System and Method for Determining Three Dimensional Well Position

Abstract

A system and method for improving the 3D positional description of well geometry, subsurface measurements and subsurface services as provided along the wellbore and improve the provision of the 3D positional uncertainty. The method selects a well reference point, calibrates the AHD, Incl and Az measurements, selects a measurement station positioned, observes measurements at the measurement station, selects at least one or more additional measurement station(s), repeats the measurements, transforms calibrated interval AHD, Incl. and Az observed measurement values into V, N and E interval values, summates V, N and E interval values to create a 3D positional description of each measurement station. The method then determines the AHD, Incl. and Az value uncertainties at each measurement station, calculates and concatenates the AHD, Incl. and Az value uncertainties and creates a depiction of these associated uncertainties along the length of the wellbore in terms of V, N and E positions from ZDP.

Description

FIELD OF INVENTION

The present invention relates to a system and method for determining the three dimensional (“3D”) position and in particular to the determination of position and positional uncertainty of any subsurface point along a wellbore.

BACKGROUND OF THE INVENTION

Typically, a well is created by drilling a hole 5 cm to 1 metre (2 in to 40 in) in diameter into the earth with a drilling rig or similar such device. The drilling rig operates a drill string made up of drill pipes with a drill bit attached to the end which cuts into the earth. The drill string comprises a number of pipe sections which are connected together to lengthen the drill string as the drill bit cuts further into the earth.

The 3D position of the bit and any point along the wellbore is expressed as “Vertical Depth (“V”), North separation (“N”) and East separation (“E”) from the well reference point, being often named Zero Depth Point (“ZDP”), being at the drill floor or some other specific location, also being along the wellbore below the drill floor. The well reference point is preferably referenced to a named Permanent Datum (“PD”) preferably being Ground Level, Mean Sea Level, Sea Fllor or some other defined datum.

During well drilling operations, the well direction is steered to arrive at a 3D point in the subsurface. It is highly desirable to be able to accurately determine the subsurface position of the drilled wellbore and of the drill bit at the furthest extent of the hole or any point along the wellbore. It is also highly desirable to accurately determine the 3D position of the well geometry, well constructional, geophysical and formation characteristics registered using wireline sensors and measurement while drilling (“MWD”) and/or logging while drilling (“LWD”) sensors and similarly conveyed sensors acquired along the length of the drilled well. It is highly desirable to be able to locate accurately in 3D the provision of subservice services provided by wireline or by drill pipe, such as formation and fluid sampling and pressures, seismic related services and other well construction related activities.

The 3D position cannot be measured directly and is ascertained by the mathematical manipulation of the observed measurements of Along-hole Depth (“AHD”—the linear distance along the centreline of the wellbore from the well reference point), Inclination (“Incl.”—the angle from vertical of the centreline of the wellbore) and Azimuth (“Az”—the directional downhole angle based on North of the centreline of the wellbore). AHD is defined using wireline or drill pipe length observations with or without corrections. Incl. and Az measurements are typically performed using wireline conveyed instruments, and/or using similar drill pipe conveyed MWD and LWD instruments. Environmental and measurement corrections may or may not be applied.

The observed measurements made are traceable to a recognized industry measurement standard (e.g. International Bureau of Weights and Measures (BIPM), Sevres, France, National Institute of Standards and Technology (NIST), Gaithersburg, USA). The use of environmental and measurement corrections return the observed values to values closer to the traceable calibration units recognized in industry.

The AHD, Incl. and Az observed measurements and calculations are subject to accuracies which influence the uncertainty of the calculated 3D positioning. Increased uncertainty in the 3D position leads to ambiguity and difficultly in ascertaining, for example, positional characteristics of the wellbore as applied in wellbore surveying, geological modelling, reservoir descriptions and asset value determination.

SUMMARY OF THE INVENTION

An aspect of the present invention is a system and method for improving the 3D positional description of well geometry, subsurface measurements and subsurface services as provided along the wellbore and improve the provision of the 3D positional uncertainty.

Another aspect of the invention aims to improve the description of the 3D positional results and the associated 3D positional uncertainty information.

In accordance with a first aspect of the invention there is provided a method for determining the 3D position of a wellbore, the method comprising the steps of: selecting a well reference point;

• • calibrating the AHD, Incl and Az. measurements;
  • selecting a measurement station positioned in the wellbore where AHD, Incl. and Az observations are made;
  • observing AHD, Incl and Az measurements at the measurement station; selecting at least one or more additional measurement station(s);
  • observing the AHD, Incl. and Az measurements at the additional measurement station(s);
  • transforming the calibrated interval AHD, Incl. and Az observed measurement values into V, N and E interval values;
  • summating the V, N and E interval values to create a 3D positional description of each measurement station;
  • determining the AHD, Incl. and Az value uncertainties at each measurement station over each observed interval;
  • calculating and concatenating the AHD, Incl. and Az value uncertainties at each sequential measurement station;
  • and creating a depiction of these associated uncertainties along the length of the wellbore and/or depicting these in terms of V, N and E positions from ZDP.

Preferably the well reference point comprises a surface marker position or a drill floor or at a defined position along the wellbore.

Preferably the well reference point is identified as having a defined 3D positional identification which is an elevation from a given surface datum elevation and a north and an east location identified using a geodetic positional reference.

Preferably the well reference point comprises a zero depth point (ZDP) for a drilling rig or wellbore.

