U.S. patent application number 09/866814 was filed with the patent office on 2003-02-06 for method and apparatus for determining drilling paths to directional targets.
This patent application is currently assigned to VALIDUS. Invention is credited to Schuh, Frank J..
Application Number | 20030024738 09/866814 |
Document ID | / |
Family ID | 25348476 |
Filed Date | 2003-02-06 |
United States Patent
Application |
20030024738 |
Kind Code |
A1 |
Schuh, Frank J. |
February 6, 2003 |
METHOD AND APPARATUS FOR DETERMINING DRILLING PATHS TO DIRECTIONAL
TARGETS
Abstract
A method and apparatus for recomputing an optimum path between a
present location of a drill bit and a direction or horizontal
target uses linear approximations of circular arc paths. The
technique does not attempt to return to a preplanned drilling
profile when there actual drilling results deviate from the
preplanned profile. By recomputing an optimum path, the borehole to
the target has a reduced tortuosity.
Inventors: |
Schuh, Frank J.; (Plano,
TX) |
Correspondence
Address: |
SUGHRUE, MION, ZINN
MACPEAK & SEAS, PLLC
2100 Pennsylvania Avenue, NW
Washington
DC
20037-3213
US
|
Assignee: |
VALIDUS
|
Family ID: |
25348476 |
Appl. No.: |
09/866814 |
Filed: |
May 30, 2001 |
Current U.S.
Class: |
175/45 ;
175/61 |
Current CPC
Class: |
E21B 7/04 20130101 |
Class at
Publication: |
175/45 ;
175/61 |
International
Class: |
E21B 025/16 |
Claims
What is claimed:
1. A method of drilling a borehole from an above ground surface to
one or more sub-surface targets according to a reference trajectory
plan, said method comprising: determining at predetermined depths
below the ground surface, a present location of a drill bit for
drilling said borehole; and calculating a new trajectory to said
one or more sub-surface targets based on coordinates of said
present location of the drill bit, said new trajectory being
determined independently of the reference trajectory plan.
2. The method of claim 1, wherein said new trajectory includes a
single curvature between said present location of the drill bit and
a first sub-surface target of said one or more sub-surface
targets.
3. The method of claim 2, wherein said single curvature is
determined based on a present location of the drill bit and a
position of said first sub-surface target.
4. The method of claim 3, wherein said single curvature is
estimated by a first tangent line segment and a second tangent line
segment, each of the first and second tangent line segments having
a length LA and meeting at an intersecting point, where LA=R tan
(DOG/2), wherein R=a radius of a circle defining said single
curvature, and DOG=an angle defined by a first and second radial
line of the circle defining said single curvature to respective
non-intersecting endpoints of the first and second tangent line
segments.
5. The method of claim 3, wherein said new trajectory includes said
single curvature and a tangent line from an end of the said single
curvature which is closest to said first sub-surface target.
6. The method of claim 1, wherein a first of said sub-surface
targets includes a target, having requirements for at least one of
entry angle and azimuth, and said new trajectory includes a first
curvature and a second curvature.
7. The method of claim 6, wherein said first and second curvature
are each estimated by a first tangent line segment A and a second
tangent line segment B, each of the first and second tangent line
segments having a length LA and meeting at an intersecting point C,
where LA-R tan (DOG/2), wherein R=a radius of a circle defining
said single curvature, and DOG=an angle defined by a first and
second radial line of the circle defining said single curvature to
respective non-intersecting endpoints of the first and second
tangent line segments.
8. The method of claim 7, wherein said first and second curvature
are interconnected by a straight line joining a non-intersecting
endpoint of the first and second tangent line segments
corresponding to said first curvature with a non-intersecting
endpoint of the first and second tangent line segments
corresponding to said second curvature.
9. The method of claim 4, wherein said first sub-surface target
comprises a horizontal well with a required angle of entry and
azimuth and said present location of said drill bit is at a depth
which is more shallow than said first sub-surface target.
10. The method of claim 1, wherein determining said present
location of the drill bit comprises ascertaining coordinates for a
borehole depth and measuring an inclination and an azimuth, wherein
the borehole depth is predetermined based on a number of drill
segments added together to drill said borehole to said present
location.
11. The method of claim 1, wherein determining said present
location of the drill bit comprises ascertaining coordinates for a
borehole depth and measuring an inclination and an azimuth, wherein
the borehole depth is determined based on a communication of a
depth measurement provided from a drilling station located above
ground.
12. The method of claim 1, further comprising determining an error
of the measurements for at least one of an inclination and an
azimuth, wherein said error is calculated as a weighted average,
which weights more recent error calculations more heavily than less
recent error calculations.
13. A computer readable medium operable with an apparatus for
drilling a borehole from an above ground surface to one or more
sub-surface targets according to a reference trajectory plan, said
computer readable medium comprising: computer readable program
means for determining at predetermined depths below the ground
surface, a present location of a drill bit for drilling said
borehole; computer readable program means for calculating a new
trajectory to said one or more sub-surface targets based on
coordinates of said present location of the drill bit, said new
trajectory being determined independently of the reference
trajectory plan.
14. The computer readable medium of claim 13, wherein said computer
readable program means for calculating said new trajectory
calculates a single curvature between said present location of the
drill bit and a first sub-surface target of said one or more
sub-surface targets.
15. The computer readable medium of claim 14, wherein said single
curvature is estimated by a first tangent line segment and a second
tangent line segment, each of the first and second tangent line
segments having a length LA and meeting at an intersecting point,
where LA=R tan (DOG/2), wherein R=a radius of a circle defining
said single curvature, and DOG=an angle defined by a first and
second radial line of the circle defining said single curvature to
respective non-intersecting endpoints of the first and second
tangent line segments.
16. The computer readable medium of claim 15, wherein said new
trajectory includes said single curvature and a tangent line from
an end of the said single curvature which is closest to said first
sub-surface target.
17. The computer readable medium of claim 13, wherein a first of
said sub-surface targets includes a target, having requirements for
at least one of entry angle and azimuth, and said new trajectory
includes a first curvature and a second curvature.
18. The computer readable medium of claim 17, wherein said first
and second curvature are each estimated by a first tangent line
segment A and a second tangent line segment B, each of the first
and second tangent line segments having a length LA and meeting at
an intersecting point C, where LA=R tan (DOG/2), wherein R=a radius
of a circle defining said single curvature, and DOG=an angle
defined by a first and second radial line of the circle defining
said single curvature to respective non-intersecting endpoints of
the first and second tangent line segments.
19. The computer readable medium of claim 18, wherein said first
and second curvature are interconnected by a straight line joining
a non-intersecting endpoint of the first and second tangent line
segments corresponding to said first curvature with a
non-intersecting endpoint of the first and second tangent line
segments corresponding to said second curvature.
20. The computer readable medium of claim 14, wherein said first
sub-surface target comprises a horizontal well with a required
angle of entry and azimuth and said present location of said drill
bit is at a depth which is more shallow than said first sub-surface
target.
