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Abstract: The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. In this work, the porochemoelectroelastic theory is applied to derive the solution for stress, pore pressure, strain, and displacement of the Mandel's problem for orthotropic charged saturated porous media. Numerical examples are given to demonstrate applications of the present solutions to laboratory characterization and hydraulic fracturing analysis of shale formation. The analysis shows that ignoring either the porochemoelectroelastic effects or the material anisotropy can leads to inaccurate prediction of the pore pressure and effective stress distributions in the shale sample or formations during these processes.
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Abstract: The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.
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Abstract: 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 (1D consolidation problem) subjected to either time-dependent force or time-dependent displacement loading have been derived and then transferred to poroviscoelasticity herein. Finally, a biomechanics analysis of laboratory testing on orthotropic articular cartilage illustrates the usefulness of the newly derived solutions.
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Abstract:This paper presents a novel analytical solution to the transient, z-dependent, and asymmetric problem of an infinite wellbore drilled into a fluid-saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far-field stresses are acting over a finite vertical section. The results of our solution to this case with a three-dimensional state of far-field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations.
The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity.
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Abstract: Numerous time-dependent wellbore-instability problems have been reported while drilling through the chemically active fractured shale formations in the Arabian Gulf. Very often, these shales are characterized by the abundance of not only macroscale bedding planes but also networks of microscale natural fractures. The presence of fractures weakens the shale mechanically and produces higher-permeability fluid-flow paths within the low-permeability rock formation. Because of different fluid-diffusion rates between the fractures and shale matrix, there are two distinct pore-pressure fields in saturated fractured shale. Additionally, in chemically active shale formations, osmotic pressure arises because of the imbalance in mud/shale chemical activity. Practically, it is extremely complex to isolate the fractures from the matrix for analysis or to identify fracture size and fracture density. However, a first-order approach in an attempt to understand the porous fractured-shale behavior is to use dual-porosity and dual-permeability theory of poromechanics in the analytical modeling. In this study, a poromechanical inclined-wellbore solution has been derived that incorporates time dependency, a primary porosity and permeability for the matrix, a secondary porosity and permeability for the fractures, and the chemical effect. The expressions for the stresses and pressure solutions are presented and detailed in Appendix A. These analytical solutions are used to simulate an inclined-wellbore-stability problem in a fractured-shale formation, accounting also for bedding planes in some instances in addition to the microfractures. Additionally, retrieved rock samples of fractured shale were tested by use of an innovative laboratory characterization device, the Inclined Direct Shear Testing Device (IDSTD) (integrated PoroMechanics Institute; Norman, Oklahoma; 2008). This device tests tiny shale specimens (rock volume less than 0.14 in.3) and is capable of measuring cohesion and friction angle while the sample is subjected to in-situ stresses, varying mud pressures, and mud-circulation times.
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Abstract: Natural fractures play an important role in the technical and economic performance of all hydrocarbon producing reservoirs. Generally, the presence of fractures weakens the reservoir mechanically and produces higher permeability fluid flow paths within the low permeability rock formation. In reservoir simulation, the intricate interplay between reservoir compaction and fluid flow may lead to undesirable production behavior if the effects of fractures are not properly accounted for. Due to the complexity of the physical phenomena and mathematical formulations, all naturally fractured reservoir modelings are performed numerically using discrete fracture network, finite difference and/or finite element method. While geologically realistic and practical, these numerical methods are computationally intensive and require analytical validation. These facts necessitate a dual-porosity and dual-permeability approach to analytical modeling that incorporates time-dependency and fracture networks effects on reservoir performance.
In this work, a general anisotropic dual-porosity and dual-permeability analytical formulation is presented to simulate naturally fractured reservoir accounting for fractures deformation and fluid flow in a three dimensional state of stresses. The solution is applied to simulate reservoir compaction of a fractured reservoir in the Ghawar field, Saudi Arabia. It is helpful in the estimation of time-dependent induced local permeability alteration due to wellbore production/injection. Various scenarios of fractures representations are illustrated to highlight the impacts of fractures' orientations, density, porosity and permeability on the overall reservoir response. In addition, the solution for the effective stress changes in the reservoir can be used to estimate stress on pipe/casing and formation brittle failure that precedes solid production.
