Method and system for numerical simulation of a bubbling degassing water exraction process

Abstract

The application discloses a kind of bubble degassing water analysis radon process numerical simulation method and system, by constructing two-dimensional gas-liquid radon mass transfer model including water body and bubble, introducing correction factor to dynamically correct benchmark shedding radius and establishing transient mass transfer differential equation combined with initial rising velocity, effectively solve the problem that radon concentration transient change in bubble rising process cannot be accurately simulated and radon detector theoretical reading cannot be accurately calculated due to dynamic coupling of bubble dynamics parameters (such as shedding radius and rising velocity affected by air flow) and mass transfer process in prior art;The method realizes the accurate capture of the spatio-temporal evolution law of radon concentration from the whole life cycle of bubble generation, rising to cracking, significantly improves the simulation accuracy, and the reliability of the model is verified by comparing the theoretical and experimental values, thereby providing a high-precision theoretical basis for the optimization design of bubble degassing process parameters.

Description

Technical Field

[0001] This invention relates to the field of 000 technology, specifically to a method and system for numerical simulation of the radon separation process in bubbling degassing water. Background Technology

[0002] Radon is a colorless, odorless, and tasteless radioactive inert gas, primarily originating from the decay of radium in the Earth's crust. In underground engineering, nuclear facilities, and drinking water treatment, the release and migration of dissolved radon in water are critical concerns for radiation protection and environmental monitoring. To reduce radon levels in water bodies, the bubble degassing method is widely used due to its high efficiency and ease of operation. The basic principle of this method is to introduce air into the water, using air bubbles as carriers. Through mass transfer at the gas-liquid interface, radon in the water is transferred to the air bubbles, which then escape to the surface and are discharged.

[0003] Existing research on radon separation in bubble degassing water largely relies on experimental tests or simplified empirical formulas. Experimentally, researchers typically construct physical experimental setups, change parameters such as inlet air flow rate and inlet water flow rate, and directly measure the radon concentration in the effluent or radon meter readings to assess degassing efficiency. However, experimental methods are costly, time-consuming, and struggle to reflect the microscopic mass transfer dynamics within the bubbles in real time. In theoretical simulations, existing techniques often employ simplified one-dimensional models or steady-state assumptions, neglecting the dynamic impact of the bubble's kinetic characteristics during ascent (such as changes in bubble radius and ascent velocity) on the mass transfer process. For example, traditional models often assume the bubble is a rigid sphere rising at a constant velocity, failing to consider the nonlinear correction for the bubble's fall radius affected by the inlet air flow rate, and neglecting to deeply couple the bubble's ascent velocity with the transient mass transfer differential equations under the two-film theory. This simplification makes it impossible for existing simulation models to accurately describe the spatiotemporal evolution of radon concentration throughout the entire process of bubble generation, rising and bursting. Consequently, it is difficult to accurately predict the theoretical readings of radon detectors under different operating conditions, which limits the optimization design of bubbling degassing process parameters. Summary of the Invention

[0004] This invention aims to provide a method and system for numerical simulation of the radon precipitation process in bubble degassing water, effectively solving the problems of existing technologies that fail to accurately simulate the transient changes in radon concentration during bubble rise and make it difficult to accurately calculate the theoretical readings of radon meters due to neglecting the dynamic coupling between bubble dynamics parameters and mass transfer process.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a method for numerical simulation of the radon separation process in bubbling degassing water, comprising:

[0006] S1: Based on the COMSOL Multiphysics software platform, a two-dimensional gas-liquid radon mass transfer model including water and bubbles is constructed, and the initial conditions are set as the radon concentration in the water and the radon concentration inside the bubbles;

[0007] S2: Based on the set air intake flow rate, the shedding radius and initial rising velocity of a single bubble are calculated using the two-dimensional gas-liquid radon mass transfer model, wherein the shedding radius is obtained by correcting the reference shedding radius by introducing a correction factor.

[0008] S3: Using the initial rising velocity and the fall radius, combined with the two-film theory, a mass transfer differential equation describing the migration of radon gas from the water body to the interior of the bubble is established, and the curve of the average radon concentration of the bubble changing with time during the rising process is obtained by solving the equation.

[0009] S4: Based on the aforementioned change curve, simulate the radon concentration field distribution at the instant the bubble breaks at the gas-liquid interface, and calculate the total radon activity accumulated inside the bubble.

[0010] S5: Calculate the theoretical reading of the radon detector based on the total radon activity and the number of bubbles generated per unit time, and compare the theoretical reading with the experimental measurement to verify the reliability of the model.

[0011] Preferably, in S2, the reference detachment radius is calculated using a static detachment formula based on the outlet diameter, gas-liquid density difference, and surface tension, and the correction factor is an empirical coefficient obtained by fitting measured bubble radius data under different inlet flow rates.

[0012] Preferably, in S3, the driving mechanism of the mass transfer differential equation is based on Henry's law, wherein the concentration of radon in the gas phase is the concentration in the liquid phase multiplied by the Ostwald coefficient, and when the ratio of the radon concentration in water to the radon concentration in the gas is greater than the Ostwald coefficient, radon is transferred from the liquid phase to the gas phase.

[0013] Preferably, in S4, the radon concentration field distribution at the instant the bubble breaks at the gas-liquid interface is obtained by volume normalization of the radon concentration inside the bubble using an integral operator.

[0014] Preferably, in S5, the number of bubbles generated per unit time is the bubble frequency calculated based on the air intake flow rate and the volume of a single bubble.

[0015] Preferably, the method further includes S6: establishing a mass balance differential equation based on the influent flow rate and water volume, deriving an analytical expression for the change of radon concentration in the water in the bubbling degassing device over time, and calculating the steady-state radon concentration.

[0016] On the other hand, the present invention proposes a system for numerical simulation of the radon separation process in bubbling degassing water, comprising:

[0017] The modeling module is used to build a two-dimensional gas-liquid radon mass transfer model containing water and bubbles based on the COMSOL Multiphysics software platform, and sets the initial conditions as the radon concentration in the water and the radon concentration inside the bubbles;

[0018] The parameter calculation module is used to calculate the shedding radius and initial rising velocity of a single bubble based on the set air intake flow rate using the two-dimensional gas-liquid radon mass transfer model. The shedding radius is obtained by correcting the reference shedding radius by introducing a correction factor.

[0019] The mass transfer solution module is used to establish a mass transfer differential equation describing the migration of radon gas from the water body to the interior of the bubble by using the initial ascent velocity and the detachment radius, combined with the two-film theory, and to solve for the curve of the average radon concentration of the bubble changing with time during the ascent process.

