I couldn't wait, so I tried two Alkaline batteries, Energizer Max + Power Seal, first battery has an 11 Ohm load and the second has an LTC3539 boost converter, output set to 1.5V, driving an 11 Ohm load.
From an energy supplied point of view, consider the area under the green curve, after 20.2 hours the battery voltage has dropped to 1.0V, the power available to the load is only 45% of what it was when the battery voltage was, say, 1.5V (1.0*1.0/1.5*1.5) = 45%.
The area under the green curve, up to 20.2hr, is 9.76 kJ. If that energy were used to supply a 100% efficienct boost converter with its output set to 1.5V, then for an 11 ohm resistive load, P = 1.5
2/11 = 204.5mW, time = Energy/Power = 9.76E3/.2045 s, or 9.76E3/0.2045/3600 hours or 13.25 hours. So maybe I could squeeze another 3 hours out of the battery if the converter were 100% efficient. If my battery powered product works down to 1V i.e. for 20.2 hours then the best I could get is 13.25/20.2 or 66% battery life at full power.