Overburden and Hydrostatic Pressure

Summary

Every pore pressure method starts from two reference pressures: the Overburden stress, which is the weight of everything above, and the Hydrostatic pressure, the pressure of a water column. Their difference is the normal Vertical effective stress. This page shows how to build both from a density log and a water gradient, and how to express them as equivalent mud weights.

Inputs and outputs

Equations

The principle that links pressure and rock behavior is the Terzaghi effective stress. Vertical effective stress is the total vertical stress less the pore pressure:

Biot's form replaces \(\ppPp\) by \(\alpha\,\ppPp\) with a coefficient \(\alpha \le 1\). Pore pressure methods almost always use \(\alpha = 1\).

The overburden stress is the integral of bulk density over depth. In field units, with density in g/cm³, depth in feet and stress in psi:

where 0.43353 psi/ft is the pressure gradient of 1 g/cm³ of material. Above the top of the density log, at depth \(\ppZtop\), the density is not measured and has to be extrapolated. With a mean density \(\ppRhoTop\) above the log and a mean \(\ppRhoLog\) below its top, the stress at depth \(\zdepth\) is:

The hydrostatic pressure is the water gradient times the true vertical depth:

Pressures are compared with drilling fluid density as an equivalent mud weight in ppg:

where 0.052 is the rounded value of 0.0519 psi/ft per ppg.

Single-value calculator

Behavior

Overburden stress rises faster than hydrostatic pressure, and the two lines separate with depth. At 10,000 ft with the default densities the overburden is about 9,884 psi, a mean gradient of 0.988 psi/ft or 19.0 ppg, while the hydrostatic pressure at 0.465 psi/ft is 4,650 psi or 8.94 ppg. The normal effective stress is therefore about 5,234 psi. The kink in the solid curve at 2,000 ft is the change from the extrapolated density above the log to the logged density below it. The mean density of the logged interval is the main sensitivity: changing it by 0.1 g/cm³ moves the overburden at 10,000 ft by about 347 psi, or 0.67 ppg, and this error carries one-for-one into every pore pressure method that subtracts an effective stress from the overburden.

Parameter guidance

Hydrostatic gradient. 0.433 psi/ft is fresh water and 0.465 psi/ft is a typical saline brine. Use the formation water salinity of the basin. Offshore, the seawater column above the mudline has a gradient of about 0.444 psi/ft (1.025 g/cm³), and the formation water gradient applies below it. Datum. Depth is measured from the surface or, offshore, from sea level; the overburden then starts with the weight of the water column, and the hydrostatic pressure includes it. Extrapolation above the log. The density log rarely reaches the surface or the seafloor. Common choices are a constant density, a fitted compaction curve for density with depth, or a regional gradient, anchored by a seismic velocity or a nearby well with a longer density log. Check that the extrapolated section is a smooth continuation of the logged section. Bad hole. Washouts lower the density; replace density in them with a repaired or modeled curve (see the data preparation stage) before integrating. Deviated wells. Integrate over true vertical depth, not measured depth.

Worked example

Offshore well with 3,000 ft of water, 2,000 ft of extrapolated section below the mudline at a mean density of 1.95 g/cm³, and two logged intervals. Depths are below the mudline; the pressure units are psi and ppg.

G = 0.43353        # psi/ft per g/cm3
water_depth, rho_w = 3000.0, 1.025
layers = [  # (thickness ft below mudline, mean density g/cm3)
    (2000.0, 1.95),   # extrapolated, above the top of the log
    (3000.0, 2.15),   # logged
    (4000.0, 2.30),   # logged
]
sv = G * rho_w * water_depth
print(f'overburden at the mudline = {sv:.0f} psi')
depth = water_depth
for h, rho in layers:
    sv += G * rho * h
    depth += h
    print(f'at {depth:6.0f} ft: overburden = {sv:7.0f} psi  ({sv / depth:.3f} psi/ft)')
g_sea, g_form = 0.4443, 0.465   # psi/ft, seawater and formation water
ph = g_sea * water_depth + g_form * (depth - water_depth)
print(f'hydrostatic at {depth:.0f} ft = {ph:.0f} psi')
print(f'normal effective stress = {sv - ph:.0f} psi')
print(f'overburden = {sv / (0.052 * depth):.2f} ppg, hydrostatic = {ph / (0.052 * depth):.2f} ppg')

Output

overburden at the mudline = 1333 psi
at   5000 ft: overburden =    3024 psi  (0.605 psi/ft)
at   8000 ft: overburden =    5820 psi  (0.728 psi/ft)
at  12000 ft: overburden =    9809 psi  (0.817 psi/ft)
hydrostatic at 12000 ft = 5518 psi
normal effective stress = 4291 psi
overburden = 15.72 ppg, hydrostatic = 8.84 ppg

Assumptions and limitations

• Stress is vertical and lithostatic: the overburden is the weight of the column and no support from the sides is considered.
• Density is representative of the rock including its pore fluid (bulk density), and the log is not affected by washouts.
• The extrapolated density above the top of the log is a model, not a measurement, and is accurate to a few hundredths of a g/cm³ at best.
• Water pressure is hydrostatic: a continuous column of water of constant gradient, with no temperature or salinity change with depth.
• Depth is true vertical depth from the same datum for the stress and the pressure.

QC checks

• The overburden gradient (stress divided by depth) increases smoothly with depth and typically ends between 0.9 and 1.1 psi/ft at 10,000 ft or more onshore, lower offshore.
• There are no steps in the overburden curve at the top of the log or at casing points where the density source changes.
• A density spike in a washout does not produce a visible kink in the integrated stress.
• Hydrostatic pressure and the formation water gradient agree with measured pressure in a water-bearing sand in normally pressured rock.
• Overburden and hydrostatic are in the same units (psi or ppg) and on the same depth datum as the pore pressure being compared.

Going Deeper

The extrapolation above the log matters more than its short length suggests. In deep water a long, soft, high-porosity section separates the mudline from the top of the log; its density is lower than the extrapolation of the logged section, and an extrapolation that is too dense gives an overburden that is too high. Practitioners often use a compaction curve, with density rising from near 1.6 g/cm³ at the mudline to the logged values, rather than a constant density. The same overburden feeds the vertical stress in the geomechanical model, so the choice made here is carried to horizontal stress and wellbore stability.

References

1. Terzaghi, K., 1943. Theoretical Soil Mechanics. John Wiley & Sons, New York.
2. Zhang, J., 2011. Pore pressure prediction from well logs: methods, modifications, and new approaches. Earth-Science Reviews, 108(1–2), 50–63.

Python reference implementation

Related methods

• Eaton (Sonic and Resistivity)
• Bowers
• Equivalent Depth
• Normal Compaction Trendlines
• Loading vs Unloading