# Pore pressure analysis

The field of pore pressure analysis is the study of how pressures within rock pores vary with depth inside the subsurface. In the field of exploration, pore pressure holds particular significance for drilling and discovery purposes. Modern drilling teams often need a subsurface pore pressure map in order to drill safely and efficiently. Anomalous pressures, especially overpressures, can pose a large threat to both life and the drilling prospect. Hazards like well blowouts, pressure kicks, and fluid influx are dangerous risks which can be avoided by studying pore pressure geometries prior to drilling[1].

Besides safety concerns, prior knowledge of the subsurface pressure layout can allow for optimization of the drilling and extraction process to save time and resources. High variability in pressures can cause high instability inside of the borehole, leading to poorer quality measurements if well logs are being recorded while drilling.

For reservoir discovery, abnormal pressures can also provide additional evidence for hydrocarbons. For example, determining a high pressure zone below a structural trap could increase confidence in a certain prospect.

## Units of Measurement

Pore pressures can be expressed as a gradient, either psi/ft or Pa/m. However, in the field of pore pressure analysis, pressures are often colloquially called equivalent mud weight or mud weight for short, which is defined as lbs/gal. The term was originally coined by the drillers, who need to pump mud into the well to counteract pressures. For the drillers, being able to relate mud weight with subsurface pressures is much more convenient than using psi units. Eventually, the term mud weight gained traction and is commonly observed in pore pressure analysis. But lbs/gal is not a proper representation of pressure change with depth, so geophysicists may prefer to use psi/ft or some other pressure unit per unit depth.

## Theory

There are several key types of pressures involved in pore pressure analysis: hydrostatic pressure, overburden pressure, fracture pressure, and pore pressure. These pressures will be expressed as the gradient of pressure change with unit depth [2].

Depth vs. Pressure plot depicting the relationship between various types of pressures
Depth vs. Pressure Gradient plot depicting the relationship between various types of pressures. Black curve is the overburden gradient.

### Hydrostatic Pressure

Hydrostatic pressure, alternatively called normal pressure, is represented as the pressure exerted by a vertical column of water. This column of water must be connected to the surface to be considered hydrostatic. This can be simply expressed as:

${\displaystyle P_{n}=pgh}$

where:

${\displaystyle P_{n}}$ = hydrostatic pressure
${\displaystyle p}$ = density of water
${\displaystyle g}$ = force of gravity
${\displaystyle h}$ = height of the water column

A typical hydrostatic pressure gradient is around 0.465 psi/ft. In the Depth vs. Pressure Gradient plot, the hydrostatic gradient is assumed to be constant and therefore it is a vertical line.

### Overburden Pressure

Overburden pressure is the pressure due to the sum of all overlying rocks and fluids. This can be expressed as:

${\displaystyle P(z)=g\int _{0}^{z}p(z)dz}$

where:

${\displaystyle P(z)}$ = pressure as a function of depth
${\displaystyle g}$ = force of gravity
${\displaystyle z}$ = depth
${\displaystyle p(z)}$ = density as a function of depth

### Pore Pressure

Pore pressure is the pressure exerted by the fluids within a rock’s pore space. Pore pressure can be calculated via a variety of methods from either well logs or seismic velocities. The gradient is called PPG or pore pressure gradient. Pore pressure gradient can be determined either from well logs (Resistivity log and Sonic log) or from seismic interval velocity.

There are several pore pressure techniques already in use, but one of the most popular methods was designed by Ben Eaton. These pore pressure equations can be converted from using either well logs or interval velocity as input.

For sonic log data, Eaton’s method is expressed as[3][4]:

${\displaystyle PPG=OBG-(OBG-HG)\times ({\dfrac {\Delta t_{norm}}{\Delta t_{obs}}})^{X}}$

where:

${\displaystyle PPG}$ = pore pressure gradient (psi/ft)
${\displaystyle OBG}$ = overburden gradient (psi/ft)
${\displaystyle HG}$ = hydrostatic gradient (psi/ft)
${\displaystyle \Delta _{normal}}$ = normal sonic log value (us/ft)
${\displaystyle \Delta _{obs}}$ = observed sonic log value (us/ft)
${\displaystyle X}$ = exponent value which is dependent on formation properties

For seismic velocity data, Eaton's method is expressed as [1]:

${\displaystyle PPG=OBG-(OBG-HG)\times ({\dfrac {IV_{obs}}{IV_{nor}}})^{X}}$

where:

${\displaystyle PPG}$ = pore pressure gradient (psi/ft)
${\displaystyle OBG}$ = overburden gradient (psi/ft)
${\displaystyle HG}$ = hydrostatic gradient (psi/ft)
${\displaystyle IV_{obs}}$ = observed interval velocity (ft/s)
${\displaystyle IV_{nor}}$ = interval velocity from normal compaction trend (ft/s)
${\displaystyle X}$ = exponent value which is dependent on formation properties

### Fracture Pressure

Fracture pressure is the pressure limit at which the internal pore pressure causes fractures and cracks to split open the rock. Fracture pressure is a complex property which depends on many factors including overburden pressure and pore pressure. Other factors include rock properties and anisotropy. The gradient is called FG or fracture gradient.

### Overpressure and Effective Stress

From the above pressures we can derive overpressure and effective stress. Overpressure is defined as the difference between the internal fluid pressures of a rock's pore space and the hydrostatic or normal pressure.

${\displaystyle {\text{Overpressure}}={\text{Pore pressure}}-{\text{Hydrostatic pressure}}}$

High overpressures can be particularly dangerous and is one of the reasons why pore pressure analysis is necessary in order to protect the well-being of bystanders and to avoid drilling catastrophes.

The effective stress is defined as the difference between the pressure caused by the overburden material and the internal fluid pressures of a rock's pore space.

${\displaystyle {\text{Effective stress}}={\text{Overburden pressure}}-{\text{Pore pressure}}}$

## Application

Note the relationship between the various pressures illustrated in the Depth vs. Pressure and Depth vs. Pressure Gradient plots. Drillers tend to prefer using the Depth vs. Pressure Gradient plot. The reason they do so can be explained by the mud weight curve. In this orientation, it is much easier for drillers to interpret and apply the data to their physical task. The ultimate goal is to keep the mud weight appropriately between the pore pressure and fracture gradient curves. Straying too close to the fracture gradient curve will increase the risk of large fractures and mud loss. Stray too close to the pore pressure gradient curve and the possibility of blowouts increases along with the risk of higher instability inside the borehole. Higher overpressures push the two gradient curves closer, making the job of balancing the mud weight that much more difficult.

Being able to determine the danger zone from a pore pressure map is a very valuable application of pore pressure analysis. The added advantage of pore pressure analysis is how it can accept seismic velocities as an input. This allows for the generation of large scale maps depicting subsurface pore pressure geometries.

## References

1. Zhang, Jincai. 2011. “Pore Pressure Prediction from Well Logs: Methods, Modifications, and New Approaches.” Earth-Science Reviews 108 (1–2):50–63. https://doi.org/10.1016/j.earscirev.2011.06.001.
2. Bruce, Bob, and Glenn Bowers. 2002. “Pore Pressure Terminology.” The Leading Edge 21 (2): 170–173.
3. van Ruth, P., and R. Hillis. 2000. "Estimating Pore Pressure In The Cooper Basin, South Australia: Sonic Log Method In An Uplifted Basin". Exploration Geophysics 31 (2): 441. doi:10.1071/eg00441.
4. Eaton, Ben A. 1975. “The Equation for Geopressure Prediction from Well Logs.” In . Society of Petroleum Engineers. https://doi.org/10.2118/5544-MS.