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I'm thinking about the scalability of the system with regard to the transaction volume. Is it possible to predict future blockchain size for a certain future transaction volume? Is the relationship directly proportional?

Are there any estimates compared to traditional fiat currencies transaction volumes?

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The Bitcoin wiki page on scalability looks at what things would be like if transaction volume was similar to that of Visa. It states:

Today the Bitcoin network is restricted to a sustained rate of 7 tps by some artificial limits. These were put in place to stop people from ballooning the size of the block chain before the network and community was ready for it. Once those limits are lifted, the maximum transaction rate will go up significantly.

The page also contains various calculations on what the implications are of the Bitcoin network matching Visa's rate of transaction processing (which the page states as being around 2,000 transactions/sec). Figures on storage required for the blockchain are included in the calculations, but it's clear that as Bitcoin grows the core backend nodes will require commercial levels of investment in hardware & systems.

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Well, there are upper per-block size limits (about 500KB per block) based on the currently implemented protocol. So max levels might be 5x or 10X current levels.

When those levels get hit, then it will be levels of fees that determine transaction volumes, and the many microtransactions seen today will no longer be justifiable.

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