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1.
Using one- and two-dimensional homogeneous simulations, this paper addresses challenges associated with sensitivity analysis and parameter estimation for virus transport simulated using sorptive-reactive processes. Head, flow, and conservative- and virus-transport observations are considered. The paper examines the use of (1) observed-value weighting, (2) breakthrough-curve temporal moment observations, and (3) the significance of changes in the transport time-step size. The results suggest that (1) sensitivities using observed-value weighting are more susceptible to numerical solution variability, (2) temporal moments of the breakthrough curve are a more robust measure of sensitivity than individual conservative-transport observations, and (3) the transport-simulation time step size is more important than the inactivation rate in solution and about as important as at least two other parameters, reflecting the ease with which results can be influenced by numerical issues. The approach presented allows more accurate evaluation of the information provided by observations for estimation of parameters and generally improves the potential for reasonable parameter-estimation results.  相似文献   

2.
Organic substrates in reactive barrier systems are often heterogeneous material mixtures with relatively large contrasts in hydraulic conductivity and porosity over short distances. These short-range variations in material properties imply that preferential flow paths and diffusion between regions of higher and lower hydraulic conductivity may be important for treatment efficiency. This paper presents the results of a laboratory column experiment where denitrification is investigated using a heterogeneous reactive substrate (sawdust mixed with sewage sludge). Displacement experiments with a non-reactive solute at three different flow rates are used to estimate transport parameters using a dual porosity non-equilibrium model. Parameter estimation from breakthrough curves produced relatively consistent values for the fraction of the porosity consisting of mobile water (β) and the mass transfer coefficient (α), with average values of 0.27 and 0.42 d(-1), respectively. The column system removes >95% of the influent nitrate at low and medium flow, but only 50-75% of the influent nitrate at high flow, suggesting that denitrification kinetics and diffusive mass transfer rates are limiting the degree of treatment at lower hydraulic residence times. Reactive barrier systems containing dual porosity media must therefore consider mass transfer times in their design; this is often most easily accommodated by adjusting flowpath length.  相似文献   

3.
Hydraulic conductivity and sorption coefficients for chlorinated hydrocarbons (chloroform, carbon tetrachloride and tetrachloroethylene) were evaluated for 216 sediment samples collected across a 15 m transect and a 21 m depth interval in a contaminated aquifer near Schoolcraft, Michigan. Relationships between hydraulic conductivity, linear sorption partition coefficients, grain size classes, and spatial location were investigated using linear regression analysis and geostatistical techniques. Clear evidence of layering was found in sorption properties, hydraulic conductivity and grain sizes. Conductivity correlated well with grain size, as expected, but sorption varied inversely with grain size, contrary to some previous reports. No significant correlation was found between sorption properties and hydraulic conductivity. This is likely due to the unexpected presence of small amounts of highly sorptive coal-like solids, which dominate the sorption behavior but have little effect on conductivity. The results demonstrate that recent findings regarding the high sorption capacity of coal materials found in soils can exert a controlling influence on contaminant transport. Designers of in situ remediation systems should be cautioned that 1) it is not reasonable to assume that sorption capacity and hydraulic conductivity are related, 2) sorption capacity and hydraulic conductivity are critical measurements for contaminant site characterization and subsequent transport modeling, 3) estimating sorption capacity from organic carbon measurement may lead to greater errors than performing sorption isotherms, and 4) it is more important to characterize vertical heterogeneity rather than horizontal heterogeneity because both sorption and hydraulic conductivity are correlated across longer distances in the horizontal plane.  相似文献   

4.
Data from 90 tracer experiments performed in low-permeability fractured media have been studied to explore correlations among parameters controlling flow and transport. The original data had been interpreted by different authors using different models, which prevents direct comparison of their estimated parameters. In order to produce comparable parameters, the data have been reexamined using simple models (homogeneous domain, steady-state flow regime, single porosity). Specifically, hydraulic conductivity has been derived as the ratio of water flux to head gradient and apparent porosity as the ratio of water velocity to water flux; the former estimated from both first and peak arrival times. Hydraulic conductivity and porosity correlate along a straight line of slope 1:3 in log scale. While the regression is too noisy to be of predictive use, it lends some support to the use of a generalized cubic law. The fact that correlation for first arrival time porosity (0.77) is larger than for peak arrival porosity (0.62) suggests that first arrival is controlled by the same flow paths as hydraulic conductivity. Apparent porosity derived from peak arrival time is found to grow with travel time along a line of 0.55 slope (again log scale). The correlation coefficient ranges between 0.73 and 0.80 (depending on the data set) for hard rocks. The fact that this correlation is maintained when varying the flow rate at a given site leads us to suggest that it is caused by diffusion mechanisms. This conclusion is further supported by the increase of apparent porosity with the matrix porosity of the rock on which the experiments were performed.  相似文献   

