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Drilling Hydraulics Calculators

Use 49 drilling hydraulics petroleum engineering calculators with formulas, inputs, outputs, units, and source references.

Drilling hydraulics calculations help estimate pressure losses, ECD, annular velocity, pump output, bit hydraulics, circulation timing, and pump power efficiency.

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Annular Capacity - bbl/ft

ACbbl=Dh2−Dp21029.4AC_{bbl}=\frac{D_h^2-D_p^2}{1029.4}
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Annular Capacity - gal/ft

ACgal=Dh2−Dp224.51AC_{gal}=\frac{D_h^2-D_p^2}{24.51}
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Annular Capacity Between Casing and Multiple Strings of Tubing

Ca=Di2−(T12+T22)1029.4C_a=\frac{D_i^2-(T_1^2+T_2^2)}{1029.4}
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Annular Velocity from Pump Output

AV=24.5QDh2−Dp2AV = \frac{24.5Q}{D_h^2 - D_p^2}
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Annular Volume Capacity of Pipe

Va=0.7854(Dh2−Do2)L808.5V_a=\frac{0.7854(D_h^2-D_o^2)L}{808.5}
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Apparent Viscosity from 600 RPM Reading

AV=θ6002AV=\frac{\theta_{600}}{2}
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Bit Nozzle Impact Force

IF=MWVnQ1930IF=\frac{MWV_nQ}{1930}
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Bit Nozzle Jet Velocity

Vn=417.2QN12+N22+N32V_n = \frac{417.2 Q}{N_1^2 + N_2^2 + N_3^2}
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Bit Nozzle Pressure Loss

Pb=156.5Q2MW(N12+N22+N32)2P_b = \frac{156.5Q^2MW}{(N_1^2+N_2^2+N_3^2)^2}
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Bit-to-Surface Lag Time from Annular Volume

tlag=VAVPO⋅SPMt_{lag}=\frac{V_{AV}}{PO\cdot SPM}
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Critical Flow Rate for Flow Regime Change

Qc=2.448VcDi2Q_c=2.448V_cD_i^2
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Cuttings Carrying Capacity Index

CCI=MW AV Keff400000CCI=\frac{MW\,AV\,K_{eff}}{400000}
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Cuttings Net Rise Velocity

Vnet=AV−VsV_{net}=AV-V_s
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Cuttings Slip Velocity

Vs=0.45PVMWDcut(36800Dcut(DenP/MW−1)(PV/(MWDcut))2+1−1)V_s=0.45\frac{PV}{MWD_{cut}}\left(\sqrt{\frac{36800D_{cut}(DenP/MW-1)}{(PV/(MWD_{cut}))^2}+1}-1\right)
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Depth of a Washout - Method 1

Dw=NsPoCpD_w=\frac{N_sP_o}{C_p}
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Depth of a Washout - Method 2

Dw=NsPoCp+CaD_w=\frac{N_sP_o}{C_p+C_a}
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Drill Pipe or Drill Collar Capacity

C=ID21029.4C=\frac{ID^2}{1029.4}
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Drill Pipe or Drill Collar Displacement and Weight

Disp=OD2−ID21029.4Disp=\frac{OD^2-ID^2}{1029.4}
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Drill String Volume

B=ID21029.4PLB = \frac{ID^2}{1029.4}PL
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Duplex Pump Output per Stroke

PO=0.000162S(2Dl2−dr2)PO=0.000162S(2D_l^2-d_r^2)
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Duplex Pump Output Rate with Volumetric Efficiency

Qgpm=0.000162S(2Dl2−dr2)EvSPM⋅42Q_{gpm}=0.000162S(2D_l^2-d_r^2)E_vSPM\cdot42
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Equivalent Circulating Density

ECD=MW+ΔPa0.052TVDECD = MW + \frac{\Delta P_a}{0.052TVD}
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Hydraulic Horsepower at Bit

HHP=PsQ1714HHP = \frac{P_s Q}{1714}
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Hydraulic Horsepower per Unit Bit Area

