A simulation method and system for nitrogen migration in a saturated water layer of a snow-soil interface

Abstract

The application provides a snow-soil interface saturated water layer nitrogen migration simulation method and system, and belongs to the technical field of frozen soil hydrology and non-point source pollution simulation. The application firstly constructs a micro adsorption model based on a double electric layer compression theory, and solves Poisson-Boltzmann equation to analyze the influence of ion intensity on soil colloid surface potential and Debye length, and establishes a dynamic correction function of desorption rate constant; then constructs a macro migration model of coupling non-constant flow complete mixing reactor and modified reversible first-order kinetics, and forms an equation set in parallel, describes the convection transport and mixing process of solute in a variable volume water body, dynamically selects a solving strategy by introducing a quasi-steady state approximation mechanism, and obtains the non-equilibrium migration process and leaching efficiency of nitrogen in the saturated water layer. The application effectively reveals the superimposed driving mechanism of "ion intensity effect" and "flow rate pulse effect" on nitrogen loss during the snow melting period, and significantly improves the precision of the cold region snow melting area source pollution simulation.

Description

Technical Field

[0001] This invention relates to the fields of frozen soil hydrology and non-point source pollution simulation technology, specifically to a simulation method and system for nitrogen migration in saturated water layers at the snow-soil interface based on double-layer theory coupled with reversible single-section kinetics and a fully mixed reactor model. Background Technology

[0002] In seasonally frozen soil regions, spring snowmelt is a crucial hydrological process and a high-risk period for agricultural non-point source pollution. Due to the presence of a weakly permeable layer in the frozen soil, snowmelt water cannot infiltrate rapidly, instead forming a very thin saturated water zone between the snow and the frozen soil. The kinetics and driving mechanisms of solute leaching from the soil within this interface still require further investigation.

[0003] Existing simulation methods typically suffer from the following two types of drawbacks:

[0004] First, it ignores the unsteady flow characteristics of snowmelt runoff. Existing models often simplify it to steady-state flow, failing to capture the impact of flow pulses caused by diurnal temperature variations during the snowmelt period on solute transport and mixing processes, resulting in significant deviations in the simulation of peak concentrations.

[0005] Second, there is a lack of support from microscopic physicochemical mechanisms. Existing models often use fixed adsorption / desorption coefficients (linear partition coefficients), neglecting the perturbation of the electrochemical properties (electric double layer) of soil colloidal surfaces by rapid changes in ion intensity in snowmelt water. Experiments show that high-concentration ion influxes compress the electric double layer, producing an "electrostatic shielding effect," thereby promoting nitrogen desorption. Traditional models cannot reflect this "concentration-positive correlation" kinetic mechanism, leading to a significant decrease in accuracy when simulating high-concentration pulsed influxes. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a simulation method and system for nitrogen migration in saturated water layers at the snow-soil interface. This invention employs a coupled simulation strategy of "macroscopicizing microscopic mechanisms," constructing a fully mixed reactor model with coupled reversible first-order dynamics. It creatively introduces double-layer compression theory and a quasi-steady-state approximate adaptive algorithm to achieve refined and highly stable simulation of the non-equilibrium nitrogen migration process in the frozen soil surface during snowmelt. This solves the problems of neglecting dynamic water chemistry feedback mechanisms and being unable to adapt to non-steady-flow calculations in existing technologies.

[0007] To achieve the above objectives, the specific technical solution of the present invention is as follows:

[0008] A first aspect of the present invention provides a method for simulating nitrogen migration in a saturated water layer at the snow-soil interface, comprising the following steps:

[0009] A physical generalized model of the saturated water layer at the snow-soil interface is constructed to determine the system's basic state variables and boundary conditions; wherein, the state variables include the instantaneous volume of the saturated water layer (i.e., the liquid phase). saturated water layer temperature Nitrogen concentration in saturated water layer and soil solid phase adsorption nitrogen amount The boundary conditions include the inflow rate. With the inflow nitrogen concentration ;

[0010] Based on the double-layer compression theory and the Gouy-Chapman model, and according to the saturated water layer temperature Constructing an ion strength correction factor Used to correct the desorption rate constant To establish the response function of micro-electrostatic interaction to macro-dynamic parameters, so as to characterize the promoting effect of double-layer compression and electrostatic shielding effect caused by increased ionic strength on desorption;

[0011] According to the ion strength correction factor A modified reversible first-order kinetic equation was constructed to describe the current amount of nitrogen adsorbed in the soil solid phase. Non-equilibrium adsorption-desorption rate at the solid-liquid interface;

[0012] Based on Reynolds' transport theorem and the determined boundary conditions, a nonsteady flow field is coupled to construct the governing equations for a fully mixed reactor, which describe the instantaneous volume of the saturated water layer. nitrogen concentration in saturated water layer Convection transport and mixing processes in variable volume water bodies;

[0013] By combining the governing equations of the completely mixed reactor with the modified reversible first-order kinetic equations, a system of nonlinear ordinary differential equations is established. A solution strategy is selected using a quasi-steady-state approximation discrimination mechanism to obtain the instantaneous volume of the saturated water layer. Nitrogen concentration in saturated water layer Current amount of nitrogen adsorbed in the soil solid phase The nitrogen migration flux was then calculated. and cumulative extraction efficiency .

