Method and system for regulating water-extracted radon concentration by gas-liquid flow

Abstract

The application discloses a method and system for regulating water-extracted radon concentration by adjusting gas-liquid flow, wherein a water source containing radon is introduced into a bubbling degassing device, air is pumped into the bubbling degassing device, and the air forms bubbles in the water source, so that radon is transferred from the liquid phase to the gas phase. By adjusting the air inlet flow and the water inlet flow of the water source, the radon concentration extracted from the bubbling degassing device is regulated. The ratio of the air inlet flow to the water inlet flow determines the radon concentration. The decisive influence of the gas-liquid ratio (i.e. the ratio of the air inlet flow to the water inlet flow) on the extracted radon concentration enables accurate, stable and active regulation of the radon concentration, thereby effectively solving the problem of inaccurate concentration control caused by isolated parameter regulation in the prior art.

Description

Technical Field

[0001] This invention relates to the field of radon gas observation technology, specifically to a method and system for regulating the concentration of radon in water by controlling gas-liquid flow rate. Background Technology

[0002] In non-radium source radon chamber systems that utilize groundwater as a radon source, existing technologies generally employ bubbling degassing devices to achieve radon separation from water. This method involves continuously pumping air into the radon-containing water source to form bubbles, utilizing the gas-liquid two-phase mass transfer principle to release and enrich radon dissolved in the water into the gas phase.

[0003] However, existing technologies for controlling radon concentration typically rely on adjusting only a single parameter, either the inlet gas flow rate or the inlet water flow rate, without effectively utilizing their synergistic effect. This approach results in the system's inability to achieve precise, proactive, and stable control of the radion concentration in the gas phase, presenting a technical challenge in achieving accurate control of radon concentration in water through the coordinated regulation of gas and liquid flow parameters. Summary of the Invention

[0004] The present invention aims to provide a method and system for regulating the concentration of radon in water by controlling the gas-liquid flow rate. By coordinating the control of the air inlet flow rate and the water inlet flow rate, and utilizing the decisive influence of the gas-liquid ratio on the concentration of radon released, the present invention can achieve precise, stable and proactive control of the radon concentration.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for regulating the concentration of radon in water by adjusting the gas-liquid flow rate, comprising: providing a bubbling degassing device; introducing a radon-containing water source into the bubbling degassing device; pumping air into the bubbling degassing device, causing the air to form bubbles in the water source, so that radon is transferred from the liquid phase to the gas phase; and regulating the radon concentration precipitated from the bubbling degassing device by adjusting the air inlet flow rate and the water inlet flow rate; wherein the ratio of the air inlet flow rate to the water inlet flow rate jointly determines the precipitated radon concentration.

[0006] Preferably, the method of regulating the radon concentration by adjusting the air flow rate and the water flow rate includes: under the condition of a fixed water flow rate, increasing the air flow rate to reduce the radon concentration.

[0007] Preferably, the method of regulating the radon concentration by adjusting the air intake flow rate and the water intake flow rate includes: increasing the water intake flow rate to increase the radon concentration under a fixed air intake flow rate.

[0008] Preferably, the ratio of the air intake flow rate to the water intake flow rate is the gas-liquid ratio, and the radon concentration released is negatively correlated with the gas-liquid ratio.

[0009] Preferably, the process of radon being transferred from the liquid phase to the gas phase is affected by the residence time of the bubbles in the water source, and the residence time is determined by the air intake flow rate.

[0010] Preferably, the water source is groundwater.

[0011] Preferably, the air intake flow rate is adjustable in the range of 0.5-5.0 L / min, and the water intake flow rate is adjustable in the range of 0.3-1.3 L / min.

[0012] On the other hand, the present invention proposes a system for regulating the concentration of radon in water by controlling the gas-liquid flow rate, comprising:

[0013] Bubble degassing device;

[0014] A water supply unit connected to the bubbling degassing device is used to provide radon-containing water to the bubbling degassing device;

[0015] An air supply unit connected to the bubbling degassing device is used to pump air into the bubbling degassing device to form bubbles;

[0016] The flow control units respectively installed on the water supply unit and the air supply unit are used to independently control the inlet water flow and the inlet air flow to coordinately control the radon concentration output from the bubbling degassing device.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] This invention introduces radon-containing water into a bubbling degassing device and pumps air into the device, causing the air to form bubbles in the water, thus transferring radon from the liquid phase to the gas phase. By adjusting the air inlet flow rate and the water inlet flow rate, the concentration of radon released from the bubbling degassing device is controlled. The ratio of the air inlet flow rate to the water inlet flow rate jointly determines the released radon concentration. By utilizing the decisive influence of the gas-liquid ratio (i.e., the ratio of the air inlet flow rate to the water inlet flow rate) on the released radon concentration, precise, stable, and proactive control of the radon concentration can be achieved, thereby effectively solving the problem of inaccurate concentration control caused by isolated parameter control in existing technologies. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method for regulating the concentration of radon in water by gas-liquid flow rate according to the present invention;

[0020] Figure 2 This is a block diagram of the system for regulating the concentration of radon in water by gas-liquid flow rate according to the present invention;

[0021] Figure 3 This is a schematic diagram of the structure of the bubbling degassing device of the present invention;

[0022] Figure 4This is a schematic diagram of the gas-water mixing pipe of the present invention;

[0023] Figure 5 The intake air flow rate (Q) of this invention w The effect of 1.3 L / min on the radon concentration in the bubbling degassing unit is shown in the figure.

[0024] Figure 6 The intake air flow rate (Q) of this invention w The effect of 1.0 L / min on the radon concentration in the bubbling degassing unit is shown in the figure.

[0025] Figure 7 The intake air flow rate (Q) of this invention w The effect of 0.7 L / min on the radon concentration in the bubbling degassing unit is shown in the figure.

[0026] Figure 8 The intake air flow rate (Q) of this invention w The effect of 0.5 L / min on the radon concentration in the bubbling degassing unit is shown in the figure.

[0027] Figure 9 This is a graph showing the effect of the influent flow rate (Qg=0.5 L / min) on the radon concentration in the bubbling degassing device of the present invention;

[0028] Figure 10 This is a graph showing the effect of the influent flow rate (Qg = 1.0 L / min) on the radon concentration in the bubbling degassing device of the present invention.

[0029] Figure 11 This is a graph showing the effect of the influent flow rate (Qg = 1.5 L / min) on the radon concentration in the bubbling degassing device of the present invention.

[0030] Figure 12 This is a graph showing the effect of the influent flow rate (Qg = 2.0 L / min) on the radon concentration in the bubbling degassing device of the present invention.

[0031] Figure 13 This is a graph showing the effect of the influent flow rate (Qg = 2.5 L / min) on the radon concentration in the bubbling degassing device of the present invention.

[0032] Figure 14 This is a graph showing the effect of the influent flow rate (Qg = 3.0 L / min) on the radon concentration in the bubbling degassing device of the present invention.

[0033] Figure 15 This is a graph showing the effect of the influent flow rate (Qg = 5.0 L / min) on the radon concentration in the bubbling degassing device of the present invention.

[0034] Figure 16This is a graph showing the effect of air intake flow rate and water intake flow rate on the concentration of radon released from the water body according to the present invention.

[0035] Figure 17 This is a 3D surface projection diagram showing the effect of influent water flow rate and influent air flow rate on the radon concentration released by the degassing device according to the present invention.

[0036] Figure 18 This is a graph showing the effect of the gas-liquid ratio on the concentration of radon released in this invention.

[0037] Figure 19 This is a diagram showing the competition between the dilution effect and the mass transfer effect in this invention.

[0038] Figure 20 This is a diagram showing the effect of the influent flow rate on radon concentration according to the present invention.

[0039] Figure 21 This is a 3D surface projection diagram showing the effect of influent water flow rate and influent air flow rate on the radon concentration released by the degassing device according to the present invention.

