4th Lecture on Separation Processes

Unit Operations and Separation Processes

Lecture 4 Calculation of Height of Gas Absorption Column and Material Balance for Plate Towers

Characteristics of an Absorption Tower Let us consider gas – liquid absorption tower operated in a counter current design mode We can define the following quantities; – moles of solute gas per mole of inert gas in the gas phase – moles of solute gas per mole of solute free liquid in liquid phase – Area of interface between the two phases is unknown – Interfacial area per unit volume of column

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Characteristics of an Absorption Tower Equation (11) NA = k G (PAG – PAi) = k L (CAi – CAL)………………(11) Can be rewritten as follows;

NAdZa = kGa(PAG − PAi)A dZ………………………(31) = kLa(CAi − CAL)A dZ • where: NA= kmol of solute absorbed per unit time and unit interfacial area, a = surface area of interface per unit volume of column, A = cross-sectional area of column, and Z = height of packed section.

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Absorption Tower (Counter current flow)

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Calculation of Column Height based on conditions in the gas film

• Assumptions Gm = moles of inert gas/(unit time) (unit cross-section of tower), Lm = moles of solute-free liquor/(unit time) (unit cross-section of tower)

Y = moles of solute gas A/mole of inert gas B in gas phase, and X = moles of solute A/mole of inert solvent in liquid phase.

where • Molar ratios of the diffusing material in the gas and liquid phases are Y and X respectively, 5

Calculation of Column Height(Gas film conditions) • Over a small height dZ, the moles of gas leaving the gas phase will equal the moles taken up by the liquid. • This behaviour is described by AGm dY = ALm dX………………………….(32) But AGmdY = NA = kGa(PAi − PAG)A dZ...............(33) (a) Substituting for PAG in terms of gas partial pressure and moles of solute gas (b) Rearranging Gm dY in terms of partial pressure and moles of solute gas (c) And integrating the height of column Z required to achieve a change from Y1 (bottom of column)to Y2 (top of column)

Calculation of Column Height(Gas film conditions)

• Z (Height of column required to achieve a change in Y from Y1 at the bottom to Y2 at the top of the column is; • Z=

𝑌2 𝑑𝑌 𝐺𝑚 ………………………….(34) 𝑌 𝑘𝐺𝑎𝑃 1 𝑌𝑖 −𝑌

• kG is assumed to be constant throughout the column

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Calculation of Column Height(Liquid film conditions) • Over a small height dZ, the moles of gas leaving the gas phase will equal the moles taken up by the liquid. • This behaviour is described by ALm dX = kLa(CAi − CAL)A dZ………..….(35) where

Concentration C (moles of solute per unit volume of liquid). • If CT = (moles of solute + solvent) (volume of liquid), then: CA CT −CA

=

moles of solute moles of solvent

=X 8

Calculation of Column Height(Liquid film conditions)

• Z (Height of column required to achieve a change in Y from Y1 at the bottom to Y2 at the top of the column is; • Z=

X2 dX Lm ………………………….. X kLaCT 1 X−Xi

(36)

• kL and CT is assumed to be constant throughout the column

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Plate Towers for Gas Absorption • Sieve trays and bubble cap columns are similar to those used for distillation • Preferred to packed towers when; – the load is excessive; diameter of column > 2m – there is likelihood of deposition of solids which could choke packed tower – liquid flow rate is very high and could cause flooding in packed towers

• Ratio of liquid rate to gas rate is higher with plate towers than in distillation however, plate efficiencies are lower than with distillation equipment

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Definition of Tower Characteristics

– Lm is the molar rate of flow per unit area of solute free liquid – Gm is the molar rate of flow per unit area of inert gas – n refers to the plate numbered from the bottom upwards (and suffix n refers to material leaving plate n) – x defines the mole fraction of the absorbed component in the liquid – y defines the mole fraction of the absorbed component in the gas

– s is the total number of plates in the column. 13

Material Balance for Absorbed Component for Plate Towers

• Material balance for the absorbed component from the bottom to a plane above plate n gives:

• Gmyn + Lmx1 = Gmy0 + Lmxn+1……………………….(37)

• Material leaving plate 𝐿𝑚 𝐿𝑚 𝑥𝑛+1 + y0 - x1 ……..(38) yn = 𝐺 𝐺 𝑚

𝑚

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Number of Transfer Units/Height of Transfer Units • Height (HOG ) of an overall transfer unit for a Packed Column Gm = HOG = ………………………………………….(39) KGaP where Gm is the molar gas flow rate KGa is the overall transfer coefficient P is the partial pressure of Gas • Number of transfer units (NOG) in a Packed Column is expressed as an integral value of the change in composition of the gas in the column per unit driving force y2 d𝑦 ………………………….. y1 ye−𝑦

where y is mole fraction of A in gas phase ye is mole fraction of A at equilibrium

(40)

Height of Column (Z) No of Transfer units

Height of Column (NOG) = Height of Transfer Unit

Therefore column height (Z) = NOG x HOG

=

Z HOG