KR101793216B1 - Method for displaying pollutant concentration in ground water due to tidal fluctuation in coastal area - Google Patents

Abstract

The present invention relates to a method for displaying a pollutant concentration in underground water due to tidal fluctuation in a coastal area, and more particularly, to a method for displaying a pollutant concentration in underground water due to tidal fluctuation in a coastal area, capable of displaying the pollutant concentration by calculating the pollutant concentration using a general integral transformation technique (GITT) in a situation in which nuclides leaked from a nuclear power plant and a radioactive waste storage space adjacent to the coast and pollutants resulting from various kinds of chemical accidents are influenced by tides in a confined aquifer.

Description

TECHNICAL FIELD The present invention relates to a method for displaying a pollutant concentration in a groundwater,

The present invention relates to a method of indicating the concentration of pollutants in groundwater by fluctuation of the tide in a coastal area. Especially, the pollutants leaked from radioactive waste reservoirs and nuclear power plants adjacent to the coast, The present invention relates to a method for displaying the concentration of contaminants in the groundwater due to fluctuation of the tide in the coastal area using the General Integral Transformation Technique (GITT) technique.

In general, the behavior of various pollutants that are leaked by chemical accidents and pollution accidents in various industrial complexes, radioactive waste repositories and nuclear power plants adjacent to the coasts is inherently very complicated. The groundwater flow in the aquifer adjacent to the shore undergoes a fluctuation in the direction and magnitude of the groundwater velocity in a period of about 12 hours due to the fluctuation of the tidal currents. As a result, the transport and diffusion of the pollutants are caused by the unidirectional groundwater velocity Very different aspect. In addition to the periodic fluctuations of groundwater caused by algae fluctuations, aquifers affected by various factors such as brine interface, concentration difference of seawater and fresh water, wave fluctuations besides algae, coastal slope and aquifer bottom slope Various efforts have been made to identify the behavior of contaminants.

However, most studies on pollutants in aquifers have been conducted in laboratory experiments (eg, Wrenn et al., 1997; Uchiyama et al., 2000; Boufadel et al., 2006, (2008), which is based on the assumption that the aquifer is a part of the coastal aquifer, There is not yet a technique for evaluating the behavior of contaminants under groundwater velocity controlled by fluctuations. Although Yadav et al. [2012] developed an analytical solution for evaluating the pollutant behavior based on the assumption of fluctuation of the algae. However, considering the fluctuation amplitude of the groundwater level decreased along the distance from the coast to inland, it was too simple to consider only the periodic pattern There was a problem.

