Special Issue "Water Flow, Solute and Heat Transfer in Groundwater"

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydrology and Hydrogeology".

Deadline for manuscript submissions: closed (30 April 2020).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Alexander Yakirevich
E-Mail Website
Guest Editor
Ben-Gurion University of the Negev, J. Blaustein Institutes for Desert Research, Zuckerberg Institute for Water Research, Sede Boqer campus, 8499000, Israel
Interests: experimental and theoretical investigation of water flow, solute and heat transfer in porous and fractured media; formulation of mathematical models for multiphase and multicomponent flow and transport in the vadose zone and groundwater system; simulation of saltwater-intrusion problems; simulation of overland flow, solutes transport in runoff and streams; estimating mass-transfer parameters from laboratory- or field-measured water and solute distribution data

Special Issue Information

Dear Colleagues,

This Special Issue on “Water Flow, Solute and Heat Transfer in Groundwater” of Water, focuses on recent advances and future perspectives of groundwater studies, including, but not limited to:

Fundamental investigations addressing multi-phase and multi-component interactions using various experimental techniques, mathematical and numerical modeling of physical mechanisms, management strategies, and experience learned from case studies.  

Monitoring and predictions of groundwater flow, solute and heat transfer at different spatial and temporal scales, hydrogeochemistry, well hydraulics, hydraulic fracturing, karst, freshwater-saltwater interactions, groundwater contamination, remediation and protection.

Effect of heterogeneity on dynamic and distribution of contaminants, calibrating flow and transport models, and uncertainty associated with predictions and observations.

Contributions are solicited from hydrogeologists, geophysicists, geochemists, climatologists, microbiologists, ecologists, and others involved with experimental and theoretical aspects linked to flow, solute and heat transport in heterogeneous media, with application to water resources, groundwater contamination and remediation, mining and hydrocarbon geology, geothermal resources, and related areas. By presenting this integrative and multidisciplinary volume we aim at transferring knowledge to hydrologists, hydraulic engineers, water resources planners, managers, and policy makers, who are engaged in the sustainable development of groundwater resources.

Prof. Alexander Yakirevich
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Water is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Porous and fractured media 
  • groundwater 
  • hydrology 
  • geochemistry 
  • contaminant transport 
  • heat transfer 
  • field and laboratory studies 
  • conceptual and mathematical modeling 
  • heterogeneity 
  • climate 
  • water resources

Published Papers (13 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Editorial

Jump to: Research, Other

Open AccessEditorial
Water Flow, Solute and Heat Transfer in Groundwater
Water 2020, 12(7), 1851; https://doi.org/10.3390/w12071851 - 28 Jun 2020
Cited by 1 | Viewed by 540
Abstract
Groundwater is an essential and vital water resource for drinking water production, agricultural irrigation, and industrial processes. The better understanding of physical and chemical processes in aquifers enables more reliable decisions and reduces the investments concerning water management. This Special Issue on “Water [...] Read more.
Groundwater is an essential and vital water resource for drinking water production, agricultural irrigation, and industrial processes. The better understanding of physical and chemical processes in aquifers enables more reliable decisions and reduces the investments concerning water management. This Special Issue on “Water Flow, Solute and Heat Transfer in Groundwater” of Water focuses on the recent advances in groundwater dynamics. In this editorial, we introduce 12 high-quality papers that cover a wide range of issues on different aspects related to groundwater: protection from contamination, recharge, heat transfer, hydraulic parameters estimation, well hydraulics, microbial community, colloid transport, and mathematical models. By presenting this integrative volume, we aim to transfer knowledge to hydrologists, hydraulic engineers, and water resources planners who are engaged in the sustainable development of groundwater resources. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)

