One Dimensional Stochastic Inversion (ODiSI) for Improved Lithology Prediction
How a One Dimensional Stochastic Inversion (ODiSI) was performed on a central North Sea field to quantify the extent of high-quality sand successfully.
The presence of relatively high impedance over- and under-burden combined with a low acoustic differentiation within the reservoir are often major challenges to any seismic analysis. These challenges were also some of the difficulties linked to an Upper Fulmar reservoir, where ODiSI was applied to delineate the presence and lateral extent of the range of lithology types within the field.
A Reservoir Bounded by Mixed Lithology
The reservoir is an Upper Jurassic Fulmar interpod (depocenter), which is flanked by Triassic Smith Bank shale pods. Triassic shales and Zechstein Evaporites underlie the field, and Cretaceous lithologies overlay it, which provides a challenge for seismic analysis, particularly with regards to inversion and Quantitative Interpretation (QI).
The ODiSI parameterization was performed on four wells located within the field and crossing the reservoir. All wells had the suite of well logs needed for an ODiSI parameterization: Vp, Vs, density, total porosity, Vsh, water and HC saturation, and a facies log.
The provided facies logs represented four lithologies within the reservoir:
- Clean sand
- Shaley sand
- Cemented sand
- Shale
The uppermost Fulmar have alternations of thin Clean sands and thicker Shaley sands. A new lithofacies called Clean + Shaley Sands was created to facilitate this higher net fraction, a lithofacies that is only present in the upper reservoir zone.
ODiSI: A New Approach to Seismic Inversion
Originally developed by BP and re-engineered as a Petrel E&P software platform* plug-in by Cegal, ODiSI is a novel approach to seismic inversion. The method captures all associated prior knowledge about a given field, prospect or reservoir and allows its users to build robust and comprehensive models of the subsurface, produce high-quality property estimates, and capture associated uncertainties for any given reservoir output.
ODiSI jointly estimates facies, reservoir properties, and impedances, and their associated uncertainties, by creating a set of pseudo-wells, typically between 1,000 to 50,000, at each seismic trace position. Physical properties are generated for each pseudo-well from robust prior information utilizing Rock Physics Models (RPM), and synthetics derived from the pseudo-wells using Extended Elastic Impedance (EEI) are then matched to the appropriate seismic volume.
The statistically best-matched pseudo-wells are selected (based on RMSE value), and their properties averaged to provide an estimate at each sample of the mean reservoir properties, their associated uncertainties and the probability of the presence of each lithofacies at every trace location.
Applying ODiSI
In this particular case, ODiSI was applied in an attempt to delineate the presence and lateral extent of the range of lithology types within the field.
Delineation is generally complicated by the relatively high impedance contrasts at the top and the base of the reservoir and poor acoustic differentiation of the Fulmar facies themselves. Figure 1, a cross-plot of Vp/Vs versus Acoustic Impedance (AI) shows very limited Vp/Vs contrast between the facies, suggesting a small gradient signal and limited AVO information. On the other hand, Acoustic Impedance shows differentiation of the cemented sands and highest quality reservoir sands from the shaley facies and is, therefore, the preferred elastic property for inversion.
Figure 1: Vp/Vs versus Acoustic Impedance (AI) cross plot, data colored by facies.
ODiSI makes use of the extended elastic impedance (EEI) concept to derive synthetics from the pseudo-wells. A Chi angle stack was created from three angle stacks (near, mid, far) at a Chi projection of 5 degrees to mimic the central angle of the full-stack (no notable AVO effects were observed). The Chi 5 stack was conditioned for utilization within ODiSI through the application of Colored Inversion (figure 2).
Figure 2: EEI Chi 5° projection, colored inverted NW/SE transept.
ODiSI also uses Rock Physics Models (RPM) to generate physical properties for each pseudo-well from robust prior information. Each lithofacies was associated with a Rock Physics Model calibrated to known well data. Three types of Rock Physics Models were used depending on the lithology:
- Reservoir: Clean sand and Shaley + Clean sand were modeled by defining the porosity versus depth trend (TWT), then Shear Modulus versus porosity, and finally Dry Bulk Modulus versus Shear Modulus.
- Non-reservoir: Shale was defined using P-wave versus depth trend (TWT), then S-wave versus P-wave trend, and density (rho) versus P-wave trend.
- Laminated: Shaley sand was modeled as a laminated formation, an effective medium mix between Clean sand and Shale according to the shale fraction (Backus averaging).
Results
The inversion was performed on the color inverted Chi angle stack at 5 degrees to obtain several output volumes:
- Most Probable Lithofacies
- Mean Net Reservoir Fraction
- Standard deviation of the Net Reservoir Fraction
- The probability of each lithofacies
ODiSI also created EEI Synthetics and residual traces to validate the matching of pseudo-wells. At each seismic trace, 5000 pseudo-wells were created and compared to the EEI Chi 5 CI input. The results at each trace are the average of the properties from the 50 best pseudo-wells, based on the lowest residual energy, RMSE (Root Mean Square Error), value.
ODiSI successfully delineated the regions of high net reservoir quality sand within the field, and these are consistent with blind wells. The results also show good lateral continuity, and the differentiation between the expected lithologies is consistent with the expectations of the overall geological model.
An analysis of the lithofacies and net volume outputs (figure 3 and figure 4) together highlights the extent of the high fraction of clean sand within the field. Correlation with the well data is strong and supports the robustness of the results.
Figure 3: Probable lithofacies output with faults. This volume shows a good delineation of high net reservoir quality sands (Clean and Shaley + Clean).
Figure 4: Net Mean. This volume highlights the delineation of high net sands.
As the process is a one-dimensional trace-by-trace method with no spatial smoothing, the lateral continuity confirms the stability of the algorithm. The quality inherent in the map views in figures 5 and 6 clearly shows the benefit of retaining the lateral resolution of the seismic data.
Figure 5: The Probable Lithofacies cube in 3D view. Dotted lines represent faults. The figure shows the probable lithofacies and the strong link observed between facies depositions and faults.
Figure 6: Demonstrates the chronostratigraphic slices for the cemented sand probability (left) and the probability of clean sand within the transition zone (right). The output shows clear facies discrimination while retaining the full spatial resolution of the seismic data.
Impact
Applying ODiSI solved two notable challenges encountered in the field: the presence of relatively high impedance over- and under-burden in combination with low acoustic differentiation within the reservoir.
ODiSI worked by creating a set of pseudo-wells at each seismic trace position and then by matching the best pseudo-wells to the trace, which allowed the output of different 3D volumes such as Probable Lithofacies and Net-to-Gross. The different volumes showed a good lateral continuity providing a strong validation of the ODiSI method and process.
Moreover, the ODiSI inversion results showed a very good delineation of high-quality sands and were therefore incorporated in the screening of the next water injector location drilled in 2017.
*Petrel is a mark of SLB.
