Enter temperature in Kelvin (283.15 to 313.15 Kelvin):

Select temp in °C 10°C 15°C 20°C 25°C 30°C 35°C 40°C K

Enter the water flow rate to be treated (1 to 70 m3/hr): 

   m3/h                                                                                                                                                                             m3/s

Enter the airflow (0.05 to 1.5 m3/s):

m3/s

Enter the desired removal percentage (0.90 to 0.99):

Select gasket type:

2 inch Nor-Pac (12) 2 inch TriPack (15) 1.5 inch Nor-Pac (17) 2 inch FlexRing (24) 2 inch plastic PallRing (25)

De Stripping Factor is:                                                                                                                                                            

The x and y values on the Eckert curve are:

x: y:

Specific Surface Packing:                 m2/m3

Nominal Diameter of Gasket:             m

Cross section and Diameter:

Cross-section: m2          Diameter: m

Column Height:                                                                                                                                                                         m

When extracting water, there can sometimes be talk of dissolved CO₂ in the groundwater. CO₂ forms an equilibrium together with HCO₃^- and CO₃^2- . When purifying water in which CO₂ and HCO₃^- are dissolved, the dissolved HCO₃^- largely removed by the semipermeable membrane of the reverse osmosis process. The HCO₃^- is entrained with the unwanted concentrate. The CO₂ that is dissolved in the water largely passes through the membrane. As a result, the water that has come out of the reverse osmosis process has become more acidic. Before the acidic water is again passed through a second reverse osmosis process, the dissolved CO₂ must first be removed from the water. This is done via so-called strip towers. By removing the dissolved CO₂, the acidity decreases again. This is necessary, among other things, because the membranes used for purifying water are poorly resistant to acid water. The balance between CO₂, HCO₃^- and CO₃^2- is shown below.

The Eckert Pressure Drop Curve

The temperature determines the concentration of CO₂ in air which is in equilibrium with the concentration of CO₂ in water

The ratio between these two equilibrium concentrations is called Henry's constant. Henry's dimensionless constant at a given temperature can be found using the formula given below:

Here, ΔH is the standard enthalpy change for solution in water in [kcal/kmol].R is the universal gas constant, 1.987 [kcal/kmolK]. K_c is a substance dependent constant. H is Henry's dimensionless constant at 20 degrees Celsius. T is the absolute temperature in Kelvin.

For a number of common substances, these data are listed in the table below

Dimensionless Henry constants of a number of substances at 20 degrees Celsius.

ΔH in 10³ [kcal/kmol] .

Component	ΔH	Kc	H
Ammonia	8.63	1526	0.0006
Carbon Dioxide	4.77	4013	1,1
Chlorine	4.01	420	0.43
Chlorine dioxide	6.75	4300	0.04
Hydrogen sulfide	4.26	567	0.38
Methane	3,55	12402	28,41
Oxygen	3,34	9627	32.15
ozone	5.80	83848	3.74
Sulphur dioxide	5.53	358	0.03
Carbon tetrachloride	7.85	8580096	0.96
tetrachloroethylene	7.85	290732	0.41
Benzene	8.47	357678	0,18
Chloroform	9,21	940789	0,13

A minimum ratio between the air and water flow is required to achieve a certain desired final concentration of the "pollution" in the water.

This is given by:

Air/water ratios smaller than this minimum value will not reach the desired final concentration, because an equilibrium has then been established before the desired initial concentration is reached.

The minimum air/water ratio therefore changes with the temperature. If the entry C(0) concentration of the contaminant is known and the desired exit concentration    C(u) is also known, then, if the Henry constant of the substance is known, the minimum air/water ratio needed to reach the desired starting concentration can be determined.

Another concept commonly used is the so-called stripping factor, which is defined as the number of minimum air/water ratios required to achieve a high removal level. At a high removal level, the desired concentration at the exit is many times smaller than the entering concentration

The minimum air/water ratio can then be written as:

The stripping factor S is then defined as:

With a stripping factor S equal to 1, the stripping column operates at the minimum air/water ratio required to achieve a certain desired concentration at the exit. If S is less than 1, the stripping column will not be able to reach the target concentration because equilibrium is reached earlier than the target concentration.

The cross-section/diameter of a strip column can be determined with the following procedure.

