A method and apparatus for simulating the hydrologic legacy time of nitrate contaminated water in a groundwater system

Abstract

The application discloses a simulation method and equipment for nitrate pollution hydrological residual time in a groundwater system, and relates to the field of hydrogeology and environmental simulation. The method comprises the following steps: obtaining the geometric size, hydrological physical parameters and geochemical parameters of a target groundwater system, establishing an ideal basin conceptual model of a flux upper boundary, and constructing a mathematical model coupling water flow, solute transport and groundwater age distribution; simulating the groundwater flow, solute transport and transformation process, groundwater age, expected life distribution under steady-state conditions and the solute transport and transformation process under non-steady-state conditions based on the constructed model; and determining the nitrate characteristic hydrological residual time under steady-state conditions and the nitrate hydrological residual time under non-steady-state conditions. The application provides a simulation method for nitrate hydrological residual time, realizes quantitative calculation of the nitrate pollution lag time in the groundwater system, and provides direct basis for pollution tracing, treatment scheme formulation and effectiveness prediction.

Description

Technical Field

[0001] This application relates to the field of hydrogeology and environmental simulation technology, and in particular to a method and equipment for simulating the hydrological persistence time of nitrate pollution in groundwater systems. Background Technology

[0002] Agricultural activities and excessive application of nitrogen fertilizers lead to the accumulation of large amounts of nitrogen in the soil. This nitrogen undergoes complex biogeochemical processes in the soil environment (such as mineralization and fixation) and is leached into the groundwater system by precipitation and irrigation water. Nitrate nitrogen (NO3-N) is the main form of leached nitrogen, accounting for 76.9% to 88.1% of the total leached nitrogen. Nitrates entering the groundwater system are transported along groundwater flow paths of different levels and lengths, exerting a long-term impact on the water quality of groundwater discharge areas. To improve groundwater nitrate pollution, enacting pollution control policies is an effective method.

[0003] However, due to the influence of groundwater solute transport processes, nitrates leached into aquifers can take months or even tens of thousands of years to reach the discharge area, resulting in a significant lag in the water quality improvement effects of pollution control measures. The time it takes for nitrates to migrate from the water table to the discharge area or to be completely removed through denitrification by gaseous loss (N2, N2O, etc.) is defined as the hydrological residence time of nitrates in the water flow system. Currently, quantitative studies on nitrate residence time largely rely on statistical models based on historical input-output data, lacking a detailed characterization of water flow paths and solute transport and transformation processes in groundwater systems. To achieve nitrate pollution reduction targets in water bodies, the nitrate residence process should be fully considered, and management policies should be formulated based on the hydrological residence time of nitrates in groundwater systems. Summary of the Invention

[0004] The purpose of this application is to provide a method and equipment for simulating the hydrological retention time of nitrate pollution in groundwater systems, which can realize the quantitative calculation of the lag time of nitrate pollution in groundwater systems.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] Firstly, this application provides a method for simulating the hydrological persistence time of nitrate pollution in groundwater systems, including:

[0007] Obtain the geometric dimensions, hydrophysical parameters, and geochemical parameters of the target groundwater system;

[0008] Based on the geometric dimensions, hydrophysical parameters, and geochemical parameters, an ideal basin concept model for the flux upper boundary is established, and a mathematical model coupling water flow, solute transport, and groundwater age distribution is constructed.

[0009] Based on the ideal basin conceptual model and the mathematical model, the groundwater flow, solute transport and transformation process, groundwater age, expected lifetime distribution under steady-state conditions and the solute transport and transformation process under unsteady-state conditions are simulated to obtain the nitrate concentration, groundwater age, expected lifetime of groundwater and nitrate penetration curve of the discharge area at various locations in the groundwater system.

[0010] Based on the nitrate concentration, groundwater age, and expected lifespan at various points in the groundwater system, the characteristic hydrological legacy time of nitrate under steady-state conditions is determined.

[0011] Based on the nitrate breakthrough curve of the excretion zone, the nitrate salt retention time under unsteady-state conditions is determined.

[0012] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method for simulating the hydrological persistence time of nitrate pollution in a groundwater system.

[0013] According to the specific embodiments provided in this application, this application has the following technical effects: by acquiring multiple key parameters such as geometric dimensions, hydrophysical and geochemical parameters, an ideal basin conceptual model is established, and a mathematical model coupling water flow-solute transport-age distribution is constructed. Based on the constructed model, the groundwater flow, solute transport and transformation process, groundwater age and expected life distribution are simulated. It can not only simulate groundwater flow and solute transformation processes, but also output multi-dimensional data such as nitrate concentration, groundwater age, expected life and discharge zone penetration curve. It realizes the quantitative calculation of nitrate pollution lag time in the groundwater system, and constructs a dimensionless characteristic retention time to eliminate the influence of spatial scale, which facilitates the comparison of pollution retention time in different groundwater systems and provides a direct basis for pollution source tracing, treatment plan formulation and effectiveness prediction. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart illustrating a method for simulating the hydrological persistence time of nitrate pollution in a groundwater system, as provided in an embodiment of this application.

[0016] Figure 2 This is a conceptual schematic diagram illustrating the hydrological persistence time of nitrate pollutants in a groundwater system according to one embodiment of this application.

