METHODS FOR ESTIMATING A POSITION OF A WELL PATH WITHIN A SUBSURFACE FORMATION

Abstract

A method of estimating a position of a well path within a subsurface formation of the Earth, the method comprising determining a well path estimate using navigation measurements from a downhole tool and a position estimate derived from seismic data. A method of geosteering comprising: estimating a position of the well path and controlling a drill bit in response to the estimated position of the well path to follow a desired well trajectory.

Claims

1-21. (canceled)

22. A method of estimating a position of a well path within a subsurface formation of the Earth, the method comprising determining a well path estimate using navigation measurements from a downhole tool and a position estimate of a point lying on the well path derived from seismic data, the method further comprising determining the well path estimate using the minimum curvature method with a parameter obtained using an optimisation process.

23. The method of claim 22, wherein the navigation measurements from a downhole tool comprise orientation and/or measured depth measurements.

24. The method of claim 22, wherein the navigation measurements from a downhole tool comprise magnetic and/or gyroscopic measurements.

25. The method of claim 22, wherein the position estimate is derived from passive seismic data.

26. The method of claim 22, further comprising collecting seismic data from a plurality of seismic sensors spread across a region of the surface of the Earth above the downhole tool and/or located in one or more nearby wells; and deriving the position estimate from the seismic data.

27. The method of claim 22, wherein: the well path estimate comprises a vertical path component and a lateral path component; the vertical path component is determined using the navigation measurements from a downhole tool; and the lateral path component is determined using the position estimate derived from seismic data.

28. The method of claim 27, wherein: the position estimate derived from seismic data is also used when determining the vertical path component; and/or the navigation measurements from a downhole tool are also used when determining the lateral path component.

29. The method of claim 22, wherein the optimisation process comprises: determining a distance between a general definition of a well path modelled using the minimum curvature method and the position estimate derived from seismic data; and minimising an objective function based on the distance and starting from the navigation measurements to obtain the parameter for the well path estimate.

30. The method of claim 29, wherein the distance is a lateral distance.

31. The method of claim 30, wherein determining the lateral distance between a general definition of a well path modelled using the minimum curvature method and the position estimate derived from seismic data comprises: identifying an arc of the general definition of a well path modelled using the minimum curvature method that is closest to the position estimate derived from seismic data; projecting the position estimate derived from seismic data vertically on to the plane spanned by the arc; and using the geometry of the plane spanned by the arc to derive the minimum lateral distance between the position estimate derived from seismic data and the arc; using this derived minimum lateral distance as the lateral distance.

32. The method of any of claim 22, wherein the parameter obtained using an optimisation process is an azimuth value.

33. The method of claim 29, wherein the parameter obtained using an optimization process is an inclination value.

34. The method of claim 22, wherein using the minimum curvature method to determine the well path estimate further comprises using a second parameter, the second parameter being from the navigation measurements from a downhole tool.

35. The method of claim 22, further comprising determining a measure of uncertainty of the well path estimate, wherein the lateral measure of uncertainty of the well path estimate is independent of a measured depth.

36. The method of claim 35, wherein determining a measure of the uncertainty comprises calculating a single measure for the entire well path estimate using a statistical distribution of residuals between the well path estimate and position estimates derived from seismic data.

37. The method of claim 35, wherein determining a measure of the uncertainty comprises calculating a plurality of independent measures for different sections of the well path estimate using a statistical distribution of residuals between the well path estimate and position estimates derived from seismic data.

38. The method of claim 22, comprising using the well path estimate to predict the path that the well will take ahead of the downhole tool

39. The method of claim 22, further comprising deriving the position estimate from seismic data, wherein deriving the position estimate from seismic data comprises: a) collecting seismic data from a plurality of seismic sensors spread across a region of the surface of the Earth above a drill bit or other noise source and/or located in one or more nearby wells; b) pre-processing the seismic data to enhance a contribution of drill bit or noise source generated noise; c) defining a set of points on a grid in 3-dimensional space that includes an expected position of the drill bit or noise source; d) computing travel times for seismic waves from each said point to each seismic sensor location; e) for each said point, using the pre-processed seismic data, sensor location data, and computed travel times to compute a semblance stack of travel-time corrected seismic data in a time window; f) determining the grid location of the maximum semblance and fitting a 3-dimensional function around this grid location; and g) identifying the location of a maximum of the 3-dimensional function and using that as the estimate derived from seismic data.

