New impressive supercapacitor -but is my calculations of it correct?

http://phys.org/news/2014-05-flexible-supercapacitor-bar-volumetric-energy.html
“...
The device is a supercapacitor—a cousin to the battery. This one packs an interconnected network of graphene and carbon nanotubes so tightly that it stores energy comparable to some thin-film lithium batteries—an area where batteries have traditionally held a large advantage.
...
the storage capacity by volume (called volumetric energy density) is the highest reported for carbon-based microscale supercapacitors to date: 6.3 microwatt hours per cubic millimeter.
….
The device also maintains the advantage of charging and releasing energy much faster than a battery. The fiber-structured hybrid materials offer huge accessible surface areas and are highly conductive.
….
To improve the energy density by volume, the researchers designed a hybrid fiber.
A solution containing acid-oxidized single-wall nanotubes, graphene oxide and ethylenediamine, which promotes synthesis and dopes graphene with nitrogen, is pumped through a flexible narrow reinforced tube called a capillary column and heated in an oven for six hours.
Sheets of graphene, one to a few atoms thick, and aligned, single-walled carbon nanotubes self-assemble into an interconnected prorous network that run the length of the fiber.
….
The researchers have made fibers as long as 50 meters and found they remain flexible with high capacity of 300 Farad per cubic centimeter.

Using a polyvinyl alcohol /phosphoric acid gel as an electrolyte, a solid-state micro-supercapacitor made from a pair of fibers offered a volumetric density of 6.3 microwatt hours per cubic millimeter, which is comparable to that of a 4-volt-500-microampere-hour thin film lithium battery.

…

The fiber supercapacitor demonstrated ultrahigh energy-density value, while maintaining the high power density and cycle stability.
….
"We have tested the fiber device for 10,000 charge/discharge cycles, and the device retains about 93 percent of its original performance," Yu said, " while conventional rechargeable batteries have a lifetime of less than 1000 cycles."
...”

Now, it says above it has an energy density of “6.3 microwatt hours per cubic millimeter”.
But surely this cannot be! Because, when I do the calculations, and please would someone check I have done these calculation correctly and coorect any error here, what I get is:

6.3 microwatt hours per cubic millimeter = 6.3 watt hours per cubic centimeter
= 6300 watt hours per litre = 22.68 MJ per litre (because 1 watt hour = 0.0036 MJ )

Now, even assuming this supercapacitor has about the same density at of the densest type of graphene which is about 2.7g/cm3 , that still gives an energy density by mass of ; 8.4 MJ/Kg which, if true, would be a MASSIVE energy density for any electric storage system because that compares with 40.9 MJ/Kg for octane (which is a very energy dense fuel ) and thus would be a massive ~20% of that of octane!
This doesn't look realistic to me but, if it really is that energy dense, this would surely be a game-changing technological revolution and could lead to very cost effective off-the-grid energy storage! -right? Am I missing something here because this looks too good to be true?

Originally posted by humy
http://phys.org/news/2014-05-flexible-supercapacitor-bar-volumetric-energy.html
“...
The device is a supercapacitor—a cousin to the battery. This one packs an interconnected network of graphene and carbon nanotubes so tightly that it stores energy comparable to some thin-film lithium batteries—an area where batteries have traditionally held a large advantage. ...[text shortened]... grid energy storage! -right? Am I missing something here because this looks too good to be true?

Originally posted by sonhouse
This link says lithium-air batteries have a power density of 40+Mj/kg:

http://en.wikipedia.org/wiki/Lithium%E2%80%93air_battery

Originally posted by humy
I had forgotten about lithium-air batteries. But lithium-air batteries are not technically true batteries but fuel cells and the lithium batteries mentioned in the OP link were lithium-ion batteries, not lithium-air batteries.

http://en.wikipedia.org/wiki/Thin_film_rechargeable_lithium_battery

I would expect lithium-air batteries to have impressive ener ...[text shortened]... e energy densities of around 5 Wh/kg compared to around 100 Wh/kg for lithium-ion batteries...."

Originally posted by humy
http://phys.org/news/2014-05-flexible-supercapacitor-bar-volumetric-energy.html
“...
The device is a supercapacitor—a cousin to the battery. This one packs an interconnected network of graphene and carbon nanotubes so tightly that it stores energy comparable to some thin-film lithium batteries—an area where batteries have traditionally held a large advantage. ...[text shortened]... grid energy storage! -right? Am I missing something here because this looks too good to be true?

6.3 microwatt hours per cubic millimeter = 6.3 watt hours per cubic centimeter

Originally posted by DeepThought

6.3 microwatt hours per cubic millimeter = 6.3 watt hours per cubic centimeter

A microwatt is one millionth of a watt and a cubic millimetre is one thousandth of a cubic centimetre so that should be 6.3 milliwatts per cc.