Biological mathematical modeling and application of aerobic granular sludge process

Abstract

This invention belongs to the field of water treatment technology, specifically relating to a biomathematical modeling and application of an aerobic granular sludge process. It includes the following steps: S1, collecting parameter data required for constructing the biomathematical model of the aerobic granular sludge process; S2, establishing a biomathematical model of the aerobic granular sludge based on the parameter data, including a sludge microbial metabolism module and a sludge migration module; S3, establishing a batch-cycle aerobic granular sludge reactor model for the influent, aeration, sedimentation, and sludge discharge stages of the aerobic granular sludge process, combining the above modules; S4, using the constructed aerobic granular sludge reactor model to simulate and optimize the aerobic granular sludge process, with optimization data including influent flow rate, aeration intensity and time, sludge discharge start-up time and duration. The method provided by this invention, through the construction of a dedicated biomathematical model and through parameter optimization and real-time control, achieves improved process efficiency, reduced energy consumption, and enhanced granular sludge stability.

Description

Technical Field

[0001] This invention relates to a biomathematical modeling and application of aerobic granular sludge process, belonging to the field of water treatment technology. Background Technology

[0002] With the continuous growth of urban populations, urban wastewater treatment plants need to increase treatment capacity and reduce energy consumption within limited space. Therefore, aerobic granular sludge (AGS) technology is becoming increasingly popular. Compared to using activated sludge to treat wastewater, using AGS can potentially reduce the volume of the bioreactor by 30% and save up to 63% of energy. To date, more than one hundred wastewater treatment plants worldwide have adopted AGS technology. However, the design and operation of AGS currently rely heavily on the experience of relevant personnel, i.e., based on practical experience. This experience-based design is often non-standard and limited. Biomodeling can effectively predict and simulate the operating conditions and effluent quality of AGS. Researchers can use the model to guide future research and better understand the underlying mechanisms. Engineers can also use the model for the planning, design, optimization, and evaluation of existing or new wastewater treatment plants.

[0003] Due to its unique sludge morphology, hydraulic conditions, and operating mode, the aerobic granular sludge process differs fundamentally from the traditional activated sludge process in biological process modeling, making conventional activated sludge models (ASMs series models) unsuitable for direct application. Its core modeling challenges and special requirements are mainly reflected in the following three aspects:

[0004] (1) Differences in sludge morphology and reaction mechanisms: In aerobic granular sludge processes, both immature flocculent sludge (<200μm) and mature granular sludge (>200μm) coexist. The core issue is that the dense structure of granular sludge leads to significant diffusion restrictions on dissolved oxygen and substrate within it, resulting in a stable stratified structure with an aerobic exterior, an anoxic interior, and an anaerobic interior, where differentiated biochemical reactions occur in each layer. In contrast, traditional ASMs series models, based on the assumption of "complete mixing," treat activated sludge as uniform flocculents, completely ignoring the spatial stratification concentration differences and reaction mechanisms caused by diffusion.

[0005] (2) Differences in reactor flow regime and particle migration process: Aerobic granular sludge processes often adopt a bottom influent mode. This influent method provides upward hydraulic shear force, a substrate gradient environment, and settling selective pressure, promoting sludge granulation and maintaining particle stability. This is completely different from the "front-end influent, complete mixing" flow regime of traditional processes such as AAO (anaerobic-anoxic-aerobic three-stage process) and oxidation ditches. Therefore, aerobic granular sludge models must consider material transport and sludge distribution in the vertical direction of the reactor, rather than a single uniform reaction tank. In addition, considering that flocs with a particle size of less than 200 micrometers and particles with a particle size of more than 200 micrometers have different hydraulic characteristics in their migration processes, they should be considered separately in granular sludge process models.

[0006] (3) Differences in operating mode and process dynamics: The mainstream aerobic granular sludge process adopts a sequencing batch reactor (SBR), whose periodic operation of "influent-effluent-aeration-sedimentation-sludge discharge" leads to significant and intermittent changes in substrate concentration, dissolved oxygen, and sludge concentration over time. Traditional wastewater treatment process models are mainly developed for continuous flow (steady-state or dynamic) processes, and their solution logic and periodic boundary conditions cannot directly describe the intermittent and highly transient characteristics of the sequencing batch aerobic granular sludge process.

[0007] In summary, effective simulation of aerobic granular sludge processes relies on a comprehensive mathematical model that can simultaneously characterize three key features: stratified reactions within the granules, vertical mass transfer in the reactor, and sequencing batch reactor (SBR) cyclic operation. However, current research largely focuses on local descriptions of single mechanisms and lacks a complete biological modeling system that covers the entire process, the entire cycle, and multiple particle sizes.

[0008] Therefore, developing a method specifically for simulating aerobic granular sludge processes is imperative. A scientific mathematical model can accurately and dynamically simulate the distribution changes of particles of different sizes within the reactor, substrate consumption, and effluent quality. This allows for the quantitative identification of the impact of key operational variables such as influent flow rate, aeration intensity and time, and sludge discharge on system performance and particle stability, thus optimizing operating parameters. The establishment of this method will provide indispensable quantitative basis and decision support for the rapid start-up, shock-resistant control, and optimized design of aerobic granular sludge processes, possessing significant engineering application value. Summary of the Invention

[0009] (a) Technical problems to be solved

[0010] To address the aforementioned problems in the prior art, this invention provides a biomathematical modeling and application of aerobic granular sludge process.

[0011] (II) Technical Solution

[0012] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0013] A biomathematical modeling and application of an aerobic granular sludge process, comprising the following steps:

[0014] S1. Collect the parameter data required to construct the biomathematical model of the aerobic granular sludge process;

[0015] S2. Based on the parameter data, establish a biomathematical model of aerobic granular sludge, which includes a granular sludge microbial metabolism module and a sludge migration module.

[0016] S3. Based on the above-mentioned microbial metabolism module and sludge migration module of granular sludge, establish an aerobic granular sludge reactor model for the sequential batch operation of the influent, aeration, sedimentation and sludge discharge stages of the aerobic granular sludge process.

[0017] S4. The aerobic granular sludge reactor model was constructed to simulate and optimize the aerobic granular sludge process. The optimized data included influent flow rate, aeration intensity and time, sludge discharge start-up time and duration.

[0018] As described above, in a preferred application, the parameters required for the biomathematical model include influent water quality, sludge characteristics, and tank parameters; wherein, the influent water quality includes influent nitrogen composition, phosphorus composition, and organic matter composition;

[0019] The sludge characteristics include the particle size distribution of the sludge and the proportion and specific gravity of sludge within the defined particle size range; the sludge particles are grouped according to size into {0~200, 200~400, 400~800, 800~1200, 1200~1900, 1900~2000 and greater than 2000 μm}, and the sludge density and weight percentage of each group are measured, with the median value of the upper and lower limits of each group representing the average particle size of that group; sludge smaller than 200 micrometers is defined as flocculent sludge, and sludge larger than 200 micrometers is defined as granular sludge.

[0020] The pool parameters include the pool drainage height H, the pool area A, and the sludge discharge pipe height Hp.

[0021] As described above, preferably, in step S2, the biomathematical model can be constructed using languages ​​such as Python, R, C++, and C#;

[0022] The construction of the granular sludge microbial metabolic module includes the following steps:

[0023] (1) Based on the sludge characteristics measured in step S1, the sludge is divided into two parts according to the sludge particle size: flocculent sludge with a particle size of less than 200 micrometers and granular sludge with a particle size of more than 200 micrometers. The internal mass transfer resistance of the flocculent sludge is set to 0. The changes in phosphorus, nitrogen and organic matter, as well as the changes in the amount of sludge flocs themselves, are calculated based on the ASMs activated sludge.

[0024] For granular sludge larger than 200 micrometers, the sludge particles are modeled as spheres subdivided into N layers (10>N>5); the thickness of the outermost three layers of the model is constant at 30 micrometers, and the thickness of the inner layer Zin=(Rm-3×30 / N-3), where Rm is the particle radius;

[0025] (2) Establish a reaction-diffusion coupling model to simulate the most typical concentric stratified structure of granular sludge, consisting of an aerobic outer layer and an anoxic / anaerobic inner layer, and the simultaneous nitrification-denitrification, denitrification, and efficient nitrogen and phosphorus removal phenomena achieved therefrom; for the change of concentration of any component i within the granules over time, the diffusion-reaction equation in the spherical coordinate system is as follows:

[0026] ,

[0027] in:

[0028] C k The concentration of component k at the particle's inner radius r corresponds to the nine soluble and particulate components in the ASMs model, including fermentation products (S... A Rapidly biodegradable organic matter (S) F Inert dissolved organic matter (S) I ), ammonia nitrogen S NH4 Nitrate nitrogen (S) NO3 Dissolved oxygen (S) O2 ), soluble inorganic phosphorus (S) PO4 ), nitrifying bacteria (X) AUT ), heterotrophic bacteria (X) H )wait;

[0029] t: time (s)

[0030] r: Radial coordinate (m), determined according to the layering in the above steps, from the particle center (r=0) to the surface (r=Rm), the thickness of the inner layer Zin=(Rm-3×30 / N-3);

[0031] D k : Effective diffusion coefficient of component k within the particle (m 2 The classical diffusion coefficient of each component in pure water at 25°C is D ( / s), and the reference value for the diffusion coefficient of each component is D. O2 =2.1×10 -9 m 2 / s、D NH4 =1.8×10 -9 m 2 / s、D NO3 =1.90×10 -9 m 2 / s、D PO4 =0.89×10-9 m 2 / s, due to the influence of porosity and tortuosity, the effective diffusion coefficient in granular sludge is usually 30-70% of the free water diffusion coefficient;

[0032] r k The growth or decay reaction rate of component k (g / (m)) 3 ·s), calculated based on the ASM model matrix, with the core formula being r k =Σ(ν kj ·ρ j ), where ν kj The stoichiometric coefficients and ρ of component k in the model matrix under process j j The rate expression for process j is given. The ASMs model involves 21 reaction processes, including hydrolysis (aerobic, anaerobic, and anoxic), heterotrophic growth decay (aerobic growth, anoxic growth, fermentation, and decay), polyphosphate growth decay (anaerobic storage, aerobic growth, anoxic growth, and decay), nitrifying bacteria growth decay (aerobic growth and decay), and the chemical precipitation and redissolution of phosphorus.

