Pore pressure is not hydrostatic everywhere. In fact, many times pore pressure is an unknown! In a system of “connected pores” under hydrostatic equilibrium (water does not move), pore pressure increases hydrostatically. Non-hydrostatic variations of pore pressure are usually located adjacent to low permeability barriers (e.g., shale formations) that do not allow pore pressure to achieve hydrostatic equilibrium fast enough compared to the rate of sedimentation and pore pressure relief. Hence, pore pressure gets locked-in. In the example in Figure 2.9, pore pressure is hydrostatic until ft. Overpressure develops from ft to ft (likely due to a low permeability mudrock). Pore pressure below ft is quite different from hydrostatic!
A convenient parameter to relate pore pressure and total vertical stress is the dimensionless overpressure parameter :
In stationary conditions cannot be larger than , hence, . In onshore conditions means hydrostatic pore pressure ( in hydrostatic conditions offshore, why?). Reservoir overpressure is good for hydrocarbon recovery (more energy to flow to the wellbore), however, it may cause geomechanical challenges for drilling (kicks). Parameter means little effective stress. We will see later that rocks have effective stress-dependent strength. Hence, overpressure leads to weak rocks, especially if they are not well cemented, difficult to drill.
There are several mechanisms that may contribute to overpressure . First, hydrocarbon accumulations create overpressure due to buoyancy. Overpressure is proportional to hydrocarbon column height and difference in mass density of pore fluids
Second, changes in temperature cause fluids to dilate. If the fluids cannot escape quickly enough, then pore pressure increases. Third, clay diagenesis can expell water molecules. For example, when montmorillonite converts to illite at high pressure and temperature, previously bound water molecules get “added” to the pore space. Under constant pore volume conditions, such addition will result in increases of pore pressure. Fourth, hydrocarbon generation also induces overpressure. With hydrocarbon generation, the original organic compounds transform in another phase which occupies more volume at the same pressure conditions. Overpressure in organic-rich shales is a good indicator of hydrocarbon presence.
Changes of vertical and horizontal stresses can induce pore pressure changes. Pore pressure increases when a rock/sediment is compressed (such that the pore volume decreases) under conditions in which the fluid cannot escape quickly enough. Figure 2.12 shows a schematic representation of this concept.
Imagine now a sediment layer saturated with water. There is an impervious layer at the bottom. Water cannot escape from the sides either. Water can only escape from the top.
An overburden is placed quickly on the sediment so that it compacts an amount . Initially, the pore pressure increases everywhere the same amount. The pore pressure decreases preferentially at the top boundary (where it can flow) and the rate of pore pressure change is proportional to the hydraulic diffusivity parameter
The solution of the partial differential equation above give us a characteristic time for which of the pore pressure is relieved,
EXAMPLE 2.5: Calculate the characteristic time of pore pressure diffusion for a 100 m thick sediment with top drainage considering
(a) a sand with 100 mD and 1 GPa, and
(b) a mudrock with 100 nD and 1 GPa.
The water viscosity is 1 mPa s.
(a) Sand: 1.1 day.
(b) Mudrock: 3000 years.
The example in Figure 2.16 is a measurement of pore pressure that utilizes measurements of porosity in mudrocks (Track 3) to predict overpressure (Track 4). The concept is simple: the porosity of clay-rich rock decreases with effective stress (Figure 2.15). Let us assume the following equation for such dependence
Under hydrostatic pore pressure conditions, vertical effective stress will always increase with depth. However, in the presence of overpressure, effective stress may increase less steeply or even decrease with depth. Hence, mudrocks with porosity higher than the porosity expected at that depth (in hydrostatic conditions) indicate overpressured sediment intervals (Figure 2.17).
Figure 2.18 shows maps of pressure gradients in the Gulf of Mexico. Data from offshore locations show that overpressure (gradient 0.44 psi/ft ) starts to develop at 2 to 3 km of depth below seafloor.
EXAMPLE 2.6: Calculate the pore pressure and overpressure parameter in a muddy sediment located offshore with porosity . The total depth is 2000 m and the water depth is 500 m (assume a lithostatic gradient of 22 MPa/km below the seafloor). Laboratory tests indicate a compaction curve with parameters MPa and . How much higher than expected hydrostatic value is the pore pressure?
First, calculate total vertical stress:
|MPa/km km MPa/km km MPa|
Second, calculate effective vertical stress from using the measured porosity and Equation 2.19:
Third, calculate pore pressure from , so
|MPa MPa MPa|
Hence, the overpressure parameter is
Opposite to overpressure, “underpressure” occurs when pore pressure is lower than hydrostatic. The most common reason of underpressure is reservoir depletion. In compartmentalized reservoirs with poor water recharge drive, pore pressure may stay low for long periods of time. Reservoir depletion usually brings along lower total horizontal stresses which lower the fracture gradient and make drilling problematic because of decreased difficulty to create open-mode fractures.