A method for coupling calculation of dissolved oxygen and nitrification reaction in a pipeline pressure and non-pressure mixed water delivery process

Abstract

This invention discloses a coupled calculation method for dissolved oxygen and nitrification reactions in a mixed pressurized and unpressurized water conveyance process in a pipeline. First, the topology and geometry of the water conveyance pipeline, along with hydrodynamic and water quality parameters, are input, and the pipeline is spatially discretized along its length. Then, a one-dimensional transient flow dynamic equation is solved to obtain the hydrodynamic simulation results. Next, at each time step and in each computational unit, the pressurized and unpressurized flow states are determined based on the relationship between pressure head and the top elevation of the pipe. Finally, under the constraints of the hydrodynamic results and the flow state switching, one-dimensional convection-diffusion reaction equations are solved for dissolved oxygen, ammonia nitrogen, nitrite nitrogen, and nitrate nitrogen, respectively, outputting the hydrodynamic forces along the pipeline, flow state segments, and the spatiotemporal distribution of the four water quality indicators. This invention consistently couples the reoxygenation switching mechanism with the two-stage nitrification oxygen consumption process for modeling and numerical solution, overcoming the shortcomings of existing methods that are difficult to adapt to alternating pressurized and unpressurized operating conditions, numerical oscillations caused by sudden changes in the reoxygenation source term, and large prediction deviations due to decoupling of nitrification and dissolved oxygen.

Description

Technical Field

[0001] This invention belongs to the field of coupled calculation of pipeline hydrodynamics and water quality processes in long-distance water transmission projects. It relates to a method for simulating the water quality evolution of long-distance water transmission pipelines under alternating pressurized and unpressurized flow conditions. Specifically, it is a coupled calculation method for dissolved oxygen and nitrification reaction in a pipeline mixed pressurized and unpressurized water transmission process. Background Technology

[0002] Long-distance water pipelines are typically characterized by their length, significant elevation variations along the route, and frequent changes in operating conditions. Under varying operational conditions such as pump station startup and shutdown, valve regulation, and water distribution and return, the pipeline system may experience complex hydraulic states where free surface flow (unpressurized sections) and pressurized flow (pressurized sections) coexist and alternate. These changes in hydraulic state significantly alter the connectivity between the water body and the atmosphere, the gas-liquid interface area, and the hydraulic residence time, thereby affecting the spatiotemporal evolution of water quality within the pipeline. This is particularly evident in alterations to the dissolved oxygen supply and consumption balance, and engineering problems such as the limitation of dissolved oxygen in the nitrification process using ammonia nitrogen as a substrate, leading to water quality risks including odor.

[0003] To address the aforementioned issues, engineering projects require the implementation of combined hydrodynamic and water quality simulations of water pipelines. This simulation aims to obtain the spatiotemporal distribution of hydrodynamic processes such as flow rate, velocity, and pressure, as well as water quality processes such as dissolved oxygen and nitrogen content. This data will provide a basis for identifying unfavorable sections, assessing operational conditions, and ensuring water quality safety. However, current technologies still have significant limitations in simulating the mechanistic mechanisms of water quality under alternating pressurized and depressurized conditions.

[0004] In existing modeling software, some computing platforms possess the capability for open-flow and full-flow correlation in hydraulic calculations, simulating various flow regimes such as backflow, underflow, and reverse flow. However, in water quality calculations, they often employ a simplified framework that treats the pipeline as a continuous stirred reactor with mixing at nodes. The built-in support for biochemical reactions tends to be biased towards coarse estimations of a few parameters such as the diffusion coefficient, making it more suitable for conservative substances or index transport calculations that can be approximated by first-order decay. For biochemical processes where dissolved oxygen and nitrification are significantly coupled and require switching reoxygenation mechanisms between pressurized and depressurized states, the above implementation methods lack directly reusable mechanistic modules and unified switching rules.

[0005] To bridge the gap between software capabilities and on-site requirements, engineering applications often employ manual segmentation and fixed assumptions: pre-defining which pipe sections are pressurized or depressurized, and assigning different biochemical reaction parameters to each. However, this approach struggles to adapt to the shifting pressurized / depressurized boundary over time due to changes in operating conditions. Furthermore, the lack of unified state discrimination criteria and source term calculation methods easily leads to discontinuities or accumulated errors at the boundary, thus affecting the reliability of dissolved oxygen and ammonia nitrogen conversion predictions. The limitations of existing computing platforms can be summarized as follows: 1) Lack of unified expression and automatic switching of reoxygenation mechanism: It is difficult to characterize the difference mechanism of reoxygenation supply under unpressurized free water surface conditions and reoxygenation suppression under pressurized isolation conditions within the same calculation framework, which can easily lead to deviations in dissolved oxygen prediction along the way.

[0006] 2) Insufficient coupling between dissolved oxygen and nitrification: Water quality calculations often focus on convection, diffusion, transport, and simplified attenuation, making it difficult to reflect the limiting effect of dissolved oxygen on the nitrification reaction rate and the oxygen consumption feedback of the nitrification reaction on dissolved oxygen. This makes it difficult to reliably predict the spatiotemporal evolution of ammonia nitrogen conversion.

