Geomechanical Simulation Research Articles

Composite wedge failure using photogrammetric measurements and DFN-DEM modelling

Analysis and prediction of structural instabilities in open pit mines are an important design and operational consideration for ensuring safety and productivity of the operation. Unstable wedges and blocks occurring at the surface of the pit walls may be identified through three-dimensional (3D) image analysis combined with the discrete fracture network (DFN) approach. Kinematic analysis based on polyhedral modelling can be used for first pass analysis but cannot capture composite failure mechanisms involving both structurally controlled and rock mass progressive failures. A methodology is proposed in this paper to overcome such limitations by coupling DFN models with geomechanical simulations based on the discrete element method (DEM). Further, high resolution photogrammetric data are used to identify valid model scenarios. An identified wedge failure that occurred in an Australian coal mine is used to validate the methodology. In this particular case, the failure surface was induced as a result of the rock mass progressive failure that developed from the toe of the structure inside the intact rock matrix. Analysis has been undertaken to determine in what scenarios the measured and predicted failure surfaces can be used to calibrate strength parameters in the model.

Investigation of the influence of geomechanical and hydrogeological properties on surface uplift at In Salah

Coupled reservoir and geomechanical simulations are significantly important to understand the long-term behavior of geologic carbon storage (GCS) systems. In this study, we performed coupled fluid flow and geomechanical modeling of CO2 storage using available field data to (1) validate our existing numerical model and (2) perform parameter estimation via inverse modeling to identify the impact of key geomechanical (Young's modulus and Biot's coefficient) and hydrogeological (permeability and anisotropy ratio) properties on surface uplift and the pore pressure buildup at In Salah in Algeria. Two sets of surface uplift data featuring low and high uplifts above two injection wells and the maximum change in the pore pressure due to CO2 injection were used to constrain the inverse model. Forward simulation results with representative parameter values from the literature match both low and high surface uplifts reasonably well and predicted the maximum change in the pore pressure. In particular, forward modeling results with estimated Biot's coefficients for reservoir and caprock layers, match the observed uplift well, highlighting the significance of Biot's coefficient in coupled reservoir and geomechanical models. Parameter estimation with 12 parameter sets for both low and high uplift data demonstrates that multiple sets of parameters can match the observed data equally well and the inclusion of the pore pressure data is critically important to constrain the parameter solution during inverse modeling. For a majority of cases, estimation results for both low and high uplift data show the vertical intrinsic permeability and Young's modulus of the reservoir remained close to 13mD (1.3×10−14m2) and 10GPa, respectively, suggesting that these parameters may represent the actual effective properties. Additionally, higher correlations between reservoir permeability and caprock's Biot's coefficient with high surface uplift data were observed consistently under the pore pressure constraint, suggesting the inclusion of the pore pressure constraint is required to estimate the proper values of coupled flow and geomechanical properties associated with different surface uplift data. Overall, this study suggests that given limited data, including Biot's coefficient, in addition to permeability and Young's modulus can enhance parameter estimation of the geomechanical response during GCS.

Reservoir stress path and induced seismic anisotropy: results from linking coupled fluid-flow/geomechanical simulation with seismic modelling

We present a workflow linking coupled fluid-flow and geomechanical simulation with seismic modelling to predict seismic anisotropy induced by non-hydrostatic stress changes. We generate seismic models from coupled simulations to examine the relationship between reservoir geometry, stress path and seismic anisotropy. The results indicate that geometry influences the evolution of stress, which leads to stress-induced seismic anisotropy. Although stress anisotropy is high for the small reservoir, the effect of stress arching and the ability of the side-burden to support the excess load limit the overall change in effective stress and hence seismic anisotropy. For the extensive reservoir, stress anisotropy and induced seismic anisotropy are high. The extensive and elongate reservoirs experience significant compaction, where the inefficiency of the developed stress arching in the side-burden cannot support the excess load. The elongate reservoir displays significant stress asymmetry, with seismic anisotropy developing predominantly along the long-edge of the reservoir. We show that the link between stress path parameters and seismic anisotropy is complex, where the anisotropic symmetry is controlled not only by model geometry but also the nonlinear rock physics model used. Nevertheless, a workflow has been developed to model seismic anisotropy induced by non-hydrostatic stress changes, allowing field observations of anisotropy to be linked with geomechanical models.