[0014] Furthermore, the ion strength correction factor Used to correct the desorption rate constant The corrected desorption rate constant was obtained. The formula is as follows:

[0015] ;

[0016] In the formula, This is the corrected desorption rate constant. Let be the desorption rate constant. This is the ion strength correction factor.

[0017] Furthermore, the ion strength correction factor Based on Debye-Hückel length The changes in are constructed, and their calculation formula is as follows:

[0018] ;

[0019] ;

[0020] ;

[0021] In the formula, This is the ion strength correction factor. Based on ionic strength The determined Debye-Hückel length, and For fitting parameters related to soil colloidal properties, For Debye-Hückel length, The vacuum permittivity, The relative permittivity, Boltzmann's constant, Where K is the absolute temperature, and T is the temperature measured in the saturated water layer. Let Avogadro's constant be 1. For elementary charge, The ionic strength of the solution.

[0022] Furthermore, based on the Langmuir isotherm adsorption hypothesis, and combined with the aforementioned ion strength correction factor... A modified reversible first-order kinetic equation was derived; among which, the classical Langmuir equilibrium equation, when adsorption reaches thermodynamic equilibrium, represents the current amount of nitrogen adsorbed in the soil solid phase. nitrogen concentration in saturated water layer Satisfy the following standard equation:

[0023] ;

[0024] in, This represents the current amount of nitrogen adsorbed in the solid phase of the soil. The nitrogen concentration in the saturated water layer varies over time. This is the Langmuir equilibrium constant. This represents the maximum adsorption capacity of the soil.

[0025] The physical essence of the Langmuir equilibrium equation above is that the adsorption rate is equal to the desorption rate, where the equilibrium constant is... It is the adsorption rate constant. With desorption rate constant The ratio, that is:

[0026] ;

[0027] To describe the time-varying process under non-equilibrium conditions, this invention reduces the above equilibrium relationship to a microscopic kinetic mechanism, wherein the adsorption term is proportional to the nitrogen concentration of the saturated water layer. and remaining adsorption sites ( The desorption term is proportional to the current amount of nitrogen adsorbed in the soil solid phase. ;

[0028] At this point, surface coverage is introduced. Substituting the above physical process into the law of mass action, we obtain the modified reversible first-order dynamic equation. The following is the form of expression:

[0029] ;

[0030] in, For surface coverage, For time, The adsorption rate constant is . This is the corrected desorption rate constant. The nitrogen concentration in the saturated water layer varies over time.

[0031] Furthermore, based on Reynolds' transport theorem and after coupling in the non-steadiness of snowmelt runoff, the following volume conservation equation and solute mass conservation equation are obtained:

[0032] ;

[0033] ;

[0034] In the formula, The instantaneous volume of the saturated water layer. For time, Inflow rate changing over time The outflow rate varies over time. The nitrogen concentration in the saturated water layer varies over time. The inflow nitrogen concentration varies over time. For the soil quality involved in the reaction, This represents the current amount of nitrogen adsorbed in the solid phase of the soil.

[0035] Expanding the volume conservation equation and the solute mass conservation equation, we obtain the following governing equations for a completely mixed reactor:

[0036] ;

[0037] In the formula, The nitrogen concentration in the saturated water layer varies over time. For time, The instantaneous volume of the saturated water layer. Inflow rate changing over time The outflow rate varies over time. The inflow nitrogen concentration varies over time. For the soil quality involved in the reaction, This represents the current amount of nitrogen adsorbed in the solid phase of the soil.

[0038] Furthermore, the dimensionless parameter As a criterion for the quasi-steady-state approximation discrimination mechanism, the dimensionless parameter Defined as reaction time scale With the flow time scale The ratio:

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, For the reaction time scale, For the time scale of flow, The adsorption rate constant is . The nitrogen concentration in the saturated water layer varies over time. This is the corrected desorption rate constant. The instantaneous volume of the saturated water layer. The outflow rate varies over time;

[0043] when When the reaction rate is equal to the flow rate, the fourth-order Runge-Kutta method is used to solve the nonlinear ordinary differential equation system by complete integration.

[0044] when When the system is determined to have entered a quasi-steady state, the rate of change of the solid phase is... The nonlinear ordinary differential equation system is reduced to an algebraic equation for solution; the algebraic equation is as follows:

[0045] ;

[0046] In the formula, The nitrogen concentration in the saturated water layer varies over time. For inflow traffic, The inflow nitrogen concentration, This is the corrected desorption rate constant. This represents the current amount of nitrogen adsorbed in the solid phase of the soil. For the soil quality involved in the reaction, For outflow volume, The adsorption rate constant is . This represents the maximum adsorption capacity of the soil.

[0047] Furthermore, the migration flux The calculation formula is as follows:

[0048] ;

[0049] In the formula, For migration flux, The outflow rate varies over time. The nitrogen concentration in the saturated water layer varies over time;

[0050] The cumulative extraction efficiency The calculation formula is as follows:

[0051] ;

[0052] ;

[0053] In the formula, To accumulate extraction efficiency, To simulate the total amount of nitrogen lost at the end of the simulation, This represents the initial adsorbed nitrogen content. For the soil quality involved in the reaction, To simulate the end time, The integral variable represents the time variable within the integral. for Inflow rate at any given moment for The inflow nitrogen concentration at time , for The cumulative nitrogen loss over time. for outflow rate at any given moment for The effluent nitrogen concentration at any given time.