[0017] Figure 3 This is a steady-state groundwater flow field distribution diagram under the local-intermediate-regional nested water flow system model in Implementation Case 1 of this application.

[0018] Figure 4 This is a stable spatial distribution diagram of nitrate concentration in the local-intermediate-region nested water flow system mode in Implementation Case 1 of this application.

[0019] Figure 5 This is a spatial distribution map of the nitrate characteristic hydrological legacy time under the local-intermediate-regional nested flow system model in Implementation Case 1 of this application.

[0020] Figure 6 This is a frequency statistical histogram of nitrate characteristic hydrological legacy time in the local-intermediate-regional nested flow system model in Implementation Case 1 of this application.

[0021] Figure 7 This is a breakthrough curve and hydrological retention time diagram of nitrate concentration in the discharge area under the control measures of immediately stopping the input of nitrate pollution in Case 2 of this application.

[0022] Figure 8 This is a breakthrough curve of nitrate concentration and hydrological retention time diagram of the discharge area under the control measures of gradually stopping the input of nitrate pollution in Case 2 of this application. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] In one exemplary embodiment, such as Figure 1 As shown, a method for simulating the hydrological legacy time of nitrate pollution in a groundwater system is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. The method includes the following steps 101 to 105.

[0026] Step 101: Obtain the geometric dimensions, hydrophysical parameters, and geochemical parameters of the target groundwater system. Specifically, this includes basin length, elevation of the lowest discharge point, regional undulation amplitude, permeability coefficient, porosity, current and input concentrations of dissolved oxygen and nitrate in the groundwater, dispersion, molecular diffusion coefficient, reaction kinetic constant, initial nitrate concentration distribution, and input concentration at the upper boundary, as shown in Table 1.

[0027] Table 1

[0028]

[0029] Step 102: Based on the geometric dimensions, hydrophysical parameters, and geochemical parameters, establish an ideal basin concept model for the flux upper boundary, and construct a mathematical model coupling water flow, solute transport, and groundwater age distribution.

[0030] In a specific application example, the ideal basin conceptual model is as follows: Figure 2 As shown, the horizontal axis represents horizontal distance, the vertical axis represents elevation, and the arrowed curves represent groundwater flow lines. Among them, solid lines, dense dotted lines, and sparse dotted lines correspond to local (L), intermediate (M), and regional (R) water flow systems, respectively. S1~S4 represent different discharge zones, and RZ1~RZ3 represent different recharge zones.

[0031] Rainfall and irrigation water carry large amounts of dissolved oxygen and nitrates, which infiltrate the soil and replenish groundwater. During the transport of nitrates from the recharge zone to the discharge zone of the groundwater system, denitrification is the main mechanism for reducing and removing nitrogen. Dissolved or particulate organic carbon is the main electron donor in denitrification; organic carbon is preferentially oxidized by O2, hindering electron transfer to NO3. - The transfer of oxygen is crucial; therefore, denitrification only begins when oxygen is almost completely consumed. Electron donors sequentially reduce dissolved oxygen, nitrate, and other substances, resulting in corresponding redox zones (oxygen reduction zone, nitrate reduction zone, etc.) in groundwater. Differences in flow paths and hydrochemical zoning across different flow systems directly affect the retention of nitrate in groundwater, and the mixing of groundwater from different flow stages in the discharge zone directly influences the nitrate concentration there.

[0032] Step 103: Based on the ideal basin conceptual model and the mathematical model, simulate groundwater flow, solute transport and transformation processes, groundwater age, expected lifetime distribution under steady-state conditions, and solute transport and transformation processes under unsteady-state conditions to obtain nitrate concentrations, groundwater ages, expected lifetimes, and nitrate penetration curves in the discharge zone at various locations in the groundwater system. The nitrate penetration curve in the discharge zone is a curve showing the change of nitrate concentration in the discharge zone over time.

[0033] In a specific application example, the mathematical model includes a two-dimensional groundwater steady flow model, a solute transport and reaction model, and a groundwater age distribution model. The solute transport and reaction model uses a convection-dispersion-reaction equation to simulate the solute transport and transformation process; the groundwater age distribution model uses a convection-dispersion equation to simulate the groundwater age and expected lifespan. Step 103 includes steps 31 to 33.

[0034] Step 31: Construct a two-dimensional groundwater steady flow model based on the geometric dimensions and hydrophysical parameters, and simulate groundwater flow under steady-state conditions based on the ideal basin concept model and the two-dimensional groundwater steady flow model to obtain the groundwater flow velocity at various points in the groundwater system.

[0035] In this embodiment, a linear combination of cosine functions is used to describe the change in ground elevation at the upper boundary: .in, This represents the topographic elevation of the upper boundary, in meters. x The horizontal direction represents the horizontal distance, in meters (m). z The vertical direction represents elevation, in meters (m). The elevation of the lowest discharge point is in meters (m). L This represents the length of the basin, in meters. The amplitude of the regional undulation is expressed in meters (m). The amplitude of the local fluctuation is expressed in meters (m). k For local fluctuation frequency, k When taking even values, both the left and right boundaries correspond to valleys.

[0036] The groundwater dynamic equation is: ;in, H The water head of the basin is expressed in meters (m). K The value is the permeability coefficient, expressed in m / d.

