Comparison of Borehole Velocity-Prediction Models and Estimation of Fluid Saturation Effects: From Rock Physics to Exploration Problem
Authors: Sun S.Z. , Stretch S.R. , Brown R.J. 
Published: March 2010

Abstract
We analyzed three types of elastic-wave velocity-prediction models by means of well-log synthetics and seismic-section ties by considering fluid saturation in five wells, including clastic and carbonate reservoirs. The elastic moduli of a formation are functions of the elastic moduli of the solid matrix and the fluid components, as well as the pore geometry. By using the volumes of different minerals and fluids obtained from log analysis, we calculated the elastic moduli of the matrix and fluid. Changes in velocities between invaded and uninvaded zones are quite signifi cant and often ignored in well-to-seismic ties.
We applied three different models (time-average, Gassmann, and Kuster-Toks?z), seeking a best velocity-prediction model. The time-average equation is not recommended for velocity prediction and is especially inaccurate for gas-reservoir intervals. The Gassmann equation is usually the most appropriate for low-frequency seismic data. The Kuster-Toks?z model is best for high-frequency data. Also, because it takes pore geometry intoccount, it should be considered when the pore shape is signifi - cant in determining formation velocity (pore aspect ratio &lt; 0.3).
There can be a trade-off between low-frequency dispersion effects, favouring the Gassmann application, and pore geometry effects, favouring the Kuster-Toks?z application. Our exploration case study indicates that the high-frequency (Kuster-Toks?z) model may usually be a better choice. This case study yields good agreement between the predicted pore aspect ratio (0.12) and that from a laboratory measurement (0.166) in the study area.
Comprehensive research encompassing borehole-velocity prediction models, laboratory study of core such as pore geometry statistics, well-log analysis, and study of seismic response is required.

Introduction
A question of considerable interest in seismic lithology studies is how best to predict elastic-wave velocities, both compressional (or P, sonic, or acoustic) and shear (or S), for composite media (e.g., porous rocks) in cases where there are no velocity logs available. Nuclear logs have sometimes been used to derive sonic and shear logs(1) but, unfortunately, estimation of velocities by thisalgorithm is quite inaccurate. For one thing, it does not take intoccount fluid saturation. For wells in western Canada, sonic logs re commonly available but shear logs are rarely available. And S wave logs are often required in seismic lithology studies that seek to understand the effects of reservoir fluid content, such as in AVO studies. The purpose of this paper is twofold. First, by comparing different velocity-prediction models for composite media, it tries to find a best model to predict P-wave and S-wave velocities, VP and VS. Second, by considering fluid-saturation effects, it applies predictions to exploration problems by tying into field seismic data with synthetic seismograms that incorporate velocities predicted from different porous-rock models.
Laboratory studies show that there are significant changes in elastic-wave velocities in a porous rock depending on whether it is dry, gas-saturated, water-saturated, or oil-saturated(2-6). Figureshows P- and S-wave velocity comparisons between laboratory measurements and predictions from rock-physics models(7, 8).