[0040] Figure 22 This invention establishes a nonlinear unified relationship between radon concentration and gas-liquid ratio (H=0.58).

[0041] Figure 23 This is a graph showing the influence of influent water flow rate and influent air flow rate on the concentration of radon in water precipitation and the model fitting analysis of this invention.

[0042] Figure 24 This invention demonstrates the nonlinear effect of equal air-water flow rate on radon removal efficiency in water (n<1).

[0043] Figure 25 This invention relates to the nonlinear effect of equal air-water flow rate on the radon removal efficiency in water (n>1). Detailed Implementation

[0044] 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.

[0045] like Figure 1 As shown, this invention proposes a method for regulating the concentration of radon in water by adjusting the gas-liquid flow rate, comprising the following steps:

[0046] A bubbling degassing device is provided, into which a radon-containing water source (groundwater) is introduced; air is pumped into the bubbling degassing device, causing the air to form bubbles in the water source, so that radon is transferred from the liquid phase to the gas phase; the concentration of radon released from the bubbling degassing device is controlled by adjusting the air inlet flow rate and the water inlet flow rate.

[0047] The ratio of air inlet flow rate to water inlet flow rate jointly determines the concentration of radon released. The process of radon transfer from the liquid phase to the gas phase is affected by the residence time of the bubbles in the water source, which is determined by the air inlet flow rate.

[0048] like Figure 3 and Figure 4 As shown, the bubbling degassing device includes a water inlet 1, an air inlet 2, an air-water mixing chamber 3, an air-water mixing pipe 4, an air-water separation hole 5, an air collecting chamber 6, an air outlet 7, an overflow outlet 8, and a housing 9.

[0049] The lower end of the gas-water mixing pipe 4 is connected to the inside of the outer pipe 9, the overflow port 8 is opened on the surface of the outer shell 9, and the inside of the outer shell 9 is used to store water containing radon.

[0050] The gas-water mixing pipe 4 consists of an inner pipe 401 and an outer pipe 402, which are connected at their upper ends and have an open structure at their lower ends. Both the air inlet 2 and the water inlet 1 are connected to the inner pipe 401 for injecting gas and water. A gas collecting chamber 6 is formed between the inner pipe 401 and the outer pipe 402. An air outlet 7 is located on the surface of the outer pipe 402 to allow the separated gas to be discharged. A gas-water separation hole 5 is located at the lower end of the inner pipe 401, allowing the injected gas and water to mix with radon-containing water. The junction of the water inlet 1 and the air inlet 2 forms the gas-water mixing chamber 3.

[0051] In one embodiment, the concentration of radon released is controlled by adjusting the air intake flow rate and the water intake flow rate, including: under the condition of a fixed water intake flow rate, increasing the air intake flow rate to reduce the concentration of radon released.

[0052] In one embodiment, the concentration of radon released is controlled by adjusting the air intake flow rate and the water intake flow rate, including: increasing the water intake flow rate to increase the concentration of radon released under a fixed air intake flow rate.

[0053] Specifically, the ratio of inlet air flow rate to inlet water flow rate is the gas-liquid ratio, and the radon concentration released is negatively correlated with the gas-liquid ratio. The inlet air flow rate can be adjusted within the range of 0.5-5.0 L / min, and the inlet water flow rate can be adjusted within the range of 0.3-1.3 L / min.

[0054] This invention achieves precise, proactive, and stable control of radon concentration in water by synergistically regulating the inlet air flow rate and the inlet water flow rate, utilizing the decisive role of their ratio (gas-liquid ratio) in the radon concentration. By adjusting the gas-liquid ratio, the target radon concentration can be flexibly increased or decreased as needed. Furthermore, the clear negative correlation between radon concentration and the gas-liquid ratio makes the regulation process predictable and highly repeatable, significantly improving the accuracy of radon concentration control and the stability of the system.

[0055] On the other hand, this invention proposes a system for regulating the concentration of radon in water by controlling the gas-liquid flow rate, such as... Figure 2 As shown, it includes:

[0056] Bubble degassing device;

[0057] A water supply unit connected to the bubbling degassing device is used to provide radon-containing water to the bubbling degassing device;

[0058] An air supply unit connected to the bubbling degassing device is used to pump air into the bubbling degassing device to form bubbles;

[0059] The flow control units respectively installed on the water supply unit and the air supply unit are used to independently control the inlet water flow and the inlet air flow to coordinately control the radon concentration output from the bubbling degassing device.

[0060] In this embodiment, the principle of the bubbling degassing device is to introduce stabilized water and mix it with pumped air. Radon gas is mainly transferred from the liquid phase (water) to the gas phase (bubbles) in the water through bubbles generated by the air. This system aims to clarify the independent action mechanism of water flow rate and air flow rate through the controlled variable method, as follows:

[0061] The effect of gas flow rate on radon precipitation is as follows:

[0062] Figure 5 Figure (a) shows a fixed influent flow rate of 1.3 L / min, with the air inlet flow rate Q adjusted. g (Adjustment range: 0.5-3.0 L / min) Relationship between radon concentration released by the bubbling desorption device and air flow rate. The blue discrete hollow circles represent the original measured values, and the red continuous solid line represents the smoothed data after processing with a Savitzky-Golay filter.

[0063] Figure 5 In Figure (a), the original curve shows a clear decreasing trend: the generated radon concentration decreases with increasing pumped air flow rate. As the air flow rate increases from 0.5 L / min to 3.0 L / min, the radon radioactivity concentration decreases from 58 Bq / L to 35 Bq / L. Further smoothing of the original data (continuous red solid line) makes Q more clearly visible. g When the concentration of radon gas was increased from 1.0 L / min to 1.5 L / min, the radioactive concentration of radon gas decreased significantly, with a decrease of 16%.

[0064] To more intuitively reflect the impact of pumped air flow rate on degassing, the effect of changes in air flow rate on the concentration of radon gas released during bubbling degassing was plotted as a bar chart. Figure 5 (b)). The figure clearly shows the effect of pumped air flow rate Q. g With the increase of Q, the concentration of radium released decreased significantly. gWhen Q = 0.5 L / min, the maximum concentration of radon radioactivity precipitated in water is 58 Bq / L. g When the concentration is 5.0 L / min, the minimum is 24.6 Bq / L.

[0065] The measured radon concentrations were plotted as a scatter plot, and confidence and prediction intervals were defined. Figure 5 (c) and (d) show the polynomial and nonlinear fittings of the relationship between radon concentration and airflow rate, respectively. The radon concentration and airflow rate were normalized. The resulting polynomial model is: C Rn = 2.1Q g 2 -17.7Q g + 67.8; The fitted nonlinear model is: C Rn = 51.9e -Qg / 2.8 +15.8. Whether it's polynomial fitting or nonlinear fitting, the coefficient of determination R... 2 Both reached 0.98, proving that the fitting results are quite consistent.

[0066] Figure 6 Figure (a) shows the relationship between the concentration of radon gas released during bubbling degassing and the air flow rate. The blue discrete hollow circles represent the original measurements, and the red continuous solid line represents the smoothed data after processing with a Savitzky-Golay filter. The experiment was conducted with a fixed influent flow rate Q. w =1.0 L / min, adjust the pumped air flow rate Q g (Adjustment range: 0.5-5.0 L / min), completed at a temperature of 25℃.

[0067] Figure 6 (a) shows the effect at a constant influent flow rate Q w At a flow rate of 1.0 L / min, the radon concentration generated by bubbling increases with the pumped air flow rate Q. g It increases and decreases, exhibiting a clear negative correlation. When Q g The radon concentration is highest when Q = 0.5 L / min; g =5.0 L / min, the radon concentration is the lowest; compared with other pumped air flow conditions, when Q g The radon concentration changes significantly at concentrations of 1.5 L / min and 5.0 L / min.

