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

Hydrostatic Pressure (Field)

NEWIntermediate
P=0.052×MW×TVDP = 0.052 \times MW \times TVD

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

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API Gravity

NEWBasic
API=141.5SG131.5API = \frac{141.5}{SG} - 131.5

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

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Buoyancy Factor

NEWIntermediate
BF=1MW65.5BF = 1 - \frac{MW}{65.5}

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

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Equivalent Circulating Density

NEWAdvanced
ECD=MW+ΔP0.052×TVDECD = MW + \frac{\Delta P}{0.052 \times TVD}

Effective mud density while circulating, including friction pressure.

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Annular Velocity

NEWAdvanced
Va=24.5QDh2Dp2V_a = \frac{24.5 \, Q}{D_h^2 - D_p^2}

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

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Triplex Pump Output

NEWAdvanced
Q=0.000243×D2×S×NQ = 0.000243 \times D^2 \times S \times N

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

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Original Oil in Place

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

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

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Recovery Factor

NEWIntermediate
RF=NpOOIP×100RF = \frac{N_p}{OOIP} \times 100

Percentage of oil in place that can actually be produced.

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Exponential Production Decline

NEWAdvanced
q=q0eDtq = q_0 e^{-D t}

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

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Gas-Oil Ratio

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

Volume of gas produced per barrel of oil.

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Pressure Gradient

NEWIntermediate
G=0.433×SGG = 0.433 \times SG

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

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Balanced Mud Weight

NEWIntermediate
MW=Ppore0.052×TVDMW = \frac{P_{pore}}{0.052 \times TVD}

Mud weight needed to just balance formation pore pressure.

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Pipe Capacity

NEWAdvanced
C=D21029.4C = \frac{D^2}{1029.4}

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

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Formation Pressure

NEWIntermediate
Pf=Gf×TVDP_f = G_f \times TVD

Pore pressure of a formation from its gradient and depth.

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Reservoir Flow (Darcy Radial)

NEWAdvanced
q=kh(PePw)141.2μBln(re/rw)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.

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Cuttings Transport Ratio

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

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

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