40. A method of geosteering, the method comprising: estimating a position of the well path using the method of claim 22; and controlling a drill bit in response to the well path estimated to follow a desired well trajectory.

41. A carrier medium comprising computer readable code configured to cause a computer to perform the method of claim 22.

Description

BRIEF DESCRIPTION OF FIGURES

[0108] FIG. 1 is a flow diagram which illustrates the general steps of deriving a position estimate from seismic data;

[0109] FIG. 2 illustrates schematically a procedure for estimating the position of a drill bit whilst drilling a subsea well using subsea data;

[0110] FIG. 3 shows, for an exemplary well, the observed maximum semblance value and the rate of penetration (ROP) and rotations per minute (RPM) of the drill bit as a function of time;

[0111] FIG. 4 shows the maximum semblance position for an exemplary well at a measured depth of approximately 1500 m;

[0112] FIG. 5 shows the maximum semblance position for an exemplary well at a measured depth of approximately 3500 m;

[0113] FIG. 6 shows maximum semblance position for an exemplary well at a measured depth of approximately 6500 m;

[0114] FIG. 7 is a flow diagram which illustrates the actions for estimating a position of a well path according to the disclosure;

[0115] FIG. 8 shows positions derived from seismic data, an initial well path estimate and an improved well path estimate;

[0116] FIGS. 9A and 9B schematically illustrate minimum curvature methods for estimating well path positions;

[0117] FIGS. 10A through 10D show positions derived from seismic data, an initial well path estimate, an improved well path estimate, an uncertainty ellipse for the initial well path estimate and an uncertainty ellipse for the improved well path estimate for an exemplar well;

[0118] FIGS. 11A through 11G show comparisons of the initial well path estimate and improved well path estimate; and

[0119] FIGS. 12A through 12G show the differences between the initial well path estimate and the improved well path estimate.

DETAILED DESCRIPTION

[0120] FIGS. 1 to 6 generally demonstrate methods for deriving position estimates from seismic data, for use in the present disclosure.

[0121] A method of estimating the current position of a drill bit or other noise source within the drill string or bottom hole assembly (BHA) or in a subsurface formation of the Earth is described below. This method may provide the position estimate derived from seismic data used methods for estimating a well position.

[0122] The proposed method tracks noise from drilling operations or other noise sources within passive seismic data. The data is analysed to obtain independent measurements of a well position, which do not suffer from an accumulation of error with measured depth. This allows the well path to be localized laterally with a higher accuracy than can be obtained with conventional gyroscopic and magnetic measurements. For a horizontal well 6500 m in length for example, the lateral positional uncertainty of the well path may be reduced from over 60 m to approximately 15 m. The proposed method supports improved well placement by reducing the lateral position uncertainty while drilling, in real time. The risk of adverse events, e.g. drilling infill wells too close to already existing producers or hazard zones such as faults, gas pockets, stringers etc, may also be reduced.

[0123] Permanently-deployed reservoir monitoring (PRM) arrays provide continuous background noise recordings, amounting to Terabytes of passive seismic data every day. Passive data can, therefore, be measured using an existing PRM system. Hence for PRM-equipped fields, the method provides accurate, complementary information at minimal extra costs, for real-time well positioning that can be used for decision making during drilling operations.

[0124] The method for providing a position estimate derived from seismic data is based on computing, using a known semblance analysis technique, the semblance stack of passive seismic data. The stack is computed along travel time curves from each grid point in a subsurface volume to selected seismic sensors at the seabed (or land surface). The method can also be used for detecting sudden, transient drilling issues (e.g. liner failure) and drilling-induced events in the analysed subsurface volume.

[0125] FIG. 1 is a flow diagram illustrating the general steps of the sub-surface well location determination method. The method comprises the steps of:

S1) Collecting passive seismic data;
S2) Pre-processing the collected data;
S3) Defining a 3D grid around the expected drill bit position;
S4) Computing travel times from each grid point to selected sensors;
S5) Computing a semblance stack of travel-time corrected data for each grid point;
S6) Locating the maximum semblance on the grid and fitting a 3D polynomial through the grid points at and around the grid maximum; and
S7) Locating the maximum of the fitted 3D polynomial.

[0126] This method is further illustrated in FIG. 2, which shows an offshore drilling platform 1, with a drill string 2 extending from the platform into a well 3 extending through the subsurface formation.

