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Comprehensive Drilling Calculator

Operations & Technical Reference Manual

180 Formulas Field · SI · Metric 7 Engineering Sections Lapeyrouse Reference API Standards

This manual provides complete operational guidance and technical formula derivations for the Comprehensive Drilling Calculator web application. It covers all 180 unique drilling engineering formulas (140 core plus 40 additional, Part C) across six disciplines plus a merged Section 7: Hydrostatics, Well Control, Pump & Hydraulics, Mud Engineering, Mechanical Engineering, and Directional Drilling.

The calculator supports three simultaneous unit systems — Field (US Imperial), SI (International System), and Metric (Oilfield) — with real-time switching. All formulas are sourced from industry-standard references including Lapeyrouse: Formulas & Calculations for Drilling, Production & Workover, API RP 13D (rheology), API RP 65 (cementing), IADC Well Control Manual, and Baker Hughes/Schlumberger operational guides.

180

Unique Formulas

3

Unit Systems

6

Engineering Sections

Document Type: Operations & Technical Reference Version: 1.0 Application: drilling_calc_v2.html
References: Lapeyrouse (2002), API RP 13D, IADC Well Control Manual, API Spec 5CT, Baker Hughes TechFacts
Units: Field (US) · SI · Metric Oilfield Classification: Technical Reference — Drilling Engineering

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Table of Contents

PART A — OPERATIONS GUIDEpg 3

1. Getting Started — Interface Overview3

2. Unit System Selection (Field / SI / Metric)3

3. Section 1 — Hydrostatics & Pressure Calculations4

4. Section 2 — Well Control & Kick Management4

5. Section 3 — Pump, Volume & Hydraulics5

6. Section 4 — Mud & Drilling Fluids5

7. Section 5 — Mechanical & Engineering6

8. Section 6 — Directional Drilling & Surveys6

9. Worked Examples (All Unit Systems)7

PART B — TECHNICAL REFERENCEpg 8

10. Hydrostatics — Formula Derivations & Constants8

11. Well Control — Formula Derivations & Constants10

12. Pump & Hydraulics — Formula Derivations12

13. Mud Engineering — Formula Derivations14

14. Mechanical Engineering — Formula Derivations16

15. Directional Drilling — Formula Derivations18

APPENDICESpg 19

A. Unit Conversion Tables19

B. Common Constants & Material Properties20

C. Quick-Reference Formula Summary Card21

D. Calculator Input/Output Summary22

PART C — ADDITIONAL CALCULATIONS (SECTION 7)pg 25

C.1–C.5 Overview, Usage, Unit Handling & Corrections25

C.6 Formula Reference — all 40 calculators26

E. Section 7 Input/Output Examples (Field / SI / Metric)33

ℹ️ How to use this document
Part A (Operations) — Step-by-step guide for field personnel to enter data and interpret results for each calculator section.
Part B (Technical) — Full formula derivations with field constants, SI equivalents, and industry references for engineers and QA.
Appendices — Unit conversions, material constants, and quick-reference cards for on-the-rig use.

A

Part A — Operations Guide

Step-by-step instructions for using the Comprehensive Drilling Calculator

1. Getting Started — Interface Overview

The Comprehensive Drilling Calculator is a standalone browser-based application (drilling_calc_v2.html). No internet connection or server is required — open the file directly in any modern web browser (Chrome, Edge, Firefox, Safari).

Interface Elements

Header bar — Title and unit system toggle (Field / SI / Metric)
Left sidebar — Navigation between 6 formula sections
Main area — Formula cards with input fields and Calculate buttons
Result boxes — Green = result, Yellow = warning, Red = error/critical

Result Color Codes

■ Green — Valid result, within normal operating range
■ Yellow — Result computed but warrants attention
■ Red — Critical condition (e.g. negative MAASP, kick indicators)
■ Purple — Informational multi-result output

2. Unit System Selection

The unit toggle at top-right switches all labels, formula displays, and output units simultaneously. Select your unit system before entering any values.

Button	Pressure	Density	Depth/Length	Volume	Flow Rate	Temperature
Field (US)	psi	ppg (lb/gal)	ft	bbl	bbl/min	°F / °R
SI	kPa	kg/m³	m	m³	L/min	°C / K
Metric	bar	kg/L (SG≡kg/L)	m	m³	L/min	°C / K

⚠️ Important — Consistent Units
All inputs within a single calculator card must use the same unit system. The calculator does not auto-convert between systems mid-calculation. When switching unit systems, re-enter values using the correct unit equivalents shown in Appendix A.

ℹ️ Unit Conversion Quick Guide (Density)
ppg × 119.83 = kg/m³ | ppg ÷ 8.33 = SG = kg/L | ppg × 7.481 = lb/ft³ | 1 SG = 8.33 ppg = 1000 kg/m³ = 1 kg/L

3. General Workflow for Any Calculator

Click the appropriate section in the left navigation panel (e.g. "Well Control")
Select your unit system (Field / SI / Metric) using the top-right toggle
Locate the relevant formula card (cards are numbered to match this manual)
Enter all input values in the labeled fields — all fields must be filled for results
Press the Calculate button — the result appears immediately in the green box below
If the result is red, read the error message and check your inputs
For multi-output results, all values are displayed in a single result box with line breaks

✅ Best Practice
For well control calculations, always use the Mud Density Converter (Section 1, Card 20) to verify your density unit conversions before entering values into kill calculations. A density error of 0.1 ppg equates to ~50 psi per 1000 ft TVD.

4. Section 1 — Hydrostatics & Fundamental Pressure (22 Formulas)

This section contains the foundational pressure and density calculations used throughout drilling operations. These values feed directly into well control and hydraulics calculations.

#	Calculator	Key Inputs	Output	Primary Use
1	Pressure Gradient	Mud weight/density	psi/ft · kPa/m · bar/m	Daily mud check
2	Hydrostatic Pressure	MW, TVD	psi · kPa · bar	Pre-trip planning
3	EMW from LOT/FIT	MW at test, LOT pressure, shoe TVD	ppg · kg/m³	Casing design, shoe strength
4	Specific Gravity	Mud density (any unit)	SG (dimensionless)	Fluid property checks
5	Formation Pressure	Ph_DS, SIDPP	psi · kPa	Kick analysis
6	BHP Shut-In	Ph_DS, SIDPP	psi · kPa	Well control
7	BHP Circulating	Ph_Ann, APL	psi · kPa	ECD management
8	BHP Killing (Subsea)	Ph_Ann, P_Ann, CLFL	psi · kPa	Subsea well control
9	ECD	MW, APL, TVD	ppg · kg/m³	Overburden monitoring
10	Formation Temperature	Surface temp, TVD, geothermal grad	°F / °C	BHA design, cement design
11	Temperature Converter	°F or °C	°R, °K, °C, °F	Gas calculations
12	API Crude Density	°API gravity	SG, ppg, kg/m³	Influx density estimation
13	Gas Pressure at Depth	Surface P, gas gravity, depth, temp	psi · kPa	Gas migration modeling
14	Gas Gradient	Pressures at two depths, interval	psi/ft · kPa/m	Kick characterization
15–18	Gas Density Constants	— (reference card)	SG, gradient	Kick type identification
19	HP Difference	Two MWs, TVD	psi · kPa	Mud weight change impact
20	Density Converter	Any density value + unit	All units	Daily use
21	Pressure Converter	Any pressure value + unit	psi, kPa, bar, kg/cm²	Daily use
22	MAASP	FG, MW, shoe TVD	psi · kPa · bar	BOP pressure limits

5. Section 2 — Well Control & Kick Management (25 Formulas)

🔴 Safety Critical — Read Before Use
Well control calculations must be performed under competent supervision. Calculator results should be verified independently using secondary methods. Never rely solely on a single calculation tool during a live well control event.

Kill Sheet Workflow Using This Calculator

Confirm kick — Record SIDPP, SICP, pit gain volume
Influx Height (Card 6) — Pit gain ÷ annular capacity
Kill Mud Weight (Card 1) — From SIDPP, TVD, OMW
ICP (Card 2) — SIDPP + SCRP
FCP (Card 3) — SCRP × (KMW ÷ OMW)
MAASP check (Sec 1 Card 22) — Verify KMW does not exceed FG at shoe
Influx Density (Card 4) — Confirm influx type (gas/oil/water)
Kick Tolerance (Card 5) — Maximum kick volume that can be taken safely

#	Calculator	Key Inputs	Output
1	Kill Mud Weight (KMW)	SIDPP, TVD, OMW	ppg · kg/m³ · kg/L
2	ICP	SIDPP, SCRP	psi · kPa · bar
3	FCP	SCRP, KMW, OMW	psi · kPa · bar
4	Influx Density	MW, SICP, SIDPP, influx height	ppg (identifies gas/oil/water)
5	Kick Tolerance	MAASP, MW, influx height, TVD	ppg · kg/m³
6	Influx Height	Pit gain, annular capacity	ft · m
7	Boyle's Law	P₁, V₁, P₂ (or V₂)	V₂ or P₂ · expansion ratio
8	Gas Migration Rate	Pressure rise rate, mud gradient	ft/hr · m/hr
9	U-Tube Balance	SIDPP, Ph_DS, SICP, Ph_ann	Ph_gas in annulus
10	Driller's Method ICP & FCP	SIDPP, SCRP, KMW, OMW	ICP and FCP simultaneously
11	Tapered String Pressure	ICP, FCP, strokes pumped/total	Interim circulating pressure
12	Pill Strokes	Pill vol, chase vol, pump output	Pump strokes (pill + chase + total)
13	Volumetric Method	Allow ΔP, MW, annular capacity	Bleed volume + bubble rise
14	Lubricate & Bleed	Target ΔP, MW, annular capacity	Lubrication volume per step
15	Riser Margin	Seawater density, MW, water depth, TVD	Riser margin (ppg)
16–25	Additional WC References	Various	Max shoe pressure, CLFL, formation P

6. Section 3 — Pump, Volume & Hydraulics (30 Formulas)

#	Calculator	Key Inputs	Output & Notes
1	Triplex Pump Output	Liner ID, stroke length, efficiency%	bbl/stk · L/stk; also shows output at 60 spm
2	Duplex Pump Output	Bore, rod diameter, stroke, efficiency	bbl/stk · L/stk
3	Flow Rate from SPM	Pump output, strokes/min	bbl/min · L/min
4	Annular Velocity	Flow rate, hole ID, pipe OD	ft/min · m/min; warns if below minimum
5	Hydraulic Horsepower	Pump pressure, flow rate	HP (horsepower)
6	HHP at Bit	Bit pressure drop, flow rate	HP; target ≥2.5 HP/in² for PDC
7	Nozzle Pressure Drop	MW, flow rate, TFA	psi · kPa; enter TFA in in² (Field)
8	Jet Velocity & Impact Force	Flow rate, TFA, MW	ft/s and lbs impact force
9	Pipe Capacity	Pipe ID	bbl/ft, gal/ft, ft/bbl, L/m
10	Annular Capacity	Hole ID, pipe OD	bbl/ft, gal/ft, L/m
11	Lag Strokes (S→Bit)	DS volume, pump output	Strokes (surface to bit)
12	Return Lag Strokes	Annulus volume, pump output	Strokes (bit to surface)
13	Pressure vs. SPM	Old P, old SPM, new SPM	New pump pressure (SPM² relationship)
14	Pressure vs. MW	Old P, old MW, new MW	New pump pressure (linear relationship)
15	Rectangular Tank	L, W, D (depth)	bbl · m³
16	Cylindrical Tank	Radius, height	bbl · m³
17	APL from ECD	ECD, MW, TVD	Annular pressure loss (psi · kPa)
18	Cuttings Slip Velocity	MW, cutting size, apparent viscosity	ft/min slip velocity + transport ratio
19	Shear Rates	Velocity, pipe ID, (Dh-Dp)	Pipe and annular wall shear rates (s⁻¹)
20	Reynolds Number	Density, velocity, diameter, viscosity	Re + flow regime (laminar/turbulent)
21	Fanning Friction Factor	Reynolds number Re	f_laminar and f_turbulent (Blasius)
22	Power Law n & K	θ600, θ300 (viscometer readings)	Flow index n, consistency K
23	PV & YP	θ600, θ300, θ6, θ3	PV (cP), YP (lb/100ft²), gel strength
24	Trip Volume Monitor	OD, ID, length pulled, actual fill	Expected fill + discrepancy warning

