Arithmetically it seems to me that the percentage cannot exceed 50%: in fact it should reach 50% asymptotically.
If x is the average of the last block number seen for any bitcoin, the percentage is (x- N/2) divided by N (N being the current block number).
x should be close to N as velocity increases.
I'm not sure your math is right. Since a theoretical series of transactions which move 100% of the existing bitcoin to some previously-unknown wallet address would reduce the BTCDD figure to 0%, I don't believe the figure is asymptotic to 50%. Please explain further.
Even if you consider that there are lost coins, the theoretical BTCDD figure approaches zero as the number of days goes to infinity.
Today all bitcoins have been mined at a steady rate of 50 BTC per block.
If none have been spent to date and all are spent today we would have the maximum of BTCDD (i.e minimum monetary velocity).
The percentage of DD for each bitcoin amount would be today's block number (N) minus the block number of the block generating it which we average by halving today's block number (because we have a linear growth rate), divided by N.
Hence the maximum percentage is currently 50%.
When the reward is halved next year from 50 to 25 BTC, then there will be fewer "young" bitcoins: the weighted average will get tilted towards the first bitcoins generated, increasing the maximum BTCDD percentage to 66% at the end of the next period (2016).