Modular electromagnetic simulations with applications to steel cased wells

Interest in using electromagnetic methods for reservoir monitoring problems such as hydraulic fracturing, en- hanced oil recovery or carbon-capture and storage is motivating the need to examine the behaviour of electro- magnetic fields and fluxes in the presence of steel cased wells. In many of these scenarios, a transmitter is placed on or in the steel cased well. Such a scenario has large physical property contrasts, both in electrical conduc- tivity and magnetic permeability that are atypical of most geologic settings. Using this problem as motivation, we discuss a modular framework for simulating and computing sensitivities for electromagnetic problems. The implementation is a part of SimPEG, an open source package for Simulation and Parameter Estimation in Geophysics (Cockett et al., 2015). Two applications of EM simulations and inversions in reservoir monitoring settings are discussed. The first example demonstrates forward simulations on a cylindrically symmetric mesh to interrogate and visualize electromagnetic fields and fluxes in the presence of steel cased wells. The second example demonstrates a sensitivity analysis for a parametric model of a target within a reservoir layer.

Extended abstract available at: http://nebula.wsimg.com/d08e4f75db1a3988252f35a74b79db9d?AccessKeyId=C1B15BD8D0A222F3993D&disposition=0&alloworigin=1

Transcript

1. Modular electromagnetic simulations with applications to steel cased wells Lindsey Heagy, Rowan Cockett, Doug Oldenburg & the SimPEG team Geophysical Inversion Facility University of British Columbia
2. eg. Reservoir monitoring + steel casing eg. Airborne TDEM Oldenburg, BIRS 2016
3. building for researchers • Flexibility to experiment ◦ Prioritize organization and flexibility • Integration of information ◦ Geologic ◦ Multiple physics • Reproducible and transparent
4. • Modular: building blocks ◦ organized in a framework ◦ pieces available to manipulation • Declarative: express intent ◦ write what you mean ◦ looks like the math • Extensible: new research ◦ quantitative communication ◦ built in feedback loops • Open: for the future ◦ reproducible ◦ opportunities for collaboration building for researchers
5. building for researchers • Modular: building blocks ◦ organized in a framework ◦ pieces available to manipulation • Declarative: express intent ◦ write what you mean ◦ looks like the math • Extensible: new research ◦ quantitative communication ◦ built in feedback loops • Open: for the future ◦ reproducible ◦ opportunities for collaboration
6. (Cockett et al., 2015)
7. Implemented in Python! framework
8. forward simulation Survey: Data collection and geometry Problem: Physics
9. finite volume
10. create a mesh
11. discretize & solve continuous discrete
12. framework
13. Data Misfit Regularization Inverse Problem inversion elements
14. inversion as optimization
15. For second order optimization techniques, need data: And sensitivities: sensitivities
16. em + steel casing This is a problem. Want to characterize this (SEG Abstract: Heagy et al, 2015) Physical Properties • highly conductive • significant (variable) magnetic permeability Geometry • cylindrical • thin compared to length
17. • Fields magnetic flux density current density • Physical Properties • Fluxes Constitutive Relations Maxwell’s Equations (quasi-static) electric field magnetic field electrical conductivity magnetic permeability Time Frequency math!
18. primary magnetic flux density Interpolate secondary source current density Casing 3D Geology Data Simulate
19. Forward Inverse
21. ?
22. Model & Physical Properties: What should we invert for? (SEG Abstract: Kang et al, 2015) Derivatives using chain rule: or : • Active reservoir layer • Parametric representation • ... inversion model physical properties
23. ?
24. grounded electric inductive loop point dipole (electric or magnetic) fields from a primary problem natural source Sources: How do we excite the Earth?
25. ?
26. Solve 2nd order system Solve E-B, H-J ? or and compute derivative Physics: How do we solve Maxwell’s equations
27. ?
28. compute fields everywhere: what we solved for from source derivative Fields: How do we calculate the EM fields and fluxes? from source from physics
29. ?
30. ... Data: Receivers: What, and where, do we measure?
31. Plug in the pieces
32. Sensitivities
33. How do we know it works? Testing! • Taylor series
34. for example: casing & sensitivities What is the sensitivity with respect to the… • conductivity of the ◦ Block? ◦ Layer? ◦ Background? • Depth and thickness of the layer? • Location and widths of the block? Heagy et al. 2017 - in review
35. for example: casing & sensitivities
36. for example: casing & sensitivities
37. data
38. sensitivities • Need background model • Collect data away from the
39. summary • Modular, composable pieces ◦ Compartmentalize concerns ◦ All pieces available to manipulation ◦ extensible • Testing! ◦ Test pieces ◦ Test composite http://www.flickr.com/photos/13403905@N03/2080281038/
40. using numerical tools in education
42. http://em.geosci.xyz/apps.html
43. http://em.geosci.xyz/apps.html
46. thank you! simpeg.xyz geosci.xyz lheagy@eos.ubc.ca @
48. example: permeable casing 2Hz source, return electrode 10km away
49. Implemented in Python! framework
52. Airborne TEM example:
53. Ground loop TEM example
54. SimPEG MT: Magnetotellurics Rosenkjær et al 2015
55. eg. Reservoir monitoring + steel casing eg. Airborne TDEM