Optionally, the well reference point is a wellbore sub-surface point identified as having a defined 3D position.

Preferably, the position of the well reference point are subject to a given accuracy which is defined by a fixed uncertainty value for each dimensional measurement (“ToolJointError”).

Preferably, the measurement stations are positions in the wellbore between which the wellbore trajectory is regarded as being constant or near-constant.

Preferably, each wellbore trajectory between measurement stations is characterized by having constant or near-constant AHD correction, Incl. and Az values such that the whole wellbore to ZDP can be characterized geometrically as a continuum of constant or near-constant trajectory lines.

Preferably, the measurement station is positioned at the end of constant or near-constant AND correction, Incl. and Az values.

Alternatively, the measurement station is positioned to account for changes in well geometry, well architecture, or proximity to other well bores. For example, at positions where it is known that the well direction changes, where there are changes to the well casing or other subsurface tubulars, or where there is a proximity to other wellbores.

Alternatively, the measurement station is positioned to account for changes in geology intercepted by the wellbore.

Alternatively, the measurement station is positioned to account for the location of zones of interest to the observer. For example, at positions where it is known that there are geological boundaries or changes in reservoir characteristics.

Alternatively, the measurement station is positioned by user selection.

Advantageously, a user may control the number of measurement stations and measurement station positions and therefore control the associated uncertainty.

Preferably, each measure station is identified along the wellbore at given well depths whereby the interval to each subsequent measure station has a constant, or near-constant AHD correction, Incl. and Az values.

Preferably the parameter values measured are AHD, Incl and Az.

Preferably, where AHD correction, Incl. and Az values depart to different values beyond a defined tolerance, a new measure station is identified at a defined AHD.

Optionally, where additional measurement stations may be located at positions along the wellbore where there are well construction, geological or reservoir property reasons for including a measurement station.

Optionally, where additional measurement stations may be located where the concatenation of the interval uncertainties results in an improved uncertainty value.

Optionally, AHD is measured using an observed drill pipe depth measurement.

Optionally, the observed drill pipe depth measurement is based on drill pipe length, preferably expressed as a “pipe tally” record.

Optionally, the observed drill pipe depth measurement is calibrated and corrected for environmental and measurement influences such as temperature and drill pipe axial tension, included in the reporting process.

Optionally, AHD is measured using a wireline measurement.

Optionally, the observed wireline length measurement is calibrated and corrected for environmental and measurement influences such as temperature and wireline tension, included in the process.

Optionally, Az is measured using an observed drill pipe depth measurement.

Optionally, Az is measured using a wireline measurement.

Preferably, the Az as measured is calibrated and corrected for environmental and measurement influences such as offset orientation, measurement drift, directional measurement anomalies, and/or so-called “sag”, included in the reporting process.

Optionally, Incl. is measured using an observed drill pipe depth measurement.

Optionally, Incl. is measured using a wireline measurement.

Preferably, the Incl. as measured is calibrated and corrected for environmental and measurement influences such as offset orientation, measurement drift, directional measurement anomalies, and/or so-called “sag”, included in the reporting process.

Optionally, inter-measure stations may be comprised of observed AHD, Incl. and Az measurements, or may be derived from protractions of observed measurement values.

Preferably, the step of transforming the calibrated and corrected AHD, Incl. and Az values into V, N and E values comprises identifying those individual contributory elements of V, N and E from the observed values of AHD, Incl. and Az and transforming them into a summated V, N and E values.

Preferably, the step of ascertaining the calibrated measurement value uncertainties of the V, N and E values is comprised of transforming the calibrated AHD, Incl and Az values and their accuracies into V, N and E uncertainty values through identifying those individual contributory elements of V, N and E from the observed values and the accuracies of AHD, Incl. and Az measurements.

Preferably, the transformations are as defined in the table of FIG. 10 attached hereto.

Preferably, the interval V uncertainty (Δ.V_i) comprises the combined contributions of AHD and Incl. uncertainties.

Preferably, interval V value uncertainty is given by the following expression for any interval “i” where Δ.u refers the component uncertainty,

$\Delta .V_i=\sqrt{{\left(\Delta .u_{{\mathrm{AHD}}_i}^V\right)}^2+{\left(\Delta .u_{\mathrm{Incl}{.}_i}^V\right)}^2},$

Preferably the interval north (N) value comprises the combined contributions of AHD, Incl. and Az uncertainties for any interval Preferably the interval north (N) value uncertainty (Δ.N_i) is given by the expression for any interval “i”,

$\Delta .N_i=\sqrt{{\left(\Delta .u_{{\mathrm{AHD}}_i}^N\right)}^2+{\left(\Delta .u_{\mathrm{Incl}{.}_i}^N\right)}^2+{\left(\Delta .u_{{\mathrm{Az}}_i}^N\right)}^2}$

Preferably the interval east (E) value uncertainty (Δ.E_i) comprises the combined contributions of AHD, Incl. and Az uncertainties for any interval “i”,

Preferably the interval east (E) value uncertainty is given by the expression for any interval “i”,

$\Delta .E_i=\sqrt{{\left(\Delta .u_{{\mathrm{AHD}}_i}^E\right)}^2+{\left(\Delta .u_{\mathrm{Incl}{.}_i}^E\right)}^2+{\left(\Delta .u_{{\mathrm{Az}}_i}^E\right)}^2}$

Preferably, an inter-measure station continuum of V, N and E values between measure stations is created.

