BTC Parameters

BTC Solute-Transport Parameters for three Sediments

Mohamed Fahmy Hussein
Cairo University, Egypt

Abstract
Solute transport is concerned with irrigation and soil salinization, fertilization and pollution.
A locally manufactured fraction-collector was used for BTC runs on three disturbed sediments from
Egypt to get transient chloride-transport parameters under steady-state saturated flow. 30-cm long
columns were packed with dune Sands, Nile-bank sediments, and clayey Calcareous-aggregates.
Experimental BTC data were fitted to two analytical solutions in CfitM code that solves the
CDE equation corresponding to boundary conditions. The parameters included the retardation
factor, Peclet number, longitudinal dispersivity, hydrodynamic dispersion coefficient and tortuosity.
RETC was used to get the hydraulic parameters by fitting the samples’ pF data.
Sands showed retardation factor of about unity (no reaction), intermediate values for both
Peclet number (49-61) and dispersivity (0.49-0.62cm) (moderate leaching-efficiency). Smaller
dispersivity (better leaching) would be expected if saturation was realized. Nile-bank sediments
monitored high Peclet number (117-180), small dispersivity (0.17-0.26cm) (efficient leaching) and
slightly less than unity retardation-factor (some anion exclusion). The Clayey-aggregates have
shown wide range of small Peclet numbers (9-34), large dispersivity (0.90-3.4cm) increasing with
aggregate size (low leaching in large aggregates) and retardation factor significantly less than unity
(rapid exit due to high anion-exclusion). In contrast to Clayey-aggregates, the high Peclet number
of the Nile-bank and Sands reflects dominant mass-flow transport compared to dispersive transport.

Introduction
Water percolation into soils induces solute-transport and soil modifies the process. Aquifers
receive recharge accompanied by solutes and pollutants passed via soil. Farmers are interested in
removing salts below the root-zone while retaining nutrients. Mass-flow is a major solute
translocation-mode and dispersion occurs due to differences in pore-sizes whereas diffusion and
chemical reactions also take place. Second-order differential equations describe the phenomena.
With the advent of computer codes, the use of soil columns became a helpful lab tool in studying
solute transport.
Before simulating solute transport in soils, one must get the concerned parameters through
experimentation. The hydrodynamic dispersion coefficient, the retardation factor, the dispersivity,
etc… may be obtained by iterative best fit of the BTC curve. Hydraulic parameters [θ(ψ), K(θ) and
the K(ψ)] are obtained by best-fit of pF, and/or K(θ) data. We used soil columns to follow-up the
change of C/C0 in function of PV of three samples and their dry-sieve size fractions.

Review of Literature
1. Qualitative and Quantitative BTC Techniques
Two major types of column experiments are in use; qualitative and quantitative. The
qualitative (Swarp et al, 1983, Shehata et al, 1983, Timmons, 1984 and Ozturk and Ozkan, 2002) is
used for studying the effect amendments (e.g. Freitas et al, 1984), testing coated fertilizers (Hanafi
et al, 2002) or for detecting the depth to which solutes would be leached (Deverajani et al, 1995),
etc…. In the quantitative technique, the tracer concentration is measured during BTC runs and the
C/C0 is plotted in function of PV.
The popular approach for the non-linear best fit of BTC data is the convection-dispersion
equation (CDE) based on Fick’s second law. Computer codes are useful for analytically solving the
CDE either for the direct problem (finding the BTC corresponding to a known set of physical and
chemical parameters) or for the inverse-problem (finding the unknown parameters corresponding
to the boundary conditions.) In such codes, the presence of immobile water in dead-end pores is
generally ignored.

