A method for calculating phosphorus transport and distribution based on suspended sediment settling probability

Abstract

The present application provides a kind of phosphorus transport and distribution calculation method based on suspended sediment settling probability, comprising the following steps: selecting a typical section, field determination section sediment particle size distribution, sediment concentration and water velocity;According to the sediment concentration, etc., the settling velocity of single-component sediment is calculated and checked, and the settling velocity of full particle size suspended sediment is obtained by particle size distribution composition;According to the settling velocity of sediment and the sediment settling probability function, the particle state phosphorus transport trajectory is analyzed;Based on the phase separation model, the functional relationship between different particle size groups of sediment, i.e. different sediment concentrations and adsorption phase phosphorus is determined through laboratory experiment;The sediment particle size distribution grouping information and the settling velocity of full particle size suspended sediment are introduced into the hydrodynamic water quality model to analyze the transport process and distribution characteristics of particle phosphorus and dissolved phase phosphorus. This method realizes the numerical analysis of the particle phosphorus transport trajectory, settling velocity and solid-liquid two-phase distribution of full particle size sediment.

Description

Technical Field

[0001] This invention relates to the field of water environment simulation and control, specifically a method for calculating phosphorus transport and distribution based on the sedimentation probability of suspended sediment. Background Technology

[0002] Changes in sediment movement, particle size distribution, and pollutant adsorption characteristics directly affect the content and form of pollutants. Phosphorus in water can be divided into soluble and particulate forms, and it migrates along with sediment movement in water bodies. On the one hand, particulate phosphorus settles to the bottom of the sediment, reducing the amount of pollutants in the water. Under certain conditions, pollutants deposited on the bottom can re-enter the water body with the flushed sediment. On the other hand, when external conditions such as hydrochemistry and hydrodynamics change, adsorbed phosphorus on the sediment will dynamically exchange with dissolved phosphorus in the water. The movement and transport of suspended sediment in the water directly affect the distribution and spatiotemporal distribution of phosphorus between the solid and liquid phases. Sediment is a mixture with a wide particle size distribution, and its particle size composition is one of the main factors affecting the settling rate and the adsorption and desorption rate of pollutants.

[0003] Mathematical models of river sediment phosphorus transport processes are effective tools for solving reservoir engineering management problems. The earliest model to simulate the impact of sediment on water quality was the Thomas model, followed by the Velez-Gannon model and the Dobbins-Comp model. However, these models describe various sediment movement processes with a single constant parameter, failing to reflect the impact of sediment transport on pollutant migration (He Yong, Li Yitian, Gao Huicai, Wang Jiasheng. Research on sediment pollution water quality models [J]. Journal of Sichuan University (Engineering Science Edition), 2004, 6: 12-17.). Many researchers have proposed and established water quality models for sediment-laden water bodies, introducing different parameters to consider the impact of sediment movement on phosphorus transport. Chu Junda et al. (Chu Junda, Xu Huici. Study on the impact of river sediment scouring and settling on water quality. Journal of Hydraulic Engineering, 1994, 11, 42-47, 69.) started from the pollution convection and diffusion equation, introduced particulate pollutants, and considered the influence of sediment scouring, settling and release, and derived a one-dimensional water quality model; Yu Xuezhong established a one-dimensional transport and transformation phase separation model of dissolved and adsorbed pollutants (Yu Xuezhong, Yang Zhifeng, Zhong Deyu, Peng Qidong. Mathematical model of interaction between river sediment and pollutants [J]. Journal of Hydraulic Engineering, 2006, 1: 10-15.). Huang Lei et al. introduced the theory of bed sediment-suspended sediment exchange in river dynamics and established a phase-separation model of the river hydrodynamic-sediment-phosphorus transport process (Huang Lei, Fang Hongwei, Wang Jingyu, et al. Mathematical model study on river sediment-phosphorus transport process [J]. Journal of Hydraulic Engineering, 2014, 4: 394-402.). This model considers the different distribution ratios of phosphorus in the bottom sediment from a mechanistic perspective, focusing on the phosphorus exchange between the aerobic and anoxic layers of the bottom sediment layer under scouring and deposition. However, the sedimentation coefficient in the phosphorus transport transformation equation of this model is only a fixed empirical constant (i.e., the steady settling velocity of the population). This generalized approach ignores the obstruction of sedimentation of particulate phosphorus in the water layer and the multiphase interactions of sediments of different particle sizes, and lacks the basic theory of sedimentation process. Therefore, this type of model is more suitable for studying the environmental behavior of phosphorus in sediments of large lake-type reservoirs with less external disturbance. However, for natural rivers or river-type reservoirs, due to the large annual variation of hydrodynamic conditions in the reservoir area and the obvious spatial variation along the route, the transport and sedimentation characteristics of sediments of different particle sizes and the particulate phosphorus they carry under the influence of human water and sediment regulation have significant spatiotemporal differences. The simplified treatment of the sedimentation process may have a significant impact on the simulation results.