21. The computer readable medium of claim 13, wherein said computer
readable program means for determining said present location of the
drill bit comprises ascertaining coordinates for a borehole depth,
wherein the borehole depth is predetermined based on a number of
drill segments added together to drill said borehole to said
present location.
22. The computer readable medium method of claim 13, wherein
computer readable program means for determining said present
location of the drill bit comprises ascertaining coordinates for a
borehole depth, wherein the borehole depth is determined based on a
communication of a depth measurement provided from a drilling
station located above ground.
23. The computer readable medium of claim 13, further comprises a
computer readable program means for determining an error of
measurements for at least one of an inclination and azimuth,
wherein said error is calculated as a weighted average, which
weights more recent error calculations more heavily than less
recent error calculations.
24. An apparatus for drilling a borehole from an above ground
surface to one or more sub-surface targets according to a reference
trajectory plan, comprising: a device for determining at
predetermined depths below the ground surface, a present location
of a drill bit for drilling said borehole; and a device for
calculating a new trajectory to said one or more sub-surface
targets based on coordinates for said present location of the drill
bit, said new trajectory being independent of the reference
trajectory plan.
25. The device of claim 24, wherein said device for calculating a
new trajectory calculates a single curvature between said present
location of the drill bit and a first sub-surface target of said
one or more sub-surface targets.
26. The apparatus of 25, wherein said device for calculating said
new trajectory approximates said single curvature by a first
tangent line segment and a second tangent line segment, each of the
first and second tangent line segments having a length LA and
meeting at an intersecting point, where LA=R tan (DOG/2), wherein
R=a radius of a circle defining said single curvature, and DOG=an
angle defined by a first and second radial line of the circle
defining said single curvature to respective non-intersecting
endpoints of the first and second tangent line segments.
27. The apparatus of claim 26, wherein said device for calculating
said new trajectory calculates said single curvature and a tangent
line from an end of the said single curvature which is closest to
said first sub-surface target.
28. The apparatus claim 24, wherein a first of said sub-surface
targets includes a target, having requirements for at least one of
entry angle and azimuth, and said device for calculating said new
trajectory calculates a first curvature and a second curvature.
29. The apparatus claim 28, wherein said device for calculating
said new trajectory estimates each of said first and second
curvature are each estimated by a first tangent line segment A and
a second tangent line segment B, each of the first and second
tangent line segments having a length LA and meeting at an
intersecting point C, where LA=R tan (DOG/2), wherein R=a radius of
a circle defining said single curvature, and DOG=an angle defined
by a first and second radial line of the circle defining said
single curvature to respective non-intersecting endpoints of the
first and second tangent line segments.
30. The apparatus of claim 29, wherein said device for calculating
said new trajectory determines a straight line segment joining
first and second curvatures, said straight line joining a
non-intersecting endpoint of the first and second tangent line
segments corresponding to said first curvature with a
non-intersecting endpoint of the first and second tangent line
segments corresponding to said second curvature.
31. The apparatus of claim 25, wherein said first sub-surface
target comprises a horizontal well with a required angle of entry
and azimuth and said present location of said drill bit is at a
depth which is more shallow than said first sub-surface target.
32. The apparatus of claim 24, wherein said device for determining
said present location of the drill bit comprises means for
ascertaining coordinates for a borehole depth, wherein the borehole
depth is predetermined based on a number of drill segments added
together to drill said borehole to said present location.
33. The apparatus of claim 24, wherein said device for determining
said present location of the drill bit comprises means for
ascertaining coordinates for a borehole depth, wherein the borehole
depth is determined based on a communication of a depth measurement
provided from a drilling station located above ground.
34. The apparatus of claim 24, further comprising means for
measuring at least one of an azimuth and depth of the drill bit;
and means for determining an error of the measurements for at least
one of the inclination and azimuth, wherein said error is
calculated as a weighted average, which weights more recent error
calculations more heavily than less recent error calculations.
35. The method of claim 1, wherein the predetermined depths are
anticipated depths, said method further comprising loading the
anticipated depths into a processor that is lowered into the
borehole, said loading occurring while the processor is at the
above ground surface prior to being lowered into the borehole.
36. The method of claim 35, wherein the anticipated depths are
determined based on an average length of drill pipe segments.
Description
FIELD OF THE INVENTION
[0001] This invention provides an improved method and apparatus for
determining the trajectory of boreholes to directional and
horizontal targets. In particular, the improved technique replaces
the use of a preplanned drilling profile with a new optimum profile
that maybe adjusted after each survey such that the borehole from
the surface to the targets has reduced tortuosity compared with the
borehole that is forced to follow the preplanned profile. The
present invention also provides an efficient method of operating a
rotary steerable directional tool using improved error control and
minimizing increases in torque that must be applied at the surface
for the drilling assembly to reach the target.
BACKGROUND
[0002] Controlling the path of a directionally drilled borehole
with a tool that permits continuous rotation of the drillstring is
well established. In directional drilling, planned borehole
characteristics may comprise a straight vertical section, a curved
section, and a straight non-vertical section to reach a target. The
vertical drilling section does not raise significant problems of
directional control that require adjustments to a path of the
downhole assembly. However, once the drilling assembly deviates
from the vertical segment, directional control becomes extremely
important.
[0003] FIG. 1 illustrates a preplanned trajectory between a
kick-off point KP to a target T using a broken line A. The kickoff
point KP may correspond to the end of a straight vertical segment
or a point of entry from the surface for drilling the hole. In the
former case, this kick-off point corresponds to coordinates where
the drill bit is assumed to be during drilling. The assumed
kick-off point and actual drill bit location may differ during
drilling. Similarly, during drilling, the actual borehole path B
will often deviate from the planned trajectory A. Obviously, if the
path B is not adequately corrected, the borehole will miss its
intended target. At point D, a comparison is made between the
preplanned condition of corresponding to planned point on curve A
and the actual position. Conventionally, when such a deviation is
observed between the actual and planned path, the directional
driller redirects the assembly back to the original planned path A
for the well. Thus, the conventional directional drilling
adjustment requires two deflections. One deflection directs the
path towards the original planned path A. However, if this
deflection is not corrected again, the path will continue in a
direction away from the target. Therefore, a second deflection
realigns the path with the original planned path A.
[0004] There are several known tools designed to improve
directional drilling. For example, BAKER INTEQ'S "Auto Trak" rotary
steerable system uses a closed loop control to keep the angle and
azimuth of a drill bit oriented as closely as possible to
preplanned values. The closed loop control system is intended to
porpoise the hole path in small increments above and below the
intended path. Similarly, Camco has developed a rotary steerable
system that controls a trajectory by providing a lateral force on
the rotatable assembly. However, these tools typically are not used
until the wellbore has reached a long straight run, because the
tools do not adequately control curvature rates.
[0005] An example of controlled directional drilling is described
by Patton (U.S.Pat.No. 5,419,405). Patton suggests that the
original planned trajectory be loaded into a computer which is part
of the downhole assembly. This loading of the trajectory is
provided while the tool is at the surface, and the computer is
subsequently lowered into the borehole. Patton attempted to reduce
the amount of tortuosity in a path by maintaining the drilling
assembly on the preplanned profile as much as possible. However,
the incremental adjustments to maintain alignment with the
preplanned path also introduce a number of kinks into the
borehole.
