Two-region Non-equilibrium Model Research Articles

Investigating advection–dispersion behavior for simulation of HTO and 238Pu transport in argillaceous shale with different varying degrees of weathering

Abstract Exploring the migration behavior of radioactive nuclides in the surrounding rock media of the disposal site is the basis for the safety evaluation of radioactive waste disposal sites. In this study, the column experiment was employed to evaluate the nuclide migration behavior in the surrounding rock medium of a near-surface disposal site in China and to investigate the advection–dispersion behavior of tritium (HTO) and plutonium-238 (238Pu) in highly weathered argillaceous shale with different degree of weathering. A reasonable numerical model was selected to fit the experimental breakthrough curves (BTCs) and obtain relevant migration parameters. The results showed that: (1) the breakthrough curves of HTO and 238Pu in fractured media with varying degrees of weathering exhibited clear “peak forward” and “tail dragging” phenomena; (2) the stream tube model can better fit the BTCs of the nuclides in the highly weathered fractures and obtain the average dispersion coefficient <D>, average distribution coefficient <K d>, and other parameters; (3) the two-region non-equilibrium model can better fit the BTCs of the nuclides in the penetrating fractures and weak weathering fractures and obtain the volumetric water content of the mobile liquid region (θ m), distribution coefficient (K d), and other parameters.

Transport-based source tracking of contaminants in a karst aquifer: Model implementation, proof of concept, and application to event-based field data

Identification and location of contamination sources is crucial for water resource protection — especially in karst aquifers which provide 25% of the world´s population with water but are highly vulnerable to contamination. Transport-based source tracking is proposed and verified here as a complementary approach to microbial and chemical source tracking in karst aquifers for identifying and locating such sources of contamination and for avoiding ambiguities that might arise from using one method alone. The transport distance is inversely modelled from contaminant breakthrough curves (BTC), based on analytical solutions of the 1D two-region non-equilibrium advection dispersion equation using GNU Octave. Besides the BTC, the model requires reliable estimates of transport velocity and input time. The model is shown to be robust, allows scripted based, automated 2D sensitivity analyses (interplay of two parameters), and can be favourable when distributed numerical models are inappropriate due to insufficient data. Sensitivity analyses illustrate that the model is highly sensitive to the input time, the flow velocity, and the fraction of the mobile fluid region. A conclusive verification approach was performed by applying the method to synthetic data, tracer tests, and event-based field data. Transport distances were correctly modelled for a set of artificial tracer tests using a discharge-velocity relationship that could be established for the respective karst catchment. For the first time such an approach was shown to be applicable to estimate the maximum distance to the contamination source for coliform bacteria in karst spring water combined with microbial source tracking. However, prediction intervals for the transport distance can be large even in well-studied karst catchments mainly related to uncertainties in the flow velocity and the input time. Using a maximum transport distance is proposed to account for less permeable, “slower” pathways. In general, transport-based source tracking might be used wherever transport can be described by the 1D two-region non-equilibrium model, e.g. rivers and fractured or porous aquifers.

Effects of flow rate variation on solute transport in a karst conduit with a pool

To investigate the effects of flow rate variation on solute transport in a karst conduit, three pipe structures of a constant diameter pipe, the pipe connected to a symmetrical pool and an asymmetrical pool respectively were chosen, and several tracer experiments were conducted separately in each of the three pipe structures at nine flow rates. Experimental results show that the peak of the breakthrough curve (BTC) increased and the tailing decreased with increasing discharge. Three models, the advection–dispersion equation (ADE), the two-region nonequilibrium model (TRNM) and the transient storage model (TSM), were used to simulate BTCs and explore the change of transport parameters with increasing flow rate. Simulations show that ADE was capable of replicating the almost symmetrical BTCs of the single pipe but incapable of fitting the appreciable BTC tails for the pools. Nevertheless, TRNM and TSM can reproduce all BTCs of single pipe and pipe with a pool very well. The research demonstrates the significant effect of the pool on solute transport. The parameters in the two models (TRNM and TSM) exhibited similar trends with increasing discharge in either pool. In the TRNM, a clear positive correlation with discharge emerged for the partition coefficient and mass transfer coefficient. Meanwhile, the main channel cross-sectional area and exchange coefficient in TSM increased gradually with discharge. The storage zone area decreased generally with increasing flow rate. The relationship between solute transport and the flow rate is more complex in the asymmetrical pool than in the symmetrical pool.

