One-dimensional Solute Transport Equation Research Articles

Long-term simulation of some soil chemical properties under continuous wheat cultivation irrigated with waters of different qualities

The use of low-quality waters for irrigation in arid and semiarid regions is increasing due to the shortage of good-quality water supplies. Geochemical simulations are cost-effective ways to determine the suitable strategies for sustainable water and soil management. In the first step of this study, the combination of one-dimensional solute transport equation and cation exchange model in PHREEQC was used to predict breakthrough curves of the exchangeable sodium percentage (ESP) of nine soil columns during the leaching with 20 pore volumes of a solution with sodium adsorption ratio (SAR) of 10. In the second step, the trend of changes in solution and exchangeable phases of a non-sodic agricultural soil was simulated over 20 years of continuous wheat cultivation irrigated with waters of different qualities. The graphical and statistical comparison (RMSE values ranged from 0.36 to 0.95) between experimental and predicted results showed that the geochemical simulations in the first step were successful. Simulation results of the second step indicated that the soil ESP decreased from 10.1 to 5.6% after a 20-year consecutive application of water with SAR 2.5, while the long-term use of irrigation waters with SAR 10 and SAR 40 increased the final soil ESP to 27.8 and 88.5%, respectively. In the case of application of irrigation water with SAR 10, the final ESP values of wheat residues-, gypsum-, and calcite-amended soils were 18.5, 16.9, and 20.2% which were less than that obtained for control soil.

Simulation of Diffusive Transport of Radionuclides in the Soil of a Radioactive Waste Disposal Site

The diffusive transport of 137Cs, 90Sr, and 60Co in the clay of a radioactive waste disposal site at PINSTECH was studied to assess the safety of the underlying permeable zone against the release of these radionuclides from buried waste containers in the clay. Diffusion coefficients of these radionuclides were estimated by reservoir to sediment diffusion method via their stable counterparts in a laboratory experiment. A curve-fitting procedure was applied on the measured concentration-time profiles of the reservoir using the one-dimensional solute transport equation with a nonlinear least squares technique. Distribution coefficients were determined in laboratory batch experiments. Diffusive transport simulations were performed with the estimated values of diffusion coefficients and distribution coefficients using the one-dimensional solute transport equation describing Fickian diffusion, equilibrium adsorption, and radioactive decay. The transport simulation results showed that 137Cs, 90Sr, and 60Co will transport distances of 4.33, 3.77, and 1.51 meters, respectively, in the clay before their activity concentrations will drop to clearance levels set by the International Atomic Energy Agency (IAEA), below which the waste is treated as non-radioactive. This showed that concentrations more than clearance levels will not be able to transport to the permeable zone at a minimum depth of seven meters from the ground surface if the waste containers are disposed in a trench below which a clay layer with a thickness of 4.33 meters or more exists.

Determination of diffusion coefficient and analysis of diffusion factors of Cr(VI) ion in clay soil

Some laboratory diffusion tests were conducted with diffusion device to determine the diffusion coefficient of Cr(VI) ion passing through Dalian red clay samples. The concentrations of Cr(VI) at different places of the samples were then measured spectrophotometrically after a standing time of 1 000 d. A one-dimensional solute transport equation was used to simulate the transport of Cr(VI) through clay samples. Back-calculation of diffusion coefficient of Cr(VI) was made with finite difference method. Parametric analysis was conducted to simulate variations in soil dry density, temperature, pH and standing time. The results show that the method used in this paper is simple and effective. The diffusion coefficient of Cr(VI) in Dalian red clay varies from 1.50×10−7 cm2/s to 2.08×10−7 cm2/s. After 1 000 d diffusion, the concentration of the source solution drops down to 1.27 mg/L from 62.5 mg/L, and the diffusion distance is only 3.5 cm. Under the assumption that diffusion coefficient is constant, the diffusion effect becomes more obvious with lower density, lower temperature, higher pH value, and much more time.

Transport of dissolved methoxy-nonafluorobutane through a saturated column

Solute transport experiments were conducted in a one-dimensional saturated column using dissolved methoxy-nonafluorobutane (HFE-7100), a Novec engineered fluid developed by the 3M Corporation, as the solute. Novec engineered fluids are considered dense non-aqueous phase liquids (DNAPLs) because they are immiscible with water and have a specific gravity greater than one. The HFE-7100 fluid is safer and environmentally friendlier than common DNAPL contaminants such as tetrachloroethylene (PCE) or trichloroethylene (TCE); thus, it is an ideal substitute DNAPL for laboratory groundwater contamination research. Three sets of solute transport experiments were conducted. The first set of experiments was conducted in a glass-bead-packed column using dissolved HFE-7100 as the solute. The second set of experiments was conducted in a sand-packed column using dissolved HFE-7100 as the solute. The third set of experiments was conducted in a sand-packed column using dissolved PCE as the solute. The dissolved HFE-7100 column breakthrough concentrations were compared with dissolved PCE breakthrough concentrations. Results show that the one-dimensional solute transport equation was successful in describing the transport behavior of dissolved HFE-7100. This study demonstrates that the HFE-7100 fluid can be used as a safer substitute DNAPL for groundwater contaminant dissolution and transport research.

Incorporating convection into one-dimensional solute redistribution during crystal growth from the melt I. The steady-state solution

A one-dimensional mathematical analysis is made of the redistribution of solute which occurs during crystal growth from a convected melt. In this analysis, the important contribution from lateral melt convection to one-dimensional solute redistribution analysis is taken into consideration via an annihilation/creation term in the one-dimensional solute transport equation. Calculations of solute redistribution under steady-state conditions have been carried out analytically. It is found that this new solute redistribution model overcomes several weaknesses that occur when applying the Burton, Prim and Slichter solute segregation equation (1953) in real melt growth situations. It is also found that, with this correction, the diffusion coefficients for solute's in liquid silicon are now found to be in the same range as other liquid metal diffusion coefficients.

Transformation kinetics of trace-level halogenated organic contaminants in a biologically active zone (BAZ) induced by nitrate injection

Laboratory experiments and numerical modeling were conducted to evaluate the secondary utilization of eight trace-concentration halogenated solvents in a denitrifying biologically active zone (BAZ) induced by nitrate injection into an acetate-fed porous-medium column. Results of column experiments indicated that carbon tetrachloride was removed most completely by the denitrifying BAZ, while bromoform, dibromoethane, tetrachloroethene, trichloroethene, and 1,2- and 1,3-dichlorobenzenes were removed, but to lesser degrees. 1,1,1-trichloroethane removal was slight. Compounds were removed to higher degrees when the BAZ contact time was increased. The steady-state, one-dimensional solute-transport equation was solved using an iterative finite-difference scheme and by employing a quasilinearization technique for the biofilm-reaction term. The model solved directly for the steady-state profiles of secondary substrates. One set of experimental results was used to obtain best-fit values of kinetic parameteres, which were then used to predict the removal at different liquid velocities. The model predictions correctly described all experimental trends: removal of the halogenated compounds in the BAZ, greater removal with increased BAZ contact time, and reduced specific removal rates caused by diffusion limitation in the biofilm.