- Get link
- X
- Other Apps
The purpose of this article is to provide a practical, rate-based workflow for sizing packed absorption or stripping columns using HTU/NTU with overall mass transfer coefficients, including the key equations, assumptions, and common pitfalls engineers face in real designs.
1. Why HTU/NTU is the practical design language for packed columns.
Packed columns do not have discrete equilibrium stages, so a stage-count approach is often a modeling convenience rather than a physical description of what happens inside the bed.
HTU/NTU design treats separation as a distributed mass-transfer process driven by a local driving force that varies with height, and it converts that distributed problem into a simple product of “how hard the separation is” times “how good the packing is at transferring mass.”
The core sizing statement is the packed height equation, where packing height equals a height-of-transfer-unit times a number-of-transfer-units for a consistent basis.
Z = H_OG * N_OG = H_OL * N_OL.Here, the “O” indicates an overall coefficient basis, and the “G” or “L” indicates whether the driving force is expressed on the gas side or liquid side.
2. Minimum definitions and notation you must keep consistent.
Most HTU/NTU mistakes come from mixing bases, mixing units, or mixing definitions of “overall coefficient,” so it helps to lock down notation at the start.
| Symbol. | Meaning. | Typical unit basis in design. |
|---|---|---|
| y, x. | Bulk gas and liquid solute composition, often mole fraction or solute ratio. | Dimensionless. |
| y*, x*. | Equilibrium composition corresponding to the opposite phase bulk condition. | Dimensionless. |
| m. | Equilibrium slope for a linear relation, commonly y* = m x for dilute systems. | Dimensionless. |
| G, L. | Gas and liquid molar mass velocity, meaning molar flow rate per column cross-sectional area. | mol/(m²·s) or kmol/(m²·h). |
| a. | Interfacial area per packed volume used with volumetric coefficients, often interpreted as effective area rather than geometric area. | m²/m³. |
| K_y a. | Overall gas-phase volumetric mass transfer coefficient on a y-driving-force basis. | mol/(m³·s·(driving force in y)). |
| K_x a. | Overall liquid-phase volumetric mass transfer coefficient on an x-driving-force basis. | mol/(m³·s·(driving force in x)). |
| H_OG, H_OL. | Overall gas- or liquid-based height of a transfer unit. | m. |
| N_OG, N_OL. | Overall gas- or liquid-based number of transfer units. | Dimensionless. |
Note : Use molar mass velocities G and L, not total molar flows, inside HTU definitions, or you will accidentally scale height with column diameter and get a nonphysical result.
3. Overall coefficients and the resistance-in-series structure.
In gas–liquid mass transfer, the flux is commonly written using either a gas-side driving force or a liquid-side driving force, and “overall” means the two-film resistances have been combined into one effective coefficient referenced to a single phase basis.
For dilute systems with a linear equilibrium relation y* = m x, the classic resistance-in-series relationships are.
1 / K_y = 1 / k_y + m / k_x. 1 / K_x = 1 / k_x + 1 / (m k_y).If you use volumetric forms, the same relationships apply when each coefficient is paired with a consistent interfacial area basis, such as k_y a and k_x a, producing K_y a and K_x a.
In many industrial packed-column designs, K_y a or K_x a is obtained from vendor data or correlations that already embed wetting, area effectiveness, and hydrodynamic effects, which is why overall coefficients are often the most reliable “engineering input” for HTU sizing.
3.1 How to choose a gas-based versus liquid-based overall formulation.
You can compute height using either Z = H_OG N_OG or Z = H_OL N_OL, and both should agree if the same physical assumptions are used.
In practice, engineers often choose the side that makes equilibrium and operating-line calculations simpler and matches the available coefficient data.
Gas-based overall driving forces are commonly used for absorption of dilute solutes from gases, while liquid-based overall driving forces are common when liquid-phase data or liquid-phase limitations are the focus.
Note : If you compute N_OG on a gas basis but you only have H_OL data, do not mix them, and instead convert or recompute to a consistent basis, or you will silently embed the equilibrium slope twice or not at all.
4. HTU definitions on an overall basis.
The overall gas-based HTU is the gas molar mass velocity divided by the overall gas-based volumetric coefficient.
H_OG = G / (K_y a).The overall liquid-based HTU is the liquid molar mass velocity divided by the overall liquid-based volumetric coefficient.