Optionally, subsurface data is synchronised to the calculated and presented 3D positional and positional uncertainty results.

Optionally, subsurface services are provided at a required 3D locations using the calculated and presented 3D positional results.

Optionally the 3D position and positional uncertainty can be incrementally ascertained by making AHD, Incl. and Az measurements by drilling the wellbore deeper and then adding (a) further measure station(s), so that the position and positional uncertainty data is a series of increments defined by sequential additional of measure station 3D positions and associated uncertainties.

A computer system comprising program instructions or process logic instructions for the operation of the method in accordance with the first aspect of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way of example only, with reference to the drawings, in which:

FIG. 1 is a flow diagram which illustrates a first example of a method in accordance with the present invention;

FIG. 2 is a flow diagram which illustrates a second example of a method in accordance with the present invention;

FIG. 3 is a flow diagram which illustrates a third example of a method in accordance with the present invention;

FIG. 4 is a schematic diagram of an example wellbore showing measurement points of a drilled well where the interim lengths of wellbore have the same, or close to the same, AHD correction, Incl. and Az directions, and the measure stations represent the calculation basis for the 3D based positional determination and associated uncertainty;

FIGS. 5a and 5b are schematic diagrams illustrating AHD and the AHD value uncertainty, showing this uncertainty in the line of the wellbore and illustrating its 3D transformation based on the measurement accuracy (not to scale);

FIGS. 6a and 6b are schematic diagrams illustrating Az and the Az value uncertainty based on North, showing this uncertainty perpendicular to the wellbore in a horizontal plane and illustrating its 3D transformation based on the measurement accuracy (not to scale);

FIGS. 7a and 7b are schematic diagrams illustrating Incl. and Incl. value uncertainty from vertical, showing this uncertainty perpendicular and in the same vertical plane of the wellbore and illustrating its 3D transformation based on the measurement accuracy (not to scale);

FIG. 8 is a schematic diagram illustrating V transformation, the geometric relationship that describes V based on AHD and Incl;

FIG. 9 is a schematic diagram illustrating N and E transformation and the geometric relationship that describes N and E based on the horizontal displacement of the wellbore from the vertical V;

FIG. 10 is a graph of V positional uncertainty result measured in metres; and

FIG. 11 is a table of transformation of AHD, Az and Incl. uncertainties to V, N and E uncertainties.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

An aspect of the present invention provides a method and system for determining the 3D position of a wellbore and the associated uncertainty of this depiction. This is done by observing AHD, Incl. and Az values at identified measure stations and applying corrections to these values to arrive at calibrated measurement values. These interval values are subject to accuracies that result in uncertainties of the resulting calibrated values per measure station. These interval values and associated uncertainties are transformed into V, N and E values and the values are summated to arrive at a 3D positional description of each measure station. The associated 3D interval V, N and E value uncertainties are concatenated to arrive at uncertainties of the summated V, N and E positional values. In some examples, the interval between measure stations are subject to negligible differences in Incl. and Az. The then resulting positional 3D positions and uncertainties can be interpolated, resulting in a continuum of 3D positional values and 3D positional uncertainties. All three components, AHD, Incl. and Az are equally incorporated into the transformation process, the weighting of each of these measurements is equally distributed giving a balanced interpretation of the 3D dimensional position and uncertainty description.

As discussed herein, an observation is a value without an assigned uncertainty and a measurement is an observation with an assigned uncertainty this based on the accuracy of the observation equipment and process projected over the values being observed.

In the examples provided below, the well reference point is the start of the wellbore, typically identified as being the drill floor, a surface marker position, or the like. The well reference point is typically identified as having a defined 3D positional identification as being an elevation from a given surface datum elevation, and a north and an east location identified using a geodetic positional reference. For a drilling rig, this is often referred to as the ZDP.

The reference point may also be a wellbore sub-surface point identified as having a defined 3D position (e.g. sea bed, casing shoe, side track Y-spilt point, or a wellbore transgression of a defined geological marker). In this case the (subsurface) reference point uncertainty is defined accordingly.

Along the wellbore from the reference point, intervals are identified where the wellbore trajectory can be described as being constant or near-constant. These intervals are characterized by having constant or near-constant Incl. and Az such that the wellbore can be characterized geometrically as a continuum of constant or near-constant trajectory straight-lines. The end of each straight-line is identified as being a measure station. Each measure station is identified along the wellbore at given AHD points where by the interval to each subsequent measure station has a constant or near-constant Incl. and Az values. Where these Incl. and Az values depart to different values beyond a defined tolerance, a new measure station may be identified.

At the surface, there is an inherent uncertainty in the AHD, Az and Incl. measurements at the reference point for these measurements. This uncertainty is the referred to as the “ToolJointError” and represents a fixed uncertainty value for each dimensional measurement i.e. as if the uncertainty is taken at surface with no wellbore effect.

At the well reference point the ToolJointError for AHD is the same as that for V, ToolJointError(AHD). The ToolJoinError(s) for Incl. and Az are equal to the uncertainty of both Incl. and Az combined defined at the start of the measurement and dependent on the characteristics of each Incl. and Az measurement. These lateral horizontal uncertainties are expressed as ToolJointError(N) and ToolJointError(E).

