A method for predicting concentration distribution in a thickener settling zone

Abstract

The present application relates to the technical field of concentration prediction, in particular to a kind of thickener sedimentation zone concentration distribution prediction method, comprising: constructing thickener numerical calculation model;Extract the solid phase pressure and solid phase volume fraction of each height plane of thickener after flow field stabilizes, construct interface characteristic index curve based on solid phase volume fraction and its gradient, construct pressure gradient curve based on solid phase pressure and solid phase volume fraction, find clarification point and gel point according to gradient change;According to clarification point and gel point, fluid model is divided into clarification zone, sedimentation zone and compression zone;According to clarification point height and gel point height, construct sedimentation zone normalized height variable in sedimentation zone, carry out nonlinear fitting according to sedimentation zone normalized height variable and solid phase volume fraction, construct sedimentation zone concentration distribution function, realize the concentration distribution prediction of thickener sedimentation zone.The present application accurately defines the boundary of sedimentation zone based on concentration gradient characteristics and pressure mutation characteristics.

Description

Technical Field

[0001] This invention relates to the field of concentration prediction technology, and specifically to a method for predicting the concentration distribution in the settling zone of a thickener. Background Technology

[0002] As a solid-liquid separation device based on the principle of gravity sedimentation, the thickener exhibits a typical three-layer structure in its internal flow field in the vertical direction: the top clarification zone is dominated by clear liquid, the middle sedimentation zone is the key area for the transition of particles from free sedimentation to interference sedimentation, and the bottom compression zone forms the particle skeleton structure. As the transition zone connecting the clarification and compression zones, the concentration distribution in the sedimentation zone directly affects the overflow mass and underflow discharge concentration. Accurately understanding the concentration distribution and boundary position of the sedimentation zone is crucial for optimizing the thickener's operating parameters. From a physical perspective, the upper and lower boundaries of the sedimentation zone correspond to the clarification point (the termination point of free sedimentation) and the gel point (the critical position where particles begin to form a continuous force network), respectively. Precise positioning of these two characteristic points is the theoretical basis for effective control of the sedimentation zone.

[0003] Existing technologies mainly employ a combination of laboratory static tests and online monitoring to assess the internal condition of thickeners. Static graduated cylinder sedimentation tests estimate sedimentation characteristics by visually observing changes in the mud layer interface, but they have inherent limitations, such as limited sample volume and inability to reflect dynamic changes under continuous operating conditions. Online monitoring systems typically deploy discrete measuring points such as pressure sensors and turbidimeters at different heights on the tank wall. For example, patent CN120079149A uses a wall turbidimeter to monitor suspended particle concentration, patent CN120208383A uses a gravity sensor to identify the interface of the clarification zone, and patent CN119827720A utilizes a lifting monitoring box to obtain concentration data at different heights. These methods generally suffer from three technical bottlenecks: First, the data gaps between discrete measurement points make it difficult to reconstruct a complete concentration distribution curve, especially with insufficient accuracy in capturing gradual gradients within the settling zone; second, conventional sensors can only acquire local absolute concentration values ​​and lack the ability to specifically identify clarification points and gel points that reflect abrupt changes in the stress state of particles; third, although computational fluid dynamics simulations can reconstruct multiphase flow fields across the entire domain, existing studies mostly focus on macroscopic parameter predictions and lack a systematic method for automatically extracting the boundary of the settling zone and establishing a mathematical model of the concentration distribution from simulation data, making it difficult to transform numerical simulation results into quantitative indicators required for engineering control. Summary of the Invention

[0004] To address the aforementioned technical problems of poor representativeness and monitoring blind spots in physical detection methods, difficulty in accurately capturing the physical boundaries of the settling zone, and low utilization rate of existing numerical simulation results, this invention provides a method for predicting the concentration distribution in the settling zone of a thickener. This invention, without relying on a multi-point sensor layout inside the tank, utilizes pressure and concentration field data obtained from numerical simulation. By identifying interface characteristic indices and abrupt changes in solid-phase pressure gradients, it determines the clarifying point and gel point, thereby clarifying the effective height range of the settling zone. Based on this, a mathematical descriptive model of the concentration distribution in the settling zone is established, enabling rapid prediction and quantitative characterization of the settling zone state, providing a basis for the operation and control of the thickener.

