Modeling of E.coli transport on homogenous clay influenced by permeability has been carried out. The transport of the microbes on uniform clay formation was developed to monitor the migration process of the microbes in the clay region. The model explains the behaviour of the microbes with respect to time of transport on homogenous clay, and determines the rate of concentration including the rate of permeability influence. The results show that without any regeneration of the microbes in the study area, the concentration at the period from 10 – 100 days may be insignificant on homogenous clay formation. From the simulation results it has explain the behaviour in physical process where the contaminant express it deposition from high to low concentration, while in other deposition the heterogeneous setting of some minerals developed high accumulation of E.coli in eighty days thus decreasing slightly in hundred days. The models were compared with the experimental values and both parameters compared favourably well.

1. http://www.iaeme.com/IJCIET/index.asp 315 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 7, Issue 1, Jan-Feb 2016, pp. 315-323, Article ID: IJCIET_07_01_026
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=1
Journal Impact Factor (2016): 9.7820 (Calculated by GISI) www.jifactor.com
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
MODELING OF E. COLI TRANSPORT ON
HOMOGENEOUS CLAY FORMATION
INFLUENCED BY PERMEABILITY IN
AHAODA EAST RIVERS STATE OF
NIGERIA
Eluozo, S. N
Subaka Nigeria Limited, Port Harcourt, Rivers State of Nigeria
F.E.Ezeilo
Department of Civil Engineering,
Rivers State University of Science and Technology,
Port Harcourt, Rivers State, Nigeria
ABSTRACT
Modeling of E.coli transport on homogenous clay influenced by
permeability has been carried out. The transport of the microbes on uniform
clay formation was developed to monitor the migration process of the
microbes in the clay region. The model explains the behaviour of the microbes
with respect to time of transport on homogenous clay, and determines the rate
of concentration including the rate of permeability influence. The results show
that without any regeneration of the microbes in the study area, the
concentration at the period from 10 – 100 days may be insignificant on
homogenous clay formation. From the simulation results it has explain the
behaviour in physical process where the contaminant express it deposition
from high to low concentration, while in other deposition the heterogeneous
setting of some minerals developed high accumulation of E.coli in eighty days
thus decreasing slightly in hundred days. The models were compared with the
experimental values and both parameters compared favourably well.
Key words: Mathematical Modeling, E. Coli Transport, Clay Formation and
Permeability
Cite this Article: Eluozo, S. N and F.E.Ezeilo, Modeling of E. Coli Transport
on Homogeneous Clay Formation Influenced by Permeability in Ahaoda East
Rivers State of Nigeria, International Journal of Civil Engineering and
Technology, 7(1), 2016, pp. 315-323.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=1

2. Eluozo, S. N and F.E.Ezeilo
http://www.iaeme.com/IJCIET/index.asp 316 editor@iaeme.com
1. INTRODUCTION
Microorganisms have conquered the biosphere for 3.5 billion years. This observation
is for 3.5 billion years of microbial evolution; it seems that there are several types of
microorganisms than anyone can imagine (Hackl et al. 2004; Schloss and Handelsman
2004; Spear et al. 2003; Ward 2002; Ward et al. 1998). In addition, the earth’s
habitats present multifaceted gradients of environmental circumstances that comprise
extreme variations in heat, light, pH, pressure, salinity, and both inorganic and
organic compounds. Evolutionary mechanisms have made it feasible for
microorganisms continue to exist these extreme variations by means of genetic
adaptation (Bond et al. 2000; Brofft et al. 2002; Hallberg and Johnson 2001; Ward et
al. 1998). Microorganisms play very imperative roles in environmental preservation
and safety. Interest in predicting the fate and transport of bacteria in the subsurface
area is motivated by either a concern that microbes can pollute drinking water
supplies or their role in bioremediation (Fontes et al. 1991). Bacterial transport is
affected by the propensity for cell sorption within the pore environment in the
subsurface (Grasso and Smets 1998; Grasso et al. 1996; Karickhoff et al. 1979; Smets
et al. 1999). Bacterial strains with different cell surface properties show different
adhesion kinetics and affinity for substrate (Chen and Strevett 2001). Bacterial surface
physicochemical properties can be chemically modified to stimulate or impede
bacterial adhesion to the substratum (Powelson and Mills 1998; van der Mei et al.
2001; Whitekettle 1991). For various industrial and environmental protection
applications it would be advantageous if bacteria could be made to adhere to a
substratum surface, when their cell surface properties would not normally allow them
to adhere. Similarly, different probiotic bacteria have been found to slow down fungal
biofilm formation on silicone rubber voice prostheses, but the adhesion of different
probiotic bacteria to silicone rubber is not ideal (van der Mei et al. 2000). Therefore, it
would be advantageous to have a methodology available through which bacterial cell
surfaces could be chemically modified to tailor their cell surface for optimal adhesion
to a given substratum surface. (Doyle et al, 1980).
2. MATERIALS AND METHOD
Column experiments were also performed using soil samples from forty (7) different
borehole locations, the soil samples were collected at intervals of three metres each
(3m). An E.coli solute was introduced at the top of the column and effluents from the
lower end of the column were collected and analyzed for E.coli, and the effluent at the
down of the column were collected at different days, analysis, velocity of the
transport were monitored at different days. Finally, the results were collected to be
compared with the theoretical values.
Developed Mathematical Model
t
C
V
t
V
CK
xx
x




