offshore well design mud pumps

1. Offshore well 17-1/2" Intermediate section
≔ρSteel 65.4 ――
lb
gal
≔bbl 42 gal
1. Well and string Capacities data INPUT
Enter well tubular data into table as shown. From this table,
annular capacity and volumes are calculated.
Tod
((in))
5
5
5
5
8
9.5
Tid
((in))
4.1778
4.1778
4.1778
3
2.812
3
Wo
((in))
18.75
18.415
Wb
((in))
21
17.5
17.5
17.5
17.5
17.5
TL
((m))
30
970
820
90
60
30
Buoyancy, buoyed weight, buoyancy factor
≔ρmw 9.2 ――
lb
gal
≔ρsw 8.33 ――
lb
gal
≔Pumprate 1050 ――
gal
min
≔Bf =
⎛
⎜
⎝
-1 ――
ρmw
ρSteel
⎞
⎟
⎠
0.859
=ρmw 1102 ――
kg
m3
=ρsw 998 ――
kg
m3
=Pumprate
⎛⎝ ⋅3.975 103 ⎞⎠ ――
liter
min
String and wellbore
component volumes ≔Intvol =―――
⋅π Tid
2
4
0.0088
0.0088
0.0088
0.0046
0.004
0.0046
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
m3
m
≔Annvol =――――――
⋅π ⎛
⎝ -Wb
2
Tod
2 ⎞
⎠
4
0.2108
0.1425
0.1425
0.1425
0.1227
0.1094
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
m3
m
≔Wellvol =―――
⋅π ⎛
⎝Wb
2 ⎞
⎠
4
0.2235
0.1552
0.1552
0.1552
0.1552
0.1552
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
m3
m
1a) Internal string volumes 1b) Annular volumes 1c) Well volume ONLY
≔DPid
⟨
0
⟩
=――――
⋅π
⎛
⎜⎝Tid
2
⟨
0
⟩
⎞
⎟⎠
4
0.0088[[ ]] ――
m3
m
≔DPvol
⟨
0
⟩
=⋅――――
⋅π
⎛
⎝DPid
⟨
0
⟩
⎞
⎠
4
TL
⟨
0
⟩
0.21[[ ]] m3
≔DPann
⟨
0
⟩
=⋅―――――――
⋅π
⎛
⎜⎝ -
⎛
⎝Wb
⟨
0
⟩
⎞
⎠
2
⎛
⎝Tod
⟨
0
⟩
⎞
⎠
2 ⎞
⎟⎠
4
TL
⟨
0
⟩
6.32[[ ]] m3
≔Wbore
⟨
0
⟩
=⋅――――
⋅π
⎛
⎝Wb
⟨
0
⟩
⎞
⎠
2
4
TL
⟨
0
⟩
6.7[[ ]] m3
≔DPid
⟨
1
⟩
=――――
⋅π
⎛
⎜⎝Tid
2
⟨
1
⟩
⎞
⎟⎠
4
0.0088[[ ]] ――
m3
m
≔DPvol
⟨
1
⟩
=⋅――――
⋅π
⎛
⎝DPid
⟨
1
⟩
⎞
⎠
4
TL
⟨
1
⟩
6.74[[ ]] m3
≔DPann
⟨
1
⟩
=⋅―――――――
⋅π
⎛
⎜⎝ -
⎛
⎝Wb
⟨
1
⟩
⎞
⎠
2
⎛
⎝Tod
⟨
1
⟩
⎞
⎠
2 ⎞
⎟⎠
4
TL
⟨
1
⟩
138.24[[ ]] m3
≔Wbore
⟨
1
⟩
=⋅――――
⋅π
⎛
⎝Wb
⟨
1
⟩
⎞
⎠
2
4
TL
⟨
1
⟩
150.52[[ ]] m3
≔HWDPid
⟨
2
⟩
=――――
⋅π
⎛
⎜⎝Tid
2
⟨
2
⟩
⎞
⎟⎠
4
0.0088[[ ]] ――
m3
m
≔HWDPvol
⟨
2
⟩
