• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2002.04a
• /
• pp.102-105
• /
• 2002

A new finite difference model is developed for solute transport in a fractured medium that can consider advection, adsorption, first-order decay, and scale-dependent dispersivity of individual fractures. In the model, the dispersivity of individual fractures is employed as a variable increasing with travel distance from a source. The model is verified using an analytical solution for a single fracture. A solution from the new model is independent of the outlet boundary condition of fractures, and has little numerical dispersion error.

• Journal of Soil and Groundwater Environment
• /
• v.22 no.3
• /
• pp.27-41
• /
• 2017

This study dealt with the characteristics and the interrelations of hydrogeological parameters such as hydraulic conductivity, dispersivity and effective porosity of unconsolidated sediments for providing the basic data necessary for the planning of the management and preservation of groundwater quality in the Nakdong River Delta of Busan City, Korea. Groundwater quality in this area has been deteriorated due to seawater intrusion, agricultural fertilizer and pesticide, industrial wastewater, and contaminated river water. The physical properties (grain size distribution, sediment type, sorting) and aquifer parameters (hydraulic conductivity, effective porosity, longitudinal dispersivity) were determined from grain size analysis, laboratory permeability test and column tracer test. Among 36 samples, there were 18 Sand (S), 7 Gravelly Sand (gS), 5 Silty Sand (zS), 5 Muddy Sand (mS), and 1 Sandy Silt (sZ). Hydraulic conductivity was determined through a falling head test, and ranged from $9.2{\times}10^{-5}$ to $2.9{\times}10^{-2}cm/sec$ (0.08 to 25.6 m/day). From breakthrough curves, dispersivity was calculated to be 0.35~3.92 cm. Also, effective porosity and average linear velocity were obtained through the column tracer test, and their values were 0.04~0.46 and 1.06E-04~6.49E-02 cm/sec, respectively. Statistical methods were used to understand the interrelations among aquifer parameters of hydraulic conductivity, effective porosity and dispersivity. The relation between dispersivity and hydraulic conductivity or effective porosity considered the sample length, because dispersivity was affected by experimental scale. The relations between dispersivity and hydraulic conductivity or effective porosity were all in inverse proportion for all long and short samples. The reason was because dispersivity was in inverse proportion to the groundwater velocity in case of steady hydrodynamic dispersion coefficient, and groundwater velocity was in proportion to the hydraulic conductivity or effective porosity. This study also elucidated that longitudinal dispersivity was dependent on the scale of column tracer test, and all hydrogeological parameters were low to high values due to the sand quantity of sediments. It is expected that the hydrogeological parameter data of sediments will be very useful for the planning of groundwater management and preservation in the Nakdong River Delta of Busan City, Korea.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.215-241
• /
• 2003

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.

• Journal of Soil and Groundwater Environment
• /
• v.12 no.6
• /
• pp.17-25
• /
• 2007

Convergent flow tracer test for 2 m (IW-1 well) and 5 m (IW-2 well) of test scale was conducted at the alluvial aquifer with high permeability and storativity. Pumping rate for convergent flow tracer test were $2,500m^3/day$, and the chloride tracer of 5 kg was instantaneously injected into IW-1 and IW-2 wells. Differences of first arrival time and peak concentration were analyzed by using the concentration breakthrough curves of chloride. Recovered chloride mass were analyzed by recovered cumulative mass curves. And, increment and decrement for chloride concentration were analyzed through chloride concentration versus recovered cumulative mass ratio graphs. Also, increment and decrement ratios of chloride concentration were estimated through linear regression analyses for increment and decrement intervals of chloride concentration. Longitudinal dispersivities were estimated by quot;Converging Radial Flow With Instantaneous Injectionquot; method using CATTI code. Longitudinal dispersivities estimated by CATTI code were 0.4152 m between pumping well and IW-1 well, and 3.2665 m between pumping well and IW-2 well. Longitudinal dispersivity was increased according to far distance from the pumping well. The longitudinal dispersivity according to distance were estimated as 0.21 between pumping well and IW-1 well, and 0.65 between pumping well and IW-2 well.

• Journal of Soil and Groundwater Environment
• /
• v.13 no.4
• /
• pp.1-7
• /
• 2008

This study analyzed for hydrodynamic dispersion characteristics of multi-soil layer (Silt and clay, Find sand, Coarse sand), data of a field tracer test on the multi-soil layer and data of laboratory column experiments on the samples on each soil layers. Through the analysis of permeability and flow, MS (Silt and clay) and FS (Fine sand), which were low effective porosity, were higher average linear velocity while CS (Coarse sand), which was high effective porosity, was higher hydraulic conductivity. Hydraulic conductivity function based on average soil particle diameter was assumed Y=$3.49{\times}10^{-8}e^{15320x}$ and coefficient of determination was 0.90. Average linear velocity function based on average soil particle diameter was assumed Y=$1.88{\times}10^{-7}e^{11459x}$ and coefficient of determination was 0.81. Longitudinal dispersivity function based on average soil particle diameter was Y = 0.00256$e^{5971x}$ and coefficient of determination was 0.98. According to the linear regression analysis of average linear velocity and longitudinal dispersivity, assumed function was Y = 21.7527x + 0.0063, and coefficient of determination was 0.9979. The ratio of field scale/laboratory scale was 54.09, it exhibited scale-dependent effect of hydrodynamic dispersion. Field longitudinal dispersivity (1.39m) was 7.47 times as higher than longitudinal dispersivity estimated by the methods of Xu and Eckstein (1995). Hydrodynamic dispersion on CS layer was occurred mainly by diffusion flow in the test aquifer.

