A pipeline fouling analysis method, device and electronic equipment

Abstract

The application provides a pipeline fouling analysis method and device and electronic equipment, and relates to the technical field of pipeline fouling analysis. The pipeline fouling analysis method comprises the following steps: based on smooth particle hydrodynamics, constructing a steady-state velocity field of fluid in a pipeline according to obtained pipeline characteristic data; based on near-field dynamics, constructing a reaction transport model of solute in the pipeline according to the steady-state velocity field; obtaining a converted solid-state material point through threshold comparison according to a solid-phase concentration output by the reaction transport model; and obtaining fouling data of the pipeline through geometric measurement according to all the converted solid-state material points. The application can improve the accuracy of pipeline fouling analysis.

Description

Technical Field

[0001] This invention relates to the field of pipe scaling analysis technology, and more specifically, to a pipe scaling analysis method, apparatus, and electronic equipment. Background Technology

[0002] Pipeline scaling is a common engineering problem in oil, natural gas, chemical, and water transportation systems. During oil and gas extraction and transportation, fluids often contain high concentrations of scale-forming ions such as calcium, magnesium, and carbonate. When conditions such as temperature, pressure, and flow rate change, these ions are prone to supersaturation and precipitation, forming inorganic salt scale layers such as calcium carbonate and calcium sulfate on the inner wall of the pipeline. The continuous accumulation of scale layers leads to a reduction in the effective flow cross-sectional area of ​​the pipeline, an increase in flow resistance, and a decrease in transportation efficiency. In severe cases, it can even cause pipeline blockage, equipment failure, and safety accidents.

[0003] In related technologies, existing pipe scaling analysis is usually based on analytical models that assume macroscopic continuity. Because the scaling process is simplified to uniform deposition or one-dimensional growth, the analysis results obtained by simplified one-dimensional deposition calculations or empirical formulas deviate from the actual scaling data of the pipe, affecting the accuracy of scaling analysis. Summary of the Invention

[0004] The problem addressed by this invention is how to improve the accuracy of pipe scaling analysis.

[0005] To address the above problems, this invention provides a method, apparatus, and electronic device for analyzing pipe scaling.

[0006] In a first aspect, the present invention provides a method for analyzing pipe scaling, comprising: Based on smooth particle fluid dynamics, a steady-state velocity field of the fluid inside the pipe is constructed according to the acquired pipe feature data; Based on peri-field dynamics, a reaction transport model of solute in the pipeline is constructed according to the steady-state velocity field. The conversion point of the solid material is obtained by comparing the solid phase concentration output by the reaction transport model with a threshold. The scaling data of the pipeline is obtained through geometric measurements based on all the converted solid material points.

[0007] Optionally, the pipeline characteristic data includes pipeline geometric parameters, physical property parameters, and numerical discrete parameters; the step of constructing the steady-state velocity field of the fluid inside the pipeline based on the acquired pipeline characteristic data includes: A coupled discrete model of the pipeline is constructed based on the pipeline geometric parameters and the numerical discrete parameters. Based on a preset viscous relaxation solver, the steady-state velocity field is obtained according to the pipeline coupled discrete model, the physical property parameters, and the numerical discrete parameters.

[0008] Optionally, the construction process of the pipeline coupling discrete model includes: A pipeline model is constructed based on the pipeline geometry parameters, and the fluid domain and solid domain of the pipeline model are determined. Based on the smooth particle spacing in the numerical discrete parameters, smooth particles are uniformly distributed in the fluid domain and the solid domain, and the smooth particles in the fluid domain are assigned fluid particle properties, and the smooth particles in the solid domain are assigned wall particle properties. Based on the material point spacing in the numerical discretization parameters, material points are uniformly distributed in the fluid domain and the solid domain, and liquid point attributes are assigned to liquid material points in the fluid domain and solid point attributes are assigned to solid material points in the solid domain.

[0009] Optionally, the pipeline characteristic data further includes inlet concentration parameters; the process of constructing the reaction transport model includes: Based on the normalized interpolation method, the steady-state velocity field is interpolated from the smooth particle to the liquid material point; The initial liquid phase concentration is assigned to the liquid material points in the inlet region of the pipeline coupled discrete model based on the inlet concentration parameter.

[0010] Optionally, the step of obtaining the conversion solid material point by comparing the solid phase concentration output from the reaction transport model with a threshold includes: Based on a preset time step, the reaction transport model is controlled to perform simulation to obtain the solid phase concentration of the liquid material point; Based on the threshold comparison result of the solid phase concentration, the corresponding liquid material point is subjected to liquid-solid conversion to obtain the converted solid material point.

[0011] Optionally, the step of performing liquid-solid conversion on the corresponding liquid material point based on the threshold comparison result of the solid phase concentration to obtain the converted solid material point includes: The corresponding solid volume fraction is obtained by comparing the solid concentration at the liquid material point with the preset maximum equivalent solid concentration. The liquid material point is judged to meet the liquid-solid conversion condition based on the comparison result between the solid volume fraction and the preset conversion threshold. If so, the liquid material point is converted from a fluid state to a solid state to obtain the converted solid material point.

[0012] Optionally, determining whether the liquid material point meets the liquid-solid conversion condition based on the comparison result of the solid volume fraction and the preset conversion threshold includes: When the solid volume fraction is greater than the preset conversion threshold, it is determined that the liquid material point satisfies the liquid-solid conversion condition. When the solid volume fraction is less than or equal to the preset conversion threshold, it is determined that the liquid material does not meet the liquid-solid conversion condition.

[0013] Optionally, obtaining the scaling data of the pipe through geometric measurement based on all the converted solid material points includes: The corresponding equivalent blockage thickness is obtained by summing the characteristic dimensions of the converted solid material points in the wall normal of the pipe. The remaining flow area of ​​the pipeline is obtained by statistical analysis of the area occupancy based on the spatial distribution of all the converted solid material points. The scaling mass is obtained by summing and integrating the solid phase concentration and characteristic volume of all the aforementioned solid material points. The scaling data is generated based on the equivalent blockage thickness, the remaining flow area, and the scaling quality.

[0014] Secondly, the present invention provides a pipe scaling analysis device, comprising: The module is used to construct the steady-state velocity field of the fluid inside the pipe based on the acquired pipe feature data, using smooth particle fluid dynamics. The modeling module is used to construct a reaction transport model of solute in the pipeline based on near-field dynamics and the steady-state velocity field. The conversion module is used to obtain the conversion point of the solid material by comparing the solid phase concentration output by the reaction transport model with a threshold. The measurement module is used to obtain the scaling data of the pipeline through geometric measurement based on all the converted solid material points.

[0015] Thirdly, the present invention provides an electronic device, including a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the pipe scaling analysis method as described in the first aspect when executing the computer program.

[0016] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the pipe scaling analysis method as described in the first aspect.

[0017] The beneficial effects of the pipe scaling analysis method of the present invention are as follows: Based on smooth particle fluid dynamics, a steady-state velocity field of the fluid inside the pipe is constructed, which can accurately capture the details of fluid motion and velocity gradient distribution under complex pipe geometric boundaries, providing high-fidelity flow field boundary conditions for subsequent analysis; based on near-field dynamics, a solute reaction transport model is constructed using the steady-state velocity field, overcoming the singularity problem of traditional continuum mechanics methods in dealing with discontinuous solute diffusion and reaction, and using its nonlocal action concept to more accurately describe the microscopic migration and chemical evolution behavior of solute driven by the flow field; by comparing solid phase concentration thresholds to determine the conversion solid material point, the critical state of solute transformation from liquid to solid phase is accurately quantified, effectively identifying the scaling initiation location; based on the conversion solid material point, geometric measurements are performed to obtain scaling data, which can accurately quantify the spatial distribution and thickness variation of the scaling layer. By accurately mapping from the macroscopic flow field to the microscopic reaction transport, this method not only solves the problem that traditional methods cannot simultaneously account for complex fluid flow and discontinuous solute phase change processes, but also achieves a refined reconstruction of the scaling evolution process in pipelines. This significantly improves the accuracy of scaling prediction and provides reliable data support for pipeline maintenance. Attached Figure Description

[0018] Figure 1 This is a schematic flowchart of a pipe scaling analysis method according to an embodiment of the present invention; Figure 2 This is a schematic diagram comparing the steady-state SPH velocity field with the Poiseuille analytical solution in an embodiment of the present invention; Figure 3 This is a schematic diagram of the cross-sectional concentration distribution curve according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the total deposition mass variation in an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of a pipe scaling analysis device according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0020] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0021] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0022] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0023] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0024] In related technologies, existing pipe scaling analysis is typically based on analytical models that assume macroscopic continuity. Because this simplifies the scaling process as uniform deposition or one-dimensional growth, it ignores the complexity of the actual flow state in the pipe, the non-uniformity of ion concentration distribution, and the irregular morphology of the scale layer. This leads to significant discrepancies between the analytical results obtained through simplified one-dimensional deposition calculations or empirical formulas and the actual pipe scaling data, affecting the accuracy of scaling analysis. Such simplified models struggle to capture localized supersaturation changes in the near-wall region, cannot accurately describe the dynamic phase transition process between fluid and solid, and cannot accurately reflect the data changes after pipe scaling.