✅ TFA Calculation Tip (Card 7 & 8)
For Field units: TFA (in²) = number of nozzles × (nozzle_size_32nds ÷ 32)² × π/4
Example: Three 12/32" nozzles: TFA = 3 × (12/32)² × 0.7854 = 3 × 0.1406 × 0.7854 = 0.331 in²

7. Section 4 — Mud & Drilling Fluids (28 Formulas)

#	Calculator	Key Inputs	Output
1	Barite to Raise MW	Current MW, target MW, active volume	lb/bbl required + total lbs
2	Fluid Mixing	V₁, ρ₁, ρ₂ (weighting material), ρ_target, V_total	Volume of fluid 2 required
3	Slug Design	Slug vol, slug density, mud density, DP ID	Dry pipe length above slug
4	PV, YP & Rheology	θ600, θ300, θ6, θ3	PV, YP, AV, n, K, gel strengths
5	Average Specific Gravity	%vol water, oil, solids; individual SGs	ASG + density in ppg and kg/m³
6	Low Gravity Solids	Total solids %, ASG of mud	LGS % vol, HGS (barite) % vol
7	Oil/Water Ratio Adjustment	Current volume, current oil%, target oil%	Oil volume to add
8	Bentonite Content	Mud CEC (MBT), shale CEC, drilled sol%, bent CEC	Bentonite % vol, lb/bbl
9	Complete Solids Analysis	Retort oil, water, solids; LGS, bentonite	Full breakdown: DS, barite, bentonite
10	Saltwater from Chlorides	Cl⁻ content (ppm)	Estimated saltwater % vol
11	Dilution Rate	Pit vol, current LGS%, target LGS%	Dilution volume required
12	Centrifuge Evaluation	Feed/overflow density and volumes	Underflow density
13	Weighted Cement	Base slurry density, target density	Barite per sack
14	Slurry Weight Check	Cement lb, mix water gal, additives	Slurry density (ppg) + volume

8. Section 5 — Mechanical & Engineering (22 Formulas)

#	Calculator	Key Inputs	Output
1	Buoyancy Factor	Mud weight, string weight in air	BF (dimensionless) + buoyed weight
2	Ton-Mile (Round Trip)	Depth, DS length, DP weight, BHA weight	Ton-miles (for line replacement)
3	Free Point (Stuck Pipe)	Pipe weight, measured stretch, pull force	Free point depth
4	D-Exponent	ROP, RPM, WOB, bit size	d-exponent + pore pressure indicator
5	Hookload	Weight in air, BF, block weight	Expected hookload
6	Casing Length Change	Piston force, area, length, ΔT	ΔL_piston + ΔL_thermal + total
7	Cement Volume	Hole size, casing OD, length, excess%, yield	Annular volume + sack count
8	Balanced Cement Plug	Plug vol, pipe cap, annular cap	Plug length + displacement volume
9	Cement Differential HP	Slurry density, mud density, TVD	ΔP cement vs mud (check vs MAASP)
10	DC Length for WOB	Required WOB, BF, DC weight/ft	DC length needed (add 15–25%)
11	Matthews & Kelly FG	Pore pressure grad, overburden grad, Ki	Fracture gradient (psi/ft + ppg EMW)

9. Section 6 — Directional Drilling & Surveys (13 Formulas)

#	Calculator	Key Inputs	Output
1	Dogleg Severity	MD interval, I₁, I₂, Az₁, Az₂	DLS (°/100ft or °/30m) + dogleg angle
2	Radius of Curvature	DLS	Radius (ft or m)
3	Min. Curvature Survey	MD, I₁, I₂, Az₁, Az₂	ΔNorth, ΔEast, ΔVertical, RF
4	Average Angle Survey	MD, avg inclination, avg azimuth	ΔNorth, ΔEast, ΔVertical
5	Departure & HD	Inclination, build distance, ΔN, ΔE	Departure, horizontal distance, closure Az
6	Required Build Rate	Target departure, TVD from KOP, MD build	Required inclination + BUR
7	Well Path Planning	KOP, target inclination, BUR, target TVD	Build TVD/MD, tangent TVD/MD, total departure
8	Radius of Curvature Method	MD, I₁, I₂, Az₁, Az₂	ΔNorth, ΔEast, ΔVertical
9	Effective WOB (Deviated)	Surface WOB, inclination, FF, BHA weight	Effective WOB at bit

9. Worked Examples — All Unit Systems

Example A — Kill Sheet Calculation (Driller's Method)

Scenario: Kick taken while drilling at 8,200 ft TVD. SIDPP = 380 psi, SICP = 480 psi, pit gain = 12 bbl, SCRP at 30 spm = 580 psi, OMW = 10.2 ppg, annular capacity (8½" × 5") = 0.0505 bbl/ft.

🇺🇸 Field Units

KMW = 380/(0.052×8200) + 10.2 KMW = 11.09 ppg ICP = 380 + 580 = 960 psi FCP = 580 × (11.09/10.2) = 631 psi h_i = 12/0.0505 = 238 ft d_inf = 10.2 − (480−380)/(0.052×238) d_inf = 2.13 ppg ≈ Gas kick

🌍 SI Units

TVD = 8200 ft × 0.3048 = 2499 m SIDPP = 380 psi × 6.895 = 2620 kPa OMW = 10.2 × 119.83 = 1222 kg/m³ KMW = 2620/(0.00981×2499) + 1222 KMW = 1329 kg/m³ ICP = 2620 + 4000 = 6620 kPa FCP = 4000 × (1329/1222) = 4350 kPa

📐 Metric Units

TVD = 2499 m SIDPP = 380 psi × 0.06895 = 26.2 bar OMW = 10.2/8.33 = 1.224 kg/L KMW = 26.2/(0.0981×2499) + 1.224 KMW = 1.330 kg/L ICP = 26.2 + 40.0 = 66.2 bar FCP = 40.0 × (1.330/1.224) = 43.5 bar

Example B — ECD Calculation During Drilling

Scenario: Circulating at 8,000 ft TVD. MW = 10.5 ppg, measured annular pressure loss = 200 psi.

🇺🇸 Field Units

ECD = 10.5 + 200/(0.052×8000) ECD = 10.5 + 0.481 ECD = 10.98 ppg SG = 10.98/8.33 = 1.318

🌍 SI Units

ρ = 10.5 × 119.83 = 1258 kg/m³ TVD = 8000 × 0.3048 = 2438 m APL = 200 × 6.895 = 1379 kPa ECD = 1258 + 1379×102/2438 ECD = 1316 kg/m³

📐 Metric Units

ρ = 10.5/8.33 = 1.261 kg/L APL = 200 × 0.06895 = 13.79 bar ECD = 1.261 + 13.79×10.2/2438 ECD = 1.318 kg/L

Example C — Pump Output & Annular Velocity

Scenario: Triplex pump, 6" liner, 12" stroke, 95% efficiency. Circulating 8½" hole with 5" DP at 60 spm.

🇺🇸 Field Units

PO = 0.000243 × 6² × 12 × 0.95 PO = 0.000243 × 36 × 12 × 0.95 PO = 0.0999 bbl/stk Q = 0.0999 × 60 = 5.99 bbl/min Ann Cap = (8.5² − 5²)/1029.4 = 0.0457 bbl/ft AV = 24.51 × 5.99/(8.5²−5²) AV = 131 ft/min ✓ (above 100 min)

🌍 SI (liner 15.24 cm, stroke 30.48 cm)

PO = π/4 × 15.24² × 30.48 ÷ 1000 × 3 × 0.95 PO = 0.7854 × 232.3 × 30.48/1000 × 2.85 PO = 15.88 L/stk Q = 15.88 × 60 = 952.8 L/min Dh = 216 mm, Dp = 127 mm Area = π(216²−127²)/4×10⁻⁶ = 0.00728 m² AV = (0.953/1000)/0.00728 × 60 = 7.85 m/min ✓

Example D — Well Planning (Directional)

Scenario: KOP at 3,000 ft TVD, build to 30° at 3°/100ft, target TVD = 10,000 ft.

🇺🇸 Field Units

R = 5730/3 = 1910 ft TVD_build = 1910 × sin(30°) = 955 ft MD_build = 1910 × 30×π/180 = 1000 ft TVD_tangent = 10,000−3,000−955 = 6045 ft MD_tangent = 6045/cos(30°) = 6980 ft Total MD from KOP = 7980 ft Departure_build = 1910×(1−cos30°) = 256 ft Departure_tangent = 6980×sin(30°) = 3490 ft Total Departure = 3746 ft

🌍 SI Units (KOP 914 m, target 3048 m)

R = 1746/3 = 582 m TVD_build = 582 × sin(30°) = 291 m MD_build = 582 × 30×π/180 = 305 m TVD_tangent = 3048−914−291 = 1843 m MD_tangent = 1843/cos(30°) = 2128 m Total MD from KOP = 2433 m Total Departure = 1141 m

✅ Verification — Cross-Check Results
Always verify kill sheet calculations using the U-Tube equation (Section 2, Card 9): SIDPP + Ph_DS = SICP + Ph_ann + Ph_influx
If the equation does not balance, recheck your influx height calculation and annular capacity values.

Drilling Calculator v2 — Documentation

PART B

Technical Reference

Formula Derivations & Constants
Sections 10–15: Hydrostatics · Well Control · Pump & Hydraulics
Mud Engineering · Mechanical · Directional Drilling

CONFIDENTIAL — INTERNAL USE

Section 10 — Hydrostatics: Formula Derivations

All formulas based on hydrostatic pressure principle: pressure = fluid density × gravitational constant × true vertical depth

10.1 Hydrostatic Pressure

P = k × MW × TVD Field: P(psi) = 0.052 × MW(ppg) × TVD(ft) SI: P(kPa) = 0.00981 × MW(kg/m³) × TVD(m) [≡ ρgh, g=9.81 m/s²] Metric:P(bar) = 0.0981 × MW(kg/l) × TVD(m)

Derivation: 1 psi = 1 lbf/in² = 144 lbf/ft². For water at 8.34 ppg: k = 8.34/144 = 0.0579 ≈ 0.052 (industry standard for drilling mud). SI: k = ρg/1000 = 1000×9.81/1,000,000 = 0.00981 kPa·m/kg/m³.

10.2 Equivalent Mud Weight (EMW) & Equivalent Circulating Density (ECD)

EMW = P / (k × TVD) ECD = MW + ΔP_ann / (k × TVD) Field: ECD(ppg) = MW + ΔP_ann(psi) / (0.052 × TVD) SI: ECD(kg/m³) = MW + ΔP_ann(kPa) / (0.00981 × TVD)

ECD accounts for annular friction pressure losses added to static mud weight. Must remain below fracture gradient and above pore pressure to maintain well control.

