For more than 50 years, computer simulations have been used to understand and forecast fluid flow in petroleum reservoirs. Somewhat simplified, a simulation model consists of three parts: (i) a volumetric grid with cell/face properties that describes the given porous rock formation; (ii) a flow model given as a set of partial differential equations expressing conservation of mass or volumes together with appropriate closure relations; and (iii) a well model that describes the flow in and out of the reservoir.
In this talk, I will discuss the basics of the three parts and some of the related challenges. In particular, I will introduce the black-oil equations, which is the basic flow model used in industry, try to explain why numerical solution of these equations is surprisingly difficult and remains an interesting research topic. In doing so, I will touch upon extensions to basic EOR processes.