Separation Process Principles- 2n - Seader & Henley - Solutions Manual

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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 10-6 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 shrinking-core 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 shrinking-core model. CuO is uniformly distributed in the particles. Pseudo-steady-state assumption is valid. Find: Effect of particle size on leaching time for 98% of the Cu. Analysis: Equation (16-34) 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 10-6 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 pseudo-steady-state 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 shrinking-core model. Given: Particles of 10 mm (1.0 cm) in diameter. Data from Example 16.8. Assumptions: Applicability of the shrinking-core model. CuO is uniformly distributed in the particles. Pseudo-steady-state assumption is valid. Find: Effect of % recovery over the range of 50 to 100% of Cu on leaching time. Analysis: Equation (16-34) 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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