[0068] Figure 6 Figure (b) is a bar chart showing the effect of changes in inlet flow rate on the radon evolution characteristics in the bubbling degassing unit. It clearly demonstrates a negative correlation between the evolved radon concentration and the inlet flow rate. From Q... g=0.5 L / min to Q g =5.0 L / min, the percentage decreases in radon concentration were 7.5%, 24.5%, 18.9%, 3.3%, 6.9%, and 27.4%, respectively; overall, the radon concentration decreased from a maximum of 53 Bq / L to a minimum of 19.6 Bq / L, a decrease of 63%. As mentioned in the previous analysis, in terms of the magnitude of radon concentration change, at Q g At concentrations of 1.5 L / min and 5.0 L / min, the radon concentration decreased by 24.5% and 27.4%, respectively.

[0069] Figure 6 In equations (c) and (d), respectively, are the polynomial and nonlinear equations fitted to the radon concentration and inlet flow rate. The polynomial model is: C Rn =2.1Q g 2 -18.8Q g +67.5, R 2 =0.97( Figure 6 (c)); The fitted nonlinear model is: C Rn =50.3e -Qg / 1.8 +16.8, R 2 =0.97( Figure 6 (d) shows that the fitting results are relatively consistent.

[0070] Figure 7 (a) shows the curves of radon concentration with a fixed influent flow rate of 0.7 L / min and adjusted pumped air flow rate. The blue hollow circles represent the raw radon data; the red solid line represents the radon concentration trend after smoothing. The red solid line trend graphs show the radon concentration at seven different air flow rates. At the pumped air flow rate Q... g The radon concentration decreased significantly at pumped air flow rates of 1.0, 1.5, and 5.0 L / min; the decrease was more pronounced when the pumped air flow rate Q... g At concentrations of 2.5 L / min and 3.0 L / min, the radon concentration decreased relatively slowly.

[0071] Figure 7 Figure (b) more intuitively demonstrates the effect of different airflow rates on radon concentration. Airflow rate Q gFrom 0.5 L / min to 5.0 L / min, the radon concentrations were 47, 40, 29.6, 22.6, 21.4, 19.7, and 12.3 Bq / L, respectively. The percentage decreases in radon concentration were 14.9%, 26.0%, 23.6%, 5.3%, 7.9%, and 37.6%, respectively. This is consistent with the significant changes in radon concentration mentioned earlier at inlet flow rates of 1.0, 1.5, and 5.0 L / min.

[0072] Performing polynomial fitting and nonlinear fitting respectively, the following results were obtained: The polynomial fitting model is C Rn =2.2Q g 2 -19.4Q g +55.7, R 2 =0.97( Figure 7 (c)); The nonlinear fitting model is: C Rn =51.2e -Qg / 1.6 +10.5, R 2 =0.98( Figure 7 (d) The coefficients of determination for polynomial fitting and nonlinear fitting are 0.97 and 0.98, respectively, proving that the fitting results are relatively ideal.

[0073] Figure 8 (a) shows the curves of radon concentration with the pumped air flow rate adjusted when the influent flow rate is fixed at 0.5 L / min. The blue hollow circles represent the original measured values ​​of radon concentration; the red solid line represents the trend of radon concentration change. Radon concentration still shows a clear negative correlation with the influent flow rate. The maximum radon concentration is 43.7 Bq / L when the influent flow rate is 0.5 L / min; the minimum radon concentration is 9.6 Bq / L when the influent flow rate is 5 L / min.

[0074] Bar chart showing the effect of intake flow rate gradient on radon gas evolution ( Figure 8 Figure (b) more clearly shows the changes in radon concentration. The inlet flow rates were 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, and 5.0 L / min, corresponding to radon concentrations of 43.7, 34.9, 26.1, 21.9, 19.1, 15.9, and 9.6 Bq / L, respectively. The percentage decreases in radon concentration were 20.1%, 25.2%, 16.1%, 12.7%, 16.8%, and 39.6%, respectively. The most significant decreases in radon concentration were observed at inlet flow rates of 1.0 and 1.5 L / min. Then, polynomial and nonlinear fitting were performed, with the following results: The polynomial fitting model is: C Rn =1.6Q g 2 -15.8Qg +47.8, R 2 =0.99( Figure 8 (c)); The nonlinear fitting model is: C Rn =48.9e -Qg / 1.7 +7.6, 0.99 ( Figure 8 (d)

[0075] The effect of water flow rate on radon precipitation is as follows:

[0076] To further investigate the influence mechanism of gas flow rate and water flow rate on radon gas evolution, a method was used to determine the radon concentration evolved in the degassing device by fixing the inlet gas flow rate and adjusting the inlet water flow rate. For example... Figure 9 As shown in (a), the air inlet flow rate was maintained at 0.5 L / min, and the water inlet flow rate ranged from 1.3 to 0.3 L / min. The blue hollow circles in the figure represent the initial radon concentration data, and the red solid line represents the radon concentration trend. The trends in radon concentration and water inlet flow rate show that, under a fixed air inlet flow rate, radon concentration and water inlet flow rate exhibit a positive correlation. Furthermore, compared to the traditional method where low flow rates and low water heads easily lead to decreased radon stability and reliability, the radon concentration in the degassing device demonstrates good stability.

[0077] The effect of adjusting the influent flow rate (1.3-0.3 L / min) on radon precipitation was tested. (See bar chart). Figure 9 As shown in (b), the radon concentration (55-28.5 Bq / L) is significantly positively correlated with the influent flow rate: when the influent flow rate decreases from 1.3 L / min to 0.5 L / min, the radon concentration decreases by about 48.2%. The rate of decrease slows down after the flow rate decreases to 0.7 L / min, for example, the concentration decrease is 14% when the flow rate decreases from 1.0 to 0.7 L / min, and 10.5% when the flow rate decreases from 0.7 to 0.5 L / min.

[0078] Figure 10 (a) The radon concentration was measured by adjusting the influent flow rate (1.3-0.3 L / min) under the condition that the influent flow rate was fixed at 1.0 L / min. The blue hollow circles represent the original data, and the red solid line represents the trend after smoothing. First, the graph shows that the entire bubbling degassing device exhibits good stability under different head conditions. Second, the radon concentration also shows a clear positive correlation with the influent flow rate.

[0079] A clearer bar chart ( Figure 10(b) further demonstrates that the overall variation in radon concentration reached 91%, exhibiting a non-linear decrease: the concentration decreased by 10.7% during the high flow rate phase (1.3–1.0 L / min), significantly higher than the 1.3% decrease during the low flow rate phase (0.5–0.7 L / min).

[0080] Figure 11 (a) The radon concentration in the water was measured with the inlet water flow rate adjusted from 1.3 to 0.3 L / min while the inlet air flow rate was fixed at 1.5 L / min. The blue hollow circles represent the original data, and the red solid line represents the trend after smoothing. (Compared to Q) g The radon concentration measured at 0.5 and 1.0 L / min conditions showed both similarities and differences. The similarity lies in the significant positive correlation between radon concentration and influent flow rate. The difference is that, judging from the trend graph, the radon concentration decreased rapidly from 1.3 to 0.3 L / min.

[0081] Figure 11 (b) It shows that: 1. There is a clear positive correlation between the influent flow rate and the radium concentration; 2. The radium concentration decreases rapidly and significantly as the influent flow rate decreases. When the influent flow rate is 1.3 L / min, the radium concentration is 33.5 Bq / L, and when the influent flow rate is 0.3 L / min, the radium concentration is 12.8 Bq / L, a decrease of 161%.