[0025] To address the problems existing in the aforementioned related technologies, embodiments of the present invention provide a method, apparatus, and electronic device for analyzing pipe scaling.

[0026] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for analyzing pipe scaling, comprising: S110, based on smooth particle fluid dynamics, constructs the steady-state velocity field of the fluid inside the pipe based on the acquired pipe characteristic data.

[0027] Specifically, the steady-state velocity field of the fluid inside the pipe is constructed based on Smoothed Particle Hydrodynamics (SPH), a meshless Lagrangian numerical method. Its core idea is to discretize the fluid domain into a series of particles carrying mass, momentum, and energy. The fluid motion control equations are solved by approximating the kernel function of the interactions between particles, thus avoiding the mesh distortion and reconstruction problems faced by traditional mesh methods when dealing with large deformations or complex boundaries. First, an SPH particle model is generated based on the pipe's geometric characteristics (such as pipe diameter, length, wall shape, and internal obstacle distribution), and fluid properties (such as density and viscosity) and boundary conditions (such as inlet velocity, outlet pressure, and no-slip condition) are set. Then, a body-force-driven SPH viscous relaxation solver is used to solve the incompressible viscous flow control equations in Lagrangian particle form. The process iterates until the velocity field converges, obtaining the steady-state flow field distribution.

[0028] For any physical quantity f, its SPH kernel function is approximately expressed as: ; Using a two-dimensional cubic spline kernel function: ; The viscosity term uses the SPH Laplace operator: ; Among them, f i Let m be any physical quantity (such as velocity, density, or concentration) to be approximated at particle i, j be the neighboring particle number within the influence domain of particle i, and m be the mass of particle i. j Let ρ be the mass of particle j. j Let W(x) be the density of particle j. i x j Let r(x, h) be a kernel function with the distance between particles i and j as the independent variable and the smooth length h as the scale parameter. This kernel function performs a weighted average of the contributions of neighboring particles within the influence domain. i x j | represents the spatial distance between the two particles, q = r / h is the normalized distance, and α2 is the normalization constant in two-dimensional space (usually taken as 10 / (7πh2)). This piecewise function ensures the compact support (only works when q < 2) and smoothness of the kernel function.

[0029] For example, in the simulation of Poiseuille flow in a two-dimensional parallel plate channel, the channel is first discretized into uniformly distributed SPH particles. Wall particles are fixed to satisfy the no-slip condition, while internal fluid particles begin to move under a given fluid acceleration. The viscous force between particles is approximated using the SPH Laplace operator. After several time steps of relaxation iteration, the velocity distribution of the fluid particles exhibits a parabolic shape in the transverse direction, with the maximum velocity at the channel center and zero velocity at the wall. This steady-state velocity field can be directly compared and verified with the analytical solution of Poiseuille flow. Furthermore, in non-uniform pipes with bottom protrusions or local necking, the SPH method can naturally adapt to complex geometric boundaries. Particles form a low-velocity backflow zone upstream of the protrusion, while the velocity increases significantly at the top of the protrusion and in the narrow downstream region. This accurate capture of the non-uniform velocity field provides crucial flow input conditions for subsequent solute transport and scaling / deposition analysis. The steady-state velocity field established by the SPH method not only avoids the tedious process of mesh generation, but also accurately describes the flow characteristics under low Reynolds number laminar flow conditions, laying a reliable kinetic foundation for the convection-diffusion-reaction process in pipe scaling analysis.

[0030] S120, based on peri-field dynamics, constructs a reaction transport model of the solute in the pipeline according to the steady-state velocity field.

[0031] Specifically, constructing a reaction transport model of solute in a pipe based on peri-field dynamics is a non-local integral form of numerical method. Its core idea is to discretize the solute concentration field into a series of material points. Each material point is characterized by the diffusion flux through the concentration difference of other material points in its neighborhood. This avoids the local differential approximation of the spatial derivative in the traditional grid method and is naturally suitable for dealing with discontinuous interfaces, moving boundaries and multiphase coupling problems. First, within the framework of the aforementioned pipeline coupled discrete model, each peridynamic (PD) material point, i.e., the liquid material point, is assigned an initial ion concentration (such as the inlet concentration values ​​of calcium ions and carbonate ions), and physicochemical parameters such as diffusion coefficient, reaction rate constant, and solubility product are set. Then, within each time step, based on the steady-state velocity field obtained from SPH particle interpolation, the convection contribution, PD diffusion contribution, and reaction source term are calculated for each material point. The convection term is discretized using a local first-order upwind scheme, the diffusion term is obtained by summing the concentration difference of the material points in the peridynamic domain and the bond diffusion coefficient, and the reaction source term is calculated based on the local supersaturation and surface-constrained precipitation rate formula to calculate the precipitation rate, thereby synchronously updating the liquid phase ion concentration and solid phase concentration.

[0032] For example, in the simulation of scaling deposition in a straight pipe, the pipe is first discretized into uniformly distributed PD material points, and the calcium ion concentration at the inlet is set to 8.0 × 10⁻⁶. -3 mol / L, carbonate ion concentration is 6.0 × 10⁻⁶-4 mol / L, with an inlet saturation ratio as high as 1.45 × 10⁻⁶. 3 The system is in a state of obvious supersaturation. Then, the Poiseuille velocity field pre-calculated using the SPH method is interpolated to each PD material point as input for the flow velocity transport. Next, within each time step, the PD diffusion flux is calculated for each liquid material point based on the concentration distribution of its neighboring material points. Simultaneously, the concentration change caused by convection is calculated based on the local velocity, and the saturation index SI is calculated based on the current ion concentration. When SI exceeds a critical value, a precipitation reaction is triggered. The calcium carbonate formation rate is calculated according to the surface-limited precipitation rate formula, and the liquid phase ion concentration is reduced and the solid phase concentration is increased accordingly. Through iterative calculations over consecutive time steps, it can be observed that: in the pipe inlet region, due to sufficient ion supply, the solid phase concentration accumulates rapidly; along the flow direction, as ions are consumed by precipitation, the rate of increase in solid phase concentration gradually slows down; in the near-wall region, due to the velocity gradient leading to relatively sufficient ion replenishment, the solid phase concentration is higher than in the pipe center region. Compared to traditional reaction transport models based on the finite difference method, reaction transport models based on peri-field dynamics do not require explicit tracking of the solid-liquid interface. When the solid concentration at a certain material point accumulates to a level that causes its solid volume fraction to exceed a preset threshold (e.g., φ), the reaction transport model will proceed as planned. crit =2.0×10 -3 When the material point is in a liquid state, it can be directly converted into a solid state, becoming a new reaction surface and participating in subsequent deposition reactions. This natural nonlocal integral framework enables the model to automatically handle the dynamic growth, morphological evolution, and feedback effects on flow and transport of the scale layer, providing an efficient and robust computational tool for the fully coupled analysis of pipe scaling.

[0033] The formula for the surface-constrained sedimentation rate is: ; Among them, R scale For surface-constrained sedimentation rate, i.e., the rate of calcium carbonate formation, I surf This is a surface indicator parameter; it takes a value of 1 when the liquid element is adjacent to an initial wall, obstacle, or existing fouling element, and 0 otherwise. α s ρ represents the reactive surface area density. calcite M is the density of calcite. calcite k is the molar mass of calcium carbonate. p The equivalent normal growth rate is given by SR, which is the saturation ratio, i.e., the ratio of the ion activity product to the solubility product, used to characterize the degree of supersaturation of the solution. crit The critical saturation ratio is the threshold saturation ratio that triggers the precipitation reaction; precipitation occurs when this value is exceeded.

[0034] S130, the solid concentration output by the reaction transport model is used to obtain the conversion solid material point through threshold comparison.

[0035] Specifically, the solid-phase concentration output by the reaction transport model is used to determine the solid material points to be converted through threshold comparison. This involves using the accumulated solid-phase concentration at each liquid material point calculated by the reaction transport model as the criterion. By comparing this concentration with a preset maximum equivalent solid-phase concentration and a conversion threshold, material points meeting the phase transition conditions are selected and converted from liquid to solid. Specifically, within each time step, the reaction transport model synchronously updates the liquid-phase ion concentration and solid-phase concentration based on the convection-diffusion-reaction equation. The solid-phase concentration represents the equivalent number of moles of calcium carbonate solid generated at that liquid material point per unit volume. As the precipitation reaction continues, the solid-phase concentration gradually accumulates from its initial zero value. However, due to differences in ion supply, flow state, and wall proximity at different locations, the rate of solid-phase concentration increase varies among material points. Therefore, a unified criterion is needed to identify which material points have accumulated sufficient solid and should be considered solid blockage units rather than continuing to be treated as fluid. This criterion introduces a solid-phase volume fraction φ. s =C s / C s，max To achieve this, where φ s C is the solid volume fraction. s C is the solid phase concentration. s,max The theoretical maximum solid equivalent concentration is given by the calcite density ρ. calcite and molar mass M calcite Calculation yields (C) s，max =ρ calcite / (1000×M calcite ), representing the solid concentration when the material point is completely filled with solid; when φ s Reaching the preset conversion threshold φ crit (e.g., 2.0 × 10) -3 When the solid content (i.e., 0.2%) is reached, the material point is considered to meet the liquid-solid transition condition. This threshold setting reflects the physical nature of the scaling process: the material point does not need to be completely filled with solid, but the state transition is triggered in the initial scale layer formation stage (accounting for only two-thousandths of the characteristic volume of the material point), so that the newly formed scale layer can become a new reaction surface as early as possible and participate in subsequent deposition, thereby accurately simulating the gradual growth process of the scale layer.