[0004] During the process of developing this invention, the inventors discovered that existing water-sediment pollutant coupling models or technologies have significant shortcomings:

[0005] (1) Existing sediment-water quality mathematical models overgeneralize the key influencing factor of sediment particle size. In the simulation, the median particle size is used as the sediment particle size. This simplification is more suitable for sediment with short transport distance and relatively uniform particle size. However, sediment can usually be divided into clay, silt, very fine sand, fine sand and coarse sand according to particle size. The median particle size often cannot reflect the true particle composition of sediment. Moreover, for long-distance sediment transport, as the hydrodynamic conditions change, the range of movement, settling distance and movement state of sediment with different particle sizes show huge differences. For example, coarse sand usually settles at the tail of the reservoir, while fine sand is deposited in front of the dam and can adsorb and enrich more pollutants.

[0006] (2) Secondly, during the movement of sediment particles, pollutants such as phosphorus are redistributed between the particulate and dissolved phases. The distribution coefficient is usually determined by selecting representative particle sizes and calculating it using Langmuir adsorption models through isothermal oscillation adsorption and desorption experiments. The sediment particle size is normally distributed, and the particle size after oscillation has changed significantly from that before the experiment. Therefore, the distribution coefficient cannot scientifically reflect the influence of sediment particle size or composition on the interconversion between particulate phosphorus and dissolved phosphorus. Summary of the Invention

[0007] To address the aforementioned deficiencies in existing technologies, this invention provides a method for calculating phosphorus transport and distribution based on the settling probability of suspended sediment. This method considers the full particle size composition of sediment, analyzes the particle size distribution of river sediment, calculates the settling rate and transport distance of sediment of all particle sizes based on the sediment settling probability, obtains the phosphorus distribution coefficient of sediment particles of different sizes based on indoor experiments, and constructs a phosphorus transport model based on sediment settling probability, which can comprehensively analyze the environmental effects of sediment transport of all particle sizes.

[0008] A method for calculating phosphorus transport and distribution based on the settling probability of suspended sediment includes the following steps:

[0009] Step 1: Select a typical cross section, measure the topographic data on site, and simultaneously measure the suspended sediment concentration S, water temperature T, and flow velocity U. The topographic data includes the river width B and water depth H. Use an in-situ laser particle size analyzer to monitor changes in sediment particle size distribution in real time.

[0010] Step 2: Initially determine the flow regime based on the particle size of the grouped sediment particles, calculate the sediment particle settling velocity based on the flow regime, and then verify the accuracy of the determined flow regime by calculating the Reynolds number. If it does not belong to the discriminant flow layer, assume another flow regime and calculate the settling velocity until the correct result is obtained. Correct the sediment mass settling velocity based on the suspended sediment concentration and synthesize the sediment settling velocities of different particle size groups.

[0011] Step 3: Calculate the particle phosphorus settling probability using the sediment settling probability density function based on the settling velocity of sediment of all particle sizes.

