Drilling Calculator: 180 Formulas

Hydrostatics & Fundamental Pressure 22 Formulas

1. Pressure Gradient

psi/ft = MW(ppg) × 0.052kPa/m = ρ(kg/m³) ÷ 102kg/cm²/m = ρ(kg/l) ÷ 10

Mud Weight (ppg)Fluid Density (kg/m³)Fluid Density (kg/l)

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Field: psi/ft · SI: kPa/m · Metric: kg/cm²/m

2. Hydrostatic Pressure

HP(psi) = MW × 0.052 × TVD(ft)HP(kPa) = ρ(kg/m³) × 0.00981 × TVD(m)HP(bar) = ρ(kg/l) × 0.0981 × TVD(m)

Mud Weight (ppg)Fluid Density (kg/m³)Fluid Density (kg/l)

TVD (ft)TVD (m)TVD (m)

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3. Equivalent Mud Weight from LOT/FIT

EMW(ppg) = MW_LOT + LOT_psi ÷ 0.052 ÷ TVD_shoeEMW(kg/m³) = ρ_LOT + LOT_kPa × 102 ÷ TVD_shoeEMW(kg/l) = ρ_LOT + LOT_bar × 10.2 ÷ TVD_shoe

Mud Weight at LOT (ppg)Mud Density at LOT (kg/m³)Mud Density at LOT (kg/l)

LOT Pressure (psi)LOT Pressure (kPa)LOT Pressure (bar)

Shoe TVD (ft)Shoe TVD (m)Shoe TVD (m)

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4. Specific Gravity from Mud Density

SG = MW(ppg) ÷ 8.33SG = ρ(kg/m³) ÷ 1000SG = ρ(kg/l)

Mud Weight (ppg)Fluid Density (kg/m³)Fluid Density (kg/l)

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5. Formation Pressure

Pf(psi) = Ph_DS(psi) + SIDPP(psi)Pf(kPa) = Ph_DS(kPa) + SIDPP(kPa)Pf(bar) = Ph_DS(bar) + SIDPP(bar)

Hydrostatic Pressure in Drill String (psi)Ph DS (kPa)Ph DS (bar)

SIDPP — Shut-In Drill Pipe Pressure (psi)SIDPP (kPa)SIDPP (bar)

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Also: MW required = (Pf ÷ 0.052 ÷ TVD) ppg

6. Bottom-Hole Pressure — Shut-In

BHP = Ph_DS + SIDPP = Ph_Ann + SICPBHP(kPa) = Ph_DS + SIDPPBHP(bar) = Ph_DS + SIDPP

Ph Drill String (psi) = MW×0.052×TVDPh DS (kPa)Ph DS (bar)

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

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Verify: Ph_Ann + SICP should equal Ph_DS + SIDPP

7. BHP While Circulating

BHP_circ = Ph_Ann + APL (psi)BHP_circ = Ph_Ann + APL (kPa)BHP_circ = Ph_Ann + APL (bar)

Annular Hydrostatic Pressure (psi)Ph Ann (kPa)Ph Ann (bar)

Annular Pressure Loss APL (psi)APL (kPa)APL (bar)

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8. BHP — Killing Well (Subsea)

BHP_kill = Ph_Ann + P_Ann + CLFL (psi)BHP_kill(kPa) = Ph_Ann + P_Ann + CLFLBHP_kill(bar) = Ph_Ann + P_Ann + CLFL

Annular HP (psi)Ann HP (kPa)Ann HP (bar)

Annular Pressure (psi)Ann Pressure (kPa)Ann Pressure (bar)

Choke Line Friction Loss CLFL (psi)CLFL (kPa)CLFL (bar)

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9. Equivalent Circulating Density (ECD)

ECD(ppg) = MW + APL ÷ 0.052 ÷ TVDECD(kg/m³) = ρ + APL(kPa) × 102 ÷ TVD(m)ECD(kg/l) = ρ + APL(bar) × 10.2 ÷ TVD(m)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Annular Pressure Loss (psi)APL (kPa)APL (bar)

TVD (ft)TVD (m)TVD (m)

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10. Formation Temperature

FT(°F) = Surface_Temp + (0.012°F/ft × TVD)FT(°C) = Surface_Temp + (0.022°C/m × TVD)FT(°C) = Surface_Temp + (0.022°C/m × TVD)

Surface Temperature (°F)Surface Temperature (°C)Surface Temperature (°C)

TVD (ft)TVD (m)TVD (m)

Geothermal Gradient (°F/ft, default 0.012)Geothermal Gradient (°C/m, default 0.022)Geothermal Gradient (°C/m, default 0.022)

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11. Temperature Conversions

°R = °F + 460 · °K = °C + 273°K = °C + 273 · °F = (°C × 9/5) + 32°K = °C + 273

Temperature (°F)Temperature (°C)Temperature (°C)

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12. Crude Oil Density from °API

SG = 141.5 ÷ (131.5 + °API) · Density(ppg) = SG × 8.33

°API Gravity

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13. Gas Pressure at Depth (Charles/Boyle)

P_d = P_s × e^(0.2085 × Gg × D ÷ (T_avg + 460))P_d = P_s × e^(0.03415 × Gg × D_m ÷ (T_avg + 273))P_d = P_s × e^(0.03415 × Gg × D_m ÷ (T_avg + 273))

Surface Pressure (psi)Surface Pressure (kPa)Surface Pressure (bar)

Gas Gravity (SG, air=1.0)

Depth (ft)Depth (m)Depth (m)

Average Temperature (°F)Average Temperature (°C)Average Temperature (°C)

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14. Gas Gradient

Gas Grad (psi/ft) = (P_deep − P_shallow) ÷ Depth_intervalGas Grad (kPa/m) = (P_deep − P_shallow) ÷ Interval(m)Gas Grad (bar/m) = (P_deep − P_shallow) ÷ Interval(m)

Deep Pressure (psi)Deep Pressure (kPa)Deep Pressure (bar)

Shallow Pressure (psi)Shallow Pressure (kPa)Shallow Pressure (bar)

Depth Interval (ft)Depth Interval (m)Depth Interval (m)

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15. Gas / Fluid Gradient Calculator

G(psi/ft) = SG × 0.4335G(kPa/m) = SG × 9.81G(bar/m) = SG × 0.0981

Gas / Fluid Type (sets SG below)

Gas/Fluid SG (relative to water=1)

Column Height (ft)Column Height (m)Column Height (m)

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16. Influx Type Identification

d_inf(ppg) = MW − (SICP−SIDPP) ÷ (0.052 × h_i)d_inf(kg/m³) = ρ − (SICP−SIDPP) ÷ (0.00981 × h_i)d_inf(kg/l) = ρ − (SICP−SIDPP) ÷ (0.0981 × h_i)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

SICP (psi)SICP (kPa)SICP (bar)

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

Influx Height h_i (ft)Influx Height (m)Influx Height (m)

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17. Gas Volume — Boyle-Charles Combined

V₂ = (P₁ × V₁ × T₂) ÷ (P₂ × T₁) · T in absolute (°R or K)

P₁ (psi)P₁ (kPa)P₁ (bar)

V₁ (bbl)V₁ (m³)V₁ (m³)

T₁ (°F)T₁ (°C)T₁ (°C)

P₂ (psi)P₂ (kPa)P₂ (bar)

T₂ (°F)T₂ (°C)T₂ (°C)

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18. Pressure Gradient from Any Fluid Density

G(psi/ft) = ρ(ppg) × 0.052G(kPa/m) = ρ(kg/m³) × 0.00981G(bar/m) = ρ(kg/l) × 0.0981

Fluid Density (ppg)Fluid Density (kg/m³)Fluid Density (kg/l)

Column Depth / TVD (ft)Depth (m)Depth (m)

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19. Hydrostatic Pressure Difference

ΔHP(psi) = (MW₁ − MW₂) × 0.052 × TVDΔHP(kPa) = (ρ₁ − ρ₂) × 0.00981 × TVDΔHP(bar) = (ρ₁ − ρ₂) × 0.0981 × TVD

Mud Weight 1 (ppg)Density 1 (kg/m³)Density 1 (kg/l)

Mud Weight 2 (ppg)Density 2 (kg/m³)Density 2 (kg/l)

TVD (ft)TVD (m)TVD (m)

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20. Mud Density Unit Converter

ppg × 119.83 = kg/m³ · ppg ÷ 8.33 = SG · ppg × 7.48 = pcf

Input Value

Input Unit

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21. Pressure Unit Converter

psi × 6.895 = kPa · psi × 0.06895 = bar · psi × 0.0703 = kg/cm²

Pressure Value

Input Unit

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22. MAASP — Max Allowable Annular Surface Pressure

MAASP(psi) = (FG − MW) × 0.052 × TVD_shoeMAASP(kPa) = (FG − ρ) × 0.00981 × TVD_shoeMAASP(bar) = (FG − ρ) × 0.0981 × TVD_shoe

Fracture Gradient / EMW (ppg)Fracture Gradient (kg/m³)Fracture Gradient (kg/l)

Current Mud Weight (ppg)Current Density (kg/m³)Current Density (kg/l)

Shoe TVD (ft)Shoe TVD (m)Shoe TVD (m)

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MAASP is the maximum pressure allowed on the annulus at surface before fracturing the formation at the shoe

Well Control & Kick Management 25 Formulas

1. Kill Mud Weight (KMW)

KMW(ppg) = SIDPP(psi) ÷ (0.052 × TVD) + OMWKMW(kg/m³) = SIDPP(kPa) ÷ (0.00981 × TVD) + OMWKMW(kg/l) = SIDPP(bar) ÷ (0.0981 × TVD) + OMW

SIDPP — Shut-In Drill Pipe Pressure (psi)SIDPP (kPa)SIDPP (bar)