[0033] (3) Based on the above reaction-diffusion coupling model, a differentiated classification modeling strategy is adopted to describe its material transformation process;

[0034] For flocculent sludge, the biotransformation of phosphorus, nitrogen, and organic matter, as well as the dynamic changes in sludge quantity, are calculated based on the reaction kinetics of ASMs. For granular sludge, a reaction-diffusion coupling model is used: the granules are radially discretized into multiple shells, and diffusion and reaction terms are calculated in each layer. The diffusion term describes the interlayer transfer of substrates (dissolved oxygen, organic matter, nitrogen, phosphorus, etc.) based on Fick's law. The reaction term calculates the concentration changes of each component, biomass growth, and decay based on ASMs kinetics.

[0035] As described above, preferably, in step S2, the sludge migration module calculates the migration process of flocculent sludge and granular sludge separately in the reactor. When the particle size of the sludge is less than 200 micrometers, the rising process in the influent process and the sedimentation process in the sedimentation stage are described by a conventional activated sludge settling model.

[0036] When the particle size of granular sludge is greater than 200 micrometers, its movement and migration characteristics are described according to the granular sludge description:

[0037] (1) Under influent conditions, granular sludge generates influent items. And two fluxes, the upward flux J generated by the "bottom inlet, top outlet" mode. up The gravity settlement flux caused by gravity settlement is J. sg ; Calculate according to the following formula:

[0038] ;

[0039] Among them, v in X represents the inlet water upflow velocity. k Q represents the concentration of particulate components k in the reaction tank. in Where A is the influent flow rate and A is the bottom area of ​​the reaction tank.

[0040] ;

[0041] Where v up X represents the top water outlet velocity. k Q represents the concentration of particulate components k in the reaction tank. e The effluent flow rate (Q in the aerobic granular sludge process) in =Q e A is the bottom area of ​​the reaction tank;

[0042] ;

[0043] Where v sg X represents the settling velocity of granular sludge. k The concentration of particulate matter k in the reaction tank; the settling velocity v of sludge particles with a particle size greater than 200 micrometers. sg The formula is as follows:

[0044] ;

[0045] Where g is the acceleration due to gravity, ρ s and ρ l Let d be the density of granular sludge and water, d be the diameter of the sludge particles, and C be the density of the granular sludge and water. d This is the drag coefficient;

[0046] Drag coefficient C d It can be derived from the following formula, where Re is the Reynolds number, μ is the viscosity of water, and C... d =22.75×Re-0.7, Re=ρdv sg / μ, from which the gravitational settling velocity v is obtained. sg The formula is

[0047] ;

[0048] For granular sludge with a particle size of less than 200 micrometers, the gravity settling velocity v was calculated using a bi-exponential settling model. sg The formula is as follows:

[0049] ;

[0050] Where v'0 is the maximum settling velocity, v0 is the maximum theoretical velocity, and r h To interfere with the sedimentation parameters of the precipitate, rp f is the sedimentation parameter for slow sedimentation. ns The percentages representing non-sedimentation ratios are all parameters from the stratified sedimentation model; X floc,i X represents the concentration of particulate components in the flocculent sludge in the reaction tank. a,k The concentration of particulate components with a particle size of less than 200 micrometers in the influent layer of the reaction tank;

[0051] (2) Under sedimentation conditions, granular sludge generates two fluxes. The gravity settling flux caused by gravity settling is J. sg The flux J caused by the discharge of residual sludge in the later stage dn Among them, the gravity settling flux J sg The calculation formula is the same as above, sludge discharge loss flux J dn The formula is as follows:

[0052] ;

[0053] Where v dn X represents the sludge discharge rate. k Q represents the concentration of particulate component k in the reaction tank. w , where A is the sludge discharge flow rate and A is the bottom area of ​​the reaction tank.

[0054] As described above, preferably, in step S3, the establishment of the sludge migration module includes the following steps:

[0055] (1) Discretize the reactor with height H and area A into M layers along the vertical direction. Each layer is regarded as a completely mixed reactor with height z of H / M. They are named R1, R2, R3...Ri...RM from bottom to top. The height range of the sub-reactor Ri is {(i-1)×H / M~i×H / M}. The sub-reactor containing the sludge discharge pipe is Rw. The dynamic process of each stage in the reactor is simulated by calculating the sludge concentration and substrate concentration in each layer.

[0056] (2) Based on the establishment of the microbial metabolism module and sludge migration module of granular sludge in step S2 above, according to the actual operation mode of the aerobic granular sludge process of "water inlet, water outlet, aeration, sedimentation, and sludge discharge", the macroscopic aerobic granular sludge reactor model is integrated into three dynamic stages: water inlet-water outlet stage, aeration stage and sedimentation-sludge discharge stage.

[0057] Furthermore, the aerobic granular sludge reactor model for the influent-outfluent stage is established: a multi-scale coupled model is established to calculate the mass transfer within each granular layer, the interlayer migration of granules, and the liquid phase material balance, and the concentration of each layer and the effluent concentration are obtained by iterative solution.

[0058] Specifically, the mass transfer flux on the surface of each granular layer is calculated using the granular sludge microbial metabolism module, as shown in the following formula:

[0059] ,

[0060] ;

[0061] in:

[0062] C k The concentration of component k at the inner radius r of the particle.

[0063] D k : The effective diffusion coefficient of component k within the particle,

[0064] r k The growth or decay reaction rate of component k.

[0065] J g,i,k In the i-th layer, the net mass transfer flux of component k from the particle surface into the liquid phase per unit external surface area;

[0066] r m : The radius of the particle;

[0067] Cn represents the nth sub-reactor;

[0068] The granular sludge migration module describes the macroscopic movement of granular sludge between different layers of the reactor under the hydraulic condition of "bottom inlet and top outlet"; the reactor is uniformly divided into M layers along its height, and the interlayer flux of particulate components is driven by both the influent upflow and gravity settling.

[0069] Bottom layer: The first layer at the bottom of the reaction tank is the influent layer (i=1), with two fluxes and one influent term, J. in The upward flux J of this layer up,1 Upper-layer gravity settlement flux J sg,2 The increase in particle mass per unit area in the first layer is .

[0070] ,

[0071] Intermediate layer: Layers 2 to (M-1) of the reaction tank are the influent layer (i=2-(M-1)), with four fluxes. The flux J transferred upwards in this layer is J. up,i Gravity settlement flux of this layer (J) sg,i Upper-layer gravity settlement flux J sg,i+1 The flux J transferred from the lower layer upwards up,i-1 .

[0072] The rate of increase in particle mass per unit area in the i-th layer is

[0073] ,

[0074] Top layer: The Mth layer of the reaction tank is the effluent layer (i=M), with three fluxes. This layer transfers flux J to the upper layers. up,M The flux J transferred from the lower layer upwards up,M-1 and gravity settlement flux J of this layer sg,M The rate of increase in particle mass per unit area in the Mth layer is...

[0075] ,

[0076] The above J in J up J sg Calculations from the granular sludge migration module show that all fluxes generated by hydraulic mixing and gravity settling apply only to the particulate components in the reactor, while soluble components are transported only through influent / effluent convection and interlayer upflow.

[0077] For any component k in the i-th liquid phase within the reactor, the dynamic material balance equation as a function of time is as follows:

[0078] ,

[0079] in:

[0080] C k,i Let k be the concentration of component k in the i-th layer;

[0081] ∑F in,i,k and ∑F out,i,k These represent the total mass flow rates of component k into and out of the i-th layer, respectively.

[0082] A g,i The total external surface area of ​​the i-th layer of sludge particles with a diameter greater than 200 micrometers;

[0083] J g,i,k The net exchange flux between component k on the surface of the i-th layer of granular sludge and the liquid phase is determined by the diffusion-reaction process inside the granules.

[0084] r f,i,k Let be the biochemical reaction rate of component k in the i-th layer of flocculent sludge (following ASMs kinetics).

[0085] V i Let V be the volume of the i-th layer. i =z×A;

[0086] S g,i,k The increase rate of particle mass per unit area in the i-th layer due to interlayer migration of particles;

[0087] z i Let be the height of the i-th layer.

[0088] The model solution employs an iterative coupling framework. First, the bulk concentrations of each liquid phase (including soluble and particulate components) and reactor parameters are initialized. In each iteration, the following steps are executed sequentially: using the current liquid phase concentrations of each layer as boundary conditions, the reaction-diffusion coupling model within the particles is solved to obtain the radial concentration distribution and surface mass transfer flux within the particles; based on the current particle concentration distribution, the interlayer particle flux driven by influent upflow and gravity settling is calculated, thereby determining the net increase rate of particle mass per unit area in each layer; at a macroscopic scale, the above fluxes are substituted into the steady-state material balance equations for each layer, which simultaneously integrate the contributions of liquid phase refluxing, particle-liquid phase mass transfer, flocculent sludge biochemical reactions, and particle migration, and the liquid phase concentrations of each layer are updated by solving these equations. Iteration continues until the concentration changes in each layer satisfy the convergence tolerance, ultimately outputting the radial concentration field within the particles, the surface mass transfer flux of each particle layer, and the concentration C of each liquid phase component in the reactor during the influent-drainage stage. k,i The concentration of the liquid phase component in the Mth layer is C M,k This is the concentration of the effluent.

[0089] Furthermore, the aerobic granular sludge reactor model for the aeration stage is established as follows: it is simplified to a completely mixed reactor (CSTR), ignoring liquid relativity and particle migration, and only calculating the diffusion-reaction within the particles and the floc biochemical reaction, which is solved by numerical integration.

[0090] Specifically, in the aerobic granular sludge reactor model during the aeration stage, the dynamic material balance equation for component k in the liquid phase within the reactor is:

[0091] ,

[0092] in:

[0093] C k The concentration of component k in the liquid phase;

[0094] A g The total external surface area of ​​sludge particles with a diameter greater than 200 micrometers;

[0095] J g,k The net exchange flux between the surface component k of the granular sludge and the liquid phase is determined by the diffusion-reaction process inside the granules and is calculated by the microscopic biological metabolism module of the granular sludge mentioned above.

