Younane N. Abousleiman

Merging sequence stratigraphy and geomechanics for unconventional gas shales

The recent revelation of vast global quantities of potentially gas- (and oil-) productive shales has paved the way for rapid advancements in understanding their geological properties, many of which affect their geomechanical properties, and ultimately reservoir operations and performance. Because of shales unique and very intricate geological, physical and mechanical properties at all scales (from nano- to macro-scale (Abousleiman et al., 2010) compared with sandstones and carbonates, the ad-jective “unconventional” has often been applied to their characterization. Although many shale characteristics are different than those of sandstones and carbonates, and require new technologies to measure them, other characteristics, mentioned below, are similar. As such, customized conventional methodologies and concepts can be applied to exploration and production of shale gas (and oil).

Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium

A porothermoelastic solution of the general problem of the inclined borehole in a transversely isotropic porous material is presented herein and compared with the isotropic porothermoelastic solution. The governing equations are outlined for the case of general anisotropy and specialized for a transversely isotropic poroelastic material under nonhvdrostatic and nonisothermal in situ conditions. A superposition scheme is employed to obtain the analytical solutions within the isotropic and transversely isotropic poromechanics theory. The borehole generator is assumed to coincide with the material axis of symmetry, in the case of transverse isotropy, yet subjected to a three-dimensional state of stress. A systematic analysis has been carried out to evaluate the effect of the anisotropy of the poromechanical material parameters as well as the thermal material properties on stress and pore pressure distributions and the potential impact on the overall stability of deep wellbore drilling.

The nanogranular acoustic signature of shale

A multiscale, micromechanics model has been developed for the prediction of anisotropic acoustic properties of shale. The model is based on the recently identified nanogranular mechanical response of shale through indentation experiments. It recognizes the dominant role of the anisotropic elastic properties of compacted clay in the anisotropic elasticity of shale at different length scales compared to contributions of shape and orientation of particles. Following a thorough validation at multiple length scales using mineral elasticity data, nanoindentation experiment results, and ultrasonic pulse velocity tests, the model predictions compare adequately with measurements on kerogen-free and kerogen-rich shales and shaley sandstones. The acoustic signature of shale thus is found to be controlled by two volumetric parameters that synthesize the porosity and mineralogy information: the clay-packing density and the silt inclusion volume fraction. Through a series of dimensionless isoparametric plots, the micromechanics model predicts trends of increasing elastic anisotropy with increasing clay-packing density (or decreasing porosity), which correspond to the intrinsic mechanical response of unfractured shale, and quantifies the stiffness reduction induced by the presence of kerogen.

Pore-to-regional-scale Integrated Characterization Workflow for Unconventional Gas Shales

Based on recent studies of Barnett and Woodford gas shales in Texas and Oklahoma, a systematic characterization workflow has been developed that incorporates lithostratigraphy and sequence stratigraphy, geochemistry, petrophysics, geomechanics, well log, and three-dimensional (3-D) seismic analysis. The workflow encompasses a variety of analytical techniques at a variety of geologic scales. It is designed as an aid in identifying the potentially best reservoir, source, and seal facies for targeted horizontal drilling. Not all of the techniques discussed in this chapter have yet been perfected, and cautionary notes are provided where appropriate. Rock characterization includes (1) lithofacies identification from core based on fabric and mineralogic analyses (and chemical if possible); (2) scanning electron microscopy to identify nanofabric and microfabric, potential gas migration pathways, and porosity types/distribution; (3) determination of lithofacies stacking patterns; (4) geochemical analysis for source rock potential and for paleoenvironmental indicators; and (5) geomechanical properties for determining the fracture potential of lithofacies. Well-log characterization includes (1) core-to-log calibration that is particularly critical with these finely laminated rocks; (2) calibration of lithofacies and lithofacies stacking patterns to well-log motifs (referred to as gamma-ray patterns or GRPs in this chapter); (3) identification and regional to local mapping of lithofacies and GRPs from uncored vertical wells; (4) relating lithofacies to petrophysical, geochemical, and geomechanical properties and mapping these properties. Three-dimensional seismic characterization includes (1) structural and stratigraphic mapping using seismic attributes, (2) calibrating seismic characteristics to lithofacies and GRPs for seismic mapping purposes, and (3) determining and mapping petrophysical properties using seismic inversion modeling. Integrating these techniques into a 3-D geocellular model allows for documenting and understanding the fine-scale stratigraphy of shales and provides an aid to improved horizontal well placement. Although the workflow presented in this chapter was developed using only two productive gas shales, we consider it to be more generically applicable.

Generalized Biot's theory and Mandel's problem of multiple-porosity and multiple-permeability poroelasticity

This paper finds in Biots theory of poroelasticity a complete and consistent extension to the general case of multiple-porosity and multiple-permeability, fluid-saturated, and linearly elastic media. The constitutive stress-strain relations for a medium identified with this extension are presented, and the coefficient matrix of mechanical properties associated with these relations is derived from the corresponding intrinsic properties of its single-porosity constituents. The closed form analytical solution to Mandels problem is upgraded to the case being considered in this study. This problem addresses the transient consolidation of a porous elastic slab of rectangular geometry, when confined from the top and bottom. A numerical example solution for shale with laboratory setup of Mandels problem is provided. Results are compared for the cases of single-, double-, and triple-porosity solutions.

Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium

The two-dimensional Mandel-type problem geometry is well-known to bio-geomechanicians for testing rocks, cartilages, and bones with solutions in Cartesian coordinates for rectangular specimens or polar coordinates for cylindrical and disk samples. To date, all existing solutions are only applicable to single-porosity and single-permeability models, which could fall short when the porous material exhibits multi-porosity and/or multipermeability characteristics, such as secondary porosity or fracture. This paper extends the plane strain and axisymmetric Mandel-type solutions from single-to dual-porosity and dual-permeability poromechanics. The solutions are presented in explicit analytical forms and account for arbitrary time-dependent external loading conditions, e.g., cyclic and ramping. The derived analytical solutions and results exhibit general behaviors characterized by two time scales. Stresses, pore pressures, and displacements are plotted for various time scale ratios to illustrate the interplaying effects of permeability and stiffness contrast of both porous regions, in addition to the interporosity exchange, on the overall responses of the system. Also, examples with realistic loading conditions for laboratory testing or field simulation such as cyclic and ramping are provided to demonstrate the engineering applications of the presented dual-poroelastic formulation and solutions.

Boundary element solution for steady and unsteady Stokes flow

Abstract This paper represents a boundary element formulation for steady and unsteady slow viscous flow of incompressible Newtonian fluid. The steady flow completely ignores the inertial effect, while the unsteady flow retains the local acceleration term. The boundary integral equations and fundamental solutions are presented in two and three dimensions. A Laplace transform and numerical inversion approach is used for the unsteady problem. Two-dimensional internal flow problems are solved to illustrate the capability of the developed algorithms.

Geomechanics field characterization of woodford Shale and Barnett Shale with advanced logging tools and nano-indentation on drill cuttings

The Woodford Shale and Barnett Shale have emerged as prolific gas plays in the US midcontinent. However, the intrinsically low permeability of these gas shales hinders profitable pro-duction unless horizontal well drilling and multistage hydraulic fracturing are employed. The success of these operations depends on accurate de-terminations of the anisotropic elastic and poroelastic properties of these shale formations.

Correspondence principle between anisotropic poroviscoelasticity and poroelasticity using micromechanics and application to compression of orthotropic rectangular strips

In this paper, the correspondence principle between poroviscoelasticity and poroelasticity in both time domain and Laplace transform domain is established for the general case of matrix anisotropy as well as solid constituent anisotropy using micromechanics considerations. Using this correspondence principle, any constitutive relation or formula for material coefficient of linear anisotropic poroviscoelasticity can be obtained from the corresponding expression in poroelasticity. Numerical examples of the complex behavior of the poroviscoelastic Biot’s effective stress coefficient for geomaterials and biomaterials are included as illustration. Moreover, analytical solutions for initial and boundary value problems in the Laplace transform domain in poroelasticity can now be readily transferred to poroviscoelasticity and vice versa. To illustrate this technique, analytical solutions for orthotropic poroelastic rectangular strips under either unconfined compression (Mandel’s problem) or confined compression (...

General solutions to poroviscoelastic model of hydrocephalic human brain tissue.

Hydrocephalus is a well-known disorder of brain fluidic system. It is commonly associated with complexities in cerebrospinal fluid (CSF) circulation in brain. In this paper, hydrocephalus and shunting surgery which is used in its treatment are modeled. Brain tissues are considered to follow a poroviscoelastic constitutive model in order to address the effects of time dependence of mechanical properties of soft tissues and fluid flow hydraulics. Our solution draws from Biots theory of poroelasticity, generalized to account for viscoelastic effects through the correspondence principle. Geometrically, the brain is conceived to be spherically symmetric, where the ventricles are assumed to be a hollow concentric space filled with cerebrospinal fluid. A generalized Kelvin model is considered for the rheological properties of brain tissues. The solution presented is useful in the analysis of the disorder of hydrocephalus as well as the treatment associated with it, namely, ventriclostomy surgery. The sensitivity of the solution to various factors such as aqueduct blockage level and trabeculae stiffness is thoroughly analyzed using numerical examples. Results indicate that partial aqueduct stenosis may be a cause of hydrocephalus. However, only severe occlusion of the aqueduct can cause a significant increase in the ventricle and brains extracellular fluid pressure. Ventriculostomy shunts are commonly used as a remedy to hydrocephalus. They serve to reduce the ventricular pressure to the normal level. However, sensitivity analysis on the shunts fluid deliverability parameter has shown that inappropriate design or selection of design shunt may cause under-drainage or over-drainage of the ventricles. Excessive drainage of CSF may increase the normal tensile stress on trabeculae. It can cause rupture of superior cerebral veins or damage to trabeculae or even brain tissues which in turn may lead to subdural hematoma, a common side-effect of the surgery. These Post-Surgery Reaction (PSR) patterns might occur on much larger time scales than those of the surgery itself, depending on the flow conductivity parameters of the brain. The viscoelastic effects can be significant contingent on the long term tissue moduli and their contrast with the initial ones.