Predicting the Hydraulic Conductivity of Metallic Iron Filters: Modeling Gone Astray

Since its introduction about 25 years ago, metallic iron (Fe0) has shown its potential as the key component of reactive filtration systems for contaminant removal in polluted waters. Technical applications of such systems can be enhanced by numerical simulation of a filter design to improve, e.g., the service time or the minimum permeability of a prospected system to warrant the required output water quality. This communication discusses the relevant input quantities into such a simulation model, illustrates the possible simplifications and identifies the lack of relevant thermodynamic and kinetic data. As a result, necessary steps are outlined that may improve the numerical simulation and, consequently, the technical design of Fe0 filters. Following a general overview on the key reactions in a Fe0 system, the importance of iron corrosion kinetics is illustrated. Iron corrosion kinetics, expressed as a rate constant kiron, determines both the removal rate of contaminants and the average permeability loss of the filter system. While the relevance of a reasonable estimate of kiron is thus obvious, information is scarce. As a conclusion, systematic experiments for the determination of kiron values are suggested to improve the database of this key input parameter to Fe0 filters.


Introduction
Due to their low-cost components, metallic iron-based filtration systems (Fe 0 filters) have a broad range of applications from small-sized units for the production of safe drinking water in remote and/or low-income communities (e.g., Africa, Latin America and South-East Asia) to large-scale reactive walls for groundwater remediation, progress in numerical simulation of such systems may reasonably be expected to increase the application potential of this proven environmentally-friendly technology.
Fe 0 `2H + ñ Fe 2+ `H2 Water Iron corrosion is well-known as a major nuisance reaction in the present iron-based world causing billions of Euro of damage per year [20].This reaction is quantitative even in situations where water is present as moisture only [21].It is therefore clear that iron corrosion by water has to be considered as a major reaction in a context (water treatment or Fe 0 /H 2 O system) where water is the solvent ([H 2 O] = ~55.5 mol L ´1).Even if more powerful oxidizing agents (e.g., Cr VI , Cu 2+ , NO 3 ´, O 2 , RCl) should be present as solutes (even at the mg L ´1 level), Equation (2) still needs to be considered a dominant reaction in Fe 0 /H 2 O systems.
2 Fe 2+ `RCl `H+ ñ Fe 3+ `RH `Cl - H 2 `RCl ñ RH `HCl The fact that the Fe 0 surface is constantly shielded by a multi-layered oxide scale (see [11] and the references cited therein) implies that, even under oxic conditions (O 2 is available), Fe 0 oxidizes according to Equation (2).This reaction is even accelerated if reaction products (e.g., Fe II species) are consumed (Le Chatelier's principle).Further details about this aspect of the iron corrosion process are summarized in [21].
The presentation above clearly shows that rate constants for modeling contaminant reductive transformations in Fe 0 /H 2 O systems should be exclusively based on Equations ( 3) and (4).Alternative strategies have been discussed in [16,19,[27][28][29][30].These alternative strategies are based on Equation (1) and mentioned herein for the sake of completeness.
Electrochemical reduction alone (Equation ( 1)) cannot explain all reported observations as (i) the generation of iron hydroxides and oxides for As or U removal [31,32] or (ii) the porosity loss of Fe 0 beds flushed with distilled water [33,34].These obvious discrepancies between various modeling approaches for Fe 0 filters, however, had been a motivation for the discussion herein.
The following four facts suggest that it may be sufficient to characterize the long-term behavior of Fe 0 corrosion while considering the coupled removal efficiency of selected species added as contaminants to have a realistic picture of Fe 0 filters [10,11,25]: (i) Fe 0 corrosion by water is quantitative; (ii) contaminants are chemically reduced by some iron corrosion products; (iii) contaminants are present in trace amounts; and (iv) contaminants without redox properties are quantitatively removed.Thus, the most important parameter to design a Fe 0 filter is the long-term corrosion rate (k iron ; cf.Section 2) of the material to be used.
The aim of the present communication is to demonstrate that no reliable model for Fe 0 filters can be presented without relevant k iron values.Domga et al. [35] recently summarized the results of mathematical modeling of the spatial description of the process of permeability loss in Fe 0 filters.Herein, it is shown that related temporal changes depend on k iron values that are yet to be determined.The significance of k iron will be first presented, followed by the specificity of Fe 0 materials as used in water treatment and environmental remediation.

Descriptive Aspects
Kinetic studies on contaminant reductive transformation in Fe 0 /H 2 O systems currently use relationships like the following based on reactions similar to Equation (5): drRCls dt " ´k ˆrRCls ˆrH `s (5) Water 2016, 8, 162 3 of 21 Following this approach, k values for individual contaminants (e.g., k RCl ) have been determined and partly tabulated for modeling purposes [16]; however, considering that Equation ( 1) is faulty as Equations ( 3) and ( 4) are the main sources of electrons for any contaminant in a Fe 0 /H 2 O system (indirect reduction).Accordingly, properly modeling the kinetics of any reductive transformation in Fe 0 /H 2 O systems depends on the accurate characterization of the kinetics of the production of Fe 2+ and H 2 or the determination of the kinetics of Fe 0 corrosion by water (Equation ( 6)).The relationship defining k iron can be written as: where k iron is the rate of iron corrosion and [H + ] the concentration of protons.Reardon [36,37] has positively correlated k iron and the volume of H 2 generated in the Fe 0 /H 2 O system.However, properly correlating both values depends on the description of individual systems and the characterization of possible H 2 sinks [38].In other words, characterizing the kinetics of iron corrosion (at pH > 4.0) by determining the volume of generated H 2 is just an approximation.This approach is arguably nearer to reality than any reasoning based on Equation ( 5) [39].
The abundant literature on aqueous iron corrosion reveals that there are three basic kinetics laws that characterize the oxidation rates of Fe 0 : (i) the parabolic rate law; (ii) the logarithmic rate law; and (iii) the linear rate law.These laws are modeled respectively as follows [40,41]: x " Kp ˆlogpc ˆt `bq x " K L ˆt where x is the thickness of the oxide scale on Fe 0 ; Kp is the parabolic rate constant for scale growth; K L is the linear rate constant for scale growth; t is time; a and c are constants.As a rule, the x values (scale thickness) are correlated to the Fe 0 weight loss (metal loss) without considering the presence of individual corrosive species (e.g., Cl ´, CO 2 , H 2 O, H 2 S, O 2 ).The parabolic rate law assumes that the concentrations of diffusing species at the oxide/metal and oxide/water interfaces are constant and that the oxide scale is uniform, continuous and of the single phase type [41].This law is applicable to high temperature engineering problems and is recalled here only for the sake of completeness.
The logarithmic and the linear rate laws are more likely to be applicable to Fe 0 water filters and are both empirical relationships.It is essential to notice that the corrosion rate (k iron ) is not investigated as a function of the amount of individual corrosive species (e.g., Cl ´, contaminants, H 2 S), but rather as the extent of iron corrosion as influenced by these and all other operational parameters (flow velocity, system design, temperature).In other words, considering that contaminants are the main corroding agents for Fe 0 is alien to corrosion science [10,13,14,25,40,41].