Step 1

In order to determine the cross section of a strip column, there are a number of important design criteria in advance. These are:

1. The so-called packing factor of the type of packing chosen.
2. Air/Water ratio
3. Pressure drop of the gas , typical value is 50 [Pa/m]

The table below lists the data for some commonly used gasket types

Data of some commonly used gaskets

Gasket type	nominal diameter   [m]	Packing factor  C f	Specific Surface   [m 2/m 3]	Critical Surface Tension  [N/m]
Nor-Pac	0.0508	12.0	102.0	0.033
Plastic Tri-Pac	0.0508	15.0	157.0	0.033
Nor-Pac	0.0381	17.0	144.0	0.033
Flex ring	0.0508	24.0	115.0	0.033
Pall Ring	0,0508	25,0	102,0	0,033

Step 2

The Eckert pressure drop curve is used to determine the cross-section/diameter of the stripping column. The x coordinate of the Eckert curve is associated with a particular equation. The x value of the Eckert curve is given by:

Herein is:

• ρ _l = The density of the water, in [kg/m³]
• ρ _g = The density of the gas , in [kg/m³]
• G_m / L _m = mass flux ratio gas/water

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If the density of water and air at a certain temperature is not known, these extra steps should be followed.

The density of a substance depends on the temperature. For solids and liquids, the volume change can be determined to a good extent using the cubic expansion coefficient. The volume change is given by the equation below:

Herein is:

• ΔV = volume change of the substance at temperature T₂ in [m³]  relative to a certain reference temperature T₁
• β = coefficient of cubic expansion, for water this is 0.21·10^-3 K^-1 at 293 Kelvin (20 degree Celsius)
• V₀ original volume of water at reference temperature of 293 K, to be taken as 1 m³
• ΔT is the temperature difference between T₂ and T ₁

The density of water can then be calculated using the well-known formula for density: mass / volume. The volume here is the old volume + the change in volume.

The density of air at a certain temperature T can be determined using the ideal gas law.
It reads:

Herein is:

• p = the prevailing air pressure, for atmospheric strippers this is the outside air pressure, 101 kPa
• M = molar mass of air , 28.97 [kg/kmol]
• R = universal gas constant , 8314 [J/(kmol·K)]
• T = the absolute temperature in Kelvin.

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The value G_m / L_m can be determined if the air/water ratio is known.

Herein is:

• Q_a = The airflow in [m³ / s]
• Q = waterflow in [m³ / s]

Step 3

At a known x value (between 0.02 and 3.0), the y value on the Eckert curve can be determined graphically. Using Excel, the
y value can be approximated with the formula below. This formula gives the red curve in the Eckert graph.

Step 4

The mass flux of the gas per unit time can be determined with the relation for the y value on the Eckert curve.
This is given by:

The mass flux of the gas is then given by:

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If the dynamic viscosity of water at a certain temperature in the temperature range from 283 to 293 K is unknown, it can be determined
using the formula below.
The prescription for this empirical formula is ¹:

Here, μ_l is the dynamic viscosity of water in [kg/m·s] and T is the temperature in Kelvin< /p>

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The mass flux of the gas G_m can then be calculated.

Step 5

The mass flux per unit time of the water L_m can then be calculated from:

The cross section of the strip column can then be determined from:

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The mass transfer of the CO₂ that is transferred from the water to the air takes place by diffusion. The driving force for diffusion is the difference in concentration of the CO₂ in the water with the concentration of the CO₂ in the air. The degree to which a substance diffuses depends on the temperature. In a stripping column, two phases are always in contact with each other. Diffusion in the liquid and diffusion in the gas then takes place. For the calculation of the diffusion coefficient of the CO₂ in the water the empirical Hayduk-Laudie relation is used, the prescription is given by:

Herein is:

• D_L the diffusion coefficient of the CO₂ in water, in [cm²/s]
• μ_w is the dynamic viscosity of water in {cP], [1 kg/(m·s] = 1000 cP]
• V_b is the molar volume of CO₂ at the standard boiling point (the vapor pressure is then equal to 1 atm), expressed in {litre/mole]

The diffusivity of a given substance in a gas can be determined by using the Wilke-Lee modification of the empirical Hirschfelder-Bird-Spotz relation. The prescription of this is given by:

Herein is:

• D_g = diffusion coefficient of CO₂ in the stationary gas (here that is air), in [cm^{2< /sup>/s]}
• T = the temperature in [Kelvin]
• M_A = molecular weight of CO₂ in [g/mol]
• M_B = molecular weight of air in [g/mol]
• P_l = air pressure in [Pa]
• r_AB = average distance between two molecules colliding, equal to ( r_A + r_B ) / 2 , expressed in [nm]
• r_A = the average collision distance between the CO₂S , in [nm]
• r_B = the average collision distance between the air "molecules" , in [nm]
• ε_AB = molecular attraction energy equal to √(ε_A· ε_B) in ergs (1 erg = 10^-7 J)
• ε_A = the molecular attraction energy for CO₂ in [ergs] (1 erg = 10^{-7< /sup> J )}
• ε_B = the molecular attraction energy for air in [ergs] ( 1 erg = 10^-7 J )
• k = Boltzmann's constant, (1.38·10^-16 [g·cm² / s² ·K ]
• f(k·T/ε_AB) = collision function

