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added Category:Methods in Exploration 10 using HotCat
|+ {{table number|1}}Definitions of terms and abbreviations used in this chapter
|+ {{table number|1}}Definitions of terms and abbreviations used in this chapter
|-
|-
! Term
! Term || Definition || Unit
|-
|-
| P
| P || Hydrostatic pressure at depth d || psi
| Hydrostatic pressure at depth d
| psi
|-
|-
| MW
| MW || Mud weight || lb/gal
| Mud weight
| lb/gal
|-
|-
| D
| D || Vertical depth || ft
| Vertical depth
| ft
|-
|-
| V<sub>bpf</sub>
| V<sub>bpf</sub> || Volume || bbl/ft
| Volume
| bbl/ft
|-
|-
| <sup>D</sup><sub>1</sub>
| <sup>D</sup><sub>1</sub> || Larger diameter || in.
| Larger diameter
| in.
|-
|-
| <sup>D</sup> s
| <sup>D</sup> s || Smaller diameter || in.
| Smaller diameter
| in.
|-
|-
| V<sub>h</sub>
| V<sub>h</sub> || Hole volume; the volume of the open or cased hole || bbl/ft
| Hole volume; the volume of the open or cased hole
| bbl/ft
|-
|-
| V<sub>a</sub>
| V<sub>a</sub> || Annular volume; the volume of the annulus, the area between the outside of the drillpipe or collar and the open or cased hole || bbl/ft
| Annular volume; the volume of the annulus, the area between the outside of the drillpipe or collar and the open or cased hole
| bbl/ft
|-
|-
| V<sub>d</sub>
| V<sub>d</sub> || Displacement volume; the volume displaced by the steel volume of drillpipe or collar. Displacement is the volume between the outside diameter and inside diameter of a drillpipe or collar. || bbl/ft
| Displacement volume; the volume displaced by the steel volume of drillpipe or collar. Displacement is the volume between the outside diameter and inside diameter of a drillpipe or collar.
| bbl/ft
|-
|-
| V<sub>c</sub>
| V<sub>c</sub> || Capacity volume; the volume contained inside a drill pipe or collar || bbl/ft
| Capacity volume; the volume contained inside a drill pipe or collar
| bbl/ft
|-
|-
| W
| W || Weight of collars or casing || lb/ft
| Weight of collars or casing
| lb/ft
|-
|-
| od
| od || Outside diameter of pipe || in.
| Outside diameter of pipe
| in.
|-
|-
| id
| id || Inside diameter of pipe || in.
| Inside diameter of pipe
| in.
|-
|-
| D<sub>t</sub>
| D<sub>t</sub> || Triplex mud pump output || bbl/stroke
| Triplex mud pump output
| bbl/stroke
|-
|-
| D<sub>d</sub>
| D<sub>d</sub> || Duplex mud pump output || bbl/stroke
| Duplex mud pump output
| bbl/stroke
|-
|-
| L<sub>s</sub>
| L<sub>s</sub> || Length of pump stroke || in.
| Length of pump stroke
| in.
|-
|-
| D<sub>1</sub>
| D<sub>1</sub> || Diameter of pump liner || in.
| Diameter of pump liner
| in.
|-
|-
| D<sub>r</sub>
| D<sub>r</sub> || Diameter of pump rod (duplex only) || in.
| Diameter of pump rod (duplex only)
| in.
|-
|-
| AV
| AV || Annular velocity || ft/min
| Annular velocity
| ft/min
|-
|-
| GPM
| GPM || Mud pump output || gal/mi n
| Mud pump output
| gal/mi n
|-
|-
| Dh
| Dh || Hole diameter || in.
| Hole diameter
| in.
|-
|-
| An
| An || Jet nozzle area || in.<sup>2</sup>
| Jet nozzle area
| in.<sup>2</sup>
|-
|-
| J<sub>1</sub> … J<sub>n</sub>
| J<sub>1</sub> … J<sub>n</sub> || Size of jet nozzles, “32nd” omitted || 32nd in.
