Distillation & Crystallization Notes

4.1. Introduction

• Distillation is a unit operation separating liquid mixture constituents using thermal energy.
• Separation relies on differences in vapor pressures, boiling points, or volatility of constituents at the same temperature.
• Also known as “fractional distillation or fractionation”.
• Commonly used in chemical and petroleum industries to separate liquid mixtures.
• Examples:
  • Separation of ethanol and water.
  • Production of absolute alcohol from 95% ethyl alcohol using benzene.
  • Separation of petroleum crude into gasoline, kerosene, fuel oil, etc.

Boiling Point

• For a given pressure, a pure liquid boils/vaporizes at a specific temperature called its “boiling point”.
• Boiling points vary for different liquids; e.g., water (100°C), toluene (110°C), and methanol (64.7°C) at 1 atm.
• In a binary mixture:
  • The component with a lower boiling point or higher vapor pressure is the “more volatile or lighter component”.
  • The component with a higher boiling point or lower vapor pressure is the “less volatile or heavier component”.
• Example: In a methanol-water system, methanol is more volatile, and water is less volatile.

Raoult’s Law

• Used to predict vapor-liquid equilibrium for an ideal solution in equilibrium with an ideal gas mixture, based on vapor pressure data.
• States that in a binary system of A and B, the equilibrium partial pressure of a constituent at a given temperature equals the product of its vapor pressure in a pure state and its mole fraction in the liquid phase.
• Mathematically:
  • pA = PA^{vap} . x_A
  • pB = PB^{vap} . x_B
  • pB = PB^{vap} . (1 - xA), as xA + x_B = 1
  • Where:
    • pA & pB - Equilibrium partial pressure of A and B, respectively.
    • PA^{vap} & PB^{vap} - Vapor pressure of A and B in pure state, respectively.
    • xA & xB - Mole fraction of A and B in the liquid phase, respectively.

Relative Volatility (\alpha_{AB})

• Volatility of A:
  • Defined as the ratio of the partial pressure of A to the mole fraction of A in the liquid phase.
  • Volatility
    of
    A = \frac{pA}{xA} = \frac{Partial pressure of 'A'}{mole fraction of A in the liquid phase}
• Volatility of B:
  • Defined as the ratio of the partial pressure of B to the mole fraction of B in the liquid phase.
  • Volatility of B = \frac{pB}{xB} = \frac{Partial pressure of 'B'}{mole fraction of B in the liquid phase}
• Relative volatility:
  • The ratio of the volatility of A (more volatile) to that of B (less volatile).
  • Denoted by \alpha_{AB}.
  • \alpha{AB} = \frac{\left( \frac{pA}{xA} \right)}{\left( \frac{pB}{xB} \right)} = \frac{pA}{pB} . \frac{xB}{x_A}

4.2. Methods of Distillation

• Common methods:
  • Simple batch (or) differential distillation
  • Flash (or) equilibrium distillation
  • Continuous distillation

4.2.1. Simple Batch (or) Differential Distillation

• A known quantity of liquid mixture is charged into a still or jacketed kettle.
• The mass is heated using steam in the jacket, and boiled slowly.
• Vapors are withdrawn, liquefied in a condenser, and collected as distillate.
• Initially, vapors are richest in the more volatile component. As distillation proceeds, the liquid becomes lean in the more volatile component.
• The composition of the less volatile component increases, raising the boiling point.
• The distillate can be collected in several receivers (cuts) to obtain products of various purities.
• Distillation continues until the boiling point reaches a predetermined value.
• The remaining liquid in the still, containing mainly the less volatile component, is removed as residue.
• Mathematical approach is differential due to changing composition during operation.

4.2.3. Continuous Rectification - Binary System

• Common in industrial practice for obtaining almost pure products.
• Enrichment of the vapor stream through the column in contact with reflux is termed “rectification”.
• Part of the condensed liquid is returned as reflux.
• Maximum enrichment of the more volatile component is achieved through successive partial vaporization and condensation via multi-stage contact of vapor and liquid.
• This is achieved in a "fractionating column".

Fractionating Column

• Components:
  1. Cylindrical shell divided into sections by perforated trays
  2. Reboiler
  3. Condenser
• The liquid mixture enters the column approximately centrally.
• The column is divided into a rectifying section and a stripping section.
• Rectifying section (above feed plate):
  • Vapor is washed to remove the less volatile component using liquid (reflux) from the top.
  • Also called the absorption/enriching section as the feed is enriched.
  • The top product or distillate is richer in the more volatile component.
• Stripping section (below feed plate):
  • Liquid is stripped of the more volatile component by rising vapor.
• Perforated trays facilitate gas-liquid contact for mass transfer.
• Vapors are generated in the reboiler and fed to the bottom of the column.
• Liquid removed from the fractionator, rich in the less volatile component, is the bottom product.
• Vapor from the top is fed to the condenser, where latent heat is removed using a coolant.
• Part of the condensed liquid is returned as reflux, and the rest is withdrawn as the distillate.
• The vapor becomes richer in the more volatile component moving up the column, while the liquid becomes richer in the less volatile component moving down.
• Temperature is maximum at the bottom (bubble point) and minimum at the top (dew point).

4.3. Crystallization

• Introduction:
  • A unit operation involving the separation of a solute from a solution in the form of crystals.
  • Involves simultaneous mass and heat transfer.
  • Yields a pure product.
  • Requires less energy than other purification methods like distillation.
• Principle: Saturation
  • Example: Dissolving copper sulfate in water.
  • Initially, salt dissolves completely.
  • Further addition leads to saturation, where no more salt dissolves without temperature change.
  • A saturated solution at different temperatures contains different amounts of dissolved salt.
  • Cooling a saturated solution at a higher temperature causes the salt to crystallize out.

