There is a significant shift toward high-pressure direct injected gasoline engines. An analysis of the octane requirements for such fuels would be timely and very useful. This would require a (commercially available) engine and a series of fuels with differing octane numbers. This is simple by my definition.
The field of petrochemicals is fertile for basic research as well as applied research. Since you are interested in using simple laboratory analysis, then I suggest basic research on solid heterogeneous catalysts that can be used to improve the preparation of important chemicals.
Few years ago, developing a new manufacturing method for caprolactam (important monomer in making nylon-6) made a big story.
I would highly suggest doing research on developing integral strategies for the management and disposal of lube oils and oil filters in vehicles. There's still no unified criteria and strategies for oil filters and there are some changes that can be made in the life cycle of these products to improve their capability of being recycled.
I would suggest to look into the desulfurization of heavy residue streams, which is a challenging topic and important for every refinery, because the legislation for the sulfur content is heavy has became really strict.
I think you need to explore the field based on your qualification in terms of expertise and interest. nothing is impossible, every field has plenty of research gaps available you just read the literature related to your field and decide what do you really want to do a task or just easy going task go for it, at the end everything can be finished because someone is there who is really waiting to help you.
Most Petroleum processes (Hydrotreating(from Naphtha to Vac Resid), Naphtha Reforming Cat Cracking, HF and H2SO4 alkylation, Hydrocracking, Delayed and Fluid coking etc) have been thoroughly studied for at least 50 years. Gas to Liquid /Fischer-Tropsch is interesting but has also been thoroughly researched.
Technology that hasn't been implemented yet in many refineries like solid catalyst/fixed bed Alkylation may still have some room for new discoveries and can probably be explored at a typical university lab. Information. Reliability analysis to develop optimum sparing philosophy could be valuable if you have access to the right information. There has been a lot of work done on deasphalting but combining deasphalting with other technologies is still a more fertile area for research than most other refinery processes.
Most refineries are very old and as a result are not optimized for energy conservation. This area is ripe for study but to do it properly you will need information from actual refineries that they normally would be reluctant to share. You may be able to make some reasonable assumptions and produce useful research.
I just would like to extend Mr. Julio Vargas words. Really that is a need of time to re-refine "Used Lube Oil" as industrialization, vehicles and population is exploding day by day like anything.
Used Lube oil is 'The most neglected liquid though of utmost important in it's working condition and even after use'.
Still we don't have any firm technology which can claim a best refining techniques. So, it's an high time to understand this and Re-refine used lube oil which can add a life to Reservoirs as well as Base oil which is adding life to Engines and which ultimately leads to a sustainable World for future generations.
But nowadays market is looking at it as a product of great value due to increasing prices of base stock. A Reformation has been started and you can be a valuable part of it.