Designing laboratory metallic iron columns for better result comparability 1 
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Noubactep C.*(a,c), Caré S.(b)
(a) Angewandte Geologie, Universität Göttingen, Goldschmidtstraße 3, D - 37077 Göttingen, Germany; 
(b) Université Paris-Est, Laboratoire Navier, (ENPC/IFSTTAR/CNRS), 2 allée Kepler, 77420 Champs sur Marne, 
France; 
(c) Kultur und Nachhaltige Entwicklung CDD e.V., Postfach 1502, D - 37005 Göttingen, Germany. 
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* corresponding author: e-mail: cnoubac@gwdg.de; Tel. +49 551 39 3191, Fax: +49 551 399379 
Abstract 
Despite the amount of data available on investigating the process of aqueous contaminant 
removal by metallic iron (Fe0), there is still a significant amount of uncertainty surrounding 
the design of Fe0 beds for laboratory testing to determine the suitability of Fe0 materials for 
field applications. Available data were obtained under various operating conditions (e.g. 
column characteristics, Fe0 characteristics, contaminant characteristics, oxygen availability, 
solution pH) and are hardly comparable to each other. The volumetric expansive nature of 
iron corrosion has been univocally reported as major drawback for Fe0 beds. Mixing Fe0 with 
inert materials has been discussed as an efficient tool to improve sustainability of Fe0 beds. 
This paper discusses some problems associated with the design of Fe0 beds and proposes a 
general approach for the characterization of Fe0 beds. Each Fe0 column should be 
characterized by its initial porosity, the composition of the steady phase and the volumetric 
proportion of individual materials. Used materials should be characterized by their density, 
porosity, and particle size. This work has introduced simple and reliable mathematical 
equations for column design, which include the normalisation of raw experimental data prior 
to any data treatment. 
Key words: Deep bed filtration, Operational parameters, Results comparability, Water 
Filtration; Zerovalent iron. 
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Metallic iron (Fe0) as reactive medium for aqueous contaminant removal has been intensively 
investigated during the last two decades [1-6]. These studies have demonstrated the potential 
of Fe0 for use in (i) subsurface permeable reactive barriers [1], (ii) above ground wastewater 
treatment [3,5], (iii) household water filters [7-10], and (iv) drinking water treatment plants 
[11-13]. The fundamental mechanisms of contaminant removal in Fe0 beds are adsorptive 
size-exclusion and co-precipitation [5,6,13-19]. 
Data for pilot- and full-scale remediation scheme are mostly obtained from laboratory 
columns [20-22]. Laboratory column studies are in turn conventionally designed based on 
batch treatability studies [21,23,24]. A major problem of available data from batch studies is 
the poor comparability of results from different laboratories using different conditions. Most 
experimental conditions are not relevant for field situations [25,26]. For example, only 
shaking intensity lower than 50 m-1 could enable the formation of a universal oxide-scale in 
the vicinity of the Fe0 surface as observed in column studies and in full-scale barriers [25]. A 
careful look behind published data on laboratory column experiments ([27-32]; see Tab. 1) 
also demonstrates large variability in the experimental design. General design procedures are 
not available. Differences in design procedures may cloud interpretations of reported data. 
Therefore, any effort to ensure the comparability of laboratory results over time and space 
would accelerate the development of the Fe0 remediation technology. 
The objective of the present communication is to improve the comparability of laboratory 
column results by offering the scientific community tools for a common basis for the design 
of Fe0 beds. Previous theoretical works [9,31,32] have demonstrated that mixing Fe0 and other 
materials (gravel, pumice, sand, quartz) is the prerequisite for long service life. This mixture 
should be characterized by the volumetric proportion of Fe0 (Fig. 1) and other materials 
(additives) and the initial porosity [32]. The specific objective of this communication is to 
establish equations for the evaluation of the mass of the materials to be used. 
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2 Basis for comparable results 52 
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Cylindrical columns usually used for laboratory experiments primarily differ in their size 
(diameter * length). For example, columns with 5 cm internal diameters exist with lengths 
varying from 30 to 100 cm (Tab. 1). Completely filling the six different columns from Tab. 1 
with reactive materials (e.g. Fe0) will yield 0.2 to 9.8 kg of Fe0 for the experiment. The 
question is how to objectively compare results obtained with various amount of the same 
materials? The situation is exacerbated when the materials are different (particle size, shape, 
chemical composition or generally intrinsic reactivity). When material mixture should be 
performed, the rationale for purposeful mixing should be developed. 
