Numerical Modelling of Capillary Transition Zones

Abstract

Abstract For a large number of reservoirs, a vertical transition zone between water and oil exists. In this zone, both water saturation and capillary pressure vary with height. Traditionally one assumes that there is a relation between capillary pressure and water saturation, given by a Pc-S primary drainage curve prior to any production in the reservoir. The vertical fluid distribution is found by assuming equilibrium between capillary forces and gravity. This paper will focus on numerical modelling of the fluid distribution as production is started in a reservoir. As wells may be open and shut during the (field) lifetime of a reservoir, both imbibition and drainage may occur in different parts of a reservoir. The numerical model will take into account the irreversibility of imbibition and drainage, commonly known as hysteresis, which applies for both capillary pressure and relative permeability. Our test examples will deal with three different production rate regimes; capillary-dominated, capillary-viscous and viscous. We investigate the fluid distribution in the transition zones as the wells are shut down and equilibrium again is reached for the different cases. The tests will show that the fluid distribution differs for different injection-and production rates. For the case where the production in the reservoir is very close to equilibrium, we also show how the fluid distribution can be found analytically.