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

• Geomechanics and Engineering
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• v.9 no.4
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• pp.465-481
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• 2015

Three-dimensional simulation of flow through dam foundation is performed using finite element (Seep3D model) and artificial neural network (ANN) models. The governing and discretized equation for seepage is obtained using the Galerkin method in heterogeneous and anisotropic porous media. The ANN is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning, using the water level elevations of the upstream and downstream of the dam, as input variables and the piezometric heads as the target outputs. The obtained results are compared with the piezometric data of Shahid Abbaspour's Dam. Both calculated data show a good agreement with available measurements that demonstrate the effectiveness and accuracy of purposed methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.95-105
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• 2007

A mathematical modeling for the drying process of hygroscopic porous media, such as wood, has been developed in the past decades. The governing equations for wood drying consist of three conservation equations with respect to the three state variables, moisture content, temperature and air density. They are involving simultaneous, highly coupled heat and mass transfer phenomena. In recent, the equations were extended to account for material heterogeneity through the density of the wood and via the density variation of the material process, capillary pressure, absolute permeability, bound water diffusivity and effective thermal conductivity. In this paper, we investigate the drying behavior for the three primary variables of the drying process in terms of control volume finite element method to the heterogeneous transport model on one-dimensional grid.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 1999.10a
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• pp.39-43
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• 1999

불포화대에서 LNAPL의 이동과 분포를 수치 모의를 통하여 예측하였다. 균질한 매질에서 LNAPL의 이동은 조립질 매질에서 빠르고, 세립질 매질에서 더 많은 면적으로 확산되며, 더 많은 LNAPL이 불포화대에 잔류한다. 조립질 매질내에 세립질층이 존재할 경우, 이 층이 지하수면으로부터 멀수록 LNAPL이 많이 포획된다. 조립질 매질에 세립질 또는 더 조립질인 매질이 렌즈 상으로 존재하는 환경에서는, LNAPL이 이들 렌즈를 통과하지 못한다. 불균질한 렌즈가 존재할 때의 LNAPL 분포를 초기조건으로 이용하여, 지하수 면의 수직 이동과 물의 침투에 따른 LNAPL의 이동을 모의하였다. 두 경우 모두 불포화대에 잔류되어 있던 LNAPL의 수직방향 이동이 증가되었다. 특히, 지하수면의 하강 시 LNAPL이 조립질 렌즈를 통해 이동하나, 세립질 렌즈를 통해서는 이동하지 못한다.

• New & Renewable Energy
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• v.2 no.4 s.8
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• pp.56-63
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• 2006

In this paper, heat and mass transfer characteristics through experimental and numerical study are extensively investigated in steam reforming reactor under given operating conditions. In order to get simulated data at outlet of the reformer, heterogeneous reactor model is incorporated. As the reaction also takes place in porous media, two medium approach is used to take into account thermally non-equilibrium phenomena between catalyst and bulk gas. From various parametric studies, significance of heat transfer is emphasized in steam reforming reaction.

• 한국신재생에너지학회:학술대회논문집
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• 2008.10a
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• pp.25-28
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• 2008

Steam reforming reaction is a matured technology to get hydrogen from hydrocarbon fuels compared with other reforming reactions such as partial oxidation(POX), autothermal reforming(ATR). It is so endothermic that it needs heat source to activate the reaction. Due to the reaction characteristics, heat transfer limitation phenomena generally occur in the steam reformer. As one of new ideas, the effect of discontinuous gas feeding is investigated based on heat transfer characteristics. The new operating method is usually favorable at high GHSV region(i.e. over $10,000h^{-1}$). In order to numerically simulate the physical issues, numerical approach is adopted based on heterogeneous reaction model, two-equation model in energy equation, and other constitutive models in porous media.