5.
Matrix diffusion is an important transport process in geologic materials of low hydraulic conductivity. For predicting the fate and transport of contaminants, a detailed understanding of the diffusion processes in natural porous media is essential. In this study, diffusive tracer transport (iodide) was investigated in a variety of geologically different limestone and sandstone rocks. Porosity, structural and mineralogical composition, hydraulic conductivity, and other rock properties were determined. The effective diffusion coefficients were measured using the time-lag method. The results of the diffusion experiments indicate that there is a close relationship between total porosity and the effective diffusion coefficient of a rock (analogous to Archie's Law). Consequently, the tortousity factor can be expressed as a function of total porosity. The relationship fits best for thicker samples (> 1.0 cm) with high porosities (> 20%), because of the reduced influence of heterogeneity in larger samples. In general, these correlations appear to be a simple way to determine tortuosity and the effective diffusion coefficient from easy to determine rock porosity values.  相似文献   

6.
A study was conducted to assess key factors to include when modeling porosity reductions caused by mineral fouling in permeable reactive barriers (PRBs) containing granular zero valent iron. The public domain codes MODFLOW and RT3D were used and a geochemical algorithm was developed for RT3D to simulate geochemical reactions occurring in PRBs. Results of simulations conducted with the model show that the largest porosity reductions occur between the entrance and mid-plane of the PRB as a result of precipitation of carbonate minerals and that smaller porosity reductions occur between the mid-plane and exit face due to precipitation of ferrous hydroxide. These findings are consistent with field and laboratory observations, as well as modeling predictions made by others. Parametric studies were conducted to identify the most important variables to include in a model evaluating porosity reduction. These studies showed that three minerals (CaCO3, FeCO3, and Fe(OH)2 (am)) account for more than 99% of the porosity reductions that were predicted. The porosity reduction is sensitive to influent concentrations of HCO3-, Ca2+, CO3(2-), and dissolved oxygen, the anaerobic iron corrosion rate, and the rates of CaCO3 and FeCO3 formation. The predictions also show that porosity reductions in PRBs can be spatially variable and mineral forming ions penetrate deeper into the PRB as a result of flow heterogeneities, which reflects the balance between the rate of mass transport and geochemical reaction rates. Level of aquifer heterogeneity and the contrast in hydraulic conductivity between the aquifer and PRB are the most important hydraulic variables affecting porosity reduction. Spatial continuity of aquifer hydraulic conductivity is less significant.  相似文献   

7.
When soil structure varies in different soil types and the horizons of these soil types, it has a significant impact on water flow and contaminant transport in soils. This paper focuses on the effect of soil structure variations on the transport of pesticides in the soil above the water table. Transport of a pesticide (chlorotoluron) initially applied on soil columns taken from various horizons of three different soil types (Haplic Luvisol, Greyic Phaeozem and Haplic Cambisol) was studied using two scenarios of ponding infiltration. The highest infiltration rate and pesticide mobility were observed for the Bt1 horizon of Haplic Luvisol that exhibited a well-developed prismatic structure. The lowest infiltration rate was measured for the Bw horizon of Haplic Cambisol, which had a poorly developed soil structure and a low fraction of large capillary pores and gravitational pores. Water infiltration rates were reduced during the experiments by a soil structure breakdown, swelling of clay and/or air entrapped in soil samples. The largest soil structure breakdown and infiltration decrease was observed for the Ap horizon of Haplic Luvisol due to the low aggregate stability of the initially well-aggregated soil. Single-porosity and dual-permeability (with matrix and macropore domains) flow models in HYDRUS-1D were used to estimate soil hydraulic parameters via numerical inversion using data from the first infiltration experiment. A fraction of the macropore domain in the dual-permeability model was estimated using the micro-morphological images. Final soil hydraulic parameters determined using the single-porosity and dual-permeability models were subsequently used to optimize solute transport parameters. To improve numerical inversion results, the two-site sorption model was also applied. Although structural changes observed during the experiment affected water flow and solute transport, the dual-permeability model together with the two-site sorption model proved to be able to approximate experimental data.  相似文献   

