J.-C. Roegiers

Evaluation of mechanical rock properties using a Schmidt Hammer

The Schmidt Hammer was developed in 1948 for non-destructive testing of concrete hardness [1], and was later used to estimate rock strength [2,3]. It consists of a spring-loaded mass that is released against a plunger when the hammer is pressed onto a hard surface. The plunger impacts the surface and the mass recoils; the rebound value of the mass is measured either by a sliding pointer or electronically. Hammer rebound readings are considered consistent and reproducible [4‐6]. Such fast, non-destructive and in situ evaluations of rock mechanical parameters reduce the expenses for sample collection and laboratory testing. Consequently, the mechanical parameters can be determined in dense arrays of field measurements that reflect the real inherent inhomogeneity of rock masses [7]. Schmidt Hammers were used to estimate the strength of concrete and rocks [2,8‐11] via empirical correlations between rebound readings and compressive strength determined from standard tests [2,8,11]. This Technical Note extends these correlations, and we present new correlations between rebound readings of seven rock types and their measured laboratory values of Young’s modulus, uniaxial compressive strength and density. The studied rocks include soft chalk, limestones, sandstone and stiA igneous rocks, covering a wide range of rock elasticity. These new correlations have already been used for a detailed field study of rock damage [7].

Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs

This paper presents an array of deformation-dependent flow models of various porosities and permeabilities relevant to the characterization of naturally fractured reservoirs. A unified multiporosity multipermeability formulation is proposed as a generalization of the porosity- or permeability-oriented models of specific degree. Some new relationships are identified in the parametric investigation for both single-porosity and dual-porosity models. A formula is derived to express Skemptons constant B by Biots coefficient H and relative compressibility ϕ*. It is found that the recovery of the original expression for Skemptons constant B is largely dependent on the choice of ϕ*, representing relative compressibility. The dual-porosity/dual-permeability model is evaluated through an alternative finite element approximation. The deformation-dependent fracture flow mechanism is introduced where the rock matrix possesses low permeability and fracture flow is dominant. A preliminary study of the reservoir simulation identifies the strong coupling between the fluid flow and solid deformation.

Fracture toughness of a soft sandstone

Abstract Fracture toughness of a rock/material is important in the design of rock drilling/boring equipment, rock bursting, prediction of rock drilling forces, hydraulic fracturing, wellbore stability and stability of jointed rock masses. A series of fracture toughness tests under mode-I, mode-II and mixed-mode (I–II) loading conditions were conducted on straight-edge notch Brazilian disk (SENBD) specimens in an attempt to develop an empirical failure envelope under both tension-shear and compression-shear conditions. This series of tests is the first of its kind on a naturally weakly-cemented Antler sandstone. Even though there have been published data on artificially cemented sandstones, there are no data on mixed-mode fracture toughness of such soft formations. The SENBD specimen configuration used herein provides consistent failure patterns and development of a failure envelope in the compression-shear zone, as well. Microscopic studies using thin sections of tested and untested specimens were carried out to study the fracture propagation at micro-level.

Dual-porosity poroelastic analyses of wellbore stability

This paper presents a numerical solution of dual-porosity poroelastic formulations that couple solid deformations with fluid flow in both matrix and fracture systems of naturally fractured reservoirs. The finite element numerical method was applied to solve the inclined wellbore problem in which mud weight was considered for both permeable and impermeable boundary conditions. Failure criteria relevant to tensile, collapse, and shear failure modes were introduced into the numerical model and resulting failure areas around boreholes were subsequently defined. Several related applications, including the stability of inclined and horizontal wellbores under various in situ stress regimes, were evaluated. Upper and lower mud weight bounds and the most stable borehole orientations were determined. The best trajectory selections for horizontal boreholes were also investigated.

