SPE-140119-PA_Joint Stiffness and Deformation Behaviour of Discontinuous Rock

78 Journal of Canadian Petroleum T echnology Introduction Mechanical behaviour of the jointed rock in naturally fractured reservoirs or in rock bodies stimulated by hydraulic fracturing (i.e., an artificially fractured well in a tight gas reservoir) is highly influenced by the presence of joints. Because joints are the main flow conduit in jointed rocks and single-joint permeability is a quadratic function of its aperture size, it is crucial to investigate the variations in a joint aperture size under different loading conditions. Change in the pore pressure is the main source of the load acting on a jointed rock in fractured reservoirs. The question of how aperture size of the joints varies with the applied load is an- swered by investigating the stress-deformation of the jointed rock. Increasing in pore pressure usually results in the opening of fracture aperture and enhancement in the fractured block permeability and vice versa. Mechanical behaviour of a joint is characterized by its normal- shear mechanical deformation and is defined in the form of a joint constitutive model. Here we will firs t review the literature related to normal and shear rock joint deformations. Different techniques by which the composite system of rock and joints (jointed rock) are mechanically modelled will be reviewed in the next section. Normal deformation of a joint has been the subject of many studies in the early investigations on jointed rock mechanical behaviour. It w as first f ormulated by Goodman (1) and later by Swan (2) in an empirical approach by power-law mathematical functions. Afterward, based on numerous experimental results, Bandis et al. (3) proposed an empirical hyperbolic model for normal deformation of a rock joint. This model is similar, in both formulation approach a nd funct ional form, to Goodman’s model; howe ver, each fits best their own experimental results. It is obvious that an empirical model cannot provide a reasonable simulation of joint behaviour under all laboratory testing conditions. A general exponential function was later suggested by Malama and Kulatilake (4) . The model proved to be the best fit for their experimental data in comparison wit h other empirical models. However, other models only require two experimental data points to be defined, whereas the general exponential function requires at least three experimental data points. Some theoretical models have also been developed using theories of different branches of solid mechanics; for ex- ample, the theor y of plasticity, damage mechanics and Her tz’ s con- tact theory of elasticity [Plesha (5) , Amadei and Saeb (6) and Jing (7) ]. This approach suffers from the limitation of the existing mathematical theory of classical solid mechanics, which today cannot conveniently represent all aspects of rock joint behaviour. Hence, both appr oaches r ely on the experi mental data and are valid only under the certain experimental conditions under which they can fit the experiments. To model the shear behaviour of a rock joint, one needs to know the peak shear stress and the respective shear displacement. Patton (8) , Ladanyi and Archambault (9) and Barton (10) were among the first to develop a rock joint’s shear strength criterion. Patton conducted a series of tests to study regular tooth-shaped artifi- cial joints under constant-normal load. In his study he showed that the shear strength of a saw-tooth joint is controlled by the effec- tive friction angle, summation of basic joint friction angle and the angle asperities’ build with fracture plane or dilation angle. Pat- ton’s finding is only valid at low-normal stresses where no asperities are worn off. Jaeger (11) proposed a nonlinear failure criterion instead of a bilinear form of Patton’s. At higher-normal stress his criterion approaches Patton’s model as shown in Fig. 1. An empirical s hear strength criterion was proposed by Barton (10) , which represents a continuous failure envelope from low- to high-normal stresses. This criterion is advantageous because it is defined in Joint Stiffness and Deformation Behaviour of Discontinuous Rock M. Nassir, A. Settari, and R. Wan, University of Calgary Abstract Some rock masses are characterized by joints, fractures and other planes of weakness which reduce the strength and deformation properties of rock structure. Under different loading conditions, joints with weaker than normal and shear deformation strength undergo a relatively higher strain than intact rock. Because permeability of jointed rock masses in fractured reservoirs is a strong function of joint aperture size, one may expect a major change in the permeability when sub- jected to confining load variation. Therefore, it is important to establish the relation between the stress-strain of the jointed rock mass and the reser voir permeability. This relation is par- ticularly important to model hydraulic fracturing and produc- tivity decline in tight gas wells. In this paper, a new relation is proposed to model prepeak shear stiffness of the joint based on the conven tional joint sur- face parameters and the confining load. Furthermore, constitutive matrices for evaluating deformation behaviour of a single-joint and regularly jointed rock are presented as the results of an analytical study. Based on the concept of joint stiffness, an equivalent stiffness for regularly jointed rock masses was derived, assuming that the deformation of the jointed rock mass equals the sum of the deformation of the rock ma- trix and the joints. Finite element technique is used to numer- ically model the deformation behaviour of the jointed rock under various loading conditions. The applicability of the constitutive model to represent jointed rock mass was con- firmed from comparison of the numerical results with some of the existing experimental data. The model presented here will be the key element for inte- grated geomechanical modelling of tight gas wells, naturally fracture reservoirs and other fracturing processes in stress- sensitive reservoirs.

SPE-140119-PA_Joint Stiffness and Deformation Behaviour of Discontinuous Rock

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