[0127] In S1, sensors 4, which may be part of an existing permanently-deployed reservoir monitoring (PRM) array, are used to collect passive seismic data. Such an array may be primarily used, in a known way, for periodic 4D seismic monitoring of a reservoir and the overburden. A known system has been developed, for example, to use passively monitored seismic data for detecting and locating microseismic events induced by injection into wells (Bussat et al., 2016, Bussat et al., 2018) to support safe operations and prevent out-of-zone injection. The sensors 4 may be of a conventional or fibre-optic distributed acoustic sensing (DAS) type. This known PRM array, and the data it provides, is used in a new way to track the well location.

[0128] Typically, for periodic microseismic monitoring by semblance analysis, a temporal semblance window is defined. Passive data collected with the sensors is processed and stacked over the sensors and the semblance window for semblance analysis. In the present case, since the drilling operation (or other noise generating process) is expected to produce a continuous signal, a longer semblance window is used compared to that used for conventional microseismic monitoring. The window should be sufficiently long to be able to pick up the continuous but rather weak noise, but sufficiently short such that the drill bit does not move substantially, which would cause the image of the noise source to be blurred. Although the present example relates to the noise emitted from a drill bit, it is understood that in alternative examples the noise may instead be emitted from an alternative noise source. An example of a suitable semblance window is in the range of to 120 seconds in duration depending on drilling parameters, for example 90 seconds to scan through the passive data.

[0129] In alternative examples, the window may be between 5 and 300 seconds in duration.

[0130] As well as the noise from the drill bit, the passive seismic data contains noise from a range of different sources that are not of interest for the positional monitoring, such as interference from nearby seismic acquisitions, noise from the platform, and noise from vessels in the neighbourhood. To be able to track the drilling noise therefore, the passive data is pre-processed after collection (S2). This may be achieved by the use of a bandpass filter, an FX median filter, PZ-summation, and a subspace filter prior to computing the semblance. Except for the bandpass filter, the filters are data-driven; that is, filter parameters are computed continuously during operation. The parameters for these filters can, therefore, be optimized for the noise present in the data at any given time. By appropriate pre-processing, a significant amount of background noise is removed from the passive data.

[0131] For each time interval corresponding to the semblance window length, a processing grid that covers a limited monitoring volume around the current expected drill bit position 6 is then defined (S3), as shown in FIG. 2. The method by which the initial expected position is obtained is not limited, although this may be known from the well-planning phase in combination with the current length of the drill string. Conventional magnetic MWD or gyroscopic techniques may be used to estimate the drill bit position more accurately. The estimate may then be stored in a database, along with real-time drilling parameters such as rate of penetration (ROP) and bit rotations per minute (RPM). The expected position is fetched for the construction of the processing grid. The spatial extent of the monitoring volume should be large enough to cover possible revisions of the planned well path, and the grid spacing can be relatively coarse. For example, the extension of the volume may be ±200 m along the well path (MD axis) with 20 m grid spacing, and ±80 m laterally (R axis) and 140 m vertically (Z axis) away from the well path with 20 and 35 m grid spacing, respectively.

[0132] P-wave travel times between the sensors 4 and all points on the processing grid are then obtained (S4), for example by ray tracing or wavefield modelling through a velocity model. For this step, an optimal subset 4b of the available PRM nodes may be selected and used for a given expected drill bit position. The selected nodes may be, for example, all nodes within an area centred above the drill bit with a radius equal to the current vertical depth of the drill bit. By reducing the amount of data for analysis, both in terms of the number of sensors and in terms of the number of grid points on the processing grid, the amount of computational power and computational time required for processing is reduced. The travel times are then used to travel time-correct the seismic data (the vertical component of the geophone after pre-processing). For each grid point on the processing grid, the travel time-corrected data from the selected nodes are then stacked to compute the semblance by known methods (S5). This procedure may be repeated for consecutive semblance windows, whether or not partially overlapping, with a potentially new optimal subset of receivers.

[0133] The location and value of the maximum semblance on the processing grid is then determined (S6). The finer the grid, the higher the positional precision achieved. A finer grid, however, requires higher computational power and longer computational time. Therefore, to obtain sub-grid resolution, in particular when using a relatively coarse processing grid, the exact location of the maximum semblance and its value may be estimated by fitting a second-degree polynomial in 3D through the 3×3×3 grid points around the grid maximum. A coarse grid used in combination with this 3D fitting gives very similar results to a finer grid, and is much faster to compute. This is an important benefit for real-time implementation and positional decision-making.

