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It really depends on where you are at in the world. If you live within the European Union you know that 134a was phased out back in 2011 for all new model vehicles and it will be phased out completely from all vehicles 2017. The preferred replacement in the EU is the new HFO refrigerant 1234YF. (Unless you’re in Germany!)
If you are located in the United States then you don’t have too much to worry about, yet. I say yet as just last year (2014) the three North American Countries (United States, Mexico, & Canada.) filed an amendment to the Montreal Protocol. The filed amendment would add all HFC refrigerants to the mandatory phase out that CFCs and HCFCS went through. The amendment did not pass in 2014, mainly due to no votes by China and India.
In 2015 there was a change of heart by India and China. India filed a similar amendment that the United States filed in 2014 to phase out HFCs across the world and China said that they would be in favor of such amendment as well. This clears the path to a yes vote on the amendment at the end of 2015. The only remaining opposition of the HFC phase out was the middle east, but with China and India aboard I see no reason why this amendment won’t pass.
So, to answer your question. If you are in the US there is no set date on when 134a will be completely phased out. Some vehicle manufacturers have already begun using 1234YF instead of 134a. (General Motors for one.) Not to mention that the Obama administration is actively pushing to lower the usage of all HFC refrigerants. (This includes 134a, R410A, and R404A.)
If I was to put a year on when the 134 phase out process will begin in the United States I would say 2017-2018. The amendment is expected to be approved towards the end of this year and then I believe the new regulations and phase out protocols will be initiated the following year in 2017.
One thing to note is that if and when an amendment to ban HFCs does pass it will not be an on/off switch approach. Governments of the world aren’t just going to flip it to off and ban all 134a instantly. History has shown us that they will schedule the phase out over ten to fifteen years. The intention here is to cause as little pain as possible for manufacturers, suppliers, and businesses. So, if and when it does pass you don’t need to panic. It will be a gradual phase out just as R-12 and R-22 was. You will have plenty of time to prepare and retrofit.
In the European Union the final date of any 134a vehicle usage is 2017. Here in the states I would predict our phase-out to begin in 2017 and that our final date would be 2025-2026. The other HFC refrigerants would follow soon after 134a.