[0005] The technical means employed in this invention are as follows:

[0006] A method for predicting the concentration distribution in the settling zone of a thickener includes the following steps:

[0007] A numerical calculation model of a thickener is constructed, which includes a thickener fluid domain model and a solution control model. The solution control model considers a gas-liquid-solid three-phase flow model and a particle flow model. The particle flow model adopts particle kinetic theory based on particle temperature.

[0008] A numerical model of the thickener is run to extract the solid pressure and solid volume fraction at each height plane of the thickener after the flow field stabilizes. An interface characteristic index curve is constructed based on the solid volume fraction and its gradient. The first main peak position is found on the interface characteristic index curve and determined as the clarification point. A solid pressure gradient curve is constructed based on the solid pressure and solid volume fraction. The position of the maximum main peak is found on the solid pressure gradient curve and determined as the gel point. The clarification point is the boundary between the clarification zone and the sedimentation zone, and the gel point is the boundary between the sedimentation zone and the compression zone.

[0009] Based on the clarification point and the gel point, the internal flow field of the thickener is divided into a clarification zone, a settling zone, and a compression zone;

[0010] Based on the clarification point height and gel point height in the settling zone, a normalized height variable for the settling zone is constructed. Then, a nonlinear fitting is performed on the normalized height variable and the solid volume fraction to construct a concentration distribution function for the settling zone, thereby enabling the prediction of the concentration distribution in the settling zone of the thickener.

[0011] Furthermore, based on the principles of mass conservation and residual stability, the relative deviation of the mass-weighted average flow rate between the thickener's horizontal cross-sections at different heights and the feed inlet is used to determine whether flow field stability has been achieved. The formula for calculating the relative deviation is as follows:

[0012]

[0013] in, This is a relative deviation. The mass-weighted average flow rate is the flow rate at the cross-sectional height. The quality-weighted average flow rate at the feed inlet. This is the index for the section height.

[0014] Furthermore, the calculation process of the interface feature index curve includes:

[0015] The interface characteristic index curve is defined as the reciprocal modulus of the solid volume fraction gradient, and the initial solid volume fraction gradient curve is calculated using the following formula:

[0016]

[0017] in, This is the initial solid volume fraction gradient curve. In order to be in The gradient of solid volume fraction at a point as a function of thickener height. This represents the increase in the volume fraction of the solid phase. For the first solid volume fraction For the first solid volume fraction For the increase in the height of the thickener, For the first The height of the dense machine, For the first The height of the dense machine, Index of the extracted data points;

[0018] After smoothing the initial solid volume fraction gradient curve, the solid volume fraction gradient curve is obtained.

[0019] Based on the solid phase volume fraction gradient curve, the interface characteristic index curve is obtained:

[0020]

[0021] in, This is the interface feature index curve. This is the solid volume fraction gradient curve. It is a positive number.

[0022] Furthermore, the calculation process for the solid-phase pressure gradient curve includes:

[0023] An initial solid-phase pressure gradient curve is constructed based on the aforementioned solid-phase pressure and solid-phase volume fraction. The calculation formula for the initial solid-phase pressure gradient curve is as follows:

[0024]

[0025] in, This is the initial solid-phase pressure gradient curve. In order to be in The gradient of solid pressure at a point as a function of solid volume fraction. For the solid phase pressure increment, This represents the increase in the volume fraction of the solid phase. For the first Solid-phase pressure, For the first Solid-phase pressure, For the first solid volume fraction For the first solid volume fraction Index of the extracted data points;

[0026] After smoothing the initial solid pressure gradient curve, the solid pressure gradient curve is obtained.

[0027] Furthermore, the formula for calculating the solid volume fraction at the clarification point is:

[0028]

[0029] in, The solid volume fraction at the clarification point. This represents the volume fraction of the solid phase. The interface feature exponential curve function is used, and the clarification point height is calculated by interpolation.

