Modelling electromagnetic problems in the presence of cased wells

Electrical conductivity can be a diagnostic physical property for distinguishing geologic units and delineating the distribu- tion of fluids such as hydrocarbons and saline water within these units. Electromagnetic (EM) methods are sensitive to conductivity contrasts and can be used to characterize them. They are increasingly being applied in settings where cased wells are present. Most commonly-used casing materials, such as steel, are highly conductive, have a significant, often vari- able, magnetic permeability, and therefore significantly impact the behavior of the EM fields and fluxes. The aim of this pa- per is to revisit numerical modelling strategies to investigate the role of various properties and complexities due to the cas- ing, and present a modelling and inversion strategy, using a primary-secondary approach, for capturing the impacts of both the variable casing and three dimensional geologic structures on EM data.

Extended abstract available at: http://library.seg.org/doi/abs/10.1190/segam2015-5931035.1

Transcript

1. Modelling electromagnetic problems in the presence of cased wells Lindsey J. Heagy1, Rowan Cockett1, Douglas W. Oldenburg1 and Michael Wilt2 1University of British Columbia Geophysical Inversion Facility 2GroundMetrics
2. Why? Electrical conductivity can be a diagnostic physical property • e.g. Monitoring applications ◦ CO 2 sequestration ◦ Locating missed pay ◦ Enhanced Oil Recovery ▪ ie. water floods ◦ Hydraulic fracturing Source: http://www.oil-price.net/en/articles/novel-crude-oil-recovery.php
3. Why? Electrical conductivity can be a diagnostic physical property • e.g. Monitoring applications ◦ CO 2 sequestration ◦ Locating missed pay ◦ Enhanced Oil Recovery ▪ ie. water floods ◦ Hydraulic fracturing • EM sensitive to conductivity • Inversion: characterize conductivity distribution Want to characterize this
4. Why? This is a problem. Electrical conductivity can be a diagnostic physical property • e.g. Monitoring applications ◦ CO 2 sequestration ◦ Locating missed pay ◦ Enhanced Oil Recovery ▪ ie. water floods ◦ Hydraulic fracturing • EM sensitive to conductivity • Inversion: characterize conductivity distribution Want to characterize this
5. Steel casing in EM This is a problem. Physical Properties • highly conductive • significant (variable) magnetic permeability Significant impact on signals Geometry • cylindrical • thin compared to length Numerically challenging Want to characterize this
6. Overview Motivation: How do we characterize 3D conductivity distributions in settings with steel cased wells? Modelling 3D geology Modelling Maxwell’s equations Modelling the Casing Approaching the inverse problem
7. Constitutive Relations Electromagnetics: Maxwell’s Equations Maxwell’s Equations (frequency domain, quasi-static) electric field magnetic field magnetic flux density current density electrical conductivity magnetic permeability • Physical Properties • Fluxes • Fields
8. • Fields • Fluxes • Physical Properties Finite Volume Forward Modelling electric field magnetic field magnetic flux density current density electrical conductivity magnetic permeability
9. Two Formulations of Maxwell E-B Formulation: H-J Formulation:
10. Cylindrical mesh
11. Primary: Cylindrical Symmetry - Dipole Magnetic Dipole
12. Primary: Cylindrical Symmetry - Dipole Electric Dipole
13. Two Formulations of Maxwell E-B Formulation: H-J Formulation:
14. Modelling the casing
15. Modelling the casing: Source types magnetic flux density current density current density current density
16. Impact of magnetic permeability: magnetic flux density
17. Impact of magnetic permeability: current density
18. Impact of magnetic permeability: current density
19. Impact of Variable Magnetic Permeability
20. Variable Magnetic Permeability
21. Modelling with 3D geology What we have done • cylindrically symmetric • variable Casing & Source, Layered Earth • Steel casing has a significant impact on the signal ◦ conductivity and magnetic permeability ✓
22. Modelling with 3D geology What we have done • cylindrically symmetric • variable ,, Casing & Source, Layered Earth ✓ Want to model geologic structures • 3 dimensional • variable ? Fields from casing, 3D Earth
23. Modelling with 3D geology: Primary Secondary Primary: Secondary: 0 Casing & Source, Layered Earth Fields from casing, 3D Earth ✓ Interpolate
24. Modelling with 3D geology: Primary Secondary Primary: Secondary: Casing & Source, Layered Earth ✓ Interpolate
25. Primary-Secondary: 3D geology (magnetic dipole) Primary: Secondary: magnetic flux density secondary source current density Interpolate
26. Interpolate magnetic flux density Primary-Secondary: 3D geology (magnetic dipole) Primary: Secondary: Data Source in 3D Solve
27. Approaching the Inverse Problem ✓ ?
28. Approaching the Inverse Problem Estimate: Solve for: Interpolate to compute source Invert for 3D conductivity : Model dependence on RHS → need to include in sensitivities
29. Generalizing • Time domain EM ◦ similar approach can be applied • Non-symmetric settings: ◦ deviated or horizontal wells ◦ source outside of casing Source: http://docs.simpeg.xyz/en/latest/api_Mesh.html Source: http://www.drillingformulas.com/introduction-to-well-control-for-horizontal-wells/
30. Summary Motivation: How do we characterize 3D conductivity distributions in settings with steel cased wells? Modelling 3D geology Modelling Maxwell’s equations Modelling the Casing Approaching the inverse problem
31. Thank you! Thanks to: • developers of SimPEG and simpegEM • UBC GIF
32. References:
33. Using Conductivity Permeability product