[0037] For groundwater flow, the target groundwater system is a homogeneous and isotropic Quaternary porous unconfined aquifer. The upper boundary of the two-dimensional steady-state groundwater flow model is an open boundary receiving atmospheric precipitation and irrigation recharge, the properties of which are determined by the relative magnitudes of the hydraulic head and surface elevation at the upper boundary, evaporation is ignored. When the groundwater level is higher than the surface, groundwater drains from low-lying areas, forming a free outflow boundary, i.e., a convection boundary; when the hydraulic head is lower than the elevation, it forms a flux boundary receiving infiltration recharge. The basin topography is undulating, including multiple potential sources and potential sinks. As the intensity of infiltration recharge increases, the groundwater level rises. When the groundwater level is higher than the potential sink elevation, groundwater drains from the low-lying potential sinks. The left and right boundaries and the bottom boundary are set as impermeable boundaries. ; ; .

[0038] in, This represents the infiltration flux of the upper boundary recharge zone, in m / d. The discharge flux of the discharge area is expressed in m³ / d. This is the upper boundary supply area; For excretion area; The entire area, including the left, right, and bottom boundaries; Fluid density, in kg / m³ 3 ; I (･) is an indicator function; it is assigned a value of 1 if the condition inside the parentheses is true, and 0 otherwise. ε The infiltration recharge intensity is expressed in m / d. l The coupling length scale, in meters, represents the thickness of the infiltration boundary; p The pore water pressure on the lower surface of the upper boundary is expressed in Pa. g This is the acceleration due to gravity, measured in m / s². 2 ; n It is the outward normal vector.

[0039] Specifically, the groundwater head in the basin is obtained by solving the above formula. H Furthermore, based on the groundwater head in the basin H Determine the groundwater flow velocity, i.e., the pore water flow velocity vector. u .

[0040] Step 32: Based on the geochemical parameters and the groundwater flow velocity, the ideal basin conceptual model and the solute transport and reaction model are used to simulate the solute transport and transformation process under steady-state and unsteady-state conditions, respectively, to obtain the nitrate concentration at various points in the groundwater system and the nitrate penetration curve of the discharge area.

[0041] The convection-dispersion-reaction equation used in the solute transport reaction model is as follows: .in, solute i The mass concentration is expressed in mg / L. i Represents dissolved oxygen or nitrate; t For time; for jb The hydrodynamic dispersion coefficient tensor in the direction, in units of m 2 / d, including dispersion and molecular diffusion. j = x , z , b = x , z In groundwater systems with significant groundwater flow velocities (such as sandy basins), the contribution of mechanical dispersion is far greater than that of molecular diffusion. Therefore, the hydrodynamic dispersion coefficient tensor no longer depends on the solute.i To distinguish; for j The actual velocity component of pore water flow in the direction, in m / d; This refers to chemical reaction terms, with units of mg / (L•d).

[0042] In this application, the simulation under steady-state conditions does not include partial derivatives with respect to time, i.e. The simulation of nitrate solute transport under unsteady conditions includes a partial derivative with respect to time.

[0043] Specifically, the formula for calculating the hydrodynamic dispersion coefficient tensor is: ; ; ;in, Longitudinal dispersion, in meters; This refers to lateral dispersion, expressed in meters (m). Molecular diffusion coefficient, in units of m 2 / d; Pore ​​water velocity vector u The component in the horizontal direction, with units of m / d; Pore ​​water velocity vector u The component in the vertical direction, in m / d; This represents the actual flow velocity of the pore water, expressed in m / d.

[0044] In this embodiment, for solute transport simulation, DO and NO3 - Following a first-order kinetic decay process, the denitrification reaction starts when the dissolved oxygen concentration is <2 mg / L. ; .in, The rate at which dissolved oxygen is consumed by biogeochemical reactions, expressed in mg / (L·a); The rate at which nitrates are consumed by biogeochemical reactions is expressed in mg / (L·a). The first-order kinetic constant for dissolved oxygen is represented by the rate constant of reduction of organic carbon by oxygen, expressed in a (a). -1 ; The first-order kinetic constant for nitrates represents the reduction rate constant of nitrates consuming organic carbon, and its unit is a. -1 ; Dissolved oxygen concentration, in mg / L; This represents the nitrate concentration, expressed in mg / L.

[0045] In the groundwater recharge zone, nitrate and dissolved oxygen concentrations are given values, i.e., known concentration boundaries; in the groundwater discharge zone, solute free outflow boundaries are set; all other boundaries are zero flux boundaries. ; ; ; .

[0046] in, for solute at position i mass concentration, for t time solute at position i mass concentration, for Groundwater solutes at the location i The initial mass concentration, in mg / L; for t time Solute at location recharge area i The input concentration is expressed in mg / L. For gradient operators, The concentration gradient vector points in space. The direction in which the concentration increases most steeply; D Let be the hydrodynamic dispersion coefficient tensor.

[0047] Specifically, at the initial moment, the initial concentration at each location within the simulation range is known, and the concentration is... The solute concentration at the upper boundary replenishment portion is a given value, and the concentration is... That is, the solute input concentration at the upper boundary is ; The upper boundary discharge zone is the free outflow boundary, meaning the diffusion flux is 0. The left and right boundaries and the lower boundary are the zero flux boundaries, meaning that both diffuse flux and convective flux are 0.

[0048] The concentrations of dissolved oxygen and nitrate solutes at various points in the groundwater system can be obtained by solving the above formulas.

