Geomechanical Applications Research Articles

Improved Gridding Technique for Coupling Geomechanics to Reservoir Flow

SummaryThe application of geomechanics in reservoir flow simulation has increased substantially since it was recognized that the modeling of geomechanical effects was necessary to predict important phenomena such as compaction, subsidence, wellbore failure. However, its application is strongly limited because of the use of a single-grid system for both reservoir flow and geomechanics deformation. In the case of a large field-scale simulation, the use of a single-grid system gives rise to an extremely large number of gridblocks. On one hand, for an accurate modeling of fluid flow, the gridblocks need to be reasonably small around wells and sharp fronts. Yet, these small gridblocks may not be essential for geomechanics computations. On the other hand, accurate geomechanics calculations may require many gridblocks in the overburden, underburden, and sideburden (country rock) that are not necessary for fluid flow. In this work, a dual-grid technique is combined with an iterative coupling method to resolve the problem. In this dual-grid technique, the reservoir flow grid and the geomechanics grid are distinct in order to model efficiently both fluid flow phenomena and geomechanics deformations. A method to couple the two grid systems is described. The use of this grid coupling approach reduces the simulation run time substantially with results that are very close to the single-grid method. A series of examples illustrating the application of this dual-grid concept and the corresponding runtime reduction are described.

Applications of multiphysical geomechanics in underground nuclear waste storage

ABSTRACT Deep geological disposal in suitable host rocks is the favoured strategy for the storage and disposal of heat-emitting high level nuclear waste. A rational design of repositories requires a good understanding of the interacting thermo-hydro-mechanical phenomena that occur in the engineered barrier and adjacent rock. To this end, a multiphysical formulation is described that allows the performance of coupled THM analyses capable of reproducing observed phenomena. The formulation and computer code is applied to the simulation of two large scale tests: a mine-by test involving the excavation of a shaft in an argillaceous rock and a large-scale high- temperature heating test in fractured rock.

Applications of multiphysical geomechanics in underground nuclear waste storage

Applications of multiphysical geomechanics in underground nuclear waste storage

Applications of multiphysical geomechanics in underground nuclear waste storage

Deep geological disposal in suitable host rocks is the favoured strategy for the storage and disposal of heat-emitting high level nuclear waste. A rational design of repositories requires a good understanding of the interacting thermo-hydro-mechanical phenomena that occur in the engineered barrier and adjacent rock. To this end, a multiphysical formulation is described that allows the performance of coupled THM analyses capable of reproducing observed phenomena. The formulation and computer code is applied to the simulation of two large scale tests: a mine-by test involving the excavation of a shaft in an argillaceous rock and a large-scale high- temperature heating test in fractured rock.

Rock-Strength Data From Cores and Logs

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 121972, "Rock Strength From Cores and Logs: Where We Stand and Ways To Go," by A. Khaksar, P.G. Taylor, Z. Fang, T. Kayes, A. Salazar, and K. Rahman, SPE, Helix RDS, prepared for the 2009 SPE Europec/EAGE Annual Conference and Exhibition, Amsterdam, 8-11 June. The paper has not been peer reviewed. Accurate rock-strength knowledge is essential for in-situ stress estimation, wellbore-stability analysis, sand-production prediction, and other geomechanical applications. When sufficient rock-strength core data exist, computing techniques, such as fuzzy logic and cluster-pattern recognition, coupled with sedimentary-facies analysis and diagenetic classification, can improve strength estimation. Semicontinuous impact-energy logs from portable nondestructive testing tools can be correlated with petrophysical logs to generate mechanical facies and improved sampling for conventional rock testing pattern. Introduction Rock mechanical properties are essential for accurate in-situ stress analysis and geomechanical evaluations including wellbore-stability analysis, sand-production prediction and management, hydraulic-fracturing design, fault-stability and -reactivation analysis, and other geomechanical applications. The rock mechanical (strength) parameters typically required to populate a geomechanical model that is based on the linear Mohr-Coulomb failure criterion are unconfined compressive strength (UCS), friction angle or coefficient of internal friction, and thick-wall- (hollow) cylinder (TWC) strength, which may be needed for sanding evaluation and calibration. Laboratory-based rock-strength values typically are determined with triaxial tests on cylindrical samples that are cut from cores obtained at depths of interest. Continuous profiles of rock strength vs. depth can be estimated by use of well logs and empirical core/log relationships. In most cases, core-strength databases are limited, discontinuous, and biased toward stronger intervals. Quality core plugs of nonreservoir formations (e.g., mudstones and shales), where most hole-instability problems occur, are rarely available for testing. The full-length paper outlines good practices for obtaining quality rock-strength data from core tests then presents common empirical rock-strength equations and discusses ways to improve rock-strength estimates. Rock Strength From Core Tests Often, samples for rock-mechanics testing are taken only after the initial slab cut is made. This process reduces the core diameter and, hence, the plug length, usually making the length/diameter ratio unacceptable. It is even worse when no samples for rock-mechanics tests are cut and the core is allowed to dry out and, possibly, deteriorate, depending on mineralogy. The rock-mechanics program must be planned well in advance of the core being cut because many interests must be accommodated and potential pitfalls overcome. Good communications between different departments will help streamline the process, maximize the benefits of geomechanics, and avoid repeated work.