Applications of time-dependent pseudo-3D stress analysis in evaluating wellbore stability

Abstract Recent studies have shown that the coupled fluid-deformation effects may significantly influence stress and pore pressure distributions around the wellbore in fluid saturated porous media, as well as its stability. Therefore, the poroelastic effect must be considered in stability analysis of inclined wellbores, especially when time-dependent/delayed borehole failure is considered. However, a complicated numerical technique is required to evaluate stress and pore pressure distributions around the wellbore based on the poroelastic model. It may not be convenient to perform the aforementioned analysis of the deviated wellbore in industry applications without a computer aided engineering (CAE) software. A window based software, PBORE-3D, has been developed recently for poroelastic analysis of inclined boreholes. The applications and capabilities of PBORE-3D are described in the present paper. The poroelastic effects on the pore pressure and the stress concentration around the wellbore, and the wellbore stability, are analyzed using this friendly CAE software.

Fluid flow and heat flow in deformable fractured porous media

Abstract Analtyical solutions based on a porothermomechanical formulation for double-porosity media have been presented. Complete coupling is ensured among fluid flow, heat flow, and solid deformation in the conservation of momentum. Partial coupling between fluid flow and deformation is justified for the problems solved in infinite media or media with a relatively distant boundary. Full decoupling in heat flow is implemented for the convenience of obtaining the analytical solutions sequentially and is justifiable for the temperature distribution anywhere but in close proximity of the loading. This coupling can be readily restored through numerical means. In comparison with previous publications, the model presented provides more realistic characterization of reservoir storage changes in the fluid flow. The double-porosity behaviors of fractured porous media for both fluid flow and heat flow have been identified. The corresponding effect due to thermal and fluid pressure changes on solid deformation, particularly in the vicinity of the flow and/or heat source(s), has been emphasized. The significant impact of thermal loading and reservoir mechanical properties on the reservoir porothermomechanical environment has been demonstrated.

Influence of anisotropies in borehole stability

Abstract This paper discusses an anisotropic model for assessing the mechanical stability of a deep borehole subjected to an internal wellbore pressure and a far-field stress tensor. The model consists of a three-dimensional stress analysis around an inclined borehole combined with a generalized three-dimensional anisotropic strength criterion for assessing shear fracturing. Parametric studies indicated that the stability of a wellbore is influenced significantly by rock anisotropy, rock strength anisotropy, and in-situ stress differentials when it is highly inclined and oriented in the direction parallel to the maximum horizontal in-situ stress. The influence of anisotropies is more pronounced on passive shear failure caused by wellbore pressurization.

Poroviscoelastic analysis of borehole and cylinder problems

SummaryThis paper addresses the phenomena of mechanical creep and deformation in rock formations, coupled with the hydraulic effects of fluid flow. The theory is based on Biots poroelasticity, generalized to encompass viscoelastic effects through the correspondence principle. Based on the resultant poroviscoelastic theory, stress and deformation analyses are performed. The interactions between the fluid pore pressure diffusion and the elastic/viscoelastic rock matrix deformation are illustrated via two important examples. First, the problem of a borehole subject to a non-hydrostatic stress state, but deforming under plane strain condition, is examined. Second, a cylinder under generalized plane strain conditions is solved. Three rocks, Berea Sandstone, Danian Chalk, and a deep water Gulf of Mexico Shale, covering a wide range of permeabilities, are considered. The significance of poro-and viscoelastic time-dependent effects is discussed.

Modeling of naturally fractured reservoirs using deformation dependent flow mechanism

Abstract As special cases of a multi-porosity/multi-permeability formulation based on the mixture theory, an array of deformation-dependent flow models of various porosities and permeabilities relevant to the characterization of naturally fractured reservoirs is presented. Some key relationships are identified in the parametric investigation. A finite element discretization is developed for the multi-porosity/multi-permeability media. A case study is focused on a reservoir simulation using dual-porosity/dual-permeability model. The preliminary study identifies the strong coupling between fluid flow and solid deformations. The effect of this coupling is also controlled by the constitutive properties of the formation.

FINITE ELEMENT ANALYSES OF ANISOTROPIC POROELASTICITY: A GENERALIZED MANDEL'S PROBLEM AND AN INCLINED BOREHOLE PROBLEM

The finite element equations for non-linear, anisotropic poroelasticity are cast in the form of measurable engineering constants. Two problems of importance to the rock and petroleum industry are analysed by the FEM. First, the classical Mandels problem with an extension to transversely isotropic case is investigated. Second, the problem of an inclined borehole is explored. In particular, the effect of material anisotropy on stress concentration near the wall with implication to borehole instability is examined in detail.