How Engineers Determine the Number of Transfer Units (NTU) for Packed Tower Absorption

The HTU/NTU method is widely used to estimate packing height for gas absorption and stripping.

The basic packed-height relationship is:

Z=HTU×NTUZ = HTU \times NTU

where:

• ZZ = required packed height;
• HTU = height of a transfer unit;
• NTU = number of transfer units.

These two terms represent different parts of the design problem.

HTU is related primarily to:

• packing performance;
• mass-transfer coefficients;
• effective interfacial area;
• gas and liquid loading.

NTU is related primarily to:

• inlet composition;
• required outlet composition;
• phase equilibrium;
• operating conditions;
• available mass-transfer driving force.

Therefore:

NTU describes how demanding the separation is, while HTU describes how effectively the packed bed provides mass transfer per unit height.

Engineers should calculate or determine the required NTU before converting the separation duty into physical packing height.

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What Does NTU Mean?

A transfer unit is not a physical section inside the packing.

NTU is a mathematical representation of the total mass-transfer duty relative to the available driving force.

Conceptually:

Large Driving Force

→ fewer transfer units may be required.

Small Driving Force

→ more transfer units may be required.

As the required outlet approaches equilibrium more closely, the driving force decreases and the required NTU can increase significantly.

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NTU Is Not a Packing Property

This distinction is critical.

Two different packing types installed in the same absorber can face approximately the same:

required separation NTU

because the process duty is unchanged.

What changes between the packings may be:

HTU

Therefore:

Packing A:

ZA=HTUA×NTUZ_A=HTU_A\times NTU

Packing B:

ZB=HTUB×NTUZ_B=HTU_B\times NTU

If Packing A provides a lower applicable HTU, less packing height may be required for the same separation duty.

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1. Define the Absorption Duty First

Before calculating NTU, engineers need to know what must be removed from the gas.

Typical information includes:

• gas inlet composition;
• required gas outlet composition;
• gas flow;
• liquid inlet composition;
• liquid flow;
• temperature;
• pressure.

For example:

Gas inlet:

1.0 mol% contaminant

Required outlet:

0.1 mol%

The calculation must determine how much gas–liquid contact is required to achieve that reduction.

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2. Define the Transferring Component

NTU calculations are normally performed for a particular transferred species.

Examples include:

• CO₂;
• H₂S;
• NH₃;
• SO₂;
• HCl;
• VOC components.

In a multicomponent absorber, different components can require different transfer considerations.

The component controlling the design may not always be the one with the highest inlet concentration.

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3. Establish Material Balance

The gas and liquid streams are connected through the absorbed component balance.

A simplified differential or overall material balance relates:

• gas concentration change;
• liquid concentration change.

This determines the operating relationship between the two phases.

Without a consistent material balance, the NTU calculation cannot represent the actual absorber.

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4. Define the Operating Line

The operating line describes how bulk gas and liquid compositions relate through the tower.

For simplified dilute systems with approximately constant gas and liquid molar flow, the operating relationship may be represented in a relatively simple form.

Real systems may require more rigorous treatment when:

• gas flow changes;
• liquid flow changes;
• absorption is large;
• reaction occurs;
• temperature changes.

The operating line is important because it describes the actual bulk compositions inside the tower.

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5. Define the Equilibrium Line

The equilibrium relationship describes what gas composition would be in equilibrium with a particular liquid composition.

For some dilute systems:

y∗=mxy^*=mx

may be used as a simplified equilibrium relation.

Where:

• y∗y^* = gas composition in equilibrium with liquid;
• xx = liquid composition;
• mm = equilibrium slope.

Other systems may require:

• Henry's law;
• vapor–liquid equilibrium data;
• thermodynamic models;
• reactive equilibrium.

The correct equilibrium relationship is fundamental to NTU.

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6. Operating Composition and Equilibrium Composition Are Different

At any location in the tower:

y

represents the actual bulk-gas composition.

y*

represents the gas composition that would be in equilibrium with the local liquid.

The difference:

y−y∗y-y^*

is one possible expression of the gas-phase mass-transfer driving force.

If this difference becomes small:

mass transfer becomes increasingly difficult.

