CO2 sequestration crosswell monitoring based upon spectral-element and adjoint methods Christina Morency Department of Geosciences, Princeton University Collaborators: Jeroen Tromp & Yang Luo Computational Geosciences Seminar Series- Sept. 27, 2010 - Stanford
34
Embed
CO2 sequestration crosswell monitoring based upon …cees.stanford.edu/docs/CEES-Morency.pdf · CO2 sequestration crosswell monitoring based upon spectral-element and adjoint methods
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
CO2 sequestration crosswell monitoring basedupon spectral-element and adjoint methods
Christina Morency
Department of Geosciences, Princeton UniversityCollaborators: Jeroen Tromp & Yang Luo
1) Numerical simulation of wave propagation:spectral-element method (SEM)
2) Imaging and inversion:finite-frequency sensitivity kernels based on adjoint method
3) Application: CO2 sequestration monitoring
=> using seismic data for imaging & inversion of subsurface properties
Forward wave propagationbased on SEM
Three rheologies
Elastic:
Poroelastic [Biot, 1962]:
Acoustic, inviscid fluid and neglecting gravity effects [Chaljub and Valette, 2004;Komatitsch et al., 2005]:
where the displacement and the acoustic pressure
{B, C and M are the Biot coefficientsdefined in terms of solid, fluid, andframe properties
In an isotropic case:and
where
Three & 1/2 rheologies continued
Elastic with Gassmann’s formulae [Gassmann, 1951]:
In an isotropic case:and
Effective saturated bulk & shear moduli:
Poroelastic governing equations
Microscopic equations for the solid and fluid phase:• Conservation of mass• Constitutive relationships (Hooke’s law, Navier-Stokes)• Conservation of momentum
Macroscopic equations of the biphasic porous medium:
=> Access to different information depending on the measurements used
Final model update
P-wavespeed
S-wavespeed
Final model update
Bulk density
Final model update
Fluid bulk modulus
Fluid density
Conclusions
1) Forward & adjoint wave propagation:- SEM highly suitable for parallel computation- Sensitivity kernels defined based upon an adjoint method
2) CO2 sequestration monitoring:=> poroelastic signature in data- full iteration procedure- poroelastic inversion: accurate + fluid properties- next: use real data- next: use the full signal (FLEXWIN software, Maggi et al. 2009)- next: strategy to take advantage of all poroelastic kernels