FLV
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Chapter 10
Gas–Liquid Contactors
Every earlier chapter counted stages. None of them told you how wide the column has to be, how much pressure it drops, or how hard you can push it before it stops working.
By the end of this chapter you should be able to
- Describe the parts of a tray and say what each is for.
- Name the four ways a tray stops working — jet flooding, downcomer flooding, weeping and dumping.
- Estimate the flooding velocity from a force balance and the Fair correlation.
- Size a column diameter from the vapour load.
- Break the tray pressure drop into its dry, holdup and surface-tension terms.
- Correct a Murphree efficiency for entrainment.
- Choose between sieve, valve and bubble-cap trays.
How big is the column?
McCabe–Thiele and FUG answer one question: how many equilibrium stages? Divide by an efficiency and you have a number of real trays; multiply by a tray spacing and you have a height. But the height is only one of the two dimensions, and it is the cheaper one. Nothing in Chapters 4 to 6 says how wide the column must be, what it costs in pressure drop, or how far the throughput can be turned down before the trays stop working at all.
The two questions, and where they are answered
How many stages? — thermodynamics and mass balances, Chapters 2 to 6. How big is each stage? — hydraulics, this chapter. They are almost completely decoupled, which is why the course could leave the second one until last. The first sets the height; the second sets the diameter, the pressure drop and the operating range. A design is not a design until you have both.
10.1 What a contactor has to do
Three requirements, and as usual they conflict:
- High efficiency — the best possible contact between the two phases, so that a real tray comes close to an equilibrium stage.
- Low energy consumption — the least possible pressure drop, because in a distillation column every pascal dropped raises the reboiler temperature.
- Operational flexibility — the plant will not run at the design rate. It must work over a range, and the width of that range is the turndown ratio.
| Family | Types | Suits |
|---|---|---|
| Tray columns | Sieve, valve, bubble-cap | Large diameters, high liquid loads, dirty or fouling service, where you need to see what is happening |
| Packed columns | Random packing, structured packing | Low pressure drop (vacuum service), corrosive duty, small diameters, high-efficiency separations |
10.2 Tray anatomy
| Part | What it does | What happens if it is wrong |
|---|---|---|
| Shell | The pressure vessel. | — |
| Bubbling area | Where gas and liquid meet. Sets the mass transfer. | Too small → poor efficiency; too large → not enough downcomer. |
| Downcomer | Carries liquid down and disengages vapour from it. | Too small → it backs up and floods the tray above. |
| Weir | Maintains a liquid depth on the tray. | Too low → poor contact; too high → pressure drop and flooding. |
| Perforations | Distribute the vapour across the deck. | Too large a hole area → weeping; too small → high pressure drop. |
10.3 Operating regimes
| Failure | What is happening | What you see |
|---|---|---|
| Jet (entrainment) flooding | The rising vapour carries liquid drops up to the tray above. | Efficiency collapses — the carried-up liquid undoes the separation that tray just achieved. |
| Downcomer flooding | The downcomer cannot pass the liquid fast enough and backs up to the tray above. | Liquid level climbs the column; pressure drop rises sharply. |
| Weeping | The vapour is too slow to hold the liquid up, so some rains through the holes. | Efficiency falls, gradually. |
| Dumping | All the liquid rains through and none reaches the downcomer. | The tray has stopped working entirely. |
Entrainment is not a leak — it is undone work
Stages are numbered from the top down, so entrainment carries liquid up: a drop thrown from tray to tray is liquid of composition arriving where the liquid should be . Since the liquid gets richer in heavies going down, is the heavier of the two — that drop is carrying heavies back up, the wrong way. Entrainment does not lose material; it partly undoes the separation the tray just performed, which is why §10.7 corrects the efficiency rather than the flow.
10.4 The flooding velocity
Consider a drop of liquid in the rising vapour. Three forces act on it: gravity down, buoyancy up, and drag up. At the flooding velocity they balance and the drop is held in suspension:
10.1
The square root does the physical work here, and it is worth reading. A dense vapour — a high-pressure column — gives a small and therefore a low flooding velocity, so high-pressure columns are fat and slow. A vacuum column has a very light vapour and floods only at high velocity, but its volumetric flow is enormous, so it is fatter still.
is not a constant. It is read from a correlation — the Fair correlation — as a function of the tray spacing and a flow-ratio parameter, and then corrected:
10.2
with in dyn/cm, for a non-foaming system (0.75 for a moderate foamer), and when the hole area is at least 10 % of the active area. is the ratio of liquid to vapour momentum: small when the vapour dominates, large when the liquid does.
