For the needs of the whole region’s emergency regulation of the nullah sudden water pollution event, the emergency regulation strategy of the accident section and upstream and downstream of the sudden water pollution event is studied. For the accident section, the duration of the whole emergency event is calculated using the parameter quantification method; for the upstream of the accident section, the NSGA-II is used to adjust the gate opening to ensure the water level stability of the upstream pools; for the downstream section, the optimized partition method is used to identify the unfavorable pools and close the unfavorable pool to extend the water supply time. Based on the example of an emergency event in the section of the Liyanghe gate–Guyunhe gate of the middle line project, the research results are as follows: the accident section is identified as the Xiaohe gate–Hutuohe gate, the upstream of the accident section is the Liyanghe gate–Xiaohe gate, and the downstream of the accident section is the Hutuohe gate–Gangtou Tunnel gate. The duration of the emergency event in the accident section is 7.9 h; the maximum average water level deviation before the gate upstream of the accident section is 0.05 m; two unfavorable canal pools are identified in the stream of the accident section, and the water supply time of the unfavorable pools is extended by 6.13 and 5.61 d.

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.

Due to the temperature of shallow aquifers being affected by atmospheric temperature, groundwater source heat pumps (GWSHPs) become unstable and the operation efficiency of GWSHP is constrained. In the study, the coupling numerical simulation model of the groundwater flow field and temperature field is established based on the continuous monitoring results in an actual experimental site, and the water and thermal migration of shallow aquifer is simulated under the influence of the atmospheric environment. The influence of the dynamic change in ground temperature is analyzed on a GWSHP. The results indicated that the temperature of the shallow aquifer is affected by the external temperature, and the recharge temperature in the summer cooling period was 33°C, and that in the winter heating period was 6°C in the actual site, to avoid the occurrence of thermal penetration when there is a gap between the actual situation and the design situation, the single cooler can balance the insufficient cooling capacity in summer under the most unfavorable situation. The research results can also provide a reference for the development and utilization of geothermal energy resources in shallow aquifers.

The effect of water temperature variation in a river channel on groundwater temperature in the confined aquifer it cuts can be generalized to a one-dimensional thermal convection-conduction problem in which the boundary water temperature rises instantaneously and then remains constant. The basic equation of thermal transport for such a problem is the viscous Burgers equation, which is difficult to solve analytically. To solve this problem, the Cole–Hopf transform was used to convert the second-order nonlinear thermal convection-conduction equation into a heat conduction equation with exponential function-type boundary conditions. Considering the difficulty of calculating the inverse of the image function of the boundary function, the characteristics and properties of the Laplace transform were used to derive the theoretical solution of the model without relying on the transformation of the boundary function, and the analytical solution was obtained by substituting the boundary condition into the theoretical solution. The analytical solution was used to analyze the temperature response laws of aquifers to parameter variation. Subsequently, a 40-day numerical simulation was conducted to analyze the boundary influence range and the results from the analytical method were compared to those from the numerical method. The study shows that: (1) the greater the distance from the river canal and the lower the aquifer flow velocity, the slower the aquifer temperature changes; (2) the influence range of the river canal boundary increases from 18.19 m to 23.19 m at the end of simulation period as the groundwater seepage velocity v increases from 0.08 m/d to 0.12 m/d; (3) the relative errors of the analytical and numerical methods are mostly less than 5%, confirming the rationality of the analytical solution.

The function of boundary temperature variation with time, f(t) is generally defined according to measured data. For f(t), which has a complicated expression, a corresponding one-dimensional heat conduction model was constructed under the first type of boundary conditions (Dirichlet conditions) in a semi-infinite domain. By taking advantage of the Fourier transform properties, a theoretical solution was given for the model, under the condition that f(t) does not directly participate in the transformation process. The solution consists of the product of erfc(t) and f(0) and the convolution of erfc(t) and the derivative of f(t). The piecewise linear interpolation equation of f(t), based on the measured data of temperature, was substituted into the theoretical solution, thus quickly solving the model and deriving a corresponding analytical solution. Based on the analytical solution under the linear decay function boundary condition, the inflection point method and curve fitting method for calculating the thermal diffusivity were introduced and exemplified, and the variation laws of the appearance moment of the inflection point were discussed. The obtained results show that the values of thermal diffusivity calculated by the two methods are basically consistent, and that the inflection point values rise with the increasing values of the initial temperature variation of the boundary, the decrease in boundary temperature velocity, and the distance from the boundary, respectively.