Empirical estimation of viscoelastic seismic parameters from petrophysical properties of sandstone

Abstract

Viscoelastic seismic parameters are expressions of underlying petrophysical properties. Theoretical and empirically derived petrophysical/seismic relations exist, but each is limited in the number and the range of values of the variables used. To provide a more comprehensive empirical model, we combined lab measurements from 18 published data sets and well log data for sandstone samples, and determined least‐squares coefficients across them all. The dependent variables are the seismic parameters of bulk density (ρ), compressional and shear wave velocities ([Formula: see text] and [Formula: see text]), and compressional and shear wave quality factors ([Formula: see text] and [Formula: see text]). The independent variables are effective pressure, porosity, clay content, water saturation, permeability, and frequency. As the derived expressions are empirical correlations, no causal relations should be inferred. Prediction of ρ is based on volumetric mixing of the constituents. For [Formula: see text] and [Formula: see text] predictions, separate sets of coefficients are fitted for three water saturation conditions: dry, partially saturated, and fully saturated. Predictions of [Formula: see text] and [Formula: see text] are fitted as functions of porosity, clay content, effective pressure, saturation, and frequency. Predictions of [Formula: see text] are fitted as a function of porosity, clay content, permeability, saturation, frequency, and pressure. Interactions between effective pressure, saturation, and frequency are included. Predictions of [Formula: see text] are obtained from [Formula: see text] and [Formula: see text]. The result is a composite model that is more comprehensive than previous models and that predicts seismic properties from the petrophysical properties. Empirically estimated values of ρ, [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the composite data over all saturations predict the measurements with correlation coefficients [Formula: see text] that range from a low of 0.65 (for [Formula: see text],) to a high of 0.90 (for [Formula: see text]). As the fitted relations have been derived from data with limited parameter ranges, extrapolation is not advised, and they are not intended to substitute for locally derived relations based on site‐specific data. Nevertheless, the derived expressions produce representative values that will be useful when approximate, internally consistent predictions are sufficient. Potential future applications include building of seismic reservoir models from petrophysical data and analysis of the sensitivity of seismic data to changes in reservoir properties.

Petro‐seismic inversion for sandstone properties

“…This paper takes the next step beyond the sequence described above. By rearranging the empirical equations of Koesoemadinata and McMechan (2001), the equations can be solved for any desired unknown parameters. With these, and some additional equations, we obtain a robust inversion scheme that, provided sufficient input data are given, can solve for all the remaining unknowns.…”

“…Comprehensive models that encompass a wide range (and various combinations) of multiple parameters are important to Manuscript provide an understanding of the observed behaviors and the sensitivity of the seismic data to the petrophysical properties. Using primarily published laboratory data, Koesoemadinata and McMechan (2001) develop a composite model of the empirical relationships between the petrophysical properties [porosity (φ), clay content (C), permeability (k), water saturation (S) and effective pressure (P)] and the viscoelastic seismic parameters [frequency ( f ), density (ρ), P-wave velocity (V p ), S-wave velocity (V s ), V p /V s , P-wave quality factor (Q p ), S-wave quality factor (Q s ), and Q s /Q p ]. These data are limited to low-clay sandstones, and to water as the pore fluid.…”

An experimental study on seismic monitoring of a CO2 flooding in two sandstones

“…Wave velocity and attenuation in sandstone are widely studied in fields of reservoir engineering and geo-engineering [1]. In oil reservoir field, there is a practical need to identify non-flooded compartments within the reservoir during an enhanced oil recovery operation.…”

Characterization of Seismoacoustic Properties of Marine Sediments

“…10). Koesoemadinata and McMechan [42] provided an empirial formula for the dispersion of P waves in sandstone with the dispersion part following 0.388f where f is the frequency in MHz for the frequency range 400 Hz to 1 Mhz. Further research is needed to find the physical mechanism explaining the controversial high-frequency dispersion in water-saturated sediments.…”