[0030] Furthermore, the formula for calculating the solid volume fraction of the gel point is:

[0031]

[0032] in, The solid volume fraction at the gel point. This represents the volume fraction of the solid phase. The pressure gradient curve function is used to calculate the height of the gel point through interpolation.

[0033] Furthermore, the formula for calculating the normalized height variable of the settlement zone is as follows:

[0034]

[0035] in, For the normalized height variable of the settlement zone, For the height of the thickener, For the clarification point height, This represents the gel point height.

[0036] Furthermore, using the inverse function form of the Hill normalized model, based on the normalized height variable of the settlement zone, the concentration distribution function of the settlement zone is calculated. The formula for calculating the concentration distribution function of the settlement zone is as follows:

[0037]

[0038] in, Let be the concentration distribution function in the settling zone. For the inflection point position parameters, The steepness of the curve, This represents the volume fraction of the solid phase. The solid volume fraction at the gel point. The solid volume fraction at the clarification point.

[0039] Furthermore, the clarifying point and gel point can divide the internal flow field of the thickener into a clarifying zone, a settling zone, and a compression zone. The area above the clarifying point is the clarifying zone, located in the upper part of the thickener; the area from the clarifying point to the gel point is the settling zone, located in the middle part of the thickener; and the area below the gel point is the compression zone, located in the lower part of the thickener.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. This invention explicitly introduces a particle flow model based on particle kinetics into the numerical simulation of multiphase flow in a thickener. Solid pressure is used as a key physical quantity to characterize the stress state of particles. The distribution characteristics of solid pressure with solid volume fraction are obtained, which are used to characterize the stress differences in each zone and provide a mechanical basis for distinguishing between the clarification zone, the settling zone and the compression zone.

[0042] 2. This invention innovatively uses the interface characteristic index and the solid phase pressure gradient abrupt change feature to define the physical boundary of the thickener settling zone: the first characteristic abrupt change of the interface characteristic index function is used to determine the clarification point, that is, the interface between the clarification zone and the settling zone; the maximum gradient abrupt change of the solid phase pressure is used to determine the gel point, that is, the interface between the settling zone and the compression zone, so as to automatically and accurately identify the upper and lower boundaries of the settling zone based on the physical nature in the numerical simulation results.

[0043] 3. This invention performs nonlinear fitting on the solid volume fraction data between the clarification point and the gelation point to construct a concentration distribution function in the sedimentation zone, and combines it with a visualization interface to transform the numerical results into graphical information that can be directly used for engineering operation control.

[0044] Compared with existing boundary determination methods that rely on empirical concentration thresholds or local sensor measurement points, this invention utilizes the essential abrupt change characteristics of multi-physics parameters to identify boundaries. Specifically, it identifies the settling point and gel point by using the abrupt change in the solid phase volume fraction and solid phase pressure gradient, avoiding subjective errors caused by simply relying on concentration thresholds or empirical judgments. This makes the determination of the upper and lower boundaries of the settling zone more consistent with the mechanisms of fluid mechanics and particle kinetics. Simultaneously, this invention directly outputs the concentration-height-pressure distribution inside the thickener based on numerical calculations and software processing. It eliminates the need for multi-layer sensor arrays or expensive tomographic scanning equipment inside the tank, allowing for a direct presentation of the effective height and concentration distribution of the settling zone on the display terminal, providing a reference for adjusting the underflow pump speed and feed rate. Furthermore, this invention obtains a settling zone concentration distribution model that reflects the concentration variation with height under actual operating conditions by performing nonlinear fitting on the concentration data between the settling point and gel point. This overcomes the traditional simplistic assumption of treating the settling zone concentration as a constant value, improving the accuracy and applicability of thickener operation state prediction.

[0045] Based on the above reasons, this invention can be widely applied in fields such as concentration prediction. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating a method for predicting the concentration distribution in the settling zone of a thickener according to the present invention.

[0048] Figure 2 This is a schematic diagram of the fluid domain division of the thickener of the present invention.

[0049] Figure 3(a) is a relative deviation diagram of the present invention.

[0050] Figure 3(b) is a cloud map showing the simulation effect of the present invention.