[0054] The simulation method for nitrogen migration in saturated water layers at the snow-soil interface provided by this invention is based on the construction of a complete mathematical and physical framework that includes microscopic electrochemistry, macroscopic hydrodynamics, and numerical calculation strategies. Specifically, it comprises the following three parts:

[0055] Part 1: Constructing a dynamic parameter correction model based on the microscopic double-layer mechanism, including:

[0056] Traditional models often assume that soil adsorption-desorption parameters are constant. This invention, however, analyzes the driving mechanism of ionic strength changes on the kinetic process from the perspective of microscopic colloidal chemistry.

[0057] First, considering the charged characteristics of the frozen soil colloid surface, the Gouy-Chapman-Stern double-layer theory is introduced. This invention posits that the potential distribution on the soil surface... It is not fixed, but rather satisfies the nonlinear Poisson-Boltzmann equations:

[0058] ;

[0059] In the formula, Distance from surface The potential at that point, This refers to the distance from the surface of the soil colloid. The vacuum permittivity, The relative permittivity, For the first The valence of the ions. For elementary charge, This represents the number density of the ion in the bulk solution. Boltzmann's constant, Kelvin is the absolute temperature.

[0060] Secondly, by solving the aforementioned nonlinear Poisson-Boltzmann equation, this invention defines the Debye-Hückel length. As a characteristic physical quantity of the electric double layer thickness, this characteristic physical quantity With solution ionic strength There is a clear negative correlation in mathematical relationships:

[0061] ;

[0062] This relationship reveals the physical nature of how high concentrations of ions entering the body during the initial stages of snowmelt lead to significant compression of the electric double layer.

[0063] Finally, based on this, the present invention proposes a quantitative expression for the "electrostatic shielding effect": when As the concentration decreases, the electrostatic binding energy of nitrogen ions on the colloidal surface also decreases. This invention macroscopically transforms this microscopic mechanism into an effect on the desorption rate constant. Dynamic correction function:

[0064] ;

[0065] In the formula, for The effect on the corrected desorption rate constant. The term representing the change in activation energy caused by the change in ionic strength. The reference rate under pure water conditions. The gas constant is Kelvin is the absolute temperature.

[0066] This step achieves unidirectional coupling between water chemistry processes and physical migration processes.

[0067] Part Two: Constructing the macroscopically coupled governing equations for the adaptive variable volume process, including:

[0068] To address the problem that traditional steady-state models cannot describe the pulse characteristics of snowmelt runoff, this invention establishes a volumetric... A fully mixed reactor system that changes dynamically over time.

[0069] 1. Mass conservation equation for a non-steady flow perfectly mixed reactor

[0070] This invention takes into account the inflow rate. outflow The volume fluctuation caused by the imbalance is expressed by the following equation regarding the conservation of solute mass:

[0071] ;

[0072] In the formula, The instantaneous volume of the saturated water layer varies with time. The nitrogen concentration in the saturated water layer varies over time. For time, Inflow rate that varies over time The inflow nitrogen concentration varies over time. The outflow rate varies over time. To control the net reactive source term in vivo, This represents the volume of the saturated water layer.

[0073] To achieve numerical solutions, this invention expands the solution into concentration. Total differential form:

[0074] ;

[0075] In the formula, The nitrogen desorption rate per unit mass of soil. Effective soil density;

[0076] The equation clearly deconstructs the three driving forces of concentration change: external input exchange, dilution / concentration effect caused by changes in water volume, and soil desorption and release.

[0077] 2. Reversible first-order kinetic equations based on the Langmuir isothermal adsorption hypothesis

[0078] For source and sink items This invention abandons the simple linear distribution assumption and adopts the Langmuir monolayer adsorption theory. Soil surface cover is defined. Based on the law of mass action, the net desorption rate equation is constructed as follows:

[0079] ;

[0080] In the formula, In actual calculations, this invention equates the outflow concentration to the nitrogen concentration of the saturated water layer. .

[0081] The net desorption rate equation is introduced by... This reflects the saturation effect of soil adsorption sites, that is, when the adsorption amount approaches... At this point, the adsorption rate approaches zero. This not only conforms to physical facts, but also mathematically guarantees the boundedness and stability of the model.

[0082] Part Three: Introducing an adaptive solution strategy with multi-scale time coupling, including:

[0083] In response to the coexistence of extremely fast flow velocity (physical process) and extremely fast adsorption reaction (chemical process) in the extremely thin water layer at the snow-soil interface, the model equations are prone to exhibiting stiffness. This invention introduces a numerical strategy based on time scale comparison.

[0084] Define the system's reaction time scale With the flow time scale :

[0085] ;

[0086] ;

[0087] Constructing reaction timescales With the flow time scale The ratio dimensionless parameter As a criterion for judging the degree of rigidity:

[0088] ;

[0089] This invention is based on dimensionless parameters Real-time value dynamic switching solution algorithm:

[0090] Non-equilibrium calculation mode: when When the reaction rate is equal to the flow rate, the fourth-order Runge-Kutta method is used to solve the nonlinear ordinary differential equation system by complete integration.

[0091] Quasi-steady-state approximation mode: when When the chemical reaction rate is much greater than the flow rate, the system instantaneously reaches local equilibrium. At this point, the quasi-steady-state approximation is applied, and the solid phase change rate is set to... The differential equation is reduced to an algebraic equation for solution.

