CN108931465B - Method for measuring diffusion coefficient and transportable radon generation rate in porous emanation medium - Google Patents

Method for measuring diffusion coefficient and transportable radon generation rate in porous emanation medium Download PDF

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CN108931465B
CN108931465B CN201810487727.5A CN201810487727A CN108931465B CN 108931465 B CN108931465 B CN 108931465B CN 201810487727 A CN201810487727 A CN 201810487727A CN 108931465 B CN108931465 B CN 108931465B
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radon
collecting space
measuring system
porous
diffusion coefficient
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CN108931465A (en
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叶勇军
吴文浩
李实�
丁德馨
谢超
冯胜洋
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University of South China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume, or surface-area of porous materials
    • G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
    • G01N15/082—Investigating permeability by forcing a fluid through a sample
    • G01N15/0826—Investigating permeability by forcing a fluid through a sample and measuring fluid flow rate, i.e. permeation rate or pressure change
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
    • G01N2013/003—Diffusion; diffusivity between liquids

Abstract

The invention discloses a method for measuring a radon diffusion coefficient and a transportable radon generation rate in a porous emanation medium, which uses the following devices for measurement: the device comprises a test body, a first radon collecting space, a second radon collecting space, a first radon measuring system and a second radon measuring system; the inner side of the inner arc surface is provided with a first radon collecting space, the outer side of the outer arc surface is provided with a second radon collecting space, the first radon measuring system is communicated with the first radon collecting space to form a closed loop, and the second radon measuring system is communicated with the second radon collecting space to form a closed loop. The invention provides a method for determining the radon diffusion coefficient of a porous emanator and the generation rate of transportable radon without measuring physical parameters such as radium content, density, porosity and the like, so that the workload can be greatly reduced, and the method is simple in equipment and very convenient and fast.

Description

Method for measuring diffusion coefficient and transportable radon generation rate in porous emanation medium
Technical Field
The invention relates to a method for measuring diffusion coefficient and migration radon generation rate in a porous emanation medium, belonging to the technical field of nuclear radiation detection.
Background
Radon is colorless, odorless, radioactive inert gas which is 7.5 times heavier than air, has a half-life period of about 3.85 days, and when people inhale radon, the radon decays in a human body and releases α particles to cause radiation damage to the respiratory system of people, so that lung cancer is caused.
The diffusion coefficient, which is a physical quantity related to the pore structure, temperature and humidity of the porous medium itself, is often used to describe the migration capability of radon in the porous medium, and its size affects the radon exhalation rate of the surface of the porous emanation medium. The transportable radon production rate is an important physical quantity determining the radon release potential of porous emanation media, and is related to the content of radium in the media, the microstructure of pores, and the temperature and humidity. At present, methods for measuring the diffusion coefficient and the generation rate of transportable radon are complex, parameters such as radium content, density, porosity and water content need to be measured, and measurement difficulty and measurement workload are high. Therefore, the invention provides a method for determining the radon diffusion coefficient of the porous emanation medium and the generation rate of transportable radon without measuring physical parameters such as radium content, density, porosity and the like, so that the workload can be greatly reduced, and the equipment is simple and very convenient.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: firstly, providing an accurate solution to the radon diffusion coefficient in a porous medium; and secondly, resolving the radon generation rate of the transportable emanation medium without measuring parameters such as radium content.
The technical scheme of the invention is to provide a method for measuring the diffusion coefficient of radon in a porous emanation medium, which uses the following devices for measurement: the device comprises a test body, a first radon collecting space, a second radon collecting space, a first radon measuring system and a second radon measuring system; the testing body is a straight cylinder, the bottom surface of the testing body is a quarter of ring, the side surface of the testing body is composed of two opposite planes and two opposite cambered surfaces, wherein the cambered surface close to the center of a circle is an inner cambered surface, and the cambered surface far away from the center of a circle is an outer cambered surface; a first radon collecting space is arranged on the inner side of the inner cambered surface and used for collecting radon separated out from the inner cambered surface; a second radon collecting space is arranged on the outer side of the outer arc surface and used for collecting radon separated out from the outer arc surface; the first radon measuring system is communicated with the first radon collecting space to form a closed loop, and the second radon measuring system is communicated with the second radon collecting space to form a closed loop;
the first radon collecting space and the second radon collecting space are relatively closed spaces and are communicated with a radon measuring instrument and other structures (a gas flowmeter, a drying device, a filtering device and the like) through pipelines to form a first radon measuring system and a second radon measuring system.
