# Formulae Sheets

**FUNDAMENTAL CONCEPTS**

To link the following formula to worked examples, just click on the number beside the formula for example click on [1]

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**INDEX API - API FIELD UNITS FORMULAE SHEET**

Hydrostatic Pressure

Pressure Gradient

Mud Density

True Vertical Distance

Maximum Allowable Mud Density & ECD

Maximum Allowable Annular Surface Pressure (MAASP)

Formation Pressure

Volumes, Capacities, Displacements, Outputs & Velocities

Circulating Pressures

Tripping

Volumetric & Migration

Boyle's Law

Shut-in Casing Pressure

Riser Margin

**INDEX SI METRIC - **SI METRIC FORMULAE SHEET

Hydrostatic Pressure

Pressure Gradient

Mud Density

True Vertical Depth

Maximum Allowable Mud Density & ECD

Maximum Allowable Annular Surface Pressure (MAASP)

Formation Pressure

Volumes, Capacities, Displacements, Outputs & Velocities

Circulating Pressures

Tripping

Volumetric & Migration

Boyle's Law

Shut-in Casing Pressure

Riser Margin

**The following formulae are written in a programming or calculator mode and need to be entered into your calculator form left to right exactly as the formula dictates.**

**API FIELD UNITS FORMULAE SHEET**

[1] HSP (psi) = Mud Density (ppg) x 0.052 (lb.gal/sqin/ft) x True Vertical Depth (ft)

[2] Mud Gradient (psi/ft) = Mud Density (ppg) x 0.052

[3] Formation Fracture Gradient (psi/ft) = Maximum Allowable Mud Density (ppg) x 0.052

[4] Influx Gradient (psi/ft) = Mud Gradient (psi/ft) - ((SICP - SIDPP) / True Vertical Influx Height (ft))

[5] Mud Density (ppg) = HSP (psi) / 0.052 / TVD (ft)

[6] Mud Density (ppg) = Mud Gradient (psi/ft) / 0.052

[7] Kill Mud Density (ppg) = SIDPP(psi) / 0.052 / TVD (ft) + Current Mud Density (ppg)

[8] TVD (ft) = HSP (psi) / 0.052 / Mud Density (ppg)

[9] TVD (ft) = Cosine Deviation (degrees) x Measured Distance (ft)

[10] Influx Length in annulus (ft) = Pit Gain (Bbls) / Annular Capacity (Bbls/ft)

[11] True Vertical Influx Height (ft) = Cosine Deviation (degrees) x Influx Length (ft)

*Maximum Allowable Mud Density & Equivalent Circulating Density*

[12] MAMD (ppg) = Leak-off Pressure (psi) / 0.052 / TVD of Shoe (ft) + Test Fluid Density (ppg)

[13] MAMD (ppg) = Total Pressures @ Shoe (psi) / 0.052 / TVD of Shoe (ft)

[14] ECD (ppg) = Annular Friction Loss (psi) / 0.052 / TVD (ft) + Current Mud Density (ppg)

*Maximum Allowable Annular Surface Pressure*

** Before Kill**

[15] MAASP (psi) = (MAMD (ppg)- Current Mud Density (ppg)) x 0.052 x Shoe TVD (ft)

** After Kill**

[16] MAASP (psi) = (MAMD (ppg) - Kill Mud Density (ppg)) x 0.052 x Shoe TVD (ft)

[17] Formation Pressure (psi) = HSP (psi) + SIDPP (psi)

*Volume, Capacity, Displacement, Output, Velocity*

[18] Volume (Bbls) = Capacity (Bbls/ft) x Length (ft)

[19] Pipe or Hole Capacity (Bbls/ft) = ID2 (inches) / 1029.4

[20] Annular Capacity (Bbls/ft) = (Hole ID2 (inches) - Pipe OD2 (inches)) / 1029.4

[21] Pipe Displacement (Bbls/ft) = (Pipe OD2 (inches) - Pipe ID2 (inches)) / 1029.4

[22] Pump Output (Bbls/min) = Pump Displacement (Bbls/stk) x Pump Speed (spm)

[23] Annular Velocity (ft/min) = Pump Output (Bbls/min) / Annular Capacity (Bbls/ft)

[24] Initial Circulating Pressure (psi) = Dynamic Pressure Loss (psi) + SIDPP (psi)