[0092] This strategy significantly improves computational efficiency while ensuring computational accuracy, and effectively prevents numerical oscillations caused by excessively large time steps.

[0093] A second aspect of the present invention provides a simulation system for nitrogen migration in a saturated water layer at the snow-soil interface, comprising:

[0094] Experimental parameter acquisition module: used to determine the basic state variables and boundary conditions of the system based on the physical generalization model of the saturated water layer at the snow-soil interface;

[0095] The module for constructing governing equations for a fully mixed reactor is used to establish governing equations for a fully mixed reactor by coupling an unsteady flow field with the determined boundary conditions based on Reynolds' transport theorem.

[0096] Modified reversible first-order kinetic equation construction module: used to establish an ion strength correction factor based on the double-layer compression theory and the Gouy-Chapman model, and then establish a modified reversible first-order kinetic equation based on the ion strength correction factor.

[0097] The solution module is used to combine the governing equations of the fully mixed reactor with the modified reversible first-order kinetic equations to establish a set of nonlinear ordinary differential equations. Based on the quasi-steady-state approximation discrimination mechanism, the solution strategy is selected to solve the set of nonlinear ordinary differential equations to obtain the instantaneous volume of the saturated water layer, the nitrogen concentration of the saturated water layer, and the current amount of nitrogen adsorbed in the soil solid phase, thereby obtaining the nitrogen migration flux and cumulative leaching efficiency.

[0098] A third aspect of the present invention provides an electronic device, including a memory and a processor; wherein the memory stores program instructions, and the processor is configured to execute the program instructions to perform a simulation method for nitrogen migration in a saturated water layer at the snow-soil interface.

[0099] Compared with the prior art, the advantages of the present invention are:

[0100] 1. Completeness of physical mechanisms: This invention is the first to introduce the Poisson-Boltzmann equation into a snowmelt hydrological model, successfully quantifying the relationship between "ionic strength and double layer thickness". Desorption activation energy The micro-chain of "macro-release flux" fills the gap in traditional models that neglect the hydrochemical feedback mechanism, and fundamentally explains the phenomenon that "high concentration of influent leads to high extraction efficiency".

[0101] 2. High accuracy of non-steady flow simulation: The model constructed by coupling a variable volume fully mixed reactor with modified reversible first-order kinetics can not only simulate steady-state processes, but also accurately reproduce the concentration "tailing phenomenon" and concentration rebound characteristics under flow pulse conditions, and significantly improve the simulation Nash efficiency coefficient.

[0102] 3. Robustness and efficiency of the algorithm: The introduction of the quasi-steady-state adaptive discrimination mechanism in this invention solves the problem of solving rigid equations, enabling the model to maintain numerical stability and avoid overflow or oscillation under extreme snowmelt flow or high reaction rate conditions. Attached Figure Description

[0103] Figure 1 A schematic diagram illustrating the mechanism of double-layer compression effect and its influence on soil nitrogen adsorption-desorption;

[0104] Figure 2 This is a flowchart illustrating the overall computational logic of the simulation method for nitrogen migration in the saturated water layer at the snow-soil interface in this embodiment of the invention.

[0105] Figure 3 This is a comparison and residual analysis diagram of the simulated effluent concentration curve and measured data in an embodiment of the present invention;

[0106] Figure 4 This is a comparison and error distribution diagram between the simulated cumulative extraction efficiency and the measured data in the embodiments of the present invention. Detailed Implementation

[0107] To enable those skilled in the art to clearly and completely understand the technical solution of the present invention, the present invention will be further described in detail below with reference to embodiments. Obviously, the embodiments described herein are only for explaining the present invention and are not intended to limit the scope of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0108] This invention provides a method for simulating nitrogen migration in a saturated water layer at the snow-soil interface, comprising the following steps:

[0109] A physical generalized model of the saturated water layer at the snow-soil interface is constructed to determine the system's basic state variables and boundary conditions; wherein, the state variables include the instantaneous volume of the saturated water layer. saturated water layer temperature Nitrogen concentration in saturated water layer and the current amount of nitrogen adsorbed in the soil solid phase The boundary conditions include the inflow rate. With the inflow nitrogen concentration .

[0110] Based on the double-layer compression theory and the Gouy-Chapman model, and according to the saturated water layer temperature Constructing an ion strength correction factor Establish the response function of microscopic electrostatic interaction to macroscopic dynamic parameters;

[0111] The ion strength correction factor Based on Debye-Hückel length The changes in are constructed, and their calculation formula is as follows:

[0112] ;

[0113] ;

[0114] ;

[0115] In the formula, This is the ion strength correction factor. Based on ionic strength The determined Debye-Hückel length, and For fitting parameters related to soil colloidal properties, For Debye-Hückel length, The vacuum permittivity, The relative permittivity, Boltzmann's constant, Where K is the absolute temperature, and T is the temperature measured in the saturated water layer. Let Avogadro's constant be 1. For elementary charge, The ionic strength of the solution;

[0116] The ion strength correction factor Used to correct the desorption rate constant That is, the corrected desorption rate constant. To characterize the promoting effect of double-layer compression and electrostatic shielding effect caused by increased ionic strength on desorption.