[0020] The field distribution simulation module is used to simulate the radon concentration field distribution at the moment the bubble breaks at the gas-liquid interface based on the curve of the average radon concentration changing with time during the rising process of the bubble, and to calculate the total radon activity accumulated in the bubble.

[0021] The results analysis module is used to calculate the theoretical reading of the radon detector based on the total radon activity accumulated in the bubbles and the number of bubbles generated per unit time, and to compare the theoretical reading with the experimental measurement to verify the reliability of the model.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] This invention constructs a two-dimensional gas-liquid radon mass transfer model incorporating water and bubbles, introduces a correction factor to dynamically correct the baseline shedding radius, and establishes a transient mass transfer differential equation in conjunction with the initial rise velocity. This effectively solves the problem in existing technologies where the dynamic coupling between bubble dynamics parameters (such as the shedding radius and rise velocity affected by the inlet flow rate) and the mass transfer process is neglected, resulting in the inability to accurately simulate the transient changes in radon concentration during bubble rise and the difficulty in accurately calculating the theoretical readings of radon meters. This method achieves precise capture of the spatiotemporal evolution of radon concentration throughout the entire life cycle of bubbles, from generation and rise to collapse, significantly improving simulation accuracy. The reliability of the model is verified by comparing theoretical and experimental values, thus providing a high-precision theoretical basis for the optimized design of bubbling degassing process parameters. Attached Figure Description

[0024] Figure 1 This is a diagram showing the bubble distribution (inlet flow rate = 0.5 L / min) of the bubbling degassing device of the present invention.

[0025] Figure 2 This is a diagram showing the bubble distribution (inlet flow rate = 1.0 L / min) of the bubble degassing device of the present invention.

[0026] Figure 3 This is a diagram of the gas-liquid mass transfer model for a single bubble in this invention. , );

[0027] Figure 4 The concentration distribution of the bubbles at the moment they reach the liquid surface (t=0.25 s) is shown in the figure. )picture;

[0028] Figure 5 The curve showing the change of average bubble concentration over time in this invention ( , )picture;

[0029] Figure 6 This refers to the time it takes for a single bubble to reach the interface under different influent flow rates according to the present invention. a-f represent the influent flow rates, respectively. =1.0, 1.5, 2.0, 2.5, 3.0-5.0 L / min time graph for bubbles reaching the liquid surface;

[0030] Figure 7 This is a graph showing the effect of the influent flow rate on the concentration of radon gas at the outlet and its saturation verification.

[0031] Figure 8 The trend of radon concentration change in the water body of the degassing device of the present invention ( =1.3L / min, =75.71Bq / L) Figure;

[0032] Figure 9 The graph shows the variation of radon concentration in the water of the degassing device of the present invention, where ad represents the influent flow rates of 1.0, 0.7, 0.5 and 0.3 L / min, respectively.

[0033] Figure 10 The concentration distribution of the bubbles at the moment they reach the liquid surface (t=0.27s) is shown in the figure. )picture;

[0034] Figure 11 The curve showing the change of average bubble concentration over time in this invention ( , )picture;

[0035] Figure 12 The time for a single bubble to reach the interface under different inlet water flow rates in this invention is given by a-f, where a-f represent the inlet air flow rates, respectively. =1.0, 1.5, 2.0, 2.5, 3.0-5.0 L / min, the time it takes for bubbles to reach the liquid surface;

[0036] Figure 13 This is a flowchart of the numerical simulation method for the radon separation process of bubbling degassing water according to the present invention. Detailed Implementation

[0037] The following description is intended to disclose the invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art.

[0038] like Figure 13 As shown, this invention proposes a method for numerical simulation of the radon separation process in bubbling degassing water, comprising:

[0039] S1: Based on the COMSOL Multiphysics software platform, a two-dimensional gas-liquid radon mass transfer model including water and bubbles is constructed, and the initial conditions are set as the radon concentration in the water and the radon concentration inside the bubbles;

[0040] S2: Based on the set air intake flow rate, the shedding radius and initial rising velocity of a single bubble are calculated using the two-dimensional gas-liquid radon mass transfer model, wherein the shedding radius is obtained by correcting the reference shedding radius by introducing a correction factor.

[0041] The reference detachment radius is calculated using a static detachment formula based on the outlet diameter, gas-liquid density difference, and surface tension. The correction factor is an empirical coefficient obtained by fitting measured bubble radius data under different inlet flow rates.

[0042] S3: Using the initial rising velocity and the fall radius, combined with the two-film theory, a mass transfer differential equation describing the migration of radon gas from the water body to the interior of the bubble is established, and the curve of the average radon concentration of the bubble changing with time during the rising process is obtained by solving the equation.

[0043] The driving mechanism of the mass transfer differential equation is based on Henry's law, in which the concentration of radon in the gas phase is the concentration in the liquid phase multiplied by the Ostwald coefficient, and when the ratio of the radon concentration in water to the radon concentration in the gas is greater than the Ostwald coefficient, radon is transferred from the liquid phase to the gas phase.

[0044] S4: Based on the aforementioned change curve, simulate the radon concentration field distribution at the instant the bubble breaks at the gas-liquid interface, and calculate the total radon activity accumulated inside the bubble; the radon concentration field distribution at the instant the bubble breaks at the gas-liquid interface is obtained by volume normalizing the radon concentration inside the bubble using an integral operator.

[0045] S5: Based on the total radon activity and the number of bubbles generated per unit time, calculate the theoretical reading of the radon meter, and compare the theoretical reading with the experimental measurement to verify the reliability of the model. The number of bubbles generated per unit time is the bubble frequency calculated based on the airflow rate and the volume of a single bubble.

[0046] Furthermore, the above method also includes S6: establishing a mass balance differential equation based on the influent flow rate and water volume, deriving an analytical expression for the change of radon concentration in the water body with time in the bubbling degassing device, and calculating the steady-state radon concentration.

[0047] This invention constructs a two-dimensional gas-liquid radon mass transfer model that includes water and bubbles, introduces a correction factor to dynamically correct the baseline drop radius, and establishes a transient mass transfer differential equation in conjunction with the initial rise velocity. This effectively solves the problem that existing technologies cannot accurately simulate the transient changes in radon concentration during bubble rise and are difficult to accurately calculate the theoretical reading of the radon meter because they ignore the dynamic coupling between bubble dynamic parameters (such as the drop radius and rise velocity affected by the air flow rate) and the mass transfer process.

[0048] This method accurately captures the spatiotemporal evolution of radon concentration throughout the entire lifecycle of bubbles, from generation and rise to rupture, significantly improving simulation accuracy. The reliability of the model is verified by comparing theoretical and experimental values, thus providing a high-precision theoretical basis for the optimized design of bubbling degassing process parameters.