The values of r_A and ε_A can be estimated using the following relationships:

Herein is:

• r_A = the average distance between the colliding CO₂ molecules in [nm]
• T_b,A = temperature of the boiling point of CO₂ where the vapor pressure is equal to 1 atm, expressed in [Kelvin]
• V_b,A = the molar volume of CO₂ that at the boiling point T_{b,A< /sub>} should be expressed in [liter/mol]

For CO₂ the boiling point is 194.6 Kelvin and the molar volume at this temperature is 0.0340 [liter/mol]

The diffusivity of a given substance (here CO₂ ) can be determined by assuming that air behaves as a single substance with regard to molecular collisions.
The required parameters for being air:

• r_B = 0,3711 [nm]
• ε_B / k = 78,6

So:

The collision function can be determined by:

Where ee is given by:

This allows the diffusion coefficients of CO₂ in water and CO₂ in air to be determined.

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In stripping processes, the mass balances on the liquid side are involved. The total mass transfer constant can be determined using the equation below.

Herein is:

• K_L·a = total mass transfer constant per [s^-1]
• k_l = the local mass transfer coefficient of the CO₂ in the water in [m/s]
• k_g = the local mass transfer coefficient of the CO₂ in the air in [m/s]
• a_w = the wetted surface of the gasket in [m² / m³]
• H = Henry's dimensionless constant

The local mass transfer coefficients k_l and k_g and the wetted surface of the gasket a _w can be found using the Onda correlations.

The wetted surface of the gasket a_w is given by:

Herein is:

• σ = the surface tension of the water in [kg/s²]
• σ_c = the critical surface tension of the gasket in [kg/s²]
• a_t is the specific area of the gasket used in [m² / m³]< /li>
• Re = the dimensionless Reynolds number
• Fr = the dimensionless Froude number
• We = the dimensionless Weber number

These dimensionless key figures are given by:

Herein is:

• L_m = mass flux of the water in [kg/m²s].
• a_t = specific surface area of the gasket in [m²/m³]
• μ_l = the dynamic viscosity of the water in [kg/m·s]
• ρ_l = density of water in [kg/m³]
• g = gravitational acceleration , 9.81 [m/s²

The local mass transfer coefficient k_l of the CO₂ in water can be found by:

• L_m = mass flux of the water in [kg/m²s].
• D_l = Diffusion coefficient of the CO₂ in water in [m²/s]
• d_p = nominal diameter of the gasket type used in [m]

The local mass transfer coefficient of the CO₂ in air can be determined with:

Herein is:

• G_m = the mass flux of the air in [kg/m²·s]
• D_g = the diffusion coefficient of the CO₂ in air in [m²/s]
• μ_g = the dynamic viscosity of air in [kg/m·s]
• ρ_g = density of air in [kg/m³]

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The dynamic viscosity μ_g of air depends on the temperature, if this is not known it can be determined with the relation below.

Herein is:

• m = 4.79·10^-26 [kg], the mass of an "air molecule"
• δ = 3.7·10^-10 [m] diameter of an "air molecule"
• P_L = the air pressure in [Pa]

k

= the boltzmann constant , 1,38·10

^-23

[Y/K]

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The use of the Onda relations is subject to a number of conditions:

• The nominal diameter of the gasket must be less than 0.0508 [m]
• The mass flux L_m of the water should be between 0.8 and 43 [kg/m²s].< /li>
• The mass flux G_m of the air should be between 0.014 and 1.7 [kg/m²s].< /li>

When using gaskets that are 2 inches ( 0.0508 m ) or larger, the K_L·a value obtained using the Onda relationships multiplied by a safety factor of 0.75.

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The height L of the strip column can now be determined using the formula below:

In this, S is the so-called stripping factor, which depends on the air and water flow rates and the temperature at which the treatment will be carried out. Furthermore, C₀ is the incoming concentration of the substance to be removed
(here CO₂), for this calculation it is 100 % asked.

The outgoing concentration C_u is the desired concentration that one wishes to achieve of the contaminant in the water and this is
with the formula (1 - removal rate).

Q is the water flow rate to be treated and A is the cross section of the stripping column. The K_L·a value should be obtained from the Onde relations.