I'll try to do a very naive (napkin) calculation. (The way the question is formed does not warranty -IMHO- a more detailed/diligent calculation).
(Also, apologies in advance, but it's been over a decade since I worked for a wind farm so my numbers and estimates might be outdated).
Example of a Wind turbine of 1.5 MW.
1. Weight of the blades
For a 1.5-MW turbine, typical blades should measure 110 ft to 124 ft (34m to 38m) in length, typically weigh about 5000 kg each source: Composites world.
That means that the total mass of the blades is about 15000kg. (although approximately 75% of it is by weight glass, but let's assume that all of it is from PE - it won't matter in the end).
2. How much Crude Oil is required to make the blades
Let's assume that the wind blade is made from PP (usually a thermosetting epoxy system is used, but I don't have access to reliable data regarding this, and PP is a good thermoplastic alternative).
For each kg of PP, about 0.54 to 0.68 lit of petrol is required. (Let's take the worst case 0.54). For each lt of petrol 0.9 kg of crude oil is required. (source: THE USE OF CRUDE OIL IN PLASTIC MAKING CONTRIBUTES TO GLOBAL WARMING)
This means that for each kg or crude oil about 0.6 kg of PP is made.
So this means that for the 15000kg of the blades about 25000 kg of crude oil are required.
Additionally 1kg of crude oil produces about 44 MJ. Therefore the energy in the crude oil required to make the plastic of the blades is about $1.1\cdot 10^{12}J $ or (the less impressive) 0.3056 GWh. (UPDATE: I found on the following article, for the wind blade system, the estimated energy per metric ton is about 170GJ/t)
Again please make a note that there are gross simplifications/assumptions:
- the blades are assumed to be from PP (not epoxy)
- All the weight of the blades is assumed to be plastic (only about 25% actually is)
- There is no consideration about energy required to shape/transfer mold the blades
- There is no consideration about the tower or gear/box system
All things considered, the assumptions should even out, given the accepted worst case values, they might even be overly conservative.
3. Energy produced per year by the wind farm.
A properly placed wind generator has a capacity factor of about .25 to 0.5. Assuming the lowest $C_F =0.25$, a 1.5 MW wind generator in a year would produce about:
$$E_{WG} = 1.5 [MW]\cdot 365[days]\cdot 24[hr]\cdot C_F = 3.285 [GWh]$$
So the 1.5MW turbine would produce over 10 times more energy annually.
Additional benefits of wind turbines
Not burning the Oil has the added benefit that greenhouse gases are not produced. This is a significant environmental benefit, and if you add the benefit from the reduced carbon taxes, it adds an economic incentive.