Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology. Numerous approaches have been proposed to characterize heterogeneity in the last several decades. However, little attention has...Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology. Numerous approaches have been proposed to characterize heterogeneity in the last several decades. However, little attention has been paid to correlate permeability heterogeneity with geological information. In the present study, several causes of permeability heterogeneity, that is, lithology, tectonism, and depth, are identified. The unit absorption values （denoted as ω）, which are results obtained from the packer test, are employed to represent permeability. The variability of permeability in sandstone-mudstone is so significant that the value of unit absorptions span 3-4 orders of magnitude at any depth with several test sections. By declustering, it has been found that under a similar tectonic history, the means of permeability differ greatly at different formations as a result of different mudrock contents. It has also been found that in the same formation, permeability can be significantly increased as a result of faulting. The well-known phenomenon, the decrease in permeability with depth, is found to be caused by the fractures in the rock mass, and the relationship between permeability and depth can be established in the form of logoω-logd. After subtracting the trend of ω with absolute depth, the mean of the residual value at each relative depth can be well correlated with the distribution of mudstone. The methods proposed in this paper can be utilized to research in similar study areas.展开更多
Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsi...Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.展开更多
Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e...Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.展开更多
Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different gra...Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,Darcy and Non-Darcy)were observed.The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the Non-Darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For Non-Darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.展开更多
Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1238-1255)developed exact first and second nonlocal moment equations for advective-dispersive transport in finite,randomly heterogeneous geologic media.The velocity an...Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1238-1255)developed exact first and second nonlocal moment equations for advective-dispersive transport in finite,randomly heterogeneous geologic media.The velocity and concentration in these equations are generally nonstationary due to trends in heterogeneity,conditioning on site data and the influence of forcing terms.Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1399-1418)solved the Laplace transformed versions of these equations recursively to second order in the standard deviationσY of(natural)log hydraulic conductivity,and iteratively to higher-order,by finite elements followed by numerical inversion of the Laplace transform.They did the same for a space-localized version of the mean transport equation.Here we recount briefly their theory and algorithms;compare the numerical performance of the Laplace-transform finite element scheme with that of a high-accuracy ULTIMATE-QUICKEST algorithm coupled with an alternating split operator approach;and review some computational results due to Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1399-1418)to shed light on the accuracy and computational efficiency of their recursive and iterative solutions in comparison to conditional Monte Carlo simulations in two spatial dimensions.展开更多
Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology and numerous approaches had been proposed to characterize heterogeneity in the past several decades.However。
One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is ...One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is considered. Due to heterogeneity velocity and dispersivity coefficient of the advection dispersion equation are considered functions of space variable and time variable. Analytical solution is obtained using Laplace transform technique when dispersivity depended on velocity. The effects of first order decay term and adsorption are studied. The graphical representations are made using展开更多
Coal was considered rock matrix-fractured media composed of rock matrix and fractures, and the rock matrix-fractured media model for heterogeneous and fractured coal bed was presented. In this model the rock matrix is...Coal was considered rock matrix-fractured media composed of rock matrix and fractures, and the rock matrix-fractured media model for heterogeneous and fractured coal bed was presented. In this model the rock matrix is heterogeneous, and the mechanical parameters such as elastic modulus and strength follow Weibull distribution. Fractures in coal bed were generated with the discrete fracture network method, and the properties of fractures were simulated with Desai element. Then the virtual generating system (VGS) of natural heterogeneous and fractured coal bed was developed in Matlab 6.0. The coupled model of gas flow and deformation process based on the rock matrix-fractured media model method and VGS for heterogeneous and fractured coal bed was presented, and the numerical code was developed in Matlab 6.0. The gas flow process in the heterogeneous and fractured coal bed was simulated in a numerical case. The main conclusions are: 1) The natural heterogeneous and fractured coal bed could be simulated by the rock matrix-fractured media model and VGS; 2) The fractures connected with the well have much more effects on gas flow than those non-connected.展开更多
Using the Maxwell＇s equations, we carry out theoretical analysis on the maximum incident and refractive angles at which negative refraction can be realized at the interfaces associated with conventional uniaxial medi...Using the Maxwell＇s equations, we carry out theoretical analysis on the maximum incident and refractive angles at which negative refraction can be realized at the interfaces associated with conventional uniaxial media. In the numerical analysis, the largest incident and refractive angles at which refraction arises are obtained by optimizing directions of the optical axis of the uniaxial bicrystal. Meanwhile, the optical parameters of the ordinary uniaxial bicrystals （including homogeneity- junction and heterogeneity-junction） are given, and some representative laser wavelengths, the largest incident and refractive angles are obtained. The relation between the largest incident angles （or refractive angles） and refractive index is also discussed.展开更多
基金support by the National Natural Science Foundation of China(No.40528003 and 50639090)
文摘Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology. Numerous approaches have been proposed to characterize heterogeneity in the last several decades. However, little attention has been paid to correlate permeability heterogeneity with geological information. In the present study, several causes of permeability heterogeneity, that is, lithology, tectonism, and depth, are identified. The unit absorption values （denoted as ω）, which are results obtained from the packer test, are employed to represent permeability. The variability of permeability in sandstone-mudstone is so significant that the value of unit absorptions span 3-4 orders of magnitude at any depth with several test sections. By declustering, it has been found that under a similar tectonic history, the means of permeability differ greatly at different formations as a result of different mudrock contents. It has also been found that in the same formation, permeability can be significantly increased as a result of faulting. The well-known phenomenon, the decrease in permeability with depth, is found to be caused by the fractures in the rock mass, and the relationship between permeability and depth can be established in the form of logoω-logd. After subtracting the trend of ω with absolute depth, the mean of the residual value at each relative depth can be well correlated with the distribution of mudstone. The methods proposed in this paper can be utilized to research in similar study areas.
