A Method for 3D Saturation Modeling with Drainage and Imbibition Cycles

Darous, Christophe (Schlumberger) | Raina, Ishan (Schlumberger)



Typical saturation height modeling assumes that the migrated hydrocarbon has displaced water under primary drainage until pressure equilibrium controlled by buoyancy, pore throat size, and the position of the free water level (FWL) is reached. When leakage of the caprock or a structural tilting after migration occurs, a shallower position of the new FWL involves an imbibition cycle to represent the initial saturation distribution in a 3D reservoir model.

The methodology starts at the well level by building drainage saturation height functions (SHFs) typically from core capillary pressures (Pc) experiments, in relationship with the reservoir rock typing scheme. The following step involves the construction of the scanning curves that will revert any primary drainage saturation into an imbibition cycle. Then, considering the position of the actual FWL defined from pressure gradients, the position of the paleo-FWL (PFWL) in each well is solved to best match the water saturation profile computed from logs. The resulting PFWL is mapped to implement the saturation height modeling in 3D.

A synthetic case, of tilting after migration is used to illustrate the methodology. The rock typing scheme and the petrophysical properties from logs are coupled with the saturation height modeling defined from Pc core experiments. The typical inconsistencies between the saturation profiles computed from logs and the position of the FWL from pressure gradient that cannot be resolved with drainage SHF are described. The interpretation of the PFWL improves the understanding of the migration episodes and geological events. The implementation of the methodology in a 3D model provides a more accurate hydrocarbon in-place calculation and perspectives for improving recovery and field development strategy.

Methodologies to build 3D saturation height models in drainage consistent with reservoir rock types are common practices. The equations for modeling water saturation by including an imbibition cycle have also already been defined. The developed workflow combines both methodologies to initialize a 3D static saturation model that honors the fluid fill history associated with imbibition and is consistent with petrophysical properties of the reservoirs. The method has been fully coded into commercial software and can be readily implemented to real case studies.