Using the material apparent specific weight tabulated by Noubactep and Caré [9], Tab. 1 
clearly shows that a given volume (e.g. Vsolid in the same column) is occupied by a mass m of 
pumice, 4.14*m of sand, and 12.19*m of Fe0. The coefficients are the ratios of the apparent 
specific weights (ρi/ρj). This observation confirms that the volumetric ratio is the sole 
appropriate approach to design column studies. Accordingly, an approach to have comparable 
results could be to fix the Fe0 volume. A given Fe0 volume corresponds to various heights 
depending on the column internal diameter. Accordingly, beside used Fe0 mass 
(corresponding to a volumetric fraction of solid), the column dimensions should always be 
specified. Three examples are given below for illustration.  
In the laboratory, the Fe0 amount is commonly given in weight (g or kg). Therefore, a 
practical approach is to fix a mass of Fe0 (m0) which is likely to enable observable effects 
within a reasonable time (e.g. 6 weeks). 
- An experiment is designed to compare the reactivity of different Fe0 materials. Parallel 
column experiments have to be conducted in which Fe0 is the sole variable and the same mass 
(m0) is used in individual columns.  
- An experiment is designed to compare the impacts of chloride (Cl-) and sulphates (SO42-) on 
the efficient of a Fe0 for methylene blue (MB) discoloration. The three following parallel 
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experiments could be conducted with the mass m0 of a Fe0 sample: (i) MB in deionised water, 
(ii) MB in a Cl
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- solution, and (iii) MB in a SO42- solution. The MB concentration is the same 
in all experiments, Cl- and SO42- solutions have the same equivalent concentration. 
- An experiment is designed to compare the impact of mixing Fe0 with additives. The 
reference system should be the mass m0 of Fe0, and volumetric proportions of Fe0 have to be 
replaced by appropriated additives. Tab. 1 shows that each column is characterized by a 
constant pore volume which is the external or inter-granular porosity. For porous materials the 
internal porosity or intra-granular porosity has been discussed as a storage room for in-situ 
generated corrosion products and thus a tool to sustain Fe0 reactivity [9,10,32]. Similarly, 
mixing Fe0 and non-porous inert additives is beneficial for the system because inert material 
will not contribute to pore filling or filter clogging. 
The next section will establish some general equations to support design operations. 
3 Mathematical equations for column design 
A hypothetical cylindrical filter having an inner diameter D, a length L, and a reactive zone 
hrz is considered. The reactive zone is the fraction of L (L > hrz) containing the reactive 
material, possibly mixed with selected additives. The filter is filled by spherical particles 
(reactive materials and non-reactive additives) having a constant diameter d. Considering the 
granular material as composed of mono-dispersed spheres subjected to soft vibrations, the 
column compactness (or packing density) C ranges between 0.60 and 0.64 for a random close 
packing  but it is generally considered to be equal to 0.64 (limit value). It can be noticed that 
the value of the compactness depends on various parameters as the distribution size of 
particles, their shape [33-34]. The theoretical value of C = 0.64 is strictly valid for particles 
with spherical shape and similar sizes. It is assumed in this study that ratio of cylinder 
diameter (D = 2*R) to particle diameter (d), β = 2*R/d is optimal for axial hydrodynamic 
dispersion [36,37]. 
