Patent Publication Number: US-9429506-B2

Title: Apparatus and method of measuring effective porosity using radon

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority from Korean Patent Application No. 10-2013-0107469 filed on Sep. 6, 2013, which is incorporated herein by reference in its entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     The present invention relates to an apparatus and method of measuring effective porosity using radon, and more particularly, to an apparatus and method of measuring effective porosity of various media such as rock or soil using radon that is an inert gas. 
     2. Description of the Prior Art 
     The porosity of rock, which refers to a capability of storing fluid, provides a basis for determining economic feasibility of petroleum, natural gas, subsurface water, or mineral resource and is used in a variety of fields other than that, and thus, it is very important to accurately calculate the porosity. 
     For example, recently, studies on underground storage of carbon dioxide for solving global warming are actively carried out, and an investigation for selecting proposed sites for storing carbon dioxide is performed along therewith. In order to find an underground storage place of carbon dioxide in a commercialized scale, evaluations for a scale of a quantitative storage space and a storage capacity should be carried out. To this end, it is preferentially required to find a stratum having a porosity of at least 8%. 
     In addition, weathering and permeability of rock plays an important role in terms of stability securement and long-term management of a bedrock structure and disposal of radioactive waste in subterranean caves. The weathering and permeability of rock is greatly influenced depending on internal structure properties of the rock. That is, the weathering may proceed rapidly depending on the quantity of pores, fine cracks and the like inside rock. In addition, a quantitative evaluation of an internal structure of rock may be a means capable of quantitatively evaluating the degree of weathering of the rock. Therefore, in terms of long-term management of a bedrock structure, it is very important to accurately understand the internal structure of rock in three dimensions. 
     Carbonate rock is very important reservoir rock, and the understanding of lithological properties of carbonate rock is very important in evaluating economic feasibility of a mining area and oil deposits. Particularly, techniques of analyzing and predicting permeability of carbonate reservoir rock may be helpfully used in greatly reducing capital risk when developing a mining area. The permeability of carbonate reservoir rock is mainly influenced by porosity of reservoir rock, connectivity between pores, temperature of reservoir rock, precipitation of asphaltene and the like. However, it has been known that among the factors, the porosity of reservoir rock most greatly influences the permeability of reservoir rock. 
     The liquid substances in the ground permeate through pores connected between soil particles constituting the ground. In addition, it has been known that the liquid substances in bedrock moves depending on cracks and fine cracks formed by weathering, fault activity, discontinuity surface, joint, and the like. Therefore, all spaces connected to one another that relate to a mechanism of such movement may be represented as spatial meaning of the effective porosity. The effective porosity is one of the very important parameters capable of estimating a contaminant penetration pathway, the subsurface water content, and the like. 
     Even in order to evaluate the subsurface water content in the ground for rain and the inflow of contaminants leaked from the ground surface, it is preferentially necessary to understand porosity and effective porosity, which are physical properties of the ground. Further, in the case of subsurface dam in the course of construction in an alluvium region that is an unconsolidated, unconfined aquifer for the purpose of emerging conservation and effective use of water resources, in order to estimate storage capability of subsurface water in the target area, the measurement of porosity and effective porosity of the ground should be preceded. 
     The porosity may be classified into absolute porosity or total porosity and effective porosity depending on whether or not geotechnically isolated pores are included. The absolute porosity is a ratio of the volume of all empty spaces in a sample to the total volume thereof with or without connectivity between the spaces. On the contrary, the effective porosity is defined as a ratio of the total volume of the pores connected to one another allowing fluid to pass, except isolated pores, to the total volume. 
     Indoor measurement of porosity of rock is generally performed using a saturation method. According to the definition of porosity, it can be seen that the porosity calculated by a saturation method is effective porosity. The volume of pores is calculated using a difference in weight between a saturated state and a dried state of rock according to the saturation method. Thus, the accuracy in measuring the porosity depends on whether rock is saturated 100%. In Korean Society for Rock Mechanics and International Society for Rock Mechanics, a saturation method using vacuum is employed as a standard test method, in which a test specimen is immersed in water in a vacuum state below 800 Pa (6 torr) for one or more hours to saturate the test specimen. 
