Shocks and Bifurcations in Black-Oil Models

Abstract

Abstract Here, it is shown that the ‘traditional’ approach to variable bubble-point problems is not consistent, because it does not incorporate important kinds of shocks that occur in black-oil models. This paper contains an exhaustive analysis of shocks that black-oil models may develop and it is shown that a considerable variety of them may indeed occur; a bifurcation mechanism is also exhibited. Except for the class of shocks described by Buckley-Leverett theory, all other kinds may be developed even if capillary forces are present. Modelers must be aware of these pathologies in order to handle them properly. This paper also supplies a basis for the developement of consistent black-oil models, applicable to variable bubble-point reservoirs. The analysis and results here presented, also contribute to a better understanding of limitations imposed by the simplifying assumptions of black-oil models.