In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a ge...In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.展开更多
In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators bas...In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.展开更多
An elastomeric gel is a mixture of a polymer network and a solvent. In response to changes in mechanical forces and in the chemical potential of the solvent in the environment, the gel evolves by two concurrent molecu...An elastomeric gel is a mixture of a polymer network and a solvent. In response to changes in mechanical forces and in the chemical potential of the solvent in the environment, the gel evolves by two concurrent molecular processes： the conformational change of the network, and the migration of the solvent. The two processes result in viscoelasticity and poroelasticity, and are characterized by two material-specific properties： the time of viscoelastic relaxation and the effective diffusivity of the solvent through the network. The two properties define a material- specific length. The material-specific time and length enable us to discuss macroscopic observations made over different lengths and times, and identify limiting conditions in which viscoelastic and poroelastic relaxations have either completed or yet started. We formulate a model of homogeneous deformation, and use several examples to illustrate viscoelasticity-limited solvent migration, where the migration of the solvent is pronounced, but the size of the gel is so small that the rate of change is limited by viscoelasticity. We further describe a theory that evolves a gel through inhomogeneous states. Both infinitesimal and finite deformation are considered.展开更多
Seismic amplitude variation with offset(AVO) inversion is an important approach for quantitative prediction of rock elasticity,lithology and fluid properties.With Biot-Gassmann's poroelasticity,an improved statist...Seismic amplitude variation with offset(AVO) inversion is an important approach for quantitative prediction of rock elasticity,lithology and fluid properties.With Biot-Gassmann's poroelasticity,an improved statistical AVO inversion approach is proposed.To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients,the AVO equation of reflection coefficients parameterized by porosity,rock-matrix moduli,density and fluid modulus is initially derived from Gassmann equation and critical porosity model.From the analysis of the influences of model parameters on the proposed AVO equation,rock porosity has the greatest influences,followed by rock-matrix moduli and density,and fluid modulus has the least influences among these model parameters.Furthermore,a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity,rock-matrix modulus,density and fluid modulus.Besides,the Laplace probability model and differential evolution,Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework.Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters,which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.展开更多
Abstract Hydrogel can swell to many times of its dry volume, resulting in large deformation which is vital for its function. The swelling process is regulated by many physical and chemical mechanisms, and can, to some...Abstract Hydrogel can swell to many times of its dry volume, resulting in large deformation which is vital for its function. The swelling process is regulated by many physical and chemical mechanisms, and can, to some extent, be fairly described by the poroelasticity theory. Implementation of the poroelastieity theory in the framework of finite element method would aid the design and optimization of hydrogel-based soft devices. Choosing chemical potential and displacement as two field variables, we present the implementation of poroelastieity tailored for hydrogel swelling dynamics, detail the normalization of physical parameters and the treatment of boundary conditions. Several examples are presented to demonstrate the feasibility and correctness of the proposed strategy.展开更多
In this paper,a multirate time iterative scheme with multiphysics finite element method is proposed and analyzed for the nonlinear poroelasticity model.The original problem is reformulated into a generalized nonlinear...In this paper,a multirate time iterative scheme with multiphysics finite element method is proposed and analyzed for the nonlinear poroelasticity model.The original problem is reformulated into a generalized nonlinear Stokes problem coupled with a diffusion problem of a pseudo pressure field by a new multiphysics approach.A multiphysics finite element method is adopted for the spatial discretization,and the generalized nonlinear Stokes problem is solved in a coarse time step and the diffusion problem is solved in a finer time step.The proposed algorithm is a decoupled algorithm,which is easily implemented in computation and reduces greatly computation cost.The stability analysis and the convergence analysis for the multirate iterative scheme with multiphysics finite element method are given.Some numerical tests are shown to demonstrate and validate the analysis results.展开更多
Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential...Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.展开更多
In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space.We choose N´ed´elec edge elemen...In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space.We choose N´ed´elec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem.In constructing multigrid algorithm,a distributive Gauss-Seidel iteration method is applied.Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size h and parameter dt on regular meshes.展开更多
