Anelastic attenuation is the process by which rocks convert compressional waves into heat and thereby modify the amplitude and phase of the waves. Understanding the causes of compressional wave attenuation is important in the acquisition, processing, and interpretation of high‐resolution seismic data, and in deducing the physical properties of rocks from seismic data. We have measured the attenuation coefficients of compressional waves in 42 sandstones at a confining pressure of 40 MPa (equivalent to a depth of burial of about 1.5 km) in a frequency range from 0.5 to 1.5 MHz. The compressional wave measurements were made using a pulse‐echo method in which the sample (5 cm diameter, 1.8 cm to 3.5 cm long) was sandwiched between perspex (lucite) buffer rods inside the high‐pressure rig. The attenuation of the sample was estimated from the logarithmic spectral ratio of the signals (corrected for beam spreading) reflected from the top and base of the sample. The results show that for these samples, compressional wave attenuation (α, dB/cm) at 1 MHz and 40 MPa is related to clay content (C, percent) and porosity (ϕ, percent) by α=0.0315ϕ+0.241C−0.132 with a correlation coefficient of 0.88. The relationship between attenuation and permeability is less well defined: Those samples with permeabilities less than 50 md have high attenuation coefficients (generally greater than 1 dB/cm) while those with permeabilities greater than 50 md have low attenuation coefficients (generally less than 1 dB/cm) at 1 MHz at 40 MPa. These experimental data can be accounted for by modifications of the Biot theory and by consideration of the Sewell/Urick theory of compressional wave attenuation in porous, fluid‐saturated media.

Compressional-and shear-wave attenuation data were calculated from sonic waveforms in three wells. The results show that at similar porosities and at in-situ conditions, gas and condensate sandstone reservoirs exhibit higher P-wave attenuation (lower P-wave quality factor, Qp) than either fully-water or partially "oil + water" saturated sandstones. However, S -wave attenuation and quality factor Qs do not show such a strong dependence on pore fluids. Furthermore, Qp/Qs < 1 indicates presence of gas or condensate, while Qp/Qs -1 indicates "full water" or "oil + water" saturation. These field data are INTRODUCTION

A general theory for the propagation of elastic waves in porous, fluid‐filled media was derived by Biot (1956a, b). A fundamental prediction of this theory is the existence of three body waves: a shear wave, a fast compressional wave, and a slow compressional wave.

Summary We developed an experimental method to obtain the Biot elastic constant of rocks from laboratory dynamic and static measurements. The Biot constant often has been calculated with various empirical equations. The experimental determination of the Biot elastic constant is very important to engineering problems associated with sand control, hydraulic fracturing, wellbore stability, earth stresses, sonic porosity, and estimation of compressional-, P, and shear-, S, wave velocity. Both the dynamic and static moduli of actual reservoir sandstone core samples, jacketed and mounted in a triaxial cell under vacuum, were measured at various confining and overburden stresses. The results obtained show that the Biot constant is a complex function of porosity, permeability, pore-size distribution, and overburden and confining stress, which means that it is not really a constant. Also, the static Biot constant is greater than the dynamic one and their difference increases with increasing overburden stress according to the equation astatic =[1+0.05*(sz)ef]*adynamic (where sz is in Ksi). Moreover, both the experimental static and dynamic Biot constants may be significantly different from values calculated with empirical equations. This study suggests that quantifying the Biot constant in the laboratory may enhance the determination of rock-strength/fracturing, earth stresses, rock subsidence, sanding predictions, P- and S-wave velocities, porosity, and pore fluid from sonic and seismic data. Introduction The Biot1–7 elastic constant, a, of a rock is an important poroelastic parameter that relates stress and pore pressure and describes how compressible the dry skeletal frame is with respect to the solid material composing the dry skeletal frame of the rock. Biot1 measures the ratio of the fluid volume squeezed out to the volume change of the rock if the latter is compressed while allowing the fluid to escape. It is described as Because the petroleum-related rocks are usually saturated, it is important to know how the saturation and pore pressure affect their mechanical and flow properties. Terzaghi's8 effective-stress principle for soils states that we can obtain the effective stress by simply subtracting the fluid pressure from the total stress; i.e., se=st -ap, which means that a=1. This implies that increasing the external stress by some amount produces the same volume change of the porous material as reducing the pore pressure with the same amount. This principle appears to be valid for most properties of soils. However, in petroleum-related rocks, Terzaghi's effective-stress principle may not be valid. Then, a modified effective stress is a function of the Biot constant, a, and given by sef=st -ap. Despite the great significance of a, only a limited amount of laboratory work on its determination has been reported in the literature.9–13 The failure criteria for a saturated rock with a pore pressure are obtained by introducing the effective stress into the dry form of the failure criteria. This means that all rock failure and sand-production prediction models require a known static Biot constant value. So far, researchers, engineers, and geophysicists quite often assume that a=1 (Terzaghi's principle), which is not necessarily true. Alternatively, for the determination of a, they may use various empirical equations.14–17 These equations, however, yield different values that may vary by up to 100% or more depending on the equation used. The primary objective of this study was to determine the Biot elastic constant experimentally, both by dynamic and static measurements, and to establish a correlation between the dynamic and static a. Another objective was to identify any rock properties controlling the Biot elastic constant. Experimental Determination of the Biot Constant In this experimental method, we determined both the dynamic and static moduli of actual reservoir sandstone core samples under high vacuum (&lt;0.15 mbar) and at various confining (s2=s3=sx) and axial (s1=sx) stresses. The vacuum was obtained and maintained in-situ while the rock sample was mounted and tested with a triaxial system. The rock sample is prepared, jacketed, and mounted in the triaxial cell. Then, the cell is closed firmly to prevent leaks and filled with the confining fluid. Vacuum is then pulled out of the sample with a high-power vacuum pump. Once the desired vacuum condition (&lt;0.15 mbar) is established, a multistage triaxial compression test is performed, as discussed in details elsewhere.18 Axial and confining stresses were applied hydraulically. The dynamic and static data were generated at various axial and confining stresses. At each confining-stress stage, several P and S waveforms were recorded as the axial (overburden) stress was increased. The measured P - and S-wave velocities were used to calculate the dynamic Poisson's ratio and the dynamic Bulk, Shear, and Young's moduli of the dry skeletal frame of the rock, Ksk.

In this paper we present data from several offshore wells, which have experienced wellbore stability related problems, especially over intervals with higher angles of deviation. We performed a wellbore stability evaluation for several angles of deviation using log, core and drilling data from all the existing wells, in order to predict the optimum drilling parameters to be used in the next wells to be drilled in this area. The answers provided by this study included properties such as, recommended mud-weights (minimum & maximum) as a function of angle of deviation, rock strength, and pore pressure. The determination of the rock strength along with the optimum mud-weight windows improved overall the drilling performance by minimizing washouts, loss of circulation, and optimizing casing design by elimination of unnecessary casing strings. Moreover, improvement of bit performance was achieved by using the predicted rock-strength values. As a result, drilling time and well construction costs were reduced significantly.