 Cotta, R.M., 1993. Integral Transforms in Computational Heat and Fluid Flow, CRC Press, Inc., Florida.  Jacob, C. E., 1950. Flow of ground water, Chapter 5 in Engineering Hydraulics, p. 365, New York, John Wiley and Sons, Inc.  Perez Guerrero, J.S., Skaggs, T. H., 2010. Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients. J. Hydrol. 390 (1), 57-65. https://doi.org/10.1016/j.jhydrol.2010.06.030.  Robinson, C., Gibbes, B., Li, L., 2006. Driving mechanisms for flow and transport in a subterranean estuary. Geophys. Res. Lett. 33, L03402. http://dx.doi.org/10.1029/2005GL025247.  Robinson, C., Li, L., Barry, D. A., 2007. Effect of tidal forcing on a subterranean estuary. Adv. Water Resour. 30, 851-365. http://dx.doi.org/10.1016/J.Advwatres.2006.07.006.  Robinson, C., Brovelli, A., Barry, D. A., Li, L., 2009. Tidal influence on BTEC biodegradation in sandy coastal aquifers. Adv. Water Resour. 32 (1), 16-28. .  Rugh, W.J., 1996. Linear system theory, Prentice-Hall.  Xia, Y., Li, H., Boufadel, M. C., Sharifi, Y., 2010. Hydrodynamic factors affecting the persistence of the Exxon Valdez oil in a shallow bedrock beach. Water Resour. Res. 46, W10528.  Li, H. L., Zhao, Q. H., Boufadel, M. C., Venosa, A.D., 2007. A universal nutrient application strategy for the bioremediation of oil-polluted beaches. Marine Pollut. Bull. 54 (8), 1146-1161.  Li, H., Boufadel, M.C., 2011. A tracer study in an Alaskan gravel beach and its implications on the persistence of the Exxon Valdez oil. Mar. Pollut. Bull. 62 (6), 1261-1269.  Liu, C., Szecsody, J.E., Zachara, J.M., Ball, W.P., 2000. Use of the generalized integral transform method for solving transport in porous media. Adv. Water Resour. 23 (5), 483-492. http://dx.doi.org/10.1016/S0309-1708(99)00048-2.  Bakhtyar, R., Brovelli, A., Barry, D. A., Robinson, C., Li, L., 2013. Transport of variable-density solute plumes in response to oceanic forcing. Adv. Water Resour. 53, 208-224. http://dx.doi.org/10.1016/j.advwatres.2012. 11.009.  Uchiyama, Y., Nadaoka, K., Rolke, P., Adachi, K., Yagi, H., 2000. Submarine groundwater discharge into the sea and associated nutrient transport in a sandy beach. Water Resour. Res. 36 (6), 1467-1479. http://dx.doi.org/10.1029/000WR900029.  Boufadel, M. C., Siudan, M.T., Venosa, A.D., 2006. Tracer studies in laboratory beach simulating tidal influences. J. Environ. Eng. 132 (6), 616-623. http://dx.doi.org/10.1061/(ASCE) 0733-9372 (2006) 132: 6 (616).  Boufadel, M. C., Bobo, A. M., Xia, Y., 2011. Feasibility of deep nutrients delivery into a Prince William Sound Beach for the bioremediation of the Exxon Valdez Oil Spill. Ground Water Monit. R. 31 (2), 80-91.  Boufadel, M. C., Suidan, M.T., Venosa, A.D., 1999. A numerical model for density-and-viscosity-dependent flows in two-dimensional variably-saturated porous media. J. Contam. Hydrol. 37 (1-2), 1-20.  Brovelli, A., Mao, X., Barry, D. A., 2007. Numerical modeling of tidal influence on density-dependent contaminant transport. Water Resour. Res. 43, W10426.  Geng, X., Boufadel, M.C., 2015. Numerical study of solute transport in shallow beach aquifers subjected to waves and tides. J. Geophys. Res. Oceans 120, 1409-1428.  Wrenn, B. A., Suidan, M.T., Strohmeier, K.L., Eberhart, B.L., Wilson, G.J., Venosa, A.D., 1997. Nutrient transport during bioremediation of contaminated beaches: Evaluation with lithium as a conservative tracer. Water Res. 31 (3), 515-524.  L., Jackson, N. L., Miller, R. S., 2014. Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach. J. Contam. Hydrol. 165, 37-52. http://dx.doi.org/10.1016/j.jconhyd.2014.07.001.  Geng, X., Boufadel, M.C., 2015. Numerical study of solute transport in shallow beach aquifers subjected to waves and tides. J. Geophys. Res. Oceans 120, 1409-1428.  Suk, H., 2013. Developing semianalytical solutions for multispecies transport coupled with a sequential first-order reaction network under variable flow velocities and dispersion coefficients. Water Resour. Res. 49 (5), 3044-3048. http://dx.doi.org/10.1002/wrcr.20230.  Suk, H., 2016. Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction networks with spatially or temporally variable transport and decay coefficients. Adv. Water Resour. 94, 412-423. http://dx.doi.org/10.1016/J.Advwatres.2016.06.004.  Yadav, R. R., Jaiswal D. K. and Gulrana, 2012. An analytical solution for contaminant transport with a periodic boundary condition in one-dimensional porous media. Int. J. Environ. Sciences 3 (2), 1208-1222.

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a method and apparatus for rapidly and accurately displaying the concentration of contaminants under groundwater velocity controlled by periodic tidal fluctuations in coastal aquifers through mathematical interpretation The present invention relates to a method for indicating the concentration of pollutants in groundwater by fluctuation of the tide in the coastal area.

을 적용하고, 그린 이론, 상기 지하수내 오염물의 초기 조건식, 오른쪽 경계 조건식 및 왼쪽 경계 조건식을 적용하여 상기 지배 방정식을 변환하는 단계; GITT의 전향 변환식을 규정하는 단계; 상기 GITT의 후향 변환식을 규정하는 단계; 상기 후향 변환식을 상기 지배 방정식 변환 단계에서 획득된 지배 방정식의 변환식에 대입하는 단계; 상기 대입 단계의 결과식을 M개 항을 가진 콤팩트한 행렬 형태로 표현하는 단계; 상기 콤팩트한 행렬 형태 표현 단계의 결과식의 해석해를 선형 이론에 따라 계산하는 단계; 상기 계산된 해석해의 지수 함수 내의 행렬은 MATLAB7의 expm() 함수를 이용하여 계산하여서 전향 변수인 S(t)를 획득하는 단계; 상기 S(t)로부터 상기 후향 변환식을 이용하여 상기 지하수내 오염물 농도인 c(x, t)를 획득하는 단계; 및 상기 표시부에서 상기 c(x, t)에 대한 데이터를 입력받아 지하수내 오염물 농도를 디스플레이하는 단계를 포함하는 것을 특징으로 한다.In order to achieve the above object, according to an embodiment of the present invention, a method of indicating a pollutant concentration in a groundwater by fluctuation of a tide in a coastal area is performed by a pollutant concentration calculation unit using a GITT technique A method for displaying a pollutant concentration in a groundwater by a tidal fluctuation in a coastal area, the method comprising: setting a conceptual model; Defining a groundwater level variation variable that is varied by algae variation; Obtaining the groundwater velocity [v (x, t)] by differentiating the groundwater level variation; Obtaining a diffusion coefficient [D (x, t)] using the groundwater velocity; Defining a governing equation that is a one-dimensional transfer spreading equation; Defining an initial condition formula of the contaminants in the groundwater; Defining a right boundary condition equation corresponding to an inland side of the conceptual model diagram; Defining a left boundary condition equation corresponding to the coast of the conceptual model diagram; In the governing equations,