TVD (ft)TVD (m)TVD (m)

Original Mud Weight (ppg)Original Density (kg/m³)Original Density (kg/l)

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Metric alt: KMW(kg/m³) = (SIDPP(psi) × 10 ÷ TVD(m)) + OMW(kg/l×1000)

2. Initial Circulating Pressure (ICP)

ICP = SIDPP + SCRP (Slow Circulating Rate Pressure)

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

Slow Circulating Rate Pressure SCRP (psi)SCRP (kPa)SCRP (bar)

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SCRP must be recorded at the kill rate (typically 25–50 spm) BEFORE the kick occurs

3. Final Circulating Pressure (FCP)

FCP = SCRP × (KMW ÷ OMW)

SCRP at Kill Rate (psi)SCRP (kPa)SCRP (bar)

Kill Mud Weight (ppg)KMW (kg/m³)KMW (kg/l)

Original Mud Weight (ppg)OMW (kg/m³)OMW (kg/l)

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4. Estimated Influx Density

d_inf(ppg) = MW − (SICP − SIDPP) ÷ (0.052 × h_i)d_inf(kg/m³) = ρ − (SICP − SIDPP) ÷ (0.00981 × h_i)d_inf(kg/l) = ρ − (SICP − SIDPP) ÷ (0.0981 × h_i)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

SICP (psi)SICP (kPa)SICP (bar)

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

Influx Height h_i (ft)Influx Height (m)Influx Height (m)

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Gas: <3 ppg · Oil: 3–7 ppg · Saltwater: 8.3–9.0 ppg

5. Kick Tolerance

KT(ppg) = (MAASP ÷ 0.052 ÷ TVD) − (MW × h_i ÷ TVD)KT = [MAASP(kPa) ÷ (0.00981 × TVD)] − [ρ × h_i ÷ TVD]KT = [MAASP(bar) ÷ (0.0981 × TVD)] − [ρ × h_i ÷ TVD]

MAASP (psi)MAASP (kPa)MAASP (bar)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Influx Height h_i (ft)Influx Height (m)Influx Height (m)

TVD (ft)TVD (m)TVD (m)

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6. Influx Height

h_i(ft) = Pit Gain(bbl) ÷ Ann Capacity(bbl/ft)h_i(m) = Gain(m³) ÷ Ann Cap(m³/m)h_i(m) = Gain(m³) ÷ Ann Cap(m³/m)

Pit Gain (bbl)Pit Gain (m³)Pit Gain (m³)

Annular Capacity (bbl/ft) = (Dh²−Dp²)÷1029.4Annular Cap (m³/m) = π(Dh²−Dp²)÷4Annular Cap (m³/m)

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7. Boyle's Law — Gas Expansion

P₁ × V₁ = P₂ × V₂ → V₂ = (P₁ × V₁) ÷ P₂

Initial Pressure P₁ (psi)P₁ (kPa)P₁ (bar)

Initial Volume V₁ (bbl)V₁ (m³)V₁ (m³)

Final Pressure P₂ (psi)P₂ (kPa)P₂ (bar)

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Also: P₂ = P₁V₁÷V₂. Critical for gas migration and kick handling

8. Gas Percolation / Migration Rate

Mig Rate(ft/hr) = ΔP(psi/hr) ÷ Mud Gradient(psi/ft)Mig Rate(m/hr) = ΔP(kPa/hr) ÷ Mud Grad(kPa/m)Mig Rate(m/hr) = ΔP(bar/hr) ÷ Mud Grad(bar/m)

Pressure Rise Rate (psi/hr)Pressure Rise Rate (kPa/hr)Pressure Rise Rate (bar/hr)

Mud Gradient (psi/ft) = MW×0.052Mud Gradient (kPa/m)Mud Gradient (bar/m)

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Typical gas migration: 100–1000 ft/hr. Monitor SICP rise rate.

9. U-Tube Balance Equation

SIDPP + Ph_mud(DS) = SICP + Ph_mud(ann) + Ph_gas(ann)

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

Ph mud in DS (psi)Ph DS (kPa)Ph DS (bar)

SICP (psi)SICP (kPa)SICP (bar)

Ph mud in Annulus (psi)Ph ann (kPa)Ph ann (bar)

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10. Driller's Method — ICP & FCP

ICP = SIDPP + SCRP · FCP = SCRP × (KMW÷OMW) · Max BHP = const

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

SCRP at Kill Rate (psi)SCRP (kPa)SCRP (bar)

KMW (ppg)KMW (kg/m³)KMW (kg/l)

OMW (ppg)OMW (kg/m³)OMW (kg/l)

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11. Tapered String — Interim Circulating Pressure

P_interim = ICP − (Strks_pumped ÷ Strks_DS) × (ICP − FCP)

ICP (psi)ICP (kPa)ICP (bar)

FCP (psi)FCP (kPa)FCP (bar)

Strokes Pumped

Total Strokes to Displace DS

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12. Strokes to Pump & Spot a Pill

Strokes_pump = Vol_pill(bbl) ÷ PO(bbl/stk) · Strokes_chase = chase_vol ÷ PO

Pill Volume (bbl)Pill Volume (m³)Pill Volume (m³)

Chase Volume (bbl)Chase Volume (m³)Chase Volume (m³)

Pump Output (bbl/stk)Pump Output (m³/stk)Pump Output (L/stk)

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13. Volumetric Well Control Method

ΔV(bbl) = ΔP(psi) ÷ (MW×0.052) · Allow P rise, bleed ΔV, maintain BHP

Allowable Pressure Increment (psi)Allowable ΔP (kPa)Allowable ΔP (bar)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Annular Capacity at Bubble (bbl/ft)Ann Cap (m³/m)Ann Cap (m³/m)

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14. Lubricate & Bleed — Volume per Step

Vol_lub(bbl) = ΔP_target(psi) ÷ (MW×0.052) × Ann_cap(bbl/ft)

Target Pressure Drop (psi)Target ΔP (kPa)Target ΔP (bar)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Annular Capacity (bbl/ft)Ann Cap (m³/m)Ann Cap (m³/m)

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15. Riser Margin (Offshore)

RM(ppg) = (ρ_sea×0.052×D_sea − ρ_mud×0.052×(D_sea−TVD)) ÷ (0.052×TVD)RM(kg/m³) = (ρ_sw×D_sea×0.00981 − ρ_mud×0.00981×(D_sea−TVD)) ÷ (0.00981×TVD)RM(kg/l) = same with 0.0981

Seawater Density (ppg, typ. 8.6)Seawater Density (kg/m³, typ. 1030)Seawater Density (kg/l, typ. 1.03)

Current Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Water Depth (ft)Water Depth (m)Water Depth (m)

Well TVD (ft)Well TVD (m)Well TVD (m)

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16. Max Pressure at Shoe (Driller's — Gas Kick)

P_shoe_max = Ph_mud_above_shoe + Ph_gas + Csg_pressure

Ph mud above shoe (psi)Ph above shoe (kPa)Ph above shoe (bar)

Gas Gradient (psi/ft)Gas Gradient (kPa/m)Gas Gradient (bar/m)

Gas Column Height (ft)Gas Column Height (m)Gas Column Height (m)

Casing Shoe Pressure (psi)Shoe Pressure (kPa)Shoe Pressure (bar)

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17. Choke Line Friction Loss (CLFL) — Subsea

CLFL(psi) ≈ K × (ρ × Q²) — use pressure gauge readingsCLFL(kPa) ≈ measured at kill rate on choke lineCLFL(bar) ≈ measured at kill rate

Circulating Pressure (full rate) (psi)Circulating Pressure (kPa)Circulating Pressure (bar)

Slow Rate Pressure (kill rate) (psi)Slow Rate P (kPa)Slow Rate P (bar)

Full Rate (spm)

Kill Rate (spm)

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CLFL = SPR × (Kill_Rate/Full_Rate)² where SPR = slow pump rate pressure

18. BOP Accumulator Sizing (API 16D)

Usable Vol(gal) = Close_Vol × P_precharge ÷ (P_min − P_precharge)Usable Vol(L) = Close_Vol × P_pre ÷ (P_min − P_pre)Usable Vol(L) = Close_Vol × P_pre ÷ (P_min − P_pre)

Required Closing Volume (gal)Closing Volume (L)Closing Volume (L)

Pre-charge Pressure (psi)Pre-charge (kPa)Pre-charge (bar)

Min Operating Pressure (psi)Min Op Pressure (kPa)Min Op Pressure (bar)

Number of Closing Operations Required

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API 16D: Total accumulator = Usable Vol ÷ 0.5 (50% usable factor). Min precharge = 200 psi above seabed hydrostatic.