[0007] 3) Insufficient applicability and weak section identification capability: Under alternating pressurized and depressurized conditions, it is difficult to stably output the results of key water quality processes such as dissolved oxygen and ammonia nitrogen and support the identification of unfavorable sections, which affects its application effect in operation management and risk assessment.

[0008] 4) The parameter system is either too simplified or too complex: Some methods rely on only a few empirical parameters (such as diffusion coefficient) and cannot characterize key biochemical mechanisms; other methods introduce a large number of ecological processes and parameters, which leads to problems such as difficulty in calibration and high engineering deployment costs, making it difficult to meet the needs of rapid field application.

[0009] In response to the actual situation where pressurized and unpressurized flows may coexist and alternate under the changing operating conditions of long-distance water pipelines such as scheduling, operation, pump and valve operation, existing technologies in water quality simulation generally have the ability to handle changes in open and full flow states through hydraulic calculations, but water quality calculations are mostly limited to the level of convection, diffusion and transport and simplified attenuation, lacking the problem of coupling biochemical reaction mechanisms and handling the switching between pressurized and unpressurized states, which makes it difficult to reliably predict dissolved oxygen and nitrification processes.

[0010] In summary, there is an urgent need for a computational method for long-distance water pipelines that operates under both pressurized and depressurized conditions and alternates between them. This method should be able to perform hydrodynamic calculations, identify and switch between open and closed states within a unified framework, and achieve consistent coupling between dissolved oxygen processes and nitrification kinetics, thereby improving the accuracy, stability, and engineering applicability of predictions. Summary of the Invention

[0011] To address the shortcomings of existing technologies in water quality simulation, such as the lack of coupling of biochemical reaction mechanisms and handling of pressurized and unpressurized state switching, which makes it difficult to reliably predict dissolved oxygen and nitrification processes, this invention provides a method for coupled calculation of dissolved oxygen and nitrification reactions in a pipeline process involving mixed pressurized and unpressurized water transportation.

[0012] A coupled calculation method for dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water transport process in a pipeline includes four steps: hydrodynamic calculation, identification and switching of open and full flow regimes, coupled solution of water quality convection-diffusion reaction, and result output. The details are as follows: (1) Data input and discrete modeling Obtain the topological and geometric information of the water pipeline, including at least the length, diameter, node elevation, and top elevation of each pipe segment for determining whether the pipeline is open or full. Simultaneously input hydrodynamic parameters (roughness / friction, local losses, etc.) and water quality parameters (diffusion coefficient, overall oxygen consumption coefficient, etc.). Based on this, divide the pipeline into several computational units and set the time step size. Given the hydrodynamic boundary conditions and initial water quality conditions, establish a one-dimensional discrete computational model for coupled solution.

[0013] (2) Hydrodynamic transient calculation After inputting the pipeline topology and geometric parameters and discretizing them along the pipeline, a one-dimensional transient flow dynamic equation set with cross-sectional flow rate and pressure head as the main variables is used to solve the pipeline over time. This yields hydrodynamic simulation results such as flow rate, pressure head, and velocity along the pipeline at each time step. The one-dimensional transient flow dynamic equation set can be expressed as a continuity equation and a momentum equation: (1) (2) In the formula, x is the axial coordinate of the pipeline; t is time; H is the pressure head (or total head); Q is the cross-sectional flow rate; A is the cross-sectional area of ​​the pipeline; D is the pipe diameter; c is the water flow wave velocity; g is the acceleration due to gravity; f is the Darcy friction coefficient; ∑K L This is the sum of the local loss coefficients for valves, elbows, tees, etc. The above equation is used to output the value at any given time. Q ( x,t ), H ( x, t And further obtain the cross-sectional average flow velocity. u ( x,t )= Q / A。

[0014] To facilitate numerical solutions, equations (1)-(2) are written as the following vector form of a system of conservation equations: (3) in: (4) 1) Finite volume spatial discretization Divide the pipeline along its length into N control volume elements according to a spatial step Δx, with the center of the i-th element being x. i The left and right interfaces are x i-1 / 2 x i+1 / 2 Define the unit average: (5) Integrating equation (3) over the control volume and approximating the interface flux using numerical flux, we obtain the first-order finite volume update scheme: (6) In the formula, and For numerical flux, Discretize the source terms of the unit.

[0015] 2) Interface numerical flux To ensure stability and robustness under hydrodynamic wave propagation conditions, this invention can employ a local Rusanov-type numerical flux: (7) in, To determine the maximum characteristic wave velocity at the interface, we can take: (8) 3) Source terms (friction and local loss) discretization In equation (4), the source term only acts on the momentum equation, and the source term for the i-th element is discretized as follows: (9) When friction terms lead to increased rigidity in time progression, the source terms can be handled semi-implicitly.

