The recovery of zinc with this level of CaCO3 is possible; however it is economically viable we cannot say. For that truly do the calculations of zinc cleaning process, however as you will not have mining costs but the extraction of the sludge may help us end costs. Another idea is to use this product for CaCO3 as a soil amendment or cement. 

Thank you for your answers, The Tailing pile characteristics were as follows: 300.000 per cubic meter (size), contains higher amounts (65 %) of fine fraction <63 μm,

Chemistry

2.5 % Pb

8.2 % Zn

300 ppm Cd

Mineralogy

80 wt % Calcite

2 wt % Quartz

2 wt % Cerussite

6.5 wt % Hemimorphite

2 wt % Smithsonite

1 wt % oxy-hydroxydes of iron

0.5 wt % barite

0.5 wt % Celestine

I think a primary process for concentration of zinc will be beneficial, isn’t it? For example a procedure can remove a lot of carbonic gangue (maybe another regrinding stage and a flotation process). It will be reduce your acid consumption in leaching stage but as you stated it must be tested to get a better idea on cost of methods against profit.

Proposed analysis are promising and should be tried, but he small disadvantage that complete dissolution of carbonates may consume a lot of acid to maintain a low pH of the pulp. I agree that depressing carbonates may eliminate smithsonite in the residues.

I have worked in a company in VEDANTA where Pb was 3%, Zinc was 5%, but you have valuable cadmium most costly metal. Why not we beneficiate it? Before doing all kinds of tests. Do simple flotations test? We call bulk flotation of all minerals Pb,+ Zn+ Cd.

Lab tests:

Condition it with a Collector called as Xanthates few mg , add few drops of Frother, you get a froth of bulk. Send concentrate for analysis.

Yes waste from froth flotation can be used for Iron ore pellet making as flux. Or sold to cement plants where ca Co3 is less. Or you can make cement if quantity is large. Or you can supply for water treatment in mining industry. Or you can make 20 no. chemicals out of it.

But most important is not theory practical. Start doing you gets solution.

Since the specific gravity are:

Calcite = 2.71 g/cc

Hemimorphite = 3.48 g/cc

Smithsonite = 4.45 g/cc

You should reject calcite by gravity concentration (spiral Humphrey work well), the next step could be leaching and so on. I don't think froth flotation can work.

You might find that the CaCO3 is well worth extracting /separating on its own as it has many applications in various particle sizes as low cost filler. Naturally you need to establish which market and grades will maximize your ROI but to save cost of regrinding it you could spray dry slurry. Ultrasonic spray drying is an option and has good control on the particle size.

Since your goal is to recover zinc minerals, the easiest first step is bulk flotation of the metals using xanthate collector (preferably isobutyl xanthate for zinc minerals). The particle size distribution looks good although mineral liberation tests may be required depending on your flotation results. Start by simple lab. Flotation tests!