Dual continuum model

Several options are available in FLOTRAN for representing fractured media. The equivalent continuum model (ECM) formulation represents fracture and matrix continua as an equivalent single continuum. Two distinct forms of dual continuum models also are available, defined in terms of connectivity of the matrix. These models are the dual continuum connected matrix (DCCM) and the dual continuum disconnected matrix (DCDM) options. A parallel version of the code, PFLOTRAN, has been developed based on the PETSC parallel library at Argonne National Laboratory. 

The dual continuum model (DCM) formulation is comparable to the dual permeability model (DKM) formulation (TRW Environmental Safety Systems, Inc., 2000). The DCM and DKM conceptualizations provide separate continua for the matrix and the fractures. The dual continua are coupled throughout the model domain by transfer functions for heat and mass transfer between the fractures and matrix. Use of a DCM increases the complexity of the numerical model used in the simulations, but offers the potential to realistically partition flow between matrix and fractures. Mass flow across the matrix/fracture interface is directionally dependent. When liquid pressure in the matrix exceeds the pressures in the fractures (i.e., P > P//), liquid flow, Qi, from the matrix to the fracture continuum is defined by... 

Figure 13 represents an instrument having dual-channel optics. This means that there are facilities for two line sources and one continuum source, each line source having its own monochromator and detector. Many workers have advocated the usefulness of this type of instrument. Certainly the recently introduced microcomputerised dual channel models are easier to use than their earlier counterparts, so it is worthwhile to summarise the possible attractions of simultaneous dual element analysis. One obvious possibility is the analysis of two elements in a sample at the same time, thus halving analysis time. A less obvious attraction is the possibility of analysing via an internal standard. This is where a second element, either already present or added to the sample, is measured and ratioed to the analytical element. The... 

We applied the dual VFA approach to a neutral form (NF) glycine molecule in aqueous solution and compared the calculation results with those estimated by the conductor-like polarizable continuum model (CPCM) method in order to extract the explicit solvation effects. Table 8.1 shows a triple of typical vibrational frequencies (cugas, cocpcMi coee) of glycine molecule in the isolated state and in aqueous solution with their vibrational frequency shifts, (AcocpcM) Acofe). evaluated by two types of solute-solvent interactions, i.e., the CPCM and QM/MM method, scaled by the recommended factor of 0.9418 [43]. In addition, they were compared with the experimental values Acoexp obtained by the Fourier transform infrared (FT-IR)... 

This simple mixing rule demonstrates satisfactory agreement with experimental evidence from experiments with binary fluid blends [. l Furthermore, it is similar in form with the result from a continuum theory approach by Davis [ ], applicable for IPN with dual phase continuity but which are not mixed on a molecular level. This last model involves an exponent equal to 1/5 instead of 1/2 and is quite successful in predicting the experimental evidence [1 ] from permanent networks. 

Abstract Results from the four-year long heating phase of the Drift-Scale Heater Test at the Exploratory Studies Facility at Yucca Mountain, Nevada, provide a basis to evaluate conceptual and numerical models used to simulate thermal-hydrological coupled processes expected to occur at the proposed repository. A three-dimensional numerical model was built to perform the analyses. All model simulations were predicated on a dual (fracture and matrix) continuum conceptualization. A 20-percent reduction in the canister heat load to account for conduction and radiation heat loss through the bulkhead, a constant pressure boundary condition at the drift wall, and inclusion of the active fracture model to account for a reduction in the number of fractures that were hydraulically active provided the best agreement between model results and observed temperatures. The views expressed herein are preliminary and do not constitute a final judgment of the matter addressed or of the acceptability of its use in a license application... 

Matrix temperature, matrix saturation, and fracture saturation are calculated after four years of heating using the 3D model with dual continua, an active fracture model, and an open boundary at the drift wall (Figures 6-8). This model conceptualization provided the best agreement with temperatures measured during the DST at boreholes 158, 160, andl62. Temperatures calculated for the fracture continuum are the same as those calculated for the... 

Vieth W, Howell J, Hsieh J (1976) Dual sorption theory. J Memb Sci 1 177-220 Weitsman YJ (1990) A continuum diffusion model for viscoelastic materials. J Phys Chem 94 (2) 961-968... 

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