The method calculates the diffusion coefficient D of radon in the porous emanation medium according to the following formula:
Figure BDA0001667192910000021
wherein:
Figure BDA0001667192910000022
Figure BDA0001667192910000031
I0、I1respectively representing 0-order and 1-order virtual vector Bessel functions of a first class;
K0、K1respectively representing a second class of 0-order and 1-order virtual vector Bessel functions;
r1represents the radius of the inner circular arc in the circular ring; r is2The radius of the outer arc in the ring is represented;
J1、J2respectively showing the radon exhalation rates of the inner arc surface and the outer arc surface;
respectively testing the radon concentration C of the first radon collection space at two moments by using a first radon measuring system11And C12Calculating the radon exhalation rate J of the intrados according to the following formula1,
Figure BDA0001667192910000032
t1Representing the time interval, S, of two moments of testing a first set of radon spaces1Denotes the surface area of the intrados of the test body, V1Representing a first set of radon spacesThe total volume of the closed loop;
respectively testing the radon concentration C of the second radon collection space at two moments by using a second radon measuring system21And C22Calculating the radon exhalation rate J according to the following formula2，
Figure BDA0001667192910000033
t2Representing the time interval, S, of two moments of testing a second set of radon spaces2Representing the surface area of the extrados of the test body; v2Representing the total volume of the closed loop in which the second radon collection space is located.
Preferably, t is1＝10-30min；t2＝10-30min。
Preferably, the test body is prepared by mixing uranium tailings and cement, adding water and uniformly mixing.
Preferably, the particle size of the uranium tailings is less than 1 mm.
Preferably, the mass ratio of the uranium tailings to the cement is 3-7: 1.
Preferably, r1＝80-150mm；r2＝300-500mm。
Preferably, the radon concentration in the radon collecting space is simultaneously tested by using the first radon measuring system and the second radon measuring system.
Preferably, the first radon collecting space and the second radon collecting space are homocylinders, and the bottom surface of the first radon collecting space is in a fan shape with a central angle of 90 degrees; the bottom surface of the second radon collecting space is a quarter of a circular ring.
The invention provides a method for measuring the generation rate of transportable radon in a porous emanation medium, which comprises the steps of firstly calculating the diffusion coefficient D of radon in the porous emanation medium, then calculating the generation rate α of transportable radon according to the following formula,
Figure BDA0001667192910000041
the invention provides a method for measuring the generation rate of transportable radon in a porous emanation medium, which comprises the steps of firstly calculating the diffusion coefficient D of radon in the porous emanation medium, then calculating the generation rate α of transportable radon according to the following formula,
Figure BDA0001667192910000042
the invention uses a straight cylinder formed by one quarter of circular rings as a test body, and the bottom surface of the straight cylinder, namely the cylinder, is vertical to the side surface. The bottom surface of the column body is a quarter of a circular ring, one side close to the center of the circular ring is the inner side, and one side far away from the center of the circular ring is the outer side.
