Submit an article to a conference, which contains a section that has been already published I want to submit an article to a conference, however, let's say 50% of the content of such article has been already published. The reason of such 'variation', is that after some suggestions, we applied some modifications to the methodology and the way to analyse the data, so basically a variation of the study resulted from that, but the core remains the same. 

I actually never had the opportunity to present this study in a conference before or after the publication, so this is something that I'd really like to do; but I'd prefer to submit the 'second version' of the study, since I think that it is more complete than the published one.

I know that (if accepted) the entire article would not be published in the  conference proceedings (only the abstract), since its related to a published article, still I  would like to know if submitting an article that contains some part of a previously published article is something acceptable to do. 

I'd appreciate your comments on this.
You could treat it as a new paper. Maybe after the conference, you could add more results and publish a paper from it.