Passive-magnetic ranging capability for relief wells in salt formations

Ranging and homing-in methods are required for intercepting target wells by a relief well, as survey position uncertainty is commonly too large for enabling first-time successful direct interception. An interception might be needed to make a hydraulic connect with a blowout well or to re-enter an abandoned well. Passive homing-in methods often use measurement-while-drilling (MWD) survey data for steering a relief well toward a target well.^1,2 The methods rely on the magnetism from steel casings in the target well. The magnetism can be of remnant nature or can be artificially induced prior to casing installation. Furthermore, explicit assumptions are made regarding the magnetism, especially on the strength and distribution of the magnetic poles along the casing. These methods are complex³, and experience shows that they can result in sub-optimal estimates of the distance to, and the direction toward the target well, potentially resulting in significant operational time delays.

This publication addresses a new method that uses MWD survey data for estimation of the distance to, and the direction toward the target well, using only qualitative assumptions for the magnetic field from the casing. The method is referred to as passive-magnetic triangulation ranging (PMTR). Application of PMTR is preferred over industry-proven active ranging methods in salt formations; for example, in Brazil, the Gulf of Mexico, Oman and the North Sea areas. In these areas, active ranging methods cannot be (easily) utilized, as the non-conductive nature of salt formation hampers electric current injection when using active ranging tools. PMTR is now a viable ranging and homing-in option in operators' well control contingency plans.

METHOD

When drilling a relief well toward a target well (Fig. 1), the magnetic field b_MWD as measured by the MWD tool in the relief well, will be a combination of Earth's magnetic field b_earth (known from models or in-situ measurements), the interference ∆b_BHA from the Bottom Hole Assembly (BHA) (is calibrated) and the disturbance Δb due to the target well casing magnetism. PMTR determines the disturbance Δb at each “measurement station” by:

which applies in absence of crustal magnetic anomalies. Note that vector quantities are written in a boldface font.

Fig. 1. MWD survey instrument nearing a target well.

As the magnetic MWD measurements are used for well ranging, it is required that a gyro is also used along the relief well, where there exists magnetic interference from the target well. The gyro data then forms the basis for the calculation of the 3D well path and associated geometric properties of the relief well.

Figure 2A shows the cross-wellbore plane of the target well and illustrates the magnetic field originating from two assumed magnetic (North and South) poles along the target well casing. Figure 2B shows the radial plane and field line through a “measurement station”, i.e. at which an MWD-measurement is taken. The position x_r represents the location of one measurement station on the relief well path. The vectors h_r, r_r and a_r are the corresponding high-side, high-side-right (together determining the local cross-wellbore plane) and axial directions of the relief well. The position x_t is the intersection location of the target well path, with the cross-wellbore plane of the relief well being considered.

The remnant field is assumed to be axisymmetric about the target well, and thus Δb only has axial and radial components within the radial plane (Fig. 2B). Therefore, the vector Δb and the relative well position x_t-x_r must be within the same radial plane of the target well. This is the only information of the casing magnetic field that is used by the PMRT method.

Figure 3 extends this concept for a multi-measurement station context, when the relief well has been drilled for some distance along the target well, i.e. the “ranging interval.” The positions x_r, the corresponding local direction vectors h_r, r_r, a_r, cross-wellbore plane and interference Δb are shown for the two measurement stations with numbers i and j (Fig. 3A), but in a practical application, several thousands of stations and associated cross-wellbore planes may be used. As the relief well path can build and/or turn along the ranging interval, the cross-well bore planes for the local h_r and r_r vectors at the subsequent measurement stations change accordingly, i.e. are not all parallel. For each measurement station, there also exists the position x_t at which the target well path intersects the relief cross-wellbore plane under consideration.

Figure 3B further illustrates the situation in the cross-wellbore plane of a single measurement station. PMTR only uses the components of Δb along the high-side and high-side right directions in the relief cross-wellbore plane:

and thus, that any component of ∆b along the axial direction a_r can be ignored, including Δb_BHA.

The magnitude of the transverse component Δb_t within a relief cross-wellbore plane is calculated by:

The corresponding magnetic interference toolface angle τ_m is determined by:

and the corresponding unit direction vector d_m is calculated by:

Based on the axisymmetry properties of the magnetic field around the target well casing, the target well position x_t, which is the key unknown to be found using PMTR, should be located relative to x_r somewhere along the direction d_m. However, as the direction of Δb depends on the axial position relative to the magnetic poles (Fig. 2B), one does not know whether it is located in the positive direction d_m, or perhaps in the opposite direction –d_m. Thus, the calculated toolface angle τ_m, or the direction d_m, can be in error by 180˚, as compared to the actual orientation between the two wells.

Fig. 2. Axisymmetric magnetic field, due to assumed South and North poles on the target well and a measurement station on the relief well. View in the target well cross-wellbore plane (A) and the field line in the radial plane through the measurement station (B).

Fig. 3. Multiple measurement stations on the relief well and the corresponding positions of the target well in the relief cross-wellbore plane (A) and the various (vector) quantities in the relief cross-wellbore plane of a single measurement station (B).