[0134] The resulting estimates (fitted maximum semblance position and value) may then be stored in a database, together with the median semblance value on the grid to represent the background noise level. When the estimated location in any direction is far from the maximum semblance on the grid, it is a sign of low-quality data without a clear maximum in the semblance volume. For example, when the estimated location in any direction is farther than one grid point away from the grid point with maximum semblance. Any such observations may be flagged as ‘bad data’ and replaced with their original maximum value and location on the grid. The value of the fitted maximum semblance, or, if replaced in case of bad data, the original grid maximum, may be used as a measure of the amount of noise detected from the drilling operation. The position of the maximum of the 3-dimensional polynomial or, if replaced in the case of bad data, the original grid position of the maximum, may be used as the estimate for the location of the noise source, i.e. the current position of the drill bit or other noise source in the BHA (S7).

[0135] FIG. 3 shows results collected from an exemplary well, where a bandpass filter, an FX median filter, PZ-summation, and a subspace filter have been applied to the passive data. The lower panel shows the rate of penetration (ROP) (upper trace) and rotations per minute (RPM) (lower trace) of the drill bit as a function of time. The upper panel shows the observed maximum semblance value, also as a function of time. The data for both panels is aligned along a common time scale for comparison. There is a clear correlation between maximum semblance and drill bit activity. When the drill bit is rotating and advancing (ROP>0), the semblance is high, while the semblance is low when drilling is paused (these low semblance values are typically flagged as bad data). This confirms that the detected noise comes from the drilling operation, and the pre-processing preserves the drilling noise.

[0136] FIGS. 4-6 show results of the maximum semblance positions obtained for three wells (at approximately 1500, 3500, and 6500 m along the length of the well path respectively) after carrying out the method as described. Each of the figures shows a map view of the estimated drilled well path 7 and corresponding 95% uncertainty ellipse 9 from gyroscopic measurements. The fitted location of the maximum semblance 8 for 90 second intervals of data, the grid points at which the semblance is computed, and the PRM nodes, are plotted. Threshold values for the semblance and signal-to-noise ratio (SNR) (represented by maximum divided by median semblance) and the ‘bad data’-flag are used to filter measurements before plotting. Over time, the observations are located at increasing measured depth (length along well path), following the progress of the drilling.

[0137] FIGS. 4-6 show that the lateral extent of the error ellipse 9 for the gyroscopic measurements for horizontal wells increases from less than 10-15 m at around 1500 m measured depth (FIG. 4) to over 60 m at 6500 m measured depth (FIG. 6). The position of the (filtered) maximum semblance 8 obtained by the method described above is close to the drilled well path 7, as estimated by gyroscopic measurements, and well within the corresponding uncertainty ellipse. The lateral spread of the observations, however, shown by the spread of the region 8, is far smaller than the width of the error ellipse for the gyroscopic measurements, and is independent of measured depth (that is, independent of the position along the well path). This indicates that the passive data can be used to reduce the lateral well positional uncertainty significantly, by approximately a factor 4 for a 6500 m long well, compared to the gyroscopic measurements. The reduction in uncertainty may be even higher during favourable (quiet) ambient noise conditions.

[0138] Instead of the drill bit, any other suitable source may be used to produce the noise used for localisation. For example, an acoustic source may be gradually lowered into an already drilled well whilst generating noise. Such alternative noise sources may be introduced to the well bore alone, or they may be introduced by equipment to be used for other downhole operations, for example cement bond logging tools. In this way, the cost of operation would be reduced. Furthermore, additional noise sources may be used simultaneously with a drill bit. This may, for example, be used to supplement the noise produced by the drill bit during operation, and could be useful in situations where the noise reaching the surface sensors from the drill bit itself is weak or insufficient for proper localisation.

[0139] Instead of a permanently-deployed PRM system, the method can also be used with temporarily deployed cables. This method may be also used to provide depth estimates for the noise source. Depth estimates may be improved by including passive data from sensors (conventional sensors or a fiber-optic DAS systems) which are located downhole in the same or one or more nearby wells as well as from those at the surface. It is further noted that, by reducing the semblance window length, this method may also be used to detect sudden, transient, drilling-related events.

[0140] The above-described method provides a position estimate for a drill bit or an associated well path, derived from seismic data.

[0141] The present disclosure provides a method of estimating a position of a well path within a subsurface formation of the Earth comprising calculating a well path estimate using navigation measurements from a downhole tool and a position estimate derived from seismic data. Accordingly, in the examples of the present disclosure described below, the position estimate derived from seismic data is combined with navigation measurements from a downhole tool to calculate a well path estimate.

