REMOVAL OF COLOIDAL PARTICLES IN SAND ABSTRACTION SYSTEMS (SAS)
*C. Mutsvangwa1, M. Kubare1 and B. Mtaurwa1
1Department
of Civil and Water Eng., National University of Science & Tech., P. O. Box
AC 939 Ascot, Bulawayo, Zimbabwe. cmutsvangwa@nust.ac.zw, FAX: 263-9-286803
Abstract
Sand Abstraction Systems (SAS) are infiltration galleries installed in sandy rivers with
intermittent flow and are common in the Southern Africa region. They are a source of potable
water for small rural communities. It’s a cheap appropriate technology because of the minimal
capital and operation costs. Although the sand acts as a natural filter, the water quality is
susceptible to contamination from continuous inflow of colloidal particles from the various
contaminant sources within the catchment areas of the sandy rivers. The colloidal particles are
an important parameter in assessing the water quality because they act as sorbents for other
hazardous water contaminants. The advection-dispersion equation with the colloidal theory was
applied to relate the time-space removal of the suspended solids. The numerical solution of the
equation was compared with field results. The overall objective was to establish whether the
removal of colloids in sand abstraction systems is consistent with the principles of colloidal
transport. An existing SAS called Nkayi, in the Matabeleland region of Zimbabwe, was used to
test and verify the mathematical model. Samples of the subsurface water from Nkayi SAS were
collected from observation wells and were analyzed for the indigenous colloidal particles. The
simulation results of the model reasonably accounted for the concentration histories of the
indigenous colloidal particles appearing in the samples from the observation wells. The removal
efficiency of the colloidal particles in SAS was found to be above 85% which is very high and the
margin of error of the model was ±0.04. Therefore the advection-dispersion equation with the
colloidal filtration theory can be applied in the modelling of the removal of colloidal particles in
SAS with confidence. At the same time the advection-dispersion model can be localized for any
SAS to predict the water quality at existing and new schemes at low cost, which is the concept
inherent with consideration of SAS.
Key words: infiltration gallery; advection-dispersion; colloidal particles; colloidal attachment
rate coefficient.
* To whom all correspondence should be addressed.
1
INTRODUCTION
Ephemeral sand rivers are a common drainage feature in the semi-arid to arid regions of
Southern Africa. They form a major historical source of underutilized groundwater for the small
rural communities. These systems are known as sand abstraction systems (SAS), or infiltration
galleries and are composed of a naturally deposited porous sandy medium. They are a result of
siltation in areas where soil erosion is prominent, coupled with poor conservation practices.
These systems are recharged by infrequent wet season rainfall, which results in short lived flow
or mere trickles along the surface of the channel. Other sources of recharge include the channelaquifer interactions as well as riverbank inflow. During the dry season the river bed becomes
dry and the deposited sand bed will now act as a natural filter. The naturally filtered water is
potable, although at some schemes disinfection is necessary.
Infiltration galleries which are
installed at depths ranging from 4-8m will collect the filtered water into a sump from which the
collected water is pumped into the distribution network. It’s a low cost technology because of
the minimal capital and operational costs. A typical illustration of an infiltration gallery is
shown in Fig. 1.
Although the water is of high quality, the schemes are susceptible to
contamination especially from suspended particles. Problems have been experienced with a
number of existing schemes where the yield has dropped rapidly due to clogging by suspended
solids (Clanahan, 1977). The mobile colloidal particles in sand abstraction systems mostly
originate from external sources and enter the sandy aquifer through gravity dominated flow and
infiltration of silted surface runoff and mainly during the rain season. The major source of
colloidal particles is from soil erosion which is continuously taking place in the catchment areas.
The colloidal particles are an important parameter in assessing the water quality and are defined
as small particles with dimensions roughly ranging between 1nm and 1μm (Hunter, 1986;
2
Rajagopolan, 1977). They have some unique properties like a very large specific surface area
(>10m2/g) and therefore present important sorbents for other water contaminants. In fact more
contaminants would be attached to colloids than to the solid surface (McDowell, 1986).
River bank
Pump
To tertiary
treatment
and
distribution
plant
Concrete Sandbed top
slab
Phreatic
surface
Pump
Mainfold
Gravel
Tapping
well points
Impermeable
strata
Fig. 1: Typical schematic illustration of a typical SAS.
Source: Modelling the removal of suspended solids in SAS, Kubare and Mutsvangwa (2005)
Such particles provide sites for certain viruses and bacteria and therefore become hazardous
pollutants (Kretzschmar et., al, 1997). They also provide means of transport for nutrients and
toxic contaminants by chemical processes such as adsorption, exchange and precipitation and
bacterial growth (Mutsvangwa et al., 2005; Golterman, 1983; Maunz and Poillon, 1992). Also
suspended particles can protect microorganisms from effects of disinfection. Due to all these
negative impacts on water quality from SAS, there is need to have an understanding on the
removal mechanisms of colloidal particles in SAS. This will enable designers of such schemes
