Bayesian inversion of pressure diffusivity from microseismicity

We have considered the problem of using microseismic data to characterize the flow of injected fluid during hydraulic fracturing. We have developed a simple probabilistic physical model that directly ties the fluid pressure in the subsurface during the injection to observations of induced microseismicity. This tractable model includes key physical parameters that affect fluid pressure, rock failure, and seismic wave propagation. It is also amenable to a rigorous uncertainty quantification analysis of the forward model and the inversion. We have used this probabilistic rock failure model to invert for fluid pressure during injection from synthetically generated microseismicity and to quantify the uncertainty of this inversion. The results of our analysis can be used to assess the effectiveness of microseismic monitoring in a given experiment and even to suggest ways to improve the quality and value of monitoring

A Fully Analytical Solution of the Wellbore Stability Problem under Undrained Conditions Using a Linearised Cam-Clay Model

This paper presents a linearised version of the Cam-Clay model fully integrated in the scope of the general theory of poroplasticity. The constitutive law which is developed in the scope of the effective plastic stress concept, only contains two plastic parameters (hardening modulus and slope of the critical state line). To be validated, the model is integrated over homogeneous stress paths (hydrostatic, drained triaxial and undrained triaxal) then compared with experimental data issued from conventional laboratory triaxial tests. In the second part, a simplified version of the model is applied to the wellbore boundary problem (vertical well) in an axisymmetric horizontal stress field and under undrained conditions. Given the linearity of the constitutive law and the a priori knowledge of the shape of the plastic region, the solution (stress, strain and pore pressure) is fully analytical. The solution shows that for an overconsolidated material (overconsolidation degree less than 2) the hoop stress is strongly relaxed in the plastic zone. The higher the compressibility of the saturating fluid, the larger the relaxation of the hoop stress. In terms of stability, the more compressible the fluid saturating the porous medium is, the more stable the well will be. Finally the larger the overconsolidation ratio is, the less stable the well will be

A Fully Analytical Solution of the Wellbore Stability Problem under Undrained Conditions Using a Linearised Cam-Clay Model

International audienceThis paper presents a linearised version of the Cam-Clay model fully integrated in the scope of the general theory of poroplasticity. The constitutive law which is developed in the scope of the effective plastic stress concept, only contains two plastic parameters (hardening modulus and slope of the critical state line). To be validated, the model is integrated over homogeneous stress paths (hydrostatic, drained triaxial and undrained triaxal) then compared with experimental data issued from conventional laboratory triaxial tests. In the second part, a simplified version of the model is applied to the wellbore boundary problem (vertical well) in an axisymmetric horizontal stress field and under undrained conditions. Given the linearity of the constitutive law and the a priori knowledge of the shape of the plastic region, the solution (stress, strain and pore pressure) is fully analytical. The solution shows that for an overconsolidated material (overconsolidation degree less than 2) the hoop stress is strongly relaxed in the plastic zone. The higher the compressibility of the saturating fluid, the larger the relaxation of the hoop stress. In terms of stability, the more compressible the fluid saturating the porous medium is, the more stable the well will be. Finally the larger the overconsolidation ratio is, the less stable the well will be