Thus, the magnetic toolface angle τ_m cannot be used directly as the orientation for drilling the relief well toward the target well for making the actual intercept. Also, the magnetic toolface angle τ_m can only be accurately calculated at measurement stations at which ∆b_t is sufficiently large. This condition is not met at locations where Δb is directed predominantly parallel to the relief well; for example, when located about half-way between opposite magnetic poles along the target well casing. Therefore, PMTR combines the usable data on τ_m with the calculated well paths.

Calculated target well position. Survey measurements are taken during drilling operations in the wells. Together with the known surface locations, the 3D well path of both wells is calculated in a common coordinate reference system and depth reference system.⁴ However, the survey measurements carry an uncertainty in well position. Figure 3 illustrates the calculated position x_t,calc of the target well in a relief cross-wellbore plane. Note that x_t,calc contains a position uncertainty in the target well position, whereas the x_t is the target well position without position uncertainty, which is unknown.

Uncertainty correction approach. The position uncertainty of both wells along the ranging interval are represented in PMRT by a single, to-be-solved relative position uncertainty u, which lumps the position uncertainties of both wells together. This is accounted for by assuming that the position uncertainties of the relief well are zero, and thus the target well position is approximated by:

and thus, no longer represents an absolute position, as in reality the relief well position x_r contains an uncertainty too. The objective is to solve u, in order to calculate the exact position of the target well, relative to the relief well. This is discussed in the following.

Relative well positions. The well position difference Δx between the relief well position x_r and the target well position x_t,calc in the relief cross-wellbore plane at a measurement station is defined by:

The components of Δx along the high-side and high-side-right directions of the local cross-wellbore plane are given by (Fig. 3B):

The transverse component Δx_t in the plane is calculated by:

and corresponds to the calculated center-to-center distance between the wells. The corresponding geometric toolface angle τ_x is determined by:

Due to position uncertainties, this toolface orientation τ_x is generally different from the magnetic interference toolface angle τ_m toward the target well, as following from the magnetic interference calculations (even when ignoring the 180° ambiguity therein).

Calculated target well position uncertainty. As discussed in the above, PMTR approximates the relative well position uncertainty u as constant for the entire ranging interval. This is first-order correct, as the ranging interval is only short as compared to the along-hole distance from surface to the ranging interval / interception point. Thus, u represents the mean, combined position uncertainty as accumulated along the well trajectories from their surface location to the ranging / interception depth. Position uncertainty variations / differences within the ranging interval are thus considered of second order and are thus neglected.

From Fig. 3B, it can be inferred that when the target well position x_t,calc  is shifted / corrected by u, then the corresponding toolface angle τ_x would become equal to τ_m. Furthermore, the toolface angle τ_m, or equivalently the direction d_m, resulting from a single MWD measurement does not fully define u. Namely, any shifted well position x_t,calc+u located along the d_m direction (relative to x_r) will achieve consistency between the toolface angles τ_m and τ_x. Therefore, multiple measurement stations, having distinct toolface angles τ_m, must be combined to fully solve u. This can be achieved using non-linear least-squares fitting, which is outlined in the following.

Solving the target well position. In the context of near-parallel well intercepts, the lateral position uncertainties are particularly relevant. Furthermore, as the PMTR method essentially uses toolface orientation information, it is deemed less accurate in estimating the axial position uncertainties. Therefore, the position uncertainty / target well shift u is solved only in 2D sub-space as:

where h_t,int and r_t,int are respectively the (fixed) high-side and high-side right direction vectors of the target well at a chosen depth near the interception location and the corresponding (to-be-solved) lateral position uncertainties are u_h and u_r. By this approach, the target well is shifted parallel to itself within a single, representative cross-wellbore plane, but there are also other approaches possible (e.g. shifting the well in the horizontal plane).

It is assumed that at a certain stage of the solution process, the trial / estimate u'for the shift vector u is available, (Fig. 3B). This vector is determined by only two trial / estimate values u'_h and u'_r for the lateral position uncertainties and chosen directions as per equation (11). The corresponding (trial) shifted target well position for a measurement station is defined by:

whereby the 'un-shifted' position x_t,calc must be calculated / adjusted, such that the resulting shifted position x'_t,calc is located within the relief cross-wellbore plane under consideration. Namely, the along-hole depth (AHD) of the calculated plane position may change, due to the applied shift. Furthermore, the shift vector u' applied to the entire target well may not be perfectly parallel to the cross-wellbore plane of the station under consideration, and thus x_t,calc may become located slightly off-plane to compensate for this.

Least-squares fitting, based on differences between the magnetic interference toolface angle τ_m and the toolface angle for the shifted position x'_t,calc is impractical, as τ_m can be off by 180°. Therefore, the following alternative approach is used. The unit direction vector p_m is calculated at each measurement station by:

which is perpendicular to d_m. The shifted (trial) position x'_t,calc for a measurement station may not (yet) be located along the direction d_m, (Fig. 3B). This is quantified during the solution process by means of the projected error y for the trial position that is defined by:

The cumulative quadratic error Q over all measurement stations along the ranging interval is defined by:

where the index i for quantities refers to the number of a measurement station and n is the total number of measurement stations along the ranging interval. In practice, only stations should be incorporated at which the magnitude of the transverse component Δb_t exceeds a minimum value, and so the resulting direction p_m is well-defined.

