Kocabas Ibrahim, Bulbul Mahmut
Petroleum and Natural Gas Engineering Department, Izmir Katip Celebi University, Izmir, Turkey,
Environ Sci Pollut Res Int. 2015 Mar;22(5):3298-313. doi: 10.1007/s11356-014-3827-2. Epub 2014 Nov 22.
A fissured aquifer may be considered as a dense network of fissures separated by low permeability matrix blocks. A conceptual modeling of such a system consists of an infinite number of parallel fractures separated by constant width matrix slabs. While the fissures are assumed to be main flow conduits, the fluid in the porous matrix blocks are considered to be virtually immobile. The mathematical model of the transport of a solute and/or contaminant which assumes a purely convective flow in fissures and diffusion into the matrix blocks consists of two coupled differential equations. An analytical solution of this model for the case of solute entering into the system at a constant concentration has been presented by Skopp and Warrick in Soil Sci Soc Am Proc 38:545-550, 1974. Note however, Skopp and Warrick (Soil Sci Soc Am Proc 38:545-550, 1974) have not considered the additional processes of adsorption and radioactive decay. Unfortunately, their solution had computational limitations as it involved numerical integration of a quite complex expression. Therefore, one had to turn to employing numerical Laplace transform inverters to compute the solutions. This work presents simple real space analytical solutions for the contaminant transport model described above including the adsorption and radioactive decay. The real space solutions have been developed using the method of double Laplace transform and binomial series approximation. An accurate approximate solution has also been presented which converges to the exact solution only after computing three terms in the series full solution. The developed model has been used for 1) assessment of the efficiency of numerical Laplace transform algorithms and 2) investigation of the degree and scale of contamination, and 3) designing remediation schemes for the already contaminated aquifers.
裂隙含水层可被视为由低渗透基质块分隔的密集裂隙网络。这种系统的概念模型由无数个由恒定宽度基质板分隔的平行裂缝组成。虽然裂隙被假定为主要流动通道，但多孔基质块中的流体被认为基本不流动。溶质和/或污染物传输的数学模型假定裂隙中为纯对流流动且扩散进入基质块，该模型由两个耦合的微分方程组成。Skopp和Warrick在《土壤科学协会美国分会会刊》38:545 - 550, 1974中给出了该模型在溶质以恒定浓度进入系统情况下的解析解。然而，请注意，Skopp和Warrick（《土壤科学协会美国分会会刊》38:545 - 550, 1974）未考虑吸附和放射性衰变的附加过程。不幸的是，他们的解存在计算局限性，因为它涉及到一个相当复杂表达式的数值积分。因此，人们不得不求助于使用数值拉普拉斯变换反演器来计算解。这项工作给出了上述污染物传输模型的简单实空间解析解，包括吸附和放射性衰变。实空间解是使用双拉普拉斯变换和二项式级数近似方法开发的。还给出了一个精确的近似解，该近似解仅在计算级数全解中的三项后才收敛到精确解。所开发的模型已用于1）评估数值拉普拉斯变换算法的效率，2）调查污染程度和规模，以及3）为已受污染的含水层设计修复方案。