| Size of jet nozzles, “32nd” omitted
| 32nd in.
|-
|-
| JNV
| JNV || Jet nozzle velocity || ft/sec
| Jet nozzle velocity
| ft/sec
|-
|-
| THhp
| THhp || Total hydraulic horsepower || hp
| Total hydraulic horsepower
| hp
|-
|-
| Pp
| Pp || Mud pump pressure || psi
| Mud pump pressure
| psi
|-
|-
| JNPL
| JNPL || Jet nozzle pressure loss || psi
| Jet nozzle pressure loss
| psi
|-
|-
| % Hhpb
| % Hhpb || Percentage of total horsepower expended at bit || %
| Percentage of total horsepower expended at bit
| %
|-
|-
| BHhp
| BHhp || Hydraulic horsepower at the bit || hp
| Hydraulic horsepower at the bit
| hp
|-
|-
| Hhp/in.<sup>2</sup>
| Hhp/in.<sup>2</sup> || Hydraulic horsepower per square inch area of bit || hp/in.<sup>2</sup>
| Hydraulic horsepower per square inch area of bit
| hp/in.<sup>2</sup>
|-
|-
| Ob
| Ob || Bit diameter || in.
| Bit diameter
| in.
|-
|-
| JIF
| JIF || Jet impact force || lb
| Jet impact force
| lb
|-
|-
| FFP
| FFP || Formation [[fracture]] pressure || psi
| Formation fracture pressure
| psi
|-
|-
| T% Hhpb
| T% Hhpb || Total percentage hydraulic horsepower at the bit || %
| Total percentage hydraulic horsepower at the bit
| %
|}
|}
* The density of the liquid (mud weight)
* The density of the liquid (mud weight)
The total volume of liquid or shape of the hole have no influence on hydrostatic pressure, but the height of the liquid column (depth) must be measured in the same direction as the force due to gravity, that is, true vertical. This consideration is important in highly deviated and horizontal wellbores. The hydrostatic pressure (P) at any depth in a wellbore is calculated as follows:
The total volume of liquid or shape of the hole have no influence on hydrostatic pressure, but the height of the liquid column (depth) must be measured in the same direction as the force due to [[gravity]], that is, true vertical. This consideration is important in highly deviated and horizontal wellbores. The hydrostatic pressure (P) at any depth in a wellbore is calculated as follows:
:<math>\mbox{P} = 0.052 \times \mbox{MW} \times \mbox{D}</math>
:<math>\mbox{P} = 0.052 \times \mbox{MW} \times \mbox{D}</math>
If the equation for hydrostatic pressure is solved for mud weight (MW), then the equivalent mud weight can be calculated, which has several important wellsite applications. Solving for MW, the equation becomes
If the equation for hydrostatic pressure is solved for mud weight (MW), then the equivalent mud weight can be calculated, which has several important wellsite applications. Solving for MW, the equation becomes
:<math>\mbox{MW} = \mbox{P}/(0.052 \times \mbox{D})</math>
:<math>\mbox{MW} = \frac{\mbox{P}}{(0.052 \times \mbox{D})}</math>
''Example'': Assume a formation at [[depth::10,000 ft]] has a known hydrostatic pressure of 6292 psi. The mud weight needed to drill this formation “balanced” (hydrostatic pressure equal to formation pressure) is calculated as follows:
'''''Example''''': Assume a formation at [[depth::10,000 ft]] has a known hydrostatic pressure of 6292 psi. The mud weight needed to drill this formation “balanced” (hydrostatic pressure equal to formation pressure) is calculated as follows:
:<math>\mbox{MW} = 6292/(0.052 \times 10{,}000) = 12.1 \mbox{ ppg}</math>
:<math>\mbox{MW} = \frac{6292}{(0.052 \times 10{,}000)} = 12.1 \mbox{ ppg}</math>
===Kill weight of mud===
===Kill weight of mud===