Multi‐level incomplete factorizations for the iterative solution of non‐linear finite element problems

AbstractSeveral engineering applications give rise quite naturally to linearized FE systems of equations possessing a multi‐level structure. An example is provided by geomechanical models of layered and faulted geological formations. For such problems the use of a multi‐level incomplete factorization (MIF) as a preconditioner for Krylov subspace methods can prove a robust and efficient solution accelerator, allowing for a fine tuning of the fill‐in degree with a significant improvement in both the solver performance and the memory consumption. The present paper develops two novel MIF variants for the solution of multi‐level symmetric positive definite systems. Two correction algorithms are proposed with the aim of preserving the positive definiteness of the preconditioner, thus avoiding possible breakdowns of the preconditioned conjugate gradient solver. The MIF variants are experimented with in the solution of both a single system and a long‐term quasi‐static simulation dealing with a multi‐level geomechanical application. The numerical results show that MIF typically outperforms by up to a factor 3 a more traditional algebraic preconditioner such as an incomplete Cholesky factorization with partial fill‐in. The advantage is emphasized in a long‐term simulation where the fine fill‐in tuning allowed for by MIF yields a significant improvement for the computer memory requirement as well. Copyright © 2009 John Wiley & Sons, Ltd.

State and origin of present-day stress fields in sedimentary basins

The present-day stress field provides fundamental insight into the forces driving plate tectonics and intra-plate deformation. Furthermore, Knowledge of the present-day stress field is essential in petroleum, geothermal and mining geomechanics applications such as the stability of boreholes and tunnels, and improving production through natural and induced fractures. The World Stress Map (WSM) Project has, for over 20 years, compiled a public global database of present-day tectonic stress information to determine and understand the state of stress in the Earth?s lithosphere. The WSM database has revealed that plate-scale stress fields are controlled by forces exerted at plate boundaries (e.g. mid-ocean ridges, continental collision zones), commonly resulting in regional stress orientations sub-parallel to plate motion. However, the state and origin of present-day stress fields at smaller scales, such as within sedimentary basins, remains poorly understood in comparison. Detailed analysis of present-day stresses from within 70 sedimentary basins commonly reveals significant and complex variations in the present-day stress orientation, both across basins and within fields. For example, borehole breakouts in the North German Basin, Nile Delta and the Baram Delta province of northwest Borneo indicate broad regional rotations in the horizontal stress orientation. The present-day maximum horizontal stress orientations in the Gulf of Thailand are approximately north-south at the basin-scale (perpendicular to plate motion) and are perturbed locally to be sub-parallel to fault strike. The North Sea and Permian Basin of Texas display widely varying stress orientations between fields, with some neighbouring fields exhibiting perpendicular stress orientations. Basin- and field-scale stress fields result from the complex combination of numerous factors acting at different scales, including far-field forces (e.g. plate boundary forces), basin geometry (e.g. the shape of deltaic wedges), geological structures (e.g. diapirs, faults), mechanical contrasts (e.g. evaporites, overpressured shales, detachment zones), topography and deglaciation.