Wellbore depth is measured using drill pipe or wireline. The drill pipe is typically measured using a recorded length of drill pipe, typically expressed as a pipe tally, which, preferably, may be ascertained using tape measure or laser length measurement. The wireline length is typically recorded making use of fixed wireline length intervals or recording of the movement of a calibrated measurewheel, or a combination of both. The temperature and tension at which these surface measurements are made is recorded. The observed drill pipe and wireline depth values are corrected for measurement and environmental influences, typically including temperature and tension, resulting in returning calibrated values, being AHD. The way in which the length observation correction is created and applied is not the subject of this current invention, only that a correction is applied. The applied correction may be zero.

FIG. 1 is a flow diagram which illustrates a first example of a method in accordance with an aspect of the present invention. In a first step, well reference point is selected 2. Arrow 1 shows the order of steps in the method.

The measurement station position in the wellbore is selected 3 AHD, Incl. and Az measurements are calibrated and measurement accuracies ascertained 4.

AHD, Incl. and Az are measured at the measurement station 5.

V, N and E positions references are calculated to well reference point 6.

AHD, Incl. and Az positional uncertainties are calculated and transformed to V, N and E positional uncertainty reference to well reference point 7.

Optionally, additional measurement station(s) position(s) in the wellbore are selected. Subsequently calculate V, N and E positions reference to well reference point using then already defined previous measurement station(s).8.

AHD, Incl. and Az are measured at (optional) additional measurement station(s) 9.

Calculate AHD, Incl. and Az positional uncertainties and transform to V, N and E positional uncertainties per interval and sequentially concatenate these reference to the well reference point. 10.

V, N and E positional results are depicted 11.

V, N and E positional uncertainty results are depicted 1.

FIG. 2 is a flow diagram 21 which illustrates a second example of a method in accordance with the present invention.

Firstly ToolJointError for AHD, Incl. and Az are defined 23. The accuracy of the AHD, Incl. and Az measurements is defined (25).

Measurement stations and intervals a.-f. are defined 27. For each measurement station a.-f., 29:

• • Observe AHD, Incl and Az values;
  • Calculate AHD, Incl. and Az corrected values;
  • Transform and summate V, N and E values;
  • Model-fit accuracy: calculate and summate area under departure curve along
  • measurement station interval for AHD correction, incl. and Az;
  • Uncertainty: calculate AHD; Incl. and Az interval uncertainties;
  • Transform and concatenate V, N and E uncertainties;
  • Depict results for V, N and E values against AHD;
  • Depict results for V, N and E uncertainty against AHD 31;
  • is Depict results for V, N and E values against V;
  • Depict results for V, N and E uncertainty against V 33.

Calibration accuracy: for each observation of AHD, Incl., and AZ a calibration accuracy is used representing the calibration and observation accuracies of these individual parameters.

Correction accuracy: for each observation made of AHD, Incl., and Az, a correction accuracy is used representing the accuracy of the calculated correction based on the measured correction parameter accuracy and the accuracy of the correction algorithm used.

FIG. 3 is a flow diagram 18 which illustrates a third example of a method in accordance with the present invention. Arrow 20 shows the order of steps in the method.

• • Step 1. Define ToolJointError for AHD, Incl. and Az 22,
  • Step 2. Define accuracy of AHD, Incl. and Az measurements 24,
  • Step 3. Define measurement stations and intervals a.-f 26,
  • Step 4. For each measurement station a.-f., observe AHD, Incl. and Az values 28,
  • Step 5. For each measurement station: calculate AHD, Incl. and Az corrected values 30,
  • Step 6. Transform and summate V, N and E values 32,
  • Step 7. Based on AHD, Incl. and Az measurement accuracies, calculate interval value uncertainties 34,
  • Step 8. Calculate and summate area under departure curve along measurement station interval of AHD correction, Incl. and Az to create model-fit accuracy per measurement interval 36,
  • Step 9. From model-fit accuracy area calculate interval model-fit uncertainty per AHD correction, Incl. and Az measurement 38,
  • Step 10. Uncertainty: calculate interval AHD, Incl. and Az uncertainties and transform and sequentially concatenate V, N and E uncertainties 40.
  • Depict results for V, N and E values against pipe length,
  • Depict results for V, N and E uncertainties against pipe length.
  • Depict results for V, N and E values against AHD,
  • Depict results for V, N and E uncertainties against AHD.
  • Depict results for N and E values against V,
  • Depict results for N and E uncertainty against V. 42

Model-fit accuracy: for each interval there may be a difference between the assumed constant or nearly-constant straight-line representing the AHD correction, Incl. and Az values along the interval being considered and the suspected or known variances of AHD correction, Incl. and Az over that interval. This also describes what is known, or suspected, to be the difference between the constant or nearly-constant straight-line AHD correction, Incl. and Az behaviour over each straight-line interval. These may be represented by actual points of AHD correction, Incl. or Az data or a continuum of data or assumed data expressed as a curve. The differences between the straight-line and the suspected or known responses are expressed as an area. This area represents the variance of the straight-line assumption from the suspected, or actual, behavior of AHD correction, Incl. and Az over the observation interval and is called the model-fit accuracy. The area representing this difference is divided by the length of the interval and hence results in an uncertainty value called the model-fit uncertainty for that observation interval.

The terms calibration accuracy, correction accuracy, and model-fit accuracy are used to arrive at uncertainties that describe each of the AHD correction, Incl. and Az values per interval considered.

AHD, Incl. and Az uncertainties are transformed to V, N and E uncertainties per interval considered.