[0036] The convection-diffusion-reaction equation satisfies: ; Among them, C a Let a be the concentration of component a, where a is the calcium ion concentration (C). aOr carbonate ions (CO3), t is the time variable of reaction transport, in seconds, u is the velocity field, the local velocity vector of the fluid, calculated by the SPH method and interpolated to the PD material point, in m / s, D a The diffusion coefficient is the molecular diffusion coefficient of component a, expressed in m³. 2 / s, R a is the reaction term, representing the rate at which component a is generated or consumed due to a chemical reaction, expressed in mol / (L·s), and ▽ is the vector differential operator.

[0037] In the convection-diffusion-reaction equation, the reaction term R is the key bridge connecting the liquid and solid phases. α Different components have different symbols and physical meanings: for calcium ions in the liquid phase (C... a 2+ ) and carbonate ions (CO3) 2- The reaction term takes a negative value, i.e., R Ca =R CO3 =-R scale This indicates that these ions are consumed and removed from the liquid phase due to the calcium carbonate precipitation reaction; meanwhile, for solid-phase calcium carbonate (C... a CO3), the reaction term takes a positive value, i.e., Rs = +R scale This indicates that the same amount of substance is converted into the solid phase and accumulates at a material point. This "negative-positive" correspondence ensures the conservation of mass during the chemical reaction; for every calcium ion and carbonate ion consumed, exactly one calcium carbonate solid unit is generated, making the decrease in liquid phase ion concentration precisely equal to the increase in solid phase concentration. Therefore, the reaction term R... scale It not only determines the decay rate of liquid-phase ion concentration during transport, but also directly controls the solid-phase concentration C. s The accumulation rate of Rc tightly couples the chemical changes in the fluid phase with the physical accumulation in the solid phase. It is through this reaction term that the reaction transport model can synchronously update the liquid ion concentration and solid concentration at each time step, providing fundamental data for subsequent calculations of the solid volume fraction and determination of liquid-solid phase transitions. scale R is the calcium carbonate precipitation rate, a non-negative scalar value. a It is the source / sink term of component a, and its value is determined by R. scale The signs are assigned based on the different components.

[0038] For example, in a simulation of non-uniform pipe scaling with a bottom protrusion, the calcium ion concentration at the inlet is 8.0 × 10⁻⁶. -3 mol / L, carbonate ion concentration is 6.0 × 10⁻⁶ -4 mol / L, corresponding to an inlet saturation ratio as high as 1.45 × 10⁻⁶. 3The solution is in a significantly supersaturated state. After the reaction transport model is started, calcium carbonate precipitation begins at each liquid material point in the pipeline, and the solid concentration C... s Gradually accumulating. Near the wall in the pipe inlet region, due to ample ion supply and active wall-induced deposition reactions, the C content at certain material points increases. s It grows to the point where φ s Reaching 2.0×10 -3 These material points, marked as meeting the conversion conditions, are transformed from liquid to solid, becoming new scaling units. In the central region of the pipe, although supersaturation also occurs, the limited surface area due to distance from the pipe wall results in a lower sedimentation rate. s Accumulation is slow, φ s For an extended period below the threshold, the material remains in a liquid state and continues to participate in transport. As time progresses to the preset simulation time (e.g., 3.0 seconds), it can be observed that: upstream of the bottom protrusion, due to flow deceleration and sufficient ion replenishment, a large number of liquid material points are sequentially converted into solid material points, forming a significant scale accumulation zone, with a substantial increase in the equivalent blockage height; at the top of the protrusion, flow acceleration leads to relatively insufficient ion replenishment, resulting in fewer converted material points and a thinner scale layer; while downstream of the protrusion, due to the large consumption of ions upstream and the high flow rate, almost no material points meet the conversion conditions, and scale is negligible. The mechanism of selective material point conversion through solid phase concentration threshold comparison allows the spatial distribution and morphological evolution of the scale layer to be naturally determined by the coupling effect of local flow, ion concentration, and reaction kinetics, without the need for artificially preset scale shape or growth direction, thus enabling accurate capture of scale hotspot locations and local blockage characteristics. Furthermore, material points converted to solid state are marked as new exposed reaction surfaces (I1). surf =1), its velocity is set as a no-slip boundary condition (velocity is zero), and it serves as the boundary condition for solid obstacles to participate in flow and transport in subsequent time steps. The liquid-solid conversion only affects the boundary state in the PD transport module, and the SPH steady-state velocity field remains unchanged, truly reflecting the self-accelerated growth phenomenon of scale during actual pipeline scaling. The set of converted solid material points obtained through this solid concentration threshold comparison constitutes the basic data for subsequent geometric measurements. Based on this, macroscopic scaling indicators such as equivalent blockage thickness, remaining flow area, and total solid scale mass can be statistically analyzed, providing a quantitative basis for pipeline scaling assessment and control design.

[0039] The saturation ratio and critical condition are satisfied: ; ; ; Wherein, SR is the saturation ratio (dimensionless) of calcium carbonate, used to characterize the degree of supersaturation of the solution relative to calcite minerals; C Ca For calcium ions C in solution a 2+ Concentration (unit: mol / m³) 3 ), C CO3 Carbonate ions CO3 2 Concentration (unit: mol / m³) 3 The product of these two is the ion activity product (under practical conditions, concentration is usually used to approximate activity); K sp The solubility product constant of calcite (unit: mol) 2 / m 6 (), depending on thermodynamic conditions such as temperature, pressure, and ionic strength, when the product of ion concentrations in the solution is less than K. sp When the temperature is above a certain threshold, the solution is unsaturated (no tendency to sediment); when the temperature is above a certain threshold, it is supersaturated. I The saturation index (SI, dimensionless) quantitatively describes the degree of supersaturation or undersaturation on a logarithmic scale. When SI = 0, the solution is in equilibrium; SI > 0 indicates supersaturation (prone to scaling); and SI < 0 indicates undersaturation (prone to dissolution). crit The critical saturation ratio threshold (dimensionless) required to trigger the precipitation reaction, SI crit The corresponding critical saturation index threshold (dimensionless, usually taken as an empirical value such as 0.1-0.5, indicating that the solution needs to exceed the equilibrium point to a certain degree of supersaturation before overcoming the nucleation energy barrier and effective precipitation can occur) is given by this formula. This establishes the reciprocal conversion relationship between the saturation index and the saturation ratio, which is used in the subsequent precipitation rate formula to determine whether the reaction has started (i.e., only when SR > SR). crit The precipitation reaction only has a forward rate when the precipitation reaction occurs.

[0040] S140, the scaling data of the pipeline is obtained by geometric measurement based on all the converted solid material points.

[0041] Specifically, by obtaining the scaling data of the pipeline through geometric measurements of all converted solid material points, the changes in the state of micro-particles are transformed into macro-engineering indicators. Essentially, this is a discretized description of the spatial distribution of the scale layer and the amount of solid accumulation. However, in engineering practice, what is truly of concern is the thickness of the scale layer, the extent of pipe blockage, and the total amount of scale. These macro-indicators cannot be directly read from the state identifiers of the material points and must be obtained through systematic geometric measurements and statistical analysis of the spatial location, solid concentration, and characteristic dimensions of all converted solid material points. First, the equivalent blockage thickness is calculated. Along the normal direction of the pipe wall, the characteristic dimensions (i.e., the PD material point spacing) of the continuously arranged converted solid material points from the inner wall to the pipe center at each axial position are summed to obtain the equivalent blockage thickness at that location. This thickness directly reflects the degree of local encroachment of the scale layer on the pipe's flow cross-section. Second, the remaining flow area is statistically analyzed. Based on the spatial distribution of all converted solid material points, the total area occupied by all converted solid material points at each pipe cross-section is calculated. The remaining flow area at that cross-section is obtained by subtracting the occupied area from the original cross-sectional area of ​​the pipe. The severity of the blockage is then visually characterized by the area loss rate (i.e., the ratio of occupied area to the original cross-sectional area). Finally, the total solid scale mass is converted. Based on the solid phase concentration of all converted solid material points and the characteristic volume they represent (i.e., the product of the material point spacing in the two-dimensional model, representing the area unit controlled by that material point), the product of the solid phase concentration and characteristic volume of each converted solid material point is summed and then multiplied by the molar mass of calcium carbonate to obtain the total solid scale mass in the pipe.