HHPba=QPb1.271714B2HHP_{ba} = \frac{QP_b1.27}{1714B^2}
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Impact Force per Unit Bit Area

IFa=MWVnQ1.271930B2IF_a = \frac{MWV_nQ1.27}{1930B^2}
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Linear Annular Capacity of Pipe

Co=0.7854(Dh2−Do2)808.5C_o=\frac{0.7854(D_h^2-D_o^2)}{808.5}
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Linear Pipe Capacity

Ci=0.7854Di2808.5C_i=\frac{0.7854D_i^2}{808.5}
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Maximum Drilling Rate for Larger Holes

MDR=67(MWo−MWi)qcDh2MDR = \frac{67(MW_o - MW_i)q_c}{D_h^2}
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New Pump Circulating Pressure

Pc=Pp(qnqo)2P_c=P_p\left(\frac{q_n}{q_o}\right)^2
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New Pump Circulating Pressure - Square Law

Pnew=Pcurrent(NnewNold)2P_{new}=P_{current}\left(\frac{N_{new}}{N_{old}}\right)^2
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New Pump Circulating Pressure with Friction Exponent

Pnew=Pcurrent(QnewQold)nP_{new}=P_{current}\left(\frac{Q_{new}}{Q_{old}}\right)^n
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Nozzle Area from Three Jet Sizes

Na=N12+N22+N321303.8N_a=\frac{N_1^2+N_2^2+N_3^2}{1303.8}
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Open-Ended Displacement Volume of Pipe

Vo=0.7854(Do2−Di2)L808.5V_o=\frac{0.7854(D_o^2-D_i^2)L}{808.5}
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Overall Diesel-to-Mud-Pump Efficiency

ηo=ηeηlηmηv\eta_o=\eta_e\eta_l\eta_m\eta_v
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Overall Power System Efficiency

Ei=PQiE_i=\frac{P}{Q_i}
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Percentage Pressure Loss at Bit

Ppsib=100PbPsP_{psib} = \frac{100P_b}{P_s}
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Plastic Viscosity from 600 and 300 RPM Readings

PV=θ600−θ300PV=\theta_{600}-\theta_{300}
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Power Law Consistency Index from 300 RPM Reading

Keff=5111−nθ300K_{eff}=511^{1-n}\theta_{300}
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Power Law Flow Behavior Index from Rheometer Readings

n=3.322log⁡10(θ600θ300)n=3.322\log_{10}\left(\frac{\theta_{600}}{\theta_{300}}\right)
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Pump Input Power from Fuel Consumption Rate

Pi=QfH2545P_i=\frac{Q_fH}{2545}
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Pump Pressure Exponent from Two Pump Tests

n=ln⁡(P1/P2)ln⁡(Q1/Q2)n=\frac{\ln(P_1/P_2)}{\ln(Q_1/Q_2)}
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Pump Pressure from Bit Drop and Friction Losses

Pp=ΔPbit+PdP_p=\Delta P_{bit}+P_d
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Strokes per Minute Required for Target Annular Velocity

SPM=AV ACqoSPM=\frac{AV\,AC}{q_o}
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Total Circulation Strokes from Drillstring and Annular Volume

S=VDS+VAVOS=\frac{V_{DS}+V_{AV}}{O}
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Triplex Pump Output per Stroke

PO=0.000243Dl2LsPO=0.000243D_l^2L_s
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Triplex Pump Output Rate with Volumetric Efficiency

Qgpm=0.000243Dl2LsEvSPM⋅42Q_{gpm}=0.000243D_l^2L_sE_vSPM\cdot42
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Tubular and Open-Hole Capacity

Cbbl=Di21029.4C_{bbl}=\frac{D_i^2}{1029.4}
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Velocity of Fluid in Annulus

va=Q2.448(Do2−Dp2)v_a = \frac{Q}{2.448(D_o^2-D_p^2)}
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Yield Point from 600 and 300 RPM Readings

YP=2θ300−θ600YP=2\theta_{300}-\theta_{600}
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