Corrosion Rate and Extent of Mass Loss
The extent of aqueous Fe 0 corrosion under environmental conditions is generally expressed either in terms of [40,41] (i) the change in Fe 0 weight (mass loss), (ii) the dimensions of the corroded crevices, (iii) the number and quantity of formed pits or (iv) the amount of corrosion products (e.g., the thickness of the oxide scale; Equations ( 7)-( 9)).Equation (10) expresses the corrosion rate (k iron ) in terms of mass loss: where k iron (mm/y) is the corrosion rate; m b (g) is the mass before exposure; m a (g) is the mass after exposure; A (mm 2 ) is exposed surface area; t (years) is the exposure time; ρ (g/cm 3 ) is density and K a constant.Expressing the time in years suggests that, to be relevant, experiments should ideally last for several years.
Another conventional way to access k iron uses the Faraday law.Here, k iron is quantified through the relationship between the corrosion current density and the extent of metal dissolution [41,42].

Oxide Scale Formation and Its Effects on k iron : Modeling Aspects
Equation (10) shows that k iron depends on ∆m = m b -m a , A and t. ∆m is related to the amount of corrosion products within the system or the thickness of the oxide scale (x value; Equations ( 7)-( 9)).The time-dependent changes of ∆m and A render corrosion processes very complex.Generally, one should consider the following processes [40,41,43]: (i) the Fe 0 dissolution (anodic reaction) at the free metal surface; (ii) water reduction (cathodic reaction) at the Fe 0 surface; (iii) the precipitation equilibria yielding the oxide scale on the Fe 0 surface; (iv) the dissolution of the oxide scale (abiotic and biotic); (v) chemical reactions within the oxide scale (including Equations ( 3) and ( 4)); (vi) adsorption, co-precipitation and mass transfer across and within the oxide scale; and (vii) electro-migration (ionic transport) through the oxide-scale.The latter depends on the permeability and the surface charge of the precipitates building the scale [43].
A comprehensive model for the corrosion process should take into account all of these phenomena.Such a model would contain a large number of parameters.Relevant parameters could not be unequivocally determined on the basis of the limited amount of data that is available in the literature.This is an argument for new, holistic and systematic investigations.However, appropriate simplifications could be made.For example, Anderko and Young [44] considered that separate species form on the corroding Fe 0 surface in order to derive a mathematical model that represents the effects of scale formation on corrosion rates.The time-dependent change of each Fe 0 surface fraction is mathematical expressed.Similarly appropriate assumptions could be made on the reaction orders, the absorption behavior (e.g., Freundlich, Langmuir) and all other relevant aspects [44,45].
The approach conventionally used in the Fe 0 water filtration literature [16,19,[27][28][29][30] is not derived from Equation (10) and related simplifications.Moreover, the presentation above reveals that chemical reactions yielding contaminants reductive transformation in Fe 0 /H 2 O systems (Equations (3) and ( 4)) are included in just one of seven processes making up the dynamics of oxide scale formation and transformation.For this reason, it would be difficult to find a model really describing an actual Fe 0 /H 2 O system within the remediation literature.

Major Characteristics of Fe 0 Materials for Water Filters
Reactive Fe 0 materials used for water filters are characterized mostly by their size/thickness of less than 5.0 mm [46][47][48][49].A widely-used Fe 0 sample from iPuTech (Rheinfelde, Germany) has a grain size varying from 0.3 to 2.0 mm [16,47].This diameter represents less than 1/10 of the thickness of the buried cast iron pipes investigated by Mohebbi and Li [50].The pipe presented pits having widths varying from 13 to 117 mm and depths from 1.6 to 9.1 mm after a service life of 90 years.From the study of Mohebbi and Li [50], an average rate constant (k iron ) for a cast iron pipe under service conditions can be derived (Equation (10)), but such k iron values cannot be extrapolated to Fe 0 materials for water filters, even when they result from the same cast iron.Many material and application-dependent k iron values can be found in the broad literature [51,52] using Fe 0 , but none of them can be adopted for Fe 0 filters.Relevant fields include metal recovery by the cementation process, which was established in 1890s [53,54].In the cementation process, metal (e.g., Fe 0 , Zn 0 ) particles are used in technical devices for some weeks or months and the major (controlled) operating conditions (e.g., high temperatures or low pH values) are not comparable to those of water filters.In particular, high metal ion concentrations warrant the formation of an electronic conductive layer of recovered metals at the Fe 0 surface, while in the water filtration industry, a multi-layered, nonconductive oxide scale ("passive" film) is inevitably formed [55], rendering quantitative direct reduction (electrons from Fe 0 ) simply impossible.

Coping with the Singularity of Fe 0 Filters
In order to assess the service life of Fe 0 filters, it is imperative to determine corrosion rates (k iron ) of relevant Fe 0 materials over the long term and to develop models for Fe 0 depletion to be correlated with the extent of contaminant removal under operational conditions.Although many studies have been performed to determine the rate constant of the degradation (chemical reduction) of individual contaminants (k contaminant ; based on reactions similar to Equation ( 1)) (Section 2), little research has been undertaken, which could be used to derive k iron values over longer time scale than days, weeks or a few months.The intention herein is to pave the way to fill the gap regarding the long-term corrosion rate of materials for Fe 0 filters in the absence of historical data.Clearly, long-term experiments for the determination of k iron values are urgently needed to assist the development of reliable models to predict the service life of Fe 0 filters and/or describe their operation.
It is understood that the k iron value is not an intrinsic property of the material, but depends on several inter-related site-specific parameters.For example, the same material will exhibit different k iron values in reactive zones containing the same amount of Fe 0 , but having different volumetric Fe 0 :sand ratios, e.g., 10:90, 25:75 and 50:50.The rationale is that the long-term kinetics of iron corrosion also depends on the pressure within the filter (P H2 in Equation ( 6)).The initial k iron value (k 0 iron ) could be identical in the three systems, but with increasing service life, systems with higher Fe 0 ratios will exhibit lower k iron values.Remember that in designing Fe 0 filters, the goal is to work with the material, for which k iron value implies efficient decontamination under the operational conditions (e.g., bed thickness, flow velocity, water chemistry).Clearly, selecting an appropriate material for a given site is not seeking for the most reactive one.

