Back when I was living in the boonies with an extended power failure every 2 weeks, I just bought a car battery and charger. Thing weighed almost 50 pounds, but it was "portable" in that I could lug it to my car and take it with me. Wouldn't want to take it in a bag though.
When the power was out for more than a few minutes, I'd clip the 12V leads to the cigarette lighter plug of a car power inverter (rated at enough watts to power the laptop). Then plug the laptop's AC adapter into the inverter's 110 Volt outlet.
It held about 1000 Watt-hours (12V * 85 Amp-hours), which is about 20x what the built-in battery on that laptop holds (49 Wh). So in theory it has enough juice to last 20x longer. Maybe 2/3rds that after figuring...