I am trying to perform a particular reaction. As a result, I am using a methodology applied in a 1976 Paper. However, I see that someone (not the authors of that paper) has patented a process very similar to that paper (with some minute differences like the temperature of the reaction, etc.). If I replicate what is done in the 1976 paper with some modifications, what are the chances of patent infringement?
Without a patent number it is hard to be authoritative. That said, patents expire. Since about 1995, patents in the US and pretty everywhere else expire 20 years after the filing date. Before that it was 17 years from the grant date in the US. Either way, a patent on something published in 1976 would have to be expired by now and not enforceable. This is because anything publicly disclosed becomes prior art to a patent filed after it. Another thing to remember about patents is only what is in the claims is protected. So just because a reaction is described in the body of the patent doesn't mean the whole reaction is necessarily patented. In many cases, only a minor improvement might be claimed. Also, patents are territorial so a US patent wouldn't be relevant to you if you were in another country.
So as to your specific question:
If I replicate what is done in the 1976 paper with some modifications, what are the chances of patent infringement?
What is in the original 1976 paper is sure to be available for use. What I can't say is if the "modifications" are unprotected by patent. If you provide the actual patent number to the patent you found I can look it up and provide better guidance. Also, there is always the possibility of other patents you aren't aware of. Lastly, I am not a lawyer so this isn't legal advice.