Method of drilling a directonal well bore

The invention relates to a method of drilling a directional well bore with a drill string. According to the invention, at least a part of the trajectory of the well bore is drilled with a constant build rate so that the part has substantially a constant curvature shape.

The invention relates to a method of drilling a directional well bore, 
usually in order to produce a fluid, such as oil and/or gas, contained in 
an underground formation. 
Many oil or gas wells are not drilled vertically but with a certain angle 
or inclination to vertical. The target location, determined before 
drilling, does not lie vertically below the surface location of the 
drilling rig. This is particularly true when drilling offshore when a 
cluster of wells is drilled from the same rig. The majority of these 
deviated wells are of the "build and tangent" type, depicted in FIG. 1. 
From the rig R located at the surface S, the well is first drilled 
downwards vertically to a prescribed depth D.sub.1. Then, the well 
trajectory kicks off and the angle of inclination to vertical is built, 
ideally at some fixed rate, to some predetermined angle .theta. formed 
between a vertical line and the longitudinal axis of the well bore. This 
part of the borehole is called the build section. Then, the hole is 
drilled straight at the target T in the oil or gas producing formation F, 
maintaining the inclination angle as close to .theta. as possible until 
the target is reached. This last part of the hole is called the tangent 
section. 
The drilling assembly, or drill string, used to drill a well is mainly 
composed of a pipe string with a drilling bit at its lower end and drill 
collars located just above the bit. Drill collars are heavy tubes 
(compared with drill pipes), used to put weight on the drill bit. Usually, 
all the available weight is not applied to the bit, i.e. the drill string 
is retained at the surface. Consequently, the upper part of the drill 
string is under tension and the lower part is under compression. The point 
in-between, where the stress changes from tension to compression is the 
neutral point which is usually located in the upper part of the drill 
collars section. 
However, for deviated wells, the hook load when drawing the drill string 
out of the hole (tripping out) is substantially greater than the free 
(rotating) weight of the string. In addition, the torque required at the 
surface to achieve a given (lower) torque at the bit is substantially 
greater in the case of a deviated well than in the case of a vertical well 
of similar length. 
In general, drag and torque loss in a drill string system are associated 
with the side forces acting along the drill string giving rise to a 
frictional interaction between the string and the well bore. The side 
forces are comprised of two components depicted in FIG. 2 and associated 
with: 
the local curvature c of the string (which is taken to lie in a vertical 
plane) giving rise to a term T.c where T is the local tension and 
the component of the buoyed mass of the string acting orthogonally to the 
tangent to the trajectory. This gives rise to a term of the form mg sin 
(.theta.) where .theta. is the inclination angle and m the buoyed mass of 
the drill string per unit length. 
The total contribution of these two terms to the drag or the torque loss is 
given by a term depending on the coefficient of friction of the form: 
EQU .mu..vertline.mg sin (.theta.)-Tc.vertline. 
integrated over the entire length of the string. 
In certain circumstances, particularly in long reach wells, the induced 
drag can be of such a magnitude that the drilling process is hindered. 
This can occur either because it becomes difficult or impossible to trip 
out or because the torque required to rotate the drill string exceeds the 
rating of the rotary table. 
U.S. Pat. No. 4,440,241 describes a method of drilling a well bore that 
substantially reduces the likelihood of the drill string becoming stuck 
and reduces the frictional forces between the drill string and the well 
bore. According to this method, the well bore is drilled along the path of 
a catenary curve. However, this method is very difficult to implement, 
because for a catenary curve, the variation of the inclination angle is 
not constant but has to increase continuously. In practice, drilling a 
borehole along a catenary path is an impossible task. For instance, if two 
stabilizers are used to deviate the trajectory of the borehole, the 
distance between the two stabilizers has to be increased regularly in a 
predetermined way. This is not easily achieved and it requires fine 
control from the directional driller. In addition, frequent correction 
runs to return the trajectory to catenary could readily give rise to 
regions of local dog legs which, in turn, would increase drag and torque. 
Another drawback of the method is that the inclination of the borehole 
when reaching the target location is often very large: the borehole lies 
nearly horizontally. This large inclination might not be appropriate with 
an efficient production of the formation fluid. It also increases the drag 
of the bottom hole assembly and therefore the side forces acting on the 
bore hole string, making worse the problems of borehole stability and 
stabilizer sticking. 
The primary object of the invention is to provide a method of drilling a 
well bore that substantially reduces the drag and torque loss in the drill 
string system and that can be implemented easily. 
According to the present invention, at least a portion of the borehole 
ending at the target location is drilled with a constant build rate (the 
build rate is the change of inclination per unit of pipe string length), 
so that said portion of the borehole has substantially a constant 
curvature shape.