19. Formation Pressure from DST / Wireline

Pf(psi) = FBHP or = MW×0.052×TVD + SIDPPPf(kPa) = ρ×0.00981×TVD + SIDPPPf(bar) = ρ×0.0981×TVD + SIDPP

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

TVD (ft)TVD (m)TVD (m)

SIDPP (psi) — 0 if known FBHPSIDPP (kPa)SIDPP (bar)

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20. Additional Mud Weight for Kill (Over-balance)

ΔMW(ppg) = SIDPP ÷ (0.052 × TVD)Δρ(kg/m³) = SIDPP(kPa) ÷ (0.00981 × TVD)Δρ(kg/l) = SIDPP(bar) ÷ (0.0981 × TVD)

SIDPP (psi)SIDPP (kPa)SIDPP (bar)

TVD (ft)TVD (m)TVD (m)

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21. A-Factor — Gas Migration in Annulus

A = BHP − [Mud_Grad × (D − X) − P_influx]A = BHP − [Mud_Grad × (D − X) − P_influx] (kPa)A = BHP − [Mud_Grad × (D − X) − P_influx] (bar)

BHP / Formation Pressure (psi)BHP (kPa)BHP (bar)

Mud Gradient (psi/ft)Mud Gradient (kPa/m)Mud Gradient (bar/m)

Total Depth D (ft)Total Depth D (m)Total Depth D (m)

Influx Top Position X from surface (ft)Influx Top X (m)Influx Top X (m)

Influx Pressure P_i (psi)Influx Pressure (kPa)Influx Pressure (bar)

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22. New MAASP After Mud Weight Increase

MAASP_new = (FG − KMW) × 0.052 × TVD_shoeMAASP_new = (FG − KMW) × 0.00981 × TVD_shoeMAASP_new = (FG − KMW) × 0.0981 × TVD_shoe

Fracture Gradient / EMW (ppg)FG (kg/m³)FG (kg/l)

Kill Mud Weight KMW (ppg)KMW (kg/m³)KMW (kg/l)

Shoe TVD (ft)Shoe TVD (m)Shoe TVD (m)

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23. Pressure to Break Circulation (Gel Strength)

P_gel(psi) = (YP × L) ÷ (300 × D) + (PV × V × L) ÷ (90000 × D²)P_gel(kPa) = (τ_gel(Pa) × L) ÷ (300 × D) × 47.88P_gel(bar) = P_gel_psi × 0.06895

Yield Point / Gel Strength YP (lb/100ft²)

Plastic Viscosity PV (cP)

String Length L (ft)Length (m)Length (m)

Pipe ID D (in)Pipe ID (m)Pipe ID (m)

Annular Velocity V (ft/min)Velocity (m/min)Velocity (m/min)

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24. Gas Migration & Shut-In Pressure Rise

Mig_Rate(ft/hr) = ΔP_rate(psi/hr) ÷ MW(ppg) ÷ 0.052Mig_Rate(m/hr) = ΔP_rate(kPa/hr) ÷ (ρ × 0.00981)Mig_Rate(m/hr) = ΔP_rate(bar/hr) ÷ (ρ × 0.0981)

SICP rise rate (psi/hr)SICP rise (kPa/hr)SICP rise (bar/hr)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Time monitored (hrs)Time (hrs)Time (hrs)

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Typical gas migration: 100–1500 ft/hr. Monitor SICP trend every 15 min when shut in.

25. Pressure at Shoe — Gas Migrating to Shoe

P_shoe = P_surf + Ph_mud_above_shoe + Ph_gas_at_shoeP_shoe = P_surf + Ph_mud + Ph_gas (kPa)P_shoe = P_surf + Ph_mud + Ph_gas (bar)

Surface Pressure (psi)Surface Pressure (kPa)Surface Pressure (bar)

Mud Col above shoe (ft)Mud Col (m)Mud Col (m)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Gas Col height at shoe (ft)Gas Col (m)Gas Col (m)

Gas Gradient (psi/ft)Gas Gradient (kPa/m)Gas Gradient (bar/m)

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Pump, Volume & Hydraulics 30 Formulas

1. Triplex Pump Output

PO(bbl/stk) = 0.000243 × Liner_ID²(in) × Stroke_Length(in)PO(L/stk) = 0.000785 × Liner_ID²(cm) × Stroke_Length(cm)PO(L/stk) = 0.000785 × Liner_ID²(cm) × Stroke(cm)

Liner Internal Diameter (inches)Liner ID (cm)Liner ID (cm)

Stroke Length (inches)Stroke Length (cm)Stroke Length (cm)

Volumetric Efficiency (%, default 98)

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2. Duplex Pump Output

PO(bbl/stk) = 0.000162 × (2×Bore² − Rod²) × StrokePO(L/stk) = 0.000524 × (2×Bore² − Rod²) × Stroke (cm)PO(L/stk) same formula

Bore/Liner ID (inches)Bore ID (cm)Bore ID (cm)

Piston Rod Diameter (inches)Rod Diameter (cm)Rod Diameter (cm)

Stroke Length (inches)Stroke Length (cm)Stroke Length (cm)

Volumetric Efficiency (%, default 90)

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3. Flow Rate from Pump SPM

Q(bbl/min) = PO(bbl/stk) × SPMQ(L/min) = PO(L/stk) × SPMQ(L/min) = PO(L/stk) × SPM

Pump Output (bbl/stk)Pump Output (L/stk)Pump Output (L/stk)

Pump Strokes per Minute (spm)

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4. Annular Velocity (AV)

AV(ft/min) = (24.51 × Q_bbl/min) ÷ (Dh² − Dp²) in²AV(m/min) = Q(L/min) ÷ [π(Dh²−Dp²)÷4×1000] (Dh,Dp in mm)AV(m/min) = Q(m³/min) ÷ [π(Dh²−Dp²)÷4] (Dh,Dp in m)

Flow Rate Q (bbl/min)Flow Rate (L/min)Flow Rate (m³/min)

Hole/Csg ID Dh (inches)Hole ID Dh (mm)Hole ID Dh (m)

Pipe OD Dp (inches)Pipe OD Dp (mm)Pipe OD Dp (m)

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Minimum AV for hole cleaning: ~100 ft/min (0.5 m/s) in vertical, higher in deviated wells

5. Hydraulic Horsepower (HHP)

HHP = (P_psi × Q_bbl/min) ÷ 1714HHP = (P_kPa × Q_L/min) ÷ 44,742HHP = (P_bar × Q_L/min) ÷ 447.4

Pump Pressure (psi)Pump Pressure (kPa)Pump Pressure (bar)

Flow Rate (bbl/min)Flow Rate (L/min)Flow Rate (L/min)

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6. HHP at Bit (HHPb)

HHPb = (Pb_psi × Q_bbl/min) ÷ 1714HHPb = (Pb_kPa × Q_L/min) ÷ 44,742HHPb = (Pb_bar × Q_L/min) ÷ 447.4

Bit Pressure Drop Pb (psi)Pb (kPa)Pb (bar)

Flow Rate (bbl/min)Flow Rate (L/min)Flow Rate (L/min)

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Target: ≥2.5 HHP/in² of bit area for PDC; ≥1.0 for rollercone

7. Bit Nozzle Pressure Drop

Pb(psi) = 156.5 × MW(ppg) × Q²(bbl/min) ÷ TFA²(in²)Pb(kPa) = 0.8 × ρ(kg/m³) × v_n²(m/s)Pb(bar) = Pb_kPa ÷ 100

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Flow Rate Q (bbl/min)Flow Rate Q (m³/min)Flow Rate Q (m³/min)

TFA — Total Flow Area (in²) = sum of (d/32)²×π/4 per nozzleTFA (m²)TFA (m²)

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Field TFA(in²): count nozzle sizes in 32nds. Three 12/32" nozzles → TFA = 3×(12/32)²×π/4 ≈ 0.332 in²

8. Nozzle Jet Velocity & Impact Force

v_n(ft/s) = Q(bbl/min) × 0.3208 ÷ TFA(in²)v_n(m/s) = Q(m³/s) ÷ TFA(m²)v_n(m/s) = Q(m³/s) ÷ TFA(m²)

Flow Rate (bbl/min)Flow Rate (m³/s)Flow Rate (m³/s)

TFA (in²)TFA (m²)TFA (m²)

Mud Weight (ppg) for Impact ForceMud Density (kg/m³)Mud Density (kg/l)

—

9. Pipe Internal Capacity

Cap(bbl/ft) = ID²(in) ÷ 1029.4Cap(L/m) = π × ID²(mm) ÷ 4000Cap(m³/m) = π × ID²(m) ÷ 4

Pipe ID (inches)Pipe ID (mm)Pipe ID (m)

—

10. Annular Capacity

Ann Cap(bbl/ft) = (Dh² − Dp²)(in²) ÷ 1029.4Ann Cap(L/m) = π(Dh²−Dp²)(mm²) ÷ 4000Ann Cap(m³/m) = π(Dh²−Dp²)(m²) ÷ 4

Hole/Csg ID Dh (inches)Dh (mm)Dh (m)

Pipe OD Dp (inches)Dp (mm)Dp (m)

—

11. Surface to Bit — Lag Strokes

Lag Strokes = DS_Volume ÷ Pump Output

Drill String Volume (bbl)DS Volume (m³)DS Volume (m³)

Pump Output (bbl/stk)Pump Output (m³/stk)Pump Output (L/stk)

—

12. Bit to Surface — Return Lag Strokes

Return Strokes = Annulus Volume ÷ Pump Output

Annulus Volume (bbl)Annulus Volume (m³)Annulus Volume (m³)

Pump Output (bbl/stk)Pump Output (m³/stk)Pump Output (L/stk)

—

13. Pump Pressure vs. SPM (Roughneck Formula)

P_new = P_old × (SPM_new ÷ SPM_old)²

Current Pressure P_old (psi)P_old (kPa)P_old (bar)

Current SPM

New SPM

—

14. Pump Pressure vs. Mud Weight Change

P_new = P_old × (MW_new ÷ MW_old)

Old Pressure (psi)Old Pressure (kPa)Old Pressure (bar)

Old Mud Weight (ppg)Old Density (kg/m³)Old Density (kg/l)

New Mud Weight (ppg)New Density (kg/m³)New Density (kg/l)

—

15. Rectangular Pit Capacity

Vol(bbl) = L(ft) × W(ft) × D(ft) ÷ 5.615Vol(m³) = L × W × D (m)Vol(m³) = L × W × D (m)

Length (ft)Length (m)Length (m)

Width (ft)Width (m)Width (m)

Depth / Fill Height (ft)Depth (m)Depth (m)

—

16. Cylindrical Tank Capacity

Vol(bbl) = π × r²(ft) × H(ft) ÷ 5.615Vol(m³) = π × r²(m) × H(m)Vol(m³) = π × r²(m) × H(m)