Numerical simulation of soil–water interaction using smoothed particle hydrodynamics (SPH) method

An application of smoothed particle hydrodynamics (SPH) to simulation of soil–water interaction is presented. In this calculation, water is modeled as a viscous fluid with week compressibility and soil is modeled as an elastic–perfectly plastic material. The Mohr–Coulomb failure criterion is applied to describe the stress states of soil in the plastic flow regime. Dry soil is modeled by one-phase flow while saturated soil is modeled by separate water and soil phases. Interaction between soil and water is taken into account by means of pore water pressure and seepage force. Simulation tests of soil excavation by a water jet are calculated as a challenging example to verify the broad applicability of the SPH method. The excavations are carried out in two different soil models, one is dry soil and the other is fully saturated soil. Numerical results obtained in this paper have shown that the gross discontinuities of soil failure can be simulated without any difficulties. This supports the feasibility and attractiveness of this a new approach in geomechanics applications. Advantages of the method are robustness, conceptual simplicity and relative ease of incorporating new physics.

Analyse microstructurale au MEB environnemental d’une craie soumise à chargement hydrique et mécanique

The Electron Scanning Environmental Microscope (ESEM) allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Unlike the traditional Scanning Electron Microscopy (SEM), ESEM technology does not require any preliminary treatment of the observed samples (i.e. dehydration, and eventually conductive coating). This has undeniable advantages to the analysis of geomaterials’ microstructure. Although ESEM applications are nowadays recurrent in many research fields related to materials science, this investigation tool is still seldom used in geomechanics. In this note, we discuss some aspects associated with this technology when used for geomaterials. Examples of applications are presented for the particular case of partially saturated chalks observed under variable environmental conditions. Some perspectives on the development of this instrument in relation with geomechanical applications are also discussed.

From pore-pressure prediction to reservoir characterization: A combined geomechanics-seismic inversion workflow using trend-kriging techniques in a deepwater basin

To optimize drilling decisions and well planning in overpressured areas, it is essential to carry out pore-pressure predictions before drilling. Knowledge of pore pressure implies knowledge of the effective stress, which is a key input for several geomechanics applications, such as fault slip and fault seal analysis and reservoir compaction studies. It is also a required input for 3D and 4D seismic reservoir characterization. Because the seismic response of shales and sand depends on their compaction history, the effective stress will govern the sedimentary seismic response. This is in contrast to normally pressured regimes, where the depth below mudline (or overburden stress) is typically used to characterize the compaction effect.