Where the chart comes from, and what the app uses
Fair's chart is a set of curves, one per tray spacing, plotted against on log axes. The apps here evaluate the standard closed-form fit to it,
with the tray spacing in mm and in m/s. It reproduces the published chart to within a few per cent across the useful range. Chart and fit alike are correlations — treat the answer as ±10 % and add a design margin.
10.5 Column diameter
Design at a fraction of flooding, typically 0.75 to 0.85. The vapour has to pass through the column cross-section minus the downcomers:
10.3
with the downcomer typically 10 % of the total area at each end. Round the answer up to a standard vessel size; nobody builds a 1.623 m column.
Sizing the column
The whole Fair calculation, live, with the C3 splitter of Seminar 7 as the default. Watch the flooding velocity collapse as you raise the pressure — a dense vapour is much harder to hold liquid up in — and watch what tray spacing buys you. The right-hand panel is the chart itself, with your operating point on it.Diameter against tray spacing
And what the fraction of flooding costs you.
The Fair capacity chart
Csb against the flow parameter, one curve per spacing.
Diameter
—m
Flooding velocity
—m/s
Design velocity
—m/s
Csb
—m/s
Total area
—m²
✓—
10.6 Pressure drop across a tray
The total drop is conventionally expressed as a head of clear liquid and split into three parts:
10.4
| Term | What it is | Estimated by |
|---|---|---|
| Drop through the dry perforations. | — a modified orifice equation, the hole velocity | |
| The weight of liquid held on the tray. | — weir height plus crest over it | |
| Surface tension: the pressure to make a bubble. | — usually the smallest of the three |
Here is the fraction of the froth that is liquid — about 0.6 — the weir height and the weir length. The whole calculation is a correlation stack, and the point of App 2 is not the number but which term dominates.
Watch the units in the orifice term
Every equation in this section is SI: in m/s, in kg/m³, in N/m, and every head comes out in metres of clear liquid. Older texts write the dry-tray drop as ; that is the same equation, but the 0.186 is with in ft/s², so it takes in ft/s and returns in inches. Feed it SI and read metres and you are out by a factor of 3.65. The SI coefficient is .
Why a chemical engineer cares about 0.6 kPa
The tray in App 2 drops 133 mm of clear liquid — 0.63 kPa — at its design load. A hundred trays drop a hundred times that, and every pascal at the bottom of a distillation column raises the boiling temperature there. In a vacuum column separating heat-sensitive material, pressure drop is the difference between a product and a tar — which is exactly why packed columns exist.
Pressure drop and the operating window
The three contributions to the tray pressure drop, and the two ways out of the operating window. The geometry is the C₃ splitter of Worked example 10.1 at its design point — 1.62 m diameter, 0.6 m tray spacing, 484.8 kg/m³ liquid — with the hole area taken as 6 % of the active area rather than the 10 % used for the capacity correlation, because a tight perforation is exactly what buys a sieve tray the 2:1 turndown quoted in §10.8. Push the vapour rate up towards flooding, or down until the tray starts to weep, and watch the window close as you open the holes up. Flooding is held fixed at 125 % of design (the column was sized at 80 % of flooding); only the weep point moves.Where the pressure goes
The three terms, stacked, against vapour load.
The operating window
Between weeping and flooding.
Total drop
—kPa
Dry tray
—mm
Liquid holdup
—mm
Surface tension
—mm
Hole velocity
—m/s
Turndown
—
✓—
10.7 Entrainment and efficiency
Let be the fractional entrainment — the ratio of entrained liquid to gross liquid flow. The Murphree efficiency you actually get is
10.5
which is the correction that connects this chapter to the Murphree efficiency of Chapter 4b4b §4b.5. Below about 10 % entrainment the penalty is small; above 20 % it becomes the dominant loss, and it climbs very steeply as you approach flooding. This is the quantitative reason the design point sits at 75–85 % of flooding rather than at 95 %.
itself is read from a second Fair chart, and it is a strong function of two things: the approach to flooding, which is what App 3 varies, and the flow parameter , which App 3 holds fixed. At a given per cent of flooding, falls by more than an order of magnitude as rises across the chart — a liquid-loaded tray entrains far less than a vapour-loaded one at the same fraction of flooding. The curve in App 3 is a low- one (), so read it for the shape of the approach to flooding, not for an absolute to put in a design.
