System and Method for Combined Streaming Potential and Controlled-Source Electromagnetic Modeling

A method of imaging saturation or permeability of a formation, comprising:

• positioning a controlled source electromagnetic (CSEM) transmitter on a surface of the earth relative to a borehole;
• positioning a plurality of CSEM receivers relative to the borehole, synchronized with the CSEM transmitter;
• transmitting signals from the CSEM transmitter into a subsurface formation about the borehole;
• receiving by the plurality of CSEM receivers a secondary electromagnetic (EM) field corresponding to the signals transmitted from the CSEM transmitter coupled with a streaming potential at a location where fluid is being injected into the subsurface formation;
• measuring the secondary EM field;
• and
• calculating a saturation or permeability of the formation by performing an inversion on an objective function based on the secondary EM field and a function transforming saturation or permeability into the secondary EM field.

A method of determining an injection or flowback rate into or from a subsurface formation, comprising:

• positioning a controlled source electromagnetic (CSEM) transmitter on a surface of the earth relative to a borehole;
• positioning a plurality of CSEM receivers relative to the borehole, synchronized with the CSEM transmitter;
• transmitting signals from the CSEM transmitter into a subsurface formation about the borehole;
• receiving by the plurality of CSEM receivers a secondary electromagnetic (EM) field corresponding to the signals transmitted from the CSEM transmitter coupled with a streaming potential at a location where fluid is being injected into the subsurface formation;
• measuring the secondary EM field;
• and
• performing a reservoir simulation based on the injection or flowback rate by performing an inversion on an objective function based on the secondary EM field and a function transforming a pressure or gradient of a pressure field to the secondary EM field.

A method of calculating electrical and magnetic fields in a subsurface formation, comprising:

• positioning a controlled source electromagnetic (CSEM) transmitter on a surface of the earth relative to a borehole;
• positioning a plurality of CSEM receivers relative to the borehole, synchronized with the CSEM transmitter;
• transmitting signals from the CSEM transmitter into a subsurface formation about the borehole;
• receiving by the plurality of CSEM receivers a secondary electromagnetic (EM) field corresponding to the signals transmitted from the CSEM transmitter coupled with a streaming potential at a location where fluid is being injected into the subsurface formation;
• measuring the secondary EM field;
• and
• calculating a streaming potential current from a cross-coupling coefficient between a fluid and electric flow and a pressure field;
• calculating electrical and magnetic fields based on an exciting current and a streaming potential current.