sorry for late.
I came across the fact that balance drums/piston as well as division walls in back to back compressors have a balance line from compressor discharge side at the shaft end back to the low pressure suction side. Is the settle out pressure for stages driven by the same shaft also driven by this balance drum? Or that the combined settle out pressure is only driven by having the various stages within the same casing.
For interstate balance piston, the balance flow goes from discharge 2nd stage to discharge first stage. The line is not external (does not run 'around' the casing). At stop, both leakages (shaft end and interstate drums) will contribute to establish an equalized pressure in the two casing compartments.
I have experienced designs with two compressor stages/sections driven by the same shaft but fitted in separate casing with separate seal gas system but still with a combined settle out instructed by vendor.
Like explained in another thread I guess, the casing's pressures can equalize via process too (not tight shut off valve, check valves, etc.).
Also I would like to ask about the difference between seal balance and gas balance within the same compressor section.
Not sure about what you mean. Try check 1st response, possibly there is some element of answer. Otherwise please re-clarify or give more context.