     Here, when a vacuum pump with low pumping rate is used or a plurality of test specimens are saturated in a lump, the test specimens should be immersed in water for a long time in a vacuum state. Particularly, if a test specimen contains substances soluble in water, a surface-dried water saturation weight is reduced. In addition, there may be various disadvantages according to the vacuumization by the water-immersion. One of the disadvantages is air bubbles captured on the surface of the test specimen when it is immersed in water and saturated. In the standard test, the test specimen is periodically disturbed in order to remove the air bubbles, which is practically extremely difficult operation. Moreover, vacuum efficiency is deteriorated and influenced even by the amount of water because of water serving as buffer along with the air. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention is conceived to solve the aforementioned problems in the prior art. An objective of the present invention is to provide an apparatus and method of relatively simply and accurately measuring porosity of various media using radon. 
     According to an aspect of the present invention for achieving the objectives, there is provided an apparatus of measuring porosity, including: a gas component detector having two ports and configured to measure a concentration of a predetermined gas; a gas vessel having two ports and configured to accommodate the predetermined gas; a medium vessel having two ports and configured to accommodate a medium, of which the porosity is desirous to be measured; pipe lines connecting the ports of the gas component detector, the gas vessel and the medium vessel; and valves installed on the pipe lines, wherein the pipe lines and the valves are arranged and installed to form a first loop wherein the gas component detector is not connected to both the gas vessel and the medium vessel, a second loop wherein the gas component detector is connected to the gas vessel and not connected to the medium vessel, and a third loop wherein the gas component detector is connected to the medium vessel and not connected to the gas vessel, and the valves switches between the loops. 
     Preferably, the two ports of the gas component detector are respectively connected to the two ports of the gas vessel through two pipe lines, the valves are respectively installed on the two pipe lines, the valves are connected to each other through a pipe line, the valves are respectively connected to the two ports of the medium vessel through two pipe lines, and each of the valves is a four-way valve. 
     Preferably, the gas component detector, the gas vessel, and the medium vessel are serially connected to one another through pipe lines to form a single closed loop, the valves are respectively installed at the pipe lines in the vicinity of the two ports of the gas vessel and connected to each other through a pipe line, the valves are respectively installed at the pipe lines in the vicinity of the two ports of the medium vessel and connected to each other through a pipe line, and each of the valves is a three-way valve. 
     The apparatus may further include a pump installed adjacent to the gas component detector. 
     The gas component detector and the pump may be integrally formed. 
     Each port of the gas vessel may be provided with an opening/closing valve. 
     The apparatus may further include a drying tube installed on the first loop. 
     The apparatus may further include a drying tube installed on the third loop. 
     The predetermined gas may include at least one of radon and helium. 
     According to another aspect of the present invention, there is provided a method of measuring porosity, including: providing the above-described apparatus of measuring porosity, accommodating the predetermined gas and the medium, of which the porosity is desirous to be measured, in the gas vessel and the medium vessel, respectively; forming the second loop and maintaining it for a predetermined time; forming the first loop, maintaining it for a predetermined time, and measuring a concentration of the predetermined gas in the first loop by the gas component detector; forming the third loop, maintaining it for a predetermined time so that pores of the medium are filled with the predetermined gas, and measuring a concentration of the predetermined gas in the third loop by the gas component detector; and calculating porosity of the medium based on the respective gas concentrations in the first and third loops, respective internal volumes of these loops, a volume of the medium, and a mass balance equation for the predetermined gas in these loops. 
     Before the second loop is formed, the method may further include additionally forming the first loop to measure a background concentration of the predetermined gas in the additional first loop by the gas component detector, wherein after forming the second loop, the gas concentrations measured in the first and third loops by the gas component detector are corrected by subtracting the background concentration therefrom. 
     The predetermined gas may include at least one of radon and helium. 
     A solid substance generating the predetermined gas may be accommodated in the gas vessel. 
     A drying tube may be further installed on the first loop of the apparatus of measuring porosity, and before forming the second loop, the method may further include additionally forming the first loop to allow air to circulate in the first loop, thereby removing moisture within the third loop. 
     A drying tube may be further installed on the third loop of the apparatus of measuring porosity, and before forming the second loop, the method may further include additionally forming the third loop to allow air to circulate in the third loop, thereby removing moisture within the third loop. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objectives, features and advantages of the present invention will become apparent from the following description of a preferred embodiment given in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic view of an apparatus of measuring porosity of a medium according to an embodiment of the present invention; 
         FIG. 2  is a flowchart illustrating a method of measuring porosity of a medium using the apparatus shown in  FIG. 1 ; 
         FIGS. 3A to 3D  are views showing loops formed in respective steps for measuring porosity of a medium using the apparatus shown in  FIG. 1 ; 
         FIG. 4  is a schematic view of an apparatus of measuring porosity of a medium according to a modified embodiment of the present invention; and 
         FIGS. 5A to 5D  are views showing loops formed in respective steps for measuring porosity of a medium using the apparatus shown in  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are provided only for illustrative purposes so that those skilled in the art can fully understand the spirit of the present invention. Therefore, the present invention is not limited to the following embodiments but may be implemented in other forms. In the drawings, the widths, lengths, thicknesses and the like of elements may be exaggerated for convenience of illustration. Like reference numerals indicate like elements throughout the specification and drawings. 