Transforming the governing equation by applying green theory, an initial condition equation of a contaminant in the groundwater, a right boundary condition equation and a left boundary condition equation; Defining the forward conversion equation of GITT; Defining a backtranslation equation of the GITT; Assigning the backward conversion equation to a conversion equation of the governing equation obtained in the governing equation conversion step; Expressing the resultant expression of the substitution step in the form of a compact matrix having M terms; Calculating a solution expression of a result expression of the compact matrix form representation step according to a linear theory; Calculating a matrix in an exponential function of the computed analysis solution using an expm () function of MATLAB 7 to obtain a forwarding variable S (t); Obtaining a contaminant concentration c (x, t) in the groundwater from the S (t) using the backward conversion equation; And displaying the concentration of the contaminant in the groundwater by receiving data on the c (x, t) from the display unit.

In the method of displaying the pollutant concentration in the groundwater by the tide fluctuation in the coastal area according to the above embodiment, the conceptual model diagram is such that the left boundary corresponding to the coast is the Neumann boundary, and the right boundary corresponding to the inland side is the zero- Boundary condition, the length of the entire area is L, and the initial contaminant may be located between L1 and L1 + L2 from the coastline.

In the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the groundwater level fluctuation equation is expressed by the following equation 1

[Equation 1]

은 해안가로부터 내륙 쪽으로 거리 x에서 시간 t에 따른 지하수 수위를 나타내고,

는 조류의 진폭이며,

은 조류의 주기를 나타내며,

는 대수층의 물리적인 계수로서 다음의 수학식 2[here,

Indicates the groundwater level according to the time t from the distance x from the coast to the inland,

Is the amplitude of the bird,

Represents the cycle of the bird,

Is the physical coefficient of the aquifer,

&Quot; (2) "

는 저류계수이고,

는 투수계수임)(here,

Is a storage coefficient,

Is the permeability coefficient)

Expressed as]

.

In the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the tide in the coastal area according to the above embodiment, the groundwater velocity [v (x, t)] is calculated by the following equation

&Quot; (3) "

,

이며, ω는 조석의 각 진동수이며,

는 유효공극율임][here,

,

Ω is the angular frequency of the tide,

Is the effective porosity]

. ≪ / RTI >

The diffusion coefficient [D (x, t)] is expressed by the following equation (4): " (4) "

&Quot; (4) "

,

이며,

은 종분산 계수임][here,

,

Lt;

Is the longitudinal dispersion coefficient]

As shown in FIG.

In the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water of the coastal area according to the above embodiment, the governing equation is expressed by the following equation 5

&Quot; (5) "

.

In the method of displaying the pollutant concentration in the groundwater by fluctuation of the fresh water of the coastal area according to the above embodiment, the initial condition formula of the pollutant in the groundwater is expressed by the following equation 6

&Quot; (6) "

[Where F (x) represents the initial pollutant concentration distribution function formula]

.

In the method for displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the right boundary condition equation is expressed by the following equation 7

&Quot; (7) "

.

In the method for displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the left boundary condition equation is expressed by the following equation 8

&Quot; (8) "

.

In the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the resultant expression converted in the governing equation converting step is expressed by the following equation

&Quot; (9) "

이고,

는 m번째 고유함수이며,

는 m번째 노름임][here,

ego,

Is an m-th eigenfunction,

Is the m-th gambling]

Lt; / RTI >

In the method of displaying the pollutant concentration in the groundwater by fluctuation of the fresh water of the coastal area according to the above embodiment, the forward conversion formula of the GITT is expressed by the following equation 10

&Quot; (10) "

는 m번째 GITT의 전향 변수임][here,

Is the forward variable of the m-th GITT]

.

In the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the backward conversion formula of the GITT is expressed by the following equation 11

&Quot; (11) "

.

In the method for displaying the pollutant concentration in the groundwater caused by the fluctuation of the fresh water in the coastal area according to the above embodiment, the resultant expression at the step of substituting for the conversion equation of the governing equation is expressed by the following equation 12

&Quot; (12) "

이고,

는 r번째 고유함수이며,

는 r번째 노름이며, S_r(t)는 r번째 GITT의 전향 변수임][here,

ego,

Is an r-th eigenfunction,

Is the r-th gambling, and S _r (t) is the forward variable of the r-th GITT.