Inverse modeling of ground surface uplift and pressure with iTOUGH-PEST and TOUGH-FLAC: The case of CO2 injection at In Salah, Algeria

Ground deformation, commonly observed in storage projects, carries useful information about processes occurring in the injection formation. The Krechba gas field at In Salah (Algeria) is one of the best-known sites for studying ground surface deformation during geological carbon storage. At this first industrial-scale on-shore CO2 demonstration project, satellite-based ground-deformation monitoring data of high quality are available and used to study the large-scale hydrological and geomechanical response of the system to injection. In this work, we carry out coupled fluid flow and geomechanical simulations to understand the uplift at three different CO2 injection wells (KB-501, KB-502, KB-503). Previous numerical studies focused on the KB-502 injection well, where a double-lobe uplift pattern has been observed in the ground-deformation data. The observed uplift patterns at KB-501 and KB-503 have single-lobe patterns, but they can also indicate a deep fracture zone mechanical response to the injection.The current study improves the previous modeling approach by introducing an injection reservoir and a fracture zone, both responding to a Mohr-Coulomb failure criterion. In addition, we model a stress-dependent permeability and bulk modulus, according to a dual continuum model. Mechanical and hydraulic properties are determined through inverse modeling by matching the simulated spatial and temporal evolution of uplift to InSAR observations as well as by matching simulated and measured pressures. The numerical simulations are in agreement with both spatial and temporal observations. The estimated values for the parameterized mechanical and hydraulic properties are in good agreement with previous numerical results. In addition, the formal joint inversion of hydrogeological and geomechanical data provides measures of the estimation uncertainty.

Effects of in situ stress measurement uncertainties on assessment of predicted seismic activity and risk associated with a hypothetical industrial-scale geologic CO2 sequestration operation

Carbon capture and storage (CCS) in geologic formations has been recognized as a promising option for reducing carbon dioxide (CO2) emissions from large stationary sources. However, the pressure buildup inside the storage formation can potentially induce slip along preexisting faults, which could lead to felt seismic ground motion and also provide pathways for brine/CO2 leakage into shallow drinking water aquifers. To assess the geomechanical stability of faults, it is of crucial importance to know the in situ state of stress. In situ stress measurements can provide some information on the stresses acting on faults but with considerable uncertainties. In this paper, we investigate how such uncertainties, as defined by the variation of stress measurements obtained within the study area, could influence the assessment of the geomechanical stability of faults and the characteristics of potential injection-induced seismic events. Our modeling study is based on a hypothetical industrial-scale carbon sequestration project assumed to be located in the Southern San Joaquin Basin in California, USA. We assess the stability on the major (25 km long) fault that bounds the sequestration site and is subjected to significant reservoir pressure changes as a result of 50 years of CO2 injection. We present a series of geomechanical simulations in which the resolved stresses on the fault were varied over ranges of values corresponding to various stress measurements performed around the study area. The simulation results are analyzed by a statistical approach. Our main results are that the variations in resolved stresses as defined by the range of stress measurements had a negligible effect on the prediction of the seismic risk (maximum magnitude), but an important effect on the timing, the seismicity rate (number of seismic events) and the location of seismic activity.

An overview of TOUGH-based geomechanics models

After the initial development of the first TOUGH-based geomechanics model 15 years ago based on linking TOUGH2 multiphase flow simulator to the FLAC3D geomechanics simulator, at least 15 additional TOUGH-based geomechanics models have appeared in the literature. This development has been fueled by a growing demand and interest for modeling coupled multiphase flow and geomechanical processes related to a number of geoengineering applications, such as in geologic CO2 sequestration, enhanced geothermal systems, unconventional hydrocarbon production, and most recently, related to reservoir stimulation and injection-induced seismicity. This paper provides a brief overview of these TOUGH-based geomechanics models, focusing on some of the most frequently applied to a diverse set of problems associated with geomechanics and its couplings to hydraulic, thermal and chemical processes.