2. Water Flow Conditions
The CDE model gives good results in the saturated and the close-to-saturation columns
(Mermoud et al, 1991). Constant water-application rate (or constant head) results in a steady-state-
flow, whereas a free pond that gradually drains-out will result in a transient flow. Under all water
flow regimes, solute transport is always transient (Minhas and Sharma, 1989). Under transient flow
the solute will move deeper than under steady-state water flow. Saturated flow enhances rapid Cl
breakthrough and induces a smearing of solute peak in sandy loam soils, Hamid, (1988). Under
unsaturated flow there is early tracer exit and large mixing due to non-completion of displacement
(since velocity is high leading to the increase of the hydrodynamic dispersion that decreases
leaching). It has been shown (Saigusa et al, 1996) that Cl diffusion-coefficient increases with the
increase of the moisture-content and with the diminution of anion exchange capacity. Under
unsaturated flow, if the initial moisture content was low, leaching efficiency is high in small
aggregates (Katou and Akiyama, 1990) (almost no diffusion takes place inside the large aggregates
under transient flow). However, the general role is that when the moisture content is low
dispersivity is high (Peclet number is low) and the leaching efficiency is low (Toride et al, 2003).
Dispersivity will be at its lowest value only at saturation (and the leaching efficiency is at its
highest level). There is no dispersivity when solute-transport is piston-type. Sharp pulse (less
dispersion) takes place under saturated-flow than under unsaturated-conditions (more dispersion).
Higher dispersion (high values for dispersivity and the dispersion coefficient but small values for
Peclet number) indicates the presence of widely different pore-water velocities (poor leaching). The
close–to–symmetrical BTC’s show that immobile-water is trivial (Wierenga and Van Genchten,
1989). Asymmetrical BTC’s for a conservative tracer indicate non-equilibrium process (Beigel and
Pietro, 1999) and strongly asymmetrical BTC (shifted to the right with a broad extended tailing) for
the organic-agrochemicals (measured by 14C labeling) argue for the presence of “non-equilibrium
sorption” and “kinetic decay.”
3. Leaching Efficiency
Anions are more strongly leached than cations (Ferreira et al, 1990) due to anion exclusion
which is important in fine-textured soils (Verma and Gupta, 1989). Anions exit the column early
(before 1 PV) whereas cations breakthrough is retarded. Solute will early exit a saturated column
under low water-flow velocity. Smaller the water velocity, shorter – and more flattened – will be
the bell-shaped BTC of a pulse event. The early exit of solute is a sign of “non-efficient leaching”
(and/or presence of immobile-water in dead-end pores). On the contrary, high pore-water velocity
results in decreasing the time of anion-reaction with soil, increasing solute kinetic-energy and
inducing more dragging of water from micro-pores. This leads to a relative retardation on anions
and makes the bell-shaped pulse narrower and higher (efficient leaching). Jacobsen et al, 1992
mentioned that despite the presence of no significant difference between NO3 and Cl, dispersivity of
Cl was slightly higher (less leached) than NO3. Smaller dispersivity (higher leaching) was observed
for Cl compared to tritium (Porro et al, 1993) due to Cl exclusion and to the cation exchange of H+
of tritiated water. Tritium peak is always shorter and more flattened than Cl peak due to more 3H
dispersion. Mayer et al, (1991) mentioned that Cl dispersion increases as water-velocity increases.
Small dispersivity (α = 0.06 cm) was obtained for Cl in saturated clay-loam under high pore-
velocity (Beigel and Pietro, 1999) indicating high leaching efficiency. Under unsaturated-
conditions, dispersivity is larger than saturated-conditions (lower leaching under unsaturated flow.)
For anions when R >1 this indicates adsorption on soil positive charges (Mayer et al, 1991).
The usual trend is to obtain R<1 (anion-exclusion induced leaching). When R=1 this indicates lack
of solute chemical-reaction with soil. In unsaturated columns, the wetting front moves first
followed by anions then cations (lagged behind depending on selectivity-coefficient, concentration
and water-flux, Zhou-ZhiJun et al, 1999). Cl retardation factor was found to be less than that of
Tritium by 10% due to Cl anion-exclusion (Jacobsen et al, 1992). H+ cation-exchange results in
Tritium lag behind (flattened 3H-BTC to the right of Cl BTC). Length of soil columns do not affect