[0012] Step 4: Calculate the transport distance of particulate phosphorus before sedimentation based on the sedimentation probability of particulate phosphorus and the sedimentation rate of the synthesized full-size particles;

[0013] Step 5: Obtain the adsorption rate k of sediment under different particle size groups through indoor experiments. p and sediment adsorption rate k under different suspended sediment concentrations S The overall adsorption rate k was obtained through polynomial fitting. α ;

[0014] Step 6: Use a phosphorus phase transport model to analyze the changes in dissolved and adsorbed phosphorus along the process, extract specific cross-sectional data to obtain phosphorus distribution characteristics, and obtain the distribution characteristics of dissolved and adsorbed phosphorus based on the ratio of the two forms of phosphorus.

[0015] Furthermore, in step 2, formula (7) is used to correct the settling velocity of the sediment group, and formula (8) is used to synthesize the settling velocities of sediment groups with different particle sizes:

[0016]

[0017]

[0018] In the formula, For sediment mass settling velocity; P i ω represents the percentage of the i-th particle size group; i ω represents the settling velocity of sediment with particle size i in the i-th group; S0 S represents the settling velocity of sediment particles under the experimental conditions. f α represents the suspended sediment concentration under experimental conditions, and α is a coefficient related to the Reynolds number.

[0019] Furthermore, step 3 specifically includes:

[0020] The model assumes that sediment particles settle to the bottom with a certain probability, which varies between 0 and 1. The velocity of the sediment particles follows a Gaussian normal distribution with the following density function:

[0021]

[0022] In the formula, x is the particle velocity; u is the mean; σ is the standard deviation. Particle phosphorus and sediment are interdependent. Integrating the Gaussian density function yields the particle phosphorus sedimentation probability function:

[0023]

[0024] In the formula, Ps is the settling probability of particulate phosphorus; x is the velocity of sediment particles; ω is the settling velocity of particulate phosphorus, i.e., the settling velocity of sediment of all particle sizes; σ ν The standard deviation of vertical turbulence intensity.

[0025] Furthermore, in step (4), the transport distance of particulate phosphorus before sedimentation is calculated using equation (11):

[0026] Average velocity of sediment particles along the vertical of the water flow At a settling velocity ω, the longitudinal transport distance when sinking from a distance h from the riverbed to the riverbed is:

[0027]

[0028] In the formula L c ω represents the longitudinal transport distance of sediment deposition; ω represents the settling velocity. β is the vertical average velocity of the water flow; β is a parameter representing the following behavior of sediment particles with water flow turbulence.

[0029] Furthermore, in step 5, the adsorption rate k α The adsorption kinetics were obtained through indoor experiments. The kinetic equations were fitted using the intraparticle diffusion model, first-order kinetics, and second-order kinetics, respectively. The optimal fitting parameters were selected based on the coefficient of determination.

[0030] in:

[0031] k p =f(d,P i (12)

[0032] k s =f(S) (13)

[0033] k α =f(k) p ,k s (14).

[0034] Furthermore, the phosphorus adsorbate in step 6 is expressed as follows:

[0035]

[0036]

[0037] In the formula C s The phosphorus content of the adsorbed phase of sediment is N, which represents the sediment particle size group, and Q is the phosphorus content of the adsorbed phase. si P represents the phosphorus content of the adsorbed phase of the i-th sediment group. i The mass percentage of sediment in the i-th group;

[0038] The governing equations for phosphorus transport employ a phase-separation model, including dissolved phosphorus C in the water body. w Phosphorus C adsorbed on suspended sand s The specific expression is as follows:

[0039]

[0040]

[0041] In the formula, A is the control cross-sectional area; C b C s C w These represent the contents of bed sand, suspended sediment, and pollutants in the water body, respectively; S is the average sediment concentration of the cross section; S * D represents the average sand-carrying capacity of the cross section. x ω is the longitudinal dispersion coefficient; α is the recovery saturation coefficient; ω is the particle settling velocity, i.e., the particle settling velocity containing information on sediment particle size grouping; B is the river width; k α The adsorption rate, i.e., the rate of change of the amount of sediment adsorbed per unit mass per unit time, is k. α >0 indicates sediment adsorption, and vice versa; U is the average cross-sectional velocity; dC w / dt represents the biochemical reaction term; σ represents the pollutant release rate per unit river length; r represents the emission source strength;

