- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
Modeling flow and solute transport in large-scale (e.g.) on the order of 103 m heterogeneous porous media involves substantial computational burden. A common approach to alleviate the problem is to utilize an upscaling method that generates models that require less intensive computations. The method must also preserve the important properties of the spatial distribution of the hydraulic conductivity (K) field. We use an upscaling method based on the wavelet transformations (WTs) that coarsens the computational grid based on the spatial distribution of K. The technique is applied to a porous formation with broadly distributed and correlated K values, and the governing equation for solute transport in the formation is solved numerically. The WT upscaling preserves the resolution of the initial highly-resolved computational grid in the high K zones, as well as that of the zones with sharp contrasts between the neighboring K, whereas the low-K zones are averaged out. To demonstrate the accuracy of the method, we simulate fluid flow and nonreactive solute transport in both the high-resolution and upscaled grids, and compare the concentration profiles and the breakthrough times. The results indicate that the WT upscaling of a K field generates non-uniform upscaled grids with a number of grid blocks that on average is about two percent of the number of the blocks in the original high-resolution computational grids, while the concentration profiles, the breakthrough times and the second moment of the concentration distribution, computed for both models, are virtually identical. A systematic parametric study is also carried out in order to investigate the sensitivity of the method to the broadness of the K field, the nature of the correlations in the field (positive versus negative), and the size of the computational grid. As the broadness of the K field and the size of the computational domain increase, better agreement between the results for the high-resolution and upscaled models is obtained.
This work presents the application of a methodology for upscaling of the spatial distribution of a hydraulic conductivity or permeability field in a computational grid for simulation of solute transport in spatially-heterogeneous geological formations. The methodology is based on the wavelet transforms that preserve the resolution of the high-conductivity paths, as well as that of the regions in which there are sharp contrasts between the conductivities. The performance of the method was tested for a wide range of the important parameters of the simulations, ranging from the order of magnitude variations in the conductivities and the nature of their correlations (positive versus negative), to the size of the computational grid. We demonstrated in all cases that the upscaled grid constructed by the wavelet transform reproduces the concentration breakthrough curves very accurately when compared with the same in the initial highly-resolved grids. In particular, the breakthrough times are predicted extremely accurately. From a computational point of view, the wavelet transform upscaling method generates non-uniform grids with a number of grid blocks that represent, on average, only about 2.1% of the number of grid blocks in the original high-resolution models. Thus, given any reasonable method of solving the advection-dispersion equation, the upscaling method results in an enormous reduction in the computational time of such simulations.