[0142] Turning now to FIG. 7, an overview of a method according to the disclosure is shown.

[0143] The method shown in FIG. 7 comprises: [0144] S71—Obtain navigation measurements from a downhole tool; [0145] S72—Estimate a well path position using seismic data; [0146] S73—Determine a generalised distance between a minimum curvature well path and a position estimate derived from seismic data; [0147] S74—Minimise an objective function based on the generalised distance, starting from the navigation measurements, to obtain a well path estimate parameter; [0148] S75—Use the well path estimate parameter to determine a well path estimate; and [0149] S76—Calculate the uncertainty of the well path estimate.

[0150] While FIG. 7 shows steps S71 to 76 as sequential actions, it is to be understood that this is only for illustration. In practice, certain actions may be undertaken in alternative orders, or undertaken simultaneously.

[0151] Navigation measurements from a downhole tool are obtained in S71. These measurements may be obtained directed from a downhole tool, or provided by a third party. These measurements may, in some examples, be provided in the form of a well path trajectory calculated using the navigation measurements—this will be referred to herein as an initial well path estimate. An initial well path estimate, as used here, refers to an estimated well trajectory derived from navigation measurements from a downhole tool (i.e. without use of seismic data position estimates).

[0152] Example navigation measurements include inclination, azimuth and measured depth values. The navigation measurements are readings from, or derived from readings from, magnetic and/or gyroscopic sensors in a drill bit or other downhole tool, as well as the measured depth (which may be considered as the length of the wellbore). These magnetic and/or gyroscopic measurements may be filtered, processed or otherwise ‘cleaned-up’ prior to use (e.g. to calculate the initial well path estimate).

[0153] In the examples described herein, an initial well path estimate calculated from the navigation measurements from a downhole tool is calculated using the minimum curvature method. The minimum curvature method is also used to determine the well path estimate, as described above. The minimum curvature method is described in “A compendium of directional calculations based on the minimum curvature method”, Sawaryn & Thorogood, SPE 2005 Drilling & Completion.

[0154] FIG. 9A schematically illustrates the minimum curvature method. In brief, calculating the initial well path estimate using measurements from the downhole tool and the minimum curvature method comprises assuming that the well path between two consecutive survey points is a circular arc, and that this arc is defined by the position at the first survey point, the inclination and azimuth angles at the two survey points and the measured depth (MD) difference between the two survey points. Using this method and the measurements of the inclination, azimuth and measured depth from the downhole tool, an estimate for the locations of each sequential survey point along the well path can be calculated. This estimated well path based on inclination, azimuth and MD values from the navigation measurements is referred to herein as the initial well path estimate.

[0155] Using the minimum curvature method, any point on the circular arc, and thus the absolute location of any point along the well path can be calculated.

[0156] The minimum curvature method will now be very briefly described with reference to FIG. 9A. As noted above, the estimated well trajectory is completely defined by the spatial location (e.g. Northing coordinate, Easting coordinate, depth coordinate (N.sub.0,E.sub.0,Z.sub.0)) at MD=MD.sub.0 together with a list of (MD,Inclination(θ),Azimuth(φ)) values measured at specific points (i) along the entire length of the well path, referred to as survey points or station survey points (starting at MD=MD.sub.0). The typical distance between survey points is around 30 m, but this may be greater or less in certain cases.

[0157] The inclination (θ) is the angle between the estimated well path and the vertical axis; and the azimuth (φ) is the angle between the estimated well path, projected on a horizontal (lateral) plane, and the Northing axis.

[0158] The azimuth and inclination define the tangential unit vector along the estimated well path at the survey point i: {circumflex over (t)}.sub.i=(sin θ.sub.i cos φ.sub.i, sin θ.sub.i sin φ.sub.i, cos θ.sub.i).

[0159] The minimal curvature method assumes that the estimated well path between two consecutive survey points (i, i+1) is a circular arc completely defined by the position (N.sub.i,E.sub.i,Z.sub.i) at survey point i, the tangential vectors {circumflex over (t)}.sub.i and {circumflex over (t)}.sub.i+1 at i and i+1, and the MD difference S.sub.ii+1=MD.sub.i+1−MD.sub.i (which is considered to be the arc length).

[0160] With given position at MD.sub.0 and the list (MD.sub.i, θ.sub.i, φ.sub.i) all points (N.sub.i,E.sub.i,Z.sub.i) along the estimated well path can be uniquely computed. As such, the position (N.sub.0,E.sub.0,Z.sub.0) at MD=MD.sub.0 and list (MD.sub.i, θ.sub.i, φ.sub.i) define the estimated trajectory of the well path.