[0049] Step 33: Based on the hydrophysical parameters and the groundwater flow velocity, the groundwater age distribution is simulated using the ideal basin concept model and the groundwater age distribution model to obtain the groundwater age and expected lifespan at various points in the groundwater system.

[0050] The convection-diffusion equation for groundwater age in the groundwater age distribution model is: .

[0051] The convection-diffusion equation for expected lifetime in the groundwater age distribution model is: .

[0052] in, Porosity; The age of groundwater is expressed in years (a). u The pore water velocity vector is... and The composite vector; The expected lifespan of groundwater is expressed in years (a).

[0053] In this embodiment, the simulation of groundwater age and expected lifespan is generalized as the solute continuously generated as it migrates with the water flow. At the impermeable boundary of the flow model, the mass flux of age and expected lifespan is... All are 0, for groundwater age, the recharge zone of the upper flux boundary. The value is 0, the discharge zone is a convective boundary, and the diffusion flux is 0. =0; for the expected life of groundwater, the discharge zone at the upper flux boundary. The flux is 0, the recharge region is the convective boundary, and the diffuse flux is 0. It is 0.

[0054] The biogeochemical processes of nitrates can be controlled by dissolved oxygen and nitrate concentrations. Denitrification removes nitrates during their migration with groundwater flow, thus reducing their residence time in the groundwater system. It is related to the nitrate substrate concentration, the first-order kinetic constant of denitrification, and the dissolved oxygen concentration. Reducing dissolved oxygen decay and denitrification to a first-order kinetic reaction, denitrification occurs in groundwater when dissolved oxygen is less than 2 mg / L.

[0055] This application can use the finite element method to numerically solve the formulas in steps 31 to 33 above.

[0056] Step 104: Determine the hydrological legacy time of nitrate characteristics under steady-state conditions based on the nitrate concentration, groundwater age, and expected lifespan of the groundwater system at various locations.

[0057] In a specific application example, the finite element method (FEM) is used for mesh generation and calculation to simulate groundwater flow, nitrate concentration, and age distribution under steady-state conditions. Statistical methods are employed to obtain the spatiotemporal distribution range and mean of nitrate hydrological legacy time in the groundwater system. Based on the basin characteristic time of the groundwater system, the dimensionless characteristic hydrological legacy time of nitrate in the groundwater system is calculated. When calculating the mean legacy time, since the nitrate input concentration is constant, the spatial distribution of nitrate concentration in the groundwater system eventually tends to stabilize. Step 104 includes steps 41 to 43.

[0058] Step 41: Calculate the basin characteristic time based on the basin volume and total groundwater recharge. ;in, The time period representing basin characteristics is expressed in years (a). The volume of the basin is expressed in meters (m). 3 ; Total groundwater recharge, in cubic meters (m³). 3 / a.

[0059] Step 42 involves statistically analyzing the nitrate concentration, groundwater age, and expected lifespan at various points in the groundwater system to determine the hydrological retention time of nitrates under steady-state conditions. The hydrological retention time of nitrates refers to their residence time in the groundwater system, i.e., the time it takes for nitrates to migrate from the groundwater surface to the discharge sink or be completely removed through denitrification gaseous losses (N2, N2O, etc.).

[0060] Specifically, such as Figure 2 As shown on the left, with The critical threshold is used as the minimum standard for complete nitrate removal. When the nitrate concentration is below this value, it is considered that the lower limit standard for complete removal has been met. The residence time of nitrate at each location is statistically analyzed to obtain its numerical distribution, and the arithmetic mean is calculated. The residence time of nitrate at each location depends on whether it can completely traverse the groundwater system: if the nitrate particles can completely traverse the groundwater system, then the hydrological residence time of the nitrate particles is the sum of the groundwater age and the expected lifespan of the groundwater, i.e. If nitrates are completely denitrified during their migration with groundwater flow and are removed before flowing out, their hydrological retention time is equal to the time required for complete denitrification, i.e., the total time for dissolved oxygen and nitrate reduction. .

[0061] The formula for calculating the retention time of nitrate solution under steady-state conditions is: ; ; .

[0062] in, The time of nitrate salt retention under steady-state conditions is expressed in years (a). The time taken for dissolved oxygen to be consumed, expressed in years (a), i.e., the denitrification lag time; The time required for the reaction of nitrate reduction is measured in a (a). Groundwater retention time, measured in years (a). The first-order reaction kinetic constant for dissolved oxygen; The first-order reaction kinetic constant for nitrates; This represents the input concentration of dissolved oxygen, expressed in mg / L. This represents the input concentration of nitrate, in mg / L. Dissolved oxygen threshold concentration at the start of denitrification, in mg / L; The threshold concentration for complete removal of nitrate is expressed in mg / L.

[0063] Step 43: The ratio of the nitrate hydrological persistence time under steady-state conditions to the basin characteristic time is taken as the nitrate characteristic hydrological persistence time under steady-state conditions. .Right now .

[0064] The nitrate retention time based on simulation calculations in this application can quantitatively predict the time required for groundwater bodies and discharge areas to recover to environmental background or target concentrations after implementing specific pollution reduction measures. Furthermore, by calculating dimensionless characteristic retention times, it enables the comparison of nitrate pollution lag effects in different hydrogeological units, providing a basis for decision-making regarding land development and utilization, and land use control. This method provides a reliable timescale for long-term assessment of regional groundwater pollution risks, safety planning for drinking water sources, and setting water quality restoration targets.