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which c...We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.展开更多
Development and production from fractured reservoirs require extensive knowledge about the reservoir structures and in situ stress regimes.For this,this paper investigates fractures and the parameters(aperture and den...Development and production from fractured reservoirs require extensive knowledge about the reservoir structures and in situ stress regimes.For this,this paper investigates fractures and the parameters(aperture and density)through a combination of wellbore data and geomechanical laboratory testing in three separate wells in the Asmari reservoir,Zagros Belt,Iran.The Asmari reservoir(Oligo-Miocene)consists mainly of calcitic and dolomitic rocks in depths of 2000e3000 m.Based on the observation of features in several wellbores,the orientation and magnitude of the in situ stresses along with their influence on reservoir-scale geological structures and neotectonics were determined.The study identifies two regional tectonic fracture settings in the reservoir:one set associated with longitudinal and diagonal wrinkling,and the other related to faulting.The former,which is mainly of open fractures with a large aperture,is dominant and generally oriented in the N45°-90°W direction while the latter is obliquely oriented relative to the bedding and characterized by N45°-90°E.The largest aperture is found in open fractures that are longitudinal and developed in the dolomitic zones within a complex stress regime.Moreover,analysis of drilling-induced fractures(DIFs)and borehole breakouts(BBs)from the image logs revealed that the maximum horizontal stress(SHmax)orientation in these three wells is consistent with the NE-SW regional trend of the SHmax(maximum principal horizontal stress)in the Zagros Belt.Likewise,the stress magnitude obtained from geomechanical testing and poroelastic equations confirmed a variation in stress regime from normal to reverse,which changes in regard to active faults in the study area.Finally,a relationship between the development degree of open fractures and in situ stress regime was found.This means that in areas where the stress regime is complex and reverse,fractures would exhibit higher density,dip angle,and larger apertures.展开更多
In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role ...In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role in determining flow dynamics and the resulting formation deformation.Existing models of the wellbore skin zone generally assume a constant permeability throughout,resulting in a sharp permeability discontinuity at the skin-reservoir interface.This paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic medium.Analytical solutions are derived using the Laplace transform method,addressing both positive and negative skin zones.Numerical results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a wellbore.The results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.展开更多
Injection-induced seismicity has been a focus of industry for decades as it poses great challenges to the associated risk mitigation and hazard assessment.The response surface methodology is integrated into the geo-me...Injection-induced seismicity has been a focus of industry for decades as it poses great challenges to the associated risk mitigation and hazard assessment.The response surface methodology is integrated into the geo-mechanical model to analyze the effects of multiple factors on induced seismicity during the post shut-in period.We investigate the roles of poroelastic stress and pore pressure diffusion and examine the differences in the controlling mechanism between fault damage zones and the fault core.A sensitivity analysis is conducted to rank the selected factors,followed by a Box‒Behnken design to form response surfaces and formulate prediction models for the Coulomb stress and its components.Reservoir properties significantly affect the potentials of induced seismicity in the fault by changing pore pressure diffusion,which can be influenced by other factors to varying degrees.Coulomb stress is greater in pressurized damage zones than in fault cores,and the seismicity rate exhibits a consistent variation.Poroelastic stress plays a similar role to pore pressure diffusion in the stability of the fault within the pressurized damage zones.However,pore pressure diffusion dominates in the fault core due to the low rigidity,which limits the accumulation of elastic energy caused by poroelastic coupling.The slip along the fault core is a critical issue to consider.The potential for induced seismicity is reduced in the right damage zones as the pore pressure diffusion is blocked by the low-permeability fault core.However,poroelastic stressing still occurs,and in deep basements,the poroelastic effect is dominant even without a direct increase in pore pressure.The findings in this study reveal the fundamental mechanisms behind injection-induced seismicity and provide guidance for optimizing injection schemes in specific situations.展开更多