[0042] For example, the equivalent blockage thickness: ; Remaining circulation area: ; Scale quality ; Output scaling data: ; Among them, h scale (x) represents the equivalent blockage thickness of the scale layer at location x along the pipeline flow direction (unit: m), N solid (x) represents the number of solid material points (i.e., the number of blocking unit layers) on the cross-section at this flow location, along the wall normal direction, Δy PD The initial spacing (in meters) of the PD material points along the wall normal direction is given. This formula estimates the local scale thickness by statistically counting the number of solid material point accumulation layers. A flow The remaining effective flow area of ​​the pipe after scaling (unit: m) 2 Aoriginal Initial cross-sectional area of ​​the pipe (unit: m) 2 A scale A represents the total area occupied by the scale layer on the cross-section (obtained by summing the areas of all solid material points on that cross-section). scale =∑A i Unit: m 2 A i M represents the area contribution of the i-th solid material point (scaling unit) on the cross-section. This formula quantifies the reduction in pipe flow capacity by subtracting the scaling blockage area from the original area. solid C represents the total mass (kg) of calcite scale corresponding to the points where solid materials have been converted within the pipeline. s Solid concentration of solid material at a given point (unit: mol / m³) 3 V represents the volume of a single PD material point (unit: m³). 3 M calcite The molar mass of calcite (unit: kg / mol, usually taken as 100.09 g / mol, i.e., 0.10009 kg / mol) is calculated by summing the mass contributions of all points in the solid-state material conversion process. The final output is the scaling dataset {h}. scale A flow M solid This includes three key geometric statistics: equivalent blockage thickness distribution, remaining flow area, and total scale quality, used to comprehensively assess the severity of pipe scaling. It should be noted that geometric measurement is not a simple arithmetic operation, but is based on the physical premise that "the converted solid material points accurately represent the actual spatial distribution of the scale layer". The position of each converted solid material point accurately records the spatial coordinates of the scale occurrence, and its solid concentration reflects the amount of solid accumulated at that point. The continuous arrangement along the wall normal naturally constitutes the thickness of the scale layer. Although this information exists in the form of solid concentration before conversion (i.e. when the material points are still in a liquid state), it has not yet formed a solid geometric structure with blocking function, so it cannot be directly used for geometric measurement.

[0043] In this embodiment, a steady-state velocity field of the fluid within the pipeline is constructed based on smooth particle fluid dynamics. This accurately captures the details of fluid motion and velocity gradient distribution under complex pipeline geometry, providing high-fidelity flow field boundary conditions for subsequent analysis. A solute reaction transport model is constructed using the steady-state velocity field based on near-field dynamics, overcoming the singularity problem of traditional continuum mechanics methods when dealing with discontinuous solute diffusion and reaction. Its nonlocal interaction concept more accurately describes the microscopic migration and chemical evolution behavior of the solute driven by the flow field. By comparing solid concentration thresholds to determine the conversion solid material point, precise quantitative determination of the critical state of solute transition from liquid to solid phase is achieved, effectively identifying the scaling initiation location. Geometric measurements based on the conversion solid material point are used to obtain scaling data, accurately quantifying the spatial distribution and thickness variation of the scaling layer. Through a step-by-step precise mapping from the macroscopic flow field to microscopic reaction transport, not only is the problem of traditional methods struggling to simultaneously handle complex fluid flow and discontinuous solute phase transition processes solved, but also a refined reconstruction of the pipeline scaling evolution process is achieved, significantly improving the accuracy of scaling prediction and providing reliable data support for pipeline maintenance.

[0044] Optionally, the pipeline characteristic data includes pipeline geometric parameters, physical property parameters, and numerical discrete parameters; the step of constructing the steady-state velocity field of the fluid inside the pipeline based on the acquired pipeline characteristic data includes: A coupled discrete model of the pipeline is constructed based on the pipeline geometric parameters and the numerical discrete parameters. Based on a preset viscous relaxation solver, the steady-state velocity field is obtained according to the pipeline coupled discrete model, the physical property parameters, and the numerical discrete parameters.

[0045] In this optional embodiment, the pipeline feature data includes at least three categories: pipeline geometric parameters, physical property parameters, and numerical discrete parameters. Pipeline geometric parameters define the spatial extent and boundary shape of the computational domain, physical property parameters describe the physical properties of the fluid, and numerical discrete parameters control computational accuracy and resolution. Based on this, a pipeline coupled discrete model is constructed according to the pipeline geometric parameters and the numerical discrete parameters. This coupled discrete model serves as the basic framework for numerically representing a real pipeline. Subsequently, based on a preset viscous relaxation solver, the steady-state velocity field is obtained according to the pipeline coupled discrete model, physical property parameters, and numerical discrete parameters. Specifically, using the Smooth Particle Hydrodynamics (SPH) method, a volume acceleration g along the flow direction is applied to each SPH fluid particle on the established pipeline coupled discrete model. x To drive the flow, the viscous response of the particles is set according to the kinematic viscosity v in the physical property parameters, and the particle spacing Δx in the SPH parameter is used for numerical discretization. SPH and Δy SPH Determine the scope of the kernel function (smoothing length h = ηΔx) SPHBy approximating the viscous contribution through the SPH Laplace operator, a zero-velocity condition is applied at the wall particles to satisfy the no-slip boundary. A linear equation system is established for all fluid particles and solved iteratively until the velocity field converges to a steady state. The steady-state velocity field constructed through the above process provides key flow input conditions for subsequent solute transport and scaling / deposition analysis. Furthermore, since the SPH method uses meshless Lagrangian particle discretization, it can naturally adapt to arbitrary geometric boundaries such as pipe walls, protrusions, and necks without generating complex mesh structures. This avoids the velocity field calculation errors caused by mesh distortion or boundary fitting difficulties in traditional mesh methods, ensuring high-precision prediction of velocity distribution under low Reynolds number laminar flow conditions and providing reliable convective velocity input for the calculation of the convection term in the reactive transport model.

[0046] Optionally, the construction process of the pipeline coupling discrete model includes: A pipeline model is constructed based on the pipeline geometry parameters, and the fluid domain and solid domain of the pipeline model are determined. Based on the smooth particle spacing in the numerical discrete parameters, smooth particles are uniformly distributed in the fluid domain and the solid domain, and the smooth particles in the fluid domain are assigned fluid particle properties, and the smooth particles in the solid domain are assigned wall particle properties. Based on the material point spacing in the numerical discretization parameters, material points are uniformly distributed in the fluid domain and the solid domain, and liquid point attributes are assigned to liquid material points in the fluid domain and solid point attributes are assigned to solid material points in the solid domain.

[0047] Specifically, based on the pipe's geometric parameters (such as channel length L, channel height H, wall thickness, bottom protrusion size and location, etc.), a numerical geometric model corresponding perfectly to the actual pipe geometry is established in the computational space. Based on this geometric model, a region where the fluid can flow freely (fluid domain Ω_f) and a region representing fixed walls or internal obstacles (solid domain Ω_s) are clearly defined, thus providing a spatial basis for subsequent particle placement and boundary condition application. Subsequently, according to the smooth particle spacing in the numerical discretization parameters, smooth particles are uniformly placed in the fluid and solid domains. Fluid particle properties are assigned to the smooth particles in the fluid domain, and wall particle properties are assigned to the smooth particles in the solid domain. That is, within the defined fluid and solid domains, according to the SPH particle spacing Δx... SPH and Δy SPHSPH particles are generated in two domains, arranged in a regular pattern. Particles in the fluid domain are assigned fluid properties to participate in solving the flow control equations, while particles in the solid domain are assigned wall properties to keep their velocity constant at zero, achieving no-slip boundary conditions. Simultaneously, wall particles, acting as fixed boundaries, participate in the kernel function summation of the fluid particles to apply wall repulsion and viscous forces. Next, based on the material point spacing in the numerical discretization parameters, material points are uniformly distributed in both the fluid and solid domains. Liquid material point properties are assigned to the material points in the fluid domain, and solid material point properties are assigned to the material points in the solid domain, i.e., within the same geometric region, according to the PD material point spacing Δx... PD and Δy PD Another independent particle system is generated, which is independent of the SPH particle system. Material points located in the fluid domain are set as liquid material points for subsequent ion transport and reaction calculations, while material points located in the solid domain (including walls and obstacles) are set as solid material points, serving as flux-free boundaries that do not participate in reaction transport but can be used as deposition surfaces to participate in surface indicator parameters I. surf The judgment.

[0048] For example, in a two-dimensional pipe scaling simulation case with a bottom Gaussian protrusion, the pipe geometry parameters are: channel length L = 0.100m, height H = 0.040m, bottom protrusion center position xc = 0.046m, width wb = 0.008m, height hb = 0.006m, and the SPH spacing Δx is a numerical discrete parameter. SPH =Δy SPH =0.0016m, PD spacing Δx PD =Δy PD=0.0010m; First, construct a pipe model based on the above geometric parameters, define a fluid domain within the range of y=0 to y=0.040m, define the bottom edge and bottom convex outline of y=0 and the top edge of y=0.040m as a solid domain, and determine the specific boundary shape of the solid domain according to the Gaussian convexity function; then, generate about 15,000 fluid SPH particles in the fluid domain and about 3,000 wall SPH particles in the solid domain according to the SPH spacing of 0.0016m, and assign different properties to the two types of particles; then, generate about 40,000 PD material points in the same geometric area according to the PD spacing of 0.0010m, set the material points located in the fluid domain as liquid material points and assign them liquid phase point properties, and set the material points located in the solid domain as solid material points and assign them solid point properties. It is important to emphasize that although the two particle systems overlap geometrically, their functions are completely separate and independent: the SPH fluid particles are only used to solve the velocity field and do not involve any transport or phase change calculations; the PD material points do not participate in the velocity field solution, but instead obtain convection velocity information from the SPH particles through subsequent velocity interpolation for transport and reaction calculations. The liquid material points can accumulate solid phase concentration and be converted into solid material points when certain conditions are met, while the solid material points always maintain solid properties.

