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Drilling Hydraulics Equations

Browse 49 drilling hydraulics petroleum engineering equations with formulas, inputs, outputs, units, and sources.

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

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Drilling EngineeringDrilling Hydraulics

Annular Capacity - bbl/ft

AC_{bbl}=\frac{D_h^2-D_p^2}{1029.4}

Drilling EngineeringDrilling Hydraulics

Annular Capacity - gal/ft

AC_{gal}=\frac{D_h^2-D_p^2}{24.51}

Drilling EngineeringDrilling Hydraulics

Annular Capacity Between Casing and Multiple Strings of Tubing

C_a=\frac{D_i^2-(T_1^2+T_2^2)}{1029.4}

Drilling EngineeringDrilling Hydraulics

Annular Velocity from Pump Output

AV = \frac{24.5Q}{D_h^2 - D_p^2}

Drilling EngineeringDrilling Hydraulics

Annular Volume Capacity of Pipe

V_a=\frac{0.7854(D_h^2-D_o^2)L}{808.5}

Drilling EngineeringDrilling Hydraulics

Apparent Viscosity from 600 RPM Reading

AV=\frac{\theta_{600}}{2}

Drilling EngineeringDrilling Hydraulics

Bit Nozzle Impact Force

IF=\frac{MWV_nQ}{1930}

Drilling EngineeringDrilling Hydraulics

Bit Nozzle Jet Velocity

V_n = \frac{417.2 Q}{N_1^2 + N_2^2 + N_3^2}

Drilling EngineeringDrilling Hydraulics

Bit Nozzle Pressure Loss

P_b = \frac{156.5Q^2MW}{(N_1^2+N_2^2+N_3^2)^2}

Drilling EngineeringDrilling Hydraulics

Bit-to-Surface Lag Time from Annular Volume

t_{lag}=\frac{V_{AV}}{PO\cdot SPM}

Drilling EngineeringDrilling Hydraulics

Critical Flow Rate for Flow Regime Change

Q_c=2.448V_cD_i^2

Drilling EngineeringDrilling Hydraulics

Cuttings Carrying Capacity Index

CCI=\frac{MW\,AV\,K_{eff}}{400000}

Drilling EngineeringDrilling Hydraulics

Cuttings Net Rise Velocity

V_{net}=AV-V_s

Drilling EngineeringDrilling Hydraulics

Cuttings Slip Velocity

V_s=0.45\frac{PV}{MWD_{cut}}\left(\sqrt{\frac{36800D_{cut}(DenP/MW-1)}{(PV/(MWD_{cut}))^2}+1}-1\right)

Drilling EngineeringDrilling Hydraulics

Depth of a Washout - Method 1

D_w=\frac{N_sP_o}{C_p}

Drilling EngineeringDrilling Hydraulics

Depth of a Washout - Method 2

D_w=\frac{N_sP_o}{C_p+C_a}

Drilling EngineeringDrilling Hydraulics

Drill Pipe or Drill Collar Capacity

C=\frac{ID^2}{1029.4}

Drilling EngineeringDrilling Hydraulics

Drill Pipe or Drill Collar Displacement and Weight

Disp=\frac{OD^2-ID^2}{1029.4}

Drilling EngineeringDrilling Hydraulics

Drill String Volume

B = \frac{ID^2}{1029.4}PL

Drilling EngineeringDrilling Hydraulics

Duplex Pump Output per Stroke

PO=0.000162S(2D_l^2-d_r^2)