[0096] r f,k The biochemical reaction rate of component k in flocculent sludge (following ASMs kinetics);

[0097] V is the volume of the reactor (liquid phase);

[0098] The initial uniform concentration of each component during the aeration stage is the volume-weighted average of the concentrations of each liquid phase remaining in the reactor at the end of the influent-effect stage; the calculation formula is as follows:

[0099] ,

[0100] Among them, C k 0 is the initial concentration of component k in the aeration stage, and C i,k is the concentration of each liquid-phase component calculated in the influent - effluent stage. Vi is the volume of the i-th layer, H is the total height of the reactor, and A is the area of the reactor;

[0101] The model solution uses the numerical integration method for initial value problems. First, the initial concentration of each component is calculated based on the stratified concentration at the end of the influent - effluent stage. Subsequently, time stepping is performed during the aeration duration. In each step, the microscopic biological metabolism module of granular sludge is used to couple the internal microscopic model of granular sludge with the floc reaction kinetics, and the material balance equation is substituted to update the liquid-phase concentration. Finally, the uniform concentration at the end of aeration will be used as the initial condition for the next process stage to achieve the dynamic connection of the full-cycle model.

[0102] Furthermore, the establishment of the reactor model in the sedimentation - sludge discharge stage: The diffusion - reaction process inside the granular sludge and the biochemical reaction process of floc sludge are ignored, and only the gravitational sedimentation and sludge discharge flux are calculated. The change in the concentration of each granular component in each layer is solved based on the stratified mass conservation.

[0103] Specifically, the reactor is uniformly divided into M completely mixed reaction layers along the vertical height direction, numbered from 1 to M from bottom to top. The first layer is the bottom layer, and the M-th layer is the top layer. The w-th layer (1 < w < M) is set as the dedicated sludge discharge operation layer; the dynamic core of the model is based on the mass conservation of each layer of sludge components;

[0104] For the bottom layer (i = 1), there is no flux entering from the lower layer, and it only receives the sludge settling from the upper layer (the second layer). The increase rate of the particle mass per unit area is ;

[0105] For all intermediate layers i (i.e., i = 2, …, M - 1 and i ≠ w), the increase rate of the mass per unit area is determined by the difference between the sedimentation input from the upper layer and the sedimentation output from this layer, expressed as ;

[0106] Especially for the sludge discharge layer (i = w), the increase rate of the particle mass per unit area is ;

[0107] For the top layer (i = M), the increase rate only reflects the loss of the sludge settling downward in this layer, and the formula is ;

[0108] Based on this, according to the mass conservation, the change rate of each granular component in each layer with time is

[0109] ;

[0110] in:

[0111] C i,k Let k be the concentration of the particulate component k in the i-th layer;

[0112] J sg,i,k Let be the gravitational settling flux of particulate component k in the i-th layer;

[0113] J dn The sludge flux discharged from the sludge discharge layer (the wth layer) is greater than 0 during the sludge discharge stage and equal to 0 during the sedimentation stage.

[0114] z i Let be the thickness of the i-th layer;

[0115] The core variables driving the model include the sludge flux (J) caused by gravity settling in each layer. sg ) and the forced discharge flux of the sludge layer (J dn The sludge migration module in step S2 obtains the sludge.

[0116] The aerobic granular sludge reactor model in the sedimentation-sludge discharge stage is tested using the sludge discharge flux J. dn This configuration enables dynamic simulation and precise characterization of the two operational stages: sedimentation and sludge discharge. Specifically, during the sedimentation stage simulation, the sludge discharge flow rate Q is... w The value is 0, meaning the sludge discharge flux J is 0. dn =0; During the simulated sludge discharge stage, set the sludge discharge flow rate Q. w Then the sludge discharge layer has a sludge discharge flux J. dn This model, through reasonable simplification and a clear reactor stratification structure, provides a scientific basis for optimizing sludge discharge location, settling time, and sludge discharge strategy, while significantly improving computational efficiency while ensuring simulation accuracy.

[0117] This model can systematically evaluate and optimize key operational parameters such as sludge discharge location, duration, and volume, providing a reliable quantitative analysis tool for setting sedimentation time and formulating sludge discharge strategies. Therefore, this invention not only provides a scientific basis for process design optimization and operational control, but also significantly improves computational efficiency while ensuring simulation accuracy, demonstrating good engineering applicability.

[0118] In the application described above, preferably, in step S4, the process of optimizing the influent flow rate is as follows: Set the filling ratio parameter, where the filling ratio is the ratio of a single influent volume to the total reactor volume, and the range of the filling ratio is 20%–50%; set the influent time for each filling ratio, with the influent time parameter ranging from 20 to 60 minutes; input the filling ratio and influent time into the aerobic granular sludge biomathematical model and run 10–15 cycles; under the condition of meeting the treatment water volume requirements, the parameter with the lowest effluent pollutant concentration is the preferred parameter.

[0119] As described above, preferably, in step S4, the optimization of the aeration stage is as follows: the aeration stage is divided into low dissolved oxygen aeration and high dissolved oxygen aeration; wherein, the dissolved oxygen concentration range of low dissolved oxygen aeration is 0.1 to 1 mg / L; the low dissolved oxygen aeration optimization process includes inputting the dissolved oxygen parameters into the aerobic granular sludge reactor model and running it for 10 minutes; calculating the change in total nitrogen (the sum of ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen) before and after the operation; and selecting the dissolved oxygen concentration with the largest change in total nitrogen as the preferred dissolved oxygen concentration;

[0120] Input the optimal low dissolved oxygen parameters into the system and run it continuously; calculate the change in total nitrogen within every 5 minutes of operation. When this value is less than 5% of the initial total nitrogen concentration, the total low dissolved oxygen aeration time is the optimal low dissolved oxygen aeration time; then start aeration with dissolved oxygen parameters of 1-2.5 mg / L; the time until the system ammonia nitrogen is lower than the target ammonia nitrogen concentration is the optimal aeration time.

[0121] In a preferred embodiment, the sludge discharge process is optimized as follows: the sludge discharge volume is determined based on the sludge retention time; the planned sludge discharge start time and duration are input into the system; the sludge discharge start time is the time from the start of the sedimentation stage to the start of sludge discharge; the sludge discharge start time is set to 10–45 minutes; the sludge discharge duration is 5–15 minutes; a target sludge concentration is set in the reactor, and sludge discharge is initiated when the sludge concentration is higher than the target value; the process is continuously run for 20–50 cycles, and the parameter with the highest proportion of particles larger than 200 micrometers is the preferred sludge discharge parameter.

[0122] (III) Beneficial Effects

[0123] The beneficial effects of this invention are:

[0124] The biomathematical model for aerobic granular sludge processes provided by this invention constructs a complete simulation system covering the entire process, the entire cycle, and multiple particle sizes. This system can accurately and dynamically simulate the distribution and evolution of particles of different sizes within the reactor, the degradation process of key substrates, and the final effluent quality. It quantitatively reveals the impact mechanisms of key variables such as influent flow rate, aeration strategy, and sludge discharge operation on system treatment performance and particle stability. Based on this model, process operating parameters can be precisely optimized, providing indispensable quantitative basis and decision support for the rapid start-up, long-term stable operation, and enhanced resistance to shock loads of aerobic granular sludge processes, as well as for process design and control. Ultimately, this achieves the goals of improved treatment efficiency, reduced operating costs, and optimized effluent quality, demonstrating significant engineering application value. Attached Figure Description

[0125] Figure 1 Flowchart for biomathematical modeling and application of aerobic granular sludge process;

[0126] Figure 2 This is a schematic diagram of granular sludge stratification.

[0127] Figure 3 A schematic diagram of the reactor configuration and modeling;

[0128] Figure 4 The results show the changes in nitrate and ammonia nitrogen concentrations in each sub-reactor during the simulation process;

[0129] Figure 5 This is a comparison of the changes in nitrate and ammonia nitrogen concentrations in the simulation results of the method of this invention and other methods;

[0130] Figure 6 This is a comparison of the sludge removal effect simulation results between the method of this invention and other methods.

[0131] [Explanation of Labels in the Attached Image]

[0132] 3-1: Sub-reactor C1;

[0133] 3-2: Sub-reactor C2;

[0134] 3-3: Sub-reactor C3;

[0135] 3-4: Sub-reactor C4;

[0136] 3-5: Mother reactor;

[0137] 3-6: Outflow weir;

[0138] 3-7: Sludge discharge pipe;

[0139] 3-8: Water inlet system;

[0140] 3-9: Aeration system. Detailed Implementation

[0141] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0142] Example 1

[0143] This embodiment provides a method for biomathematical simulation and application of aerobic granular sludge processes, the flowchart of which is shown below. Figure 1 As shown, the specific steps include the following:

[0144] S1. Collect the parameter data required for constructing the aerobic granular sludge process biomathematical model. The collected parameter data includes influent water quality, sludge characteristics, and tank parameters. Among them, the influent water quality indicators include influent nitrogen composition, phosphorus composition, and organic matter composition.

[0145] The sludge characteristics include the particle size distribution of the sludge and the proportion and specific gravity of sludge within the defined particle size range. Sludge particles are grouped according to size into {0~200, 200~400, 400~800, 800~1200, 1200~1900, 1900~2000, and greater than 2000 μm}. The sludge density and weight percentage of each group are measured, and the average particle size of each group is represented by the median value of its upper and lower limits.

[0146] The pool parameters include the pool drainage height H, the pool area A, and the sludge discharge pipe height Hp.

[0147] S2. Based on the obtained parameter data, a biomathematical model of aerobic granular sludge is established. The biomathematical model includes a granular sludge microbial metabolism module and a granular sludge migration module. The biomathematical model is constructed using Python software.

[0148] The granular sludge microscopic biological metabolism module simulates the complex biological processes within granular sludge, with its core being the establishment of a coupled model capable of characterizing microscopic stratified reactions. This module mainly consists of two parts: first, a stratified diffusion model describing the diffusion and transport of substrates and dissolved oxygen within the granules; and second, a bioreaction kinetic model based on activated sludge mathematical models (ASMs series models). The ASMs model was chosen primarily to accurately characterize typical enhanced biological phosphorus removal processes within the aerobic granular sludge system, thereby more precisely reflecting its biochemical reaction processes during actual operation.

