Petroleum & Drilling

Oilfield maths: hydrostatic pressure, mud weight, API gravity, buoyancy, ECD and production decline

Petroleum & Drilling brings together the core oilfield formulas used to understand pressure, mud properties, flow in the wellbore, and how reservoirs produce over time. It’s useful for students, exam prep, and engineers working in drilling or production, because quick, accurate calculations for things like hydrostatic pressure, ECD, API gravity, and decline forecasting help improve safety, efficiency, and decision-making in the field.

Hydrostatic Pressure (Field)

NEWIntermediate

P = 0.052 \times MW \times TVD

Bottom-hole pressure from mud weight and depth in oilfield units.

API Gravity

API = \frac{141.5}{SG} - 131.5

Standard measure of how light or heavy a crude oil is relative to water.

Buoyancy Factor

NEWIntermediate

BF = 1 - \frac{MW}{65.5}

Reduction in a steel pipe string's weight when submerged in drilling mud.

Equivalent Circulating Density

ECD = MW + \frac{\Delta P}{0.052 \times TVD}

Effective mud density while circulating, including friction pressure.

Annular Velocity

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

Speed of mud returning up the annulus, key to carrying cuttings out.

Triplex Pump Output

Q = 0.000243 \times D^2 \times S \times N

Mud volume per minute from a triplex pump's bore, stroke and speed.

Original Oil in Place

OOIP = \frac{7758 \, A h \phi (1 - S_w)}{B_o}

Volume of oil originally in a reservoir (in stock-tank barrels).

Recovery Factor

NEWIntermediate

RF = \frac{N_p}{OOIP} \times 100

Percentage of oil in place that can actually be produced.

Exponential Production Decline

q = q_0 e^{-D t}

Falling production rate of a well over time at a constant decline rate.

Gas-Oil Ratio

NEWIntermediate

GOR = \frac{V_{gas}}{V_{oil}}

Volume of gas produced per barrel of oil.

Pressure Gradient

NEWIntermediate

G = 0.433 \times SG

Rate at which fluid pressure rises with depth (psi per foot).

Balanced Mud Weight

NEWIntermediate

MW = \frac{P_{pore}}{0.052 \times TVD}

Mud weight needed to just balance formation pore pressure.

Pipe Capacity

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

Internal volume of pipe per foot of length (barrels per foot).

Formation Pressure

NEWIntermediate

P_f = G_f \times TVD

Pore pressure of a formation from its gradient and depth.

Reservoir Flow (Darcy Radial)

q = \frac{k h (P_e - P_w)}{141.2 \, \mu B \ln(r_e/r_w)}

Steady oil flow rate into a well from radial Darcy flow.

Cuttings Transport Ratio

CTR = 1 - \frac{V_{slip}}{V_a}

Fraction of annular velocity effectively lifting cuttings out of the hole.