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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