The aim of the proposed method is to reduce the drag and torque loss 
experienced in most of the directional wells. 
There are mainly two means of ameliorating the drag problems of a well. The 
first is to counter some of the load force in the tangent section while 
the second is to reduce the extent of the build section. The second of 
these is important since the build section is high in the drill string, 
tension is consequently large and the side force and associated drag is 
high in this region. Reduction of the side forces not only reduces drag 
but also reduces the wear on the casing (the steel tube which lines the 
well bore). 
The method of the present invention combines both of the options outlined 
above. First, the conventional tangent section (also called "hold 
section") depicted in FIG. 1 is replaced by a constant (upward) curvature 
section to target. Second, the initial build section is reduced in extent 
so that the angle achieved at the end of the initial build section is 
lower than that required for a conventional build/tangent well. This 
reduction of the initial build section is the consequence of the use of a 
constant curvature section for the last part of the borehole. 
In practice, the building characteristics of a well trajectory are achieved 
by the strategic placement of stabilizers in the bottom hole assembly of 
the drill string. In general, a given bottom hole assembly, at constant 
weight on bit, will tend to build angle at a fairly constant rate. In 
order to change slightly the inclination of the borehole, the driller 
modifies the weight on bit. For a substantial change of inclination, the 
driller has to modify the distance between the stabilizers. The drill 
string is therefore tripped out, the stabilizers positions in the borehole 
assembly is modified and the drill string lowered again in the borehole to 
resume the drilling operation. 
The method for drilling a constant build trajectory well is illustrated on 
FIG. 3. 
The initial vertical section 12 is drilled from the rig R to the desired 
detph 1 at which point 14 the well kicks off. The initial build section 16 
is then drilled at a build rate b (degrees per hundred feet) generating an 
arc of radius r.sub.1 where 
EQU r.sub.1 18000/.pi.b 
The initial build section is continued until point 18, where some 
pre-determined inclination angle .theta. is achieved. In general, the 
initial build section 16 will be a necessary requirement as it serves two 
purposes: to clear neighbouring wells as quickly as possible, in the case 
of high density of wells, such as for cluster wells, and to define an 
initial compass bearing for the well. The driller needs, as a matter of 
fact, to determine fairly quickly the azimuth of the borehole. This last 
requirement will normally constrain .theta. to take some value greater 
than about 15.degree.-20.degree.. Notwithstanding these comments, a well 
with no initial build section can be planned by taking .theta.=0 in the 
following formulae. 
At the end 18 of the initial build section, the vertical depth v is given 
by: 
EQU v=1+rly sin .theta. 
and a horizontal displacement d given by 
EQU d=r.sub.1 (1-Cos .theta.) 
For a well with a target (at some vertical depth y.sub.t and some 
horizontal displacement x.sub.t the quantities .DELTA.x and .DELTA.y are 
defined by: 
EQU .DELTA.x=x.sub.t -d 
and 
EQU .DELTA.y=y.sub.t -v 
The constant build trajectory 20 from the end 18 of the initial build 
section 16 to the target T (with matching tangent at the end of the 
initial build section) is given by: 
EQU (x-d-x).sup.2 =(y-v-y).sup.2 =R.sup.2 
where x and y are the horizontal and vertical components relative to the 
rig location, and where: 
##EQU1## 
The radius of curvature R is given by: R=(x.sup.2 +y.sup.2).sup.1/2 
To achieve this trajectory in practice, an appropriate bottom hole assembly 
is run at the end of the initial build section and the well is caused to 
build angle constantly at a rate of 18000/.sub.R degrees per hundred feet 
until the target is reached. For a typical well, this value of the build 
rate would be between 0.2.degree. and 0.degree.5 per 100 feet. 
Calculations of the total hook load, when tripping out from full depth, and 
of the rotary torque were made for a typical model, well shown in FIG. 4, 
to exhibit the possible reduction in drag and torque loss gained by using 
curved trajectories. The well is drilled vertically to a kick off point 30 
at 2400 feet. The inclination was then build at a rate of 5.degree. per 
100 feet to some angle .theta. at point 32. This angle would be typically 
between 2.degree. and 8.degree. per 100 feet. The target T was at a total 
vertical depth of 9000 ft with a step out from the rig of 6000 feet. 
Drilled as a conventional build and hold trajectory (such as the well 
trajectory shown on FIG. 1) this would correspond to an inclination angle 
of 44.5.degree.. 
The model drill string was configured with 372 feet of 61/2 inch drill 
collar and 840 feet of 5 inch heavyweight pipe with 5 inch drill pipe to 
surface. A mud weight of 9.8 lb per gallon was used. The drag and torque 
loss are a function of the coefficient of friction and this would normally 
be expected to lie in the range 0.2-0.4. In this example, a value of 0.4 
was used to simulate harsh drag conditions. The torque loss calculation 
was made assuming a weight on bit of 38000 lb. 
FIG. 5 shows, for this model well, the hook load in 10K lb when tripping 
out from full depth as a function of the angle .theta. at the end of the 
5.degree. per 100 foot section, between points 30 and 32. The upper curve 
34 is the hook load for the constant curvature trajectory while the lower 
curve 36 depicts the hook load for a catenary trajectory. The two curves 
34 and 36 are virtually coincident for inclination angles above 
30.degree.. With a conventional trajectory (.theta.=44.5.degree.), a hook 
load of about 320K lb would be expected. For a curved section well with 
.theta.=30.degree., both the catenary and the constant build trajectory 
reduce this figure by about 55K lb. 
FIG. 6 shows the rotary torque as a function of .theta. for a well bore 
drilled according to the present invention. For the conventional 
trajectory, the torque loss from the surface to the bit is in the region 
of 22,500 foot lb while the constant build trajectory from inclinations of 
about 30.degree. reduces this loss by about 4,500 foot lb. 
While it has been shown and described in FIG. 3 what is considered to be 
the preferred embodiment of the invention, it will be apparent to those 
skilled in the art that various changes and modifications may be made 
therein without departing from the spirit or scope of the invention.