[0016] 4) Time step selection and boundary handling Time progression can be achieved using explicit Euler or second-order Runge-Kutta methods. To ensure stability, the time step Δt is selected based on the CFL condition. (10) Boundary conditions can be achieved using a constant flow rate method: a flow rate is given upstream or downstream, and boundary constraints are applied by setting virtual units, thereby completing the numerical solution of the hydrodynamic transients of the entire pipeline and outputting the spatiotemporal distribution results of flow rate, pressure head, and velocity along the pipeline.

[0017] (3) Mingman flow state identification and switching weight construction After obtaining the transient calculation results of hydrodynamics along the route, in order to realize the automatic switching of the reoxygenation process under the coexistence of pressurized and depressurized conditions, this invention distinguishes the flow state at each time step and each calculation unit, and constructs a switching weight for controlling the reoxygenation term.

[0018] 1) Flow pattern discrimination The top elevation inside the pipe is used as the criterion for determining whether the pipe is fully open. For the i-th calculation unit, at time t... nThe pressure head of the unit is compared with the elevation of the top of the pipe: when the pressure head is not lower than the elevation of the top of the pipe, it is determined to be a full-pipe pressurized flow; when the pressure head is lower than the elevation of the top of the pipe, it is determined to be an unpressurized open flow. This criterion is used to determine whether the unit has the conditions for reoxygenation connected to the atmosphere and to provide a basis for subsequent reoxygenation calculations.

[0019] For ease of expression, the above judgment can be written as: (11) 2) Switch weight construction To avoid abrupt changes in source terms when the boundary between light and full shifts over time, this invention constructs a switching weight w∈[0,1] to achieve a smooth transition of the reoxygenation term: where w=1 indicates pressure (reoxygenation off), w=0 indicates no pressure (reoxygenation on), and the light-full transition region takes the value 0. <w<1。

[0020] This invention uses a simple and engineering-feature-featured weight construction method for piecewise linear transition. The transition bandwidth Δh is set to > 0, and then... (12) The above structure allows the weights to change continuously within a finite bandwidth when the pressure head approaches the top elevation of the pipe, thereby avoiding abrupt changes in the reoxygenation source term at the boundary between the bright and full.

[0021] 3) Application of weights in the reoxygenation term The switching weights are used to control the start, stop, and transition of the reoxygenation coefficient. Specifically, under depressurized, ventilable conditions, reoxygenation is supplied according to the preset reoxygenation coefficient; under pressurized, full-pipe, closed conditions, reoxygenation is shut off or reaches a minimum value. A smooth transition is achieved in the transition zone through weights. Preferably, the reoxygenation coefficient can be written in an equivalent form of weighted control: (13) This ensures that reoxygenation plays a full role in the pressureless section, automatically shuts off in the pressurized section, and achieves continuous transition in the Mingman conversion zone.

[0022] (4) Solution of water quality convection-diffusion-reaction coupling and construction of source term consistency After obtaining the flow rate, pressure head, and velocity along the flow path through hydrodynamic transient calculations, and completing the identification of the full flow regime and the construction of switching weights, this invention performs convection-diffusion-reaction coupling solutions for four indicators—dissolved oxygen, ammonia nitrogen, nitrite nitrogen, and nitrate nitrogen—in each time step and each calculation unit to obtain their spatiotemporal distribution along the flow path.

[0023] For any water quality index concentration C(x,t), establish a one-dimensional convection-diffusion reaction equation: (14) In the formula, E is the longitudinal dispersion (equivalent diffusion) coefficient; R jThe source and sink terms (reaction terms) of this indicator can be calibrated using first-order decay, compound kinetics, or other methods according to engineering requirements.

[0024] Ammonia nitrogen: (15) Nitrate nitrogen: (16) Nitrite nitrogen: (17) Dissolved oxygen: (18) In the formula, Nitrification consumes oxygen; This is the total oxygen consumption item; For the reoxygenation term, among which, Given by the Mingman state recognition module, the value is 1 for the unpressed segment and 0 for the pressurized segment. The transition segment uses weighted smoothing.

[0025] Dissolved oxygen in natural water bodies is typically influenced by multiple processes, including oxygen production through photosynthesis, oxygen consumption from respiration and organic matter degradation, oxygen consumption from nitrification, and reoxygenation. Considering that the long-distance water pipelines addressed in this invention are opaque sections without effective lighting, the oxygen production term for photosynthesis is not considered in the model. For other oxygen-consuming processes besides nitrification (including respiration from pipe wall biofilms and oxygen consumption on the pipe wall), to reduce parameter dimensionality and ensure engineering feasibility, this invention combines them into a comprehensive oxygen consumption term, using a first-order oxygen consumption coefficient. k bg Characterization. The oxygen consumption caused by nitrification is consistently coupled with the speciation of ammonia nitrogen and nitrite nitrogen. The reoxygenation phase is only activated under unpressurized free water surface or aeration conditions. Under pressurized full-pipe closed conditions, the reoxygenation coefficient is 0 or a minimum value, and automatic switching is achieved through the open / full state identification and switching module, thereby ensuring the continuity and traceability of water quality source items in the open / full transition section.