The accuracy of drill pipe and wireline length measurements contribute to the uncertainty of the AHD value as described with reference to FIGS. 4a and 4b.

FIG. 4 is a schematic diagram of an example well 41 showing a reference point 43 and a number of measurement stations a-f numbered 45 to 55. N 57 and E 59 are also shown. Double headed arrow 51 shows the position along the hole and the along hole depth with length measurement accuracy Δ.AHD_i. Double headed arrow 53 shows the position along the hole and A degrees N with accuracy +/− metres. Double headed arrow 55 shows the position along the hole and I degrees vertical with accuracy +/− degrees Δ.li_uncertainty+/− metres.

FIG. 5a is a schematic diagram 61 illustrating AHD 65 and Δ.AHD 67, FIG. 4b is a schematic diagram 63 illustrating Δ.u_AHDi the 3D uncertainty transformation. The accuracy with which the temperature and tension measurements are made, and the mathematical formulation of the correction, contribute to the correction value uncertainty. The difference of the AHD correction parameters used from the actual continuum of well temperature and tension contribute to the accuracy of the applied correction resulting in a model-fit uncertainty. The AHD model-fit uncertainty is the difference between the area under the continuum curve of correction and under the measure station interval lines of correction due to temperature and tension.

These AHD uncertainties are summated and include the depth measurement ToolJointErrorto arrive at the AHD uncertainty applicable to each measure station.

The expressions to arrive at AHD and AHD uncertainty are:

AHD_i=Obs.Depth_i+AHD.Corr_i,

• • where
  • AHD; =along-hole depth over any wellbore interval, i, with constant or near-constant Incl. and Az 67,
  • Obs.Depth; =observed depth without correction over any wellbore interval with constant or near-constant Incl. and Az,
  • AHD.Corr; =observed depth value correction over any wellbore interval with constant or near-constant Incl. and Az.

The AHD of any interval is described as:

${\mathrm{AHD}}_i=\sqrt{V_i^2+{\mathrm{AHD}}_i^{h^2}}=\sqrt{V_i^2+N_i^2+E_i^2},$

• • (see FIG. 8, a schematic diagram 121 illustrating V transformation) where
  • V_i=vertical depth over any wellbore interval with constant or near constant Incl. and Az,
  • AHD^h_i=horizontal distance from vertical over any wellbore interval with constant or near-constant Incl. and Az,
  • N_i=north directional distance over any wellbore interval with constant or near constant Incl.,
  • E_i=east directional distance over any wellbore interval with constant or near-constant Incl. (FIG. 9, 131).

The north (N) and east (E) dimensions of any interval are described as

$N_i={\mathrm{AHD}}_i^h\times \cos {\mathrm{Az}}_i=\left({\mathrm{AHD}}_i\times \sin \mathrm{Incl}{.}_i\right)\times \cos {\mathrm{AZ}}_i,$ $E_i={\mathrm{AHD}}_i^h\times \cos {\mathrm{Az}}_i=\left({\mathrm{AHD}}_i\times \sin \mathrm{Incl}{.}_i\right)\times \sin {\mathrm{AZ}}_i,$

• • where
  • Az; =azimuth over any wellbore interval with constant or near-constant Incl. and Az,
  • Incl._i=inclination over any wellbore interval with constant or near-constant Incl.

The V dimension of any interval is described as

$V_i={\mathrm{AHD}}_i\times \cos \left(\mathrm{Incl}{.}_i\right),$

(see FIG. 8).

The V, N and E dimension of any series of intervals is described as

$V_n={\sum }_{n=0}^i{V}_i,$

• • where
  • V_n=true vertical depth over all sequential wellbore intervals considered, and

$N_n={\sum }_{n=0}^i{N}_i,$

• • where
  • N_n=north directional distance over any sequential wellbore intervals considered, and

$E_n={\sum }_{n=0}^i{E}_i,$

• • where
  • E_n=east directional distance over any sequential wellbore intervals considered.

The AHD uncertainty of any interval is described as

$\Delta .{\mathrm{AHD}}_i=\sqrt{\left(\Delta .{\mathrm{Calb}}_{{\mathrm{AHD}}_i}{ }^2\right)+\left(\Delta .{\mathrm{Corr}}_{{\mathrm{AHD}}_i}{ }^2\right)+\left(\Delta .{\mathrm{Mod}}_{{\mathrm{AHD}}_i}{ }^2\right)}+{\mathrm{ToolJointError}}_{\mathrm{AHD}},$

• • (see FIGS. 5a and 5b) where for any interval
  • Δ.AHD_i=AHD value uncertainty over any wellbore interval with constant or near-constant Incl. and Az,
  • Δ.Calb_AHDi=Observed length calibration value uncertainty over any wellbore interval with constant or near-constant Incl. and Az,
  • Δ.Corr_AHDi=Observed length correction value uncertainty over any wellbore interval with constant or near-constant Incl. and Az,
  • Δ.Mod_AHDi=Observed AHD correction value model-fit uncertainty over any wellbore interval with constant or near-constant Incl. and Az due to difference between observed and used correction parameters,
  • ToolJointError_AHD=Fixed uncertainty associated with any observed wellbore length.