to implement adequate measures to reduce the inflows of colloidal particles in SAS.
Monitoring of the water quality at most SAS is not carried out due to financial constraints and
relevant expertise. The quality also varies throughout the year due to changes in recharge and
surface runoff. Hence a model is required that can predict accurately the movement of the
3
subsurface contaminants in order to take the necessary precautionary measures like disinfection
or other forms of tertiary treatment. Extensive studies have been carried out on the transport and
deposition of colloidal particles in porous media (Elimelech and O’melia, 1991; Ryan and
Elimelech, 1996). However most studies were for deep bed filtration in conventional water and
wastewater treatment (Tan et al.; Iwasaki, 1937; Yao et al, 1971; Rajagopolan and Tien, 1976;
Trussel and Chang, 1999).
Application of filtration theory alone to colloidal transport in
subsurface systems will not be adequate because SAS can be classified as unconfined sandy
aquifers and the topographical geometry of the SAS is different from conventional filters. The
areal extent is large and on average, the effective length is about 500m with depths of about 48m (Mutsvangwa and Kubare, 2005). Evaluating the removal rates of colloidal particles in SAS
therefore strongly relies in numerical models and field data.
The aim of the study was to determine the efficiencies of SAS in the removal of colloidal
particles in existing SAS through field studies and application of colloidal transport equations.
The numerical solutions were compared with field results to establish whether the removal of
colloids in sand abstraction systems is consistent with the principles of colloidal transport
equations. The overall objective was to evaluate their applicability in predicting the water
quality for SAS.
MATERIALS AND METHODS
Theoretical considerations
Suspended solids have sorption properties which are adsorption and desorption. The adsorption
being the attachment or deposition of particles on the solid phase of the porous medium resulting
in a decrease in concentration of the colloidal particles a process described as filtration in water
4
treatment. The desorption is the release of the colloids from the solid phase back into the fluid
flow.
Transport and removal of suspended solid particles in a porous medium is by advection,
hydrodynamic dispersion and interactive processes between colloids and soil surfaces. For
colloidal particles, deposition is negligible at high velocities but is significant when the
concentration of the particles is high. (Grolimund and Borkovec, 2001). The adsorption and
release processes are generally described by a sorption isotherm, which is the relationship
between the suspended solid concentration in the adsorbed phase and in the fluid phase. Also the
adsorption and release process in most of the models are described by a first-order kinetic
process with fixed rate constants and has been found to be accurate in many situations
(Grolimund and Borkovec, 2001; Kretzschmar et., al, 1997). The velocity of flow in SAS is low
and hence particles are carried along the flow streamlines, and therefore the flow can be
considered as one-dimensional unless a transport mechanism causes transport across the
streamline. The contaminant transport in SAS is under saturated flow conditions and the media
is assumed to be homogenous for a single population of suspended solids. The reason being that
it is assumed that the parent material is homogenous in the catchment area where SAS are
located. The one dimensional transport equation for advection-dispersion and for steady-state in
saturated conditions for such a process is given as:
C
 2C
C
 D 2  vp
 kaC
t
x
x
(1)
where C is the colloid concentration in solution, t is the time of travel, x is the travel distance, D
is the hydrodynamic dispersion coefficient for the colloidal particles and is equivalent to the
5
product of the longitudinal dispersivity (αL) and the Darcy velocity, vp which is the average
travel velocity of colloidal particles through connected interstices, ka is the colloidal attachment
rate coefficient. The term kC is the attachment flux governed by the first-order rate law.
Straining has been identified as the fundamental mechanism that is operative in the removal of
suspended solids (Adin and Rebhin, 1977; 1986, Harvey and Garabedian, 1991 and
Tchobanoglous, 1970). The detachment of suspended particles in porous medium is unimportant
compared to the attachment process.
Carbo-Maldonaldo et al. (1998) reported that the
detachment coefficient is practically zero, implying that the particles do not detach significantly
after removal. This has been observed in many colloidal transport experiments (Kretzschmar et.,
al, 1997; Mutsvangwa and Kubare, 2005). Therefore the release process of the suspended
particle can be neglected. Also filter blocking and ripening are neglected.
A number of models have been developed to determine the colloidal attachment rate coefficient
which accounts for the permanent removal of colloids by filtration onto the solid phase (Harter et
al, 2000). For first order deposition kinetics with step-inflow of colloidal particles into the sand
column for a clean filter bed, the clean filter bed coefficient (λo) can be evaluated from Iwasaki
equation (1937):
1
C 
o   ln  f 
L  Co 
(2)
Where L is the column length, Co is the influent colloidal concentration; Cf is the final colloidal
concentration after the breakthrough curve has reached a plateau. For columns with high Peclet
numbers, the colloidal deposition rate coefficient ka can be estimated as:
6
ka  ov p  o
L
tp
(3)
Substituting equation 2 into 3, we get
ka  
1  Cf
ln 
t p  Co