[0117] Based on the Langmuir isotherm adsorption hypothesis, combined with the aforementioned ion strength correction factor A modified reversible first-order kinetic equation was derived; among which, the classical Langmuir equilibrium equation, when adsorption reaches thermodynamic equilibrium, represents the current amount of nitrogen adsorbed in the soil solid phase. nitrogen concentration in saturated water layer Satisfy the following standard equation:

[0118] ;

[0119] in, This represents the current amount of nitrogen adsorbed in the solid phase of the soil. The nitrogen concentration in the saturated water layer varies over time. This is the Langmuir equilibrium constant. This represents the maximum adsorption capacity of the soil.

[0120] The physical essence of the Langmuir equilibrium equation above is that the adsorption rate is equal to the desorption rate, where the equilibrium constant is... It is the adsorption rate constant. With desorption rate constant The ratio, that is:

[0121] ;

[0122] To describe the time-varying process under non-equilibrium conditions, this invention reduces the above equilibrium relationship to a microscopic kinetic mechanism, wherein the adsorption term is proportional to the nitrogen concentration of the saturated water layer. and remaining adsorption sites ( The desorption term is proportional to the current amount of nitrogen adsorbed in the soil solid phase. ;

[0123] At this point, surface coverage is introduced. Substituting the above physical process into the law of mass action, we obtain the following: The modified reversible first-order kinetic equation is used to describe the current amount of nitrogen adsorbed in the soil solid phase. Non-equilibrium adsorption-desorption rate at the solid-liquid interface:

[0124] ;

[0125] in, For surface coverage, For time, The adsorption rate constant is . This is the corrected desorption rate constant. The nitrogen concentration in the saturated water layer varies over time.

[0126] Based on Reynolds' transport theorem and according to the determined boundary conditions, by coupling the unsteady flow field, the following volume conservation equation and solute mass conservation equation are obtained:

[0127] ;

[0128] ;

[0129] In the formula, The instantaneous volume of the saturated water layer varies with time. For time, Inflow rate changing over time The outflow rate varies over time. The nitrogen concentration in the saturated water layer varies over time. The inflow nitrogen concentration varies over time. For the soil quality involved in the reaction, This represents the current amount of nitrogen adsorbed in the solid phase of the soil.

[0130] Expanding the volume conservation equation and the solute mass conservation equation yields the following governing equations for a completely mixed reactor, used to describe the instantaneous volume of the saturated water layer. nitrogen concentration in saturated water layer Convective transport and mixing processes in variable volume water bodies:

[0131] ;

[0132] In the formula, The nitrogen concentration in the saturated water layer varies over time. For time, The instantaneous volume of the saturated water layer varies with time. Inflow rate changing over time The outflow rate varies over time. The inflow nitrogen concentration varies over time. For the soil quality involved in the reaction, This represents the current amount of nitrogen adsorbed in the solid phase of the soil.

[0133] By combining the governing equations of the completely mixed reactor with the modified reversible first-order kinetic equations, a system of nonlinear ordinary differential equations is established; a quasi-steady-state approximation discrimination mechanism is introduced to address the dimensionless parameters. As a criterion for the quasi-steady-state approximation discrimination mechanism, the solution strategy is dynamically selected to obtain the instantaneous volume of the saturated water layer. Nitrogen concentration in saturated water layer Current amount of nitrogen adsorbed in the soil solid phase The nitrogen migration flux was then calculated. and cumulative extraction efficiency ;

[0134] The dimensionless parameter Defined as reaction time scale With the flow time scale The ratio:

[0135] ;

[0136] ;

[0137] ;

[0138] In the formula, For the reaction time scale, For the time scale of flow, The adsorption rate constant is . This is the corrected desorption rate constant. The instantaneous volume of the saturated water layer varies with time. The outflow rate varies over time;

[0139] when When the reaction rate is equal to the flow rate, the fourth-order Runge-Kutta method is used to solve the nonlinear ordinary differential equation system by complete integration.

[0140] when When the system is determined to have entered a quasi-steady state, the rate of change of the solid phase is... The nonlinear ordinary differential equation system is reduced to an algebraic equation for solution; the algebraic equation is as follows:

[0141] ;

[0142] In the formula, The nitrogen concentration in the saturated water layer varies over time. For inflow traffic, The inflow nitrogen concentration, This is the corrected desorption rate constant. This represents the current amount of nitrogen adsorbed in the solid phase of the soil. For the soil quality involved in the reaction, For outflow volume, The adsorption rate constant is . This represents the maximum adsorption capacity of the soil.

[0143] The migration flux The calculation formula is as follows:

[0144] ;

[0145] In the formula, For migration flux, The outflow rate varies over time. The nitrogen concentration in the saturated water layer varies over time;

[0146] The cumulative extraction efficiency The calculation formula is as follows:

[0147] ;

[0148] ;

[0149] In the formula, To accumulate extraction efficiency, To simulate the total amount of nitrogen lost at the end of the simulation, This represents the initial adsorbed nitrogen content. For the soil quality involved in the reaction, To simulate the end time, The integral variable represents the time variable within the integral. for Inflow rate at any given moment for The inflow nitrogen concentration at time , for The cumulative nitrogen loss over time. for outflow rate at any given moment for The effluent nitrogen concentration at any given time.

[0150] Example 1

[0151] This embodiment is combined with the appendix Figure 1-4 The mathematical construction logic and implementation process of the simulation method of the present invention are described in detail.

