Saturation Modeling Under a Complex Fluid-Fill History: Drainage and Imbibition
Authors: Wilson Adam 
Published: October 2018

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 188594, “Saturation Modeling Under Complex Fluid-Fill History—Drainage and Imbibition,” by H. Xian, SPE, L. Beugelsdijk, SPE, and A. Kohli, SPE, Shell; E. Fokkema, SPE, Nederlandse Aardolie Maatschappij; and A. Cense, Shell, prepared for the 2017 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 13–16 November. The paper has not been peer reviewed.
This paper presents a saturation-modeling approach for fields and reservoirs with complex hydrocarbon-charging histories. The model resolves saturation-height functions for the primary-drainage, imbibition, and secondary-drainage equilibriums. As part of the approach, a method of evaluating the residual-hydrocarbon saturation below the initial free-water level (FWL) is proposed. The developed theory is based on the principle of capillary-pressure/saturation hysteresis on the drainage/imbibition process in a water-wet system.
Introduction
Many discovered oil and gas fields are found to have gone through complex fluid-fill histories where residual hydrocarbons are observed below the FWL. To add to the complexity, some of these are giant fields and are divided into compartments with varying contacts and FWLs.
To model saturation-height dependencies for reservoirs in fields under imbibition equilibrium, one of the adopted practices is to use a drainage model built from core data or log data to compute the saturation starting from the original FWL contact but only calculate the hydrocarbon-in-place volumes above the initial FWL. Another common practice is to build log-based drainage models using the current FWL while ignoring the uncertainties in the transition zone from the imbibition effect. These approaches typically lead to an inappropriate estimation of the hydrocarbon saturation in the transition zone and normally require separate models for different segments of the field.
In this paper, an approach is presented for modeling the core capillary-pressure imbibition and secondary drainage cycles, integrating with log-based saturation-height models, and designing a work flow for upscaling and implementation in 3D reservoir models.
Imbibition and Secondary-Drainage-Model Theory
Hysteresis of Saturation/Capillary Pressure and Analytical Imbibition Model Method. Modeling of saturation/capillary pressure of primary-drainage-imbibition hysteresis is more complicated than other types of hysteresis effects because its cycle is not a closed loop; the imbibition route does not end at the starting point of the primary drainage route. Fig. 1 shows the multi cycle drainage/imbibition scanning curves in mixed-wet or strongly water-wet rock systems. Saturation changes caused by the imbibition-hysteresis effect are larger at lower capillary pressures in the transition zone but become insignificant over the higher capillary pressures across the main nonwetting-phase column.
The primary-drainage capillary pressure can be measured by high-pressure mercury injection, porous plate, and centrifuge. Spontaneous imbibition can be measured only by use of the porous-plate technique or by use of an Amott cell. The forced imbibition part of the imbibition capillary pressure can be measured by porous plate and centrifuge.