• The Journal of Engineering Geology
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• v.19 no.1
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• pp.81-88
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• 2009

Two dimensional Monte-Carlo simulations of a non-reactive solute plume in isotropic porous media which are physically and chemically heterogeneous are conducted to determine the variations of moment. Retardation factors of 1, 2 and 5 are given to ascertain how the second moments are changed as adsorption increased. Retarded longitudinal second spatial moment, ${Z_{11}}^{'R}(t',l')$, increased during the transport process and as the dimensionless lengths of line plume source, $l_2'$, increased. ${Z_{11}}^{'R}(t',l')$ decreased as the retardation factors increased, and the simulated moments fit well to the first-order analytical results. Retarded longitudinal plume centroid variance, ${Z_{11}}^{'R}(t',l')$, decreased as the dimensionless lengths of line plume source, $l_2'$, increased and as the retardation factor increased. The result indicates that the uncertainty about the plume center decreased, and the ergodic condition for the second spatial moments is far from reaching. Simulated longitudinal one particle displacement covariance, ${Z_{11}}^{'R}(t')$, well consistent with the first-order analytical results for the three degrees of retardation factors of 1, 2 and 5 respectively. It is, consequently, concluded that the retarded longitudinal second moments could be produced by stochastic simulation, and that the first-order analytical results definitely provides very close values of the longitudinal retarded moments.

• The Journal of Engineering Geology
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• v.13 no.1
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• pp.51-65
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• 2003

A series of numerical simulations were carried out using STOMP( Subsurface Transport over Multiple Phase) simulator. The flow and distribution of LNAPL were analyzed in homogeneous fine and coarse sand. Vertical movement of LNAPL is faster in the coarser sand. But the total volume of LNAPL retained in the unsaturated zone is larger in the finer sand. A fine layer in the coarse sand domain is also simulated. The results showed that the retained LNAPL volume and shape are highly influenced by the Position of the fine layer. Flow and distributions of LNAPL were simulated when there were heterogeneous lenses in the sand domain. Water table fluctuation was also considered. In these cases, it was found that the heterogeneous lens was a barrier to LNAPL flow, and water table fluctuation stimulated the downward movement of retained LNAPL. The LNAPL flow and distribution observed in these numerical experiments show that in the subsurface environment, the behaviors of LNAPL highly depend on heterogeneities of unsaturated zone and the dynamic hydrogeologic condition such as water table fluctuation. These results can explain some of the complexity of LNAPL flow and distribution Patterns in LNAPL contaminated field sites.

• The Journal of Engineering Geology
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• v.28 no.1
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• pp.35-45
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• 2018

Imaging technologies are applied at various geological scales including pore scale, core scale and intermediate scale in order to characterize pore space of rocks as well as to map the fluid distribution in porous media. This technical report presents experimental results using core-flooding apparatus suited with imaging technology. Three different core samples, that are homogeneous, fractured and heterogeneous cores, were used to assess the two-phase fluid migration behavior as $CO_2$ displaces resident brine. We show that imaging technology can be effective in characterizing salt-precipitation, capillary pressure and spatio-temporal variation of trapping mechanisms.

• Nuclear Engineering and Technology
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• v.25 no.4
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• pp.529-538
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• 1993

A stochastic way using continuous time Markov process is presented to model the one-dimensional nuclide transport in fractured rock matrix as an extended study for previous work ［1］. A nuclide migration model by the continuous time Markov process for single planar fractured rock matrix, which is considered as a transient system where a process by which the nuclide is diffused into the rock matrix from the fracture may be no more time homogeneous, is compared with a conventional deterministic analytical solution. The primary desired quantities from a stochastic model are the expected values and variance of the state variables as a function of time. The time-dependent probability distributions of nuclides are presented for each discretized compartment of the medium given intensities of transition. Since this model is discrete in medium space, parameters which affect nuclide transport could be easily incorporated for such heterogeneous media as the fractured rock matrix and the layered porous media. Even though the model developed in this study was shown to be sensitive to the number of discretized compartment showing numerical dispersion as the number of compartments are decreased, with small compensating of dispersion coefficient, the model agrees well to analytical solution.