The derivation process of the invention is as follows:
according to the differential equation of the formula (1),
Figure BDA0001667192910000043
in the formula: C-Radon concentration in porous emanation media, Bq/m3；
D-diffusion coefficient of Radon in porous emanation media, m2/s；
λ -decay constant of radon, λ 2.1 × 10-6s-1；
α -Radon generation rate, Bq/(m) produced by porous emanation medium3s)；
The general solution of this differential equation is shown in equation (2):
Figure BDA0001667192910000051
in the formula: i is0-a first type zero order imaginary vector Bessel function;
K0-a second class of zero order imaginary vector Bessel functions;
A. b-integral constant;
solving the integral constant by using a boundary condition, wherein the boundary condition is that r is r1Where C is ═ C1；r＝r2Where C is ═ C2。C1，C2-measuring the radon concentration in and on the external surface of the body, i.e. the radon concentration in the first and second radon collecting spaces, Bq/m3；
Figure BDA0001667192910000052
Figure BDA0001667192910000053
When the radon concentration in the air environment on the inner and outer surfaces of the medium of the circular tube body is lower, namely when C1And C2Close to 0Bq/m3Then, the equations (3) and (4) are simplified as follows:
Figure BDA0001667192910000061
Figure BDA0001667192910000062
from the Fick's first law:
radon exhalation rate J of inner cambered surface of test body1The formula:
Figure BDA0001667192910000063
testing radon exhalation rate J of extrados surface2The formula:
Figure BDA0001667192910000064
testing the ratio of the radon exhalation rates of the internal cambered surface and the external cambered surface:
Figure BDA0001667192910000071
wherein, in formula (9), J1And J2The radon diffusion coefficient D can be calculated, and then the obtained radon diffusion coefficient D is substituted into the formula (7) or (8), so that the transportable radon generation rate α generated by the porous emanation medium is obtained.
Wherein the content of the first and second substances,J1and J2Calculated according to the following equation (10):
Figure BDA0001667192910000072
j is the radon exhalation rate, Bq/m2s；C1The radon concentration in the radon collecting space at the 1 st moment, Bq/m3；C2The radon concentration in the radon collecting space at the 2 nd moment, Bq/m3(ii) a S is the surface area of a certain surface of the test body, and radon enters a corresponding radon collecting space through the surface; v is the total volume of the closed loop where the corresponding radon collecting space is located, m3(ii) a t is the sampling interval time, s, of two time instants.
The method can determine the radon diffusion coefficient of the porous emanation medium and the generation rate of transportable radon without measuring physical parameters such as radium content, density, porosity and the like, so that the workload can be greatly reduced, and the equipment is simple and very convenient.
Drawings
FIG. 1 is a schematic diagram of a simplified structure of an apparatus for testing according to the present invention;
FIG. 2 is a schematic diagram of a closed-loop radon exhalation rate measurement system according to the present invention;
FIG. 3 is a front view of a test body and a radon collecting space in the manufacturing process of the present invention;
FIG. 4 is a schematic structural diagram of the apparatus according to the present embodiment;
illustration of the drawings: 1-a first radon measuring system, 2-a second radon measuring system, 3-a first radon collecting space, 4-a wedge, 5-a test body and 6-a second radon collecting space; 11-radon measuring instrument, 12-filtering device, 13-drying tube and 14-gas flowmeter.
Detailed Description
The present invention will be further described with reference to the following examples.
Examples
As shown in fig. 1, the experimental apparatus mainly comprises: the radon measuring device comprises a first radon measuring system 1, a second radon measuring system 2, a first radon collecting space 3, a second radon collecting space 6 and a test body 5, wherein the test body 5 is fixed by a wedge 4. The first radon measuring system 1 is communicated with the first radon collecting space 3 through a hose, and the second radon measuring system 2 is communicated with the second radon collecting space 6 through a hose.
The first radon measuring system 1 and the second radon measuring system 2 have the same structure, and as shown in fig. 2, both the first radon measuring system 1 and the second radon measuring system 2 include a radon measuring instrument 11, a filtering device 12, a drying pipe 13, and a gas flow meter 14. The radon measuring instrument 11, the filtering device 12, the drying pipe 13, the gas flowmeter 14 and the first radon collecting space 3 are connected in series through a hose to form a closed loop to form a first radon measuring system 1. Similarly, the radon measuring instrument 11, the filtering device 12, the drying pipe 13, the gas flow meter 14 and the second radon collecting space 6 are connected in series through a hose and form a closed loop to form the second radon measuring system 2.
(1) And (3) manufacturing a die to be tested in the experiment:
1) experimental Material
Uranium tailings with the particle size of less than 1mm are screened and uniformly mixed with cement according to the ratio of 5:1, and a proper amount of water is added to be used as a test body (namely a sample to be tested).
