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```operating cost of the
drilling operation. For example, an operator may
find from experience that operating a rig on a given
lease offshore Louisiana requires expenditures that
will average about \$30,000/day. Included in this
daily operating cost are such things as rig rentals,
crew boat rentals, work boat rentals, helicopter
I
ROTARY DRILLING PROCESS 33
TABLE 1.7- AVERAGE 1978 COSTS OF DRILLING AND EQUIPPING WELLS
IN THE SOUTH LOUISIANA AREA
Dry Holes
Mean
Depth Interval Number Depth, D;
(ft) of Wells, n; (ft)
0 to 1,249 1 1,213
1 ,250 to 2,499 1 1,542
2,499 to 3,749 8 3,015
3, 750 to 4,999 11 4,348
5,000 to 7,499 43 6,268
7,500 to 9,999 147 8,954
10,000 to 12,499 228 11,255
12,500 to 14,999 125 13,414
15,000 to 17,499 54 16,133
17,500 to 19,999 21 18,521
20,000 and more 7 21,207
rentals, well monitoring services, crew housing,
routine maintenance of drilling equipment, drilling
fluid treatment, rig supervision, etc. The depth of the
well will govern the lithology that must be penetrated
and, thus, the time required to complete the well.
An excellent source of historical drilling-cost data
presented by area and well depth is the annual joint
API. Shown in Table 1. 7 are data for the south
Louisiana area taken from the 1978 joint association
survey. Approximate drilling cost estimates can be
based on historical data of this type.
Drilling costs tend to increase exponentially with
depth. Thus, when curve-fitting drilling cost data, it
is often convenient to assume a relationship between
cost, C, and depth, D, given by
C=aebD, .......................... (1.17)
where the constants a and b depend primarily on the
well location. Shown in Fig. 1.65a is a least-square
curve fit of the south Louisiana completed well data
given in Table 1. 7 for a depth range of 7,500 ft to
about 21,000 ft. For these data, a has a value of
about 1 x 105 dollars and b has a value of 2 x 10- 4
ft- 1 . Shown in Fig. 1.65b is a more conventional
cartesian representation of this same correlation.
When a more accurate drilling cost prediction is
needed, a cost analysis based on a detailed well plan
must be made. The cost of tangible well equipment
(such as casing) and the cost of preparing the surface
location usually can be predicted accurately. The cost
per day of the drilling operations can be estimated
from considerations of rig rental costs, other
equipment rentals, transportation costs, rig
supervision costs, and others. The time required to
drill and complete the well is estimated on the basis
of rig-up time, drilling time, trip time, casing
placement time, formation evaluation and borehole
survey time, completion time and trouble time.
Trouble time includes time spent on hole problems
such as stuck pipe, well control operations, for-
mation fracture, etc. Major time expenditures always
are required for drilling and tripping operations.
An estimate of drilling time can be based on
historical penetration rate data from the area of
interest. The penetration rate in a given formation
Completed Wells
Mean
Cost, C; Number Depth, D; Cost, C;
(\$) of Wells, n; (ft) (\$)
64,289 0
65,921 9 1,832 201,416
126,294 20 3,138 212,374
199,397 20 4,347 257,341
276,087 47 6,097 419,097
426,336 117 9,070 614,510
664,817 165 11,280 950,971
1,269,210 110 13,659 1,614,422
2,091,662 49 16,036 2,359,144
3,052,213 17 18,411 3,832,504
5,571,320 11 20,810 5,961,053
varies inversely with both compressive strength and
shear strength of the rock. Also, rock strength tends
to increase with depth of burial because of the higher
confining pressure caused by the weight of the
overburden. When major unconformities are not
present in the subsurface lithology, the penetration
rate usually decreases exponentially with depth.
Under these conditions, the penetration rate can be
related to depth, D, by
dD
_ =K e -2.303a 2D, ................... (1.18)
dt
where K and a2 are constants. The drilling time, td,
required to drill to a given depth can be obtained by
separating variables and integrating. Separating
variables gives
0 0
Integrating and solving for t d yields
1
td = (e2.203a 2 D -1). . .......... (1.19)
2.303a 2K
As experience is gained in an area, more accurate
predictions of drilling time can be obtained by
plotting depth vs. drilling time from past drilling
operations. Plots of this type also are used in
evaluating new drilling procedures designed to reduce
drilling time to a given depth.
Example 1. 6. The bit records for a well drilled in
the South China Sea are shown in Table 1.8. Make
plots of depth vs. penetration rate and depth vs.
rotating time for this area using semilog paper. Also,
evaluate the use of Eq. 1.19 for predicting drilling
time in this area.
Solution. The plots obtained using the bit records
are shown in Fig. 1.66. The constants K and a2 can
be determined using the plot of depth v~. penetration
rate on semilog paper. The value of 2.303a 2 is 2.303
divided by the change in depth per log cycle:
2.303
2.303a 2 = -- =0.00034. 6,770
The constant 2.303 is a convenient scaling factor since
•
34 APPLIED DRILLING ENGINEERING
5000~--~---r---,----r---,---~
10,000
...: ~ IL
:I:
:I: 1-1- ll. ll. 15,000 ILl ~ 0
20,000 20,000
0.1 1.0 10.0 0 2 3 4 5 6
MILLION DOLLARS MILLION DOLLARS
(a) CURVE FIT (b) CARTESIAN REPRESENTATION
Fig. 1.65 _Least-square curve fit of 1978 completed well costs for wells below 7,500 ft in the south Louisiana area.
semilog paper is based on common logarithms. The
value of K is equal to the value of penetration rate at
the surface. From depth vs. penetration rate plot,
K=280. Substitution of these values of a 2 and Kin
Eq. 1.19 gives
td = 10.504 (e0·00034D- 1).
The line represented by this equation also has been
plotted on Fig. 1.66. Note that the line gives good
agreement with the bit record data over the entire
depth range.
------------------
A second major component of the time required to
drill a well is the trip time. The time required for
tripping operations depends primarily on the depth of
the well, the rig being used, and the drilling practices
followed. The time required to change a bit and resume
drilling operations can be approximated using the
relation
tr =2( ~ )n. . .................... (1.20)
Is
where t t is the trip time required to change bits and
resume drilling operations, fs is the average tim5!
required to handle one stand of the drillstring, and Is
is the average length of one stand of the drillstring.
The time required to handle the drill collars is greater
than for the rest of the drillstring, but this difference
usually does not warrant the use of an additional term
in Eq. 1.20. Historical data for the rig of interest are
needed to determine t s .
The previous analysis shows that the time required
per trip increases linearly with depth. In addition, the
footage drilled by a single bit tends to decrease with
depth, causing the number of trips required to drill a
given depth increment also to increase with depth.
The footage drilled between trips can be estimated if
the approximate bit life is known. Integrating Eq.
1.18 between Di, the depth of the last trip, and D,
the depth of the next trip, gives the following
equation:
1
D= 1n(2.303a 2 Ktb +e 2 J03a,D, ). . (1.21) 2.303a 2
The total bit rotating time, t b, generally will vary
with depth as the bit size and bit type are changed.
Eqs. 1.20 and 1.21 can be used to estimate the total
trip time required to drill to a given depth using
estimated values of fs, t b, a2 and K. As experience is
gained in an area using a particular rig, more accurate```