[0051] Figure 4(a) is a graph showing the relationship between concentration, altitude, and pressure in an embodiment of the present invention.

[0052] Figure 4(b) is a schematic diagram of the feeding process of the present invention.

[0053] Figure 5 This is a schematic diagram of the interface feature index and pressure gradient curve of the present invention.

[0054] Figure 6 This is a schematic diagram of the concentration distribution function in the sedimentation zone of this invention.

[0055] Figure 7 This is a flowchart illustrating the visualization function of the sedimentation zone concentration distribution function in this invention.

[0056] Figure 8 This is a schematic diagram illustrating the evaluation error of the concentration distribution function in the sedimentation zone according to the present invention. Detailed Implementation

[0057] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0058] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0059] like Figure 1 As shown, this invention provides a method for predicting the concentration distribution in the settling zone of a thickener, comprising the following steps:

[0060] S1. Construct a numerical calculation model for the thickener. The numerical calculation model for the thickener includes a fluid domain model and a solution control model. The solution control model considers a three-phase flow model of gas, liquid, and solid and a particle flow model. The particle flow model adopts particle kinetic theory based on particle temperature.

[0061] Furthermore, the dense mechanical fluid domain model includes a geometric model and mesh generation;

[0062] The geometric model is strictly based on the actual size parameters of the thickener on site. The feed well and barrel are generated separately using 3D modeling software. Geometric components with little impact on the internal flow field are omitted, and the features of the simplified geometric model are grouped and classified.

[0063] The mesh generation includes the feed well mesh and the barrel mesh. During feed well mesh generation, the portion of the feed pipe tangentially entering the feed well undergoes special segmentation, improving the mesh quality to above 0.5. The barrel mesh generation employs a multi-layer O-shaped meshing method to ensure the generation of a high-quality structured mesh. The surfaces where the feed well and barrel contact each other undergo topological processing, and the meshes are merged using the Interface method. Data is transferred through interpolation, ultimately generating a high-quality structured mesh for the entire thickener. Figure 2 As shown.

[0064] Furthermore, the gas-liquid-solid three-phase flow model includes the Eulerian-Eulerian multiphase flow model, the RNG k-ε turbulence model, and an extensible wall function, comprehensively considering the independent adjustability and correlation of parameter settings;

[0065] The Eulerian-Eulerian multiphase flow model can treat the solid and liquid phases as a continuous medium that permeates each other, and directly solve for the volume fraction, velocity field and pressure field of each phase. It describes the floc settling and compaction process of high solid content and strong interphase coupling while greatly reducing the amount of computation.

[0066] The RNG k-ε turbulence model can balance computational efficiency and accuracy, and is especially suitable for simulating strong swirling flow, high shear zone near the thickener feed well, and complex turbulent structures with separation and backflow inside the barrel.

[0067] The scalable wall function can employ logarithmic near-wall processing when the dimensionless distance y+ in the first layer of the wall mesh is in the range of 30~300. It also sets a lower limit protection when the local mesh is too fine and y+ is below the critical value, ensuring that the calculation of wall shear stress and turbulent flow remains physically reasonable. Thus, under the condition of large-scale dense and non-uniform mesh, it significantly improves the robustness and convergence stability of numerical simulation.

[0068] Furthermore, the constitutive relations of particle temperature-based particle kinetics (KTGF) include physical property parameters such as solid-phase shear viscosity, bulk viscosity, solid pressure, friction viscosity, and friction pressure, which are used to characterize the rheological behavior of solid particles in collision-dominated and friction-dominated regions.

[0069] The solid-phase shear viscosity was modeled using the Gidaspow model, while the particle bulk viscosity, solid pressure, and radial distribution function were modeled using the kinetic model proposed by Lun et al. The particle temperature was determined using a closed-loop algebraic equation, the frictional viscosity using the Schaeffer model, and the frictional pressure using a frictional pressure model based on particle kinetics. The particle packing limit, frictional packing limit, and internal friction angle of the solid phase were set according to the material characteristics (e.g., packing limit approximately 0.60~0.65°, frictional packing limit approximately 0.58~0.62°, and internal friction angle approximately 25°~35°). This ensures that the solid-phase pressure and equivalent viscosity can increase continuously and non-linearly as the solid volume fraction changes from a dilute phase to a near-packed state, thus more realistically reflecting the floc compaction and skeleton bearing behavior during the transition from the thickener settling zone to the compression zone.

