Intercept Method for Accurately Estimating Critical Fluid Saturation and Approximate Transient Solutions with Production Time Scales in Centrifuge Core Plug Experiments
Authors: Andersen Pål Østebø 
Published: June 2023

Abstract
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 critical 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. Practical speed limitations include maintaining core integrity and avoiding unrepresentative capillary desaturation. In tight or strongly wetted media the capillary forces are strong and more challenging to overcome.
Firstly, we demonstrate an ‘intercept method’ to estimate critical saturation. It states that average saturation is proportional to inverse squared rotation speed (at high speeds) allowing to determine critical saturation by linear extrapolation of a few measurements to the intercept where inverse squared speed is zero. The linear trend is valid once the core saturation profile contains the critical saturation. The result follows as the saturation profile near the outlet is invariant and only compressed while the other saturations equal the critical saturation. Although it was assumed the gravitational acceleration is uniform (reasonable for short cores and long centrifuge arm), the result was highly accurate even for extremely non-uniform gravity along the core: the data are linear and the correct critical saturation value is estimated. This was justified by that the end effect profile is uniformly compressed even under those conditions since most of it is located in a narrow part of the core.
Secondly, an analytical solution is derived for transient production after the rotation speed is increased starting from an arbitrary initial state towards equilibrium. For this result we assume the outlet profile compresses also during the transient stage. The two regions have fixed mobilities, while the regions occupy different lengths with time. Time as function of production has a linear term and logarithmic term (dominating late time behavior). An analytical time scale is derived which scales all production curves to end (99.5 % production) at same scaled time.
We validate the intercept method for high rotation speed data with synthetical and experimental data. For the synthetical data, the input critical saturation is reproduced both for uniform and highly non-uniform gravity along the core. Given the same input as a reservoir simulator, including saturation functions, the analytical transient solution is able to predict similar time scales and trends in time scale (with e.g. rotation speed and viscosity) as numerical simulations. The numerical simulations however indicate that the saturations travel with highly different speeds rather than as a uniformly compressed profile. Especially saturations near the critical saturation are very slow and caused production to span 5 log units of time (the analytical solution predicted 2-3) when the critical saturation was in the core. The correlation better matched low speed data where the critical saturation had not entered the core.