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Applied Drilling Engineering

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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 
association survey on drilling costs published by 
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