State of stress

4.6.2.1 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. It can be shown that there is a certain orientation of this volume element, for which only normal stresses exist. These stresses are called the principal stresses, and their orientations are called the principal stress directions.

In rock mechanics most of the stresses are compressive (for example, overburden in the field and confining stress in the laboratory). It is therefore convenient to chose compressive stresses and pore pressures as positive. In order to be consistent with the literature [1,2], this convention is used in this guide.

Effective stress: Schematically, external forces applied on a rock will be of "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. It is denoted with a "dash", and can be expressed according to Terzaghi's relationship as follows:

σ'= σ - po (App. 3-1) where :

σ' = effective stress

σ = the stress corresponding to the external force (total stress) po = the pore pressure.

This concept is very important in rock mechanics because the overall behaviour of rocks is governed by the effective stresses.

4.6.2.2 In situ-stress state

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.

In this report we use the following convention:

Normally stressed : σ1 = overburden, vertical σ2, σ3 horizontal

σ1 > σ2 > σ3

Tectonically stressed areas will typically be zones where there are active faults, salt domes, or zones with compressive regimes (e.g. foothills). In these zones, the principal stress directions may not be vertical or horizontal and their determination, although more important in such a case, may be more difficult than in a normally stressed zone.

Methods exist to determine the state of stress in a formation. The vertical stress (the stress exerted by the overburden) can be obtained by the integration of a density log. Fracture closure data (from formation breakdown tests, mini or micro-frac tests or well stimulation operations) will give the magnitude of the minimum in-situ stress. The intermediate in-situ stress magnitude and orientation can be deduced using a variety of laboratory techniques (e.g. Differential strain analysis or Acoustic velocity anisotropy).

In many cases the in-situ stress is not known. For wells where no formation breakdown data from offset-wells is available, regional stress models and stress trend curves may be used. These curves give the magnitude of the minimum in-situ stress with depth from correlations based on regional data [10,11]. They are representative for certain tectonic conditions only, and may not be generally applicable.

It is recommended that Opcos develop these regional stress models and trend curves as a joint effort between petrophysics, geology and operations departments.

4.6.2.3 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, see also Figure C-4). The pore pressure gradient can be expressed as follows:

PPG =

For drilling operations, and well control specifically, the pore pressure is often expressed as an equivalent mud gradient relative to the derrickfloor:

ρo =

ρo = equivalent mudweight of pore pressure Po = pore pressure

dform = true vertical depth of the formation below derrick floor dFWL = true vertical depth of Free Water Level, below derrick floor

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:

TABLE OF PRESSURE REGIMES TYPES AND PORE PRESSURE GRADIENTS

A discussion of the geological causes of the different pore pressure regimes falls outside the scope of this report; for reviews, see [5,6,7].

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. Various other techniques may give indications of over pressures, (geophysical/geological studies, seismic interpretation studies).

During the drilling of the well, pore pressures can inferred from an analysis of the drilling operation during a reservoir fluid influx (e.g. drilling kick or swabbed kick). In addition, most mudlogging contractors offer pore pressure evaluation services. These are based on an analysis of drilling data, mud properties, gas indications, cuttings and cavings observations. Most of the techniques have been developed for pore pressure evaluation in areas where over pressures are related to undercompaction (Gulf Coast), and may not work in other environments (for example the North Sea).

In reservoirs of sufficient porosity and permeability, pore pressures can be measured with wireline tools (eg. RFT) after the well has been drilled. Evaluation of petrophysical (wireline and MWD) data sometimes allows the determination of the behaviour of pore pressures in shales [8].

4.6.3 Borehole failure - rock mechanics