[0149] The granular sludge microbial metabolic module includes the following steps:

[0150] (1) Based on the sludge characteristics measured in step 1, i.e., sludge particle size, the sludge is divided into two parts: flocculent sludge with a particle size of less than 200 micrometers and granular sludge with a particle size of more than 200 micrometers. The internal mass transfer resistance of the flocculent sludge is set to 0, and the changes in phosphorus, nitrogen, and organic matter, as well as the changes in the sludge volume of the flocculent itself, are calculated according to the widely used ASM2d activated sludge model in ASMs. For granular sludge with a particle size of more than 200 micrometers, the sludge particles are modeled as spheres subdivided into N layers (10>N>5); the thickness of the outermost three layers of the model is constant at 30 micrometers, and the thickness of the inner layer Zin=(Rm-3×30 / N-3), where Rm is the particle radius. Figure 2 As shown, in this embodiment, granular sludge particles larger than 200 micrometers are modeled as spheres subdivided into 6 layers. The thickness of the outermost three layers is constant at 30 micrometers, and the thickness of the other inner layers is Zin = (Rm - 3 × 30) / 6 - 3, where Rm is the particle radius. The diffusion process and concentration of nitrogen, phosphorus, organic matter, and dissolved oxygen in each layer of the particle are calculated based on the reaction-diffusion coupling model. The changes in phosphorus, nitrogen, and organic matter in each layer, as well as the changes in the amount of sludge in the sludge particles themselves, are calculated based on the existing and widely used ASM2d activated sludge model.

[0151] (2) A reaction-diffusion coupling model is established. Its core principle is to combine the mathematical model of activated sludge describing biological reaction kinetics with the diffusion model describing mass transfer, so as to quantitatively characterize the substrate concentration gradient caused by the size effect inside the granular sludge and the resulting stratified metabolic phenomenon. Dissolved oxygen and substrates in the reaction tank diffuse from the surface of the granular sludge to the interior, and are rapidly consumed by the aerobic microorganisms in the outer layer, resulting in a sharp decrease in oxygen concentration with increasing depth. At a certain depth, the oxygen concentration drops to near zero, and the environment changes to anoxic or anaerobic state. The most typical concentric stratified structure of the granular sludge, consisting of an aerobic outer layer and an anoxic / anaerobic inner layer, can be simulated, as well as the efficient nitrogen and phosphorus removal phenomena such as simultaneous nitrification and denitrification, and denitrification phosphorus removal achieved by it. For the change of concentration of any component i in the granules with time, the diffusion-reaction equation in the spherical coordinate system is as follows:

[0152] ,

[0153] in:

[0154] C k The concentration (mg / L) of component k at the inner radius r of the particle corresponds to the nine soluble and particulate components in the ASM2d model of ASMs, such as S. A (Fermentation products), S F (Rapidly biodegradable organic matter), S I (Inert soluble organic matter), S NH4 (ammonia nitrogen), S NO3 (nitrate nitrogen), SO2 (Dissolved oxygen), S PO4 (Dissolved inorganic phosphorus), X AUT (nitrifying bacteria), X H (Heterotrophic bacteria), etc.;

[0155] t: time (s)

[0156] r: Radial coordinate (m), determined according to the layering in the above steps, from the particle center (r=0) to the surface (r=Rm), the thickness of the inner layer Zin=(Rm-3×30 / N-3);

[0157] D k : Effective diffusion coefficient of component k within the particle (m 2 / s), the classical diffusion coefficient of each component in pure water at 25°C is generally referenced as D. O2 =2.1×10⁻ 9 m 2 / s、D NH4 =1.8×10⁻ 9 m 2 / s、D NO3 =1.90×10⁻ 9 m 2 / s、D PO4 =0.89×10⁻ 9 m 2 / s, due to the influence of porosity and tortuosity, the effective diffusion coefficient in granular sludge is usually 30-70% of the free water diffusion coefficient;

[0158] r k The growth or decay reaction rate of component k (g / (m)) 3 ·s), calculated based on the ASM model matrix, with the core formula being r k =Σ(ν kj ·ρ j ), where ν kj The stoichiometric coefficients and ρ of component k in the model matrix under process j j Let be the rate expression for process j. The ASM2d model in ASMs involves 21 reaction processes, including hydrolysis (aerobic, anaerobic, anoxic), heterotrophic growth decay (aerobic growth, anoxic growth, fermentation, decay), polyphosphate growth decay (anaerobic storage, aerobic growth, anoxic growth, decay), nitrifying bacteria growth decay (aerobic growth, decay), and the chemical precipitation and redissolution of phosphorus.

[0159] (3) In view of the structural differences between flocculent sludge and granular sludge, a differentiated classification modeling strategy is adopted based on the above reaction-diffusion coupling model to accurately describe their material transformation process.

[0160] For flocculent sludge, given its small particle size and negligible internal mass transfer resistance, it is assumed that the components are uniformly distributed within the flocs with no concentration gradient. The model is based solely on the reaction terms of the above model, namely the ASM2d reaction kinetics in ASMs, to calculate the biotransformation of phosphorus, nitrogen, and organic matter, as well as the dynamic changes in sludge quantity. The effective diffusion coefficient of each component is set to zero, i.e., diffusion terms are not considered.

[0161] For granular sludge, the large particle size (typically >200 μm) leads to significant diffusion limitation, resulting in a concentration gradient during substrate transport from the surface to the interior. To address this, a reaction-diffusion coupled model is employed: the particles are radially discretized into multiple shells, with diffusion and reaction terms calculated within each shell. The diffusion term describes the interlayer transport of substrates (dissolved oxygen, organic matter, nitrogen, phosphorus, etc.) based on Fick's law; the reaction term calculates the concentration changes, biomass growth, and decay of each component based on the ASM2d kinetics in ASMs. Depending on the required computational accuracy and available computing power, the number of shells, N, can be selected between 5 and 10. A larger N results in higher computational accuracy but also a greater computational load, and vice versa. The outermost shell of the granular sludge is defined as three fixed 30-micron shells, as ammonia oxidation primarily occurs at the 90-micron surface of the granular sludge. Defining the sludge into three fixed 30-micron shells ensures the accuracy of the nitrification process. This stratification method accurately characterizes the concentration gradient within the granules while effectively controlling the computational scale.

[0162] This classification modeling strategy can accurately characterize the overall reaction dynamics of flocculent sludge and reveal the spatial stratification metabolic mechanism inside granular sludge, thereby significantly improving the accuracy of the model in simulating composite sludge systems and providing a more reliable quantitative basis for process design and operation control.

[0163] Granular sludge migration module: The unique physicochemical properties of granular sludge cause it to exhibit distinctive movement behavior within the reactor. On a macroscopic scale, granular sludge undergoes periodic rising and settling processes, and the reactor simultaneously contains particles with excellent settling properties and flocs with slower settling. When the particle size of granular sludge is less than 200 micrometers, the rising process during the influent process and the settling process during the sedimentation stage can be described using a conventional activated sludge settling model. However, when the particle size of granular sludge is greater than 200 micrometers, a granular sludge migration module should be introduced to more accurately characterize its movement and migration features.

[0164] (1) Under influent conditions, granular sludge generates an influent term and two fluxes. The upward flux J generated by the "bottom influent, top effluent" mode is... up The gravity settlement flux caused by gravity settlement is J. sg Influent flux J in Calculate using the following formula:

[0165] ;

[0166] Where v in X represents the inlet water upflow velocity. k Q represents the concentration of particulate components k in the reaction tank. in A represents the influent flow rate, and A represents the bottom area of ​​the reaction tank.

[0167] ;

[0168] Where v up X represents the top water outlet velocity. k Q represents the concentration of particulate components k in the reaction tank. e The effluent flow rate (Q in the aerobic granular sludge process) in =Q e A represents the bottom area of ​​the reaction tank.

[0169] ;

[0170] Where v sg X represents the settling velocity of granular sludge. k The concentration of particulate matter, k, in the reaction tank. The settling velocity, v, of sludge particles with a diameter greater than 200 micrometers. sg The formula is as follows:

[0171] ,

[0172] Where g is the acceleration due to gravity, ρ s and ρ l Let d be the density of granular sludge and water, d be the diameter of the sludge particles, and C be the density of the granular sludge and water. d This is the drag coefficient;

[0173] Drag coefficient C d It can be derived from the following formula, where Re is the Reynolds number, μ is the viscosity of water, and C... d =22.75×Re-0.7, Re=ρdv sg / μ, from which the gravitational settling velocity v is obtained. sg The formula is

[0174] .

[0175] For flocculent sludge with a particle size of less than 200 micrometers, the gravity settling velocity v was calculated using a conventional double-exponential settling model. sg The formula is as follows:

[0176] ,

[0177] Where v'0 is the maximum settling velocity, v0 is the maximum theoretical velocity, and r h To interfere with the sedimentation parameters of the precipitate, r pf is the sedimentation parameter for slow sedimentation. ns The values ​​represent the non-sedimentation proportions, all parameters from the stratified sedimentation model. X floc,i X represents the concentration of particulate components in the flocculent sludge in the reaction tank. a The concentration of particulate components with a particle size of less than 200 micrometers in the influent layer of the reaction tank.

[0178] (2) Under sedimentation conditions, granular sludge generates two fluxes. The gravity settling flux caused by gravity settling is J. sg The flux J caused by the discharge of residual sludge in the later stage dn Among them, the gravity settling flux J sg The calculation formula is the same as above, sludge discharge loss flux J dn The formula is as follows:

[0179] ;

[0180] Where v dn X represents the sludge discharge rate. k Q represents the concentration of particulate component k in the reaction tank. w , where A is the sludge discharge flow rate and A is the bottom area of ​​the reaction tank.

[0181] The core function of the granular sludge migration module is to simulate the dynamic vertical distribution of different sludge components during the influent and sedimentation stages of the reactor. Because flocs smaller than 200 micrometers and particles larger than 200 micrometers differ significantly in their hydraulic properties (such as settling velocity), they must be described and calculated separately in the model. Traditional activated sludge models are typically based on assumptions of complete mixing or uniform settling, lacking the ability to simulate sludge stratification and classification. Therefore, they cannot accurately reflect the crucial migration-driven sludge distribution and transformation processes in aerobic granular sludge systems.

