EP3978721A1 - Method of drilling a relief well - Google Patents

Abstract

A method of drilling a relief well to intercept a target well in an Earth formation, wherein Measurement While Drilling (MWD) survey data is used for estimation of the distance to and the direction towards the target well without assumptions for the remnant magnetic field. The method uses a combination of MWD measurements and calculated 3D well paths for the accurate estimation of the distance to and the direction towards the target well.

Description

FIELD OF THE INVENTION
• The present invention relates to a method of drilling a relief well to intercept a target well in an Earth formation.
BACKGROUND TO THE INVENTION
• 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. Measurement While Drilling (MWD) survey data are often used for steering relief wells towards a target well. Examples of such methods are disclosed in D.L. Jones, G.L. Hoehn, A.F. Kuckes, "Improved Magnetic Model for Determination of Range and Direction to a Blowout Well", Society of Petroleum Engineers, SPE-14388, 1987; and J.D. Robinson, J.P. Vogiatzis, "Method for determining distance and direction to a cased borehole using measurements made in an adjacent boreholes", US Patent 3725777 (1973 ). These methods make explicit assumptions on the remnant casing magnetism of the target well, especially regarding the strength and distribution of the magnetic poles. These methods are complex and experience shows that they can result in sub-optimal estimates of the distance to and the direction towards the target well, potentially resulting in significant operational time delays.
SUMMARY OF THE INVENTION
• In accordance to one aspect of the present invention, there is provided a method of homing in drilling a relief well to a target well in a subsurface Earth formation, which target well is lined with a steel casing; comprising:
• drilling a relief well alongside a target well over a 'ranging interval' along a relief well trajectory that comprises non-parallel sections in proximity with and relative to to the target well, under varying relative lateral orientations, using a bottom hole assembly which comprises a drill bit;
• carrying out magnetic MWD measurements at multiple measurement stations along the relief well trajectory;
• defining a radial plane of the target well for each measurement station, spanned by two points on the target well and the measurement station;
• determining a remnant magnetic field vector of the target well at said multiple measurement stations along the relief well by subtracting contributions from Earth magnetic field and the bottom hole assembly magnetic field from the magnetic MDW measurements within said radial plane;
• providing calculated 3D well paths for both the target well and the relief well in a common coordinate reference system based on survey data;
• using the remnant magnetic field vector in said multiple measurement stations and least-squares fitting to determine a position shift vector of the target well, relative to the relief well by minimizing a position error measure that is associated with the orientation of the remnant magnetic field vector;
• steering the bottom hole assembly towards the target well after applying the position shift vector to the 3D target well path.
BRIEF DESCRIPTION OF THE DRAWINGS
• The drawing figures depict one or more implementations in accordance with the present teachings, by way of example only, not by way of limitation. In the figures, like reference numerals refer to the same or similar elements.
• Fig. 1 schematically shows an impression of MWD Survey instrument nearing a target well;
• Fig. 2A schematically shows a view in the direction of the target well of the axisymmetric magnetic field due to assumed South and North poles on the target well and a measurement station on the relief well;
• Fig. 2B schematically shows a view of the situation of Fig. 2A in a direction transverse to the relief well;
• Fig. 3A schematically shows multiple measurement stations on the relief well and the corresponding positions of the target well in the relief cross-wellbore plane;
• Fig. 3B schematically shows various (vector) quantities in the relief cross-wellbore plane of a single measurement station (B).
DETAILED DESCRIPTION OF THE INVENTION
• The person skilled in the art will readily understand that, while the detailed description of the invention will be illustrated making reference to one or more embodiments, each having specific combinations of features and measures, many of those features and measures can be equally or similarly applied independently in other embodiments or combinations.
• The present description addresses a new method that uses MWD survey data for estimation of the distance to and the direction towards the target well without assumptions for the remnant magnetic field. The method is referred to as Passive-Magnetic Triangulation Ranging (PMTR).
• 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 towards the target well. Several building blocks that may contribute to the method include:
• 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 used, as the MWD magnetic measurements are used for ranging.
• The remnant 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.
• Application of PMTR is preferred over industry proven active ranging methods in salt formations, for example in Brazil, Gulf of Mexico, Oman and the North Sea areas. In these areas, active ranging methods cannot be (easily) utilized, as the nonconductive nature of salt formation hampers electric current injection when using active ranging tools. PMTR is now a viable ranging and homing-in option in operator's well control contingency plans.
• When drilling a relief well towards a target well, see 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 Δ b _BHA from the Bottom Hole Assembly (BHA) (is calibrated) and the disturbance Δ b due to target well remnant magnetism. PMTR determines the disturbance Δ b at each 'measurement station' by: $$\mathrm{\Delta }\mathit{b}={\mathit{b}}_{\mathit{MWD}}-{\mathit{b}}_{\mathit{earth}}-{\mathrm{\Delta }\mathit{b}}_{\mathit{BHA}},$$