Drilling EngineeringDrilling Hydraulics

Duplex Pump Output Rate with Volumetric Efficiency

Q_{gpm}=0.000162S(2D_l^2-d_r^2)E_vSPM\cdot42

Drilling EngineeringDrilling Hydraulics

Equivalent Circulating Density

ECD = MW + \frac{\Delta P_a}{0.052TVD}

Drilling EngineeringDrilling Hydraulics

Hydraulic Horsepower at Bit

HHP = \frac{P_s Q}{1714}

Drilling EngineeringDrilling Hydraulics

Hydraulic Horsepower per Unit Bit Area

HHP_{ba} = \frac{QP_b1.27}{1714B^2}

Drilling EngineeringDrilling Hydraulics

Impact Force per Unit Bit Area

IF_a = \frac{MWV_nQ1.27}{1930B^2}

Drilling EngineeringDrilling Hydraulics

Linear Annular Capacity of Pipe

C_o=\frac{0.7854(D_h^2-D_o^2)}{808.5}

Drilling EngineeringDrilling Hydraulics

Linear Pipe Capacity

C_i=\frac{0.7854D_i^2}{808.5}

Drilling EngineeringDrilling Hydraulics

Maximum Drilling Rate for Larger Holes

MDR = \frac{67(MW_o - MW_i)q_c}{D_h^2}

Drilling EngineeringDrilling Hydraulics

New Pump Circulating Pressure

P_c=P_p\left(\frac{q_n}{q_o}\right)^2

Drilling EngineeringDrilling Hydraulics

New Pump Circulating Pressure - Square Law

P_{new}=P_{current}\left(\frac{N_{new}}{N_{old}}\right)^2

Drilling EngineeringDrilling Hydraulics

New Pump Circulating Pressure with Friction Exponent

P_{new}=P_{current}\left(\frac{Q_{new}}{Q_{old}}\right)^n

Drilling EngineeringDrilling Hydraulics

Nozzle Area from Three Jet Sizes

N_a=\frac{N_1^2+N_2^2+N_3^2}{1303.8}

Drilling EngineeringDrilling Hydraulics

Open-Ended Displacement Volume of Pipe

V_o=\frac{0.7854(D_o^2-D_i^2)L}{808.5}

Drilling EngineeringDrilling Hydraulics

Overall Diesel-to-Mud-Pump Efficiency

\eta_o=\eta_e\eta_l\eta_m\eta_v

Drilling EngineeringDrilling Hydraulics

Overall Power System Efficiency

E_i=\frac{P}{Q_i}

Drilling EngineeringDrilling Hydraulics

Percentage Pressure Loss at Bit

P_{psib} = \frac{100P_b}{P_s}

Drilling EngineeringDrilling Hydraulics

Plastic Viscosity from 600 and 300 RPM Readings

PV=\theta_{600}-\theta_{300}

Drilling EngineeringDrilling Hydraulics

Power Law Consistency Index from 300 RPM Reading

K_{eff}=511^{1-n}\theta_{300}

Drilling EngineeringDrilling Hydraulics

Power Law Flow Behavior Index from Rheometer Readings

n=3.322\log_{10}\left(\frac{\theta_{600}}{\theta_{300}}\right)

Drilling EngineeringDrilling Hydraulics

Pump Input Power from Fuel Consumption Rate

P_i=\frac{Q_fH}{2545}

Drilling EngineeringDrilling Hydraulics

Pump Pressure Exponent from Two Pump Tests

n=\frac{\ln(P_1/P_2)}{\ln(Q_1/Q_2)}

Drilling EngineeringDrilling Hydraulics

Pump Pressure from Bit Drop and Friction Losses

P_p=\Delta P_{bit}+P_d

Drilling EngineeringDrilling Hydraulics

Strokes per Minute Required for Target Annular Velocity

SPM=\frac{AV\,AC}{q_o}

Drilling EngineeringDrilling Hydraulics

Total Circulation Strokes from Drillstring and Annular Volume

S=\frac{V_{DS}+V_{AV}}{O}

Drilling EngineeringDrilling Hydraulics

Triplex Pump Output per Stroke

PO=0.000243D_l^2L_s

Drilling EngineeringDrilling Hydraulics

Triplex Pump Output Rate with Volumetric Efficiency

Q_{gpm}=0.000243D_l^2L_sE_vSPM\cdot42

Drilling EngineeringDrilling Hydraulics

Tubular and Open-Hole Capacity

C_{bbl}=\frac{D_i^2}{1029.4}

Drilling EngineeringDrilling Hydraulics

Velocity of Fluid in Annulus

v_a = \frac{Q}{2.448(D_o^2-D_p^2)}

Drilling EngineeringDrilling Hydraulics

Yield Point from 600 and 300 RPM Readings

YP=2\theta_{300}-\theta_{600}