8.
A two-dimensional model for virus transport in physically and geochemically heterogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considers virus inactivation in the solution, as well as virus removal at the solid matrix surface due to attachment (deposition), release, and inactivation. Two surface inactivation models for the fate of attached inactive viruses and their subsequent role on virus attachment and release were considered. Geochemical heterogeneity, portrayed as patches of positively charged metal oxyhydroxide coatings on collector grain surfaces, and physical heterogeneity, portrayed as spatial variability of hydraulic conductivity, were incorporated in the model. Both layered and randomly (log-normally) distributed physical and geochemical heterogeneities were considered. The upstream weighted multiple cell balance method was employed to numerically solve the governing equations of groundwater flow and virus transport. Model predictions show that the presence of subsurface layered geochemical and physical heterogeneity results in preferential flow paths and thus significantly affect virus mobility. Random distributions of physical and geochemical heterogeneity have also notable influence on the virus transport behavior. While the solution inactivation rate was found to significantly influence the virus transport behavior, surface inactivation under realistic field conditions has probably a negligible influence on the overall virus transport. It was further demonstrated that large virus release rates result in extended periods of virus breakthrough over significant distances downstream from the injection sites. This behavior suggests that simpler models that account for virus adsorption through a retardation factor may yield a misleading assessment of virus transport in "hydrogeologically sensitive" subsurface environments.  相似文献   

9.
The present Spanish concept of a deep geological high level waste repository includes an engineered clay barrier around the canister. The clay presents a very high sorption capability for radionuclides and a very small hydraulic conductivity, so that the migration process of solutes is limited by sorption and diffusion processes. Therefore, diffusion and distribution coefficients in compacted bentonite (i.e. in "realistic" liquid to solid ratio conditions) are the main parameters that have to be obtained in order to characterise solute transport that could be produced after the canister breakdown. Through-Diffusion (TD) and In-Diffusion (ID) experiments with HTO, Sr, Cs and Se were carried out using compacted FEBEX bentonite, which is the reference material for the Spanish concept of radioactive waste disposal. Experiments were interpreted by means of available analytical solutions that allow the estimation of diffusion coefficients and, in some cases, distribution coefficients. Analytical solutions are simple to use, but rely on hypotheses that do not hold in all the experiments. These experiments were interpreted also using an automatic parameter estimation code that overcomes the limitations of analytical solutions. Numerical interpretation allows the simultaneous estimation of porosity, diffusion and distribution coefficients, accounts for the role of porous sinters and time-varying boundary concentrations, and can use different types of raw concentration data.  相似文献   

10.
Model predictions of pesticide transport in structured soils are complicated by multiple processes acting concurrently. In this study, the hydraulic, physical, and chemical nonequilibrium (HNE, PNE, and CNE, respectively) processes governing herbicide transport under variably saturated flow conditions were studied. Bromide (Br-), isoproturon (IPU, 3-(4-isoprpylphenyl)-1,1-dimethylurea) and terbuthylazine (TER, N2-tert-butyl-6-chloro-N4-ethyl-1,3,5-triazine-2,4-diamine) were applied to two soil columns. An aggregated Ap soil column and a macroporous, aggregated Ah soil column were irrigated at a rate of 1 cm h(-1) for 3 h. Two more irrigations at the same rate and duration followed in weekly intervals. Nonlinear (Freundlich) equilibrium and two-site kinetic sorption parameters were determined for IPU and TER using batch experiments. The observed water flow and Br- transport were inversely simulated using mobile-immobile (MIM), dual-permeability (DPM), and combined triple-porosity (DP-MIM) numerical models implemented in HYDRUS-1D, with improving correspondence between empirical data and model results. Using the estimated HNE and PNE parameters together with batch-test derived equilibrium sorption parameters, the preferential breakthrough of the weakly adsorbed IPU in the Ah soil could be reasonably well predicted with the DPM approach, whereas leaching of the strongly adsorbed TER was predicted less well. The transport of IPU and TER through the aggregated Ap soil could be described consistently only when HNE, PNE, and CNE were simultaneously accounted for using the DPM. Inverse parameter estimation suggested that two-site kinetic sorption in inter-aggregate flow paths was reduced as compared to within aggregates, and that large values for the first-order degradation rate were an artifact caused by irreversible sorption. Overall, our results should be helpful to enhance the understanding and modeling of multi-process pesticide transport through structured soils during variably saturated water flow.  相似文献   