2

the value of R, but will affect dispersivity (Wierenga and Van Genchten, 1989) since the last is
scale-dependent.
4. Impact of Texture and Structure
Soil texture is impressive on the BTC shape. Sandy soils show symmetrical pulse BTC,
whereas loamy and clayey soils (in particular in presence of Smectites) show asymmetrical BTC for
reactive solutes (e.g. herbicides) indicating low leaching (Gonzalez and Ukrainczyk, 1999). Coarse-
textured soil has non-immobile water whereas heavy soils have significant immobile water and
sorption (so the non-equilibrium models are more successful). BTC asymmetry increases in fine-
textured soil as flux-density increases. In poorly structured clayey soils flow-velocity is slow and
results in early solute exit and increase of mixing (longer time is available for diffusion). In fine-
grained soils the stagnant moisture leads to high mixing (early solute exit, small slope for the BTC,
and poor leaching). Dispersivity under unsaturated-flow was 0.58cm for coarse sand but larger
(1.3-1.9cm) for sandy loam (lower leaching in finer texture), Jacobsen et al, (1992). Dispersivity
increases with the increase of sediment non-homogeneity (Bear and Verruijt, 1987.)
It was observed (Starrett et al, 1995) that chloride leaching from undisturbed soils was twice
larger than that from disturbed columns. A possible failure of the BTC (Mayer et al, 1991) is due to
diffusive solute exchange between inter- and intra-aggregate pores. The main part of the
hydrodynamic dispersion-coefficient is mechanical (due to different pore-sizes). This induces the
deviation of any BTC from the piston-type. Hydrodynamic-dispersion increases in the case of wide
distribution of pore-velocities, the increase of tortuosity and the presence of different velocities in
neighbor pores; the two last factors are associated with fine-grained soils. Katou and Akiyama,
1990 showed that, under unsaturated transient flow, higher dispersivity is obtained with the increase
of aggregate diameter. Large-aggregates monitored high unsaturated-flow velocity and were poorly
leached whereas the fine-aggregates monitored low flow-velocity and were efficiently leached (low
dispersivity). They concluded that inefficient leaching is due to restriction of diffusion within the
large aggregates. Mayer et al, 1991 stated that high pore-velocity in aggregated soil will flatten the
pulse BTC and make it shorter. Disturbed soil will monitor low velocity, low dispersion and long
and sharp pulse BTC, whereas the same undisturbed soil monitors higher velocity, higher
dispersion and shorter and flattened pulse BTC. Well-structured soils have smaller dispersivity
(higher leaching) than weakly structured soils, so dispersivity could be used as a “structure index”.
They added that weakly structured soils have more immobile-water than well-structured soils. For a
layered column (without preferential flow) Porro et al, 1993 reported that water velocity is smaller
(and dispersivity is smaller) than in a uniform column that has a significant bypass flow. This
reflects high leaching in layered soils (keeping in mind that the criterion is the presence, or absence,
of bypass).
Advices (such as the best way to preserve agrochemicals) may be derived from column
experiments. Ressler et al (1998) found that when the agrochemical is applied in the solid-state its
loss will be reduced given that macro-pores are limited to topsoil. It has been reported (LevAnon et
al, 1993) that preferential flow (under plough-tillage or no tillage management) increases
agrochemicals’ movement in soil surface. On the contrary, the reaction between solutes and soil
leads to the increasing water and solute retardation and increases the spatial variability of moisture
and solute distribution across the field (Russo, 1989). Short-cut flow is not well reproduced in the
lab (Booltink, 1995) but may be responsible for 30- 80% of the water reaching soil and enhances
nitrate leaching to groundwater in structured clayey soils. Kluitenberg and Horton (1990) had
shown that solute application method (solute boundary conditions) has a net effect on the BTC that
diminishes with the increase of macro-pores. The transport of oocysts (of certain protozoa that
gives the waterborne disease Cryptosporidiosis when passing to groundwater via soils) was
monitored to occur by preferential flow (Darnault et al, 2003). Herbicides are not leached unless
there are macro-pores (Czapar et al, 1992) available for bypass, so disturbed columns may give
misleading conclusions. Unfortunately, in some cases contradictory conclusions would be reported
by the same authors due to differences in the setup and the type of soil material used in column
runs, or through misleading interpretation of the experimental work (Starrett et al, 1995 and 1996.)
3