Spatial resolution of transport parameters in a subtropical karst conduit system during dry and wet seasons

Karst aquifers are characterized by a high degree of hydrologic variability and spatial heterogeneity of transport parameters. Tracer tests allow the quantification of these parameters, but conventional point-to-point experiments fail to capture spatiotemporal variations of flow and transport. The goal of this study was to elucidate the spatial distribution of transport parameters in a karst conduit system at different flow conditions. Therefore, six tracer tests were conducted in an active and accessible cave system in Vietnam during dry and wet seasons. Injections and monitoring were done at five sites along the flow system: a swallow hole, two sites inside the cave, and two springs draining the system. Breakthrough curves (BTCs) were modeled with CXTFIT software using the one-dimensional advection-dispersion model and the two-region nonequilibrium model. In order to obtain transport parameters in the individual sections of the system, a multi-pulse injection approach was used, which was realized by using the BTCs from one section as input functions for the next section. Major findings include: (1) In the entire system, mean flow velocities increase from 183 to 1,043 m/h with increasing discharge, while (2) the proportion of immobile fluid regions decrease; (3) the lowest dispersivity was found at intermediate discharge; (4) in the individual cave sections, flow velocities decrease along the flow direction, related to decreasing gradients, while (5) dispersivity is highest in the middle section of the cave. The obtained results provide a valuable basis for the development of an adapted water management strategy for a projected water-supply system.

Laboratory investigation and simulation of breakthrough curves in karst conduits with pools

A series of laboratory experiments are performed under various hydrological conditions to analyze the effect of pools in pipes on breakthrough curves (BTCs). The BTCs are generated after instantaneous injections of NaCl tracer solution. In order to test the feasibility of reproducing the BTCs and obtain transport parameters, three modeling approaches have been applied: the equilibrium model, the linear graphical method and the two-region nonequilibrium model. The investigation results show that pools induce tailing of the BTCs, and the shapes of BTCs depend on pool geometries and hydrological conditions. The simulations reveal that the two-region nonequilibrium model yields the best fits to experimental BTCs because the model can describe the transient storage in pools by the partition coefficient and the mass transfer coefficient. The model parameters indicate that pools produce high dispersion. The increased tailing occurs mainly because the partition coefficient decreases, as the number of pools increases. When comparing the tracer BTCs obtained using the two types of pools with the same size, the more appreciable BTC tails that occur for symmetrical pools likely result mainly from the less intense exchange between the water in the pools and the water in the pipe, because the partition coefficients for the two types of pools are virtually identical. Dispersivity values decrease as flow rates increase; however, the trend in dispersion is not clear. The reduced tailing is attributed to a decrease in immobile water with increasing flow rate. It provides evidence for hydrodynamically controlled tailing effects.

Sorption and retardation of strontium in saturated Chinese loess: experimental results and model analysis

Geological burial and landfill have been widely practiced for disposal of nuclear wastes. However, radionuclides in the waste leachate from landfill facilities can contaminate soil and groundwater. Chinese loess is widely distributed in China and has been involved in large-scale disposal of nuclear wastes. Consequently, there has been an urgent need for understanding and predicting the fate and transport of contaminants in both vadose and saturated zones in the loess. In this paper, the distribution coefficient (Kd) values of Strontium between a Chinese loess and groundwater were determined in batch experiments. The isotherm could be described with nearly linear isotherm model, which resulted in a Kd value of 40.0 cm3/g. Based on this Kd value, the retardation factor (Rd, the ratio of pore water velocity to solute transport velocity) value was calculated to be 112.6. As an alternative approach, the Rd value was also determined through independent column experiments and transport modeling. Bromide (Br−) was used as a non-reactive tracer, and reagent SrCl2 was used as a surrogate for the radioactive isotope (99Sr) in the experiment because they share the same adsorption and transportation characteristics. An equilibrium-based model and a two-region non-equilibrium model were employed to interpret the column sorption data of Sr. The computer program, CXTFIT 2.1, was used to estimate the parameters by simulating the breakthrough and retention curves of Br and Sr, respectively. The resultant D (dispersion coefficient) value for Sr transport was much lower than that of Br−, indicating the important effect of chemical non-equilibrium of Sr in the loess system. The observed Sr retention curves in the loess were best modeled by the two-site transport model. The Rd value determined from batch equilibrium tests differed markedly from that determined from the column transport experiments, and the Rd value decreased with increasing pore-water velocity. The relationship between D and pore water flow velocity (v) was determined as a D = 1.192v1.26. The results from this work indicate that the strong flow and non-equilibrium effects on the transport parameters (Rd and D) must be taken into account in Sr transport modeling.

Una nueva interpretación cuantitativa de curvas de avance con mesetasy largos limbos de recesión a partir de ensayos de trazadoren el acuífero cárstico artesiano de Stuttgart, Alemania

In 1998 and 1999, two multi-tracer experiments were conducted in the artesian karst aquifer of the mineral springs of Stuttgart, Germany. The breakthrough curves (BTCs) monitored at the springs showed very long tails or developed plateau-like concentration levels for more than 200 days. Initially, this observation was qualitatively explained by exchange between cavities with stagnant water and the active conduits. Since then, a new analytical solution for tracer transport in karst aquifers has become available, the “two-region non-equilibrium model” (2RNE), which assumes the presence of mobile and immobile fluid regions, and mass transfer between these two regions. The experiments were thus revisited, and it was possible to provide a more quantitative explanation of the observed behaviour. The new model simulated all BTCs very well, thus confirming the earlier qualitative explanation. The prolonged BTCs can be attributed to intermediate storage in cavities containing quasi-immobile groundwater, and slow release into active fractures and conduits. The results also demonstrate that karst aquifers are not always fast-flushing systems, but contaminants can sometimes remain in immobile fluid regions for long periods.