2) Constitution of the experimental apparatus
The quarter-circle tubular porous emanation medium radon pure diffusion precipitation experimental device is shown in figure 1. The device consists of a quarter-pipe-shaped test block containing container, a first radon measuring system and a second radon measuring system. The container is a quarter cylindrical container (inner dimension: 500mm in radius, 200mm in height) made of stainless steel plates, the stainless steel plates (40 mm in width) are welded on the top of the container, and the container is divided into three parts from inside to outside: a first radon collecting space (radius 100mm) and a quarter-round tubular test body (inner radius r)1100mm, outer radius r2400mm) and a second radon collection space (inner radius 400mm, outer radius 500 mm). The fan-shaped cover with the radius of 540mm is connected with the container through bolts, and the fan-shaped cover and the container are sealed through rubber gaskets. Two metal connecting pipes with the diameter of 4mm are respectively arranged on the wall surfaces of the two radon collecting spaces inside and outside the container, and the radon measuring instrument, the drying pipe and the (first or second) radon collecting space form a closed cycle radon exhalation rate measuring system through the hose.
And finally, additionally manufacturing two quarter arc surface stainless steel baffles, wherein one is 100mm in radius and the other is 400mm in radius.
3) Preparation of test pieces
Step 1: the plastic paper with the same size as the arc surface stainless steel baffle is attached to the outer surface of the arc surface stainless steel baffle with the radius of 100mm, and the plastic paper with the same size as the arc surface stainless steel baffle is attached to the inner surface of the arc surface stainless steel baffle with the radius of 400 mm.
Step 2: putting two circular arc stainless steel baffles into the container and closing to the wedge; then, pouring the prepared concrete in proportion into the container to ensure that the height of the test block is higher than that of the container; after the test block is dried, cutting off the part of the test block exceeding the height of the container to enable the height of the test block to be flush with the height of the container; and taking out the stainless steel baffles with the circular arc surfaces on the two sides of the test sample, and slightly scraping the residual plastic paper on the test block.
(2) Experiment of
1) Preparation phase
Step 1: sealing the top surface of the test block by using aluminum foil paper with the same size as the test block; then, the test block is opened in the atmosphere and is placed for 30 days under natural conditions, so that the radon in the test block can be stably diffused; then a quarter round surface rubber pad (thickness 6mm) with the radius of 540mm is placed above the container, then a rubber pad (thickness 3mm) with the same size as the test block is placed, aligned with the test block, covered with a quarter fan-shaped stainless steel cover with the radius of 540mm, and finally connected through bolts.
Step 2: and the gas flowmeter, the drying pipe, the filtering device and the Rad7 radon measuring instrument are connected with the radon collecting space in the test block through hoses to form two closed loops.
2) Measuring
In this experiment, the surface area S of the inner surface (intrados) of the quarter-circle tubular test piece1＝0.0314m2Surface area S of the outer surface (extrados)2＝0.1257m2The volume of the first radon collecting space is 1.6L, and the volume of the external circuit is V11.05L (including Rad7 Radon instrument lumen volume, drying tube internal volume and hose internal volume) and total circulation volume V22.65L, the volume of the second radon collecting space is 14.1L, and the volume of the external circuit is 1.06L (including the inner cavity volume of the Radon measuring instrument Radon 7, the volume in the drying tube,Volume in hose), total circulation volume is 15.16L, opening radon measuring instrument, and measuring radon concentration parts in the first radon collecting space and the second radon collecting space for 2 times, and setting the measuring period as t1＝t2＝15min。
(3) Calculating the radon exhalation rate measured value of the inner surface and the outer surface of the circular tube
Calculating the radon exhalation rate J of the inner and outer arc surfaces of the circular tube by using the following formula (10)1And J2：
Radon concentration measurement result of first radon collection space and radon exhalation rate J1The calculation results are as follows:
cumulative time t1 C11(Bq/m3) C12(Bq/m3) J1(Bq/m2s)
15min 1420 3360 0.1819
Radon concentration measurement result and radon exhalation rate J of second radon collection space2The calculation results are as follows:
cumulative time t2 C21(Bq/m3) C22(Bq/m3) J2(Bq/m2s)
15min 810 1650 0.1126
(4) Calculating radon diffusion coefficient and transportable radon generation rate