Research

Jump to: Editorial, Other

Open AccessArticle
Seepage Characteristics of a Single Ascending Relief Well Dewatering an Overlying Aquifer
Water 2020, 12(3), 919; https://doi.org/10.3390/w12030919 - 24 Mar 2020
Cited by 2 | Viewed by 982
Abstract
The application of groundwater relief, i.e., dewatering, ascending wells, drilled upward from the mining tunnel into the overlying aquifer, is common in underground mining engineering. In this study, the seepage characteristics of single ascending partially and fully penetrating relief wells are investigated using [...] Read more.
The application of groundwater relief, i.e., dewatering, ascending wells, drilled upward from the mining tunnel into the overlying aquifer, is common in underground mining engineering. In this study, the seepage characteristics of single ascending partially and fully penetrating relief wells are investigated using a series of laboratory sand-tank experiments and numerical simulations. The seepage characteristics of ascending wells dewatering an overlying aquifer are different from those of conventional pumping wells descending from the ground surface into the underlying aquifer, because of the pronounced influence of the seepage face boundary condition along the seepage boundary of the ascending dewatering well. The seepage face of the ascending well is formed as the well casing remains open and water is discharged under the action of gravity through the well casing. The results of laboratory sand-tank experiments and modeling show that when the degree of penetration of an ascending relief well does not exceed a critical value, the effect of the seepage face cannot be ignored. In particular, the seepage flux increases as the degree of penetration increases following an exponential function, and the relationship between the seepage flux and the well radius can be described using a power law function. The results of numerical simulations are used to develop a series of type curves to evaluate the effects of the critical degree of penetration for different well radii and different aquifer water levels. Modified versions of the Dupuit and Dupuit–Thiem formulae for a single ascending partially well for the degree of penetration less than the critical one for the unconfined, confined, and confined-unconfined aquifers are developed. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
The Impact of Capillary Trapping of Air on Satiated Hydraulic Conductivity of Sands Interpreted by X-ray Microtomography
Water 2020, 12(2), 445; https://doi.org/10.3390/w12020445 - 07 Feb 2020
Cited by 2 | Viewed by 937
Abstract
The relationship between entrapped air content and the corresponding hydraulic conductivity was investigated experimentally for two coarse sands. Two packed samples of 5 cm height were prepared for each sand. Air entrapment was created by repeated infiltration and drainage cycles. The value of [...] Read more.
The relationship between entrapped air content and the corresponding hydraulic conductivity was investigated experimentally for two coarse sands. Two packed samples of 5 cm height were prepared for each sand. Air entrapment was created by repeated infiltration and drainage cycles. The value of K was determined using repetitive falling-head infiltration experiments, which were evaluated using Darcy’s law. The entrapped air content was determined gravimetrically after each infiltration run. The amount and distribution of air bubbles were quantified by micro-computed X-ray tomography (CT) for selected runs. The obtained relationship between entrapped air content and satiated hydraulic conductivity agreed well with Faybishenko’s (1995) formula. CT imaging revealed that entrapped air contents and bubbles sizes were increasing with the height of the sample. It was found that the size of the air bubbles and clusters increased with each experimental cycle. The relationship between initial and residual gas saturation was successfully fitted with a linear model. The combination of X-ray computed tomography and infiltration experiments has a large potential to explore the effects of entrapped air on water flow. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
Speeding up the Computation of the Transient Richards’ Equation with AMGCL
Water 2020, 12(1), 286; https://doi.org/10.3390/w12010286 - 18 Jan 2020
Cited by 2 | Viewed by 859
Abstract
The Richards’-equation is widely used for modeling complex soil water dynamics in the vadose zone. Usually, the Richards’-equation is simulated with the Finite Element Method, the Finite Difference Method, or the Finite Volume Method. In all three cases, huge systems of equations are [...] Read more.
The Richards’-equation is widely used for modeling complex soil water dynamics in the vadose zone. Usually, the Richards’-equation is simulated with the Finite Element Method, the Finite Difference Method, or the Finite Volume Method. In all three cases, huge systems of equations are to be solved, which is computationally expensive. By employing the free software library AMGCL, a reduction of the computational running time of up to 79% was achieved without losing accuracy. Seven models with different soils and geometries were tested, and the analysis of these tests showed, that AMGCL causes a speedup in all models with 20,000 or more nodes. However, the numerical overhead of AMGCL causes a slowdown in all models with 20,000 or fewer nodes. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
Numerical Investigation of Techno-Economic Multiobjective Optimization of Geothermal Water Reservoir Development: A Case Study of China
Water 2019, 11(11), 2323; https://doi.org/10.3390/w11112323 - 06 Nov 2019
Cited by 2 | Viewed by 716
Abstract
Renewable geothermal utilization is a significant approach for residential heating with two principal modes, direct geothermal district heating systems (DGDHSs) and indirect geothermal district heating systems (IGDHSs). The key principle of geothermal development design is to prevent premature thermal breakthrough, which could result [...] Read more.
Renewable geothermal utilization is a significant approach for residential heating with two principal modes, direct geothermal district heating systems (DGDHSs) and indirect geothermal district heating systems (IGDHSs). The key principle of geothermal development design is to prevent premature thermal breakthrough, which could result in low efficiency of geothermal heating systems. In this paper, a new approach considering building heating demand, geothermal water resource protection, and optimal economic benefits is presented systematically. The results simulated by OGS software show that well spacing, reinjection temperature, and production rate are the most significant parameters affecting thermal breakthrough in geothermal reservoirs. In addition, production rate and reinjection temperature have a huge effect on the payback period of investment. Comparing IGDHS to DGDHS, the investment in construction of geothermal wells and the annual water consumption decrease by up to 10% and 50%, respectively. Additionally, electricity costs increase by 5% to 30%. The indirect geothermal district heating system with a well spacing of 300 m, a production rate of 100 m3/h, and a reinjection temperature of 301.15 K is much better for this case, both technically and economically. The systematic calculation approach can be reasonably applied to other regions with geothermal energy utilization. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
The Spatial Distribution of the Microbial Community in a Contaminated Aquitard below an Industrial Zone
Water 2019, 11(10), 2128; https://doi.org/10.3390/w11102128 - 14 Oct 2019
Cited by 4 | Viewed by 871
Abstract
The industrial complex Neot Hovav, in Israel, is situated above an anaerobic fractured chalk aquitard, which is polluted by a wide variety of hazardous organic compounds. These include volatile and non-volatile, halogenated, organic compounds. In this study, we characterized the indigenous bacterial population [...] Read more.
The industrial complex Neot Hovav, in Israel, is situated above an anaerobic fractured chalk aquitard, which is polluted by a wide variety of hazardous organic compounds. These include volatile and non-volatile, halogenated, organic compounds. In this study, we characterized the indigenous bacterial population in 17 boreholes of the groundwater environment, while observing the spatial variations in the population and structure as a function of distance from the polluting source. In addition, the de-halogenating potential of the microbial groundwater population was tested through a series of lab microcosm experiments, thus exemplifying the potential and limitations for bioremediation of the site. In all samples, the dominant phylum was Proteobacteria. In the production plant area, the non-obligatory organo-halide respiring bacteria (OHRB) Firmicutes Phylum was also detected in the polluted water, in abundancies of up to 16 %. Non-metric multidimensional scaling (NMDS) analysis of the microbial community structure in the groundwater exhibited clusters of distinct populations following the location in the industrial complex and distance from the polluting source. Dehalogenation of halogenated ethylene was demonstrated in contrast to the persistence of brominated alcohols. Persistence is likely due to the chemical characteristics of brominated alcohols, and not because of the absence of active de-halogenating bacteria. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Graphical abstract