[0161] Using this method, the initial well path estimate is obtained.

[0162] Referring to the figure, the following is provided, for clarity.

[0163] The angle arc angle α.sub.12 is given by:

[00003] $α_{12} = 2 \sin^{- 1} {\sqrt [\sin^{2} (\frac{θ_{2} - θ_{1}}{2}) + \sin θ_{1} \sin θ_{2} \sin^{2} (\frac{ϕ_{2} - ϕ_{1}}{2})]} R_{12} = \frac{S_{12}}{α_{12}}$

where R.sub.12 is the radius and S.sub.12 is the arc length and α.sub.12 is in radians (although where a small a straight line approximation may be used, resulting in different formulae as described in “A compendium of directional calculations based on the minimum curvature method”, Sawaryn & Thorogood, SPE 2005 Drilling & Completion.)

[00004] ${\hat{n}}_{12} = \frac{{\hat{t}}_{1} + {\hat{t}}_{2}}{\sin (α_{12})}$

where n.sub.12 is the normal vector

{right arrow over (C)}.sub.12={right arrow over (P)}.sub.1−R.sub.12({circumflex over (t)}.sub.1×{circumflex over (n)}.sub.12)

where C.sub.12 is the location of the centre of the circle and P.sub.1 is the location of the first survey point being considered (at MD.sub.1)

[00005] ${\overset{.fwdarw.}{P}}_{2} = {\overset{.fwdarw.}{P}}_{1} + \frac{S_{12}}{α_{12}} \tan (\frac{α_{12}}{2}) ({\hat{t}}_{1} + {\hat{t}}_{2}) and$

where P.sub.2 is the location of the second survey point being considered (at MD.sub.2).

[0164] Turning back to FIG. 7, in S72, an estimate for a well path position is obtained using seismic data. In this example, a plurality of points, each representing an estimate for the well path position, are provided using seismic data. This plurality of points are provided using the method described above with reference to FIGS. 1 to 6.

[0165] Before providing the well path estimate it must be decided the minimum MD from which the improved well path estimate should be calculated (minMD). This may be from the start of the wellbore (e.g. MD=0), or at a specified measured depth. This may be selected by an operator, for example.

[0166] The minimum curvature method is used to determine the well path estimate. In order to determine the well path estimate using the minimum curvature method, values for the inclination, azimuth and measured depth are required (as well as the location of the well path estimate starting point). At least one of these values will be obtained using an optimisation process based on the seismic data position estimates. The navigation measurements will be used as starting points for the optimisation process.

[0167] In certain embodiments, both the inclination and azimuth may be obtained using an optimisation process based on the seismic data position estimates. However, in the present example only the azimuth values will be obtained using an optimisation process.

[0168] In S73, a generalised distance between a general definition of a well path defined using the minimum curvature method and a position estimate derived from seismic data is determined. This distance will be the function that is optimised to obtain the well path estimate.

[0169] In the present example, the estimated well path positions derived from the seismic data are known to be accurate with regard to their lateral location, but have a larger spread in the vertical, or depth, dimension. The estimated lateral position of the well path derived from seismic data is more accurate than that calculated using magnetic and/or gyroscopic measurements from the downhole tool. As such, the well path positions estimated from seismic data are used to determine the lateral component of the well path estimate (also referred to herein as an “improved well path estimate”).

[0170] The estimated depth and inclination of the well path estimate are determined using the navigation measurements from the downhole tool, because in this specific case the depth and inclination estimates derived using magnetic and/or gyroscopic measurements from the downhole tool are more accurate than those provided by the seismic data well position estimates.

[0171] Accordingly, the lateral position component of the improved well path estimate is derived using the position estimates from seismic data, and the vertical position component of the improved well path estimate is derived using navigation measurements from a downhole tool.

[0172] FIG. 8 shows the initial well path estimate derived from the navigation measurements, position estimates derived from seismic data and the improved well path estimate, in a horizontal plane.

[0173] In FIG. 8, the improved well path estimate is seen to follow the position estimates derived from seismic data in a lateral dimension (e.g. in a horizontal plane). The position estimates derived from seismic data are known to be more accurate in a lateral dimension than those obtained from magnetic and/or gyroscopic measurements. One reason for this is that inaccuracies are cumulative when using navigation measurements from a downhole tool, whereas each data point is independent when using position estimates derived from seismic data, and so inaccuracies are not cumulative.