[0152] Part 1: Construction of Microscopic Physicochemical Mechanisms

[0153] like Figure 1 As shown, soil colloid surfaces are typically negatively charged, and the distribution of ions in their vicinity follows a Boltzmann distribution. This invention first constructs a Poisson-Boltzmann equation describing the microscopic potential distribution:

[0154]

[0155] In the formula, Distance from surface The potential at that point, This refers to the distance from the surface of the soil colloid. Let x be the volume charge density at a distance x from the surface. The vacuum permittivity, The relative permittivity, For the first The valence of the ions. For elementary charge, This represents the number density of the ion in the bulk solution. Boltzmann's constant, Kelvin is the absolute temperature.

[0156] Solving the Poisson-Boltzmann equation yields the Debye-Hückel length (a characteristic value of the double-layer thickness). Its relationship with the ionic strength of the solution The relationship is:

[0157] ;

[0158] ;

[0159] In the formula, For Debye-Hückel length, The vacuum permittivity, The relative permittivity, Boltzmann's constant, Kelvin absolute temperature, Let Avogadro's constant be 1. For elementary charge, The ionic strength of the solution. Let be the molar concentration of the i-th ion. Let be the valence of the i-th ion.

[0160] Reference Figure 1 Left side (Low Ionic Strength): Ionic strength in snowmelt water At lower levels, The soil double layer is relatively large, and the electrical double layer is in an expanded state (Expanded EDL). Soil colloids are less sensitive to nitrogen (e.g., ... It has strong electrostatic adsorption force, and is characterized as a "strong adsorption phase".

[0161] Reference Figure 1 Right side (High Ionic Strength): Ionic strength during the initial stage of snow melting. At higher levels, As the electrical double layer (EDL) decreases, it is compressed, resulting in an electrostatic shielding effect. This reduces the binding energy of adsorption sites on the soil surface, leading to a "desorption phase".

[0162] Based on this mechanism, the present invention... Figure 1 The "double-layer regulation" module introduces a correction formula:

[0163] ;

[0164] This modified formula maps microscopic electrochemical changes to changes in macroscopic kinetic parameters.

[0165] Part Two: Derivation of the Macroscopic Dynamic Equations

[0166] like Figure 2 As shown in the flowchart, the simulation method of the present invention is not a simple linear calculation, but a complete logical closed loop that includes state discrimination.

[0167] 1. Modified Reversible First-Order Dynamics (RFO) Equations (Based on the Langmuir Assumption)

[0168] Define coverage .like Figure 1 As shown in the "RFO kinetics" module, according to the law of mass action, the adsorption rate is related to the number of vacancies. The desorption rate is directly proportional to the coverage. Proportional:

[0169] ;

[0170] In the formula, For surface coverage, For time, The adsorption rate constant is . This is the corrected desorption rate constant. The outflow concentration is [value].

[0171] 2. Governing equations for a variable volume completely mixed reactor (CSTR)

[0172] Treating the saturated water layer as the control volume, according to Reynolds' transport theorem, the mass conservation equation is:

[0173] ;

[0174] In the formula, For time, For the saturated water layer volume, For inflow traffic, Inflow concentration, For outflow volume, For the outflow concentration, To control the net reactive source term in the body.

[0175] After expansion, the ordinary differential equation for the saturated water concentration is obtained (e.g.) Figure 2 (The "Coupled with CSTR" module)

[0176] ;

[0177] In the formula, For the outflow concentration, For time, For the saturated water layer volume, For inflow traffic, Inflow concentration, For outflow volume, For the soil quality involved in the reaction, This represents the maximum adsorption capacity of the soil. This is the corrected desorption rate constant. The adsorption rate constant is . For the outflow concentration, For surface coverage.

[0178] 3. Quasi-steady-state approximation (QSSA) adaptive discrimination ( Figure 2 The right-hand branch is used to solve the rigidity problem. Figure 2 The flowchart includes “(4) QSSA criterion”: Calculate the dimensionless parameter .

[0179] when When the reaction rate is much greater than the flow rate, the system is deemed to meet the quasi-steady-state condition. At this point, the model automatically switches to algebraic mode:

[0180] ;

[0181] In the formula, For the outflow concentration, For inflow traffic, Inflow concentration, For the soil quality involved in the reaction, This is the corrected desorption rate constant. This represents the current amount of nitrogen adsorbed in the solid phase of the soil. For outflow volume, The adsorption rate constant is . This represents the maximum adsorption capacity of the soil.

[0182] This strategy greatly improves the computational efficiency of the model under rigid conditions.

[0183] Part Three: Numerical Solution and Result Analysis

[0184] This invention employs the fourth-order Runge-Kutta (RK4) algorithm to discretely solve the above system of equations.

[0185] Define state vector ,exist arrive step size Inside:

[0186] ;

[0187] ;

[0188] …

[0189] ;

[0190] In the formula, Based on the current time t n The calculated rate of change Based on The estimated rate of change at the midpoint. Based on The corrected rate of change at the midpoint. Based on The predicted next moment rate of change, This is the time node of the current calculation step. For the time step of the calculation, for The state vector value at time t. for The state vector value at time t.

[0191] The simulation results are verified as follows:

[0192] 1. Effluent concentration simulation

[0193] Figure 3 Showing outflow concentration Changes over time.