[0065] Step 105: Determine the nitrate residue time under unsteady-state conditions based on the nitrate penetration curve of the excretion zone.

[0066] In a specific application example, such as Figure 2 As shown on the right, based on the nitrate penetration curve of the groundwater system discharge zone, the hydrological retention time of nitrate in the discharge zone is defined as the time required from the moment of intervention (reduction) of groundwater nitrate input to the time required for the discharge zone to recover to the nitrate background value. This time characterizes the time required for the nitrate concentration in the groundwater system discharge zone to be reduced and restored to the environmental background concentration after the implementation of control measures to control nitrate pollution input. Step 105 includes steps 51 and 52.

[0067] Step 51: Based on the nitrate breakthrough curve of the excretion area, determine the moment when the nitrate concentration first drops to the environmental background concentration, and obtain the endpoint time of the residue in the excretion area. This refers to the moment, on the nitrate breakthrough curve of the excretion area, when the nitrate concentration first drops to the environmental background concentration after the implementation of nitrate control measures.

[0068] Step 52, record the endpoint time of the excretion area. Timing of nitrate control measures The difference is used as the nitrate residue time under unsteady-state conditions. : .

[0069] In this application, step 104 assesses the range and average nitrate retention time throughout the groundwater system. The calculation result indicates how long nitrate remains in the entire groundwater system, providing a general and holistic view. Step 105, based on the nitrate concentration change curve over time in the discharge area (nitrate penetration curve), calculates the time required for nitrate to recover to the environmental background level after the implementation of nitrate input control (such as immediate or gradual cessation of input). This calculates the nitrate retention time at a specific location in the groundwater system (the streamline cluster that ultimately reaches the discharge area), making it more specific and useful for assessing the recovery time required after nitrate pollution control in discharge areas (such as rivers) primarily recharged by groundwater.

[0070] The hydrological persistence time calculated in this application is based on extrapolation under existing scenarios. Specifically, the simulation of nitrate contaminant transport and persistence is based on steady-state groundwater flow, where the groundwater flow velocity does not change over time. This method predicts the duration of contamination or the natural recovery time. The simulation method for nitrate contamination hydrological persistence time in groundwater systems can be applied to groundwater systems of different geometric dimensions and hydrogeological conditions, and can assess different lithologies or topography (with different permeability coefficients). K and local fluctuation frequency k The numerical range of nitrate retention time can be used to determine which groundwater system is more suitable for agricultural development and can more quickly reduce nitrate pollution naturally. It can also be applied to the same groundwater system to calculate the nitrate retention time in each discharge zone under different nitrate input control measures. The simulation results can directly determine the number of years required to immediately stop pollution input before the concentration returns to a certain level (such as the environmental background level).

[0071] In summary, this application has achieved a quantitative assessment and cross-sectional comparison of the lag effect of nitrate pollution under different scales and hydrogeological conditions, providing a scientific and quantitative basis for policy formulation on groundwater pollution control, and a unified scientific benchmark for achieving regional water environment zoning management and formulating differentiated protection and restoration strategies.

[0072] This application also provides two implementation cases to test the method for simulating the hydrological legacy time of nitrate pollution in the groundwater system provided in this application based on a two-dimensional Tóth model.

[0073] The two-dimensional Tóth model is an ideal basin model proposed by Tóth. Its upper boundary and various boundary conditions are consistent with the formulas in step 31. It is a classic model for simulating groundwater flow in the study area and provides a physical basis and computational domain for subsequent simulations such as solute transport.

[0074] In both implementation cases, the parameter is set to: basin length L 3600m ，The aspect ratio is approximately 10:1, the aquifer medium is homogeneous and isotropic sandy sediment, and the permeability coefficient is... K =0.25m / d, porosity θ= 0.40. Infiltration recharge intensity at the upper boundary. ε A groundwater system model of local-intermediate-regional nesting was established using a density of 1.64 mm / d. Vertical dispersion... approximate basin length L 1 / 100, lateral dispersion Take longitudinal dispersion 1 / 10 of the molecular diffusion coefficient Take 1.16 × 10 -9 m 2 / s. Assuming the dissolved oxygen in the vadose zone reaches saturation with air, the dissolved oxygen concentration at this saturation equilibrium ( The dissolved oxygen input concentration serves as the upper boundary of the model. Dissolved oxygen in groundwater decays due to reactions with organic carbon during transport; when the dissolved oxygen concentration falls below a certain level... At this time, organic carbon, acting as an electron donor, participates in denitrification mediated by microorganisms. This is to simulate DO and NO3 in sandy unconfined aquifers. - The first-order kinetic decay process, taking =0.04a -1 , =0.02a -1 Furthermore, it does not change with time and space. Numerical solutions are obtained using the finite element method.

[0075] Implementation Case 1: Based on the two-dimensional Tóth model, the application was tested by calculating the nitrate salt retention time in a small sandy basin with a multi-level groundwater system under steady-state conditions.