[0174] For these reasons, in the present example the lateral distance between a generic definition of a well path and a position estimate derived from seismic data is used for the optimisation process, so as to capture the lateral accuracy of the seismic data locations while relying on the navigation measurements for the vertical component. In particular, the lateral distance is used to generate an objective function that is minimised to determine a parameter for the well path estimate.

[0175] Once an equation for the lateral distance is derived, an objective function incorporating the distance can be optimised to determine the lateral component of the (improved) well path estimate.

[0176] FIG. 9B schematically illustrates the method by which an expression for the lateral distance between the generic definition of a minimum curvature well path and the seismic data position estimate is obtained.

[0177] As discussed above, a plurality of seismic data position estimates are provided. The below method will be discussed with respect to a single seismic data position estimate j. In practice, the following method will be undertaken for a plurality, or all, of the seismic data position estimates.

[0178] In order to obtain a formula for the distance between a general definition of a well path modelled using the minimum curvature method and the position estimate derived from seismic data, the nearest two survey points P.sub.1, P.sub.2 along the general definition of a well path are identified for the seismic data position estimate j. The arc S.sub.12 between these two survey points P.sub.1, P.sub.2 is identified as the closest arc segment to the seismic data position estimate j. The position estimate j is associated with this arc S.sub.12. When undertaking this method for a plurality of seismic data position estimates, each will be associated with its nearest arc.

[0179] The seismic data position estimate j is projected vertically in the plane spanned by the circle associated with arc S.sub.12—this projected point is shown as j.sub.P.

[0180] The seismic data position estimate j and has a position (n.sub.j,e.sub.j,z.sub.j) and the projected seismic data position j.sub.P has a position (n.sub.j,e.sub.j,z.sub.j,proj), where

[00006] $z_{j, proj} = \frac{{\overset{.fwdarw.}{P}}_{1} .Math. {\hat{n}}_{12} - n_{j} n_{12} (1) - e_{j} n_{12} (2))}{n_{12} (3)} {\overset{.fwdarw.}{Q}}_{j} = {\overset{.fwdarw.}{C}}_{12} + R_{12} .Math. \frac{({\overset{.fwdarw.}{C}}_{12} - (n_{j}, e_{j}, z_{j, proj}))}{.Math. {\overset{.fwdarw.}{C}}_{12} - (n_{j}, e_{j}, z_{j, proj}) .Math.}$

where Q.sub.i is the point on the arc closest to the projected point j.sub.P
and

d.sub.j=√{square root over ((Q.sub.j(1)−n.sub.j).sup.2+(Q.sub.j(2)−e.sub.j).sup.2)}

[0181] This allows us to derive the lateral distance between the well path and the seismic data position estimate in terms of the parameters used to define the minimum curvature well path and the seismic data position estimates.

[0182] To obtain the azimuth values for the (improved) well path estimate, an optimisation process is used to minimise an objective function based on the sum of the lateral distances of a plurality of seismic data position estimates and thus, effectively, find the azimuth values for the best well path estimate that passes through the seismic data position estimates. To achieve this, an optimisation procedure is employed, to minimise an objective function based on generalised definition of the lateral distances d.sub.j (i.e. between the seismic data position estimates and the associated arc of the generic definition of a minimum curvature well path).

[0183] The optimisation process starts with the navigation measurements from a downhole tool, S74. By starting with the azimuth values from the navigation measurements, and optimising this function with respect to the azimuth values, optimised azimuth values are calculated to fit the (improved) well path estimate to the position estimates derived from seismic data in the lateral plane.

[0184] The improved well path estimate is calculated using these values.

[0185] In this example, an optimising procedure is used to minimize the objective function:

[00007] $J (ϕ_{minMD}, .Math., ϕ_{N}) = \underset{j}{.Math.} d_{j}^{2}$

[0186] Where N is the number of survey points along the well path, (φ.sub.minMD, . . . , φ.sub.N) are the azimuth values for each of the survey points from minMD to N with φ.sub.minMD being the azimuth value at the first survey point being considered and φ.sub.N being the azimuth value at the last survey point being considered, and d.sub.j is the lateral distance between the seismic data position estimate j and the closest point on the generic definition of a minimum curvature well path estimate (i.e. arc S.sub.12).

[0187] The azimuth values φ.sub.l are constrained, for example with an upper and lower bound around the navigation measurements from a downhole tool. The upper and lower bound may be determined by the uncertainty associated with the measurements (e.g. the gyroscopic measurements) of the downhole tool. In the present example, the upper and lower bounds for the azimuth are ±0.74° around their measured value.