[0070] S2. Run the thickener numerical calculation model, extract the solid phase pressure and solid phase volume fraction at each height plane of the thickener after the flow field stabilizes, construct the interface characteristic index curve based on the solid phase volume fraction and the solid phase volume fraction gradient, find the first main peak position in the interface characteristic index curve and determine it as the clarification point; construct the solid phase pressure gradient curve based on the solid phase pressure and solid phase volume fraction, find the maximum main peak position in the high concentration region of the solid phase pressure gradient curve and determine it as the gel point; the clarification point is the boundary between the clarification zone and the sedimentation zone, and the gel point is the boundary between the sedimentation zone and the compression zone.

[0071] Furthermore, the flow field stability criteria include convergence analysis of the solution process and relative deviation analysis of the mass-weighted average flow rate across multiple cross sections;

[0072] Convergence analysis showed that the sum of the inlet and outlet mass flow rates was approximately zero, the mass conservation equation, and the residual fluctuation of the continuity equation was less than 1 × 10⁻⁶. -3 The residual is stable;

[0073] Relative deviation analysis involves setting up sampling planes at predetermined heights in the vertical direction of the thickener, calculating the mass flow rate of each sampling plane, and considering the flow field to be stable when the relative deviation between the mass flow rate of each sampling plane and the inlet mass flow rate is within a set threshold.

[0074] Specifically, relative deviation can quantitatively determine whether the flow field has reached a steady state. A sampling plane is set at a predetermined height (e.g., 2 m) in the vertical direction to cover the height range of the thickener and is compared with the mass-weighted average flow rate of the inlet section. When the relative deviation of the mass-weighted average flow rate of each plane is within a set threshold (e.g., 10%) and remains within a certain period of time, the flow field can be considered to have reached a steady state. The relative deviation of the mass-weighted average flow rate of the section shows large oscillations in the early stage of the simulation, and shows a damping decay trend as the calculation progresses, eventually converging within the set threshold, indicating that the flow field has reached statistical stability. Figure 3(a) is the relative deviation diagram, and Figure 3(b) is the simulation effect cloud diagram.

[0075] The formula for calculating the quality-weighted average is:

[0076]

[0077]

[0078] in, A discrete mass-weighted average of a certain physical quantity; i The index of the face element; Bulk density; Volume velocity; The area of ​​the face element; Porosity of the medium; j For the index of phase, , , They represent the first j Volume fraction, density, and velocity components of the normal phase;

[0079] The formula for calculating relative deviation is:

[0080]

[0081] in, This is a relative deviation; Cross-section height Quality-weighted average flow rate; The mass-weighted average flow rate at the feed inlet; This is the index for the section height.

[0082] Furthermore, the boundary delineation of the settling zone based on physical properties includes the determination of the clarification point and the gel point. Solid volume fraction and solid pressure data are extracted from the central axis of the thickener, and a concentration-height-pressure correlation curve is established, as shown in Figure 4(a). It can be clearly observed that in the upper clarification zone, the solid pressure curve is close to the zero axis, indicating that the particles are in a suspended state of free or interfered settling. However, after reaching a certain critical depth (gel point), the solid pressure exhibits an exponential increase, indicating the formation of a contact skeleton between the particles. This significant pressure stratification characteristic verifies the reliability of using the abrupt change in solid pressure as the physical criterion for defining the lower boundary of the settling zone; Figure 4(b) shows the feed diagram.

[0083] The determination of the clarifying point and the gel point is based on the physical characteristics of the abrupt change in the solid phase volume fraction gradient and the solid phase pressure gradient: the clarification point is determined by the first characteristic abrupt change of the interface characteristic exponential function, that is, the interface between the clarifying zone and the sedimentation zone; the gel point is determined by the abrupt change point of the solid phase pressure gradient in the high concentration region, that is, the interface between the sedimentation zone and the compression zone.