[0042] The sand-carrying capacity is calculated using Zhang Ruijin's formula, with a particle size distribution correction factor introduced:

[0043]

[0044] S * The sand-carrying capacity is expressed in kg / m³. 3 U is the average flow velocity across the cross section, in m / s; g is the acceleration due to gravity, in m / s². 2 h is the average water depth in meters (m); ω is the average settling velocity in meters per second (m / s); m is the sediment-carrying capacity index, typically taken as 0.92; k is the sediment-carrying capacity coefficient; P i denoted as the mass percentage of the i-th group of sediment; N represents the number of sediment particle size groups.

[0045] The content relationships of adsorbed phosphorus in different sediment components are as follows:

[0046]

[0047] In the formula C s The phosphorus content of the adsorbed phase of sediment is N, which represents the sediment particle size group, and Q is the phosphorus content of the adsorbed phase. si P represents the phosphorus content of the adsorbed phase of the i-th sediment group. i Let be the percentage of sediment mass in the i-th group.

[0048] By employing the above-mentioned scheme, this invention can simulate the process of phosphorus transported with sediment, and has the following beneficial effects:

[0049] (1) Combining underwater in-situ monitoring technology of suspended sediment particle size and particle settling velocity formula, the settling velocity of a particle with particle size distribution is calculated to obtain the real process of sediment settling rate change of all components; by using real-time observed particle size data, the limitation of the fixed constant given in the traditional water and sediment nutrient model is solved, and the accurate simulation of sediment and biogenic elements of all particle size in the sedimentation and transport process in the main water body is realized, which is more in line with the actual situation;

[0050] (2) The sedimentation trajectory of phosphorus particles of different sizes was simulated, the transport distance of phosphorus particles of the whole component was calculated, and the sedimentation probability and interception efficiency of phosphorus particles were analyzed. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the framework of the phosphorus transport model based on the settling probability of suspended sediment constructed in this invention;

[0052] Figure 2 This is a graph showing the probability distribution of phosphorus particle sedimentation under different turbulence velocities;

[0053] Figure 3 This is a diagram showing the trajectory of phosphorus particles.

[0054] Figure 4 It is the trajectory of particulate phosphorus transport in the surface layer of each cross section during the flood season;

[0055] Figure 5 This is a comparison chart of simulated and measured values ​​of particulate phosphorus in an embodiment of the present invention;

[0056] Figure 6 This is a flowchart of one embodiment of the method for calculating phosphorus transport and distribution based on the sedimentation probability of suspended sediment according to the present invention. Detailed Implementation

[0057] The technical solutions of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.

[0058] Please see Figure 1 The phosphorus transport model based on the settling probability of suspended sediment established in this invention includes three parts: a hydrodynamic module, a suspended sediment transport module, and a phosphorus transport and distribution module. The hydrodynamic module and the phosphorus transport and distribution module both consider the influence of sediment gradation and sediment content. The particle phosphorus settling rate is represented by the Gauss equation.

[0059] The hydrodynamic module includes the flow continuity equation and the flow motion equation, as detailed below:

[0060] Continuity equation for water flow:

[0061]

[0062] Equations of water flow:

[0063]

[0064] The sediment transport in the suspended sediment transport module is calculated using the unsaturated sediment transport method, considering the exchange between suspended sediment and bottom sediment, as well as the sediment particle size distribution. The governing equations for sediment transport are continuous equations, as follows:

[0065]

[0066]

[0067] In the formula, ω is the sediment settling velocity, subscript i represents the sediment group number for different particle size groups; Q is the flow rate; A is the flow area; t is the time; x is the coordinate along the flow path; Z is the water level; K is the cross-sectional flow modulus; S is the sediment concentration; S * ρ is the sediment-carrying force of the water flow; B is the dry density of the sediment; g is the cross-sectional width; u is the gravitational acceleration; α is the regenerative saturation coefficient; A d d represents the suspended sediment deposition area; d represents the particle size; U represents the flow velocity; A represents the flow velocity. b To reduce the area of ​​riverbed erosion and sedimentation.