The summated AHD uncertainty of any interval is described as

$\Delta .\mathrm{AHD}=\sqrt{{\left(\Delta .u_{{\mathrm{AHD}}_i}-{\mathrm{ToolJointError}}_{\mathrm{AHD}}\right)}^2+{\left(\Delta .u_{{\mathrm{AHD}}_i}\right)}^2}+{\mathrm{ToolJointError}}_{\mathrm{AHD}},$

• • where
  • Δ.AHD=total uncertainty over the wellbore for any n sequence of intervals to the reference point,
  • Δ.AHD_i-1=AHD value uncertainty for any sequence of i−1 intervals to the reference point.

The AHD uncertainty resolved in V of any interval is described as

$\Delta .u_{{\mathrm{AHD}}_i}^V=\Delta .{\mathrm{AHD}}_i\times \cos \mathrm{Incl}{.}_i,$

• • where
  • Δ.u_AHDi^V=V value uncertainty due to AHD value uncertainty over any wellbore interval with constant or near-constant AHD correction, Incl. and Az.

The AHD uncertainty resolved in north (N) of any interval is described as

$\Delta .u_{{\mathrm{AHD}}_i}^N=\left(\Delta .{\mathrm{AHD}}_i\times \sin \mathrm{Incl}{.}_i\right)\times \cos {\mathrm{Az}}_i,$

• • where
  • Δ.u_AHDi^N=north value uncertainty due to AHD value uncertainty over any wellbore interval with constant or near-constant Incl. and Az.

The AHD uncertainty resolved in east (E) of any interval is described as

$\Delta .u_{{\mathrm{AHD}}_i}^E=\left(\Delta .{\mathrm{AHD}}_i\times \sin \mathrm{Incl}{.}_i\right)\times \sin {\mathrm{Az}}_i,$

where

• • Δ.u_AHDi^E=east value uncertainty due to AHD value uncertainty over any wellbore interval with constant or near-constant Incl. and Az.

Az is measured using drill pipe or wireline conveyed sondes aligned parallel to the centre line of the wellbore. Az measurements are that of the downhole direction of the plane of any inclination of the wellbore based on a specified North reference. The Az measurement may be made continuously and is relevant to an aspect of the current invention at each measure station. The observed Az values may be corrected for measurement and environmental influences, typically including offset orientation (including so-called “sag”), measurement drift, and/or directional measurement anomalies. The way in which the Az correction is created and applied is not the subject of an aspect of this current invention, only that a correction is applied. The correction may be zero.

The accuracy of Az measurements contribute to the uncertainty of the Az value (see FIGS. 6a and 6b, schematic diagrams 81, 83 illustrating Azimuth and the and the azimuth Δ.Az_i uncertainty 3D transformation). The accuracy of the corrections contribute to the correction value uncertainty. The deviation of the used Az correction from the actual continuum of well Az measurements contribute to the accuracy of the measure station Az values resulting in a model-fit uncertainty. The Az model-fit uncertainty is the ratio of the difference between the area under the continuum curve and under the measure station interval lines compared to the area under the continuum Az curve line.

These Az uncertainties are summated and include the azimuth ToolJointErrorto arrive at the Az uncertainty applicable to each measure station.

The expressions to arrive at Az and Az uncertainty are:

$A{z}_i=\mathrm{Obs}.{\mathrm{Az}}_i+\mathrm{Az}.{\mathrm{Corr}}_i,$

• • where
  • Az_i=Az value over any wellbore interval with constant or near-constant Az,
  • Obs.Az_i=Observed Az value without correction over any wellbore interval with constant or near-constant Az,
  • Az.Corr_i=Az correction over any wellbore interval with constant or near-constant Az.

The Az measurement value uncertainty of any interval is described as

$\Delta .{\mathrm{Az}}_i=AH{D}_i\times \tan \left(\Delta .A{z}^o\right)$

• • (see FIGS. 6a and 6b) where
  • Δ.Az_i=Az value uncertainty over any length of wellbore interval with constant or near-constant Az,
  • Δ.Az^o=Az measurement accuracy.

The Az uncertainty resolved in north (N) of any interval is described as

$\Delta .u_{{\mathrm{Az}}_i}^N=\mathrm{AH}{D}_i\times \tan \left(\Delta .{\mathrm{Az}}^o\right)\times \sin {\mathrm{Az}}_i$

where

• • Δ.u_Az^N=north value uncertainty due to Az value uncertainty over any wellbore interval with constant or near-constant Az.

The Az uncertainty resolved in east (E) of any interval is described as

$\Delta .u_{{\mathrm{Az}}_i}^E=\mathrm{AH}{D}_i\times \tan \left(\Delta .{\mathrm{Az}}^o\right)\times \cos A{z}_i$

• • where
  • Δ.u_Az^E=east value uncertainty due to Az value uncertainty over any wellbore interval with constant or near-constant Az.

Incl. is measured using drill pipe or wireline-conveyed sondes aligned parallel to the centre line of the wellbore. Incl. measurements are based on the deviation from vertical of the wellbore at the point of measurement. Incl. measurements may be made continuously and are relevant to an aspect of the current invention at each measure station. Observed Incl. values may be corrected for measurement and environmental influences, typically including offset orientation (including so-called “sag”), measurement drift and/or directional measurement anomalies The way in which the Incl. correction is created and applied is not the subject of an aspect of this current invention, only that a correction is applied. The correction may be zero. The accuracy of Incl. measurements contribute to the uncertainty of the Incl. value (see FIGS. 7a and 7b schematic diagrams 101, 103 illustrating Inclination and the Δ.Incl._i uncertainty 3D transformation).