Lessons from Monitored Aquifer Recharge
In many regions of the world, monitored aquifer recharge (MAR) is applied as a tool to (i) overcome the over-exploitation of groundwater or (ii) store excess storm water in the subsurface [56,57].While injecting water into an aquifer, clogging does often occur, possibly rendering MAR inefficient in the long-term.There are three clogging types: (i) biological clogging due to growing biofilms; (ii) chemical clogging due mostly to precipitation reactions; and (iii) physical clogging caused by suspended solids.In many cases, it has been demonstrated that physical clogging accounts for about 70% of the permeability loss [58].
A particular case of water injection into the aquifer is that of the re-circulation of iron-rich groundwaters.Here, the precipitation of Fe II /Fe III mineral phases significantly reduces the porosity of the aquifer system after a certain operation duration.The removal of dissolved iron by several techniques was proven efficient in sustaining MAR operations [59].In the context of Fe 0 filters, dissolved iron generates and precipitates within the system (in situ).Accordingly, dissolved iron cannot be removed, but only properly considered.Thus, the two major lessons from the MAR technology are that: (i) suspended substances should be filtered out; and (ii) the generation, migration and transformation of Fe species should be carefully considered (mass balance, including volumetric expansion).

Lessons from the Merrill-Crowe Process
The century-old zinc cementation for gold recovery from a pregnant leach liquor (the Merrill-Crowe process) reveals that clarification and deaeration (O 2 removal) of the leach liquor are two decisive stages to optimize the efficiency of Fe 0 filters.Clarification corresponds to the elimination of suspended substances (Section 4.1) to avoid physical clogging.
In its original version, the cementation process involved the filtration of a gold-bearing cyanide solution through a packed bed of zinc shavings.This operation was proven to have little efficiency because the reaction rate was very slow and the Zn 0 surface was soon "passivated".The problem of Water 2016, 8, 162 6 of 21 passivation was solved by the addition of a lead salt (e.g., Pb(NO 3 ) 2 ).This allowed a Zn 0 /Pb 0 bimetallic system to form at the Zn 0 surface (shavings), enabling continued gold cementation (deposition).
Two further improvements were realized later: (i) using zinc dust rather than shavings; and (ii) the deaeration of the gold-bearing solution to O 2 levels lower than 1.0 mg L ´1.Zn 0 dust provided a much larger surface area ("A" in Equation ( 10)) for gold precipitation (Equation ( 11)), while the deaeration significantly reduced Zn 0 consumption through O 2 .Clearly, a concurrent reaction for Zn 0 consumption is eliminated.
Replacing Zn 0 by Fe 0 , in the context of Fe 0 filters, iron corrosion by water (Equation ( 2)) is the main reaction and corresponds to Equation (11).
It has been established that disturbance through dissolved O 2 results from the acceleration of Equation ( 2) by consumption of Fe II species that are the effective reducing agents for O 2 .Considering permeability loss, Fe 0 corrosion in the presence of O 2 yields more voluminous Fe III oxides (e.g., Fe 2 O 3 , FeOOH) and hydroxides (Table 1).Table 1 summarizes the densities of iron corrosion products and the corresponding coefficient of volumetric expansion.If it is assumed that all oxidized Fe remains in the system (no transport of Fe II /Fe III ), then it becomes evident that, for a constant volume (initial porosity of a Fe 0 filter), the systems with more oxygen will clog early [7,60].

Table 1. Theoretical ratios (η values) between the volume of expansive corrosion products (V oxide )
and the volume of iron consumed during the corrosion process (V Fe ).η values are compiled by Caré et al. [60].The ratios of ρ values (densities) indicate that corrosion products are 1.5 to 2.2 times larger in volume than the parent Fe 0 .The logical consequence of the presentation above is that the use of O 2-poor leach liquors is a prerequisite for efficient Au recovery through Zn 0 cementation in packed beds.This process is ultimately known as the Merrill-Crowe precipitation process.Coming back to Fe 0 filters, it becomes evident that the analysis of the chemistry of the system would have enabled the proper consideration of the volumetric expansive nature of iron corrosion (Table 1) prompted at the start of the technology some 25 years ago.

Species
The major lesson from the Merrill-Crowe precipitation process for Fe 0 filters is that controlling the O 2 level is essential for the efficiency of a filter.O 2 accelerates corrosion and can be beneficial in some cases.Where necessary, even stronger oxidizing agents can be used [32,61].However, it should be carefully considered that more corrosion products implies rapid clogging, such that it is certain that long-term permeable systems should operate at low O 2 levels.

Conventional Approach
Conventionally, numerical models are used to predict the long-term behavior of Fe 0 filters (see [19] and the references cited therein).Data for such models should be derived from well-designed laboratory column experiments performed under operational conditions (e.g., experimental duration, flow velocity, temperature and water chemistry) mimicking as closely as possible those expected in the field.However, such studies currently provide at best information for understanding the early service life of Fe 0 filters (some months).In fact, experiments lasting for more than one year are very scarce [19,62,63], while it is not established that k iron determined under such conditions would describe the behavior of Fe 0 filters for 10 or 15 years.Moreover, according to Alamilla et al. [51], it is even not likely that this will be the case because of the well-documented non-linearity of the kinetics of iron corrosion [64] (Section 2).
It has been unambiguously demonstrated that all tools used to accelerate lab-scale experiments collectively impair the reliability of the obtained test results [35,[65][66][67].Relevant tools include adding oxidizing agents to accelerate corrosion [58], increasing flow velocity [34] and using Fe 0 of smaller particle sizes and/or rapid small-scale column tests [65].For the early phase of column operation, methylene blue (MB) discoloration has been proven a powerful indicator of reactivity [68][69][70][71][72][73][74].Actually, the longest experiment with MB in this context lasted only for 4 months [69].Accordingly, the suitability of MB discoloration for characterizing the long-term behavior of Fe 0 filters is yet to be investigated.
While the reliability of data currently used to model processes in Fe 0 filters is questioned, there is evidence that used k iron values are inaccurate.For example, Moraci et al. [19] critically reviewed available approaches and presented a new modeling tool to simulate the permeability loss in Fe 0 filters.The presented model takes into account: (i) the volumetric expansive nature of iron corrosion; (ii) the precipitation of foreign species; and (iii) gas formation.However, a look at the used k iron values suggests that there are still misunderstandings to be addressed before acceptable models are presented.

