Matrix model permeability pressure

Comparing the curves in Fig. 2 shows that representing the permeability versus pressure data by either model provides a satisfactory fit to the data over the pressure range of 1 to 20 atm. However, at pressures less than 1 atm. the two models differ in their prediction regarding the behavior of the permeability-pressure curve [Fig. 2]. While the matrix model predicts a strong apparent pressure dependence of the permeability in this range (solid line), the dual-mode model predicts only a weak dependence (broken line). 

The fit of these expressions to experimental results is very good. At low pressure regimes, the fit was shown to be even better than that of dual sorption expressions. Except for these regimes, the two models seem to do equally well in describing sorption and permeability data. Concentration dependent diffusivity and permeability have been considered before mainly for vapors. The new aspect of the matrix model is that it broadens these effects to fixed gases. The important difference between the matrix and dual sorption models is in the physical picture they convey of gas transport and interaction with the polymer. Additional experimental evidence will be needed to determine the preference of these different physical representations. 

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... 

The thermo-hydrological calculations have indicated that it is possible to choose appropriate hydrological parameters in order to obtain a distribution of saturation similar to the one prevailing in the in situ test. Intrinsic permeability was taken from the fractures and retention curve was taken from the matrix. Relative permeability for gas and for liquid had to be modified. None of the functions valid for the matrix or the fracture were appropriate. The problem in fact, is that relative permeabilities are controlled by degree of saturation in the fracture and this model used a global degree of saturation. Therefore, relative permeability functions should undergo variations near full saturation because the fractures desaturate for low capillary pressures compared to the matrix. 

The jointed rock is treated as a hydraulically discontinuous mass. According to this model the rock matrix is not permeable and the seepage flow is limited in fractures. Taking into account the contribution of water saturation and seepage pressure, the total strain and constitutive equations of the rock mass was obtained. 

In the second case, the fault model, the same matrix mesh is employed, but with the addition of a single 2-D embedded planar fault. The orientation and dip of the fault have been estimated from the seismic location data for cluster a. The matrix permeability is held constant at a typical value for intact crystalline rock and the fault diffusivity is calibrated to match the observed 4.5 month time delay of the pressure wave to 2 km depth. 

A conceptual and numerical model of fluid flow beneath A u reservoir has been developed to model RIS. Model simulations show that for pressure-diffusion to be a hydrogeologically consistent mechanism for RIS, preferential flow must occur within 2D fault planes embedded in a 3D low permeability matrix. Further, the observed... 

A realistic prediction of the permeability distribution in three dimensions in sedimentary basins seems impossible given the wide ranges of values for different types of sediments and the heterogeneities of the basins. Pore pressures and fluid fluxes in three dimensions can not be modelled reliably. When the fracture pressure is reached at high overpressure, the fluid flow becomes decoupled from the permeability of the rock matrix and is mostly a function of the permeability of very thin hydrofractures. The permeability is then coupled to the fracture spacing and width which again is a function of the fluid flux and the rate of compaction. 

Figure 2(b) contains the resulting information on required compaction time and pressure to reach a void content of less than 2%. Experimentally determined data enable a comparison to the calculated curves. The most significant sources of error in the latter are the viscosity and the perme-abiUty constant. The viscosity depends strongly on the temperature and the shear rate. Neither are constant at any point of the matrix. As the calculation estimated the processing time too short, it can be stated that both viscosity and the permeability constant have been chosen as too low. By a further development of the model, errors can be reduced, although the former model will then lose its advantage of simplicity. 

Extensive numerical studies were carried out by Fu etal. (2007) to model the thermal stresses and cracks in a cement-based matrix with inclusions under elevated temperature. A mechanical thermal-elastic damage 2D model with heat transfer was built to study these phenomena. It has been established that the temperature gradient is dependent on the heating rate and the thermal conductivity. The cracks open and propagate when the thermal stress reaches the tensile strength of the matrix. The crack pattern is closely related to the heating rate and thermal coefficients of the phases. The cracks play a double role they increase the permeability of the matrix and allow the pore pressure... 

Steady-state permeability is defined as the flux of penetrant per unit pressure difference across a sample of unit thickness. Permeation through polymers is generally a three step process absorption of penetrant into the polymer matrix, diffusion of penetrant through the matrix and desorption of penetrant at the other side (Kirwan and Strawbridge, 2003). Thus, permeability is influenced both by the dissolution and the diffusion of the penetrant in the polymer matrix. In this sorption-diffusion model of penetrant transport across the polymer, permeability (P) is given as the product of diffusion coefficient () and solubility coefficient () (Callister and Rethwisch, 2010), that is ... 

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