H_OL = L / (K_x a).Both definitions are most useful when K_y a and K_x a are expressed on the same concentration scale used in the NTU integral, such as y and x being mole fractions or solute ratios consistently across the design.
4.1 What HTU physically means for packed beds.
H_OG is the packed height required for the gas phase to experience one transfer-unit worth of “exponential-like” approach to equilibrium at the local conditions.
Smaller HTU means more effective mass transfer per height, which usually corresponds to higher effective area, stronger turbulence, better wetting, or smaller characteristic diffusion distances.
HTU is not purely a property of the packing, because it depends on liquid and gas rates, fluid properties, and sometimes solute loading, so it should be checked at the intended operating point.
5. NTU definitions and how to compute them correctly.
NTU captures how much “driving-force effort” is required by the separation specification and the chosen operating line.
For an overall gas-based method, the definition is.
N_OG = ∫(from column top to bottom) [ dy / (y - y*) ].For an overall liquid-based method, the definition is.
N_OL = ∫(from column bottom to top) [ dx / (x* - x) ].The driving force must match the chosen basis and sign convention, and the integration direction must match how the compositions change with height in countercurrent flow.
5.1 Operating line and equilibrium line setup for countercurrent absorption.
For absorption, gas enters at the column bottom with higher solute content and leaves at the top with lower solute content, while lean solvent enters at the top and becomes richer as it flows downward.
A common approach is to label gas inlet and outlet as y_in at the bottom and y_out at the top, and liquid inlet and outlet as x_in at the top and x_out at the bottom.
With constant molar flow approximations, the operating line in composition form is often written as.
y = y_out + (L / G) (x - x_in).For a linear equilibrium y* = m x, you can compute y* along the bed once x is obtained from the operating line, which allows direct evaluation of y - y* inside the integral.
Note : If gas or liquid molar flow rates change significantly due to absorption, stripping, heating, or reaction, a constant G and L assumption can bias NTU, so use solute ratios, variable flow models, or a rate-based simulator when the solute loading is not dilute.
6. Closed-form NTU for the common dilute linear case.
When equilibrium is linear, y* = m x, and the operating line is also linear under constant molar flow assumptions, the driving force can be expressed as a linear function of y, enabling a closed-form expression for N_OG.
Define an absorption factor A as.
A = L / (m G).Then, for countercurrent absorption with x_in known and y_out specified, the overall gas-based NTU can be written in a compact log form once the end driving forces are computed consistently.
N_OG = (1 / (1 - 1/A)) * ln( (y_in - y*_in) / (y_out - y*_out) ).This form is sensitive to how you define end driving forces, so many engineers prefer direct numerical integration of dy/(y - y*) using a small grid in y or in height for robustness.
6.1 Practical numerical integration template.
A simple trapezoidal integration in composition space is often sufficient for preliminary sizing, and it avoids algebraic mistakes when equilibrium is nonlinear or when L and G vary with loading.
1) Create N points from y_out to y_in. 2) For each y_i, compute x_i from the operating line. 3) Compute y*_i from equilibrium at x_i. 4) Compute integrand_i = 1 / (y_i - y*_i). 5) Integrate N_OG ≈ Σ 0.5 * (integrand_i + integrand_{i+1}) * (y_{i+1} - y_i).7. Step-by-step packed height sizing workflow using overall HTU/NTU.
7.1 Step 1, define separation targets and the governing equilibrium.
Specify gas inlet solute level y_in, required gas outlet level y_out, gas and liquid flow rates, pressure, temperature, and the solvent inlet composition x_in.
Obtain or fit an equilibrium relation y* = f(x) at the operating temperature and pressure, and confirm whether a linear approximation y* = m x is acceptable across the expected loading range.
7.2 Step 2, choose the liquid rate using Lmin logic and a safety margin.
For absorption, the minimum solvent rate corresponds to the operating line that just touches the equilibrium line at a pinch point, creating an infinite NTU requirement at that point.
In design, choose L as a multiple of Lmin, commonly by selecting an absorption factor A greater than one to avoid pinch behavior and reduce required height.
As A approaches one, the log-mean driving force collapses and N_OG grows rapidly, so small errors in equilibrium or coefficient estimates create large height swings.