[0049] On the other hand, the present invention proposes a system for numerical simulation of the radon separation process in bubbling degassing water, the system comprising:

[0050] The modeling module is used to build a two-dimensional gas-liquid radon mass transfer model containing water and bubbles based on the COMSOL Multiphysics software platform, and sets the initial conditions as the radon concentration in the water and the radon concentration inside the bubbles;

[0051] The parameter calculation module is used to calculate the shedding radius and initial rising velocity of a single bubble based on the set air intake flow rate using the two-dimensional gas-liquid radon mass transfer model. The shedding radius is obtained by correcting the baseline shedding radius by introducing a correction factor.

[0052] The mass transfer solution module is used to establish a mass transfer differential equation describing the migration of radon gas from the water body to the interior of the bubble by using the initial rising velocity and the falling radius, combined with the two-film theory, and to solve for the curve of the average radon concentration of the bubble changing with time during the rising process.

[0053] The field distribution simulation module is used to simulate the radon concentration field distribution at the moment the bubble breaks at the gas-liquid interface based on the curve of the average radon concentration changing with time during the rising process of the bubble, and to calculate the total radon activity accumulated in the bubble.

[0054] The results analysis module is used to calculate the theoretical reading of the radon detector based on the total radon activity accumulated in the bubbles and the number of bubbles generated per unit time, and to compare the theoretical reading with the experimental measurement to verify the reliability of the model.

[0055] This study employed COMSOL Multiphysics to simulate the radon mass transfer process between bubbles and water in a bubbling degassing device. Its core advantage lies in its highly integrated modular structure, providing a unified interface for solving coupled problems between various physical phenomena. Furthermore, COMSOL Multiphysics' multiphysics simulation capabilities make it an indispensable tool in research and industrial applications, particularly in the analysis of interdisciplinary studies involving electromagnetics, fluid mechanics, structural mechanics, chemistry, acoustics, and thermodynamics. The modeling process in COMSOL Multiphysics is primarily based on the Finite Element Method (FEM).

[0056] The specific numerical simulation process for radon separation in bubbling degassing water is as follows:

[0057] The water radon desorption model is constructed as follows:

[0058] Considering that the bubbling degassing process in this embodiment mainly occurs under low flow and low speed conditions, the main gas-liquid two-phase region can be approximated as fully mixed, while the main mass transfer resistance is concentrated in the thin interfacial layer region near the bubble surface. Therefore, the basic assumption of the two-film theory regarding "the existence of a stable mass transfer boundary layer on both sides of the interface" is largely consistent with this embodiment. Compared to the permeation theory and surface renewal theory, the two-film theory has fewer parameters and clearer physical meaning, making it easier to implement in COMSOL Multiphysics and compare with experimental results. Since the parameters such as contact time and surface renewal rate involved in the permeation theory and surface renewal theory are difficult to determine independently under the conditions of this study and would increase model uncertainty, the subsequent gas-liquid mass transfer model adopts the two-film theory as the descriptive basis.

[0059] In the process of bubble degassing, the mechanism by which radon gas is removed from the water can be divided into two key stages: mass transfer during bubble rise and release after bubble collapse at the gas-liquid interface.

[0060] Mass transfer during bubble ascent is the core stage: radon gas is primarily transferred from the liquid phase (water) to the gas phase (bubbles) as the bubbles rise in water. This process is dominated by the following physical mechanisms: 1. Dissolution equilibrium and Henry's Law. Radon gas is mainly transferred through the solubility C of the bubbles in water. H2O Its partial pressure P within the bubble Rn Obeying Henry's Law:

[0061] (1)

[0062] In formula (1), H: Henry's constant for radon (approximately 0.23 mol / (m3·Pa) at 25℃); P Rn: The partial pressure of radon gas inside the bubble (initially 0, gradually increasing with mass transfer).

[0063] The driving mechanism is that the radon concentration in the water is higher than the equilibrium concentration inside the bubbles, causing radon gas to enter the bubbles through diffusion and convection. Furthermore, this involves radon exchange at the gas-liquid interface, which can also be expressed as flux.

[0064] (2)

[0065] In formula (2), Radon transport flux, Bq / (m2·s); Radon transport rate at the gas-liquid interface, m / s; Radon concentration in water, Bq / m³ 3 ; Radon concentration in gas, Bq / m³ 3 ; The Ostwald coefficient, also known as the radon dissolution equilibrium coefficient at the gas-liquid interface, is an important parameter describing the solubility of a gas in the liquid phase during gas-liquid two-phase equilibrium. It is defined as follows:

[0066]

[0067] That is, when the gas and liquid phases reach dynamic equilibrium, the ratio of the concentration of a specific gas in the liquid phase to the concentration in the gas phase.

[0068] According to formula (2) and definition: at the gas-liquid interface, there are three cases: 1) C water / C gas >α, at this point, radon dissolved in water is transferred to the gas; 2)C water / C gas <α, at this point, dissolved radon in the gas is transferred to the water; 3)C water / C gas =α, at which point radon in the gas and liquid phases is in equilibrium and radon mass transfer stops.

[0069] According to Fick's law, the radon concentration gradient in a liquid film will induce diffusion mass transfer. Fick's first law describes steady-state diffusion, meaning that when the concentration does not change with time, the diffusion flux is linearly related to the concentration gradient.

[0070] (3)

[0071] In formula (3), Diffusion flux, g / (cm³) 2 ·s) or mol / (cm 2 ·s); : Diffusion coefficient, which is related to material and temperature, in cm 2 / s; Concentration gradient.

[0072] Fick's second law describes unsteady diffusion, i.e., the change of concentration over time, and is expressed as:

[0073] (4)

[0074] According to Fick's Law, the direction of diffusion is the direction of concentration decrease, leading to a eventually uniform concentration distribution. However, in the bubbling degassing process, radon mass transfer follows Fick's First Law. This is because: 1) During bubble ascent, diffusion within the liquid film can generally be considered quasi-steady-state, meaning the concentration gradient within the liquid film remains stable for a short time. This aligns with the core argument of the two-film theory, that liquid film mass transfer is the rate-controlling step of the process, and is calculated using Fick's First Law. 2) Radon diffuses from the high-concentration liquid phase to the low-concentration gas phase, driven by the concentration difference at the interface. The diffusion rate is directly proportional to the concentration gradient, which conforms to Fick's First Law. 3) Although bubble motion may lead to unsteady-state effects, a steady-state approximation is typically used to simplify calculations, hence Fick's First Law is also employed. Finally, when the bubble bursts at the gas-liquid interface, the accumulated radon gas is released directly into the air, completing the degassing process.