An Alternative Approach
The process of permeability loss should be investigated at the micro-scale [35].The size of the Fe 0 particles, the volume of the space between individual grains and their modifications with the service life of the filter should be simultaneously considered.

Descriptive Aspects
Spherical Fe 0 particles are considered.Each particle has an initial diameter of d 0 (t 0 = 0).At t > t 0 , the residual diameter of the particle (non-corroded Fe 0 ) is d.The in situ generated amount of corrosion products corresponds to ∆d = d 0 -d.The initial mass of each particle is m p = ρ iron ˆV0 (V 0 = π ˆd0 3 /6) A certain Fe 0 mass (m 0 ) is made up of N 0 particles, such that m 0 = N 0 ˆρiron ˆπ ˆd0 3 /6.Assuming uniform corrosion, all N 0 particles corrode with the same kinetics (k iron ).At each time (t), the mass of non-corroded Fe 0 can be determined and the corresponding decrease in diameter (∆d) deduced.The average corrosion rate is given by Equation (12).The best scenario is the one in which ∆d is directly measured (in situ).
The surface area of a Fe 0 particle (A p ) with a diameter d is given by Equation ( 13): The number of Fe atoms covering A p can be deduced using Equation ( 14), while considering that each Fe atom (r atom = 1.24Å or d atom = 2.48 Å) covers an effective area equal to a square (d atom 2 ).
This reasoning has intentionally ignored the evidence that isolated Fe 0 atoms do not exist; instead, each unit cell of Fe 0 (BCC) contains two (2) Fe atoms.
One major challenge for the Fe 0 filtration technology has been to properly consider the contribution of (volumetric expansive nature of) iron corrosion to permeability loss [16,[33][34][35]75].That is coupling ∆d to the diminution of the porosity (Challenge 1).Challenge 1 has been resolved using mass balance equations [7,8,35,76] open question (Challenge 2) is how to correlate this spatial porosity loss to the service life of Fe 0 filters (temporal porosity loss).Thus, determining k iron is the key to model the operation of Fe 0 filters.In the context of Fe 0 filters, "permeability loss" and "porosity loss" can be randomly interchanged as permeability loss is mostly mediated by the occupation of the inter-granular pore space (porosity) and, thus, to reduced interconnectivity of available pores (physical clogging).This is the reason why the entrance zone of a filter comparatively experiences increased porosity loss as a rule.This evidence alone makes the discussion of common column parameters like Reynold or Peclet numbers a complex task.

On the Significance of k iron Values
The k iron values used by Moraci et al. [19] as calibration parameters are expressed in mmol kg ´1 d ´1.According to the references cited by these authors, such expressions are common in the Fe 0 literature.Each k iron value should be given in mmol particle ´1 d ´1.The reason being that all Fe 0 particles are corroded by water (H + or H 2 O) with the same kinetics.Admittedly, in the entrance zone, dissolved O 2 and/or other oxidizing agents, including contaminants (e.g., Cu II , Cr VI , NO 3 ´) and co-solutes (e.g., Ca 2+ , Cl ´, NO 3 ´), will accelerate iron corrosion and, thus, the extent of permeability/porosity loss.However, permeability loss due to Equation (2) [7,9,[33][34][35] is ideally uniform.For example, a k iron value of 30 mmol kg ´1 d ´1 corresponding to 1680 mg kg ´1 d ´1 implies a daily dissolution of 1.57 ˆ10 ´2 mmol or 0.88 mg of iron from individual spherical particles having a diameter of 1.0 mm (d value).The equations used for calculations are summarized in the previous section, and the results of all k iron values used by Moraci et al. [19] are summarized in Table 2.   [19] assuming uniform corrosion for d = 1.0 mm.It is seen that t 8 varies from 0.2 to 69.1 years.Keeping in mind that subsurface Fe 0 reactive walls (Fe 0 filters) should have a service life in the range of decades, Table 2 suggests that, for d = 1.0 mm, a material exhibiting a k iron value averaging 4.0 mmol particle ´1 d ´1 should be used.Such a material would last for 12.22 years (t 8 value).These calculations suggest that in a cross-disciplinary approach, a challenge for material scientists (Challenge 3) would be to manufacture a (possibly porous) spherical material with a 1.0 mm diameter exhibiting an average of 0.12 µg particle ´1 d ´1.The same reasoning suggests that a material exhausting within one year (t 8 ) should have a k iron value of 1.47 µg particle ´1 d ´1.Such a material could be useful for household water filters [77].
It is understood that solving Challenge 3 will just be the first step in designing Fe 0 filters.In fact, the target k iron value (e.g., 4.0 mmol particle ´1 d ´1) depends on a myriad of operational parameters, including the porosity of the Fe 0 materials, the Fe 0 ratio in the reactive layer, the nature of the admixing aggregates (e.g., MnO 2 , pumice, sand, TiO 2 ), the water flow velocity (residence time), the water chemistry (the composition of the electrolyte) and the thickness of the reactive layer.The next section proposes an approach for a systematic investigation yielding suitable materials for Fe 0 filters.Table 3 and Figure 1 summarize the trend of the expected changes in efficiency as a function of d values.It is seen that the number of particles decreases exponentially with increasing d values, while the number of atoms at the surface increases.The objective of this communication is to outline that the law of efficiency change as d 0 changes to d in a Fe 0 filter is not yet established.