Materials and Methods
A preparatory stage started with manufacturing of a fraction-collector and its components
(air-compressor, vacuum pump, columns, solution reservoir, etc.). Three soil materials were
selected, namely: sand dune materials (Salam city, northeast of Cairo), Nile-bank sediments (Giza,
Abbas Bridge) and Calcareous topsoil (Noubarya. northwestern flanks of the Nile Delta). Each of
these sediments was size-fractionated using the standard dry-sieve technique.
The sediments and their size-fractions with the highest masses were used in the BTC runs,
Tables 1 and 2 (except for the Calcareous sediment where the finest faction, <0.25mm, was
excluded due to its slow discharge). For each sample, pF data was obtained using a pressure-cocker,
Table 4, where eight volumetric moisture points were defined versus their pneumatic potentials to
get the θ(ψ) function on the pF drying branch. RETC code (RETC version 6.0, IGWMC, 2001) was
used for non-linear best fit of pF data. BTC data was introduced into CfitM (CFITM, IGWMC,
2001). Solute transport simulation would be run using another code (CHEMFLO, v 1.3, 1989) to
solve the direct problem. The studied samples are listed in Table 1 and 2. Dry-sieve results are
given in Figure 1 and Table 2. The effective diameter (d10) and the d60 are the 10% and 60%
cumulative finer, respectively. The CU (=d60/d10) is the “uniformity coefficient.
Table 1 (left) Samples and their dry-sieve fractions, mm
Table 2 (Right) d10, d60 and CU. A high CU value means low uniformity
d10 , mm
Nile-bank 0.058
Salam Sand 0.180
B-Salam Sand 0.190
Calcareous 0.068
B-Calcareous 0.100
d60 , mm
Nile-bank 0.150
1 Nile bank fine earth < 2.000 Salam Sand 0.350
2 Nile bank 0.250 - 0.125 B-Salam Sand 0.410
3 Nile bank 0.125 - 0.053 Calcareous 0.600
4 Salam fine earth < 2.000 B-Calcareous 0.720
5 Salam sand 1.000 - 0.500 CU
6 Salam sand 0.500 - 0.250 Nile-bank 2.586
7 Calcareous fine earth < 2.000 Salam Sand 1.944
8 Calcareous 2.000 - 1.000 B-Salam Sand 2.158
9 Calcareous 1.000 - 0.500 Calcareous 8.824
10 Calcareous 0.500 - 0.250 B-Calcareous 7.200

4

100
90
80
70 Nile bank
60 Salam sand
50 B-Salam sand
40 Calcareous
30 B-Calcareous
20
%
w
h
b
n

10
g
y
r
e
t
f
i

0
10.000 1.000 0.100 0.010
Particle size, mm
Figure 1 Dry-sieve results
3. Models and parameters
Fahmy Hussein (1995) described modeling in environmental hydrology in two components.
First, a “conceptual model” represents our understanding of the system; it includes a set of
assumptions that simplify the natural phenomena. Second, the processes are expressed by
“governing equations” that include certain parameters. Those equations may be solved, under
pertinent initial and boundary conditions corresponding to a specific problem. Initial conditions are
dropped in the steady-state flow problems. The second-order partial-differential equations together
with the algebraic or differential equations representing the initial and/or boundary conditions
define the “mathematical model” which describes system behavior. Under certain assumptions
(applicable for few constrained cases), the governing equations may be analytically solved as
closed-form algebraic equations. The governing equations are solved on computer for more
practical situations. The solution is obtained via finite-differences or finite-elements techniques.
The code is considered as the numerical part of the model. Chen Zhu and Anderson (2002) stated
that “modeling” is a continuous effort based on a concept aided by a computer program. That effort
should not stop at running the software but must start at choosing consistent input data, picking
appropriate program, selecting reasonable results and coherently evaluating the output.
Accordingly, the prediction capability of a model is admitted when the output is, at least partially,
observable or experimentally verifiable. CfitM code (IGWMC, 2001) was used to get the inverse
analytical-solution of the CDE (Van Genchten and Wierenga, 1986) using non-linear best-fit
technique for optimizing BTC parameters. The retardation factor, R, and Peclet number, P, are the
main output parameters. We used two solutions (the constant concentration and the constant flux
models). Most of the parameter given below is scale-dependent (except R, k, and νc.)
3.1 Peclet number, P, dimensionless
It is the ratio of the mass-flow induced transport (by convection with water, νxL) relative
to that induced by hydrodynamic dispersion (expressed by DL). P increases when mass-flow
surpasses dispersive-flow (efficient leaching).
ν
xL (q/θ L
) L
P = = ≈
DL DL α
With νx mean pore-water velocity, cm/hr
L column length, cm
DL effective hydrodynamic dispersion coefficient, cm2/hr
q Darcy velocity, cm/hr
θ Bulk moisture-content, fraction
α Longitudinal dispersivity, cm
3.2 Effective hydrodynamic dispersion coefficient, DL, cm2/hr