10.3 Pressure Gradient

G = k × MW Field: G(psi/ft) = 0.052 × MW(ppg) → water ≈ 0.433 psi/ft (8.33 ppg) SI: G(kPa/m) = 0.00981 × MW(kg/m³) Normal formation pore pressure gradient: 0.433–0.465 psi/ft (fresh–salt water)

10.4 U-Tube Pressure Balance (Kill Sheet Foundation)

SIDPP + Ph_DS = SICP + Ph_ann Where: Ph_DS = k × MW_ds × TVD Ph_ann = k × MW_ann × TVD + P_influx Rearranged: SIDPP − SICP = Ph_ann − Ph_DS (+) SIDPP > SICP → influx lighter than mud (gas) (−) SIDPP < SICP → influx heavier than mud (brine)

10.5 Influx Height & Type Identification

H_influx = V_influx / Ca (Ca = annular capacity, bbl/ft or m³/m) G_influx = (SICP − SIDPP) / (k × H_influx) + MW Gas: G < 2 ppg (0.24 kg/l) Brine: G ≈ MW_formation ≈ 8.5–10 ppg Oil: G ≈ 6–7 ppg

10.6 Formation Integrity Test (FIT) & Leak-Off Test (LOT)

EMW_LOT = (P_surface + Ph_shoe) / (k × TVD_shoe) = P_surface / (k × TVD_shoe) + MW Max MAASP = (EMW_LOT − MW) × k × TVD_shoe LOT gradient typically 0.5–0.8 psi/ft above pore pressure gradient

10.7 Annular Pressure While Circulating (Pressure Loss Sources)

P_circ_total = P_bit + P_pipe + P_annulus + P_surface_equip ECD = MW + (P_pipe_ann + P_annulus_ann) / (k × TVD) Surge/Swab (Ormsby approximation): P_surge = 0.000162 × MW × v_pipe × (D_h² + D_p²)/(D_h² − D_p²) (Field: psi; v in ft/min; D in inches)

Section 11 — Well Control: Formula Derivations

11.1 Kill Mud Weight (KMW)

KMW = MW + SIDPP / (k × TVD) Field: KMW(ppg) = MW + SIDPP(psi) / (0.052 × TVD(ft)) Origin: To bring well to static equilibrium, kill mud hydrostatic must equal pore pressure. Pore Pressure = MW × k × TVD + SIDPP → KMW = (PP) / (k × TVD)

11.2 Initial Circulating Pressure (ICP) & Final Circulating Pressure (FCP)

ICP = SIDPP + P_slow_pump (SCR pressure at kill rate) FCP = SCR × KMW / MW Origin: Pressure drop across bit nozzles ∝ ρQ². Keeping flow rate constant: P_bit_new / P_bit_old = (KMW / MW) → FCP = SCR × KMW/MW ICP ensures full annular kill before increasing MW.

11.3 Driller's Method Pressure Schedule

Stroke 1 (1st Circulation): Hold casing pressure constant at SICP Purpose: Circulate influx out with original MW Stroke 2 (2nd Circulation): Ramp drill pipe pressure from ICP → FCP P at stroke n = ICP − (ICP − FCP) × n / n_total n_total = pipe volume / pump output (strokes to bit)

11.4 MAASP (Maximum Allowable Annular Surface Pressure)

MAASP = (FG − MW) × k × TVD_shoe FG = fracture gradient (ppg or equivalent) As kill mud is pumped: MAASP_new = (FG − KMW) × k × TVD_shoe MAASP reduces as KMW increases — monitor continuously during kill.

11.5 Boyle's Law — Gas Influx Expansion

P₁V₁ = P₂V₂ (isothermal, constant Z) P₁ = bottom hole pressure when influx taken V₁ = influx volume at bottom hole P₂ = pressure at any point during migration V₂ = expanded volume = P₁V₁/P₂ Boyle-Charles (with temperature correction): P₁V₁/T₁ = P₂V₂/T₂ → V₂ = P₁V₁T₂/(P₂T₁)

11.6 Volumetric Method (Gas Migration Control)

Gas migration rate ≈ 500–2000 ft/hr (empirical; use actual from annulus pressure rise) Step 1: Allow pressure to build by ΔP (typically 100 psi) Step 2: Bleed mud volume = ΔP × annular capacity / G_mud Step 3: Lubricate same volume of kill mud in Repeat until gas reaches surface or well is killed. Bleed vol = ΔP / (k × MW) × Ca (bbl per step)

11.7 BOP Accumulator Sizing (API 16D)

V_total_accum = V_usable / (1 − P_precharge/P_min) V_usable = V_BOP_ops × safety_factor (≥1.25) P_precharge = 1000 psi (typical N₂ charge) P_min = 1200 psi (minimum operating pressure) P_max = 3000 psi (max accumulator pressure) Usable vol fraction = 1 − 1000/3000 = 0.667 per bottle API requirement: ≥45 gal usable volume + 25% reserve

11.8 Kick Tolerance & Influx Volume Limits

KT = (FG_shoe − MW) × k × TVD_shoe / (k × h_influx_max) Max kick volume before shoe fracture: V_max = KT × Ca_shoe where Ca_shoe = annular capacity at shoe (bbl/ft) Kick tolerance decreases as MW increases and as TD increases.

Section 12 — Pump & Hydraulics: Formula Derivations

12.1 Pump Output

PO = (π/4) × D_liner² × L_stroke × n_cylinders × e_vol Field: PO(bbl/stk) = 0.000243 × D_liner(in)² × L_stroke(in) × n × e_vol SI/Metric: PO(L/stk) = π/4 × D(cm)² × L(cm) / 1000 × n × e_vol Origin: displacement volume per stroke = bore area × stroke length. Volumetric efficiency (e_vol) ≈ 0.90–0.98 for piston pumps.

12.2 Annular Velocity (AV)

AV = Q / A_annular Field: AV(ft/min) = 24.51 × Q(gpm) / (D_h² − D_p²) [D in inches] OR = 0.408 × Q(bbl/min) / (D_h² − D_p²) SI: AV(m/min) = Q(m³/min) × 10⁶ / (π(D_h²−D_p²)/4) × 0.001 Minimum AV for cuttings transport: 100–200 ft/min in most conditions. Critical AV (laminar/turbulent transition) depends on Reynolds number.

12.3 Reynolds Number & Flow Regime

Re_pipe = 928 × ρ × v × D / μ_eff (Field: ρ ppg, v ft/s, D in, μ cp) Re_ann = 109 × ρ × v × (D_h − D_p) / μ_eff Re < 2100: Laminar flow (Hagen-Poiseuille) Re > 3000: Turbulent flow (Fanning friction) 2100–3000: Transition zone — assume turbulent for safety μ_eff(Bingham) = PV + 5 × YP × D / (96 × v) (pipe, Field units)

12.4 Bingham Plastic Pressure Loss — Laminar

ΔP_pipe = (PV × v / 1500 × D²) + (YP / 225 × D) [psi/100ft, Field] ΔP_ann = (PV × v / 1000 × (D_h−D_p)²) + (YP / 200 × (D_h−D_p)) Exact Buckingham equation (pipe, Field): ΔP = [PV × v + 225 × YP × D] / (1500 × D²) psi/100ft Origin: Navier-Stokes for Bingham plastic in cylindrical geometry with plug flow core.

12.5 Power Law Pressure Loss

n = 3.32 × log(θ₆₀₀/θ₃₀₀) (flow behavior index, dimensionless) K = 511^(1-n) × θ₃₀₀ / 511 (consistency index, eq. cp) ΔP_pipe = K × v^n × (3n+1/4n)^n × 144000/(144 × D^(n+1) × 96^n) Power law better models shear-thinning fluids at high and low shear rates. K and n from 600/300 rpm Fann VG readings.

12.6 Hydraulic Horsepower & Bit Nozzle Sizing

HHP_bit = P_bit × Q / 1714 (Field: psi, gpm → HP) HHP/in² = HHP_bit / A_bit (optimize: ≥1.0 HP/in² in soft, ≥3.0 in hard) P_bit = 0.000156 × ρ × Q² / (Cd² × A_nozzles²) Cd ≈ 0.95 (discharge coefficient for jet nozzles) Impact Force = 0.000516 × ρ × Q × v_nozzle (lbf, Field) v_nozzle = 0.32 × Q / A_nozzles (ft/s, gpm, in²)

12.7 Surge & Swab Pressure

P_surge = C_surge × (v_pipe + 0.45 × v_pipe) × MW × L / 1000 Simplified Ormsby (Field): P_surge(psi) = 0.000162 × MW × v × (D_h² + D_p²)/(D_h² − D_p²) v = tripping speed (ft/min), D in inches, MW in ppg Safe tripping speed: typically < 500 ft/min to keep P_surge < 50–100 psi Swab = negative surge; can cause wellbore breathing or kick.

Section 13 — Mud Engineering: Formula Derivations

13.1 Mud Weighting — Adding Barite

Barite(sacks) = [V_final × (MW₂ − MW₁)] / [MW_bar − MW₂] × (35.8/100) Field simplified: Sacks = 1470 × V_pit(bbl) × (MW₂−MW₁) / (35.8−MW₂) Derivation (mass balance): MW₁×V₁ + MW_bar×V_bar = MW₂×(V₁+V_bar) V_bar = V₁(MW₂−MW₁)/(MW_bar−MW₂) Convert m³ → sacks: ×(1/0.04756 m³/sack) MW_barite = 35.8 ppg (SG 4.3); MW_calcium carbonate = 22.6 ppg (SG 2.71)

13.2 Dilution — Reducing Mud Weight

V_water = V_pit × (MW_current − MW_desired) / (MW_desired − MW_water) MW_water = 8.34 ppg (fresh) or 8.55–9.0 ppg (brine) Note: Dilution always increases pit volume. Plan for pit capacity. Solids content after dilution: %sol = %sol_orig × V_pit/(V_pit + V_water)

13.3 Retort Analysis — Solids Content

%Oil + %Water + %Solids = 100% %LGS = %Solids − %HGS (Low-gravity vs High-gravity solids) %HGS = (%Solids × SGsolids − %LGS × 2.6) / (SGbar − 2.6) MBT (bentonite equivalent): API bentonite content via methylene blue test Bentonite equiv. (ppb) = MBT × 5 (approximate for field use) Colloidal solids: bentonite equivalent / (total clay + bentonite)

13.4 Plastic Viscosity & Yield Point (Fann VG Meter)

PV(cp) = θ₆₀₀ − θ₃₀₀ (600 rpm − 300 rpm readings) YP(lbf/100ft²) = θ₃₀₀ − PV Gel strength: 10-sec gel = θ₁₀s, 10-min gel = θ₁₀m (at 3 rpm) Apparent Viscosity: AV = θ₆₀₀ / 2 (cp) High PV → excess solids; High YP → good cuttings suspension but high ECD

13.5 Filtration (API Filter Press)

Spurt loss ≈ 2 × V₇.₅ − V₃₀ (extrapolation to t=0) Filtration coefficient: k = V₃₀ / √30 × factor API fluid loss: V_fl = 2 × V₇.₅ (corrected from 7.5 min to 30 min via √t) HPHT filter loss (230°F, 500 psi): divide by 2 to compare with API Target: API FL < 15 cm³/30min; HPHT < 20 cm³/30min

13.6 Chemical Treatments — pH & Alkalinity

Caustic soda (NaOH) to raise pH: NaOH(lbm/bbl) = 0.056 × (pH_target − pH_current) (approximate) Lime (Ca(OH)₂) for CO₂/H₂S contamination: Lime(lbm/bbl) = 0.26 × CO₂_content(mg/l) / 1000 Soda ash (Na₂CO₃) for Ca²⁺ contamination: Soda ash(lbm/bbl) = Ca²⁺(mg/l) × 0.00094 KCl concentration for shale inhibition: 3–7% by weight (typical)

13.7 Oil-Based Mud (OBM) & Synthetic-Based Mud (SBM)

O:W ratio = (vol oil / vol water) × 100 e.g. 80:20 = 80% oil, 20% brine Electrical stability (ES): field measure of emulsion quality; target >400V OBM mud weight: same weighting formulas apply Chloride check: titrate with silver nitrate; indicates brine influx Cl⁻(mg/l) = ml AgNO₃ × N × 35450 / ml sample

Section 14 — Mechanical Calculations: Formula Derivations

14.1 Pipe Capacities & Displacements

Capacity(bbl/ft) = ID²(in) / 1029.4 → C = π/4 × D² / 144 / 5.6146 Displacement(bbl/ft) = (OD²−ID²) / 1029.4 Open-end displacement = ID² / 1029.4 (same as capacity — displaces fluid equal to bore) Metric: C(L/m) = π/4 × ID(mm)² / 1,000,000 Annular capacity: Ca = (D_h²−D_p²) / 1029.4 (Field)

14.2 Casing String Length Change (4-Effect Model)

ΔL₁ (Piston/Ballooning pressure effect): ΔL₁ = −(Δp_i × A_i − Δp_o × A_o) × L / (E × A_s) Δp_i = change in internal pressure, A_i = πID²/4 ΔL₂ (Ballooning — radial stress): ΔL₂ = −2ν/E × (Δp_i×A_i − Δp_o×A_o) × L / A_s ΔL₃ (Buckling — helical): ΔL₃ = −r_b² × F_sb² / (8 × E × I × w_n) ΔL₄ (Temperature): ΔL₄ = α × ΔT_avg × L α(steel) = 6.9×10⁻⁶ /°F = 12.4×10⁻⁶ /°C Total: ΔL = ΔL₁ + ΔL₂ + ΔL₃ + ΔL₄ E(steel) = 30×10⁶ psi = 207 GPa; ν = 0.3

14.3 Casing Design — Burst, Collapse & Tension

Burst (Barlow): P_b = 2 × t × σ_y / OD × SF (SF ≥ 1.1) Collapse (API): based on D/t ratio → elastic/plastic/transitional formulas D/t < 15: yield-strength collapse 15–25: plastic collapse 25–35: transition collapse >35: elastic (Lamé) collapse Tension: F_t = A_s × σ_y → check hook load margin Biaxial correction: σ_y_eff = σ_y × √(1 − 0.75(F_a/F_y)² − 0.5(F_a/F_y))

14.4 Ton-Miles Calculation (Drill String Fatigue)

TM_round_trip = W_s × D × 2 / 5280 / 2000 W_s = total string weight in mud (lbf) D = drill depth (ft) Cumulative TM tracked per string component; replace/inspect at API TM limits: Drill pipe: 3000–5000 TM (depends on grade and conditions) Heavy-weight DP: 1000–2000 TM Connection inspection every 500 TM or after each coring run.