[0026] The rates of the first and second nitration reactions are as follows: (19) (20) In the formula, k1 and k2 are reaction rate coefficients; The dissolved oxygen limiting function is as follows: (twenty one) To facilitate numerical solutions, the one-dimensional convection-diffusion reaction equation described in equation (14) is written in a conservation form: (twenty two) The total interface flux G consists of convective flux and diffusion flux: (twenty three) In the formula, C(x,t) represents the concentration of any water quality index (corresponding to dissolved oxygen, ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen, respectively); u is the average cross-sectional velocity obtained from hydrodynamic calculations; E is the diffusion coefficient; R j The source and sink terms of this indicator are constructed according to equations (15)-(18) and in combination with equations (19)-(21).

[0027] 1) Finite volume spatial discretization Divide the pipeline along its length into N control volume elements according to a spatial step Δx, with the center of the i-th element being x. i The left and right interfaces are x i-1 / 2 x i+1 / 2 Define the unit average: (twenty four) Integrating equation (22) over the control volume and approximating the interface flux using numerical flux, we obtain the first-order finite volume update scheme: (25) In the formula, and For numerical flux; The discrete values ​​of the unit source terms are given. Equation (25) can be used to advance the four equations for dissolved oxygen, ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen using the same discrete framework.

[0028] 2) Interface numerical flux To maintain consistency with the flux construction method in hydrodynamic solutions, this invention expresses interface numerical fluxes in the form of convective fluxes and diffusion fluxes: (26) The flux can be obtained by solving using the Rusanov type: (27) in, The interface velocity can be obtained by interpolating the hydrodynamic results at the interface. The maximum convective characteristic velocity at the interface can be taken as: (28) The diffusion flux can be obtained using the central difference scheme: (29) In the formula, The diffusion coefficient is the interface diffusion coefficient, which can be taken as the arithmetic mean of the diffusion coefficients of adjacent units.

[0029] 3) Source term discrete (reaction term synchronously coupled) The source term in equation (25) Constructed according to equations (15)–(18), wherein the two-stage nitration reaction rate is determined according to equations (19)–(21) at unit i and time t. n The calculated values ​​are used for the synchronous coupling update of source and sink terms of the four indices within the same time step. Furthermore, to avoid negative concentrations in the reaction step, an upper limit constraint can be imposed on the two-stage reaction rate, thereby ensuring the physical feasibility and numerical stability of the source term update process.

[0030] (30) 4) Time step selection and boundary handling The water quality equation can use the same time step Δt as the hydrodynamic equation. When it is necessary to satisfy the stability of the explicit advancement of the water quality equation alone, Δt can simultaneously consider convection and diffusion constraints, taking the following value: (31) Boundary conditions can be achieved using constant concentration or zero gradient methods, and C is assigned values ​​by setting virtual cells to apply boundary constraints and complete the time-progressed solution of the water quality equation for the entire pipeline.

[0031] Time step stability constraints and numerical solution strategies: Both the hydrodynamic equations and the water quality equations are solved using numerical discretization and time-stepping. The time step is adaptively determined based on the spatial discretization step size and in combination with the current flow velocity level, hydraulic wave propagation characteristics, and diffusion intensity to satisfy stability constraints, thus ensuring the numerical stability and engineering feasibility of the coupled solution process.

[0032] In terms of numerical solution strategy, the present invention preferably adopts a consistent coupled update of transport and reaction: firstly, the convective and diffuse transport updates of dissolved oxygen, ammonia nitrogen, nitrite nitrogen, and nitrate nitrogen are completed in the current time step; then, in the same time step and the same computing unit, the two-stage nitrification process is calculated based on the updated concentration state, and the reaction source and sink terms of each index are constructed synchronously to achieve a unified reaction update of each water quality.

[0033] To ensure consistent coupling between dissolved oxygen consumption and nitrogen-containing form conversion, this invention uses the same set of two-stage nitration calculation results during the reaction update stage, simultaneously driving: the conversion of ammonia nitrogen to nitrite nitrogen, the conversion of nitrite nitrogen to nitrate nitrogen, and the nitration oxygen consumption term in the dissolved oxygen equation; wherein the nitration oxygen consumption is contributed by the two-stage nitration and converted by the corresponding oxygen consumption equivalent coefficient, so that the form conversion and oxygen consumption feedback occur synchronously in the same time step, avoiding decoupling errors caused by mismatch between form conversion and oxygen consumption processes.

[0034] To avoid non-physical negative values ​​caused by reaction updates, this invention applies a substrate-limited upper limit control to the reaction amount in the two-stage nitration at each time step, ensuring that the reaction amount does not exceed the ammonia nitrogen or nitrite nitrogen that can be consumed in that time step, thereby guaranteeing the physical feasibility of the calculation results and improving numerical stability.