'''''Example''''': Assume a well has taken a kick at [[depth::10,000 ft]] while drilling with 11.5-ppg mud. The well is shut-in, and the drill pipe pressure reads 312 psi. The excess in pounds per gallon mud weight equivalent is calculated as follows:
'''''Example''''': Assume a well has taken a kick at [[depth::10,000 ft]] while drilling with 11.5-ppg mud. The well is shut-in, and the drill pipe pressure reads 312 psi. The excess in pounds per gallon mud weight equivalent is calculated as follows:
:<math>\mbox{MW} = 312/(0.052 \times 10{,}000) = 0.6 \mbox{ ppg}</math>
:<math>\mbox{MW} = \frac{312}{(0.052 \times 10{,}000)} = 0.6 \mbox{ ppg}</math>
Adding the calculated excess of 0.6 ppg to the current mud weight of 11.5 ppg results in 12.1 ppg necessary to control the well. The mud weight is typically increased beyond the calculated kill weight to allow for the negative pressure (swab) exerted on the hole when tripping the drill string.
Adding the calculated excess of 0.6 ppg to the current mud weight of 11.5 ppg results in 12.1 ppg necessary to control the well. The mud weight is typically increased beyond the calculated kill weight to allow for the negative pressure (swab) exerted on the hole when tripping the drill string.
'''''Example''''': Assume a leak-off test conducted in a 10,000-ft wellbore containing 11.5-ppg mud with a leak-off pressure of 1040 psi. The formation fracture pressure is estimated as
'''''Example''''': Assume a leak-off test conducted in a 10,000-ft wellbore containing 11.5-ppg mud with a leak-off pressure of 1040 psi. The formation fracture pressure is estimated as
:<math>\mbox{MW} = 1040/(0.052 \times 10{,}000 = 2.0 \mbox{ ppg}</math>
:<math>\mbox{MW} = \frac{1040}{(0.052 \times 10{,}000)} = 2.0 \mbox{ ppg}</math>
The formation fracture pressure is equivalent to an 11.5 + 2.0 = 13.5 ppg mud weight, or
The formation fracture pressure is equivalent to an 11.5 + 2.0 = 13.5 ppg mud weight, or
All important wellbore volumes are calculated with a single formula:
All important wellbore volumes are calculated with a single formula:
:<math>\mbox{V}_{\rm bpf} = (\mbox{D}_{\rm L}{}^{2} - \mbox{D}_{\rm S}{}^{2})/1029.4</math>
:<math>\mbox{V}_{\rm bpf} = \frac{(\mbox{D}_{\rm L}{}^{2} - \mbox{D}_{\rm S}{}^{2})}{1029.4}</math>
Volumes are reported in units of barrels and can be calculated for an in-gauge hole by using this equation to determine volume in barrels per foot, then multiplying that value by the length of the section of hole in feet. (Note: washouts and thick mud cake can substantially alter hole volume.)
Volumes are reported in units of barrels and can be calculated for an in-gauge hole by using this equation to determine volume in barrels per foot, then multiplying that value by the length of the section of hole in feet. (Note: washouts and thick mud cake can substantially alter hole volume.)
:<math> \mbox{Bbl/min} = \mbox{Bbls/stroke} \times \mbox{Strokes/min}</math>
:<math> \mbox{Bbl/min} = \mbox{Bbls/stroke} \times \mbox{Strokes/min}</math>
:<math> \mbox{Gal/stroke} = \mbox{Bbls/stroke} \times 42
:<math> \mbox{Gal/stroke} = \mbox{Bbls/stroke} \times 42</math>
:<math> \mbox{Gal/min} = \mbox{Gal/stroke} \times \mbox{Strokes/min}</math>
:<math> \mbox{Gal/min} = \mbox{Gal/stroke} \times \mbox{Strokes/min}</math>
Bottoms-up circulation, or ''lag time'', is the time for samples or gas created at the bit to arrive at the surface (via the drilling fluid) for examination. This calculation is dependent on the volume and rate.