[0076] First, substitute the parameters obtained in step 101 (Table 1) into the mathematical model established in step 102. Then, execute step 103 to perform numerical solutions using the finite element method, obtaining a series of steady-state distribution results, such as... Figures 3 to 6 As shown. Among them, Figure 5 and Figure 6 The nitrate characteristic hydrological persistence times shown are dimensionless results. Simulation results demonstrate that this application can accurately capture the response of nitrate hydrological persistence times to different flow system orders during the simulation process.

[0077] Figure 3 To implement the steady-state groundwater flow field distribution under the local-intermediate-regional nested flow system model in Case 1, this result was obtained by solving the two-dimensional steady-state groundwater flow model in step 102. The horizontal axis represents the horizontal distance. x (m), with the vertical axis representing elevation. z (m). Figure 3Solid lines with arrows represent groundwater flow lines, indicating the trajectory of groundwater flow; dashed lines with numbers represent isohead lines, with the numbers indicating the corresponding hydraulic head values ​​(m); and dotted lines represent the groundwater level of the groundwater system. This diagram visually illustrates a multi-level groundwater system driven by topography, where different discharge zones are the confluence of groundwater flows at different levels (local, intermediate, and regional). This steady-state flow field distribution is one of the direct outputs of step 103, providing essential and fundamental physical field data for subsequent calculations of solute transport and hydrological retention time.

[0078] Figure 4 To implement the stable spatial distribution of nitrate concentration in the local-intermediate-region nested flow system model of Case 1. The results are based on Figure 3 The flow field shown is obtained by solving the convection-dispersion-response equation in step 102. The horizontal axis represents the horizontal distance. x (m), with the vertical axis representing elevation. z (m). Figure 4 The solid lines with arrows represent groundwater flow lines, indicating the trajectory of groundwater flow; the dashed lines with numbers represent nitrate concentration contour lines, with the numbers indicating the corresponding concentration values ​​(mg / L); the solid lines represent the threshold for denitrification initiation (dissolved oxygen concentration of 0.02 mg / L); and the dotted lines represent the groundwater level in the groundwater system. This figure illustrates the spatial distribution of nitrate in the groundwater system under continuous pollution input. Figure 4 As can be seen, the nitrate reduction range in groundwater is approximately 230m–270m, with nitrate mainly distributed in localized and intermediate flow systems with relatively high flow velocities. These results validate that the model can accurately capture the coupled processes of transport and reaction, and provide direct input data for subsequent calculations of nitrate retention time.

[0079] Figure 5 This result is one of the final outputs of step 104, used to illustrate the spatial distribution of nitrate characteristic hydrological legacy time under the local-intermediate-regional nested flow system model in Case 1. The horizontal axis represents horizontal distance. x (m), with the vertical axis representing elevation. z (m); the dashed line with numbers represents the hydrological legacy time of nitrate characteristics. The base-10 logarithm, i.e., log10( The map shows contour lines, with numbers representing the corresponding values; the dashed lines represent the groundwater level in the groundwater system. This map identifies the main distribution locations of "residual nitrates," which pose a long-term threat to future water quality. Figure 5The data shows that residual nitrates occupy 72% of the spatial area of ​​the groundwater system, mainly distributed in localized, intermediate, and some regional water flow systems where denitrification is insufficient. Areas with longer residual nitrates (yellowish-green in color) are concentrated in slow-flowing, long-course water flow systems. This map, by spatially visualizing and dimensionlessly representing the residual time of nitrates, provides a scientific basis and decision-making support for accurately identifying contaminated areas requiring priority attention and remediation.

[0080] Figure 6 To implement the frequency statistical histogram of nitrate characteristic hydrological persistence time in Case 1, it is based on the... Figure 5 The spatial data of the characteristic hydrological retention time of nitrate and the characteristic retention time of groundwater are statistically analyzed, which is one of the final outputs of step 104. Figure 6 The x-axis represents logarithmic time, and the y-axis represents frequency, indicating the overall proportion of groundwater retention time or nitrate hydrological legacy time within a certain interval. Compared to groundwater retention time, which reflects the physical transport process of groundwater, nitrate hydrological legacy time has a shorter and more concentrated distribution. This means that the proportion of "old water" containing nitrates is lower, indicating that longer transport paths and slower flow velocities are conducive to sufficient denitrification. In local and intermediate flow systems, more nitrates reach the discharge area directly without undergoing sufficient denitrification. The average hydrological legacy time for nitrates is 421 years, and the dimensionless average characteristic hydrological legacy time is 1.01 years. When influenced by longer transport paths, longer nitrate hydrological legacy times account for the largest proportion of the overall total.

[0081] Groundwater systems are inherently multi-level (e.g., the local-intermediate-regional three-level flow system in Case Study 1), with groundwater in different discharge zones being the confluence of different levels of groundwater flows. For example, the flow from the rightmost recharge zone RZ3 to the downstream discharge zone S1 is a regional flow system, while the flow from the recharge zone to the nearest discharge zone is a local flow system (e.g., from RZ3 to S3). The hydrological pathways correspond to... Figure 3 The streamlines (including the arrowed curves) in the image.

