Research on the Contaminant Breakthrough Time Algorithm Based on Thermal Penetration Theory

Abstract

The current calculation method of breakthrough time calculates the concentration value of the measuring point at different times based on the model solution, which is determined by approaching the concentration value corresponding to the breakthrough standard through trial calculations. However, it is necessary to research the breakthrough standard with practical applications of mathematical and physical significance, especially a one-dimensional mathematical model of contaminant migration under Dirichlet boundary conditions. A general algorithm for directly calculating the breakthrough time was established in this research. Moreover, the calculation standard of the breakthrough time was also discussed based on the similarity between the analytical solution and the mathematical law of thermal conduction. This research considered parameters of the seepage velocity, dispersion coefficient and characteristics of the impervious layer, and the sensitivity analysis of these factors were investigated. The results show that the proposed algorithm was basically consistent with the current method, and the concept of thermal penetration depth is also feasible for the calculation standard. This is not only suitable for different breakthrough standards, but also simple and convenient. This study can provide a reference for the design, management and subsequent remediation of actual sites. INDEX TERMSBreakthrough time, mathematical model, convection dispersion, analytical solution, general algorithm. I.

Analytical solution for one‐dimensional steady‐state VOCs diffusion in simplified capillary cover systems

“…In this section, sensitivity analysis was introduced to investigate the effects of various parameters on the performance of the unsaturated landfill cover system. The sensitivity is expressed by a dimensionless index (e.g., I ), which is calculated as the ratio between the relative change in model output and the relative change in a parameter 74,75 . The expression of the sensitivity index I can be given by $$$$\begin{equation}I = \frac{{\left( {{y_2} - {y_1}} \right)/{y_0}}}{{\left( {{x_2} - {x_1}} \right)/{x_0}}}\end{equation}$$$$where, y 0 is the model output calculated with an initial value x 0 of the parameter x ; y 2 and y 1 are the model outputs calculated with the inputted parameter values x 2 and x 1 , respectively.…”

“…The sensitivity is expressed by a dimensionless index (e.g., I), which is calculated as the ratio between the relative change in model output and the relative change in a parameter. 74,75 The expression of the sensitivity index I can be given by 𝐼 = (𝑦 2 − 𝑦 1 ) ∕𝑦 0 (𝑥 2 − 𝑥 1 ) ∕𝑥 0 (40) where, y 0 is the model output calculated with an initial value x 0 of the parameter x; y 2 and y 1 are the model outputs calculated with the inputted parameter values x 2 and x 1 , respectively. In this study, the relative width of the ranges is achieved by varying x by Δ𝑥 = 10%, with x 0 chosen as the mean.…”