Abstract

The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete ordinates method. For the inverse Laplace transform, the double-exponential formula is employed. In this paper, we consider the travel distance of tracer particles whereas the half-space geometry was assumed in our previous paper [Amagai et al. (2020 Amagai, K., M. Yamakawa, M. Machida, and Y. Hatano. 2020. The linear Boltzmann equation in column experiments of porous media. Transp. Porous Med. 132 (2):311–31.[Crossref], [Web of Science ®] , [Google Scholar]). Trans. Porous Media 132:311–331].

摘要

开发了线性输运理论来描述多孔介质中示踪粒子数密度的时间依赖性。平流被考虑在内。输运方程通过解析离散坐标法进行数值求解。对于逆拉普拉斯变换，采用双指数公式。在本文中，我们考虑了示踪粒子的行进距离，而在我们之前的论文中假设了半空间几何形状 [Amagai et al. ( 2020 Amagai、K.、M. Yamakawa、M. Machida和Y. Hatano。2020 年。多孔介质柱实验中的线性Boltzmann方程。转运 多孔医学。132 (2): 311 – 31。[Crossref]、[Web of Science®]、[  Google Scholar]）。翻译 多孔介质 132:311-331]。