Non-linear behaviour for naturally fractured carbonates and frac-stimulated gas-shales

Gas-shales and naturally fractured reservoirs usually produce from several kilometers depth, with fracing-stimulation and eventual water-drive respectively. Due to porosity, the matrix is generally weaker than is typical for basement rocks. The potential pore pressure reduction of tens of MPa during the early life of the fields, may therefore be a significant proportion of the strength of the matrix. Inevitable non-linear rock strength behaviour for the matrix should not then be ignored. It is therefore unrealistic to utilize a linear Mohr-Coulomb strength criterion as so frequently seen. The joints or natural fractures in the shales and carbonates, which are so important for production, will have producing fracture sets with different roughness and aperture, and few of them are planar enough to follow the frequently used linear Mohr-Coulomb behaviour. Non-linearity especially applies to the favourable shear strength-dilation-permeability coupling which is relevant for both NFR and gas-shales, and to the less desirable stress-closure-permeability coupling of a stress-sensitive reservoir. Non-linear constitutive modelling, partly based on the joint- or fracture-roughness coefficient (JRC) used widely in rock mechanics, also applies to the conversion from hydraulically interpreted theoretical smooth-wall apertures (e) to the larger and non-planar-non-smooth-wall physical apertures (E) through which the oil or gas actually flows to the wells. Simple index tests which can also be applied on joints or fractures recovered in occasional and inevitably expensive core, and which can also be estimated when mapping fractured pavement analogues, have been available in rock mechanics for several decades. They were already incorporated in coupled distinct element (jointed) non-linear modelling routines in 1985. However, their implementation in petroleum industry geomechanics seems to be very rare judging by numerous workshops attended in the last seven to eight years on both sides of the Atlantic. Application of non-linear (non Mohr-Coulomb) rock mechanics, using recovered core from Ekofisk in 1986-1987 in order to model fracture shear-dilation coupling with simplified E and e tracking during compaction, may be the earliest example.