[0188] In the present example the objective function is based on the lateral distance (residual) between the, or each, seismic data position estimate and the minimum curvature well path estimate. However, in alternative examples where the initial well path estimate is optimised with respect to both the azimuth and inclination, the objective function may be based on the total distance vector (i.e. including both depth, northing and easting dimensions) between the position estimate derived from seismic data and a general definition of a well path modelled using the minimum curvature method.

[0189] Once azimuth values are obtained from the optimisation process, they are used—together with inclination and measured depth values from navigation measurements from a downhole tool—to calculate a well path estimate using the minimum curvature method, as outlined in S75.

[0190] Once the optimisation process is complete and the improved well path estimate has been calculated, a measure of the uncertainty is calculated, S76.

[0191] The measure of the uncertainty for the improved well path estimate is calculated for the improved well path estimate from the minimum MD from which the improved well path estimate was calculated (minMD). For sections of the well where an improved well path estimate is not provided, the uncertainty measurement (e.g. the uncertainty ellipse) for the initial well path estimate is used (which may be derived from the uncertainty inherent in the measurements from the downhole tool).

[0192] Any suitable statistic distribution may be used to provide a measure of the uncertainty. In the present case, the uncertainty is measured using the student distribution. The global P % lateral uncertainty ellipse along the improved well path estimate (from minMD) is given by the constant value as follows:

[00008] $Uncertainty (P) = t (1 - (1 - P) / 2, M - (N - minMD + 1)) \sqrt{\frac{1}{M} {.Math.}_{j = 1}^{M} d_{j}^{2}}$

where M is the number of position estimates derived from seismic data for the portion of the well being considered and t(P,df) gives the P % student distribution for df degrees of freedom.

[0193] In the present example, a value of P=0.99 (99% uncertainty ellipse) is used.

[0194] In other examples, the uncertainty can be computed per arc segment (i.e. between consecutive survey points). This can be done by summing the M.sub.i position estimates derived from seismic data belonging to segment i, and M.sub.i−1 degrees of freedom in t(P,df).

[0195] FIGS. 10A through 12G relate to an example well.

[0196] FIGS. 10A through 10D show the initial well path estimate (based solely on the navigation measurements from a downhole tool) and improved well path estimate (using azimuth values obtained by an optimisation process based on the seismic data position estimates) along with their associated uncertainty ellipses, the seismic data positions estimates and the PRM nodes. FIGS. 10A through 10D show varying sections and magnifications of the well path. In FIGS. 10A and 10B, a single uncertainty ellipse is calculated for the whole improved well path estimate. In FIGS. 100 and 10D, an independent uncertainty value is determined for each arc segment (i.e. for each survey point pair). For the purpose of clarity, the uncertainties for each segment are plotted block-wise, rather than with a smooth curve.

[0197] FIGS. 10A through 10D show that the lateral uncertainty values are much lower for the improved well path estimate compared to the initial well path estimate.

[0198] FIGS. 11A through 11G show comparisons of the initial well path estimate and the improved well path estimate. The following parameters are plotted with respect to MD: MD, inclination, azimuth, DogLeg, TVDSS, Northing and Easting. As can be seen, at this scale the differences are relatively small. The most noticeable differences are in the Easting values, depicted in FIG. 11G.

[0199] FIGS. 12A through 12G plot the differences in MD, inclination, azimuth, DogLeg, TVDSS, Northing and Easting between the initial well path estimate and the improved well path estimate with respect to MD. The differences in the azimuth (bounded by the upper and lower bound of ±0.74° around the downhole measurements are clearly shown in FIG. 12C. The resulting change in DogLeg can also be seen. The resulting differences in Northing and Easting values along the estimated well paths are shown in FIGS. 12F and 12G.

[0200] FIGS. 12B and 12E show differences in the inclination and TVDSS, however, given the scale used in FIGS. 12B and 12E, the differences shown in these Figures are de minimis. They are mainly due to data collection/processing phenomena, rather than intentional differences between the estimated well paths, per se.

[0201] The present invention has been described above purely by way of example. Modifications in detail may be made to the present invention within the scope of the claims as appended hereto. Furthermore, features from one example may be combined with an alternative example unless such a combination is explicitly precluded.

METHODS FOR ESTIMATING A POSITION OF A WELL PATH WITHIN A SUBSURFACE FORMATION

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