For the Burners, the conversion factor usually used to evaluate the operating conditions is the Wobbe Number.
Wobbe Nr = [Calorific Value (volumetric)]/[sq rt(Specific gravity)]
To maintain the same furnace heat release which you have now, adjust the operating pressure according to the square of ratio of the Wobbe Nrs of the gas
For Ethane W = 1641/sqrt(1.018) = 1627
For Methane W = 913 /sqrt(0.553) = 1228 (using Btu/scf)
Methane pressure = (1627/1228)^2 x ethane pressure = 1.755x
Alternatively, to keep the same pressures, change the burner tip flow area in the ratio of the Wobbe Nrs = (1627/1228) = 1.325x.
For example 6 x 2mm holes becomes 6 x 2.3mm. If you are changing tips, call the burner manufacturer rather than drill them out yourself. He may know of a reason (or previous bad experience) why you should not exceed a particular hole size or number of holes per tip.
If you fire the same heat release you should almost expect the same furnace results. Just two things change the balance a little. Jonkatz already mentioned that the stoichiometric flue gas goes up by 30%. That's not really entirely true for your case because the air you use is more closely related to the total heat release in the furnace than it is to the fuel being used. Stoichiometry works out at (roughly) 1 cu ft of air per 100 Btu/h (+/-) regardless of the fuel. The excess air (ratio) which you use can swamp the figures so you may not even notice the difference.
Ethane, being a little heavier than methane with more carbon, can produce slightly more luminous flames than methane. You may not notice this in the convective section of the furnace but, if the furnace is natural draft, you may have a less radiant flame with methane and have to adjust the air registers to change the flame shape a little and force some heat transfer back down into the radiant section, (if you need it there). Overall, with a little juggling, you should find something which works.
If you are sooting in the stack or coking in the tubes, both of those might reduce.
Good luck
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David