Open AccessArticle
Interplays between State and Flux Hydrological Variables across Vadose Zones: A Numerical Investigation
Water 2019, 11(6), 1295; https://doi.org/10.3390/w11061295 - 20 Jun 2019
Cited by 4 | Viewed by 1133
Abstract
Knowledge of both state (e.g., soil moisture) and flux (e.g., actual evapotranspiration (ETa) and groundwater recharge (GR)) hydrological variables across vadose zones is critical for understanding ecohydrological and land-surface processes. In this study, a one-dimensional process-based vadose zone [...] Read more.
Knowledge of both state (e.g., soil moisture) and flux (e.g., actual evapotranspiration (ETa) and groundwater recharge (GR)) hydrological variables across vadose zones is critical for understanding ecohydrological and land-surface processes. In this study, a one-dimensional process-based vadose zone model with generated soil hydraulic parameters was utilized to simulate soil moisture, ETa, and GR. Daily hydrometeorological data were obtained from different climate zones to drive the vadose zone model. On the basis of the field phenomenon of soil moisture temporal stability, reasonable soil moisture spatiotemporal structures were reproduced from the model. The modeling results further showed that the dependence of ETa and GR on soil hydraulic properties varied considerably with climatic conditions. In particular, the controls of soil hydraulic properties on ETa and GR greatly weakened at the site with an arid climate. In contrast, the distribution of mean relative difference (MRD) of soil moisture was still significantly correlated with soil hydraulic properties (most notably residual soil moisture content) under arid climatic conditions. As such, the correlations of MRD with ETa and GR differed across different climate regimes. In addition, the simulation results revealed that samples with average moisture conditions did not necessarily produce average values of ETa and GR (and vice versa), especially under wet climatic conditions. The loose connection between average state and flux hydrological variables across vadose zones is partly because of the high non-linearity of subsurface processes, which leads to the complex interactions of soil moisture, ETa, and GR with soil hydraulic properties. This study underscores the importance of using soil moisture information from multiple sites for inferring areal average values of ETa and GR, even with the knowledge of representative sites that can be used to monitor areal average moisture conditions. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer
Water 2019, 11(6), 1168; https://doi.org/10.3390/w11061168 - 04 Jun 2019
Cited by 4 | Viewed by 984
Abstract
Various delineation methods, ranging from simple analytical solutions to complex numerical models, have been applied for wellhead protection area (WHPA) delineation. Numerical modeling is usually regarded as the most reliable method, but the uncertainty of input parameters has always been an obstacle. This [...] Read more.
Various delineation methods, ranging from simple analytical solutions to complex numerical models, have been applied for wellhead protection area (WHPA) delineation. Numerical modeling is usually regarded as the most reliable method, but the uncertainty of input parameters has always been an obstacle. This study aims at examining the results from different WHPA delineation methods and addressing the delineation uncertainty of numerical modeling due to the uncertainty from input parameters. A comparison and uncertainty analysis were performed at two pumping sites—a single well and a wellfield consisting of eight wells in an unconfined coastal aquifer in Israel. By appointing numerical modeling as the reference method, a comparison between different methods showed that a semi-analytical method best fits the reference WHPA, and that analytical solutions produced overestimated WHPAs in unconfined aquifers as regional groundwater flow characteristics were neglected. The results from single well and wellfield indicated that interferences between wells are important for WHPA delineation, and thus, that only semi-analytical and numerical modelling are recommended for WHPA delineation at wellfields. Stochastic modeling was employed to analyze the uncertainty of numerical method, and the probabilistic distribution of WHPAs, rather a deterministic protection area, was generated with considering the uncertain input hydrogeological parameters. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
Sensitivity of Potential Groundwater Recharge to Projected Climate Change Scenarios: A Site-Specific Study in the Nebraska Sand Hills, USA
Water 2019, 11(5), 950; https://doi.org/10.3390/w11050950 - 06 May 2019
Cited by 6 | Viewed by 1290
Abstract
Assessing the relationship between climate forcings and groundwater recharge (GR) rates in semi-arid regions is critical for water resources management. This study presents the impact of climate forecasts on GR within a probabilistic framework in a site-specific study in the Nebraska Sand Hills [...] Read more.