[0194] Curve analysis: The model simulation curve (purple solid line) is in high agreement with the measured data (green solid line), and both are located within the uncertainty zone (light-colored area).

[0195] Mechanism verification: The curve exhibits a typical "rapid rise, slow fall" characteristic. By introducing reversible first-order kinetics, the model successfully captures the "tailing effect" under non-equilibrium conditions, avoiding the problem of excessively rapid concentration decreases in traditional first-order models. The residual plot in the upper right corner shows that the error fluctuates within a very small range.

[0196] 2. Extraction efficiency simulation

[0197] Figure 4 Demonstrates cumulative extraction efficiency The dynamic changes.

[0198] Early non-linear growth: Please note the first 4 hours ( Figure 4 (On the left), the extraction efficiency shows a rapid, non-linear increase. This is because the influent ion intensity is high at this point, triggering the process in Equation 1. The correction term (double-layer compression) leads to a significant increase in the desorption rate.

[0199] Accuracy verification: If the double-layer effect is not considered, the simulated curve will be linear and lower than the measured value. However, the curve (purple) obtained by the method of this invention closely follows the measured value (green). The APE (absolute percentage error) statistics in the upper left corner show that most of the error is concentrated around 0, and the Nash efficiency coefficient (NSE) exceeds 0.85.

[0200] In summary, this invention achieves accurate reproduction of the complex solute migration process at the snow-soil interface by constructing a coupled mathematical model of "double electric layer microscopic mechanism + CSTR macroscopic transport + RFO non-equilibrium dynamics".

[0201] The implementation of the above embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a simulation system for nitrogen migration in a saturated water layer at the snow-soil interface, used to execute the simulation method for nitrogen migration in a saturated water layer at the snow-soil interface described in the above embodiments. The simulation system includes: an experimental parameter acquisition module, used to determine the basic state variables and boundary conditions of the system based on a physical generalization model of the saturated water layer at the snow-soil interface; a complete mixing reactor control equation construction module, used to establish the control equations of the complete mixing reactor based on Reynolds transport theorem and the determined boundary conditions, coupled with a non-steady flow field; a modified reversible first-order kinetic equation construction module, used to establish an ion strength correction factor based on the double-layer compression theory and the Gouy-Chapman model, and then establish a modified reversible first-order kinetic equation based on the ion strength correction factor; and a solution module, used to combine the complete mixing reactor control equations and the modified reversible first-order kinetic equations to establish a set of nonlinear ordinary differential equations, and select a solution strategy based on the quasi-steady-state approximation discrimination mechanism to solve the nonlinear ordinary differential equations to obtain the instantaneous volume of the saturated water layer, the nitrogen concentration of the saturated water layer, and the current amount of nitrogen adsorbed in the soil solid phase, thereby obtaining the nitrogen migration flux and cumulative leaching efficiency.

[0202] It should be noted that the simulation system embodiments provided by the present invention are used not only to implement the simulation methods in the above-described simulation method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is the setting of corresponding functional modules. The principle is basically the same as that of the above-described system embodiments provided by the present invention. As long as those skilled in the art can improve the modules in the above-described system embodiments by referring to the specific technical solutions in other method embodiments, combining technical features to obtain corresponding technical means and technical solutions composed of these technical means, and ensuring the practicality of the technical solutions, they can obtain corresponding system-class embodiments for implementing the methods in other method-class embodiments.

[0203] The method described in this invention is implemented using an electronic device; therefore, it is necessary to introduce the relevant electronic device. To this end, this invention provides an electronic device comprising: at least one processor and at least one memory; wherein the memory stores program instructions, and the processor executes the program instructions to perform the simulation method for nitrogen migration in the saturated water layer at the snow-soil interface described in the above embodiments. The storage medium can be any non-volatile storage device such as a hard disk, solid-state drive, flash drive, or optical disk, used to store computer program code and necessary data files. The stored computer program includes: an experimental parameter acquisition module, a module for constructing the control equations of a fully mixed reactor, a module for constructing modified reversible first-order kinetic equations, and a solution module.

[0204] The above detailed embodiments describe the implementation of the present invention; however, the present invention is not limited to the specific details described in the above embodiments. Within the scope of the claims and technical concept of the present invention, various simple modifications and changes can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

Claims

1. A method for simulating nitrogen migration in a saturated water layer at the snow-soil interface, characterized in that, Includes the following steps: A physical generalized model of the saturated water layer at the snow-soil interface is constructed to determine the system's basic state variables and boundary conditions; wherein, the state variables include the instantaneous volume of the saturated water layer. saturated water layer temperature Nitrogen concentration in saturated water layer and the current amount of nitrogen adsorbed in the soil solid phase The boundary conditions include the inflow rate. With the inflow nitrogen concentration ; Based on the double-layer compression theory and the Gouy-Chapman model, and according to the saturated water layer temperature Constructing an ion strength correction factor Used to correct the desorption rate constant The ion strength correction factor Based on Debye-Hückel length The formula is constructed based on the changes in , as follows: ； ； ； In the formula, This is the ion strength correction factor. Based on ionic strength The determined Debye-Hückel length, and For fitting parameters related to soil colloidal properties, For Debye-Hückel length, The vacuum permittivity, The relative permittivity, Boltzmann's constant, Where K is the absolute temperature, and T is the temperature measured in the saturated water layer. Let Avogadro's constant be 1. For elementary charge, The ionic strength of the solution; According to the ion strength correction factor A modified reversible first-order kinetic equation was constructed to describe the current amount of nitrogen adsorbed in the soil solid phase. Non-equilibrium adsorption-desorption rate at the solid-liquid interface; Based on Reynolds' transport theorem and the determined boundary conditions, a nonsteady flow field is coupled to construct the governing equations for a fully mixed reactor, which describe the instantaneous volume of the saturated water layer. nitrogen concentration in saturated water layer Convection transport and mixing processes in variable volume water bodies; By combining the governing equations of the completely mixed reactor with the modified reversible first-order kinetic equations, a set of nonlinear ordinary differential equations is obtained. A solution strategy is selected using a quasi-steady-state approximation discrimination mechanism to obtain the instantaneous volume of the saturated water layer. Nitrogen concentration in saturated water layer Soil solid-phase adsorption nitrogen content The nitrogen migration flux was then calculated. and cumulative extraction efficiency .