Radius (ft)Radius (m)Radius (m)

Height / Fill (ft)Height (m)Height (m)

—

17. Annular Pressure Loss (from ECD)

APL(psi) = (ECD − MW) × 0.052 × TVDAPL(kPa) = (ECD − ρ) × 0.00981 × TVDAPL(bar) = (ECD − ρ) × 0.0981 × TVD

ECD (ppg)ECD (kg/m³)ECD (kg/l)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

TVD (ft)TVD (m)TVD (m)

—

18. Cuttings Slip Velocity & Transport Ratio

V_slip(ft/min) ≈ 0.45×[(65.4−MW)÷MW]^0.5 × d_cut(in)^0.667 ÷ μ_app^0.333V_slip(m/min) = V_slip(ft/min) × 0.3048same

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Cutting Size (inches, typ 0.25)Cutting Size (mm, typ 6)Cutting Size (mm)

Apparent Viscosity μ_app (cP, from PV + YP)

—

19. Shear Rate in Pipe & Annulus

γ_pipe = 96×V(ft/s) ÷ ID(in) · γ_ann = 144×V(ft/s) ÷ (Dh−Dp)(in)γ_pipe = 8V(m/s) ÷ D(m) · γ_ann = 12V(m/s) ÷ (Dh−Dp)(m)same as SI

Fluid Velocity (ft/s)Fluid Velocity (m/s)Fluid Velocity (m/s)

Pipe ID (in) — for pipe shear ratePipe ID (m)Pipe ID (m)

(Dh − Dp) in inches — for annular shear rate(Dh − Dp) in m(Dh − Dp) in m

—

20. Reynolds Number

Re = 928 × ρ(ppg) × V(ft/s) × D(in) ÷ μ(cP)Re = ρ(kg/m³) × V(m/s) × D(m) ÷ μ(Pa·s)same as SI

Mud Density (ppg)Mud Density (kg/m³)Mud Density (kg/m³)

Fluid Velocity (ft/s)Velocity (m/s)Velocity (m/s)

Diameter (inches)Diameter (m)Diameter (m)

Apparent Viscosity μ (cP / Pa·s)

—

Laminar: Re < 2100 · Transitional: 2100–3000 · Turbulent: >3000

21. Fanning Friction Factor

f_lam = 16÷Re (laminar) · f_turb = 0.0791÷Re^0.25 (Blasius, turbulent)

Reynolds Number Re

—

22. Power Law n and K Indices

n = 3.32 × log(θ600 ÷ θ300) · K = θ300 ÷ (511)^n

θ600 — 600 RPM Viscometer Reading (dial units)

θ300 — 300 RPM Viscometer Reading (dial units)

—

23. Plastic Viscosity & Yield Point (Bingham Plastic)

PV(cP) = θ600 − θ300 · YP(lb/100ft²) = θ300 − PV

θ600 — 600 RPM Reading

θ300 — 300 RPM Reading

—

24. Trip Volume Monitoring

Expected Fill(bbl) = Pipe Displacement(bbl/ft) × Stands Pulled × ft/standExpected Fill(m³) = Pipe Displacement(m³/m) × m pulledsame

Pipe OD (in)Pipe OD (mm)Pipe OD (mm)

Pipe ID (in)Pipe ID (mm)Pipe ID (mm)

Length Pulled (ft)Length Pulled (m)Length Pulled (m)

Actual Fill Volume (bbl)Actual Fill (m³)Actual Fill (m³)

—

25. Laminar Pressure Loss — Pipe (Bingham Plastic)

ΔP(psi) = PV×V×L ÷ (90000×ID²) + YP×L ÷ (225×ID)ΔP(kPa) = μ_p×v×L ÷ (3000×D²) + τ_y×L ÷ (6×D)ΔP(bar) = ΔP_kPa ÷ 100

Plastic Viscosity PV (cP)

Yield Point YP (lb/100ft²)

Fluid Velocity V (ft/min)Velocity (m/min)Velocity (m/min)

Pipe Length L (ft)Length (m)Length (m)

Pipe ID (in)Pipe ID (m)Pipe ID (m)

—

26. Laminar Pressure Loss — Annulus (Bingham)

ΔP(psi) = PV×V×L ÷ (60000×(Dh−Dp)²) + YP×L ÷ (200×(Dh−Dp))ΔP(kPa) = μ_p×v×L ÷ (2000×(Dh−Dp)²) + τ_y×L ÷ (6×(Dh−Dp))ΔP(bar) = ΔP_kPa ÷ 100

Plastic Viscosity PV (cP)

Yield Point YP (lb/100ft²)

Annular Velocity V (ft/min)Ann Velocity (m/min)Ann Velocity (m/min)

Annular Length L (ft)Length (m)Length (m)

Hole ID Dh (in)Dh (m)Dh (m)

Pipe OD Dp (in)Dp (m)Dp (m)

—

27. Critical Velocity — Laminar/Turbulent Transition

Vc = [97×PV + √(97²×PV² + 8.2×D²×YP×ρ)] ÷ (6.7×ρ×D)Vc(m/s) = Vc_ft/min × 0.00508same

Plastic Viscosity PV (cP)

Yield Point YP (lb/100ft²)

Mud Density ρ (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Pipe ID or (Dh−Dp) (in)Diameter (m)Diameter (m)

—

28. System HHP & Parasitic Pressure Loss

HHP_sys = P_surf × Q ÷ 1714 · HHP_parasitic = (P_surf − Pb) × Q ÷ 1714kW_sys = P(kPa) × Q(m³/s) ÷ 1000kW = P(bar) × Q(L/s) ÷ 10

Surface Pump Pressure (psi)Surface Pressure (kPa)Surface Pressure (bar)

Bit Pressure Drop Pb (psi)Bit ΔP (kPa)Bit ΔP (bar)

Flow Rate Q (bbl/min)Q (m³/s)Q (L/s)

—

Optimal: 65% of system HHP at bit. Parasitic loss should be 35% for efficient drilling.

29. Fluid Velocity from Flow Rate & Area

V(ft/s) = Q(bbl/min) × 0.3208 ÷ A(in²)V(m/s) = Q(m³/s) ÷ A(m²)V(m/s) = Q(L/s) ÷ (A(cm²) × 0.0001)

Flow Rate Q (bbl/min)Q (m³/s)Q (L/s)

Cross-Section Area A (in²)Area (m²)Area (cm²)

—

30. Minimum Flow Rate for Hole Cleaning

Q_min(bbl/min) = AV_min(ft/min) × (Dh²−Dp²) ÷ 24.51Q_min(L/min) = AV_min(m/min) × π(Dh²−Dp²)÷4000 (mm)Q_min(m³/min) = AV_min(m/min) × π(Dh²−Dp²)÷4 (m)

Min Annular Velocity Required (ft/min)Min AV (m/min)Min AV (m/min)

Hole ID Dh (in)Dh (mm)Dh (m)

Pipe OD Dp (in)Dp (mm)Dp (m)

—

Vertical: 100–120 ft/min min AV · Deviated 30–60°: 150–180 ft/min · Horizontal: 200+ ft/min

Mud & Drilling Fluids Engineering 28 Formulas

1. Barite Required to Raise Mud Weight

Barite(lb/bbl) = 1470 × (MW_new − MW_old) ÷ (35 − MW_new)Barite(kg/m³) = 4200 × (ρ_new − ρ_old) ÷ (4200 − ρ_new)Barite(kg/m³) = 4200 × (ρ_new − ρ_old) ÷ (4200 − ρ_new)

Current Mud Weight (ppg)Current Density (kg/m³)Current Density (kg/l)

Target Mud Weight (ppg)Target Density (kg/m³)Target Density (kg/l)

Volume of Active Mud (bbl)Volume (m³)Volume (m³)

—

Barite SG = 4.2 (35 ppg). Formula valid up to ~19 ppg

2. Mixing Two Fluids — Volume Balance

(V₁ × ρ₁) + (V₂ × ρ₂) = V_F × ρ_F → V₂ = (V_F × ρ_F − V₁ × ρ₁) ÷ ρ₂

Volume of Fluid 1 V₁ (bbl)V₁ (m³)V₁ (m³)

Density of Fluid 1 ρ₁ (ppg)ρ₁ (kg/m³)ρ₁ (kg/l)

Density of Fluid 2 ρ₂ (ppg)ρ₂ (kg/m³)ρ₂ (kg/l)

Target Density ρ_F (ppg)ρ_F (kg/m³)ρ_F (kg/l)

Target Total Volume V_F (bbl)V_F (m³)V_F (m³)

—

3. Drill Pipe Slug Design

Dry Pipe (ft) = Slug_Vol × (ρ_slug − ρ_mud) × 1029.4 ÷ DP_ID²Dry Pipe (m) = Slug_Vol × (ρ_slug − ρ_mud) × 1000 ÷ Cap_m³/msame

Slug Volume (bbl)Slug Volume (m³)Slug Volume (m³)

Slug Density (ppg)Slug Density (kg/m³)Slug Density (kg/l)

Mud Density (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Drill Pipe ID (in)DP ID (mm)DP ID (mm)

—

4. Plastic Viscosity & Yield Point

PV(cP) = θ600 − θ300 · YP(lb/100ft²) = θ300 − PV · AV(cP) = PV + YP

θ600 — Fann VG Reading at 600 RPM

θ300 — Reading at 300 RPM

θ6 — Reading at 6 RPM (gel strength)

θ3 — Reading at 3 RPM

—

5. Average Specific Gravity of Mud

ASG = (%vol_water × SG_water + %vol_oil × SG_oil + %vol_solids × SG_solids) ÷ 100

Water Content (% by volume)

Oil Content (% by volume)

