Absorption Column with Water:
Diagrams:
Figure 1 below shows a diagram of an absorption column. The inlet gas in this case is our mixture of 13%
methane with 87% carbon dioxide. The inlet liquid is our absorbent, pure water while the outlet liquid is
water with dissolved carbon dioxide. This leaves our gas outlet to contain whatever purity of methane is
desired with carbon dioxide making up the remainder. The column is to be packed with 1” Raschig rings.
Figure 1: Absorption Column Diagram1
Operation Assumptions:
The water used in the absorption process can be recycled each day, therefore only enough water is
needed for 24 hours rather than 6000 hours per year. The Henry’s law constant for carbon dioxide in
water was assumed to be constant at each of the temperatures tested 25˚C, 5˚C and 45˚C. The mass
transfer coefficients Kx and Ky used to calculate the volume of the column needed were assumed to be
the same as those values given in Problem Set 4 because that problem had the same geometry and the
MDEA solution used was mostly water.3
Kx = 8.6 mol/(m2*s)
Ky = 0.56 mol /(m2*s)
When the profit was calculated, the carbon dioxide that was dissolved in the water was neglected due
to complexity. Carbon dioxide would somehow have to be extracted out of the water and sold. The
resources were not given for this analysis and thus we assumed that the water containing CO2 yields no
profit.
Figure 2 below displays the Henry’s law constant in water at various temperatures. This model is said to
be relatively accurate for the solubility of carbon dioxide in water at pressures up to 100MPa or roughly
14,500 psi. The pressure of our feed is well below this threshold at 334.7psi.
Figure 2: Henry’s Law Constant for CO2 in Water2
Based upon graph and dividing by our running temperature of 334.7psi or 2307.7kPa the henry’s law
constants used for calculation were:
At 25˚C
At 5˚C
At 45˚C
H=65.00
H=34.66
H=104.00
Calculation:
The minimum water flow Lmin for each purity was calculated using:
Lmin = V H(yCO2,in-yCO2,out)/YCO2,in
In order to find the best Liquid flow rate, Lmin was multiplied by 1.2, 1.3, and 1.1 for each desired purity
gas and was used as Lin in all following calculations.
𝑉𝑝𝑟𝑖𝑚𝑒 = 𝑉𝑖𝑛 (1 − 𝑌𝑖𝑛 )
𝐿𝑝𝑟𝑖𝑚𝑒 = 𝐿𝑖𝑛 (1 − 𝑋𝑖𝑛 )
These two equations are used to account for the variable nature of the vapor and liquid flow rates as the
respective streams travel through the absorption column. The Vprime and Lprime values are constant
throughout the column.
In order to evaluate the volume of the column needed based solely on changing the Yin and YCO2,out,X
must be converted into a function of Y.
𝑋=
𝑉𝑝𝑟𝑖𝑚𝑒 (𝑌 − 𝑌𝑜𝑢𝑡 )
𝐿𝑝𝑟𝑖𝑚𝑒 (𝑌 − 1)(𝑌𝑜𝑢𝑡 − 1) + 𝑉𝑝𝑟𝑖𝑚𝑒 (𝑌 − 𝑌𝑜𝑢𝑡 )
This equation is derived by performing a mass balance on the entire system with respect to CO2. The
equation was then solved for the XCO2 variable to simplify the calculations.
Henry’s Law constants were obtained from above graph in Figure 2 and then used to calculate the
overall mass transfer coefficient, K0.
𝐾0 =
1
1
𝐻
+
𝐾𝑌 𝐾𝑋
Using the mass transfer coefficient along with the Henry’s constants, the volume required to produce
the various YCO2,out fractions needed was calculated in Wolfram Mathematica by evaluating the following
integral:
𝑌𝑖𝑛
−𝑉𝑝𝑟𝑖𝑚𝑒
1
(
)
2
(1 − 𝑌) (𝑌 − 𝐻𝑋)
𝑌𝑜𝑢𝑡 𝐾0 𝑎
𝑉𝑜𝑙𝑢𝑚𝑒 = ∫
This equation is traditionally expressed as Height of column = (Height of a transfer unit)*(Number of
transfer units). It was reformatted so that the equation could be used to solve for the overall volume of
the column instead of just the height of the column by removing the cross sectional area from the
integral and multiplying it to the LHS of the equation or the height of the column.
