Fluidized Beds for 1 Gtonne Removal of Dilute CO2 using Mg-MOF-74 Particles

I used the dimensionless time[1] to calculate time needed for a cycle to saturate the sorbent. This is a back of the envelope calculation since I am learning Fluidized beds. This is a working document process. I had made an error with my density and I corrected the typo in my excel file.

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 998 seconds, with a minimum fluidization velocity 8.1 m/s for 0.75 void fraction of, but I double that to 8.12 to elicit carryover. I estimated the molCO2/kgAir to be 0.0049. Since 2.273e13 molCO2/y needed to be processed, the former and latter lead to 1.49e8 kgAir/sec 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 solidsdoubled velocity(3.14(D/4)^2) (1-voidage) to find the inlet area 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 during all cycles(time of year in seconds/988 s/cycle), which is 4.4e10 kg. I took the ratio of total kgsorbet/yr divided by 4.4e10 and multiplied that value (61.5) times the number of reactors estimated from the mass flow rate per second, which gave me a goal seek of 2.27e13 molCO2/year which was an Ideal 1 reactor. This is 62 fluidized bed adsorption and 124 beds including regenerators. I am assuming the 62 fluidized adsorption beds have the same mass flow rate as the other beds. So, I took the total kg sorbent overall all cycles and multiplied it by 61.5 beds and came up with the 2.780e12 kgsorbent/year value from the top of the spreadsheet[SS].

The land area for 5.44 m diameter and 18 meter tall fluidized bed is (3.71e3 m^2) or 0.00371 km^2. This assumes 30% the Total area for spacing or 3.71e3*(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.

References:

[SS] Fluidized Adsorption Bed Number https://1drv.ms/x/s!AiVJ2x5-aoWykNo32gdRgG4R5nE-iA?e=DBomfQ

[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

Green Energy Fuels, MACA, v1.0

Hello,

‘The MIT Alumni for Climate Action group on Advocacy and Policy led by Jeremy Grace, PhD, published a position paper on Green Alternative Fuels. (See https://maca.earth/). This paper examines the appropriate production and use of green alternative fuels in the context of a transition to a net-zero economy. General points articulated in the paper written for maximum clarity for citizens and government representatives include (i) Hydrogen and other green alternative fuels are not a one-to-one substitution for fossil fuels; and (ii) They should be used appropriately only where direct electrification is not possible. Any green alternative fuel, including hydrogen and ammonia, must be produced in a manner that complies with the “three pillars” of the 45V Hydrogen Production Tax credit. These pillars are necessary to ensure that scale-up of green hydrogen production does not impede the needed deep cuts in CO2 emissions.'[MACA]

I am a co-author of the above-mentioned paper. I am excited to share this important information with you.

Here is the paper: https://maca.earth/wp-content/uploads/2023/10/MACAGreenAlternativeFuels.pdf

MITx 18.03 Introduction to Differential Equations

I have a BS in chemical engineering. I averaged 96% over the 5 units of study. The material was mostly new to me. Although I had a high average, I only averaged so high because I took copious notes from the lecture notes, practice problems, and videos.

A BS in electrical engineering said in the discussion that this course is too hard for a first time learner. That was his opinion, and he made the comment after a section on imaginary concepts. It was new to me. I found it difficult, but I tend to, so far, do well with mathematics. Still, I took a total of 303 full pages of notes that I referenced often to solve the very difficult homework problems. I find note taking useful since there is no PDF textbook download. Also, it helps me remember the material.

I am an official Friend of MIT. I have been awarded an MIT Infinite Connection account by MIT after I completed numerous MITx courses and completed a MIT Digital Learning survey. Although I am not an alumnus, I can participate in the MIT Alumni Forums. I can also watch, as an example, videos from the MIT Alumni website. In one video about volunteering, the presenter joked about MIT students being used to taking copious notes. I find it useful as well.

As of March 06, 2022, the edx syllabus is not accurate. So, be prepared for a little change in the organization of course topics. I found the material increased in difficulty as the course progressed, with the exception of Unit 5 on nonlinear differential equations graphical methods.

Dr. Jennifer French, MIT Lecturer, agreed with the BS in electrical engineering that the course is hard, it has a lot of material, and it is the same as taught on MIT campus. I have read that 99% of MIT students have taken a MITx course. MIT is no joke. It is high quality material.

There are two homework styles. The mechanics are covered in homework A(s), and homework B(s) are often harder with more mathematics and physics.

I put in the suggested time for completion. I worked hard.

References:

[1] https://www.edx.org/course/introduction-to-differential-equations-2

MITx 18.03x Introduction to Differential Equations Notes

I Am Now A Friend of MIT

Can you believe it? I have an MIT Infinite Connection [1]. The often ranked number 1 technical university in the world gave me an MIT Infinite Connection account. I could even join the Oregon Southwestern Washington MIT Alumni club once I created my account.