Solute and Colloid Transport in Karst Conduits under Low‐ and High‐Flow Conditions

Solute and colloid transport in karst aquifers under low and high flows was investigated by tracer tests using fluorescent dyes (uranine) and microspheres of the size of pathogenic bacteria (1 microm) and Cryptosporidium cysts (5 microm), which were injected into a cave stream and sampled at a spring 2.5 km away. The two types of microspheres were analyzed using an epifluorescence microscope or a novel fluorescence particle counter, respectively. Uranine breakthrough curves (BTCs) were regular shaped and recovery approached 100%. Microsphere recoveries ranged between 27% and 75%. During low flow, the 1-microm spheres displayed an irregular BTC preceding the uranine peak. Only a very few 5-microm spheres were recovered. During high flow, the 1-microm-sphere BTC was regular and more similar to the uranine curve. BTCs were modeled analytically with CXTFIT using a conventional advection dispersion model (ADM) and a two-region nonequilibrium model (2RNE). The results show that (1) colloids travel at higher velocities than solutes during low flow; (2) colloids and solutes travel at similar velocities during high flow; (3) higher maximum concentrations occur during high flow; and (4) the 2RNE achieves a better fit, while the ADM is more robust, as it requires less parameters.

Multitracer Test Approach to Characterize Reactive Transport in Karst Aquifers

A method to estimate reactive transport parameters as well as geometric conduit parameters from a multitracer test in a karst aquifer is provided. For this purpose, a calibration strategy was developed applying the two-region nonequilibrium model CXTFIT. The ambiguity of the model calibration was reduced by first calibrating the model with respect to conservative tracer breakthrough and later transferring conservative transport parameters to the reactive model calibration. The reactive transport parameters were only allowed to be within a defined sensible range to get reasonable calibration values. This calibration strategy was applied to breakthrough curves obtained from a large-scale multitracer test, which was performed in a karst aquifer of the Swabian Alb, Germany. The multitracer test was conducted by the simultaneous injection of uranine, sulforhodamine G, and tinopal CBS-X. The model succeeds to represent the tracer breakthrough curves (TBCs) of uranine and sulforhodamine G and verifies that tracer-rock interactions preferably occur in the immobile fluid region, although the fraction of this region amounts to only 3.5% of the total water. However, the model failed to account for the long tailing observed in the TBC of tinopal CBS-X. Sensitivity analyses reveal that model results for the conservative tracer transport are most sensitive to average velocity and volume fraction of the mobile fluid region, while dispersion and mass transfer coefficients are least influential. Consequently, reactive tracer calibration allows the determination of sorption sites in the mobile and immobile fluid region at small retardation coefficients.

A TWO-REGION MATHEMATICAL MODEL FOR BATCH DRYING OF GRAINS IN A TWO-DIMENSIONAL SPOUTED BED

A two-region non-equilibrium model of a two-dimensional spouted bed dryer has been developed. The model, based on heat and mass transfer interactions between the spout and downcomer regions, predicts the air and grain temperatures and moisture content throughout each elementary thin layer of grain in the spouted bed. The model was validated with the experimental results on batch drying of corn. Drying and heating processes are shown to occur in both the spout and downcomer regions. Overall, the agreement between experimental and simulated results is satisfactory.

A two-region nonequilibrium model for solute transport in solution conduits in karstic aquifers

A two-region nonequilibrium model was used to calibrate initial solute-transport parameter estimates generated from tracer-breakthrough curves (TBCs) developed from tracer tests conducted in uni-axial solution conduits in karstic aquifers. Two-region nonequilibrium models account for partitioning of solute into mobile- and immobile-fluid regions to produce a more representative model fit to the strong tails associated with TBCs than do equilibrium models. The nonequilibrium model resulted in an increase in average flow velocities and a decrease in longitudinal dispersion coefficients over comparable estimates using an equilibrium model. Increases in velocity and decreases in dispersion were obtained at the expense of including parameters that describe solute partitioning and mass transfer rate for the mobile- and immobile-fluid regions. In addition, nonidentifiable sorption and mass transfer parameters for the immobile-fluid regions could only be described in terms of upper and lower bounds using readily determined identifiable ratios representing solute partitioning and system constraints based on known physical properties. The identifiable ratios and system constraints serve to minimize model nonuniqueness and renders the nonidentification problem trivial.