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Offshore well intermediate

This document provides calculations for the capacities, volumes, and weights of components in an offshore well. It includes: 1) Calculations of internal string volumes, annular volumes, and wellbore volumes based on tubular dimensions. 2) Calculations of displacement volumes for individual components and the total string based on wall thicknesses, diameters, and lengths. 3) Calculations of component and total string weights in mud based on tubular dimensions, material density, and a buoyancy factor. The document contains input data for tubular dimensions and properties, and outputs detailed volumetric and mass calculations for well design and drilling fluid management.

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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
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
≔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
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
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

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Offshore well intermediate

  • 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 endeddisplacement 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 rigand 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; Fora 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