[0006] As the number of deflections in a borehole increases, the
amount of torque that must be applied at the surface to continue
drilling also increases. If too many corrective turns must be made,
it is possible that the torque requirements will exceed the
specifications of the drilling equipment at the surface. The number
of turns also decreases the amount of control of the directional
drilling.
[0007] In addition to Patton '405, other references have recognized
the potential advantage of controlling the trajectory of the tool
downhole. (See for example, Patton U.S. Pat. No. 5341886, Gray,
U.S. Pat. No. 6109370, W093112319, and Wisler, U.S. Pat. No.
5812068). It has been well recognized that in order to compute the
position of the borehole downhole, one must provide a means for
defining the depth of the survey in the downhole computer. A
variety of methods have been identified for defining the survey
depths downhole. These include:
[0008] 1. Using counter wheels on the bottom hole assembly,
(Patton, 5341886)
[0009] 2. Placing magnetic markers on the formation and reading
them with the bottom hole assembly, (Patton, 5341886)
[0010] 3. Recording the lengths of drillpipe that will be added to
the drillstring in the computer while it is at the surface and then
calculating the survey depths from the drillpipe lengths downhole.
(Witte, 5896939).
[0011] While these downhole systems have reduced the time and
communications resources between a surface drilling station and the
downhole drilling assembly, no technique is known that adequately
addresses minimizing the tortuosity of a drilled hole to a
directional or horizontal target.
SUMMARY OF THE INVENTION
[0012] Applicant's invention overcomes the above deficiencies by
developing a novel method of computing the optimum path from a
calculated position of the borehole to a directional or horizontal
target. Referring to FIG. 1, at point D, a downhole calculation can
be made to recompute a new trajectory C, indicated by the dotted
line from the deviated position D to the target T. The new
trajectory is independent of the original trajectory in that it
does not attempt to retrace the original trajectory path. As is
apparent from FIG. 1, the new path C has a reduced number of turns
to arrive at the target. Using the adjusted optimum path will
provide a shorter less tortuous path for the borehole than can be
achieved by readjusting the trajectory back to the original planned
path A. Though a downhole calculation for the optimum path C is
preferred, to obviate delays and to conserve communications
resources, the computation can be done downhole or with normal
directional control operations conducted at the surface and
transmitted. The transmission can be via a retrievable wire line or
through communications with a non-retrievable
measure-while-drilling (MWD) apparatus.
[0013] By recomputing the optimum path based on the actual position
of the borehole after each survey, the invention optimizes the
shape of the borehole. Drilling to the target may then proceed in
accordance with the optimum path determination.
[0014] The invention recognizes that the optimum trajectory for
directional and horizontal targets consists of a series of circular
arc deflections and straight line segments. A directional target
that is defined only by the vertical depth and its north and east
coordinates can be reached from any point above it with a circular
arc segment followed by a straight line segment. The invention
further approximates the circular arc segments by linear elements
to reduce the complexity of the optimum path calculation.
Preferred Embodiments of Invention
[0015] Preferred embodiments of the invention are set forth below
with reference to the drawings where:
[0016] FIG. 1 illustrates a comparison between the path of a
conventional corrective path and an optimized path determined
according to a preferred embodiment of the present invention;
[0017] FIG. 2 illustrates a solution for an optimized path
including an arc and a tangent line;
[0018] FIG. 3 illustrates a solution for an optimized path
including two arcs connected by a tangent line;
[0019] FIG. 4, illustrates a solution for an optimized path
including an arc landing on a sloping plane;
[0020] FIG. 5 illustrates a solution for an optimized path
including a dual arc path to a sloping plane;
[0021] FIG. 6 illustrates the relationship between the length of
line segments approximating an arc and a dogleg angle defining the
curvature of the arc to determine an optimized path according to a
preferred embodiment of the invention;
[0022] FIG. 7 illustrates a first example of determining optimum
paths according to a preferred embodiment of the invention;
[0023] FIG. 8 illustrates a second example of determining optimum
paths according to a preferred embodiment of the invention;
[0024] FIG. 9 illustrates a bottom hole assembly of an apparatus
according to a preferred embodiment of the invention; and
[0025] FIG. 10 illustrates a known geometric relationship for
determining minimum curvature paths.
[0026] The method of computing the coordinates along a circular arc
path is well known and has been published by the American Petroleum
Institute in "Bulletin D20". FIG. 10 illustrates this known
geometric relationship commonly used by directional drillers to
determine a minimum curvature solution for a borehole path.
[0027] In the known relationship, the following description
applies:
[0028] DL is the dogleg angle, calculated in all cases by the
equation:
cos (DL)=cos (I.sub.2-I.sub.1).multidot.sin (I.sub.1).multidot.sin
(I.sub.2).multidot.(1-cos (A.sub.2-A.sub.1))
[0029] or in another form as follows:
cos(DL).about.cos(A.sub.2-A.sub.1).circle-solid.sin(I.sub.1).circle-solid.-
sin (I.sub.2)+cos(I.sub.1).circle-solid.cos(I.sub.2)
[0030] Since the measured distance (.DELTA.MD) is measured along a
curve and the inclination and direction angles (I and A) define
straight line directions in space, the conventional methodology
teaches the smoothing of the straight line segments onto the curve.
This is done by using the ratio factor RF. Where RF=(2/DL) Tan
(DL/2); for small angles (DL<0.25.degree.), it is usual to set
RF=1. 1 T h e n : N o r t h = MD 2 [ sin ( I 1 ) cos ( A 1 ) + sin
( I 2 ) cos ( A 2 ) ] R F E a s t = MD 2 [ sin ( I 1 ) sin ( A 1 )
+ sin ( I 2 ) sin ( A 2 ) ] R F V e r t = MD 2 [ cos ( I 1 ) + cos
( I 2 ) ] R F
[0031] Once the curvature path is determined, it is possible to
determine what coordinates in space fall on that path. Such
coordinates provide reference points which can be compared with
measured coordinates of an actual borehole to determine deviation
from a path.
[0032] The methods and tools to obtain actual measurements of the
bottom hole assembly, such as measured depth, azimuth and
inclination are generally well-known. For instance, Wisler U.S.
Pat. No. 5,812,068, Warren U.S. Pat. No. 4,854,397, Comeau U.S.
Pat. No. 5,602,541, and Witte U.S. Pat. No. 5,896,939 describe
known MWD tools. To the extent that the measurements do not impact
the invention, no further description will be provided on how these
measurements are obtained.
[0033] Though FIG. 10 allows one skilled in the art to determine
the coordinates of an arc, the form of the available survey
equations is unsuitable for reversing the process to calculate the
circular arc specifications from actual measured coordinates. The
present invention includes a novel method for determining the
specifications of the circular arc and straight line segments that
are needed to calculate the optimum trajectory from a point in
space to a directional or horizontal target. The improved procedure
is based on the observation that the orientations and positions of
the end points of a circular arc are identical to the ends of two
connected straight line segments. The present invention uses this
observation in order to determine an optimum circular arc path
based on measured coordinates.