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The volume of the reactive zone (Vrz), the volume of solid (Vsolid), the volume of inter-
granular pores (V
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pore), the volume of individual solids (Vi) with the apparent specific weight 
ρi, and the thickness of the reactive zone (hrz) are given by Eq. 1 through Eq. 6: 
  Vrz = π*D2*hrz/4       (1) 
 Vrz = Vsolid + Vpore      (2) 
 Vsolid = C*Vrz       (3a)  
 Vpore = (1 - C)*Vrz      (3b) 
 Vsolid = ΣVi = Vsolid1 + Vsolid2 + Vsolid3 + …   (4) 
 Vi = mi/ρi        (5) 
  hrz = 4Vrz/ π*D2 = 4Vsolid/(C*π*D2)    (6) 
3.1 Volumetric solid fractions in the reactive zone 
Replacing Vsolid in Eq. 2 by its expression from Eq. 4 yields: 
Vrz = Vsolid + Vpore = Vpore + ΣVi ⇒ αpore + Σαi = 1  (7) 
where αpore and αi are the volumetric fractions of the inter-granular pores and of the individual 
solid phase “i” in the column respectively. The fractions are related to the volume of the 
reactive zone Vrz.( αpore = Vpore/Vrz and  αi = Vsolid i/Vrz).  
Eq. 7 suggests that Σαi  is necessarily equal to C. Thus, Eq. 2 should be written: 
  Vrz = Vsolid + Vpore = Vrz (αpore + Σαi)   (8) 
For instance, for a system containing a mixture of four solid phases, Eq. 7 should read: 
  αpore + α1 + α2 + α3 + α4 = 1     (8a) 
or   α1 + α2 + α3 + α4 = 1 - αpore = C    (8b) 
Eq. 8 is very important for the calculations of the amounts of individual additives to achieve 
wished material mixtures as will be discussed in the next section. Eq. 8b suggests that αi  is 
necessarily a fraction of C. Thus, a simple rule of proportion can be established to calculate αi 
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for each proportion Pi of the solid phase. C necessarily corresponds to 100 % solid. The 
relation between α
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i  and Pi is given by Eq. 9: 
  αi = C*Pi/100       (9) 
Tab. 2 gives some values of αi for selected relevant Pi values. For example, if a quaternary 
system should be made up of 40 % of material A, 30 % material B, 20 % material C and 10 % 
material D, the coefficients to be used are: 0.256, 0.192, 0.128 and 0.064 respectively. A 
quaternary system seems to be strange or complicated. However, such a system could 
comprise Fe0 as basic reactive material, MnO2 to sustain Fe0 reactivity, pumice as storage 
solid and quartz as non-porous inert filling material. 
3.2 Initial porosity of reactive the zone 
In the case of non porous spherical particles, the initial porosity of the reactive zone Φ0 is the 
inter-granular porosity αpore and is given by Eq. 10 [32]. 
Φ0 = 1 – C       (10) 
If individual particles are porous, the intra-granular porosity should be considered [32]. In this 
case the initial porosity should read: 
Φ0 = (1 – C) + Σαiφi      (11) 
where C is the compactness of the reactive zone, αi the volumetric fraction of the solid i (Tab. 
2) and φi its internal porosity. 
Equations 1 to 11 are the basis for purposeful experimental design as will be discussed below 
for selected cases. 
4 Designing some Fe0 systems 
4.1 A four component system 
For the design of a quaternary system of Fe0, sand, pumice and MnO2, Eq. 8 can be used: 
  Vrz = Vrz (αpore + αFe + αsand + αpumice + αMnO2) 
Vrz = αpore* Vrz + αFe*Vrz + αsand*Vrz + αpumice*Vrz + αMnO2* Vrz
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Vrz = Vpore + VFe + Vsand + Vpumice + VMnO2  
Assuming Vrz = 1000 mL, αFe = 0.192 (PFe = 30 %), αsand = 0.256 (Psand = 40 %), αpumice = 
0.128 (Ppumice = 20 %), and αMnO2 = 0.064 (PMnO2 = 10 %), the volume of the materials are 
192, 256, 128 and 64 mL respectively and Vpore = 360 mL. 
Using Eq. 5 (mi = ρi*Vi), the needed mass of each material can be calculated. Results showed 
that 1498 g of Fe, 678 g of sand, 82 g of pumice and 224 g of MnO2 will be used and 
homogeneously mixed to design the desired column. 
The initial porosity of the resulted column is given by Eq. 11 
Φ0 = (1 – C) + αFeφFe + αsandφsand + αpumiceφpumice + αMnO2φMnO2
But Fe and sand (quartz) are non-porous, therefore Φ0 is given by: 
Φ0 = (1 – C) + αpumiceφpumice + αMnO2φMnO2
Using values above (αpumice = 0.128 and αMnO2 = 0.064), φ = 0.80 (80 %) for pumice, and φ = 
0.25 (25 %) for MnO2, give an initial porosity of 0.48 (vs. 0.36 in a pure Fe0 column).  