[0049] In this optional embodiment, by constructing the above two discrete systems, the pipeline coupled discrete model not only provides a meshless Lagrangian particle framework for solving the velocity field, but also provides a discrete material point carrier with a nonlocal integral format for reaction transport and liquid-solid phase transition. The two systems are coupled through velocity interpolation, avoiding the problems of complex mesh generation, difficult boundary fitting, and cumbersome tracking of moving interfaces in the traditional mesh method, and laying an efficient and robust discrete foundation for subsequent steady-state velocity field solution and reaction transport simulation.

[0050] Optionally, the pipeline characteristic data further includes inlet concentration parameters; the process of constructing the reaction transport model includes: Based on the normalized interpolation method, the steady-state velocity field is interpolated from the smooth particle to the liquid material point; The initial liquid phase concentration is assigned to the liquid material points in the inlet region of the pipeline coupled discrete model based on the inlet concentration parameter.

[0051] In this optional embodiment, the pipeline characteristic data also includes inlet concentration parameters, specifically the calcium ion concentration and carbonate ion concentration at the inlet, used to set the initialization conditions for the reaction transport model. The construction process of the reaction transport model includes two key steps: normalized interpolation and assignment based on the inlet concentration parameters. First, based on the normalized interpolation method, the steady-state velocity field is interpolated from smooth particles to liquid material points. This step is necessary because the SPH particle system and the PD material point system are two independently generated discrete systems. SPH particles only carry velocity information and are used for flow field solving, while PD liquid material points are the actual carriers for subsequent reaction transport calculations. Interpolation is needed to transfer the velocity information at the SPH particles to each PD liquid material point. Specifically, the normalized interpolation method (i.e., Shepard normalized interpolation) is used. The reciprocal of the distance between the SPH particle and the target PD liquid material point is used as the weight to perform a weighted average of the velocities of all SPH particles in the neighborhood, and the average is only applied when the sum of the weights exceeds a preset capacity. Interpolation is performed only when there is a time difference; otherwise, the output velocity is zero. For solid material points located in the solid domain, the velocity is directly set to zero without interpolation, thus assigning each liquid material point the velocity vector required for convective transport. Subsequently, based on the inlet concentration parameter, the liquid material points in the inlet region of the pipe coupled discrete model are assigned initial liquid phase concentration values. That is, the initial concentrations of calcium ions and carbonate ions of each liquid material point are set near the pipe inlet section according to the inlet concentration parameter, serving as the initial concentration conditions for the time-progression solution of the reaction transport model. The initial concentrations of liquid material points outside the inlet region are set to zero or assigned according to preset conditions, while solid material points are not assigned liquid phase concentration values ​​and do not participate in reaction transport calculations. Through the inverse distance weighted interpolation step, seamless transfer of physical quantities is achieved between the SPH particle system and the PD material point system. This enables the reaction transport model to obtain high-fidelity convection velocity input without sharing the same set of discrete points, avoiding velocity information loss due to discrepancy in discrete systems. Through the inlet concentration assignment step, the reaction transport model obtains initialization conditions that conform to physical reality, ensuring the rationality and convergence of ion concentration evolution during subsequent time progression. These two steps together constitute the complete data preparation process before the reaction transport model is started, laying the initial condition foundation for the velocity and concentration fields for the subsequent time-progression solution of the convection-diffusion-reaction equation.

[0052] For example, the Shepard normalized interpolation method satisfies: ; Among them, u i PD Here, is the velocity vector (in m / s) at point i in the PD material after interpolation, 'a' is the SPH particle number (traversing all SPH particles that contribute to point i in PD), 'Va' is the volume of SPH particle 'a', and 'u' is the velocity vector at point i in the PD material after interpolation. aW(x) is the velocity vector of SPH particle a (unit: m / s). i x a，h Let x be the position of point i in PD. i Position x of SPH particle a a The difference is the independent variable, and the kernel function (usually the same cubic spline kernel function as in the SPH solver) is used as the scale parameter. This kernel function determines the weight contribution of SPH particles to PD points (the closer the distance, the greater the weight). The denominator is the normalization factor, ensuring that the sum of all weights is 1, thus achieving zero-order consistency (i.e., accurate interpolation of constants). This formula is essentially a specific application of the Shepard normalization interpolation method within the SPH framework. By using the SPH kernel function to perform a weighted average of the velocities of SPH particles in the neighborhood, the discrete SPH velocity field is smoothly and physically consistently mapped onto the PD material points.

[0053] Optionally, the step of obtaining the conversion solid material point by comparing the solid phase concentration output from the reaction transport model with a threshold includes: Based on a preset time step, the reaction transport model is controlled to perform simulation to obtain the solid phase concentration of the liquid material point; Based on the threshold comparison result of the solid phase concentration, the corresponding liquid material point is subjected to liquid-solid conversion to obtain the converted solid material point.

[0054] Specifically, based on a preset time step, the solid concentration of liquid material points is obtained through simulation using the reaction transport model. This is done after both the pipeline coupled discrete model and the reaction transport model have been constructed, the velocity field has been interpolated to each liquid material point, and the initial inlet concentration has been assigned to each liquid material point in the inlet region. Then, a time-progression cycle is initiated. Within each preset time step Δt, for each liquid material point, the convection term (based on the interpolated velocity field using a local first-order upwind discretization scheme), the PD diffusion term (based on a near-field dynamics nonlocal integral scheme, obtained by summing the concentration difference and bond diffusion coefficient of neighboring material points in the near-field domain), and the reaction source term (calculated based on the local supersaturation and surface-constrained sedimentation rate formula to determine the sedimentation rate R) are calculated sequentially. scale ), thereby synchronously updating the liquid phase ion concentration (Ca ), 2+ and CO3 2- Consumed due to precipitation reaction) and solid concentration (C) s (Accumulated growth due to precipitation reaction), after several time steps of iterative advancement, the accumulated solid concentration C at each liquid material point... sThe concentration gradually increases from an initial zero value to different levels; subsequently, based on the threshold comparison results of the solid concentration, the corresponding liquid material points are converted to solid material points through liquid-solid transformation. That is, after the solid concentration is updated at each time step, all liquid material points are traversed, and for each liquid material point, its current solid concentration C is determined. s Calculate the solid volume fraction φ s , will φ s With the preset volume fraction threshold φ crit (e.g., 2.0×10) -3 The comparison is performed to determine whether the liquid material point meets the liquid-solid transition condition. The state of the liquid material point that meets the condition is then switched from liquid to solid to obtain the solid material point, with its velocity set to zero to satisfy the no-slip boundary condition. This solid material point is then marked as a new exposed reaction surface (I). surf =1) to participate in subsequent deposition reactions, thereby realizing the transformation of liquid material points into solid material points, while liquid material points that have not reached the threshold continue to remain in the liquid state and participate in subsequent transport calculations.

[0055] Furthermore, the liquid-solid conversion criterion is specifically based on the solid phase concentration C. s Calculate the solid volume fraction: ; ; in, s The volume fraction of solid phase at a point in a liquid material (dimensionless) characterizes the degree of solid calcium carbonate filling within that point and is a direct criterion for liquid-solid phase transition; C s The concentration of solid calcium carbonate accumulated within a point of liquid material (unit: mol / m). 3 ), from the reaction source term R scale The integral is updated within each time step; C s，max Maximum solid-phase equivalent concentration (unit: mol / m³) 3 This represents the limiting solid concentration at which the material completely transforms into a solid state. The maximum equivalent solid concentration is C0. s，max , ρ calcite The density of calcite crystals (usually taken as 2710 kg / m³) 3 M calcite The molar mass of calcite (usually taken as 100.09 g / mol) is divided by 1000 to convert the density unit from kg / m³ to g / cm³ to match the molar mass of the unit system, thus obtaining the maximum solid concentration corresponding to the completely solid material point. When the near-wall liquid material point... s Reaching or exceeding the preset conversion threshold critAt that time, the material point is converted into a static equivalent blocking element. When the following conditions are met: ; Then the liquid material point is converted into a solid material point.

[0056] The converted solid-state material point: velocity is set to zero (no-slip condition), marked as solid domain, and I is set. surf =1, becoming a new reaction surface, wherein: if (the liquid material point) is adjacent to the initial wall, obstacle, or existing scale unit, I surf =1, otherwise I surf =0, thus forming a positive feedback mechanism of "deposition - surface renewal - accelerated deposition".