       FIG. 1  is a schematic view of an apparatus of measuring porosity of a medium according to an embodiment of the present invention;  FIG. 2  is a flowchart illustrating a method of measuring porosity of a medium using the apparatus shown in  FIG. 1 ; and  FIGS. 3A to 3D  are views showing loops formed in respective steps for measuring porosity of a medium using the apparatus shown in  FIG. 1 . 
     First, referring to  FIG. 1 , a porosity measuring apparatus  100  according to an embodiment of the present invention includes a radon component detector  110  for measuring the concentration of radon gas, a drying tube  115 , a radon vessel  130  for accommodating radon gas, a medium vessel  150  for accommodating a medium  160 , of which the porosity is desirous to be measured, pipe lines PL for connecting the radon component detector  110 , the radon vessel  130  and the medium vessel  150  to one another, and a plurality of valves  172  and  174  installed at predetermined positions of the pipe lines PL to switch between a plurality of predetermined loops formed by the radon component detector  110 , the radon vessel  130 , the medium vessel  150 , and the pipe lines PL. Unless otherwise specified herein, radon refers to radon (Rn-220). 
     The radon component detector  110  is a pump built-in type and includes a component detection part for detecting the concentration of radon gas and input and out ports  112  and  114  respectively connected to pipe lines PL. Since the radon component detector  110  used in the embodiment has a pump installed therein, the pump operates to allow radon gas to flow into the radon component detector  110  through the pipe line PL connected to the input port  112  and to allow the radon gas to flow out through the output port  114  after the concentration of the radon gas is measured by the component detection part. 
     The drying tube  115  is optionally provided in order to remove moisture from the radon component detector  110 , the medium vessel  150 , and/or the medium  160 . The drying tube  115  is filled with a desiccant, which changes color if the desiccant contains moisture. It is possible to confirm a dried state from a ratio of a discolored desiccant with moisture contained therein to a desiccant without moisture. Although in the embodiment, the drying tube  115  is disposed adjacent to the radon component detector  110 , the present invention is not limited thereto, but the drying tube  115  may be disposed at any other various positions. However, in order to remove moisture from the radon component detector  110 , it is preferred that the drying tube  115  be disposed adjacent to the radon component detector  110 . 
     The radon vessel  130 , which is an airtight container for accommodating radon gas, accommodates radon gas itself, but it may be preferred that a solid substance generating radon gas, such as a radon-enriched mineral, be accommodated in the radon vessel  130 . The radon vessel  130  is provided with two ports  132  and  134 , which in turn are respectively connected to the pipe lines PL. The two ports  132  and  134  of the radon vessel  130  are preferably equipped with opening/closing valves. 
     The medium vessel  150  is an airtight container for accommodating the medium  160 , of which the porosity is desirous to be measured. The medium vessel  150  is provided with two ports  152  and  154 , which in turn are respectively connected to the pipe lines PL. 
     The input and output ports  112  and  114  of the radon component detector  110  are respectively connected to the two ports  132  and  134  of the radon vessel  130  through the two pipe lines PL. Here, the valves  172  and  174  are respectively installed in the middles of the two pipe lines PL, and the valves  172  and  174  are connected to each other through a pipe line PL. In addition, the valves  172  and  174  are connected to the two ports  152  and  154  of the medium vessel  150  through the pipe lines PL. Here, each of the valves  172  and  174  installed in the pipe lines PL is a four-way valve. 
     By controlling the valves  172  and  174  in the state that the pipe lines PL and the valves  172  and  174  are connected and installed, predetermined loops Loop-0, Loop-1, Loop-2 and Loop-3 for measuring the radon concentration necessary for calculating the porosity of the medium  160 . 
