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Simulation of an Electromagnetic Sounding Method for Oil Prospecting
Introduction
The marine controlled source electromagnetics method (CSEM) for oil prospecting has emerged as a promising technique during recent years. This example demonstrates one variant of it. It uses a mobile horizontal 1 Hz electric dipole antenna that is towed 150 m above the sea floor. An array of sea floor receivers measure the electric field at various distances away from the antenna. When measuring at sufficiently large distance, some of the transmitted energy is reflected/guided by the resistive reservoir and results in a higher received signal than if no reservoir were present.
Model Definition
The computational domain is a sphere of 5 km radius. The top region of this sphere represents air. At such a low frequency as 1 Hz, some numerical stabilization is required in this domain so an artificial conductivity of 0.001 S/m is specified. A 100 m deep ocean water domain with a conductivity of 3 S/m and a relative permittivity of 80 is specified above the midplane of the sphere. Below the midplane, a conductivity of 1.5 S/m and a relative permittivity of 30 is specified for the rock. Embedded in the rock at an average depth of 250 m, there is a block-shaped, 100 m deep and 4 km-by-1 km wide hydrocarbon reservoir. The conductivity of the hydrocarbon layer is 0.01 S/m and the permittivity is 4. The transmitter is modeled as a short 10 kA amplitude AC line current segment 150 m above the midplane. At the external spherical boundaries, a scattering type boundary condition absorbs outgoing spherical waves. The following equation is solved for the electric field vector E inside the computational domain:
where μr denotes the relative permeability, j the imaginary unit, σ the conductivity, ω the angular frequency, εr the relative permittivity, and ε0 the permittivity of free space.
Results and Discussion
The first figure below shows a slice plot of the electric field magnitude on a dB scale where the guiding effect of the hydrocarbon layer is clearly visible.
Figure 1: The electric field magnitude is plotted in a slice containing the antenna (red spot). The guiding effect of the hydrocarbon layer is clearly visible.
The effect is shown quantitatively in the next plot, where a comparison of the electric field magnitude on the sea floor is plotted as a function of distance for simulations with and without a hydrocarbon layer. The maximum is obtained right under the antenna where there is little difference between the two cases. When you move away from the antenna, there is a notably higher signal strength when the hydrocarbon layer is present.
Figure 2: Electric field magnitude on the sea floor as a function of distance. The dashed line represents the case without a hydrocarbon layer.
Notes about the COMSOL Implementation
This example uses the 3D Electromagnetic Waves formulation available in the RF Module although the wavelength is much larger than the computational domain. You could also create this example using a quasi-static formulation in the AC/DC Module.
Application Library path: RF_Module/Scattering_and_RCS/marine_csem
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Frequency Domain.
6
Click  Done.
Geometry 1
Sphere 1 (sph1)
1
In the Geometry toolbar, click  Sphere.
2
In the Settings window for Sphere, locate the Size section.
3
In the Radius text field, type 5e3.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 6e3.
4
In the Height text field, type 1e3.
Intersection 1 (int1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Intersection.
2
Click in the Graphics window and then press Ctrl+A to select both objects.
Sphere 2 (sph2)
1
In the Geometry toolbar, click  Sphere.
2
In the Settings window for Sphere, locate the Size section.
3
In the Radius text field, type 5e3.
Block 1 (blk1)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 4e3.
4
In the Depth text field, type 1e3.
5
In the Height text field, type 100.
6
Locate the Position section. From the Base list, choose Center.
7
In the z text field, type -250.
Line Segment 1 (ls1)
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
Locate the Endpoint section. From the Specify list, choose Coordinates.
5
Locate the Starting Point section. In the x text field, type -10 and z to 150.
6
Locate the Endpoint section. In the x text field, type 10 and z to 150.
Line Segment 2 (ls2)
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
Locate the Endpoint section. From the Specify list, choose Coordinates.
5
Locate the Starting Point section. In the x text field, type -5e3.
6
Locate the Endpoint section. In the x text field, type 5e3.
7
Click  Build All Objects.
8
Click the  Wireframe Rendering button in the Graphics toolbar.
Materials
Sea Water
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Sea Water in the Label text field.
3
Select Domain 1 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
80
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
3
S/m
Basic
Rock
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Rock in the Label text field.
3
Select Domains 2 and 4 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
30
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
1.5
S/m
Basic
Oil
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Oil in the Label text field.
3
Select Domain 4 only.