Analyses reveal that production may induce up to 7-percent permeability reduction which can affect the production rate. Thus, accounting for reservoir compaction facilitates future production forecast and/or stimulation planning. For a vertical well, horizontal fractures orientation show higher degree of compaction and permeability damage than vertically oriented fractures. Discounting the effect of fractures will largely underestimate the decline in reservoir performance and complicate future field-development options.
This unique analytical model and solution can be directly applied to real field analyses in naturally fractured reservoirs. The impact of fractures on the overall reservoir performance can be investigated using the solution and approach presented. Finally, the analytical solution can be used as a benchmark for validation of available reservoir simulation numerical codes.
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Abstract: Drilling and production optimization are two interconnected operations for successful well construction and reservoir management, in particular for extended reach of multilateral wells. Formation damage, especially permeability reduction induced during drilling, greatly affect well completion and future potential reserve production. Reservoir pressure depletion and the consequent increase in effective stresses around the well branches are the main reasons behind solid production or total wellbore collapse. Unfortunately, to date, analytical study for the stability of multilaterals has been very limited due to the complex geometry and stress state involved. This work entails a recently derived analytical solution to estimate the safe mudweight window for wellbore stability during drilling, as well as to predict the maximum pressure drawdown for a stable junction during production. The presented solution is capable of handling the complexity of 3D anisotropic state of stress as well as any mother and lateral size, inclination, and azimuth. The study shows that the design of multilateral junction, especially inclination and azimuth of both wellbores with respect to regional in-situ stresses play a crucial role in the multilateral junction stability and the critical pressure drawdown estimation to prevent solid production and wellbore collapse. A field case study of a multilateral well drilled in the Khuff-C formation, Ghawar field, Saudi Arabia, is analyzed herein with drilling data, core-retrieved rock properties, and pressure drawdown and production estimates. The results showed alternate optimized completions that could have been applied early in the drilling and branching of the laterals. Practical guidelines concerning branching optimization have been established for junction planning and execution. The new analytical modeling has also been calibrated with a published peer-reviewed large-scale experimental program simulating both the anisotropy of far-field stresses and complex junction geometry with exceptional qualitative and quantitative results.
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Abstract: Even with the emerging gas and oil shale plays, little laboratory data exists for the simulation of openhole completion and production accounting for the inherent anisotropy of shale. Contrary to the success of the thick wall cylinder test in simulating openhole production stability and/or solids production in sandstone and carbonate formations, the application and modeling of this test in shale, while subjecting the sample to in-situ openhole conditions, presents considerably greater complexity. Shale in general possesses anisotropic mechanical material properties that will alter the stress distribution around an open hole. Moreover, time-dependent pore pressure and permeability effects will modify the effective stresses and can cause delayed formation failure. In this study, the response of anisotropic hollow cylindrical shale samples under laboratory time-dependent loading, simulating near-wellbore production stresses, is investigated under the realm of coupled fluid and shale matrix interaction to address these challenging issues. Experimental results on thick wall cylinder testing of an anisotropic and low permeability shale were analyzed using the developed physical and mathematical model. The results showed that significant pore pressure could be generated and sustained in even small shale specimens (3.81 cm outer diameter and 1.27 cm inner diameter), depending on shale anisotropic properties, permeability, and loading rate, and cannot be ignored when the collapse strength from thick wall cylinder tests is interpreted for field conditions. Furthermore, commonly employed elasticity analyses for the thick wall cylinder test fail to account for the coupled fluid and shale matrix interaction under time-dependent loading condition and produce oversimplified and inaccurate results for not only the effective stress distribution but also failure analysis. The new modeling, therefore, will be essential for designing, simulating, and interpreting laboratory thick wall cylinder tests on shales as well as the subsequent modeling of sustainable gas and oil production from these formations.
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Abstract: The importance of accurate determination of in-situ maximum and minimum horizontal stress orientations and magnitudes can never be over-emphasized in geomechanics-related operations in the oil and gas industry. In this paper, the Anelastic Strain Recovery (ASR) test is revisited, and for the first time, the analytical solution for the relaxation evolution of recovered cores from deep wells is extended to fully cover the poroviscoelastic nature of formation rocks, i.e., viscoelasticity of not only the porous matrix moduli but also the grain bulk modulus, as well as a realistic description of the coring, retrieving, and testing processes, i.e., practical time-dependent stress and pore pressure boundary condition evolution instead of the common Heaviside step unloading used in previous studies. Furthermore, the solution also incorporates material transverse isotropy which is frequently encountered in sedimentary formations yet regularly overlooked in previous works. The study identifies several key parameters for accurate determination of in-situ horizontal stresses from ASR test and serves as a reference for future operations.