Geomechanical effects of CO2 storage in depleted gas reservoirs in the Netherlands: Inferences from feasibility studies and comparison with aquifer storage

In this paper, the geomechanical impact of large-scale carbon dioxide (CO2) storage in depleted Dutch gas fields is compared with the impact of CO2 storage in saline aquifers. The geomechanical behaviour of four potential CO2 storage sites is examined using flow and geomechanical simulations. Many gas reservoirs in the Netherlands are found in fault blocks, one to a few kilometres wide, laterally bounded by sealing faults. Aquifer depletion or re-pressurization in the lateral direction is seldom an issue because of a lack of active aquifers. Reservoir pressure changes are therefore limited to a gas-bearing fault block, while the induced stress changes affect the gas reservoir and extend 1–3 km away into the surrounding rock. Arguments in favour of CO2 storage in depleted gas fields are: proven seal quality, availability of field data, no record of seal integrity failure by fault reactivation from the seismically active producing Dutch gas fields, and the potential benefits of restoring the virgin formation pressure and stress state to geomechanical stability. On the other hand, CO2 injection in saline aquifers causes pressure build-up that exceeds the virgin hydrostatic pressure. Stress perturbations resulting from pressure build-up affect large areas, extending tens of kilometres away from the injection wells. Induced stresses in top seals are, however, small and do not exceed a few tenths of megapascal for a pressure build-up of a few megapascals in the storage formation. Geomechanical effects on top seals are weak, but could be enhanced close to the injection zone by the thermal effects of injection. Uncertainties related to characterisation of large areas affected by pressure build-up are significant, and seal quality and continuity are more difficult to be demonstrated for aquifers than for depleted gas reservoirs that have held hydrocarbons for millions of years.

Implementation of an Empirical Joint Constitutive Model into Finite-Discrete Element Analysis of the Geomechanical Behaviour of Fractured Rocks

An empirical joint constitutive model (JCM) that captures the rough wall interaction behaviour of individual fractures associated with roughness characteristics observed in laboratory experiments is combined with the solid mechanical model of the finite-discrete element method (FEMDEM). The combined JCM-FEMDEM formulation gives realistic fracture behaviour with respect to shear strength, normal closure, and shear dilatancy and includes the recognition of fracture length influence as seen in experiments. The validity of the numerical model is demonstrated by a comparison with the experimentally established empirical solutions. A 2D plane strain geomechanical simulation is conducted using an outcrop-based naturally fractured rock model with far-field stresses loaded in two consecutive phases, i.e. take-up of isotropic stresses and imposition of two deviatoric stress conditions. The modelled behaviour of natural fractures in response to various stress conditions illustrates a range of realistic behaviour including closure, opening, shearing, dilatancy, and new crack propagation. With the increase in stress ratio, significant deformation enhancement occurs in the vicinity of fracture tips, intersections, and bends, where large apertures can be generated. The JCM-FEMDEM model is also compared with conventional approaches that neglect the scale dependency of joint properties or the roughness-induced additional frictional resistance. The results of this paper have important implications for understanding the geomechanical behaviour of fractured rocks in various engineering activities.

Coupled solid and fluid mechanics simulation for estimating optimum injection pressure during reservoir CO2-EOR

Reservoir geomechanics can play an important role in hydrocarbon recovery mechanism. In CO2-EOR process, reservoir geomechanics analysis is concerned with the simultaneous study of fluid flow and the mechanical response of the reservoir under CO2 injection. Accurate prediction of geomechanical effects during CO2 injection will assist in modeling the Carbon dioxide recovery process and making a better design of process and production equipment. This paper deals with the implementation of a program (FORTRAN 90 interface code), which was developed to couple conventional reservoir (ECLIPSE) and geomechanical (ABAQUS) simulators, using a partial coupling algorithm. A geomechanics reservoir partially coupled approach is presented that allows to iteratively take the impact of geomechanics into account in the fluid flow calculations and therefore performs a better prediction of the process. The proposed approach is illustrated on a realistic field case. The reservoir geomechanics coupled models show that in the case of lower maximum bottom hole injection pressure, the cumulative oil production is more than other scenarios. Moreover at the high injection pressures, the production rates will not change with the injection bottom hole pressure variations. Also the FEM analysis of the reservoir showed that at CO2 injection pressure of 11000 Psi the plastic strain has been occurred in the some parts of the reservoir and the related stress path show a critical behavior.