14.5 Free Point Calculation

Free Point Constant (FPC) = E × A_s / (L_unit × 144) E = 30×10⁶ psi (steel), A_s = pipe cross-section area (in²) L_unit = pipe length per unit (ft) Free Point Depth = FPC × ΔL / ΔF ΔL = stretch measured (in), ΔF = pull force applied (lbf) FPC (drill pipe): depends on weight/grade. Example: 5" 19.5 lb/ft S-135: FPC≈16,000

14.6 Cement Calculations

Slurry volume(bbl) = V_annulus + V_shoe_track + V_excess V_annulus = Ca × (L_casing − L_shoe_track) Slurry yield(ft³/sack) = 1 / (% cement/100 / 0.0382 + WCR / 5.615) Mix water(gal/sack) = WCR × 7.48 WCR = water:cement ratio by weight No. sacks = V_slurry / slurry_yield Mixing water(bbl) = sacks × WCR × 0.0453

14.7 Matthews-Kelly Fracture Gradient

FG = G_ob − σ_v × (1 − 2ν)/(1 − ν) + Pp × 2ν/(1 − ν) / TVD Simplified (Hubbert-Willis): FG = (G_ob − Pp)/3 + Pp/TVD Eaton (preferred): FG = Pp/TVD + (G_ob − Pp/TVD) × ν/(1 − ν) ν varies by region/depth: typically 0.25 (shallow) to 0.45 (overpressured) G_ob (overburden): integrate bulk density log or use 1.0 psi/ft (shallow) to 0.95 psi/ft

Section 15 — Directional Drilling: Formula Derivations

15.1 Minimum Curvature Method (Industry Standard)

β = arccos[cos(I₂−I₁) − sin(I₁)×sin(I₂)×(1−cos(A₂−A₁))] RF = 2/β × tan(β/2) (ratio factor — approaches 1 as β→0) ΔTVD = ΔMD/2 × (cos(I₁) + cos(I₂)) × RF ΔNorth = ΔMD/2 × (sin(I₁)cos(A₁) + sin(I₂)cos(A₂)) × RF ΔEast = ΔMD/2 × (sin(I₁)sin(A₁) + sin(I₂)sin(A₂)) × RF More accurate than radius of curvature method; handles azimuth changes correctly. β in radians for RF calculation; angles in degrees for ΔTVD.

15.2 Dogleg Severity (DLS)

DLS(°/100ft) = 100/ΔMD × arccos[cos(I₁−I₂) − sin(I₁)×sin(I₂)×(1−cos(ΔA))] SI: DLS(°/30m) = 30/ΔMD × (same arccos formula) Simplified (in-plane): DLS = ΔI/ΔMD × 100 (when azimuth unchanged) API RP 7G limits: S-135 DP: 8°/100ft max fatigue; <3°/100ft preferred Heavy-weight DP: 6°/100ft max BHA: evaluate case-by-case; rotary assemblies <5°/100ft

15.3 Build Rate & Radius of Curvature

R = 5730 / BR (Field: BR in °/100ft, R in ft) = 1746 / BR (SI: BR in °/30m, R in m) MD_build = R × θ × π/180 (arc length for angle θ) TVD_build = R × sin(θ) Horiz_departure = R × (1 − cos(θ)) J-curve profile: KOP → build → tangent → drop → horizontal

15.4 Horizontal Well Planning

TVD_target = TVD_KOP + R×sin(90°) + TVD_tangent×cos(inc) For 90° horizontal wells: TVD_target = TVD_KOP + R + 0 Departure_total = R×(1−cos(inc_final)) + TVD_tangent×sin(inc_final) Landing depth check: TVD_reservoir ± 10ft vertical accuracy typical Turn rate (azimuth change) adds to DLS: DLS² = BR² + TR² (vector sum)

15.5 Anti-Collision — Separation Factor

SF = (C₁₂ − r₁ − r₂) / σ_total C₁₂ = center-to-center distance between wellbores r₁, r₂ = wellbore radii σ_total = √(σ₁² + σ₂²) (combined positional uncertainty ellipsoid) SF > 1.5 — accept; SF 1.0–1.5 — caution; SF < 1.0 — stop and remediate Separation calculated along Ellipsoid of Uncertainty (EOU) surface.

15.6 Casing Setting Depth — Pore Pressure / Fracture Gradient Method

CSD = P_next_zone / (FG_at_shoe × k) Steps: 1. Identify next zone pore pressure (PPG) 2. Find shallowest depth where FG > next-zone PP + safety margin (0.5 ppg) 3. Set casing such that kick from next zone can be circulated to surface without fracturing shoe: MW_kill < FG_shoe 4. Repeat for all casing strings (surface, intermediate, production)

15.7 Riser Margin (Deepwater)

Riser Margin = (MW_drill − MW_seawater) × k × TVD_shoe / TVD MW_seawater ≈ 8.55 ppg (1025 kg/m³) When riser is disconnected, seawater replaces riser mud above mudline. The lost hydrostatic head reduces BHP: ΔBHP = (MW_drill − 8.55) × k × D_water Must maintain ΔBHP + PP_margin < FG × k × TVD for safe disconnect. Deepwater DW: typically 0.3–1.0 ppg riser margin.

Appendix A — Unit Conversion Tables

A.1 Pressure

From	To psi	To kPa	To bar	To atm
1 psi	1.000	6.895	0.06895	0.06805
1 kPa	0.1450	1.000	0.01000	0.009869
1 bar	14.504	100.00	1.000	0.9869
1 atm	14.696	101.33	1.0133	1.000
1 MPa	145.04	1000.0	10.000	9.869

A.2 Density / Mud Weight

From	To ppg	To kg/m³	To kg/l (SG)	To lb/ft³
1 ppg	1.000	119.83	0.11983	7.481
1 kg/m³	0.008345	1.000	0.001000	0.06243
1 kg/l (SG)	8.345	1000.0	1.000	62.43
8.34 ppg	8.34 (FW)	999.5 (FW)	0.9995 (FW)	—
8.55 ppg	8.55 (SW)	1025 (SW)	1.025 (SW)	—

A.3 Length / Depth

From	To ft	To m	To in	To cm
1 ft	1.000	0.3048	12.00	30.48
1 m	3.2808	1.000	39.37	100.00
1 in	0.08333	0.02540	1.000	2.540
1 cm	0.03281	0.01000	0.3937	1.000

A.4 Volume / Flow Rate

From	To bbl	To m³	To L	To gal (US)
1 bbl	1.000	0.15899	158.99	42.00
1 m³	6.2898	1.000	1000.0	264.17
1 L	0.006290	0.001000	1.000	0.26417
1 gal (US)	0.02381	0.003785	3.785	1.000
1 ft³	0.17811	0.028317	28.317	7.481

A.5 Gradient Constants (k)

Unit System	Formula	k value	Example (10 ppg/1020 kg/m³, 1000 ft/305 m)
Field (psi/ppg/ft)	P = 0.052 × MW × TVD	0.052 psi/ppg/ft	520 psi
SI (kPa/kg/m³/m)	P = 0.00981 × MW × TVD	0.00981 kPa·m³/kg/m	2996 kPa
Metric (bar/kg/l/m)	P = 0.0981 × MW × TVD	0.0981 bar·l/kg/m	29.96 bar

A.6 Viscosity & Torque

From	To cP (mPa·s)	Notes
1 cP	1 mPa·s	Water at 20°C ≈ 1 cP
1 lbf/100ft²	0.4788 Pa	Yield Point unit (YP)
1 ft·lbf	—	1 ft·lbf = 1.3558 N·m (torque)
1 klbf·ft	—	1000 ft·lbf = 1.3558 kN·m

Appendix B — Common Constants & Material Properties

B.1 Physical & Mathematical Constants

Constant	Symbol	Value	Units
Gravitational acceleration	g	9.80665	m/s² (32.174 ft/s²)
Pi	π	3.141593	—
Atmospheric pressure	P_atm	14.696 / 101.325	psia / kPa
Fresh water density	ρ_fw	8.34 / 1000 / 1.000	ppg / kg/m³ / SG
Sea water density	ρ_sw	8.55 / 1025 / 1.025	ppg / kg/m³ / SG
Steel elastic modulus	E	30×10⁶ / 207	psi / GPa
Steel Poisson ratio	ν	0.30	—
Steel thermal expansion	α	6.9×10⁻⁶ / 12.4×10⁻⁶	/°F / /°C
R gas constant	R	10.73 / 8.314	psi·ft³/(lb-mol·°R) / J/(mol·K)

B.2 Drilling Fluid Material Densities

Material	SG (kg/l)	ppg	lb/sack	Remarks
Barite (BaSO₄)	4.20–4.35	35.0–36.3	100	Primary weighting agent; API spec: SG ≥ 4.20
Calcium Carbonate	2.71	22.6	50	Acid-soluble; used in completion/drill-in
Hematite (Fe₂O₃)	5.05	42.1	100	High-density; abrasive; high-pressure wells
Ilmenite	4.45	37.1	100	Low abrasion; alternative to barite
Bentonite	2.60	21.7	100	Yields ≈ 90 bbl/ton with 3 ppb treatment
Cement (Class G)	3.14	26.2	94	Slurry yield ≈ 1.15 ft³/sack at normal WCR
Diesel oil	0.84	7.0	—	Base oil; OBM/SBM systems
KCl solution (10%)	1.064	8.88	—	Shale inhibition; common in HPWBM

B.3 Steel Drill String Properties (API Grades)

Grade	Min Yield (psi)	Min Tensile (psi)	Typical Use
E-75	75,000	100,000	General purpose; shallow-medium wells
X-95	95,000	105,000	Medium-deep wells; offshore
G-105	105,000	115,000	Deep wells; high angle
S-135	135,000	145,000	Deep HPHT; horizontal; extended reach
V-150	150,000	160,000	Ultra-deep; extreme conditions

B.4 Formation Pressure & Gradient Reference

Formation Type	Gradient (psi/ft)	Equivalent MW (ppg)
Normal pore pressure (fresh water)	0.433	8.33
Normal pore pressure (salt water)	0.465	8.94
Geopressured (typical)	0.500–0.700	9.6–13.5
Overpressured (extreme)	0.700–0.900	13.5–17.3
Fracture gradient (typical carbonate)	0.800–0.900	15.4–17.3
Fracture gradient (typical shale)	0.650–0.750	12.5–14.4
Salt formations	1.000	19.2 (litho. overburden)

Appendix C — Quick-Reference Formula Summary

All Field-unit formulas. For SI: replace 0.052→0.00981, 1029.4→1×10⁶/π, 1714→kW·factor. See Appendix A for conversion constants.

