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

3€

G = kGΔcγ

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B = kBΔcβ

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Δc = c(t) − ceq (T) =mini −ms(t)

V− ceq (T)