Exploring the physics of electromagnetics with steel-cased wells using open-source tools Lindsey Heagy & Doug Oldenburg IUGG 2019 

A motivating example Subsurface injections (hydraulic fracturing) 2 

A motivating example 3 Maxwell’s equations (quasi-static) time frequency constitutive relations Subsurface injections (hydraulic fracturing) 

Outline ● Numerical modelling ● DC Resistivity ● Electromagnetics ○ Conductivity ○ Permeability 4 

Modelling EM on cylindrical meshes ● Finite volume discretization ○ cylindrically symmetric ○ 3D cylindrical meshes ● DC, FDEM, TDEM ● Open source ● Implemented in SimPEG 5 Heagy & Oldenburg, 2018 

DC resistivity 6 Kaufman, 1990 Validating the physics ● Kaufman (1990): Charges, currents, electric fields ● Augustin (1989): magnetic permeability 

7 currents charges short well long well DC Resistivity DC Resistivity: fundamentals ● Kaufman (1990), Kaufman & Whitman (1993), Schenkel & Morrison (1994) ● Cross-sectional conductance (S · m) ● Implications ○ Survey design ○ Approximating wells (to reduce computation) ○ Sensitivity in an inversion 

DC Resistivity: casing integrity 8 

DC Resistivity: data at the surface Intact well 9 primary Secondary (flawed - intact) 

DC resistivity with steel-cased wells ● Casing integrity ● Survey design considerations ● Detecting a target ○ Conductor, resistor ○ Electrical connection vs. not 10 Signal due to target resistor conductor 

EM: conductive well 11 Current density (A/m2) 

EM: permeable well 12 t = 5ms t = 10ms t = 1ms conductive permeable 

EM: permeable well 13 conductive permeable 

EM: permeable well 14 

EM: permeable well 15 conductive permeable difference 

Summary DC 16 EM: conductive t = 10ms permeable conductive EM: permeability currents: galvanic + image + channelled 

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