Relations between static and dynamic moduli of sedimentary rocks

Abstract

Static moduli of rocks are usually different from the corresponding dynamic moduli. The ratio between them is generally complex and depends on several conditions, including stress state and stress history. Different drainage conditions, dispersion (often associated with pore fluid effects), heterogeneities and strain amplitude, are all potential reasons for this discrepancy. Moreover, comparison of static and dynamic moduli is often hampered and maybe mistaken due to insufficient characterization of anisotropy. This paper gives a review of the various mechanisms causing differences between static and dynamic moduli. By careful arrangements of test conditions, it is possible to isolate the mechanisms so that they can be studied separately. Non‐elastic deformation induced by the large static strain amplitudes is particularly challenging, however a linear relationship between non‐elastic compliance and stress makes it possible to eliminate also this effect by extrapolation to zero strain amplitude. To a large extent, each mechanism can be expressed mathematically with reasonable precision, thus quantitative relations between the moduli can be established. This provides useful tools for analyses and prediction of rock behaviour. For instance, such relations may be used to predict static stiffness and even strength based on dynamic measurements. This is particularly useful in field situations where only dynamic data are available. Further, by utilizing the possibility for extrapolation of static measurements to zero strain amplitude, dispersion in the range from seismic to ultrasonic frequencies may be studied by a combination of static and dynamic measurements.

Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid-Saturated Porous Sandstones

“…For nonporous, homogeneous materials like metal and glass, dynamic and static moduli are experimentally found to be equal (Simmons and Brace 1965;Ledbetter 1993). In contrast, the dynamic modulus is almost always larger than the static one for many rocks (Simmons and Brace 1965;King 1969;Cheng and Johnston 1981;Coyner 1984;Fjaer 2009Fjaer , 2019. Recently, Fjaer (2019) summarized some potential reasons for the discrepancy between static and dynamic moduli of rocks, including the different strain rates, drainage conditions, as well as the heterogeneity of rock properties.…”

Identification of stress regimes by using 1D geomechanical modeling of clastic and carbonate reservoirs

“…There exists a relationship between static and dynamic Young's moduli, and it depends upon stress path, the stress history and lithology. [12].…”

Anisotropic Wellbore Stability Analysis: Impact on Failure Prediction

“…In the present case, log data were available from the overburden. Sonic log data provide dynamic elastic moduli, which are known to be different from their static counterparts due to dispersion and strain dependence (Fjaer 2019). These moduli represent upper limits to undrained static stiffnesses and may provide information about shale strength through empirical correlations (Horsrud 2001).…”