# December 2020 /// Vol 12 No. 241

## Special Focus

# Passive-magnetic ranging capability for relief wells in salt formations

A new triangulation method, using MWD survey data, provides operators a viable ranging and homing option for well control contingency planning.

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 complex^{3}, 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**(known from models or in-situ measurements), the interference ∆*

_{earth}

*b**from the Bottom Hole Assembly (BHA) (is calibrated) and the disturbance Δ*

_{BHA}**due to the target well casing magnetism. PMTR determines the disturbance Δ**

*b***at each “measurement station” by:**

*b** *

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

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**and*

_{r}

*a**are the corresponding high-side, high-side-right (together determining the local cross-wellbore plane) and axial directions of the relief well. The position*

_{r}

*x**is the intersection location of the target well path, with the cross-wellbore plane of the relief well being considered.*

_{t}The remnant field is assumed to be axisymmetric about the target well, and thus Δ** b** only has axial and radial components within the radial plane (

**Fig. 2B**). Therefore, the vector Δ

**and the relative well position**

*b*

*x**-*

_{t}

*x**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.*

_{r}**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**, cross-wellbore plane and interference Δ*

_{r}**are shown for the two measurement stations with numbers**

*b**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**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*

_{r}

*x**at which the target well path intersects the relief cross-wellbore plane under consideration.*

_{t}**Figure 3B** further illustrates the situation in the cross-wellbore plane of a single measurement station. PMTR only uses the components of Δ** b** 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**can be ignored, including Δ*

_{r}

*b**.*

_{BHA}The magnitude of the transverse component Δ*b _{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**somewhere along the direction*

_{r}

*d**. However, as the direction of Δ*

_{m}**depends on the axial position relative to the magnetic poles (**

*b***Fig. 2B**), one does not know whether it is located in the positive direction

*d**, or perhaps in the opposite direction*

_{m}

*–d**. Thus, the calculated toolface angle*

_{m}*τ*, or the direction

_{m}

*d**, can be in error by 180˚, as compared to the actual orientation between the two wells.*

_{m}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*can only be accurately calculated at measurement stations at which

_{m}*∆b*is sufficiently large. This condition is not met at locations where Δ

_{t}**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**

*b**τ*with the calculated well paths.

_{m}**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**contains a position uncertainty in the target well position, whereas the*

_{t,calc}

*x**is the target well position without position uncertainty, which is unknown.*

_{t}**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

**, in order to calculate the exact position of the target well, relative to the relief well. This is discussed in the following.**

*u***Relative well positions.** The well position difference Δ** x** between the relief well position

*x**and the target well position*

_{r}

*x**in the relief cross-wellbore plane at a measurement station is defined by:*

_{t,calc}* *

The components of Δ** x** along the high-side and high-side-right directions of the local cross-wellbore plane are given by (

**Fig. 3B**):

* *

The transverse component Δ*x** _{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*toward the target well, as following from the magnetic interference calculations (even when ignoring the 180° ambiguity therein).

_{m}**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,

**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.**

*u*From **Fig. 3B,** it can be inferred that when the target well position *x** _{t,calc }* is shifted / corrected by

**, then the corresponding toolface angle**

*u**τ*would become equal to

_{x}*τ*. Furthermore, the toolface angle

_{m}*τ*, or equivalently the direction

_{m}

*d**, resulting from a single MWD measurement does not fully define*

_{m}**. Namely, any shifted well position**

*u*

*x**+*

_{t,calc}**located along the**

*u*

*d**direction (relative to*

_{m}

*x**) will achieve consistency between the toolface angles*

_{r}*τ*and

_{m}*τ*. Therefore, multiple measurement stations, having distinct toolface angles

_{x}*τ*, must be combined to fully solve

_{m}**. This can be achieved using non-linear least-squares fitting, which is outlined in the following.**

*u***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**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*

_{t,int}*u*and

_{h}*u*. 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).

_{r}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'*and

_{h}*u'*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:

_{r}* *

whereby the 'un-shifted' position *x** _{t,calc}* must be calculated / adjusted, such that the resulting shifted position

*x**'*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

_{t,calc}

*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**may become located slightly off-plane to compensate for this.*

_{t,calc}Least-squares fitting, based on differences between the magnetic interference toolface angle *τ _{m}* and the toolface angle for the shifted position

*x**'*is impractical, as

_{t,calc}*τ*can be off by 180°. Therefore, the following alternative approach is used. The unit direction vector

_{m}

*p**is calculated at each measurement station by:*

_{m}* *

which is perpendicular to *d** _{m}*. The shifted (trial) position

*x**'*for a measurement station may not (yet) be located along the direction

_{t,calc}

*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 Δ*b _{t}* exceeds a minimum value, and so the resulting direction

*p**is well-defined.*

_{m}The sought solutions for the lateral position uncertainties *u' _{h}* and

*u'*minimize

_{r}*Q*through their effect on the position

*x**'*at each station as per equation (12). The final trial position

_{t,calc}

*x**'*at each station then corresponds to the sought target well position

_{t,calc }

*x**relative to the relief well position*

_{t}

*x**. This (non-linear) minimization problem can be solved using standard numerical methods.*

_{r}^{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*≈ 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 Δ

_{m }*b*as per equation (3) of the calculated magnetic interference is small.

_{t }**Figure 4A**also shows the toolface angles

*τ*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.

_{m}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 Δ*b _{t}*>2

*µT*, such that the used toolface angle

*τ*and the associated direction vectors

_{m}

*d**and*

_{m}

*p**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*

_{m}

*u**= –5.15 ft and*

_{h }

*u**= –8.36 ft.*

_{r }**Figures 4B**and

**4C**show, respectively, the toolface angles

*τ*and the relative well distances Δ

_{x'}*x'*at the measurements stations after solving and correcting for the position uncertainties. The series

_{t}*τ*now has the 180° ambiguity for the magnetic toolface angle resolved.

_{m,corr }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**

- Jones, D.L., G.L. Hoehn and A.F. Kuckes, “Improved magnetic model for determination of range and direction to a blowout well” SPE paper 14388, Society of Petroleum Engineers, 1987.
- 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.
- Eatough, O., M. Alahmad, F. Momot, A.S. Sikal, and D. Reynaud, “Advanced well positioning with magnetic interference, based on passive magnetic MWD ranging: Case study,” SPE paper 191503, Society of Petroleum Engineers, 2018.
- Sarawyn, S.J., and J.L. Thorogood, “A compendium of directional calculations, based on the minimum curvature method,” SPE paper 84246, Society of Petroleum Engineers, 2005.
- Press, W.H., S.A. Teulosky, W.T. Vetterling, and B.P. Flannery, “Numerical recipes in C++–the art of scientific computing,” Cambridge University Press, 2nd ed., 2002.

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