[0075] The analysis of radon concentration in water under different influent flow rates is as follows:

[0076] Steady-state radon concentration in water from the bubbling degassing device:

[0077] The continuous variation in water and air flow rates means that the radon concentration in the degassing device is not a fixed value. Therefore, it is necessary to derive the radon concentration in the device under different conditions.

[0078] Table 1 Parameter Table of Bubble Degassing Unit

[0079]

[0080] Because of the residence time of water inside the device Since its half-life is much shorter than that of radon, the decay term can be ignored. Assume the aqueous phase is completely mixed and the radon concentration in the water is uniform. .

[0081] Under steady state, the inflow and outflow of radon per unit time:

[0082] (5)

[0083] According to Henry's equilibrium law, when equilibrium is reached at the gas-liquid interface:

[0084] (6)

[0085] This indicates that the concentration of radon in the gas phase is four times that in the liquid phase, suggesting that radon is preferentially allocated to the gas phase.

[0086] In reality, bubbles have a limited time to rise in water and may not reach complete equilibrium. Mass transfer efficiency is defined. :

[0087] (7)

[0088] In formula (7), The bubbles and water are completely in equilibrium; The bubbles have only partially reached equilibrium. Solving equations 5-5 and 5-7 simultaneously yields:

[0089] (8)

[0090] (9)

[0091] (10)

[0092] Outlet gas phase concentration:

[0093] (11)

[0094] Define equivalent airlift parameters:

[0095] (12)

[0096] Formula (12) shows that the gas flow rate Q g Mass transfer efficiency and solubility coefficient A joint decision.

[0097] Then formula (10) simplifies to:

[0098] (13)

[0099] (14)

[0100] Formula (14) shows that: 1. Increase the influent flow rate Q w , Increase, or conversely, 1. Decrease; 2. Increase intake airflow Q g , 3. Decrease; 4. Increase , 4. Decrease; Increase temperature Reduced, leading to Decrease.

[0101] Mass transfer efficiency :

[0102] For a diameter Bubbles rise from the bottom to the surface of the water. Contact time:

[0103] (15)

[0104] The differential equation for the change of radon concentration inside the bubble over time:

[0105] (16)

[0106] in For measuring the mass transfer coefficient in the liquid phase, This represents the specific surface area of ​​the bubble.

[0107] Initial conditions The solution is:

[0108] (17)

[0109] Therefore, the mass transfer efficiency is:

[0110] (18)

[0111] Classic bubble diameter produced by air stone Take the median value The rising speed of the bubbles, because they are small bubbles, is in the middle Reynolds number region, therefore... Mass transfer coefficient on the liquid surface:

[0112] (19)

[0113] Contact time: t e = 0.25 s, mass transfer efficiency: η ≈ 10.7%.

[0114] The calculation results are shown in Table 2.

[0115] Table 2 Equivalent gas stripping parameters

[0116]

[0117] Gas-liquid balance ( , )hour:

[0118] (20)

[0119] (twenty one)

[0120] The data are shown in Table 3:

[0121] Table 3. Parameter values ​​for the complete gas-liquid equilibrium condition.

[0122]

[0123] Mass transfer efficiency ( , )hour:

[0124] (twenty two)

[0125] (twenty three)

[0126] The data are shown in Table 4:

[0127] Table 4. Parameter values ​​for incomplete gas-liquid equilibrium.

[0128]

[0129] The bubble radius and initial ascent velocity are analyzed as follows:

[0130] In simulating gas-liquid mass transfer processes in two-phase flow, bubble size and rising velocity are key factors. Air ejected from micropores in a bubble stone forms bubbles below the liquid surface. The size of a single bubble is determined by the following factors: 1. the diameter of the outlet (d0); 2. the gas-liquid density difference. 3. Surface tension σ; 4. Gas flow rate in the pores (compared to the inlet flow rate Q) g (Related). The rising speed of a bubble is determined by buoyancy, resistance, inertia, and other factors.

[0131] When the intake airflow changes, the amount of air ejected from the outlet varies, resulting in different volumes of each bubble detaching, thus altering the radius. A change in the radius alters the balance between buoyancy and resistance in the bubble, thus affecting its initial ascent speed. .

[0132] With a fixed intake airflow At (L / min), the bubble formation process can be approximated as follows:

[0133] (twenty four)

[0134] In formula (24), The number of bubbles formed per unit time; Volume of a single bubble.

[0135] Bubble volume:

[0136] (25)

[0137] have:

[0138] (26)

[0139] Formula (26) shows that if the intake flow rate Increase the number of bubbles This will also increase, and the volume of a single bubble will also increase accordingly.

[0140] For slowly formed bubbles, the buoyancy and surface tension balance when the bubble falls out:

[0141] (27)

[0142] Simplify:

[0143] (28)

[0144] Formula (28) gives the static detachment radius (which is independent of flow rate). However, under high-speed airflow conditions, the flow rate will increase the detachment volume of the bubble, so the actual radius will be larger than the static value. In this case, a correction term needs to be introduced.

[0145] The effects of buoyancy, drag, and mass on the bubble in water. Initially, immediately after detachment, it can be approximated as having reached a quasi-steady-state velocity. For Reynolds number For larger, medium-sized bubbles, the terminal velocity can be calculated using the method of balancing buoyancy and drag, i.e., buoyancy equals drag:

[0146] (29)

[0147] Simplify:

[0148] (30)

[0149] In formula (30), C d The drag coefficient depends on: Re, which characterizes the relative interaction between inertial and viscous forces during bubble motion; and Eo, which characterizes the relative interaction between buoyancy and surface tension. Both factors jointly affect the bubble shape, flow state, and the drag it experiences.

[0150] for bubbles, This formula shows The larger the initial rate of ascent The larger.

[0151] Calculation results:

[0152] 1) Calculate the radius based on the flow rate:

[0153] (31)

[0154] 2) Static limiting radius (applicable to conditions of slow gas release):

[0155] (32)

[0156] 3) Initial ascent velocity (applicable to millimeter-scale bubbles) ):

[0157] (33)

[0158] Because a larger flow rate results in a larger volume of detached bubbles, the formula for the reference radius is as follows:

[0159] (34)

[0160] A correction factor needs to be introduced; the empirical model can be as follows:

[0161] (35)

[0162] In formula (35), , This is an empirical coefficient.

[0163] Based on known parameters , , , , The baseline detachment radius can be obtained. .

[0164] like Figure 1 and 2 The images show bubble swarms in a bubbling degassing device under inlet flow rates of 0.5 L / min and 1.0 L / min, respectively. The black and white grid background in the images is 6 mm × 6 mm. The median bubble radius in the images is 2 mm (0.5 L / min) and 2.2 mm (1.0 L / min). It is clear that the bubble radius at an inlet flow rate of 0.5 L / min is smaller than the baseline shedding radius of 3.32 mm. Therefore, correction is needed.