HYDROSTATICS

P = 0.052 × MW × TVD
ECD = MW + ΔP_ann/(0.052×TVD)
G_grad = 0.052 × MW
EMW = P/(0.052×TVD)
MAASP = (FG−MW)×0.052×TVD_shoe
KT = MAASP/(0.052×H_influx)
Overbalance = (MW−PPG)×0.052×TVD
Underbalance = (PPG−MW)×0.052×TVD

WELL CONTROL

KMW = MW + SIDPP/(0.052×TVD)
ICP = SIDPP + SCR
FCP = SCR × KMW/MW
H_inf = V_inf/Ca  [Ca=annular cap bbl/ft]
G_inf = (SICP−SIDPP)/(0.052×H_inf)+MW
P₁V₁ = P₂V₂  (Boyle's Law)
BleedVol = ΔP×Ca/(0.052×MW)

PUMP & HYDRAULICS

PO = 0.000243×D²×L×n×eff  [bbl/stk]
AV = 24.51×Q/(Dh²−Dp²)  [ft/min]
P_bit = 0.000156×ρ×Q²/(Cd²×An²)
HHP = P×Q/1714
ΔP_pipe = (PV×v+225×YP×D)/(1500×D²)
Re = 928×ρ×v×D/μ  [<2100=lam]
n=3.32log(θ600/θ300); K=510^(1-n)×θ300

MUD ENGINEERING

PV = θ600 − θ300   [cP]
YP = θ300 − PV   [lbf/100ft²]
Barite sks = 1470×V×(MW₂−MW₁)/(35.8−MW₂)
Dil water = V×(MWc−MWd)/(MWd−8.34)
Retort: %Oil+%Water+%Sol = 100
ECD_sol = MW + 0.029×%LGS (approx)

MECHANICAL

Cap = ID²/1029.4  [bbl/ft]
Disp = (OD²−ID²)/1029.4  [bbl/ft]
Burst = 2×t×σy/OD  [psi]
FP_depth = FPC×ΔL(in)/ΔF(klbf)
ΔL_temp = α×ΔT×L  [α=6.9e-6/°F]
TM = W_str×D/(5280×2000×2)
Slurry_Y = 1/(C%/0.0382+WCR/5.615)

DIRECTIONAL

β=arccos[cosΔI−sinI₁sinI₂(1−cosΔA)]
RF = 2/β×tan(β/2)  [min curv factor]
ΔTVD = ΔMD/2×(cosI₁+cosI₂)×RF
DLS = 100/ΔMD×β(deg)  [°/100ft]
R = 5730/BR  [ft; BR in °/100ft]
MD_build = R×θ×π/180
CSD: MW_kill < FG_shoe → set casing

Appendix D — Core 140 Calculator Inputs & Outputs (Sections 1–6; Section 7 is in Appendix E)

Quick lookup table — every calculator card in the app. Inputs listed first, then → output(s).

D.1 Section 1 — Hydrostatics (22 Calculators)

#	Calculator	Key Inputs	Output(s)
1	Hydrostatic Pressure	MW, TVD	P (psi/kPa/bar)
2	Mud Weight from P	P, TVD	MW (ppg/kg/m³)
3	Pressure Gradient	MW	G (psi/ft etc.)
4	EMW	P, TVD	EMW (ppg equiv.)
5	ECD	MW, ΔP_ann, TVD	ECD (ppg/kg/m³)
6	Overbalance / UB	MW, PPG, TVD	Overbalance P
7	Formation Pressure	PPG, TVD	PP (psi/kPa)
8	Fracture Pressure	FG, TVD	FP (psi/kPa)
9	Kill Mud Weight	MW, SIDPP, TVD	KMW (ppg)
10	MAASP	FG, MW, TVD_shoe	MAASP (psi)
11	Influx Height	V_inf, Ca	H_inf (ft/m)
12	Influx Gradient	SICP, SIDPP, H_inf, MW	G_inf → type
13	U-Tube Balance	SIDPP, MW, TVD, SICP, MW_ann	Balance check
14	LOT / FIT EMW	P_surface, MW, TVD_shoe	EMW_test (ppg)
15	Gas Gradient	SG_gas	Gas grad (psi/ft)
16	Influx Type ID	SIDPP, SICP, H_inf, MW	Gas/brine/oil
17	Boyle-Charles Gas	P1,V1,T1,P2,T2	V2 expanded
18	Fluid Pressure Gradient	Fluid SG	G (psi/ft/kPa/m)
19	Kick Tolerance	FG_shoe, MW, TVD_shoe, Ca	KT (bbl/m³)
20	Surge Pressure	MW, v_pipe, Dh, Dp	P_surge (psi)
21	Swab Pressure	MW, v_pipe, Dh, Dp	P_swab (psi)
22	Subsea Hydrostatic	MW, TVD, D_water	BHP, WH_P

D.2 Section 2 — Well Control (25 Calculators)

#	Calculator	Key Inputs	Output(s)
1	Kill Mud Weight	MW, SIDPP, TVD	KMW
2	ICP	SIDPP, SCR	ICP (psi)
3	FCP	SCR, KMW, MW	FCP (psi)
4	Strokes to Bit	V_pipe, PO	Strokes
5	Strokes to Shoe	V_annulus, PO	Strokes
6	Pressure Schedule	ICP, FCP, strokes_bit	P vs stroke table
7	Influx Volume	Pit gain, surface correction	V_inf (bbl)
8	Influx Height	V_inf, Ca	H_inf
9	U-Tube Pressure	SIDPP, SICP, MW, TVD	Balance
10	Gas Expansion (Boyle)	P1,V1,P2	V2
11	Choke Pressure	SICP, ΔP_pump	P_choke
12	Bleed Volume	ΔP, Ca, MW	V_bleed (bbl)
13	Volumetric Method	SICP, ΔP_step, Ca, MW	Steps to surface
14	Striper/Snubbing Force	P_wellhead, A_pipe	F_snub (lbf)
15	BHP During Circ.	MW, TVD, ΔP_ann	BHP
16	Shoe Fracture Check	MW_kill, TVD_shoe, FG	Safe/unsafe
17	MAASP Reduction	FG, KMW, TVD_shoe	MAASP_new
18	Lubricate & Bleed	V_lube, G_kill_mud, G_gas	Steps needed
19	Wait & Weight Strokes	V_string, V_ann, PO	Total strokes
20	Kick Tolerance	FG_shoe, MW, TVD, Ca	KT (bbl)
21	A-Factor (Gas Migration)	MW, Dh, Dp	A (dimensionless)
22	New MAASP	FG, KMW, TVD_shoe	New MAASP
23	Break Circ. Pressure	SCR, gel_10min, L_pipe, D	P_break
24	Gas Migration Rate	P_rise/hr, G_mud	v_mig (ft/hr)
25	Shoe Pressure (Kick)	MW, TVD, SICP, H_inf, G_inf	P_shoe

D.3 Section 3 — Pump & Hydraulics (30 Calculators)

#	Calculator	Key Inputs	Output(s)
1	Pump Output	D_liner, L_stroke, n, eff	PO (bbl/stk, gpm)
2	Annular Velocity	Q, Dh, Dp	AV (ft/min)
3	Pipe Capacity	ID	Cap (bbl/ft)
4	Annular Capacity	Dh, Dp	Ca (bbl/ft)
5	Strokes to Fill	V_target, PO	Strokes
6	Bit HHP	P_bit, Q	HHP (HP/kW)
7	HHP per in²	HHP, D_bit	HHP/in²
8	Nozzle Velocity	Q, An	v_n (ft/s)
9	Nozzle Pressure Drop	ρ, Q, An	P_bit (psi)
10	Impact Force	ρ, Q, v_n	IF (lbf)
11	Reynolds Number (pipe)	ρ, v, D, PV, YP	Re, regime
12	Reynolds Number (ann)	ρ, v, Dh, Dp, PV, YP	Re, regime
13	Bingham ΔP Pipe	PV, YP, v, D	ΔP (psi/100ft)
14	Bingham ΔP Annulus	PV, YP, v, Dh, Dp	ΔP (psi/100ft)
15	Power Law n & K	θ600, θ300	n, K
16	Power Law ΔP	K, n, v, D	ΔP (psi/100ft)
17	Surge/Swab Pressure	MW, v_pipe, Dh, Dp	P_surge/swab
18	Penetration Rate Hydraulics	WOB, N, D_bit	MSE, ROP
19	Flow Rate Optimization	pump_pressure, string data	Q_opt
20	Pressure Loss (surface equip)	Q, ρ, L_equip	ΔP_se
21	String Pressure Loss	Q, fluid props, string dims	ΔP_string
22	Annulus Pressure Loss	Q, fluid, Dh, Dp, L	ΔP_ann
23	ECD from Hydraulics	MW, ΔP_ann, TVD	ECD
24	Jet Nozzle Sizing	Q, P_bit_desired	TFA, nozzle combo
25	Laminar ΔP Pipe (Bingham)	PV, YP, v, D	ΔP detailed
26	Laminar ΔP Annulus	PV, YP, v, Dh, Dp	ΔP ann detailed
27	Critical Velocity (Bingham)	PV, YP, ρ, D	v_c, Re_c
28	System HHP & Parasitic	Q, P_total, P_bit	HHP_sys, HHP_par
29	Velocity from Q & Area	Q, Dh, Dp	v (ft/min)
30	Min Flow for Hole Cleaning	MW, ROP, Dh, Dp, inc	Q_min (gpm)

D.4 Section 4 — Mud Engineering (28 Calculators)

#	Calculator	Key Inputs	Output(s)
1–4	Add Barite / CaCO₃ / Hematite / Dilution Water	V_pit, MW₁, MW₂	Material quantity
5	PV & YP from Fann	θ600, θ300	PV, YP, AV
6	Power Law n & K	θ600, θ300	n, K
7	Retort Analysis	%oil, %water	%solids, %LGS, %HGS
8	Solids Dilution	%sol_c, %sol_d, V_pit	V_water to add
9	MW after Dilution	V_pit, V_water, MW, MW_water	MW_new
10	O:W Ratio	%oil, %water	O:W ratio
11	Mixing Two Muds	V₁, MW₁, V₂, MW₂	MW_blend, V_total
12	Methylene Blue Test	MBT reading	Bentonite equiv (ppb)
13	Chloride Titration	ml AgNO₃, N, ml sample	Cl⁻ (mg/l)
14	pH / Caustic Soda	pH_current, pH_target	NaOH (lbm/bbl)
15	Shear Stress (Power Law)	K, n, shear rate	τ (lbf/100ft²)
16	Apparent Viscosity	θ600	AV (cP)
17	Filter Loss Coefficient	V7.5, V30	k_spurt, V_API
18	pH / Alkalinity	Pm, Pf, Mf	CO₂, OH⁻, HCO₃⁻
19	MBT Bentonite	MBT, V_mud	Bentonite (ppb)
20	Barite %Vol	SG_mud, %solid	%vol barite
21	Chloride Analysis	ml titrant, N, V_sample	Cl⁻ (mg/l), formation water
22	Lime Treatment	CO₂/H₂S content	Lime (lbm/bbl)
23	Soda Ash	Ca²⁺ (mg/l)	Na₂CO₃ (lbm/bbl)
24	KCl Concentration	V_mud, KCl%_target	KCl sacks needed
25	Mass Rate / Pit Balance	ρ_in, Q_in, ρ_out, Q_out	Mass flow balance
26	Additive per Sack	concentration (ppb), V_pit	Sacks to add
27	Turbulent ΔP	PV, ρ, v, D	ΔP_turb (psi/100ft)
28	LCM Pill Volume	Dh, D_lost_circ_zone, L_pill	V_LCM (bbl)

D.5 Section 5 — Mechanical (22 Calculators)