7.3 Step 3, compute NTU on a consistent basis.
Use either numerical integration or a verified closed form to compute N_OG or N_OL, and document the definitions of end points, flow assumptions, and equilibrium used.
Confirm that the computed driving force y - y* remains positive throughout the bed for absorption, or the chosen operating line is infeasible.
7.4 Step 4, estimate HTU using overall coefficients at the intended hydraulic point.
Use vendor curves, pilot data, or correlations to obtain K_y a or K_x a, then compute H_OG or H_OL using the correct G and L mass velocities.
Recognize that H_OG and H_OL vary with packing type, size, liquid distribution quality, wetting, viscosity, surface tension, and gas and liquid loads.
7.5 Step 5, compute packed height and apply practical allowances.
Compute Z = H_OG N_OG, then add allowances for maldistribution sensitivity, end effects, and performance uncertainty appropriate to the project stage.
For tall beds, consider splitting into multiple packed sections with redistributors to control liquid maldistribution and preserve the assumed effective area.
Note : Liquid distribution quality can dominate performance, and a perfect HTU estimate cannot compensate for a poor distributor, so ensure distributor turndown, drip point density, and redistribution spacing are treated as first-order design inputs.
8. Typical HTU levels and what drives them in real packed columns.
HTU values are strongly system- and packing-dependent, so any single “typical” number is only a starting point for screening.
Still, rough ranges help sanity-check results before deeper vendor engagement.
| Service and conditions. | Common packing family. | Order-of-magnitude H_OG screening range. | Main drivers. |
|---|---|---|---|
| Dilute physical absorption at moderate rates. | Random packing, moderate specific area. | About 0.5 m to 1.5 m. | Wetting quality, effective area, gas turbulence, solvent properties. |
| High-efficiency service with structured packing. | Structured packing, high specific area. | About 0.2 m to 0.8 m. | High effective area, lower channeling, better redistribution practices. |
| Viscous solvent or foaming tendency. | Robust packing with larger passages. | Often above 1.0 m. | Reduced wetting, higher liquid-side resistance, maldistribution sensitivity. |
| Reactive absorption with fast liquid reaction. | Structured or random depending on fouling risk. | Can be lower than physical absorption at same hydraulics. | Enhanced liquid-side driving force and effective k_L, with possible heat effects. |
9. A worked example using overall gas-based HTU/NTU.
This example illustrates the mechanics of the method rather than serving as a universal design template.
Assume a dilute solute is absorbed from a gas into a solvent with linear equilibrium y* = m x.
Given y_in = 0.060 and y_out = 0.010 as gas-phase mole fractions, x_in = 0.000 as fresh solvent, and choose absorption factor A = 1.6 as a preliminary operating point.
Compute the required solvent-to-gas ratio from A = L/(m G), meaning L/G = A m.
For a linear system under constant molar flow assumptions, compute end driving forces consistently by using the operating line to obtain x at each end, then using equilibrium to obtain y* at each end.
1) Choose m from equilibrium data at operating T and P. 2) Compute L/G = A m. 3) From operating line, compute x_out = x_in + (G/L) (y_in - y_out). 4) Compute y*_out = m x_in and y*_in = m x_out. 5) Compute end driving forces: Δ_out = y_out - y*_out. Δ_in = y_in - y*_in. 6) Compute N_OG by numerical integration or a verified log form. 7) Obtain H_OG from K_y a data at the chosen G and L, using H_OG = G/(K_y a). 8) Compute Z = H_OG * N_OG.If the integration yields N_OG = 4.2 and the selected packing and hydraulics give H_OG = 0.70 m, the preliminary packed height is Z = 2.94 m.
Then apply project-appropriate allowances for distribution, end effects, and uncertainty, and check hydraulics before finalizing.
10. Hydraulics and pressure drop checks that must accompany HTU/NTU sizing.
HTU/NTU provides a mass-transfer height, but the design is only feasible if the same operating point satisfies flooding margin, pressure drop limits, foaming behavior, entrainment constraints, and mechanical internals constraints.
Hydraulic limits typically set an upper bound on gas rate for a given packing and liquid load, and the chosen operating point should include an explicit safety margin from flooding appropriate to the service.
Pressure drop constraints are especially important in vacuum service, where structured packing is often selected to reduce pressure drop per meter of packing height.