(4)
where tp is the average travel time of the colloidal particles. Yao, Habiban and O’ Melia (1971)
presented an expression which relates the single collector efficiency with the colloidal filtration
expression of Iwasaki (1937) for conventional filters (in packed beds). The equation is given as:
Cf
 ln 
 CO

 

3  1   
 c O L
2  d g 
(5)
Where: =porosity; c=collision efficiency factor; o=single collector efficiency (   o and is
the overall efficiency); dg=representative (effective) grain diameter of porous media.
Substituting 5 into 4, we get:
ka 
1 3  1  
t p 2  d g

 c O L


(6)
The single collector efficiency, o is determined analytically from the trajectory analysis for the
processes of particle diffusion, inertia impaction, and settling (Rajagopolan and Tien, 1976;
Elimelech, 1995), and the expression is given as:
 o  4 As 
1
 3

3
 B T vd p d g 
 Z

2
dp 8
  p   g 
 4H  8

 As 

0
.
00338
A
s

1
 9  v 8 d g 158
 18 
1
3
13
and As is give as:
As 
2  31  

2 1  1   
1
3
5
 31   
3
5

3
 21   
2

7
(8)
1.2
d p2 d g
0.4
v 1.2
(7)
Where: As=porous medium constant; T= temperature in Kelvin; Bz=Boltzman constant;
H=Hamaker constant; =dynamic viscosity of fluid; v-average water velocity; dp=colloidal
diameter; p=buoyant density of colloids; =solution density and =porosity.
Numerical solution
Equations 1 through to 8 were applied in determining the removal mechanisms and the efficiency
in the removal of suspended solids in SAS. The fully implicit finite difference technique was
applied to solve equation 1. The results of the computation were compared with actual filed data
to verify the model application. The solution of the equation will show how the suspended solids
concentration changes at successive distances and time intervals for the entire effective length of
the system. The effective length of the SAS is 500m, and is the distance along the river course
up to which the source of water for gravity drainage is effective. In a bid to avoid meandering, a
straight river reach is selected during the sitting of SAS, which gives the maximum length to
which gravitational drainage is effective (Fig. 2).
Meandering interrupts direct flow of
groundwater to the abstraction point of SAS (Mutsvangwa and Magombeyi, 2002).
Applying the fully implicit finite difference technique and carrying out differencing in space and
time about the point (i, k+1), then the difference approximation of equation 1 becomes:
Ci ,k 1  Ci ,k
t
Or