  

  which applies in absence of crustal magnetic anomalies. Note that vector quantities are written in boldface font.
• As the magnetic MWD measurements are used for well ranging, a gyro is used in addition, 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.
• Fig. 2 .A illustrates the remnant magnetic field originating from two assumed magnetic (North and South) poles along the target well casing. The position x _r represents the location of one 'measurement station' on the relief well path, at which an MWD-measurement is taken. The vectors h _n 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. Fig. 2.A shows the cross-wellbore plane of the target well. Fig. 2.B shows the radial plane and field line through the measurement station. The position x _t is the intersection location of the target well path with the cross-wellbore plane being considered.
• The disturbance field is assumed to be axisymmetric, and thus Δb only has axial and radial components within the radial plane ( Fig. 2.B). Therefore, the vector Δ b 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 remnant magnetic field that is used by the PMRT method.
• Fig. 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 Δ b are shown for the two measurement stations with numbers i and j ( Fig. 3.A), 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.
• Fig. 3.B 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: $${\mathrm{\Delta }\mathit{b}}_h=\mathrm{\Delta }\mathit{b}\mathrm{.}{\mathit{h}}_r{\mathrm{and}\mathrm{\Delta }b}_r=\mathrm{\Delta }\mathit{b}\mathrm{.}{\mathit{r}}_r$$

  

  and thus that any component of Δ b along the axial direction a _r can be ignored, including Δ b _BHA.
  The magnitude of the transverse component Δb_t within a relief cross-wellbore plane is calculated by: $${\mathrm{\Delta }\mathit{b}}_t=\sqrt{{{\mathrm{\Delta }\mathit{b}}_h}^2+{{\mathrm{\Delta }\mathit{b}}_r}^2}\mathrm{.}$$

  

  The corresponding magnetic interference toolface angle τ_m is determined by: $$\cos \left({\tau }_m\right)=\frac{{\mathrm{\Delta }\mathit{b}}_h}{{\mathrm{\Delta }\mathit{b}}_t}\mathrm{and\; sin}\left({\tau }_m\right)=\frac{{\mathrm{\Delta }\mathit{b}}_r}{{\mathrm{\Delta }\mathit{b}}_t}$$

  

  and the corresponding unit direction vector d _m is calculated by: $${\mathit{d}}_m=\frac{{\mathrm{\Delta }\mathit{b}}_h}{{\mathrm{\Delta }\mathit{b}}_t}{\mathit{h}}_r+\frac{{\mathrm{\Delta }\mathit{b}}_r}{{\mathrm{\Delta }\mathit{b}}_t}{\mathit{r}}_r\mathrm{.}$$

  

  Based on the axisymmetry properties of the remnant magnetic field around the target well casing, the target well position x _t should be located relative to x _r somewhere along the direction d _m . However, as the direction of Δ b depends on the axial position relative to the magnetic poles ( Fig. 2.B), 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. Thus, the magnetic toolface angle τ_m cannot be used directly as the orientation for drilling the relief well towards 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 Δb_t is sufficiently large. This condition is not met at locations where Δ b 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.
• 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. A reference is made to S.J. Sarawyn, J.L. Thorogood, "A compendium of directional calculations based on the minimum curvature method", SPE 84246, Society of Petroleum Engineers, 2005. However, the survey measurements carry an uncertainty in well position. Fig. 3 . illustrates the calculated position x _t,calc of the target well in the 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.
• 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: $${\mathit{x}}_t={\mathit{x}}_{t,\mathit{calc}}+\mathit{u},$$

  

  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.
• The well position difference Δ x 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: $$\mathrm{\Delta }\mathit{x}={\mathit{x}}_{t,\mathit{calc}}-{\mathit{x}}_r\mathrm{.}$$

  

  The components of Δ x along the local high-side and high-side-right directions of the cross-wellbore plane are given by ( Fig. 3.B): $${\mathrm{\Delta }\mathit{x}}_h=\mathrm{\Delta }\mathit{x}\mathrm{.}{\mathit{h}}_r{\mathrm{and\; \Delta }x}_r=\mathrm{\Delta }\mathit{x}\mathrm{.}{\mathit{r}}_r\mathrm{.}$$

  

  The transverse component Δx_t in the plane is calculated by: $${\mathrm{\Delta }\mathit{x}}_t=\sqrt{{{\mathrm{\Delta }\mathit{x}}_h}^2+{{\mathrm{\Delta }\mathit{x}}_r}^2},$$

  

  and corresponds to the calculated center-to-center distance between the wells. The corresponding geometric toolface angle τ_x is determined by: $$\mathit{cos}\left({\tau }_x\right)=\frac{{\mathrm{\Delta }\mathit{x}}_h}{{\mathrm{\Delta }\mathit{x}}_t}\mathrm{and\; sin}\left({\tau }_x\right)=\frac{{\mathrm{\Delta }\mathit{x}}_r}{{\mathrm{\Delta }\mathit{x}}_t}\mathrm{.}$$

