I am looking to either get my 2litre petrol engine refurbished or replaced. What are my options please?

Hello.
My Silvie is using a litre of engine oil every time I fill up the petrol tank. There doesn't seem to be any visible oil leak from the engine itself. Where else could the engine oil go? Can it get burned up internally? I've noticed that when the engine is warm and has been idilling for a while ...