 )()(
)(
(1)
t
V
CK
t
V x
x
x




 )(
)(
)(
(2)

3. Modeling of E. Coli Transport on Homogeneous Clay Formation Influenced by Permeability
in Ahaoda East Rivers State of Nigeria
http://www.iaeme.com/IJCIET/index.asp 317 editor@iaeme.com
t
V
CK
t
CV x
x
x )(
)(
)(



(3)
t
Kdt
x
C
V
V x
x



)(
)(
(4)
 


t
t
KCCV
V x
x
)(
)(
1
… (5)







t
t
KCV
V o
x
x
lnln )(
)(
(6)
V
V
K
t
t
t
t
V
V
K
C
C x
oo
x
ox
x






 lnlnln
)(
)(
)(
(7)
V
KV
t
t
C
C x
ox
x
o







)(
)(
(8)
V
V
t
tK
x
x
x
o
o
C
C 






ln
)(
)(

(9)
V
V
tK
xx
x
o
CC
1ln
)()(

 
(10)
V
VxC tK
x
1ln
)(

 
(11)
(12)
The model will be used to determine the Rte of E. coli Transport influenced by
permeability.
The equation were expressed integrating the influence parameter permeability (K)
as
KVt
xC 
 )(
(13)
Take Laplace Transform of (13) we have
SKV
C o



)(
(14)
tv
V
C x
x o
)(
)( 

4. Eluozo, S. N and F.E.Ezeilo
http://www.iaeme.com/IJCIET/index.asp 318 editor@iaeme.com
i.e.
  SKVC o)(
0)()(  SCKVC oo
(15)
By applying quadratic formula in (15), we have
KV
KVSS
C x
2
42
)(


(16)
Our equation (15) can be expressed as follows if our S = KV
KV
KVVK
KVCei x
2
4
..
22
)(


(17)
Now the general solution of (16) is
tKVVKKVtKVVKKV
x AC 


 



 



44
)(
2222

(18)
At initial point, x = 0, t = 0 and C(o) = 0
So that our (16) can give the constant A and β, values of 1 and -1. A = 1 and β = -1
So that equation (16) can be expressed as
tKVVKKVtKVVKKV
xC 


 



 

 44
)(
2222

(19)
Again ℓx
- ℓ-x
= Sin x, now our equation (19) cam ne rewritten in this form
(20)
Table 1 Comparison of theoretical and experimental values at various time
Time
Theoretical values at
different velocity
[mg/l]
Experimental values
[mg/l]
10 2.12E-06 2.20E-05
20 2.68E-06 2.26E-06
30 4.81E-08 4.42E-06
40 2.49E-04 4.75E-04
50 2.63E-04 2.36E-04
60 2.14E-05 1.19E-05
70 4.98E-05 4.37E-05
80 5.59E-03 5.38E-03
90 3.44E-05 3.65E-04
100 1.59E-04 1.42E-04
t
K
KVVK
KVSinC x







 

2
4
2
22
)(


5. Modeling of E. Coli Transport on Homogeneous Clay Formation Influenced by Permeability
in Ahaoda East Rivers State of Nigeria
http://www.iaeme.com/IJCIET/index.asp 319 editor@iaeme.com
Table 2 Comparison of theoretical and experimental values at various time
Time
Theoretical values At
Constant velocity
[mg/l]
Experimental values
[mg/l]
10 1.00E-04 1.20E-04
20 1.05E-05 1.46E-05
30 1.10E-05 1.42E-05
40 1.06E-05 1.55E-05
50 1.10E-05 1.36E-05
60 1.05E-05 1.19E-05
70 1.01E-05 1.37E-05
80 1.10E-05 1.58E-05
90 1.07E-05 1.85E-05
100 1.07E-05 1.42E-05
Table 3 Comparison of theoretical and experimental values at various time
Time
Theoretical values at
constant velocity [mg/l]
Experimental values
[mg/l]
10 2.85E-06 2.78E-06
20 5.64E-08 5.23E-07
30 2.85E-08 2.66E-08
40 2.90E-08 2.45E-07
50 2.86E-08 2.66E-07
60 2.84E-08 2.51E-08
70 2.86E-08 2.51E-08
80 2.90E-08 2.31E-08
90 2.86E-08 2.12E-08
100 2.90E-08 2.17E-08
Table 4 Comparison of theoretical and experimental values at various time
Time
Theoretical values at
Different velocity [mg/l]
Experimental values
[mg/l]
10 2.42E-06 2.78E-06
20 2.15E-06 2.30E-06
30 4.97E-09 4.66E-07
40 9.42E-07 9.45E-08
50 1.84E-05 1.66E-05
60 3.87E-05 3.51E-05
70 1.72E-04 1.51E-04
80 1.41E-05 1.31E-05
90 7.64E-09 8.12E-08
100 1.15E-05 1.17E-05

