The local analysis of changing force balances in immiscible incompressibletwo-phase flow

The balance of viscous, capillary and gravity forces strongly affects two-p hase flow through porous media and can therefore influence the choice of ap propriate methods for numerical simulation and upscaling. A strict separati on of the effects of these various forces is not possible due to the nature of the nonlinear coupling between the various terms in the transport equat ions. However, approximate prediction of this force balance is often made b y calculation of dimensionless quantities such as capillary and gravity num bers. We present an improved method for the numerical analysis of simulatio ns which recognises the changing balance of forces - in both space and time - in a given domain. The classical two-phase transport equations for immis cible incompressible flow are expressed in two forms: (i) the convection-di ffusion-gravity (CDG) formulation where convection and diffusion represent viscous and capillary effects, respectively, (ii) the oil pressure formulat ion where the viscous effects are attributed to the product of mobility dif ference and the oil pressure gradient. Each formulation provides a differen t perspective on the balance of forces although the two forms are equivalen t. By discretising the different formulations, the effect of each force on the rate of change of water saturation can be calculated for each cell, and this can be analysed visually using a ternary force diagram. The methods h ave been applied to several simple models, and the results are presented he re. When model parameters are varied to determine sensitivity of the estima tors for the balance of forces, the CDG formulation agrees qualitatively wi th what is expected from physical intuition. However, the oil pressure form ulation is dominated by the steady-state solution and cannot be used accura tely. In addition to providing a physical method of visualising the relativ e magnitudes of the viscous, gravity and capillary forces, the local force balance may be used to guide our choice of upscaling method.