This example shows an increase of the initial porosity by 33 % for the given mixture. 
4.2 Working with a constant Fe0 mass 
To work with a constant Fe0 mass, the volume (VFe) occupied by the given Fe mass is 
calculated using Eq. 5. This volume represents a certain fraction of solid in the filter (αFe in 
Eq. 8a). Knowing Vsolid, the volume of the reactive zone Vrz and its thickness hrz can be 
deduced using Eq. 3c and Eq. 6. 
It is obvious, that hrz depends on the inner diameter of the filter. Accordingly, the simplest 
way to investigate the effect of bed thickness on the efficiency of Fe0 beds is to work with a 
constant Fe0 mass, representing a fix volumetric percentage of solid and using columns of 
various internal diameters (Di). 
Working with a constant Fe0 mass can be regarded as the most powerful tool to achieve 
comparable results. For example, laboratory column experiments could be routinely 
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performed with 100 g of Fe0 representing 30 vol-% of the solid in the reactive zone. 
Calculations show that the reactive zone will occupy a volume of 20 mL. To have such a 
volume using columns with inner diameters D
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1 (2.0 cm), D2 (2.6 cm) and D3 (5.0 cm), the 
column length should be 6.37, 3.77, and 1.02 cm respectively. All columns of Tab. 1 satisfy 
this basic condition. However building an homogeneous 1.02 cm layer of “Fe0 + additive” 
could be a difficult task. While repeating the calculations above with 250 g Fe0 results show 
that needed column lengths are 15.93, 9.43, and 2.55 cm respectively. While column 1 (D = 2 
cm, L = 12 cm) is no more applicable, filling column 3 (D = 5 cm) with only 2.55 cm of 
homogeneous mixture could still be difficult to achieved. Therefore and objective could be a 
minimum reactive zone length of 5 cm. To achieve this thickness, a Fe
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0 of 500 g is needed for 
column 3. This is necessarily coupled with longer experimental duration. As a result, it is 
suggested that columns with more than 3 cm internal diameter are not suitable for short term 
laboratory experiments. This suggestion is coupled with the desire to save Fe0 costs in 
columns and to shorten experimental durations. 
4.3 Working with a constant initial porosity 
For column experiments performed with a constant Fe0 mass (e.g. 100 g), using various 
additives could enable a constant initial porosity (Φ0). The aim could be for example to 
experimentally quantify the impact of MnO2 on Fe0 bed’s hydraulic permeability. The length 
of the reactive zone will vary as a function of the porosity of the tested additive. Eq. 11 (Φ0 = 
(1 – C) + Σαiφi) should be solved while fixing one or two variables. 
For example, the reference system uses Fe0 (100 g representing 50 vol-%) and a limestone 
with φlime = 25 %. A second system having the same initial porosity (Φ0) and been made up of 
Fe (φFe = 0 %), quartz (φquartz = 0 %) and pumice should be designed. Which pumice amount 
should be used? 
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For the reference system, αFe = 0.32; φFe = 0; αlime = 0.32; and φlime = 0.25. Calculations give 
Φ
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0 = 1 – C + 0.32*0.25 = 0.44. Now, Eq. 11 (Φ0 = 0.44) should be written for the unknown 
system and solved for φpumice, given αFe = 0.32 (or αquartz + αpumice = 0.32). That is, with φFe = 
φquartz = 0: 
Φ0 = 0.44 = 1 – C + αFeφFe + αquartzφquartz + αpumiceφpumice  (11a) 
  αpumice = 0.08/φpumice       (11b) 
The pumices to be used are materials for which Eq. 11b and the fundamental conditions αquartz 
+ αpumice = 0.32 and φpumice < 0.9 are respected. There are certainly a large number of possible 
solutions but the appropriate solution will be dictated by pumice’s availability. Table 3 
summarizes 5 appropriate solutions corresponding to φpumice values varying from 0.33 to 0.80.  
Having the αpumice (and αquartz) the volumes and the masses can be derived and used as 
described above. 
