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Browse petroleum engineering formulas with units, variables, source references, worked default examples, and direct calculator links.

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Drilling Engineering9 formulasGeomechanics and Fracturing1 formulaPetrophysics2 formulasPhase Behavior and Thermodynamics4 formulasProduction Engineering5 formulasReservoir Engineering7 formulas

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Drilling Hydraulics3 formulasFluid Flow in Porous Media2 formulasFluid Properties1 formulaGas Properties1 formulaHydraulic Fracturing2 formulasIn-Situ Stress and Rock Mechanics1 formulaInflow Performance2 formulasMaterial Balance and Production1 formulaPVT and Rock-Fluid Properties2 formulasPVT Properties3 formulasResistivity Logs2 formulasWell Control6 formulasWell Performance2 formulas

In-depth formula references

Showing 28 formulas with individually written usage notes, assumptions, limitations, examples, and citations.

Drilling EngineeringWell ControlIn-depth reference

Hydrostatic Pressure from Mud Weight

HP=0.052MW⋅TVDHP = 0.052 MW \cdot TVD
MW (ppg)TVD (ft)
Formula and calculator
Drilling EngineeringDrilling HydraulicsIn-depth reference

Equivalent Circulating Density

ECD=MW+ΔPa0.052TVDECD = MW + \frac{\Delta P_a}{0.052TVD}
MW (ppg)dP_a (psi)TVD (ft)
Formula and calculator
Drilling EngineeringWell ControlIn-depth reference

Initial Circulating Pressure

ICP=SCRP+SIDPPICP=SCRP+SIDPP
SCRP (psi)SIDPP (psi)
Formula and calculator
Drilling EngineeringWell ControlIn-depth reference

Maximum Allowable Annular Surface Pressure from Shoe EMW

MAASP=(MWmax−MW)0.052TVDshoeMAASP=(MW_{max}-MW)0.052TVD_{shoe}
MW_max (ppg)MW (ppg)TVD_shoe (ft)
Formula and calculator
Drilling EngineeringWell ControlIn-depth reference

Kill Weight Mud Determination - Moore Equation

KWM=SIDPP0.052TVD+OMWKWM=\frac{SIDPP}{0.052TVD}+OMW
SIDPP (psi)OMW (ppg)TVD (ft)
Formula and calculator
Production EngineeringInflow PerformanceIn-depth reference

Vogel Inflow Performance Relationship

qo=qmax[1−0.2(PwfPr)−0.8(PwfPr)2]q_o = q_{max}\left[1 - 0.2\left(\frac{P_{wf}}{P_r}\right) - 0.8\left(\frac{P_{wf}}{P_r}\right)^2\right]
q_max (STB/day)P_wf (psi)P_r (psi)
Formula and calculator
Production EngineeringInflow PerformanceIn-depth reference

Productivity Index and Straight-Line IPR

J=qoPr−PwfJ = \frac{q_o}{P_r - P_{wf}}
q_o (STB/day)P_r (psi)P_wf (psi)
Formula and calculator
Reservoir EngineeringPVT PropertiesIn-depth reference

Gas Formation Volume Factor

Bg=0.02827zTPB_g = 0.02827 \frac{zT}{P}
z (dimensionless)T (°R)P (psia)
Formula and calculator
Phase Behavior and ThermodynamicsPVT PropertiesIn-depth reference

Standing Oil Formation Volume Factor

Bo=0.9759+0.00012F1.2B_o=0.9759+0.00012F^{1.2}
R_s (SCF/STB)gamma_g (fraction)gamma_o (fraction)t (°F)
Formula and calculator
Reservoir EngineeringPVT and Rock-Fluid PropertiesIn-depth reference

API Gravity

API=141.5SGo−131.5API = \frac{141.5}{SG_o} - 131.5
SG_o (dimensionless)
Formula and calculator
PetrophysicsResistivity LogsIn-depth reference

Archie Water Saturation from Resistivity Logs

Sw=[(aϕm)(RwRt)]1/nS_w = \left[\left(\frac{a}{\phi^m}\right)\left(\frac{R_w}{R_t}\right)\right]^{1/n}
a (dimensionless)phi (fraction)m (dimensionless)R_w (ohm m)R_t (ohm m)n (dimensionless)
Formula and calculator
Reservoir EngineeringPVT and Rock-Fluid PropertiesIn-depth reference

Capillary Number

Nc=μw⋅V⋅0.304886400⋅σowN_c = \frac{\mu_w \cdot V \cdot 0.3048}{86400 \cdot \sigma_{ow}}
mu_w (cP)V (ft/day)sigma_ow (dyn/cm)
Formula and calculator
Reservoir EngineeringFluid Flow in Porous MediaIn-depth reference

Steady-State Radial Liquid Flow Rate

qo=0.00708kh(pe−pwf)μoBo[ln⁡(re/rw)+s]q_o=\frac{0.00708kh(p_e-p_{wf})}{\mu_oB_o[\ln(r_e/r_w)+s]}
k (mD)h (ft)p_e (psi)p_wf (psi)mu_o (cP)B_o (bbl/STB)
Formula and calculator
Reservoir EngineeringFluid Flow in Porous MediaIn-depth reference

