Abstract
A three-dimensional finite-difference groundwater flow model was developed by the use of fractal theory. The model developed in this study can simulate the groundwater flow in fractured aquifers as well as in porous aquifers. The model was designed to be able to use other parameters, such as permeability, hydraulic conductivity, porosity and fractal dimension besides hydraulic parameters which are used in MODELOW. Methods which can calculate box fractal dimension used in the Baecher model and mass dimension used in Levy-Lee Fractal model were developed. The results of the model and MODFLOW agreed exactly in the case of the fractal dimension of 2.0 without regard to the use of a fractal equation. The fact that the drawdown along the distance from the well increases by increasing the fractal dimension shows the effect of fracture on groundwater flow.
Similar content being viewed by others
References
Anderson, M. P. and Woessner, W. W.,“Applied Groundwater Modeling: Simulation of Flow and Advective Transport,” Academic Press Inc., San Diego (1992).
Barker, J. A.,“A Generalized Radial Flow Model for Hydraulic Tests in Fractured Rock,”Water Resour. Res.,24(10), 1796 (1988).
Chon, B. H. and Choi, Y. S.,“A Study on the Three-Dimensional Groundwater Flow Simulation by Extension of Input Parameters in MODFLOW,”Mineral and Energy Resour. Korea,34(4), 420 (1997).
Dershowitz, W. S. et al.,“FracMan 2.6 User Documentation,” Golder Associates Inc., WA (1998).
Geier, J., Dershowitz, W. S. and Lee, K.,“Field Validation of Conceptual Models for Fracture Geometry,”Transactions of American Geophysical Union,69(44), 1177 (1988).
Hamm, S. Y.,“Hydraulic Characteristics of Fractured Aquifers in South Korea Applying Fractal Models,”Jour. Geol. Soc. Korea,31(4), 467 (1995).
Mandelbrot, B. B.,“Self-Affine Fractals and Fractal Dimension,”Physica Scripta,32, 257 (1985).
McDonald, M. G. and Harbaugh, A. W.,“A Modular Three-Dimensional Finite-Difference Ground-water Flow Model,” U.S. Geological Survey, Colorado (1994).
Sen, Z.,“Applied Hydrogeology for Scientists and Engineers,” Lewis Publishers, Florida (1995).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chon, B., Choi, YS. Modeling of three-dimensional groundwater flow using the method to calculate fractal dimension. Korean J. Chem. Eng. 18, 382–386 (2001). https://doi.org/10.1007/BF02699182
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02699182