Absorption Tower Calculations: Capacity, Pressure Drop, Column Dimensions, Mass Transfer, Example Computation

A properly designed adsorption tower helps effectively purify a gas stream of harmful impurities. However, absorption tower design is impossible without precise determinations of its parameters.

The key parameter determining the energy consumption for gas transportation and the operational capability of the equipment is the drop pressure in absorption tower. As air passes through the column, it overcomes the resistance of the trays/packing, constrictions in the flow areas, the liquid layer, etc.

The magnitude of the pressure drop depends on:

• the type of contact device (for sieve trays - 300-800 Pa/tray, for packed beds - 50-300 Pa/m);
• flow rate (at low velocities, it increases linearly; at operating velocities, it follows a quadratic function);
• liquid flow rate (minimum for dry columns, increasing as the reflux ratio rises);
• physical properties of the gas: density, temperature, viscosity;
• column parameters: number of trays, construction diameter, and orifice characteristics;
• contamination of the contact device.

Calculating pressure loss is necessary to select the optimal fan operating mode. If the pressure loss exceeds the fan pressure, the flow will not pass through the entire column and will not be purified. If the pressure loss is lower than the fan pressure, excess energy consumption will occur, which can reach up to 50%.

An increasing pressure loss during operation indicates clogged contact devices, excessive air flow rates, or a disruption in the spray pattern.

When performing absorption tower sizing, the required diameter of the structure is typically determined first. This depends on the air flow rate and permissible air velocity. The more air that needs to be purified, the wider the tower should be. The higher the velocity, the smaller the diameter. For standardization, the resulting value is rounded to the nearest standard size (0.4; 0.6; 0.8; 1.0; 1.2 m, etc.).

Next, the absorption tower height is calculated based on mass transfer, which determines how efficiently the pollutant is transferred from the air to the filter layer. Accordingly, the lower the pollutant concentration at the column outlet, the taller the structure should be (the more trays or the thicker the packing layer).

Different column types have different optimal height-to-diameter ratios:

• tray configurations– 4:15;
• packed configurations – 3:10;
• adsorbers – 1:4.

After performing these calculations, they are checked for any contradictions (for example, whether the resistance is too high for the chosen diameter and height). If any contradictions arise, the parameters are iteratively adjusted.

Calculating height and expected pressure drop of an absorption tower is accomplished through mass transfer calculations. Mass transfer occurs only when the system is not at equilibrium. The greater the deviation from equilibrium, the faster the mass transfer. The mass transfer coefficient determines how quickly a substance moves from one phase to another. The total resistance to mass transfer is determined by the sum of the resistances in the gas and liquid (or solid) phases.

The rate of mass transfer depends on turbulence (the higher the turbulence, the faster the transfer), temperature (as temperature increases, transfer accelerates), contact area (the larger the contact area, the higher the total mass flow), contact time, solubility, and porosity (for adsorption).

Mass transfer in absorption tower design calculation is determined using various methods, depending on the type of contact element:

• for trays — the tray efficiency method (Murphree efficiency);
• for packing — the HTU–NTU method (the height at which the concentration changes by one driving force unit — the number of transfer units — indicates the required degree of purification);
• for adsorbers — a moving zone model, where the concentration changes from the inlet value to the residual value.

These methods require knowledge of equilibrium relationships (isotherms) and kinetic coefficients, which are taken from reference books, determined experimentally, or obtained through correlations.

1. Parameters are specified: stream flow rate, inlet and outlet concentrations, physical properties, and column type.
2. An equilibrium line (isotherm) and an operating line are plotted.
3. The number of theoretical plates or packing thickness is calculated.
4. One of the methods specified above is used.
5. The actual number of trays or packing thickness is determined.
6. The values are checked for adequacy. If insufficient, more contact elements are added or the type of contact element is changed.

The number of trays or packing height is determined based on the calculated height. Next, the formula for operating line absorption towers is used to calculate the required tray height. This formula describes the relationship between the current pollutant concentrations in the gas and liquid phases along the height of the apparatus and is derived from the mass balance for one of the components.

The client asks us to specify the efficiency of the scrubber with the following parameters:
Capacity: 1000 m³/h
Temperature: 20–40 °C
Phenol: 10 mg/m³
Formaldehyde: 1 mg/m³
Scrubber diameter: 450 mm
Packing: 35 mm plastic Pall rings, height 1 m
Irrigation density: 20 m³/m²·h
Absorbent: 5% NaOH solution

Calculation
Absorption will be accompanied by a reaction



Using the Antoine equation, the partial vapor pressure above the solution is determined.





From the graph in Fig. 1.1 [1]




Equivalent packing diameter



Gas mass flow rate


Air density at 40 °C


Velocity in the absorber


Cross-sectional area


Determination of irrigation density (liquid velocity)


Liquid flow rate


Determination of the fraction of active packing surface
Coefficients [1 p. 343, Table IV-3] p = 0.021, q = 0.0116 (random packing)
Fraction of active packing surface


Reynolds number for the gas phase in the packing


Modified Reynolds number for the liquid film flowing down the packing


Equivalent thickness of the falling liquid film


Packing resistance coefficient
Pall rings, random packing, Re_y > 40


Next, the calculations are performed for each component, and the results are summarized in Table 1.




The calculation is performed using Excel with the successive approximation method, assuming a packing bed height of 1 m.
Absorber capacity for the absorbed component:


The final gas concentration in the liquid is determined.


Then the removal efficiency is determined as:


The driving force at the bottom of the apparatus is determined:


The driving force at the top of the apparatus is determined:


x_H = is assumed to be zero in the absence of gas in the initial solution.
The average driving force is determined as:


Table 1 – Results of calculations

v – molar gas volumes
ν_air = 29.9 cm³/mol – air [3 p. 277, Table 6.3]
ν_phenol = 103.4 cm³/mol – phenol [3 p. 277, Table 6.3]
ν_formaldehyde = 29.6 cm³/mol – formaldehyde [3 p. 277, Table 6.3]

Molecular diffusion coefficients in the gas phase


Prandtl diffusion number for the gas phase


Diffusion Nusselt number for the gas phase


Mass transfer coefficient in the selected units


Express the mass transfer coefficient in the selected units


Table 2 – Results of calculations

Molecular diffusion coefficients in the liquid phase


Prandtl diffusion number for the gas phase


Diffusion Nusselt number for the gas phase


Mass transfer coefficient in the liquid phase


Express the mass transfer coefficient in the selected units


Table 3 – Results of calculations

Mass transfer coefficient in the gas phase


Mass transfer surface area


Determining the packing height


Determination of the hydraulic resistance of dry packing:

where λ is the effective friction coefficient;
packing resistance coefficient

The hydraulic resistance of a packed absorber with wetted packing ΔP_sm, Pa, can be calculated using the formula:

where b = 126 – coefficient [3, p. 343];

Table 4 – Results of calculations