11.
Fate and mobility of pharmaceuticals in solid matrices   总被引:2,自引:0,他引:2  
The sorption and mobility of six pharmaceuticals were investigated in two soil types with different organic carbon and clay content, and in bacterial biomass (aerobic and anaerobic). The pharmaceuticals examined were carbamazepine, propranolol, diclofenac sodium, clofibric acid, sulfamethoxazole and ofloxacin. The sorption experiments were performed according to the OECD test Guideline 106. The distribution coefficients determined by this batch equilibrium method varied with the pharmaceutical tested and the solid matrix type. Ofloxacin was particularly strongly adsorbed (except of the case of using anaerobic biomass for the solid matrix) while clofibric acid was found to be weakly adsorbed. The fate of pharmaceuticals in soil was also assessed using lysimeters. Important parameters that were studied were: the pharmaceutical loading rate and the hydraulic loading rate for adsorption and the rate and duration of a "rain" event for desorption. Major differences in the mobility of the six pharmaceuticals were observed and correlated with the adsorption/desorption properties of the compounds.  相似文献   

12.
Colloid-facilitated transport has been recognized as a potentially important and overlooked contaminant transport process. In particular, it has been observed that conventional two phase sorption models are often unable to explain transport of highly sorbing compounds in the subsurface appropriately in the presence of colloids. In this study a one-dimensional model for colloid-facilitated transport of chemicals in unsaturated porous media is developed. The model has parts for simulating coupled flow, and colloid transport and dissolved and colloidal contaminant transport. Richards' equation is solved to model unsaturated flow, and the effect of colloid entrapment and release on porosity and hydraulic conductivity of the porous media is incorporated into the model. Both random sequential adsorption and Langmuir approaches have been implemented in the model in order to incorporate the effect of surface jamming. The concept of entrapment of colloids into the air-water interface is used for taking into account the effect of retardation caused due to existence of the air phase. A non-equilibrium sorption approach with options of linear and Langmuir sorption assumptions are implemented that can represent the competition and site saturation effects on sorption of multiple compounds both to the solid matrix and to the colloidal particles. Several demonstration calculations are performed and the conditions in which the non-equilibrium model can be approximated by an equilibrium model are also studied.  相似文献   

13.
The effects of biofilm growth on flow and solute transport through a sandblasted glass parallel plate fracture was investigated. The fracture was inoculated using soil microorganisms. Glucose, oxygen and other nutrients were supplied to support growth. The biomass initially formed discrete clusters attached to the glass surfaces, but over time formed a continuous biofilm. From dye tracer tests conducted during biofilm growth, it was observed that channels and low-permeability zones dominated transport. The hydraulic conductivity of the fracture showed a sigmoidal decrease with time. The hydraulic conductivity was reduced by a factor of 0.033, from 18 to 0.6 cm/s, corresponding to a 72% decrease in the hydraulic aperture, from 500 to 140 microm. In contrast, the mass balance aperture, determined from fluoride tracer tests, remained relatively constant, indicating that the impact of biomass growth on effective fracture porosity was much less than the effect on hydraulic conductivity. Analyses of pre-biofilm tracer tests revealed that both Taylor dispersion and macrodispersion were influencing transport. During biofilm growth, only macrodispersion was dominant. The macrodispersion coefficient alpha(macro) was found to increase logarithmically with hydraulic conductivity reduction.  相似文献   