[0182] S3. Based on the above modules, establish a sequential batch cycle operation model of aerobic granular sludge reactor for the influent, aeration, sedimentation, and sludge discharge stages of the aerobic granular sludge process.

[0183] The operational states of aerobic granular sludge processes differ significantly across their various stages. For instance, the influent stage employs a bottom-influent, top-exfluent method, during which mass transfer and biochemical reactions occur within the granular sludge, accompanied by sludge rising and settling within the reactor. The aeration stage involves a uniformly mixed sludge state, while the sedimentation stage involves the sorting and settling of particles of different sizes. These significant stage differences make traditional models developed for continuous flow processes difficult to apply—their steady-state or dynamic solution logic and periodic boundary conditions cannot directly describe the intermittent and highly transient characteristics of the process. Furthermore, the vertical dynamic changes in mass transfer within the granular sludge and the concentration field within the reactor make real-time calculation of the entire system's microbial metabolism and mass transfer processes extremely difficult.

[0184] To systematically characterize the process behavior, an aerobic granular sludge reactor model needs to be established for the aerobic granular sludge process.

[0185] Specifically, it includes the following steps:

[0186] (1) The reactor with height H and area A is discretized into M layers along the vertical direction. Each layer is regarded as a completely mixed reactor with height z of H / M. They are named R1, R2, R3, ..., Ri, ..., RM from bottom to top. The height range of the sub-reactor Ri is {(i-1)×H / M~i×H / M}. The sub-reactor containing the sludge discharge pipe is denoted as Rw. The sludge concentration and substrate concentration in each layer are calculated according to the sludge migration module, so that the dynamic process of each stage in the reactor can be simulated. This method can significantly reduce the computational complexity based on accurately describing the key dynamic characteristics of each stage, thereby achieving efficient simulation of aerobic granular sludge process. Usually, M can be set to 10.

[0187] (2) Based on the establishment of the granular sludge microbial metabolism module and granular sludge migration module in step 2 above, and according to the actual operation mode of the aerobic granular sludge process of "influent, effluent, aeration, sedimentation, and sludge discharge", the macroscopic reactor model is integrated into three dynamic stages: influent-effluent stage, aeration stage, and sedimentation-sludge discharge stage. This division method can more clearly correspond to the process sequence and facilitate modular modeling and simulation of the entire operation cycle.

[0188] (A) Model Establishment of Aerobic Granular Sludge Reactor in the Influent-Drainage Stage: To describe the unique behavior of the granular sludge system in the influent-drainage stage, a multi-scale coupled reactor model was established. In each reaction layer, the internal substrate concentration gradient caused by the size effect and the resulting stratified metabolic phenomena were quantitatively characterized by the granular sludge microbial metabolism module; simultaneously, the sludge migration module was used to describe its macroscopic movement as it experiences influent rising and settling within the reactor. Based on this, the model integrates the dynamics of each layer by establishing the material balance of the bulk solution in each layer, thereby achieving a full-chain quantitative simulation from the microscopic metabolism inside the granules to the macroscopic flow and reaction processes in the reactor.

[0189] It comprises three parts: a microscale granular sludge microbial metabolism module, which characterizes the substrate concentration gradient and stratified metabolism within the granular sludge due to its size; a mesoscale sludge migration module, which describes the interlayer migration of particles under the influence of influent upflow and gravity settling; and a macroscale reactor stratified material balance model, which integrates mass transfer and reaction between particles and the liquid phase, and describes the dynamic changes in the concentration of the bulk solution in each layer.

[0190] The mass transfer flux on the granular surface was calculated using the granular sludge microbial metabolism module, as shown in the following formula:

[0191] ,

[0192] ;

[0193] in:

[0194] Ck: The concentration of component k at the inner radius r of the particle.

[0195] Dk: Effective diffusion coefficient of component k within the particle.

[0196] rk: The growth or decay reaction rate of component k.

[0197] Jg,i,k: In the i-th layer, the net mass transfer flux of component k from the particle surface into the liquid phase per unit external surface area.

[0198] rm: the radius of the particle.

[0199] The sludge migration module describes the macroscopic movement of granular sludge between different layers of the reactor under hydraulic conditions of "bottom inlet, top effluent". The reactor is uniformly divided into M layers along its height, and the interlayer flux of granular components is driven by both the influent upflow and gravity settling.

[0200] Bottom layer: The first layer at the bottom of the reaction tank is the influent layer (i=1), with two fluxes and one influent term, J. in The upward flux J of this layer up,1 Upper-layer gravity settlement flux J sg,2 The increase in particle mass per unit area in the first layer is .

[0201] .

[0202] Intermediate layer: Layers 2 to (M-1) of the reaction tank are the influent layer (i=2-(M-1)), with four fluxes. The flux J transferred upwards in this layer is J. up,i Gravity settlement flux of this layer (J) sg,i Upper-layer gravity settlement flux J sg,i+1 The flux J transferred from the lower layer upwards up,i-1 The rate of increase in particle mass per unit area in the i-th layer is...

[0203] ;

[0204] Top layer: The Mth layer of the reaction tank is the effluent layer (i=M), with three fluxes. This layer transfers flux J to the upper layers. up,M The flux J transferred from the lower layer upwards up,M-1 and gravity settlement flux J of this layer sg,M The rate of increase in particle mass per unit area in the Mth layer is...

[0205] ;

[0206] The above J in J up J sg Calculations from the sludge migration module show that all fluxes generated by hydraulic mixing and gravity settling apply only to particulate components in the reactor, while soluble components are transported only through influent / effluent convection and interlayer upflow.

[0207] For any component k in the i-th liquid phase within the reactor, the dynamic material balance equation as a function of time is as follows:

[0208] ;

[0209] in:

[0210] C k,i Let k be the concentration of component k in the i-th layer;

[0211] ∑F in,i,k and ∑F out,i,k These represent the total mass flow rates of component k into and out of the i-th layer, respectively.

[0212] A g,i The total external surface area of ​​the i-th layer of sludge particles with a diameter greater than 200 micrometers;

[0213] J g,i,k The net exchange flux between component k on the surface of the i-th layer of granular sludge and the liquid phase is determined by the diffusion-reaction process inside the granules.

[0214] r f,i,k Let be the biochemical reaction rate of component k in the i-th layer of flocculent sludge (following ASMs kinetics).

[0215] V i Let Vi be the volume of the i-th layer, and Vi = z × A;

[0216] S g,i,k The increase rate of particle mass per unit area in the i-th layer due to interlayer migration of particles;

[0217] z i Let be the height of the i-th layer.

[0218] The model solution employs an iterative coupling framework. First, the bulk concentrations of each liquid phase (including soluble and particulate components) and reactor parameters are initialized. In each iteration, the following steps are executed sequentially: using the current liquid phase concentrations of each layer as boundary conditions, the reaction-diffusion coupling model within the particles is solved to obtain the radial concentration distribution and surface mass transfer flux within the particles; based on the current particle concentration distribution, the interlayer particle flux driven by influent upflow and gravity settling is calculated, thereby determining the net increase rate of particle mass per unit area in each layer; at a macroscopic scale, the above fluxes are substituted into the steady-state material balance equations for each layer, which simultaneously integrate the contributions of liquid phase refluxing, particle-liquid phase mass transfer, flocculent sludge biochemical reactions, and particle migration, and the liquid phase concentrations of each layer are updated by solving these equations. Iteration continues until the concentration changes in each layer satisfy the convergence tolerance, ultimately outputting the radial concentration field within the particles, the surface mass transfer flux of each particle layer, and the concentration C of each liquid phase component in the reactor during the influent-drainage stage. k，i The concentration of the liquid phase component in the Mth layer is C M，k This is the concentration of the effluent.

[0219] (B) Modeling of the Aerobic Granular Sludge Reactor in the Aeration Stage: In the aerobic granular sludge process, the aeration stage is a critical period where influent and effluent are stopped, and oxygen supply and mixing rely solely on gas agitation. At this time, the intense aeration disturbance causes the granular sludge and flocculent sludge to reach a completely mixed state within the reactor, with all components uniformly distributed in the liquid phase. Therefore, this stage can be simplified as a completely mixed reactor (CSTR) with no influent or effluent flow. Compared to the influent-effluent stage, the hydraulic conditions and mixing state in the aeration stage are significantly different. The effects of relative liquid flow and particle migration can be ignored, and the modeling focus can be placed on the two core mechanisms: the diffusion-reaction process within the granular sludge and the biochemical reactions of the flocculent sludge. To accurately describe the material transformation and removal in this stage, a separate model of the aerobic granular sludge reactor for the aeration stage needs to be established.

[0220] In the aerobic granular sludge reactor model during the aeration stage, the dynamic material balance equation for component k in the liquid phase within the reactor is:

[0221] ,

[0222] in:

[0223] C k The concentration of component k in the liquid phase;

[0224] A g The total external surface area of ​​sludge particles with a diameter greater than 200 micrometers;

[0225] J g,k The net exchange flux between the surface component k of the granular sludge and the liquid phase is determined by the diffusion-reaction process inside the granules and is calculated by the microscopic biological metabolism module of the granular sludge mentioned above.

[0226] r f,k is the biochemical reaction rate of component k in flocculent sludge (following ASMs kinetics);

[0227] V is the volume of the reactor (liquid phase).

[0228] The initial concentration in the aeration stage is determined by the internal state of the reactor at the end of the influent - effluent stage. At the start of aeration, intense gas agitation rapidly brings the substances in the reactor to a fully mixed state. Therefore, the initial uniform concentration of each component in the aeration stage is the volume - weighted average of the liquid - phase concentrations of each layer remaining in the reactor at the end of the influent - effluent stage. The calculation formula is as follows:

[0229] ,

[0230] where, C k 0 is the initial concentration of component k in the aeration stage, C i，k is the calculated liquid - phase component concentration of each layer in the influent - effluent stage, V i is the volume of the i - th layer, H is the total height of the reactor, and A is the area of the reactor.

[0231] The model solution uses the numerical integration method for initial - value problems. First, the initial concentration of each component is calculated based on the stratified concentration at the end of the influent - effluent stage. Subsequently, time - stepping solution is carried out during the aeration duration. In each step, the microscopic biological metabolism module of granular sludge is used to couple the internal microscopic model of granular sludge with the floc reaction kinetics, and the material balance equation is substituted to update the liquid - phase concentration. Finally, the uniform concentration at the end of aeration will be used as the initial condition for the next process stage to achieve the dynamic connection of the full - cycle model.