[25] Final Circulating Pressure (psi) = Dynamic Pressure Loss (psi) x KMD (ppg) / OMD (ppg)

[26] New Pump Pressure (psi) = Current Pressure (psi) x (New Rate (spm) / Old Rate (spm))2

[27] New Pump Pressure (psi) = Old Pressure (psi) x (New Mud Density (ppg) / Old Mud Density (ppg))

[28] Pipe To Pull Before Well Starts To Flow (ft) = (Overbalance x (Casing Capacity - Metal Displ.)) / (Mud Gradient x Metal Displ.)

psi Bbls/ft Bbls/ft psi/ft Bbls/ft

[29] Overbalance (psi) = (Hydrostatic Pressure) – (Formation Pressure)

= (Mud Density x 0.052 x TVD) – (Pore Pressure Gradient x TVD)

ppg

[30] Pressure drop per foot tripping dry pipe = (OMD x 0.052 x Metal Displ.) / (Casing Capacity - Metal Displ.)

ppg Bbls/ft Bbls/ft Bbls/ft

[31] Pressure drop per foot tripping wet pipe = (OMD x 0.052 x Closed-end Displ.) / (Casing Capacity - Closed-end Displ.)

ppg Bbls/ft Bbls/ft Bbls/ft

[32] Fluid level drop when all drill collars are removed from the well dry = (Length of Drill Collars x Metal Displ.) / Casing Capacity

ft Bbls/ft Bbls/ft

[33] Slug Drop (ft) = (Slug Density / OMD x Slug Length in Pipe) - Slug Length in Pipe

ppg ppg ft ft

[34] Slug Density (ppg) = OMD x ((Slug Drop/Slug Length in Pipe) + 1)

ppg ft ft

[35] Gain in Trip Tank (bbl) = ((Slug Density / OMD) - 1) x Pill Volume Pumped

ppg ppg bbls

[36] PSI PER BBL = Mud Gradient (psi/ft) / Hole Capacity (Bbls/ft)

[37] Volume to Bleed to Maintain BHP (Bbls)

= (Increase in Press (psi) x Pit Gain (Bblss)) / (Formation Press (psi) - Increase in Press (psi))

[38] Percolation Rate (ft/hr) = Increase in Drill Pipe Press (psi/hr) / (OMD (ppg)x 0.052)

[39] Pressure x Volume = Constant :P x V = C

[40] New Volume = Constant / New Pressure : V = C / P

**Other**

[41] **SICP** (psi) = ((Mud Gradient – Influx Gradient) x True Vertical Influx Height) + SIDPP

psi/ft psi/ft ft psi

[42] **Riser Margin** (ppg) = Pressure Differential D / 0.052 / True vertical distance from mud-line to TVD

[1] HSP (kPa) = Mud Density (sg) x 9.8 (m/s/s) x True Vertical Depth (m)

[2] Mud Gradient (kPa/m) = Mud Density (sg) x 9.8

[3] Formation Fracture Gradient (kPa/m) = Maximum Allowable Mud Density (sg) x 9.8

[4] Influx Gradient (kPa/m) = Mud Gradient (kPa/m) - ((SICP - SIDPP) / True Vertical Influx Height (m))

[5] Mud Density (sg) = HSP (kPa) / 9.8 / TVD (m)

[6] Mud Density (sg) = Mud Gradient (kPa/m) / 9.8

[7] Kill Mud Density (sg) = SIDPP / 9.8 / TVD (m) + OMD (sg)

[8] TVD (m) = HSP (kPa) / 9.8 / Mud Density (sg)

[9] TVD (m) = Cosine Deviation (degrees) x Measured Depth (m)

[10] Influx Length in annulus (m) = Pit Gain (m3) / Annular Capacity (m3/m)

[11] True Vertical Influx Height (m) = Cosine Deviation (degrees) x Influx Length (m)

*Maximum Allowable Mud Density & Equivalent Circulating Density - SI*

[12] MAMD (sg) = (kPa) / 9.8 / TVD of Shoe (m) + Test Fluid Density (sg)

[13] MAMD (sg) = Total Pressures @ Shoe (kPa) / 9.8 / TVD of Shoe (m)

[14] ECD (sg) = Annular Friction Loss (kPa) / 9.8 / TVD (m) + OMD (sg)