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Abstract: An analytical solution is presented in this paper to study the time-dependent settlement behaviour of a rigid foundation resting on a transversely isotropic saturated soil layer. The governing equations for a transversely isotropic saturated soil, within Biot's poroelasticity framework, are solved by means of Laplace and Hankel transforms. The problem is subsequently formulated in the Laplace transform domain in terms of a set of dual integral equations that are further reduced to a Fredholm integral equation of the second kind and solved numerically. The developed analytical solution is validated via comparison with the existing analytical solution for an isotropic saturated soil case, and adopted as a benchmark to examine the sensitivities of the mesh refinement and the locations of truncation boundaries in the finite element simulations using ABAQUS. Particular attention is paid to the influences of the degree of soil anisotropy, boundary drainage condition, and the soil layer thickness on the consolidation settlement and contact stress of the rigid foundation.
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Abstract:The transverse anisotropic poromechanics solution for the two-dimensional Mandel-type problem geometry is extended in this paper to account for the orthotropic nature of the porous media, thus mimicking the response of articular cartilage samples when subjected to load perturbation. The anisotropic solution presented takes into account the viscoelastic and anisotropic nature of the fluid-saturated cartilage specimen sandwiched between two impermeable rigid plates and subjected to quasi-static step loading conditions; thus simulating the unconfined compressive test responses of cartilage samples in biomechanics laboratory setups. The solution addresses the stress, fluid pressure, and displacement results due to load application through exact modeling of the intrinsic nature of the orthotropic viscoelastic matrix structure as well as the compressible interstitial fluid flow responses. Poromechanical parameter characterization and modeling of biological tissues, such as cartilage, will find this analytical solution to the two-dimensional anisotropic poroviscoelastic geometry very useful. This problem will not only serve as a benchmark for validating numerical schemes and simulations but also assist in calibrating laboratory results on biological tissues, including cyclic loadings.
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Abstract: Shale, a common type of sedimentary rock of significance to petroleum and reservoir
engineering, has recently emerged as a crucial component in the design of sustainable
carbon and nuclear waste storage solutions and as a prolific natural gas source. Despite
its importance, the highly heterogeneous and anisotropic nature of shale has challenged
the theoretical modeling and prediction of its mechanical properties. This thesis presents
a comprehensive microporomechanics framework for developing predictive models for
shale poroelasticity and strength. Modeling is accomplished through a multi-scale
approach, in which the experimental evidence gathered from novel nanoindentation
techniques and conventional macroscopic tests informs the development of a suit of
micromechanics tools for linking composition and microstructure to material
performance.
Based on a closed loop approach of calibration and validation of elastic and strength
properties at different length scales, it was possible to deconstruct shale to the scale of an
elementary material unit with mechanical behaviors governed by invariant properties, and
to upscale these behaviors from the nanoscale to the macroscale of engineering
applications. The elementary building block for elasticity is an anisotropic solid
characterizing the in situ stiffness of highly consolidated clay. This intrinsic behavior
represents the composite response of clay platelets, interlayer galleries, and interparticle
contacts, yielding an invariant stiffness with respect to clay mineralogy. The anisotropic
nanogranular nature of the porous clay in shale as inferred from nanoindentation is
confirmed through micromechanics modeling. The intrinsic anisotropy of the clay fabric
is suggested as the dominant factor driving the multi-scale anisotropic poroelasticity of
unfractured shale compared to the contributions of geometrical sources related to shapes
and orientations of particles. For strength properties, the micromechanics approach
revealed that the frictional behavior of the elementary unit of compacted clay is scale
independent, whereas a scale effect modifies its cohesive behavior.
Having established a fundamental material unit and the adequate micromechanics
representation for the microstructure, the macroscopic diversity of shale predominantly
depends on two volumetric properties derived from mineralogy and porosity: the clay
packing density and the silt inclusion volume fraction. The proposed two-parameter
microporoelastic and strength models represent appealing alternatives for use in
geomechanics and geophysics applications.
