Closed-Form Solution for the Reconstruction Problem in Porous Media

AIChE Journal

Volumn 42, Issue 5, 1996, Pages 1407-1415

  Giona, Massimiliano ^a,b   Adrover, Alessandra ^a,c  

^a Ctro Interuniversitario sui S   (Italy)

^b UNIVERSITY OF CAGLIARI   (Italy)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

LATTICE MODELS; MODELLING-MATHEMATICAL; POROUS MEDIA-FLOW THROUGH;

CORRELATION METHODS; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING; STATISTICAL METHODS; TRANSPORT PROPERTIES;

CLOSED FORM SOLUTION; CORRELATION FUNCTION; CORRELATION PROPERTIES; GAUSSIAN PROCESSES; KHINCHIN THEORY; LATTICE MODELS; LINEAR FUNCTION EQUATION; POROUS STRUCTURE THEORY; STATISTICAL RECONSTRUCTION;

POROUS MATERIALS;

EID: 0030131297     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.690420521     Document Type: Article

References (26)

1. Abramowitz, M., and I. Stegun, Handbook of Mathematical Functions, Dover, New York (1974).
2. Adler, P. M., Porous Media: Geometry and Transports, Butterworth-Heinemann, Boston (1992).
3. Adler, P. M., C. G. Jacquin, and J. A. Quiblier, "Flow in Simulated Porous Media," Int. J. Multiphase Flow, 16, 691 (1990).
4. Baldo, S., F. Normant, and C. Tricot, eds., Fractals in Engineering, World Scientific, Singapore (1994).
5. Barnsley, M. F., Fractals Everywhere, Academic Press, Boston (1988).
6. Barnsley, M. F., and L. P. Hurd, Fractal Image Compression, Peters, Wellesley, MA (1993).
7. Barrett, J. F., and J. F. Coales, "An Introduction to the Analysis of Non-linear Control Systems with Random Imputs," Proc. IEEE, Mono: 154 M, 103, 190 (1955).
8. Blumenfeld, R., and S. Torquato, "Coarse-Graining Procedure to Generate and Analyze Heterogeneous Materials: Theory," Phys. Rev. E, 48, 4492 (1993).
9. Blumenfeld, R., and R. C. Ball, "Probe for Morphology and Hierarchical Correlations in Scale-Invariant Structures," Phys. Rev. E, 47, 2298 (1992).
10. Cerofolini, G. F., and N. Re, "The Mathematical Theory of Adsorption on Non-Ideal Surfaces," Riv. Nuovo Cimento, 16, 1 (1993).
11. Dixon, D. G., and J. L. Hendrix, "A General Model for Leaching of One or More Solid Reactants from Porous Ore Particles," Met. Trans. B, 24B, 157 (1993).
12. Doob, J. L., Stochastic Processes, Wiley, New York (1953).
13. Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York (1990).
14. Forte, B., and E. R. Vrscay, "Solving the Inverse Problem for Function/Image Approximation using Iterated Function Systems: I. Theoretical Basis," Fractals, 2, 325 (1994a).
15. Forte, B., and E. R. Vrscay, "Solving the Inverse Problem for Function/Image Approximation using Iterated Function Systems: II. Algorithm and Computations," Fractals, 2, 335 (1994b).
16. Joshi, M. Y., A Class of Stochastic Models for Porous Media, PhD Diss., Univ. of Kansas, Lawrence (1974).
17. Prakash, S., S. Havlin, M. Schwartz, and H. E. Stanley, "Structural and Dynamical Properties of Long-Range Correlated Percolation," Phys. Rev. A, 46, R1724 (1992).
18. Quiblier, J. A., "A New Three-Dimensional Modeling Technique for Studying Porous Media," J. Coll. Interf. Sci., 98, 84 (1984).
19. Rugh, W. J., Nonlinear System Theory - The Volterra/Wiener Approach, Johns Hopkins Univ. Press, Baltimore, MD (1980).
20. Sahimi, M., "Long-Range Correlated Percolation and Flow and Transport in Heterogeneous Porous Media," J. Phys. I France, 4, 1263 (1994).
21. Sallés, J., J. F. Thovert, and P. M. Adler, "Transport in Reconstructed Porous Media," Characterization of Porous Solids: III, Studies in Surface Science and Catalysis, Vol. 87, J. Rouquerol, F. Rodriguez-Reinoso, K. S. W. Sing, and K. K. Unger, eds., Elsevier, Amsterdam, p. 211 (1994).
22. Stauffer, D., and A. Aharony, Introduction to Percolation Theory, Taylor & Francis, London (1992).
23. Thompson, W. E., "The Response of a Non-Linear System to Random Noise," Proc. IEE, Mono: 106 R, 46 (1954).
24. Weinrib, A., "Long-Range Correlated Percolation," Phys. Rev. B, 29, 387 (1984).
25. Weinrib, A., and B. I. Halperin, "Critical Phenomena in Systems with Long-Range-Correlated Quenched Disorder," Phys. Rev. B, 27, 413 (1983).
26. Yao, J., P. Frykman, F. Kalaydjian, J. F. Thovert, and P. M. Adler, "High-Order Moments of the Phase Function for Real and Reconstructed Model Porous Media: A Comparison," J. Coll. Interf. Sci., 156, 478 (1993).