     That is, by controlling the valves  172  and  174 , the loop Loop-0 or Loop-1 (i.e., a closed loop connecting reference numerals  110 ,  172 ,  174 ,  115  and  110  in the embodiment) is formed so that the radon component detector  110  is not connected to both the radon vessel  130  and the medium vessel  150  as shown by a bold line in  FIG. 3A or 3C , the loop Loop-2 (i.e., a closed loop connecting reference numerals  110 ,  172 ,  130 ,  174 ,  115  and  110  in the embodiment) is formed so that the radon component detector  110  is connected to the radon vessel  130  and not connected to the medium vessel  150  as shown by a bold line in  FIG. 3B , and the loop Loop-3 (i.e., a closed loop connecting reference numerals  110 ,  172 ,  150 ,  174 ,  115  and  110  in the embodiment) is formed so that the radon component detector  110  is connected to the medium vessel  150  and not connected to the radon vessel  130  as shown by a bold line in  FIG. 3D . 
     Here, the internal volumes of the loops Loop-1 and Loop-3 among the loops are used in calculating the porosity of the media. It should be noted that the internal volumes of the loops Loop-1 and Loop-3 include the volume of the internal path of the radon component detector  110  from the input port  112  to the output port  114  thereof, the volume (except the volume of the desiccant) of the internal space of the drying tube  115 , the volume of the internal space of the medium vessel  150 , the volume of the medium  160 , and/or the volume of the internal spaces of the valves  172  and  174  in addition to the internal volume of the corresponding pipe lines PL. As the internal volume of each loop, only a macroscopic space in the loop is basically taken into consideration. Therefore, in the case of the loop Loop-3 including the medium vessel  150 , the volume of the internal space of the medium vessel  150  is a volume obtained by subtracting the entire volume of the medium  160  disposed in the medium vessel  150  from the entire internal volume of the medium vessel  150 . 
     Next, a method of measuring the porosity of the medium  160  using the measuring apparatus  100  so configured will be described with reference to  FIGS. 2 and 3A to 3D . 
     First, radon gas or radon-enriched mineral and a medium  160  are accommodated in the radon vessel  130  and the medium vessel  150 , respectively (S 110 ). Here, the measuring apparatus  100  should be in the state of the loop Loop-0, in which the input port  112  of the radon component detector  110  is connected to the output port  114  thereof via the drying tube  115  through the pipe lines PL as shown in  FIG. 3A  by operating the valves  172  and  174  in order for the radon component detector  110  not to be connected to the radon vessel  130  and the medium vessel  150 . Here, if an opening/closing valve is installed at each of the ports  132  and  134  of the radon vessel  130  and is in a closed state, the measuring apparatus  100  may be in a state of any loop. Here, the accommodated medium  160  should be in a sufficiently dried state in order for moisture not to occur within the pores of the medium  160 . 
     Then, the radon component detector  110  is operated in the state of the loop Loop-0 as shown in  FIG. 3A . Here, the air of a measuring room occurs in the loop Loop-0 so configured. While the air circulates in the loop Loop-0 by means of the pump provided in the radon component detector  110  in the operation thereof, the component detection part of the radon component detector  110  measures the background concentration C 0  of radon gas that essentially occurs in the air in the loop Loop-0 (S 120 ). That is, the background concentration C 0  of radon gas refers to the concentration of the radon gas that essentially occurs in the measuring room, specifically in the measuring apparatus  100  and the pipe lines PL. The concentration of radon gas in the loop Loop-1 or Loop-3 formed later can be more precisely obtained by subtracting the background concentration C 0  from the radon concentration measured in each loop. However, if the background concentration of radon gas can be obtained from the information about the measuring room, the step of measuring the background concentration C 0  may be omitted. 
     Here, since the loop Loop-0 includes the drying tube  115 , while the air circulating in the loop Loop-0 passes through the drying tube  115 , the moisture in the radon component detector  110  and the pipe lines PL is removed. It is preferred that the background concentration C 0  of radon gas be measured after allowing the air to circulate in the loop Loop-0 until the relative humidity in the loop Loop-0 including the radon component detector  110  is less than 5%. 
     Meantime, the order of the step S 110  of respectively accommodating the radon gas and the medium in the radon vessel  130  and the medium vessel  150  and the step S 120  of measuring the background concentration C 0  of radon gas may be changed. 
     Thereafter, the loop Loop-2, in which the radon component detector  110  and the radon vessel  130  are connected to each other as shown in  FIG. 3B , is formed by operating the valves  172  and  174 , thereby allowing the radon gas concentrated in the radon vessel  130  to enter the loop Loop-2 (S 130 ). Here, if the ports  132  and  134  of the radon vessel  130  are respectively provided with opening/closing valves, these valves should be in an open state. By maintaining the loop Loop-2 for about 10 minutes, the radon gas is allowed to uniformly occur in the loop Loop-2. Here, it is possible to allow the radon gas to circulate in the loop Loop-2 and rapidly reach the uniform state by operating the pump of the radon component detector  110 . 