[0084] In the specific algorithm implementation, the interface feature exponential function is calculated. and solid-phase pressure gradient curve The first main peak of the interface characteristic index curve was selected as the clarifying point, and the position of the maximum main peak of the solid phase pressure gradient was selected as the gel point. The solid volume fraction and height corresponding to the clarifying point are denoted as follows: , The solid volume fraction and height corresponding to the gel point are denoted as follows: , ,like Figure 5 As shown;

[0085] Based on the abrupt change in solid pressure, the solid pressure and solid volume fraction corresponding to the height sequence are extracted based on the central axis. The data are monotonically sorted according to the solid volume fraction, and the initial solid volume fraction gradient curve and the initial pressure gradient curve are constructed by the difference between adjacent points.

[0086] The initial solid volume fraction gradient curve can be obtained by the following formula:

[0087]

[0088] in, This is the initial solid volume fraction gradient curve. In order to be in The gradient of solid volume fraction at a point as a function of thickener height. This represents the increase in the volume fraction of the solid phase. For the first solid volume fraction For the first solid volume fraction For the increase in the height of the thickener, For the first The height of the dense machine, For the first The height of the dense machine, Index of the extracted data points;

[0089] To reduce differential noise, the Loess method was used to smooth the initial solid volume fraction gradient curve, resulting in the solid volume fraction gradient curve. ;

[0090] The interface feature index curve can be obtained by the following formula:

[0091]

[0092] in, For interface feature index curves; This is the solid phase volume fraction gradient curve; To prevent tiny positive numbers with a denominator of zero;

[0093] The initial pressure gradient curve can be obtained by the following formula:

[0094]

[0095] in, This is the initial solid-phase pressure gradient curve. In order to be in The gradient of solid pressure at a point as a function of solid volume fraction. For the solid phase pressure increment, This represents the increase in the volume fraction of the solid phase. For the first Solid-phase pressure, For the first Solid-phase pressure, For the first solid volume fraction For the first solid volume fraction Index of the extracted data points;

[0096] To reduce differential noise, the Savitzky-Golay method is used to smooth the initial pressure gradient curve, resulting in the pressure gradient curve. .

[0097] Furthermore, the formula for calculating the solid volume fraction at the clarification point is:

[0098]

[0099] in, For interface feature exponential curve function; The solid volume fraction at the clarification point, i.e., the interfacial characteristic exponential curve function. The concentration at which the first local maximum value is achieved; This represents the volume fraction of the solid phase.

[0100] Furthermore, the formula for calculating the solid volume fraction at the gel point is:

[0101]

[0102] in, This is a function representing the pressure gradient curve; The solid volume fraction at the gel point, i.e., the pressure gradient curve function. The concentration corresponding to the maximum value; This represents the volume fraction of the solid phase.

[0103] S3. Based on the clarifying point and gel point, the internal flow field of the thickener is divided into a clarifying zone, a settling zone, and a compression zone.

[0104] Furthermore, the gel point height and clearing point height can be obtained by interpolation. Using the clearing point height... With gel point height Using this as a boundary, the interior of the thickener can be divided sequentially along the height direction into a clarification zone, a settling zone, and a compression zone: among which... The upper region is the clarification zone, where the solid volume fraction is close to the clear liquid value and the solid pressure is approximately zero. The central region is a settling zone, where the solid volume fraction continuously increases with height, and the solid pressure remains at a low level. The lower region is the compression zone, where the solid volume fraction is close to the packing limit and the solid pressure increases significantly.

[0105] S4. Based on the gel point height and clarification point height, a normalized height variable for the settling zone is constructed. Based on the normalized height variable for the settling zone and the solid volume fraction, a nonlinear fitting is performed to construct the concentration distribution function for the settling zone, so as to predict the concentration distribution in the settling zone of the thickener.

[0106] Furthermore, at the clarification point height With gel point height Define the normalized height variable of the settlement zone as the upper and lower boundaries of the settlement zone. for:

[0107]

[0108] in, The normalized height variable for the settlement zone is defined in the range [0,1]. For the height of the thickener; The height of the thickener corresponding to the clarification point; This represents the height of the thickener corresponding to the gel point.