5

It consists of “mechanical dispersion” (resulting from the variability of pore-sizes giving
rise to pore-water velocity change) and “molecular diffusion”, D*, (diffusion from a high to a low
concentration point.), which is usually small and neglected.
* νx L
DL = D +
P
ν x d10
DL = + α νx
P
DL ≈ α νx
With D* the effective molecular diffusion coefficient, cm2/hr,
d10 soil particles effective-diameter (10% cumulative finer)
3.3 Effective molecular diffusion coefficient, D*, cm2/hr
It is always lower than the molecular diffusion coefficient for the same solute in free-
water.
* ν
x d10
D =
P
3.4 Retardation factor, R, dimensionless
ρ
k
R = 1 +
θ
Where ρ bulk density, gm/cm3
k distribution coefficient, cm3solution/g soil
R<1 implies anion exclusion, precipitation or immobile moisture. For R>1, k is positive
(cation exchange or anion adsorption). R=1 indicates lack of solute reaction with soil.
3.5 Distribution coefficient, k, cm3 solution /g soil
R-1
k =
ρ/θ
When R<1, k will be negative (solute precipitation or anion exclusion, (-k) is the “specific
anion exclusion” (cm3/g soil) and (1–R) is the “relative volume of anion exclusion”
(dimensionless). The BTC may give a better appreciation of adsorption than batch technique
where soil is mixed with a volume of solution to determine kd by Frundlich equation:
q = kd C1/n
With q concentration of adsorbed solute, mmol/kg soil,
C concentration of added solution, mmol/kg soil
n power term (generally considered as unity)
3.6 Solute velocity, ν c, cm/hr
νx
ν
c =
R
3.7 Omega, ω, dimensionless fraction
It represents the ratio of effective molecular diffusion, D*, in soil to molecular diffusion,
D, in free water (for example D=7.2*10-2cm2/hour for Cl- in free-water). Due to the diminishing of
D* in soil compared to D in free water, omega is always a fraction.
D*
ω
=
D
3.8 Longitudinal dispersivity, α, cm
A length represents soil non-homogeneity due to presence of different particle and void
sizes that define the microscopic configuration of the solid-liquid interface.
(DL - D*) L
α
L = ≈
ν P
x
It may be obtained from the slope of the BTC at its inflection point (at C/C0 = 0.50 in simple
cases), Bear and Verruijt (1987). It may be close to the mean diameter of soil particles if soil was
homogeneous, but it becomes larger when soil is non-homogeneous. It may appear small in
numerical models due to a technical problem known as “numerical dispersion”.
3.9 Tortuosity, τ, dimensionless

6

An expression of the longer flow pathway, Le, compared to straight distance, L, in the
porous medium, so its value is always >1,
φ Le
τ= =
ω L
Where φ bulk porosity, fraction

Results and Discussion
1. Hydraulic behavior and pore-size distribution
The hydraulic data and pF curve parameters were obtained by solving the inverse-problem
(RETC version 6, STANMOD, Van Genuchten model) under the constraint (m = 1 - 1/n). To get
better retention curves fit for some samples, the observed saturation moisture was introduced as a
fixed value. Figure 2 illustrates the pF curves of the studied samples. These curves were used to
explore pore-size distribution (Figure 3). For the Sandy samples, we expected high average pore-
water flow velocity due to the high contribution of macro-pores. In the Nile Set, the average pore-
water velocity is lower than in the Sand. The pF curve of Sand has a sharp shape near air-entry
potential (1/α) whereas the Nile-bank pF curve is smooth. Pore-water velocity distribution is
bimodal in the Calcareous sample and flow velocity was the lowest (dominance of micro-pores.)
The macro-pores (1-100cm suction) is about twice greater in the Sand than in the Nile bank
(the values based on total porosity were ~ 81 and 46%, respectively). However, the values based on
soil volume were comparable (~27 and 23%, respectively). The meso-pores (100-1000cm tension)
are slightly greater in the Nile bank sediment than in the Sand (~15% and 10% of total porosity,
respectively, and 8% and 3% of soil volume, respectively). The micro-pores (>1000cm suction) are
~4 to 6 times higher in the Nile sample (39% of total porosity and 19% of soil volume) than in the
Sand (9% of total porosity and 3% of soil volume.). The pore-size distribution of the raw samples
and their 2 to 3 dry-sieve size-fractions are given in Figure 3.
100
80 macro
60
meso
40
20 micro
0
100000
1 2 3
Salam sand RETC 1 = sand, 2 = 1.0-.05mm, 3 = 0.5-0.25mm
10000 OBS
100
1000 80 macro
60
meso
Nile total RETC 40
100 20 micro
OBS 0
1 2 3
10 1=Nil,2=0.25-0.125mm,3=0.125-0.053mm
m
d
h
u
p
a
c
e
r
s
,