v
D
Ci1,k 1  2Ci,k 1  Ci1,k 1   p Ci,k 1  Ci1,k 1   K a Ci,k 1
2
x
x
ZCi ,k 1  Ci1,k 1  Ci1,k 1  Ci ,k
Where:   D
t
;
x 2
  vp
t
;
x
(9)
(10)
Z  1  2  K a t  
  
(11)
A grid of six observation wells was applied at Nkayi SAS for the verification process of the
model. For a grid of six observation wells, the matrix equation to solve for Ci ,k 1 for i=1,2…,6 is
8
formed successively by implementing equation (10) at (2,k+1), (3,k+1)….., (5,k+1) and making
use of known initial concentrations at Ci ,k . The resulting general matrix equation becomes:
z 
0
0
 
 0  z  0

 0
0  z 

0
0  z
 0





 
0
0
0
 C1,k 1 
C 
 2,k 1   C2,k 
C3,k 1   C3,k 


=


C
C
4 ,k 1
 4,k 1 

C5,k 1  C5,k 1 


 
C
 6,k 1 
(12)
The additional information comes from the boundary conditions and in this case the first-type or
Dirichlet boundary conditions have been specified at both boundaries. That is to say suspended
solids concentration are known at x=0 or (1,k): k=1,2,… and at x=L or (L,k), when L is the
distance to the last observation well (x=500m). In other words C1,k 1 and C6,k 1 are known.
With these initial and boundary conditions the matrix equation 12 is modified and transformed
into the following matrix equation:
0 
 Z  0
  Z   0 


 0  Z  


0  Z 
 0
C2,k 1  C1,k 1  C2,K 

C  
C3,k

 3,k 1  = 
C4,k 1  

C 4 ,k


 
C5,k 1  C6,k 1  C5,k 
(13)
Model testing and verification
The model was tested on an existing SAS called Nkayi along the Shangani River, in the
Matebeleland Region of Zimbabwe and the study area is shown in Fig. 2 and Fig. 3. The scheme
supplies about 400 households with a daily demand of about 3400m3/day.
9
Water samples were collected from a grid of observation wells along the effective length at
various depths and time (Fig. 3). The observation wells were positioned 100m apart (∆x) along
the river length for the entire effective length of the filter bed. The infiltration galleries of the
scheme are at a depth of 1.9m below the riverbed surface, which is the unconfined aquifer
thickness (ZINWA, 2004). The standard vacuum filtration procedure was carried out with a
gravimetric analysis in the laboratory to determine the concentration of suspended solids.
Fig 2(a) Nkayi SAS Locality map
105.00
Fig 2(b): 3-Dimensional locality map of
Nkayi SAS.
104.00
Makalandoda school
Mazhebe
103.00
Shangani
102.00
101.00
LEGEND
LEGEND
Road
position of SAS
Position of infiltration arm
100.00
IntakeNkayi
well Aerodrome
Shangani river
Nkayi Business centre
Communal homesteads
Police Camp
99.00
98.00
99.00
100.00
101.00
102.00
103.00
104.00
105.00
Fig. 2 Locality map and three dimensional profile of Nkayi scheme.
A sieve analysis was carried out to establish the media characteristics. The analysis showed that
the aquifer is made up of predominantly well-graded coarse sand with fine particles, and the
effective size is 0.42mm. The aquifer can be considered as homogeneous. The filtration velocity
was estimated from Darcy’s law using the medium permeability and hydraulic gradient. The
values of the hydraulic gradient and the permeability for Nkayi were taken as 0.0013m/m and
10
252m/day respectively and are from previous research work (Magombeyi and Mutsvangwa,
2001). The porosity of sandy materials was taken to be 0.35 (Boonstra, 1981).
2
Eastings
80.00
4
3
1
5
6
60.00
9
40.00
11
7
8
20.00 12
10
0.00
0.00
50.00
100.00
KEY
Ground level contour (m)
150.00
200.00
250.00
300.00
350.00
400.00
450.00
500.00
Northings
Water level contour (m)
Observation well
Fig. 3: The study section of the river reach for the Nkayi SAS (Mutsvangwa et al, 2005).
A laboratory longitudinal dispersivity was used and was determined from columns of PVC pipes
of diameter 100mm and length of 600mm. A constant head setup was used to maintain constant
velocity during the tracer tests. The laboratory apparatus used is shown in Fig. 4. The columns
were packed with soil samples collected from Nkayi SAS. The choice of material was such that
no distortion due to corrosion, leakage and external influence would affect conductivity of the
liquid. The soil samples were cleaned using both an acid (HCL) and a base (NaOH) to remove
impurities and to neutralize the soil grains. Sodium chloride (NaCl) was used as the conservative
tracer. A known concentration of the tracer was passed through the sand columns and the
effluent concentrations were determined using electrical conductance from a calibrated curve
obtained from the NaOH solution (Fig. 5). For a pulse input of tracer with a first order decay,
the dispersivity is determined from the solution to the one-dimensional advection-dispersion
equation with all other processes set to zero.
conditions were assumed;
11
In this case, Dirichlet (type-one) boundary
C x  0, t   C1,k  C 0
C  x, t  0   C i , 0
Where: C0 is the concentration in the reservoir. For such boundary conditions, Ogata and Banks
(1961) gave the solution as:
C
Where: v 
 x  vt
CO
erfc
 4vt
2
L

