Estimation of Biot’s effective stress coefficient from well logs

Abstract

Effective stress governs the mechanical response of rock formations to variations in stress and pore pressure, which affect wellbore stability and reservoir integrity during drilling and production. Biot's coefficient is employed to calculate effective stresses from total stress and pore pressure. Therefore, the measurement of Biot's coefficient becomes crucial. However, the laboratory measurement of Biot's coefficient is expensive and laborious. This paper presents three methods for computing Biot's coefficient using logging data. The first method calculates Biot's coefficient using the existing empirical correlations between porosity and Biot's coefficient. The second and third methods calculate Biot's coefficient using dynamic rock and solid bulk modulus, computed using rock and solid wave velocities, respectively. However, the second and third methods calculate the necessary solid wave velocities in different ways. The second method calculates solid shear and compressive velocities (V s and V p ) using a newly developed correlation between the differential pressure, porosity and wave velocity of sandstone.The third method calculates solid wave velocities based on the significant finding that the V p /V s ratio with respect to the S-wave velocity is constant for sediments including highly compacted sand. Case studies were undertaken using logging data from the Gulf Coast Gas Wells. It was found that Biot's coefficient calculated using the first method was highly dependent on the chosen relation, while the coefficients calculated using the second and third methods were related to well logs. Results from the third method show that Biot's coefficient deflects to higher values in situations where gamma ray surveys read low API values. This is in agreement with the phenomenon that rocks with a smaller API should have lower a clay content and bigger value of Biot's coefficient. Therefore, the third method is more reliable and also requires fewer input parameters. Keywords Biot's coefficient measurement Á Well logging Á Measurement while drilling Á Effective stress Á Acoustic logging List of symbols r eff Effective stress [MPa] r total Total stress [MPa] a Biot's coefficient [-] p Pore pressure [MPa] / Rock porosity [-] K rock Rock bulk modulus [MPa] K solid Solid bulk modulus [MPa] E Young's modulus [MPa] t Poisson's ratio [-] V s Shear wave velocity [m/s] V p Compressive wave velocity [m/s] P d Differential pressure [MPa] C Clay content [-] X. Rock compressive wave velocity [m/s] V p solid Solid compressive wave velocity [m/s] V s rock Rock shear wave velocity [m/s] V s solid Solid shear wave velocity [m/s] V constant Constant wave velocity under high confining pressure [m/s] V solid Solid wave velocity [m/s]

Models of overpressure build-up in shallow sediments by glacial deposition and glacial loading with respect to chimney formation

“…Zweigel and Heill (2003) assumed that = 1 for the caprock. There have been reports of Biot coefficients for clay/shale with values of less than 0.5 (Luo et al 2015); however, these values are for more deeply buried rocks than the Nordland Shale, and with much less porosity. It is not unreasonable that the Biot coefficient could tend towards 1 for the Utsira caprock.…”

Anisotropic Rock Poroelasticity Evolution in Ultra‐low Permeability Sandstones under Pore Pressure, Confining Pressure, and Temperature: Experiments with Biot's Coefficient

“…The higher the Biot coefficient is, the bigger the stiffness of the pore is, the more difficult the pore is to be compressed. On the contrary, the lower the Biot coefficient, the smaller the stiffness of the pore is, the easier the pore is to be compressed (Tan et al, 2014;Yang et al, 2015;Luo et al, 2015;Pimienta et al, 2015;Straughan et al, 2018).…”

A framework for assessing the uncertainty in wave energy delivery to targeted subsurface formations

“…(21a), (21b), α is Biot's effective stress coefficient. Various correlations between the effective stress coefficient (α) and the porosity of the poroelastic solid (ϕ) are available in the literature (Luo et al, 2015;Lee, 2002). In this work, we use α = 1 − (1− ϕ) 3.8 .…”