1 Calc. total RETC
100
OBS 80 macro
60
0.1 40
meso
20 micro
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0

θv 1 2 3 4
1=cal,2=2-1mm,3=1-0.5mm,4=0.5-0.25mm

Figure 2 (Right) Retention curves for three main samples. The smooth fitted-lines are obtained by RETC.
Figure 3 (Left) Pore-size distribution relative to total porosity. Sand is in the upper plot. Nile-bank is in the middle plot.
Calcareous is in the bottom plot. In each case, the raw sample is on the left-hand side followed by its size-fractions.

Total porosity was used as the saturation state of the pF data. The differences in pore-size
distribution had serious impact on water flow and solute transport (Darcy velocity, the shape of the
breakthrough curve, solute velocity, retardation factor, Peclet number, etc…). The pore-size
distribution of the Nile bank is towards the fine side contrasting to that of Sand. This favored solute
dispersion by Nile sediment relative to Sand (Soil Science Coarse 107, University California Davis,
7

2004). Tortuosity is high for Nile sample due to its relatively finer texture relative to the Sand
sample, high total porosity and to its low value of omega than Sand. Low omega reflects high
reduction of ion-diffusion in the Nile bank relative to that in free water.
2. BTC Runs
The BTC (Figure 4) was constructed according to observations and the parameters obtained
by iterative fitness in CfitM code (IGWMC, 2001). For the sand samples we observed instability of
leachate discharge (due to non-completer saturation or fraction-collector mal-function) and this had
a serious effect on the cumulative PV and resulted in the deformation of the retardation factor and
the modification of the hydrodynamic dispersion coefficient (but to a less extent). We rectified
these errors by visually averaging the discharge. The Calcareous sample had the lowest and the
most stable discharge in conformity with its heavy texture and structure (aggregation). The Nile-
bank sample had intermediate discharge between that of Sand and that of the Calcareous sample.
Both the Nile-bank and Sand have single-grain structure. Nile-bank had a discharge that showed
slight upward drift during the BTC run, whereas the discharge of Sand had significantly drifted. It
was impossible to attain complete and sustainable saturation in the sand sample during BTC runs.
One of the possible solutions of pseudo-saturation was the use of a column supplied with tracer
solution at column bottom in order to expel air-bubbles. However, we did not adopt this mode for
the following reasons: a) to test the workability of the downward flow that resembles water flow in
natural soils, b) to keep track for simple machining of the columns, c) to keep track for adding dry
salts on column top, and d) bottom-feeding do not fix the fraction-collector mal-function.
Dispersivity showed the lowest values for the Nile bank sediment (and its size-fractions)
whereas its largest values were for the aggregated Calcareous samples (and its size-fractions). The
Sand samples showed intermediate values for α. This observation may be explained on the basis of
soil texture. The Nile bank sediment has about 80% of its mass mostly <0.25mm in diameter
whereas the Sand sample has about 80% of its mass in a coarser size-range 1.00-0.50mm (Figure
1). This means a larger non-homogeneity of Sands compared to the Nile bank. However, high the
non-homogeneity of the Calcareous samples due to aggregation is outstanding. There were large
differences in pore-water velocity distribution in Sand compared to Nile bank. This affected solute
transport through relatively low Peclet number value for Sand compared to Nile-bank.
For the effective hydrodynamic dispersion coefficient, we observed an opposite trend of the
Peclect number in the Sand and Nile bank samples. The reason is not only that the relative
contribution of less dispersion in the Nile bank (giving smaller DL for the Nile-bank sample) but
also that the average flow velocity (νx) is smaller in Nile-bank sample compared to Sand. The shape
of the pF curve for Sand and Nile-bank support that explanation. Figures 2 and 3 show a more
smooth distribution for the Nile bank pore-sizes. The Peclet number was higher for the Nile-bank
sediment than for Sand. This may be seen as a discrepancy. However, it seems that the Sand has a
significant dispersive effect on solute transport exceeding the dispersion imposed by Nile-bank
sediments. High transport of solutes with mass-flow in Sand is justified by the dominance of macro-
pores. However, solute dispersion by Sand is also high. This explains the lower Peclet number
value for Sand compared to the Nile-bank. Despite the finer texture of the Nile bank, the convective
solute transport in Nile bank is greater than in Sand.