The Problem
The main problem of the Fe 0 filtration technology is the lack of appropriate standard tools to characterize the reactivity of used materials [47][48][49].In other words, ill-defined materials have been used by various research groups and remediation companies for the past two decades.Accordingly, it is not surprising that only highly qualitative results have been presented.Considering this vacuity, the intention herein is to pave the way for the determination of kiron values useful for modeling purposes.Clearly, while determining kiron values useful for models, experiments should be designed to characterize as much parameters as possible in a systematic approach [77,78].The major advantage

The Problem
The main problem of the Fe 0 filtration technology is the lack of appropriate standard tools to characterize the reactivity of used materials [47][48][49].In other words, ill-defined materials have been used by various research groups and remediation companies for the past two decades.Accordingly, it is not surprising that only highly qualitative results have been presented.Considering this vacuity, the intention herein is to pave the way for the determination of k iron values useful for modeling purposes.Clearly, while determining k iron values useful for models, experiments should be designed to characterize as much parameters as possible in a systematic approach [77,78].The major advantage of this approach is that the same set of experiments will generate data enabling the discussion of the appropriateness of current approaches, as well.For example, in a three-contaminant system employing arsenic, fluoride and uranium, the correlation of k iron values to the time-dependent extent of the removal of each contaminant can be properly discussed.In a similar way, repeating the experiments of Luo et al. [34] for the long term will enable the determination of k iron of the same sample in deionized water, groundwater and acid mine drainage (AMD).
In the absence of a reference material, an operational reference can be selected; for example, one of the materials commercialized by iPuTech mbH (Rheinfelde, Germany) and widely used in laboratory and field studies [47,79].A material scientist solving Challenge 3 would manufacture Fe 0 materials to be characterized (k iron values) and compared to the operational reference.Following this approach, available Fe 0 materials could be classified according to their k iron values, which are only indirectly correlated to the intrinsic reactivity.It is understood that neither the reference nor one of the individual materials could be the material for all situations.The objective is to come out with various materials exhibiting various k iron values, such that selection to meet site-specificity would be simplified.Section 4.3 suggested for Fe 0 materials with a 1.0 mm diameter, k iron = 0.12 µg particle ´1 d ´1 is suitable for subsurface-reactive Fe 0 walls, whereas k iron = 1.47 µg particle ´1 d ´1 is suitable for household water filters.

Ways to Reliable k iron Values
A proven tool to determine k iron values is to allow Fe 0 materials (initial diameter d 0 ) to corrode under specific conditions and to determine the time-dependent variation of either (i) the residual diameter (d) or (ii) the amount of generated corrosion product (corresponding to ∆d = d 0 -d).The latter can be also expressed by the thickness of the oxide scale (x in Equations ( 7) to ( 9)).In essence, a good estimation can be realized by just weighing the dried materials at the start (t 0 ) and the end (t 8 ) of the experiments (mass balance) [80].In this approach, ∆m = m 8 -m 0 represents (approximately) the mass of generated corrosion products when the column is flushed by deionized water.Depending on the operational conditions (oxic/anoxic), reliable assumptions can be made on the nature of corrosion products to enable modeling porosity loss.If the system is flushed by other solutions, the mass balance of individual species must be considered.Proper assumptions on all reactions likely to occur in the system and their contribution to changes in porosity must be made.
Recent data have proven that (i) the residual diameter (d), (ii) the amount of generated corrosion products and (iii) the nature of corrosion products can be determined by in situ measurements/observations of both d and changes in the pore diameters [34].In their excellent work using X-ray computed tomography (RX-CT), Luo et al. [34] used three different model waters: (i) distilled water, (ii) synthetic groundwater and (iii) synthetic AMD.Luo et al. [34] also investigated the impacts of three different Fe 0 /sand ratios (w/w): 10:90, 50:50 and 100:0.Duplicating the experiments of Luo et al. [34] for longer experimental durations and more applicable experimental set-ups (for water treatment) will certainly allow the determination of reliable k iron values for predictive models.In this effort, a pure Fe 0 column (100 % Fe 0 ) could be used just as a tool to shorten the experimental duration or as a negative reference.For long-term basic experiments, a volumetric Fe 0 :aggregate ratio of 25:75 should be used.Such experiments should not be stopped because contaminant breakthrough has occurred.In fact, the focus herein is on the efficiency of tested Fe 0 materials [69,71,72] and possibly characterizing the time to Fe 0 exhaustion (t 8 ).There is certainly an infinity of possibilities of experimental designs; the present effort will be limited to two approaches: (i) the sampling-port approach (in one column); (ii) the column-in-series approach.

