Fractured porous media

Schery, S. D., Holford, D. J., Wilson, J. L., and Phillips, F. M. (1988). The flow and diffusion ofradon isotopes in fractured porous media Part 2, Semi-infinite media. Radiation Protection Dosimetry, 24(1/4), 191-197. 

Natural and man-made porous media usually possess formidably complex microstructure, often hierarchical. In this paper we shall not discuss hierarchical microstructures revealed, for instance by fractured porous media and biological tissues like bone and soft tissue. However, recently developed stochastic reiterated homogenisation enables one to determine macroscopic properties of random porous media with hierarchical architecture, cf. [11],... 

Sudicky, E.A. and Frind, E.O., Contaminant transport in fractured porous media Analytical solutions for a system of parallel fractures. Water Resour. Res., 18, 1634, 1982. 

PORFLOW A software tool for multiphase fluid flow, heat and mass transport in fractured porous media. User s manual. Version 3.07. -Analytic Computational Research, Inc. (ACRi). 

A)jS, whether sampled from probability distribution functions or calculated by regression equations or surface-complexation models, can be used in many contaminant transport models. Alternate forms of the retardation factor equation that use a (Equation (3)) and are appropriate for porous media, fractured porous media, or discrete fractures have been used to calculate contaminant velocity and discharge (e.g., Erickson, 1983 Neretnieks and Rasmuson, 1984). An alternative approach couples chemical speciation calculations... 

The approach for unsaturated conductivity outlined in previous sections was extended to modeling the unsaturated hydraulic conductivity of rough fracture surfaces (Or Tuller, 2000). Flow on rough fracture surfaces is an essential component required for deriving constitutive relationships for flow in unsaturated fractured porous media (Or Tuller, 2001). The detailed derivations are obtained by consideration of a dual porosity model (matrix - fracture) and the proportional contributions to flow from these different pore spaces. 

The results for flow on a single fracture surface are incorporated in the derivation of hydraulic properties of unsaturated fractured rock mass. Liquid retention and hydraulic conductivity in partially saturated fractured porous media are modeled in angular pores and slit-shaped spaces representing rock matrix and fractures, respectively. A bimodal distribution of pore sizes and apertures accounts for the two disparate pore scales and porosity. These considerations provide a framework for derivation of retention and hydraulic conductivity functions for fractured porous media (Or Tuller, 2001). 

Or, D., and M. Tuller. 2000. Flow in unsaturated fractured porous media Hydraulic conductivity of rough surfaces. Water Resour. Res. 35 1165-1177. 

Di Pietro, L. 1996. Application of a lattice gas numerical algorithm to modelling water transport in fractured porous media. Transp. Por. Media 22 307-325. 

Logan, J.D., V.A. Zlotnik, and S. Cohn. 1996. Transport in fractured porous media with time-periodic boundary conditions. Math. Comput. Model. 24 1-9. 

NUMERICAL SIMULATION OF VARIABLY COUPLED THERMO-HYDRO-MECHANICAL PROCESSES IN FRACTURED POROUS MEDIA... 

Abstract motif is a three-dimensional finite-element code developed to simulate groundwater flow, heat transfer and solute transport in deformable fractured porous media. The code has been subjected to an extensive verification and updating programme since the onset of its development. In this paper, additional verification and validation works with an emphasis on thermo-hydro-mechanical processes are presented. The verification results are based on cases designed to verify thermo-hydro-mechanical coupling terms, and isothermal and non-isothermal consolidations. A number of validation case studies have been conducted on the code. Example results are repotted in this paper. 

Over the past two decades AECL has developed a three-dimensional code, MOTIF (Model Of Transport In Fractured/porous media), for detailed modelling of groundwater flow, heat transport, mechanical equilibrium and solute transport in a fractured rock mass. The initial development was completed in 1985 (Guvanasen 1985). Since then the code has undergone extensive updating, verification - comparison with known analytical or numerical solutions - and validation - comparison with experiments - (Chan et al. 2(XX)). In the latter document sixteen test cases were repotted to verify the code for groundwater flow, heat transfer and solute transport in fractured or porous rock. In this paper, additional verification and validation studies with an emphasis on thermo-hydromechanical (T-H-M) processes are presented. 

