Influence of Effective Stress on the Acoustic Velocity and Log Derived Porosity
Authors: Khaksar A. , Griffiths C.M. 
Published: December 2007

Abstract
Experimental studies indicate that when effective stress increases, compressional wave velocity in porous rocks increases. As a consequence, porosity values derived from sonic transit times measured in reservoir rocks in hydrocarbon producing fields will vary. The in-situ pressure condition has rarely been considered as a parameter in conventional velocity porosity transforms. Reservoir pressure reduction, resulting from hydrocarbon production, increases effective stress. Consequently for a given reservoir rock at a given depth and porosity the sonic log may show decreasing values as the pressure in the reservoir decreases. This in turn may lead to underestimation of the actual porosity of the reservoir rocks in partially pressure depleted reservoirs. The range of such underestimation for liquid saturated reservoirs may not be significant, but since the influence of effective stress on velocity increases as fluid saturation changes to gas, porosity underestimation by conventional velocity-porosity transforms for gas bearing rocks may increase. As a result, porosity assigned to partially pressure depleted gas reservoirs may be several porosity units too low. Examples are taken from partially depleted gas reservoirs in the Cooper Basin in South Australia. The stress dependent nature of velocity requires that the in-situ pressure condition should be considered when the sonic log is used to determine the porosity of gas producing reservoir rocks. We conclude that where other porosity tools are not available, and where the formation pressure of the reservoir varies in different wells, or different reservoirs in the same well show markedly varying pressures, it is necessary to calibrate the sonic tool response to pressure variation.

Introduction
A knowledge of the elastic velocities in porous media is of considerable interest in many research fields including rock mechanics, geological engineering, geophysics and petroleum exploration. In petroleum exploration this concept mainly concerns the relationship between reservoir rock characters and the acoustic velocity. Porosity estimation is one of the most common application of acoustic velocity data in hydrocarbon wells. Numerous equations have been introduced to convert sonic travel time (Dt) to porosity. It is well known that the P-wave velocity (Vp) for a rock with a given porosity, is also controlled by several other factors such as pore filling minerals, internal and external pressures, pore geometry and pore fluid saturation etc. These factors may have significant effect on measured Dt and thus on porosity interpretation from the sonic log.
Several investigators (see references 2 through 4) have studied the effect of clay content and the type and saturation of pore fluids on acoustic velocity and the sonic log derived porosity in reservoir rocks. In contrast, the in situ pressure condition has rarely been considered as a parameter in the commonly used velocity-porosity equations. This paper addresses the influence of effective stress on the elastic wave velocities in rocks and its implications on porosity determination from the sonic log in hydrocarbon bearing reservoirs. Examples from the literature and a case study in a gas producing reservoir are used to highlight the importance of the issue.
Effective stress is the arithmetic difference between lithostatic pressure and hydrostatic pressure at a given depth. It may normally be considered equivalent to the difference between confining pressure (Pc) and pore pressure (Pp). Experimental studies indicate that as effective stress increases, VP increases. This increase depends on the rock type and pore fluid. The change in Vp due to effective stress increase is more pronounced when the pore fluid is gas. Current sonic porosity methods do not account for the variation of Vp due to pressure change in hydrocarbon producing fields.

Effective Stress Versus Velocity
Wyllie et al. measured ultrasonic P-wave velocity as a function of effective pressure in water saturated Berea sandstone.
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