Reduced range at low altitudes?

[xpell]

Hello to everybody, I'm a total newbie and just a huge fan of aviation with limited technical knowledge. But I'm a very curious person, I have a question, and I thought it was better to ask the professionals. :)

(I think) I know that an aircraft has an optimal cruise altitude and speed, and that different altitudes and speeds will significantly shorten its range and endurance (please correct me if I'm wrong.) I was thinking in an scenario where a modern jetliner (let's say an A350 or B787 or the like) experiences decompression during an intercontinental flight above the ocean so the crew is forced to descend to safe altitude (that's 8,000 ft I think?)

My question is basic: how much would this diminish its range or endurance? Would this aircraft still be able to land in an alternative airport if it happens "deep into the ocean"? (I mean, are transoceanic flight plans calculated predicting this possibility?) And, if you're so kind, how would all of this affect its speed?

I know there are performance tables to calculate all this, but I've been unable to find any and I'm not sure I would be able to properly use them. So, since I wouldn't like to bother you too much, just a "back of the envelope" estimate will be enough.

Thank you all in advance, sorry if I made any stupid error (quite probable!) and please moderators move this post if it isn't in the correct forum. :)

[Meikleour]

xpell: following a depressurisation a descent would be required to 14,000ft/10,000ft
depending on the oxygen fit. When I used to fly the North Pacific routes between Asia and North America the available alternates were often a considerable distance away from the planned route therefore additional fuel had to be added to the route calculation to take in to account the much increased fuel consumption at the lower flight levels required for the diversion. This would have been precalculated as a "depres. critical point" to the diversion. The extra fuel plus the unused onward fuel would have to be sufficient to arrive at the diversion with 30 minutes holding fuel remaining. In very broad brush terms the increased fuel burn at the lower levels compared to the cruise burn was in the region of +40%.
I expect other ppruners will come on here and quote much more rules and regs. ro you but that is the simple answer to your query. Hope that helps?

[Intruder]

"Back of the envelope" -- which means these are approximations, not absolutes:

Fuel flow at a constant INDICATED airspeed is constant, regardless of altitude. TRUE airspeed at a constant IAS increases approx 2% per 1000' altitude. Therefore, if you maintain the same "efficient" IAS, your time to destination will increase 2%/1000' of altitude reduction.

[xpell]

Thank you both very much, certainly useful! :) Actually I've noticed that both of your estimations are quite close: Meikleour says about a 40% reduction in range and Intruder says around 2%/1000', which everything else being equal, would be 32-50% too if descending from FL300-400 to FL100-140. I knew asking the professional was the best! ;)))