Assessing the relationship between climate forcings and groundwater recharge (GR) rates in semi-arid regions is critical for water resources management. This study presents the impact of climate forecasts on GR within a probabilistic framework in a site-specific study in the Nebraska Sand Hills (NSH), the largest stabilized sand dune region in the USA containing the greatest recharge rates within the High Plains Aquifer. A total of 19 downscaled climate projections were used to evaluate the impact of precipitation and reference evapotranspiration on GR rates simulated by using HYDRUS 1-D. The analysis of the decadal aridity index (AI) indicates that climate class will likely remain similar to the historic average in the RCP2.6, 4.5, and 6.0 emission scenarios but AI will likely decrease significantly under the worst-case emission scenario (RCP8.5). However, GR rates will likely decrease in all of the four emission scenarios. The results show that GR generally decreases by ~25% under the business-as-usual scenario and by nearly 50% in the worst-case scenario. Moreover, the most likely GR values are presented with respect to probabilities in AI and the relationship between annual-average precipitation and GR rate were developed in both historic and projected scenarios. Finally, to present results at sub-annual time resolution, three representative climate projections (dry, mean and wet scenarios) were selected from the statistical distribution of cumulative GR. In the dry scenario, the excessive evapotranspiration demand in the spring and precipitation deficit in the summer can cause the occurrence of wilting points and plant withering due to excessive root-water-stress. This may pose significant threats to the survival of the native grassland ecology in the NSH and potentially lead to desertification processes if climate change is not properly addressed. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
Dynamic Variation Characteristics of Seawater Intrusion in Underground Water-Sealed Oil Storage Cavern under Island Tidal Environment
Water 2019, 11(1), 130; https://doi.org/10.3390/w11010130 - 12 Jan 2019
Cited by 3 | Viewed by 1542
Abstract
In the case of constructing underground water-sealed oil storage caverns in island environments, the groundwater seepage characteristics are more complicated under the influence of seawater and tidal fluctuations. It also faces problems such as seawater intrusion. This research is based on multi-physical field [...] Read more.
In the case of constructing underground water-sealed oil storage caverns in island environments, the groundwater seepage characteristics are more complicated under the influence of seawater and tidal fluctuations. It also faces problems such as seawater intrusion. This research is based on multi-physical field coupling theory and analyzed the influence of tidal fluctuation and water curtain systems on the temporal-spatial variations of seawater intrusion in an island oil storage cavern in China using the finite element method. The results show that the operation of an underground water-sealed oil storage cavern in an island environment has a risk of inducing seawater intrusion. The tidal fluctuation has a certain degree of influence on the seepage field of the island. The water curtain system can decrease seawater intrusion and reduce the influence of tidal fluctuation on the seepage field inside the island. The research results provide a theoretical basis for the study of seawater intrusion in underground oil storage caverns under island tidal environments. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Open AccessArticle
Colloid Transport in a Single Fracture–Matrix System: Gravity Effects, Influence of Colloid Size and Density
Water 2018, 10(11), 1531; https://doi.org/10.3390/w10111531 - 27 Oct 2018
Cited by 7 | Viewed by 1267
Abstract
A numerical model was developed to investigate the influence of gravitational force on the transport of colloids in a single horizontal fracture–matrix system. Along with major transport phenomena, prominence was given to study the mass flux at the fracture–matrix interface, and colloid penetration [...] Read more.
A numerical model was developed to investigate the influence of gravitational force on the transport of colloids in a single horizontal fracture–matrix system. Along with major transport phenomena, prominence was given to study the mass flux at the fracture–matrix interface, and colloid penetration within the rock matrix. Results suggest that the gravitational force significantly alters and controls the velocity of colloids in the fracture. Further, it was shown that the colloid density and size play a vital part in determining the extent that gravity may influence the transport of colloids in both fracture and rock matrix. The mass flux transfer across the fracture–matrix interface is predominantly dependent on the colloidal size. As large as 80% reduction in penetration of colloids in the rock matrix was observed when the size of the colloid was increased from 50–600 nm. Similarly, the farther the density of colloid from that of the fluid in the fracture (water), then the higher the mitigation of colloids in the fracture and the rock matrix. Finally, a non-dimensional parameter “Rock Saturation Factor” has been presented in the present study, which can offer a straightforward approach for evaluating the extent of penetration of colloids within the rock matrix. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Graphical abstract