Solids Content (% by volume)

SG Water (typ 1.0–1.2)

SG Oil (typ 0.8–0.85)

SG Solids (typ 2.6–4.2)

—

6. Low Gravity Solids (LGS) Content

LGS(%vol) = [%vol_solids × (4.2 − ASG)] ÷ (4.2 − 2.6)

Total Solids (% volume)

Average Specific Gravity of Mud (ASG)

—

LGS (SG 2.6) includes bentonite + drilled solids. HGS = Barite (SG 4.2)

7. Oil/Water Ratio Adjustment

Oil volume to add: V_oil = V_total × (%oil_target − %oil_current) ÷ 100

Current Volume (bbl)Current Volume (m³)Current Volume (m³)

Current Oil % (by volume)

Target Oil % (by volume)

—

8. Bentonite Content Determination

Bent(%vol) = (Mud_CEC − Shale_CEC × %drill_sol) ÷ Bent_CEC

Mud CEC (meq/100mL) from Methylene Blue Test

Shale CEC (meq/100g, typ 3–5)

Drilled Solids (% vol)

Bentonite CEC (meq/100g, typ 70–90)

—

9. Complete Mud Solids Analysis

Drilled Solids = %LGS − %Bentonite · Barite = %Suspended − %LGS

Retort Total Solids (% vol)

Retort Oil (% vol)

Retort Water (% vol)

LGS (% vol, from formula 6)

Bentonite (% vol, from formula 8)

—

10. Saltwater Content from Chlorides

SW(%vol) ≈ Cl_ppm ÷ (NaCl_sat_ppm × 0.01) — approx for NaCl

Chloride Content (mg/L or ppm)

Retort Water Volume (% vol)

—

Sat. NaCl ≈ 315,000 ppm. 3.5% seawater ≈ 19,000 ppm Cl

11. Dilution Rate to Remove Drilled Solids

V_dilute = V_pit × (%LGS_curr − %LGS_target) ÷ (%LGS_target − %LGS_diluent)

Current Pit Volume (bbl)Pit Volume (m³)Pit Volume (m³)

Current LGS (% vol)

Target LGS (% vol)

LGS in Diluent (% vol, typ 0)

—

12. Centrifuge Evaluation — Underflow Density

ρ_underflow ≈ (Mass_in − Mass_overflow) ÷ Volume_underflow

Feed Mud Density (ppg)Feed Density (kg/m³)Feed Density (kg/l)

Feed Volume (bbl/hr)Feed Rate (m³/hr)Feed Rate (m³/hr)

Overflow Density (ppg)Overflow Density (kg/m³)Overflow (kg/l)

Overflow Volume (bbl/hr)Overflow (m³/hr)Overflow (m³/hr)

—

13. Barite for Weighted Cement Slurry

Barite(lb/sk) = [Target_density(ppg) − Base_density] × 94 ÷ (35 − Target)

Base Slurry Density (ppg)Base Slurry (kg/m³)Base Slurry (kg/l)

Target Slurry Density (ppg)Target (kg/m³)Target (kg/l)

—

14. Cement Slurry Weight Check

Slurry ρ(ppg) = Total Weight ÷ Total Volume (gal)

Cement (lb, typ 94 lb/sk)

Mix Water (gal, typ 4.3–6.0 gal/sk)

Additive 1 — Weight (lb)

Additive 1 — Volume (gal)

Additive 2 — Weight (lb)

Additive 2 — Volume (gal)

—

15. Shear Stress (Power Law & Bingham)

Power Law: τ = K × γⁿ · Bingham: τ = YP + PV×γ÷478.8

Shear Rate γ (s⁻¹)

Power Law K (consistency index)

Power Law n (flow behavior index)

Yield Point YP (lb/100ft² for Bingham)

Plastic Viscosity PV (cP for Bingham)

—

16. Apparent Viscosity at Shear Rate

AV(cP) = τ(lb/100ft²) × 478.8 ÷ γ(s⁻¹) · Or: AV = PV + YP (at 511 s⁻¹)

Shear Rate γ (s⁻¹) — e.g. 511 = 300 RPM, 1022 = 600 RPM

Shear Stress τ (lb/100ft²) — or enter PV + YP below

PV (cP) — for PV+YP method

YP (lb/100ft²) — for PV+YP method

—

17. API Filter Loss & Spurt Loss

V_filtrate = 2 × C_w × √t · Spurt Loss = V_30min − 2×(V_7.5min − V_1min)

API 30-min filtrate volume (mL)

7.5-min filtrate volume (mL)

1-min filtrate volume (mL)

—

API spec: fresh water mud <15 mL/30min · OBM <2 mL/30min

18. Mud pH & Alkalinity Analysis

Excess lime (lb/bbl) = 0.26 × (Pm − 0.5×Pf) · Carbonate = 0.026×(2×Pf − Pm) · Bicarbonate = 0.012×(Mf − 10×Pm)

Pm — Phenolphthalein alkalinity of mud (cc/cc)

Pf — Phenolphthalein alkalinity of filtrate (cc)

Mf — Methyl orange alkalinity of filtrate (cc)

—

19. Methylene Blue Test (MBT) — Bentonite

Bentonite(lb/bbl) = MBT_reading × 5 · Bentonite(%vol) = lb/bbl ÷ 9.1

MBT Reading (cc of 0.01N methylene blue)

Mud Volume (bbl) — for total bentoniteMud Volume (m³)Mud Volume (m³)

—

API grade bentonite: 22–32 lb/bbl typical · High yield: 10–15 lb/bbl · Native clay: 3–5 lb/bbl

20. Barite Volume % from Solids Analysis

%Barite = %Suspended_Solids − %LGS · Suspended = 100 − %oil − %water

Retort Oil (% vol)

Retort Water (% vol)

LGS (% vol) — from LGS calculator

—

21. Chloride Analysis & Salt Content

NaCl(ppm) = Cl⁻(ppm) × 1.65 · CaCl₂(ppm) = Cl⁻(ppm) × 1.56 · KCl(ppm) = Cl⁻(ppm) × 1.91

Chloride Cl⁻ content (ppm or mg/L)

Salt Type in Mud

Formation water chlorides (ppm) — for comparison

—

22. Lime Treatment for CO₂ / H₂S

Lime(lb/bbl) = CO₂(mg/L) ÷ 1000 × 0.74 · H₂S(lb/bbl) = H₂S(ppm) × Vol × 0.000034

CO₂ content (mg/L or ppm)

Mud Volume (bbl)Mud Volume (m³)Mud Volume (m³)

H₂S content (ppm) — if applicable

—

23. Soda Ash for Ca²⁺ Treatment

Soda Ash(lb/bbl) = Ca²⁺(ppm) × 0.00094 · Total(lbs) = lb/bbl × Volume(bbl)

Calcium Ca²⁺ content (ppm or mg/L)

Mud Volume (bbl)Mud Volume (m³)Mud Volume (m³)

—

Target Ca²⁺: <200 ppm for WBM · High Ca²⁺ causes flocculation and viscosity increase

24. KCl Concentration for Shale Inhibition

KCl(lb/bbl) = %KCl × 3.5 · KCl(kg/m³) = %KCl × 10 · Activity of water: Aw = 1 − 0.00345×%KCl

Target KCl Concentration (%wt)

Mud Volume (bbl)Mud Volume (m³)Mud Volume (m³)

Current Mud Density (ppg)Current Density (kg/m³)Current Density (kg/l)

—

25. Mass Rate Balance — Solids Removal Pit

Q_B(lb/min) = Q_m×ρ_m − Q_c×ρ_c − Q_w×ρ_w · (Vm=mud in, Vc=centrifuge out, Vw=water in)

Mud Feed Rate Q_m (bbl/min)Q_m (m³/min)Q_m (m³/min)

Mud Density ρ_m (ppg)ρ_m (kg/m³)ρ_m (kg/l)

Centrifuge Output Rate Q_c (bbl/min)Q_c (m³/min)Q_c (m³/min)

Centrifuge Output Density ρ_c (ppg)ρ_c (kg/m³)ρ_c (kg/l)

Water Addition Rate Q_w (bbl/min)Q_w (m³/min)Q_w (m³/min)

—

26. Additive Concentration per Cement Sack

%Additive = W_add(lb) ÷ 94 × 100 · lb/sk = %add × 0.94 · gal/sk = V_add(gal)/sk

Additive Weight per sack (lb/sk)

Additive Volume per sack (gal/sk) — if liquid

Number of sacks

—

27. Turbulent Pressure Loss (Pipe)

ΔP(psi) = 7.7×10⁻⁵ × f × ρ⁰·⁸ × PV⁰·² × Q¹·⁸ × L ÷ D⁴·⁸ΔP(kPa) = ΔP_psi × 6.895ΔP(bar) = ΔP_psi × 0.06895

Fanning Friction Factor f (from Card 21)

Mud Density ρ (ppg)ρ (kg/m³)ρ (kg/l)

Plastic Viscosity PV (cP)

Flow Rate Q (bbl/min)Q (m³/min)Q (m³/min)

Pipe Length L (ft)Length (m)Length (m)

Pipe ID D (in)Pipe ID (m)Pipe ID (m)

—

28. LCM Pill & Loss Circulation Treatment

Pill Vol(bbl) = Ann_Cap(bbl/ft) × Pill_Length(ft) · Barite to weight pill = standard formula

Required Pill Length (ft)Pill Length (m)Pill Length (m)

Annular Capacity (bbl/ft)Ann Cap (m³/m)Ann Cap (m³/m)

Pill Density (ppg)Pill Density (kg/m³)Pill Density (kg/l)

Base Mud Density (ppg)Base Mud (kg/m³)Base Mud (kg/l)