Why?

After I took a calculus course, after several MITx courses, where I earned As and finished one course in half the allotted time, I was asked to fill out a survey. In that survey, MIT asked me questions about my professional life and academic life. After I completed the survey, I started receiving MIT News and MIT Technology Review for free. I thought it was because of the survey. The magazine costs 13 dollars a pop. I continued my calculus courses from MITx on edx.org.

Recently, I received an Email from MIT, with a special number associated with my Email address, asking me to create an MIT Infinite Connection account. I was dumbfounded. I gave it a go, created the account, and joined my regional MIT alumni club. I am an official MIT Friend of MIT to one of the most prestigious technical universities in the world. I am proud.

I am proud that someone from MIT recognized my work. I assume that is why I was given an MIT Infinite Connection account, which was verified by MIT Alum help. To be recognized by them is quite special indeed.

With that said, I am most proud of my Oregon State University School of Chemical Engineering alum status.

References:

[1] https://alum.mit.edu/aboutfaqs/registration-faq

A Positive Outlook: Professor Hrvoje Jasak

Can you believe Professor Jasak[https://www.lsc.phy.cam.ac.uk/staff/dr-hrvoje-jasak] is a professor and researcher at the same University of Cambridge that Dr. Stephen Hawking, famous theoretical physicist, researched and taught at. Cambridge has a 21% acceptance rate.

I am excited because he has been a LinkedIn contact of mine for more than a year. In the last couple months, he contacted me and offered to supervise my OpenFOAM learning. He said he would share his lectures from University of Cambridge too.

I told him my goals, my desires, and that I needed to complete them before I accept his offer. He didn’t say no. I need to complete MIT differential equations series, MIT advanced fluid mechanics from MIT mechanical engineering graduate school, and MIT analysis and transport from MIT chemical engineering graduate program. I also need to complete my self study of Fox and McDonald’s introduction to fluid dynamics. Then, I plan to self study a book on Finite Volume Method, a book on computational fluid dynamics, and two books on turbulence. Then, I might pay for an OpenFOAM introductory course from OpenFOAM foundation or ESI. I also need to successfully draft my waterjet propulsion system. After all that, I said I will ask for his supervision.

He didn’t say no. Instead, he looked at my profile. I have grand plans, but I don’t want to waste the opportunity to learn from Dr. Jasak. I want to be an intelligent and educated student and well prepared. If I do, my chances of successfully modeling the waterjet propulsion system will be greater. I share my successes on LinkedIn because success are more fun when shared and celebrated, but I also want Dr. Jasak to know that I am working my goals. He is a brilliant engineer, CFD expert, and mathematician. He is a world class researcher in CFD. I am lucky he offered to supervise me.

A New Goal: To understand waterjet propulsion via computational fluid dynamics and OpenFOAM

Tuesdays and Thursdays are my short study days. It helps me reset. MWF are my 7 hour days. TTH are 5 hours on average.

After studying my fluid mechanics today, and watching several videos, I feel good about my fluid mechanics path. I am so dependent on feeling good about my studies. It affects my whole day.

Although I succeeded yesterday in MITx introduction to differential equations, it was a grueling day that I didn’t enjoy that much. Was making so many tiny errors, and I got the concept right for a really difficult problem, but failed to simply distribute correctly. A simple algebra error caused me to miss a very challenging problem. Although I got some dopamine rush from getting the concept correct, I felt horrible because I made errors like that all day yesterday. I had to check and recheck my problems multiple times, which drug the day out significantly. Anyhow, it is over.

Today has been a much better day, but I did watch a really boring video on shock waves. I should have chosen a more entertaining video since I have control. Anyhow, note taking went well, and I am learning fluid mechanics well. I have to get through the book so that I can study Introduction to Turbulence.

I am spoiled with PDFs. I don’t like reading from textbooks. My computer and monitor, along with my makeshift desk, is set up for PDFs and not books. MIT Press Introduction to Turbulence is not in electronic format, but it is a great book to work my way into turbulence. Then I can study the bible–Pope’s book on turbulent flows. Most flows in real life are turbulent.

It is quite difficult to properly model turbulent flows in OpenFOAM. Especially if the geometry is complicated. What will all this do for me? Pass time. I doubt anybody will benefit from my studies, but I will have fun. I hope to get published. That way it might be used. I will share it on cfd-online and other open-access document servers. I hope to be sound mathematically and physics wise. I am excited that Dr. Jasak, the creator of OpenFOAM, has offered to supervise me and share his valuable lectures on OpenFOAM. The man is a professor at Cambridge, which has a 21% acceptance rate. Exciting!

A Review of Vector Calculus for Engineers

Although I earned a BS degree in chemical engineering in 1999 and have taken multivariable calculus, Professor Jeffrey Chasnov’s Vector Calculus for Engineers[1] was a great challenging learning process.

