Presently, it is not possible to replace batteries with capacitors.
The storage capacity of the new capacitors is starting to get somewhat closer to the capacity of small batteries.
Example : capacitor with 1000 Farads Capacitor loaded with a 10 ohm resistor will drop its voltage to 37% of the initial value in 10,000 seconds or 2 hours, 46 minutes and about 40 seconds.
The same "time" size storage battery may be several times smaller in volume.
A 1000 Farads 2.5 Volts capacitor is big !. and the price bigger.
So the industry has not being able to replace the storage capacity of the chemical batteries -- one day may happen -- to some capacity.
A dream that many want.
We, in the electronic industry, have been using the large Farads capacitors, replacing Nickel based batteries, for low energy circuits, where the life of the capacitors DO out perform the batteries in charge cycles and energy storage without short time self discharge periods.
Nando