=⋅―――――
⋅π
⎛
⎝HWDPid
⟨
2
⟩
⎞
⎠
4
TL
⟨
2
⟩
5.7[[ ]] m3
≔HWDPann
⟨
2
⟩
=⋅―――――――
⋅π
⎛
⎜⎝ -
⎛
⎝Wb
⟨
2
⟩
⎞
⎠
2
⎛
⎝Tod
⟨
2
⟩
⎞
⎠
2 ⎞
⎟⎠
4
TL
⟨
2
⟩
116.86[[ ]] m3
≔Wbore
⟨
2
⟩
=⋅――――
⋅π
⎛
⎝Wb
⟨
2
⟩
⎞
⎠
2
4
TL
⟨
2
⟩
127.25[[ ]] m3
≔DC2id
⟨
3
⟩
=――――
⋅π
⎛
⎜⎝Tid
2
⟨
3
⟩
⎞
⎟⎠
4
0.0046[[ ]] ――
m3
m
≔DC2vol
⟨
3
⟩
=⋅――――
⋅π
⎛
⎝DC2id
⟨
3
⟩
⎞
⎠
4
TL
⟨
3
⟩
0.32[[ ]] m3
≔DC2ann
⟨
3
⟩
=⋅―――――――
⋅π
⎛
⎜⎝ -
⎛
⎝Wb
⟨
3
⟩
⎞
⎠
2
⎛
⎝Tod
⟨
3
⟩
⎞
⎠
2 ⎞
⎟⎠
4
TL
⟨
3
⟩
12.83[[ ]] m3
≔Wbore
⟨
3
⟩
=⋅――――
⋅π
⎛
⎝Wb
⟨
3
⟩
⎞
⎠
2
4
TL
⟨
3
⟩
13.97[[ ]] m3
≔DC1id
⟨
4
⟩
=――――
⋅π
⎛
⎜⎝Tid
2
⟨
4
⟩
⎞
⎟⎠
4
0.004[[ ]] ――
m3
m
≔DC1vol
⟨
4
⟩
=⋅――――
⋅π
⎛
⎝DC1id
⟨
4
⟩
⎞
⎠
4
TL
⟨
4
⟩
0.19[[ ]] m3
≔DC1ann
⟨
4
⟩
=⋅―――――――
⋅π
⎛
⎜⎝ -
⎛
⎝Wb
⟨
4
⟩
⎞
⎠
2
⎛
⎝Tod
⟨
4
⟩
⎞
⎠
2 ⎞
⎟⎠
4
TL
⟨
4
⟩
7.36[[ ]] m3
≔Wbore40 =⋅――――
⋅π
⎛
⎝Wb
⟨
4
⟩
⎞
⎠
2
4
TL
⟨
4
⟩
9.31 m3
1.) Pumping times Total volumes
≔ΣTid =⋅―――
⋅π ⎛
⎝Tid
2 ⎞
⎠
4
TL 16.9 m3
≔ΣAnnvol =⋅――――――
⋅π ⎛
⎝ -Wb
2
Tod
2 ⎞
⎠
4
TL 284.9 m3
≔ΣWellvol =⋅―――
⋅π ⎛
⎝Wb
2 ⎞
⎠
4
TL 312.4 m3
≔ΔStime =―――
ΣTid
Pumprate
4.248 min ≔ΔAnntime =―――
ΣAnnvol
Pumprate
71.677 min ≔Totaltime =+ΔStime ΔAnntime 75.92 min
Peter Aird

2. 2a.) Open ended displacement of steel
tubular based on the wall thickness od and id
string dimensions as input. Total 'open and closed ended'
displacement volumes≔OEDS =――――――
⋅π ⎛
⎝ -Tod
2
Tid
2 ⎞
⎠
4
0.0038
0.0038
0.0038
0.0081
0.0284
0.0412
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
m3
m
≔ΣOEDS =⋅OEDS TL 10.63 m3
2b.) Close ended displacement of steel tubular
based on the od string dimensions as input. ≔ΣCEDS =⋅――――
⋅π ⎛
⎝Tod
2 ⎞
⎠
4
TL 27.51 m3
≔CEDS =――――
⋅π ⎛
⎝Tod
2 ⎞
⎠
4
0.0127
0.0127
0.0127
0.0127
0.0324
0.0457
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
m3
m
2c1) Total open ended displacement of all steel tubulars
based on the wall thicknesses and lengths input .