As shown in FIG.

In the method for displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the resultant expression in the step of expressing in the form of the compact matrix is expressed by the following equation 13

&Quot; (13) "

는 크로네커의 델타이고, [here,

Is the Kronecker's delta,

이고,

ego,

이며,

Lt;

임]

being]

As shown in FIG.

In the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the above embodiment, the resultant expression at the step of calculating according to the linear theory is expressed by the following equation 14

&Quot; (14) "

임]Where S (T) is the forward vector of GITT,

being]

Lt; / RTI >

을 적용하고, 그린(Green) 이론, 상기 지하수내 오염물의 초기 조건식, 오른쪽 경계 조건식 및 왼쪽 경계 조건식을 적용하여 상기 지배 방정식을 변환하는 단계; GITT의 전향 변환식을 규정하는 단계; 상기 GITT의 후향 변환식을 규정하는 단계; 상기 후향 변환식을 상기 지배 방정식 변환 단계에서 획득된 지배 방정식의 변환식에 대입하는 단계; 상기 대입 단계의 결과식을 M개 항을 가진 콤팩트한 행렬 형태로 표현하는 단계; 상기 콤팩트한 행렬 형태 표현 단계의 결과식의 해석해를 선형 이론에 따라 계산하는 단계; 상기 계산된 해석해의 지수 함수 내의 행렬은 MATLAB7의 expm() 함수를 이용하여 계산하여서 전향 변수인 S(t)를 획득하는 단계; 상기 S(t)로부터 상기 후향 변환식을 이용하여 상기 지하수내 오염물 농도인 c(x, t)를 획득하는 단계; 및 상기 표시부에서 상기 c(x, t)에 대한 데이터를 입력받아 지하수내 오염물 농도를 디스플레이하는 단계;를 포함하여 구성됨으로써,According to an embodiment of the present invention, there is provided a method for displaying a pollutant concentration in a groundwater by fluctuation of fresh water in a coastal area, comprising: setting a conceptual model diagram; Defining a groundwater level variation variable that is varied by algae variation; Obtaining the groundwater velocity [v (x, t)] by differentiating the groundwater level variation; Obtaining a diffusion coefficient [D (x, t)] using the groundwater velocity; Defining a governing equation that is a one-dimensional transfer spreading equation; Defining an initial condition formula of the contaminants in the groundwater; Defining a right boundary condition equation corresponding to an inland side of the conceptual model diagram; Defining a left boundary condition equation corresponding to the coast of the conceptual model diagram; In the governing equations,

Transforming the governing equation by applying the Green theory, the initial condition equation of the contaminants in the groundwater, the right boundary condition equation and the left boundary condition equation; Defining the forward conversion equation of GITT; Defining a backtranslation equation of the GITT; Assigning the backward conversion equation to a conversion equation of the governing equation obtained in the governing equation conversion step; Expressing the resultant expression of the substitution step in the form of a compact matrix having M terms; Calculating a solution expression of a result expression of the compact matrix form representation step according to a linear theory; Calculating a matrix in an exponential function of the computed analysis solution using an expm () function of MATLAB 7 to obtain a forwarding variable S (t); Obtaining a contaminant concentration c (x, t) in the groundwater from the S (t) using the backward conversion equation; And displaying the concentration of the pollutant in the groundwater by receiving data on the c (x, t) from the display unit,

First, there is an excellent effect that the concentration of pollutants can be displayed quickly and accurately under the groundwater velocity, which is controlled by periodic tidal fluctuations in coastal aquifers through mathematical interpretation.

Second, in order to establish pollution cleanup and pollution prevention measures, it is possible to perform calculations that are much quicker, easier, and more accurate than conventional numerical simulation techniques (usually from several hours to several days) (In other words, in the conventional numerical simulation method, the calculation time usually takes from several hours to several days, while in the case of using the method according to the present invention, calculation can be performed within 5 minutes). Especially, it is expected that a program made by using the method according to the present invention can be very useful when a countermeasure is taken in the case of a chemical accident occurring in a nuclear power plant adjacent to a coastal area and an industrial complex dealing with a chemical substance having a toxicity do.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram showing a hardware structure for implementing a method of displaying a pollutant concentration in a groundwater by fluctuation of fresh water in a coastal area according to an embodiment of the present invention. FIG.
FIG. 2 is a flowchart illustrating a method for displaying a pollutant concentration in a groundwater by fluctuation in fresh water in a coastal area according to an embodiment of the present invention.
FIG. 3 is a diagram showing a conceptual diagram set in S10 of FIG.
Fig. 4 is a view showing a screen in which the concentration of contaminants is displayed on the display unit at S170 in Fig. 2, showing the concentration distribution of contaminants according to the bird's amplitude. Fig.
5 is a view showing a calculation result of the center position of the polluted cloud according to the bird's amplitude based on the concentration of the pollutant obtained in the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the embodiment of the present invention.
FIG. 6 is a view showing a calculation result of the degree of contamination concentration dispersion according to the bird's amplitude based on the concentration of the obtained pollutant in the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the embodiment of the present invention.
FIG. 7 is a graph showing a calculation result of contamination macro dispersion coefficient according to algae amplitude based on the concentration of the pollutant obtained in the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the fresh water in the coastal area according to the embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram showing a hardware structure for implementing a method of displaying a pollutant concentration in a groundwater by fluctuation of fresh water in a coastal area according to an embodiment of the present invention. FIG.

