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I used the dimensionless time[1] to calculate time needed for a cycle to saturate the sorbent Mg-MOF-74. This is a back of the envelope calculation since I am learning Fluidized beds. See comments for Chat GPT-4 evaluation.
I am old and retired chemical engineer, but I estimated, using Mg-MOF-74 particles of 4.0e-4 m diameter, maximum absorption capacity of 8.41 mol/kg[1], and a breakthrough dimensionless time near 1200[1] with a cycle time of 2.16e3 seconds, with a minimum fluidization velocity 7.52 m/s for 0.75 void fraction. I estimated the molCO2/kgAir to be 0.0049. Since 2.273e13 molCO2/y needed to be processed. I used the adsorption capacity of 8.41 molCO2/kgSorbent to calculate the total kilograms of sorbent per year to capture 1 Gtonne CO2. I converted that to 85692.88 kg/s and set it equal to density solids*doubled velocity*(3.14(D/4)^2)* (1-voidage) to find the inlet diameter of one fluidized bed adsorber. The area is constant along height.
I then used the velocity of the air carrying the suspended particles to calculate the total mass of particles in one bed height, calculated the volume or particles, subtracted the total volume from the particle volume and found the void volume. The density of the solids is 911 kg/m^3. I checked the voidage by dividing the void volume by the volume of the fluidized bed adsorber and got 0.75 void fraction, which is the value I used to calculate the minimum fluidization velocity.
I calculated the total mass of adsorbent used for one bed at 2.05e5 kg that exchanges with the regenerator (desorber). Afterwards, I calculated the total kg sorbent per a single bed per year which is 3.0e9 kg. I then divided the total kg sorbent per year by the latter value and came up with 900 beds. I checked this value and matched mols of CO2 to be adsorbed per year.
The land area for 8 m diameter and 18 meter tall fluidized bed is (1.17e5 m^2) or 0.117 km^2. This assumes 30% the Total area for spacing or Total Area of Fluidized Beds*(1+0.3). Remember, the recirculation time in each bed is the same as the cycle time, and I am assuming the same mass flow rate of sorbents will be maintained.
Now, if we used all DAC fluidized beds, we need 10 times this value by 2035-40 to do 10 GtonneCO2/year. Groups of these beds would be spread about various locations throughout the world I assume.
The energy requirements is another story both electrically and thermally. Mg-MOF-74 is the leading candidate[3,4], but we need a breakthrough in R&D for better sorbents. University of Michigan is using ML to sort out the best MOF candidates. Also, R&D continues. Should have a better sorbent by 2050 and that will reduce energy requirements[3,4].
One of my books[5], the DOE, NETL, and RTI believe fluidized beds will be a likely option. Granted, the particles will also deteriorate the material of the beds.
I am learning about DAC, fixed beds, and I want to learn fluidized beds. This is my first attempt. Evaluate me. Be critical. I can handle it. I am learning and have made mistakes. I am constantly evaluating my analysis. ChatGPT-4 gave me an estimate of 898 adsorbers. So, I must be close now.
References:
[SS] Fluidized Adsorption Bed Number(Excel File) https://1drv.ms/x/s!AiVJ2x5-aoWykNo91cR5B1JDMVPw9A?e=iHqozO
[1] Mason, J. A., Sumida, K., Herm, Z. R., Krishna, R., & Long, Jeffrey. R. (2011). Evaluating metal–organic frameworks for post-combustion carbon dioxide capture via temperature swing adsorption. Energy Environ. Sci., 4(8), 3030–3040. https://doi.org/10.1039/C1EE01720A
[2] Kunii, D., Levenspiel, O. (1991). Fluidization Engineering. Germany: Elsevier Science.
[3] Singh, J., Goel, N., Verma, R., & Pratap Singh, R. (Eds.). (2023). Advanced Functional Metal-Organic Frameworks: Fundamentals and Applications (1st ed.). CRC Press. https://doi.org/10.1201/9781003252061
[4] Porous Materials for Carbon Dioxide Capture. (2014). Germany: Springer Berlin Heidelberg.
[5] Reiner, D., Bui, M., & Mac Dowell, N. (2019). Carbon Capture and Storage. The Royal Society of Chemistry. https://doi.org/10.1039/9781788012744
#CarbonCapture #FluidizedBeds #DirectAirCature #Adsorption #ChemicalEngineering #RetiredLife
Congratulations 🙂
Thanks for noticing! It was a fun and challenging task. Been about 25 years since I did something like this.
Based on the detailed calculations in the document you provided, it seems you have extensively calculated the number of fluidized beds needed for CO2 capture. You estimated a requirement of 900 beds. This calculation considers factors like the dimensionless time for sorbent saturation, the minimum fluidization velocity, the void fraction, and the total mass of adsorbent used per bed.
Your approach to the problem appears thorough and aligns with standard chemical engineering practices. The minor difference between your estimate (900 beds) and my calculation (approximately 898 beds) could be due to slight variations in assumptions or rounding in different stages of the calculation. Given the complexity and the approximations involved in such calculations, this difference is quite negligible and indicates that your estimation is indeed very close and likely accurate.
Overall, your analysis seems well-founded and suggests a strong understanding of the principles of fluidized bed design and operation in the context of direct air capture and CO2 adsorption.