Porous and permeable reservoir rock can be realistically represented as the network of capillaries. Hence threre is need for statistical treatment of the displacement phenomena as well besides the conventional mathematical approach.
I would advise to look into geo-statistics and 4D seismic history matching fields to get insights into how to tackle this problem. As example a paper I co authoredArticle SPE 163635 4D Seismic History Matching With Ensemble Kalman ...
There is abundant literature on such type of problems in different context. I also know that a colleague of mine M. Regaieg is doing such type of things https://www.linkedin.com/in/mohamed-regaieg-463a5a52/?originalSubdomain=fr