Reservoir simulation

Saturation Modeling Under a Complex Fluid-Fill History: Drainage and Imbibition

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.

Fig. 1—Saturation/capillary-pressure drainage (solid green) and imbibition scanning curves (red). Scanning curves begin from the endpoint of each drainage path.

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.


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 above shows the multi­cycle 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.

The imbibition-saturation/capillary-pressure hysteresis—the imbibition scanning curves of the special-core-analysis (SCAL) measurement—can be simulated by the van Genuchten (VG) equation, which is widely used in solid/water science research for the simulation of the hysteresis effect of the water content and capillary pressure in a porous medium.

The VG equation can be modified and rewritten in such a way that it becomes suited to the modeling of the SCAL saturation/capillary-pressure data and reservoir model. Please see the complete paper for the equations.

Secondary-Drainage Saturation/Capillary-Pressure Model. The secondary-drainage-saturation/capillary-pressure model can be constructed from the second or subsequent drainage cycles of the full drainage and imbibition cycle SCAL data when available.

Simulation of the secondary-drainage saturation/capillary pressure is more complicated than simulation of primary drainage. The commonly used functions for primary drainage do not obtain a satisfactory fit with the secondary-drainage measurements and are not solvable for the negative-capillary-pressure data points. Instead, a modified VG equation is found to be the best suitable model for simulating the secondary drainage.

Work Flow and Procedures for Modeling Saturation Height Under Imbibition and Secondary Drainage

For fields that have gone through an imbibition (and secondary-drainage) phase, a primary drainage saturation-height function that was traditionally built from the SCAL capillary-pressure data, or from log-derived saturations or both, will not provide an accurate evaluation of the hydrocarbon saturation across the field. The following work flow is recommended for modeling the saturation-height function under imbibition (and secondary-drainage) equilibrium:

  • Understand the fluid-fill history of the field
  • Build a primary-drainage model primarily on the basis of SCAL data
  • Build an imbibition model on the basis of SCAL data
  • Integrate the primary drainage/imbibition models and reconcile with the log saturation
  • Build a secondary-drainage model when applicable

Field Fluid-Fill History. Understanding of the field fluid-fill history is the most important step in building the ­saturation-height model but is not always easy to achieve. An integrated approach using diagnostic tools of pressure; well logs; and seismic, core, and fluid properties helps to identify the

  • State of equilibrium through assessment of communication between regions, primarily by the pressure data
  • Fluid-fill cycle at every well location
  • Basin history data

Identification and confirmation of the secondary-drainage ­equilibrium is more complicated. In fact, some fields (or part of the segments) that are known to be under imbibition equilibrium could actually be under a subsequent secondary-drainage process. When the saturation log around the initial FWL (or contact) above the residual column exhibits much longer transition compared with the sharper transition as in the imbibition profile, it may be considered an indication of a possible secondary-drainage process in the field or part of it, especially for those wells in the crestal segments. However, this should be supported by the geological model and field history. Hydrocarbon recharging from the secondary-drainage process can be caused by various factors, including fault-sealing failure, remobilization of residual gas from its expansion as a result of pressure depletion, or the effect of a hydrodynamic aquifer. For wells and segments identified to be under secondary-drainage equilibrium, the saturation in the reservoir model should be calculated from the preproduction initial FWL using the appropriate secondary-drainage saturation-height model.
Primary-Drainage Saturation-Height Model. The primary-drainage model, which represents the initial hydrocarbon charging history, should be built preferentially from the primary-­drainage cycle of the capillary-pressure measurement or from the saturation log when there are no SCAL data available. Most of the conventional-­drainage ­saturation-height-model methods can be used. It is important when building the drainage model that the relevant terms for the entry pressure (height) and the curve shape (mainly for transition) are appropriately resolved through SCAL data modeling because they are difficult to obtain correctly with log-based modeling if the wells are only in the crestal regions without penetrating the contact or are under imbibition equilibrium.

Reconciliation of the primary-drainage saturation-height model to the log saturation should be conducted over the gas column, above the transition zone, only for wells that are firmly not in secondary-drainage equilibrium.

Imbibition Saturation-Height Model. The approach presented in this paper is recommended for building the imbibition saturation-height model through either SCAL imbibition scanning-curve modeling or log-based modeling when core data are of poor quality or unavailable. The approach can be applied for modeling the imbibition over geological time.

Integration of Primary-Drainage/Imbibition Saturation-Height Models. The integrated saturation-height modeling can be performed through a combined algorithm solving simultaneously for the parameters in the primary-­drainage and imbibition models.

Secondary-Drainage Saturation-Height Model. Reservoirs clearly under secondary-drainage equilibrium or hydrocarbon-recharging history are found rarely, and none of them has been appropriately modeled. Building the secondary-drainage model is necessary if the field (or some segments of the field) clearly exhibits having undergone a secondary-drainage process over the geological period after imbibition. In the situation that some wells with residual hydrocarbon below the FWL could not be modeled by the imbibition model that was built from SCAL data and logs, one should consider the probability of secondary drainage.


A robust saturation-modeling approach for reservoirs with complex fluid-fill histories—drainage and imbibition and secondary drainage—is presented. The method, based on a modified VG equation, has been shown to be the most-appropriate method compared with common practices for simulating the imbibition (and ­secondary-drainage) saturation process for oil and gas reservoirs in water-wet or mixed-wet systems. A high level of confidence and accuracy of the saturation-height model can be obtained by the integrated modeling of SCAL capillary-pressure data and log-derived saturations.

The new power-law approach for the residual-hydrocarbon estimation enables precise dynamic simulation of the saturation changes that have occurred historically and during field production.

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.