All of these equations were utilized in conjunction with each other to deduce the volume of the column
at varying values of YCO2,out and Lin. The degrees of freedom involved in the calculation allowed for these
two variables to be altered maximizing results. The remaining calculations are relating to costs and will
be covered in the cost analysis section.
Cost Analysis:
The results for the volumes needed for purification from the integral above as well as a summary of all
costs of the column and materials needed can be found in Tables 1-3 for each respective temperature of
the feed. All costs and profits are given in $/yr.
The building price of the column is proportional to the Raschig ring price given as $1800/ft3 which is
equivalent to $63520/m3. Therefore the total cost of the column was simply the volume needed for
each given Liquid flow rate and purity multiplied by this price.
Column Cost($) = Volume needed(m3)* Raschig ring price($/m3)
The cost of the water was determined by the Liquid flow rate needed. The price of process water given
was $0.15/1000gal which is equivalent to $0.000659/mol.
Cost of water ($/yr) = price of water ($/mol)*flow rate (mol/hr)*running time (24 hr/yr)
The equipment cost column accounts for any equipment required to change the pressure or the
temperature. For all pipeline quality gas and liquefied natural gas, the exiting gas stream needs to be
compressed to 600psi in order to be sold. A compressor uses electric power at a price of $0.12/kilowatthr. All streams 45°C must be heated before entering the absorption column and all streams at 5°C must
be cooled. The price of heating as given in the project specs is $3/MMBtu and the price of refrigeration
(cooling) to 5°C is $12/MMBtu.
Cost of Compressor ($/yr) = Price of Electric ($/kw-hr)*Vout(mol/hr)*running time (6000 hr/yr)*energy
needed (kw-h/mol)
Cost of Heating ($/yr) = Price of heating ($/MMBtu)*Vin (mol/hr)*heating job(Btu/mol)*running
time(6000 hr/yr)
Cost of Cooling ($/yr) = Price of refrigeration ($/MMBtu)*Vapor flow rate (mol/hr)*cooling job
(Btu/mol)*running time (6000 hr/yr)
The gross income generated in absorption with water comes from selling the gas product at the various
purities (eg. High Energy Gas, Medium Energy Gas, etc…). In order to sell the carbon dioxide it would
have to be extracted from the water which is outside the scope of this project. The price of each
product grade is given in $/MMBtu of methane.
Gross Income ($/yr) = price of methane ($/Btu)*XCH4,out*Energy of Combustion for Methane (782.6
Btu/mol)*Vout (mol/hr)*running time (6000 hr/yr)
Analysis:
Upon review of the profit for each gas product in tables 1-3 it can be seen that none of the combinations
make any more money than just selling the feed as a Low Energy Gas. In fact, many of the outlet purity
and flow rate combinations listed actually lose money overall. This result is due to the fact that carbon
dioxide is not very soluble in water and therefore the Henry’s Law constants are large. Our feed stream
is very high in carbon dioxide and low in methane therefore, it takes very, very large amounts of water
to dissolve enough carbon dioxide. So much water costs a lot of money.
Based upon the data, the most significant costs to consider in building an absorption column to purify
natural gas at our feed concentration are the building costs of the column and the water used. In
general, the better quality gas stream desired, the more the column and the water costs yielding a
smaller profit.
The results suggest that as temperature decreases, the absorption of carbon dioxide in water improves
and profits are slightly better. Although this yields higher profits, cooling to 5°C still does produce more
profit than just selling the feed as is. Based upon this analysis cooling the feed further would not
outweigh the profit obtained from selling the feed as is by a significant enough amount to be worth
building an water-absorption column.
The initial price of building the column is only a one-time cost every 30 years, therefore the profits for
the years where it is not required to replace the Raschig rings would be higher. Still this profit would not
be enough to ultimately be worth building and maintaining the column using water because of the
obnoxious amount of water needed.
References:
1. "Packed Bed." - Encyclopedia Article. MediaWiki, n.d. Web. 23 Apr. 2014.
2. John J. Carroll and Alan E. Mather, "The System Carbon Dioxide-Water and the KrichevskyKasarnovsky Equation," Journal of Solution Chemistry, vol. 21, pp. 607-621, 1992.
3. Zydney, Andrew “CHE 410 Problem Set 4”. Problem 2. 2014