[0082] Figure 12 (a) The concentration of radon gas released into the water was measured by adjusting the influent flow rate (1.3-0.3 L / min) with the influent flow rate fixed at 2.0 L / min. The blue hollow circles represent the original data, and the red solid line represents the trend after smoothing. (Compared with Q) g The measured radon concentrations under the conditions of 0.5, 1.0, and 1.5 L / min showed both similarities and differences. The similarity lies in the significant positive correlation between radon concentration and influent flow rate. The differences are that, judging from the trend graph, the radon concentration decreased rapidly from 1.3 to 1.0 L / min; the decrease was not significant from 1.0 to 0.7 L / min; and the decrease was substantial from 0.7 to 0.7 L / min.

[0083] Bar chart of influent flow rate versus radon concentration ( Figure 12(b) shows that when the influent flow rate increased from 1.3 to 1.0 L / min, the radon concentration decreased by 24.5%; when the influent flow rate increased from 1.0 to 0.7 L / min, the radon concentration decreased by 9.3%; and when the influent flow rate increased from 0.7 to 0.3 L / min, the radon concentration decreased by 32.1%. The radon concentration decrease was greatest when the influent flow rate decreased from 1.3 to 1.0 L / min, indicating that radon release in the high flow rate range (>1.0 L / min) is more sensitive to changes in flow rate, which may be related to the accelerated radon diffusion caused by water turbulence. When the influent flow rate decreased from 1.0 to 0.7 L / min, the radon concentration decrease was significantly smaller in this range, indicating that the radon release process in the medium flow rate range may be regulated by a dynamic equilibrium mechanism, such as a slowdown in the gas-liquid phase exchange rate. When the influent flow rate decreased from 0.7 to 0.3 L / min, the radon concentration decreased more significantly. This may be because when the flow rate is below the critical threshold (about 0.5 L / min), the residence time of radon in the liquid phase is significantly prolonged, leading to an enhanced reverse dissolution effect.

[0084] With a fixed air inlet flow rate of 2.5 L / min, the inlet water flow rate was adjusted (1.3-0.3 L / min), and the radon concentration in the water was measured. Figure 13 (a)). The blue hollow circles represent the original data, and the red solid line represents the trend after smoothing. The trend graph shows a significant decrease in radon concentration at each influent flow rate, and the two still show a significant positive correlation.

[0085] Figure 13 (b) It shows that: 1. When the influent flow rate decreased from 1.3 to 0.3 L / min, the radon concentration decreased by 10.8%; 2. When the influent flow rate decreased from 1.0 to 0.7 L / min, the radon concentration decreased by 19.4%; 3. When the influent flow rate decreased from 0.7 to 0.5 L / min, the radon concentration decreased by 28.4%; and when the influent flow rate decreased from 0.5 to 0.3 L / min, the radon concentration decreased by 38.6%.

[0086] The significant differences in radon concentration reduction across these four stages may be due to several reasons: 1. In the high flow rate region, where the water flow rate decreases from 1.3 L / min to 1.0 L / min, strong turbulence accelerates radon's two-phase mass transfer; 2. When the water flow rate decreases from 1.0 L / min to 0.7 L / min, which may be near the critical threshold, the gas residence time increases, leading to a reverse dissolution effect, i.e., radon precipitates from the water, which gradually intensifies; 3. When the water flow rate decreases from 0.7 L / min to 0.5 L / min, below the threshold, the residence time of radon in the liquid phase increases, and Henry's law dominates the continuous precipitation of radon; 4. When the water flow rate decreases from 0.5 L / min to 0.3 L / min, at this very low level, the system approaches quasi-static equilibrium, the redistribution of dissolved radon is completed, and the remaining radon rapidly precipitates in a free state, resulting in the maximum reduction.

[0087] With a fixed air inlet flow rate of 3.0 L / min, the inlet water flow rate was adjusted (1.3-0.3 L / min), and the radon concentration in the water was measured. Figure 14 (a)). The blue hollow circles represent the original data, and the red solid line represents the trend after smoothing. The radon concentration trend chart shows a significant decrease in radon concentration at each influent flow rate, with a significant positive correlation between the two. In the figure, the radon concentration decrease is very significant when the influent flow rate decreases from 1.3 to 1.0 L / min and from 0.5 to 0.3 L / min; however, the decrease in radon concentration is less significant when the influent flow rate decreases from 1.00 to 0.7 L / min and from 0.7 to 0.5 L / min.

[0088] Figure 14 (b) Clearly demonstrated: When the influent flow rate decreased from 1.3 L / min to 0.5 L / min, the radon concentration decreased by 25.9%; when the influent flow rate decreased from 1.0 L / min to 0.7 L / min, the radon concentration decreased by 21.5%; when the influent flow rate decreased from 0.7 L / min to 0.5 L / min, the radon concentration decreased by 17.6%; and when the influent flow rate decreased from 0.5 L / min to 0.3 L / min, the radon concentration decreased by 42.9%. It should be noted that one possible reason for the significant decrease in radon concentration when the influent flow rate decreased from 0.5 L / min to 0.3 L / min is the nonlinear effect caused by the sudden reduction in flow rate.

[0089] Figure 15(a) The change in radon concentration in the water was measured when the influent flow rate was adjusted (1.3-0.3 L / min) with the influent flow rate fixed at 5.0 L / min. The blue hollow circles represent the original data, and the red solid line represents the trend after smoothing. The trend graph shows a significant decrease in radon concentration under each influent flow rate condition, with a significant positive correlation between the two. In this graph, the decrease in radon concentration was significant when the influent flow rate decreased from 1.3 to 1.0 L / min; while the changes in radon concentration were less significant when the influent flow rate decreased from 1.0 to 0.7 L / min, 0.7 to 0.5 L / min, and 0.5 to 0.3 L / min.

[0090] A bar chart of influent flow rate and radon concentration ( Figure 15 (b) shows that when the influent flow rate decreased from 1.3 to 1.0 L / min, the radon concentration decreased by 28.4%; when the influent flow rate decreased from 1.0 to 0.7 L / h, the radon concentration decreased by 21.9%; when the influent flow rate decreased from 0.7 to 0.5 L / h, the radon concentration decreased by 20.2%; and when the influent flow rate decreased from 30 to 0.3 L / min, the radon concentration decreased by 26.4%. Compared with the previous six sets of data, the radon concentration decrease was largest when the influent flow rate decreased from 1.3 to 1.0 L / min; while the largest decrease in radon concentration was observed when the influent flow rate decreased from 1.0 to 0.7 L / min among the previous six sets of data.

[0091] The effect of gas flow rate on radon precipitation is analyzed as follows:

[0092] Based on measured radon concentration data, the variation of radon concentration with air flow rate under different influent flow rates is shown in the following figures. Figure 16 As shown.

[0093] contrast Figure 16 The trends in radon concentration were measured under four different influent flow rates, and the results are as follows:

[0094] 1) Under four arbitrary influent flow rates, the radon concentration in the water showed a significant decreasing trend with the increase of the influent flow rate, and the radon concentration change trend was consistent across the four groups.

[0095] 2) Under the same air inlet flow rate, a lower water inlet flow rate usually corresponds to a lower radon concentration, which reflects the combined effect of hydraulic residence time or air-to-water ratio on radon release efficiency.

[0096] 3) The rate of change of radon concentration is fastest when the inlet flow rate increases from 1.0 to 2.0 L / min. When the inlet flow rate increases from 2.0 to 5.0 L / min, the change of radon concentration tends to level off.

[0097] 4) The inlet air flow rate has a significant dilution effect on the concentration of radium released. At any inlet water flow rate (taking 1.3 L / min as an example), as the inlet air flow rate increases from 0.5 to 5.0 L / min, the concentration of radium released decreases from 58.0 Bq / L to 33.0 Bq / L, a reduction of 43.1%.

[0098] 5) The concentration of radon in water is negatively correlated with the inlet air flow rate, and this trend is highly consistent under different inlet water flow rate conditions.