基金the National Natural Science Foundation of China(No.52274048)Beijing Natural Science Foundation(No.3222037)+1 种基金the CNPC 14th Five-Year Perspective Fundamental Research Project(No.2021DJ2104)the Science Foundation of China University of Petroleum,Beijing(No.2462021YXZZ010).
文摘Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.
基金Iranian Offshore Oil Company (IOOC) for financial support of this work
文摘Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.
基金financially supported by the National Key Research and Development Program of China(No.2019YFC1804303)the National Natural Science Foundation of China(Grant Nos.41877171 and 41831289)。
文摘Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,Darcy and Non-Darcy)were observed.The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the Non-Darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For Non-Darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.
基金This work was supported in part by NSF/ITR Grant EAR-0110289through a scholarship granted to the lead author by CONACYT of Mexico.
文摘Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1238-1255)developed exact first and second nonlocal moment equations for advective-dispersive transport in finite,randomly heterogeneous geologic media.The velocity and concentration in these equations are generally nonstationary due to trends in heterogeneity,conditioning on site data and the influence of forcing terms.Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1399-1418)solved the Laplace transformed versions of these equations recursively to second order in the standard deviationσY of(natural)log hydraulic conductivity,and iteratively to higher-order,by finite elements followed by numerical inversion of the Laplace transform.They did the same for a space-localized version of the mean transport equation.Here we recount briefly their theory and algorithms;compare the numerical performance of the Laplace-transform finite element scheme with that of a high-accuracy ULTIMATE-QUICKEST algorithm coupled with an alternating split operator approach;and review some computational results due to Morales-Casique et al.(Adv.Water Res.,29(2006),pp.1399-1418)to shed light on the accuracy and computational efficiency of their recursive and iterative solutions in comparison to conditional Monte Carlo simulations in two spatial dimensions.
文摘Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology and numerous approaches had been proposed to characterize heterogeneity in the past several decades.However。
文摘One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is considered. Due to heterogeneity velocity and dispersivity coefficient of the advection dispersion equation are considered functions of space variable and time variable. Analytical solution is obtained using Laplace transform technique when dispersivity depended on velocity. The effects of first order decay term and adsorption are studied. The graphical representations are made using
基金Projects(50874064,50804026)supported by National Natural Science Foundation of ChinaProject(E2011208036)supported by the Natural Science Foundation of Hebei Province,China
文摘Coal was considered rock matrix-fractured media composed of rock matrix and fractures, and the rock matrix-fractured media model for heterogeneous and fractured coal bed was presented. In this model the rock matrix is heterogeneous, and the mechanical parameters such as elastic modulus and strength follow Weibull distribution. Fractures in coal bed were generated with the discrete fracture network method, and the properties of fractures were simulated with Desai element. Then the virtual generating system (VGS) of natural heterogeneous and fractured coal bed was developed in Matlab 6.0. The coupled model of gas flow and deformation process based on the rock matrix-fractured media model method and VGS for heterogeneous and fractured coal bed was presented, and the numerical code was developed in Matlab 6.0. The gas flow process in the heterogeneous and fractured coal bed was simulated in a numerical case. The main conclusions are: 1) The natural heterogeneous and fractured coal bed could be simulated by the rock matrix-fractured media model and VGS; 2) The fractures connected with the well have much more effects on gas flow than those non-connected.
基金supported by the National Natural Science Foundation of China （Grant Nos.60407007, 60377025） the Science Foundation of Shanghai Municipal Commission of Education （Grant No.A03Q23）, and the Shanghai Leading Academic Discipline Project （Grant No.T0104）
文摘Using the Maxwell＇s equations, we carry out theoretical analysis on the maximum incident and refractive angles at which negative refraction can be realized at the interfaces associated with conventional uniaxial media. In the numerical analysis, the largest incident and refractive angles at which refraction arises are obtained by optimizing directions of the optical axis of the uniaxial bicrystal. Meanwhile, the optical parameters of the ordinary uniaxial bicrystals （including homogeneity- junction and heterogeneity-junction） are given, and some representative laser wavelengths, the largest incident and refractive angles are obtained. The relation between the largest incident angles （or refractive angles） and refractive index is also discussed.
