It all depends;- for a small tank you can use some circular bracing. For a larger tank you could build the external cladding around the tank, using various supporting methods. Then fill in the gap with insulation material. Obviously, you cannot use large strakes of cladding, unless you can make sure to fill in correctly the gap.
I suggest to use the corrugated cladding, because it can offer  a good circular flexibility and a better vertical stability (similar to the building the circular corrugated iron water storage tanks).
You also can build around the tank a self supporting structure, for the support of the insulation material.
It all comes down to the buck;- if you have enough, any of this might make it for technical solution, otherwise this will become a big symbol for wasting money.
Cheers,
gr2vessels

Contact some tank insulation contractors, if it can be done, they're the ones that would know.

As posted above any good insulation contractor should be able to insulate any tank unless it is too tall.  Being tall normally requires an insulation support ring.
There are a lot of other considerations that need to be addressed besides just getting the insulation on the tank.

Can you comeback with type, size. MOC, temp, and contents.
Question that will need to addressed like do you need to insulate the top.

99491...

When you get a finals solution, please come back and finish this thread....we are all curious

Regards

-MJC

   

As long as the liquid level is 3 feet or more above where you are welding, you should be OK.  I believe API has guidelines somewhere...

You can use a cable system utilizing 3/16 diam. cables on the sidewalls spaced on 4' centers. and also a cable system for the deck. Standing seam insulation is then tied to the cables.  No welding needed. We do it all the time!   

MATI22....

Sounds like an excellent idea but how do you secure the cladding?

Metal strips are wrapped around the cable between the seams of the panels. The panels are then seamed tying the strips to the panels.  I uploaded a attachment showing this, hopefully you can see it. By the way the panels are 24" wide and up to 50' in length. The insulation is glued to the panels.  

• http://files.engineering.com/getfile.aspx?folder=d80cb6db-8c45-45a6-b32f-a4

We have used the system indicated by MATI22 above.  It is more costly up front, but the installation was much quicker and it would be well suited for your situation.  Attached is the brochure of the system we used.

• http://files.engineering.com/getfile.aspx?folder=4b15633b-c1c8-4893-bf8e-77

Would a spray-on insulation work in this application.