P.M. Adler, C.G. Jacquin, J.A. Quiblier, Flow in simulated porous media, Int. J. Multiphase Flow. 16(4) (1990) 691-712.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....( u Z R depends only upon the vector u being independent of position x. Moreover, when the porous media is isotropic, Z R is a function of only u = u , and does not depend on the direction of u. A simple method to calculate the correlation function and normalized covariance function was used by [7], 8] Let S be a section of a porous medium, given by a 2 D binary representation, porous phase is represented in black and the solid matrix in white. The binary image S is divided into two halves S 1 and S 2 . Hence, S=S 1 S 2 , S 1 S 2 = 5) In order to calculate R z (u) S 1 is first ....

....as only integers are stored in resident memory. Balls generated with d 3 4 distance that are used to perform opening operation are octagonal in shape. 2. 4 Three dimensional reconstruction Three dimensional reconstruction is based on a modification of Adler et al. Gaussian truncated method [7] proposed by [1] In Adler s method, three dimensional stochastic simulation of porous structure is based on the generation of a random non correlated field X(x) which gives the correct binary phase function Z(x) after the successive application of a linear and a non linear filters. Linear ....

Adler, P.M., Jacquin C.G. and Quiblier J.A., 1990. Flow in Simulated Porous Media. Int. J. Multiphase Flow, 16: 691-712.

....distance is related to the lower computer storage as only integers are stored in resident memory. Balls generated with d 3 4 distance that are used to perform opening operation are octagonal in shape. Three Dimensional Reconstruction Three dimensional reconstruction are developed by autor s like [3, 4], using a Gaussian truncated method, by assuming homogeneity and isotropy. The 3 D pore structure can thus be constructed from 2 D porous sections, preserving porosity and autocorrelation function. Imago use a metodology based in [4] that use a Fast Fourier Transform algorithm that eliminates ....

Adler P.M., Jacquin C.G. and Quiblier J.A., 1990, Flow in Simulated Porous Media., Int. J. Multiphase Flow., 16: 691-712.

....tortuosity) the random nature of the pore space requires understanding of the spatial distribution (auto covariance) of geometry descriptive parameters and of the correlation between parameters. The n point covariance functions have played an especially prominent role in this characterisation [63, 5, 6, 2, 3, 12, 7, 13]. Measurements of the 2 point covariance function from digitised rock images have been used to generate arti cial samples, and the properties of these reconstructed rocks have been studied [2, 3, 82, 72] Such correlation functions have been important analytic tools for theoretical description of ....

.... functions have played an especially prominent role in this characterisation [63, 5, 6, 2, 3, 12, 7, 13] Measurements of the 2 point covariance function from digitised rock images have been used to generate arti cial samples, and the properties of these reconstructed rocks have been studied [2, 3, 82, 72]. Such correlation functions have been important analytic tools for theoretical description of porous media. In his review paper, Torquato [75] discusses the role the n point covariance and other correlation functions have played in rigorous theoretical estimates of upper bounds on bulk medium ....

P.M. Adler, C.J. Jacquin, and J.A. Quiblier. Flow in simulated porous media. Int. J. Multiphase Flow, 16:691-712, 1990.

....s Gamma2 = const Theta V 2=3 . Avellaneda and Torquato [1991] provide a different insight into the role of formation factor in estimates of permeability. Thus, H OE 2 =F = OE 2 m and n 2 m. Recalling that m 2, we find this estimate is in good agreement with empirical results of Adler, Jacquin, and Quiblier [1990] who found the permeability correlated well with the relation k OE n where n 4:15. Bourbi e, Coussy and Zinszner [1987] find n 7 for OE 0:05, 4 n 5 for 0:10 OE 0:25, and n 3 for sintered glass and some sandstones with porosities in the range 0:15 OE 0:30. A nominal value of n 4 ....

Adler, P. M., C. G. Jacquin, and J. A. Quiblier, Flow in simulated porous media, Int. J. Multiphase Flow 16, 691--712, 1990.

....that its correlation function G GF (r) equals a prescribed reference correlation function G 0 (r) In our case G 0 (r) G EX (r) the reference is the correlation function of the experimental sample described above. The method of Gaussian field reconstruction is well documented in the literature [20,36,9,37], and we shall only make a few remarks that the reader may find of interest when implementing the method. Given the reference correlation function G EX (r) and porosity OE(S EX ) of the experimen10 tal sample the three main steps of constructing the sample S GF with correlation function G GF (r) ....

....function G EX (r) and porosity OE(S EX ) enter into the mathematical construction of this linear filter. 3. The correlated field Y (r) is then passed through a nonlinear discretization filter which produces the reconstructed sample S GF . Details of these three main steps are documented in Ref. [20,36]. However, in these traditional methods the process described in step 2 is computationally difficult because it requires the solution of a very large set of non linear equations. We have followed an alternate and computationally more efficient method proposed in Ref. 9] which uses Fourier ....

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P. Adler, C. Jacquin, and J. Quiblier, "Flow in simulated porous media," Int.J.Multiphase Flow, vol. 16, p. 691, 1990.

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P.M. Adler, C.G. Jacquin, J.A. Quiblier, Flow in simulated porous media, Int. J. Multiphase Flow. 16(4) (1990) 691-712.

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