The Sampling-Port Approach
Experiments could be performed with a single column (ID = 5.0 cm, L > 50 cm) having a reactive zone (Fe 0 -bearing) of 50 cm and equipped with five (5) sampling ports S 1 , S 2 , S 3 , S 4 and S 5 at 10, 20, 30, 40 and 50 cm from the inlet, respectively (Figure 2).The influent solution is pumped upwards from a reservoir and at pre-defined time intervals.Effluents from each sample port are analyzed for pH value, dissolved iron, dissolved oxygen and concentrations of contaminants and co-solutes (e.g., Ca 2+ , Cl ´, HCO 3 ´, H 2 PO 4 ´, SO 4  2´) .In addition to aqueous analysis, time-dependent changes of the morphology of Fe 0 and the pore structure should be documented by RX-CT, for example at the following distances from the inlet: 5 (S' 1 ), 15 (S' 2 ), 25 (S' 3 ), 35 (S' 4 ) and 45 cm (S' 5 ) of the reactive zone.
Water 2016, 8, 162 Cl − , HCO3 − , H2PO4 − , SO4 2− ).In addition to aqueous analysis, time-dependent changes of the morphology of Fe 0 and the pore structure should be documented by RX-CT, for example at the following distances from the inlet: 5 (S'1), 15 (S'2), 25 (S'3), 35 (S'4) and 45 cm (S'5) of the reactive zone.This approach enables a reliable characterization of processes implying the well-documented increased porosity loss in the entrance zone of the Fe 0 filters (e.g., at S1 vs. higher Si stations) and how it is influenced by the presence of oxidizing agents (e.g., Cr VI , dissolved O2) in the influent solution.Moreover, by individually varying the influent O2 concentration and other oxidizing agents, while monitoring its profile in the whole column (S1 through S5), a better discussion of its impact on the porosity loss is realized.The last important feature from this experimental approach is that, before O2 breakthrough at S4, the porosity loss at S'5 is attributed solely to corrosion through water (Equation ( 1)) under the experimental conditions (anoxic conditions).Accordingly, by purposefully varying the composition of influent solution, the impact of relevant operational parameters (e.g., Cl − , HCO3 − , SO4 2− ) on the extent of porosity loss through water can be characterized.
In the absence of RX-CT, or complementary to this tool, other approaches for monitoring changes of the water flow velocity at individual sample ports can be used.The reduction of the pore size is then deduced from the Darcy equation.At the end of the experiments (at least two years), the 0 This approach enables a reliable characterization of processes implying the well-documented increased porosity loss in the entrance zone of the Fe 0 filters (e.g., at S 1 vs. higher S i stations) and how it is influenced by the presence of oxidizing agents (e.g., Cr VI , dissolved O 2 ) in the influent solution.Moreover, by individually varying the influent O 2 concentration and other oxidizing agents, while monitoring its profile in the whole column (S 1 through S 5 ), a better discussion of its impact on the porosity loss is realized.The last important feature from this experimental approach is that, before O 2 breakthrough at S 4 , the porosity loss at S' 5 is attributed solely to corrosion through water (Equation ( 1)) under the experimental conditions (anoxic conditions).Accordingly, by purposefully varying the composition of influent solution, the impact of relevant operational parameters (e.g., Cl ´, HCO 3 ´, SO 4  2´) on the extent of porosity loss through water can be characterized.
In the absence of RX-CT, or complementary to this tool, other approaches for monitoring changes of the water flow velocity at individual sample ports can be used.The reduction of the pore size is then deduced from the Darcy equation.At the end of the experiments (at least two years), the column is dismantled after the last RX-CT analysis, and the non-corroded Fe 0 materials and the corrosion products are characterized by various analytical tools, including selective extraction.This effort characterizes the changes of the following parameters as a function of the distance from the inlet: (i) the extent of Fe 0 depletion (e.g., in %); (ii) the average size of non-corroded Fe 0 ; (iii) the nature, the abundance and the reactivity of individual corrosion products; and (iv) the extent the reduction of pore sizes.

The Column-In-Series Approach
The sample-port approach requires sophisticated equipment, including the column and the pump.For less equipped laboratories (e.g., in the developing world), this could be prohibitively expensive.For these situations, small research units could be made up of five shorter columns (e.g., ID = 5.0 cm; L = 30 cm) in series (Figure 3).Individual columns are mostly filled with sand and contain a 10 cm-thick reactive layer.In this embodiment, each column corresponds roughly to 10 cm of the sample-port approach (Figure 2).The larger sand mass between the reactive layers enables the characterization of the impact of in situ-coated sand on the filter's efficiency.For Columns 1 through 4, the effluent from one column is routed to the next through a tubing system comprising a sampling station/valve (Figure 3).The sample-port approach requires some sophisticated equipment, including the column and the pump.For less equipped laboratories (e.g., in the developing world), this could be prohibitively expensive.For these situations, small research units could be made up of five shorter columns (e.g., ID = 5.0 cm; L = 30 cm) in series (Figure 3).Individual columns are mostly filled with sand and contain a 10 cm-thick reactive layer.In this embodiment, each column corresponds roughly to 10 cm of the sample-port approach (Figure 2).The larger sand mass between the reactive layers enables the characterization of the impact of in situ-coated sand on the filter's efficiency.For Columns 1 through 4, the effluent from one column is routed to the next through a tubing system comprising a sampling station/valve (Figure 3).The results are exploited similarly as for the sample-port approach, the main objective being to determine the long-term kinetics of iron corrosion (kiron).In this approach the system can be gravity fed.For example, it can be daily fed by 1000 mL of a model solution.For both approaches, the level of dissolved O2 in the influent solution can be regulated by pre-filters: a relevant pre-filtration system is a slow sand filter (SSF) in which O2 is consumed within a biofilm [81].However, working with an SSF implies a low water flow velocity.Alternative approaches to decrease/lower the O2 level include using a sacrificial Fe 0 column containing up to 10 vol% Fe 0 possibly of a smaller particle size.In fact, Fe 0 is a well-documented O2 scavenger that is used in food packaging [82,83].

The Significance of the Short-Term Kinetics of Fe 0 Corrosion
The effort herein is to prepare the way for the determination of kiron values of crucial importance for modeling scenarios to design long-term, efficient Fe 0 filters.Before being efficient for the long term, however, Fe 0 filters have to be pre-conditioned in a "maturation" phase.Data from Kowalski and Sogaard [84] suggest that in their case, this maturation phase has lasted for six months.In the subsurface context, this means that the filtration system must contain short-term, efficient materials to assure contaminant removal in the initial service life of Fe 0 filters.Examples are adsorbents or more reactive Fe 0 materials, possibly with smaller particle sizes.The presentation above demonstrates that the short-term rate constants of Fe 0 corrosion (k 0 iron) have been mistakenly used to interpret results The results are exploited similarly as for the sample-port approach, the main objective being to determine the long-term kinetics of iron corrosion (k iron ).In this approach the system can be gravity fed.For example, it can be daily fed by 1000 mL of a model solution.For both approaches, the level of dissolved O 2 in the influent solution can be regulated by pre-filters: a relevant pre-filtration system is a slow sand filter (SSF) in which O 2 is consumed within a biofilm [81].However, working with an SSF implies a low water flow velocity.Alternative approaches to decrease/lower the O 2 level include using a sacrificial Fe 0 column containing up to 10 vol% Fe 0 possibly of a smaller particle size.In fact, Fe 0 is a well-documented O 2 scavenger that is used in food packaging [82,83].

