An Analytical Model for Analysis of Capillary Pressure Measurements by Centrifuge

作者：Andersen Pal Ostebo^*; Skjaeveland Svein Magne; Standnes Dag Chun

来源：Petrophysics, 2017, 58(4): 366-375.

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.

• 出版日期2017-8