Intercept Method for Accurately Estimating Residual Fluid Saturation and Approximate Transient Solutions with Production Time Scales in Centrifuge Core Plug Experiments

Abstract

Summary The centrifuge experiment is used to measure capillary pressure in core plugs by forced displacement (imbibition or drainage): Strong gravitational forces (imposed by rotation) displace fluid held in place by capillary forces. This setup is also used to measure and establish residual saturation, the saturation where a fluid loses connectivity and can no longer flow. Obtaining this saturation is challenging as the capillary end effect causing outlet fluid accumulation theoretically only vanishes at infinite rotation speed. First, we derive a novel “intercept method” to estimate residual saturation with a centrifuge: Plotting steady-state average saturation data against inverse squared rotation speed gives a straight line at high speeds where the intercept equals the residual saturation. The linear behavior starts once the core saturation profile contains the residual saturation. The result is theoretically valid for all input parameters and functions, derived assuming uniform gravity along the core at a given speed. Then the saturation profile near the outlet is invariant and compresses at a higher speed. The method was, however, demonstrated numerically to be highly accurate even for extremely nonuniform gravity: The saturation data are linear and the correct residual saturation value is estimated. This is because when the residual saturation enters, most of the end effect profile is located in a narrow part of the core and thus uniformly compressed. Several experimental and numerical data sets validated the method. Second, an analytical solution (using all relevant input) is derived for transient production toward equilibrium after the rotation speed is increased starting from an arbitrary initial state. For this result, we assume the outlet (or initial) profile compresses also transiently. The displacing and displaced regions have fixed mobilities but occupy different lengths with time. Time as a function of production has a linear term and logarithmic term (dominating late time behavior). Production rate can thus be constant most of the time or gradually reducing, resulting in very distinct profiles. The correlation could fit experimental data well and confirmed the possible profile shapes. A time scale was derived analytically that scales all production curves to end (99.5% production) at same scaled time. The solution predicted similar time scales and trends in time scale with rotation speed and viscosity as numerical simulations. Numerical simulations indicated that the saturations near the residual saturation traveled slowly, which caused production to tail and span 5 log units of time (the analytical solution predicted 2–3). The correlation better matched low-speed data where the residual saturation had not entered.