The sought solutions for the lateral position uncertainties u'_h and u'_r minimize Q through their effect on the position x'_t,calc at each station as per equation (12). The final trial position x'_t,calc at each station then corresponds to the sought target well position x_t relative to the relief well position x_r. This (non-linear) minimization problem can be solved using standard numerical methods.⁵

METHOD VALIDATION

In a recent North Sea offshore well intervention project, a relief well was drilled to successfully intersect a target well above the reservoir. During this project, the measurements, as required for applying PMTR, were collected. The operator shared these data, which offered the opportunity to validate PMTR. The relief well was drilled along the target well over a ranging interval of about 800 ft long, before the interception was made. During this, the well inclination increased from about 32° to 42°. Figure 4A shows toolface angles τ_m resulting from the magnetic interferences as per equations (4).

At the depth of 11,400 ft-AHD, the relief well was positioned approximately above the target well (τ_m ≈ 172°) after which relative steering was applied to the left and downwards (τ_m ≈ 235° at 11,800 ft-AHD). Jumps of 180° occur at many locations (and also erroneous intermediate values occur) at locations where the magnitude of the transverse component Δb_t as per equation (3) of the calculated magnetic interference is small. Figure 4A also shows the toolface angles τ_m calculated from the original surface position and directional data set for both wells using equation (10). The agreement between the toolface angle profiles is poor, which is attributed to well position uncertainties.

The PMTR method has been applied, using the stations on the relief well on the depth range 11,400 to 11,807 ft-AHD for the least-squares fitting. Furthermore, only stations have been incorporated in the fitting for which Δb_t>2 µT , such that the used toolface angle τ_m and the associated direction vectors d_m and p_m were well-defined. The target well was shifted within its cross-wellbore plane at the depth of 11,363 ft-AHD on the target well (approximately half-way on the ranging interval). No axial shift has been incorporated, and the solutions for the lateral well shifts were u_h = –5.15 ft and u_r = –8.36 ft. Figures 4B and 4C show, respectively, the toolface angles τ_x' and the relative well distances Δx'_t at the measurements stations after solving and correcting for the position uncertainties. The series τ_m,corr now has the 180° ambiguity for the magnetic toolface angle resolved.

Fig. 4. Application of the PMTR method for a field case. (A) Shows the toolface angles between the wells resulting from the magnetic interferences and position calculations without application of PMTR. (B) and (C) show the calculated toolface angles and center-to-center distance after solving and correcting for the lateral position uncertainties. Also shown are results of the gyro surveyed proximity between the two wells, projected back over the PMTR interval after tying the surveys to the same coordinates at the interception depth.

Based on the intersection position actually encountered, the actual relative well positions, toolface and center-to-center distance could also be calculated in a backward manner. For the toolface angles, the agreement between both methods is excellent. For the calculated relative distances, there exists a difference in trends over the first part of the ranging interval, up to 11,500 ft-AHD, but over the ranging interval, the agreement is good. As the profiles of the toolface angles are consistent and the same geometric calculation principles are used for the relative well distances, it is reasoned that this trend difference is caused by factors other than the PMTR method.

CONCLUSIONS

The passive-magnetic triangulation ranging method (PMTR) can be used for homing-in to a target well. It uses a combination of MWD measurements and calculated 3D well paths for the accurate estimation of the distance to, and the direction toward the target well. The key building blocks that are found to be sufficient for the applicability of method are:

• Prior to the interception, the relief well should follow the target well over a “ranging interval” in close proximity and under varying relative lateral orientation, i.e. significantly non-perfectly parallel.
• An independent relief well (gyro) survey is required, as the MWD magnetic measurements are used for ranging.
• The magnetic field of the casings of the target well is assumed to be axisymmetric. The corresponding MWD-measured magnetic field disturbance vector should then theoretically be within the same radial plane of the target well as the relative position between the wells.
• The well position uncertainties of both wells over the ranging interval are lumped into a single, to-be-solved relative position uncertainty.
• This relative position uncertainty is accounted for as a (lateral) shift that is applied to the entire 3D well path of the target well.
• Least-squares fitting, using a large number of MWD measurements, allows solving the relative position uncertainty and thus the calculation of the exact (shifted) position of the target well, relative to the relief well.

PMTR is preferred over the industry standard active ranging method in the salt formations that are common in many basins worldwide. The method is considered a viable option in an operator's well control contingency plans. In the near future the PMTR capability will also be applied for well anti-collision design and drilling execution. This opportunity enables to obtain further experience and to achieve continuous operational implementation.

REFERENCES

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2. Robinson, J.D., and J.P. Vogiatzis, “Method for determining distance and direction to a cased borehole using measurements made in an adjacent boreholes,” US 3725777, 1973.
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