*Maximum Allowable Annular Surface Pressure - SI*

** After Kill**

[16] MAASP (kPa) = (MAMD (sg) - KMD (sg)) x 9.8 x Shoe TVD (m)

[17] Formation Pressure (kPa) = HSP (kPa) + SIDPP (kPa)

*Volume, Capacity, Displacement, Output, Velocity - SI*

[18] Volume (m3) = Capacity (m3/m) x Length (m)

[19] Length (m) = Volume (m3) / Capacity (m3/m)

[20] Annular Capacity (m3/m) = ((Hole ID2 (m) - Pipe OD2 (m)) / 4) x 3.14159

[21] Pipe Displacement (m3/m) = ((Pipe OD2 (m) - Pipe ID2 (m)) / 4) x 3.14159

[22] Pump Output (m3/min) = Pump Displacement (m3/stk) x Pump Speed (spm)

[23] Annular Velocity (m/min) = Pump Output (m3/min) / Annular Capacity (m3/m)

[24] Initial Circulating Pressure (kPa) = Dynamic Pressure Loss (kPa) + SIDPP (kPa)

[25] Final Circulating Pressure (kPa) = Dynamic Pressure Loss (kPa) x KMD (sg) / OMD (sg)

[26] New Pump Pressure (kPa) = Current Pressure (kPa) x (New Rate(spm) / Old Rate(spm))2

[27] New Pump Pressure (kPa) = Old Pressure (kPa) x (New Mud Density (sg) / Old Mud Density (sg))

[28] Pipe To Pull Before Well Starts To Flow (m) = (Overbalance x (Casing Capacity - Metal Displ.)) / (OMD x 9.8 x Metal Displ.)

kPa m3/m m3/m sg m3/m

[29] Overbalance (kPa) = (Hydrostatic Pressure) – (Formation Pressure) = (OMD x 9.8 x TVD) – (Pore Pressure Gradient x TVD)

sg m kPa/m m

[30] Pressure Drop per ft Tripping Dry Pipe (kPa/m) = (OMD x 9.8 x Metal Displ.) / (Casing Capacity - Metal Displ.)

sg m3/m m3/m m3/m

[31] Pressure Drop per ft Tripping Wet Pipe (kPa/m) = (OMD x 9.8 x (Metal Displ. + Pipe Capacity)) / Annular Capacity

sg m3/m m3/m m3/m

[32] Level Drop For POOH Drill Collars (Dry) (m) = (Length of Drill Collars x Metal Displ.) / Casing Capacity

m m3/m m3/m

[33] Slug Drop (m) = (Slug Density / OMD x Slug Length in Pipe) - Slug Length in Pipe

sg sg m m

[34] Slug Density (sg) = OMD x ((Slug Drop/Slug Length in Pipe) + 1)

sg m m

[35] Gain in Trip Tank (m3) = ((Slug Density / OMD) - 1) x Slug Volume Pumped

sg sgm3

[36] kPa PER M³ = Mud Gradient (kPa/m) / Hole Capacity (m3/m)

[37] Volume to Bleed to Maintain BHP (m3)

= (Increase in Press (kPa) x Pit Gain (m3)) / (Formation Press (kPa) - Increase in Press (kPa))

[38] Percolation Rate (m/hr) = Increase in Drill Pipe Press (kPa/hr) / (OMD x 9.8)

[39] Pressure x Volume = Constant : P x V = C

[40] New Volume = Constant / New Pressure : V = C / P

[41] **SICP** (kPa) = ((Mud Gradient – Influx Gradient) x Influx Height) + SIDPP

kPa/m kPa/m m kPa

[42] **Riser Margin** (sg) = Pressure Differential D / 9.8 / True vertical distance from mud-line to TVD

**The following fundamental concepts are the basis of many a formula. These concepts will assist in understanding the construction of the formulae presented above.**

Pressure = mud density x constant x true vertical distance

Pressure = gradient x true vertical distance

Gradient = mud density x constant

Mud Density = pressure / constant / true vertical distance

Mud Density = gradient / constant

True Vertical Distance = pressure / constant / mud density

True Vertical Height = Cos deviation x measured distance

Length = volume / capacity

Volume = length x capacity

Strokes = volume / pump displacement per stroke

Time = strokes / pump rate in strokes per minute

mud density / old mud density

New Pressure = old pressure x (new stroke rate / old stroke rate)²