the definition certainly depends how your deaerator is defined. Can you give me some information which streams (condensate, stripping steam, etc.) you are considering in your analysis?
There is a basic idea of fuel and product . for any devices, there is a fuel exergy (input or inlet or exergy enters to component) and (product , our outlet or wanted exergy). If you find exergy fuel and product then you can define :
efficiency= exergy product / exergy fuel;
this formula works for any components to my knowledge. for get more inside through this concept you may find Thermal design and optimization by Proff.A.Bejan useful.
I strongly advice to consult Perry's Chemical Engineers' Handbook; chapter 4 (thermodynamics), in the title "Thermodynamic analysis of processes". This will give you a complete path to calculate what is the minimum amount of "exergy" nedded to perform your separation. You will need a thermodynamic software to predict entropy and enthalpy of your mixtures (HYSYS, Prosim-Simulis, Pro-II, Chem-station), do you have someone? have you access to Perry's book?
I agree with Hassan, In deaerator we have only one output (the product), the rest (other streams) are the fuel, so the effectiveness is equal to the exergy of the product divided by the fuel exergy ( exergy of the other streams).