L
t 50
 CO
 x  vt
 x 

erfc
exp 
 2
 4vt
L 
L






(14)
; =average velocity (m/s); t50=time at which 50% of solute has left the column
(sec); C0=influent NaCl concentration (M/L3); C=effluent NaCl concentration (M/L3), t=elapsed
time (sec); L=dispersivity (L).
The results of both the tracer to determine the longitudinal dispersivity and the colloidal filtration
to establish the irreversible filtration coefficient were averaged over several runs and break
through curves were plotted (Fig 6), with the effluent concentrations approaching a constant
maximum value. The laboratory average longitudinal dispersivity, L, for Nkayi SAS was found
to be 6.07cm. Charbeneau (2000) and Bobba(1995) reported laboratory values ranging from
0.01 to 1.0cm whilst Packmen (2000) reported a range of 0.19 to 0.25cm. Harvey (2000)
reported in-situ values ranging from 2.2 to 5.5cm. Also rough approximation of longitudinal
dispersivity is given as (Todd, 2005):
 L  0.1L
(15)
 L  0.0175L1.46
(16)
12
Equations 15 and 16 gave values of 6cm and 0.83cm respectively. The value from equation 15 is
almost similar to the laboratory value which was applied in this research.
Fig. 4: The laboratory Constant head setup to determine the longitudinal dispersivity
The values of the collector efficiency o and collision efficiency c were found to be 6.86x10-4
and 4.48x10-3 respectively from equations 5 and 7. These are typical of laboratory values, which
range from 5.4 x 10-3 to 9.7 x 10-3 (Harvey, 1991). However experimental errors are likely as
careful controlled chemistry is required like pH, which is supposed to be close to neutral and a
high ionic strength of the solution is needed to avoid colloidal media repulsion (Packman, 2000).
From equations 3 to 8, the irreversible filtration coefficient was found to be 0.0077. The
summary of the transport parameters are in Table 1.
With the input parameters in Table 1 the variation of the suspended solids with distance and time
were computed from equation 13. The results of the simulated values of the colloidal particles
13
and field data are shown in Table 2.1.
A comparison of the advection-dispersion model
prediction and field data is also graphically illustrated in Fig. 7, which shows the plotted
regression lines for the model and superposed on field data. The simulated results of the model
reasonably accounted for the concentration histories of the suspended solids appearing in the
samples from the observation wells as demonstrated by a good match between the model and
field results.
The advection-dispersion equation under-estimated the concentration of the
suspended solids at the inlet but became closer at approximately half the effective length. This
can be explained by the fact that the dispersion front is not sharply marked but rather elongated
and shows a gradual concentration variation with distance from the contaminant source towards
the abstraction point. Therefore advection will be dominant at head and this phenomenon, of
advection dominance at shorter distances and advection-dispersion equal dominance at large
distances is also evident in an earlier work (Kubare, 2004). For the transport process under
consideration in this research, flow is laminar and as such dispersion is less pronounced than
advection.
When advection is dominant steeper concentration profiles are encountered as
depicted in the graphical illustration, where the advection-dispersion model simulations are less
steep than the field results.