[0035] Near the boundary between open and full flow, to suppress numerical oscillations caused by abrupt changes in the reoxygenation term, this invention employs the aforementioned switching weights to smoothly transition the reoxygenation supply: reoxygenation is activated under unpressurized, aerated conditions and shut off under pressurized, full-pipe, closed conditions. Smooth switching is achieved in the transition zone by continuously changing the weights, thereby improving computational robustness under alternating open and full flow conditions. If necessary, the water quality equations can be substepped within the hydrodynamic time step to meet stricter transport stability constraints while maintaining consistency with the hydrodynamic results.

[0036] Output results: After completing the hydrodynamic-water quality coupling calculation, the output shows the hydrodynamic characteristics such as flow rate, velocity, pressure and head along the pipeline at different times, as well as the spatiotemporal distribution results of water quality indicators such as dissolved oxygen, ammonia nitrogen, nitrite nitrogen and nitrate nitrogen. These results are used to support the operation and management of water transmission pipelines, water quality safety assessment and control decisions.

[0037] Beneficial effects: (1) Under the condition of alternating pressurized and unpressurized operation of long-distance water transmission pipelines, establish a water quality numerical simulation method that can identify the hydraulic state of pressurized and unpressurized pipelines and switch the dissolved oxygen supply mechanism accordingly, and couple it with the nitrification reaction kinetics. This method can be used to predict the water quality evolution along the pipeline, so as to improve the accuracy, stability and engineering applicability of the prediction of dissolved oxygen and nitrification processes.

[0038] (2) This invention is applicable to long-distance water transmission pipelines operating under both pressurized and unpressurized conditions. The coupled calculation method of dissolved oxygen and nitrification reaction enables the hydrodynamic transient process and the water quality biochemical process to be solved collaboratively within a unified framework, thereby accurately depicting the spatiotemporal evolution of dissolved oxygen replenishment and consumption, ammonia nitrogen two-stage nitrification conversion, and oxygen consumption feedback along the pipeline. Furthermore, it achieves automatic identification of pressurized and unpressurized flow states and establishes a start-up and continuous switching mechanism for the reoxygenation process under the condition of pressurized-full transition, avoiding the insufficient applicability caused by manual segmentation settings and numerical oscillations caused by sudden changes in source terms at the boundary, thus improving the stability and consistency of the model under complex scheduling conditions. Therefore, while ensuring the feasibility of the project, it outputs the distribution results of hydrodynamics, flow state segments, and dissolved oxygen and nitrogen content along the pipeline, and identifies unfavorable sections with low dissolved oxygen or excessive nitrogen content, providing reliable computational support for water transmission pipeline operation management, water quality safety assessment, and control decisions. Attached Figure Description

[0039] Figure 1This is a schematic diagram of the long-distance water pipeline described in this invention.

[0040] Figure 2 This is a schematic diagram of the hydrodynamic simulation results described in this invention.

[0041] Figure 3 This is a schematic diagram of the dissolved oxygen distribution along the line as described in this invention.

[0042] Figure 4 This is a schematic diagram of the ammonia nitrogen distribution along the line as described in this invention.

[0043] Figure 5 This is a schematic diagram of the distribution of nitrate nitrogen along the line as described in this invention.

[0044] Figure 6 This is a schematic diagram of the distribution of nitrite nitrogen along the line as described in this invention.

[0045] Figure 7 This is a flowchart of the present invention. Detailed Implementation

[0046] The principles and technical advantages of the present invention will be further explained below with reference to specific implementation examples and corresponding drawings. It should be noted that these examples are only used to illustrate the function of the present invention and are not intended to limit the scope of application of the present invention. After reading the relevant principles and functions of the present invention, any modifications to the present invention in various equivalent forms should be within the scope limited by the claims appended to this application.

[0047] Figure 7 As shown, this invention discloses a method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water conveyance process in a pipeline. The method first inputs the topology and geometry of the water conveyance pipeline, as well as hydrodynamic and water quality parameters, and spatially discretizes the pipeline along its length. Then, it solves the one-dimensional transient flow dynamic equation to obtain hydrodynamic simulation results such as flow rate, pressure head, and velocity along the pipeline. Further, at each time step and in each calculation unit, it determines the pressurized and unpressurized flow states based on the relationship between pressure head and the top elevation of the pipe, and generates switching weights to control the start-up and smooth transition of the reoxygenation process. Finally, under the constraints of the hydrodynamic results and flow state switching, it solves the one-dimensional convection-diffusion reaction equations for dissolved oxygen, ammonia nitrogen, nitrite nitrogen, and nitrate nitrogen respectively. The reaction terms simultaneously consider the coupled effects of the two-stage nitrification reaction and its oxygen consumption, the overall background oxygen consumption, and the reoxygenation supply, and output the spatiotemporal distribution of the hydrodynamic forces along the pipeline, the flow state segments, and the four water quality indicators.

