Subsurface resistivity modeling with electromagnetic fields using a conductive casing
A method for efficiently calculating a subsurface distribution of electrical resistivity or conductivity generated by an electromagnetic (EM) source is provided wherein a significant fraction of the electric current produced by a source flows along a casing of a borehole. The method is comprised of two steps: calculating EM fields produced by the casing in the background lithology; and calculating EM fields caused by a resistivity anomaly in the presence of an EM field produced by the casing within a subsurface or survey model that does not include the casing.
1. A method for conducting an electromagnetic survey of subsurface targets of interest by calculating AC electromagnetic fields below an earth surface comprising:
modeling the earth below the earth surface using a known distribution of electrical resistivity, or a representative approximation of the electrical resistivity distribution derived from current or historical data, to form a subsurface model;
transmitting current from a source, at least in part, along a conducting casing of a borehole to produce a primary electromagnetic field, said field being a DC electric field;
calculating the primary electromagnetic field produced by the casing to determine a casing model and then create an equivalent electromagnetic source based on the casing model;
representing the casing within the subsurface model with the equivalent electromagnetic source embedded in the subsurface model, wherein the casing is removed from the subsurface model and the equivalent electromagnetic source is located where the casing was located;
calculating the AC electromagnetic fields produced by the equivalent electromagnetic source; and
determining a depth, thickness or lateral extent of the target of interest based on the AC electromagnetic fields produced by the equivalent electromagnetic source.
2. The method of claim 1 , wherein the electromagnetic fields are calculated at, or near to, the earth surface.
3. The method of claim 1 , wherein the electromagnetic fields include at least one horizontal electric field radial to the casing.
4. The method of claim 1 , wherein the equivalent electromagnetic source is one or more current dipoles.
5. The method of claim 4 , wherein the equivalent electromagnetic source is a series of current dipoles distributed along an axis where the casing was located.
6. The method of claim 1 , wherein the equivalent electromagnetic source is a series of potential values.
7. The method of claim 1 , wherein the equivalent electromagnetic source is a series of potentials distributed along an axis where the casing was located.
8. The method of claim 1 , wherein the equivalent electromagnetic source is a series of current dipoles distributed orthogonal to an axis where the casing was located.
9. The method of claim 1 , wherein the primary electromagnetic field is a DC field and the equivalent electromagnetic source has a time dependent component.
10. The method of claim 1 , wherein the primary electromagnetic field is a DC field, and the equivalent electromagnetic source is a current dipole having an amplitude determined from the DC field and a time dependent component determined by a waveform of the equivalent electromagnetic source.
11. The method of claim 1 , further comprising: establishing the primary electromagnetic field between two well casings.
12. The method of claim 1 , further comprising: including a resistivity anomaly which is a feature of the targets of interest within the subsurface model.
13. The method of claim 12 , wherein the targets of interest include a hydrocarbon reservoir produced by a process of hydraulic fracturing or established by an injected fluid, gas, proppant, tracer or marker.
14. The method of claim 12 , wherein the resistivity anomaly is at a depth of greater than 1 km, preferably greater than 1.5 km and most preferably greater than 2 km.
15. The method of claim 1 , wherein the subsurface model has more than 10,000 voxels, preferably more than 200,000 voxels, and even greater than 10,000,000 voxels.
16. The method of claim 1 , further comprising: individually calculating an effect of each electromagnetic source in a survey model and totaling the electromagnetic field at each measurement location by summing the effects of all sources.
17. The method of claim 1 , further comprising: employing a borehole to surface electromagnetic sounding configuration.
18. The method of claim 1 , further comprising: employing an electrode at depth within the borehole and distant counter electrodes at the earth surface as a sounding configuration.
19. The method of claim 1 , further comprising: employing a connection at or near a top of the borehole and distant counter electrodes at the earth surface as a sounding configuration.
20. The method of claim 1 , wherein calculating the primary electromagnetic field produced by the casing includes calculating an electric current distribution along an axis of the casing.
21. The method of claim 20 , wherein representing the casing within the subsurface model by the equivalent electromagnetic source includes representing the casing within the subsurface model by a set of equivalent current dipoles embedded at the location where the casing was located.
22. The method of claim 21 , further comprising, prior to calculating the electromagnetic fields produced by the equivalent electromagnetic source, calculating a current flow caused by the set of equivalent current dipoles in the subsurface model considering a presence of subsurface inhomogeneities.
23. The method of claim 22 , wherein calculating the electromagnetic fields produced by the equivalent electromagnetic source includes calculating the electromagnetic field at the surface that is caused by the current flow in the subsurface model including the presence of the subsurface inhomogeneities.