Dear Mehdi

Hi

Please find and attached your file.

Please not

Your response are in Shrinking Particle Model (SPM) at Leaching Process, Because Recovery concept is not in SCM.

Kind Regard

Dear Dr Sajjad,

thanks for your file. But, How is Calculated the X?

Dear Mahdi the attached publication may be of your interest:

Article Critical Evaluation of Coupling Particle Size Distribution w...

Hello Mahdi,

Find attached the following publications for answer to your question.

Hope it helps you!

Hi Mahdi,

I’d like to give a suggestion; you can use the equation to find the reaction time for heterogeneous phases, from Levenspiel (Chemical Reaction Engineering). This equation considers the radius of the particle without reaction. If you have this data for different reaction times and the chemical and mineralogical analysis, then you can estimate the fractions that reacted and not reacted (Those equations are for spherical shapes, could be necessary a shape factor).  

For theoretical analysis, you can use the diffusion speed of the leaching solution.

 If you have the reaction times to different radius without reaction; then, you can to do the curves showing the reaction time vs radius,; the reaction time vs recovery or radius vs recovery.

After that if necessary;  you could use the Ponchon Savarit method to find the number of leaching stages, only if the leaching process is to discard the solids.

Practically the fraction reacted is recovery. The X is defined between 0 and 1 and recovery usually defined between 0 and 100.