The Significance of the Short-Term Kinetics of Fe 0 Corrosion
The effort herein is to prepare the way for the determination of k iron values of crucial importance for modeling scenarios to design long-term, efficient Fe 0 filters.Before being efficient for the long term, however, Fe 0 filters have to be pre-conditioned in a "maturation" phase.Data from Kowalski and Sogaard [84] suggest that in their case, this maturation phase has lasted for six months.In the subsurface context, this means that the filtration system must contain short-term, efficient materials to assure contaminant removal in the initial service life of Fe 0 filters.Examples are adsorbents or more reactive Fe 0 materials, possibly with smaller particle sizes.The presentation above demonstrates that the short-term rate constants of Fe 0 corrosion (k 0 iron ) have been mistakenly used to interpret results and/or to predict the behavior of long-term experiments.According to Alamilla et al. [51], the function describing the instantaneous rate of iron corrosion is expressed as follows: vptq " k iron `pk 0 iron ´kiron q ˆexpp´q 0 ˆtq (15) where q 0 is a constant, k 0 iron is the short-term and k iron the long-term Fe 0 average corrosion rate.It can be seen that the instantaneous rate drops exponentially from k 0 iron to k iron (k 0 iron > k iron ).The real significance of k 0 iron values for subsurface Fe 0 filters is that materials should be selected such that after the initial rapid corrosion, the permeability of the reactive zone is still superior to that of the surrounding areas.If this condition is not satisfied, preferential flow would render the filter useless before the long-term corrosion rate (k iron ) is established.
While the short-term corrosion rate (k 0 iron value) is to be properly considered in designing subsurface Fe 0 filters, it could be sufficient to design some filters for the treatment of wastewaters from various sources (agriculture, industry, mine, residential area).Here, filters may be designed to operate just for some days to weeks, and material "regeneration" consists of just letting "used" materials be "activated" by humidity and air O 2 for a certain time before being re-used.k 0 iron values would be also sufficient to design several decontamination options using Fe 0 particles in batch or fluidized column systems.In this context, the system efficiency can be purposefully enhanced by using more or less powerful oxidizing agents [10,61], because bed clogging is not an important issue.All that is needed is increased Fe 0 corrosion to generate more contaminant scavengers [11,85,86].k 0 iron values are also sufficient to design cementation beds for metal ion recovery.

Contaminant Removal in Fe 0 /H 2 O Systems
The reliance of modelers on direct reduction by Fe 0 (electrons from the core metal) is not only of concern for modeling the long-term permeability of Fe 0 filters [3,87,88].It strongly masks the real mechanisms of contaminant removal as that is a complex interplay between Fe 0 particles, Fe II released into solution and Fe II /Fe III precipitation [89][90][91][92][93][94][95][96].In particular, the transformation of Fe 0 to Fe oxides goes through colloids and hydroxides.The transformation "colloids to hydroxides" is accompanied by contaminants enmeshment (co-precipitation).In fact, whether they are reduced or not, contaminants are removed by adsorption, co-precipitation and size exclusion.On the other hand, regarding the abundance of (partly nascent) adsorbing sites and continuous generation of Fe II species, contaminant chemical reduction by so-called structural Fe II (adsorbed Fe II ) is favored [96].The abundance of Fe II /Fe III hydroxides/oxides in Fe 0 /H 2 O systems has been experimentally demonstrated by [92].However, the authors have suggested adsorptive removal as an important removal mechanism accompanying direct reduction, which is in contradiction to the mechanisms presented in Section 2. Accordingly, coming models for Fe 0 /H 2 O systems should be adjusted to address the main contaminant removal pathways.

The Shortcomings of Current Modeling Efforts
An overview of the Fe 0 filtration literature reveals conflicting information regarding the causes of permeability loss [7,75].There is always a discrepancy between the observed and the predicted porosity loss; the actual porosity loss being higher than that predicted [75].Two examples for illustration: (i) Mackenzie et al. [82] measured a 5 to 10% porosity loss using tracer tests, while calculations based on mineral precipitation predicted only 1 %; and (ii) Kamolpornwijit and Liang [97] measured porosity losses of 25 to 30% based on tracer tests and attributed 1.3% to trapped gas.Mackenzie et al. [82] attributed the remaining porosity loss (up to 9%) to H 2 gas production.Henderson and Demond [75] realized that available models for Fe 0 filters [98][99][100] do not account for the effects of H 2 on permeability loss.In a series of carefully-designed experiments, Henderson and Demond [75] could validate their working hypothesis that the majority of porosity loss is not attributable to precipitates, but to gas.
The problem with the data of Henderson and Demond [75] is that they have not considered that each individual Fe 0 atom corrodes and produces both volumetric expansive precipitates and H 2 gas [35].Moreover, the pore filling by Fe precipitates was evaluated using tabulated molar volume values (ν = 7.6 cm 3 mol ´1 for Fe 0 ), which are not necessarily relevant for Fe 0 particles confined in a packed bed (Fe 0 filter).For example, the coefficient of volumetric expansion (η = V oxide /V iron ) for magnetite (Fe 3 O 4 ; ν = 45.0 cm 3 mol ´1) using ν values is 5.0, while the η value for confined system is close to 2.2 [60].This combined with the lack of appropriate k iron values has diminished the value of the models presented.

The True Value of Mathematical Modeling
Mathematical modeling constitutes the third pillar of science and engineering, achieving the fulfilment of the two more traditional disciplines: (i) theoretical analysis; and (ii) experimentation [101].Mathematical models explore new solutions in a very short time period.This increases the speed of innovation cycles.However, this is only possible when theoretical analysis and experimentation are perfectly performed.The presentation herein has recalled that for Fe 0 filters, both theoretical analysis [102,103] and experimentation [104] have been unsatisfactory.This suggests that there is a huge gap between calculations and understanding [105].Admittedly, all modelers are not chemists nor electrochemists, but even in the absence of a real cross-disciplinary approach, self-critical scientists should have realized that something fundamental is missing.Moreover, consultations with material and corrosion engineers would have been necessary in the fitness of things to save millions of money (mostly from tax payer) spent in intensive research on a biased basis.The damage is huge, as the credibility of modeling could be questioned [105].This communication advocates for saving the credibility of mathematical modeling through the generation of credible data for Fe 0 filters.
The true value of mathematical models was recalled by Grauer [106] by the following wording: "theory and models cannot be validated in the strict sense but only refuted".The presentation herein has collectively refuted all modeling efforts regarding the design and operation of Fe 0 filters for the past two decades.The reason is the very poor theoretical analysis.The equation currently used for k iron (corresponding to Equation ( 1)) is simply wrong, and the reductive transformation of contaminants is at best a side process (Equations ( 3) and ( 4)) (Section 2).
Better models are possible, they should be based on a systematic analysis of the Fe 0 /H 2 O system.A sound analysis [102,103] has demonstrated that contaminants are removed by adsorption, co-precipitation and size exclusion.Accordingly, chemical reduction when it occurs is not responsible for (quantitative) contaminant removal and is rather a side reaction occurring within the oxide scale in the vicinity of Fe 0 and not at its surface.The evidence that the surface of Fe 0 and oxides changes with time and the Fe 0 surface is not accessible to the contaminant question of the normalization of rate constants to the surface area [107].Lastly, k iron values are the pillar for modeling the temporal realization of permeability loss.These values are yet to be determined in well-designed long-term experiments.

