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Petroleum engineering formula sheet

Fifteen frequently used equations with direct links to variable definitions, units, assumptions, worked examples, sources, and working calculators.

Drilling EngineeringWell Control

Hydrostatic Pressure from Mud Weight

HP=0.052MW⋅TVDHP = 0.052 MW \cdot TVD
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Drilling EngineeringDrilling Hydraulics

Equivalent Circulating Density

ECD=MW+ΔPa0.052TVDECD = MW + \frac{\Delta P_a}{0.052TVD}
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Drilling EngineeringDrilling Hydraulics

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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Drilling EngineeringWell Control

Initial Circulating Pressure

ICP=SCRP+SIDPPICP=SCRP+SIDPP
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Reservoir EngineeringFluid Flow in Porous Media

Darcy's Law for Linear Single-Phase Flow

q=0.001127kAΔPμLq = \frac{0.001127 k A \Delta P}{\mu L}
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Reservoir EngineeringFluid Flow in Porous Media

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]}
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Reservoir EngineeringWell Performance

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]}
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Production EngineeringInflow Performance

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]
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Reservoir EngineeringPVT Properties

Gas Formation Volume Factor

Bg=0.02827zTPB_g = 0.02827 \frac{zT}{P}
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Phase Behavior and ThermodynamicsPVT Properties

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)
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Phase Behavior and ThermodynamicsFluid Properties

Beggs-Robinson Live Oil Viscosity Correlation

μo=AμodB\mu_o=A\mu_{od}^{B}
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PetrophysicsResistivity Logs

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}
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PetrophysicsResistivity Logs

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}
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Production EngineeringWell Performance

API RP 14E Erosional Velocity

Ve=CρmV_e=\frac{C}{\sqrt{\rho_m}}
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Production EngineeringHydraulic Fracturing

Carter Leakoff Volume for Hydraulic Fracturing

VL=AL(2CLt+Sp)V_L=A_L\left(2C_L\sqrt{t}+S_p\right)
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Use note

Constants and units belong to each equation's declared unit system. Verify the full source, variables, assumptions, and limits before engineering use. This sheet supports calculation review and study; it is not an operating procedure or design standard.