[0068] The phosphorus transport and distribution module uses a phase-separation model to describe the phosphorus transport process, including dissolved phosphorus (C) in the water body. w ), phosphorus adsorbed on suspended sand (C) s The specific expression is as follows:

[0069]

[0070]

[0071] In the formula, A is the control cross-sectional area; C b C s C w These represent the contents of bed sand, suspended sediment, and pollutants in the water body, respectively; S is the average sediment concentration of the cross section; S * D represents the average sand-carrying capacity of the cross section. x α is the longitudinal dispersion coefficient; ω is the recovery saturation coefficient; B is the particle settling velocity; k is the river width; α The adsorption rate, i.e., the rate of change of the amount of sediment adsorbed per unit mass per unit time, is k. α >0 indicates sediment adsorption, and vice versa; U is the average cross-sectional velocity; dC w / dt represents the biochemical reaction term; σ represents the pollutant release rate per unit river length; and r represents the emission source strength.

[0072] Please continue reading. Figure 6 This invention provides a method for calculating phosphorus transport and distribution based on the settling probability of suspended sediment, comprising the following steps:

[0073] Step 1: Select a typical cross section, measure topographic data such as river width B and water depth H on site, and simultaneously measure suspended sediment concentration S, water temperature T, flow velocity U, etc., and use an in-situ laser particle size analyzer to monitor changes in sediment particle size distribution in real time.

[0074] Step 2: Initially determine the flow regime based on the particle size of the grouped sediment particles, calculate the sediment particle settling velocity based on the flow regime, and then verify the accuracy of the determined flow regime by calculating the Reynolds number. If it does not belong to the discriminant flow layer, assume another flow regime and calculate the settling velocity until the correct result is obtained; correct the sediment mass settling velocity according to the suspended sediment concentration using the formula (Equation 7), and synthesize the settling velocities of sediment groups with different particle sizes (Equation 8):

[0075]

[0076]

[0077] In the formula, For sediment mass settling velocity; P i ω represents the percentage of the i-th particle size group; i ω represents the settling velocity of sediment with particle size i in the i-th group; S0 S represents the settling velocity of sediment particles under the experimental conditions. f The suspended sediment concentration is given under experimental conditions, and α is a coefficient related to the Reynolds number.

[0078] Step 3: Calculate the particle phosphorus settling probability using the sediment settling probability density function (Equation 10) based on the sediment settling velocity of all particle sizes (Equation 8).

[0079] The model assumes that sediment particles settle to the bottom with a certain probability, varying between 0 and 1. Extensive experimental observations confirm that the velocity of sediment particles follows a Gaussian normal distribution, with the following density function:

[0080]

[0081] In the formula, x represents the particle velocity; u is the mean; and σ is the standard deviation. Particle phosphorus and sediment are interdependent. Integrating the Gaussian density function yields the particle phosphorus sedimentation probability function:

[0082]

[0083] In the formula, Ps is the settling probability of particulate phosphorus; x is the velocity of sediment particles; ω is the settling velocity of particulate phosphorus (i.e., the settling velocity of sediment of all particle sizes); σ ν The standard deviation of vertical turbulence intensity.

[0084] When v s When taking different values, the corresponding sediment (or particulate phosphorus) settling probability is as follows: Figure 2 As shown.

[0085] Step 4: Based on the particle phosphorus sedimentation probability (Equation 10) and the sedimentation rate of the synthesized full-size particles (Equation 8), calculate the transport distance of the particle phosphorus before sedimentation using Equation (11).

[0086] Average velocity of sediment particles along the vertical of the water flow At a settling velocity ω, the longitudinal transport distance when sinking from a distance h from the riverbed to the riverbed is:

[0087]

[0088] In the formula L c ω represents the longitudinal transport distance of sediment deposition; ω represents the settling velocity. β is the vertical average velocity of the water flow; β is a parameter representing the following behavior of sediment particles with water flow turbulence.

