This work is concerned, for the first time, with estimating the transverse dispersion coefficient under non-Darcy laminar flow conditions in porous media using pore-network modeling. The pore-network modelling approach and the mixed cell method are adopted to simulate both the steady laminar flow and the transient transport of solute for Berea and Bentheimer sandstone samples. For non-Darcy flow, the inertial effect is attributed to the quadratic increase of the pore throat mean velocity, which is embedded in the pressure head losses at either expansion or contraction located at the two ends of any pore throat. A time dependent function, based on both Péclet number and average residence time within the pore throat, is used to incorporate the effect of nonuniform pore throat velocity in the dispersion coefficient. A restrictive upper limit of the time step interval is introduced to prevent numerical overshoots of the concentrations calculated over time. For the same pressure gradient through the sample, the results show a decrease in both Péclet number and the coefficient of transverse dispersion in case of adopting the non-Darcy flow condition instead of the Darcy flow one. The percentage of decrease is up to 20% for the maximum applied pressure gradient through the sample.

这项工作首次涉及使用孔隙网络建模来估计多孔介质中非达西层流条件下的横向色散系数。采用孔隙网络建模方法和混合单元方法模拟伯里亚和本泰默砂岩样品的稳定层流和溶质的瞬态输运。对于非达西流，惯性效应归因于孔喉平均速度的二次增加，其嵌入在位于任何孔喉两端的膨胀或收缩时的压头损失中。基于佩克莱数和孔喉内平均停留时间的时间相关函数用于将不均匀孔喉速度的影响纳入分散系数中。引入时间步长间隔的限制性上限，以防止随时间计算的浓度出现数值超调。结果表明，对于相同的样品压力梯度，采用非达西流条件代替达西流条件时，佩克莱数和横向色散系数均下降。对于通过样品的最大施加压力梯度，下降百分比高达 20%。