The similarities and differences in inherent mechanism and characteristic frequency between the onedimensional(1D)poroelastic model and the layered White model were investigated.This investigation was conducted under ...The similarities and differences in inherent mechanism and characteristic frequency between the onedimensional(1D)poroelastic model and the layered White model were investigated.This investigation was conducted under the assumption that the rock was homogenous and isotropic at the mesoscopic scale.For the inherent mechanism,both models resulted from quasi-static flow in a slow P-wave diffusion mode,and the differences between them originated from saturated fluids and boundary conditions.On the other hand,for the characteristic frequencies of the models,the characteristic frequency of the 1D poroelastic model was first modified because the elastic constant and formula for calculating it were misused and then compared to that of the layered White model.Both of them moved towards higher frequencies with increasing permeability and decreasing viscosity and diffusion length.The differences between them were due to the diffusion length.The diffusion length for the 1D poroelastic model was determined by the sample length,whereas that for the layered White model was determined by the length of the representative elementary volume(REV).Subsequently,a numerical example was presented to demonstrate the similarities and differences between the models.Finally,published experimental data were interpreted using the 1D poroelastic model combined with the Cole-Cole model.The prediction of the combined model was in good agreement with the experimental data,thereby validating the effectiveness of the 1D poroelastic model.Furthermore,the modified characteristic frequency in our study was much closer to the experimental data than the previous prediction,validating the effectiveness of our modification of the characteristic frequency of the 1D poroelastic model.The investigation provided insight into the internal relationship between wave-induced fluid flow(WIFF)models at macroscopic and mesoscopic scales and can aid in a better understanding of the elastic modulus dispersion and attenuation caused by the WIFF at different scales.展开更多
In this paper,we develop a fully discrete virtual element scheme based on the local pressure projection stabilization for a three-field poroelasticity problem with a storage coefficient c00.We not only provide the wel...In this paper,we develop a fully discrete virtual element scheme based on the local pressure projection stabilization for a three-field poroelasticity problem with a storage coefficient c00.We not only provide the well-posedness of the proposed scheme by proving a weaker form of the discrete inf-sup condition,but also show optimal error estimates for all unknowns,whose generic constants are independent of the Lam´e coefficient.Moreover,our proposed scheme avoids pressure oscillation and applies to general polygonal elements,including hanging-node elements.Finally,we numerically validate the good performance of our virtual element scheme.展开更多
In order to quantify the poroelastic mechanical signals conduction and evaluate the biomechanical effectiveness of functional units(osteocyte processes,canaliculi and lacuna)in lacunar-canalicular system(LCS),a multis...In order to quantify the poroelastic mechanical signals conduction and evaluate the biomechanical effectiveness of functional units(osteocyte processes,canaliculi and lacuna)in lacunar-canalicular system(LCS),a multiscale poroelastic finite element model was established by using the Comsol Multiphysics software.The poroelastic mechanical signals(pore pressure,fluid velocity,von-Mises stress,strain)were analyzed inside the osteon-osteocyte system.The effects of osteocyte(OCY)’s shape(ellipse and circle),long axis directions(horizontal and vertical)and mechanical properties(Elastic modulus and permeability)on its poroelastic responses were examined.It is found that the OCY processes is the best mechanosensor compared with the OCY body,lacunae and canaliculi.The mechanotransduction ability of the elliptic shaped OCY is stronger than that of circular shaped.The pore pressure and flow velocity around OCYs increase as the elastic modulus and permeability of OCY increase.The established model can be used for studying the mechanism of bone mechanotransduction at the multiscale level.展开更多
Connecting earthquake nucleation in basement rock to fluid injection in basal,sedimentary reservoirs,depends heavily on choices related to the poroelastic properties of the fluid-rock system,thermo-chemical effects no...Connecting earthquake nucleation in basement rock to fluid injection in basal,sedimentary reservoirs,depends heavily on choices related to the poroelastic properties of the fluid-rock system,thermo-chemical effects notwithstanding.Direct constraints on these parameters outside of laboratory settings are rare,and it is commonly assumed that the rock layers are isotropic.With the Arbuckle wastewater disposal reservoir in Osage County,Oklahoma,high-frequency formation pressure changes and collocated broadband ground velocities measured during the passing of large teleseismic waves show a poroelastic response of the reservoir that is both azimuthally variable and anisotropic;this includes evidence of static shifts in pressure that presumably relate to changes in local permeability.The azimuthal dependence in both the static response and shear coupling appears related to tectonic stress and strain indicators such as the orientations of the maximum horizontal stress and faults and fractures.Using dynamic strains from a nearby borehole strainmeter,we show that the ratio of shear to volumetric strain coupling is~0.41 which implies a mean Skempton's coefficient of A=0.24 over the plausible range of the undrained Poisson's ratio.Since these observations are made at relatively low confining pressure and differential stress,we suggest that the hydraulically conductive fracture network is a primary control on the coupling between pore pressure diffusion and elastic stresses in response to natural or anthropogenic sources.展开更多
