By Jackson Sweeney, Monash University
We drill a well, and the oil is initially driven out of the reservoir by natural mechanisms. Unfortunately, these natural mechanisms don’t last forever, so eventually we have to confront the problem of extracting what remains of the oil. The solution is to drill a secondary well elsewhere in the reservoir. We then pump a second fluid, called a solvent, into this secondary well, displacing the oil towards our original production well.
There are three basic processes at work in this system. Firstly, fluid is pumped in and out of the reservoir via the two wells. This is simple to model since it is localised – the wells themselves are typically much smaller than the reservoir. Second is the transport of fluid mass by that fluid’s bulk motion, known as advection. As an example, consider water flowing down a river. Finally, the spreading of a fluid from regions of high concentration to regions of low concentration, this is known as diffusion. Consider for example if some ink were spilled into a lake. The ink would undergo diffusion and slowly disperse throughout the water.
These three processes, when coupled with the fact that there are two fluids present, result in some very complex equations. In fact, these equations cannot be solved exactly. However, finding ways to approximate their solution allows us to figure out, amongst other things, how much oil can be extracted in a given period of time, what kind of solvent to use, and where to drill our secondary well.
In this project I studied and implemented codes for two methods of finding approximate solutions to these equations: the modified method of characteristics, or MMOC, and the Eulerian-Lagrangian localised adjoint method, or ELLAM.
My tests yielded some interesting results. The ELLAM handled advection and diffusion very well, but had severe difficulties handling the injection well. Moreover, the results produced by my code did not agree with those published in the paper, which originally presented the ELLAM. I was able to confirm my results by slightly modifying a code by another author for a similar method, so at this stage I have some very strong doubts as to the veracity of the results published in the original paper.
The MMOC, on the other hand, produced very good results even with injection and production wells. It was not without problems though; it sometimes produced large, unrealistic spikes in solvent concentration. In future, it would be worth investigating whether aspects of the MMOC could be combined with other methods that do not have this problem. The hope is that a combined method will produce superior results to any of the methods we have at present.
Jackson Sweeney was one of the recipients of a 2013/14 AMSI Vacation Research Scholarship.