[0232] (C) Establishment of the aerobic granular sludge reactor model in the sedimentation - sludge discharge stage: In this stage of sedimentation and sludge discharge, the model focuses on the physical migration process of granular sludge and flocculent sludge in the reactor, namely gravitational sedimentation and sludge discharge, and ignores the complex processes such as the diffusion - reaction process inside granular sludge and the biochemical reaction of flocculent sludge in this stage to achieve efficient simulation of the dynamic sludge distribution. Consistent with the "reactor model in the influent - effluent stage", the reactor is evenly divided into M completely mixed reaction layers along the vertical height direction, numbered from 1 to M from bottom to top. The first layer is the bottom layer, and the M - th layer is the top layer. The w - th layer (1 < w < M) is set as the dedicated sludge discharge operation layer. The dynamic core of the model is based on the mass conservation of sludge components in each layer.

[0233] For the bottom layer (i = 1), there is no flux from the lower layer and it only receives the sludge sedimented from the upper layer (the second layer). The rate of increase in the granular mass per unit area is S g,1,k =J sg,2,k .

[0234] For all intermediate layers i (i.e., i = 2, ..., M−1 and i ≠ w), the rate of increase in mass per unit area is determined by the difference between the settlement input of the upper layer and the settlement output of the current layer, expressed as: .

[0235] Specifically, the sludge discharge layer (i=w) not only receives sediment from the upper layer and outputs sediment to the lower layer, but also includes sludge discharge losses, and its particle mass increase rate per unit area is... .

[0236] For the top layer (i=M), its mass increase rate is only reflected in the loss due to downward settling of the sludge in this layer, as shown in the formula: .

[0237] Based on this, according to the principle of mass conservation, the rate of change of particulate components in each layer over time is...

[0238] ,

[0239] in:

[0240] C i，k Let k be the concentration of the particulate component k in the i-th layer;

[0241] J sg，I，k Let be the gravitational settling flux of particulate component k in the i-th layer;

[0242] J dn The sludge flux discharged from the sludge discharge layer (the wth layer) is greater than 0 during the sludge discharge stage and equal to 0 during the sedimentation stage.

[0243] z i Let be the thickness of the i-th layer.

[0244] The core variables driving the model include the sludge flux (J) caused by gravity settling in each layer. sg ) and the forced discharge flux of the sludge layer (J dn The data is obtained from the sludge migration module in step S2. This module can distinguish the different settling characteristics of granular sludge and flocculent sludge, thereby achieving a refined description of the settling behavior of different sludge groups.

[0245] The aerobic granular sludge reactor model for the sedimentation-sludge discharge stage is analyzed using the sludge discharge flux J. dn This configuration enables dynamic simulation and precise characterization of the two operational stages: sedimentation and sludge discharge. Specifically, during the sedimentation stage simulation, the sludge discharge flow rate Q is... w The value is 0, meaning the sludge discharge flux J is 0. dn =0; During the simulated sludge discharge stage, set the sludge discharge flow rate Q. w Then the sludge discharge layer has a sludge discharge flux J. dn Sludge discharge flux, i.e., the mass of sludge discharged, is determined by the sludge discharge flow rate Q.w The model also determined the sludge concentration in the sludge discharge layer at that time. Through reasonable simplification and a clear reactor stratification structure, the model provides a scientific basis for optimizing sludge discharge location, settling time, and sludge discharge strategy, while significantly improving computational efficiency while ensuring simulation accuracy.

[0246] This model can systematically evaluate and optimize key operational parameters such as sludge discharge location, duration, and volume, providing a reliable quantitative analysis tool for setting sedimentation time and formulating sludge discharge strategies. Therefore, this invention not only provides a scientific basis for process design optimization and operational control, but also significantly improves computational efficiency while ensuring simulation accuracy, demonstrating good engineering applicability.

[0247] S4. Use the constructed model to simulate and optimize the process. The optimized aerobic granular sludge process parameters include: influent flow rate, aeration intensity and time, and sludge discharge time.

[0248] The specific optimization process for the influent flow rate is as follows: Set the filling ratio parameter, which is the ratio of the single influent volume to the total reactor volume, with a range of 20% to 50%; set the influent time for each filling ratio, with a range of 20 to 60 minutes; input the data for the filling ratio (range of 20% to 50%) and the influent time (range of 20 to 60 minutes) into the aerobic granular sludge reactor model and run it for 10 to 15 cycles; under the condition of meeting the treatment volume requirements, the parameter with the lowest effluent pollutant concentration is the preferred parameter;

[0249] The optimized aeration process is as follows: The aeration stage is divided into low dissolved oxygen aeration and high dissolved oxygen aeration; the dissolved oxygen concentration range for low dissolved oxygen aeration is 0.1–1 mg / L; the optimization process for low dissolved oxygen aeration includes inputting the dissolved oxygen parameters into the aerobic granular sludge reactor model and running it for 10 minutes; calculating the change in total nitrogen (the sum of ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen) before and after the operation; selecting the dissolved oxygen concentration with the largest change in total nitrogen as the optimal dissolved oxygen concentration; inputting the optimal low dissolved oxygen parameters into the aerobic granular sludge reactor model and running it continuously; calculating the change in total nitrogen every 5 minutes of operation; when this value is less than 5% of the initial total nitrogen concentration, the total low dissolved oxygen aeration operation time is the optimal low dissolved oxygen aeration time; then, aeration is carried out with dissolved oxygen parameters of 1–2.5 mg / L; the optimal aeration time is the time when the system ammonia nitrogen is lower than the target ammonia nitrogen concentration.

[0250] The sludge discharge process is optimized as follows: Determine the sludge discharge volume based on the sludge retention time; input the planned sludge discharge start time and duration into the aerobic granular sludge reactor model; the sludge discharge start time is the time from the start of the sedimentation stage to the start of sludge discharge; the sludge discharge start time is set to 10–45 minutes; the sludge discharge duration is 5–15 minutes; set the target sludge concentration in the reactor, and start sludge discharge when the sludge concentration is higher than the target value; run continuously for 20–50 cycles, and the parameter with the highest proportion of particles larger than 200 micrometers in the results is the preferred sludge discharge parameter.

[0251] Example 2

[0252] This embodiment is based on Embodiment 1, dividing the reactor into 4 layers in terms of height, such as... Figure 3 As shown, each layer in the model is calculated as a fully mixed sub-reactor with a height of H / 4, named C1, C2, C3, and C4 from bottom to top. That is, the mother reactor 3-5 is sub-reactors C1 3-1, C2 3-2, C3 3-3, and C4 3-4. The height range of sub-reactor Ci is {(i-1)×H / 4~i×H / 4}, where i is the level of the i-th sub-reactor, and the volume of each sub-reactor is A×H / 4. The sludge discharge pipe 3-7 is located within sub-reactor C3 3-3. The reactor operation consists of four stages: influent, aeration, sedimentation, and sludge discharge.

[0253] During the influent stage, influent enters the reactor through the influent pipe 3-8 at the bottom via the granular sludge process. Simultaneously, water from the upper part of the reactor is discharged through the drain pipe connected to the outlet of the effluent weir 3-6. The influent enters sub-reactor C1 3-1 from the bottom of the reactor. Based on the influent flow rate and the concentrations of nitrogen, phosphorus, and organic matter in the influent, the amounts of nitrogen, phosphorus, and organic matter (K) entering sub-reactor C1 3-1 are calculated. C1 At this point, based on the sludge quantity and nitrogen, phosphorus, organic matter, and dissolved oxygen content in 3-1 C1, the change in nitrogen, phosphorus, and organic matter (L) is calculated using the biological metabolism module. C1 At this point, nitrogen, phosphorus, and organic matter in C13-1 are N. C1 =(J C1 +K C1 - L C1 ) / V C1 , where J C1 V represents the amount of nitrogen, phosphorus, and organic matter before influent. C1 Let C1 be the reactor volume. Correspondingly, the amounts K of nitrogen, phosphorus, and organic matter entering C2 are calculated based on the influent flow rate and the nitrogen, phosphorus, and organic matter concentrations in C1. C2 At this point, based on the sludge quantity and nitrogen, phosphorus, organic matter, and dissolved oxygen content in C23-2, the change in nitrogen, phosphorus, and organic matter (L) is calculated using the biological metabolism module. C2At this point, nitrogen, phosphorus, and organic matter in C23-2 are N. C2 =(J C2 +K C2 - L C2 ) / V C2 , where J C2 V represents the amount of nitrogen, phosphorus, and organic matter before influent. C2 Let C2 be the reactor volume. Similarly, calculate the nitrogen, phosphorus, and organic matter concentrations from C33-2 to C43-4 after the influent. The concentration at reactor C4 at this point represents the effluent condition.

[0254] In the above process, the sludge distribution and quantity in each sub-reactor Ci are obtained from the sludge migration module: At the beginning of the influent stage, sludge accumulates in reactor C1. After the influent enters, the sludge experiences an upward velocity due to the influent. This upward velocity can be obtained from the sludge migration module. Therefore, during the influent stage, the sludge height of different groups of sludge at time Tf after the influent start-up can be obtained by Hu = Vug * Tf. The sludge in sub-reactor Ci at different times is the sludge of all Hu within the Ci height range at that time.

[0255] During the aeration stage, air enters the tank through aeration system 3-9. The sludge is agitated by the gas, achieving a completely mixed state. Changes in nitrogen, phosphorus, and organic matter, along with changes in sludge volume, are calculated using the sludge microbial metabolism module.

[0256] During the settling stage, the sludge settles at the Vsg velocity described in the sludge migration module. The sludge height of different sludge groups at time Ts after settling can be obtained by Hs = H0 - Vsg * Ts, where H0 is the initial sludge height. The sludge in sub-reactor Ci at different times represents all sludge with Hs within the Ci height range at that time. When sludge discharge begins, the amount and distribution of discharged sludge are calculated based on the sludge in sub-reactor C3, where sludge discharge pipes 3-7 are located.

