No, you will consume/use/spend Durantium when you build ships or improvements/buildings, which use Durantium including Durantium Refinery.
If you want to get more Durantium, you will either need to upgrade your starbase, which mines Durantium, or you will have to build another starbase, which can mine Durantium.
Further in the upper right corner of the screen you should see a list of resources, which you harvest. Here you should see that you are harvesting/mining 1 Durantium. You can also see the Durantium used in ships and improvements/buildings.