Bottoms-up circulation, or ''lag time'', is the time for samples or gas created at the bit to arrive at the surface (via the drilling fluid) for examination. This calculation is dependent on the volume and rate.
After calculating wellbore volumes and mud pump output, several parameters for the circulating time of the drilling fluid can be estimated. The most routinely used of these parameters are
After calculating wellbore volumes and mud pump output, several parameters for the circulating time of the [[drilling fluid]] can be estimated. The most routinely used of these parameters are
* surface-to-bit pump strokes,
* surface-to-bit pump strokes,
Because drilling fluid is pumped down the inside of the drill string to the bit, surface-to-bit (s-to-b) calculations are made as follows:
Because drilling fluid is pumped down the inside of the drill string to the bit, surface-to-bit (s-to-b) calculations are made as follows:
:<math>\mbox{S-to-b strokes} = (\mbox{Total capacity in bbl})/(\mbox{pump output in bbl/stroke})</math>
:<math>\mbox{S-to-b strokes} = \frac{\mbox{Total capacity in bbl}}{\mbox{pump output in bbl/stroke}}</math>
[[Drilling fluid]] is then pumped back up the hole to the surface via the annulus, therefore bit-to-surface (b-to-s) or lag calculations are made as follows:
[[Drilling fluid]] is then pumped back up the hole to the surface via the annulus, therefore bit-to-surface (b-to-s) or lag calculations are made as follows:
:<math>\mbox{B-to-s strokes} = (\mbox{Total annular volume in bbl})/(\mbox{pump output in bbl/stroke})</math>
:<math>\mbox{B-to-s strokes} = \frac{\mbox{Total annular volume in bbl}}{\mbox{pump output in bbl/stroke}}</math>
:<math>\mbox{B-to-s min} = (\mbox{B-to-s strokes})/(\mbox{pump rate in strokes/min})</math>
:<math>\mbox{B-to-s min} = \frac{\mbox{B-to-s strokes}}{\mbox{pump rate in strokes/min}}</math>
'''''Example''''': Using the previously calculated data, we can calculate circulating time as follows:
'''''Example''''': Using the previously calculated data, we can calculate circulating time as follows:
:<math>\mbox{S-to-b strokes} = (155.4 \mbox{ bbl})/(\mbox{0.914-in. bbl/stroke}) = 1700 \mbox{ strokes}</math>
:<math>\mbox{S-to-b strokes} = \frac{155.4 \mbox{ bbl}}{\mbox{0.914-in. bbl/stroke}} = 1700 \mbox{ strokes}</math>
:<math>\mbox{S-to-b min} = (1700 \mbox{ strokes})/(98 \mbox{ strokes/min}) = 17.35 \mbox{ min}</math>
:<math>\mbox{S-to-b min} = \frac{1700 \mbox{ strokes}}{98 \mbox{ strokes/min}} = 17.35 \mbox{ min}</math>
:<math>\mbox{B-to-s strokes} = (378.9 \mbox{ bbl})/(\mbox{0.0914-in. bbl/stroke}) = 4146 \mbox{ strokes}</math>
:<math>\mbox{B-to-s strokes} = \frac{378.9 \mbox{ bbl}}{\mbox{0.0914-in. bbl/stroke}} = 4146 \mbox{ strokes}</math>
:<math>\mbox{B-to-s min} = (4146 \mbox{ strokes})/(98 \mbox{ strokes/min}) = 42.30 \mbox{ min}</math>
:<math>\mbox{B-to-s min} = \frac{4146 \mbox{ strokes}}{98 \mbox{ strokes/min}} = 42.30 \mbox{ min}</math>
Lag time can also be measured at the wellsite by placing calcium carbide in the pipe when a connection is made. The carbide reacts with the water in the mud and forms acetylene gas that is readily detected by the chromatograph. The stroke counter is reset when the carbide is “dropped” down the pipe, and the number of strokes needed for the acetylene return is noted. The actual and calculated lags are then compared, and an interpretation is made.