[0099] Figure 17 The response surface and contour projection of radium concentration as a function of influent and influent flow rates are shown. The figure shows that: 1) the highest radium concentration is found at the highest influent flow rate and the lowest influent flow rate; 2) the contour thermogram of radium concentration shows the densest contour lines between influent and influent flow rates of 1.0 and 2.0.

[0100] Figure 17 The study also revealed a significant gradient in the spatial distribution of radon concentration. When the influent flow rate remained constant, the surface smoothly transitioned from a red region representing high concentration to a purple region representing low concentration as the influent air flow rate increased. This directly reflects the dilution effect of the influent air flow rate on the radon concentration. Furthermore, the contour lines below the surface show that the high concentration area was mainly concentrated under the combined operating conditions of "high water flow - low air flow".

[0101] The above analysis reveals the independent influence of inlet air flow rate and inlet water flow rate on the radon concentration. However, in actual operating conditions, the two often work synergistically, jointly determining the contact state between the gas and liquid phases. To quantitatively characterize this coupling effect, a gas-to-water ratio parameter is introduced to further explore its regulatory mechanism on the radon concentration.

[0102] Figure 18The graph showing the relationship between radon concentration and gas-water ratio indicates that: 1) Under low gas-water ratio conditions, the radium concentration is higher; under high gas-water ratio conditions, the radium concentration is lower. This means that the radium concentration and the gas-water ratio are negatively correlated. 2) The red fitted curve in the graph shows a clear exponential decreasing trend, indicating that in the high-sensitivity region (gas-water ratio between 0 and 2), the curve is very steep, meaning that in the low gas-water ratio stage, even a small change in gas flow rate will cause drastic fluctuations in radon concentration; when the gas-water ratio increases to 6, the curve becomes flatter, indicating that the efficiency of diluting or changing the radium concentration by continuously increasing the gas flow rate is constantly decreasing, exhibiting diminishing marginal returns. 3) When the gas-water ratio is small (<2), the distribution of points corresponding to different water flow rates is relatively wide. This indicates that at low gas-to-water ratios, the water flow rate itself contributes significantly to the absolute value of the radium concentration. However, as the gas-to-water ratio increases, the points of different colors (different influent flow rates) gradually converge and become consistent. This suggests that at high gas-to-water ratios, the gas-to-water ratio becomes the primary factor determining the concentration, offsetting the impact of changes in the single water flow rate. 4) At the same gas-to-water ratio, the radium concentration corresponding to the green points in the figure is generally higher than that of the purple points. This indicates that the radium concentration is affected not only by the gas-to-water ratio but also by the absolute influent flow rate. That is, at high influent flow rates, even with a consistent gas-to-water ratio, a higher baseline radium content in the water or differences in contact time can lead to a higher final radium concentration. This phenomenon is termed the proportional inequality phenomenon.

[0103] In summary, the gas-to-water ratio exhibits a significant nonlinear characteristic in regulating the concentration of radon released: in the low gas-to-water ratio range (<2), the radon concentration is extremely sensitive to changes in the gas-to-water ratio; when the ratio exceeds 6, the dilution effect becomes less pronounced. Furthermore, although the gas-to-water ratio is the primary controlling parameter, at the same ratio, the radon concentration under high influent flow rate conditions is still slightly higher than under low flow rate conditions, demonstrating the cumulative effect of absolute influent flow rate on mass transfer balance.

[0104] Based on the distribution characteristics of experimental data, empirical formulas are derived to describe the effects of water flow rate and gas flow rate on the concentration of radon gas released from water. Since most of the fitting models for the four sets of data presented above are suitable for nonlinear fitting, it is assumed that the radon concentration (C...) Rn ) and water flow (Q) w ) and air flow rate (Q) g The relationship is power function:

[0105] (1)

[0106] In the formula, k: proportionality coefficient; a, b: numbers to be specified.

[0107] Taking the natural logarithm of the formula, we have:

[0108] (2)

[0109] Transform the original data into logarithmic form. Then, use matrix form:

[0110] (3)

[0111] Solve for the parameters. Matrix X contains constants, ln(Q) g ) and ln(Q w Y = ln(Rn). The final regression results are: a = 0.715 (air flow index), b = 0.928 (water flow index), ln(k) = 3.902, k ≈ 49.6, R 2 =0.961.

[0112] Substitute into formula (1):

[0113] (4)

[0114] Q w ∈[0.5,1.3] L / min, Q g ∈[0.5,5.0] L / min.

[0115] Mean absolute error (MAE): ±3.8 Bq / L.

[0116] This empirical formula quantifies the contribution weight of gas-water flow rate to the radium concentration. Exponential analysis shows that 1) the influent flow rate (Q) w The influence weight of ) (0.928) is slightly higher than that of gas flow (Q). g 1) The influence weight (0.715) indicates that the radon concentration released by the bubbling degassing device is more sensitive to fluctuations in the influent flow rate. 2) The indices of influent flow rate and influent air flow rate respectively indicate that increasing the influent flow rate will bring more radon sources, which is beneficial to increasing the radon concentration in the water; increasing the influent air flow rate will produce a dilution effect, leading to a decrease in the radon concentration in the water. 3) The indices of both influent flow rate and influent air flow rate are not 1, indicating that it is not a simple linear proportional relationship. That is, in the bubbling degassing device, the mass transfer between the gas and liquid phases is jointly constrained by complex factors such as flow field fluctuations and changes in bubble specific surface area. 4) In addition, the coefficient of determination R 2 The value of 0.961 indicates that the formula can accommodate most of the experimental data variation and has a good fit. The mean absolute error (MAE) is only ±3.8 Bq / L, which is of great guiding significance for the automated control of bubbling degassing devices, especially in maintaining a constant radon concentration output.

[0117] To better study the role of the dilution effect, a key variable is now introduced: the radon release rate E, which is the radon activity transferred from water to air per minute (Bq / min). According to the law of conservation of mass:

[0118] (5)

[0119] In the formula, : Total radon gas released, Bq / min; Q g Intake airflow, L / min; ; Radon concentration at the outlet, Bq / L.

[0120] Transform the formula into a concentration calculation form:

[0121] (6)

[0122] Discussion Q g When C increases, out The changes can be divided into three cases: 1) Pure dilution effect (ideal case, E remains constant), if the amount of radon gas extracted from the water is constant, then C out Will with Q g Inversely proportional, i.e., Q g Double, C out (Half-reduced). 2) Enhanced mass transfer effect (E increases). Increasing the gas flow rate usually increases the gas-liquid contact area and turbulence, improving the mass transfer coefficient and leading to an increase in the total amount of radon gas E released from the water. 3) Actual observation results show that the inlet gas flow rate Q... g The total amount of radon gas is increasing. It is also increasing.

[0123] The total amount of radon gas released under different influent flow rates is shown in the table below.

[0124] Table 1 Radon gas emission rate (Q) under different inlet flow rates L =1.3 L / min)

[0125] 0.5 58.0 29.0 1.0 55.0 55.0 1.5 46.0 69.0 2.0 40.0 80.0 2.5 36.0 90.0 3.0 35.0 105.0 5.0 33.0 165.0

[0126] As shown in Table 1, based on an intake flow rate of 0.5 L / min, the total radon gas volume Q is calculated as follows: g From 0.5 to 1.0 L / min, the gas flow rate increased by 100%, and the total amount of radon released almost doubled, but the concentration only decreased from 58.0 to 55.0 (a decrease of about 5%). This indicates that the mass transfer enhancement effect was extremely significant at this point, almost offsetting the dilution effect. When the gas flow rate was increased, there was no significant dilution of the gas; on the contrary, because there were more bubbles, most of the radon gas in the water was carried out.