From 2009 to 2017,parts of Central America experienced marked increase in the number of small to moderate-sized earthquakes.For example,three significant earthquakes(~Mw 5)occurred near Prague,Oklahoma,in the U.S.in 2...From 2009 to 2017,parts of Central America experienced marked increase in the number of small to moderate-sized earthquakes.For example,three significant earthquakes(~Mw 5)occurred near Prague,Oklahoma,in the U.S.in 2011.On 6 Nov 2011,an Mw 5.7 earthquake occurred in Prague,central Oklahoma with a sequence of aftershocks.The seismic activity has been attributed to slip on the Wilzetta fault system.This study provides a 3 D fully coupled poroelastic analysis(using FLAC3 D)of the Wilzetta fault system and its response to saltwater injection in the underpressured subsurface layers,especially the Arbuckle group and the basement,to evaluate the conditions that might have led to the increased seismicity.Given the data-limited nature of the problem,we have considered multiple plausible scenarios,and use the available data to evaluate the hydromechanical response of the faults of interest in the study area.Numerical simulations show that the injection of large volumes of fluid into the Arbuckle group tends to bring the part of the Wilzetta faults in Arbuckle group and basement into near-critical conditions.展开更多
A linear viscoporoelastic model is developed to describe the problem of reflection and transmission of an obliquely incident plane P-wave at the interface between an elastic solid and an unsaturated poroelastic medium...A linear viscoporoelastic model is developed to describe the problem of reflection and transmission of an obliquely incident plane P-wave at the interface between an elastic solid and an unsaturated poroelastic medium, in which the solid matrix is filled with two weakly coupled fluids （liquid and gas）. The expressions for the amplitude reflection coefficients and the amplitude transmission coefficients are derived by using the potential method. The present derivation is subsequently applied to study the energy conversions among the incident, reflected, and transmitted wave modes. It is found that the reflection and transmission coefficients in the forms of amplitude ratios and energy ratios are functions of the incident angle, the liquid saturation, the frequency of the incident wave, and the elastic constants of the upper and lower media. Numerical results are presented graphically. The effects of the incident angle, the frequency, and the liquid saturation on the amplitude and the energy reflection and transmission coefficients are discussed. It is verified that in the transmission process, there is no energy dissipation at the interface.展开更多
A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In part...A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.展开更多
Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to reduce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitori...Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to reduce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitoring is essential on ascertaining movement, volumes and locations of injected CO2 in the sequestration reservoir. One technique is to use time-lapsed seismic survey mapping to provide spatial distribution of seismic wave velocity as an indicator of CO2 migration and volumes in a storage reservoir with time. To examine the use of time-lapsed seismic survey mapping as a monitoring tool for CO2 sequestration, this paper presents mathematical and experimental studies of the effects of supercritical CO2 injection on the seismic velocity of sandstone initially saturated with saline water. The mathematical model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the modeling of the acoustic velocity of porous rocks containing two-phase immiscible pore fluids. The experimental study uses a high pressure and high temperature triaxial cell to clarify the seismic response of a sample of Berea sandstone to supercritical CO2 injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO2 injection in the sandstone sample show the effects of pore fluid distribution in the seismic velocity of porous rocks. CO2 injection was shown to decrease the P-wave velocity with increasing CO2 saturation whereas the S-wave velocity was almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity of sandstone containing different mixtures of supercritical CO2 and saline water provided the distribution of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus. The empirical relation of Brie et al. for the bulk modulus of mixtures of two-phase immiscible fluids, in combination with the Biot-Gassmann theory, was found to satisfactorily represent the pore-fluid dependent acoustic P-wave velocity of sandstone.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.12371393,11971150 and 11801143)Natural Science Foundation of Henan Province(Grant No.242300421047).
