So what happens if you have revalued an asset and as a result you now have a revaluation surplus on your statements, namely in equity? What happens with the depreciation of the asset and with this surplus over the period the asset is in use? 

I would say that first it depends on the accounting framework you’re using. Generally speaking there could be two options (both allowed under IAS 16):

Keeping the surplus as it is until asset is disposed

The first option would be to keep the revaluation surplus there as it is until you dispose of the asset and then recognize the surplus in retained earnings in full (Db Revaluation Surplus and Cr Retained Earnings – both equity accounts, so movement would be within equity).

Accounting depreciation difference into retained earnings over the useful life

Another option is to account the difference of the depreciation arising from the new revalued value compared to the original value from the surplus to the retained earnings. For an example, if the new depreciation charge would be 20,000 as compared to 18,000, which it was originally, you have difference in depreciation charges. You would still account 20,000 as an expense and to accumulated depreciation on the balance sheet, however you’d also debit the difference (2,000) to retained earnings (again using the same entry as mentioned above).

Note here that the second option reduces the revaluation surplus therefore leaving a lower buffer in the accounts in case the value of the asset falls and a potentially an impairment loss needs to be recognized.