#	Calculator	Key Inputs	Output(s)
1	Pipe Capacity	ID	Cap (bbl/ft, L/m)
2	Annular Capacity	Dh, Dp	Ca (bbl/ft)
3	Pipe Displacement	OD, ID	Disp (bbl/ft)
4	String Weight in Air	wt/ft, L	W_air (lbf)
5	String Weight in Mud	W_air, BF	W_mud (lbf)
6	Buoyancy Factor	MW, ρ_steel	BF (dimensionless)
7	Hook Load	W_mud + BHA components	HL (lbf)
8	Ton-Miles	W_string, depth	TM
9	Free Point	ΔL, ΔF, pipe specs	FP depth (ft/m)
10	Burst Pressure	OD, t, σ_y	P_burst (psi)
11	Collapse Pressure	OD, t, grade	P_collapse (psi)
12	Piston Effect ΔL₁	Δp_i, A_i, Δp_o, A_o, L, E, A_s	ΔL₁ (ft/m)
13	Ballooning ΔL₂	Same as ΔL₁ + Poisson ratio	ΔL₂ (ft/m)
14	Temperature ΔL₄	α, ΔT_avg, L	ΔL₄ (ft/m)
15	Buckling ΔL₃	r_b, F_sb, E, I, w_n	ΔL₃ (ft/m)
16	Total ΔL	ΔL₁, ΔL₂, ΔL₃, ΔL₄	ΔL_total (ft/m)
17	Yield at Temperature	σ_y_room, T_op, T_room	σ_y_T (psi)
18	Cement Mix Water	WCR, n_sacks	V_water (bbl)
19	Slurry Yield	%cement, WCR	ft³/sack
20	Torque & Drag	W_mud, μ, sin(inc)	T (ft·lbf), drag (lbf)
21	Neutral Point	W_BHA, BF, WOB	NP depth (ft)
22	Critical Buckling Force	EI, w_n, r_b	F_c (lbf)

D.6 Section 6 — Directional Drilling (13 Calculators)

#	Calculator	Key Inputs	Output(s)
1	Min Curvature ΔTVD	ΔMD, I₁, I₂, A₁, A₂	ΔTVD, ΔNorth, ΔEast
2	Dogleg Severity	I₁, I₂, A₁, A₂, ΔMD	DLS (°/100ft or °/30m)
3	Build Rate & Radius	BR	R (ft/m)
4	Build Section MD & TVD	KOP_TVD, BR, inc_final	MD_build, TVD_build
5	Departure	R, inc_final	Horiz departure (ft/m)
6	Total MD to Target	All well profile inputs	TD_MD
7	Wellbore Position	Survey stations array	TVD, N, E at each station
8	Closure Distance	ΔNorth, ΔEast	Closure, azimuth
9	Horizontal Section	TVD_target, lateral_length	MD_horizontal
10	Casing Setting Depth	PP_next, FG_shoe, MW_safety	CSD (ft/m)
11	Riser Margin	MW, D_water, TVD_shoe	Riser margin (ppg)
12	Tool Face Angle	ΔI, ΔA, I_current	TF (° from high side)
13	Tortuosity Index	DLS values along survey	TI (°/100ft avg)

📊 Total: 180 Interactive Calculators across 7 Sections (140 core + 40 additional, see Part C)
All calculators support Field, SI, and Metric unit systems via the toggle at the top of the app. Results update instantly on input change. No server required — fully offline capable.

C

Part C — Additional Calculations (Section 7)

40 calculators merged from the Lapeyrouse and Pressure calculators

C.1 Overview

Section 7 of the Comprehensive Drilling Calculator (7 · Additional Calculations in the left sidebar) adds 40 calculators that were previously only in the Lapeyrouse and Pressure calculators. Together with the original 140 formulas the application now holds 180 calculators. They are grouped as: Pressure & Mud Weight, Pore Pressure & Fracture Gradient, Well Control, Hydraulics, Volumes & Displacement, Cementing, Casing Design, Drill String & Pipe, and Directional.

C.2 How to use a Section 7 calculator

Choose the unit system with the toggle at top right (Field / SI / Metric). Every Section 7 label shows the unit of the selected system.
Click 7 · Additional Calculations in the sidebar and find the card.
Enter the inputs. The grey example values are in the selected unit system. Optional inputs may be left blank.
Press Calculate. The result box shows the answer in the selected unit system, and an animated illustration appears below it.
Read the colour: green = normal result, yellow = estimate or result that needs attention, red = missing input or a limit exceeded.

C.3 Unit handling

Inputs are converted to field units, calculated with the formula shown on the card, and each result is converted back to the selected system. The formulas are printed in field units. Switching unit system does not change the answer, only its units. This was verified for all 40 calculators by running each in all three unit systems and comparing the internal values.

Quantity	Field	SI	Metric
Pressure	psi	kPa	bar
Mud / fluid density	ppg	kg/m³	kg/l
Depth / length	ft	m	m
Diameter / wall thickness	in	mm	mm
Volume	bbl	m³	m³
Force / weight	lbs	kN	kN
Force (large)	klbs	kN	kN
Weight per length	lb/ft	kN/m	kN/m
Stress / yield strength	psi	MPa	MPa
Area	in²	cm²	cm²
Temperature	°F	°C	°C
Velocity	ft/min	m/min	m/min
Pressure gradient	psi/ft	kPa/m	bar/m
Dogleg / turn rate	°/100ft	°/30m	°/30m
Pump output	bbl/stk	m³/stk	L/stk
Hydraulic horsepower	hp	kW	kW
Horsepower per area	hp/in²	kW/cm²	kW/cm²
Ton-miles	ton-mi	t-km	t-km
Cement yield	ft³/sk	m³/sk	m³/sk
Capacity	bbl/ft	m³/m	m³/m

C.4 Corrections made while merging

Eaton pore pressure (d-exponent and resistivity). The earlier Pressure Calculator used normal ÷ observed. Eaton's method uses observed ÷ normal, so overpressured zones now correctly give pore pressure above normal.
Bending stress in pipe. The earlier formula omitted the conversion from inches to feet and returned 12 times the correct value. The merged card uses σ = E·OD·α ÷ 24 (about 218 × OD × DLS).

C.5 Estimates

Annular Pressure Loss (Simplified), Surge & Swab Pressure (Approx.) and the WOC estimate are screening estimates and always show a yellow result. Use rheology-based or simulator results for design.

C.6 Section 7 — Formula Reference (all 40 calculators)

Formulas are in field units; each calculator converts to and from the selected unit system automatically.

Pressure & Mud Weight

C.6.1 Required Mud Weight from Pressure

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

Back-calculates the mud weight that produces a known pressure at a given true vertical depth. Use it to find the density needed to balance a measured formation or shut-in pressure.

Inputs: Known Pressure [psi | kPa | bar]; TVD [ft | m]
Note: Result is an equivalent density; add a trip or safety margin separately. (source: Lapeyrouse calculator)

C.6.2 Lost Returns Pressure Change

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

Pressure change at depth when mud weight changes from old to new, for example after weighting up or after losing returns and replacing the column with lighter fluid.

Pore Pressure & Fracture Gradient

C.6.3 Overburden Gradient from Bulk Density

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

Overburden (lithostatic) gradient from the average bulk density of the rocks above, taken from density logs.

Inputs: Average Bulk Density (g/cc)
Note: 1 g/cc = 8.33 ppg = 0.433 psi/ft. Typical sediments 2.0–2.5 g/cc, deepwater columns lower. (source: Pressure Calc calculator)

C.6.4 Pore Pressure from d-exponent (Ratio Method)

PP = MW_normal × (dc_normal ÷ dc_observed)

Ratio-method pore pressure from the drilling-rate d-exponent: pore pressure rises in proportion to how far the observed d-exponent falls below the normal trend.

Inputs: Normal Mud Weight [ppg | kg/m³ | kg/l]; d-exponent (normal trend); d-exponent (observed)
Note: A quick screening method; use the Eaton cards for design values. (source: Lapeyrouse calculator)

C.6.5 Pore Pressure from d-exponent (Eaton)

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

Eaton's method for pore pressure from the corrected d-exponent (dc). The observed-to-normal ratio is raised to the 1.2 power and scales the gap between overburden and normal pressure.

Inputs: Overburden Gradient [ppg | kg/m³ | kg/l]; Normal PP Gradient [ppg | kg/m³ | kg/l]; dc Normal (on trendline); dc Observed (actual)
Note: Corrected 2026: the earlier Pressure Calculator inverted the ratio (normal ÷ observed), which put overpressured zones below normal. Overpressure now plots above normal, as expected. Yellow result = more than 30 % above normal. (source: Pressure Calc calculator)

C.6.6 Pore Pressure from Resistivity (Eaton)

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

Eaton's method with formation resistivity: lower-than-normal resistivity in a shale indicates higher pore pressure.

Inputs: Overburden Gradient [ppg | kg/m³ | kg/l]; Normal PP Gradient [ppg | kg/m³ | kg/l]; Normal Resistivity Ro (Ω·m); Observed Resistivity Robs (Ω·m)
Note: Corrected 2026: ratio is observed ÷ normal resistivity. Use shale points only; clean sands and gas zones distort it. (source: Pressure Calc calculator)

C.6.7 Effective Stress

σ_eff = Total stress (OBP) − Pore pressure

Terzaghi effective stress: the part of the total (overburden) stress carried by the rock matrix rather than by pore fluid.

Inputs: Total Stress, OBP [psi | kPa | bar]; Pore Pressure [psi | kPa | bar]
Note: As pore pressure rises toward overburden, effective stress falls and the rock gets weaker and easier to fracture. (source: Pressure Calc calculator)

C.6.8 Fracture Gradient (Eaton / Poisson)

FG = [ν ÷ (1 − ν)] × (OBG − PP) + PP

Eaton fracture gradient from Poisson's ratio. The matrix stress ratio ν/(1−ν) scales the effective overburden, then pore pressure is added back.

Inputs: Overburden Gradient [psi/ft | kPa/m | bar/m]; Pore Pressure Gradient [psi/ft | kPa/m | bar/m]; Poisson's Ratio ν (0.25–0.45)
Note: Inputs are gradients (psi/ft or kPa/m). Result also shown as an equivalent mud weight. (source: Lapeyrouse calculator)

C.6.9 Fracture Pressure at Depth

P_frac (psi) = FG (ppg) × 0.052 × TVD

Converts a fracture gradient (equivalent mud weight) into the actual fracture pressure at a given depth.

Inputs: Fracture Gradient [ppg | kg/m³ | kg/l]; TVD [ft | m]
Note: Use the TVD of the weakest point, normally the casing shoe. (source: Pressure Calc calculator)

C.6.10 Mud Weight Window

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

Mud weight window between pore pressure (floor) and fracture gradient (ceiling), with an optional collapse gradient that raises the floor.

Inputs: Pore Pressure Gradient [ppg | kg/m³ | kg/l]; Fracture Gradient [ppg | kg/m³ | kg/l]; Collapse Gradient (optional) [ppg | kg/m³ | kg/l]
Note: Red below 1 ppg window, yellow below 2 ppg. Remember ECD, surge and swab all eat into the window. (source: Pressure Calc calculator)

C.6.11 Overbalance & Margin Check

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

Overbalance and margin check: how far mud weight sits above pore pressure and below fracture gradient.

Inputs: PP Gradient [ppg | kg/m³ | kg/l]; Mud Weight [ppg | kg/m³ | kg/l]; Fracture Gradient [ppg | kg/m³ | kg/l]
Note: Negative overbalance = underbalanced (kick risk). Under 0.3 ppg is marginal. (source: Pressure Calc calculator)

C.6.12 Poisson's Ratio from Depth (Empirical)

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

Empirical Poisson's ratio from depth for Gulf Coast sediments, used as an input to fracture-gradient estimates.

Inputs: TVD [ft | m]
Note: Regional approximation only; replace with log- or test-derived values when available. (source: Pressure Calc calculator)

Well Control

C.6.13 Choke Pressure During Kill

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

Target choke (casing) pressure during a kill, interpolated between ICP and FCP according to how much of the drill string has been filled with kill mud.

Inputs: ICP [psi | kPa | bar]; FCP [psi | kPa | bar]; Total Strokes to fill DP; Current Strokes Pumped
Note: Applies to the drill-string fill stage. Always follow the rig's approved kill sheet. (source: Pressure Calc calculator)

C.6.14 Kick Tolerance (Subsea BOP)

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

Kick tolerance for a subsea BOP: fracture pressure at the shoe minus mud hydrostatic, less the riser-margin pressure lost when returns are taken through the choke line.