[0257] In step S4, preset parameters are input into the aerobic granular sludge reactor model to obtain optimal parameters. The process of optimizing the influent flow rate is as follows: The input parameters, the filling ratio (the ratio of a single influent volume to the total reactor volume), are divided into four groups based on filling ratios of 20%, 30%, 40%, and 50%. Influent times are set for each group at 20, 30, 40, 50, and 60 minutes respectively. The data is input into the program and run for 10-15 cycles. First, the optimal filling ratio is determined: the parameter with the lowest effluent pollutant concentration while meeting the treatment volume requirements is the preferred parameter. Then, the influent time under the optimal filling ratio is determined: with a constant influent volume, a longer influent time results in a longer biochemical reaction time and a lower effluent pollutant concentration. The effluent pollutant concentration for a 60-minute influent time parameter is defined as N. 60mg / L. Reducing the influent time may also meet the time required for the biochemical reaction. Screening is performed to ensure the effluent concentration is less than 1.1*N. 60 The shortest influent time among the mg / L influent times is selected as the optimal influent time.

[0258] After the water intake is complete, the aeration system is turned on for aeration. Due to the agitation of the gas, the aeration process is a completely mixed state, and the sludge is uniformly distributed in the reaction. The biological metabolic process during the aeration stage is calculated under these conditions.

[0259] Unlike conventional activated sludge processes, aerobic granular sludge processes utilize a substrate concentration gradient in the granular sludge. The dissolved oxygen concentration decreases towards the center of the granule, allowing denitrification to occur within the granules. This process is known as simultaneous nitrification and denitrification. The presence of simultaneous nitrification and denitrification reduces the energy consumption of the aeration process. The biological metabolism module can effectively calculate this process. If the external dissolved oxygen concentration is low, there will be more anoxic zones within the granules.

[0260] To promote simultaneous nitrification and denitrification, the sludge aeration stage was divided into two phases: low dissolved oxygen (DO) aeration and high dissolved oxygen (DO) aeration. The optimization process for the low DO stage is as follows: Dissolved oxygen levels were set to 0.1, 0.3, 0.5, and 0.7 mg / L. The optimization process for low DO aeration was as follows: First, the low DO concentration was optimized. The dissolved oxygen parameters were input into the aerobic granular sludge biological mathematical model and run for 5 minutes. The change in total nitrogen (the sum of ammonia nitrogen, nitrate nitrogen, and nitrite nitrogen) before operation was calculated. The dissolved oxygen concentration with the largest change was selected as the optimal dissolved oxygen concentration. The optimal low DO parameters were then input into the system and continuously run.

[0261] Then, the low dissolved oxygen (DO) aeration time was optimized: the change in total nitrogen (TNO) every 5 minutes was calculated, and the operating time when this value was less than 5% of the initial TNO concentration was the optimal low DO aeration time. As mentioned above, as the reaction proceeds, the ammonia nitrogen concentration gradually decreases, so the change in TNO every 5 minutes will become increasingly lower. When this value is less than 5%, it indicates that the simultaneous nitrification and denitrification process has become very weak.

[0262] Aeration was then initiated with dissolved oxygen at a concentration of 1–2.5 mg / L. The optimal aeration time was defined as the time it took for the system's ammonia nitrogen concentration to fall below the target ammonia nitrogen concentration by 1 mg / L.

[0263] During the settling stage, sludge will be discharged from the system after the sludge discharge pipe is opened. The sludge discharge start time and duration are input into the system. The sludge discharge start time is set to the time from the start of the settling stage to the start of sludge discharge, specifically set to 10, 15, 20, 25, and 30 minutes after settling. The sludge discharge duration is set to 5, 7, 9, 11, and 15 minutes. A target sludge concentration is set in the reactor; sludge discharge is initiated when the sludge concentration exceeds the target value. After 20–50 cycles of continuous operation, the parameter with the highest proportion of particles larger than 200 micrometers is the optimal sludge discharge parameter. The optimal sludge discharge parameters need to be updated every 3–15 days based on changing sludge characteristics.

[0264] The optimal parameters can also be obtained using the overall optimization method. For example, inputting the parameter matrix set shown in Table 1 into the aerobic granular sludge biomathematical model constructed above will directly simulate the results. The parameter set includes: water filling ratio, influent time, dissolved oxygen concentration and aeration time for low dissolved oxygen aeration, dissolved oxygen concentration and aeration time for high dissolved oxygen aeration, sludge discharge start-up time and duration, and then running continuously for 10-20 cycles. Afterwards, the optimal parameters are selected based on a comprehensive consideration of treated water volume, effluent quality, and operating energy consumption. The input parameter table is as follows.

[0265] Table 1

[0266]

[0267] All optimal parameters are time-sensitive and have boundary conditions. When boundary conditions change or the process has been running for a period of time, a new simulation optimization should be performed when boundary conditions such as influent pollutant concentration, influent water temperature, etc., exceed the limits, or when the simulation results deviate significantly from the actual results.

[0268] This embodiment improves reactor treatment efficiency through an optimized fill ratio. Optimized influent time ensures both proper mixing of sludge and substrate while allowing sufficient time for biological reactions. Optimized aeration process enhances simultaneous nitrification and denitrification capabilities. Optimized sludge discharge process improves settling performance. The optimal conditions, as determined by this embodiment, are: a fill ratio of 40%, influent time of 20 minutes, low dissolved oxygen level of 0.5 mg / L, low dissolved oxygen aeration time of 40 minutes, high dissolved oxygen aeration time of 80 minutes, sludge discharge start-up time of 10 minutes, and sludge discharge duration of 5 minutes. Under these conditions, reactor treatment capacity increases by 25%, effluent nitrate decreases by 10%, the contribution rate of simultaneous nitrification and denitrification increases by 50%, aeration system energy consumption decreases by 20%, and the proportion of particles larger than 200 micrometers increases by 30%.

[0269] To verify the effectiveness and innovation of the aerobic granular sludge and biomathematical model in this method, the optimal conditions of 40% water filling ratio, 20-minute influent time, low dissolved oxygen value of 0.5 mg / L, 40-minute low dissolved oxygen aeration time, 80-minute high dissolved oxygen aeration time, 10-minute sludge discharge start-up time, and 5-minute sludge discharge duration were input into the model, and the widely used Biowin was used as a comparison. Figure 4 As shown, this illustrates the changes in nitrate nitrogen and ammonia nitrogen during an influent / aeration stage. For nitrate nitrogen, it can be seen that as the influent flows, the nitrate concentration at the bottom of C1 immediately decreases, followed by a decrease in C2. The nitrate concentrations in C3 and C4 show little change. After aeration, C1 and C4 mix rapidly within a short period. During the low dissolved oxygen aeration stage, the nitrate concentration does not change significantly, indicating that simultaneous nitrification and denitrification occur at this stage. After high dissolved oxygen aeration, nitrate increases significantly. For ammonia nitrogen, it can be seen that since the ammonia nitrogen concentration in the original reactor was 0, all ammonia nitrogen enters the reactor through the influent. As the influent flows, the ammonia nitrogen in the bottom of C1 rises rapidly, followed by C2. There is no change in C3 and C4 because the water filling ratio is 40%, and the influent does not reach the upper two sub-reactors. After aeration, the ammonia nitrogen in C1 and C4 mixes rapidly and gradually decreases to 0. This indicates that the aerobic granular sludge biological metabolism model and reactor module are functioning normally and achieving their intended effect.

[0270] The model values ​​studied in this invention are compared with those of the commonly used Biowin model, and the effectiveness of the simulated values ​​in this study is explained in conjunction with actual reactor operating conditions. For example... Figure 5As shown, after influent, the ammonia nitrogen in the biowin gradually increases, while the ammonia nitrogen in the actual effluent is essentially zero. This is because the biowin lacks a function similar to the reactor module, resulting in immediate and complete mixing of the influent, leading to discrepancies with actual results. During the aeration phase, the ammonia nitrogen in the biowin decreases significantly faster than in reality. This is because the biochemical reactions in the biowin do not account for the mass transfer gradient within the granules. In reality, the dissolved oxygen in the sludge inside the granules is very low or zero, preventing nitrification. The model studied in this invention matches the actual results, indicating that the biological metabolism module is functioning. Regarding nitrate, it can be seen that the nitrate in the biowin continuously decreases until it reaches zero. This is because the influent in the biowin is immediately and completely mixed and diluted, leading to denitrification. However, in reality, the effluent is not mixed with the influent, and no denitrification occurs because the sludge does not diffuse to the top layer; therefore, the effluent nitrate changes little. This model matches the actual results. During the low dissolved oxygen aeration stage, nitrates accumulate rapidly in the biowin, while the actual nitrate levels are not significantly different from those in the model of this invention. This is because a simultaneous nitrification and denitrification process exists, where nitrates are simultaneously converted into nitrogen gas. This indicates that the biowin lacks the relevant functions of a biological metabolism module and cannot effectively simulate the aerobic granular sludge process. In contrast, the modules in the model of this invention can effectively simulate aerobic granular sludge.

[0271] like Figure 6 As shown, the sludge discharge effect is compared using the method of this invention, Biowin, and actual results. It can be seen that the original sludge particles and flocs accounted for 62% and 38%, respectively. After 20 cycles, the results in this study were 68% and 32%, Biowin was 54% and 46%, while the actual results were 65% and 35%. This is because sludge discharge in Biowin is indiscriminate, with no difference in the probability of flocs and particles being discharged. However, the method of this invention distinguishes the difference in the probability of flocs and particles being discharged in the aerobic granular sludge process by using sludge and reactor modules. Therefore, the research results of this invention are more similar to the actual results.

[0272] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art can make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A biomathematical modeling and application of an aerobic granular sludge process, characterized in that, It includes the following steps: S1. Collect the parameter data required to construct the biomathematical model of the aerobic granular sludge process; S2. Based on the parameter data, establish a biomathematical model of aerobic granular sludge, which includes a granular sludge microbial metabolism module and a sludge migration module. S3. Based on the above-mentioned microbial metabolism module and sludge migration module of granular sludge, establish an aerobic granular sludge reactor model for the sequential batch operation of the influent, aeration, sedimentation and sludge discharge stages of the aerobic granular sludge process. S4. The aerobic granular sludge reactor model was constructed to simulate and optimize the aerobic granular sludge process. The optimized data included influent flow rate, aeration intensity and time, sludge discharge start-up time and duration.

