Magnetostatic Methods for Estimating Distance and Direction from a Relief Well to a Cased Wellbore
Authors: Robinson J.D. , Vogiatzis J.P. 
Published: December 2007

Remanent magnetization in casing, caused by certain casing inspection procedures, can be detected in adjacent wells by wireline surveys. Such procedures, can be detected in adjacent wells by wireline surveys. Such survey data were used to calculate both distance and direction from a relief well to the Piney Woods, Mississippi, blowout well, and made it possible to intersect the well within 9 inches of the point predicted. possible to intersect the well within 9 inches of the point predicted. Introduction
We shall consider the problem of determining the distance and direction to a cased wellbore from a relief well. The magnetic state of the casing is central to the problem, and we shall consider three possibilities in the order in which they were considered when we were asked to guide a relief well to Shell Cox No. 1, a blowout well in the Piney Woods area, Mississippi. First, we assume there is no remanent magnetization in the casing. Second, we assume a remanent magnetization of the character of that found for P-110 casing inspected by electromagnetic induction with the Tuboscope Amalog IV System. Third, we assume a remanent magnetization of the form that was found for casing inspected with the Amalog IV System, but that had also been subjected to large tensile stresses at the time of the blowout and then to the large compressive stress caused by supporting some 10,000 ft of casing from the point at which it was cemented to a depth of a few thousand feet, where the casing presumably parted. For the second and third conditions of the casing, methods will be given for determining the distance and direction to the cased well based on gyro and magnetic multishot surveys (from which is deduced an apparent magnetic declination from the difference between the azimuth readings of the gyro and magnetic compasses) and a magnetometer survey in the relief well.

Theory

Casing with No Remanent Magnetization
If the casing of the object well has no remanent magnetization, then the physical problem is to determine the magnetic field in the neighborhood of a very long hollow cylinder of material with high magnetic permeability standing vertically in the earth and subjected to the magnetic field of the earth. In Appendix A we have derived the form of the field from a scalar potential and appropriate boundary conditions. In cylindrical potential and appropriate boundary conditions. In cylindrical coordinates, with the radius, r, to any point (r, 0) measured from the axis of the cylinder and 0 measured counter-clockwise from the north, the total field exterior to a cylinder of outer radius r2 is, in the most favorable case of infinite permeability of the cylinder, given by
(1)
where B H and Br are the horizontal and vertical components of the unperturbed field of the earth, respectively; and r, and z are unit vectors. B H and B v are reckoned positive northward and downward. Consider the magnetic field at r = 3 ft. The maximum effect from the casing will be when = 0, /2, 3 /2; and the maximum deviation from unperturbed value of the field will be 160 ( = 10(−5) gauss), or about three parts per 1,000 at those locations. At r = 6 ft, the maximum deviation in total field will be 40, which is of the order of variations due to changes in lithology.
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