Simulation of two-phase flow

under consideration of the entire hysteresis cycle

GeoDict calculates the flow of two immiscible fluids (e.g., oil and water) on 3D image data of porous reservoir rocks. The calculation of the capillary pressure curve is one of the most important tasks to be solved when determining the properties of a reservoir in the context of Special Core Analysis (SCAL), especially in an industrial context. Usually, the workflow for the determination of hysteresis starts with the import image data obtained by computed tomography of a rock sample. Advanced application workflows are delivered, ready-to-use with GeoDict.

GeoDict Hysteresis Cycle Workflow

The resulting images are processed with advanced image filters (e.g., Non-Local Means) and segmentation methods (e.g., AI segmentation) to optimally map the rock structure. The created 3D structure is now ready to be used to digitally determine the capillary pressure curve. When calculating the complete hysteresis cycle of the two-phase flow, each intermediate step can be simulated, from primary drainage to secondary drainage. Taking into account the individual processes, the saturation and distribution of the oil or the water phase within the structure are determined in relation to the pressure. As part of the integrated workflow, the wettability of the minerals is also taken into account (oil-wet, water-wet, mixed-wet).

The intuitive GeoDict GUI allows easy entry into the simulation of two-phase flow in rock cores.

The hysteresis cycle maps the following processes:

  • Primary Drainage (forced): Water is displaced by oil
  • Imbibition (spontaneous+forced): Oil is displaced by water based on the preceding fluid distribution
  • Secondary Drainage (spontaneous+forced): Water is displaced by oil based on the preceding fluid distribution

Authors and application specialists

Dr. Arne Jacob

Application Engineer
for Digital Rock Physics

Dr. Christian Hinz

Business Manager
for Digital Rock Physics

Effective Automation of the Workflow

Extensive automation of the individual workflows is possible in GeoDict. In this case study, the complete hysteresis cycle was simulated using the "Hysteresis for oil-water setups" application already included in GeoDict. The simulation scenarios and input parameters used for the simulation may be freely modified according to the application requirements.

When implemented in GeoDict, the entire contact angle range (water-wet, neutrally-wet, oil-wet, mixed-wet) of the simulated fluids is mapped according to the individual wetting properties of the rock. GeoDict is also used to simulate both porous plate and centrifugal standard experiments in the calculation of the properties of two-phase flow in porous media.

In the intuitive GUI, the user has access to the following input parameters:

  • Fluid properties
  • Wetting conditions
  • Contact angle
  • Interfacial tensions
  • Flow direction

Case Study: Calculation of the relative permeability of large structures under mixed-wet conditions

Large structures of rocks are analyzed in a time- and cost-efficient way with GeoDict. The digital simulation of the capillary pressure curve and the calculation of the relative permeability derived from it avoid costly laboratory measurements.

When determining the rock properties, the saturation distribution of the phases is calculated for each pressure step. At certain saturation steps, the effective permeability is determined in order to finally predict the relative permeability in relation to the fluid saturation. The user retains full control over the data generated during the simulation, ensuring the reproducibility of the results and simulation parameters.

Simulation parameters

Contact angle (to the mineral surfaces):

  • Water-wet CA: 40°
  • Oil-wet CA: 140°

Results of the capillary pressure curve calculation:

  • Irreducible Water saturation: 19 %
  • Residual Oil saturation: 31 %

Used computer resources:

  • Duration: ~3.8 days
  • RAM: ~195 GB
  • Parallelization: 32 Cores
  • Software: GeoDict 2022 (Linux)

The relative permeability can be determined ~100 times faster using GeoDict than using conventional laboratory methods!

Reference: Mattila et al., 2016: A prospect for computing in porous material research: very large fluid flow simulations, Journal of Computational Science, 15, pp. 62-76,


Primary Drainage (forced)

Oil displaces water in a water-saturated Berea sandstone. The saturation of the oil phase increases with increasing capillary pressure


Relative permeability

Visualization of flow velocities in the relative permeability simulation


Relevant publications

  • G. Burmester, F. Zekiri, H. Jurcic, P. Arnold, H. Ott., Integration and Upscaling of Multi-Phase Fluid Flow Properties in Clastic Reservoirs, 83rd EAGE Annual Conference & Exhibition, Conference Proceedings, pages 1-5, 2022