[0048] Case Study: Hydrodynamic and Water Quality Coupling Simulation and Unfavorable Section Identification for a Long-Distance Water Transmission Pipeline As shown in Figure 1, the elevation of this long-distance water pipeline varies significantly with the distance from the starting point. The elevation rises rapidly at the starting point and enters a high-level range. A significant downward cut occurs at approximately 40 km, followed by a rebound. A deeper low-lying section appears at approximately 60 km, followed by a rapid rebound. After 60 km, the overall elevation shows a slow downward trend. Based on these elevation conditions, this embodiment uses a pipeline design flow rate of 110 m³ / h. 3 Hydrodynamic calculations were performed under the condition of / h to obtain the pressure distribution along the friction and its response to elevation control conditions.

[0049] The hydrodynamic calculation results are shown in Figure 2. The pressure along the friction path exhibits segmented characteristics: local high pressure, long-distance low pressure, local high pressure, low pressure, peak high pressure, and low pressure. Combined with... Figure 2 The changes in medium pressure levels indicate that: there is a distinct pressurized section near the starting point, followed by a relatively long depressurized section; a second pressurized section appears around 40 km, which is connected to... Figure 1 The low-lying area formed by the mid-elevation downcut corresponds to the area where the pipe is more likely to be pressurized; the pressure then drops back to an unpressurized state; a third pressurized section appears around 60 km and is characterized by a peak-like high pressure. This section corresponds to... Figure 1 The consistent height of the mid-to-deep depressions indicates that this lowest point section is a sensitive location for pressure formation and pressure rise; subsequently, the pressure recovers to low pressure and remains in a pressureless state over a relatively long downstream range. Based on the identification results of the above three pressurized and three unpressurized sections, this invention further constructs a reoxygenation switching weight according to the open-full flow pattern: reoxygenation supply is enabled in the unpressurized section, and reoxygenation supply is disabled or minimized in the pressurized section. A continuous transition is adopted near the open-full boundary to avoid numerical oscillations caused by abrupt changes in the source term, thereby providing flow pattern constraints for the subsequent coupled solution of the water quality equations.

[0050] In the water quality calculations, the inlet concentration boundary conditions for the four indicators were set as follows: dissolved oxygen 7.5 mg / L, ammonia nitrogen 0.15 mg / L, nitrate nitrogen 1.1 mg / L, and nitrite nitrogen 0.005 mg / L. Subsequently, driven by the flow velocity obtained from hydrodynamic calculations, one-dimensional convection-diffusion reaction equations were solved for dissolved oxygen, ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen, respectively. The convection term was determined by the flow velocity along the flow path, the diffusion term was characterized by longitudinal dispersion, and the reaction term included a two-stage nitrification process and its corresponding oxygen consumption feedback. The automatic start-up and smooth switching of reoxygenation supply under pressurized and depressurized conditions were realized according to the aforementioned open-closed switching weights to ensure consistent coupling between the form transformation and oxygen consumption processes within the same time step.

[0051] The calculated results of water quality distribution along the route are shown in Figures 3 to 6. Figure 3 shows that dissolved oxygen generally decreases along the route, gradually decreasing from 7.5 mg / L at the inlet to 7.217 mg / L at the outlet. A characteristic point of curve slope change / local drop can be seen around 60 km. This location corresponds to the pressurized peak section in the third segment of Figure 2, reflecting that under pressurized conditions, reoxygenation is limited and nitrification oxygen consumption is superimposed, thus making the decrease in dissolved oxygen more significant.

[0052] Figure 4 shows that ammonia nitrogen gradually decreases along the process, from 0.15 mg / L at the inlet to 0.119 mg / L at the outlet; Figure 5 shows that nitrate nitrogen increases slowly along the process, from 1.1 mg / L at the inlet to 1.114 mg / L at the outlet; Figure 6 shows that nitrite nitrogen gradually increases along the process, from 0.005 mg / L at the inlet to 0.012 mg / L at the outlet.

[0053] The aforementioned pattern of decreasing ammonia nitrogen, increasing nitrite nitrogen and nitrate nitrogen, and the accompanying dissolved oxygen consumption is consistent with the two-stage nitrification reaction pathway. Furthermore, the change points that appear around 40 km and 60 km in Figures 3 to 6 correspond to the pressurized section locations in Figure 2, indicating that the present invention can stably capture the water quality response of sensitive sections along the route under alternating bright and full conditions through hydrodynamic water quality coupling and reoxygenation switching mechanisms.

[0054] Furthermore, based on the water quality classification requirements for indicators such as dissolved oxygen and ammonia nitrogen in the "Surface Water Environmental Quality Standard" (GB 3838-2002), the water quality at the inlet section in this embodiment can be classified as Class I water, while the water quality at the outlet section can be classified as Class II water due to changes such as decreased dissolved oxygen. Therefore, the section adjacent to the outlet and the pressure-sensitive section shown in Figure 2 can be designated as key areas of concern. Combined with the distribution results along the pipeline shown in Figures 3 to 6, the location range and persistence characteristics of unfavorable sections can be output, providing a basis for water pipeline operation management, water quality safety assessment, and control decisions.

