Drilling Engineering

Complete Study Guide

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Pressure Calculations
Hydrostatic Pressure

Hydrostatic Pressure

P = 0.052 × ρ × h
Pressure Calculations
Hydrostatic Pressure

Hydrostatic Pressure (SI Units)

P = ρ × g × h
Pressure Calculations
Gas Column

Gas Column Pressure

P₂ = P₁ × e^[M(D₂-D₁)/(1544·z·T)]
Pressure Calculations
Equivalent Density

Equivalent Mud Weight from Pressure

ρ = P / (0.052 × h)
Fluid Flow
Velocity

Pipe Flow Velocity

V = q / (2.448 × d²)
Fluid Flow
Velocity

Annular Flow Velocity

V = q / [2.448 × (d₂² - d₁²)]
Fluid Flow
Velocity

Annular Velocity (ft/min)

AV = (q × 1029) / (d₂² - d₁²)
Volume Calculations
Pipe Properties

Pipe Capacity

Capacity = ID² / 1029
Volume Calculations
Pipe Properties

Pipe Displacement

Displacement = (OD² - ID²) / 1029
Volume Calculations
Annular Space

Annular Capacity

Capacity = (d₂² - d₁²) / 1029
Volume Calculations
Mud Volume

Volume in Hole

V_hole = V_wellbore - V_drillstring_displacement
Rheology
Newtonian Model

Newtonian Fluid (Shear Stress)

τ = μ × γ̇
Rheology
Newtonian Model

Newtonian Viscosity from Fann

μ = 300 × θ / N
Rheology
Bingham Plastic

Bingham Plastic Model

τ = τ_y + μ_p × γ̇
Rheology
Bingham Plastic

Plastic Viscosity

μ_p = θ₆₀₀ - θ₃₀₀
Rheology
Bingham Plastic

Yield Point

τ_y = θ₃₀₀ - μ_p
Rheology
Bingham Plastic

True Yield Point

τ_y(true) = 0.75 × τ_y(Bingham)
Rheology
Bingham Plastic

Apparent Viscosity (Bingham)

μ_a = μ_p + (47,880 × τ_y) / γ̇
Rheology
Power Law

Power Law Model

τ = K × γ̇ⁿ
Rheology
Power Law

Flow Behavior Index

n = 3.32 × log(θ₆₀₀ / θ₃₀₀)
Rheology
Power Law

Consistency Index

K = (510 × θ₃₀₀) / 511ⁿ
Rheology
Power Law

Apparent Viscosity (Power Law)

μ_a = K × γ̇^(n-1)
Rheology
Viscometer

Shear Stress (Fann)

τ = 0.01066 × N × θ
Rheology
Viscometer

Shear Rate (Fann)

γ̇ = 1.703 × RPM
Rheology
Gel Strength

Gel Strength

Gel Strength = θ₃ rpm
Flow Regime
Reynolds Number

Reynolds Number (Pipe - Newtonian)

N_Re = (928 × ρ × V × d) / μ
Flow Regime
Reynolds Number

Reynolds Number (Pipe - Bingham)

N_Re = (928 × ρ × V × d) / μ_a
Flow Regime
Reynolds Number

Reynolds Number (Annulus - Newtonian)

N_Re = (757 × ρ × V × (d₂ - d₁)) / μ
Flow Regime
Reynolds Number

Hedstrom Number

N_He = (37,100 × ρ × τ_y × d²) / μ_p²
Pressure Loss
Laminar Flow

Pressure Loss (Laminar - Newtonian Pipe)

ΔP/ΔL = (μ × V) / (1,500 × d²)
Pressure Loss
Laminar Flow

Pressure Loss (Laminar - Newtonian Annulus)

ΔP/ΔL = (μ × V) / [1,000 × (d₂ - d₁)²]
Pressure Loss
Turbulent Flow

Pressure Loss (Turbulent - Pipe)

ΔP/ΔL = (ρ^0.75 × V^1.75 × μ^0.25) / (1,800 × d^1.25)
Pressure Loss
Turbulent Flow

Pressure Loss (Turbulent - Annulus)

ΔP/ΔL = (ρ^0.75 × V^1.75 × μ^0.25) / [1,396 × (d₂ - d₁)^1.25]
Flow Calculations
Equivalent Diameter

Equivalent Diameter (Annulus)

d_e = 0.816 × (d₂ - d₁)
Pump Calculations
Output

Pump Output (Triplex)

F_p = (3 × L × d² × η) / (42 × 294)
Pump Calculations
Flow Rate

Pump Flow Rate

Q = F_p × N
Pump Calculations
Horsepower

Hydraulic Horsepower

HHP = (P × Q × 42) / 1,714
Time Calculations
Circulation

Circulation Time

t = V / Q
Time Calculations
Pump Strokes

Number of Strokes

Strokes = t × N
Mud Properties
Density

Final Mud Density (Mixing)

ρ_f = (M_total) / (V_total)
Mud Properties
Volume

Volume of Material

V = M / ρ
Mud Properties
Material Weights

Weight of Water (per barrel)

M_water = 42 × 8.33 = 350 lb/bbl
Forces
Buoyancy

Buoyant Weight

W_b = W_air × (1 - ρ_mud / ρ_steel)
Economics
Drilling Cost

Drilling Cost per Foot

C_f = [C_b + C_r × (t_t + t_b + t_c)] / D
Rock Mechanics
Stress

Axial Stress

σ = F / A
Rock Mechanics
Mohr Circle

Shear Stress on Plane

τ = 0.5 × (σ₁ - σ₃) × sin(2φ)
Rock Mechanics
Mohr Circle

Normal Stress on Plane

σ_n = 0.5 × (σ₁ + σ₃) - 0.5 × (σ₁ - σ₃) × cos(2φ)
Rock Mechanics
Rock Strength

Cohesion

C = τ - σ_n × tan(θ)