Simulating current flow through a well casing and an induced fracture

A method for determining a location of a fracture in a rock formation comprising:

• calculating an estimated electromagnetic field based at least in part on a hypothetical location of an induced fracture determined by a computer executing a model of a well system based on the rock formation;
• placing sensors above the rock formation as determined by the computer executing the model;
• electrically energizing a well casing and a fluid comprising a proppant in the fracture with an amount of electric current;
• outputting data that is indicative of an electromagnetic field caused by electric current in the well casing and proppant;
• acquiring data from a sensor that is indicative of an electromagnetic field at a location;
• causing a processor to access a computer-implemented model of a well system comprising the well casing, the computer-implemented model of the well system comprising a representation of the well casing and proppant as an energized transmission line that leaks electric current;
• and
• computing one or more characteristics of the fracture in the rock formation based at least in part upon the particular amount of electric current used to electrically energize the well casing and proppant in the fracture and the data acquired from the sensor;
• and
• wherein the representations of the electrically energized well casing and proppant comprises a plurality of two-port circuits coupled in series;
• and
• wherein computing the one or more characteristics of the fracture in the rock formation also comprises performing a comparison between the data from the sensor with the estimated electromagnetic field and outputting the one or more characteristics of the fracture relative to the comparison;
• and
• wherein the one or more characteristics are selected from the group consisting of location, size, orientation and length of the fracture.

A non-transitory computer-readable medium for determining a fracture location in a rock formation, comprising instructions that, when executed by a processor, cause the processor to perform acts comprising:

• receiving a computer-implemented model of a well system that is configured to extract natural gas from a rock formation beneath the surface of the earth, the computer implemented model comprising:
• a representation of an electrically energized well casing as a transmission line that leaks electric current;
• a representation of a hypothetical fracture in the rock formation as the transmission line that leaks electric current;
• an amount of electric current utilized to energize the well casing;
• and
• a location on the well casing where the electric current is initially applied to energize the well casing;
• computing an expected electromagnetic field at the surface of the earth caused by the electric current traversing the well casing and the hypothetical fracture leaking from the well casing and the hypothetical fracture based at least in part upon the computer implemented model;
• computing sensor locations that are optimized to receive the expected electromagnetic field;
• receiving sensor data indicative of an electromagnetic field caused by an electric current in an electrically energized well casing and proppant in a fracture;
• calculating an electromagnetic field from the received sensor data;
• comparing the computed and expected electromagnetic fields to determine one or more characteristics of the fracture in the rock formation;
• and
• wherein the one or more characteristics are selected from the group consisting of location, size, orientation and length of the fracture.