[0055] In the water quality model of the Mingman flow water pipeline of this invention, the source and sink processes of dissolved oxygen are simplified as necessary according to the actual pipeline engineering. Since long-distance water pipelines are mostly closed and opaque structures, and there is no effective light condition inside the pipe, the oxygen production term of algal photosynthesis is not considered. At the same time, other oxygen-consuming processes besides nitrification (such as biofilm respiration, pipe wall oxygen consumption, and slow degradation of organic matter) are difficult to obtain parameters for individually in engineering. To ensure the feasibility of the model and the calibrability of the parameters, they are merged into a unified comprehensive background oxygen consumption term, which is represented by a special subtraction term in the DO equation. Nitrification oxygen consumption is consistent with the two-step conversion process of ammonia nitrogen to nitrite nitrogen and nitrate nitrogen. The reoxygenation replenishment term is only activated under unpressurized free water surface or aeration conditions. Under pressurized full-pipe closed conditions, the reoxygenation coefficient is zero or takes a minimum value, and automatic switching is achieved through the pressurized and unpressurized state identification and switching module, thereby ensuring the physical consistency and numerical continuity of the DO process term under the Mingman conversion condition.

Claims

1. A method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water transport process in a pipeline, characterized in that, Includes the following steps: (1) Data input and discrete modeling Obtain the topological and geometric information of the water pipeline, including at least the length of each pipe segment, pipe diameter, node elevation, and the top elevation of the pipe along the pipeline for the geometric benchmark of open-ended filling; at the same time, input the hydrodynamic parameters and water quality parameters, and on this basis, divide the pipeline along the pipeline into several calculation units and set the time step size, give the hydrodynamic boundary conditions and the initial water quality conditions, and establish a one-dimensional discrete calculation model for coupled solution; (2) Hydrodynamic transient calculation After inputting the pipeline topology and geometric parameters and discretizing them along the pipeline, a one-dimensional transient flow dynamic equation set with cross-sectional flow rate and pressure head as the main variables is used to solve the pipeline in time progression, so as to obtain the flow rate, pressure head and velocity hydrodynamic simulation results along the pipeline at each time step. (3) Mingman flow state identification and switching weight construction After obtaining the transient calculation results of hydrodynamics along the route, in order to realize the automatic switching of the reoxygenation process under the coexistence of pressurized and depressurized conditions, the flow regime is judged at each time step and each calculation unit, and the switching weights for controlling the reoxygenation term are constructed. (4) Solution of water quality convection-diffusion-reaction coupling and construction of source term consistency After obtaining the flow rate, pressure head, and velocity along the flow path through hydrodynamic transient calculations, and completing the identification of the open flow regime and the construction of switching weights, the four indicators of dissolved oxygen, ammonia nitrogen, nitrite nitrogen, and nitrate nitrogen are coupled and solved for convection-diffusion-reaction at each time step and in each computational unit to obtain their spatiotemporal distribution along the flow path.

2. The method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water conveyance process in a pipeline as described in claim 1, characterized in that, In step (2), the one-dimensional transient hydrodynamic equations are expressed as a continuity equation and a momentum equation: （1） （2） In the formula, x is the axial coordinate of the pipeline; t is time; H is the pressure head (or total head); Q is the cross-sectional flow rate; A is the cross-sectional area of ​​the pipeline; D is the pipe diameter; c is the water flow wave velocity; g is the acceleration due to gravity; f is the Darcy friction coefficient; ∑K L This is the sum of the local loss coefficients for valves, elbows, tees, etc.

3. The method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water transportation process in a pipeline as described in claim 2, characterized in that, To facilitate numerical solutions, equations (1)-(2) are written as the following vector form of a system of conservation equations: （3） in: （4） 1) Finite volume spatial discretization Divide the pipeline along its length into N control volume elements with a spatial step size Δx, where the center of the i-th element is x. i The left and right interfaces are x i-1 / 2 x i+1 / 2 Define the unit average: （5） Integrating equation (3) over the control volume and approximating the interface flux using numerical flux, we obtain the first-order finite volume update scheme: （6） In the formula, and For numerical flux, Discretize the source terms of the unit; 2) Interface numerical flux To ensure stability and robustness under hydraulic wave propagation conditions, a local Rusanov-type numerical flux is employed: (7) in, To determine the maximum characteristic wave velocity at the interface, we can take: （8） 3) Source term discretization In equation (4), the source term only acts on the momentum equation, and the source term for the i-th element is discretized as follows: （9） When friction terms lead to increased time-progression rigidity, the source terms are treated semi-implicitly. 4) Time step selection and boundary handling The time step Δt is selected based on the CFL condition: （10） Boundary conditions can be achieved using a constant flow rate method: a flow rate is given upstream or downstream, and boundary constraints are applied by setting virtual units, thereby completing the numerical solution of the hydrodynamic transients of the entire pipeline and outputting the spatiotemporal distribution results of flow rate, pressure head, and velocity along the pipeline.

