# Formulae Sheets

FUNDAMENTAL CONCEPTS
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INDEX API

INDEX SI METRIC - SI METRIC FORMULAE SHEET

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

Hydrostatic Pressure

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

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

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

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

Mud Density

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

 Mud Density (ppg) = Mud Gradient (psi/ft) / 0.052

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

True Vertical Distance

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

 TVD (ft) = Cosine Deviation (degrees) x Measured Distance (ft)

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

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

Maximum Allowable Mud Density & Equivalent Circulating Density

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

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

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

Maximum Allowable Annular Surface Pressure

Before Kill

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

After Kill

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

Formation Pressure

 Formation Pressure (psi) = HSP (psi) + SIDPP (psi)

Volume, Capacity, Displacement, Output, Velocity

 Volume (Bbls) = Capacity (Bbls/ft) x Length (ft)

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

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

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

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

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

Circulating Pressures

 Initial Circulating Pressure (psi) = Dynamic Pressure Loss (psi) + SIDPP (psi)

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

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

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

Tripping

 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

 Overbalance (psi) = (Hydrostatic Pressure) – (Formation Pressure)
= (Mud Density x 0.052 x TVD) – (Pore Pressure Gradient x TVD)

ppg

 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

 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

 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

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

ppg ppg ft ft

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

ppg ft ft

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

ppg ppg bbls

Volumetric, Migration

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

 Volume to Bleed to Maintain BHP (Bbls)
= (Increase in Press (psi) x Pit Gain (Bblss)) / (Formation Press (psi) - Increase in Press (psi))

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

Boyle - Gay - Lusac Law

 Pressure x Volume = Constant :P x V = C

 New Volume = Constant / New Pressure : V = C / P

Other

 SICP (psi) = ((Mud Gradient – Influx Gradient) x True Vertical Influx Height) + SIDPP

psi/ft psi/ft ft psi

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

SI METRIC FORMULAE SHEET

Hydrostatic Pressure - SI

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

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

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

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

Mud Density - SI

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

 Mud Density (sg) = Mud Gradient (kPa/m) / 9.8

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

True Vertical Depth - SI

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

 TVD (m) = Cosine Deviation (degrees) x Measured Depth (m)

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

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

Maximum Allowable Mud Density & Equivalent Circulating Density - SI

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

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

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

Maximum Allowable Annular Surface Pressure - SI

After Kill

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

Formation Pressure - SI

 Formation Pressure (kPa) = HSP (kPa) + SIDPP (kPa)

Volume, Capacity, Displacement, Output, Velocity - SI

 Volume (m3) = Capacity (m3/m) x Length (m)

 Length (m) = Volume (m3) / Capacity (m3/m)

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

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

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

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

Circulating Pressures - SI

 Initial Circulating Pressure (kPa) = Dynamic Pressure Loss (kPa) + SIDPP (kPa)

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

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

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

Tripping - SI

 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

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

sg m kPa/m m

 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

 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

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

m m3/m m3/m

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

sg sg m m

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

sg m m

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

sg sgm3

Volumetric, Migration - SI

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

 Volume to Bleed to Maintain BHP (m3)
= (Increase in Press (kPa) x Pit Gain (m3)) / (Formation Press (kPa) - Increase in Press (kPa))

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

Boyle - Gay - Lussac Law - SI

 Pressure x Volume = Constant : P x V = C

 New Volume = Constant / New Pressure : V = C / P

Other - SI

 SICP (kPa) = ((Mud Gradient – Influx Gradient) x Influx Height) + SIDPP

kPa/m kPa/m m kPa

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

FUNDAMENTAL CONCEPTS

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