• Journal of Soil and Groundwater Environment
• /
• v.11 no.4
• /
• pp.48-56
• /
• 2006

Using a continuous injection tracer test at a multi-soil layer deposit, the difference of hydrodynamic dispersions in unsaturated and saturated zones were analyzed through breakthrough curves of Rhodamine WT, linear regression of concentration versus time, concentration variation rates versus time, and concentration ratio according to the distance from injection well. As a result of continuous injection tracer test, the difference of the maximum concentrations of Rhodamine WT in unsaturated and saturated zones were 13-15 times after 160 hours, and the increased rate of concentration versus time in unsaturated zone was about 10 times higher than in saturated zone. The fluctuation of Rhodamine WT breakthrough curve and concentration variation rate with time in saturated zone were larger than in unsaturated zone. Rhodamine WT concentration ratio with the distance from the injection well in saturation zone was linearly decreased faster than in unsaturated zone, and the elapsed time necessary for the concentration ratio less than 2 was longer in saturation zone. The differences resulted from the lower concentration and slower hydrodynamic dispersion of Rhodamine WT at the saturation zone of the multi-soil layer deposit, in which groundwater flow significantly flow and aquifer materials have high hydraulic heterogeneity. Effective porosity, longitudinal and transverse dispersivities were estimated $10.19{\sim}10.50%,\;0.80{\sim}1.98m$ and $0.02{\sim}0.04m$, respectively. The field longitudinal dispersivity is over 12 times larger than the laboratory longitudinal dispersivity by the scale-dependent effect.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2008.05a
• /
• pp.1899-1903
• /
• 2008

대수층의 저유량이 풍부한 강변여과수 개발 예정지역의 충적층(지표면하 $25{\sim}35\;m$ 구간)에서 수리전도도와 종분산지수의 규모종속효과를 규명하기 위해 양수시험과 수렴흐름 추적자시험이 수행 되었다. 양수시험과 추적자시험의 규모는 2 m 와 5 m 이었으며 양수시험은 5개 공, 추적자시험은 3개 공을 이용하여 수행되었다. 양수시험은 일정한 양수율($2,500\;m^3/day$)로 수행되었으며, 양수 시작 후 경과시간에 따른 수위변화 자료를 AQTESOLV 3.5 프로그램에 입력하여 해석하였다. 시험 대수층의 수리전도도는 양수정에서 $1.745{\times}10^{-3}\;m/sec$, 양수정에서 이격거리가 2 m 구간에서는 $2.161{\times}10^{-3}\;m/sec$와 $2.270{\times}10^{-3}\;m/sec$ 이었으며, 이격거리가 5 m 구간에서는 $2.452{\times}10^{-3}\;m/sec$와 $2.591{\time}10^{-3}m/sec$로 산정되었다. 그리고, 양수정에서 회복시험 시 Theis(Recovery) 방법에 의해 해석된 수리전도도는 $1.603{\times}10^{-3}\;m/sec$이었다. 양수정에서 관측정의 이격거리(d)에 따른 수리전도도(K) 증가함수는 log K=0.0693 log d-2.671와 log K=0.0817 log d-2.655로 추정되었으며, 결정 계수는 각각 0.965와 0.979로서 매우 높게 나타났다. 따라서 양수정에서의 이격거리가 멀수록 수리전도도가 증가하는 규모종속을 확인하였으며, 또한 시험대수층의 수리전도도가 방사상으로 유사하게 분포하고 있음을 알 수 있었다. 수렴흐름 추적자시험의 양수율은 $2,500\;m^3/day$ 이었으며, 2개의 주입정에 염소이온 5 kg을 순간 주입하였다. 염소이온의 농도이력곡선을 작성하여 초기도달시간과 최고농도의 차이를 분석하였으며, 누적질량회수곡선을 통해 양수 후 경과시간에 따른 염소이온의 질량회수율을 분석하였다. 그리고, 염소이온농도 대 누적질량회수율의 이력그래프를 작성하여 누적질량회수율에 따른 염소이온농도의 증가와 감소 변화를 분석하였다. 또한, 염소이온농도의 증가/감소 구간에 대한 선형회귀분석을 수행하여 농도 증가율과 감소율의 변화를 파악하였다. 양수정에서 관측된 경과시간별 염소이온농도 자료를 CATTI 코드의 "Converging Radial Flow With Instantaneous Injection" 해석법에 적용하여 종분산지수를 추정하였다. 양수정에서 이격거리가 2 m인 경우의 종분산지수는 0.4152 m, 이격거리가 5 m인 경우의 종분산지수는 3.2665 m이었다. 따라서 양수정에서 이격거리가 멀수록 종분산지수가 증가하는 규모종속효과를 확인하였으며, 또한 이격거리에 대한 종분산지수의 비는 각각 0.21과 0.65 정도로서 증가하였다.