As shown in FIG. 1, the hardware for implementing the method of displaying the pollutant concentration in the groundwater due to the fluctuation of the tide in the coastal area according to the embodiment of the present invention includes the GITT technique , And a display unit (200) for displaying the concentration of the contaminants calculated by the contaminant concentration calculation unit (100).

Hereinafter, a method for displaying the concentration of contaminants in the groundwater due to the fluctuation of the fresh water of the coastal area according to the embodiment of the present invention, which is implemented by the hardware configured as described above, will be described.

FIG. 2 is a flowchart showing an operation flow chart for explaining a pollutant concentration display method in the groundwater caused by fluctuation of fresh water in a coastal area according to an embodiment of the present invention, where S denotes a step.

First, a conceptual model diagram is set by the pollutant concentration calculation unit 100 (S10). 3, the left boundary corresponding to the coast is the Neumann boundary, and the right boundary corresponding to the inland side has the boundary condition in which the mass flow rate is 0, and the length of the entire area is L, Contamination is located between L1 and L1 + L2 from the coast.

Next, the pollutant concentration calculation unit 100 defines the groundwater level fluctuation variable varying according to the algae fluctuation according to the following equation (1) using the conventional analysis (Jacob, 1950).

[Equation 1]

은 해안가로부터 내륙 쪽으로 거리 x에서 시간 t에 따른 지하수 수위를 나타내고,

는 조류의 진폭이며,

은 조류의 주기를 나타내며,

는 대수층의 물리적인 계수로서 다음의 수학식 2로 표현됨][here,

Indicates the groundwater level according to the time t from the distance x from the coast to the inland,

Is the amplitude of the bird,

Represents the cycle of the bird,

Is the physical coefficient of the aquifer and is expressed by the following equation (2)

&Quot; (2) "

는 저류계수이고,

는 투수계수임)(here,

Is a storage coefficient,

Is the permeability coefficient)

Thereafter, the pollutant concentration calculation unit 100 differentiates the groundwater level variation equation (Equation 1) to obtain the groundwater velocity v (x, t) as shown in Equation 3 below.

&Quot; (3) "

,

이며, ω는 조석의 각 진동수이며,

는 유효공극율임][here,

,

Ω is the angular frequency of the tide,

Is the effective porosity]

Next, the pollutant concentration calculation unit 100 obtains the diffusion coefficient [D (x, t)] using the groundwater velocity (Equation 3) as shown in Equation 4 below (S40).

&Quot; (4) "

,

이며,

은 종분산 계수임][here,

,

Lt;

Is the longitudinal dispersion coefficient]

Then, the pollutant concentration calculation unit 100 defines the governing equation, which is a one-dimensional transport diffusing equation, by the following Equation 5 (S50).

&Quot; (5) "

Then, the pollutant concentration calculation unit 100 defines the initial condition formula of the pollutants in the groundwater by the following equation (6) (S60).

&Quot; (6) "

[Where F (x) represents the initial pollutant concentration distribution function formula]

Next, the pollutant concentration calculation unit 100 defines the right boundary condition equation corresponding to the inland side of the conceptual diagram of FIG. 3 by the following Equation (7) (S70).

&Quot; (7) "

Then, the pollutant concentration calculation unit 100 defines the left boundary condition equation corresponding to the coast of the conceptual model diagram of FIG. 3 as the following Equation 8 (S80).

&Quot; (8) "

을 적용하고, 그린(Green) 이론, 지하수내 오염물의 초기 조건식(수학식 6), 오른쪽 경계 조건식(수학식 7) 및 왼쪽 경계 조건식(수학식 8)을 적용하여 지배 방정식을 다음의 수학식 9와 같이 변환한다(S90).Next, the pollutant concentration calculation unit 100 calculates the pollutant concentration A

And applying the governing equation to the following equation (9) by applying the Green theory, the initial conditional equation of the pollutants in the groundwater (Equation 6), the right boundary condition equation (equation 7) and the left boundary condition equation (S90).

&Quot; (9) "

이고,

는 m번째 고유함수이며,

는 m번째 노름임][here,

ego,

Is an m-th eigenfunction,

Is the m-th gambling]

Then, the contaminant concentration calculation unit 100 determines the forward conversion equation of GITT by the following equation (10) (S100).

