Basic aspects of rock mechanics

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Borehole pressure required to reach tensile failure depends on:

  • tensile strength of the rock;
  • state of stress in the formation;
  • orientation of the wellbore with respect to the state of stress;
  • shape of the wellbore cross-section;
  • wellbore fluid penetration into the rock;
  • chemical interaction between the wellbore fluids and the rock.

1. State of stress - Definitions, conventions

State of stress:

The state of stress is a description of the internal loads in a solid (for example a rock), generated by external loads acting on the solid. For an elementary volume element with perpendicular planes and a given orientation, the state of stress is described by the normal stresses and shear stresses on each of its planes.

Effective stress:

Schematically, external forces applied on a rock will be "carried" partly by the grains of rock and partly by the pore fluid. The stress induced in the rock grains is called the effective stress.

In situ-stress rate:

The in-situ stresses are the stresses present in an undisturbed virgin formation. They are a result of the combination of the weight of the overburden, the elastic behaviour of the rock and the effect of the tectonic regime. Geological zones can be classified as normally stressed or tectonically stressed. In a normally stressed formation, the major principal stress is usually vertical, and equal to the overburden. The two other principal stresses are then horizontal, and their magnitudes are (slightly) different.

Pore pressure:

The pore pressure is the pressure of the fluid in the pore spaces of the formation. Pore pressures are often expressed as gradients relative to a reference level. In most disciplines in the industry, this is the "Free Water Level" FWL, (i.e. seawater level offshore or ground water level on land). Pore pressure gradients should not be confused with the density gradient of the pore fluid.

Pore pressure regimes are classified by their pore pressure gradients:

  • Sub-normal pressures<0.433 psi/ft(<9.8 kPa/m) Depleted horizons, areas with low water table
  • Hydrostatic pressures0.433-0.465 psi/ft(9.8-10.5 kPa/m) higher values possible Normal depositional environments
  • Abnormal pressures>0.465 psi/ft(>10.5 kPa/m) Hydrocarbon columns, tectonic activity, under compaction, salt domes, uplifting of sediments

Especially in areas where over pressures are expected, an extra effort is required to predict an accurate pore pressure profile. Information on pore pressures may be derived from offset wells and from regional geological models.

During the drilling of the well, pore pressures can be inferred from:

  • reservoir fluid influx (e.g. drilling kick or swabbed kick)
  • mudlogging contractors offering pore pressure evaluation services.
  • In reservoirs of sufficient porosity and permeability, pore pressures can be measured with wireline tools (e.g. RFT)
  • Petrophysical (wireline and MWD) data sometimes allows the determination of the behaviour of pore pressures in shales.

2. Borehole failure - rock mechanics

Rock tensile strength

Borehole failure is usually governed by tensile failure. Tensile failure is defined to occur when the wellbore fluid pressure is such that the minimum effective stress at the borehole wall reaches a negative value, equal to the rock tensile strength (T).

Although intact rocks do have a tensile strength (tensile stress needed to fail a rock sample), this strength is generally small. In addition, any small defect in the rock structure (e.g. a natural fracture) considerably lowers this value.

Theoretical relationship: wellbore strength - state of stress

If a perfectly cylindrical borehole is drilled in a normally stressed formation without fractures, and a perfect mud cake prevents flow of fluids into the formation, it is possible to calculate the FBP for a few simple cases.

It should be realised that the FBP is strongly dependent of the condition of the borehole and the mud cake. Borehole rugosity or the presence of natural or drilling induced fractures will significantly lower the FBP.

Fracture propagation

If the wellbore pressure exceeds the FBP, a fracture is initiated from the borehole wall, in a direction determined by the orientation of the in-situ stresses in the near wellbore region. After the fracture propagates away from the wellbore, it will always be oriented in a plane perpendicular to the minimum stress.

Wellbore strength in fractured formation

A fracture in the borehole wall usually reduces the strength of the wellbore. If the fracture is in communication with the wellbore, it will reopen when the wellbore pressure exceeds the stress normal to the fracture which is often the minimum in-situ principal stress: s3. It will not start propagating until the pressure exceeds the ISIP. For practical purposes, to avoid opening the fracture at all, it is recommended to limit the maximum pressure in a fractured borehole to the FCP.

Theoretically, for a vertical well in a tectonically relaxed area, the difference between the FBP and the FCP is equal to the minimum effective principal stress. For a deviated well, or a well in a tectonically stressed area, the difference will be even less.

3. Other effects

Healing

It has been observed that, with time, the strength of some formations returns after the initial reduction in strength caused by formation breakdown. In some cases the strength of the formation returns completely, in others only partially. This process has been called "clay healing", because it only occurs in shales and not in carbonates.

There are indications that it only occurs with water-based muds, and not with oil-based muds. The phenomenon can not be relied on, but justifies a repeat Leak-off test some time after formation breakdown has occurred.

Borehole fluid penetration

When borehole fluid does invade the formation pore space, the near wellbore effective stresses will change as a consequence of pore fluid pressure modification near the wellbore. This phenomenon will reduce the strength of a wellbore. The magnitude of the reduction in strength depends on the quality of the mudcake, the permeability and the poro-elastic properties of the formation. This mechanism is thought to be responsible for time dependent shale instability problems. Because of capillary pressures, penetration of oil-based muds (OBM) is less than of water-based muds (WBM). This explains the better performance of OBM. Improved understanding of these phenomena is the subject of ongoing research.

Depletion

During reservoir depletion the in-situ stresses change. The total overburden stress will remain constant, which means that the effective vertical stress increases (see Eq. 6). The two horizontal stresses will reduce, and the effective horizontal stresses increase. This will reduce the formation strength. It may have additional consequences like the initiation of shear fractures, sand failure or compaction.

Borehole shape

Formulas for calculating wellbore strength are available for circular boreholes. If the borehole is not round, the borehole possibly will fail at a lower pressure. No equations exist for out-of-shape boreholes (except for an elliptical shape). For such cases, the use of numerical programs is required.

Chemical interaction

Chemical interaction between formation rock and the wellbore fluid (e.g. a sensitive shale and a water based mud) will also alter the conditions under which breakdown occurs. However, the mechanisms and parameters affecting those mechanisms are still under investigation.

 

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