A Consistent Approach to Variable Bubble-Point Systems Ismael Herrera* Instituto de Geofísica, UNAM, Apdo. Postal 22-582, Mexico D.F. Mexico Rodolfo G. Camacho PEMEX/UNAM, Facultad de Ingeniería, M ´ exico, D.F. Received 2 March 1996; revised manuscript received 14 March 1996 Here, it is shown that the ‘‘traditional approach’’ to variable bubble-point problems, using black-oil models, is not consistent, because it violates the ‘‘bubble-point conservation law.’’ In order to have a consistent approach, it is necessary to incorporate shocks—discussed in previous papers—in which the bubble-point is discontinuous. A ‘‘consistent approach’’ is applied to specific examples, and results compared with those of the ‘‘traditional’’ one. The conclusion that the ‘‘traditional approach’’ generally yields large errors for the production rates and other parameters of interest in the oil industry, is reached. c  1997 John Wiley & Sons, Inc. I. INTRODUCTION In this article, using results of previous research [1–5], it is shown that the ‘‘traditional’’ black-oil model approach to variable bubble-point problems [6–9] is inconsistent, and computations are carried out to demonstrate that such inconsistency generally yields large errors in the evaluation of production rates and other parameters of interest for the oil industry. In addition, a consistent formulation of black-oil models, suitable for application to variable bubble-point problems, is supplied. When applying black-oil models to variable bubble-point problems, it is frequently assumed that the bubble-point pressure may vary inside the undersaturated region [6–9]. However, such an assumption is incorrect, because it contradicts the basic postulates on which black-oil models are built. Indeed, such postulates do not include molecular diffusion, nor mechanical dispersion, and it has been shown that a consequence of such omission is the ‘‘bubble-point conservation law,’’ according to which: when a gas-phase is not present, oil-particles conserve their gas content (dissolved gas:oil ratio). This result imposes very severe restrictions to the manners in which the dissolved gas:oil ratio of an oil-particle can vary, when a gas-phase is absent; physically, it means that when a gas-phase is not present, two oil particles cannot exchange dissolved gas, even if they * To whom all correspondence should be addressed. e-mail: iherrera@touatiuh.igcofeu.unam.mx Numerical Methods for Partial Differential Equations, 13, 1 18 (1997) c  1997 John Wiley & Sons, Inc. CCC 0749-159X/97/010001-18