Calibration of gradiometer tools using current loop with finite dimension and ranging operation

A method for ranging using a gradiometer tool comprising,

• providing a current loop of known finite dimensions;
• disposing a gradiometer tool, including at least one magnetic field sensor, at a known distance (R) from a primary linear current source component of said current loop;
• while flowing a known current (I) through said current loop, measuring a first set of induced measurements from said at least one sensor over a range of tool face angles (β);
• from said first set of induced measurements, generating a first sensor measurements matrix (MS);
• modeling a set of synthetic magnetic field values extent at said at least one sensor over said range of tool face angles due to said current loop of known finite dimensions, said gradiometer tool, and said current;
• calculating at least one effective distance (Reff) corresponding to at least one of said set of synthetic magnetic field values using a gradient concept of infinite line source;
• creating a calibration design matrix (DMC) using said at least one effective distance;
• calculating a tool calibration matrix (TC) characterizing said gradiometer tool from said calibration design matrix and said sensor measurements matrix;
• disposing said gradiometer tool in proximity to a second current source;
• measuring a second set of induced measurements induced by said second current source from said at least one sensor;
• from said second set of induced measurements, generating a second sensor measurements matrix (MS);
• and
• determining a design matrix (DM) from said second sensor measurements matrix and said tool calibration matrix.

A gradiometer tool comprising:

• at least one magnetic field sensor;
• a processor;
• and
• a memory storing a recovery matrix (R) obtained by modeling a set of magnetic field values extent at said at least one sensor over said range of tool face angles due to a known current (I) flowing through a current loop of known finite dimensions at a known distance with respect to said gradiometer tool and calculating at least one effective distance (Reff) corresponding to at least one of said set of synthetic magnetic field values using a gradient concept of infinite line source.

A ranging system comprising:

• a current source disposed within a target first wellbore;
• a drilling string disposed in a second wellbore proximal to said current source;
• and
• a gradiometer tool included along said drilling string and having at least one magnetic field sensor, a processor, and a memory storing a recovery matrix (R) obtained by modeling a set of synthetic magnetic field values extent at said at least one sensor over said range of tool face angles due to a known current (I) flowing through a current loop of known finite dimensions at a known distance with respect to said gradiometer tool and calculating at least one effective distance (Reff) corresponding to at least one of said set of synthetic magnetic field values using a gradient concept of infinite line source.