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# Petroleum Sciences

## Team and Interlocutors

A. Loula, D. Marchesin, A. Nachbin, M. Tygel

J. Glimm

## Research Topics

There are two important problems in petroleum science that use advanced mathematics techniques and sophisticated computer simulations. The two problems are: (i) find the petroleum and (ii) remove it efficiently. In Brazil, these problems are compounded by the fact that most of the petroleum reservoirs lie underneath deep ocean water. Actually, Brazil is a world leader in deep water petroleum production.

In order to find petroleum, it is traditional to use the seismic methods, where sound waves are sent into the underground and, from detailed analysis of the reflected waves, the nature and location of geological structures that are favorable to the presence of petroleum are found. M. Tygel has a large experience in the mathematical modeling of this problem. Worldwide, this is probably the non-defense application that consumes the largest fraction of supercomputer time. Because such reflected waves are detected at the ocean surface, the problem is even harder. Thus, improvements in the mathematical techniques, in the algorithms and in their implementation in high performance computers are essential.

Nonetheless, research on promising data processing methods as applied to electromagnetic waves is important. The mathematical methods for such new models are not yet mature.

Efficient oil recovery is very important, since petroleum almost never pours out of wells. the oil must be displaced by the injection of other fluids, or by more sophisticated methods. The cheapest method and the one of most common usage is water injection. It is widely used in Brazil and in all other oil producing countries. Water is injected in some wells, displacing oil, that is produced in other wells. However, because of several reasons, this method may leave behind more than 80% of the oil in place. Computer simulations are routinely used to find ways to improve the recovery. However, the fluid dynamics problem of oil, water and often gas flow, which exist in the porous reservoir rock is rather hard for standard numerical techniques. The numerical algorithms are not good enough, and their computer implementation may be inefficient. To make the problem even harder, the reservoirs are highly heterogeneous, and it is not easy to model this heterogeneity in a practical way for simulations. This is an important research area in petroleum engineering, in mathematics and in parallel computing.

Last but not the least, new types of reservoirs are considered for exploitation: for instance, reservoirs of very viscous oil ( such as some large reservoirs in the Campos Basin near Rio de Janeiro ), and gas condensate reservoirs to be found in the Amazon Basin. New transportation techniques ( pipelines, refrigerated tank ships ) increase the commercial value of these reservoirs. Therefore, the exploitation and transportation of these hydrocarbons are a challenge to be met with better mathematical and computational simulation tools.