Chemical Engineering 3
Lecture 3: Crystallizer types, Popula:on balance, Control of crystallisa:on
Crystallizer types and operation
Precursor phase:
- from vapour, solution, or melt
Mode of operation:
- continuous vs. batch
Means of crystal removal:
- mixed product removal vs. classifying crystallizers
Means of achieving supersaturation:
- cooled, evaporative, vacuum crystallizers
Melt crystallization - rotary drum crystallizer
Crystal growth from solution Cooling crystallizers (internal/external cooling)
Evaporating crystallizer - scheme
Evaporating crystallizer – technical arrangement
Draft-tube crystallizer (enables product classification)
Draft-tube crystallizer
Oslo-type crystalliser
Salt crystallisation
Crystallisation plant layout
Crystallisation plant layout
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Crystallisation plant layout
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Crystallisation plant layout
Crystallisation plant layout
Ammonium sulfate
Population balances mass & energy balance ⇒ amount of product
population balance ⇒ quality of product! (e.g. CSD)
number (population) density [no µm-1 m-3]
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n =dNdx
MSMPR crystalliser (mixed-suspension mixed-product removal)
- ideally mixed - steady-state, continuous operation - no crystals in feed - no agglomeration or breakage - size independent growth rate
Number balance
Accumulation = flow in - flow out + birth - death
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0 = 0 − FoutniΔxΔt +Vni−1Gi−1Δt −VniGiΔt
In differential form (∆x ! dx)
Boundary condition - nucleation rate
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d(nG)dx
=G dndx
= −FoutnV
= −nτ
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B =dNdt x= 0
= n0G
size, x [µm] 0 xi-1 xi
number density, n [no µm-1 m-3] ni-1 ni n0 growth rate, G [µm s-1] Gi-1 Gi
Number balance in MSMPR crystallizer - solution
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lnn = lnn0 −xGτ
⇒ n = n0 exp −xGτ
⎛
⎝ ⎜
⎞
⎠ ⎟
size, x [µm]
ln n
slope = - 1/Gτ
ln n0 = ln B/G
Batch cooling crystalliser
Control of temperature & seeding ! control of supersaturation ! resulting size distribution
Batch cooling crystalliser - coupled mass and population balance
Population balance:
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dnidt
=G (ni−1 − ni)Δx
Mass of crystals:
Growth and birth rates:
Solubility:
Cooling profile:
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Gn0 = B
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n(x, t = 0) = ninit
Boundary condition
Initial condition
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ms(t) = mi(t)i∑ =V ni(t)ΔxρsψV xi
3i
∑
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T = f (t)
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ceq (T) = a0 + a1T + a2T2 + a3T
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G = kGΔcγ
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B = kBΔcβ
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Δc = c(t) − ceq (T) =mini −ms(t)
V− ceq (T)