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7. Driving Force Controls NTU

A general overall gas-phase NTU concept may be expressed as:

NTUOG=∫dyy−y∗NTU_{OG} = \int \frac{dy}{y-y^*}

with the appropriate limits and assumptions.

The exact equation depends on:

• flow basis;
• concentration definition;
• system assumptions.

The principle is more important than memorizing one equation:

NTU integrates the required composition change relative to the available mass-transfer driving force throughout the packed bed.

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8. Why NTU Is an Integral

The driving force normally changes from one end of the tower to the other.

At one elevation:

y−y∗y-y^*

may be large.

At another:

it may become much smaller.

Therefore it is usually not accurate to use one arbitrary driving force for the entire bed without justification.

Integration accounts for the changing driving force.

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9. Larger Removal Does Not Increase NTU Linearly

Suppose one absorber removes:

50%

of a component.

Another removes:

99%.

The second separation is not necessarily just twice as difficult.

As outlet concentration approaches a demanding specification:

• driving force near one end may become very small;
• required NTU can increase sharply.

This is especially important for deep removal applications.

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10. Deep Removal Can Produce High NTU Requirements

Consider:

Case A

Reduce contaminant from:

1% → 0.5%

Case B

Reduce:

1% → 0.01%

Case B requires much deeper removal.

The final part of the separation may operate with a relatively small driving force.

Therefore the additional packed height required for deep polishing can be disproportionate.

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11. Solvent Condition Strongly Affects NTU

If fresh solvent enters the absorber with a low dissolved contaminant concentration:

• the top-of-column driving force may be strong.

If the entering solvent already contains significant absorbed component:

• available driving force is reduced.

Therefore solvent quality directly influences required NTU.

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12. Liquid Flow Rate Influences the Operating Line

Changing liquid flow can change:

• operating-line slope;
• local liquid composition;
• mass-transfer driving force.

Increasing solvent flow may increase driving force in some absorption systems.

This can reduce required NTU.

However, higher liquid flow also increases:

• pumping cost;
• liquid loading;
• hydraulic pressure drop;
• distributor requirements.

Therefore solvent flow should not be increased without considering hydraulics and economics.

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13. Minimum Solvent Rate Is a Special Limit

For absorption, there is generally a lower solvent-flow region below which the desired separation cannot be achieved with a practical finite tower.

Near the theoretical minimum solvent rate:

• the operating line approaches equilibrium;
• driving force becomes very small at a pinch region.

Then required NTU can become very large.

Therefore:

Designing too close to minimum solvent rate can produce an impractically tall packed bed.

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14. The Pinch Point Is Important

A pinch occurs where:

Operating Condition

approaches:

Equilibrium Condition

so closely that the local driving force becomes very small.

At a pinch:

y−y∗→0y-y^* \rightarrow 0

and the required transfer effort increases strongly.

Pinch analysis can therefore reveal why a design requires excessive packing height.

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15. More Solvent Can Move the Operating Line Away From Equilibrium

Increasing liquid-to-gas ratio can often increase the separation driving force.

This may:

• reduce NTU;
• reduce required packing height.

But it may simultaneously:

• increase liquid load;
• increase pump duty;
• increase solvent consumption or regeneration duty.

The optimum design balances process and hydraulic requirements.

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16. Equilibrium Slope Strongly Influences Absorption Difficulty

If a component has favorable solubility:

• equilibrium behavior may provide a relatively strong absorption driving force.

If equilibrium strongly favors the gas phase:

• absorption becomes more difficult.

Therefore two gases with identical inlet and outlet concentration targets may require very different NTU.

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17. Temperature Can Change NTU Through Equilibrium

Temperature can affect:

• gas solubility;
• Henry's constant;
• reaction equilibrium.

For many physical absorption systems, higher temperature can reduce gas solubility.

This may move the equilibrium relationship closer to the operating line.

Result:

• smaller driving force;
• higher required NTU.

Actual behavior depends on the system.

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18. Pressure Can Change Absorption Equilibrium

Higher pressure can improve physical absorption for many gas systems because:

• gas partial pressure increases;
• equilibrium relationships change.

This may increase available driving force.

Therefore pressurized absorption may require a different NTU than an otherwise similar atmospheric system.