Modelling of a deepwater Brazilian field to assess fault reactivation and the insitu stresses during production

Fault reactivation and stress distribution are considered during a 30-year production period on a deep-water oil field using a 3D finite element geomechanical numerical simulation. Field geometry is constructed as a geomechanical model with the simulation carried out in terms of total stress; the model incorporated a network of 54 pre-existing faults which permits actual slip to occur. The principal objective is to determine whether the existing faults would propagate through to the seabed during production. The pre-production phase aims to capture material and stress states of the field accounting for salt creep and stress realignment due to the presence of the predefined faults. Preproduction stresses show good agreement with minifrac experimental results; the 3D simulation overestimates the minimum horizontal stress by 1.7-3.7%. The production stage shows that vertical compaction of the reservoir is the major influence on fault slip; the rate and magnitude of the fault slip is directly related to the rate and magnitude of depletion. The maximum fault slip is 0.82 m with normal faulting occurring beneath and thrust faulting occurring above the reservoir. Fault slip is not significant close to the seabed and the pre-existing faults are not anticipated to propagate to the seabed.

Methodology for geomechanically controlled transmissibility through active natural fractures in reservoir simulation

Forecasting water breakthrough is a difficult task to be performed for naturally fractured reservoirs. Modeling flow through natural fractures is computationally intensive for a rigorously refined model. Hence, in many cases, it is not feasible to perform a full-field simulation considering the possibility of fracture reactivation.This work aims at applying a methodology to incorporate the flow through fractures or geomechanically active fractures in a full-field model using a commercial reservoir simulator. This is accomplished by tracking which grid blocks in a model cross the activated fractures followed by the redefinition of interblock transmissibilities. These transmissibilities are calculated using the cubic law that relates fluid flow with the fracture aperture and an average distance between crossed blocks. The methodology is well known as Embedded Discrete Fracture Model (EDFM) (Moinfar, 2013; Moinfar et al., 2014; Li et al., 2009).An in-house finite element geomechanical simulator, one-way coupled with a commercial reservoir simulator, was used to predict in-situ stresses. The classical Mohr-Coulomb failure criterion was employed to calculate fracture shear strength. The natural fracture, or a segment of the fracture, is considered permeable when the applied stress is greater than its shear strength.Various case studies indicate the efficiency and accuracy of the EDFM method in a commercial simulator. In order to demonstrate the accuracy of the method, studies were performed in five spot models, comparing the results to those with a rigorously refined fracture representation. In order to highlight the applicability of the methodology at a field-scale, three reservoir simulation case studies are presented: one comparison with the dual permeability method, one simulation of a giant field, and one simulation coupled with a geomechanical simulator. The results show that the representation of natural fractures in reservoir models may drastically change the production forecast, especially in terms of water production.

Integrated microseismic and geomechanical study in the Barnett Shale Formation

We have developed a careful chronological review of multistage stimulation treatments, in which microseismic interpretation was supported by fracture simulation and finite-element geomechanical simulation. The interpretation of a zipper frac stimulation treatment conducted in the Barnett Shale Formation in 2011 progressed from microseismic interpretation, from well-site observation, to a self-consistent understanding across multiple stages and multiple wells. Through this process, we have developed a tutorial on practical interpretation of microseismic data in the context of the hydraulic fracture treatment information (pump data) and regional structural information from interpretation of 3D seismic sections. Analysis of microseismic data included summarizing groups of events in the form of [Formula: see text]-value, [Formula: see text]-value, and extracted planar geometries. We advocate the development of a chronological interpretation, the consistency of which is tested using forward modeling. The process is iterative and relies on the forward modeling of complex fracturing and finite-element geomechanical models to inform iterations of the interpretation. Although extended case studies of this type are unsuitable for well-site analysis, we recommend their use for planning stimulation treatments for future nearby wells and to inform strategies for refracturing later in the well’s life.

A coupled geomechanical reservoir simulation analysis of CO2- EOR: A case study

Currently, there is a great interest in the coupling between multiphase fluid flow and geomechanical effects in hydrocarbon reservoirs and surrounding rocks. The ideal solution for this coupled problem is to introduce the geomechanical effects through the stress analysis solution and implement an algorithm, which assures that the equations governing the flow and stress analyses are obeyed in each time step. This paper deals with the implementation of a program (FORTRAN90 interface code), which was developed to couple conventional reservoir (ECLIPSE) and geomechanical (ABAQUS) simulators, using a partial coupling algorithm. The explicit coupled hydro-mechanical behavior of Iranian field during depletion and <TEX>$CO_2$</TEX> injection is studied using the soils consolidation procedure available in ABAQUS. Time dependent reservoir pressure fields obtained from three dimensional compositional reservoir models were transferred into finite element reservoir geomechanical models in ABAQUS as multi-phase flow in deforming reservoirs cannot be performed within ABAQUS. The FEM analysis of the reservoir showed no sign of plastic strain under production and <TEX>$CO_2$</TEX> injection scenarios in any part of the reservoir and the stress paths do not show a critical behavior.