14.
Site uncertainties significantly influence groundwater flow and contaminant transport predictions. Aleatoric and epistemic uncertainty are both identified in site characterization and represented using proper uncertainty theories. When one theory best represents one parameter whereas a different theory may be more suitable for another parameter, the hybrid propagation of aleatoric (random) and epistemic (nonrandom) uncertainties will occur. The computational challenges of joint propagation of aleatoric and epistemic uncertainty through groundwater flow and contaminant transport models are significant. A fuzzy-stochastic nonlinear model was developed in this paper to incorporate these two types of uncertain site information and reduce the computational cost. The results show that (1) the computational cost using the nonlinear model is reduced compared with that of using the sparse grid algorithm and Monte Carlo methods; (2) the uncertainty of hydraulic conductivity (K) significantly influences the water head and solute distribution at the observation wells compared to other uncertain parameters, such as the storage coefficient and the distribution coefficient (Kd); and (3) the combination of multiple uncertain parameters substantially affects the simulation results. Neglecting site uncertainties may lead to unrealistic predictions.  相似文献   

15.
Two-dimensional models for biological clogging and sorptive trace transport were used to study the progress of clogging in a sand box experiment. The sand box had been inoculated with a strip of bacteria and exposed to a continuous injection of nitrate and acetate. Brilliant Blue was regularly injected during the clogging experiment and digital images of the tracer movement had been converted to concentration maps using an image analysis. The calibration of the models to the Brilliant Blue observations shows that Brilliant Blue has a solid biomass dependent sorption that is not compliant with the assumed linear constant Kd behaviour. It is demonstrated that the dimensionality of sand box experiments in comparison to column experiments results in a much lower reduction in hydraulic conductivity (factor of 100) and that the bulk hydraulic conductivity of the sand box decreased only slightly. However, in the central parts of the clogged area, the observations and simulations clearly show a complex picture of flow diverting the injected nutrients around the clogged area as fingers. The calibration of the model demonstrates that the physical and microbiological processes (advection, dispersion, attachment-detachment, growth-decay) are all needed to capture the progress of clogging.  相似文献   

16.
Interest in coupled biodegradation and transport of organic contaminants has expanded greatly in the past several years. In a system in which biodegradation is coupled with solute transport, the magnitude and rate of biodegradation is influenced not only by properties of the microbial population and the substrate, but also by hydrodynamic properties (e.g., residence time, dispersivity). By nondimensionalizing the coupled-process equations for transport and nonlinear biodegradation, we show that transport behavior is controlled by three characteristic parameters: the effective maximum specific growth rate, the relative half-saturation constant, and the relative substrate-utilization coefficient. The impact on biodegradation and transport of these parameters, which constitute various combinations of factors reflecting the influences of biotic and hydraulic properties of the system, are examined numerically. A type-curve diagram based on the three characteristic parameters is constructed to illustrate the conditions under which steady and non-steady transport is observed, and the conditions for which the linear, first-order approximation is valid for representing biodegradation. The influence of constraints to microbial growth and substrate utilization on contaminant transport is also briefly discussed. Additionally, the impact of biodegradation, with and without biomass growth, on spatial solute distribution and moments is examined.  相似文献   

17.
A new reactive transport modelling approach and examples of its application are presented, dealing with the impact of sorption/desorption kinetics on the spreading of solutes, e.g. organic contaminants, in groundwater. Slow sorption/desorption is known from the literature to be strongly responsible for the retardation of organic contaminants. The modelling concept applied in this paper quantifies sorption/desorption kinetics by an intra-particle diffusion approach. According to this idea, solute uptake by or release from the aquifer material is modelled at small scale by a "slow" diffusion process where the diffusion coefficient is reduced as compared to the aqueous diffusion coefficient due to (i) the size and shape of intra-particle pores and (ii) retarded transport of solutes within intra-particle pores governed by a nonlinear sorption isotherm. This process-based concept has the advantage of requiring only measurable model parameters, thus avoiding fitting parameters like first-order rate coefficients.In addition, the approach presented here allows for modelling of slow sorption/desorption in lithologically nonuniform media. Therefore, it accounts for well-known experimental findings indicating that sorptive properties depend on (i) the grain size distribution of the aquifer material and (ii) the lithological composition (e.g. percentage of quartz, sandstone, limestone, etc.) of each grain size fraction. The small-scale physico-chemical model describing sorption/desorption is coupled to a large-scale model of groundwater flow and solute transport. Consequently, hydraulic heterogeneities may also be considered by the overall model. This coupling is regarded as an essential prerequisite for simulating field-scale scenarios which will be addressed by a forthcoming publication.This paper focuses on mathematical model formulation, implementation of the numerical code and lab-scale model applications highlighting the sorption and desorption behavior of an organic contaminant (Phenanthrene) with regard to three lithocomponents exhibiting different sorptive properties. In particular, it is shown that breakthrough curves (BTCs) for lithologically nonuniform media cannot be obtained via simple arithmetic averaging of breakthrough curves for lithologically uniform media. In addition, as no analytical solutions are available for model validation purposes, simulation results are compared to measurements from lab-scale column experiments. The model results indicate that the new code can be regarded as a valuable tool for predicting long-term contaminant uptake or release, which may last for several hundreds of years for some lithocomponents. In particular, breakthrough curves simulated by pure forward modelling reproduce experimental data much better than a calibrated standard first-order kinetics reactive transport model, thus indicating that the new approach is of high quality and may be advantageously used for supporting the design of remediation strategies at contaminated sites where some lithocomponents and/or grain size classes may provide a long-term pollutant source.  相似文献   