Lag time can also be measured at the wellsite by placing calcium carbide in the pipe when a connection is made. The carbide reacts with the water in the mud and forms acetylene gas that is readily detected by the chromatograph. The stroke counter is reset when the carbide is “dropped” down the pipe, and the number of strokes needed for the acetylene return is noted. The actual and calculated lags are then compared, and an interpretation is made.
''Annular velocity'' is the average speed at which the drilling fluid is moving back up the annular space as the well is circulated. Although the mud pump output remains constant, annular velocities vary at different points in the wellbore due to changes in pipe, collar, and hole sizes. Annular velocity (AV) can be calculated as
''Annular velocity'' is the average speed at which the drilling fluid is moving back up the annular space as the well is circulated. Although the mud pump output remains constant, annular velocities vary at different points in the wellbore due to changes in pipe, collar, and hole sizes. Annular velocity (AV) can be calculated as
:<math>\mbox{AV} = (24.5 \times \mbox{GPM})/(\mbox{Dh}^{2} - \mbox{od}^{2})</math>
:<math>\mbox{AV} = \frac{24.5 \times \mbox{GPM}}{\mbox{Dh}^{2} - \mbox{od}^2}</math>
'''''Example''''': If mud is circulated at 400 gal/min in an 8.5-in. hole containing a 4.5-in. drill pipe and 6.5-in. collars, the annular velocities are
'''''Example''''': If mud is circulated at 400 gal/min in an 8.5-in. hole containing a 4.5-in. drill pipe and 6.5-in. collars, the annular velocities are
:<math>\mbox{Drill pipe: AV} = (24.5 \times 400)/(8.5^{2} - 4.5^{2}) = 188.5\mbox{ ft/min}</math>
:<math>\mbox{Drill pipe: AV} = \frac{24.5 \times 400}{8.5^2 - 4.5^2} = 188.5\mbox{ ft/min}</math>
:<math>\mbox{Collars: AV} = (24.5 \times 400)/(8.5^{2} - 6.5^{2}) = 326.7 \mbox{ ft/min}</math>
:<math>\mbox{Collars: AV} = \frac{24.5 \times 400}{8.5^2 - 6.5^2} = 326.7 \mbox{ ft/min}</math>
===Jet nozzle area===
===Jet nozzle area===
Jet nozzle velocity (JNV) is the velocity of the mud exiting the jet nozzles of the bit and is estimated as
Jet nozzle velocity (JNV) is the velocity of the mud exiting the jet nozzles of the bit and is estimated as
:<math>\mbox{JNV} = (0.32086 \times \mbox{GPM})/\mbox{An}</math>
:<math>\mbox{JNV} = \frac{0.32086 \times \mbox{GPM}}{\mbox{An}}</math>
''Example'': The jet nozzle velocity for a bit with three 13's jets installed and a circulation rate of 400 GPM is
''Example'': The jet nozzle velocity for a bit with three 13's jets installed and a circulation rate of 400 GPM is
:<math>\mbox{JNV} = (0.32086 \times 400)/0.3889 = 330 \mbox{ ft/sec}</math>
:<math>\mbox{JNV} = \frac{0.32086 \times 400}{0.3889} = 330 \mbox{ ft/sec}</math>
====Total hydraulic horsepower====
====Total hydraulic horsepower====
The total hydraulic horsepower (THhp) available for drilling hydraulics is defined by the circulation rate and pressure of the mud pump. Total hydraulic horsepower is calculated as
The total hydraulic horsepower (THhp) available for drilling hydraulics is defined by the circulation rate and pressure of the mud pump. Total hydraulic horsepower is calculated as
:<math>\mbox{THhp} = (\mbox{Pp} \times \mbox{GPM})/1714</math>