5 Concluding remarks 
To date, the equivocal results published on contaminant removal in Fe0/H2O systems 
demonstrate that the physico-chemical mechanisms of the remediation process still remain 
unclear [38]. Available data were produced and interpreted based on the concept that Fe0 is a 
reducing agent [1-4]. On the other side, available data are characterized by the diversity of 
experimental conditions under which they are obtained (Tab. 1). This situation is not 
favourable for reliable data comparison. In particular, further laboratory column studies 
aiming at optimising field Fe0 bed design efforts should be acquired under reproducible 
experimental conditions. 
The present theoretical study has initiated a new path to an harmonized experimental protocol 
for column experiments. It is proposed that 100 g or 250 g of Fe0 is used in a volumetric 
proportion not larger than 50 %. The equations for material mixtures are established. It is 
hoped that researchers will use the developed tools to avoid inconsistent results which are 
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most likely the product of inaccurate experimental designs. For example, while bed clogging 
has been reported as the major drawback of the Fe
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0 technology, most researchers have used 
experimental designs favouring column clogging (Fe0 > 60 vol-%) [32].  
Once the mass of Fe0 and its volumetric proportion are fixed several other factors can be 
purposefully discussed. For example, the impact of: (i) the Fe0 average particle size, (ii) the 
solution pH, (iii) the water composition, (iv) water flow velocity. In all the case the 
description of the experimental protocol should include and extensive description of used 
materials (density, porosity, measured bed porosity). Finally, because clogging is the major 
problem of Fe0 beds, expertise from other branches of environmental science dealing with 
porous media clogging could be helpful for proper Fe0 bed design. In particular, much 
impetus could come from the impact of bio-clogging on the evolution of the porosity of 
constructed wetland [39-42]. 
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343 
344 
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 14
Table 1: Variability of the operational conditions for column experiments as illustrated by 
material masses likely to be used in six different columns. D is the internal diameter of the 
column and L its length. It is assumed that the entire column volume is filled by spherical 
particle of Fe
344 
345 
346 
347 
348 
0, sand or pumice in an ideal cubic packing (C = 0.64). 
 
D L Vcolumn Vsolid mFe msand mpumice Ref. 
(cm) (cm) (cm3) (cm3) (kg) (kg) (kg)  
2.0 12 37.7 24.1 0.19 0.06 0.015 [27] 
2.6 40 212.5 136.0 1.06 0.34 0.087 [28] 
4.1 25 330.0 211.0 1.60 0.60 0.135 [29] 
5.0 30 589.3 377.1 2.94 0.94 0.241 [30] 
5.0 50 982.1 628.6 4.90 1.57 0.402 [31] 
5.0 100 1964.3 1257.1 9.81 3.14 0.805 [32] 
349 
350 
351 
 
 
 15
Table 2: Relation between the volumetric fraction (αi) of solid materials in the column (αpore 
= 0.36) and their volumetric percent (P
351 
352 
353 
354 
i) as solid. αi is obtained by a rule of proportion 
relative to (αmax = 0.64 corresponding to 100 % solid). α values are very useful for multi-solid 
system designs (see text). 
Pi 0 10 20 30 40 50 60 70 80 90 100 
αi 0.00 0.064 0.128 0.192 0.256 0.320 0.384 0.448 0.512 0.576 0.640 
355 
356 
 
 16
Table 3: selected appropriate solutions for Eq. 11b. 356 
357  
αquartz 0.08 0.13 0.16 0.19 0.22 
αpumice 0.24 0.19 0.16 0.13 0.1 
φpumice 0.33 0.42 0.50 0.62 0.80 
358 
359 
 
 17
359 
360 
361 
362 
363 
364 
 
Figure 1: Evolution of the material weight percent in a ternary system Fe0/sand/pumice as the 
initial 50:50 sand:pumice mixture (vol) is progressively amended with Fe0. The sand:pumice 
volumetric ratio is kept constant during the whole simulation. It is evident that due to 
difference in densities the weight percent variation is different for individual materials.  
 
0 25 50 75 100
0
25
50
75
100
 Fe0
 sand
 pumice
m
at
er
ia
l /
 [w
t-%
]
Fe0 / [vol-%]
 365 
366   
 18