Acoustic Evolution Brings Full Characterization, Near-Deep Profiling

The evolution of sonic capabilities has now taken the form of a modular platform from which advanced geomechanical, petrophysical, geophysical, and reservoir measurements can be obtained, leading to actionable data about the drilling environment and the reservoir. Both short and long transmitter-to-receiver spacing and crossed dipole measurements, along with enhanced acoustic data for cement evaluation, are being obtained with the new Schlumberger sonic service. Currently in field-test, the new modular sonic imaging service, fully combinable with other wireline services, was developed to provide comprehensive, robust measurements in rock for incorporation with other formation measurements for use in reducing drilling risk, improving recovery, and maximizing productivity. Properties of elastic materials are well defined, but rock properties in formations vary with pressure and exhibit variations that are not easily predictable because of plastic and nonlinear deformation. Measurements at sonic frequencies continue to dominate evaluation efforts, with significant improvements being made since the introduction of wireline sonic tools in the 1950s. These improvements have culminated in a new sonic platform that can obtain stress information critical to wellbore placement and maximum reservoir drainage. The service provides a comprehensive, mechanical characterization of the wellbore, including 3D characterization of the compressional- and shear-wave slowness in terms of their axial, azimuthal, and radial variations that arise from nonuniform stress distributions, mechanical or near-wellbore-region alteration caused by the drilling process, and from formation intrinsic anisotropy related to the in-situ properties of the formation. The platform can be leveraged in a geomechanical application to deliver mechanical-property measurements that are derived from radial profiling using a dipole source that not only provides a large amount of energy over a wide frequency band, but also is capable of compensating for the effect of the sonic tool in the borehole (full characterization for acoustic predictability). Dipole radial profiling inverts the slowness response vs. frequency into a slowness response vs. depth into the formation. Radial profiling has not been previously available from either monopole or dipole tools. From a petrophysical perspective, monopole, dipole, and Stoneley acoustic measurements are applicable for gas detection, input to volumetrics, and permeability calculations. The new telemetry and optimized hardware and software can provide slowness measurements with enhanced reliability over an increased envelope of hole size and slowness, offering measurements from total depth to the mudline and at higher logging speeds. Benefits in Geomechanics Because shear-wave velocity responds to the solid framework of the rock and is not sensitive to fluid effects, it is important from a rock-mechanics perspective to evaluate shear velocity in both the far field and the near-wellbore region. Able to remain steady even in low-anisotropy conditions, new tool functions can discern the maximum-stress direction to as little as 2%. The importance of being able to profile shear slowness for the near-wellbore region and deep into the formation is seen when determining changes caused by drilling-induced stresses or stresses caused by intrinsic anisotropy (such as shales and fractures). It is also apparent when evaluating minimum/maximum stress direction for wellbore placement, during optimized drilling, and in oriented perforating. This is accomplished by rotating the measured waveforms into the fast (maximum stress) and slow (minimum stress) shear directions. The shear- and compression-al-wave velocity is also used as an input for calculating rock properties such as Poisson’s ratio, Young’s modulus, bulk modulus, and shear modulus. These properties, which control the physical behavior of the formation, are then used to calculate a safe mud-weight window or to reduce the uncertainty of well-bore instability ahead of the drill bit. They are also used in hydraulic-fracture design.

Gradient plasticity modeling of geomaterials in a meshfree environment. Part I: Theory and variational formulation

Deformation and strength behavior of geomaterials in the pre- and post-failure regimes are of significant interest in various geomechanics applications. To address the need for development of a realistic constitutive framework, which allows for an accurate simulation of pre-failure response as well as an objective and meaningful post-failure response, a strain gradient plasticity model is formulated by incorporating the spatial gradients of elastic strain in the evolution of stress and gradients of plastic strain in the evolution of the internal variables. In turn, gradients of only kinematic variables are included in the constitutive equations. The resulting constitutive equations along with the balance of linear momentum for the continuum are cast as a coupled system of equations, with displacements and plastic multiplier appearing as the primary unknowns in the final governing integral equations. To avoid singular stress fields along element boundaries, a finite element discretization of the governing equations would require C 2 continuous displacements and C 1 continuous plastic multiplier, which is undesirable from a numerical implementation point of view. This issue is naturally resolved when a meshfree discretization is used. Hence the developed model is formulated within the framework of a meshfree environment. The new constitutive model allows an analysis of grain size effects on strength and dilatancy of rocks. The role and effectiveness of the new gradient terms on regularizing the underlying boundary value problems of geomechanics beyond the initiation of strain localization will be assessed in a future paper.

Displacement-controlled method and its applications to material non-linearity

For the analysis of non-linear problems, the displacement-controlled method (DCM) has a more extensive application scope and more powerful abilities than the load-controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman–Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non-linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd.

Mechanical Earth Model and Integrated Geomechanics Approach as New Frontier For Petroleum Industry

Geomechanics (the study of rock deformation and failure) is gaining wide recognition in the petroleum industry worldwide. Applying geomechanics modeling allow achieving significant financial benefits to oilfield operations ranging from exploration and field development to reservoir management. Central to creating value through application of geomechanics is a closed loop process that links a mechanical earth model (MEM) with fit-for-purpose-engineering software, multi-disciplinary teamwork and knowledge management1, 2)This publication provides an introduction to a MEM based integrated geomechanics process and demonstrates how operations throughout the life cycle of field benefit from the closed loop geomechanics approach. A case study introduced in this paper illustrates how MEM integrated with iterative Real Time approach helps to overcome challenges and reduce financial risk during drilling operations and field development overall.