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Abstract: Woodford shale has recently emerged as a potential gas play in the U.S. Mid-continent, following in the footsteps of the Barnett shale. Profitable production from these formations relies on the success of horizontal well drilling and hydraulic fracturing design, which in turn depends greatly on knowledge about rock formation anisotropic elastic properties and pore pressure coefficients (poroelastic properties). In this paper, a suite of recently developed wire-line logs such as the Element Capture Spectroscopy (ECS) log, Sonic Scanner log, and porosity logs, were run on the Woodford and Barnett formations. The results were utilized to estimate the anisotropic elastic and poroelastic properties of these gas shale formations using the GeoGenome™ model, a theoretical upscaling model backed up with unique laboratory testing on field retrieved preserved shale samples at a scale that has never before been investigated; that is, observing mechanics from displacements as small as 100 nm to 100 μm, and maximum applied forces not even reaching 1000 μN. Comparison between laboratory Ultrasonic Pulse Velocity measured data, Sonic Scanner log data, and simulated data has shown excellent agreement, and thus confirmed the reliability of the GeoGenome upscaling model in obtaining shale anisotropic mechanical properties of which some parameters cannot be obtained even with the most advanced sonic log. In addition, a new technique was developed using nano-indentation to extract the Woodford shale mechanical and strength properties from drill-cuttings. The measured stiffnesses and compressibility on Woodford shale drill-cuttings-size chips have shown great potential for full mechanical characterization of rocks from just the drill-cuttings, which until recently were regarded as having little value for rock mechanical characterization besides some existing simple empirical correlations. This new shale testing technique will undoubtedly help the industry to significantly reduce the overhead associated with full core retrievals at great depths.
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Abstract: In this work, laboratory characterization of Woodford shale anisotropic elastic and poroelastic properties were conducted using quasi-static and acoustic testing procedures. The Ultra Sonic Pulse Velocity (UPV) measurements were conducted on preserved core samples obtained from a shallow well drilled in the Woodford formation, Pontatoc County, Oklahoma, USA. Despite the relatively low clay content of the Woodford shale core samples, less than 36%, as shown by XRD-mineralogy analysis, UPV results show that all samples exhibit at least 24% in compressional and shear wave anisotropy as reflected through the Thomsen's coefficients ε and γ. Also, the Middle Woodford sample with high clay content appears to have higher degree of acoustic anisotropy compared to the lower clay sample from the Upper Woodford.
The second part of this work involves utilizing the available wire-line log data from the same well where the Woodford core samples were obtained to investigate the sensitivity and accuracy of sand-shale classification methods frequently employed by petrophysicists to determine shale layers in sand-shale sequences. The results show that the majority of the Woodford shale formation will be considered as "grain-supported sands" instead of "shale" and thus showing the lack of sensitivity of these sand-shale classification methods. On the other hand, using the quantitative mineralogy composition reported by the Element Capture Spectroscopy (ECS) log and employing the clay packing density concept, 99% of the formation can be regarded as "shale" which is in accordance with both common consensus about Woodford formation and the mechanical testing results at all scales on the obtained Woodford shale samples.
In addition, the log porosity and quantitative mineralogy composition from ECS log were used to estimate the anisotropic elastic and poroelastic properties of Woodford shale using the GeoGenome approach, a coherent theoretical upscaling model backed up with unique laboratory observations that allow the estimation of the rock anisotropic mechanical properties with just mineralogy and porosity. Comparison between laboratory UPV data on core samples obtained from the same well, wire line Sonic Scanner log data and GeoGenome simulated data has shown excellent qualitative and quantitative agreement between results with relative differences less than 17%. Hence, the results have confirmed the reliability of applying GeoGenome upscaling model to obtain the anisotropic elastic and poroelastic properties of shale formations some of which cannot be accessed even with the most advanced wire-line sonic log.
