Experimental investigation on rainfall infiltration and solute transport in layered porous and fractured media

Layered structures with upper porous and lower fractured media are widely distributed in the world. An experimen- tal investigation on rainfall infiltration and solute transport in such layered structures can provide the necessary foundation for effectively preventing and forecasting water bursting in mines, controlling contamination of mine water, and accomplishing ecological restoration of mining areas. A typical physical model of the layered structures with porous and fractured media was created in this study. Then rainfall infiltration experiments were conducted after salt solution was sprayed on the surface of the layered structure. The volumetric water content and concentration of chlorine ions at different specified positions along the profile of the experiment system were measured in real-time. The experimental results showed that the lower fractured media, with a considerably higher permeability than that of the upper porous media, had significant effects on preventing water infil- tration. Moreover, although the porous media were homogeneous statistically in the whole domain, spatial variations in the features of effluent concentrations with regards to time, or so called breakthrough curves, at various sampling points located at the horizontal plane in the porous media near the porous-fractured interface were observed, indicating the diversity of solute transport at small scales. Furthermore, the breakthrough curves of the outflow at the bottom, located beneath the underlying fractured rock, were able to capture and integrate features of the breakthrough curves of both the upper porous and fractured media, which exhibited multiple peaks, while the peak values were reduced one by one with time.

Numerical treatment of temporal-fractional porous medium model occurring in fractured media

This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir.For different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates.Finally,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.

NUMERICAL MODELING FOR POSITIVE AND INVERSE PROBLEMS OF 3-D SEEPAGE IN DOUBLE FRACTURED MEDIA

Three-dimensional seepage in double fractured media was modeled in this paper. The determination of hydraulic conductivity tensor of rock mass is a vital problem for the sea water intrusion or sea water encroachment and seepage of fissured medium. According to the geological and hydrogeological conditions for the 2nd-stage construction of the Three Gorges Project (TGP), the physical and mathematical models for the groundwater movement through the 3D double fractured media of rock mass during construction were established in this paper. Based on discontinuity-control inverse theory, some related parameters of double fractured media were inversed with flux being the known quantity and calibration of water table the objective function. Synchronously, the seepage field of the construction region was systematically analyzed and simulated, the results of which exhibit that the double fractured media model of fracture water can comprehensively and correctly describe the geological and hydrogeological conditions in the construction region.

LBM simulation of fluid flow in fractured porous media with permeable matrix

To analyze and depict complicated fluid behaviors in fractured porous media with variably permeable matrix,an integrated discrete computational algorithm is proposed based on lattice Boltzmann method（LBM）.This paper combines with the external force model and statistical material physics to effectively describe the feature changes while the fluid passes through the fractures within the permeable matrix.As an application example,a two dimensional rock sample is reconstructed using the digital image and characterized with different feature values at each LBM grid to distinguish pores,impermeable and permeable matrix by stating its local physical property.Compared with the conventional LBM,the results demonstrate the advantages of proposed algorithm in modeling fluid flow phenomenon in fractured porous media with variably permeable matrix.

A Two-Phase Flow Simulation of Discrete-Fractured Media using Mimetic Finite Difference Method

Various conceptual models exist for numerical simulation of fluid flow in fractured porous media,such as dual-porosity model and equivalent continuum model.As a promising model,the discrete-fracture model has been received more attention in the past decade.It can be used both as a stand-alone tool as well as for the evaluation of effective parameters for the continuum models.Various numerical methods have been applied to the discrete-fracture model,including control volume finite difference,Galerkin and mixed finite element methods.All these methods have inherent limitations in accuracy and applicabilities.In this work,we developed a new numerical scheme for the discrete-fracture model by using mimetic finite difference method.The proposed numerical model is applicable in arbitrary unstructured gridcells with full-tensor permeabilities.The matrix-fracture and fracture-fracture fluxes are calculated based on powerful features of the mimetic finite difference method,while the upstream finite volume scheme is used for the approximation of the saturation equation.Several numerical tests in 2D and 3D are carried out to demonstrate the efficiency and robustness of the proposed numerical model.

Review of permeability evolution model for fractured porous media

The ability to capture permeability of fractured porous media plays a significant role in several engineering applications, including reservoir, mining, petroleum and geotechnical engineering. In order to solve fluid flow and coupled flow-deformation problems encountered in these engineering applications,both empirical and theoretical models had been proposed in the past few decades. Some of them are simple but still work in certain circumstances; others are complex but also need some modifications to be applicable. Thus, the understanding of state-of-the-art permeability evolution model would help researchers and engineers solve engineering problems through an appropriate approach. This paper summarizes permeability evolution models proposed by earlier and recent researchers with emphasis on their characteristics and limitations.

Permeability Heterogeneity in a Fractured Sandstone-Mudstone Rock Mass in Xiaolangdi Dam Site,Central China

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.

Modeling the efects of fracture infll on frequency‑dependent anisotropy and AVO response of a fractured porous layer

In a fractured porous hydrocarbon reservoir,wave velocities and refections depend on frequency and incident angle.A proper description of the frequency dependence of amplitude variations with ofset(AVO)signatures should allow efects of fracture inflls and attenuation and dispersion of fractured media.The novelty of this study lies in the introduction of an improved approach for the investigation of incident-angle and frequency variations-associated refection responses.The improved AVO modeling method,using a frequency-domain propagator matrix method,is feasible to accurately consider velocity dispersion predicted from frequency-dependent elasticities from a rock physics modeling.And hence,the method is suitable for use in the case of an anisotropic medium with aligned fractures.Additionally,the proposed modeling approach allows the combined contributions of layer thickness,interbedded structure,impedance contrast and interferences to frequency-dependent refection coefcients and,hence,yielding seismograms of a layered model with a dispersive and attenuative reservoir.Our numerical results show bulk modulus of fracture fuid signifcantly afects anisotropic attenuation,hence causing frequencydependent refection abnormalities.These implications indicate the study of amplitude versus angle and frequency(AVAF)variations provides insights for better interpretation of refection anomalies and hydrocarbon identifcation in a layered reservoir with vertical transverse isotropy(VTI)dispersive media.