     Then, the loop Loop-1, in which the input port  112  of the radon component detector  110  is connected to the output port  114  thereof via the drying tube  115  through the pipe lines PL as shown in  FIG. 3C , is formed by operating the valves  172  and  174 . After maintaining the loop Loop-1 for a predetermined time, the component detection part of the radon component detector  110  measures the radon concentration C 1  in the loop Loop-1 (S 140 ). Here, it is preferred that the radon concentration C 1  measured in the loop Loop-1 be corrected by subtracting the background concentration C 0  of radon gas measured in the step S 120  therefrom. In practice, since the loops Loop-0 and Loop-1 have the same route but contain the substances having different concentrations, the loops Loop-0 and Loop-1 are expressed differentially from each other. 
     Thereafter, the loop Loop-3, in which the radon component detector  110 , the drying tube  115  and the medium vessel  150  are connected to one another as shown in  FIG. 3D , is formed by operating the valves  172  and  174 . Then, after the radon gas reaches an equilibrium state in the loop Loop-3, the radon concentration C 3  in the loop Loop-3 is measured (S 150 ). Here, the equilibrium state means that if the loop Loop-3 is formed as shown in  FIG. 3D , the radon gas that has existed in the loop Loop-1 is introduced into the medium vessel  150  through the loop Loop-3, and the pores of the medium  160  accommodated in the medium vessel  150  is filled with a portion of the introduced radon gas. That is, the measured radon concentration C 3  is a value measured after the pores of the medium  160  is completely filled with radon gas. Here, it is also preferred that the radon concentration C 3  measured in the loop Loop-3 be corrected by subtracting the background concentration C 0  of radon gas measured in the step S 120  therefrom. 
     If the radon concentrations C 1 , and C 3  in the loops Loop-1 and Loop-3 are measured as described above, the porosity is calculated according to the following procedure (S 160 ). 
     A mass balance equation for radon gas in the loops Loop-1 and Loop-3 is as follows:
 
 C   1   *V   1   =C   3 *( V   3   +V   p )  (Equation 1)
 
     wherein C 1  and C 3  are respectively the radon concentrations in the loops Loop-1 and Loop-3, V 1  and V 3  are respectively the internal volumes of the loops Loop-1 and Loop-3, and V p  is the volume of the pores of the medium  160  accommodated in the medium vessel  150 . As described above, C 1  and C 3  are respectively measured in steps S 140  and S 150 , and V 1  and V 3  may be obtained from the volume of the internal path of the radon component detector  110 , the volume of the internal space (except the volume of the desiccant) of the drying tube  115 , the volume of the internal space (except the volume of medium) of the medium vessel  150 , and the internal volume of the pipe lines PL, which will be described later again. 
     If Equation 1 is rearranged to solve for V p , which is the volume of the pores in the medium, the following Equation 2 is obtained as follows:
 
 V   p   =V   1   *C   1   /C   3   −V   3   (Equation 2)
 
     Therefore, according to the definition of porosity, the porosity P is calculated as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     wherein, V m  is the volume of the medium  160 . 
     In the meantime, V 1  and V 3  may be calculated as follows. 
     First, the internal volume V 1  of the loop Loop-1, which connects reference numerals  110 ,  172 ,  174 ,  115  and  110 , is the sum of the volume of the internal path of the radon component detector  110  from the input port  112  to the output port  114  thereof, the volume of the internal space (except the volume of the desiccant) of the drying tube  115 , the internal volume of the pipe lines PL from the input port  112  of the radon component detector  110  to the output port  114  of the radon component detector  110  via the valves  172  and  174  and the drying tube  115 , and the volume of the internal path of the valves  172  and  174 . The volume of the internal path of each of the radon component detector  110  and the valves  172  and  174  and the volume of the internal space (except the volume of the desiccant) of the drying tube  115  may be obtained from its specification or a conventional method such as a weight method, and the internal volume of the pipe line PL may be obtained using its inner diameter and length or from a weight method. 
     The weight method is used to obtain the internal volume of the pipe line PL by filling the pipe line PL with a fluid, the density of which is known, such as distilled water, and then obtaining the internal volume of the pipe line PL from the mass of the distilled water. 