The accuracy of the corrections contribute to the correction value uncertainty. The deviation of the used Incl. from the actual continuum of well Incl. measurements contribute to the accuracy of the measure station Incl. values resulting in a model-fit uncertainty. The Incl. model-fit uncertainty is the ratio of the difference between the area under the continuum curve and under the measure station interval lines compared to the interval wellbore length.

These Incl. uncertainties are summated and include Incl. ToolJointErrorto arrive at the Incl. uncertainty applicable to each measure station.

The expressions to arrive at Incl. and Incl. uncertainty are:

${\mathrm{Incl}}_i=\mathrm{Obs}.\mathrm{Incl}{.}_i+\mathrm{Incl}.{\mathrm{Corr}}_i,$

where

• • Incl._i=Incl. value over any wellbore interval with constant or near-constant Incl.
  • Obs.Incl._i=Observed Incl. value without correction over any wellbore interval with constant or near-constant Incl.,
  • Incl.Corr_i=Incl. correction over any wellbore interval with constant or near-constant Incl.

The Incl. measurement value uncertainty of any interval is described as

$\Delta .{\mathrm{Incl}}_i={\mathrm{AHD}}_i\times \tan \left(\Delta .\mathrm{Incl}{.}^o\right)$

• • (see FIGS. 7a and 7b) where
  • Δ.Incl_i=Inclination value uncertainty over any length of wellbore interval with constant or near-constant Incl.
  • Δ.Incl.^o=Incl. measurement accuracy.

The Incl. uncertainty resolved in north (N) of any interval is described as

$\Delta .u_{\mathrm{Incl}{.}_i}^N=\left(\left(AH{D}_i\times \tan \left(\Delta .\mathrm{Incl}{.}^o\right)\right)\times \cos \mathrm{Incl}{.}_i\right)\times \cos {\mathrm{Az}}_i$

• • where
  • Δ.u_Incl^N=north value uncertainty due to Incl. value uncertainty over any wellbore interval with constant or near-constant Incl.

The Incl. uncertainty resolved in east (E) of any interval is described as

$\Delta .u_{\mathrm{Incl}{.}_i}^E=\left(\left({\mathrm{AHD}}_i\times \tan \left(\Delta .\mathrm{Incl}{.}^o\right)\right)\times \cos \mathrm{Incl}{.}_i\right)\times \sin {\mathrm{Az}}_i$

• • where
  • Δ.u_Incl.^E=east value uncertainty due to Incl. value uncertainty over any wellbore interval with constant or near-constant Incl.

The Incl. uncertainty resolved into V of any interval is described as

$\Delta .u_{\mathrm{Incl}{.}_i}^V=\left({\mathrm{AHD}}_i\times \tan \left(\Delta .\mathrm{Incl}{.}^o\right)\right)\times \sin \mathrm{Incl}{.}_i$

Δ.u_Incl^V=V value uncertainty due to Incl. value uncertainty over any wellbore interval with constant or near-constant Incl.

An aspect of the present invention takes the observed values of AHD, Incl. and Az and identifies those individual contributory elements of V, N and E and transforms these into a summated V, N and E uncertainty using the transform described in FIG. 11, 171.

The following arrives at the interval uncertainty for each V, N and E interval value: Summating the contributions to V interval uncertainty

$\Delta .V_i=\sqrt{{\left(\Delta .u_{AH{D}_i}^V\right)}^2+{\left(\Delta .u_{\mathrm{Incl}{.}_i}^V\right)}^2},$

where

• • Δ.V_i=the interval V uncertainty of the combined contributions of AHD and Incl.

Summating the contributions to north (N) interval uncertainty

$\Delta .N_i=\sqrt{{\left(\Delta .u_{AH{D}_i}^N\right)}^2+{\left(\Delta .u_{\mathrm{Incl}{.}_i}^N\right)}^2+{\left(\Delta .u_{{\mathrm{Az}}_i}^N\right)}^2},$

• • where
  • Δ.N_i=the interval north value of the combined contributions of AHD, Incl. and Az.

Summating the contributions to east (E) interval uncertainty

$\Delta .E_i=\sqrt{{\left(\Delta .u_{AH{D}_i}^E\right)}^2+{\left(\Delta .u_{\mathrm{Incl}{.}_i}^E\right)}^2+{\left(\Delta .u_{{\mathrm{Az}}_i}^E\right)}^2},$

• • where
  • Δ.E_i=the interval east value of the combined contributions of AHD, Incl. and Az.

Each of these dimensions is summated using for V the expression:

$\Delta .V=\sqrt{{\left(\Delta .V_{i-1}-ToolJointErro{r}_{AHD}\right)}^2+{\left(\Delta .V_i\right)}^2}+\mathrm{ToolJointErro}{r}_{AHD},$

• • where
  • Δ.V is the total locational uncertainty for V at any point i.

For north (N) the expression

$\Delta .N=\sqrt{{\left(\Delta .N_{i-1}-ToolJointErro{r}_N\right)}^2+{\left(\Delta .N_i\right)}^2}+\mathrm{ToolJointErro}{r}_N,$

• • where
  • Δ.N is the total locational uncertainty for the north locational value at any point i.

For east (E) the expression

$\Delta .E=\sqrt{{\left(\Delta .E_{i-1}-ToolJointErro{r}_E\right)}^2+{\left(\Delta .E_i\right)}^2}+\mathrm{ToolJointErro}{r}_E,$

• • where
  • Δ.E is the total locational uncertainty for the east locational value at any point i.

