Is significant repetition across multiple journal papers (intro and model) an issue? Let's say I've developed a model for some process X. Using my model I can investigate (a) the effect of changing a underlying assumption used in other literature; and (b) the effect of a different equation for calculating some part of X. The assumption and different equation are not at all related but my model is fundamentally the same. Given all this when I come to write a paper for each of my investigations my introduction and model sections of the papers will be very similar - likely with a small difference in the last few lines of each specifying what is different from the baseline case.

So my question is: is this repetition across multiple journal papers acceptable? Is it considered bad practice? Should my second paper reference my first due to plagiarism?
It will depend on a bunch of things. 

Basically these papers are not "stand alone." They are elements of a series. The way to answer such questions is to put yourself in the place of your readers. Imagine you were a researcher from a related discipline, and you were encountering these papers for the first time. What level of duplication would make your life easy?

For example, if these are 5 page papers, and you have three pages of repeated intro material, that's a problem. If these are 50 page papers, three pages of repeated intro is probably not a problem. 

For example, if the papers are in the same journal every time, you should be more inclined to simply cite a previous article for material you are considering repeating. If it's a different journal, you may want to avoid forcing your reader to hunt up that other journal to figure out what is going o n.

Maybe there's a way you can get some kind of consideration from a journal. If you are going to have several papers on the same topic in rapid succession, maybe you can get them published back-to-back. Or at least in the same volume so a reader will get them all at once. That way you could simply say "see the first paper" or something like that. It is certainly not unknown, though it is also not all the common either.

Another possible strategy is to publish a "state of the union" paper in a review journal, then reference that. When I was in grad school I wore out several volumes of Physics Reports that had review articles about my research subject. So much so that I eventually had to buy my own copies. Is there a similar journal in your field of research? You could put all your intro material and notation and introductory calculations in there and just cite it. Publishing a review article on a subject you are "pioneering" in can also be a good boost for your CV. And it will tend to get cited by a lot of people who are just getting their toes wet in a subject.