&Quot; (10) "

는 m번째 GITT의 전향 변수임][here,

Is the forward variable of the m-th GITT]

Then, the contaminant concentration calculation unit 100 determines the backward conversion formula of GITT by the following equation (11) (S110).

&Quot; (11) "

Subsequently, the pollutant concentration calculation unit 100 substitutes the backward conversion formula (Equation 11) into the conversion formula (Equation 9) of the governing equations obtained in the step S90 to obtain the following equation (12) S120).

&Quot; (12) "

이고,

는 r번째 고유함수이며,

는 r번째 노름이며, S_r(t)는 r번째 GITT의 전향 변수임][here,

ego,

Is an r-th eigenfunction,

Is the r-th gambling, and S _r (t) is the forward variable of the r-th GITT.

Then, the pollutant concentration calculation unit 100 expresses the resultant expression (expression (12)) of the step (S120) by the following expression (13) in the form of a compact matrix having M terms.

&Quot; (13) "

는 크로네커의 델타이고, [here,

Is the Kronecker's delta,

이고,

ego,

이며,

Lt;

임]

being]

Then, the pollutant concentration calculation unit 100 calculates the interpretation solution of the result formula of the step S130 according to the linear theory, and obtains the following equation (14) (S140).

&Quot; (14) "

임]Where S (T) is the forward vector of GITT,

being]

Then, the pollutant concentration calculation unit 100 calculates a matrix S (t), which is a forward parameter, by calculating a matrix in the exponential function of the step S140 using the expm () function of the MATLAB 7 (S150) , The contaminant concentration c (x, t) in the groundwater is obtained using the backward conversion formula (Equation 11) (S160).

Then, the display unit 200 receives data on c (x, t) obtained in the step S160 and displays the concentration of contaminants in the groundwater (S170).

Fig. 4 is a view showing a screen in which the concentration of contaminants is displayed on the display unit 200 in step S170, showing the concentration distribution of contaminants in accordance with the bird's amplitude. The amplitudes were assumed to be 1m, 10m, and 20m, and the concentration distributions were obtained at 15 and 30 days, respectively. As can be seen from FIG. 4, as the bird amplitude increases, the maximum contamination concentration position moves more quickly. This is interpreted as an increase in the amplitude of the current causes the feed rate. In addition, an increase in the bird amplitude causes a decrease in the maximum concentration value. This is because increasing the amplitude increases the transfer rate, which increases the local diffusion coefficient.

For three different amplitudes, the location of the contaminated cloud center, the degree of dispersion of the pollutant concentration distribution, and the macrodispersion coefficient were calculated over time in Figures 5, 6 and 7, respectively. Referring to FIG. 5, it can be seen that as the amplitude increases, the center position of the contaminated cloud moves faster. This is because, as mentioned above, as the amplitude increases, the feed rate increases.

Referring to FIG. 6, it can be seen that as the amplitude increases, the degree of dispersion of the concentration of pollutant concentration increases. It can be interpreted that the increase of the amplitude increases the conveying speed and the spread of the contamination cloud increases as the diffusion coefficient increases. It is also interesting to note that the periodicity of the dispersion over time becomes more apparent as the amplitude increases.

Referring to FIG. 7, it can be seen that the macrodispersion coefficient becomes more acute as the amplitude becomes larger, because a larger amplitude changes the spread of the pollution cloud more dramatically.

From the above analysis results, it is found that, in order to establish pollution control and pollution prevention measures through the analysis technique according to the present invention, it is much faster than conventional numerical simulation techniques (usually from several hours to several days) It is easy and accurate to perform calculations, so it can be dealt with appropriately for various pollution accidents. In particular, in the case of a chemical accident occurring in a nuclear power plant adjacent to a coastal area and an industrial complex dealing with a poisonous chemical substance, a mathematical analysis technique and MATLAB developed by the embodiment of the present invention are used It is anticipated that the program created will be very useful.