Isotropic and anisotropic velocity-model building for subsalt seismic imaging

Basin simulators have been used previously for deriving subsalt velocity models with the use of a correlation to relate effective stress to velocity. We build on this, and the work of others, to use physical models to relate porosity to velocity for migrating seismic data. This process yields a physically realizable isotropic velocity model that is consistent with the geologic model and matches the tomographic velocity model above salt and in regions where the tomographic velocity estimate is accurate. We then use a geomechanical simulator to model the stress distribution in and around allochthonous salt where material properties between salt and sediment change. Our stress model is the basis for an anisotropic velocity model using Murnaghan's theory for finite elastic deformation. This formulation, with bounds placed on the elastic coefficients, leads to significant imaging improvements adjacent to salt.

Investigation of Hydromechanical Mechanisms in Microseismicity Generation in Natural Fractures Induced by Hydraulic Fracturing

SummaryEconomic success in producing oil/gas from low-permeability shale often relies on pre-existing natural fractures (NFs) to be activated or connected by hydraulic-fracturing (HF) stimulation. In practice, the reactivated NF network is often identified with the microseismicity (MS) monitored during the stimulation. However, the fundamental mechanisms of MS generation and focal mechanisms inferred from geophysical analysis near HFs are not currently well-understood (e.g., it is not clear whether the MS observed in the field can be mainly attributed to local shear slip along NFs when leakoff occurs and/or induced by stress changes as a result of HF propagation or fluid leakoff). The exact slippage area and amount of slip displacement generating the microseismic event are not well-understood either, thus requiring a “bridge” between geomechanics and geophysics. To bridge this gap, a set of experiments is performed in a geomechanics laboratory to observe whether, when, where, and how the acoustic-emission events are generated during various scenarios. The experiments are designed with the guidance of the fracture-flow/discrete-element method (DEM), coupling geomechanical simulations. In this paper, the reliability and accuracy of the fracture-flow/DEM coupling approach is validated through solving a few fundamental problems and comparing the numerical-simulation results with the corresponding analytical solutions. The coupling approach is then applied to simulate and optimize two fundamental laboratory experiments. The simulations indicate that, despite the difference in the magnitude, one could induce the local slip along NFs by both fluid leakoff and stress changes.

Material point modelling of releasing geocontainers from a barge

Numerical modelling of thin structures combined with history-dependent material under large deformation is challenging for the traditional methods of analysis. The material point method (MPM), in which the continuum is represented by material points, is a Lagrangian–Eulerian procedure suited for granular material and geomechanical simulations. The releasing process of geocontainers within a barge is simulated, in which the split barge is modelled via boundary particles with prescribed angular velocity. Various frictional contact coefficients between the barge and geotextile material are considered. Moreover, the influence of adding wrinkles to the bottom of the container that follows practice is evaluated and the predictions are compared to that of a non-slack geotextile. The effect of soil properties on the geotextile forces are also examined.

Geomechanical simulation of the stress tensor rotation caused by injection of cold water in a deep geothermal reservoir

AbstractWe present a three‐dimensional thermohydromechanical numerical study of the evolution and distribution of the stress tensor within the northwest part of The Geysers geothermal reservoir (in California), including a detailed study of the region around one injection well from 2003 to 2012. Initially, after imposing a normal faulting stress regime, we calculated local changes in the stress regime around injection wells. Our results were compared with previously published studies in which the stress state was inferred from inverting the focal plane mechanism of seismic events. Our main finding is that changes in stress tensor orientation are caused by injection‐induced progressive cooling of the reservoir, as well as by the seasonal variations in injection rate. Because of the gravity flow and cooling around a liquid zone formed by the injection, the vertical stress reduction is larger and propagates far below the injection well. At the same time, the horizontal stress increases, mostly because of stress redistribution below and above the cooling area. These two phenomena cause the rotation of the stress tensor and the appearance of a strike‐slip regime above, inside, and below the cooling area. The cooling and the associated rotation of the stress regime can play a significant role in the observed long‐term deepening of the microseismicity below active injection wells.