[0089] Step 5: Obtain the adsorption rate k of sediment under different particle size groups through indoor experiments. p (Equation 12) and sediment adsorption rate k under different suspended sediment concentrations S (Equation 13) The comprehensive adsorption rate k is obtained by polynomial fitting. α (Equation 14). Adsorption rate k α The results can be obtained through indoor adsorption kinetic experiments. The kinetic equations are fitted using an intraparticle diffusion model, first-order kinetics, and second-order kinetics, respectively, and the best fitting parameters are selected based on the coefficient of determination.

[0090] in:

[0091] k p =f(d,P i (12)

[0092] k s =f(S) (13)

[0093] k α =f(k) p ,k s (14)

[0094] Step 6: Analyze the changes in dissolved and adsorbed phosphorus along the flow path using a phosphorus phase transport model, extract data from specific cross-sections, and obtain phosphorus distribution characteristics. The distribution characteristics of dissolved and adsorbed phosphorus are obtained based on the ratio of the two phosphorus forms.

[0095] The expression for the adsorbed phase phosphorus is as follows:

[0096]

[0097]

[0098] In the formula C sThe phosphorus content of the adsorbed phase of sediment is N, which represents the sediment particle size group, and Q is the phosphorus content of the adsorbed phase. si P represents the phosphorus content of the adsorbed phase of the i-th sediment group. i Let be the percentage of sediment mass in the i-th group.

[0099] The governing equation for phosphorus transport employs a phase-separation model, including dissolved phosphorus (C) in the water body. w ), phosphorus adsorbed on suspended sand (C) s The specific expression is as follows:

[0100]

[0101]

[0102] In the formula, A is the control cross-sectional area; C b C s C w These represent the contents of bed sand, suspended sediment, and pollutants in the water body, respectively; S is the average sediment concentration of the cross section; S * D represents the average sand-carrying capacity of the cross section. x α is the longitudinal dispersion coefficient; ω is the recovery saturation coefficient; B is the particle settling velocity; k is the river width; α The adsorption rate, i.e., the rate of change of the amount of sediment adsorbed per unit mass per unit time, is k. α >0 indicates sediment adsorption, and vice versa; U is the average cross-sectional velocity; dC w / dt represents the biochemical reaction term; σ represents the pollutant release rate per unit river length; and r represents the emission source strength.

[0103] The sand-carrying capacity is calculated using Zhang Ruijin's formula, with a particle size distribution correction factor introduced:

[0104]

[0105] S * To carry sand force, kg / m 3 U is the average flow velocity across the cross section, in m / s; g is the acceleration due to gravity, in m / s². 2 h is the average water depth, in meters; ω is the average settling velocity, in meters per second; m is the sediment-carrying capacity index, typically taken as 0.92; k is the sediment-carrying capacity coefficient; P i denoted as the mass percentage of the i-th group of sediment; N is the number of sediment particle size groups.

[0106] The content relationships of adsorbed phosphorus in different sediment components are as follows:

[0107]

[0108] In the formula C s The phosphorus content of the adsorbed phase of sediment is N, which represents the sediment particle size group, and Q is the phosphorus content of the adsorbed phase. si P represents the phosphorus content of the adsorbed phase of the i-th sediment group.i Let be the percentage of sediment mass in the i-th group.

[0109] By introducing appropriate boundary and initial conditions, and importing the topographic and hydrodynamic parameters measured in step 1, the above equations are numerically solved using the finite difference method. Since the suspended sediment concentration and turbulence parameters, as well as the dissolved phase phosphorus content and adsorbed phase phosphorus content, are mutually influential and restrictive, iterative calculations are required at each time step. When the maximum absolute error between two iterations is <10... -5 Only after this time step can the calculation proceed to the next time step. During the calculation process, the concentration of suspended sediment is first obtained through the water flow equation and the suspended sediment movement equation. Substituting this into the phosphorus transport equation, the spatiotemporal distribution of dissolved phosphorus and adsorbed phosphorus can be obtained.