[0034] As shown in FIG. 6, the two segments LA are of equal length
and each exactly parallels the angle and azimuth of the ends of the
circular arc LR. Furthermore, the length of the straight line
segments can easily be computed from the specifications of the
circular arc defined by a DOG angle and radius R to define the arc
LR and visa-versa. In particular, the present inventor determined
the length LA to be R * tan (DOG/2). Applicant further observed
that by replacing the circular arcs required to hit a directional
or horizontal target with their equivalent straight line segments,
the design of the directional path is reduced to a much simpler
process of designing connected straight line segments. This
computation of the directional path from a present location of the
drill bit may be provided each time a joint is added to the
drill-string. Optimum results, e.g. reduced tortuosity, can be
achieved by recomputing the path to the target after each
survey.
[0035] Tables 1-4, below, comprise equations that may be solved
reiteratively to arrive at an appropriate dogleg angle DOG and
length LA for a path between a current location of a drill bit and
a target. In each of the tables, the variables are defined as
follows:
1 Nomenclature AZDIP = Azimuth of the direction of dip for a
sloping deg North target plane AZ = Azimuth angle from North deg
North BT = Curvature rate of a circular arc deg/100 ft BTA =
Curvature rate of the upper circular arc deg/100 ft BTB = Curvature
rate of the lower circular arc deg/100 ft DAZ = Difference between
two azimuths deg DAZ1 = Difference between azimuth at the beginning
deg and end of the upper curve DAZ2 = Difference between azimuth at
the beginning deg and end of the lower curve DEAS = Easterly
distance between two points ft DIP = Vertical angle of a sloping
target plane deg measured down from a horizontal plane DMD =
Distance between two points ft DNOR = Northerly distance between
two points ft DOG = Total change in direction between ends of deg a
circular arc DOG1 = Difference between inclination angles of deg
the circular arc DOG2 = Difference between inclination angles of
deg the circular arc DOGA = Total change in direction of the upper
deg circular arc DOGB = Total change in direction of the lower deg
circular arc DTVD = Vertical distance between two points ft DVS =
Distance between two points projected to ft a horizontal plane EAS
= East coordinate ft ETP = East coordinate of vertical depth
measurement ft position HAT = Vertical distance between a point and
a sloping ft target plane, (+) if point is above the plane INC =
Inclination angle from vertical deg LA = Length of tangent lines
that represent the ft upper circular arc LB = Length of tangent
lines that represent the ft lower circular arc MD = Measured depth
along the wellbore from ft surface MDL = Measured depth along
tangent lines ft NOR = North coordinate ft NTP = North coordinate
of vertical depth measurement ft position TARGAZ = Target azimuth
for horizontal target deg North TVD = Vertical depth from surface
ft TVDT = Vertical depth of a sloping target plane at ft north and
east coordinates TVDTP = Vertical depth to a sloping target plane
at ft NTP and ETP coordinates
[0036] FIG. 2 and Table 1 show the process for designing a
directional path comprising a circular arc followed by a straight
tangent section that lands on a directional target.
2TABLE 1 Single Curve and Tangent to a Directional Target GIVEN:
BTA Starting position: MD(1), TVD(1), EAS(1), NOR(1), TNC(1), AZ(1)
Target position: TVD(4), EAS(4), NOR(4) LA = 0 (1) MDL(1) = MD(1)
(2) MDL(2) = MDL(1) + LA (3) MDL(3) = MDL(2) + LA (4) DVS = LA
.multidot. sin[INC(1)] (5) DNOR = DVS .multidot. cos[AZ(1)] (6)
DEAS = DVS .multidot. sin[AZ(1))] (7) DTVD = LA .multidot.
cos[INC(1)] (8) NOR(2) = NOR(1) + DNOR (9) EAS(2) = EAS(1) + DEAS
(10) TVD(2) = TVD(1) + DTVD (11) DNOR = NOR(4) - NOR(2) (12) DEAS =
EAS(4) - EAS(2) (13) DTVD = TVD(4) - TVD(2) (14) DVS = (DNOR.sup.2
+ DEAS.sup.2).sup.1/2 (15) DMD = (DVS.sup.2 + DTVD.sup.2).sup.1/2
(16) MDL(4) = MDL(2) + DMD (17) 2 INC ( 3 ) = arc tan ( DVS DTVD )
(18) 3 AZ ( 3 ) = arc tan ( DEAS DNOR ) (19) DAZ = AZ(3) - AZ(1)
(20) DOGA = arc cos{cos(DAZ) .multidot. sin[INC(1)] .multidot.
sin[INC(3)] + (21) cos[INC(1)] .multidot. cos[INC(3)]} 4 LA = 100
180 BTA tan ( DOGA 2 ) (22) Repeat equations 2 through 22 until the
value calculated for INC(3) remains constant. 5 MD ( 3 ) = MD ( 1 )
+ 100 DOGA BTA (23) MD(4) = MD(3) + DMD - LA (24) DVS = LA
.multidot. sin[INC(3)] (25) DNOR = DVS .multidot. cos[AZ(3)] (26)
DEAS = DVS .multidot. sin[AZ(3)] (27) DTVD = LA .multidot.
cos[INC(3)] (28) TVD(3) = TVD(2) + DTVD (29) NOR(3) = NOR(2) + DNOR
(30) EAS(3) = EAS(2) = DEAS (31)
[0037] FIG. 3 and Table 2 show the procedure for designing the path
that requires two circular arcs separated by a straight line
segment required to reach a directional target that includes
requirements for the entry angle and azimuth.
3TABLE 2 Two Curves with a Tangent to a Directional Target GIVEN:
BTA, BTB Starting position: MD(1), TVD(1), EAS(1), NOR(1), INC(1),
AZ(1) Target position: TVD(6), EAS(6), NOR(6), INC(6), AZ(6) Start
values: LA = 0 (1) LB = 0 (2) MDL(1) = MD(1) (3) MDL(2) = MDL(1) +
LA (4) MDL(3) = MDL(2) + LA (5) DVS = LA .multidot. sin[INC(1)] (6)
DNOR = DVS .multidot. cos[AZ(1)] (7) DEAS = DVS .multidot.