[0109] Furthermore, within the settlement zone, the volume fraction... Normalized height variable of settlement zone The relationship is nonlinearly fitted to construct a sedimentation zone concentration distribution function. Since the sedimentation zone concentration monotonically increases with height and gradually approaches the saturation characteristic of the gel point concentration, this invention uses a nonlinear function with inverse S-shaped evolution characteristics to construct a sedimentation zone concentration distribution model. This type of model can... and The boundary conditions between the gel point and the clarifying point must be strictly satisfied.

[0110] In this embodiment, the inverse function form of the Hill normalized model is preferred. This model can achieve stable fitting and repeatable prediction of the concentration distribution in the settling area with a small number of parameters. The formula for calculating the concentration distribution function in the settling area is as follows:

[0111]

[0112] in, This is the concentration distribution function in the settling zone; The inflection point position parameter is used to characterize the relative position of the rapid concentration growth zone within the sedimentation zone, and its range is defined as (0,1). The steepness of the curve is used to characterize the nonlinear characteristics of the concentration growth rate in the settling zone, and its range is defined as follows: , This represents the volume fraction of the solid phase. The solid volume fraction at the gel point. The solid volume fraction at the clarification point.

[0113] Data from sampling of the subsidence area Determine parameters by performing least squares fitting. and Thus, a continuous distribution expression for the concentration in the settling zone as a function of height is obtained. ,like Figure 6 As shown.

[0114] S5. Using programming languages ​​and their scientific computing libraries, the underlying algorithm is constructed, encapsulating the aforementioned boundary definition logic and fitting model. A visual interactive interface is developed. After the user inputs basic operating parameters, the system automatically calls the background model to plot the concentration distribution curve inside the thickener on the interface, clearly identifying the dynamic boundaries of the settling zone, clarification zone, and compression zone, achieving visualized monitoring of the internal structure. Figure 7 As shown.

[0115] Furthermore, the model encapsulation includes a backend logic building module, a frontend UI design module, a frontend-backend integration module, a testing and optimization module, and a deployment and release module;

[0116] The backend logic building module relies on scientific computing libraries (such as Math, NumPy, MapleLib, etc.) to encapsulate the underlying algorithms, boundary definition logic, and fitting models in code.

[0117] The front-end UI design module is based on initialization UI (such as Qt5, QtWidgets, etc.) development tools to complete the layout and rendering configuration of the visual interactive interface;

[0118] The front-end and back-end integration module achieves functional linkage between the back-end computing logic and the front-end interactive interface through signal mechanism connection, data format conversion, and boundary processing module docking.

[0119] The testing and optimization module sequentially conducts unit testing and boundary prototype testing, and optimizes performance based on test feedback to ensure the stability of system functions;

[0120] The deployment and release module generates the system executable file, creates the installation package, and completes the final deployment of the system.

[0121] Furthermore, through a visual interface, error analysis is performed on the fitting model of the density distribution of the concentrator based on boundary identification and the theoretical model, such as... Figure 8 As shown. Simultaneously, the mean absolute error, root mean square error, and coefficient of determination are calculated. Sensitivity tests are performed on the gradient smoothing window length, peak filtering threshold, and the range of fitting parameters. When the error index exceeds the preset threshold, the system automatically adjusts the smoothing and fitting parameters and recalculates, thereby improving the robustness and repeatability of boundary identification and concentration distribution prediction.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the concentration distribution in the settling zone of a thickener, characterized in that, Includes the following steps: A numerical calculation model of a thickener is constructed, which includes a thickener fluid domain model and a solution control model. The solution control model considers a gas-liquid-solid three-phase flow model and a particle flow model. The particle flow model adopts particle kinetic theory based on particle temperature. A numerical model of the thickener is run to extract the solid pressure and solid volume fraction at each height plane of the thickener after the flow field stabilizes. An interface characteristic index curve is constructed based on the solid volume fraction and its gradient. The first main peak position is found on the interface characteristic index curve and determined as the clarification point. A solid pressure gradient curve is constructed based on the solid pressure and solid volume fraction. The position of the maximum main peak is found on the solid pressure gradient curve and determined as the gel point. The clarification point is the boundary between the clarification zone and the sedimentation zone, and the gel point is the boundary between the sedimentation zone and the compression zone. Based on the clarification point and the gel point, the internal flow field of the thickener is divided into a clarification zone, a settling zone, and a compression zone; Based on the clarification point height and gel point height in the settling zone, a normalized height variable for the settling zone is constructed. Then, a nonlinear fitting is performed on the normalized height variable and the solid volume fraction to construct a concentration distribution function for the settling zone, thereby enabling the prediction of the concentration distribution in the settling zone of the thickener.

2. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, Based on the principles of mass conservation and residual stability, the relative deviation of the mass-weighted average flow rate between the thickener's horizontal cross-sections at different heights and the feed inlet is used to determine whether flow field stability has been achieved. The formula for calculating the relative deviation is as follows: in, This is a relative deviation. The mass-weighted average flow rate is the flow rate at the cross-sectional height. The quality-weighted average flow rate at the feed inlet. This is the index for the section height.

3. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, The calculation process of the interface feature index curve includes: The interface characteristic index curve is defined as the reciprocal modulus of the solid volume fraction gradient, and the initial solid volume fraction gradient curve is calculated using the following formula: in, This is the initial solid volume fraction gradient curve. In order to be in The gradient of solid volume fraction at a point as a function of thickener height. This represents the increase in the volume fraction of the solid phase. For the first solid volume fraction For the first solid volume fraction For the increase in the height of the thickener, For the first The height of the dense machine, For the first The height of the dense machine, Index of the extracted data points; After smoothing the initial solid volume fraction gradient curve, the solid volume fraction gradient curve is obtained. Based on the solid phase volume fraction gradient curve, the interface characteristic index curve is obtained: in, This is the interface feature index curve. This is the solid volume fraction gradient curve. It is a positive number.

4. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, The calculation process for the solid-phase pressure gradient curve includes: An initial solid-phase pressure gradient curve is constructed based on the aforementioned solid-phase pressure and solid-phase volume fraction. The calculation formula for the initial solid-phase pressure gradient curve is as follows: in, This is the initial solid-phase pressure gradient curve. In order to be in The gradient of solid pressure at a point as a function of solid volume fraction. For the solid phase pressure increment, This represents the increase in the volume fraction of the solid phase. For the first Solid-phase pressure, For the first Solid-phase pressure, For the first solid volume fraction For the first solid volume fraction Index of the extracted data points; After smoothing the initial solid pressure gradient curve, the solid pressure gradient curve is obtained.

5. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, The formula for calculating the solid volume fraction at the clarification point is: in, The solid volume fraction at the clarification point. This represents the volume fraction of the solid phase. The interface feature exponential curve function is used, and the clarification point height is calculated by interpolation.

6. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, The formula for calculating the solid volume fraction of the gel point is: in, The solid volume fraction at the gel point. This represents the volume fraction of the solid phase. The pressure gradient curve function is used to calculate the height of the gel point through interpolation.

7. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, The formula for calculating the normalized height variable of the settlement zone is: in, For the normalized height variable of the settlement zone, For the height of the thickener, For the clarification point height, This represents the gel point height.

8. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, Using the inverse function form of the Hill normalized model, and based on the normalized height variable of the settlement zone, the concentration distribution function of the settlement zone is calculated. The formula for calculating the concentration distribution function of the settlement zone is as follows: in, Let be the concentration distribution function in the settling zone. For the inflection point position parameters, The steepness of the curve, This represents the volume fraction of the solid phase. The solid volume fraction at the gel point. The solid volume fraction at the clarification point.

9. The method for predicting concentration distribution in the settling zone of a thickener according to claim 1, characterized in that, The clarifying point and gel point can divide the internal flow field of the thickener into a clarifying zone, a settling zone, and a compression zone. The area above the clarifying point is the clarifying zone, located in the upper part of the thickener. The area from the clarifying point to the gel point is the settling zone, located in the middle of the thickener. The area below the gel point is the compression zone, located in the lower part of the thickener.

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