Conductivity (mS)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
300
350
400
Concentration (mg/l)
Fig.5: Conductivity Calibration curve for NaOH solution
14
450
500
Relative concentration, c/co
1.5
1
Run 1
0.5
Run 2
0
0
100
200
300
400
Time (sec)
Fig. 6: Tracer break through curves for dispersivity
Table 1: Summary of the input parameters.
Parameter
Symbol
Unit
Time interval
∆t
days
Permeability
K
m/day
252.2
Hydraulic gradient
i
m/m
0.0013
Darcy velocity
v
m/day
0.328
Porosity
θ
-
0.35
Colloidal particles velocity
vp
m/day
0.936
Distance interval
Δx
m
100
Longitudinal dispersivity
αL
m
0.0607
Hydrodynamic dispersion coefficient
D
m2/day
0.02
Porous media constant
As
-
52.52
Collision efficiency
αc
-
4.48x10-3
Single collector efficiency
ηo
-
6.86x10-4
Effective grain size
dg
m
4.2x10-4
15
Value
13
The percentage error of the advection-dispersion model is about ±4%, which is quite low. This
high accuracy proves the fact that the detachment process can be neglected in the removal of
colloidal particles in a porous medium and this fact has been highlighted elsewhere (Kubare,
2005; Carbo-Maldonaldo, 1995; Adin and Rebin, 1977; Harvey and Garabedian, 1991). The
difference in concentration from the inlet to the abstraction point will give the efficiency
removal. In this study the overall filter efficiency in the colloidal particles was found to be 85 %
and thus SAS are very good at the removal of suspended solids.
Table 2:
Simulated values of the colloidal particles field data.
Observation
Distance,
SS from field
SS from mode
well
x(m)
results (mg/l)
(mg/l)
2
100
41.35
39.72
1.63
3
200
30.01
26.10
3.91
4
300
19.80
19.06
0.73
5
400
11.92
12.47
0.55
6
500
10.75
-
-
16
Absolute error
45
40
35
Concentration, C (mg/l)
30
25
Advection-dispersion model
Experimental results
20
15
10
5
0
0
100
200
300
400
500
600
Distance, x (m)
Fig. 7: Comparison of model simulations and field results
CONCLUSIONS
The close match between the simulated results and the field data showed that the advectiondispersion equation with the attachment component and excluding detachment can be applied in
modeling the removal of suspended solids in SAS with confidence and within a reasonable
margin of error. The attachment coefficient can also be accurately estimated from the colloidal
filtration theory.
Further research is needed on effects of infiltration of colloidal particles from the banks of the
river section. Also studies need to be carried out on how clogging of the filter bed and the
natural backwashing of the filter system during the rain season will affect the removal
efficiencies. Other areas which can be explored include the simplification in the determining of
the input parameters, which involve the development of simple empirical relationships to
estimate the model parameters.
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The advection-dispersion model thought tested for Nkayi, the procedure and methods outlined
can be localized for any other SAS to predict the water quality at low cost, which is the concept
inherent with consideration of SAS. The model will go a long way in predicting the response of
the sandy aquifers from future contamination due to the increasing inflow of suspended solids as
a result of poor catchment management. Such predictions will help in formulating mitigatory
measures to reduce the inflow of colloidal particles into future and current SAS.
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