—

Mechanical & Engineering 22 Formulas

1. Buoyancy Factor

BF = 1 − (MW_ppg ÷ 65.44) · W_buoy = W_air × BFBF = 1 − (ρ_kg/m³ ÷ 7850) · (Steel density = 7850 kg/m³)BF = 1 − (ρ_kg/l ÷ 7.85)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

String Weight in Air (klbs)String Weight in Air (kN or tonnes)String Weight in Air (tonnes)

—

2. Ton-Mile — Round Trip

TM = D×(L+D)×W + D×(M+0.5×C) ÷ 5,280,000TM = D(m)×(L+D)×W(kN) ÷ 1,000,000same as SI

Depth D (ft)Depth D (m)Depth D (m)

Drill String Length L (ft)DS Length (m)DS Length (m)

Avg DP Weight W (lb/ft)DP Weight (kN/m)DP Weight (kN/m)

BHA/BHK Weight M (lbs)BHA Weight (kN)BHA Weight (kN)

Crown-to-Crown Length C (ft)Crown dist C (m)Crown dist C (m)

—

Replace line at: 1000–2000 TM (new bit), 2000–4000 TM (no bit), 500 TM (coring)

3. Free Point — Stuck Pipe

FPD(ft) = (W_pipe_lb/ft × ΔL_stretch_in × 2,500,000) ÷ (Pull_lbs × 12)FPD(m) = (W_pipe × ΔL × E × A) ÷ Pull_forcesame formula

Pipe Weight in Air (lb/ft)Pipe Weight (kg/m)Pipe Weight (kg/m)

Measured Stretch (inches)Measured Stretch (mm)Measured Stretch (mm)

Applied Pull Force (lbs, over free hang weight)Pull Force (kN)Pull Force (kN)

—

Free Point Constant = pipe weight (lb/ft). Stretch formula: FPD = (FPC × in_stretch × 2,500,000) ÷ Pull_lbs

4. D-Exponent (Drilling Rate Analysis)

d = log(R ÷ 60N) ÷ log(12W ÷ 10⁶D)

Drilling Rate R (ft/hr)Rate (m/hr)Rate (m/hr)

Rotary Speed N (RPM)

WOB W (1000 lbs/klb)WOB W (kN)WOB W (kN)

Bit Size D (inches)Bit Size (mm)Bit Size (mm)

—

Normalized: dc = d × (ρ_normal ÷ ρ_actual). Decreasing dc_exp → abnormal pore pressure

5. Hookload & Overpull

HL_fluid = W_air × BF · Overpull = HL_measured − HL_expectedHL(kN) = W_air(kN) × BFHL(tonnes) = W_air(tonnes) × BF

String Weight in Air (lbs)String Weight Air (kN)String Weight Air (tonnes)

Buoyancy Factor BF

Block/TJ Weight (lbs)Block Weight (kN)Block Weight (tonnes)

—

6. Casing Stretch / Length Change

ΔL_total = ΔL_piston + ΔL_balloon + ΔL_buckle + ΔL_temp

Piston Force Change ΔF (lbs)ΔF (kN)ΔF (kN)

Csg Cross-Section Area A (in²)Area A (cm²)Area A (cm²)

Casing Length L (ft)Length (m)Length (m)

Temperature Change ΔT (°F)ΔT (°C)ΔT (°C)

—

E_steel = 30×10⁶ psi (207 GPa) · β_steel = 6.9×10⁻⁶ /°F (12.4×10⁻⁶ /°C)

7. Cement Volume — Annular Fill

Ann Fill(bbl/ft) = (Dh² − Csg_OD²) ÷ 1029.4 · Sacks = Vol ÷ YieldAnn Fill(m³/m) = π(Dh² − OD²) ÷ 4 (Dh,OD in m)same

Hole Size Dh (inches)Hole Size Dh (m)Hole Size Dh (m)

Casing OD (inches)Casing OD (m)Casing OD (m)

Cement Length (ft)Cement Length (m)Cement Length (m)

Excess Factor (%)Excess Factor (%)Excess Factor (%)

Cement Yield (ft³/sk, typ 1.18)Yield (m³/sk)Yield (m³/sk)

—

8. Balanced Cement Plug

Plug Length(ft) = Plug_Vol(bbl) ÷ [(DS_Cap + Ann_Cap)(bbl/ft)]Plug Length(m) = Plug_Vol(m³) ÷ [(DS_Cap + Ann_Cap)(m³/m)]same

Plug Volume (bbl)Plug Volume (m³)Plug Volume (m³)

Pipe Capacity (bbl/ft)Pipe Cap (m³/m)Pipe Cap (m³/m)

Annular Capacity (bbl/ft)Ann Cap (m³/m)Ann Cap (m³/m)

—

9. Differential Hydrostatic — Cementing

ΔP(psi) = (ρ_cement − ρ_mud) × 0.052 × TVD · Check: must not exceed MAASPΔP(kPa) = (ρ_cem − ρ_mud) × 0.00981 × TVDΔP(bar) = (ρ_cem − ρ_mud) × 0.0981 × TVD

Cement Slurry Density (ppg)Slurry Density (kg/m³)Slurry Density (kg/l)

Mud Density (ppg)Mud Density (kg/m³)Mud Density (kg/l)

TVD of Cement Column (ft)TVD (m)TVD (m)

—

10. Drill Collar Length for WOB

DC_Length(ft) = WOB(lbs) ÷ (BF × DC_Weight_lb/ft)DC_Length(m) = WOB(kN) ÷ (BF × DC_Weight_kN/m)same

Required WOB (lbs)Required WOB (kN)Required WOB (kN)

Buoyancy Factor BF

DC Weight (lb/ft)DC Weight (kN/m)DC Weight (kN/m)

—

Add 15–25% safety factor — run only 85% of DC in compression

11. Matthews & Kelly Fracture Gradient

FG(psi/ft) = Pore_Pressure(psi/ft) + Ki × σ_matrix(psi/ft) ÷ TVDFG(kPa/m) = Pp(kPa/m) + Ki × σ(kPa/m) ÷ TVDsame ratio

Pore Pressure Gradient (psi/ft)Pore Pressure Gradient (kPa/m)Pore Pressure Gradient (kPa/m)

Overburden Gradient (psi/ft)Overburden Grad (kPa/m)Overburden Grad (kPa/m)

Ki — Matrix Stress Coefficient (0.3–0.9, depth-dependent)

—

Ki ≈ 0.3 shallow · 0.5 at 5000ft · 0.8–0.9 deep. Check against LOT/FIT data.

12. Piston Effect — Casing Length Change ΔL₁

ΔL₁(in) = ΔFa(lb) × L(ft) × 12 ÷ (A(in²) × 30×10⁶)ΔL₁(mm) = ΔFa(N) × L(m) × 1000 ÷ (A(m²) × 207×10⁹)same as SI

Axial Force Change ΔFa (lbs)ΔFa (N)ΔFa (N)

Casing Cross-Section Area A (in²)Area A (m²)Area A (m²)

Casing Length L (ft)Length L (m)Length L (m)

—

E_steel = 30×10⁶ psi (207 GPa). Positive = elongation, negative = shortening.

13. Ballooning Effect — Length Change ΔL₂

ΔL₂(in) = −2ν × (ΔP_i×r_i² − ΔP_o×r_o²) ÷ (r_o²−r_i²) × L×12 ÷ EΔL₂(mm) = −2ν × ΔP_avg × L × 1000 ÷ E(Pa)same as SI

Avg Internal Pressure Change ΔP_i (psi)ΔP_i (kPa)ΔP_i (bar)

Avg External Pressure Change ΔP_o (psi)ΔP_o (kPa)ΔP_o (bar)

Casing OD (in)OD (m)OD (m)

Casing ID (in)ID (m)ID (m)

Casing Length L (ft)Length L (m)Length L (m)

—

ν (Poisson's ratio for steel) = 0.3. Negative sign = shortening when pressure increases inside.

14. Temperature Effect — Length Change ΔL₄

ΔL₄(in) = β × L(ft) × ΔT(°F) × 12 · β_steel = 6.9×10⁻⁶ /°FΔL₄(mm) = β × L(m) × ΔT(°C) × 1000 · β = 12.4×10⁻⁶ /°Csame as SI

Temperature Change ΔT (°F)ΔT (°C)ΔT (°C)

Casing Length L (ft)Length L (m)Length L (m)

—

15. Buckling Effect — Length Change ΔL₃

ΔL₃(in) = −(r_n)² × ΔP_avg × L(ft) × 12 ÷ (8 × E × I / ID²) (simplified)ΔL₃(mm) ≈ −Fa_buckling × L ÷ (2 × E × A)same

Neutral Point Force Change ΔFn (lbs)ΔFn (N)ΔFn (N)

Area A (in²)Area A (m²)Area A (m²)

Length L (ft)Length L (m)Length L (m)

—

16. Total Casing Length Change (All Effects)

ΔL_total = ΔL₁(piston) + ΔL₂(balloon) + ΔL₃(buckle) + ΔL₄(temp)

ΔL₁ Piston Effect (in)ΔL₁ (mm)ΔL₁ (mm)

ΔL₂ Ballooning Effect (in)ΔL₂ (mm)ΔL₂ (mm)

ΔL₃ Buckling Effect (in)ΔL₃ (mm)ΔL₃ (mm)

ΔL₄ Temperature Effect (in)ΔL₄ (mm)ΔL₄ (mm)

—

17. Casing Yield Strength at Temperature

Yield_T = Yield_20°C × [1 − 0.02 × (T − 200) ÷ 50] for T > 200°F

Rated Yield Strength (psi at ambient)Yield Strength (MPa)Yield Strength (MPa)

Operating Temperature (°F)Operating Temp (°C)Operating Temp (°C)

—

Reduce ~2% per 50°F above 200°F (93°C). Applies to L-80, P-110, Q-125 grades.