Supersaturation

• The quantity of solute present in solution where crystals are growing, compared to the solute quantity at equilibrium.
• S = \frac{(Parts solute / parts solvent) at prevailing condition}{(Parts solute / parts solvent) at equilibrium} * 100
• S \ge 1.0
• Crystallization requires a supersaturated solution.

Units for Supersaturation

• Supersaturation is the concentration difference between the supersaturated solution (crystal growth) and the equilibrium solution.

4.4. Methods of Supersaturation

• Four methods:
  • A. Supersaturation by cooling:
    • Used for substances with decreasing solubility as temperature decreases.
    • Most common behavior.
  • B. Supersaturation by evaporation of solvent:
    • Used for substances with nearly constant solubility with temperature.
    • Common for NaCl crystal formation.
  • C. Supersaturation by adiabatic cooling:
    • Hot solution introduced into a container with pressure lower than the solvent's vapor pressure.
    • Part of the solution flashes into vapor.
    • Heat is drawn from the solution, decreasing temperature, causing supersaturation and crystal formation.
    • Suitable for heat-sensitive materials.
  • D. Supersaturation by adding another substance:
    • Less common.
    • Adding a third substance reduces the solubility of the original salt, causing it to crystallize.

4.5. Crystallization Equipment

• 4.5.1. Agitated Tank Crystallizers:
  • Also known as stir-tank or agitated batch crystallizers.
  • Simplest and most economical.
  • Super saturation generated by cooling.
  • Commonly used in small-scale or batch processing due to low cost, simple construction, and flexibility.
  • Can have large capacities.

Construction of Agitated Tank Crystallizers

• Cylindrical tank with a low-speed agitator and a cooling coil for water circulation.
• Conical bottom for product withdrawal.
• Agitator improves heat transfer, maintains uniform temperature, and keeps crystals suspended for uniform growth.

Working of Agitated Tank Crystallizers

• A known quantity of hot solution is charged into the crystallizer.
• Cooling is applied by circulating coolant through the coil, and the agitator is started.
• The mass cools, and crystals form as the solubility decreases.
• The mixture is cooled to the predicted temperature, and the product (crystals + liquor) is withdrawn from the bottom.
• Mother liquor: The solution remaining after crystallization.

Drawbacks of Agitated Tank Crystallizers

• Deposited solids on the coil reduce heat transfer efficiency.
• High supersaturation near the cooling surface causes fouling.
• Frequent washing and scraping may be required.
• Difficulty in controlling nucleation and crystal size, high labor costs.
• Used for fine chemicals, pharmaceuticals, and dye intermediates.

4.5.2. Oslo/Krystal Cooling Crystallizer

• Super saturation generated by indirect cooling.
• Circulating liquid cooling crystallizer.
• Consists of a crystallizing chamber, circulating pump, and external cooler.
• Feed solution enters from the top.
• Mother liquor is withdrawn near the feed point and sent to a cooler.
• The cooler achieves supersaturation by cooling.
• The supersaturated solution is fed back to the bottom of the crystallizing chamber through a central pipe.
• Nucleation occurs in the crystal bed.
• Nuclei circulate with the mother liquor and are removed as product when they reach the required size.

Problem 4.1.A: K2Cr2O7 Crystallization

• Problem: A solution of K2Cr2O7 in water contains 15% K2Cr2O7 by weight. Calculate the amount of K2Cr2O7 crystals produced from 1500 kg of feed solution, evaporating 700 kg of water and cooling the remaining solution to 293 K.
• Data: Solubility of K2Cr2O7 at 293 K = 115 kg per 1000 kg of water.
• Solution:
  • Basis: 1500 kg of feed solution.
  • K2Cr2O7 = \frac{15}{100} * 1500 = 225 kg
  • Water = \frac{85}{100} * 1500 = 1275 kg
  • Water evaporated = 700 kg.
  • Material balance of water: 1275 = 700 + Water in final solution.
  • Water in final solution = 1275 - 700 = 575 kg.
  • K2Cr2O7 in solution at 293 K = \frac{115}{1000} * 575 = 66.125 kg
  • Material balance of K2Cr2O7: 225 = 66.125 + (K2Cr2O7 crystals produced).
  • K2Cr2O7 crystals produced = 225 - 66.125 = 158.9 kg.

Distillation Column Problem

• Problem: A vapor at 138°C and 1 atm containing 0.72 mole fraction benzene and 0.28 mole fraction toluene is fed to a distillation column. The distillate contains 0.995 mole fraction benzene, and the bottoms contain 0.97 mole fraction toluene. The reflux ratio is 1.45 mole per mole distillation product for a feed of 100 kg mole. Compute the overall material balance.
• Solution:
  • Basis: 100 kg mole of feed.
    • Benzene = 72 kg mole.
    • Toluene = 28 kg mole.
  • Given:
    • F = 100 kg moles
    • X_F = 0.72
    • X_D = 0.995
    • X_W = 1 - 0.97 = 0.03
  • Overall material balance: F = D + W => D = F – W D = 100 – W (a)
  • Component balance: F (XF) = D (XD) + W (X_W) (b)
  • Substitute Eqn. (a) in Eqn. (b):
    • F (XF) = (100-W) (XD) + W (X_W)
    • F (XF) = 100 (XD) -W(XD) + W(XW)
    • 100 (0.72) = 100 (0.995) – W (0.995) + W (0.03)
    • 72 = 0.03 W – 0.995 W + 99.5
    • 72 -99.5 = - 0.965 W
    • - 27.5 = - 0.965 W
    • W = 28.4 kg moles
  • Amount of bottom product W = 28.4 kg moles.
  • Put value of W in Eqn.(a):
    • D = 100 – 28.4
    • D = 71.6 kg moles.
  • Amount of Distillate D = 71.6 kg moles.