文摘In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371393 and 11971150)Natural Science Foundation of Henan(Grant No.242300421047).
文摘In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.
基金supported by the National Science Foundation (NSF) (CMMI-0800161)Multidisciplinary University Research Initiative (MURI) (W911NF-09-1-0476)the Materials Research Science and Engineering Center at Harvard University (DMR-0820484)
文摘An elastomeric gel is a mixture of a polymer network and a solvent. In response to changes in mechanical forces and in the chemical potential of the solvent in the environment, the gel evolves by two concurrent molecular processes： the conformational change of the network, and the migration of the solvent. The two processes result in viscoelasticity and poroelasticity, and are characterized by two material-specific properties： the time of viscoelastic relaxation and the effective diffusivity of the solvent through the network. The two properties define a material- specific length. The material-specific time and length enable us to discuss macroscopic observations made over different lengths and times, and identify limiting conditions in which viscoelastic and poroelastic relaxations have either completed or yet started. We formulate a model of homogeneous deformation, and use several examples to illustrate viscoelasticity-limited solvent migration, where the migration of the solvent is pronounced, but the size of the gel is so small that the rate of change is limited by viscoelasticity. We further describe a theory that evolves a gel through inhomogeneous states. Both infinitesimal and finite deformation are considered.
基金the sponsorship of National Grand Project for Science and Technology(2016ZX05024004,2017ZX05009001,2017ZX05032003)the Fundamental Research Funds for the Central Universities(20CX06036A)+1 种基金the Postdoctoral Applied Research Project of Qingdao(QDYY20190040)the Science Foundation from SINOPEC Key Laboratory of Geophysics(wtyjy-wx2019-01-04)。
文摘Seismic amplitude variation with offset(AVO) inversion is an important approach for quantitative prediction of rock elasticity,lithology and fluid properties.With Biot-Gassmann's poroelasticity,an improved statistical AVO inversion approach is proposed.To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients,the AVO equation of reflection coefficients parameterized by porosity,rock-matrix moduli,density and fluid modulus is initially derived from Gassmann equation and critical porosity model.From the analysis of the influences of model parameters on the proposed AVO equation,rock porosity has the greatest influences,followed by rock-matrix moduli and density,and fluid modulus has the least influences among these model parameters.Furthermore,a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity,rock-matrix modulus,density and fluid modulus.Besides,the Laplace probability model and differential evolution,Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework.Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters,which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.
基金supported by the National Natural Science Foundation of China(11072185,11372239,and 11021202)
文摘Abstract Hydrogel can swell to many times of its dry volume, resulting in large deformation which is vital for its function. The swelling process is regulated by many physical and chemical mechanisms, and can, to some extent, be fairly described by the poroelasticity theory. Implementation of the poroelastieity theory in the framework of finite element method would aid the design and optimization of hydrogel-based soft devices. Choosing chemical potential and displacement as two field variables, we present the implementation of poroelastieity tailored for hydrogel swelling dynamics, detail the normalization of physical parameters and the treatment of boundary conditions. Several examples are presented to demonstrate the feasibility and correctness of the proposed strategy.
基金supported by the National Natural Science Foundation of China(Grant No.11971150)partially by the National Natural Science Foundation of China(Grant No.11801143).
文摘In this paper,a multirate time iterative scheme with multiphysics finite element method is proposed and analyzed for the nonlinear poroelasticity model.The original problem is reformulated into a generalized nonlinear Stokes problem coupled with a diffusion problem of a pseudo pressure field by a new multiphysics approach.A multiphysics finite element method is adopted for the spatial discretization,and the generalized nonlinear Stokes problem is solved in a coarse time step and the diffusion problem is solved in a finer time step.The proposed algorithm is a decoupled algorithm,which is easily implemented in computation and reduces greatly computation cost.The stability analysis and the convergence analysis for the multirate iterative scheme with multiphysics finite element method are given.Some numerical tests are shown to demonstrate and validate the analysis results.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12272269, 11972257,11832014 and 11472193)the Shanghai Pilot Program for Basic Researchthe Shanghai Gaofeng Project for University Academic Program Development。
文摘Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.