[0165] (36)

[0166] By fitting two known sets of data, we can deduce... .

[0167] Therefore, the empirical formula is:

[0168] (37)

[0169] The upward velocity is calculated based on the radius.

[0170] (38)

[0171] The calculation results are shown in Table 5:

[0172] Table 5. Bubble radius and rising velocity under different airflow rates

[0173]

[0174] The influence of control parameters on radon gas emission concentration is analyzed as follows:

[0175] The effect of airflow rate on radon gas evolution is as follows:

[0176] Based on model construction, the bubbling degassing device was optimized into a two-dimensional gas-liquid radon mass transfer model, such as... Figure 3 As shown in the figure, this graph reflects the initial state (t=0) when the bubbles first enter the liquid phase. The highest concentration is found at the bubble surface (orange area), indicating that the liquid-liquid component (radon) is just beginning to enter the gas phase at the gas-liquid interface. This is the concentration distribution characteristic of the initial stage of the mass transfer process.

[0177] The radon gas obtained by the degassing device is directly fed into the P2000 radon meter for real-time measurement. Under steady-state conditions, the total amount of radon gas carried out by all bubbles per unit time, divided by the total gas flow rate per unit time, is the reading of the radon meter.

[0178] The number of bubbles generated per unit time, i.e., the frequency:

[0179] (39)

[0180] The total number of bubbles generated within a time period is:

[0181] (40)

[0182] Radioactivity:

[0183] (41)

[0184] Theoretical formula for calculating radon concentration using a radon meter:

[0185] (42)

[0186] (43)

[0187] (44)

[0188] Formula (44) shows that the concentration displayed by the radon meter is the radon concentration inside the bubble at the moment of bubble burst.

[0189] In the simulation, the radon activity inside the bubble is set as c_bubble_avg=int_bub(c * (pf.Vf2 > 0.5)) / (int_bub(pf.Vf2 > 0.5) + eps). Here, int_bub is the integral operator, physically representing the total radon activity inside the bubble; pf.Vf2 > 0.5 is a Boolean function, with 1 for the inside of the bubble and 0 for the outside. The denominator is the total bubble activity, and volume normalization is applied to the denominator. The simulation results of bubble mass transfer time under different inlet flow rates are shown in the figure (…). Figures 4-6 ).

[0190] Figure 4 The diagram shows the radon concentration field distribution at the moment the bubble breaks at the liquid surface after rising for 0.27 seconds. Compared to the initial moment (t=0s), the radon concentration inside the bubble increases significantly (by four orders of magnitude) after the 0.27-second rise. The high concentration region at the top of the bubble indicates that a large amount of radon has been transferred to the gas phase, and this enriched radon will be released into the air when the bubble breaks. The wake below the bubble shows the effect of the mass transfer process on the concentration field of the surrounding liquid phase.

[0191] exist Under these conditions, the radon concentration in the water of the device was 72.9 Bq / L (Table 4). When At that time, bubble radius Initial rising velocity of the bubble (Table 4). The bubble concentration change curve is shown below. Figure 5 As shown, this curve illustrates the change in average radon concentration inside a single bubble over time during its ascent. The entire curve comprises three stages: Initial stage (0-0.05 s): The concentration rises rapidly, exhibiting a steep growth curve. This is the stage with the fastest mass transfer rate. When the bubble first enters the liquid phase, the concentration difference between the gas and liquid phases is at its maximum, resulting in a strong driving force for mass transfer, and radon quickly dissolves into the bubble. Transition stage (0.05-0.15 s): The growth rate gradually slows down. As the radon concentration inside the bubble increases, the concentration gradient decreases, and the mass transfer rate declines. Steady stage (0.15-0.3 s): Approaching equilibrium. At 0.27 s (when the bubble reaches the liquid surface), the concentration is close to the equilibrium value, and the mass transfer process is essentially complete. Furthermore, the logarithmic coordinates of the curve show that the radon concentration increased by approximately four orders of magnitude throughout the process (from 10⁻²¹ to 10⁻¹⁷ mol / m³), which is consistent with... Figure 4 The concentration field distribution observed in the study is consistent with that observed in the study.

[0192] Other single-bubble mass transfer processes at different intake flow rates, such as Figure 6As shown in the figures, this set of figures illustrates the radon concentration field distribution characteristics at the moment of bubble rupture upon reaching the liquid surface under different inlet flow rates. 1. Time variation: As the inlet flow rate increases, the time for the bubble to reach the liquid surface gradually shortens (from 0.25 s to 0.21 s). 2. Concentration distribution characteristics: In the low flow rate range (1.0-1.5 L / min), the high concentration region at the top of the bubble is relatively concentrated; in the medium flow rate range (2.0-2.5 L / min), the concentration distribution pattern is similar, and the mass transfer efficiency is stable; in the high flow rate range (3.0-5.0 L / min), the bubble rises faster, but the mass transfer time is shortened, and the concentration distribution is slightly different. 4. The concentration gradient on the bubble surface is obvious, indicating a continuous gas-liquid mass transfer process; 5. The shorter rise time means a reduced mass transfer contact time, but an increased flow rate may bring a stronger disturbance effect. This set of comparative figures reveals the comprehensive impact of inlet flow rate on bubble dynamics and the mass transfer process. Increased flow rate accelerates bubble rise and shortens mass transfer time, but under all operating conditions, bubble collapse carries a large amount of radon to the liquid surface, which is of great significance for understanding the radon release mechanism.

[0193] The calculation results are shown in Table 5-8. From the experimental and simulation data in the table, the following significant trends can be observed:

[0194] 1) Effect of inlet air flow rate on radon concentration: Under any constant inlet water flow rate, as the inlet air flow rate increased from 0.5 L / min to 3.0 L / min, the experimental radon concentration values ​​all showed a significant decreasing trend. For example, the experimental value decreased from 40.3 Bq / L to 15.9 Bq / L. This reflects that the dilution effect generated by the high gas flow exceeds the gain in mass transfer rate. This is consistent with the nonlinear relationship between contact time and mass transfer efficiency mentioned earlier. Initially, the radon concentration inside the bubble is extremely low, the concentration gradient at the gas-liquid interface is the largest, and the mass transfer driving force is the strongest. As the bubble rises, the radon concentration inside the bubble gradually increases and tends towards the gas-liquid equilibrium concentration determined by Henry's Law. When the intake airflow While increasing the concentration of the bubble may alter fluid disturbance, it also significantly increases the rising velocity of the bubble, resulting in a shorter residence time t of the bubble in the water.