sin[AZ(1))] (8) DTVD = LA .multidot. cos[INC(1)] (9) NOR(2) =
NOR(1) + DNOR (10) EAS(2) = EAS(1) + DEAS (11) TVD(2) = TVD(1) +
DTVD (12) DVS = LB .multidot. sin[INC(6)] (13) DNOR = DVS
.multidot. cos[Az(6)] (14) DEAS = DVS .multidot. sin[AZ(6)] (15)
DTVD = LB .multidot. cos[INC(6)] (16) NOR(5) = NOR(6) - DNOR (17)
EAS(5) = EAS(6) - DEAS (18) TVD(5) = TVD(6) - DTVD (19) DNOR =
NOR(5) - NOR(2) (20) DEAS = EAS(5) - EAS(2) (21) DTVD = TVD(5) -
TVD(2) (22) DVS = (DNOR.sup.2 + DEAS.sup.2).sup.1/2 (23) DMD =
(DVS.sup.2 + DTVD.sup.2).sup.1/2 (24) 6 INC ( 3 ) = arc tan ( DVS
DTVD ) (25) 7 AZ ( 3 ) = arc tan ( DEAS DNOR ) (26) DAZ = AZ(3) -
AZ(1) (27) DOGA = arc cos{cos(DAZ) .multidot. sin[INC(1)]
.multidot. sin[INC(3)] + (28) cos[INC(1)] .multidot. cos[INC(3)]} 8
LA = 100 180 BTA tan ( DOGA 2 ) (29) DAZ = Az(6) - Az(3) (30) DOGB
= arc cos{cos(DAZ) .multidot. sin[INC(3)] .multidot. sin[INC(6)] +
(31) cos[INC(3)] + cos[INC(6)]} 9 LB = 100 180 BTB tan ( DOGB 2 )
(32) Repeat equations 3 through 32 until INC(3) is stable. DVS = LA
.multidot. sin[INC(3)] (33) DNOR = DVS .multidot. cos[AZ(3)] (34)
DEAS = DVS .multidot. sin[Az(3))] (35) DTVD = LA .multidot.
cos[INC(3)] (36) NOR(3) = NOR(2) + DNOR (37) EAS(3) = EAS(2) + DEAS
(38) TVD(3) = TVD(2) + DTVD (39) INC(4) = INC(3) (40) Az(4) = Az(3)
(41) DVS = LB .multidot. sin[INC(4)] (42) DNOR = DVS .multidot.
cos[Az(4)] (43) DEAS = DVS .multidot. sin[Az(4))] (44) DTVD = LB
.multidot. cos[INC(4)] (45) NOR(4) = NOR(5) - DNOR (46) EAS(4) =
EAS(5) - DEAS (47) TVD(4) = TVD(5) - DTVD (48) 10 MD ( 3 ) = MD ( 1
) + 100 DOGA BTA (49) MD(4) = MD(3) + DMD - LA - LB (50) 11 MD ( 6
) = MD ( 4 ) + 100 DOGB BTB (51)
[0038] FIG. 4 and Table 3 show the calculation procedure for
determining the specifications for the circular arc required to
drill from a point in space above a horizontal sloping target with
a single circular arc. In horizontal drilling operations, the
horizontal target is defined by a dipping plane in space and the
azimuth of the horizontal well extension. The single circular arc
solution for a horizontal target requires that the starting
inclination angle be less than the landing angle and that the
starting position be located above the sloping target plane.
4TABLE 3 Single Curve Landing on a Sloping Target Plane GIVEN:
TARGAZ, BT Starting position: MD(1), TVD(1), NOR(1), EAS(1),
INC(1), AZ(1) Sloping target plane: TVDTP, NTP, ETP, DIP, AZDIP
DNOR = NOR(1) - NTP (1) DEAS = EAS(1) - ETP (2) DVS = (DNOR.sup.2 +
DEAS.sup.2).sup.1/2 (3) 12 AZD = arc tan ( DEAS DNOR ) (4) TVD(2) =
TVDTP + DVS .multidot. tan .multidot. (DIP) .multidot. cos(AZDIP -
AZD) (5) ANGA = AZDIP - Az(1) (6) 13 X = [ TVD ( 2 ) - TVD ( 1 ) ]
tan [ INC ( 1 ) ] 1 - cos ( ANGA ) tan ( DIP ) tan [ INC ( 1 ) ]
(7) TVD(3) = TVD(2) + X .multidot. cos(ANGA) .multidot. tan(DIP)
(8) NOR(3) = NOR(1) + X .multidot. COS[Az(1)] (9) EAS(3) = EAS(1) +
X .multidot. sin[AZ(1)] (10) LA = {X.sup.2 + [TVD(3) -
TVD(1)].sup.2}.sup.1/2 (11) AZ(5) = TARGAZ (12) INC(5) = 90 - arc
tan{tan(DIP) .multidot. cos[AZDIP - AZ(5)]} (13) DOG = arc
cos{cos[AZ(5) - Az(1)] .multidot. sin[INC(1)] .multidot.
sin[INC(5)] + (14) cos[INC(1)] + cos[inc(5)]} 14 BT = 100 180 LA
tan ( DOG 2 ) (15) DVS = LA .multidot. sin[INC(5)] (16) DNOR = DVS
.multidot. cos[AZ(5)] (17) DEAS = DVS .multidot. sin[AZ(5)] (18)
DTVD = LA .multidot. cos[INC(5)] (19) NOR(5) = NOR(3) + DNOR (20)
EAS(5) = EAS(3) + DEAS (21) TVD(5) = TVD(3).vertline. + DTVD (22)
15 MD ( 5 ) = MD ( 1 ) + 100 DOG BT (23)
[0039] For all other cases the required path can be accomplished
with two circular arcs. This general solution in included in FIG. 5
and Table 4.
5TABLE 4 Double Turn Landing to a Sloping Target GIVEN: BT, TARGAZ
Starting position: MD(1), TVD(1), NOR(1), EAS(1), INC(1), AZ(1)
Sloping Target: TVDTP @ NTP & ETP, DIP, AZDIP TVDTP0 = TVDTP -
NTP .multidot. cos(AZDIP) .multidot. tan(DIP) - (1) ETP .multidot.
sin(AZDIP) .multidot. tan(DIP) TVDT(1) = TVDTP0 + NOR(1) .multidot.
cos(AZDIP) .multidot. tan(DIP) + (2) EAS(1) .multidot. sin(AZDIP)
.multidot. tan(DIP) INC(5) = 90 - arc tan[tan(DIP) .multidot.
cos(AZDIP - TARGAZ)] (3) AZ(5) = TARGAZ (4) DAZ = AZ(5) - Az(1) (5)
DTVD = TVDT(1) - TVD(1) (6) 16 DOG2 = ( 180 ) ( BT DTVD 100 180 ) 1
/ 2 (7) If DTVD > 0 DOG1 = DOG2 + INC(1) - INC(5) (8) INC(3) =
INC(1) - DOG1 If DTVD < 0 DOG1 = DOG2 - INC(1) + INC(5) (9)
INC(3) = INC(1) + DOG1 17 DAZ1 = ( DOG1 DOG1 + DOG2 ) DAZ (10)
AZ(3) = AZ(1) + DAZ1 (11) DAZ2 = DAZ - DAZ1 (12) DOGA = arc
cos{cos[DAZ1] .multidot. sin[INC(1)] .multidot. sin[INC(3)] + (13)
cos[INC(1)] .multidot. cos[INC(3)]} DOGB = arc cos{cos[DAZ2]
.multidot. sin[INC(3)] .multidot. sin[INC(5)] + (14) cos[INC(3)]
.multidot. cos[INC(5)]} DMD = LA + LB (15) 18 LA = 100 180 BT tan (
DOGA 2 ) (16) 19 LB = 100 180 BT tan ( DOGB 2 ) (17) DVS = LA
.multidot. sin[INC(1)] (18) DNOR = DVS .multidot. cos[AZ(1)] (19)
DEAS = DVS .multidot. sin[AZ(1))] (20) DTVD = LA .multidot.
