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Article Navigation >  CARSOLOGICA SINICA  > 2024  > Accepted Manuscript
WANG Jinli, CHEN Xi, ZHANG Zhicai, KANG Jianrong, HU Jinshan. Discrete fracture network seepage analysis based on MODFLOW[J]. CARSOLOGICA SINICA. doi: 10.11932/karst2024y043
Citation: WANG Jinli, CHEN Xi, ZHANG Zhicai, KANG Jianrong, HU Jinshan. Discrete fracture network seepage analysis based on MODFLOW[J]. CARSOLOGICA SINICA. doi: 10.11932/karst2024y043
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Discrete fracture network seepage analysis based on MODFLOW

doi: 10.11932/karst2024y043
  • 1.

    School of Geography, Geomatics and Planning, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

  • 2.

    School of Earth System Science, Tianjin University, Tianjin 300072, China

  • 3.

    College of Hydrology and Water Resources, Hohai University, Nanjing, Jiangsu 210098, China

  • Received Date: 2024-08-07
  • Accepted Date: 2024-12-02
  • Rev Recd Date: 2024-11-29
    • Available Online: 2024-12-30
    Abstract
  • Karst bedrock fractures are difficult to model in hydrological research due to their heterogeneous and anisotropic. Groundwater can mainly flow in the fractures and conduits of the karst aquifer system, and the bedrock voids and micro-fractures mainly play the role of water storage, so the ideal hydrological model of the karst area is the continuum-fracture (conduit) model. As the main path of groundwater flow, the connectivity of fractures has a great influence on the seepage of fracture media. The fracture-continuum model (FC) generated by combining the merits of the continuum model and the discrete fracture network model (DFN) can realistically describe the binary structure of karst aquifer system in principle, and the diffusion of matrix as well as the water exchange between matrix and fracture can also be considered, but there is a problem that the water exchange between matrix and fracture medium is difficult to determine.This study is based on the statistical distribution of fracture geometry and hydraulic parameters, the two-dimensional fracture network original maps were generated using Monte Carlo random simulation technology and MATLAB program with the same distribution as actual rock fractures. The adjacency matrix of undirected graph of graph theory is used to characterize the intersecting relationship between fractures in the fracture network. Using percolation theory to remove fracture segment which cannot conduct fluid, such as the 1st connected maps were generated by removing the isolated fractures (fracture clusters), and the 2nd connected maps generated by removing fractures with single nodes, as well as the 3rd connected maps generated by means of cutting fracture dead ends. The DFN model in a single-phase, saturated, steady-state flow system was established based on the connected graph of fracture network, applying the cubic law and the continuity equation of seepage. Mapping of single fractures of the connected graph onto finite difference grids, FC seepage model was built by combining DFN approach and MODFLOW software. When deleting the fracture dead ends, some nodes may be lost due to computer trade-off, as a result, the 2nd connected graph and the 3rd connected graph are used for DFN and FC approaches, respectively. The corresponding simulation programs were developed, with which reproducing cross fracture test conditions, and constructing two multi-fractures cases to analyze the impact of finite difference grid resolutions and fracture dead end on stable seepage simulation accuracy. The DFN flow solution is used as a metric to evaluate the correctness and effectiveness of FC model code writing.Research results show that the simulated total flow and head of the fine grid are in good agreement with the theoretical values of DFN under the two test conditions. The node head and total grid flow simulated by the FC model of two cases are overestimated or underestimated in the coarse grid. Although a longer path of grid flow Lg from cell to cell is corrected by increasing cell hydraulic conductivity, the coarse grid based on MODFLOW cannot accurately analyze the inclined fracture length Lf on the grid. If the selected coarse grid size is greater than the distance between two adjacent fractures, a part of the two adjacent fractures will merge in the grid, thereby shortening the actual flow path. Secondly, the overestimation or underestimation of the inclined fracture length Lf.. Inaccurate analysis of the flow path will lead to an increase in the estimation error of flow rate and head, especially in the densely fractured areas near the center of the model domain. Refining the grid can greatly eliminate this error. The fracture dead-end has non-negligible effect on MODFLOW grid flow. In this study, the MODFLOW-based FC model can be used to solve for pressure distributions both within the interconnected network of fractures and the rock matrix, and could also be a solution for the water exchange between the rock matrix and the fractures is difficult to determine. This study can achieve the expression of heterogeneity and anisotropy of fracture hydraulic conductivities in numerical calculation units and will promote the understanding of MODFLOW simulation of fracture flow based on connectivity.Furthermore, The size of the MODFLOW grid should be determined in combination with the size of the study area, which should be small enough to capture the detailed features in the flow, and large enough to reduce the computational time and cost. Generally, the grid size is determined by a trial algorithm. When FC approach is applied to the actual watershed, the spatial variability of topography and landform factors should also be considered, such as coupling surface elevation DEM data.

     

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