[0195] Figure 4 and 6 This indicates that a high airflow rate leads to a faster bubble rise, reducing the contact time between the bubble and the water phase, thereby decreasing the radon absorption efficiency of a single bubble. However, the inlet airflow rate... arrive The time it takes for bubbles to reach the interface is hardly shortened, which may be related to the turbulence caused by the increased airflow and the interaction between the bubble swarms. For example, strong water flow may cause the bubble's rising path to become distorted, increasing the bubble's residence time in the water.

[0196] 2) Effect of influent flow rate on gas phase concentration: A horizontal comparison of different influent flow rates reveals that, with... The increase (from 0.5 to 1.3) The gas phase radon concentration increased significantly under the same inlet conditions. This is because the higher inlet water flow rate maintained the stability of the water radon concentration in the bubbling degassing device, reduced the concentration drop caused by degassing, and thus maintained a higher mass transfer driving force, allowing a single bubble to carry more radon into the gas phase.

[0197] From the overall error distribution, the deviation between the simulated and experimental values ​​is mostly controlled within 20%, and the nonlinear characteristics of flow rate variation are simulated well, especially in... and In both groups, the error under moderate airflow conditions remained between 3% and 9%, verifying the reliability of the multiphase mass transfer model based on COMSOL.

[0198] Positive deviation under low intake flow conditions, such as , At that time, the error was 33.0%. The simulation result (53.6 Bq / L) was significantly higher than the experimental value (40.3 Bq / L). This result may be because, at low inlet flow rates, the kinetic energy of the bubble swarm generated by the bubble stone is insufficient, and the bubbles are prone to accumulation or local stagnation on the wall during their ascent. Simulation models usually assume that the bubbles are uniform and the path is idealized, ignoring the short-circuit flow or uneven bubble distribution that may exist in the actual device. This leads to an overestimation of the effective mass transfer area calculated in the simulation, thus overestimating the degassing concentration.

[0199] Table 5. Effect of gas flow rate on bubble mass transfer ( )

[0200]

[0201] Table 6. Effect of gas flow rate on bubble mass transfer ( )

[0202]

[0203] The deviation under high water flow rate and low air flow rate conditions, such as QW=1.3 and Qg=1.0, is 26.0%. The simulation result (40.4 Bq / L) is significantly lower than the experimental value (55.5 Bq / L). This may be related to turbulence enhancement; that is, under high water flow rate conditions, the water flow generates strong turbulent disturbances in the narrow column. This disturbance significantly reduces the thickness of the liquid-side boundary layer at the gas-liquid interface, thus increasing the mass transfer coefficient. In addition, strong water flow may also cause the bubble rise path to be more tortuous, increasing the bubble residence time in the liquid phase. This study only focused on the simulation of a single bubble, and in particular, did not consider turbulent mass transfer simulations at high Reynolds numbers, which may lead to large errors in the results.

[0204] Under high inlet flow rates, the negative deviation is 21.3%, such as when QW=0.5 and Qg=3.0. The simulation result (19.3 Bq / L) is significantly higher than the experimental value (15.9 Bq / L). When the inlet flow rate is very high, the frequency of bubble generation on the bubble stone surface is extremely high, causing a large number of tiny bubbles to merge into larger bubbles in the early stage of ascent, i.e., the bubble merging effect. The specific surface area of ​​the large bubbles is much smaller than that of the tiny bubbles. In the simulation settings, the bubble diameter is constant, and its specific surface area is also fixed. However, in reality, the bubble shape will continuously change during the ascent process, and its diameter will also increase, resulting in an increase in specific surface area. Therefore, the concentration calculated by simulation is higher than the actual concentration.

[0205] Table 7. Effect of gas flow rate on bubble mass transfer ( )

[0206]

[0207] Table 8. Effect of gas flow rate on bubble mass transfer ( )

[0208]

[0209] The effect of influent flow rate on radon gas emission is as follows:

[0210] The bubbling degassing device is cylindrical, and the radon gas change consists of three parts: water inlet, water outlet, and bubble carry-out. According to the mass balance equation:

[0211] (45)

[0212] In formula (45), V w : Water volume; C in : Influent concentration; Q w C in Q: The total amount of radon gas replenished through the inlet per unit time; w C wThe total amount of radon gas lost through the outlet per unit time; m gas : The mass of radon gas carried away by bubbles per unit time (i.e., mass transfer rate).

[0213] Formula (45) indicates the influent flow rate. This determines the turnover frequency of the water body, i.e., the residence time. .when As the flow rate increases, more high-concentration fresh water enters the device per unit time. If the degassing rate of the bubbles is constant, a larger flow rate can more effectively offset the concentration decrease caused by degassing, thus... Maintain at near (105 Bq / L) level. Conversely, when As the volume decreases, the replenishment rate slows down. Because the bubbles continuously draw out radon gas, the amount of radon in the water... It will decrease significantly until a new equilibrium is reached.

[0214] As the bubbles rise, they absorb radon gas, and their concentration satisfies the following condition:

[0215] (46)

[0216] In formula (46), This refers to the degassing efficiency. It depends on factors such as bubble residence time and mass transfer coefficient, and is considered a constant or quasi-constant under the conditions of this study.

[0217] When the influent flow rate was 1.3 L / min, the radon concentration emitted from the aerator stabilized at 55 Bq / L after 270 minutes; when the influent flow rate decreased from 1.3 L / min to 1.0 L / min, the radon concentration decreased from 55 Bq / L and stabilized at 49.4 Bq / L after 180 minutes; when the influent flow rate decreased from 1.0 L / min to 0.7 L / min, the radon concentration decreased from 49.4 Bq / L and stabilized at 42 Bq / L after 180 minutes; when the influent flow rate decreased from 0.7 L / min to 0.5 L / min, the radon concentration decreased from 42 Bq / L and stabilized at 38 Bq / L after 180 minutes; when the influent flow rate decreased from 0.5 L / min to 0.3 L / min, the radon concentration decreased from 38 Bq / L and stabilized at 28.5 Bq / L after 180 minutes. That is, the bubbling degassing device is long enough to reach a steady state, at which point... From formula (45), we can obtain:

[0218] (47)

[0219] In formula (47), Total airflow rate, which is a constant value.

