Having recently been testing an upped fire stall I calculated that for fire lances you need:
111 quanta for 6 lances,
132 quanta for 5 lances,
163 quanta for 4 lances,
221 quanta for 3 lances,
331 quanta for 2 lances,
661 quanta for 1 lance.
Now these are upped so you probably have to add up to 2*No. of lances to factor in the increased casting cost.
Just thought this might help.