[0082] It is evident that this application can accurately capture the impact of changes in hydrological pathways and denitrification capacity on nitrate hydrological persistence time under different groundwater system models. Specifically, denitrification capacity is related to the first-order reaction kinetic constant of dissolved oxygen. nitrate first-order reaction kinetic constant The rate at which solutes are consumed is related to the hydrological path and the flow velocity. Longer hydrological paths and slower flow velocities result in longer groundwater retention times, allowing sufficient time for nitrates to be consumed. If the groundwater retention time is too short, dissolved oxygen may not have been consumed below the threshold (0.02 mg / L) before nitrates reach the discharge area, meaning denitrification will not occur; or dissolved oxygen may have been consumed below the threshold, but denitrification may be insufficient to completely react with the nitrates.

[0083] In Implementation Case 1, this application demonstrated satisfactory simulation performance, exhibiting high numerical stability and effectively characterizing the influence of different flow system stages in the groundwater system on the nitrate salt retention time.

[0084] Implementation Case 2: Based on the two-dimensional Tóth model, the application was tested by calculating the nitrate salt residue time in the drainage area of ​​a small sandy basin under two input control measures: gradual cessation and immediate cessation.

[0085] Referring to the trend of nitrogen leaching per unit area of ​​agricultural area in a certain region from 1961 to 2020, and taking 2020 as the current year, the effects of two groundwater nitrate input intensity control measures were compared: Scenario (i) "Gradual cessation", referring to the change in nitrogen leaching across the entire region, assuming that the nitrate leached into the groundwater decreases at a rate of 20% per year until it drops to 0 mg / L; Scenario (ii) "Immediate cessation", assuming that nitrate input into the groundwater is immediately stopped. The initial nitrate concentration of the groundwater system is 0, and the solution is obtained using the finite element method.

[0086] Simulation results show that this application can accurately capture the response of nitrate saline residue time to different control measures during the simulation process. Figure 7 and Figure 8 This result is one of the final outputs of step 105, used to measure the nitrate breakthrough curve and hydrological persistence time in the discharge area under the two input control measures of immediate cessation and gradual cessation of nitrate pollution in Case 2. The horizontal axis represents the year, where the pollution source control year is assumed to be 2020, and the vertical axis represents the nitrate concentration (mg / L) in the discharge area. Figure 7 and Figure 8The input curve represents the nitrate input concentration in the recharge area, characterizing different control intensities. Other curves represent nitrate concentrations in different discharge areas. The first hollow circle on the input curve represents the implementation time of the control measures (2020), i.e., the starting time for calculating the nitrate retention time in the discharge area. The other hollow circles represent the time when the nitrate concentration in each discharge area reaches the background value, i.e., 0 mg / L. The difference between this time and the starting time is the nitrate retention time in the discharge area. After the implementation of the two control measures to reduce nitrate input, the discharge area of ​​the water flow system needs approximately 98–142 years to recover to the environmental background value (…). Figure 6 ).

[0087] Compared to the "gradual cessation" scenario, the "immediate cessation" scenario resulted in a faster decrease in nitrate concentration in the discharge area during the initial phase of control implementation (approximately the first 10 years), but the nitrate hydrological persistence time was not significantly reduced. In each water flow system model, the time advantage for nitrate concentration in the discharge area to recover to environmental background levels under the "immediate cessation" nitrate input scenario was only about 4–6 years. Therefore, this application can accurately capture the impact of different input control intensities on the nitrate hydrological persistence time.

[0088] In Implementation Case 2, this application demonstrated satisfactory simulation performance, high numerical stability, and the ability to effectively characterize the impact of different control scenarios in the groundwater system on the retention time of nitrate salts in the discharge area.

[0089] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0090] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0091] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0092] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0093] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0094] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0095] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0096] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for simulating the hydrological persistence time of nitrate pollution in a groundwater system, characterized in that, The method includes: Obtain the geometric dimensions, hydrophysical parameters, and geochemical parameters of the target groundwater system; Based on the geometric dimensions, hydrophysical parameters, and geochemical parameters, an ideal basin concept model for the flux upper boundary is established, and a mathematical model coupling water flow, solute transport, and groundwater age distribution is constructed. Based on the ideal basin conceptual model and the mathematical model, the groundwater flow, solute transport and transformation process, groundwater age, expected lifetime distribution under steady-state conditions and the solute transport and transformation process under unsteady-state conditions are simulated to obtain the nitrate concentration, groundwater age, expected lifetime of groundwater and nitrate penetration curve of the discharge area at various locations in the groundwater system. The basin characteristic time is calculated based on the basin volume and total groundwater recharge; statistical analysis is performed on the nitrate concentration, groundwater age, and expected lifespan of groundwater at various locations in the groundwater system to determine the nitrate hydrological legacy time under steady-state conditions; the ratio of the nitrate hydrological legacy time under steady-state conditions to the basin characteristic time is taken as the nitrate characteristic hydrological legacy time under steady-state conditions. Based on the nitrate breakthrough curve of the excretion zone, the nitrate salt retention time under unsteady-state conditions is determined.

2. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 1, characterized in that, The geometric dimensions include basin length, elevation of the lowest discharge point, regional undulation amplitude, local undulation amplitude, and local undulation frequency. The hydrophysical parameters include infiltration recharge intensity, permeability coefficient, porosity, and coupling length scale; The geochemical parameters include initial concentration, vertical dispersion, horizontal dispersion, molecular diffusion coefficient, first-order reaction kinetic constant of dissolved oxygen, and first-order reaction kinetic constant of nitrate.

3. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 1, characterized in that, The mathematical model includes a two-dimensional groundwater steady flow model, a solute transport and reaction model, and a groundwater age distribution model. The solute transport and reaction model uses a convection-diffusion-reaction equation to simulate the solute transport and transformation process. The groundwater age distribution model uses a convection-diffusion equation to simulate the groundwater age and expected lifespan. Based on the aforementioned ideal basin conceptual model and mathematical model, the groundwater flow, solute transport and transformation processes, groundwater age, and expected lifetime distribution under steady-state conditions are simulated, as well as the solute transport and transformation processes under unsteady-state conditions. This yields nitrate concentrations, groundwater ages, expected lifetimes, and nitrate penetration curves in the discharge zone at various locations within the groundwater system, including: A two-dimensional groundwater steady flow model is constructed based on the geometric dimensions and hydrophysical parameters. Groundwater flow under steady-state conditions is simulated based on the ideal basin concept model and the two-dimensional groundwater steady flow model to obtain the groundwater flow velocity at various points in the groundwater system. Based on the geochemical parameters and the groundwater flow velocity, the solute transport and transformation process under steady-state and unsteady-state conditions was simulated using the ideal basin concept model and the solute transport and reaction model, respectively, to obtain the nitrate concentration at various points in the groundwater system and the nitrate penetration curve of the discharge area. Based on the hydrophysical parameters and the groundwater flow velocity, the groundwater age distribution is simulated using the ideal basin concept model and the groundwater age distribution model to obtain the groundwater age and expected lifespan at various locations in the groundwater system.

4. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 3, characterized in that, The formulas for the two-dimensional groundwater steady flow model include: ； ； ； ； ； in, The elevation of the upper boundary terrain. x In the horizontal direction, z Vertical direction The lowest discharge point elevation. For the amplitude of regional fluctuations, For local fluctuation amplitude, L The length of the basin. k For local fluctuation frequency, K Permeability coefficient, H The groundwater head in the basin, This represents the infiltration flux to the upper boundary recharge zone. The discharge flux of the excretion area. This is the upper boundary supply area. For excretion area, The entire area, including the left, right, and bottom boundaries. For fluid density, I (･) is the indicator function. ε For infiltration recharge intensity, l For coupling length scale, p The pore water pressure on the lower surface of the upper boundary. g It is the acceleration due to gravity. n It is the outward normal vector.

5. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 3, characterized in that, The solute transport reaction model is as follows: ； ； ； ； ； ； ； ； ； ； in, solute i mass concentration, for solute at position i mass concentration, for t time solute at position i mass concentration, i Represents dissolved oxygen or nitrate. t For time, during the simulation under steady-state conditions , for jb The hydrodynamic dispersion coefficient tensor in the direction, j = x , z , b = x , z, x In the horizontal direction, z Vertical direction for j The actual velocity component of pore water flow in the direction of direction. This is a chemical reaction term. For longitudinal dispersion, For lateral dispersion, The molecular diffusion coefficient is... Pore ​​water velocity vector u The component in the horizontal direction, Pore ​​water velocity vector u The component in the vertical direction, This represents the actual flow velocity of the pore water. This represents the rate at which dissolved oxygen is consumed by biogeochemical reactions. This represents the rate at which nitrates are consumed through biogeochemical reactions. The first-order reaction kinetic constant for dissolved oxygen is... The first-order reaction kinetic constant for nitrates is given. Dissolved oxygen concentration, This refers to the nitrate concentration. I (･) is the indicator function. for Groundwater solutes at the location i The initial mass concentration, for t time Solute at location recharge area i Input concentration, This is the upper boundary supply area. For excretion area, Including the left and right boundaries and the bottom boundary, For gradient operators, n The outer normal vector, D Let be the hydrodynamic dispersion coefficient tensor.

6. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 3, characterized in that, The convection-diffusion equation for groundwater age in the groundwater age distribution model is as follows: ; The convection-diffusion equation for the expected lifespan in the groundwater age distribution model is as follows: ; in, For gradient operators, Porosity D Let be the hydrodynamic dispersion coefficient tensor. Age of groundwater u The pore water velocity vector. The expected lifespan of groundwater.

7. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 1, characterized in that, The nitrate saline residue time under steady-state conditions is determined using the following formula: ； ； ； in, The retention time of nitrate solution under steady-state conditions. The time taken for dissolved oxygen to be consumed. When used for the reaction of nitrate reduction, The residence time of groundwater Age of groundwater For the expected lifespan of groundwater, The first-order reaction kinetic constant for dissolved oxygen is... The first-order reaction kinetic constant for nitrates is given. The input concentration of dissolved oxygen. This refers to the input concentration of nitrate. This refers to the dissolved oxygen threshold concentration at the start of denitrification. This is the threshold concentration at which nitrate is completely removed.

8. The method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to claim 1, characterized in that, Based on the nitrate breakthrough curve of the excretion zone, the nitrate saturation time under unsteady-state conditions is determined, including: Based on the nitrate breakthrough curve of the excretion zone, the moment when the nitrate concentration first drops to the environmental background concentration is determined, and the end point of the residue in the excretion zone is obtained. The difference between the end time of the nitrate residue in the discharge area and the time when the nitrate control measures were implemented is taken as the nitrate residue time under non-steady-state conditions.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method for simulating the hydrological persistence time of nitrate pollution in a groundwater system according to any one of claims 1-8.

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