基金The first author is supported by the National Natural Science Foundation of China under Grant No.11501473,No.11426189the Fundamental Research Funds for the Central Universities of China(No.2682016CX108)The second author is supported by the National Natural Science Foundation of China under Grant No.11671157.
文摘In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space.We choose N´ed´elec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem.In constructing multigrid algorithm,a distributive Gauss-Seidel iteration method is applied.Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size h and parameter dt on regular meshes.
文摘We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.
文摘Development and production from fractured reservoirs require extensive knowledge about the reservoir structures and in situ stress regimes.For this,this paper investigates fractures and the parameters(aperture and density)through a combination of wellbore data and geomechanical laboratory testing in three separate wells in the Asmari reservoir,Zagros Belt,Iran.The Asmari reservoir(Oligo-Miocene)consists mainly of calcitic and dolomitic rocks in depths of 2000e3000 m.Based on the observation of features in several wellbores,the orientation and magnitude of the in situ stresses along with their influence on reservoir-scale geological structures and neotectonics were determined.The study identifies two regional tectonic fracture settings in the reservoir:one set associated with longitudinal and diagonal wrinkling,and the other related to faulting.The former,which is mainly of open fractures with a large aperture,is dominant and generally oriented in the N45°-90°W direction while the latter is obliquely oriented relative to the bedding and characterized by N45°-90°E.The largest aperture is found in open fractures that are longitudinal and developed in the dolomitic zones within a complex stress regime.Moreover,analysis of drilling-induced fractures(DIFs)and borehole breakouts(BBs)from the image logs revealed that the maximum horizontal stress(SHmax)orientation in these three wells is consistent with the NE-SW regional trend of the SHmax(maximum principal horizontal stress)in the Zagros Belt.Likewise,the stress magnitude obtained from geomechanical testing and poroelastic equations confirmed a variation in stress regime from normal to reverse,which changes in regard to active faults in the study area.Finally,a relationship between the development degree of open fractures and in situ stress regime was found.This means that in areas where the stress regime is complex and reverse,fractures would exhibit higher density,dip angle,and larger apertures.
基金the financial support from Shaanxi Key Research and Development Program under Grant No.2023-YBGY-058the Fundamental Research Funds for the Central Universities under Grant No.G2020KY05312.
文摘In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role in determining flow dynamics and the resulting formation deformation.Existing models of the wellbore skin zone generally assume a constant permeability throughout,resulting in a sharp permeability discontinuity at the skin-reservoir interface.This paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic medium.Analytical solutions are derived using the Laplace transform method,addressing both positive and negative skin zones.Numerical results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a wellbore.The results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.
基金the Major Project of Inner Mongolia Science and Technology(Grant No.2021ZD0034)National Natural Science Foundation of China(Grant No.41872210)Creative Groups of Natural Science Foundation of Hubei Province(Grant No.2021CFA030).
文摘Injection-induced seismicity has been a focus of industry for decades as it poses great challenges to the associated risk mitigation and hazard assessment.The response surface methodology is integrated into the geo-mechanical model to analyze the effects of multiple factors on induced seismicity during the post shut-in period.We investigate the roles of poroelastic stress and pore pressure diffusion and examine the differences in the controlling mechanism between fault damage zones and the fault core.A sensitivity analysis is conducted to rank the selected factors,followed by a Box‒Behnken design to form response surfaces and formulate prediction models for the Coulomb stress and its components.Reservoir properties significantly affect the potentials of induced seismicity in the fault by changing pore pressure diffusion,which can be influenced by other factors to varying degrees.Coulomb stress is greater in pressurized damage zones than in fault cores,and the seismicity rate exhibits a consistent variation.Poroelastic stress plays a similar role to pore pressure diffusion in the stability of the fault within the pressurized damage zones.However,pore pressure diffusion dominates in the fault core due to the low rigidity,which limits the accumulation of elastic energy caused by poroelastic coupling.The slip along the fault core is a critical issue to consider.The potential for induced seismicity is reduced in the right damage zones as the pore pressure diffusion is blocked by the low-permeability fault core.However,poroelastic stressing still occurs,and in deep basements,the poroelastic effect is dominant even without a direct increase in pore pressure.The findings in this study reveal the fundamental mechanisms behind injection-induced seismicity and provide guidance for optimizing injection schemes in specific situations.