I found the time needed to complete the course could be long or short. Initially, I started out as I do with all my courses and tried to solve all problems without looking at the solutions. Since the course is compressed, much is covered in a short period. There were new topics that I had to learn, and I was rusty on other topics. So, week 3 sent me a message. Don’t be afraid to learn from the solutions to meet the deadlines. This is very important for week 4, which was the most challenging week for me.

When learning from the solutions, one MUST figure out the missing steps to ensure competence on the weekly assessments. This takes knowledge of physics and mathematics for some problems, and just mathematics for other problems. In engineering, we were taught to always draw our system. I found this to be true in this course as well. At times, one cannot just memorize the equations given, and there are many great equations and tricks given, but one must take the extra step to figure out how the equations were derived. As a simple example, the last problem in the notes[1a] integrates the circle over dr and one must remember that s = r(theta) and ds = r d(theta) to get the problem fully. This is knowledge from trigonometry and basic calculus, and Professor Chasnov expects one to use known physics and mathematical relationships to solve problems. Obviously, this includes material learned in Vector Calculus for Engineers.

I found the time required to complete problems was longer than suggested, and I put in 6 hours a day on some days, but my average was near 4 hours a day. Most weekly assessments took me much longer than 45 minutes to complete. Week 4 took me 4.5 hours but note that I shot for 100% on each assessment on first attempt. Also, I have an illness that causes shaky hands so my writing can be bad. This is a huge factor in later weeks where much algebra is needed to solve the problems. Week 5 had excellent applications.

Overall, Professor Jeffrey Chasnov put together a very useful course for engineers, physicists, and people who want to learn vector calculus. He does expect familiarity with mathematics and physics, and I am happy I had refreshed my algebra, trigonometry, single variable calculus, and physics using Coursera. I also used MITx and MIT OCW. I now have more confidence going into my study of computational fluid dynamics (CFD) and fluid dynamics[2]

I earned an overall 96% in the 5 week course which means I solved 48 of the 50 weekly assessments problems. In college, I received similar grades in my calculus courses. I found that the course was challenging and on par with MITx calculus and physics courses and University of Pennsylvania Calculus Coursera courses.

References:

[1] https://www.coursera.org/learn/vector-calculus-engineers

[1a] Chasnov, Jeffrey R. Vector Calculus for Engineers: Lecture Notes for coursera. URL: https://www.math.hkust.edu.hk/~machas/vector-calculus-for-engineers.pdf

[2] Warsi, Z.U.A.. Fluid Dynamics (p. 2). Taylor and Francis CRC ebook account. Kindle Edition. Google Book: https://lnkd.in/gha_C-un

Scalar, Vector, and Tensor Mathematics of CFD

I am new to tensor mathematics and CFD mathematics, but the following books have been quite helpful. [1-3] have great reviews of the mathematics of scalars, vectors, and tensors. [2-4] together cover the mathematics of CFD. Now, I just need better comprehension. #CFDBooks #BeginningOpenFOAM

Note that equation 10b is wrong in Mathematical Exposition 1[3]. See [5] for verification by a PhD in Fluid Dynamics from University of Texas at Austin.

References:

[1] SimCenter. National Center for Computational Engineering. An Introduction to Vectors and Tensors from a Computational Perspective. URL: https://www.utc.edu/sites/default/files/2020-06/utc-cecs-simcenter-2014-01.pdf

[2] Tobias Holzmann. Mathematics, Numerics, Derivations and OpenFOAM(R), Holzmann CFD, Leoben, fourth edition, February 2017. URL: http://www.holzmann-cfd.de 

[3] Warsi, Z.U.A.. Fluid Dynamics. Taylor and Francis CRC ebook account. Kindle Edition. 

[4] Hirsch, Charles. (2007). Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics. Elsevier

[5] https://math.stackexchange.com/questions/4266972/am-i-expanding-grad-v-which-is-in-index-notation-correctly-is-equation-10b-wr

A Great CFD Book

I have just started the book[1] but I like it already. So far, it provides simple and complete derivations of the equations of fluid dynamics. The book was referenced by the authors of “OpenFOAM Technology Primer, v.2012”.

References:

[1] Hirsch, Charles. (2007). Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics. Elsevier #CFDBooks #BeginningOpenFOAM

A Great Tutorial Textbook for C++

I have read up to chapter 3 of Bjarne’s beginner book for C++ programming[1], and I really enjoy the tutorial format of the well written book. #cpplus #BeginningOpenFOAM

The book mentions that a reader will understand all of https://lnkd.in/e6KDYFgy by the time chapter 21 is finished, and I like that possibility.

References:

[1] Bjarne Stroustrup. Programming: Principles and Practice Using C++, Second Edition (Chris B Harding’s Library) . Addison-Wesley Professional.