     The internal volume V 3  of the loop Loop-3, which connects reference numerals  110 ,  172 ,  150 ,  174 ,  115  and  110 , is the sum of the volume of the internal path of the radon component detector  110  from the input port  112  to the output port  114  thereof, the volume (except the volume of the desiccant) of the internal space of the drying tube  115 , the internal volume of the pipe lines PL from the input port  112  of the radon component detector  110  to the output port  114  of the radon component detector  110  via the valve  172 , the medium vessel  150 , the valve  174  and the drying tube  115 , the volume obtained by subtracting the volume V m  of the medium  160  from the internal volume of the medium vessel  150 , and the volume of the internal path of the valves  172  and  174 . The volume of the internal path of the radon component detector  110 , the internal volume of the pipe lines PL and the volume of the internal path of the valves  172  and  174  each may be obtained in the same manner as described above, and the internal volume of the medium vessel  150  may be obtained from the specification thereof or a conventional method such as a weight method. 
     The internal volume of each component may be obtained using various methods other than the aforementioned methods. For example, the internal path volume of the radon component detector  110  may be obtained using the apparatus of the present invention as follows. 
     Using the aforementioned apparatus  100 , some (S 120  to S 150 ) of the steps of the aforementioned porosity measuring method is preformed in a state where the medium vessel  150  is filled with no media, i.e., in a state of the empty vessel. That is, radon gas is accommodated in the radon vessel  130 , the background concentration C 0  of radon gas is measured in the loop Loop-0 shown in  FIG. 3A  (corresponding to S 120 ), the loop Loop-2 is formed as shown in  FIG. 3B  and the radon gas is uniformly distributed in the loop Loop-2 (corresponding to S 130 ); the loop Loop-1 is formed as shown in  FIG. 3C  and the concentration C 1  of the radon gas is measured therein (corresponding to S 140 ); and the loop Loop-3 is formed as shown in  FIG. 3D  and maintained for a predetermined time and the concentration C 3  of the radon gas is measured in the loop Loop-3 (corresponding to S 150 ). Thereafter, the internal path volume of the radon component detector  110  may be calculated according to the following procedure. 
     A mass balance equation for the radon gas in the loops Loop-1 and Loop-3 is as follows:
 
 C   1   *V   1   =C   3   *V   3   (Equation 4)
 
     The internal volumes V 1  and V 3  of the loops Loop-1 and Loop-3 each may be specifically subdivided as follows. 
     The internal volume V 1  of the loop Loop-1 is the sum of the internal path volume V d  of the radon component detector  110 , the internal volume V P1  of the pipe lines PL constituting the loop Loop-1, and the volume V V  of the internal path of both the valves  172  and  174 . That is, V 1 =V d +V P1 +V V . 
     The internal volume V 3  of the loop Loop-3 is the sum of the internal path volume V d  of the radon component detector  110 , the internal volume V P3  of the pipe lines PL constituting the loop Loop-3, the internal volume V E  of the empty vessel  150 , and the volume V V  of the internal path of both the valves  172  and  174 . That is, V 3 =V d +V P3 +V E +V V . 
     The following Equation 5 is obtained by substituting V 1  and V 3  into Equation 4.
 
 C   1 *( V   d   +V   P1   +V   V )= C   3 *( V   d   +V   P3   +V   E   +V   V )  (Equation 5)
 
     If Equation 5 is rearranged to solve for the internal path volume V d  of the radon component detector  110 , the internal path volume V d  is obtained as follows:
 
 V   d =( C   3 *( V   P3   +V   E )− C   1   *V   P1 +( C   3   −C   1 )* V   V )/( C   1   −C   3 )  (Equation 6)
 
     Meanwhile, in the above-described embodiment, although the radon component detector  110  and the valves  172  and  174  may be individually operated by an operator, an additional controller may be provided to automatically perform the above-described measurement steps after the radon gas and the medium  160  are respectively accommodated in the radon vessel  130  and the medium vessel  150 . 
     Next, an apparatus of measuring porosity of a medium according to a modified embodiment of the present invention will be described.  FIG. 4  is a schematic view of an apparatus of measuring porosity of a medium according to a modified embodiment of the present invention; and  FIGS. 5A to 5D  are views showing loops formed in respective steps for measuring porosity of a medium using the apparatus shown in  FIG. 4 . 