≔ΣOED =⋅OEDS TL 10.63 m3
2c2) Total closed ended displacement of all steel
tubulars based on the outer diameter and lengths input .
≔ΣCED =⋅CEDS TL 27.51 m3
≔OET1 =⋅OEDS
⟨
0
⟩
TL
⟨
0
⟩
1 bbl ≔OET2 =⋅OEDS
⟨1⟩
TL
⟨
1
⟩
3.71 m3
≔CET1 =⋅CEDS
⟨
0
⟩
TL
⟨
0
⟩
0.38 m3
≔CET2 =⋅CEDS
⟨
1
⟩
TL
⟨
1
⟩
12.29 m3
≔OEHW =⋅OEDS
⟨
2
⟩
TL
⟨
2
⟩
20 bbl ≔OEDC2 =⋅OEDS
⟨
3
⟩
TL
⟨3⟩
0.73 m3
≔CEHW =⋅CEDS
⟨
2
⟩
TL
⟨
2
⟩
10.39 m3
≔CEDC2 =⋅CEDS
⟨
3
⟩
TL
⟨
3
⟩
1.14 m3
≔OEDc1 =⋅OEDS
⟨
4
⟩
TL
⟨
4
⟩
11 bbl ≔OEDS =++++OET1 OET2 OEHW OEDC2 OEDc1 9.39 m3
≔CEDc1 =⋅CEDS
⟨
4
⟩
TL
⟨
4
⟩
1.95 m3
≔CEDS =++++CET1 CET2 CEHW CEDC2 CEDc1 26.14 m3
3.) Component and Total string weights Total string weigth
(in mud)≔WS =⋅――――――
⋅π ⎛
⎝ -Tod
2
Tid
2 ⎞
⎠
4
ρSteel
30
30
30
63.5
222.7
322.6
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥⎦
―
kg
m
≔ΣWS =⋅⋅⋅――――――
⋅π ⎛
⎝ -Tod
2
Tid
2 ⎞
⎠
4
ρSteel TL Bf 79 ton
Individual Component weight calculations
≔Wdp
⟨
0
⟩
=⋅――――――
⋅π
⎛
⎜⎝ -Tod
2
⟨
0
⟩
Tid
2
⟨
0
⟩
⎞
⎟⎠
4
ρSteel 30[[ ]] ―
kg
m
≔BWdp
⟨
0
⟩
=⋅
⎛
⎝ ⋅Wdp
⟨
0
⟩
TL
⟨
0
⟩
⎞
⎠ Bf 772[[ ]] kg ≔Wdp
⟨
1
⟩
=⋅――――――
⋅π
⎛
⎜⎝ -Tod
2
⟨
1
⟩
Tid
2
⟨
1
⟩
⎞
⎟⎠
4
ρSteel 30[[ ]] ―
kg
m
≔BWdp
⟨
1
⟩
=⋅
⎛
⎝ ⋅Wdp
⟨
1
⟩
TL
⟨
1
⟩
⎞
⎠ Bf 24977[[ ]] ⋅m ―
kg
m
≔Wdp
⟨
2
⟩
=⋅――――――
⋅π
⎛
⎜⎝ -Tod
2
⟨
2
⟩
Tid
2
⟨
2
⟩
⎞
⎟⎠
4
ρSteel 30[[ ]] ―
kg
m
≔BWdp
⟨
2
⟩
=⋅
⎛
⎝ ⋅Wdp
⟨
2
⟩
TL
⟨
2
⟩
⎞
⎠ Bf 21114[[ ]] kg ≔Whwdp
⟨
3
⟩ =⋅――――――
⋅π
⎛
⎜⎝ -Tod
2
⟨
3
⟩
Tid
2
⟨
3
⟩
⎞
⎟⎠
4
ρSteel 63.5[[ ]] ―
kg
m
≔BWhwdp
⟨
3
⟩
=⋅
⎛
⎝ ⋅Whwdp
⟨
3
⟩
TL
⟨
3
⟩
⎞
⎠ Bf 4914[[ ]] ⋅m ―
