publications - How shall I report an error in a given paper?

I am currently at my last MSc year in Chemical and Process Engineering (Italy), and our last course on Industrial Chemistry has a mandatory pre-exam exercise which reads:

Find an existing, published research paper in the field of Chemical Engineering and try to autonomously replicate its results (plots, data, equations et similia).

My chosen paper X was published in the Industrial & Engineering Chemistry Research journal, and I suppose it passed peer-review. X shows the application of a new algorithm to a chemical reactor with a given physical model.

However, after my revision and replication trial, I found that using their same model, I do not obtain the paper results. There is no presence of replication error by me, since I checked every passage with the TA.

The same TA pointed out flaws (of fundamental nature, for example F = mv instead of F = ma) in the model, and once corrected allowed me to obtain the results shown in the paper.

I do not think it was a overlook error, since the same reactor model was used in X and two cited sources of X. I want to inform of this error, but I do not know what to do now.

Answer

The same TA pointed out flaws (of fundamental nature, for example F = mv instead of F = ma) in the model, and once corrected allowed me to obtain the results shown in the paper.

The fact that after correcting the model you can actually reproduce the reported results seems to suggest that the authors did implement their model correctly, but made a mistake when writing the paper.

I think that it is best to first contact the authors, politely explain what you found, and give them the chance to take an appropriate action, e.g. publish an errata in the journal where they published their article (or on their website, if the mistake was really minor).

If they do not react at all, you might contact the journal directly. The editor will typically take care that an errata is published.

When nobody is responsive (I do not expect that in this case, but with a conference article or a fishy journal that might happen), and you consider it important that the scientific community is aware of the mistakes, you could decide to publish your correction somewhere (journal, conference, website, ...).