Uncertainty Analysis of Seepage-Induced Consolidation in a Fractured Porous Medium

Numerical modeling of seepage-induced consolidation process usually encounters significant uncertainty in the properties of geotechnical materials.Assessing the effect of uncertain parameters on the performance variability of the seepage consolidation model is of critical importance to the simulation and tests of this process.To this end,the uncertainty and sensitivity analyses are performed on a seepage consolidation model in a fractured porous medium using the Bayesian sparse polynomial chaos expansion(SPCE)method.Five uncertain parameters including Young’s modulus,Poisson’s ratio,and the permeability of the porous matrix,the permeability within the fracture,and Biot’s constant are studied.Bayesian SPCE models for displacement,flow velocity magnitude,and fluid pressure at several reference points are constructed to represent the input-output relationship of the numerical model.Based on these SPCE models,the total and first-order Sobol’indices are computed to quantify the contribution of each uncertain input parameter to the uncertainty of model responses.The results show that at different locations of the porous domain,the uncertain parameters show different effects on the output quantities.At the beginning of the seepage consolidation process,the hydraulic parameters make major contributions to the uncertainty of the model responses.As the process progresses,the effect of hydraulic parameters decreases and is gradually surpassed by the mechanical parameters.This work demonstrates the feasibility to apply Bayesian SPCE approach to the uncertainty and sensitivity analyses of seepage-induced consolidation problems and provides guidelines to the numerical modelling and experimental testing of such problems.

Sensitivity of seismic attenuation and dispersion to dynamic elastic interactions of connected fractures: Quasi-static finite element modeling study

Prediction of seismic attenuation and dispersion that are inherently sensitive to hydraulic and elastic properties of the medium of interest in the presence of mesoscopic fractures and pores,is of great interest in the characterization of fractured formations.This has been very difficult,however,considering that stress interactions between fractures and pores,related to their spatial distributions,tend to play a crucial role on affecting overall dynamic elastic properties that are largely unexplored.We thus choose to quantitatively investigate frequency-dependent P-wave characteristics in fractured porous rocks at the scale of a representative sample using a numerical scale-up procedure via performing finite element modelling.Based on 2-D numerical quasi-static experiments,effects of fracture and fluid properties on energy dissipation in response to wave-induced fluid flow at the mesoscopic scale are quantified via solving Biot's equations of consolidation.We show that numerical results are sensitive to some key characteristics of probed synthetic rocks containing unconnected and connected fractures,demonstrating that connectivity,aperture and inclination of fractures as well as fracture infills exhibit strong impacts on the two manifestations of WIFF mechanisms in the connected scenario,and on resulting total wave attenuation and phase velocity.This,in turn,illustrates the importance of these two WIFF mechanisms in fractured rocks and thus,a deeper understanding of them may eventually allow for a better characterization of fracture systems using seismic methods.Moreover,this presented work combines rock physics predictions with seismic numerical simulations in frequency domain to illustrate the sensitivity of seismic signatures on the monitoring of an idealized geologic CO_(2) sequestration in fractured reservoirs.The simulation demonstrates that these two WIFF mechanisms can strongly modify seismic records and hence,indicating that incorporating the two energy dissipation mechanisms in the geophysical interpretation can potentially improving the monitoring and surveying of fluid variations in fractured formations.

Numerical study on two-phase flow through fractured porous media

Based on the flux equivalent principle of a single fracture, the discrete fracture concept was developed, in which the macroscopic fractures are explicitly described as （n-l） dimensional geometry element. On the fundamental of this simplification, the discrete-fractured model was developed which is suitable for all types of fractured porous media. The principle of discrete-fractured model was introduced in detail, and the general mathematical model was expressed subsequently. The fully coupling discrete-fractured mathematical model was implemented using Galerkin finite element method. The validity and accuracy of the model were shown through the Buckley-Leverett problem in a single fracture. Then the discrete-fractured model was applied to the two different type fractured porous media. The effect of fractures on the water flooding in fractured reservoirs was investigated. The numerical results showed that the fractures made the porous media more heterogeneous and anisotropic, and that the orientation, size, type of fracture and the connectivity of fractures network have important impacts on the two-phase flow.

Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory

A numerical procedure for the evaluation of equivalent permeability tensor for fractured vuggy porous media is presented.At first we proposed a new conceptual model,i.e.,discrete fracture-vug network model,to model the realistic fluid flow in fractured vuggy porous medium on fine scale.This new model consists of three systems:rock matrix system,fractures system,and vugs system.The fractures and vugs are embedded in porous rock,and the isolated vugs could be connected via discrete fracture network.The flow in porous rock and fractures follows Darcy’s law,and the vugs system is free fluid region.Based on two-scale homogenization theory,we obtained an equivalent macroscopic Darcy’s law on coarse scale from fine-scale discrete fracture-vug network model.A finite element numerical formulation for homogenization equations is developed.The method is verified through application to a periodic model problem and then is applied to the calculation of equivalent permeability tensor of porous media with complex fracture-vug networks.The applicability and validity of the method for these more general fractured vuggy systems are assessed through a simple test of the coarse-scale model.