基金supported by the National Natural Science Foundation of China (42030810,42104115)。
文摘The similarities and differences in inherent mechanism and characteristic frequency between the onedimensional(1D)poroelastic model and the layered White model were investigated.This investigation was conducted under the assumption that the rock was homogenous and isotropic at the mesoscopic scale.For the inherent mechanism,both models resulted from quasi-static flow in a slow P-wave diffusion mode,and the differences between them originated from saturated fluids and boundary conditions.On the other hand,for the characteristic frequencies of the models,the characteristic frequency of the 1D poroelastic model was first modified because the elastic constant and formula for calculating it were misused and then compared to that of the layered White model.Both of them moved towards higher frequencies with increasing permeability and decreasing viscosity and diffusion length.The differences between them were due to the diffusion length.The diffusion length for the 1D poroelastic model was determined by the sample length,whereas that for the layered White model was determined by the length of the representative elementary volume(REV).Subsequently,a numerical example was presented to demonstrate the similarities and differences between the models.Finally,published experimental data were interpreted using the 1D poroelastic model combined with the Cole-Cole model.The prediction of the combined model was in good agreement with the experimental data,thereby validating the effectiveness of the 1D poroelastic model.Furthermore,the modified characteristic frequency in our study was much closer to the experimental data than the previous prediction,validating the effectiveness of our modification of the characteristic frequency of the 1D poroelastic model.The investigation provided insight into the internal relationship between wave-induced fluid flow(WIFF)models at macroscopic and mesoscopic scales and can aid in a better understanding of the elastic modulus dispersion and attenuation caused by the WIFF at different scales.
基金supported in part by the National Natural Science Foundation of China(Grant No.12371405).
文摘In this paper,we develop a fully discrete virtual element scheme based on the local pressure projection stabilization for a three-field poroelasticity problem with a storage coefficient c00.We not only provide the well-posedness of the proposed scheme by proving a weaker form of the discrete inf-sup condition,but also show optimal error estimates for all unknowns,whose generic constants are independent of the Lam´e coefficient.Moreover,our proposed scheme avoids pressure oscillation and applies to general polygonal elements,including hanging-node elements.Finally,we numerically validate the good performance of our virtual element scheme.
基金supported by the National Natural Science Foundation of China(Grants 11972242,11702183,11632013,and 11572213)the Scientific and Technological Innovation Projects of Colleges and Universities in Shanxi Province(Grant 2017135)Philosophy and Social Sciences Research of Higher Learning Institutions of Shanxi(Grant 2017313).
文摘In order to quantify the poroelastic mechanical signals conduction and evaluate the biomechanical effectiveness of functional units(osteocyte processes,canaliculi and lacuna)in lacunar-canalicular system(LCS),a multiscale poroelastic finite element model was established by using the Comsol Multiphysics software.The poroelastic mechanical signals(pore pressure,fluid velocity,von-Mises stress,strain)were analyzed inside the osteon-osteocyte system.The effects of osteocyte(OCY)’s shape(ellipse and circle),long axis directions(horizontal and vertical)and mechanical properties(Elastic modulus and permeability)on its poroelastic responses were examined.It is found that the OCY processes is the best mechanosensor compared with the OCY body,lacunae and canaliculi.The mechanotransduction ability of the elliptic shaped OCY is stronger than that of circular shaped.The pore pressure and flow velocity around OCYs increase as the elastic modulus and permeability of OCY increase.The established model can be used for studying the mechanism of bone mechanotransduction at the multiscale level.