kg
m
≔Wdc2
⟨
4
⟩
=⋅――――――
⋅π
⎛
⎜⎝ -Tod
2
⟨
4
⟩
Tid
2
⟨
4
⟩
⎞
⎟⎠
4
ρSteel 222.7[[ ]] ―
kg
m
≔BWdc2
⟨
4
⟩
=⋅
⎛
⎝ ⋅Wdc2
⟨
4
⟩
TL
⟨
4
⟩
⎞
⎠ Bf 11484[[ ]] kg ≔Wdc1
⟨
5
⟩
=⋅――――――
⋅π
⎛
⎜⎝ -Tod
2
⟨
5
⟩
Tid
2
⟨
5
⟩
⎞
⎟⎠
4
ρSteel 322.6[[ ]] ―
kg
m
≔BWdc1
⟨
5
⟩
=⋅
⎛
⎝ ⋅Wdc1
⟨
5
⟩
TL
⟨
5
⟩
⎞
⎠ Bf 8317[[ ]] ⋅m ―
kg
m
≔Stringweight =+++++BWdp
⟨
0
⟩
BWdp
⟨
1
⟩
BWdp
⟨
2
⟩
BWhwdp
⟨
3
⟩
BWdc2
⟨
4
⟩
BWdc1
⟨
5
⟩
79[[ ]] ton

3. ≔Wdc2 =⋅――――――
4
ρSteel 222.7[ ] ―
m
≔BWdc2 =⋅⎝ ⋅Wdc2 TL ⎠ Bf 11484[ ] kg ≔Wdc1 =⋅――――――
4
ρSteel 322.6[ ] ―
m
≔BWdc1 =⋅⎝ ⋅Wdc1 TL ⎠ Bf 8317[ ] ⋅m ―
m
≔Stringweight =+++++BWdp
⟨
0
⟩
BWdp
⟨
1
⟩
BWdp
⟨
2
⟩
BWhwdp
⟨
3
⟩
BWdc2
⟨
4
⟩
BWdc1
⟨
5
⟩
79[[ ]] ton
Triplex mud pump calculations
Triplex mud pump calculator
Note: A triplex mud pump has three pump liners. For one revolution of the mud pump
drive, each pump piston would therefore have pumped the equivalent of one strokes total
liner volume.
≔Stroke ⋅1 Hz ≔bbl ⋅42 gal
Data input
Liner diameter, d, inches
Liner length, L, inches
Pump efficiency, η %,
≔LL ⋅14 in
≔d ⋅
5
5.5
6
6.5
7
⎡
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥⎦
in ≔Sp ⋅1 Stroke
≔η 0.95
≔Pumpvol ――――――
⋅⋅3 ⋅
⎛
⎜
⎝
――
⋅π d2
4
⎞
⎟
⎠
LL η
Sp
=Pumpvol
12.838
15.534
18.487
21.697
25.163
⎡
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥⎦
―――
liter
Stroke
Step #1; Calculates the triplex mud pump output volume (Pumpvol) for the various pump liner sizes (d, inches),
liner stroke length (L, inches) , and volumetric efficiency (η) as input.