Note : A design that meets separation by HTU/NTU but operates too close to flooding can suffer large HTU degradation due to maldistribution and entrainment, so mass-transfer performance and hydraulics must be iterated together rather than checked once at the end.
11. Common failure modes and how to prevent them.
11.1 Mixing coefficient bases and composition scales.
Overall coefficients may be reported on a partial-pressure basis, a mole-fraction basis, a concentration basis, or a solute-ratio basis, and NTU integrals must use the matching scale.
Always convert coefficients so that K_y a multiplies the same y-scale that appears in the driving force y - y* inside the NTU integral.
11.2 Treating “a” as purely geometric area.
The effective interfacial area participating in mass transfer can be much lower than the geometric area at low liquid rates or with poor wetting liquids, and that reduction is often embedded implicitly in empirical K_y a data.
Do not replace a vendor-provided K_y a with k_y times a geometric area unless you also model wetting and effective area correctly.
11.3 Ignoring temperature rise and equilibrium shifts.
Absorption can release heat, and stripping can consume heat, shifting equilibrium and changing viscosity and diffusivity, which then shifts K and thus HTU.
If the heat effect is material, evaluate property and equilibrium changes along the bed or split the column into segments with piecewise coefficients.
11.4 Treating HTU as constant across large loading swings.
HTU often varies with gas and liquid rates, and it can also vary with solute loading due to property changes or reaction effects.
For turndown and debottlenecking, evaluate HTU and NTU at multiple operating points rather than extrapolating linearly from one point.
12. Practical checklist for an engineer delivering a defensible packed-column height.
| Item. | What to confirm. | Why it matters. |
|---|---|---|
| Basis consistency. | Driving-force scale matches K basis, and G and L are mass velocities. | Prevents hidden unit and scaling errors. |
| Equilibrium validity. | Equilibrium relation covers the loading range and temperature profile. | NTU is driven by equilibrium accuracy. |
| Feasibility. | Driving force does not change sign, and A is not near pinch unless justified. | Avoids infinite or unstable heights. |
| Coefficient source. | K_y a or K_x a comes from applicable packing, hydraulics, and properties. | HTU is only as good as K data applicability. |
| Distribution internals. | Distributor type, drip density, redistribution spacing, and turndown. | Controls effective area and prevents channeling. |
| Hydraulics margin. | Flooding margin, pressure drop, entrainment, and foaming risk are acceptable. | Ensures operability and stable performance. |
FAQ
What is the difference between HTU/NTU and HETP for packed columns.
HETP translates packed performance into an equivalent number of equilibrium stages, which can be convenient for stage-based simulators but can hide how driving forces and resistances vary with height.
HTU/NTU is rate-based and explicitly uses local driving force and overall resistance, so it is better aligned with how packed beds physically transfer mass over a continuous height.
When should I use overall coefficients instead of individual film coefficients.
Overall coefficients are preferred when you have reliable empirical data for K_y a or K_x a for the packing and hydraulics of interest, or when you want to avoid separately modeling effective area and the two-film coupling through equilibrium slope.
Individual film coefficients are most useful when you need mechanistic insight into which phase controls, or when you have validated area and wetting models for your system.
How do I decide whether gas-side or liquid-side resistance controls in absorption.
A practical screening approach is to compare 1/k_y to m/k_x in the gas-based resistance-in-series expression, because m scales the liquid resistance into gas driving-force units.
If 1/k_y dominates, gas-side resistance controls, and if m/k_x dominates, liquid-side resistance controls, but the controlling side can shift with flow rates and with changes in equilibrium slope.
What is the most common reason a packed column fails to meet its predicted HTU/NTU performance.
The most common cause in practice is liquid maldistribution, especially in larger diameters or in services with poor wetting, because it reduces effective interfacial area and creates channeling that invalidates the assumed uniform contact.
Improving distribution hardware and adding redistributors often produces more reliable gains than changing packing alone.
How should I handle nonlinear equilibrium or variable flow in the NTU calculation.
Use numerical integration with equilibrium evaluated locally at each computed composition point, and update G and L or use solute ratios if the solute transfer meaningfully changes bulk flow rates.
If heat effects or reactions are present, segment the column and compute segment-wise NTU and HTU using local properties and equilibrium, then sum heights across segments.