을 적용하고, 그린(Green) 이론, 상기 지하수내 오염물의 초기 조건식, 오른쪽 경계 조건식 및 왼쪽 경계 조건식을 적용하여 상기 지배 방정식을 변환하는 단계; GITT의 전향 변환식을 규정하는 단계; 상기 GITT의 후향 변환식을 규정하는 단계; 상기 후향 변환식을 상기 지배 방정식 변환 단계에서 획득된 지배 방정식의 변환식에 대입하는 단계; 상기 대입 단계의 결과식을 M개 항을 가진 콤팩트한 행렬 형태로 표현하는 단계; 상기 콤팩트한 행렬 형태 표현 단계의 결과식의 해석해를 선형 이론에 따라 계산하는 단계; 상기 계산된 해석해의 지수 함수 내의 행렬은 MATLAB7의 expm() 함수를 이용하여 계산하여서 전향 변수인 S(t)를 획득하는 단계; 상기 S(t)로부터 상기 후향 변환식을 이용하여 상기 지하수내 오염물 농도인 c(x, t)를 획득하는 단계; 및 상기 표시부에서 상기 c(x, t)에 대한 데이터를 입력받아 지하수내 오염물 농도를 디스플레이하는 단계;를 포함하여 구성됨으로써,According to an embodiment of the present invention, there is provided a method of displaying a pollutant concentration in a groundwater by fluctuation of fresh water in a coastal area, the method comprising: setting a conceptual model; Defining a groundwater level variation variable that is varied by algae variation; Obtaining the groundwater velocity [v (x, t)] by differentiating the groundwater level variation; Obtaining a diffusion coefficient [D (x, t)] using the groundwater velocity; Defining a governing equation that is a one-dimensional transfer spreading equation; Defining an initial condition formula of the contaminants in the groundwater; Defining a right boundary condition equation corresponding to an inland side of the conceptual model diagram; Defining a left boundary condition equation corresponding to the coast of the conceptual model diagram; In the governing equations,

Transforming the governing equation by applying the Green theory, the initial condition equation of the contaminants in the groundwater, the right boundary condition equation and the left boundary condition equation; Defining the forward conversion equation of GITT; Defining a backtranslation equation of the GITT; Assigning the backward conversion equation to a conversion equation of the governing equation obtained in the governing equation conversion step; Expressing the resultant expression of the substitution step in the form of a compact matrix having M terms; Calculating a solution expression of a result expression of the compact matrix form representation step according to a linear theory; Calculating a matrix in an exponential function of the computed analysis solution using an expm () function of MATLAB 7 to obtain a forwarding variable S (t); Obtaining a contaminant concentration c (x, t) in the groundwater from the S (t) using the backward conversion equation; And displaying the concentration of the pollutant in the groundwater by receiving data on the c (x, t) from the display unit,

First, the mathematical interpretation method can display the concentration of contaminants quickly and accurately under the groundwater velocity, which is dominated by periodic algal fluctuations in coastal aquifers,

Second, in order to establish pollution cleanup and pollution prevention measures, it is possible to perform calculations that are much quicker, easier, and more accurate than conventional numerical simulation techniques (usually from several hours to several days) (In other words, in the conventional numerical simulation method, the calculation time usually takes from several hours to several days, while in the case of using the method according to the present invention, calculation can be performed within 5 minutes). Especially, it is expected that a program made by using the method according to the present invention can be very useful when a countermeasure is taken in the case of a chemical accident occurring in a nuclear power plant adjacent to a coastal area and an industrial complex dealing with a chemical substance having a toxicity do.

Although the best mode has been shown and described in the drawings and specification, certain terminology has been used for the purpose of describing the embodiments of the invention and is not intended to be limiting or to limit the scope of the invention described in the claims. It is not. Therefore, those skilled in the art will appreciate that various modifications and equivalent embodiments may be made without departing from the scope of the present invention. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

: 해안가로부터 내륙 쪽으로 거리 x에서 시간 t에 따른 지하수 수위

: 조류의 진폭

: 조류의 주기

: 대수층의 물리적인 계수

: 저류계수

: 투수계수
v(x,t): 지하수 속도
D(x,t): 확산 계수
ω: 조석의 각 진동수

: 유효공극율

: 종분산 계수

: m번째 고유함수

: m번째 노름

: m번째 GITT의 전향 변수

: r번째 고유함수

: r번째 노름
Sr(t): r번째 GITT의 전향 변수

: 크로네커의 델타
S(T): GITT의 전향변수 벡터100: pollutant concentration calculation unit
200:

: Groundwater level according to time t from distance x from coast to inland

: Amplitude of the bird

: Cycle of birds

: Physical coefficient of aquifer

: Storage coefficient

: Permeability coefficient
v (x, t): groundwater velocity
D (x, t): diffusion coefficient
ω: angular frequency of tide

: Effective porosity

: Longitudinal dispersion coefficient

: mth eigenfunction

: mth gambling

: forward variables of the m-th GITT

: rth eigenfunction

: r-th gambling
Sr (t): forward variance of rth GITT

: Kronecker's Delta
S (T): forward vector of GITT

Claims (15)

A method for displaying the concentration of contaminants in the groundwater due to the fluctuation of the tide in the coastal area by the pollutant concentration calculation unit using the GITT technique and displaying through the display unit,
Establishing a conceptual model diagram;
Defining a groundwater level variation variable that is varied by algae variation;
Obtaining the groundwater velocity [v (x, t)] by differentiating the groundwater level variation;
Obtaining a diffusion coefficient [D (x, t)] using the groundwater velocity;
Defining a governing equation that is a one-dimensional transfer spreading equation;
Defining an initial condition formula of the contaminants in the groundwater;
Defining a right boundary condition equation corresponding to an inland side of the conceptual model diagram;
Defining a left boundary condition equation corresponding to the coast of the conceptual model diagram;
In the governing equations,