Hydraulics

C.6.15 HSI — Hydraulic Horsepower per Area of Bit

HSI = HHPb ÷ (π/4 × D_bit²)

Hydraulic horsepower per square inch of bit area. A standard measure of bit hydraulic energy for cleaning the hole bottom.

Inputs: Hydraulic Horsepower at Bit (HHPb) [hp | kW]; Bit Size [in | mm]
Note: Typical target 2.5–5 hp/in² (about 0.3–0.6 kW/cm²). (source: Lapeyrouse calculator)

C.6.16 Standpipe Pressure Budget

P_s = P_surface + P_drillstring + P_bit + P_annulus

Total standpipe pressure as the sum of surface equipment, drill string, bit and annulus losses.

Inputs: Surface Equipment Loss [psi | kPa | bar]; Drillstring Loss [psi | kPa | bar]; Bit Loss [psi | kPa | bar]; Annulus Loss [psi | kPa | bar]
Note: Shows the bit's share of the total; see the Optimum Bit Pressure Drop card for the target share. (source: Lapeyrouse calculator)

C.6.17 Optimum Bit Pressure Drop

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

Optimum pressure drop at the bit as a percentage of standpipe pressure, commonly about 65 % for maximum hydraulic horsepower in soft formations.

Inputs: Standpipe Pressure [psi | kPa | bar]; Optimum % at Bit
Note: Percentage can be changed for other optimisation criteria. (source: Lapeyrouse calculator)

C.6.18 Annular Pressure Loss (Simplified)

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

Simplified annular friction pressure loss from annular velocity, mud weight, length and annular gap.

C.6.19 Surge & Swab Pressure (Approx.)

ΔP ≈ 0.4 × MW × V_trip² ÷ 25.8

Approximate surge (running in) or swab (pulling out) pressure change from mud weight and trip speed.

Inputs: Mud Weight [ppg | kg/m³ | kg/l]; Trip Speed [ft/min | m/min]
Note: Estimate only (yellow). Surge adds to, and swab subtracts from, hydrostatic pressure, so keep both inside the mud weight window. (source: Pressure Calc calculator)

Volumes & Displacement

C.6.20 Displacement Volume — Pipe Steel

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

Volume of steel displaced by a length of pipe (OD² − ID²) ÷ 1029.4 per foot. Needed for trip-tank and pit-volume tracking.

Inputs: Pipe OD [in | mm]; Pipe ID [in | mm]; Length [ft | m]
Note: Result is the steel volume only, not the pipe's internal capacity. (source: Lapeyrouse calculator)

C.6.21 Strokes to Displace / Fill

Strokes = Volume ÷ Pump output

Number of pump strokes to move a given volume at a known pump output.

Inputs: Volume to Displace [bbl | m³]; Pump Output [bbl/stk | m³/stk | L/stk]
Note: Use actual (efficiency-corrected) pump output. (source: Lapeyrouse calculator)

C.6.22 Dilution to Reduce Mud Weight

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

Volume of water to add to a given volume of mud to bring its weight down to the desired value.

Cementing

C.6.23 Sacks of Cement Required

Sacks = V_bbl × 5.615 ÷ Yield × Excess factor

Number of cement sacks from annular volume, slurry yield and an excess factor.

Inputs: Annular Volume [bbl | m³]; Cement Yield [ft³/sk | m³/sk]; Excess Factor (1.5 = 50% excess)
Note: Excess 1.5 means 50 % extra volume for washouts and losses. (source: Lapeyrouse calculator)

C.6.24 Displacement Volume (Cementing)

V (bbl) = ID² ÷ 1029.4 × Depth

Volume of fluid needed to displace cement down the casing: casing capacity × depth.

Inputs: Casing ID [in | mm]; Shoe Depth [ft | m]
Note: Also shows capacity per unit length. (source: Lapeyrouse calculator)

C.6.25 Waiting on Cement (WOC) Estimate

Rule-of-thumb WOC time from temperature at depth

Rule-of-thumb waiting-on-cement time from temperature at depth and cement class.

Inputs: Temperature at Depth [°F | °C]; Cement Class
Note: Estimate only (yellow). Confirm with lab compressive-strength data before drilling out. (source: Lapeyrouse calculator)

Casing Design

C.6.26 Burst Pressure Rating (Barlow)

P_burst = 0.875 × 2 × Ym × t ÷ OD

Barlow's formula for the internal-yield (burst) pressure rating of pipe with a 12.5 % wall tolerance (factor 0.875).

Inputs: Min Yield Strength Ym [psi | MPa]; Wall Thickness t [in | mm]; Outside Diameter OD [in | mm]
Note: Rating only; compare with the burst load and apply the design factor. (source: Pressure Calc calculator)

C.6.27 Burst Pressure on Casing (Net Load)

P_burst load = Formation/internal pressure − outside mud hydrostatic

Net burst load on casing: internal pressure minus the external mud hydrostatic that backs it up.

Inputs: Formation Pressure [psi | kPa | bar]; Outside Mud Hydrostatic [psi | kPa | bar]
Note: Use the worst case internal pressure (for example a gas-filled casing). (source: Lapeyrouse calculator)

C.6.28 Collapse Pressure (Yield Strength)

P_col = Ym × 2(D/t − 1) ÷ (D/t)²

Yield-strength collapse pressure of casing from the diameter-to-thickness ratio D/t.

Inputs: Min Yield Strength Ym [psi | MPa]; Outside Diameter OD [in | mm]; Wall Thickness t [in | mm]
Note: Valid for thick-walled (low D/t) pipe. Thin-walled pipe collapses by elastic or transition modes, so use API tables. (source: Pressure Calc calculator)

C.6.29 Collapse Pressure on Casing (Net Load)

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

Net collapse load: the difference between external and internal fluid pressure acting at a given depth.

C.6.30 Axial Tension Capacity (Yield)

F_y = Ym × 0.7854 × (OD² − ID²)

Axial yield tension capacity of a pipe body: yield strength × cross-sectional steel area.

Inputs: Yield Strength Ym [psi | MPa]; Outside Diameter OD [in | mm]; Inside Diameter ID [in | mm]
Note: Body yield only; connections often govern. (source: Pressure Calc calculator)

C.6.31 Casing Design Safety Factors

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

Casing safety factors for burst, collapse and tension: rating ÷ load, checked against minimum design factors 1.1, 1.0 and 1.6.

C.6.32 Triaxial (Von Mises) Stress

σ_VME = √(σ_a² − σ_a·σ_h + σ_h²)

Von Mises equivalent stress combining axial and hoop stress into a single value for comparison with yield strength.

Inputs: Axial Stress σ_a [psi | MPa]; Hoop Stress σ_hoop [psi | MPa]; Yield Strength Ym (optional) [psi | MPa]
Note: Biaxial form. Safety factor = yield ÷ equivalent stress. (source: Pressure Calc calculator)

Drill String & Pipe

C.6.33 Drill Pipe Tensile Safety Factor

SF = Pipe yield strength ÷ Maximum hookload

Drill-pipe tensile safety factor: pipe yield strength divided by the maximum hookload.

Inputs: Pipe Yield Strength [lbs | kN]; Maximum Hook Load [lbs | kN]
Note: Yellow below 1.3. (source: Lapeyrouse calculator)

C.6.34 Maximum Allowable Overpull

Overpull_max = Yield ÷ SF − Current hookload

Maximum allowable overpull: yield strength divided by the design factor, less the current hookload.

Inputs: Pipe Yield [lbs | kN]; Current Hook Load [lbs | kN]; Design SF (e.g. 1.3)
Note: Red when the string is already beyond the design limit. (source: Lapeyrouse calculator)

C.6.35 Maximum Pipe Length (Tension Limit)

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

Longest pipe length that can hang from surface at the yield limit, allowing for other hookload and buoyancy.

C.6.36 Drill String Weight in Mud (Hookload)

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

Buoyed weight of the drill string (hookload) from drill pipe and drill collar weights and mud weight.

C.6.37 Drill String Stretch

ΔL = W × L ÷ (As × E), E = 30×10⁶ psi

Elastic stretch of a free-hanging pipe length under load: ΔL = W·L ÷ (As·E).

Inputs: Free Pipe Load W [lbs | kN]; Free Pipe Length L [ft | m]; Pipe OD [in | mm]; Pipe ID [in | mm]
Note: Used for free-point estimates. Steel modulus E = 30×10⁶ psi. (source: Pressure Calc calculator)

C.6.38 Bending Stress in Pipe

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

Bending stress in pipe passing through a dogleg: σ = E·OD·α ÷ 24 with α in rad/ft, equivalent to about 218 × OD × DLS in field units.

Inputs: Pipe OD [in | mm]; Dogleg Severity (DLS) [°/100ft | °/30m]
Note: Corrected 2026: the earlier Pressure Calculator was 12 times too high. Add to axial stress for fatigue checks. (source: Pressure Calc calculator)

C.6.39 Ton-Miles — Setting Casing

TM = W_c × D × BF × 2 ÷ (2000 × 5280)

Ton-miles of work when running a casing string, from string weight, shoe depth and buoyancy factor.

Inputs: Casing String Weight [lbs | kN]; Shoe Depth [ft | m]; Buoyancy Factor
Note: Used with the round-trip ton-miles card to track drilling-line wear and slip-and-cut schedules. (source: Lapeyrouse calculator)

Directional

C.6.40 Turn Rate (Azimuth Change)

Turn rate = |Az₂ − Az₁| ÷ ΔMD × 100

Turn rate: change in azimuth per 100 ft (30 m) of measured depth.

Inputs: Azimuth 1 (°); Azimuth 2 (°); ΔMD [ft | m]
Note: Combine with dogleg severity when reviewing wellbore tortuosity. (source: Pressure Calc calculator)

Appendix E — Section 7: Example Inputs & Results in All Unit Systems

Inputs are the example values in field units. The same case was run in Field, SI and Metric (inputs converted); results below are exactly what the calculator displays.

