By Rafiq Islam, S.H. Moussavizadegan, Shabbir Mustafiz, Jamal H. Abou-Kassem
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Additional resources for Advanced Petroleum Reservoir Simulation (Wiley-Scrivener)
2. The relationship involves truncation of the Taylor series of the unknown variables after few terms. Such truncation leads to accumulation of error. Mathematically, it can be shown that most of the error occurs in the lowest order terms. a. The forward difference and the backward difference approximations are the first order approximations to the first derivative. b. Although the approximation to the second derivative by central difference operator increases accuracy because of a second order approximation, it still suffers from the truncation problem.
The use of virtual reality in petroleum reservoir is currently being discussed only in the context of 3-D visualization (Editorial, 1996). A more useful utilization of the technique, of course, will be in reservoir management, offshore monitoring, and production control. While a full-fledged virtual reservoir is still considered to be a tool for the future, one must concentrate on physics and mathematics of the development in order to ensure that a virtual reservoir does not become a video game.
In future, the present status of this work can be extended to a multiphase system. It is anticipated that gas reservoirs will be suitable candidates for using Forchheimer extension of the momentum balance equation, rather than the conventional Darcy's law. Similar to what was done for the liquid system (Cheema and Islam, 1995); opportunities exist in conducting experiments with gas as well as multiphase fluids in order to validate the numerical models. It may be noted that in recent years several dual-porosity, dual-permeability models have been proposed based on experimental observations (Tidwell and Robert, 1995; Saghir et al, 2001).
Advanced Petroleum Reservoir Simulation (Wiley-Scrivener) by Rafiq Islam, S.H. Moussavizadegan, Shabbir Mustafiz, Jamal H. Abou-Kassem