文摘Connecting earthquake nucleation in basement rock to fluid injection in basal,sedimentary reservoirs,depends heavily on choices related to the poroelastic properties of the fluid-rock system,thermo-chemical effects notwithstanding.Direct constraints on these parameters outside of laboratory settings are rare,and it is commonly assumed that the rock layers are isotropic.With the Arbuckle wastewater disposal reservoir in Osage County,Oklahoma,high-frequency formation pressure changes and collocated broadband ground velocities measured during the passing of large teleseismic waves show a poroelastic response of the reservoir that is both azimuthally variable and anisotropic;this includes evidence of static shifts in pressure that presumably relate to changes in local permeability.The azimuthal dependence in both the static response and shear coupling appears related to tectonic stress and strain indicators such as the orientations of the maximum horizontal stress and faults and fractures.Using dynamic strains from a nearby borehole strainmeter,we show that the ratio of shear to volumetric strain coupling is~0.41 which implies a mean Skempton's coefficient of A=0.24 over the plausible range of the undrained Poisson's ratio.Since these observations are made at relatively low confining pressure and differential stress,we suggest that the hydraulically conductive fracture network is a primary control on the coupling between pore pressure diffusion and elastic stresses in response to natural or anthropogenic sources.
文摘From 2009 to 2017,parts of Central America experienced marked increase in the number of small to moderate-sized earthquakes.For example,three significant earthquakes(~Mw 5)occurred near Prague,Oklahoma,in the U.S.in 2011.On 6 Nov 2011,an Mw 5.7 earthquake occurred in Prague,central Oklahoma with a sequence of aftershocks.The seismic activity has been attributed to slip on the Wilzetta fault system.This study provides a 3 D fully coupled poroelastic analysis(using FLAC3 D)of the Wilzetta fault system and its response to saltwater injection in the underpressured subsurface layers,especially the Arbuckle group and the basement,to evaluate the conditions that might have led to the increased seismicity.Given the data-limited nature of the problem,we have considered multiple plausible scenarios,and use the available data to evaluate the hydromechanical response of the faults of interest in the study area.Numerical simulations show that the injection of large volumes of fluid into the Arbuckle group tends to bring the part of the Wilzetta faults in Arbuckle group and basement into near-critical conditions.
文摘A linear viscoporoelastic model is developed to describe the problem of reflection and transmission of an obliquely incident plane P-wave at the interface between an elastic solid and an unsaturated poroelastic medium, in which the solid matrix is filled with two weakly coupled fluids （liquid and gas）. The expressions for the amplitude reflection coefficients and the amplitude transmission coefficients are derived by using the potential method. The present derivation is subsequently applied to study the energy conversions among the incident, reflected, and transmitted wave modes. It is found that the reflection and transmission coefficients in the forms of amplitude ratios and energy ratios are functions of the incident angle, the liquid saturation, the frequency of the incident wave, and the elastic constants of the upper and lower media. Numerical results are presented graphically. The effects of the incident angle, the frequency, and the liquid saturation on the amplitude and the energy reflection and transmission coefficients are discussed. It is verified that in the transmission process, there is no energy dissipation at the interface.
基金supported by the National Natural Science Foundation of China (Grant 11372091)China Scholarship Council (Grant 201406120086)
文摘A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.
文摘Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to reduce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitoring is essential on ascertaining movement, volumes and locations of injected CO2 in the sequestration reservoir. One technique is to use time-lapsed seismic survey mapping to provide spatial distribution of seismic wave velocity as an indicator of CO2 migration and volumes in a storage reservoir with time. To examine the use of time-lapsed seismic survey mapping as a monitoring tool for CO2 sequestration, this paper presents mathematical and experimental studies of the effects of supercritical CO2 injection on the seismic velocity of sandstone initially saturated with saline water. The mathematical model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the modeling of the acoustic velocity of porous rocks containing two-phase immiscible pore fluids. The experimental study uses a high pressure and high temperature triaxial cell to clarify the seismic response of a sample of Berea sandstone to supercritical CO2 injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO2 injection in the sandstone sample show the effects of pore fluid distribution in the seismic velocity of porous rocks. CO2 injection was shown to decrease the P-wave velocity with increasing CO2 saturation whereas the S-wave velocity was almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity of sandstone containing different mixtures of supercritical CO2 and saline water provided the distribution of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus. The empirical relation of Brie et al. for the bulk modulus of mixtures of two-phase immiscible fluids, in combination with the Biot-Gassmann theory, was found to satisfactorily represent the pore-fluid dependent acoustic P-wave velocity of sandstone.