8

Rectifed and modeled BTC's with NaCl added to three natural sediments

1
0.9
Sand total
0.8
CfitM
0.7
Nile total replicate 3
0.6
CfitM
C/C0 0.5
Calcareous total
0.4
CfitM
0.3
C/C0=0.5
0.2
0.1
1 PV
0
0.0 0.5 1.0 1.5 2.0

pore volume

Figure 4 Fitted and observed BTC of the three raw samples

Sand has wider pore-size distribution than Nile-bank resulting in a high variation in pore-
water velocity (higher dispersion) in Sand. For the Calcareous aggregates, Peclet number was much
smaller than for Sand. This shows a high contribution of dispersive transport relative to advective
one. The aggregated material has a much higher complicated pore configuration than the single-
grained materials. The small Peclet numbers for the aggregated material may push to expect that DL
parameter might be large. However, this is not the case. This contradiction may be justified by the
significant decrease of average pore-water velocity, νx, which decreased DL much more than its
increase by the decrease of Peclet number. In the case of the smaller aggregates we observed that
Peclet number is increased (less dispersion by the small aggregates that partially tend to work on
the solute as if they were single grains). DL value decreased in the small aggregates not only due to
the increase of Peclet number but also due to significant decrease of average pore-water velocity.

Conclusions
Dune sands showed a close to unity retardation factor and intermediate dispersivity
(0.49-0.62 cm) indicating moderate leaching efficiency under close to saturated flow. Finer single-
grained materials (Nile sediments) monitored small dispersivity (0.17-0.26 cm) (indicating most
efficient leaching), and very slightly less than unity retardation factor (low anion exclusion). For the
Calcareous aggregates, we observed a wide range of large dispersivity (0.90-3.4 cm) (that increased
with aggregate size, indicating lowest leaching for the largest aggregates) and the retardation factor
was significantly less than unity (indicating rapid Cl exit due to significant anion exclusion.)

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9

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Environmental Res. Lab. Ada, OK 74820. EPA, 106 pp. http://www.epa.gov/ada/download/models/chemflo.pdf.
Chen Zhu and Greg Anderson, 2002.
Environmental applications of geochemical modeling. Cambridge University Press. 294 pages.
Czapar et al, 1992.
Herbicides and tracer movement in soil columns containing an artificial macropore. J. of Env. Qual. 21: 1,
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Darnault CJG, Garnier P, Kim YJ, Oveson KL, Steenhuis TS, Parlange JY, Jenkins M Ghiorse WC and Baveye P,
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Prefrential transport of Cryptosporidium parvum oocysts in variably saturated subsurface environments. Water
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Ferreira PA, Robeiro AC, Santos CR dos, Henriques HP and Caixeta TJ, 1990.
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Leaching of chloride in soil columns. Pakistan J. of Sci. and Indust. Res. 31: 2, 97-101.
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11

‫لنمذجة مؤشرات انتقال الذائبات‬ ‫‪BTC‬‬ ‫استخدام تقنية منحنى الجتياز‬
‫أ . د . محمد فهمى حسين‬
‫جامعة القاهرة - كلية الزراعة - قسم الراضى والمياه‬

