You can get some hints about this by looking at industrial practice. Look up "Copper Anode Furnace" or "Copper Anode Smelting Furnace."
These are air or air/oxygen blown furnaces. The older ones might use tuyeres or reverb furnaces, while a lot of newer ones seem to be bottom blown (like a BBOC) or top blown (Ausmelt-type lance) furnaces.
They remove impurities by progressive oxidation. Typical copper smelter impurities are nickel, tin, zinc, lead. and iron. Impurities are oxidized to slag. Slag composition has to be controlled for fluidity (viscosity) and to have sufficient flux to dissolve the impurity oxides. Fluxing is typically Al2O3, CaO, SiO2 and MgO.
The big challenge is copper oxidation to slag. Besides slag fluxing, minimizing copper in slag requires oxygen and temperature control, and of course time (if you blow too long, you will remove most of the impurities and then build up oxygen in the copper melt, ultimately oxidizing copper to slag).
You could look at using Niter (or "Nitre") which is potassium nitrate as oxidant instead of air or air/oxygen. Nobody does that commercially as far as I am aware because of cost. You wouild be well-served to thermodynamically model the impure copper/niter system (maybe a free energy minimization model if the data is available) to see just how much oxidizing potential is available and whether you oxidize too much copper. If I remember, niter has more oxidizing potential than air.
Good luck with it!
Regards, Geraldo
PS I hope you are aware that copper impurity smelting occurs in the 1200-1400 Celsius range, so your furnace has to run at least that high.