[0127] Table 2. Radon emission amount (Q) under different inlet flow rates L =1.0 L / min)

[0128] 0.5 53.0 26.5 1.0 49.0 49.0 1.5 37.0 55.5 2.0 30.0 60.0 2.5 29.0 72.5 3.0 27.0 81.0 5.0 19.6 98.0

[0129] Table 3. Radon emission rate (Q L = 0.7 L / min)

[0130] 0.5 47.0 23.5 1.0 40.0 40.0 1.5 29.6 44.4 2.0 22.6 45.2 2.5 21.4 53.5 3.0 19.7 59.1 5.0 12.3 61.5

[0131] Table 4. Radon emission rate (Q L = 0.5 L / min)

[0132] 0.5 40.3 20.1 1.0 34.9 34.9 1.5 26.1 39.1 2.0 21.9 43.8 2.5 19.1 47.7 3.0 15.9 47.7 5.0 9.6 48.0

[0133] Tables 1 - 4 all show that as the intake air flow rate increases, the calculated total amount of radon emission E also increases. Taking Table 4 as an example, that is, when Q L = 0.7 L / min, from 0.5 to 5.0 L / min, the air flow increases by 10 times. If calculated according to pure dilution, the radon concentration should decrease from 40.3 Bq / L to 4.03 Bq / L, while the actually measured radon concentration is 9.6 Bq / L. The actual concentration is higher than the pure dilution concentration, indicating that the total amount of radon emission E has indeed increased (from 20.1 to 48.0), but due to the air flow rate Q g increasing more drastically (10 times), the growth of E (2.4 times) cannot catch up with the growth of the air flow rate Q g , so finally it shows that the radon concentration is diluted.

[0134] The competition mechanism between the dilution effect and the mass transfer efficiency is as follows:

[0135] Assume the mass transfer model of radon from the liquid phase to the gas phase is:

[0136] (7)

[0137] Among them, according to the two-film theory, the mass transfer rate is usually proportional to the power function of the air flow rate Q g (because Q g affects the bubble specific surface area and turbulence): [[ID=4x1]]

[0138] (8)

[0139] Among them, 0 < n < 1, because for the bubbling device, the mass transfer efficiency increases with the increase of the flow rate, but there is a marginal effect. Substitute it into the concentration formula: <x

[0140] (9)

[0141] Formula (9) shows that only when n < 1, that is, the growth rate of the total emission amount is slower than the growth rate of the air flow rate, the exponent (n - 1) is negative. C out will decrease monotonically with the increase of Q g . It should be noted that there seems to be a typo in the original text where "4x1" is likely a mistake. I translated it as best as possible based on the context.

[0142] Figure 19 The graph shows the trends of radon concentration and total radon precipitate in water as a function of inlet air flow rate. The solid line represents the measured radon concentration, and the dashed line represents the calculated total radon precipitate. It can be seen that although increasing the airflow brings out more radon (dashed line), the large gas volume causes the radon concentration in water to be diluted (solid line).

[0143] The analysis of the nonlinear relationship between contact time and mass transfer efficiency is as follows:

[0144] In a bubbling degassing device, air rises from the bottom to the top in the form of bubbles. The residence time of these bubbles in the water determines the time window for radon gas to diffuse from the water into the bubbles. This varies with the inlet air flow rate Q. g The increase in velocity accelerates the rise of bubbles within the device, leading to a shorter average residence time for the gas. The result is a decrease in the gas flow rate Q. g The larger the bubble, the shorter its stay in the water.

[0145] 1) Nonlinearity of mass transfer efficiency

[0146] The transfer of radon from the liquid phase to the gas phase follows the mass transfer kinetics described by the two-film theory. According to the mass transfer equation:

[0147] (10)

[0148] Initially, the radon concentration inside the bubble is extremely low, resulting in the largest concentration gradient at the gas-liquid interface and the strongest mass transfer motive force. As the bubble rises, the radon concentration inside gradually increases and tends towards the gas-liquid equilibrium concentration determined by Henry's Law. However, this is a non-linear dynamic process; the concentration accumulates exponentially over time rather than non-linearly. When the inlet flow rate Q... g While increasing radon concentration may alter fluid turbulence, it also significantly increases the rising velocity of bubbles, leading to a shorter residence time (t) of the bubbles in the water. If t is less than the characteristic time required to reach gas-liquid equilibrium, the mass transfer process will be interrupted before saturation is reached, resulting in a radon concentration in the discharged bubbles that is lower than the theoretical equilibrium value.

[0149] 2) Kinetic mechanism modeling of radon mass transfer process

[0150] To verify the above discussion, a simplified mass transfer model is now established. According to the two-film theory, the mass transfer rate is proportional to the concentration difference:

[0151] (11)

[0152] In formula (11), C g Radon concentration; K La : Overall volumetric mass transfer coefficient; C *: The theoretical saturated radon concentration in the gas phase at gas-liquid equilibrium (determined by the radon concentration in water and the Henry's law, which can be considered a constant or varies slightly with water flow; here we assume it to be a local constant); t: The residence time (contact time) of the bubble in the water.

[0153] Solving the above differential equation by integration, when t = 0, C g = 0, meaning there is no radon gas in the initial bubble. Separating the variables and integrating the above equation:

[0154] (12)

[0155] (13)

[0156] (14)

[0157] Solvable formula for instantaneous concentration inside bubbles:

[0158] (15)

[0159] 3) Establishment of a response model for outlet radon concentration with inlet air flow rate

[0160] The contact time is approximately inversely proportional to the intake flow rate, and the effective volume is assumed to be V. eff Then we have:

[0161] (16)

[0162] And order Substituting into the above equation, we obtain the final outlet radon concentration model:

[0163] (17)

[0164] Based on the model obtained above, data trends and nonlinear characteristics can be interpreted. From the above equation, when Q... g When it increases, the exponential term -β / Q g Approaching 0. According to Taylor expansion, when Q... g When the contact time is very short:

[0165] (18)

[0166] The above equation shows that at extremely high flow rates, the precipitated radon concentration does indeed exhibit a dilution effect inversely proportional to the flow rate, C∝1 / Qg. When Q g When the contact time is very long, the exponential term e^(-β / Q) g The value of C approaches 0. At this point, C... Rn ≈C * (1-0)=C *Under low airflow conditions, the bubbles remain in the water long enough that the radon gas inside them has reached complete gas-liquid equilibrium (saturation). At this point, further reducing the airflow will not cause the concentration to exceed C. * It can only be maintained at the saturation value. This explains why the rate of change of data is often not as drastic in the low flow rate range as it is in the high flow rate range. Taking Table 1 as an example, when the influent flow rate is 1.3 L / min, the measured radon concentrations are 58.0 and 33.0 Bq / L when the influent gas flow rate increases from 0.5 to 5.0 L / min. If it is a pure dilution effect (without considering the mass transfer limitation, assuming the total amount is constant): the flow rate increases by 10 times (0.5 to 5.0 L / min), and the concentration should decrease to 1 / 10 of the original, that is, 5.8 Bq / L. However, in the experiment, the concentration only decreased to 33.0 Bq / L. This shows that the above model of contact time and mass transfer efficiency is correct. When the influent gas flow rate increases, although it is diluted by air, the gas-liquid contact area increases dramatically because of the large gas volume, and although the residence time of a single bubble is short and the efficiency is low, the total amount of radon gas carried out actually increases significantly. In addition, Equation (25) explains this point, as Q g Although the amount of radon carried out per liter of gas decreases (radon concentration decreases), the rate of decrease is much slower than the rate of dilution because the system has shifted from equilibrium control to kinetic control, but has not completely lost its mass transfer capacity.

[0167] Conclusions: 1) Radon concentration change is not a simple linear dilution; 2) Radon concentration change is a nonlinear coupling between contact time and mass transfer efficiency; 3) The physical model governing this process is Equation (26). At low flow rates: long contact time, bubbles reach saturation, and the concentration is determined by thermodynamic equilibrium (Henry's Law). At high flow rates: short contact time, bubbles are not saturated, and the concentration is limited by mass transfer kinetics, showing a nonlinear decrease with increasing flow rate.