4. The method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water transportation process in a pipeline as described in claim 1, characterized in that, In step (3), 1) Flow pattern discrimination Using the top elevation inside the pipe as the criterion for determining fullness, for the i-th calculation unit, at time t n Compare the pressure head of this unit with the elevation of the top of the pipe: when the pressure head is not lower than the elevation of the top of the pipe, it is determined to be a full-pipe pressurized flow; when the pressure head is lower than the elevation of the top of the pipe, it is determined to be an unpressurized open flow. This criterion is used to determine whether the unit has the conditions for reoxygenation connected to the atmosphere. For ease of description, the above criterion is written as: Pressure: No pressure: (11) 2) Switch weight construction To avoid abrupt changes in source terms when the boundary between light and full shifts over time, a switching weight w∈[0,1] is constructed to achieve a smooth transition of the reoxygenation term: where w=1 indicates pressure (reoxygenation off), w=0 indicates no pressure (reoxygenation on), and w=0 is used in the light-full transition region. <w<1, Set the conversion bandwidth Δh > 0, and let （12） The above structure allows the weight to change continuously within a finite bandwidth when the pressure head approaches the top elevation of the pipe. 3) Application of weights in the reoxygenation term The switching weights are used to control the start, stop, and transition of the reoxygenation coefficient. Specifically, under depressurized, ventilable conditions, reoxygenation is supplied according to the preset reoxygenation coefficient; under pressurized, full-pipe, closed conditions, reoxygenation is shut off or takes a minimum value. In the transition zone, a smooth transition is achieved through weights. The reoxygenation coefficient can be written in the equivalent form of weighted control: （13） This ensures that reoxygenation plays a full role in the pressureless section, automatically shuts off in the pressurized section, and achieves continuous transition in the Mingman conversion zone.

5. The method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water transportation process in a pipeline as described in claim 1, characterized in that, In step (4), For any water quality index concentration C(x,t), establish a one-dimensional convection-diffusion reaction equation: （14） In the formula, E is the longitudinal dispersion (equivalent diffusion) coefficient; R j For the source and sink terms of this indicator, a first-order decay and composite dynamics calibration method is adopted according to engineering requirements. Ammonia nitrogen: （15） Nitrate nitrogen: （16） Nitrite nitrogen: （17） Dissolved oxygen: （18） The rates of the first and second nitration reactions are as follows: （19） （20） In the formula, k1 and k2 are reaction rate coefficients; The dissolved oxygen limiting function is as follows: （21） To facilitate numerical solutions, the one-dimensional convection-diffusion reaction equation described in equation (14) is written in a conservation form: （22） The total interface flux G consists of convective flux and diffusion flux: （23） In the formula, C(x,t) represents the concentration of any water quality index (corresponding to dissolved oxygen, ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen, respectively); u is the average cross-sectional velocity obtained from hydrodynamic calculations; E is the diffusion coefficient; R j The source and sink terms of this indicator are constructed according to equations (15)-(18) and in combination with equations (19)-(21).

6. The method for coupled calculation of dissolved oxygen and nitrification reaction in a mixed pressurized and unpressurized water transportation process in a pipeline as described in claim 5, characterized in that, 1) Finite volume spatial discretization Divide the pipeline along its length into N control volume elements with a spatial step size Δx, where the center of the i-th element is x. i The left and right interfaces are x i-1 / 2 x i+1 / 2 Define the unit average: （24） Integrating equation (22) over the control volume and approximating the interface flux using numerical flux, we obtain the first-order finite volume update scheme: （25） In the formula, and For numerical flux; As the discrete value of the unit source term, equation (25) can be used to advance the four equations of dissolved oxygen, ammonia nitrogen, nitrate nitrogen and nitrite nitrogen respectively using the same discrete framework; 2) Interface numerical flux To maintain consistency with the flux construction method in hydrodynamic solutions, the numerical fluxes at the interface are expressed in the form of convective fluxes and diffusion fluxes: （26） The flux can be obtained by solving using the Rusanov type: （27） in, The interface velocity can be obtained by interpolating the hydrodynamic results at the interface. The maximum convective characteristic velocity at the interface can be taken as: （28） The diffusion flux can be obtained using the central difference scheme: （29） In the formula, The interfacial diffusion coefficient can be taken as the arithmetic mean of the diffusion coefficients of adjacent units. 3) Source term discretization The source term in equation (25) Constructed according to equations (15)–(18), wherein the two-stage nitration reaction rate is determined according to equations (19)–(21) at unit i and time t. n The calculated values ​​were used for the synchronous coupling update of the source and sink terms of the four indices within the same time step. Furthermore, to avoid negative concentrations in the reaction step, an upper limit constraint was imposed on the two-stage reaction rate, thereby ensuring the physical feasibility and numerical stability of the source term update process. （30） 4) Time step selection and boundary handling The water quality equation can use the same time step Δt as the hydrodynamic equation. When it is necessary to satisfy the stability of the explicit advancement of the water quality equation alone, Δt can simultaneously consider convection and diffusion constraints, taking the following value: （31） Boundary conditions can be achieved using constant concentration or zero gradient methods, and C is assigned values ​​by setting virtual cells to apply boundary constraints and complete the time-progressed solution of the water quality equation for the entire pipeline.

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