cos[INC(1)] (21) NOR(2) = NOR(1) + DNOR (22) EAS(2) = EAS(1) + DEAS
(23) TVD(2) = TVD(1) + DTVD (24) TVDT(2) = TVDTP0 + NOR(2)
.multidot. cos(AZDIP) .multidot. tan(DIP) + (25) EAS(2) .multidot.
sin(AZDIP) .multidot. tan(DIP) HAT(2) = TVDT(2) - TVD(2) (26) DVS =
LA .multidot. sin[INC(3)] + LB .multidot. sin[INC(3)] (27) DNOR =
DVS .multidot. cos[Az(3)] (28) DEAS = DVS .multidot. sin[Az(3)]
(29) NOR(4) = NOR(2) + DNOR (30) EAS(4) = EAS(2) + DEAS (31)
TVDT(4) = TVDTP0 + NOR(4) .multidot. cos(AZDIP) .multidot. tan(DIP)
+ (32) EAS(4) .multidot. sin(AZDIP) .multidot. tan(DIP) TVD(4) =
TVDT(4) (33) HAT(4) = TVDT(4) - TVD(4) (34) DTVD = TVD(4) - TVD(2)
(35) IF DTVD = 0 INC(3) = 90 (36) 20 If DTVD < 0 INC ( 3 ) = 180
+ arc tan [ DVS DTVD ] (37A) 21 If DTVD > 0 INC ( 3 ) = arc tan
( DVS DTVD ) (37B) DOG1 = .vertline.INC(3) - INC(1).vertline. (38)
DOG(2) = .vertline.INC(5) - INC(3).vertline. (39) Repeat equations
10 through 39 until DMD = LA + LB DVS = LA .multidot. sin[INC(3)]
(40) DNOR = DVS .multidot. cos[Az(3)] (41) DEAS = DVS .multidot.
sin[Az(3))] (42) DTVD = LA .multidot. cos[INC(3)] (43) NOR(3) =
NOR(2) + DNOR (44) EAS(3) = EAS(2) + DEAS (45) TVD(3) = TVD(2) +
DTVD (46) TVDT(3) = TVDTP0 + NOR(3) .multidot. cos(AZDIP)
.multidot. tan(DIP) + (47) EAS(3) .multidot. sin(AZDIP) .multidot.
tan(DIP) HAT(3) = TVDT(3) - TVD(3) (48) DVS = LB .multidot.
sin[INC(3)] (49) DNOR = DVS .multidot. cos[AZ(3)] (50) DEAS = DVS
.multidot. sin[AZ(3)] (51) DTVD = LB .multidot. cos[INC(3)] (52)
NOR(4) = NOR(3) + DNOR (53) EAS(4) = EAS(3) + DEAS (54) TVD(4) =
TVD(3) + DVTD (55) TVDT(4) = TVDTP0 + NOR(4) .multidot. cos(AZDIP)
.multidot. tan(DIP) + (56) EAS(4) .multidot. sin(AZDIP) .multidot.
tan(DIP) HAT(4) = TVDT(4) - TVD(4) (57) DVS = LB .multidot.
sin[INC(5)] (58) DNOR = DVS .multidot. cos[AZ(5)] (59) DEAS = DVS
.multidot. sin[AZ(5)] (60) DTVD = LB .multidot. cos[INC(5)] (61)
NOR(5) = NOR(4) + DNOR (62) EAS(5) = EAS(4) + DEAS (63) TVD(5) =
TVD(4) + DVTD (64) TVDT(5) = TVDTP0 + NOR(5) .multidot. cos(AZDIP)
tan(DIP) + (65) EAS(5) .multidot. sin(AZDIP) .multidot. tan(DIP)
HAT(5) = TVDT(5) - TVD(5) (66) 22 MD ( 3 ) = MD ( 1 ) + 100 DOGA
BTA (67) 23 MD ( 5 ) = MD ( 3 ) + 100 DOGB BT (68)
[0040] In summary, if the directional target specification also
includes a required entry angle and azimuth, the path from any
point above the target requires two circular arc segments separated
by a straight line section. See FIG. 3. When drilling to horizontal
well targets, the goal is to place the wellbore on the plane of the
formation, at an angle that parallels the surface of the plane and
extends in the preplanned direction. From a point above the target
plane where the inclination angle is less than the required final
angle, the optimum path is a single circular arc segment as shown
in FIG. 4. For all other borehole orientations, the landing
trajectory requires two circular arcs as is shown in FIG. 5. The
mathematical calculations that are needed to obtain the optimum
path from the above Tables 1-4 are well within the programming
abilities of one skilled in the art. The program can be stored to
any computer readable medium either downhole or at the surface.
Particular examples of these path determinations are provided
below.
DIRECTIONAL EXAMPLE
[0041] FIG. 7 shows the planned trajectory for a three-target
directional well. The specifications for these three targets are as
follows.
6 Vertical Depth North Coordinate East Coordinate Ft. Ft. Ft.
Target No. 1 6700 4000 1200 Target No. 2 7500 4900 1050 Target No.
3 7900 5250 900
[0042] The position of the bottom of the hole is defined as
follows.
7 Measured depth 2301 ft. Inclination angle 1.5 degrees from
vertical Azimuth angle 120 degrees from North Vertical depth 2300
ft. North coordinate 20 ft. East Coordinate 6 ft.
[0043] Design Curvature Rates.
8 Vertical Depth Curvature Rate 2300 to 2900 ft 2.5 deg/100 ft 2900
to 4900 ft 3.0 deg/100 ft 4900 to 6900 ft 3.5 deg/100 ft 6900 to
7900 ft 4.0 deg/100 ft
[0044] The required trajectory is calculated as follows.
[0045] For the first target we use the FIG. 2 and Table 1
solution.