     Referring to  FIG. 4 , a porosity measuring apparatus  101  according to the modified embodiment of the present invention includes a radon component detector  120  for measuring the concentration of radon gas, a pump  122 , a drying tube  115 , a radon vessel  130  for accommodating radon gas, a medium vessel  150  for accommodating a medium  160 , of which the porosity is desirous to be measured, pipe lines PL for connecting the above-described components, and a plurality of valves  182 ,  184 ,  186  and  188  installed at predetermined positions of the pipe lines PL to switch between a plurality of predetermined loops formed by the radon component detector  120 , the pump  122 , the drying tube  115 , the radon vessel  130 , the medium vessel  150 , and the pipe lines PL. 
     The radon component detector  120  is the same as the radon component detector  110  of the previous embodiment except that the radon component detector  120  does not have a pump housed therein. The radon component detector  120  corresponds to the component detection part of the radon component detector  110  of the previous embodiment, and the pump  122  corresponds to the pump of the radon component detector  110 . That is, the radon component detector  120  and the pump  122  of the modified embodiment, into which the component detection part and the pump housed in the radon component detector  110  of the previous embodiment are separated, are substantially the same as the radon component detector  110 . In the apparatus of measuring porosity of a medium according to the present invention, since the pump serves to assist radon gas in the formed loop in being uniform in the loop, the pump is a substantially optional element. Therefore, the pump  122  may be omitted in the modified embodiment, and the radon component detector  110  may also have no pump housed therein in the previous embodiment. 
     The drying tube  115 , the radon vessel  130  and the medium vessel  150  are respectively the same as the drying tube  115 , the radon vessel  130  and the medium vessel  150  of the previous embodiment. 
     The radon component detector  120 , the pump  122 , the drying tube  115 , the radon vessel  130  and the medium vessel  150  are connected to one another through the pipe lines PL so that they serially form one closed loop. In addition, there are further provided paths, which do not pass through the radon vessel  130  and the medium vessel  150  but bypath them, respectively. That is, the valves  182  and  184  are respectively installed at the pipe lines PL in the vicinity of the two ports of the radon vessel  130  and connected to each other through a pipe line PL, and the valves  186  and  188  are respectively installed at the pipe lines PL in the vicinity of the two ports of the medium vessel  150  and connected to each other through a pipe line PL. 
     By controlling the valves  182 ,  184 ,  186  and  188  in the state that the pipe lines PL and the valves  182 ,  184 ,  186  and  188  are connected to one another and installed as described above, loops Loop-0, Loop-1, Loop-2 and Loop-3 each having the same path as those of the previous embodiment may be formed. 
     That is, by controlling the valves  182 ,  184 ,  186  and  188 , the loop Loop-0 or Loop-1 (i.e., a closed loop connecting reference numerals  120 ,  182 ,  184 ,  186 ,  188 ,  115 ,  122  and  120  in the modified embodiment) is formed so that the radon component detector  120  is not connected to both the radon vessel  130  and the medium vessel  150  as shown by a bold line in  FIG. 5A or 5C , the loop Loop-2 (i.e., a closed loop connecting reference numerals  120 ,  182 ,  130 ,  184 ,  186 ,  188 ,  115 ,  122  and  120  in the modified embodiment) is formed so that the radon component detector  120  is connected to the radon vessel  130  and not connected to the medium vessel  150  as shown by a bold line in  FIG. 5B , and the loop Loop-3 (i.e., a closed loop connecting reference numerals  120 ,  182 ,  184 ,  186 ,  150 ,  188 ,  115 ,  122  and  120  in the modified embodiment) is formed so that the radon component detector  120  is connected to the medium vessel  150  and not connected to the radon vessel  130  as shown by a bold line in  FIG. 5D . 
     In the modified embodiment, the connection configuration of the pipe lines and the valves is somewhat changed and the number of the valves is increased, as compare with the previous embodiment. The valves used in the modified embodiment are increased in number and are not four-way valves but three-way valves. 
     Substantially, if the valves  182  and  188  are combined and substituted by one four-way valve and the valves  184  and  186  are combined and substituted by one four-way valve, the modified embodiment has the same configuration as the previous embodiment. 
     A method of measuring porosity of a medium using the measuring apparatus  101  so configured is the same as the measuring method described in the previous embodiment. 
     That is, radon gas and a medium are respectively accommodated in the radon vessel  130  and the medium vessel  150  (S 110 ); the radon component detector  110  is dried and then the background concentration C 0  of radon gas is measured in the loop Loop-0 shown in  FIG. 5A  (S 120 ); the loop Loop-2 is formed as shown in  FIG. 5B  and the radon gas is uniformly distributed in the loop Loop-2 (S 130 ); the loop Loop-1 is formed as shown in  FIG. 5C  and the radon concentration C 1  is measured therein (S 140 ) and the loop Loop-3 is formed as shown in  FIG. 5D  and the concentration C 3  of the radon gas that reaches an equilibrium state in the loop Loop-3 is measured (S 150 ). If the radon concentrations C 1  and C 3  are measured as described above, the porosity P is calculated using the above-described Equation 3 (S 160 ). 