The MOTIF code is a three-dimensional finite-element code capable of simulating steady state or transient coupled/uncoupled variable-density, variable- saturation fluid flow, heat transport, and conservative or nonspecies radionuclide) transport in deformable fractured/ porous media. In the code, the porous medium component is represented by hexahedral elements, triangular prism elements, tetrahedral elements, quadrilateral planar elements, and lineal elements. Discrete fractures are represented by biplanar quadrilateral elements (for the equilibrium equation), and monoplanar quadrilateral elements (for flow and transport equations). 

In this study, we address the hydrodynamic control of retention in fractured porous media. The hydrodynamic control of retention in fracture networks can be reduced to the distribution of a single parameter referred to as transport resistance . Two specific objectives of the study are (i) to summarize two main modelling approaches (continuum and discrete) and conditions for their equivalence, where from linearization of P is deduced, and (ii) to lest the applicability of the linearization of for lOOm and 1000m scales using results from site-specific simulations (Gutters and Shuttle, 2000 Gutters, 2002). 

For PA applications, we need to infer P statistics based on site characterization data. More specifically, we need to infer the marginal density fip). Several approaches for estimating yf ) are possible, however, at this time there is no general consensus on which one is most preferable. In view of the heterogeneity and complexity of fractured porous media, and uncertainties involved, it is most likely that several complementary approaches for estimating fip) from field data need to be used, rather than a single approach. 

Bai, M. and Roegiers, J.C. 1994. Fluid flow and heat flow in deformable fractured porous media. Int. J. Engng Sci. 32(10) pp. 1615-1633. Callari C. Federico F. 2000. FEM validation of a double porosity elastic model for consolidation of structurally complex clayey soils. Int. J. Numer. Analy. Meth. 24 (4) pp. 367-402. 

Jahan Noorishad Mohsen Mehran. 1982. An upstream finite element method for solution of transient transport equation in fractured porous media. Water resources research. 18(3) pp. 588-596... 

The following examples illustrate the variety of geochemical problems treated with the numerical simulator. We first consider geochemical processes in porous media nitrification (Example 1), validation of the nonequilibrium model (Example 2) and TCE transformation (Example 3). After that we treat the same problems in fractured porous media matrix diffusion (Example 4), two-member decay chain (Example 5). Finally, Example 5 is extended to demonstrate the influence of parameter variation for the concentration distribution that occurs either under equilibrium or nonequilibriiun conditions (Example 6). 

In case of nonequilibrium reactions, the same effect can be obtained as above when different transfer rate coefficients are assumed, as we see in Fig. 6.14. Numerical modelling of the decay chain reactions in fractured porous media with a nonequilibrium sorption model is treated for the first time. Further there exists no analytical solution for this type of model. 

A new numerical solver RF-RTM for the reactive transport in fractured porous media was investigated. The simulator RF-RTM is a three-dimensional model, that can consider several nonequilibrium kinetic type models. This paper illustrates the accuracy with the finite element model for simulating decay reactions in fractured porous media. The presented results show the capability of RF-RTM to simulate transport of one or more species. The finite element model RF-RTM was verified for several situations when sorption occurs imder equilibrium conditions such as in Example 1 and 5, or in case of matrix diffusion such as in Example 4. Validation of the nonequilibrium model was shown in Example 3. The nonequilibrium model is verified only for homogenous media. Numerical modelling of the decay chain reactions in fractured porous media with a nonequilibrimn sorption model is treated for the first time. Especially the different penetrations of decay chain components in a fiacture-matrix system was illustrated through a series of simulations (see Example 6). Further research is needed to quantify the effect of nonlinear sorption in the migration of the contaminants with sequentially deca3ong processes in fractured porous media. 

Grisak, G. E. Pickens, J. F. (1980) Solute transport through fractured porous media 1) The effect of matrix diffusion. Water Resour. Res. 16(4), 719 730. 

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