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19. Reactive Absorption Changes the NTU Problem

In reactive absorption, the absorbed component reacts in the liquid.

Examples include absorption into:

• alkaline solutions;
• reactive amines;
• other chemical solvents.

Reaction can reduce the dissolved concentration of the transferred component.

This can maintain a stronger driving force.

However, rigorous calculation may require:

• reaction equilibrium;
• reaction kinetics;
• enhancement factors;
• solvent depletion.

A simple physical-absorption NTU equation may not be sufficient.

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20. Solvent Depletion Can Increase NTU Requirement

Reactive solvent may enter with high available capacity.

As it flows downward:

• reactant is consumed;
• absorption capacity can decrease.

Near the bottom of the tower, the solvent may become more loaded.

This changes the local equilibrium and driving force.

The calculation must represent the actual solvent chemistry.

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21. Overall Gas-Phase NTU

Engineers commonly encounter:

NTUOGNTU_{OG}

This expresses the transfer requirement using an overall gas-phase driving force.

It pairs with:

HTUOGHTU_{OG}

so that:

Z=HTUOG×NTUOGZ=HTU_{OG}\times NTU_{OG}

The HTU and NTU bases must match.

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22. Overall Liquid-Phase NTU

Similarly:

NTUOLNTU_{OL}

may be used on an overall liquid-phase basis.

Then:

Z=HTUOL×NTUOLZ=HTU_{OL}\times NTU_{OL}

The selected formulation depends on:

• process;
• correlation;
• available design method.

Do not combine:

HTUOGHTU_{OG}

with:

NTUOLNTU_{OL}

without a valid conversion.

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23. Individual-Phase NTU Forms Also Exist

Engineers may encounter:

• NTUGNTU_G;
• NTULNTU_L.

These correspond to individual-phase mass-transfer definitions.

Again, the basis of:

• coefficient;
• driving force;
• HTU;
• NTU

must remain consistent.

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24. NTU Does Not Tell You Tower Diameter

This is a major distinction.

NTU determines the separation requirement.

It does not directly determine:

• gas capacity;
• flooding;
• tower diameter.

Diameter must be checked through hydraulic evaluation.

Therefore:

NTU / HTU

→ packing height.

Gas and Liquid Hydraulics

→ tower diameter and capacity.

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25. NTU Does Not Tell You Packing Type by Itself

NTU can be calculated before the final packing is selected.

Different candidate packings may then be evaluated through their respective:

• HTU;
• pressure drop;
• capacity;
• fouling characteristics.

Therefore NTU belongs primarily to the process duty, not the packing catalog.

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26. High NTU Can Make Packing Selection More Important

If only a small separation duty is required:

• differences in HTU between packings may have modest impact on total height.

If NTU is very high:

even a small HTU difference can create a large packed-height difference.

For example:

Packing A:

HTU=0.6mHTU=0.6m

Packing B:

HTU=0.8mHTU=0.8m

If:

NTU=2NTU=2

height difference:

0.4 m

But if:

NTU=10NTU=10

height difference:

2.0 m

Therefore high-NTU services can be more sensitive to mass-transfer performance.

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27. Very High NTU Should Trigger a Design Review

If an NTU calculation produces an unusually large value, engineers should investigate why.

Possible reasons include:

• outlet target too close to equilibrium;
• solvent flow too low;
• unfavorable equilibrium;
• poor solvent condition;
• incorrect thermodynamic data;
• unrealistic specification.

The answer should not automatically be:

install much more packing.

Sometimes the process conditions should be changed instead.

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28. Increase Driving Force Before Increasing Tower Height

Suppose a design produces excessive required packing height.

Possible alternatives may include:

• increase solvent circulation;
• use fresher solvent;
• reduce operating temperature;
• increase pressure where process allows;
• change solvent;
• use reactive absorption.

Improving the process driving force can reduce NTU.

This may be more effective than simply adding packing.

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29. NTU Can Vary Across Operating Cases

Minimum, normal and maximum operation may have different:

• gas flow;
• liquid flow;
• compositions;
• temperature;
• pressure.

Therefore the required NTU may also differ.

The governing packed-height case may not be the same case that governs hydraulic diameter.