[0110] The following is a specific example to illustrate this:

[0111] Step 1: Select a typical river channel as the study area and divide it into typical monitoring sections as needed. Use an underwater laser in-situ particle size analyzer (LISST-200X) to conduct on-site online monitoring of suspended sediment gradation. Measure topographic data on-site, and simultaneously determine suspended sediment concentration (S), water temperature (T), and flow velocity (U). The topographic data includes river width (B) and water depth (H).

[0112] Step 2: Based on the sediment gradation grouping, considering parameters such as on-site temperature, sediment concentration in each group, and sediment bulk density, select an appropriate calculation formula to calculate the average sediment settling rate of each group. By combining the proportion of sediment in each group, the sediment settling rate of all particle sizes in each group is obtained.

[0113] Step 3: Based on the principle of calculating the trajectory of particulate phosphorus, considering the flow velocity along both the water flow and depth directions, calculate the trajectory of particulate phosphorus in layers and segments (e.g., Figure 3 (As shown). The distance traveled from point 1 to point 2 along the direction of the water flow is L. x The distance traveled along the water depth direction is L. z t represents the time it takes for the phosphorus particle to move from point 1 to point 2.

[0114] When Ps = 50%, the sediment transport distance can be calculated using the following formula:

[0115]

[0116] In the formula L c ω represents the longitudinal distance of sediment deposition; ω represents the particle settling velocity. The vertical average velocity of the water flow is given.

[0117] When Ps = 15.85%, take The transport distance of sediment particles is:

[0118]

[0119] j represents the hydraulic gradient.

[0120] Step 4: Based on the on-site monitoring data, set the boundary conditions for the hydrodynamic model, sediment transport model, and phosphorus transport model according to the upstream water and sediment characteristics and water quality monitoring results, and determine the values ​​of the main parameters in the model.

[0121] Step 5: Introduce the corresponding boundary conditions and initial conditions (Table 1), and use the finite difference method to numerically solve the above equations. Figure 4 The figure shows the calculated trajectories of phosphorus particles transported in the surface water at four cross-sections. The transport distance of sediment particles at these four points can reach 200–350 km. Figure 5 The comparison between the phosphorus concentration in the particulate phase of water calculated by the phase separation model and the measured phosphorus concentration in the particulate phase is shown. The difference between the model calculation result and the actual value is generally less than 20%.

[0122] Table 1 Initial conditions of the model

[0123]