Substituting the calculated radon exhalation rate into a formula (9) to calculate a radon diffusion coefficient D, substituting the calculated diffusion coefficient D into a formula (8) to calculate a porous emanation medium transportable radon production rate α, wherein the results are as follows:
J1(Bq/m2s) J2(Bq/m2s) D(m2/s) α(Bq/m3s)
0.1819 0.1126 8.41×10-8 1.03

Claims (10)

1. a method for determining the diffusion coefficient of radon in a porous emanative medium, the method comprising the steps of: the device comprises a test body, a first radon collecting space, a second radon collecting space, a first radon measuring system and a second radon measuring system; the testing body is a straight cylinder, the bottom surface of the testing body is a quarter of ring, the side surface of the testing body is composed of two opposite planes and two opposite cambered surfaces, wherein the cambered surface close to the center of a circle is an inner cambered surface, and the cambered surface far away from the center of a circle is an outer cambered surface; a first radon collecting space is arranged on the inner side of the inner cambered surface and used for collecting radon separated out from the inner cambered surface; a second radon collecting space is arranged on the outer side of the outer arc surface and used for collecting radon separated out from the outer arc surface; the first radon measuring system is communicated with the first radon collecting space to form a closed loop, and the second radon measuring system is communicated with the second radon collecting space to form a closed loop;
the method calculates the diffusion coefficient D of radon in the porous emanation medium according to the following formula:
Figure FDA0002482503000000011
wherein:
Figure FDA0002482503000000012
Figure FDA0002482503000000013
I0、I1respectively representing 0-order and 1-order virtual vector Bessel functions of a first class;
K0、K1respectively representing a second class of 0-order and 1-order virtual vector Bessel functions;
r1represents the radius of the inner circular arc in the circular ring; r is2The radius of the outer arc in the ring is represented;
J1、J2radon analysis respectively showing intrados and extradosThe yield is increased;
respectively testing the radon concentration C of the first radon collection space at two moments by using a first radon measuring system11And C12Calculating the radon exhalation rate J of the intrados according to the following formula1,
Figure FDA0002482503000000021
t1Representing the time interval, S, of two moments of testing a first set of radon spaces1Denotes the surface area of the intrados of the test body, V1Representing the total volume of the closed loop in which the first radon collection space is positioned;
respectively testing the radon concentration C of the second radon collection space at two moments by using a second radon measuring system21And C22Calculating the radon exhalation rate J according to the following formula2，
Figure FDA0002482503000000022
t2Representing the time interval, S, of two moments of testing a second set of radon spaces2Representing the surface area of the extrados of the test body; v2The total volume of the closed loop in which the second radon collection space is positioned is shown, lambda represents the decay constant of radon, and lambda is 2.1 × 10-6s-1。
2. The method of claim 1, wherein t is1＝10-30min；t2＝10-30min。
3. The method of claim 1, wherein the test body is prepared by mixing uranium tailings with cement and then adding water to mix the mixture.
4. The method of claim 3 wherein the uranium tailings have a particle size of less than 1 mm.
5. The method of claim 3, wherein the mass ratio of uranium tailings to cement is 3-7: 1.
6. The method of claim 1Method characterized in that r1＝80-150mm；r2＝300-500mm。
7. The method of claim 1, wherein the radon concentration in the radon collection space is tested simultaneously using a first radon measuring system and a second radon measuring system.
8. The method of claim 1, wherein the first radon collecting space and the second radon collecting space are homocylinders, and the bottom surface of the first radon collecting space is a sector with a central angle of 90 degrees; the bottom surface of the second radon collecting space is a quarter of a circular ring.
9. A method for determining the production rate of migratory radon in a porous emanator medium, characterized in that the radon diffusion coefficient D in the porous emanator medium is calculated according to the method of any one of claims 1 to 8, and then the production rate of migratory radon is calculated according to the following formula α,
Figure FDA0002482503000000031
10. a method for determining the production rate of migratory radon in a porous emanator medium, characterized in that the radon diffusion coefficient D in the porous emanator medium is calculated according to the method of any one of claims 1 to 8, and then the production rate of migratory radon is calculated according to the following formula α,
Figure FDA0002482503000000032
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