FIG. 10 is a graph 151 of V positional uncertainty 153 measured in metres 155. It shows possible result of application of an aspect of the current invention using example well scenario where d.V 157 is the V positional uncertainty, d.N 159 is the North positional uncertainty, d. E 161 is the East positional uncertainty graphed against AHD.

The description of an aspect of the invention including that which describes examples of the invention with reference to the drawings may comprise a computer apparatus and/or processes performed in a computer apparatus. However, an aspect of the invention also extends to computer programs, particularly computer programs stored on or in a carrier adapted to bring an aspect of the invention into practice. The program may be in the form of source code, object code, or a code intermediate source and object code, such as in partially compiled form or in any other form suitable for use in the implementation of the method according to an aspect of the invention. The carrier may comprise a storage medium such as ROM, e.g. CD ROM, or magnetic recording medium, e.g. a memory stick or hard disk, or an Internet based storage medium. The carrier may be an electrical or optical signal which may be transmitted via an electrical or an optical cable or by radio or other means.

In the specification the terms “comprise, comprises, comprised and comprising” or any variation thereof and the terms include, includes, included and including, or any variation thereof are considered to be totally interchangeable and they should all be afforded the widest possible interpretation and vice versa.

Improvements and modifications may be incorporated herein without deviating from the scope of the invention.

Claims

1-42. (canceled)

43. A method for determining the 3D position of a wellbore, the method comprising the steps of: selecting a well reference point;calibrating the AHD, Incl and Az. measurementsselecting a measurement station positioned in the wellbore where AHD, Incl. and Az observations are made;observing AHD, Incl and Az measurements at the measurement station;selecting at least one or more additional measurement station(s);observing the AHD, Incl. and Az measurements at the additional measurement station(s);transforming the calibrated interval AHD, Incl. and Az observed measurement values into V, N and E interval values;summating the V, N and E interval values to create a 3D positional description of each measurement station,determining the AHD, Incl. and Az value uncertainties at each measurement station over each observed interval;calculating and concatenating the AHD, Incl. and Az value uncertainties at each sequential measurement station;and creating a depiction of these associated uncertainties along the length of the wellbore and/or depicting these in terms of V, N and E positions from ZDP.

44. The method as claimed in claim 43 wherein the well reference point comprises a surface marker position or a drill floor or at a defined position along the wellbore.

45. The method as claimed in claim 43 wherein the well reference point is identified as having a defined 3D positional identification which is an elevation from a given surface datum elevation and a north and an east location identified using a geodetic positional reference.

46. The method as claimed in claim 43 wherein the well reference point comprises a zero depth point (ZDP) for a drilling rig or wellbore.

47. The method as claimed in claim 43 wherein, the well reference point is a wellbore sub-surface point identified as having a defined 3D position.

48. The method as claimed in claim 43 wherein, the position of the well reference point are subject to a given accuracy which is defined by a fixed uncertainty value for each dimensional measurement (ToolJointError).

49. The method as claimed in claim 43 wherein, the measurement stations are positions in the wellbore between which a wellbore trajectory is constant or near-constant.

50. The method as claimed in claim 43 wherein, the measurement station is positioned at the end of constant or near-constant and correction, AHD, Incl. or Az values.

51. The method as claimed in claim 43 wherein, the measurement station is positioned to account for changes in well geometry well architecture, or proximity to other well bores.

52. The method as claimed in claim 43 wherein, the measurement station is positioned to account for changes in geology and/or reservoir characteristics intercepted by the well bore.

53. The method as claimed in claim 43 wherein, each measurement station is identified along the wellbore at given well depths where by the interval to each subsequent measure station has a constant or near-constant AHD correction, Incl., and Az values.

54. The method as claimed in claim 43 wherein, AHD is measured using an observed drill pipe depth measurement.

55. The method as claimed in claim 44 wherein, the observed drill pipe depth measurement is calibrated and/or corrected for environmental and/or measurement influences such as temperature and drill pipe axial tension, are included in the reporting process.

56. The method as claimed in claim 44 wherein, AHD is measured using a wireline measurement and the observed wireline length measurement is calibrated and/or corrected for environmental and measurement influences such as temperature and wireline tension are included in the process.

57. The method as claimed in claim 43 wherein Az is measured using an observed drill pipe depth measurement.

58. The method as claimed in claim 43 wherein, Incl. is measured using an observed drill pipe or conveyed using any other wellbore tubular depth measurement.

59. The method as claimed in claim 43 wherein, further comprising the step of ascertaining the calibrated measurement value uncertainites of the V, N and E values is comprised of transforming the calibrated AHD, Incl and Az values and their accuracies into V, N and E uncertainty values through identifying those individual contributory elements of V, N and E from the observed values and the accuracies of AHD, Incl. and Az measurements.

60. The method as claimed in claim 43 wherein, subsurface data is synchronised to the calculated and presented 3D positional and/or positional uncertainty results.

61. The method as claimed in claim 43 wherein, the 3D position and uncertainty can be incrementally ascertained by making AHD, Incl. and Az measurements by drilling the wellbore deeper and then adding (a) further measure station(s), so that the position and uncertainty data is a series of increments defined by sequential additional of measure station 3D positions and the concatenation of sequential associated uncertainties.

62. A computer system comprising program instructions or process logic for the operation of the method of claim 43.