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30. Hydraulic Governing Case and Mass-Transfer Governing Case Can Differ

For example:

Maximum Gas Flow

may govern:

• tower diameter;
• flooding.

Low Solvent Flow

may govern:

• NTU;
• required separation height.

Therefore packed tower design should evaluate both:

Hydraulic Governing Case

and

Mass-Transfer Governing Case

rather than assuming one operating case controls everything.

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31. Multi-Bed Towers Still Use Total Separation Requirement

Splitting packing into several beds does not eliminate the required transfer duty.

Total effective packed height must still achieve the required separation.

Bed segmentation may improve:

• redistribution;
• practical installation;
• hydraulic performance.

But it does not magically reduce NTU.

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32. Redistributors Can Help Preserve Effective Performance

If a long bed develops maldistribution:

• actual usable mass-transfer performance may fall below the ideal calculation.

A redistributor can restore liquid distribution before the next bed.

Therefore bed segmentation supports realization of the calculated mass-transfer potential.

But the theoretical process NTU remains determined by the separation duty.

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33. Poor Distribution Can Make Actual Performance Worse Than NTU Design

A model may calculate:

NTU = 5

and:

HTU = 0.7 m

giving:

Z=3.5mZ=3.5m

But if the installed tower suffers from:

• gas maldistribution;
• liquid maldistribution;
• dry packing regions;

actual performance may be worse.

The NTU equation assumes the packed bed is being used effectively.

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34. Fouling Can Increase Effective HTU Rather Than NTU

This distinction helps diagnosis.

The process separation requirement may still require approximately the same NTU.

But fouling can reduce packing performance by affecting:

• effective area;
• pressure drop;
• mass-transfer coefficients.

This effectively worsens HTU or usable packed-bed performance.

Therefore:

Process requirement controls NTU; equipment condition often affects HTU and hydraulic behavior.

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35. Feed Composition Changes Can Change NTU

Suppose the original absorber was designed for:

0.5% contaminant

but the plant now sends:

1.0%

with the same outlet requirement.

The required transfer duty has increased.

NTU may therefore increase even if:

• packing;
• tower diameter;
• solvent system

remain unchanged.

This is one reason existing towers can lose separation margin after process changes.

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36. More Stringent Outlet Specifications Can Increase NTU Dramatically

An environmental or product specification may tighten from:

100 ppm

to:

20 ppm

The final low-concentration region may operate close to equilibrium.

Therefore the incremental NTU requirement can be substantial.

Engineers should not assume the new packed height changes in direct proportion to the percentage reduction.

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Example 1 — Easy Physical Absorption

A contaminant has favorable solubility in the selected solvent.

The operating line remains well separated from equilibrium throughout the tower.

Driving force is relatively strong.

The calculated NTU may therefore remain moderate.

Packing height then depends strongly on the applicable HTU.

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Example 2 — Operating Near Minimum Solvent Rate

A plant reduces solvent circulation to save energy.

The operating line approaches equilibrium.

A pinch develops.

The required NTU rises sharply.

Even though pump energy decreases:

• separation margin deteriorates;
• required theoretical tower height increases.

This illustrates why minimum solvent flow and minimum packing wetting are different issues.

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Example 3 — Deeper Emission Requirement

An absorber originally removes:

90%

of a contaminant.

A new regulation requires:

99.5%

removal.

The final outlet concentration is now much closer to the equilibrium limit.

The required additional NTU may be much larger than expected from a simple percentage comparison.

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Example 4 — Reactive Alkaline Scrubber

An acid gas is absorbed into alkaline liquid.

When alkalinity is high:

• reaction maintains strong absorption driving force.

As alkalinity falls:

• liquid becomes less effective;
• equilibrium / reaction behavior changes;
• required transfer effort increases.

The design should therefore represent the realistic solvent chemical condition.