Modelling ground rupture due to groundwater withdrawal: applications to test cases in China and Mexico

Abstract. The stress variation induced by aquifer overdraft in sedimentary basins with shallow bedrock may cause rupture in the form of pre-existing fault activation or earth fissure generation. The process is causing major detrimental effects on a many areas in China and Mexico. Ruptures yield discontinuity in both displacement and stress field that classic continuous finite element (FE) models cannot address. Interface finite elements (IE), typically used in contact mechanics, may be of great help and are implemented herein to simulate the fault geomechanical behaviour. Two main approaches, i.e. Penalty and Lagrangian, are developed to enforce the contact condition on the element interface. The incorporation of IE incorporation into a three-dimensional (3-D) FE geomechanical simulator shows that the Lagrangian approach is numerically more robust and stable than the Penalty, thus providing more reliable solutions. Furthermore, the use of a Newton-Raphson scheme to deal with the non-linear elasto-plastic fault behaviour allows for quadratic convergence. The FE – IE model is applied to investigate the likely ground rupture in realistic 3-D geologic settings. The case studies are representative of the City of Wuxi in the Jiangsu Province (China), and of the City of Queretaro, Mexico, where significant land subsidence has been accompanied by the generation of several earth fissures jeopardizing the stability and integrity of the overland structures and infrastructure.

Energy-based hydraulic fracture numerical simulation: Parameter selection and model validation using microseismicity

We have investigated the use of an energy-based numerical algorithm and its ability to simulate growth of a single planar hydraulic fracture by matching modeled dimensions to those inferred from a microseismic map. The energy-based microseismic fracture model accounts for the various physical processes expressed as a balance between the work expended (input/injected energy) and work done (output/lost energy) during growth of a vertical, 3D, laterally symmetric, planar, ellipsoidal, and tensile (mode I) fracture. These canonical fracture models provide a simple but useful proxy for more complex fracture networks that occur in reality. The tensile fracture is positioned in a three-layer geologic medium defined by elastic, material, and stress properties. Fracture half-length, half-width, half-height, and effective crack-opening pressure were computed using a time-stepping algorithm that solved energy balance equations using a Lagrangian formulation. Two parameters are adjusted to calibrate the fracture model to microseismic data; observed upward growth is fit by adjusting stress-barrier contrasts, and fracture length is fit by altering an empirical parameter, fracture toughness. In the case of a symmetric model with equivalent stress and material properties above and below the fracture, an increase in fracture toughness results in a corresponding increase in modeled net pressure and fracture width profile. In the case of a model with different stress states in the layers above and below the injection level, fracture height growth is enhanced in the layer with lower in situ stress. In both cases, net work is minimized in response to trade-offs between creation of new fracture surface area and fracture volume. Our primary objective was to incorporate microseismic observations into a geomechanical simulation of hydraulic fracture growth. Our approach is novel; it explains hydraulic-fracture behavior from an energy-balance perspective using the spatial-temporal evolution of microseismicity to constrain and validate the model.

Reservoir characterization in an underground gas storage field using joint inversion of flow and geodetic data

SummaryCharacterization of reservoir properties like porosity and permeability in reservoir models typically relies on history matching of production data, well pressure data, and possibly other fluid‐dynamical data. Calibrated (history‐matched) reservoir models are then used for forecasting production and designing effective strategies for improved oil and gas recovery. Here, we perform assimilation of both flow and deformation data for joint inversion of reservoir properties. Given the coupled nature of subsurface flow and deformation processes, joint inversion requires efficient simulation tools of coupled reservoir flow and mechanical deformation. We apply our coupled simulation tool to a real underground gas storage field in Italy. We simulate the initial gas production period and several decades of seasonal natural gas storage and production. We perform a probabilistic estimation of rock properties by joint inversion of ground deformation data from geodetic measurements and fluid flow data from wells. Using an efficient implementation of the ensemble smoother as the estimator and our coupled multiphase flow and geomechanics simulator as the forward model, we show that incorporating deformation data leads to a significant reduction of uncertainty in the prior distributions of rock properties such as porosity, permeability, and pore compressibility. Copyright © 2015 John Wiley &amp; Sons, Ltd.