[0046] BTA=2.5 deg/100 ft
[0047] MDL (1)=2301 ft
[0048] INC (1)=1.5 deg
[0049] AZ (1)=120 deg North
[0050] TVD (1)=2300 ft
[0051] NOR (1)=20 ft
[0052] EAS(1)=6 ft
[0053] LA =1121.7 ft
[0054] DOGA=52.2 deg
[0055] MDL (2)=3422.7 ft
[0056] TVD (2)=3420.3 ft
[0057] NOR (2)=5.3 ft
[0058] EAS (2)=31.4 ft
[0059] INC (3)=51.8 deg
[0060] AZ (3)=16.3 deg North azimuth
[0061] MDL (3)=4542.4 ft
[0062] MD (3)=4385.7 ft
[0063] TVD (3)=4113.9 ft
[0064] NOR (3)=850.2 ft
[0065] EAS (3)=278.6 ft
[0066] MD (4)=8564.0 ft
[0067] MDL (4)=8720.7 ft
[0068] INC (4)=51.8 deg
[0069] AZ (4)=16.3 deg North
[0070] TVD (4)=6700 ft
[0071] NOR (4)=4000 ft
[0072] EAS (4)=1200 ft
[0073] For second target we use the FIG. 2 and Table 1 solution
[0074] BTA=3.5 deg/100 ft
[0075] MD (1)=8564.0 ft
[0076] MDL (1)=8720.9 ft
[0077] INC (1)=51.8 deg
[0078] AZ (1)=16.3 deg North
[0079] TVD (1)=6700 ft
[0080] NOR (1)=4000 ft
[0081] EAS (1)=1200 ft
[0082] LA=458.4 ft
[0083] DOGA=31.3 deg
[0084] MDL (2)=9179.3 ft
[0085] TVD (2)=6983.5 ft
[0086] NOR (2)=4345.7 ft
[0087] EAS (2)=1301.1 ft
[0088] INC (3)=49.7 deg
[0089] AZ (3)=335.6 deg North
[0090] MDL (3)=9636.7 ft
[0091] MD (3)=9457.8 ft
[0092] TVD (3)=7280.1 ft
[0093] NOR (3)=4663.4 ft
[0094] EAS (3)=1156.9 ft
[0095] MD(4)=9797.7 ft
[0096] MDL (4)=9977.4 ft
[0097] INC (4)=49.7 deg
[0098] AZ (4)=335.6 deg North
[0099] TVD (4)=7500 ft
[0100] NOR (4)=4900 ft
[0101] EAS (4)=1050 ft
[0102] For the third target we also use the FIG. 2 and Table 1
solution
[0103] BTA=4.0 deg/100 ft
[0104] MD (1)=9797.7 ft
[0105] MDL (1)=9977.4 ft
[0106] INC (1)=49.7 deg
[0107] AZ (1)=335.6 deg North
[0108] TVD (1)=7500 ft
[0109] NOR (1)=4900 fit
[0110] EAS (1)=1050 ft
[0111] LA=92.8 ft
[0112] DOGA=7.4 deg
[0113] MDL (2)=10070.2 ft
[0114] TVD (2)=7560.0 ft
[0115] NOR (2)=4964.5 ft
[0116] EAS (2)=1020.8 ft
[0117] INC (3)=42.4 deg
[0118] AZ (3)=337.1 deg North
[0119] MDL (3)=10163.0 ft
[0120] MD (3)=9983.1 ft
[0121] TVD (3)=7628.6 ft
[0122] NOR (3)=50221 ft
[0123] EAS (3)=996.4 ft
[0124] MD (4)=10350.4 ft
[0125] MDL (4)=10530.2 ft
[0126] INC (4)=42.4 deg
[0127] AZ(4)=337.1 deg North
[0128] TVD (4)=7900 ft
[0129] NOR (4)=5250 ft
[0130] EAS (4)=900 ft
Horizontal Example
[0131] FIG. 8 shows the planned trajectory for drilling to a
horizontal target. In this example a directional target is used to
align the borehole with the desired horizontal path. The
directional target is defined as follows.
[0132] 6700 ft Vertical depth
[0133] 400 ft North coordinate
[0134] 1600 ft East coordinate
[0135] 45 deg inclination angle
[0136] 15 deg North azimuth
[0137] The horizontal target plan has the following specs:
[0138] 6800 ft vertical depth at 0 ft North and 0 ft East
coordinate
[0139] 30 degrees North dip azimuth
[0140] 15 degree North horizontal wellbore target direction
[0141] 3000 ft horizontal displacement
[0142] The position of the bottom of the hole is as follows:
9 Measured depth 3502 ft Inclination angle 1.6 degrees Azimuth
angle 280 degrees North Vertical depth 3500 ft North coordinate 10
ft East coordinate -20 ft
[0143] The design curvature rates for the directional hole are:
10 Vertical Depth Curvature Rate 3500-4000 3 deg/100 ft 4000-6000
3.5 deg/100 ft 6000-7000 4 deg/100 ft
[0144] The maximum design curvature rates for the horizontal well
are: 13 deg/100 ft
[0145] The trajectory to reach the directional target is calculated
using the solution shown on FIG. 3.
[0146] BTA=3.0 deg/100 ft
[0147] BTB=3.5 deg/100 ft
[0148] MDL(1)=3502 ft
[0149] MD (1)=3502 ft
[0150] INC (1)=1.6 deg
[0151] AZ (1)=280 degrees North
[0152] TVD(1)=3500 ft
[0153] NOR(1)=10 ft
[0154] EAS(1)=-20 ft
[0155] LA=672.8 ft
[0156] LB=774.5 ft
[0157] DOGA=38.8 deg
[0158] DOGB=50.6 deg
[0159] MDL(2)=4174.8 ft
[0160] TVD(2)=4172.5 ft
[0161] NOR(2)=13.3 ft
[0162] EAS(2)=-38.5 ft
[0163] INC (3)=37.2 deg
[0164] AZ (3)=95.4 deg North
[0165] MDL(3)=4847.5 ft
[0166] MD (3)=4795.6 ft
[0167] TVD(3)=4708.2 ft
[0168] NOR(3)=-25.2 ft
[0169] EAS(3)=366.5 ft
[0170] INC (4)=37.2 deg
[0171] AZ (4)=95.4 deg North
[0172] MDL(4)=5886.4 ft
[0173] MD (4)=5834.5 ft
[0174] TVD(4)=5535.6 ft
[0175] NOR(4)=-84.7 ft
[0176] EAS(4)=992.0 ft
[0177] MDL(5)=6660.8 ft
[0178] TVD(5)=6152.4 ft
[0179] NOR(5)=-129.0 ft
[0180] EAS(5)=1458.3 ft
[0181] MD (6)=7281.2 ft
[0182] MDL(6)=7435.2 ft
[0183] INC (6)=45 deg
[0184] AZ (6)=15 deg North
[0185] TVD(6)=6700 ft
[0186] NOR(6)=400 ft
[0187] EAS(6)=1600 ft
[0188] The horizontal landing trajectory uses the solution shown on
FIG. 4 and Table 3.
[0189] The results are as follows.