[0220] Then Substitute into the above equation:

[0221] (48)

[0222] The final concentration of radon gas produced was obtained. expression:

[0223] (49)

[0224] Figure 7 The nonlinear positive correlation between influent flow rate and radon concentration at the outlet is clearly demonstrated. As the influent flow rate increases, the concentration in the denominator becomes dominant, C... g tending towards the maximum value When the influent flow rate decreases, the replenishment is insufficient, C g The concentration of radon gas decreases accordingly. When the influent flow rate increases from 0.3 L / min to 1.3 L / min, the concentration of radon gas emitted jumps from 28.5 Bq / L to 55.0 Bq / L. The graph exhibits typical hyperbolic saturation characteristics. In the low flow rate range, the concentration increases rapidly with increasing flow rate; as the flow rate further increases, the slope of the curve gradually decreases, showing a trend towards the theoretical upper limit. The experimental points closely match the derived formula (49). This demonstrates that the mass balance model can accurately describe the radon mass transfer dynamics within the cylindrical bubbling device.

[0225] The supplementary item is This determines the rate at which the system acquires radon. A higher flow rate results in a higher water turnover frequency, and a faster replacement of older water with fresh, high-concentration water, offsetting the concentration loss caused by bubble degassing. The consumption item is the continuous extraction of radon from the water by bubbles through the gas-liquid interface. At low flow rates, the water residence time... The process is relatively long, allowing the bubbles ample time to evacuate the radon from the water, resulting in low concentrations in both the water and the gas phase. Equilibrium is reached, i.e., steady-state operation, when the amount of radon replenished by the influent is exactly equal to the sum of the effluent loss and the amount carried away by the bubbles. The denominator ηQ in the formula... g This reveals the inherent degassing capability of the system and its constraint on concentration balance.

[0226] The radon concentration analysis of the degassing device is as follows:

[0227] To determine the variation law of radon concentration in the water of the bubble degassing device, a differential equation was established and a functional expression for its change with time was derived. According to the law of conservation of mass, the rate of change of radon in the system = the sum of the influent input rate, the effluent output rate, and the bubble degassing rate, that is:

[0228] (50)

[0229] Formula (50) where, The volume of water in the bubbling degassing device; Inlet / outlet flow rate; Radon concentration in influent: 10⁵ Bq / L; : The radon concentration in the water inside the container at any given time.

[0230] The degassing term can be represented as k ex ·C(t), where the comprehensive degassing coefficient k ex = ηQ g Based on the fitting of experimental data, ηQ g =0.503.

[0231] The following are listed:

[0232] (51)

[0233] make ,

[0234] General solution equation:

[0235] (52)

[0236] steady-state concentration (C) ss ): hour,

[0237] Initial condition: C(0) = 105 Bq / L.

[0238] Final formula:

[0239] (53)

[0240] when =1.3 L / min; ηQ g =0.503; =105 Bq / L; V=1.5 L. Calculations show that the steady-state concentration Css≈75.71 Bq / L, and the time constant a≈1.20 min⁻¹. Figure 8 and Figure 9 The changing trend of radon concentration in the water of the degassing device is shown.

[0241] The radon concentration in the water decreased exponentially from an initial 10⁵ Bq / L, eventually stabilizing. Due to... The value is very large, and the system responds very quickly, meaning it can remain in the system for a very short nominal time ( Achieving equilibrium within, such as Figure 8 and Figure 9 The system reaches equilibrium within approximately 10 minutes. Therefore, with a fixed influent flow rate, the radon concentration in the water within the bubbling device remains constant from the start of bubbling degassing until a stable radon concentration is measured (180 minutes). Different influent flow rates result in stable radon concentrations in the water within the bubbling device of 75.71, 69.89, 61.10, 52.34, and 39.23 Bq / L, respectively. The stable radon concentrations in the water under different influent flow rates are shown in Table 9 below.

[0242] Table 9 Steady-state radon concentration in water under different influent flow rates

[0243]

[0244] Under steady-state conditions, the concentration of radon in water does not change with time, i.e. Based on the formula derived from the law of conservation of mass mentioned earlier, we have:

[0245] (54)

[0246] Among them, the degassing rate Compared with the current concentration in water It is directly proportional. Therefore, it can be expressed as... ,in To comprehensively consider the effects of degassing coefficient, bubble count, and mass transfer efficiency, the above equation can be expressed as:

[0247] (55)

[0248] Further variations:

[0249] (56)

[0250] Formula (56) clearly shows the influent flow rate Decrease As the denominator increases, the steady-state radon concentration increases. Decrease.

[0251] Simulated bubble mass transfer times under different inlet flow rates are as follows: Figure 10 and 12As shown in the figure, increasing the airflow rate from 0.5 L / min to 5.0 L / min reduces the bubble residence time in water from 0.27 s to 0.21 s. When the airflow rate increases from 2.0 L / min to 3.0 L / min, the bubble residence time remains almost unchanged; however, when the airflow rate continues to increase to 5.0 L / min, the bubble residence time decreases to 0.21 s. This indicates that the airflow rate has a significant impact on the bubble size and initial velocity, leading to changes in the bubble rise time.

[0252] A cylindrical bubble degassing device was used to remove radon from water. The initial system conditions were: radon concentration in water 10⁵ Bq / L, initial radon concentration in the bubbles 0 Bq / L, and influent radon concentration 10⁵ Bq / L. Bubble swarms were generated using 2.5cm × 2.5cm bubble stones, and 35 combinations of 7 influent flow rates (0.5–5.0 L / min) and 5 influent flow rates (0.3–1.3 L / min) were systematically investigated. The calculation and experimental results are shown in Table 10.

[0253] Table 10. Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0254]

[0255] Table 11. Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0256]

[0257] Table 10 shows the error range of 0.11-6.57%. This is the group with the smallest error among all operating conditions, indicating that the model has the highest prediction accuracy under low inlet flow rate. Small bubbles (r=2 mm) have a large specific surface area, high mass transfer efficiency, and a relatively stable flow field. The error increases slightly with increasing inlet flow rate, but overall remains within a high prediction accuracy range.

[0258] Table 11 shows an error range of 1.1-11.1%. Compared to the first group, the overall radon concentration decreased by about 30%, which is consistent with the gas dilution effect. The maximum error of 11.1% occurred when the flow rate was 0.7 L / min, which may be related to the fact that the ratio of the hydraulic residence time (about 10 seconds) to the bubble residence time (0.25 seconds) under this condition was in the critical region.

[0259] Table 12 Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0260]

[0261] Table 13 Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0262]

[0263] Table 14 Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0264]

[0265] Table 12 shows the error range as 3.1-20.8%. The error was 20.8%, the largest error in this group, with the experimental value (33.5 Bq / L) significantly higher than the simulated value (26.2 Bq / L). Possible reasons: 1. High water flow rate and medium air flow rate lead to uneven bubble distribution; 2. The jet generated at the inlet and outlet may bypass some bubble areas; 3. Short bubble residence time and insufficient mass transfer time.