[0057] In this optional embodiment, through the reaction transport simulation and solid phase concentration threshold comparison conversion mechanism based on the preset time step, the state evolution of each liquid material point is completely determined by the coupling of its local flow conditions, ion supply, and reaction kinetics: the convection term determines how ions are transported to the point, the diffusion term determines how ions are replenished from the surroundings, the reaction term determines how ions are consumed and converted into the solid phase, and the threshold comparison provides a unified conversion criterion directly linked to the local accumulation amount, so that the formation location, growth rate, and spatial distribution of the scale layer no longer depend on artificial presets, but are naturally driven by physical processes. This allows for the accurate capture of the timing and location of scale hotspots, the gradual growth process of the scale layer along the wall normal, and the differences in the degree of scale in different areas, providing a set of converted solid material points that accurately reflects the actual scale state of the pipeline for subsequent geometric measurements.

[0058] Optionally, the step of performing liquid-solid conversion on the corresponding liquid material point based on the threshold comparison result of the solid phase concentration to obtain the converted solid material point includes: The corresponding solid volume fraction is obtained by comparing the solid concentration at the liquid material point with the preset maximum equivalent solid concentration. The liquid material point is judged to meet the liquid-solid conversion condition based on the comparison result between the solid volume fraction and the preset conversion threshold. If so, the liquid material point is converted from a fluid state to a solid state to obtain the converted solid material point.

[0059] Optionally, determining whether the liquid material point meets the liquid-solid conversion condition based on the comparison result of the solid volume fraction and the preset conversion threshold includes: When the solid volume fraction is greater than the preset conversion threshold, it is determined that the liquid material point satisfies the liquid-solid conversion condition. When the solid volume fraction is less than or equal to the preset conversion threshold, it is determined that the liquid material does not meet the liquid-solid conversion condition. Specifically, obtaining the corresponding solid volume fraction based on the ratio of the solid concentration at a liquid material point to the preset maximum equivalent solid concentration is a crucial data preparation step before determining the liquid-solid conversion. The maximum equivalent solid concentration C... s，max From the density ρ of calcite calcite With molar mass M calcite The ratio of C to C represents the theoretical maximum solid concentration when the material point is completely filled with solid. Each liquid material point has accumulated a different amount of solid concentration C after reaction transport simulation. s Dividing the two yields the dimensionless solid volume fraction φ. s =C s / C s，max This ratio, ranging from 0 to 1, directly reflects the degree to which the current material point is filled with solid. Subsequently, based on the comparison between the solid volume fraction and the preset conversion threshold, it is determined whether the liquid material point meets the liquid-solid conversion condition, i.e., the calculated solid volume fraction φ... s With the preset volume fraction threshold φ crit (e.g., 2.0×10) -3 ) for comparison, when φ s ≥φ crit When the liquid material is determined to meet the liquid-solid transition condition, when φ s <φ crit If the condition is not met, the liquid material point is converted from a fluid state to a solid state to obtain a converted solid material point. That is, the state identifier of the liquid material point that meets the condition is switched from liquid to solid state, and its velocity is set to zero to meet the no-slip boundary condition. It is then marked as a new exposed reaction surface to participate in the deposition reaction in subsequent time steps. The liquid material point that does not meet the condition continues to maintain its original liquid properties and participates in subsequent transport calculations.

[0060] For example, a simulation of non-uniform pipe scaling with a bottom Gaussian bulge is used to illustrate this, where the calcium ion concentration C at the pipe inlet is... Ca，in =8.0×10 -3 mol / L, carbonate ion concentration C CO3，in =6.0×10 -4 mol / L, maximum solid-phase equivalent concentration C s，max =27.07mol / L, preset conversion threshold φ crit =2.0×10 -3For example, after a 3.0-second reaction transport simulation, the solid concentration distribution at each liquid material point in the pipeline showed significant differences: at a certain liquid material point A located in the near-wall region upstream of the bottom protrusion, the solid concentration distribution at that point was significantly different due to the decelerated flow, increased ion residence time, and proximity to the wall (I...). surf =1), precipitation reaction is active, and the solid concentration accumulates to C0. s =5.42×10 -2 mol / L, according to the formula φ s =C s / C s，max =2.00×10 -3 The calculated solid volume fraction exactly reaches the preset conversion threshold φ. crit =2.0×10 -3 The comparison result shows that the liquid-solid conversion condition is met. Therefore, material point A is converted from liquid to solid, and this point becomes the solid-conversion material point. Its velocity is set to zero. surf Point B, a liquid material located in the same region but slightly farther from the wall, has a lower reaction rate due to its distance from the wall (I). surf When C=0, the surface-limited sedimentation rate is zero, and the solid concentration is only C. s =5.0×10 -5 mol / L, φ s =1.85×10 -6 Much smaller than φ crit The comparison results show that the conversion conditions are not met, and liquid material point B continues to remain in a liquid state and participate in subsequent transport; liquid material point C, located in the central region of the inlet, although having sufficient ion supply, is not adjacent to the wall (I surf =0), no precipitation reaction occurs, C s =0, φ s =0, which also does not meet the conversion condition; the liquid material point D, located in the downstream region of the convex area, although adjacent to the wall, has a low supersaturation due to the large consumption of ions upstream, resulting in a very small precipitation rate. C s =5.0×10 -4 mol / L, φ s =1.85×10 -5 Below the threshold, it remains liquid. As time continues, the solid concentration at material points B and D continues to accumulate slowly, until their respective φ values ​​reach a certain level. s Ultimately reached 2.0×10 -3 At that time, they will also sequentially complete the liquid-solid transformation into new solid material points, while material point C, because it never satisfies the wall proximity condition, its φ s It is always zero and never changes.

[0061] In this optional embodiment, through the three-step process of calculating the solid volume fraction, comparing thresholds, and transitioning states, the fate of each liquid material point is entirely determined by its accumulated solid concentration. The higher the solid concentration, the larger the solid volume fraction, and the easier it is to reach the conversion threshold, thus achieving the transition from liquid to solid. Material points below the threshold continue to participate in transport in a liquid state and continue to accumulate solid concentration in subsequent time steps until they finally reach the threshold and complete the transition. This threshold comparison mechanism based on solid volume fraction makes the generation of converted solid material points a natural selection process driven by local flow conditions, ion replenishment, and reaction kinetics. The scale layer gradually advances outward from the wall surface. Each transition adds new solid units to the blockage structure and becomes a new reaction surface, thereby accelerating the transition of subsequent material points in the adjacent area. This forms a positive feedback growth mechanism consistent with physical reality, providing a set of converted solid material points that accurately reflects the true spatial distribution of the scale layer for subsequent geometric measurements.

[0062] Optionally, obtaining the scaling data of the pipe through geometric measurement based on all the converted solid material points includes: The corresponding equivalent blockage thickness is obtained by summing the characteristic dimensions of the converted solid material points in the wall normal of the pipe. The remaining flow area of ​​the pipeline is obtained by statistical analysis of the area occupancy based on the spatial distribution of all the converted solid material points. The scaling mass is obtained by summing and integrating the solid phase concentration and characteristic volume of all the aforementioned solid material points. The scaling data is generated based on the equivalent blockage thickness, the remaining flow area, and the scaling quality.

[0063] Specifically, the equivalent blockage thickness is obtained by accumulating the characteristic dimensions of the converted solid material points along the pipe wall normal. That is, for each axial position, the status markers of the material points are checked one by one along the normal direction starting from the pipe wall, and the continuous markers are marked as the characteristic dimensions of the converted solid material points (i.e., the PD material point spacing Δy). PD The summation is performed until the first non-solid material point is encountered, yielding the equivalent blockage thickness h at that location. scale =N solid ×Δy PD , where N solid This represents the number of continuously arranged solid-state material points along the normal direction from the wall at a certain axial position in the pipe. This thickness directly reflects the degree of spatial encroachment of the scale layer on the wall's normal direction. The remaining flow area of ​​the pipe is obtained by statistically analyzing the area occupied by all solid-state material points based on their spatial distribution. Specifically, at each pipe cross-section, the total area A occupied by all solid-state material points on that cross-section is calculated. scale(i.e., the sum of the characteristic areas Δx×Δy of each solid point), then using the original cross-sectional area A of the pipe at that section. original Subtract A scale The remaining flow area A at this cross-section is obtained. flow =A original -A scale Meanwhile, through the area loss rate p m =(A scale / A original The scale mass is obtained by summing and integrating the solid concentration and characteristic volume of all converted solid material points. That is, for each converted solid material point (including unconverted material points that carry solid concentration), its solid concentration C is calculated. s Multiplying the solid mass at that point by its characteristic volume V (Δx×Δy×unit thickness in a two-dimensional model) yields the solid mass at that point. Then, the results for all material points are summed and multiplied by the molar mass M of calcium carbonate. calcite That is, the scale quality M solid =∑(C s ×V×M calcite Based on the equivalent blockage thickness, remaining flow area, and scale quality, scale data is generated. That is, the measurement results of the above three dimensions (spatial thickness, cross-sectional flow capacity, and overall quality) are integrated into a complete scale dataset to comprehensively characterize the scale status of pipelines.