What entrainment costs
Set a dry-tray efficiency and watch what entrainment does to it — and what that does to the number of real trays you have to buy. Entrainment rises sharply near flooding, so the last few per cent of capacity are expensive in a way the capacity chart never shows. The ψ curve here is one line off Fair's entrainment chart, read at a flow parameter of about FLV = 0.03; a higher-FLV column such as the C₃ splitter of App 1 entrains an order of magnitude less at the same fraction of flooding, so take the shape rather than the absolute number.Efficiency against how hard you push
Entrainment climbs steeply near flooding.
What it costs in hardware
Real trays, and the height they need.
Entrainment ψ
—
Wet efficiency
—
Efficiency lost
—%
Real trays
—
Tray section height
—m
Extra trays vs dry
—
✓—
10.8 Choosing a tray
| Sieve | Valve | Bubble cap | |
|---|---|---|---|
| Relative cost | 1.0 | 1.2 | 2.0 |
| Pressure drop | lowest | intermediate | highest |
| Efficiency | low | high | high |
| Vapour capacity | high | high | low |
| Typical turndown | 2 | 4 | 5 |
How to read that table
The sieve tray is cheapest and drops the least pressure, and it pays for that with a turndown of only about 2 — halve the vapour rate and it weeps. The valve tray buys turndown of 4 for 20 % more money, which is why it is the default choice for most new columns. The bubble cap cannot weep at all, so it wins where the rate genuinely varies by a factor of five or where a liquid seal must be maintained no matter what — and it is otherwise obsolete, being twice the price with the worst pressure drop and the lowest capacity.
10.9 Packed columns
A packed column replaces the trays with a bed of shaped elements — random rings and saddles, or corrugated structured sheets — over which the liquid runs as a film while the gas passes up through the voids. There is no weir, no downcomer and no froth, so there is very little pressure drop: a fraction of a millibar per theoretical stage for structured packing, against several millibars for a tray. That is decisive in vacuum service, and it is why structured packing took over the vacuum end of refineries.
The sizing logic is the same in outline — find a flooding condition, design at a fraction of it, work out the area — but the correlations are different: the generalized pressure-drop correlation replaces the Fair chart, and the height comes from an HETP or a transfer-unit height rather than from a tray count and an efficiency.
Self-study
Packed-column diameter and the generalized pressure-drop correlation are left as self-study in this course. The concepts you need are all in this chapter: a capacity limit set by the two densities, a design fraction of it, and a pressure drop you would rather not pay. Only the charts change.
10.10 Worked example
Worked example 10.1Sizing a C₃ splitter
Find the internal diameter of a sieve-tray propylene–propane splitter from its top-tray conditions, operating at 80 % of flooding. Pressure 18.5 bar, temperature 42 °C; vapour 0.995 propylene at 45 000 kg/h, liquid 0.985 propylene at 38 000 kg/h. , g/mol; ; pure liquid densities 485 and 475 kg/m³; dyn/cm. Tray spacing 0.6 m, hole area 10 % of the active area, downcomers 10 % of the total.
Work it yourself first, then open
Densities first — everything depends on them.
MV = 0.995(42.08) + 0.005(44.10) = 42.09 g/mol
ρV = PM/(ZRT) = 1850(42.09)/(0.78 × 8.314 × 315.15) = 38.10 kg/m³
For the liquid, take ideal volumes on a mass basis (the mass fraction of propylene is 0.9857):
1/ρL = 0.9857/485 + 0.0143/475 → ρL = 484.8 kg/m³
The flow parameter.
FLV = (L/V)√(ρV/ρL) = (38000/45000)√(38.10/484.8) = 0.8444(0.2803) = 0.2367
The Fair correlation, at a 600 mm spacing:
Csb = 0.0105 + 8.127×10⁻⁴(600)0.755exp(−1.463 × 0.23670.842) = 0.0764 m/s
C = 0.0764(8.5/20)0.2(1)(1) = 0.0764(0.8424) = 0.0643 m/s
Flooding velocity.