Darcy's Law for Linear Single-Phase Flow

q=0.001127kAΔPμLq = \frac{0.001127 k A \Delta P}{\mu L}
k (mD)A (ft²)DeltaP (psi)mu (cP)L (ft)
Formula and calculator
Reservoir EngineeringMaterial Balance and ProductionIn-depth reference

Original Oil in Place from General Oil Material Balance

N=F−WeEo+mEg+EfwN = \frac{F-W_e}{E_o+mE_g+E_{fw}}
F (RB)W_e (RB)E_o (RB/STB)m (dimensionless)E_g (RB/STB)E_fw (RB/STB)
Formula and calculator
Drilling EngineeringWell ControlIn-depth reference

Pore Pressure Gradient - Rehm and McClendon

gp=0.398log⁡10(dcn−dco)+0.86g_p=0.398\log_{10}(d_{cn}-d_{co})+0.86
d_cn (dimensionless)d_co (dimensionless)
Formula and calculator
Production EngineeringHydraulic FracturingIn-depth reference

Treatment Fracture Gradient - Hydraulic Fracturing

Gf=Pinj+ΔPh−ΔPf−ΔPpDG_f=\frac{P_{inj}+\Delta P_h-\Delta P_f-\Delta P_p}{D}
P_inj (psi)DeltaP_h (psi)DeltaP_f (psi)DeltaP_p (psi)D (ft)
Formula and calculator
Reservoir EngineeringWell PerformanceIn-depth reference

Joshi Horizontal Well Productivity Index

Jh=0.00708khhμoBo[ln⁡Rh+βhLln⁡(βh2rw)+s]J_h=\frac{0.00708k_hh}{\mu_oB_o\left[\ln R_h+\frac{\beta h}{L}\ln\left(\frac{\beta h}{2r_w}\right)+s\right]}
k_h (mD)k_v (mD)h (ft)L (ft)A_ac (acres)r_w (ft)
Formula and calculator
PetrophysicsResistivity LogsIn-depth reference

Indonesian Water Saturation from Shaly Sand Logs

Sw=[1/RtVsh1−0.5VshRsh+ϕemaRw]2/nS_w=\left[\frac{\sqrt{1/R_t}}{\frac{V_{sh}^{1-0.5V_{sh}}}{\sqrt{R_{sh}}}+\sqrt{\frac{\phi_e^m}{aR_w}}}\right]^{2/n}
R_t (ohm m)V_sh (fraction)R_sh (ohm m)phi_e (fraction)m (dimensionless)a (dimensionless)
Formula and calculator
Drilling EngineeringDrilling HydraulicsIn-depth reference

Velocity of Fluid in Annulus

va=Q2.448(Do2−Dp2)v_a = \frac{Q}{2.448(D_o^2-D_p^2)}
Q (gpm)D_o (in)D_p (in)
Formula and calculator
Phase Behavior and ThermodynamicsPVT PropertiesIn-depth reference

Vasquez-Beggs Solution Gas-Oil Ratio from Pressure

Rs=C1γgpC2exp⁡(C3APIT+460)R_s=C_1\gamma_g p^{C_2}\exp\left(\frac{C_3API}{T+460}\right)
p (psi)T (°F)API (API)gamma_g (fraction)C_rs1 (dimensionless)C_rs2 (dimensionless)
Formula and calculator
Production EngineeringWell PerformanceIn-depth reference

API RP 14E Erosional Velocity

Ve=CρmV_e=\frac{C}{\sqrt{\rho_m}}
C (empirical)rho_m (lb/ft3)
Formula and calculator
Phase Behavior and ThermodynamicsFluid PropertiesIn-depth reference

Beggs-Robinson Live Oil Viscosity Correlation

μo=AμodB\mu_o=A\mu_{od}^{B}
mu_od (cP)R_s (SCF/STB)
Formula and calculator
Production EngineeringHydraulic FracturingIn-depth reference

Carter Leakoff Volume for Hydraulic Fracturing

VL=AL(2CLt+Sp)V_L=A_L\left(2C_L\sqrt{t}+S_p\right)
A_L (ft^2)C_L (ft/min^0.5)t (min)S_p (ft)
Formula and calculator
Drilling EngineeringDrilling HydraulicsIn-depth reference

Annular Velocity from Pump Output

AV=24.5QDh2−Dp2AV = \frac{24.5Q}{D_h^2 - D_p^2}
Q (gpm)D_h (in)D_p (in)
Formula and calculator
Drilling EngineeringWell ControlIn-depth reference

Final Circulating Pressure

FCP=SCRPKWMOMWFCP=SCRP\frac{KWM}{OMW}
SCRP (psi)KWM (ppg)OMW (ppg)
Formula and calculator
Geomechanics and FracturingIn-Situ Stress and Rock MechanicsIn-depth reference

Fracture Gradient - Zoback and Healy

Shmin=(1+μf2+μf)−2(Sv−Pp)+PpS_{hmin} = (\sqrt{1 + \mu_f^2} + \mu_f)^{-2}(S_v - P_p) + P_p
mu_f (dimensionless)S_v (psi)P_p (psi)
Formula and calculator
Phase Behavior and ThermodynamicsGas PropertiesIn-depth reference

Real Gas Density

ρg=PMgzRT\rho_g=\frac{P M_g}{zRT}
P (psia)M_g (lb/lbmol)z (dimensionless)R (psia ft³/(lbmol °R))T (°R)
Formula and calculator