Upscaling Petrophysical Properties to the Seismic Scale

Greg A. Partyka, Jack B. Thomas, and Kevin P. Turco, BP

Dan J. Hartmann, DJH Energy Consulting

Previously published by the SEG in: Extended Abstracts of the 2000 Exposition and Seventieth Annual Meeting of the Society of Exploration Geophysicists, Calgary, Canada.

Summary

Introduction

Use of 3-D seismic has revolutionized the geophysicists' ability to spatially map reservoir targets. In many cases however, seismic falls short in quantifying petrophysical variability; its use often extending only as far as mapping spatial patterns that help the geologist establish the structural and stratigraphic setting. If petrophysical reservoir characteristics can be estimated "pre-drill" with confidence, early reservoir simulations can help with proper sizing of production facilities and drilling costs.

When structural or stratigraphic patterns are exposed, there is a large (typically unrealistic) temptation to infer petrophysical reservoir models directly from bandlimited seismic scale maps and volumes. The path from core data to seismic data to reservoir flow-modeling requires understanding of the interplay between flow-unit stacking, thickness, velocity, and bandwidth. Such understanding enables the interpreter to answer two basic questions: such as:

1. Does seismic respond to the variability in petrophysical properties?
2. What scale of petrophysical variability can be resolved with what seismic bandwidth?

A great deal of uncertainty is imbedded in seismic-petrophysics calibrations because of large variations in scale of measurements. Core analyses provide information on the micron to centimetre scale; well-logs on the centimetre to metre scale, seismic on the metre to decimetre scale. In addition to these upscaling and downscaling issues, the individual datasets can contain errors such as:

• Sampling bias and sampling induced damage to core plugs,
• Washouts,
• Tool problems in well-log measurements,
• Acquisition and processing artifacts that mask the true seismic response from the reservoir.

Determining qualitative gross reservoir geometries from seismic can be relatively straight-forward and fast, but may contain large uncertainties. Determining whether seismic can delineate variability in petrophysical properties however, requires scoping work on a finer level that tackles scaling issues. One such scoping approach can be broken down into two steps:

Step #1: Cross-Plot well-log-scale acoustic properties versus petrophysical properties. Do well-log scale crossplots indicate acoustic sensitivity to petrophysical properties? If yes,...there is hope for seismic; if no,... seismic will not add value to mapping petrophysical variability.
Step #2: Perform upscaling sensitivity analysis with respect to bandwidth, flow-unit thickness, velocity and flow-unit stacking; then use derived relationships to transform seismic inversion-derived acoustic properties to petrophysical properties.

Step #1: Scoping at the Well-Log Scale

At the end of step #1, the interpreter has two pieces of information in hand:

1. Seismic data derived acoustic volumes and maps of the reservoir interval, and
2. Well-log scale crossplots between acoustic and petrophysical properties.

Step #2: Sensitivity Analysis for Upscaling

We recommend upscaling the acoustic measurements using a range of upper frequency cut-offs. This enables a sensitivity analysis of upper frequency versus petrophysical resolving power, for one particular flow-unit stacking pattern and thickness. Simply filtering a well-log interval with various hi-cut filters deals with only the frequency upscaling part of the sensitivity problem, and disregards the remaining three criteria of the upscaling sensitivity matrix (flow unit stacking pattern, thickness and velocity). Quantifying seismic resolution requires a sensitivity analysis with respect to all four criteria. In other words, Backus-averaging only one well-log-based zone of interest does not uniquely determine the resolving power of a particular seismic bandwidth with respect to petrophysical properties for all other thicknesses. It does so, only for the one particular vertical thickness and the one particular ordering of layers inherent in the well-log profile. If the thickness or stacking order of individual layers changes, the resolving power of the seismic bandwidth with respect to petrophysical properties will also change. For exampe, if you progressively decrease the wavelet bandwidth (i.e. hi-cut frequency), you also progressively decrease the resolving ability of impedance with respect to porosity. Note that by the time you cut-back the frequency to 30hz, the acoustic impedance-versus porosity relationship is relatively flat, indicating that it would be very difficult to quantify porosity variability in a 50ft bed using 30hz signal. There remains however, a contrast between porous-oil-filled sand and the shale, indicating that detection of porous sand (in a 50ft bed, using 30hz signal) is still possible. You can create a similar effect by maintaining the same bandwidth while progressively decreasing thickness. To assess the ability of bandlimited seismic to resolve the range of flow unit thicknesses and stacking patterns:

1. Establish end-member flow unit profiles (the expected range of flow unit stacking orders and flow unit thicknesses), then
2. Backus-average each model with a range of upper frequency cut-offs.

The well-log scale cross-plots created in step #1, that were used to determine whether seismic can discriminate petrophysical variability, should then be replotted; one crossplot per combination of:

• Flow-unit thickness,
• Flow-unit velocity,
• Flow-unit stacking-pattern, and
• Frequency hi-cut,

Step #3: Predicting Petrophysical Properties from Seismic Impedance

• the seismic wavelet, which can be obtained via conventional spectral analysis,
• seismic-derived impedance, which can be obtained via seismic inversion techniques,
• upscaling sensitivity relationships, from step #2 above, and
• gross thickness.

• computing a spectral decomposition Tuning Cube for the zone-of-interest,
• thickness modeling to derive local energy-vs-thickness-vs-frequency relationships, and
• calibration to determine reservoir thickness.

• interpreting a guide horizon along the zone-of-interest,
• subsetting a short, zone-of-interest volume,
• computing a zone-of-interest Tuning Cube (i.e. computing an amplitude spectrum for each time-trace), and
• animating vertically (in plan view) through the Tuning Cube to examine reservoir tuning effects.

To derive local energy-vs-thickness-vs-frequency relationships, create a wedge model for the reservoir by stretching/squeezing the well-log reservoir zone to simulate a variety of thicknesses (e.g. from 10 to 100 feet in increments of 10 feet); then compute the spectral decomposition for the wedge model, in the same manner as for the real data. At this stage you have the necessary information to calibrate the real Tuning Cube with the modeled estimates.

From the modeling you can determine the frequency below which the entire thickness range stays below resolution. Staying below resolution allows you to uniquely associate a thickness with each amplitude. If you cross-over to higher frequencies, part of the possible thickness range becomes resolved, and you will no longer be able to uniquely asociate a thickness with amplitude (i.e. the amplitude versus thickness relationship would turn over itself. So, proceeding with a low-frequency component enables less-subjective gross thickness estimation.

At this stage you have all the necessary pieces to predict petrophysical properties from the seismic. The gross thickness and wavelet hi-cut frequency determine which upscaling-sensitivity cross-plot to use.

Conclusions

References

PowerPoint slides.

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