Effective pore‐scale dispersion upscaling with a correlated continuous time random walk approach
Effective pore‐scale dispersion upscaling with a correlated continuous time random walk approach
复制标题
使用相关连续时间随机游走方法有效放大孔隙尺度分散
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Tartakovsky
中科院分区：
文献类型：
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作者：
T. Le Borgne;D. Bolster;M. Dentz;P. Anna;A. Tartakovsky
我们从拉格朗日速度的孔隙尺度分析中研究了色散的升级。升级过程中的一个关键挑战是将扩散的时间演化与孔隙尺度速度场特性联系起来。我们检验了一个假设，即人们可以将孔隙尺度上的拉格朗日速度表示为空间中的马尔可夫过程。得到的有效传输模型是一个以相关随机时间增量为特征的连续时间随机行走（CTRW），这里记为相关CTRW。我们考虑了一个简化的正弦波通道模型以及一个更复杂的非均质孔隙空间。对于这两个系统，相关CTRW模型的预测，与速度场属性（分布和相关性）定义的参数，发现在前渐近和渐近时间内与直接孔隙尺度模拟的结果很好地一致。在这个框架中，分散对孔隙边界波动的非平凡依赖关系被证明与分布效应和相关效应之间的竞争有关。特别是，在有效CTRW模型中明确包含空间速度相关性对于表示孔喉中不完全混合非常重要。
We investigate the upscaling of dispersion from a pore‐scale analysis of Lagrangian velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of spreading to the pore‐scale velocity field properties. We test the hypothesis that one can represent Lagrangian velocities at the pore scale as a Markov process in space. The resulting effective transport model is a continuous time random walk (CTRW) characterized by a correlated random time increment, here denoted as correlated CTRW. We consider a simplified sinusoidal wavy channel model as well as a more complex heterogeneous pore space. For both systems, the predictions of the correlated CTRW model, with parameters defined from the velocity field properties (both distribution and correlation), are found to be in good agreement with results from direct pore‐scale simulations over preasymptotic and asymptotic times. In this framework, the nontrivial dependence of dispersion on the pore boundary fluctuations is shown to be related to the competition between distribution and correlation effects. In particular, explicit inclusion of spatial velocity correlation in the effective CTRW model is found to be important to represent incomplete mixing in the pore throats.