[0266] Table 13 shows the error range is 5.7-22.3%. The error was 22.3%, and the experimental value (32.7 Bq / L) was significantly higher than the simulated value (25.4 Bq / L). A possible reason is that the bubble stone may have entered different operating modes at this flow rate, resulting in a wider bubble size distribution, with some large bubbles rising rapidly and some small bubbles having a longer residence time, leading to a discrepancy between the calculated average residence time and the actual effective mass transfer time.

[0267] Table 15 Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0268]

[0269] Table 16 Comparison of simulated radon concentration and experimental values ​​under different influent flow rates ( , , , )

[0270]

[0271] Table 14 shows the error range as 6.7-35.0%. The error is 35.0%. Possible reasons for this large deviation include: 1. The combination of high water flow rate and high air flow rate generates a strong third-dimensional flow field, with the water flowing directly from the bottom to the middle outlet, bypassing most of the bubble area; 2. Large bubbles are more likely to coalesce into larger bubbles at high flow rates, reducing the total specific surface area; 3. The Reynolds number is significantly increased, but the model used in the simulation is not applicable to this scale, resulting in a decrease in prediction accuracy.

[0272] Table 15 shows an error range of 7.1%–50.6%. The experimental value (40.9 Bq / L) differs significantly from the simulated value (20.2 Bq / L). This discrepancy is likely related to the fluid dynamics behavior under high flow rate combinations.

[0273] Table 16 shows an error range of 3.4-25.0%. Despite the highest intake flow rate, the error is improved compared to the previous two groups, especially... The error was reduced to 25%. Possible reasons: 1. Under extremely high air flow rates, the bubble swarm occupies the entire water body, forming a uniform gas-liquid two-phase flow, which reduces the short-circuit effect; 2. Radon concentration is reduced to a very low level (6.7-20.4 Bq / L), the influence of mass transfer resistance is relatively weakened, and the dilution effect becomes the dominant factor; 3. Some simplified assumptions of the simulation model under extreme conditions may be closer to reality.

[0274] As the intake flow rate increased from 0.5 to 5.0 L / min, the bubble characteristic parameters showed a systematic change (Table 17). The bubble radius increased by 60% (from 2.0 to 3.2 mm), which is consistent with the bubble coalescence theory. The rising velocity increased by 72% (from 0.25 to 0.43 m / s).

[0275] Table 17 Bubble kinetic parameters

[0276]

[0277] Table 18 Hydraulic Residence Time

[0278]

[0279] Based on Tables 17 and 18, we found that: 1. The HRT / BRT ratio decreased from 70:1 (high flow rate) to 8:1 (low flow rate); 2. When the HRT / BRT ratio is too low, the water does not have enough time to fully contact the air bubbles, leading to short-circuit flow. This also explains why high... Large operating error.

[0280] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for numerical simulation of the radon precipitation process in bubbling degassing water, characterized in that, include: S1: Based on the COMSOL Multiphysics software platform, a two-dimensional gas-liquid radon mass transfer model including water and bubbles is constructed, and the initial conditions are set as the radon concentration in the water and the radon concentration inside the bubbles; S2: Based on the set air intake flow rate, the shedding radius and initial rising velocity of a single bubble are calculated using the two-dimensional gas-liquid radon mass transfer model, wherein the shedding radius is obtained by correcting the reference shedding radius by introducing a correction factor. S3: Using the initial rising velocity and the fall radius, combined with the two-film theory, a mass transfer differential equation describing the migration of radon gas from the water body to the interior of the bubble is established, and the curve of the average radon concentration of the bubble changing with time during the rising process is obtained by solving the equation. S4: Based on the aforementioned change curve, simulate the radon concentration field distribution at the instant the bubble breaks at the gas-liquid interface, and calculate the total radon activity accumulated inside the bubble. S5: Calculate the theoretical reading of the radon detector based on the total radon activity and the number of bubbles generated per unit time, and compare the theoretical reading with the experimental measurement to verify the reliability of the model.

2. The method for numerical simulation of radon precipitation process in bubbling degassing water according to claim 1, characterized in that, In S2, the reference detachment radius is calculated using a static detachment formula based on the outlet diameter, gas-liquid density difference, and surface tension. The correction factor is an empirical coefficient obtained by fitting measured bubble radius data under different inlet flow rates.

3. The method for numerical simulation of radon separation process in bubbling degassing water according to claim 1, characterized in that, In S3, the driving mechanism of the mass transfer differential equation is based on Henry's law, where the concentration of radon in the gas phase is the concentration in the liquid phase multiplied by the Ostwald coefficient, and when the ratio of the radon concentration in water to the radon concentration in the gas is greater than the Ostwald coefficient, radon is transferred from the liquid phase to the gas phase.

4. The method for numerical simulation of radon precipitation process in bubbling degassing water according to claim 1, characterized in that, In S4, the radon concentration field distribution at the instant the bubble breaks at the gas-liquid interface is obtained by volume normalization of the radon concentration inside the bubble using an integral operator.

5. The method for numerical simulation of radon precipitation in bubbling degassing water process according to claim 1, characterized in that, In S5, the number of bubbles generated per unit time is the bubble frequency calculated based on the air intake flow rate and the volume of a single bubble.

6. The method for numerical simulation of radon precipitation in bubbling degassing water process according to claim 1, characterized in that, The method further includes S6: establishing a mass balance differential equation based on the influent flow rate and water volume, deriving an analytical expression for the change of radon concentration in the water of the bubbling degassing device over time, and calculating the steady-state radon concentration.

7. A system for numerical simulation of the radon separation process in bubbling degassing water as described in any one of claims 1-6, characterized in that, include: The modeling module is used to build a two-dimensional gas-liquid radon mass transfer model containing water and bubbles based on the COMSOL Multiphysics software platform, and sets the initial conditions as the radon concentration in the water and the radon concentration inside the bubbles; The parameter calculation module is used to calculate the shedding radius and initial rising velocity of a single bubble based on the set air intake flow rate using the two-dimensional gas-liquid radon mass transfer model. The shedding radius is obtained by correcting the reference shedding radius by introducing a correction factor. The mass transfer solution module is used to establish a mass transfer differential equation describing the migration of radon gas from the water body to the interior of the bubble by using the initial ascent velocity and the detachment radius, combined with the two-film theory, and to solve for the curve of the average radon concentration of the bubble changing with time during the ascent process. The field distribution simulation module is used to simulate the radon concentration field distribution at the moment the bubble breaks at the gas-liquid interface based on the curve of the average radon concentration changing with time during the rising process of the bubble, and to calculate the total radon activity accumulated in the bubble. The results analysis module is used to calculate the theoretical reading of the radon detector based on the total radon activity accumulated in the bubbles and the number of bubbles generated per unit time, and to compare the theoretical reading with the experimental measurement to verify the reliability of the model.

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