Note that this selection partly overrides the geometric scope setting that you just defined for rock. This allows you to later conveniently run the model for the case where there is no hydrocarbon reserve by simply disabling the Oil node.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
4
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0.01
S/m
Basic
Air
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Air in the Label text field.
3
Select Domain 3 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0.001
S/m
Basic
Electromagnetic Waves, Frequency Domain (emw)
Scattering Boundary Condition 1
1
In the Model Builder window, under Component 1 (comp1) right-click Electromagnetic Waves, Frequency Domain (emw) and choose Scattering Boundary Condition.
2
In the Settings window for Scattering Boundary Condition, locate the Boundary Selection section.
3
From the Selection list, choose All boundaries.
4
Locate the Scattering Boundary Condition section. From the Scattered wave type list, choose Spherical wave.
Edge Current 1
1
In the Physics toolbar, click  Edges and choose Edge Current.
You are now going to apply a current on the very short edge near the center of the geometry. This will be easier if you zoom in a few times.
2
Click the  Zoom In button in the Graphics toolbar.
3
Select Edge 17 only.
4
In the Model Builder window, click Edge Current 1.
5
In the Settings window for Edge Current, locate the Edge Current section.
6
In the I0 text field, type 1e4.
7
Click the  Zoom Extents button in the Graphics toolbar.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
In the table, clear the Use check box for Electromagnetic Waves, Frequency Domain (emw).
4
From the Element size list, choose Fine.
5
Click  Build All.
Study 1
Step 1: Frequency Domain
1
In the Model Builder window, under Study 1 click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type 1[Hz].
4
In the Home toolbar, click  Compute.
Results
Proceed to reproduce Figure 1.
Multislice
1
In the Model Builder window, expand the Results>Electric Field (emw) node.
2
Right-click Results>Electric Field (emw)>Multislice and choose Delete.
Slice 1
1
In the Model Builder window, right-click Electric Field (emw) and choose Slice.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type 20*log10(emw.normE).
4
Select the Description check box. In the associated text field, type Electric field norm, dB.
5
Locate the Plane Data section. From the Plane list, choose ZX-planes.
6
In the Planes text field, type 1.
7
In the Electric Field (emw) toolbar, click  Plot.
Cut Line 3D 1
1
In the Results toolbar, click  Cut Line 3D.
2
In the Settings window for Cut Line 3D, locate the Line Data section.
3
In row Point 1, set X to -5e3.
4
In row Point 2, set X to 5e3.
1D Plot Group 2
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose Cut Line 3D 1.
4
Click to expand the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Electric field norm, log scale.
Line Graph 1
1
Right-click 1D Plot Group 2 and choose Line Graph.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type 20*log10(emw.normE).
4
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 1 (comp1)>Geometry>Coordinate>x - x-coordinate.
5
In the 1D Plot Group 2 toolbar, click  Plot.
The plot you just generated should mimic the solid line in Figure 2. Proceed to compare this result with a model without the hydrocarbon reserve.
Materials
Oil (mat3)
In the Model Builder window, under Component 1 (comp1)>Materials right-click Oil (mat3) and choose Disable.
Study 1
Solution 1 (sol1)
1
In the Model Builder window, expand the Study 1>Solver Configurations node.
2
Right-click Solution 1 (sol1) and choose Disable.
This way you get a separate solver node for the second case.
3
In the Home toolbar, click  Compute.
Results
Multislice
1
In the Model Builder window, expand the Electric Field (emw) 1 node, then click Multislice.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type 20*log10(emw.normE).
4
Locate the Multiplane Data section. Find the X-planes subsection. In the Planes text field, type 0.
5
Find the Z-planes subsection. In the Planes text field, type 0.
6
In the Electric Field (emw) 1 toolbar, click  Plot.
Cut Line 3D 2
1
In the Results toolbar, click  Cut Line 3D.
2
In the Settings window for Cut Line 3D, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 2 (sol2).
4
Locate the Line Data section. In row Point 1, set X to -5e3.
5
In row Point 2, set X to 5e3.
Line Graph 2
1
In the Model Builder window, right-click 1D Plot Group 2 and choose Line Graph.
2
In the Settings window for Line Graph, locate the Data section.
3
From the Dataset list, choose Cut Line 3D 2.
4
Locate the y-Axis Data section. In the Expression text field, type 20*log10(emw.normE).
5
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 1 (comp1)>Geometry>Coordinate>x - x-coordinate.
6
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dashed.
7
In the 1D Plot Group 2 toolbar, click  Plot.