[0168] The effect of water flow rate on radon precipitation is as follows:

[0169] Based on the measured data of radon concentration in water, the effects of inlet air flow rate and inlet water flow rate on radon concentration in water were analyzed and studied. The results are as follows: Figure 20 As shown:

[0170] 1) Under the seven inlet flow rate conditions, the concentration of radon in water showed a significant upward trend with the increase of inlet flow rate, and the trend of radon concentration in water was consistent across the seven groups.

[0171] 2) Under the same influent flow rate, a lower influent flow rate corresponds to a higher radon concentration in the water;

[0172] 3) At any air inlet flow rate, the higher the inlet water flow rate, the greater the concentration of precipitated radon;

[0173] 4) The concentration of radon in water is positively correlated with the influent flow rate, and this trend is highly consistent under different influent flow rate conditions.

[0174] Figure 21 The results show that: 1) Under the same air flow rate, the radon concentration is positively correlated with the water flow rate; 2) The maximum radon concentration occurs when the air flow rate is minimum and the water flow rate is maximum; 3) The minimum radon concentration occurs when the air flow rate is maximum and the water flow rate is minimum; 4) The surface has not only maximum and minimum values ​​but also local maxima.

[0175] The empirical formula for the effect of water vapor flow rate on the concentration of radium released is as follows:

[0176] (19)

[0177] Q w ∈[0.3,1.3] L / min

[0178] Q g ∈[0.5,5.0] L / min

[0179] Coefficient of determination R 2 =0.976, indicating that the empirical formula can capture the driving characteristics of flow rate changes on the concentration of radium released. At the same time, the mean absolute error (MAE) is ±2.1 Bq / L, which verifies the accuracy of the empirical formula in predicting the level of radium released. Formula (27) shows that 1) the inlet flow rate Q g A negative exponent indicates that increasing the airflow rate will produce a significant dilution effect, leading to a decrease in the concentration of precipitated radon. The absolute value of the exponent is less than 1, indicating that the decrease in radon concentration due to increasing the airflow rate exhibits diminishing marginal returns; that is, simply increasing the airflow rate to improve radon precipitation efficiency will become increasingly less effective. 2) Influent flow rate Q w The index is positive and greater than 1, indicating that the concentration of radon in the water is highly sensitive to changes in the influent flow rate. It also shows that while increasing the influent flow rate shortens the hydraulic residence time (HRT), it introduces more radon sources per unit time, thus increasing the concentration of radon in the water. 3) The absolute value of the influent flow rate index (1.127) is greater than the absolute value of the air influent flow rate index (0.682), indicating that changes in the influent flow rate have a more significant impact on the concentration of radon in the water than changes in the air influent flow rate.

[0180] The theoretical model for radon precipitation concentration is as follows:

[0181] According to the law of conservation of mass, the total amount of radon entering the device per unit time is equal to the total amount of radon flowing out (neglecting decay because the residence time is very short):

[0182] (20)

[0183] In formula (20): C in Influent radon concentration, 10⁵ Bq / L; Q L : Inlet flow rate, L / min; Q g Intake airflow, L / min; C out : Radon concentration in the exhaust gas, Bq / L; C L,out Radon concentration remaining in the effluent, Bq / L.

[0184] (twenty one)

[0185] Right now:

[0186] (twenty two)

[0187] In formula (22), H: the gas-liquid partition coefficient of radon, in dimensionless form, i.e., C gas / C liquid The ratio under equilibrium conditions.

[0188] (twenty three)

[0189] Extract C out :

[0190] (twenty four)

[0191] The final theoretical model for radon precipitation concentration is obtained:

[0192] (25)

[0193] Transform into gas-liquid ratio form:

[0194] (26)

[0195] Formula (26) shows that:

[0196] 1) Water flow rate Q L The concentration of radon in water is positively correlated, exhibiting a non-linear saturation trend. Since water is the source term for radon, increasing the water flow rate Q... L This means the total number of radon atoms introduced into the device per unit time (Q) L C in Increase. At a fixed intake flow rate Q g With Q unchanged, increase L The concentration of radon in water will increase.

[0197] 2) In the limiting case, when Q L Very large (relative to Q) g When the gas-liquid ratio Q is 0, g / Q LWhen the radium concentration approaches 0, 1 / H in the denominator becomes dominant, and the concentration of radon in the water is C. out Approaching saturation value C in H. This means that the air is already saturated, and increasing the influent flow rate will not release more radon, as it is limited by solubility. In the data of this study, Q g When the flow rate is 5.0 L / min, the effect of water flow rate on the concentration of radon in water is very significant and almost linear, which is far from the saturation zone.

[0198] 3) Intake flow rate Q g It is negatively correlated with the concentration of radon in water, indicating that dilution is the dominant effect. Although increasing the airflow rate Q... g It can improve mass transfer efficiency, allowing C out It is closer to the equilibrium value, but its dilution effect far outweighs the improvement in mass transfer efficiency. According to formula (26), with a fixed inlet flow rate Q... g In this case, increase the influent flow rate Q L Radon concentration C in water precipitation out This conclusion is consistent with the following: [The number of cases will increase]. Figure 3 .16 shows the relationship between the concentration of radon in the water and the influent flow rate. When the influent flow rate Q... g When it is very large, such as Q g =5.0 L / min, Q g / Q L The term is very large, and formula (26) is approximately C. out ≈C in Q L / Q g At this point, the water concentration is inversely proportional to the gas flow rate.

[0199] Figure 22 The relationship between the gas-liquid ratio and the concentration of radon gas released is shown, with the X-axis representing the gas-liquid ratio (Q). g / Q L The Y-axis represents the concentration of radon in water, and an exponential fit was performed. It was found that the data points under all working conditions fell on the same hyperbolic characteristic curve. The fitting function is actually formula (26). The fitting degree is 0.8660, which shows that the model can describe the experimental law well. Figure 22 The results show that: 1) In the low gas-liquid ratio region (<5): the curve is very steep. Slightly increasing the gas flow rate or decreasing the water flow rate (i.e., increasing the gas-liquid ratio) will cause a sharp decrease in the radon concentration in the water phase. This indicates that in this range, the mass transfer process is mainly limited by the inlet gas flow rate (the radon concentration in the gas phase quickly reaches saturation). 2) In the high gas-liquid ratio region (>10): the curve gradually flattens out, and further increasing the gas-liquid ratio results in a smaller decrease in radon concentration (diminishing marginal returns).

[0200] Formula (26) and Figure 22 This indicates that the core variable determining the final radon concentration in the water is not simply Q.L Or Q g It's not about the liquid-gas ratio, but their ratio, i.e., the gas-liquid ratio Q. g / Q L These are the core control parameters. Figure 22 This indicates that at a low gas-liquid ratio (less gas, more water), the air is easily saturated, resulting in a high concentration of radon in the water. Conversely, at a high gas-liquid ratio (more gas, less water), the air is extremely diluted, leading to a low concentration of radon in the water. This reveals that the essential parameter controlling the concentration of radon in the water is the gas-liquid flow rate ratio. When the gas-liquid ratio increases (larger flow rate or smaller flow rate), the dilution effect dominates, and the concentration of radon in the water decreases rapidly. When the gas-liquid ratio decreases, the concentration of radon in the water is limited by the gas-liquid distribution equilibrium constant. It tends towards the theoretical maximum value.

[0201] Gas-liquid ratio parameter Q g / Q L It is the core parameter that determines the output characteristics of the system. This conclusion is consistent with the findings of Hutter et al. in the design of gas flow radon sources, namely, under a fixed source term input, increasing the gas flow rate mainly manifests as a dilution effect, resulting in the output concentration decreasing in an inversely proportional manner. Figure 22 The revealed pattern is consistent with the conclusions of Lowry and Brandow in their research on radon removal via aeration: the gas-liquid ratio (Q... g / Q L The gas-liquid ratio controls the equilibrium position of interphase mass transfer. When the gas-liquid ratio increases, the strong dilution effect masks the increase in mass transfer rate, leading to a significant decrease in gas phase concentration. The 1 / H term in the model represents the limit of thermodynamic partitioning.