     In this modified embodiment, although the radon component detector  120 , the pump  122 , and the valves  182 ,  184 ,  186  and  188  may be individually operated by an operator, an additional controller may be provided to automatically perform the above-described measurement steps after the radon gas and the medium  160  are respectively accommodated in the radon vessel  130  and the medium vessel  150 . 
     Meanwhile, if the respective components, i.e., the radon component detector  110  or  120 , the drying tube  115 , the radon vessel  130 , the medium vessel  150 , the pipe lines PL and the valves are connected to one another to form the loops Loop-0, Loop-1, Loop-2 and Loop-3, they may be changed in positions, order and/or number to be modified into any other forms. However, when the pump  122  is included, it is preferred that the pump  122  be installed adjacent to the radon component detector  120 . 
     In the meantime, since the drying tube  115  is installed adjacent to the radon component detector  110  or  120 , in the state that the loop Loop-0 is formed, the air is allowed to circulate in the loop Loop-0 to remove the moisture inside the radon component detector  110  or  120 , thereby making it possible to more accurately measure the concentration. After the loop Loop-0 is formed, the loop Loop-3 is formed before the loop Loop-2 is formed, and an additional step of allowing the air to circulate in the loop Loop-3 may be further performed. In such a case, even though the medium  160  was not sufficiently dried in the step S 110  of accommodating the medium  160  in the medium vessel  150 , the more accurate porosity of the medium  160  can be obtained by removing the moisture contained in the medium vessel  150  and the medium  160  accommodated therein by means of the drying tube  115  in the above-described additional step. Here, since the loop Loop-3 of the additional step is before the loop Loop-2 is formed, the loop Loop-3 contains the air in the measuring room. That is, the loop Loop-3 of the additional step has the same route as the loop Loop-3 formed in the step S 150  but contains compositions different therefrom. 
     According to the present invention, the concentration of radon gas changes as the pores of the medium are filled with the radon gas, and, based on such a change, the porosity of the medium is measured. Radon is generated from three types of naturally occurring radioactive decay series, i.e., uranium series (U-238), actinium series (U-235) and thorium series (Th-232), and radon occurs in the form of three isotopes, i.e., Rn-222 (having a half-life of 3.82 days), Rn-219 (having a half-life of 3.96 seconds) and Rn-220 (having a half-life of 55.6 seconds). Among the three radon isotopes, Rn-222 having the longest half-life of 3.82 days is commonly referred to as radon, and the radon used in the present invention is Rn-222. 
     The reason that in the present invention, radon is selected as the gas with which pores of a medium are filled is because the concentration of radon (Rn-222) can be relatively simply and accurately obtained by measuring radioactivity of radon. Instead of radon, helium (He) may be used as the gas with which pores of a medium are filled. 
     In addition, it can be seen that from the definition of porosity that the porosity calculated in such a manner is effective porosity. 
     An apparatus and method of measuring porosity of a medium using radon according to the present invention so configured is simple in constitution, and thus, it is possible to simply and accurately measure porosity of various media. 
     Particularly, since the porosity can be measured not in a vacuum state but an atmospheric pressure state, the measuring procedure is simple and the measuring time is also very short. Further, since radon (Rn-222) that is an inert gas is used and thus does not have a chemical reaction with the medium, it is possible to accurately measure the porosity. 
     Also, since radon generated from the uranium series that is one of the naturally occurring radioactive series and is a radioactive nuclide having a half-life of 3.82 days, it is possible to relatively simply and accurately measure porosity of a medium by measuring radioactivity of radon and using it. 
     Although some embodiments of the present invention are described for illustrative purposes, it will be apparent to those skilled in the art that various modifications and changes can be made thereto within the scope of the invention without departing from the essential features of the invention. Accordingly, the aforementioned embodiments should be construed not to limit the technical spirit of the present invention but to be provided for illustrative purposes so that those skilled in the art can fully understand the spirit of the present invention. The scope of the present invention should not be limited to the aforementioned embodiments but defined by appended claims. The technical spirit within the scope substantially identical with the scope of the present invention will be considered to fall in the scope of the present invention defined by the appended claims.