2. The application as described in claim 1, characterized in that, The parameters required for the biomathematical model include influent water quality, sludge characteristics, and tank parameters; wherein, influent water quality includes influent nitrogen composition, phosphorus composition, and organic matter composition. The sludge characteristics include the particle size distribution of the sludge and the proportion and specific gravity of sludge within the defined particle size range; the sludge particles are grouped according to size into {0~200, 200~400, 400~800, 800~1200, 1200~1900, 1900~2000 and greater than 2000 μm}, and the sludge density and weight percentage of each group are measured, with the median value of the upper and lower limits of each group representing the average particle size of that group; sludge smaller than 200 micrometers is defined as flocculent sludge, and sludge larger than 200 micrometers is defined as granular sludge. The pool parameters include the pool drainage height H, the pool area A, and the sludge discharge pipe height Hp.

3. The application as described in claim 1, characterized in that, In step S2, the construction of the granular sludge microbial metabolic module includes the following steps: (1) Based on the sludge characteristics measured in step S1, i.e. sludge particle size, the sludge is divided into two parts: flocculent sludge with a particle size of less than 200 micrometers and granular sludge with a particle size of more than 200 micrometers. The internal mass transfer resistance of flocculent sludge was set to 0, and the changes in phosphorus, nitrogen and organic matter, as well as the change in the amount of sludge flocs themselves, were calculated based on ASMs activated sludge. For granular sludge larger than 200 micrometers, the sludge particles are modeled as spheres subdivided into N layers; the thickness of the outermost three layers is constant at 30 micrometers, and the thickness of the inner layer is Zin = (Rm - 3 × 30 / N - 3), where Rm is the particle radius; (2) Establish a reaction-diffusion coupling model to simulate the most typical concentric stratified structure of granular sludge, consisting of an aerobic outer layer and an anoxic / anaerobic inner layer, and the simultaneous nitrification-denitrification, denitrification, and efficient nitrogen and phosphorus removal phenomena achieved therefrom; for the change of concentration of any component i within the granules over time, the diffusion-reaction equation in the spherical coordinate system is as follows: ， in: C k The concentration of component k at the inner radius r of the particle; t: time r: Radial coordinate, determined according to the layering in the above steps, from the particle center to the surface, the thickness of the inner layer Zin = (Rm-3×30 / N-3). D k : The effective diffusion coefficient of component k within the particle; r k The growth or decay reaction rate of component k is calculated based on the ASM model matrix, with the core formula being r. k =Σ(ν kj ·ρ j ), where ν kj The stoichiometric coefficients and ρ of component k in the model matrix under process j j Let j be the rate expression for process j; (3) Based on the above reaction-diffusion coupling model, a differentiated classification modeling strategy is adopted to describe its material transformation process; For flocculent sludge, the biotransformation of phosphorus, nitrogen, and organic matter, as well as the dynamic changes in sludge quantity, are calculated based on the reaction kinetics of ASMs. For granular sludge, a reaction-diffusion coupling model is used: the granules are radially discretized into multiple shells, and diffusion and reaction terms are calculated in each layer. The diffusion term describes the interlayer transfer of the substrate based on Fick's law, where the substrate is dissolved oxygen, organic matter, nitrogen, and phosphorus. The reaction term calculates the changes in the concentration of each component, biomass growth, and decay based on ASMs kinetics.

4. The application as described in claim 1, characterized in that, The sludge migration module calculates the sludge migration process in the reactor separately for flocculent sludge and granular sludge; when the particle size of granular sludge is less than 200 micrometers, the migration process is calculated according to flocculent sludge, specifically the rising process during the influent process and the sedimentation process during the sedimentation stage are described by a conventional activated sludge settling model. When the particle size of granular sludge is greater than 200 micrometers, its movement and migration characteristics are described according to the granular sludge description: (1) Under influent conditions, granular sludge generates influent items. And two fluxes, the upward flux J generated by the "bottom inlet, top outlet" mode. up The gravity settlement flux caused by gravity settlement is J. sg ; Calculate according to the following formula: ； Among them, v in X represents the inlet water upflow velocity. k Q represents the concentration of particulate components k in the reaction tank. in Where A is the influent flow rate and A is the bottom area of ​​the reaction tank. ； Where v up X represents the top water outlet velocity. k Q represents the concentration of particulate components k in the reaction tank. e The effluent flow rate (Q in the aerobic granular sludge process) in =Q e A is the bottom area of ​​the reaction tank; ； Where v sg X represents the settling velocity of granular sludge. k The concentration of particulate matter k in the reaction tank; the settling velocity v of sludge particles with a particle size greater than 200 micrometers. sg The formula is as follows: ； Where g is the acceleration due to gravity, ρ s and ρ l Let d be the density of granular sludge and water, d be the diameter of the sludge particles, and C be the density of the granular sludge and water. d This is the drag coefficient; Drag coefficient C d It can be derived from the following formula, where Re is the Reynolds number, μ is the viscosity of water, and C... d =22.75×Re-0.7, Re=ρdv sg / μ, from which the gravitational settling velocity v is obtained. sg The formula is ； For granular sludge with a particle size of less than 200 micrometers, the gravity settling velocity v was calculated using a bi-exponential settling model. sg The formula is as follows: ； Where v'0 is the maximum settling velocity, v0 is the maximum theoretical velocity, and r h To interfere with the sedimentation parameters of the precipitate, r p f is the sedimentation parameter for slow sedimentation. ns The percentages representing non-sedimentation ratios are all parameters from the stratified sedimentation model; X floc,i X represents the concentration of particulate components in the flocculent sludge in the reaction tank. a,k The concentration of particulate components with a particle size of less than 200 micrometers in the influent layer of the reaction tank; (2) Under sedimentation conditions, granular sludge generates two fluxes. The gravity settling flux caused by gravity settling is J. sg The flux J caused by the discharge of residual sludge in the later stage dn Among them, gravity settling flux J sg The calculation formula is the same as above, sludge discharge loss flux J dn The formula is as follows: ； Where v dn X represents the sludge discharge rate. k Q represents the concentration of particulate component k in the reaction tank. w , where A is the sludge discharge flow rate and A is the bottom area of ​​the reaction tank.

5. The application as described in claim 1, characterized in that, The establishment of the sludge migration module includes the following steps: (1) Discretize the reactor with height H and area A into M layers along the vertical direction. Each layer is regarded as a completely mixed reactor with height z of H / M. They are named R1, R2, R3...Ri...RM from bottom to top. The height range of the sub-reactor Ri is {(i-1)×H / M~i×H / M}. The sub-reactor containing the sludge discharge pipe is Rw. The dynamic process of each stage in the reactor is simulated by calculating the sludge concentration and substrate concentration in each layer. (2) Based on the establishment of the microbial metabolism module and sludge migration module of granular sludge in step S2 above, according to the actual operation mode of aerobic granular sludge process: water inlet, water outlet, aeration, sedimentation and sludge discharge, the macroscopic aerobic granular sludge reactor model is integrated into three dynamic stages: water inlet-water outlet stage, aeration stage and sedimentation-sludge discharge stage aerobic granular sludge reactor model.

6. The application as described in claim 5, characterized in that, Modeling of aerobic granular sludge reactor in the influent-effect stage: A multi-scale coupled model was established to calculate the mass transfer within each granular layer, interlayer migration, and liquid phase material balance. The concentration of each layer and the effluent concentration were obtained by iterative solution.

7. The application as described in claim 5, characterized in that, The aerobic granular sludge reactor model for the aeration stage is simplified to a completely mixed reactor. Liquid relative flow and particle migration are ignored, and only the diffusion-reaction within the particles and the floc biochemical reaction are calculated. The solution is obtained by numerical integration.

8. The application as described in claim 5, characterized in that, The aerobic granular sludge reactor model for the sedimentation-sludge discharge stage is established by ignoring the diffusion-reaction process inside the granular sludge and the biochemical reaction process of the flocculent sludge, and only calculating gravity settling and sludge discharge flux, and solving the concentration changes of particulate components in each layer based on the stratified mass conservation principle.

9. The application as described in claim 1, characterized in that, The process for optimizing the influent flow rate is as follows: Set the filling ratio parameter, which is the ratio of the single influent volume to the total reactor volume, with a range of 20% to 50%; Set the influent time for each filling ratio, with a range of 20 to 60 minutes; Input the data into the aerobic granular sludge reactor model and run 10 to 15 cycles; Under the condition of meeting the treatment volume requirements, the parameter with the lowest effluent pollutant concentration is the preferred parameter; The optimized aeration process is as follows: The aeration stage is divided into low dissolved oxygen aeration and high dissolved oxygen aeration; the dissolved oxygen concentration range for low dissolved oxygen aeration is 0.1–1 mg / L; the optimization process for low dissolved oxygen aeration includes inputting dissolved oxygen parameters into the system and calculating the change in total nitrogen before and after 10 minutes of operation; selecting the dissolved oxygen concentration with the largest change in total nitrogen as the preferred dissolved oxygen concentration; inputting the optimal low dissolved oxygen parameters into the aerobic granular sludge reactor model and running it continuously; calculating the change in total nitrogen every 5 minutes of operation, and terminating the low dissolved oxygen aeration stage when the value is less than 5% of the initial total nitrogen concentration, the total low dissolved oxygen aeration operation time is the optimal low dissolved oxygen aeration time; then aeration is started with dissolved oxygen parameters of 1–2.5 mg / L; the time when the ammonia nitrogen in the aerobic granular sludge reactor model is lower than the target ammonia nitrogen concentration is the optimal high dissolved oxygen aeration time.

10. The application as described in claim 8, characterized in that, The sludge discharge process is optimized as follows: Determine the sludge discharge volume based on the sludge retention time; input the planned sludge discharge start time and duration into the system; the sludge discharge start time is the time from the start of the sedimentation stage to the start of sludge discharge; the sludge discharge start time is set to 10–45 minutes; the sludge discharge duration is 5–15 minutes; set the target sludge concentration in the reactor, and start sludge discharge when the sludge concentration is higher than the target value; run continuously for 20–50 cycles, and the parameter with the highest proportion of particles larger than 200 micrometers in the results is the preferred sludge discharge parameter.

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