Glyph and hyperstreamline representation of stress and strain tensors and material constitutive response

AbstractResults of numerical analyses of boundary value problems in geomechanics include output of three‐dimensional stress and strain states. Two‐dimensional plots of stress–stress or stress–strain quantities, often used to represent such output, do not fully communicate the evolution of stress and strain states. This paper describes the use of glyphs and hyperstreamlines for the visual representation of three dimensional stress and strain tensors in geomechanics applications. Glyphs can be used to represent principal stress states as well as normal stresses at a point. The application of these glyphs is extended in this paper to represent strain states. The paper introduces a new glyph, called HWY glyph for the representation of shear tensor components. A load step‐based hyperstreamline is developed to show the evolution of a stress or strain tensor under a general state of loading. The evolution of stress–strain states from simulated laboratory tests and a general boundary value problem of a deep braced excavation are represented using these advanced visual techniques. These visual representations facilitate the understanding of complex multidimensional stress–strain soil constitutive relationships. The visual objects introduced in this paper can be applied to stress and strain tensors from general boundary value problems. Copyright © 2003 John Wiley & Sons, Ltd.

Space decomposition preconditioners and their application in geomechanics

This paper addresses the use of space decomposition preconditioners for the numerical solution of boundary value problems. As special cases, it deals with the displacement decomposition (DiD) and overlapping domain decomposition (DD) preconditioners. A special attention is also devoted to inexact solution of sub-problems and the use of non-symmetric preconditioners. In these cases, the generalized preconditioned congugate gradient method is shown to be efficient to use. The considered methods are applied to the solution of selected model problems as well as to a large scale problem arising from assessment of stress changes induced by mining activities.

On shakedown analysis in hardening plasticity

The extension of classical shakedown theorems for hardening plasticity is interesting from both theoretical and practical aspects of the theory of plasticity. This problem has been much discussed in the literature. In particular, the model of generalized standard materials gives a convenient framework to derive appropriate results for common models of plasticity with strain-hardening. This paper gives a comprehensive presentation of the subject, in particular, on general results which can be obtained in this framework. The extension of the static shakedown theorem to hardening plasticity is presented at first. It leads by min–max duality to the definition of dual static and kinematic safety coefficients in hardening plasticity. Dual static and kinematic approaches are discussed for common models of isotropic hardening of limited or unlimited kinematic hardening. The kinematic approach also suggests for these models the introduction of a relaxed kinematic coefficient following a method due to Koiter. Some models for soils such as the Cam-clay model are discussed in the same spirit for applications in geomechanics. In particular, new appropriate results concerning the variational expressions of the dual kinematic coefficients are obtained.

Modeling in Geomechanics

Musharraf Zaman et al. (eds). Wiley, UK 2000. £150.00 hardback; xxiv+706pp. ISBN 0-471-49218-3. Contributions by established scientists and engineers from various branches worldwide of soil and rock engineering, this book compactly presents the latest theoretical and modelling developments and their practical applications in geomechanics. It will broaden the horizons of researchers and consultants toward more effective applications of the various theories and models. The book is arranged as three parts: (i) Computational Procedures; (ii) Constitutive Modelling and Testing; and (iii) Modelling and Simulation. The first part, Computational Procedures, includes four chapters, respectively addressing coupled BE/FE methods in geomechanics, FE analysis of soil plasticity, …

Coupled Reservoir-Geomechanics Model for Wellbore Stability and Sand Prediction

This article is a synopsis of paper SPE 69718, "A Coupled Reservoir- Geomechanics Model and Applications to Wellbore Stability and Sand Prediction," by Yarlong Wang, SPE, Petro-Geotech Inc. and Baoping Lu, SPE, China New Star Co., originally presented at the 2001 SPE International Thermal Operations and Heavy Oil Symposium, Margarita Island, Venezuela, March 12-14.

Accelerated initial stiffness schemes for elastoplasticity

Iterative methods for the solution of non-linear finite element equations are generally based on variants of the Newton–Raphson method. When they are stable, full Newton–Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent stiffness scheme, but there are situations in which initial stiffness schemes are very useful. These situations include problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single-parameter techniques for accelerating the convergence of the initial stiffness scheme. Some simple but effective modifications to these procedures are also proposed. In particular, a modified version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr–Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright © 2000 John Wiley & Sons, Ltd.