‫ملخص‬
‫يؤثر انتقال المواد القابلة للذوبان على تملح وتسميد وتلوث الراضى . لتعيين قيم المؤشرات الفيزيوكيميائية‬
‫للنتقال العابر للكلوريد خلل بعض الرواسب المستثارة، مختلفة القوام والبناء، تحت ظروف السريان المائى المستقر تم‬
‫تصميم دارة معملية للتجميع التجزيئ للراشح أسفل أعمدة التربة للحصول على منحنى الجتياز ‪ . BTC‬ملنا كل عمود‬
‫- ٠٣سنتيمتر - بأحد ثلثة رواسب (أو مفصولتها الحجمية ) : ١- رمال كثبان صحراوية، ٢- غرين شط النيل‬
‫بالجيزة، ٣- تجمعات بنائية من سطح تربة طينية جيرية بالنوبارية .‬
‫عقب كل تجربة نفذنا توفيق ً رياضي ً لمنحنى الجنياز ‪( BTC‬علقة التركيز النسبى 0‪ C/C‬بحجم الراشح منسوب ً‬
‫ا‬ ‫ا‬ ‫ا‬
‫للمسام )‪ PV‬عن طريق حل تحليلى - يخص ظروف الحدود - باستخدام برنامج ‪ CfitM‬على الحاسب اللى بغرض حل‬
‫المعادلة التفاضلية الجزئية من الدرجة الثانية الخاصة بانتقال الذائبات بالمواد المسامية (معادلة الحمل والنتشار ‪CDE‬‬
‫المستندة لقانون ‪ Fick’s‬الثانى ) .‬
‫اشتملت المؤشرات (البارامترات ) التى حصلنا عليها على : معامل البطاء، رقم بيكليت، التشتتية الطولية، معامل‬
‫التشتت الهيدروينامى، النتشار الجزئى الفعال، واللتوائية . وقد استخدمنا برنامج ‪ RETC‬للحصول على قيم منمذجة‬
‫للبارامترات الهيدروليكية إستناداً لبيانات المنحنى الرطوبى ‪ pF‬لكل عينة .‬
‫كان من المستحيل عملي ً - خلل تجارب انتقال الذائب - الحفاظ على حالة التشبع الرطوبى برمال الكثبان، وظهر‬
‫ا‬
‫أن معامل البطاء الخاص بالرمال قريب للغاية من الواحد الصحيح (انعدام تفاعلها مع الذائب ) على حين كانت قيمة‬
‫رقم بيكليت متوسطة (من ٩٤ إلى ١٦) وكانت التشتتية أيض ً متوسطة (من ٩٤.٠ إلى ١٦.٠سنتيمتر) مما يعنى أن كفاءة‬
‫ا‬
‫الغسيل معتدلة تحت سريان مائى قريب من التشبع بالرمال (ولكن كان من المتوقع الحصول على قيم صغيرة لمؤشر‬
‫التشتتية للرمال - كفاءة غسيل عالية - فيما لو أن السريان تام التشبع كان قد تحقق . )‬
‫أما غرين شط النيل فقد أعطى قيم ً مرتفعة لرقم بيكليت (من ٧١١ إلى ٠٨١ ) وقيم ً صغيرة للتشتتية (من ٧١.٠‬
‫ا‬ ‫ا‬
‫إلى ٦٢.٠سنتيمتر) مما يعبر عن أعلى كفاءة غسيل شاهدناها بالرواسب المستخدمة، على حين كان معامل البطاء يقل‬
‫عن الواحد الصحيح (وجود قدر من الطرد النيونى بهذا الغرين . )‬
‫وفيما يخص التجمعات البنائية الجبرية الطينية حصلنا على مجال واسع نسبي ً لمدى رقم بيكليت وإن كانت كلها‬
‫ا‬
‫قيم ً صغيرة (من ٩ إلى ٤٣) ، فى حين كان مؤشر التشتتية كبيرً (من ٥٩.٠ إلى ٤.٣سنتيمتر) ، وتزايدت تشتتية المادة‬
‫ا‬ ‫ا‬
‫الجيرية بزيادة حجم التجمعات البنائية (انخفاض كفاءة الغسيل بزيادة حجم التجمعات)، أما معامل البطاء فكان يقل‬
‫بوضوح عن الواحد الصحيح (تعجيل اجتياز الذائبات بفعل وجود قدر ملموس من الطرد النيونى بالتجمعات الطينية‬
‫الجيرية. )‬
‫وعلى النقيض مما شاهدنه فى التجمعات الجيرية (إنخفاض رقم بيكليت) نعتقد أن ارتفاع رقم بيكليت لكل من‬
‫رواسب شط النيل ورمال الكثبان يعنى أن انتقال الذائبات مع حركة كتلة المياه - بهذين النوعين الخيرين من الرواسب‬
‫- هو اللية السائدة بهما، على حين كان انتقال الذائبات عن طريق ميكانيزم النتشار بهما ضئيل، ولكنه مؤثر‬
‫بالتجمعات الطبنية الجيرية .‬
‫من الفوارق الملموسة التى لحظناها بقيم المؤشرات المنمذجة تتضح أهمية ظاهرة انتقال الذائبات بالراضى وما‬
‫لها من مردود على الرى والموارد الرضية، فنرى اعتماد تلك التقنية بشكل منتظم عند التعامل مع رى وتملح وتسميد‬
‫وتلوث الراضى .‬

‫21‬

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