Messages to Anonymous Collaborators
There is evidence in the Fe 0 literature that the aspects challenged herein are difficult to accept [108][109][110][111][112].However, this argumentation corresponds to mainstream science (chemical thermodynamics).The first message to an anonymous collaborator (a reader) is "no single reference is a quality guarantee".Accordingly, sound scientific arguments should justify each reference.Moreover, the rationale for preferring a work to another should be known and named, if applicable.
The second message is for a reviewer either for a submitted manuscript or a grant proposal.An author/applicant is a colleague and needs collegial remarks to improve his/her manuscript/proposal.A minimal requirement is that reviewer comments focus on points that need improvements or are unacceptable [113][114][115].
The third message is to the attention of funding agencies.Each applicant should have the opportunity to write some comments on the reviewer's evaluation before the final decision is made.This is of particular importance when the majority of available comments is negative.Admittedly, this could/would lengthen the review process, but this is the way to greater fairness.This procedure is already adopted by some agencies, but should be universally adopted.The reason is that the best evaluator could not recognize an innovation at first glance.
The fourth and last message is for everyone.Research on water treatment and environmental remediation has been wrongly directed from the beginning onward.Warnings from chemists [116][117][118][119] were simply ignored.Whenever a mistake is identified, starting on a new basis is always a good decision.Individual researchers already went down this path [10,119].As an example, the author of this communication has published on reductive precipitation of U VI by Fe 0 [120], then on reduction as a removal mechanism, until 2010 [14], only with [121] and hints from anonymous reviewers did he realize that at concentrations relevant for safe drinking water, reduction cannot be a stand-alone removal mechanism for any contaminant [78,122].For environmental remediation, chemical reduction (degradation) may be sufficient when reaction products are readily degradable, for instance when nitrobenzene is quantitatively reduced to aniline.For safe drinking water provision, even reduction products (here, aniline) must be removed [123][124][125][126].

Concluding Remarks
Iron corrosion is a stochastic, probabilistic phenomenon that requires interdisciplinary concepts, including chemistry, electrochemistry, hydrodynamics, materials science, metallurgy, physics and surface science.From a pure chemical perspective, the thermodynamics and kinetics of the involved processes must be understood in order to effectively design and fabricate materials to be used for optimal (efficient and affordable) applications.This communication has recalled that the chemistry of the Fe 0 /H 2 O system is being incompletely considered while using Fe 0 as a remediation material.It is particularly disappointing/frustrating that the principles of corrosion as already understood and largely disseminated in the broad scientific literature have been simply ignored.The net result is that a fictive reaction (Equation ( 1)) has been used for dimensioning Fe 0 filters for more than two decades (25 years).
This communication has also recalled that mathematical modeling is the third and only the third pillar of science and technology.The two first pillars are theoretical analysis (system analysis) and experimentation.The best model will not correct mistakes in system analysis or experimentation.It is clear that Fe 0 filtration technology requires more accurate models that take into account the various mechanisms that underpin the process.The year-long experimentation on iron corrosion (prior to the advent of Fe 0 filters) has demonstrated that uniform corrosion assumed by almost all models is an over-simplification.In other words, even considering reliable values of k iron will only describe how Fe 0 filters would behave considering the assumptions made (without biotic processes).This evidence confirms/suggests that (independent, where necessary) monitoring of the performance of Fe 0 filters is mandatory.
To conclude, Rolf Grauer will be paraphrased as follows: It would make more sense to devote more time and energy to determine k iron values than to develop sophisticated, but unreliable numerical models.It is clearly understood that no particular Fe 0 material is a universal solution for all contaminations.Each and every case has to be considered in its totality before a decision is made on the proper material, characterized by its k iron value.Therefore, a sort of database for k iron values is needed.Establishing such a database is a scientific challenge and not just laborious work.

Figure 1 .
Figure 1.Changes of the number of particles (N0) making up 1 kg of Fe 0 and the corresponding number of atoms at the surface (NA) as a function of the d values.While the N0 values exponentially decrease with increasing d, the NA values increase.

Figure 1 .
Figure 1.Changes of the number of particles (N 0 ) making up 1 kg of Fe 0 and the corresponding number of atoms at the surface (N A ) as a function of the d values.While the N 0 values exponentially decrease with increasing d, the N A values increase.

Figure 2 .
Figure 2. Side view of a single Fe 0 /sand water filter comprising five sampling ports.To optimize the efficiency of the filtration unit, the effluent should be clarified and deaerated before being introduced into the first column.A simple device for clarification and deaeration is a slow sand filter [78].

Figure 2 .
Figure 2. Side view of a single Fe 0 /sand water filter comprising five sampling ports.To optimize the efficiency of the filtration unit, the effluent should be clarified and deaerated before being introduced into the first column.A simple device for clarification and deaeration is a slow sand filter [78].

Figure 3 .
Figure 3. Side view of a series of the Fe 0 /sand water filter comprising five individual columns and sampling valves.To optimize the efficiency of the filtration unit, the effluent should be clarified and deaerated before being introduced into the first column.A simple device for clarification and deaeration is a slow sand filter [78].

Figure 3 .
Figure 3. Side view of a series of the Fe 0 /sand water filter comprising five individual columns and sampling valves.To optimize the efficiency of the filtration unit, the effluent should be clarified and deaerated before being introduced into the first column.A simple device for clarification and deaeration is a slow sand filter [78].

Table 2 .
Values of k iron used by Moraci et al. [19] and the corresponding t 8 values.Calculations are made for d = 1.0 mm and m = 1 kg.

Table 2
also summarizes the time to complete material depletion or Fe 0 exhaustion (t 8 ) for the k iron values used by Moraci et al.

Table 3 .
Values of the number of particles (N 0 ) making up 1 kg of Fe 0 as a function of the d values.The corresponding particle area (A p ) and the number of atoms at the surface (N A ) are specified.