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Seader & Henley, Separation Process Principles

Crystallization (12.11, p.817)

•  Solid-liquid separation where solid particles are formed from a homogenous liquid phase

–  Ice crystals in freezing water

–  Snow flakes from vapor

–  Solid particles from a liquid melt (e.g. molten metals, lava)

–  Solid crystals (e.g. salt) from aqueous solution •  Typical process involves cooling a concentrated solution at a temperature past

the solute solubility limit •  Another approach is to add an antisolvent that is miscible with the liquid, but

cannot dissolve the solute (e.g. benzoic acid from ethanol using water) –  Supersaturation required for crystallization ---- Controlled by nucleation and growth

–  Rate of cooling or antisolvent addition can be used to control the rate of crystal formation

•  Yield, purity, uniform particle size, and desired shapes (e.g. needles vs. cubes) –  Permit easy powder flows, low caking in packaged product form

Solubility curves in crystallization

Crystallizer equipment

Types:

1. Supersaturation by cooling with negligible evaporation –  Solubility must have a strong T dependence

2. Supersaturation by evaporation with little or no cooling –  No T dependence needed

3. Supersaturation by combined cooling and evaporation (vacuum)

Suspending growing crystals & controlling how the liquid contacts them

Crystallizer equipment

Configurations:

1. Tank crystallizers –  Hot saturated solutions cools in open tank

–  Difficult to control nucleation and, hence, crystal size

2. Scraped surface crystallizers –  Cooling surface scraped periodically to remove crystals (e.g. ice cream)

3. Circulating-liquid evaporator-crystallizer –  Supersaturation generated by evaporation (thermal)

4. Circulating-liquid vacuum crystallizer –  Supersaturation generated by evaporation (thermal + vacuum)

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Swenson-walker scraped surface crystallizers

Crystallization theory - Reaching supersaturation

a = undersaturated b = equilibrium between saturated solution and visible crystals c = supersaturation where crystals grow, but do not nucleate c-e = supersaturation temperature difference d = spontaneous nucleation of small crystals d-f = maximum (limiting) supersaturation Temperature difference

Kelvin Eqn.

Crystallization theory - Nucleation

•  Solubility & crystal size –  Small particles, greater surface energy, greater solubility.

•  Homogeneous nucleation –  Molecules cluster together to form small particles.

–  Small particles aggregate to form a nucleus, which can grow

•  Contact (heterogeneous) nucleation –  E.g. new nuclei formed at reactor walls, by agitator blades, and/or by colliding

crystals

•  Commercial setting –  Supersaturation is low, agitation is needed to suspend crystals, contact

nucleation is predominant (little homogeneous crystallization)

Crystallization theory

•  Primary –  Molecules form a cluster, cluster can grow into a particle, particles

can grow and become a nucleus…

•  Secondary –  Nucleation caused by presence of existing crystals

Crystallization theory – Crystal growth

•  Mass flux from bulk to surface i: –  ky from “typical” correlations

–  y’A is surface concentration

•  Surface reaction is c-dependent: –  kS from reference

Crystallization theory – Crystal growth

•  ΔL law of growth (McCabe) ‒  ΔL is increase in linear length, proportional to

all crystals

–  G is a constant (e.g. mm/h)

–  Total growth, ΔL, is same for all crystals

Model for mixed suspension-mixed product removal crystallizer (MSMPR)

•  Crystal population-density – obtained experimentally using screens. Sieve fractions are weighed, between two sieves where LAV=(L1+L2)/2 and ΔL = L1-L2 (upper screen – lower).

Model for mixed suspension-mixed product removal crystallizer (MSMPR)

•  Population material balance

–  Crystals collected from CSTR (ΔnΔL) in Δt.

–  Composition of effluent = that in crystillzer (i.e. composition leaving stage = stage)

Model for mixed suspension-mixed product removal crystallizer (MSMPR)

•  Population material balance

–  Particle size and nucleation rate, plot of n vs. L gives G and n0:

–  Average particle size (50% smaller, 50% larger):

–  Predominant particle size:

–  Nucleation rate:

Model for mixed suspension-mixed product removal crystallizer (MSMPR)

•  Population material balance

–  Predicting cumulative wt fraction obtained at opening L:

–  Process design:

•  Experimental G and B0 are obtained by population material balance for a given set of conditions

•  Additional experiments performed to determine effect of τ and mixing on G and B0

•  Continue until desired Wf distribution or Ld is obtained

Example: Growth and nucleation in MSMPR

Example: Growth and nucleation in MSMPR