:<math>\mbox{THhp} = \frac{\mbox{Pp} \times \mbox{GPM}}{1714}</math>
'''''Example''''': The total hydraulic horsepower available if circulating at 400 gal/min with a pump pressure of 2000 psi is
'''''Example''''': The total hydraulic horsepower available if circulating at 400 gal/min with a pump pressure of 2000 psi is
:<math>\mbox{THhp} = (2000 \times 400)/1714 = 467 \mbox{ hp}</math>
:<math>\mbox{THhp} = \frac{2000 \times 400}{1714} = 467 \mbox{ hp}</math>
===Jet nozzle pressure loss===
===Jet nozzle pressure loss===
Pump pressure is the total pressure expended throughout the circulating system's surface equipment (such as the standpipe, kelly hose, and kelly), drill string bore, jet nozzles, and annulus. Only the pressure expended through the jet nozzles accomplishes useful work for drilling. The remaining pressure losses are referred to as ''parasitic pressure losses''. Jet nozzle pressure loss is estimated as follows:
Pump pressure is the total pressure expended throughout the circulating system's surface equipment (such as the standpipe, kelly hose, and kelly), drill string bore, jet nozzles, and annulus. Only the pressure expended through the jet nozzles accomplishes useful work for drilling. The remaining pressure losses are referred to as ''parasitic pressure losses''. Jet nozzle pressure loss is estimated as follows:
:<math>\mbox{JNPL} = (\mbox{MW} \times \mbox{GPM}^{2})/(10{,}858 \times \mbox{An}^{2})</math>
:<math>\mbox{JNPL} = \frac{\mbox{MW} \times \mbox{GPM}^2}{10{,}858 \times \mbox{An}^2}</math>
'''''Example''''': The pressure lost through three 13′s jet nozzles while circulating a 12.0-ppg mud at 400 gal/min is
'''''Example''''': The pressure lost through three 13′s jet nozzles while circulating a 12.0-ppg mud at 400 gal/min is
:<math>\mbox{JNPL} = (12 \times 400^{2})/(10{,}858 \times 0.3889^{2}) = 1169 \mbox{ psi}</math>
:<math>\mbox{JNPL} = \frac{12 \times 400^2}{10{,}858 \times 0.3889^2} = 1169 \mbox{ psi}</math>
===Hydraulic horsepower at the bit===
===Hydraulic horsepower at the bit===
The hydraulic horsepower at the bit (BHhp) is calculated as for total hydraulic horsepower (THhp), but the mud pump pressure (Pp) is replaced by the jet nozzle pressure loss (JNPL):
The hydraulic horsepower at the bit (BHhp) is calculated as for total hydraulic horsepower (THhp), but the mud pump pressure (Pp) is replaced by the jet nozzle pressure loss (JNPL):
:<math>\mbox{BHhp} = (1169 \times 400)/1714 = 273 \mbox{ hp}</math>
:<math>\mbox{BHhp} = \frac{1169 \times 400}{1714} = 273 \mbox{ hp}</math>
The ''percentage'' of the total hydraulic horsepower expended at the bit is an important parameter to determine and is calculated in two ways:
The ''percentage'' of the total hydraulic horsepower expended at the bit is an important parameter to determine and is calculated in two ways:
:<math>\% \mbox{ Hhpb} = (\mbox{BHhp/THhp}) \times 100</math>
:<math>\% \mbox{ Hhpb} = \frac{\mbox{BHhp}}{\text{THhp}} \times 100</math>
or
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[[Category:Wellsite methods]] [[Category:Pages with unformatted equations]]
[[Category:Wellsite methods]] [[Category:Pages with unformatted equations]]
[[Category:Methods in Exploration 10]]