A comparison of Young's moduli and Poisson's ratios obtained from ultrasonic laboratory measurements with static moduli obtained under identical stress conditions shows that the Young's moduli are 1 to 6 times higher under ultrasonic loading conditions. A comparison of these two laboratory measured quantities with log derived moduli measured at 20 KHz indicates that E-ultrasonic > E-sonic >E-static. The clay content and porosity of the samples varied from 1% to 54.5% and 3% to 17.5%, respectively. This clearly suggests that a wide variety of sandstones behave in a viscoelastic manner. The magnitude of the variation with frequency is a function of the clay content, grain size, shape of intergranular contacts, mineralogy and fluid saturations. A model is presented that describes this observed viscoelastic behavior.
The measured static moduli are a function of the sample length. This effect is investigated in some detail. The reported static moduli were obtained at L/d ratios of 2. When comparing log measurements to core, two inherent problems were encountered: depth correlation and sample size, These effects need to be properly accounted for when comparing logs with cores.
Two methods are commonly used to measure elastic moduli of materials: static stress-strain measurements and the measurement of acoustic velocity. The stress-strain measurements yield static elastic moduli whereas the velocity measurements provide dynamic moduli. Early studies on this matter report non-linear stress-strain relations and dynamic elastic moduli that are greater than static moduli. This was ascribed to the existence of microcracks in the body and was thus related to the microcrack density. Static moduli are affected by existing microcracks while dynamic moduli appear to be less affected by them. At large overburden stresses, most cracks are closed and the values of static and dynamic moduli approach each other.
The literature discussing the correlation between static and dynamic moduli of tight gas sandstones is very limited. Jizba and Nur and Jizba et al. reported that the relation between static and dynamic moduli in tight gas sandstones is controlled by stress and lithology.