
Particle diameter, cm
Time, seconds 0.05
193 0.5
19,300 5.0
1,930,000 All values are consistent with the assumption of a pseudosteadystate necessary for the validity
of Eq. (1), as shown in Example 16.8. Exercise 16.14
Subject: Effect of % recovery of copper on the leaching of CuO from copper ore by sulfuric
acid in Example 16.8, using the shrinkingcore model.
Given: Particles of 10 mm (1.0 cm) in diameter. Data from Example 16.8.
Assumptions: Applicability of the shrinkingcore model. CuO is uniformly distributed in the
particles. Pseudosteadystate assumption is valid.
Find: Effect of % recovery over the range of 50 to 100% of Cu on leaching time.
Analysis: Equation (1634) is applied: ρB rs2
r
t=
1− 3 c
6 DebM BcAb
rs 2 r
+2 c
rs 3 (1) where, the leaching reaction is assumed to be that of Eq. (1) in Example 16.8.
Using cgs units and data from Example 16.8, the symbols are:
t = time in s
ρB = mass of CuO per volume of ore = 0.054 g/cm3
r...
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 Spring '11
 Levicky
 The Land

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