Uf = 0.0643√[(484.8 − 38.1)/38.1] = 0.0643(3.425) = 0.220 m/s
and the design velocity is 0.80(0.220) = 0.176 m/s. That is a remarkably slow gas — the price of a dense, high-pressure vapour.
Area and diameter.
V̇ = 45000/(3600 × 38.10) = 0.3281 m³/s
Anet = 0.3281/0.1763 = 1.861 m² · AT = 1.861/0.90 = 2.068 m²
DT = √(4 × 2.068/π) = 1.62 m → specify 1.7 m
Now the sensitivities, which are the real lesson.
- Tray spacing. 450 mm gives 1.78 m and 750 mm gives 1.51 m. Wider trays make a narrower column but a taller one — and shell cost goes roughly as , so there is a genuine optimum. 600 mm is the usual starting point.
- Pressure. This column floods at 0.22 m/s because ρV is 38 kg/m³. The same duty at atmospheric pressure, with ρV near 2, would flood above 1 m/s — but you cannot condense propylene with cooling water at atmospheric pressure, which is why C₃ splitters are high-pressure columns and why they are famously among the most expensive separations in a refinery.
- Surface tension. At 8.5 dyn/cm the correction factor is 0.84. Water at 70 dyn/cm would give 1.29 — over 50 % more capacity from that term alone. Low-surface-tension systems foam and entrain, and they need bigger columns.
App 1, C₃ splitter preset. Then drag the tray spacing and the pressure and watch the diameter move.
Think about it
Why design at 80 % of flooding rather than 95 %?
Because the last 15 % is bought with efficiency, and with risk. Entrainment climbs steeply as flooding approaches — App 3 shows the curve — so a column at 95 % of flooding has a materially worse Murphree efficiency and therefore needs more trays, cancelling the saving in diameter. And a correlation good to ±10 % means a column designed at 95 % might already be flooding. At 80 % you have both a margin against the correlation and room to turn the plant up when the market is good, which is a real option with a real value.
A column floods when the feed rate goes up. Would taller trays fix it?
Sometimes — and it is a common retrofit. Wider spacing raises and therefore the flooding velocity, so a column with fewer, more widely spaced trays can pass more vapour. But you have removed trays, so the separation gets worse, and you now need a higher reflux ratio to hold the specification, which puts vapour back. Whether it helps depends on whether you were capacity-limited or separation-limited. The other retrofits are high-capacity trays (larger hole area, sloped downcomers) or replacing trays with structured packing, which usually buys 20–40 % capacity and cuts the pressure drop as a bonus.
The efficiency of a tray is 70 %. Where did the other 30 % go?
Into three places, and it is worth separating them. Mass-transfer resistance: the vapour is in contact with the froth for perhaps two seconds, which is not always long enough to reach equilibrium. Non-ideal flow: vapour is not distributed evenly across the deck and liquid is not in plug flow across it, so some gas sees liquid that has already been stripped. And entrainment, which is the one this chapter can quantify — Equation 10.5. The first two are what people mean by a "dry" Murphree efficiency, and they are correlated rather than derived; the third is the part that gets worse the harder you push the column.
Where this chapter connects
- The other half of the answer: Chapters 4 to 6 give the stage count and this one gives the size. Neither is a design on its own.
- Efficiency: Equation 10.5 is the correction to the Murphree efficiency4b §4b.5 that Chapter 4b left as a number to be looked up.
- Pressure drop: what it costs is a higher reboiler temperature — the energy argument of Chapter 11 §1.2 arriving as hardware.
- Absorbers too: everything here applies unchanged to the absorber of Chapter 66 §6.1, which is the same tower with a different operating line.
- And the alternative: a membrane contactor9 §9.10 fixes the interfacial area and removes flooding, weeping and foaming altogether — at the cost of an extra resistance.
Summary & key equations
Capacity
Flooding velocity — from a force balance on a drop
Capacity factor, in dyn/cm
Flow parameter
Fair fit, in mm
Diameter, –,
Pressure drop
Total, as a head of clear liquid
Dry tray in SI — the old 0.186 form is inches and ft/s
Holdup,
Surface tension — usually the smallest term
Limits and efficiency
Four failuresjet flooding · downcomer flooding · weeping · dumping
Entrainment
Turndownsieve ≈ 2, valve ≈ 4, bubble cap ≈ 5
Packed columnsfar lower pressure drop; GPDC replaces Fair, HETP replaces efficiency