考虑加速效应的多孔介质中颗粒三维迁移模型研究

Three-dimensional modeling of particle transport in porous media considering accelerated effects

基于已有的颗粒一维迁移模型,建立一个考虑加速效应的颗粒三维迁移模型。通过Laplace变换和Fourier变换,给出点源和面源形式下的颗粒瞬时注入和周期形式注入问题的解析表达式,分析了点源瞬时注入情况下时间、距离、沉积系数、弥散系数等的影响机理。研究结果表明:随着时间增大,迁移颗粒浓度峰值逐渐减小,并且浓度峰值所对应的x坐标值逐渐增大。其次,浓度等值线在x–y平面上呈椭圆形状,在x方向上靠近颗粒注入口的等值线排列较密,远离注入口的等值线排列较疏。随着时间增大,低浓度等值线的范围逐渐向四周扩大,高浓度的等值线的范围逐渐缩小。另外,沉积系数越大,浓度等值线的范围越小。然而,随着x方向的弥散系数增大,等值线在x方向上逐渐向两侧拉长,而等值线在y方向上的范围逐渐缩小。

Based on a one-dimensional particle transport model, a theoretical model considering accelerated transport effects of particles is established. General solutions are derived with the help of the Laplace and Fourier transforms. According to the general solutions, specific solutions (instantaneously injected and periodically injected) are presented for point and areal inflow regions. The analytical solution for point source under instantaneous injection is taken as an example of specific solutions. A detailed discussion of the effect of time, distance, deposition and dispersion on particle transport is conducted. The studies show that the peak values of concentration decrease and the corresponding distance increases with the increasing time. Furthermore, the concentration contours exhibit ellipses on x-y plane, those near the particle inlet in the x-direction are arranged densely, and those far from the particle inlet are arranged sparsely. The range of low concentration contours increases and the range of high-concentration contours decreases with the increasing time. Besides, the concentration contours decrease with the increasing deposition rate. However, the range of concentration contours decreases with the increasing deposition rate. The contours in the x-direction increase and those in the y-direction decrease with the increasing Dx.