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NTU Calculation Workflow

Define Target Component

↓

Confirm Gas Inlet Composition

↓

Confirm Required Gas Outlet

↓

Define Gas Flow

↓

Define Liquid Flow and Inlet Composition

↓

Establish Material Balance

↓

Define Operating Line

↓

Establish Equilibrium Relationship

↓

Calculate Local Mass-Transfer Driving Force

↓

Integrate Over Required Composition Change

↓

Determine NTU

↓

Select Applicable HTU

↓

Calculate Packed Height

↓

Check Hydraulics

↓

Check Distribution and Bed Segmentation

↓

Validate Against Process Requirements

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NTU Input Checklist

Gas

✓ Inlet composition✓ Outlet specification✓ Gas flow✓ Temperature✓ Pressure

Liquid

✓ Liquid flow✓ Inlet composition✓ Solvent loading✓ Reactive species concentration where relevant

Equilibrium

✓ Henry's law / VLE / appropriate equilibrium model✓ Temperature basis✓ Pressure basis

Process

✓ Physical or reactive absorption✓ Minimum / normal / maximum cases✓ Required removal efficiency

Calculation

✓ Gas-side or liquid-side basis✓ Overall or individual basis✓ Compatible HTU definition

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Common NTU Calculation Mistakes

Mistake 1 — Treating NTU as a Packing Specification

Why it fails:

NTU is primarily determined by the separation duty and driving force.

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Mistake 2 — Using One Average Driving Force Without Checking

Why it fails:

Driving force changes along the tower and can become very small near a pinch.

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Mistake 3 — Ignoring the Equilibrium Line

Why it fails:

Removal percentage alone does not determine absorption difficulty.

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Mistake 4 — Operating Too Close to Minimum Solvent Rate

Why it fails:

The driving force can approach zero and NTU can become very large.

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Mistake 5 — Using Physical Absorption Equations for Strong Reactive Absorption

Why it fails:

Chemical reaction changes the transfer mechanism and driving force.

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Mistake 6 — Mixing NTU and HTU Bases

Why it fails:

Overall gas, overall liquid and individual-phase definitions must remain consistent.

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Mistake 7 — Assuming the Hydraulic Maximum Case Also Governs NTU

Why it fails:

The worst mass-transfer case may occur at a different process condition.

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NTU vs HTU

Relationship:

Z=HTU×NTU\boxed{Z=HTU\times NTU}

But the two factors must be determined independently on a consistent basis.

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How the DAIER Engineering Assistant Fits Into NTU-Based Design

The DAIER Tower Packing Engineering Assistant can help organize preliminary information such as:

• gas flow;
• liquid flow;
• tower diameter;
• packing type;
• operating conditions.

https://www.pxdaier.com/tower-packing-engineering-assistant.html

An NTU calculation additionally requires process-specific information such as:

• inlet and outlet compositions;
• liquid composition;
• equilibrium relationship;
• solvent flow;
• reaction behavior where applicable.

Therefore the Engineering Assistant can support preliminary packed-tower evaluation, while detailed NTU determination may require:

• thermodynamic data;
• mass-balance calculations;
• process simulation;
• reactive-absorption modeling.

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Quick Guide

What does NTU represent in a packed absorber?

NTU represents the amount of mass-transfer effort required to achieve the specified separation relative to the available driving force.

Is NTU a property of tower packing?

No.

The separation duty primarily determines NTU.

What mainly affects NTU?

Inlet and outlet composition, solvent flow, liquid condition, equilibrium behavior, temperature and pressure.

Why does NTU increase near equilibrium?

Because the mass-transfer driving force becomes small.

Does more solvent reduce NTU?

It can, because changing the operating line may increase driving force, but hydraulic and economic penalties must also be considered.

Is a high NTU automatically solved by adding more packing?

Not necessarily.

Engineers should first investigate whether process conditions, solvent flow or equilibrium limitations are causing the high transfer requirement.

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From Removal Requirement to Packed Height

The engineering sequence is:

Gas Inlet Composition

•  

Required Gas Outlet

•  

Liquid Flow / Composition

•  

Equilibrium Relationship

↓

Operating Line

↓

Mass-Transfer Driving Force

↓

Required NTU

•  

Packing / System HTU

↓

Required Packed Height

↓

Hydraulic Capacity Check

↓

Distribution Check

↓

Final Packed Tower Design

The key engineering principle is:

NTU should be determined from the actual separation duty and available mass-transfer driving force—not selected from a packing catalog or assumed from removal percentage alone.