Open AccessArticle
Case Study of Heat Transfer during Artificial Ground Freezing with Groundwater Flow
Water 2018, 10(10), 1322; https://doi.org/10.3390/w10101322 - 25 Sep 2018
Cited by 12 | Viewed by 1538
Abstract
For the artificial ground freezing (AGF) projects in highly permeable formations, the effect of groundwater flow cannot be neglected. Based on the heat transfer and seepage theory in porous media with the finite element method, a fully coupled numerical model was established to [...] Read more.
For the artificial ground freezing (AGF) projects in highly permeable formations, the effect of groundwater flow cannot be neglected. Based on the heat transfer and seepage theory in porous media with the finite element method, a fully coupled numerical model was established to simulate the changes of temperature field and groundwater flow field. Firstly, based on the classic analytical solution for the frozen temperature field, the model’s ability to solve phase change problems has been validated. In order to analyze the influences of different parameters on the closure time of the freezing wall, we performed the sensitivity analysis for three parameters of this numerical model. The analysis showed that, besides the head difference, the thermal conductivity of soil grain and pipe spacing are also the key factors that control the closure time of the frozen wall. Finally, a strengthening project of a metro tunnel with AGF method in South China was chosen as a field example. With the finite element software COMSOL Multiphysics® (Stockholm, Sweden), a three-dimensional (3D) numerical model was set up to simulate the change of frozen temperature field and groundwater flow field in the project area as well as the freezing process within 50 days. The simulation results show that the freezing wall appears in an asymmetrical shape with horizontal groundwater flow normal to the axial of the tunnel. Along the groundwater flow direction, freezing wall forms slowly and on the upstream side the thickness of the frozen wall is thinner than that on the downstream side. The actual pipe spacing has an important influence on the temperature field and closure time of the frozen wall. The larger the actual pipe spacing is, the slower the closing process will be. Besides this, the calculation for the average temperature of freezing body (not yet in the form of a wall) shows that the average temperature change of the freezing body coincides with that of the main frozen pipes with the same trend. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Other