[0202] Figure 23 (a) illustrates the source term effect, as the water flow rate Q increases. L As the flow rate increases, the curve shows an upward trend. This is because the faster the water flow, the more radon is supplied, leading to an increase in the concentration of radon in the water. Although the air inlet flow rate is also increasing, Q... g / Q L The ratio decreased, resulting in a lower dilution factor. Figure 23 (b) shows the dilution effect, as the gas flow rate Q... g As the gas flow rate increases, the curve shows a clear downward trend. This is because the increased gas flow rate leads to a decrease in the dilution factor Q. g / Q L The increase is rapid. Although the total amount of radon carried away may increase slightly (due to improved removal efficiency), the increase in gas volume is more dramatic, resulting in a significant decrease in the concentration of radon in the water.

[0203] Having clarified the significant macroscopic control law of the gas-liquid ratio on the concentration of radon in water precipitation, a quantitative assessment of the internal mass transfer efficiency of the system is still needed. While empirical formulas can predict trends, they cannot reveal the momentum exchange in gas-liquid mass transfer. Therefore, this study will establish a radon kinetic theoretical model in water precipitation, identify and define key parameters affecting the degassing process, and provide a theoretical basis for optimizing the real-time control algorithm of the device.

[0204] Based on reactor design principles, the mean hydraulic retention time (HRT) This refers to the available contact time in controlled liquid-phase mass transfer, which is related to the liquid flow rate Q. L For liquid-phase controlled mass transfer processes, the residence time of the liquid is inversely proportional to the residence time of the liquid.

[0205] (27)

[0206] In formula (27), Effective volume, m 3 The above formula shows that when the water flow rate Q... w When increased, contact time Linear decrease.

[0207] Mass transfer coefficient K La It is highly dependent on the degree of fluid turbulence. According to classic empirical formulas in chemical engineering, It is usually expressed as a power function of the gas velocity (or flow rate) at the gas and liquid surface:

[0208] (28)

[0209] In formula (28), Geometric constants; and It is an empirical index, usually a positive number, indicating that an increase in flow rate will enhance turbulence, thereby increasing the mass transfer coefficient.

[0210] 1) Basic model of mass transfer efficiency

[0211] In a first-order kinetic model based on the two-film theory, the rate of change of substance concentration is proportional to the concentration difference:

[0212] (29)

[0213] (30)

[0214] Perform definite integrals on both sides simultaneously, with a time range from... arrive .

[0215] Concentration range: Assuming the initial concentration is ,time concentration .have:

[0216] (31)

[0217] Integrating the left side of the above equation, we get:

[0218] (32)

[0219] (33)

[0220] Integrating over the right side, we get:

[0221] (34)

[0222] If the left and right sides are equal, then:

[0223] (35)

[0224] Remove the logarithm from both sides and take the exponent:

[0225] (36)

[0226] Take the reciprocal:

[0227] (37)

[0228] Mass transfer efficiency E is defined as the actual concentration change divided by the theoretically maximum possible concentration change. The actual change is C. τ - C0, the theoretical change is C * - C0.

[0229] therefore:

[0230] (38)

[0231] (39)

[0232] therefore:

[0233] (40)

[0234] (41)

[0235] Equation (41) shows that efficiency depends on the rate of mass transfer (K). La The product of the mass transfer unit (MTU) and the contact time (τ). This product is called the number of transfer units (NTU).

[0236] The effect of gas-water flow rate on the concentration of precipitated radon is as follows:

[0237] and Bring it into NTU:

[0238] (42)

[0239] After sorting, we can obtain:

[0240] (43)

[0241] Substitute into the efficiency formula:

[0242] (44)

[0243] To visually demonstrate the impact of the efficiency formula (44) and the contradictory relationship between water flow and air flow, we set m=0.6 and n=0.7. A heat map is then drawn to show the combined effect of the two variables (airflow and water flow) on the result (efficiency). The darker the color, the higher the efficiency, clearly showing the nonlinear gradient change. Figure 24 and Figure 25 ).

[0244] In formula (44), Q g The exponent is m (usually m>0), therefore, increasing the air flow rate will generally simply increase K. La This improves NTU and efficiency. This is a positive relationship, but due to the exponential function... The existence of this factor means that efficiency improvements will exhibit diminishing marginal returns, i.e., non-linearity. When the water flow rate Q increases... L This increases turbulence, K La Follow Q L n Increase. Simultaneously, increase water flow rate Q. L Reduced contact time Time follows Q L -1 reduce.

[0245] Therefore, the final efficiency depends on the value of n. Under conditions of strong turbulence (n > 1), the mass transfer coefficient is extremely sensitive to flow velocity; the turbulence gains from increasing the flow rate outweigh the time loss, and the overall efficiency may increase. Under normal conditions (n ​​< 1), n ​​- 1 is negative, meaning that increasing the flow rate Q... L Although K La It got bigger, but the contact time was longer. The length is shortened even more. As a result, the total number of mass transfer units (NTU) decreases, and the radon removal efficiency (E) per pass through water actually decreases.

[0246] 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 claimed by the appended claims and their equivalents is defined.

Claims

1. A method for regulating the concentration of radon in water by controlling gas-liquid flow rate, characterized in that, include: Provide a bubbling degassing device; A radon-containing water source is introduced into the bubbling degassing device; Air is pumped into the bubbling degassing device, causing the air to form bubbles in the water source, so that radon is transferred from the liquid phase to the gas phase; The concentration of radon released from the bubbling degassing device is controlled by adjusting the air intake flow rate and the water intake flow rate. The ratio of the air intake flow rate to the water intake flow rate determines the concentration of radon released.

2. The method for regulating radon concentration in water precipitation according to claim 1, characterized in that, The method of controlling the concentration of radon released by adjusting the air flow rate and water flow rate includes: Under a fixed influent flow rate, the concentration of radon released can be reduced by increasing the influent flow rate.

3. The method for regulating radon concentration in water precipitation according to claim 1, characterized in that, The method of controlling the concentration of radon released by adjusting the air flow rate and water flow rate includes: Under the condition of fixed inlet air flow rate, the concentration of radon released can be increased by increasing the inlet water flow rate.

4. The method for regulating radon concentration in water precipitation according to claim 1, characterized in that, The ratio of the air intake flow rate to the water intake flow rate is the gas-liquid ratio, and the radon concentration released is negatively correlated with the gas-liquid ratio.

5. The method for regulating radon concentration in water precipitation according to claim 1, characterized in that, The process of radon being transferred from the liquid phase to the gas phase is affected by the residence time of the bubbles in the water source, which is determined by the air intake flow rate.

6. The method for regulating radon concentration in water precipitation according to claim 1, characterized in that, The water source is groundwater.

7. The method for regulating radon concentration in water precipitation according to claim 1, characterized in that, The air intake flow rate is adjustable within a range of 0.5-5.0 L / min, and the water intake flow rate is adjustable within a range of 0.3-1.3 L / min.

8. A system for controlling the concentration of radon in water by regulating gas-liquid flow rate as described in any one of claims 1-7, characterized in that, include: Bubble degassing device; A water supply unit connected to the bubbling degassing device is used to provide radon-containing water to the bubbling degassing device; An air supply unit connected to the bubbling degassing device is used to pump air into the bubbling degassing device to form bubbles; The flow control units respectively installed on the water supply unit and the air supply unit are used to independently control the inlet water flow and the inlet air flow to coordinately control the radon concentration output from the bubbling degassing device.

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