Vapor-Liquid and Gas-Liquid Separation Processes

More volatile component is…

the one with the lower boiling point

Volatility equation

generally considered CONSTANT

Raoult’s Law

p_i=x_ip_i,sat

the partial vapor pressure of a solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution

Binary flash (equilibrium) distillation (e.g. flash vessel, flash drum, etc.)

→ 6 DOF

energy balance: FH_F + Q_flash = VH_V + LH_L

Operating line for binary flash distillation

Fraction of feed vaporized (f)

f = V/F

Feed quality (q)

q = L/F

Vapor liquid equilibrium curve (sketch it!!!)

McCabe-Thiele diagram for binary flash distillation (sketch it!!!) → what assumption is required?

relies on the assumption of CONSTANT MOLAR OVERFLOW:

1. molar heats of vaporization of feed components are EQUAL

2. every mole condensed → a mole of vapor is condensed

3. heat & energy effects are negligible (processes adiabatic)

this can be expressed as:

L_n=L_n+1=…=L_R

V_n=V_n+1=…=V_R

L_m=L_m+1=…=L_S

V_m=V_m+1=…=V_S

→ w/ assumption, only need 1 operating line

Batch distillation (e.g. still of still pot)

Differential (Simple/Rayleigh) distillation

simplest form of batch distillation → vapor is continuously removed from a liquid, and the composition of the vapor and the remaining liquid (residue) are calculated using the Rayleigh equation

W_o is initial charge

Continuous distillation (e.g. column distillation) → sketch it!!!

→ assumes vapor/liquid leaving each stage is in equilibrium

→ pressure drop between stages is negligible

→ stages operate at different temperatures

Distillate (D)

Overhead stream → contains a greater concentration of the volatile component

Bottoms (B)

Stream from bottom of column → contains greater concentration of the less volatile component 

Partial condensor

operating equation is the same as total condenser

→ ALSO counts as a equilibrium stage at the top of the column (total condenser does not)

Partial reboiler

returns a portion of the bottoms to the column

→ counts as an equilibrium stage

Total reflux

hypothetical condition where all vapor is condensed and all bottoms are returned to column

→ maximum reflux ratio

External reflux ratio (R_D)

liquid reflux entering the first stage of distillation (L_R) divided by distillate flow rate (D)

Internal reflux ratio (L_R/V_R)

liquid reflux entering the first stage of distillation (L_R) divided by rectifying flow rate (V_R)

= R_D/(1+R_D)

Minimum reflux ratio (R_min)

reflux ratio that will result in an infinite number of stages

(graphically, this is where the top operating line touches the equilibrium curve → called pinch point)

Overall (molar) material balance for continuous distillation

How are trays numbered? (n vs m?)

from to TOP → down

n : rectifying section

m : stripping section

Rectifying (top) section material balance

Stripping section material balance

Operating lines

represents the mass balance relationship between liquid and vapor phases in a column, defined by a linear equation. In the common McCabe-Thiele method, there are two operating lines: one for the rectifying (top) section and one for the stripping (bottom) section

Equilibrium ratio (K_n)

= y_n/x_n

a function of composition, temperature, and pressure

Where does operating line intersect y = x line?

at y = x = x_B

Stepping off stages

draw lines between equilibrium curve and the operating line

rectifying: start at x_D and step DOWN

stripping: start at x_B and step UP

feed stage location should be placed where operating lines intersect

Feed quality (q)

fraction of the feed that remains LIQUID

Feed equation (q)

straight line

q = (h_g - h)/h_fg

where h_fg is latent heat

Fraction of the feed vaporized (f)

complement of the feed quality

Murphree plate efficiency, E_ME

measure of deviation from actual liquid/vapor composition from ideal (equilibrium on every stage)

→ NOT the same as overall efficiency

Absorption (general)

component in gas stream (solute) is transferred into a stream of a nonvolatile liquid (solvent, separating agent)

→ purified gas is product

Physical absorption

a gas component has greater solubility in the solvent than in its original stream

Chemical (reactive) absorption

the gas component to be removed reacts with and stays with the solvent

Stripping (desorption)

solute from liquid stream is transferred to an insoluble gas stream

→ purified liquid is product

absorption drives mass transfer here too!

Raffinate

purified flow

Extract

dirtied flow

Absorption/stripping in trayed columns: main assumptions

1. carrier gas is insoluble in the liquid phase

2. solvent is nonvolatile

3. the system is isothermal and isobaric 

Benefits of trayed columns

• can handle wider range of liquid and gas flows

• performance and efficiencies predictions are better

• easier to install cooling

• easier to clean → can be used with liquids that cause fouling or contains solids

Henry’s law

the amount of a gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid, at a constant temperature

→ valid for LOW solute concentrations and solute partial pressures (< 1 atm)

p_A = H’x_A

Benefits of packed columns

• lower liquid residual (better for flammable or toxic liquids)

• better with foaming fluids

• less expensive

• lower pressure drop

• better suited for vacuum operations

What can we assume about pack column flow rates

• solvent flow (L_s) and pure gas flow (G_s) are ~constant (NOT total liquid flow, L, or total gas flow, G)

Packing is characterized by what?

• surface-to-volume ratio (a)

• intrinsic volume drop

  • which is characterized by packing factor (C_f)

  • inversely proportional to packing size

1. HETP?

2. N_EQ?

1. Height equivalent of a theoretical plate (common measure of efficiency)

2. Number of equivalent theoretical plates

Porosity (ε)

void fraction of packed bed

ε = (V of voids in bed)/(total V of bed)

Interstitial velocity (v_i)

average velocity of fluid through the pores of the column → calculated from superficial velocity, v_o

HTU

Height of transfer unit (the smaller, the more efficient the unit) → phase dependent

NTU

Number of mass transfer units → phase dependent

Ergun equation use

used to calculate pressure drop through a layer of packing 

NTU equation from practice questions