Brian Stimpson and Dr. Hugh Hales, Chemical Engineering
Introduction
The demand for petroleum products has never been higher, despite the opposition and environmental skepticism that has been present against the petroleum industry in recent years. This requires the production of petroleum products to increase. However, as politics and nature will have it, the waning supply of petroleum is becoming ever more difficult to access and tap into. To make sure we are using our reserves in the best possible ways, this industry must adapt, create better technology, and have careful planning and predictions.
Improving reservoir simulators can greatly enhance the production efficiency of oil reservoirs and improve the economics for the petroleum industry and those that use petroleum products. Reservoir simulators are tools used to optimize the production of oil and gas from subterranean petroleum reservoirs. As reservoir simulators are very expensive to run, improving the mathematics and simulation methods is one way to make them more effective. The mathematics behind reservoir simulators is iterative, meaning one must guess some values and repeat calculations until there is no change in the values before and after calculation. This iteration can take up to a week of calculation time on expensive supercomputers, so there is a lot of room for improvement in this regard.
Methodology
To make an improvement on reservoir simulation technology, I first obtained an idea to implement from my research advisor. With this idea, I derived the mass balance equations and other required equations for simulation. This involved discretization of balance equations to be able to use the finite-difference method of iteration. The parameter I chose to study was pressure, which is the most difficult parameter to calculate in oil reservoir simulation.
The finite-difference method can be used and studied in a variety of ways. The method I chose was to create an arbitrary oil reservoir in Microsoft Excel, which I could then apply several different methods to for adequate comparison. The methods of iteration I chose to use have all been developed and used in reservoir simulators to calculate pressure distributions. The new method I explored was applied to three of these methods in order to increase their speed.
I applied the equations derived in my research to this arbitrary oil reservoir and completed many iterations. In addition, I determined the actual pressure distribution and compared this to the methods studied as the iterations progressed. The goal of this study was to obtain lower error in a fewer number of iterations.
Results
When comparing each method against the others, the new method I applied increased the speed of convergence by a significant factor. The largest improvement was increasing the speed of iteration by a factor of eight. This means that the time to get to a certain level of error was 8 times faster than current method used. The other methods studied also showed improvements when this new method was applied, by factors of three and two.
The results of the study are shown in Figure 1 below. This is a log scale, which helps to be able to see rates of convergence. The steeper downward slope indicates a faster rate, meaning that that method is faster. In every case, this new method significantly increased the speed of this reservoir simulator.
Discussion and Conclusion
The reservoir simulator studied here showed significant improvements when this new method was applied. If this method could be further developed and implemented, it could greatly increase the speed of reservoir simulators used in the petroleum industry. The time required on expensive supercomputers would at least be cut in half, saving time and money. This allows for either cheaper simulation while maintain accuracy or if the same time is still used, more accurate simulations.
This project investigated a new method of iteration that can be applied to existing methods in oil reservoir simulation to increase the speed of reservoir simulators. There are many interesting aspects of this project that could further be studied. Overall, it has added a new insight into reservoir simulation that can be added to the petroleum industry knowledge-base.