Example hand held calculation;
=――――――――――
⋅⋅⋅⋅3
⎛
⎜
⎜⎝
―――――
⋅π (( ⋅5.5 in))
2
4
⎞
⎟
⎟⎠
12 in 0.95
⋅1 Stroke
13.315 ―――
liter
Stroke =Pumpvol
12.838
15.534
18.487
21.697
25.163
⎡
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥⎦
―――
liter
Stroke

4. Comments
Depending on rig and pump conditions safe operating speeds of 100-110rpm can normally be achieved particulary if the rig has three pumps.
e.g Best practices would be to work two pumps at optimal rates,maintaining the 3rd pump as contingency back up so that continuous operations would in most cases and circumstances result.
Step #2; For a selected pump liner output (Pout, gal/stroke). This step calculates the total pumping volume of the
triplex mud pump(s) for the range of strokes (n) that can be used, presenting results in both tabular & graphical
output for 2 and 3 pumps.
Liner size = 6inches ≔Pout ⋅4.884 ―――
gal
Stroke
≔f((n)) ⋅⋅Pout
⎛
⎜
⎝
⋅n ―――
Stroke
min
⎞
⎟
⎠
2
Define pump rate range (n); ≔n , ‥30 40 110 ≔fa((n)) ⋅⋅Pout
⎛
⎜
⎝
⋅n ―――
Stroke
min
⎞
⎟
⎠
3
1.4⋅10³
1.95⋅10³
2.5⋅10³
3.05⋅10³
3.6⋅10³
4.15⋅10³
4.7⋅10³
5.25⋅10³
5.8⋅10³
300
850
6.35⋅10³
38 47 56 65 74 83 92 10120 29 110
⋅4.5 103
⋅3 103
60 90
f((n))
⎛
⎜
⎝
――
liter
min
⎞
⎟
⎠
fa((n))
⎛
⎜
⎝
――
liter
min
⎞
⎟
⎠
n
=f((n))
⋅1.109 103
⋅1.479 103
⋅1.849 103
⋅2.219 103
⋅2.588 103
⋅2.958 103
⋅3.328 103
⋅3.698 103
⋅4.067 103
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
liter
min =fa((n))
⋅1.664 103
⋅2.219 103
⋅2.773 103
⋅3.328 103
⋅3.882 103
⋅4.437 103
⋅4.992 103
⋅5.546 103
⋅6.101 103
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
liter
min

5. Step #3; For a selected pump liner output (Pout2, gal/stroke). This step calculates the total
pumping volume of the triplex mud pump(s) for the range of strokes (n2) that can be used,
presenting results in both tabular & graphical output for two and three mud pumps used.
Liner size = 6 1/2 inches ≔Pout2 ⋅5.732 ―――
gal
Stroke
≔f2((n)) ⋅⋅Pout2
⎛
⎜
⎝
⋅n ―――
Stroke
min
⎞
⎟
⎠
2
≔f3((n)) ⋅⋅Pout2
⎛
⎜
⎝
⋅n ―――
Stroke
min
⎞
⎟
⎠
3
1.6⋅10³
2.25⋅10³
2.9⋅10³
3.55⋅10³
4.2⋅10³
4.85⋅10³
5.5⋅10³
6.15⋅10³
6.8⋅10³
300
950
7.45⋅10³
38 47 56 65 74 83 92 10120 29 110
⋅4 103
⋅6 103
60 90
f2((n))
⎛
⎜
⎝
――
liter
min
⎞
⎟
⎠
f3((n))
⎛
⎜
⎝
――
liter
min
⎞
⎟
⎠
n
=f2((n))
⋅1.302 103
⋅1.736 103
⋅2.17 103
⋅2.604 103
⋅3.038 103
⋅3.472 103
⋅3.906 103
⋅4.34 103
⋅4.774 103
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
liter
min
=f3((n))
⋅1.953 103
⋅2.604 103
⋅3.255 103
⋅3.906 103
⋅4.557 103
⋅5.208 103
⋅5.858 103
⋅6.509 103
⋅7.16 103
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
――
liter
min