[0064] In this optional embodiment, through a geometric measurement and data integration process, the originally discretely distributed solid material points within the pipeline are transformed into a complete set of scaling data that can be directly applied in engineering, including the equivalent blockage thickness distribution along the pipeline, the remaining flow area and area loss rate, and the total solid scale mass. These data comprehensively characterize the scaling status of the pipeline from three dimensions: the equivalent blockage thickness visually displays the spatial distribution and local severity of the scale layer in the normal direction to the wall; the remaining flow area and area loss rate directly assess the degree of impairment to the pipeline's flow capacity; and the total solid scale mass provides a quantitative basis for assessing the workload and cost of descaling. These three elements complement each other and together constitute a complete index system for scaling analysis, providing reliable data support for scaling prevention and control design, pipeline maintenance decisions, and transport capacity assessment.

[0065] Furthermore, the constructed SPH-PD coupled model (pipeline coupled discrete model) was systematically validated through three numerical examples. All computational domains consisted of two-dimensional longitudinal pipe segments, enabling precise control of velocity field recovery, reactive transport, wall deposition, and fluid-solid phase transition processes. The three numerical examples all employed an incremental validation process: first, the SPH flow field solver (a pre-defined viscous relaxation solver) was compared with the analytical Poiseuille baseline model; second, under validated velocity field conditions, the PD transport, reactive, and wall deposition modules were compared with the finite difference method (FDM) reference solution; third, the ion transport and precipitation source terms of CaCO3 were validated in a fixed geometry; subsequently, the fluid-solid phase transition process was activated in a non-uniform channel to demonstrate the formation of localized scaling and the corresponding loss of opening area.

[0066] (1) Verification of two-dimensional Poisson leaf flow To verify the performance of the SPH internal flow field solver, a two-dimensional Poiseuille flow was simulated in a straight pipe. Periodic boundary conditions were applied in the flow direction, and no-slip conditions were set at the wall. The simulation parameters were: channel length L = 0.5 m, height H = 1.0 m, and kinematic viscosity ν = 0.02 m³ / s. 2 / s, target peak velocity U max =0.75m / s², volume acceleration g x =0.12m / s 2 Reynolds number Re=25, SPH interparticle spacing Δx SPH =Δy SPH =0.04m, smoothing length h=0.048m. For example... Figure 2As shown, (a) the velocity field is a two-dimensional velocity distribution cloud map of the fluid inside the pipe. The figure consists of many discrete dots, which represent fluid particles or nodes in the computational domain. The color bars (right side) indicate the magnitude of the velocity, from dark blue (low speed) to yellow (high speed). Typical Poiseuille flow characteristics can be clearly seen, with the highest velocity in the central region of the pipe (yellow part), while the velocity approaches zero near the upper and lower walls (dark blue part). This conforms to the "no-slip boundary condition" of fluid under viscosity. (b) The velocity distribution curve is a quantitative analysis of the data in (a), showing the velocity profile along the vertical direction (Y-axis). The horizontal axis represents the normalized velocity v1, and the vertical axis represents the normalized position height h1. The blue solid line (SPH) represents the velocity distribution calculated by numerical simulation, and the red dashed line (analytical solution) represents the accurate parabolic distribution derived from the theoretical formula. The two curves are highly overlapping, indicating that the numerical model can very accurately reproduce the theoretical parabolic velocity distribution, verifying the accuracy of the solver. (c) Normalized error quantifies the deviation between the simulation results and the theoretical values, showing the relative error between the simulated velocity and the theoretical accurate velocity at different height positions. The horizontal axis represents the normalized absolute velocity error v2, and the vertical axis represents the normalized position height h1. The error curve is wavy, but the error value is very small across the entire cross section (mostly between 0.02 and 0.08, i.e., about 2% to 8%). This further proves that the calculation method is not only correct in qualitative terms (correct shape), but also has high quantitative accuracy, meeting the accuracy requirements of engineering or scientific research calculations.

[0067] (2) PD transport-deposition verification Based on the validated SPH velocity field, a PD model was used to simulate the mass transport, reaction, and wall deposition processes. This model employed a near-field dynamics (PD) diffusion model based on a nonlocal integral form, and used the harmonic average bond diffusion coefficient for discretization calculations. The channel geometry parameters were consistent with the Poiseuille validation case, and the simulation parameters were: SPH spacing Δx SPH =Δy SPH =0.04m, PD spacing Δx PD =Δy PD =0.02m, diffusion coefficient D=5.0×10 -3 m 2 / s, reaction coefficient k r =2.5×10 -1 s -1 equilibrium concentration C eq =1.0kg / m 3 Deposition rate v dep =1.6×10 -3 m / s, end time t end =3.0s, time step Δt=5.0×10 -3The SPH velocity field was interpolated onto the PD grid as the advection input in the transport calculation. The PD concentration matched the FDM reference value, successfully reproducing the flow gradient and near-wall deposition phenomena. The final relative L2 errors for the concentration field, wall deposition distribution, and total deposition mass were 3.13 × 10⁻⁶. -2 3.66×10 -2 and 3.28×10 -2 The final relative errors were all below 4.0 × 10⁻⁶. -2 This confirms the accuracy of the PD transport-reaction-deposition module. For example... Figure 3 As shown, the horizontal axis represents the concentration C of the substance (kg / m³). 3 The larger the value, the higher the substance content at that location. The vertical axis represents the vertical height h (m) of the pipe, ranging from 0 to 1 meter, corresponding to the distance from the lower to the upper wall of the pipe. The graph shows three sets of curves in different colors, corresponding to three different cross-sectional positions along the flow direction (X-axis). Each set of colors contains two lines to compare two calculation methods: solid line (PD): representing the calculation result of the near-field dynamics method; dashed line (FDM): representing the calculation result of the finite difference method (usually used as the traditional standard method). The blue curve group represents a lower overall concentration, indicating an early stage of reaction or diffusion. The red curve group shows a higher concentration (approximately 0.10-0.25 kg / m³). 3 The yellow curve group showed the highest concentration (approximately 0.15-0.35 kg / m³). 3 This indicates that as the fluid flows forward, matter is continuously generated or accumulated. All concentration curves exhibit a parabolic shape, high in the middle and low at both ends. This aligns with the convection-diffusion law in fluid mechanics. Since the flow velocity at the pipe wall is zero (no slip boundary), matter is mainly transported by diffusion at a slower speed, while the flow velocity at the center of the pipe is high, resulting in high matter transport efficiency. Therefore, the concentration at the center is often higher than at the edges (or depends on the specific source term distribution; here, the peak concentration at the center is shown). Careful observation reveals that the solid line (PD) and the dashed line (FDM) almost completely overlap, indicating that the PD model proposed in this study achieves the same high accuracy as traditional mature methods (FDM) in simulating matter transport and concentration distribution, thus verifying the effectiveness of the PD model. Figure 4 As shown, the horizontal axis represents time t (s), in seconds, ranging from 0 to 3 seconds, indicating the duration of the simulation. The vertical axis represents the total mass of sediment M per unit area. dep(kg / m): (or sediment mass per unit length, depending on the model's dimensionality), the unit is kilograms per meter, representing a micro-deposition process. The figure contains two curves to compare the results of different calculation methods: the black solid line (PD) represents the change in sediment mass over time calculated by the numerical model proposed in this embodiment (possibly based on a near-field dynamics PD or SPH-PD coupled model), and the red dashed line (FDM reference) represents the result calculated using the traditional finite difference method as a reference standard. FDM is generally considered a mature benchmark method. Both curves show a non-linear growth trend. In the initial stage (0-0.5s), the sediment mass... The increase is relatively slow; over time, the deposition rate appears to stabilize or increase slightly (with a steeper slope), reflecting the potential influence of surface coverage, reactant concentration consumption, or changes in hydrodynamic conditions on the deposition process. Most importantly, the black solid line and the red dashed line almost completely overlap; the deviation between them is minimal and virtually indistinguishable to the naked eye throughout the entire 3-second simulation. This figure strongly demonstrates the accuracy of the newly proposed numerical model in handling the complex physicochemical process of deposition / scaling. Since it can reproduce the results of the traditional FDM method, its algorithmic logic is correct, showing that deposition is a dynamic process that accumulates over time, rather than being instantaneous. This has significant engineering implications for predicting when pipelines will become clogged and require cleaning.

[0068] (3) Verification of calcium carbonate fluid-solid scaling in non-uniform channels This validation demonstrates the ability of the SPH-PD framework to simulate the reactive CaCO3 precipitation of transported ions in an equivalent solid blockage cell. Unlike the PD transport-deposition validation, which uses a preset deposition rate, this validation explicitly represents the precipitation process using a precipitation reaction equation and indicates that solid accumulation preferentially occurs at the wall or near the existing blockage cell when the conversion threshold is reached. This numerical conversion reflects the fluid-to-solid transformation and the associated loss of opening area.