Jump to: Editorial, Research

Open AccessTechnical Note
Exploring Compatibility of Sherwood-Gilland NAPL Dissolution Models with Micro-Scale Physics Using an Alternative Volume Averaging Approach
Water 2019, 11(7), 1525; https://doi.org/10.3390/w11071525 - 23 Jul 2019
Cited by 1 | Viewed by 964
Abstract
The dynamics of NAPL dissolution into saturated porous media are typically modeled by the inclusion of a reaction term in the advection-dispersion-reaction equation (ADRE) with the reaction rate defined by a Sherwood-Gilland empirical model. This stipulates, among other things, that the dissolution rate [...] Read more.
The dynamics of NAPL dissolution into saturated porous media are typically modeled by the inclusion of a reaction term in the advection-dispersion-reaction equation (ADRE) with the reaction rate defined by a Sherwood-Gilland empirical model. This stipulates, among other things, that the dissolution rate is proportional to a power of the NAPL volume fraction, and also to the difference between the local average aqueous concentration of the NAPL species and its thermodynamic saturation concentration. Solute source models of these sorts are ad hoc and empirically calibrated but have come to see widespread use in contaminant hydrogeology. In parallel, a number of authors have employed the method of volume averaging to derive upscaled transport equations describing the same dissolution and transport phenomena. However, these solutions typically yield forms of equations that are seemingly incompatible with Sherwood-Gilland source models. In this paper, we revisit the compatibility of the two approaches using a radically simplified alternative volume averaging analysis. We begin from a classic micro-scale formulation of the NAPL dissolution problem but develop some new simplification approaches (including a physics-preserving transformation of the domain and a new geometric lemma) which allow us to avoid solving traditional closure boundary value problems. We arrive at a general, volume-averaged governing equation that does not reduce to the ADRE with a Sherwood-Gilland source but find that the two approaches do align under straightforward advection-dominated conditions. Full article
(This article belongs to the Special Issue Water Flow, Solute and Heat Transfer in Groundwater)
Show Figures

Figure 1

Back to TopTop