Transforming the governing equation by applying the Green theory, the initial condition equation of the contaminants in the groundwater, the right boundary condition equation and the left boundary condition equation;
Defining the forward conversion equation of GITT;
Defining a backtranslation equation of the GITT;
Assigning the backward conversion equation to a conversion equation of the governing equation obtained in the governing equation conversion step;
Expressing the resultant expression of the substitution step in the form of a compact matrix having M terms;
Calculating a solution expression of a result expression of the compact matrix form representation step according to a linear theory;
Calculating a matrix in an exponential function of the computed analysis solution using an expm () function of MATLAB 7 to obtain a forwarding variable S (t);
Obtaining a contaminant concentration c (x, t) in the groundwater from the S (t) using the backward conversion equation; And
And displaying the pollutant concentration in the groundwater by receiving data on the c (x, t) from the display unit. The method according to claim 1,
The conceptual model diagram
The left boundary corresponding to the coast is the Neumann boundary,
The right boundary corresponding to the inland side has a boundary condition with a mass flow rate of 0,
The length of the entire area is L,
Wherein the initial pollutant is located between L1 and L1 + L2 from the coastal area. The method according to claim 1,
The groundwater level variation equation is expressed by the following equation 1

[Equation 1]

[here,

Indicates the groundwater level according to the time t from the distance x from the coast to the inland,

Is the amplitude of the bird,

Represents the cycle of the bird,

Is the physical coefficient of the aquifer,
&Quot; (2) "

(here,

Is a storage coefficient,

Is the permeability coefficient)
Expressed as]

Of the pollutant concentration in the groundwater due to fluctuation of the tide in the coastal area. The method according to claim 1,
The groundwater velocity [v (x, t)] is calculated by the following equation

&Quot; (3) "

[here,

,

Ω is the angular frequency of the tide,

Is the effective porosity]

A method of indicating the concentration of contaminants in groundwater due to tidal fluctuations in a coastal area, The method according to claim 1,
The diffusion coefficient [D (x, t)] is calculated by the following equation 4

&Quot; (4) "

[here,

,

Lt;

Is the longitudinal dispersion coefficient]

A method of indicating the concentration of contaminants in groundwater by variation in tide in a coastal area, The method according to claim 1,
The governing equation is expressed by the following equation 5

&Quot; (5) "

Of the pollutant concentration in the groundwater due to fluctuation of the tide in the coastal area. The method according to claim 1,
The initial condition equation of the contaminants in the groundwater is expressed by the following equation 6

&Quot; (6) "

[Where F (x) represents the initial pollutant concentration distribution function formula]

Of the pollutant concentration in the groundwater due to the fluctuation of the tide in the coastal area. The method according to claim 1,
The right boundary condition equation is expressed by the following equation 7

&Quot; (7) "

Of the pollutant concentration in the groundwater due to fluctuation of the tide in the coastal area. The method according to claim 1,
The left boundary condition equation is expressed by the following equation 8

&Quot; (8) "

Of the pollutant concentration in the groundwater due to fluctuation of the tide in the coastal area. The method according to claim 1,
The resultant expression converted in the governing equation conversion step is expressed by the following equation

&Quot; (9) "

[here,

ego,

Is an m-th eigenfunction,

Is the m-th gambling]

Of the pollutant concentration in the groundwater due to fluctuation of the tide of the coastal area. The method according to claim 1,
The forward conversion equation of the GITT is expressed by the following equation 10

&Quot; (10) "

[here,

Is the forward variable of the m-th GITT]

Of the pollutant concentration in the groundwater due to the fluctuation of the tide in the coastal area. The method according to claim 1,
The backward conversion equation of the GITT is expressed by the following equation 11

&Quot; (11) "

Of the pollutant concentration in the groundwater due to fluctuation of the tide in the coastal area. The method according to claim 1,
The resultant expression at the step of substituting into the conversion equation of the governing equation is expressed by the following equation 12

&Quot; (12) "

[here,

ego,

Is an r-th eigenfunction,

Is the r-th gambling, and S _r (t) is the forward variable of the r-th GITT.

The method of indicating the pollutant concentration in the groundwater due to the fluctuation of the tide in the coastal area. The method according to claim 1,
The resultant expression in the step of expressing in the form of the compact matrix is expressed by the following equation 13

&Quot; (13) "

[here,

Is the Kronecker's delta,

ego,

Lt;

being]

The method for indicating the concentration of contaminants in the groundwater by the fluctuation of the tide of the coastal area is as follows. The method according to claim 1,
The resultant expression in the step of calculating according to the linear theory is expressed by the following equation 14

&Quot; (14) "

Where S (T) is the forward vector of GITT,

being]

Of the pollutant concentration in the groundwater due to fluctuation of the tide of the coastal area.

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