18. Mix Water for Cement — Volume & WCR

Water(gal/sk) = WCR × 94 ÷ 8.33 · WCR = water weight ÷ cement weight

Water-to-Cement Ratio WCR (decimal, e.g. 0.46)

Number of Cement Sacks

Additive Water (gal/sk) — if any liquid additives

—

Class A: WCR=0.46 (5.2 gal/sk) · Class G: WCR=0.44 (5.0 gal/sk) · Class H: WCR=0.38 (4.3 gal/sk)

19. Cement Slurry Yield (ft³/sk)

Yield(ft³/sk) = (94÷Density_cement + Water(gal/sk)÷7.481 + Additive_vol) ÷ 1 · 1 ft³ = 7.481 gal

Cement Absolute Volume (gal/lb, Class G = 0.0382)

Mix Water (gal/sk)

Total Additive Volume (gal/sk)

—

Class G typical yield: 1.15 ft³/sk (5.0 gal/sk water) = 1.06 bbl/sk

20. Drill String Torque & Drag

Drag(lbs) = μ × N × ΔL · Torque(ft-lbs) = μ × N × r_string · N = Normal force on formationDrag(kN) = μ × N × ΔLsame

Friction Factor μ (0.15–0.4 typical)

Normal Force Component (lbs) = W_buoy × sin(I)Normal Force (kN)Normal Force (kN)

String segment length (ft)Segment length (m)Segment length (m)

String radius (in) — for torqueString radius (m)String radius (m)

—

21. Neutral Point — BHA in Compression

NP_depth(ft) = TD − (WOB ÷ BF ÷ DC_wt_ppf)NP_depth(m) = TD − (WOB_kN ÷ (BF × DC_wt_kNm))same

Total Depth TD (ft)TD (m)TD (m)

WOB (lbs)WOB (kN)WOB (kN)

Buoyancy Factor BF

DC Weight (lb/ft)DC Weight (kN/m)DC Weight (kN/m)

—

Keep neutral point inside drill collars. DP should always be in tension.

22. Critical Buckling Force — Sinusoidal

F_crit(lbs) = 2 × √(E×I×W_buoy÷r_c) · r_c = (Dh−DP_OD)÷2F_crit(N) = 2 × √(E×I×W_buoy÷r_c)same

Pipe OD (in)Pipe OD (m)Pipe OD (m)

Pipe ID (in)Pipe ID (m)Pipe ID (m)

Hole ID Dh (in)Hole ID (m)Hole ID (m)

Buoyed Weight of Pipe (lb/ft)Buoyed Wt (N/m)Buoyed Wt (N/m)

—

If WOB > F_crit, sinusoidal buckling occurs. If WOB > 2×F_crit, helical buckling.

Directional Drilling & Survey Calculations 13 Formulas

1. Dogleg Severity (DLS)

DLS = (100÷MD_interval) × arccos[cos(I₂−I₁) − sin(I₁)×sin(I₂)×(1−cos(Az₂−Az₁))]

MD Interval (ft)MD Interval (m)MD Interval (m)

Inclination 1 I₁ (degrees)

Inclination 2 I₂ (degrees)

Azimuth 1 Az₁ (degrees)

Azimuth 2 Az₂ (degrees)

—

Max DLS: PDC 3°/100ft · Motor 8°/100ft · Rotary BHA 1.5°/100ft

2. Minimum Radius of Curvature

R(ft) = 5730 ÷ DLS(°/100ft)R(m) = 1746 ÷ DLS(°/30m)R(m) = 1746 ÷ DLS(°/30m)

DLS (°/100ft)DLS (°/30m)DLS (°/30m)

—

3. Minimum Curvature Method (North/East/Vertical)

ΔNorth = (MD/2) × (sinI₁cosAz₁ + sinI₂cosAz₂) × RF
ΔEast = (MD/2) × (sinI₁sinAz₁ + sinI₂sinAz₂) × RF
ΔVert = (MD/2) × (cosI₁ + cosI₂) × RF

MD Interval (ft)MD Interval (m)MD Interval (m)

I₁ (deg)

I₂ (deg)

Az₁ (deg)

Az₂ (deg)

—

4. Average Angle Method Survey

ΔN = MD × sin(AvgI) × cos(AvgAz) · ΔE = MD × sin(AvgI) × sin(AvgAz) · ΔV = MD × cos(AvgI)

MD Interval (ft)MD Interval (m)MD Interval (m)

Avg Inclination (deg) = (I₁+I₂)÷2

Avg Azimuth (deg) = (Az₁+Az₂)÷2

—

5. Departure & Horizontal Distance

Departure(CD) = sin(I) × Build_Distance · Horizontal = ΔN² + ΔE²

Inclination I (degrees)

Build Distance BD (ft)Build Distance (m)Build Distance (m)

ΔNorth (ft)ΔNorth (m)ΔNorth (m)

ΔEast (ft)ΔEast (m)ΔEast (m)

—

6. Build Rate to Hit Target TVD/Departure

BUR(°/100ft) = [arctan(Dep÷TVD_interval)] × (100 ÷ MD_build)

Horizontal Departure Target (ft)Departure (m)Departure (m)

TVD from KOP to Target (ft)TVD (m)TVD (m)

MD of Build Section (ft)MD Build (m)MD Build (m)

—

7. Well Planning — KOP, Build, Tangent Distances

R = 5730÷BUR · TVD_build = R×sin(I) · MD_build = R×I(rad) · Tangent_TVD = (TVD_target − TVD_kop − TVD_build) ÷ cos(I)

KOP Depth (ft TVD)KOP (m TVD)KOP (m TVD)

Target Inclination (degrees)

Build Rate BUR (°/100ft)BUR (°/30m)BUR (°/30m)

Target TVD (ft)Target TVD (m)Target TVD (m)

—

8. Radius of Curvature Survey Method

ΔN = [300÷(I₂−I₁)] × [sin(I₂)−sin(I₁)] × [sin(Az₂)−sin(Az₁)] ÷ (Az₂−Az₁)

MD Interval (ft)MD (m)MD (m)

I₁ (deg)

I₂ (deg)

Az₁ (deg)

Az₂ (deg)

—

9. Effective WOB in Deviated Well

WOB_eff = WOB_surface × cos(I) − FF × W_BHA × sin(I)

Surface WOB (lbs)Surface WOB (kN)Surface WOB (kN)

Inclination I (degrees)

Friction Factor FF (typ 0.2–0.4)

BHA Weight in fluid (lbs/ft × length)BHA buoyed weight (kN)BHA buoyed weight (kN)

—

10. Casing Setting Depth Design

D_shoe(ft) = (P_kick_psi) ÷ (FG_shoe × 0.052) · Check: FG_shoe(ppg) > KMW_nextD_shoe(m) = P_kick(kPa) ÷ (FG × 0.00981)D_shoe(m) = P_kick(bar) ÷ (FG × 0.0981)

Formation Pressure at Target (psi)Formation P (kPa)Formation P (bar)

Fracture Gradient at Shoe (ppg)FG at shoe (kg/m³)FG at shoe (kg/l)

Kill MW for next section (ppg)KMW (kg/m³)KMW (kg/l)

—

Shoe must be deep enough that FG_shoe exceeds KMW of the next section plus safety margin.

11. Riser Margin — Deep Water

RM(ppg) = (ρ_sw × D_water − ρ_mud × (D_water − TVD)) ÷ TVDRM(kg/m³) = (ρ_sw×D_w − ρ_mud×(D_w−TVD)) ÷ TVDsame ratio

Seawater Density (ppg, typ 8.6)Seawater Density (kg/m³, typ 1030)Seawater Density (kg/l, typ 1.03)

Mud Weight (ppg)Mud Density (kg/m³)Mud Density (kg/l)

Water Depth (ft)Water Depth (m)Water Depth (m)

Well TVD (ft)Well TVD (m)Well TVD (m)

—

If riser is disconnected, mud weight must be increased by riser margin to maintain wellbore stability.

12. Tool Face Angle — Motor Orientation

Gravity TF: clockwise from high side · Magnetic TF: clockwise from magnetic north (0–360°)

Current Azimuth (degrees, 0–360)

Target Azimuth (degrees)

Current Inclination (degrees)

Build/Turn Required — Build Rate (°/100ft) target

—

Gravity TF used when inclination >5°. Magnetic TF used when inclination <5° (near vertical).

13. Closure Distance & Azimuth

CD = √(ΔN² + ΔE²) · CL_Az(°) = atan2(ΔE, ΔN) × 180/π (corrected to 0–360°)

Total ΔNorth (ft)ΔNorth (m)ΔNorth (m)

Total ΔEast (ft)ΔEast (m)ΔEast (m)

TVD (ft) — for departure ratioTVD (m)TVD (m)

—

Bonus: Wellbore Tortuosity Index

Tortuosity = Σ(DLS_i × MD_interval_i) ÷ Total_MD · Units: °/100ft

Total Accumulated Dogleg (°)Total Accumulated Dogleg (°)Total Accumulated Dogleg (°)

Total MD drilled (ft)Total MD (m)Total MD (m)

—

Low tortuosity: <1°/100ft · Moderate: 1–3°/100ft · High (affects T&D): >3°/100ft

Additional Calculations 40 Formulas · follows the Field / SI / Metric switch

Merged from the Lapeyrouse and Pressure calculators. Inputs and results use the selected unit system; the formulas themselves are shown in field units.

