10 - Advanced Modeling Methods

Abstract

This chapter describes some research areas that will extend the power of the numerical models for fluid flow, making them even more practical for routine use. These subject areas include the treatment of complicated flow domains, convergence acceleration, fast solutions to Laplace's equation, and the use of rheological models special to petroleum applications. A unified picture of boundary value problem formulation on complicated domains is presented. It is found that in hundreds of test simulations conducted using point and line relaxation, convergence times are shorter by factors of two to three, with convergence rates far exceeding those obtained for cyclic solutions. It is found that in many oilfield applications, Laplace's equation arises on doubly-connected domains, and different values of the dependent variable are applied at inner and outer contours. It is emphasized that inner and outer contours may take any shape, and since the approach applies to any problem satisfying Laplace's equation, the applications of the new method are broad. It is suggested that with interest in deep subsea applications increasing, the effect of low temperature and high pressure on drilling fluid properties must be determined.