Integrated Saturation and Dynamic Modelling

Saturation functions for volume calculations and for multi-phase flow behavior have traditionally been separated into the petrophysical- and reservoir technology disciplines. The physical and geological relations; interaction between rock and fluid surface forces and pore-structure characteristics, remain similar for all saturation functions. We have developed workflows and related software (Sw-toolbox) that bridge the gap between working disciplines and provide physical consistent input to simulation given the problem at hand. The software meets the market demand for a more digital, automated and standardized workflow where traditional methods have been dominated by individual experts with individual spreadsheets and possible lack of consistency from asset to asset.

The workflow has been implemented in a software (Sw-toolbox) that includes both saturation functions for log- and core based saturation-height modelling, capillary pressure and relative permeability for simulation of multi-phase flow. In addition, an MICP module, is developed for rock-typing or automatic scaling to capillary pressure for reservoir fluids for both the oil-water and gas-oil system.

Log based saturation-height modelling

The log-based saturation-height modelling includes modules both for calculation of saturation from resistivity and flexible workflow for building saturation-height from well logs using:

  • J-functions or bin type scaling of reservoir quality
  • Standard equation for Sw-height suited for linear regression method
  • Skjæveland correlation for both primary drainage and imbibition
  • Pc-LET functions for primary drainage, imbibition and secondary drainage

Our experience is that the standard industry approach using simple power-function and often a J-function approach may fail in some cases, especially when it comes to individual well match between model and saturation log.  In particular, this happens for reservoirs with paleo-oil zones where the oil accumulation in proximity of the free water level is impacted by imbibition or secondary drainage.  In this case the J-function scaling will not apply, and the governing capillary pressure saturation function has a different shape than primary drainage.

Well 1-24 with typical imbibition shape for saturation-height and oil below the FWL @ 2520 m TVD.

The workflow for building the saturation function(s) from log is guided, tutorial-like user interface where the user can decide between various filtering possibilities and methods for generation of Petrophysical Rock Types (PRTs).

Automated trend-plots between various parameters for reservoir quality and water saturation. Apparent poor trends are indications for facies/pore-type variations or height dependence for the water saturation.
Same data-set as above. Apparent better trend between porosity and saturation above the transition zone.

A sophisticated QC package including statistical evaluation methods for:

  • Global scale (Hydro Carbon Pore Volume – HCPV)
  • Well by well evaluation of HCPV
  • Selected log-interval with standard deviation for match in each data points
  • Geological facies or PRT’s

The goal for the saturation-height workflow is to build the simplest possible model that maintains the overall HCPV volume, but includes enough details for local oil volume estimates and keeping important information for flow dynamics.

Building saturation-height functions using the Pc_LET formulation for imbibition with oil above and below the free water level. In this case only one facies/PRT are selected and the data is sorted by porosity bins.

A priori assumptions for PRTs vs. depth in each logging point can be given as input to the saturation-height modelling. This can typically be based on geological facies, or, in carbonates, often pore-types from thin-sections or MICP. In the case that such a method fails, or the data availability is scarce, the software can do automated rock-typing itself from the saturation-log.

QC plot for reporting showing model match to CPI.
Matching Hydro Carbon Pore Volume (HCPV) in individual models, this particular model tend to slightly underestimate the global HCPV.
Example of detailed QC plot where the model matching quality can be decoupled to wells, facies/PRT’s or porosity.

The log-based saturation height will be saved for direct implementation in Petrel or Eclipse.

Saturation functions from core data

Saturation functions from core data include all types of capillary pressure data (including MICP) and relative permeability. Such SCAL data are stored in a connected data base. The data base includes all related parameters for the given measurement for later filtering possibilities and correlation analysis.

The saturation functions can be filtered, according to user specifications, before bringing the individual SCAL data into the modelling module. The modelling module will guide the user to find the appropriate method to build a core-based Pc-model, a relative permeability model or  an analysis of MICP data by employing state-of-the-art clustering techniques.

Using this modelling module, the user can bring in all MICP data for a given geological facies. By using the clustering module, the user can then automatically test if these data group with porosity, permeability, RQI or FZI in the expected way. At a given saturation level, the appropriately grouped MICP data should have increasing values for the capillary pressure for one or several of reservoir rock quality indicators when the indicators show poorer reservoir quality. The indicator that has the most consistent grouping of the data may be used as basis for distribution of properties in geo-modelling. Capillary pressure for other fluid systems is handled the same way. A core-based saturation-height model can be directly compared with an analogue model from logs.

Relative permeability modelling uses the same clustering method for building a dynamic model for simulation from several sets of SCAL data. The user can easily test if there are relations in the data set for relative permeability, such as geological facies, wettability or one of the reservoir quality indicators. The relative permeability model is saved for implementation in Eclipse and industry standard saturation scaling methods are used for coupling the saturation-height model and relative permeability for dynamic simulations. The program also handles the full three-phase system and hysteresis between primary drainage and imbibition.