[0190] The starting position is:
[0191] NMD (1)=7281.3 ft
[0192] INC (1)=45 deg
[0193] AZ (1)=l5degNorth
[0194] TVD(1)=6700 ft
[0195] NOR(1=400 ft
[0196] EAS (1)=1600 ft
[0197] The sloping target specification is:
[0198] TVDTP=6800 ft
[0199] NTP =0ft
[0200] ETP =0ft
[0201] DIP =4 deg
[0202] AZDIP =30 deg North
[0203] The horizontal target azimuth is:
[0204] TARGAZ =15 deg North
[0205] The Table 3 solution is as follows:
[0206] DNOR =400 ft
[0207] DEAS =1600 ft
[0208] DVS =1649.2 ft
[0209] AZD =76.0 deg North
[0210] TVD (2)=6880.2 ft
[0211] ANGA=15 deg
[0212] x=193.2ft
[0213] TVD (3)=6893.2 ft
[0214] NOR (3)=586.6 ft
[0215] EAS (3)=1650.0 ft
[0216] LA=273.3 ft
[0217] AZ (5)=15 deg North
[0218] INC (5)=86.1 deg
[0219] DOG=41.1 deg
[0220] BT=7.9 deg/100 ft
[0221] DVS=272.6 ft
[0222] DNOR=263.3 ft
[0223] DEAS=70.6 ft
[0224] DTVD=18.4 ft
[0225] NOR (5)=850.0 ft
[0226] EAS (5)=1720.6 ft
[0227] TVD (5)=6911.6 ft
[0228] MD (5)=7804.1 ft
[0229] The end of the 3000 ft horizontal is determined as
follows:
[0230] DVS=2993.2 ft
[0231] DNOR=2891.2 ft
[0232] DEAS=774.7 ft
[0233] DTVD=202.2 ft
[0234] NOR=3477.8 ft
[0235] EAS=2495.3 ft
[0236] TVD=7113.8 ft
[0237] MD=10804.1 ft
[0238] It is well known that the optimum curvature rate for
directional and horizontal wells is a function of the vertical
depth of the section. Planned or desired curvature rates can be
loaded in the downhole computer in the form of a table of curvature
rate versus depth. The downhole designs will utilize the planned
curvature rate as defined by the table. The quality of the design
can be further optimized by utilizing lower curvature rates than
the planned values whenever practical. As a feature of the
preferred embodiments, the total dogleg curvature of the uppermost
circular arc segment is compared to the planned or desired
curvature rate. Whenever the total dogleg angle is found to be less
than the designer's planned curvature rate, the curvature rate is
reduced to a value numerically equal to the total dogleg. For
example, if the planned curvature rate was 3.5.degree./100 ft and
the required dogleg was 0.5.degree., a curvature rate of
0.5.degree./100 ft should be used for the initial circular arc
section. This procedure will produce smoother less tortuous
boreholes than would be produced by utilizing the planned
value.
[0239] The actual curvature rate performance of directional
drilling equipment including rotary steerable systems is affected
by the manufacturing tolerances, the mechanical wear of the rotary
steerable equipment, the wear of the bit, and the characteristics
of the formation. Fortunately, these factors tend to change slowly
and generally produce actual curvature rates that stay fairly
constant with drill depth but differ somewhat from the theoretical
trajectory. The down hole computing system can further optimize the
trajectory control by computing and utilizing a correction factor
in controlling the rotary steerable system. The magnitude of the
errors can be computed by comparing the planned trajectory between
survey positions with the actual trajectory computed from the
surveys. The difference between these two values represents a
combination of the deviation in performance of the rotary steerable
system and the randomly induced errors in the survey measurement
process. An effective error correction process should minimize the
influence of the random survey errors while responding quickly to
changes in the performance of the rotary steerable system. A
preferred method is to utilize a weighted running average
difference for the correction coefficients. A preferred technique
is to utilize the last five surveys errors and average them by
weighting the latest survey five-fold, the second latest survey
four-fold, the third latest survey three-fold, the fourth latest
survey two-fold, and the fifth survey one time. Altering the number
of surveys or adjusting the weighting factors can be used to
further increase or reduce the influence of the random survey
errors and increase or decrease the responsiveness to a change in
true performance. For example, rather than the five most recent
surveys, the data from ten most recent surveys may be used during
the error correction. The weighting variables for each survey can
also be whole or fractional numbers. The above error determinations
may be included in a computer program, the details of which are
well within the abilities of one skilled in the art.
[0240] The above embodiments for directional and horizontal
drilling operations can be applied with known rotary-steerable
directional tools that effectively control curvature rates. One
such tool is described by the present inventor in U.S. Pat. No.
5,931,239 patent. The invention is not limited by the type of
steerable system. FIG. 9 illustrates the downhole assembly which is
operable with the preferred embodiments. The rotary-steerable
directional tool 1 will be run with an MWD tool 2. A basic MWD
tool, which measures coordinates such as depth, azimuth and
inclination, is well known in the art. In order to provide the
improvements of the present invention, the MWD tool of the
inventive apparatus includes modules that perform the following
functions.
[0241] 1. Receives data and instructions from the surface.
[0242] 2. Includes a surveying module that measures the inclination
angle and azimuth of the tool
[0243] 3. Sends data from the MWD tool to a receiver at the
surface
[0244] 4. A two-way radio link that sends instructions to the
adjustable stabilizer and receives performance data back from the
stabilizer unit
[0245] 5. A computer module for recalculating an optimum path based
on coordinates of the drilling assembly.
[0246] There are three additional methods that can be used to make
the depths of each survey available to the downhole computer. The
simplest of these is to simply download the survey depth prior to
or following the surveying operations. The most efficient way of
handling the survey depth information is to calculate the future
survey depths and load these values into the downhole computer
before the tool is lowered into the hole. The least intrusive way
of predicting survey depths is to use an average length of the
drill pipe joints rather than measuring the length of each pipe to
be added, and determining the survey depth based on the number of
pipe joints and the average length.
[0247] It is envisioned that the MWD tool could also include
modules for taking Gamma-Ray measurements, resistivity and other
formation evaluation measurements. It is anticipated that these
additional measurements could either be recorded for future review
or sent in real-time to the surface.
[0248] The downhole computer module will utilize; surface loaded
data, minimal instructions downloaded from the surface, and
downhole measurements, to compute the position of the bore hole
after each survey and to determine the optimum trajectory required
to drill from the current position of the borehole to the
directional and horizontal targets. A duplicate of this computing
capability can optionally be installed at the surface in order to
minimize the volume of data that must be sent from the MWD tool to
the surface. The downhole computer will also include an error
correction module that will compare the trajectory determined from
the surveys to the planned trajectory and utilize those differences
to compute the error correction term. The error correction will
provide a closed loop process that will correct for manufacturing
tolerances, tool wear, bit wear, and formation effects.
[0249] The process will significantly improve directional and
horizontal drilling operations through the following:
[0250] 1. Only a single bottom hole assembly design will be
required to drill the entire directional well. This eliminates all
of the trips commonly used in order to change the characteristics
of the bottom hole assembly to better meet the designed trajectory
requirements.
[0251] 2. The process will drill a smooth borehole with minimal
tortuosity. The process of redesigning the optimum trajectory after
each survey will select the minimum curvature hole path required to
reach the targets. This will eliminate the tortuous adjustments
typically used by directional drillers to adjust the path back to
the original planned trajectory.
[0252] 3. The closed loop error correction routine will minimize
the differences between the intended trajectory and the actual
trajectories achieved. This will also lead to reduced
tortuosity.
[0253] 4. Through the combination of providing a precise control of
curvature rate and the ability to redetermine the optimum path, the
invention provides a trajectory that utilizes the minimum practical
curvature rates. This will further expand the goal of minimizing
the tortuosity of the hole.
[0254] While preferred embodiments of the invention have been
described above, one skilled in the art would recognize that
various modifications can be made thereto without departing from
the spirit and scope of the invention.
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