Overburden stress, also known as vertical stress or geostatic stress, is the pressure exerted by the weight of overlying rock and sediments. It is a crucial parameter in geomechanics, petroleum engineering, and geotechnical studies. One of the most common ways to determine overburden stress is by using a density log, which provides a continuous measurement of rock density as a function of depth.
This guide explains the step-by-step process of calculating overburden stress from a density log, including key formulas, practical considerations, and common mistakes to avoid.
What is Overburden Stress?
Overburden stress ( ) is the total weight of all materials above a certain depth. It is typically expressed in pounds per square inch (psi), megapascals (MPa), or kilopascals (kPa). Understanding overburden stress is essential in fields like wellbore stability, reservoir compaction, and hydraulic fracturing.
Why Use a Density Log for Overburden Stress Calculation?
A density log records the bulk density ( ) of subsurface formations. Since overburden stress is a function of density and depth, density logs provide a reliable and efficient way to estimate this parameter.
Formula for Overburden Stress Calculation
Overburden stress at a given depth ( ) is calculated using the following integral:
sigma_v (z) = int_0^z rho_b (z) g dz
Where:
- $sigma_v (z)$ = Overburden stress at depth (Pa or psi)
- $rho_b (z)$ = Bulk density from the density log (kg/m³ or g/cm³)
- = Acceleration due to gravity (9.81 m/s²)
- = Depth increment (m or ft)
For practical applications, the equation is often simplified to a summation for discrete depth intervals:
sigma_v = sum (rho_b times g times Delta z)
Where $Delta z$ is the thickness of each layer recorded in the density log.
Step-by-Step Calculation of Overburden Stress
Step 1: Obtain the Density Log Data
A density log provides bulk density values ( ) at different depths. These values are usually measured in g/cm³ or kg/m³.
Example data from a density log:
| Depth (m) | Bulk Density (g/cm³) |
|---|---|
| 100 | 2.2 |
| 200 | 2.3 |
| 300 | 2.4 |
| 400 | 2.5 |
Step 2: Convert Units (if necessary)
Density values are often given in g/cm³ but need to be converted to kg/m³ for proper calculations:
1 text{ g/cm³} = 1000 text{ kg/m³}
So, for a bulk density of 2.2 g/cm³, the converted value is:
2.2 times 1000 = 2200 text{ kg/m³}
Step 3: Apply the Overburden Stress Formula
Using the summation method, calculate the overburden stress by integrating over small depth intervals.
For example, assuming 100 m depth intervals:
sigma_v = sum (rho_b times g times Delta z)
Calculating at 400 m depth:
sigma_v = (2200 times 9.81 times 100) + (2300 times 9.81 times 100) + (2400 times 9.81 times 100) + (2500 times 9.81 times 100)
sigma_v = (2.16 times 106) + (2.26 times 106) + (2.35 times 106) + (2.45 times 106)
sigma_v = 9.22 times 10^6 text{ Pa} quad text{or} quad 9.22 text{ MPa}
Step 4: Convert to psi (if required)
Since 1 MPa = 145 psi, the overburden stress in psi is:
9.22 times 145 = 1338 text{ psi}
Thus, at 400 m depth, the estimated overburden stress is 1338 psi.
Factors Affecting Overburden Stress Calculation
1. Variation in Bulk Density
- Different lithologies (sandstone, shale, limestone) have varying densities.
- Density changes should be accounted for at small depth increments.
2. Compaction Effects
- Deeper formations experience higher compaction, increasing bulk density.
- Compaction corrections may be necessary for more accurate results.
3. Fluid Saturation
- Density logs measure bulk density, which includes fluid-filled pores.
- Overestimation may occur if fluid density is not accounted for.
Common Mistakes and How to Avoid Them
1. Ignoring Depth Resolution
- Using large depth intervals can introduce errors.
- Choose smaller depth increments for better accuracy.
2. Forgetting Unit Conversions
- Ensure consistency in density (kg/m³ or g/cm³) and depth (m or ft).
3. Assuming Constant Gravity
- Gravity varies slightly with latitude and altitude, but 9.81 m/s² is a good approximation for most calculations.
Applications of Overburden Stress Calculation
1. Wellbore Stability Analysis
- Helps determine the required mud weight to prevent wellbore collapse.
2. Reservoir Engineering
- Essential for estimating pore pressure and fracture gradient.
3. Hydraulic Fracturing Design
- Used to calculate minimum stress conditions for fracture initiation.
4. Geotechnical Engineering
- Important for foundation stability and slope stability calculations.
Final Thoughts
Calculating overburden stress from a density log is a fundamental process in geomechanics and petroleum engineering. By using bulk density values, integrating over depth, and applying the correct unit conversions, engineers can accurately estimate vertical stress.
Understanding overburden stress helps in wellbore stability, hydraulic fracturing, reservoir management, and geotechnical applications. With careful data interpretation, errors can be minimized, leading to more precise and reliable geomechanical models.