#	Calculator	Example inputs (field)	Field	SI	Metric
Pressure & Mud Weight
1	Required Mud Weight from Pressure	Known Pressure = 4368; TVD = 8000	Required MW = 10.50 ppg \| SG = 1.261	Required MW = 1258.21 kg/m³ \| SG = 1.261	Required MW = 1.26 kg/l \| SG = 1.261
2	Lost Returns Pressure Change	Old Mud Weight = 10.0; New Mud Weight = 11.0; TVD = 8000	ΔP = 416 psi	ΔP = 2868 kPa	ΔP = 29 bar
Pore Pressure & Fracture Gradient
3	Overburden Gradient from Bulk Density	Average Bulk Density = 2.30	OBG = 19.16 ppg \| 0.9959 psi/ft	OBG = 2295.82 kg/m³ \| 22.5279 kPa/m	OBG = 2.30 kg/l \| 0.2253 bar/m
4	Pore Pressure from d-exponent (Ratio Method)	Normal Mud Weight = 8.6; d-exponent = 1.8; d-exponent = 1.2	Pore pressure = 12.90 ppg	Pore pressure = 1545.81 kg/m³	Pore pressure = 1.55 kg/l
5	Pore Pressure from d-exponent (Eaton)	Overburden Gradient = 19.0; Normal PP Gradient = 8.6; dc Normal = 1.8; dc Observed = 1.2	PP gradient = 12.61 ppg \| Overpressure = 4.01 ppg above normal	PP gradient = 1510.66 kg/m³ \| Overpressure = 480.13 kg/m³ above normal	PP gradient = 1.51 kg/l \| Overpressure = 0.48 kg/l above normal
6	Pore Pressure from Resistivity (Eaton)	Overburden Gradient = 19.0; Normal PP Gradient = 8.6; Normal Resistivity Ro = 2.5; Observed Resistivity Robs = 1.0	PP gradient = 15.54 ppg \| Robs/Ro = 0.40	PP gradient = 1861.75 kg/m³ \| Robs/Ro = 0.40	PP gradient = 1.87 kg/l \| Robs/Ro = 0.40
7	Effective Stress	Total Stress, OBP = 9000; Pore Pressure = 4000	Effective stress = 5000 psi	Effective stress = 34474 kPa	Effective stress = 345 bar
8	Fracture Gradient (Eaton / Poisson)	Overburden Gradient = 1.0; Pore Pressure Gradient = 0.433; Poisson's Ratio ν = 0.25	Fracture gradient = 0.6220 psi/ft \| 11.96 ppg	Fracture gradient = 14.0700 kPa/m \| 1433.35 kg/m³	Fracture gradient = 0.1407 bar/m \| 1.44 kg/l
9	Fracture Pressure at Depth	Fracture Gradient = 14.5; TVD = 8000	Fracture pressure = 6032 psi	Fracture pressure = 41589 kPa	Fracture pressure = 416 bar
10	Mud Weight Window	Pore Pressure Gradient = 10.5; Fracture Gradient = 14.5; Collapse Gradient = 9.5	Window = 4.00 ppg \| Safe MW: 10.50 ppg to 14.50 ppg \| Collapse gradient 9.50 ppg	Window = 479.32 kg/m³ \| Safe MW: 1258.21 kg/m³ to 1737.54 kg/m³ \| Collapse gradient 1138.38 kg/m³	Window = 0.48 kg/l \| Safe MW: 1.26 kg/l to 1.74 kg/l \| Collapse gradient 1.14 kg/l
11	Overbalance & Margin Check	PP Gradient = 10.5; Mud Weight = 11.0; Fracture Gradient = 14.5	Overbalance = +0.50 ppg ✓ adequate \| Margin to fracture = 3.50 ppg \| Total window = 4.00 ppg	Overbalance = +59.91 kg/m³ ✓ adequate \| Margin to fracture = 419.41 kg/m³ \| Total window = 479.32 kg/m³	Overbalance = +0.06 kg/l ✓ adequate \| Margin to fracture = 0.42 kg/l \| Total window = 0.48 kg/l
12	Poisson's Ratio from Depth (Empirical)	TVD = 10000	ν ≈ 0.225 \| Shallow (4,500 m / 15,000 ft) ≈ 0.40+	ν ≈ 0.225 \| Shallow (4,500 m / 15,000 ft) ≈ 0.40+	ν ≈ 0.225 \| Shallow (4,500 m / 15,000 ft) ≈ 0.40+
Well Control
13	Choke Pressure During Kill	ICP = 750; FCP = 520; Total Strokes to fill DP = 1500; Current Strokes Pumped = 750	Progress = 50% kill mud in DP \| Target pressure = 635 psi	Progress = 50% kill mud in DP \| Target pressure = 4378 kPa	Progress = 50% kill mud in DP \| Target pressure = 44 bar
14	Kick Tolerance (Subsea BOP)	Fracture Gradient = 14.5; Mud Weight = 10.0; Shoe TVD = 5000; Water Depth = 3000; Seawater Density = 8.6	FP at shoe = 3770 psi \| Riser margin loss = 218 psi \| Subsea KT = 952 psi	FP at shoe = 25993 kPa \| Riser margin loss = 1506 kPa \| Subsea KT = 6561 kPa	FP at shoe = 260 bar \| Riser margin loss = 15 bar \| Subsea KT = 66 bar
Hydraulics
15	HSI — Hydraulic Horsepower per Area of Bit	Hydraulic Horsepower at Bit = 400; Bit Size = 8.5	HSI = 7.05 hp/in²	HSI = 0.81 kW/cm²	HSI = 0.81 kW/cm²
16	Standpipe Pressure Budget	Surface Equipment Loss = 100; Drillstring Loss = 500; Bit Loss = 1500; Annulus Loss = 200	Standpipe pressure = 2300 psi \| Bit share 65% of total	Standpipe pressure = 15858 kPa \| Bit share 65% of total	Standpipe pressure = 159 bar \| Bit share 65% of total
17	Optimum Bit Pressure Drop	Standpipe Pressure = 3000; Optimum % at Bit = 65	Optimum bit ΔP = 1950 psi	Optimum bit ΔP = 13445 kPa	Optimum bit ΔP = 134 bar
18	Annular Pressure Loss (Simplified)	Annular Velocity = 150; Mud Weight = 10.0; Length = 8000; Hole Dia. − Pipe Dia. = 3.5	APL ≈ 3265 psi \| Simplified estimate — use viscometer data for accuracy	APL ≈ 22513 kPa \| Simplified estimate — use viscometer data for accuracy	APL ≈ 225 bar \| Simplified estimate — use viscometer data for accuracy
19	Surge & Swab Pressure (Approx.)	Mud Weight = 10.0; Trip Speed = 30	Surge ΔP ≈ 140 psi \| Estimate only — use a surge/swab simulator for design	Surge ΔP ≈ 962 kPa \| Estimate only — use a surge/swab simulator for design	Surge ΔP ≈ 10 bar \| Estimate only — use a surge/swab simulator for design
Volumes & Displacement
20	Displacement Volume — Pipe Steel	Pipe OD = 5.0; Pipe ID = 4.276; Length = 8000	Steel displacement = 52.19 bbl	Steel displacement = 8.30 m³	Steel displacement = 8.30 m³
21	Strokes to Displace / Fill	Volume to Displace = 500; Pump Output = 0.117	Strokes = 4274	Strokes = 4274	Strokes = 4274
22	Dilution to Reduce Mud Weight	Current Volume = 1000; Current Mud Weight = 12.0; Desired Mud Weight = 11.0	Water to add = 374.5 bbl	Water to add = 59.5 m³	Water to add = 59.5 m³
Cementing
23	Sacks of Cement Required	Annular Volume = 200; Cement Yield = 1.15; Excess Factor = 1.5	Cement = 1465 sacks \| No excess: 977 sacks	Cement = 1465 sacks \| No excess: 977 sacks	Cement = 1465 sacks \| No excess: 977 sacks
24	Displacement Volume (Cementing)	Casing ID = 8.681; Shoe Depth = 8000	Displacement = 585.7 bbl \| Capacity 0.07321 bbl/ft	Displacement = 93.1 m³ \| Capacity 0.03819 m³/m	Displacement = 93.1 m³ \| Capacity 0.03819 m³/m
25	Waiting on Cement (WOC) Estimate	Temperature at Depth = 150	Estimated WOC = 12 hours at 150.0 °F \| Rule-of-thumb estimate — verify with lab data	Estimated WOC = 12 hours at 65.6 °C \| Rule-of-thumb estimate — verify with lab data	Estimated WOC = 12 hours at 65.6 °C \| Rule-of-thumb estimate — verify with lab data
Casing Design
26	Burst Pressure Rating (Barlow)	Min Yield Strength Ym = 80000; Wall Thickness t = 0.472; Outside Diameter OD = 9.625	Burst rating = 6865 psi \| D/t = 20.4	Burst rating = 47336 kPa \| D/t = 20.4	Burst rating = 473 bar \| D/t = 20.4
27	Burst Pressure on Casing (Net Load)	Formation Pressure = 6000; Outside Mud Hydrostatic = 3000	Net burst load = 3000 psi	Net burst load = 20684 kPa	Net burst load = 207 bar
28	Collapse Pressure (Yield Strength)	Min Yield Strength Ym = 80000; Outside Diameter OD = 9.625; Wall Thickness t = 0.472	Collapse (yield) = 7461 psi \| D/t = 20.4	Collapse (yield) = 51445 kPa \| D/t = 20.4	Collapse (yield) = 514 bar \| D/t = 20.4
29	Collapse Pressure on Casing (Net Load)	Depth = 8000; Outside Fluid Density = 12.0; Inside Fluid Density = 8.6	Net collapse load = 1414 psi	Net collapse load = 9752 kPa	Net collapse load = 98 bar
30	Axial Tension Capacity (Yield)	Yield Strength Ym = 80000; Outside Diameter OD = 9.625; Inside Diameter ID = 8.681	Yield tension = 1086 klbs \| Steel area = 13.572 in²	Yield tension = 4830 kN \| Steel area = 87.564 cm²	Yield tension = 4830 kN \| Steel area = 87.564 cm²
31	Casing Design Safety Factors	Burst Rating = 5000; Internal Pressure = 4000; Collapse Rating = 3500; External Pressure = 3000; Tension Rating = 800; Hookload = 400	Burst SF = 1.25 ✓ (min 1.1) \| Collapse SF = 1.17 ✓ (min 1.0) \| Tension SF = 2.00 ✓ (min 1.6)	Burst SF = 1.25 ✓ (min 1.1) \| Collapse SF = 1.17 ✓ (min 1.0) \| Tension SF = 2.00 ✓ (min 1.6)	Burst SF = 1.25 ✓ (min 1.1) \| Collapse SF = 1.17 ✓ (min 1.0) \| Tension SF = 2.00 ✓ (min 1.6)
32	Triaxial (Von Mises) Stress	Axial Stress σ_a = 30000; Hoop Stress σ_hoop = 50000; Yield Strength Ym = 80000	Von Mises = 43589 psi \| SF vs yield = 1.84 ✓	Von Mises = 301 MPa \| SF vs yield = 1.84 ✓	Von Mises = 301 MPa \| SF vs yield = 1.84 ✓
Drill String & Pipe
33	Drill Pipe Tensile Safety Factor	Pipe Yield Strength = 560000; Maximum Hook Load = 300000	Safety factor = 1.87	Safety factor = 1.87	Safety factor = 1.87
34	Maximum Allowable Overpull	Pipe Yield = 560000; Current Hook Load = 250000; Design SF = 1.3	Max overpull = 180769 lbs	Max overpull = 804 kN	Max overpull = 804 kN
35	Maximum Pipe Length (Tension Limit)	Min Yield Strength = 105000; Pipe Cross Section As = 5.275; Other Hookload = 50000; Pipe Weight in Air = 19.5; Mud Weight = 10.0	Max length = 30496 ft \| At SF = 1.0 — apply 1.6+ for design	Max length = 9295 m \| At SF = 1.0 — apply 1.6+ for design	Max length = 9295 m \| At SF = 1.0 — apply 1.6+ for design
36	Drill String Weight in Mud (Hookload)	Drill Pipe Weight = 19.5; Drill Pipe Length = 7500; Drill Collar Weight = 147; Drill Collar Length = 500; Mud Weight = 10.0	Air weight = 219.8 klbs \| BF = 0.8473 \| Hookload (buoyed) = 186.2 klbs	Air weight = 977.5 kN \| BF = 0.8473 \| Hookload (buoyed) = 828.3 kN	Air weight = 977.5 kN \| BF = 0.8473 \| Hookload (buoyed) = 828.3 kN
37	Drill String Stretch	Free Pipe Load W = 100000; Free Pipe Length L = 8000; Pipe OD = 5.0; Pipe ID = 4.276	Stretch = 60.67 in \| 5.0557 ft \| Steel area = 5.275 in²	Stretch = 1540.97 mm \| 1.5410 m \| Steel area = 34.030 cm²	Stretch = 1540.97 mm \| 1.5410 m \| Steel area = 34.030 cm²
38	Bending Stress in Pipe	Pipe OD = 5.0; Dogleg Severity = 3.0	Bending stress = 3272 psi \| Add to axial stress for fatigue assessment	Bending stress = 23 MPa \| Add to axial stress for fatigue assessment	Bending stress = 23 MPa \| Add to axial stress for fatigue assessment
39	Ton-Miles — Setting Casing	Casing String Weight = 200000; Shoe Depth = 8000; Buoyancy Factor = 0.839	Casing ton-miles = 254.24 ton-mi	Casing ton-miles = 371.17 t-km	Casing ton-miles = 371.17 t-km
Directional
40	Turn Rate (Azimuth Change)	Azimuth 1 = 90; Azimuth 2 = 100; ΔMD = 100	Turn rate = 10.00 °/100ft	Turn rate = 3.00 °/30m	Turn rate = 3.00 °/30m

Drilling Calculator v2

Complete Reference
Manual

Part A — Operations Guide
Part B — Technical Reference
Appendices A–D

180 Formulas · 3 Unit Systems · 7 Sections · Offline Capable

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