Abstract Primary drainage by centrifuge is considered where a core fully saturated with a dense wetting phase is rotated at a given rotational speed and a less dense, nonwetting phase enters. The displacement is hindered by a positive drainage capillary pressure and equilibrium is approached with time. We present general partial differential equations describing the setup and consider a multispeed drainage sequence from one equilibrium state (at a given rotational speed) to the next. By appropriate simplifications we derive that the process is driven by the distance from equilibrium state as described by the capillary pressure at the inner radius and position of the threshold pressure (transition from two to one-phase) from their equilibrium values. Further, an exponential solution is derived analytically to describe the transient production phase. Using representative input saturation functions and system parameters we solve the general equations using commercial software and compare with the predicted exponential solutions. It is seen that the match is excellent and that variations in timescale are well captured. The rate is slightly underestimated at early times and overestimated at late times, which can be related to changes in total mobility during the cycles for the given input.
Introduction Measuring capillary pressure using the centrifuge approach (Ruth and Chen, 1995) is one of several methods available for obtaining such curves. Other methods include the use of membranes/porous disks (Lenormand et al., 1996; Hammervold et al., 1998) and mercury injection capillary pressure (MICP) (Purcell, 1949). Each method has benefits and disadvantages regarding time consumption and interpretation of the measured data. Most of the methods consist of exposing a rock sample saturated with a representative fluid composition to various pressure conditions where the equilibrium state corresponds to a unique distribution of fluids and hence capillary pressure in the sample (Forbes, 1997). The fluid saturations corresponding to these equilibrium states are determined by the observed fluid production.