In the last part of this work, quasi-static methods were applied to characterize the mechanical properties of Woodford shale using the innovative Inclined Direct Shear Testing Device, IDSTD, developed by the integrated Poromechanics Institute at the University of Oklahoma. The small sample size, 20 mm x 7 mm, used in this test does not only reduce the testing time but also increase the statistic of testing from one core retrieval. The results show that the Upper Woodford sample with lower clay content has a higher shear strength compared to the Middle Woodford sample. Using inverse theories, the IDSTD acoustic measurements can be utilized to estimate the full elastic stiffness tensor of transversely isotropic material. A series of calibrations has been conducted and confirmed the reliability of the new testing method. The inverted moduli from IDSTD acoustic measurements show significant reduction of compressional wave anisotropy, as much as 10%, under application of 13.89 MPa confining pressures. On the other hand, the shear wave anisotropy does not appear to be as sensitive to applied confinement as the compressional wave anisotropy. The results also show a significant decreasing of elastic stiffness in the direction perpendicular to sample axis of symmetry toward sample failure during application of axial load as compared to a slight decrease or increase of elastic stiffness in direction parallel to sample axis of symmetry. The phenomenon is believed to be associated with micro fractures forming in direction parallel to sample axis of symmetry as revealed by SEM images taken on failure surface of a sample after IDSTD tested. The knowledge on the variation of elastic moduli during confinement obtained from IDSTD acoustic measurements has facilitated the adjustment of UPV measurements conducted at atmospheric condition for the effects of confining pressure.
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Abstract: Amultiscale, 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 kerogenrich 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.
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Abstract: Woodford shale is emerging as one of the major gas formations in the US Midwest. Despite its tremendous potential, existing data on the Woodford shale geomechanics characterization are limited at best. In this work, a well in the Woodford shale formation, 200 feet deep, was cored and logged in Oklahoma, USA. The resulting retrieved preserved cores were lab tested using standard acoustic techniques and triaxial testing for shale mechanical and poromechanical characterization in terms of compressibility, strength, pore pressure coefficient, Young’s modulus, Poisson’s ratio, etc. In addition, shale mechanical parameters alteration when in contact with drilling muds and fracturing fluids were measured using Brazilian tests and the innovative Inclined Direct Shear Testing Device (IDSTD™). Finally, mechanical Woodford shale parameters were also measured and correlated with field log results, using samples a tiny as drill cuttings (a few millimeters in size) with the newly emerging nano-indentation rock characterization techniques developed in the GeoGenome™ Industry Consortium. This newly developed methodology for rock testing and shale characterization, part of the nanotechnology wave, showed excellent results when compared with shale acoustic laboratory measurements and log data and results.
Despite a relatively high quartz content as shown by XRD and Elemental Capture Spectroscopy (ECS) log results, the Woodford shale does exhibit clear transversely isotropic mechanical characteristics, from Young’s moduli to Poisson’s ratios and other mechanical parameters. Moreover, IDSTD™ and Brazilian tensile tests on the preserved Woodford samples exposed to different drilling and hydraulic fracturing fluids showed that fluid effects play an important role on both compressive strength and tensile strength of the shale despite the fact that the Woodford clay content mainly composes of illite and chlorite.
The mechanical and poromechanical properties of Woodford shale were measured at four different scales, from field well logs to standard rock testing to the penny-size samples of IDSTD™ and down to drill cuttings scales using the nano-indentation. Furthermore, the innovative nano-indentation techniques for rock testing have allowed the construction of a GeoGenomeTM simulation model which can estimate and determine macroscopic rock properties based on porosity, packing density, and mineralogy. The simulated moduli and parameters using this model showed excellent agreement when compared to both lab and field log results.
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Abstract: Despite their ubiquitous presence as sealing formations in hydrocarbon bearing reservoirs affecting many fields of exploitation, the source of anisotropy of this earth material is still an enigma that has deceived many decoding attempts from experimental and theoretical sides. Sedimentary rocks, such as shales, are made of highly compacted clay particles of sub-micrometer size, nanometric porosity and different mineralogy. In this paper, we present, for the first time, results from a new experimental technique that allows one to rationally assess the elasticity content of the highly heterogeneous clay fabric of shales from nano- and microindentation. Based on the statistical analysis of massive nanoindentation tests, we find (1) that the in-situ elasticity content of the clayfabric at a scale of a few hundred to thousands nanometers is almost an order of magnitude smaller than reported clay stiffness values of clay minerals, and (2) that the elasticity and the anisotropy scale linearly with the clay packing density beyond a percolation threshold of roughly 50%. Furthermore, we show that the elasticity content sensed by nano- and microindentation tests is equal to the one that is sensed by (small strain) velocity measurements. From those observations, we conclude that shales are nanogranular composite materials, whose mechanical properties are governed by particle-to-particle contact and by characteristic packing densities, and that the much stiffer mineral properties play a secondary role.
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