2. The method for simulating nitrogen migration in a saturated water layer at the snow-soil interface according to claim 1, characterized in that, Ion strength correction factor Used to correct the desorption rate constant The corrected desorption rate constant was obtained. The formula is as follows: ； In the formula, This is the corrected desorption rate constant. Let be the desorption rate constant. This is the ion strength correction factor.

3. The method for simulating nitrogen migration in a saturated water layer at the snow-soil interface according to claim 2, characterized in that, Based on the Langmuir isotherm adsorption hypothesis and the aforementioned ion strength correction factor The following modified invertible first-order dynamic equation is derived: ； In the formula, For surface coverage, For time, The adsorption rate constant is . This is the corrected desorption rate constant. The nitrogen concentration in the saturated water layer varies over time.

4. The method for simulating nitrogen migration in a saturated water layer at the snow-soil interface according to claim 1, characterized in that, The governing equations for the fully mixed reactor are as follows: ； In the formula, The nitrogen concentration in the saturated water layer varies over time. For time, The instantaneous volume of the saturated water layer. Inflow rate changing over time The outflow rate varies over time. The inflow nitrogen concentration varies over time. For the soil quality involved in the reaction, This represents the current amount of nitrogen adsorbed in the solid phase of the soil.

5. The method for simulating nitrogen migration in a saturated water layer at the snow-soil interface according to claim 1, characterized in that, dimensionless parameters As a criterion for the quasi-steady-state approximation discrimination mechanism, the dimensionless parameter Defined as reaction time scale With the flow time scale The ratio: ； ； ； In the formula, For the reaction time scale, For the time scale of flow, The adsorption rate constant is . The nitrogen concentration in the saturated water layer varies over time. This is the corrected desorption rate constant. The instantaneous volume of the saturated water layer. The outflow rate varies over time; when At that time, the fourth-order Runge-Kutta method was used to solve the nonlinear ordinary differential equation system by complete integration; when When the system is determined to have entered a quasi-steady state, the rate of change of the solid phase is... The nonlinear ordinary differential equation system is reduced to an algebraic equation for solution.

6. The method for simulating nitrogen migration in a saturated water layer at the snow-soil interface according to claim 1, characterized in that, The migration flux The calculation formula is as follows: ； In the formula, For migration flux, The outflow rate varies over time. The nitrogen concentration in the saturated water layer varies over time.

7. The method for simulating nitrogen migration in a saturated water layer at the snow-soil interface according to claim 1, characterized in that, The cumulative extraction efficiency The calculation formula is as follows: ； ； In the formula, To accumulate extraction efficiency, To simulate the total amount of nitrogen lost at the end of the simulation, This represents the initial adsorbed nitrogen content. For the soil quality involved in the reaction, To simulate the end time, The integral variable represents the time variable within the integral. for Inflow rate at any given moment for The inflow nitrogen concentration at time , for The cumulative nitrogen loss over time. for outflow rate at any given moment for The effluent nitrogen concentration at any given time.

8. A simulation system for nitrogen migration in a saturated water layer at the snow-soil interface, used to implement the simulation method according to any one of claims 1-7, characterized in that, include: Experimental parameter acquisition module: used to determine the basic state variables and boundary conditions of the system based on the physical generalization model of the saturated water layer at the snow-soil interface; Modified reversible first-order kinetic equation construction module: used to establish an ion strength correction factor based on the double-layer compression theory and the Gouy-Chapman model, and then establish a modified reversible first-order kinetic equation based on the ion strength correction factor. The module for constructing governing equations for a fully mixed reactor is used to establish governing equations for a fully mixed reactor by coupling an unsteady flow field with the determined boundary conditions based on Reynolds' transport theorem. The solution module is used to combine the governing equations of the completely mixed reactor with the modified reversible first-order kinetic equations to establish a set of nonlinear ordinary differential equations. Based on the quasi-steady-state approximation discrimination mechanism, the solution strategy is selected to solve the set of nonlinear ordinary differential equations to obtain the instantaneous volume of the saturated water layer, the nitrogen concentration of the saturated water layer, and the amount of nitrogen adsorbed in the soil solid phase, thereby obtaining the nitrogen migration flux and cumulative leaching efficiency.

9. An electronic device comprising a memory and a processor, characterized in that, The memory stores program instructions, and the processor executes the program instructions to perform the simulation method according to any one of claims 1-7.

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