Pressure & Mud Weight

Required Mud Weight from Pressure

MW (ppg) = Pressure (psi) ÷ (0.052 × TVD ft)

Known Pressure (psikPabar)

TVD (ftmm)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Lost Returns Pressure Change

ΔP (psi) = (MW_new − MW_old) × 0.052 × TVD

Old Mud Weight (ppgkg/m³kg/l)

New Mud Weight (ppgkg/m³kg/l)

TVD (ftmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Pore Pressure & Fracture Gradient

Overburden Gradient from Bulk Density

OBG (psi/ft) = 0.433 × ρ_bulk (g/cc); ppg = 8.33 × ρ

Average Bulk Density (g/cc)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Pore Pressure from d-exponent (Ratio Method)

PP = MW_normal × (dc_normal ÷ dc_observed)

Normal Mud Weight (ppgkg/m³kg/l)

d-exponent (normal trend)

d-exponent (observed)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Pore Pressure from d-exponent (Eaton)

PP = OBG − (OBG − PP_n) × (dc_observed ÷ dc_normal)^1.2

Overburden Gradient (ppgkg/m³kg/l)

Normal PP Gradient (ppgkg/m³kg/l)

dc Normal (on trendline)

dc Observed (actual)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Pore Pressure from Resistivity (Eaton)

PP = OBG − (OBG − PP_n) × (R_observed ÷ R_normal)^1.2

Overburden Gradient (ppgkg/m³kg/l)

Normal PP Gradient (ppgkg/m³kg/l)

Normal Resistivity Ro (Ω·m)

Observed Resistivity Robs (Ω·m)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Effective Stress

σ_eff = Total stress (OBP) − Pore pressure

Total Stress, OBP (psikPabar)

Pore Pressure (psikPabar)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Fracture Gradient (Eaton / Poisson)

FG = [ν ÷ (1 − ν)] × (OBG − PP) + PP

Overburden Gradient (psi/ftkPa/mbar/m)

Pore Pressure Gradient (psi/ftkPa/mbar/m)

Poisson's Ratio ν (0.25–0.45)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Fracture Pressure at Depth

P_frac (psi) = FG (ppg) × 0.052 × TVD

Fracture Gradient (ppgkg/m³kg/l)

TVD (ftmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Mud Weight Window

Window = FG − PP (safe MW between PP and FG)

Pore Pressure Gradient (ppgkg/m³kg/l)

Fracture Gradient (ppgkg/m³kg/l)

Collapse Gradient (optional) (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Overbalance & Margin Check

Overbalance = MW − PP; Margin to fracture = FG − MW

PP Gradient (ppgkg/m³kg/l)

Mud Weight (ppgkg/m³kg/l)

Fracture Gradient (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Poisson's Ratio from Depth (Empirical)

ν ≈ min(0.125 + TVD ÷ 100,000 , 0.48) (Gulf Coast)

TVD (ftmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Well Control

Choke Pressure During Kill

P_choke = ICP − (strokes pumped ÷ strokes to bit) × (ICP − FCP)

ICP (psikPabar)

FCP (psikPabar)

Total Strokes to fill DP

Current Strokes Pumped

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Kick Tolerance (Subsea BOP)

KT = FP_shoe − MW×0.052×Shoe − Riser margin loss

Fracture Gradient (ppgkg/m³kg/l)

Mud Weight (ppgkg/m³kg/l)

Shoe TVD (ftmm)

Water Depth (ftmm)

Seawater Density (8.6 ppg if blank) (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Hydraulics

HSI — Hydraulic Horsepower per Area of Bit

HSI = HHPb ÷ (π/4 × D_bit²)

Hydraulic Horsepower at Bit (HHPb) (hpkWkW)

Bit Size (inmmmm)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Standpipe Pressure Budget

P_s = P_surface + P_drillstring + P_bit + P_annulus

Surface Equipment Loss (psikPabar)

Drillstring Loss (psikPabar)

Bit Loss (psikPabar)

Annulus Loss (psikPabar)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Optimum Bit Pressure Drop

ΔP_bit,opt = % × P_standpipe (≈65% for soft formations)

Standpipe Pressure (psikPabar)

Optimum % at Bit

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Annular Pressure Loss (Simplified)

APL ≈ MW × AV × L ÷ (300 × (D_h − D_p)²)

Annular Velocity (AV) (ft/minm/minm/min)

Mud Weight (ppgkg/m³kg/l)

Length (ftmm)

Hole Dia. − Pipe Dia. (inmmmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Surge & Swab Pressure (Approx.)

ΔP ≈ 0.4 × MW × V_trip² ÷ 25.8

Mud Weight (ppgkg/m³kg/l)

Trip Speed (ft/minm/minm/min)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Volumes & Displacement

Displacement Volume — Pipe Steel

V (bbl) = (OD² − ID²) ÷ 1029.4 × Length

Pipe OD (inmmmm)

Pipe ID (inmmmm)

Length (ftmm)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Strokes to Displace / Fill

Strokes = Volume ÷ Pump output

Volume to Displace (bblm³m³)

Pump Output (bbl/stkm³/stkL/stk)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Dilution to Reduce Mud Weight

V_water = V × (MW_old − MW_new) ÷ (MW_new − 8.33)

Current Volume (bblm³m³)

Current Mud Weight (ppgkg/m³kg/l)

Desired Mud Weight (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Cementing

Sacks of Cement Required

Sacks = V_bbl × 5.615 ÷ Yield × Excess factor

Annular Volume (bblm³m³)

Cement Yield (ft³/skm³/skm³/sk)

Excess Factor (1.5 = 50% excess)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Displacement Volume (Cementing)

V (bbl) = ID² ÷ 1029.4 × Depth

Casing ID (inmmmm)

Shoe Depth (ftmm)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Waiting on Cement (WOC) Estimate

Rule-of-thumb WOC time from temperature at depth

Temperature at Depth (°F°C°C)

Cement Class

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Casing Design

Burst Pressure Rating (Barlow)

P_burst = 0.875 × 2 × Ym × t ÷ OD

Min Yield Strength Ym (psiMPaMPa)

Wall Thickness t (inmmmm)

Outside Diameter OD (inmmmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Burst Pressure on Casing (Net Load)

P_burst load = Formation/internal pressure − outside mud hydrostatic

Formation Pressure (psikPabar)

Outside Mud Hydrostatic (psikPabar)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Collapse Pressure (Yield Strength)

P_col = Ym × 2(D/t − 1) ÷ (D/t)²

Min Yield Strength Ym (psiMPaMPa)

Outside Diameter OD (inmmmm)

Wall Thickness t (inmmmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Collapse Pressure on Casing (Net Load)

P_col load = (ρ_out − ρ_in) × 0.052 × Depth

Depth (ftmm)

Outside Fluid Density (ppgkg/m³kg/l)

Inside Fluid Density (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Axial Tension Capacity (Yield)

F_y = Ym × 0.7854 × (OD² − ID²)

Yield Strength Ym (psiMPaMPa)

Outside Diameter OD (inmmmm)

Inside Diameter ID (inmmmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Casing Design Safety Factors

SF = Rating ÷ Load (min: burst 1.1 · collapse 1.0 · tension 1.6)

Burst Rating (psikPabar)

Internal Pressure (psikPabar)

Collapse Rating (psikPabar)

External Pressure (psikPabar)

Tension Rating (klbskNkN)

Hookload (klbskNkN)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Triaxial (Von Mises) Stress

σ_VME = √(σ_a² − σ_a·σ_h + σ_h²)

Axial Stress σ_a (psiMPaMPa)

Hoop Stress σ_hoop (psiMPaMPa)

Yield Strength Ym (optional) (psiMPaMPa)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Drill String & Pipe

Drill Pipe Tensile Safety Factor

SF = Pipe yield strength ÷ Maximum hookload

Pipe Yield Strength (lbskNkN)

Maximum Hook Load (lbskNkN)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Maximum Allowable Overpull

Overpull_max = Yield ÷ SF − Current hookload

Pipe Yield (lbskNkN)

Current Hook Load (lbskNkN)

Design SF (e.g. 1.3)

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Maximum Pipe Length (Tension Limit)

L_max = (Ym × As − W_other) ÷ (w × BF)

Min Yield Strength (psiMPaMPa)

Pipe Cross Section As (in²cm²cm²)

Other Hookload (lbskNkN)

Pipe Weight in Air (lb/ftkN/mkN/m)

Mud Weight (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Drill String Weight in Mud (Hookload)

W_buoyed = (w_dp·L_dp + w_dc·L_dc) × BF, BF = (65.5 − MW) ÷ 65.5

Drill Pipe Weight (lb/ftkN/mkN/m)

Drill Pipe Length (ftmm)

Drill Collar Weight (lb/ftkN/mkN/m)

Drill Collar Length (ftmm)

Mud Weight (ppgkg/m³kg/l)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Drill String Stretch

ΔL = W × L ÷ (As × E), E = 30×10⁶ psi

Free Pipe Load W (lbskNkN)

Free Pipe Length L (ftmm)

Pipe OD (inmmmm)

Pipe ID (inmmmm)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Bending Stress in Pipe

σ_b = E × OD × α ÷ (2 × 12), α = DLS/100 in rad/ft (≈ 218 × OD × DLS)

Pipe OD (inmmmm)

Dogleg Severity (DLS) (°/100ft°/30m°/30m)

—

Follows the unit switch · formula shown in field units · from Pressure Calc

Ton-Miles — Setting Casing

TM = W_c × D × BF × 2 ÷ (2000 × 5280)

Casing String Weight (lbskNkN)

Shoe Depth (ftmm)

Buoyancy Factor

—

Follows the unit switch · formula shown in field units · from Lapeyrouse

Directional

Turn Rate (Azimuth Change)

Turn rate = |Az₂ − Az₁| ÷ ΔMD × 100

Azimuth 1 (°)

Azimuth 2 (°)

ΔMD (ftmm)

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Follows the unit switch · formula shown in field units · from Pressure Calc