[0069] Furthermore, under a fixed geometry and without considering liquid-solid phase transformation, the PD model and the FDM model differ in solid phase distribution, the trend of total solid mass change over time, and Ca. 2+The high consistency in concentration distribution curves and other aspects confirms that the PD model can accurately simulate ion transport processes. Under supersaturated inlet conditions, solid accumulation mainly occurs near the wall. When liquid-solid phase conversion is disabled, accumulation only manifests as an increase in solid volume fraction without changing the fluid computational domain. After enabling liquid-solid phase conversion, near-wall liquid phase units that reach the threshold are transformed into equivalent blocking units, forming local solid deposits. Comparative results of three operating conditions (supersaturated inlet with conversion process, supersaturated inlet without conversion process, and undersaturated inlet with conversion process) show that significant accumulation of blocking units only occurs under supersaturated conditions and when phase change occurs, mainly concentrated on the upstream side of the protruding structure and distributed along the downslope direction. In the two control cases, solid formation is negligible and channel area loss is minimal.

[0070] The above three verification results show that the prediction results of the SPH-PD model are highly consistent with the analytical solution and the FDM reference solution, and can accurately reproduce 10 -2 The fundamental physical mechanisms at the order of magnitude. The main conclusions are: (1) The velocity distribution curve obtained based on the SPH model is consistent with the analytical solution, and the SPH model can successfully predict the laminar flow field; (2) The PD transport-reaction-deposition model is highly consistent with the FDM simulation results in terms of flow direction concentration gradient, near-wall loss and total deposition mass, and the PD model can accurately predict component transport and wall deposition behavior; (3) The coupled SPH-PD framework can accurately describe the complete process of CaCO3 transport from the fluid phase to the solid blockage unit. Unlike the model that ignores phase change or unsaturated state, the blockage unit will only be formed under supersaturated conditions and when the liquid-solid conversion mechanism is activated; (4) The bottom convex structure can enhance the local precipitation effect, and the newly formed blockage unit is mainly concentrated on the upstream side and near the peak of the convex structure.

[0071] like Figure 5 As shown, an embodiment of the present invention provides a pipe scaling analysis device 500, comprising: Module 510 is used to construct the steady-state velocity field of the fluid inside the pipe based on the acquired pipe feature data, using smooth particle fluid dynamics. Modeling module 520 is used to construct a reaction transport model of solute in the pipeline based on peri-field dynamics and the steady-state velocity field. The conversion module 530 is used to obtain the conversion point of the solid material by comparing the solid phase concentration output by the reaction transport model with a threshold. Measurement module 540 is used to obtain scaling data of the pipeline by geometric measurement based on all the converted solid material points.

[0072] The pipe scaling analysis device of this embodiment is used to implement the pipe scaling analysis method as described above. Its advantages over the prior art are the same as the advantages of the pipe scaling analysis method over the prior art, and will not be repeated here.

[0073] like Figure 6 As shown, an electronic device 600 provided in this embodiment of the invention includes a memory 610 and a processor 620; the memory 610 is used to store a computer program; the processor 620 is used to implement the pipe scaling analysis method as described above when the computer program is executed.

[0074] Alternatively, an electronic device 600 includes a memory 610 and a processor 620 coupled to the memory 610; the memory 610 is configured to store a computer program; and the processor 620 is configured to perform the following operations when the computer program is executed: Based on smooth particle fluid dynamics, a steady-state velocity field of the fluid inside the pipe is constructed according to the acquired pipe feature data; Based on peri-field dynamics, a reaction transport model of solute in the pipeline is constructed according to the steady-state velocity field. The conversion point of the solid material is obtained by comparing the solid phase concentration output by the reaction transport model with a threshold. The scaling data of the pipeline is obtained through geometric measurements based on all the converted solid material points.

[0075] This invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the pipe scaling analysis method described above.

[0076] Alternatively, a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the following operations: Based on smooth particle fluid dynamics, a steady-state velocity field of the fluid inside the pipe is constructed according to the acquired pipe feature data; Based on peri-field dynamics, a reaction transport model of solute in the pipeline is constructed according to the steady-state velocity field. The conversion point of the solid material is obtained by comparing the solid phase concentration output by the reaction transport model with a threshold. The scaling data of the pipeline is obtained through geometric measurements based on all the converted solid material points.

[0077] Electronic device 600, which can serve as a server or client of the present invention, is described below as an example of a hardware device applicable to various aspects of the present invention. Electronic device 600 is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic device 600 can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0078] Electronic device 600 includes a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or a computer program loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0079] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc. In this application, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of the present invention according to actual needs. Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units can be implemented in hardware or as software functional units.

[0080] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for analyzing pipe scaling, characterized in that, include: Based on smooth particle fluid dynamics, a steady-state velocity field of the fluid inside the pipe is constructed according to the acquired pipe feature data; Based on peri-field dynamics, a reaction transport model of solute in the pipeline is constructed according to the steady-state velocity field. The conversion point of the solid material is obtained by comparing the solid phase concentration output by the reaction transport model with a threshold. The scaling data of the pipeline is obtained through geometric measurements based on all the converted solid material points.

2. The pipe scaling analysis method according to claim 1, characterized in that, The pipeline characteristic data includes pipeline geometric parameters, physical property parameters, and numerical discrete parameters; the construction of the steady-state velocity field of the fluid inside the pipeline based on the acquired pipeline characteristic data includes: A coupled discrete model of the pipeline is constructed based on the pipeline geometric parameters and the numerical discrete parameters. Based on a preset viscous relaxation solver, the steady-state velocity field is obtained according to the pipeline coupled discrete model, the physical property parameters, and the numerical discrete parameters.

3. The pipe scaling analysis method according to claim 2, characterized in that, The construction process of the pipeline coupling discrete model includes: A pipeline model is constructed based on the pipeline geometry parameters, and the fluid domain and solid domain of the pipeline model are determined. Based on the smooth particle spacing in the numerical discrete parameters, smooth particles are uniformly distributed in the fluid domain and the solid domain, and the smooth particles in the fluid domain are assigned fluid particle properties, and the smooth particles in the solid domain are assigned wall particle properties. Based on the material point spacing in the numerical discrete parameters, material points are uniformly distributed in the fluid domain and the solid domain, and liquid point attributes are assigned to liquid material points in the fluid domain and solid point attributes are assigned to solid material points in the solid domain.

4. The pipe scaling analysis method according to claim 3, characterized in that, The pipeline characteristic data also includes inlet concentration parameters; the construction process of the reaction transport model includes: Based on the normalized interpolation method, the steady-state velocity field is interpolated from the smooth particle to the liquid material point; The initial liquid phase concentration is assigned to the liquid material points in the inlet region of the pipeline coupled discrete model based on the inlet concentration parameter.

5. The pipe scaling analysis method according to claim 1, characterized in that, The step of obtaining the conversion point of the solid material by comparing the solid concentration output from the reaction transport model with a threshold includes: Based on a preset time step, the reaction transport model is controlled to perform simulation to obtain the solid phase concentration of the liquid material point; Based on the threshold comparison result of the solid phase concentration, the corresponding liquid material point is subjected to liquid-solid conversion to obtain the converted solid material point.

6. The pipe scaling analysis method according to claim 5, characterized in that, The step of performing liquid-solid conversion on the corresponding liquid material point based on the threshold comparison result of the solid phase concentration to obtain the converted solid material point includes: The corresponding solid volume fraction is obtained by comparing the solid concentration at the liquid material point with the preset maximum equivalent solid concentration. The liquid material point is judged to meet the liquid-solid conversion condition based on the comparison result between the solid volume fraction and the preset conversion threshold. If so, the liquid material point is converted from a fluid state to a solid state to obtain the converted solid material point.

7. The pipe scaling analysis method according to claim 5, characterized in that, The step of determining whether the liquid material point meets the liquid-solid conversion condition based on the comparison result of the solid volume fraction and the preset conversion threshold includes: When the solid volume fraction is greater than the preset conversion threshold, it is determined that the liquid material point satisfies the liquid-solid conversion condition. When the solid volume fraction is less than or equal to the preset conversion threshold, it is determined that the liquid material does not meet the liquid-solid conversion condition.

8. The method for analyzing pipe scaling according to claim 1, characterized in that, The process of obtaining the scaling data of the pipeline through geometric measurement based on all the converted solid material points includes: The corresponding equivalent blockage thickness is obtained by summing the characteristic dimensions of the converted solid material points in the wall normal of the pipe. The remaining flow area of ​​the pipeline is obtained by statistical analysis of the area occupancy based on the spatial distribution of all the converted solid material points. The scaling mass is obtained by summing and integrating the solid phase concentration and characteristic volume of all the aforementioned solid material points. The scaling data is generated based on the equivalent blockage thickness, the remaining flow area, and the scaling quality.

9. A pipe scaling analysis device, characterized in that, include: The module is used to construct the steady-state velocity field of the fluid inside the pipe based on the acquired pipe feature data, using smooth particle fluid dynamics. The modeling module is used to construct a reaction transport model of solute in the pipeline based on near-field dynamics and the steady-state velocity field. The conversion module is used to obtain the conversion point of the solid material by comparing the solid phase concentration output by the reaction transport model with a threshold. The measurement module is used to obtain the scaling data of the pipeline through geometric measurement based on all the converted solid material points.

10. An electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to implement the pipe scaling analysis method as described in any one of claims 1 to 8 when executing the computer program.

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