18.
We obtain an analytical solution for two-dimensional steady-state transport of conservative contaminant between injecting and pumping wells. Flow and transport are considered in the vertical cross-section. The Dupuit approximation and conformal mapping onto the complex potential domain are employed to determine the velocity and concentration distributions, respectively. We use this solution to derive a priori conditions under which widely used 1-D analytical solutions with constant velocity and dispersion coefficients provide accurate approximations. These conditions are formulated in terms of aquifer parameters, such as hydraulic conductivity, porosity and dispersivities, and remediation strategy, e.g., well spacing and pumping regimes.  相似文献   

19.
Numerical simulation tools have been used to study the dominating processes during transport of aromatic hydrocarbons in the unsaturated soil zone. Simulations were based on field observations at an experimental site located on a glacial delta plain with pronounced layered sedimentary structures. A numerical model for transport in the unsaturated zone, SWMS-3D, has been extended to incorporate coupled multispecies transport, microbial degradation following Monod kinetics and gas diffusive transport of oxygen and hydrocarbons. The flow field parameters were derived from previous work using nonreactive tracers. Breakthrough curves (BTC) from the hydrocarbon field experiment were used to determine sorption parameters and Monod kinetic parameters using a fitting procedure. The numerical simulations revealed that the assumption of homogeneous layers resulted in deviations from the field observations. The deviations were more pronounced with incorporation of reactive transport, compared with earlier work on nonreactive transport. To be able to model reasonable BTC, sorption had to be reduced compared to laboratory experiments. The initial biomass and the maximum utilisation rate could be adjusted to capture both the initial lag phase and the overall degradation rate. Nevertheless, local oxygen limitation is predicted by the model, which was not observed in the field experiment. Incorporation of evaporation and diffusive gas transport of the hydrocarbons did not significantly change the local oxygen demand. The main cause of the observed discrepancies between model and field are attributed to channelling as a result of small-scale heterogeneities such as biopores.  相似文献   

20.
Tracer tests were conducted in three laboratory columns to study changes in the hydraulic properties of a porous medium due to bioclogging. About 30 breakthrough curves (BTCs) for each column were obtained. The BTCs were analyzed using analytical equilibrium and dual-porosity models, and estimates of the hydrodynamic dispersion and mass transfer coefficients were obtained by curve fitting. The change in transport properties developed in three stages: an initial phase (I) with no significant changes in transport properties, phase II with growth of biomass near the inlet of the columns causing changes in dispersivity, and phase III with added growth of micro-colonies deeper in the columns causing mass transfer of solutes from the water phase to the biophase. Tracer transport changed from being uniform to more non-uniform with increase in mass transfer of the tracer between the mobile phase and the immobile biomass. An increase in the bulk dispersivity value of up to one order of magnitude was observed. Numerical simulations suggest that local dispersivity values may be as much as 40 times higher in the more severe clogged areas inside the column. The bulk hydraulic conductivities of the columns decreased by up to three orders of magnitude. The hydraulic conductivity and dispersivity parameters were almost recovered after disinfection of the columns. Different models relating the changes of the hydraulic conductivity to the changes in the mobile porosity due to bioclogging were reviewed, and the micro-colony relation of Thullner et al. [Thullner, M., Zeyer, J., Kinzelbach, W., 2002. Influence of microbial growth on hydraulic properties of pore networks, Transport in Porous Media, 49, 99-122.] was found to best describe the relation between the bulk hydraulic parameters.  相似文献   

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