  

  Due to position uncertainties this toolface orientation τ_x is generally different from the magnetic interference toolface angle τ_m towards the target well, as following from the magnetic interference calculations (even when ignoring the 180° ambiguity therein).
• 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. 3.B 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 form 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 in order to fully solve u. This can be achieved using non-linear least-squares fitting, which is outlined in the following.
• 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: $$\mathit{u}=u_h{\mathit{h}}_{t,\mathit{int}}+u_r{\mathit{r}}_{t,\mathit{int}},$$

  

  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, see Fig. 3.B. The corresponding (trial) shifted target well position for a measurement station is defined by: $${\mathit{x}}_{t,\mathit{calc}}^{ʹ}={\mathit{x}}_{t,\mathit{calc}}+\mathit{uʹ},$$

  

  whereby the 'un-shifted' position x _t,calc must be calculated / adjusted, such that the resulting shifted position ${\mathit{x}}_{t,\mathit{calc}}^{ʹ}$

  

  is located within the relief cross-wellbore plane. 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 ${\mathit{x}}_{t,\mathit{calc}}^{ʹ}$

  

  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: $${\mathit{p}}_m=-\frac{{\mathrm{\Delta }\mathit{b}}_r}{{\mathrm{\Delta }\mathit{b}}_t}{\mathit{h}}_r+\frac{{\mathrm{\Delta }\mathit{b}}_h}{{\mathrm{\Delta }\mathit{b}}_t}{\mathit{r}}_r,$$

  

  which is perpendicular to d _m. The shifted (trial) position ${\mathit{x}}_{t,\mathit{calc}}^{ʹ}$

  

  for a measurement station may not (yet) be located along the direction d_m, see Fig. 3.B. This is quantified during the solution process by means of the projected error y for the trial position that is defined by: $$y={\mathit{p}}_m\mathrm{.}\left({\mathit{x}}_{t,\mathit{calc}}^{ʹ}-{\mathit{x}}_r\right)\mathrm{.}$$

  

  The cumulative quadratic error Q over all measurement stations along the ranging interval is defined by: $$Q=\sum _{i=1}^{i=n}{y}_i^2=\sum _{i=1}^{i=n}{\left({\mathit{p}}_{m,i}\mathrm{.}\left({\mathit{x}}_{t,\mathit{calc},i}^{ʹ}-{\mathit{x}}_{r,i}\right)\right)}^2,$$

  

  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 $u_h^{ʹ}$

  

  and $u_r^{ʹ}$

  

  minimize Q through their effect on the position ${\mathit{x}}_{t,\mathit{calc}}^{ʹ}$

  

  at each station as per equation (12). The final trial position ${\mathit{x}}_{t,\mathit{calc}}^{ʹ}$

  

  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, including those described in W.H. Press, S.A. Teulosky, W.T. Vetterling, B.P. Flannery, "Numerical Recipes in C++ - The art of Scientific Computing", Cambridge University Press, 2nd ed., 2002.
• The PMTR method has been validated with field data, whereby a relief well was drilled to intersect a target well. The validation shows that the method works in practice.
• The person skilled in the art will understand that the present invention can be carried out in many various ways without departing from the scope of the appended claims.

Claims (2)

1. A method of drilling a relief well to a target well in a subsurface Earth formation, which target well is lined with a steel casing; comprising:

   - drilling a relief well alongside a target well over a 'ranging interval' along a relief well trajectory that comprises non-parallel sections in proximity with and relative to to the target well, under varying relative lateral orientations, using a bottom hole assembly which comprises a drill bit;

   - carrying out magnetic MWD measurements at multiple measurement stations along the relief well trajectory;

   - defining a radial plane of the target well for each measurement station, spanned by two points on the target well and the measurement station;

   - determining a remnant magnetic field vector of the target well at said multiple measurement stations along the relief well by subtracting contributions from Earth magnetic field and the bottom hole assembly magnetic field from the magnetic MDW measurements within said radial plane;

   - providing calculated 3D well paths for both the target well and the relief well in a common coordinate reference system based on survey data;

   - using the remnant magnetic field vector in said multiple measurement stations and least-squares fitting to determine a position shift vector of the target well, relative to the relief well by minimizing a position error measure that is associated with the orientation of the remnant magnetic field vector;

   - steering the bottom hole assembly towards the target well after applying the position shift vector to the 3D target well path.
2. The method of claim 1, wherein the error measure for said least-squares fitting is defined by a perpendicular distance of a calculated relative position vector between the wells to the radial plane as defined by the orientation of the remnant magnetic field vector to determine said position shift vector.

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