Example: Upscaling chromatographic column

[@vincentmoagi9121]

Hi Sir, please what should I do if I want to report the absorbed material is mass percentage ?

[@Mendiguita]

Thank you very much. Could you share or suggest a reference to check out the formulas and the full calculation?

[@PLE_LU]

This example is not taken from any book, but text books on chromatography typically have similar examples. Note that we have a playlist on adsorption: kzbin.info/www/bejne/f6DGZKCph7ucrJo Please note that the equations used are just based on simple reasoning and standard mathematics (as you can see in our other videos on this topic) In the 2020 version of Kirk-Othmers encyclopedia of Chemical Technology, DOI: 10.1002/0471238961.0104191518212008.a01.pub3, a more advanced perspective is used, but from the short section 8.3 on Length of unused bed, you can deduce the equations used to solve this example simply by studying the graph. Kirk-Othmer calls t* the stoichiometric time, t_st, uses t_bp for t_b and uses L_UNB for LUB. If you analyze equation 42 on page 38 you will see that that equation is in agreement with our calculations in this video: t_bp = t_st *( L - L_UNB)/L = t_st * integral_0^t (1-c/c_0) dt / (integral_0^infinity (1-c/c_0) dt ) Note that the two integral have the unit C*t, concentration multiplied with time (in this example, mg*min/litre). You can change the unit of the integrals to be the same unit as the capacity of the column (mg in this example) by multiplying the integral with the volumetric flow through the column. (But since one integral is divided by the other and volumetric flow obviously is the same, since we're dealing with the same setup, the volumetric flow can be taken away from the equation) The integral from 0 to t=t_breakpoint _is_ the amount adsorbed in the column at the breakpoint, hence the area above the breakthrough curve (up to the concentration c_0) up to t=t_b. Similarly, the integral from 0 to infinity _is_ the capacity.

[@Mendiguita]

@@PLE_LU Thank you very much for answering.

[@stambouliwalid]

i didn't get how t* is proportional to length of bed

[@PLE_LU]

See my answer to your other question kzbin.info/www/bejne/m2LYn5aJqNCor8U&lc=UgwjY2wG1HNRSJQWvsZ4AaABAg

[@oladelemayowa12]

what is t*?

[@PLE_LU]

The time for which capacity = F * C0 * t* see e.g. video "Understanding breakthrough curves" kzbin.info/www/bejne/pJW6kHt8jJlrkKM Note that there is a playlist on adsorption kzbin.info/aero/PLvpgTFzUKO49f62FlfIxOgfeiY-BxNhGj