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating phosphorus transport and distribution based on suspended sediment settling probability, characterized by, Comprising the following steps: Step 1: selecting a typical section, measuring topographic data on site, synchronously measuring suspended sediment concentration S, water temperature T, and flow velocity U, wherein the topographic data includes river width B and water depth H, and using an in-situ laser particle size analyzer to monitor the variation of the particle size distribution of the sediment in real time; Step 2: preliminarily judging the flow regime according to the size of the grouped sediment particle size, calculating the sediment particle settling velocity according to the flow regime, and then proving whether the judged flow regime is correct by calculating the Reynolds number, if it does not belong to the judged flow regime, assuming another flow regime to calculate the settling velocity until the correct result is obtained, correcting the settling velocity of the sediment group according to the suspended sediment concentration, and synthesizing the settling velocity of the sediment of different particle size groups; Step 3: calculating the particle phosphorus settling probability according to the particle size distribution of the sediment and the particle phosphorus settling probability density function; Step 4: calculating the transport distance of the particle phosphorus before settling according to the particle phosphorus settling probability and the synthesized settling velocity of the particle of the full particle size; Step 5: Obtain the adsorption rate k of sediment under different particle size groups through indoor experiments. p and sediment adsorption rate k under different suspended sediment concentrations S The overall adsorption rate k was obtained through polynomial fitting. α ; Step 6: analyzing the variation of the dissolved phase phosphorus and the adsorbed phase phosphorus along the river by using the phosphorus phase transport model, extracting the data of a specific section to obtain the distribution characteristics of the phosphorus, and obtaining the distribution characteristics of the dissolved phase phosphorus and the adsorbed phase phosphorus according to the proportion of the two forms of phosphorus; In step 2, the settling velocity of the sediment group is corrected by using formula (7), and the settling velocity of the sediment of different particle size groups is synthesized by using formula (8): ； where, is the settling velocity of the sediment population; P i is the percentage of the i-th size fraction; ω i is the settling velocity of the i-th size fraction; ω S0 is the settling velocity of the sediment particles under the experimental conditions, S f is the concentration of suspended sediment under the experimental conditions, and α is a coefficient related to the Reynolds number; In step 6, the adsorbed phase phosphorus is expressed as: ； where C s is the adsorbed-phase phosphorus content of the sediment, N is the sediment size grouping, Q si is the adsorbed-phase phosphorus content of the ith sediment size grouping, P i is the mass percentage of the ith sediment size grouping; The control equation of phosphorus transport adopts a phase model, including the dissolved phase phosphorus C w content in water and the phosphorus content C s adsorbed by sediment, and the specific expression is as follows: ； where A is the control cross-sectional area; C b , C s , and C w are the bed sediment, adsorbed phase sediment, and water body phosphorus contents, respectively; S is the average sediment concentration of the cross section; S * is the average sediment carrying capacity of the cross section; D x is the longitudinal dispersion coefficient; a is the recovery saturation coefficient; w is the particle settling velocity; B is the river width; k α is the adsorption rate, i.e., the change rate of the adsorbed amount of sediment per unit mass per unit time, k α > 0 indicates sediment adsorption, and vice versa; U is the average flow velocity of the cross section; dC w / dt is the biochemical reaction term; s is the phosphorus release rate per unit river length; and r is the source intensity. The sediment carrying capacity is calculated by using the Zhang Ruijin formula, and the particle size distribution correction coefficient is introduced: ； S * is the sediment carrying capacity, with the unit of kg / m 3 ; U is the average flow velocity in the cross section, with the unit of m / s; g is the acceleration of gravity, with the unit of m / s 2 ; h is the average water depth, with the unit of m; is the average settling velocity, with the unit of m / s; m is the sediment carrying capacity index, taking 0.92; k is the sediment carrying capacity coefficient; P i is the mass percentage of the i-th group of sediment; N is the number of sediment particle size groups; The content of the adsorbed phase phosphorus in different sediment components is related as follows: ； N is the sediment size grouping, Pi is the phosphorus content of the adsorbed phase of the i-th sediment size grouping, i Ni is the mass percentage of the i-th sediment size grouping.

2. The method for calculating phosphorus transport and distribution based on the probability of suspended sediment settling according to claim 1, wherein: Step 3 specifically includes: The model assumes that the sediment particles will settle down with a certain probability when they settle to the bottom, the settling probability varies between 0 and 1, and the movement speed of the sediment particles obeys the Gauss normal distribution, ； The distribution density function is: In the formula, x is the particle speed, u is the mean value, and sigma is the standard deviation. ； where Ps is the probability of phosphorus settling in the particulate form; x is the sediment particle velocity; ω is the particle phosphorus settling velocity, i.e., the settling velocity of the total particle size sediment; σ ν is the vertical turbulent intensity standard deviation.

3. The method for calculating phosphorus transport and distribution based on the settling probability of suspended sediment as described in claim 1, characterized in that: The particle phosphorus and the sediment are interdependent, the Gauss distribution density function is integrated to obtain the particle phosphorus settling probability function: sediment particles in the vertical average flow velocity of the water flow and settling velocity ω, the longitudinal transport distance is: ； where L c is the longitudinal distance of sediment deposition; ω is the settling velocity; is the vertical average flow velocity; β is the parameter of sediment particle and flow turbulence following.

4. The method for calculating phosphorus transport and distribution based on the probability of suspended sediment settling according to claim 1, wherein: Adsorption rate k in step 5 α The indoor adsorption kinetics experiment shows that the kinetic equation is fitted by the intraparticle diffusion model, the first order kinetics and the second order kinetics, and the best fitting parameter is selected by the coefficient of determination. In step (4), the transport distance of the particle phosphorus before settling is calculated by formula (11): Wherein: 。

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