6. Eluozo, S. N and F.E.Ezeilo
http://www.iaeme.com/IJCIET/index.asp 320 editor@iaeme.com
Figure 1 Comparison of theoretical and experimental values at various time
Figure 2 Comparison of theoretical and experimental values at various time
0.00E+00
2.00E-05
4.00E-05
6.00E-05
8.00E-05
1.00E-04
1.20E-04
1.40E-04
0 20 40 60 80 100 120
ConcentrationMg/l
Time Per Day
Theoretical values At
Constan velocity
Experimental values
-1.00E-03
0.00E+00
1.00E-03
2.00E-03
3.00E-03
4.00E-03
5.00E-03
6.00E-03
0 20 40 60 80 100 120
ConcentrationMg/l
Time Per Day
Theoretical values at
different velocity
Experimental values

7. Modeling of E. Coli Transport on Homogeneous Clay Formation Influenced by Permeability
in Ahaoda East Rivers State of Nigeria
http://www.iaeme.com/IJCIET/index.asp 321 editor@iaeme.com
Figure 3 Comparison of theoretical and experimental values at various time
Figure 4 Comparison of theoretical and experimental values at various time
-5.00E-07
0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
3.00E-06
3.50E-06
0 20 40 60 80 100 120
ConcentrationMg/l
Time Per Day
Theoretical values at
constant velocity
Experimental values
-2.00E-05
0.00E+00
2.00E-05
4.00E-05
6.00E-05
8.00E-05
1.00E-04
1.20E-04
1.40E-04
1.60E-04
1.80E-04
2.00E-04
0 20 40 60 80 100 120
ConcentrationMg/l
Time Per Day
Theoretical values at
Different velocity
Experimental values

8. Eluozo, S. N and F.E.Ezeilo
http://www.iaeme.com/IJCIET/index.asp 322 editor@iaeme.com
3. RESULTS AND DISCUSSION
Figure 1 show that the concentration of the microbes deposited very high
concentration from day one to 10 days and suddenly decrease with a slight fluctuation
from 20 days to 100 days, this condition shows that at a homogenous formation the
concentration of the microbes maintained the physical process, from high
concentration to low concentration. Thus microbes experience slight fluctuation due
to the slight variation on the soil deposit based on the soil Matrix that may have
deposited slight fluctuation in the studied area. The microbes were influenced by such
conditions based on the influence of permeability. Figure 2 experienced fluctuation on
the migration process at the homogenous formation and suddenly increased in
microbial population was observed between seventy and eighty days, based on the
deposition of substrate utilization between the region, and finally decrease between
ninety and hundred days as the substrate begin to experience degradation influenced
by other environmental factors. Figure 3 were found to maintain similar conditions
like figure 1 where the optimum growth were recorded at 10 days, fluctuation were
also experienced between thirty and forty days and finally it linearly decreased from
fifty to hundred days. These conditions shows that there region that deposited
substrate at some certain layers of the soil, and finally experience degradation base
on the environmental factors from man made activities, these factors may subject the
microbes degradation through these influences from environmental condition. Figure
4 linearly migrate in a gradual process and suddenly increased between forty and
eighty days based on the high deposition of micronutrients, when the microelement
decreased, the microbes now lack its substrate and without regeneration they
experience some degradation at ninety days and finally developed slight growth at
hundred days. The models were compared with experimental values, both the
theoretical and experimental values compared favourably well. These comparisons
with the experimental result explain the validation of the predictive model.
4. CONLUSION
The development of mathematical model of microbes E.coli in a homogeneous clay
soil is a study that has displayed the behaviour of microbial transport in a clay region,
the studies has explain the condition of microbes in homogeneous clay soil, microbial
transport in clay region are determine on the soil matrix deposition influenced by the
geological formation of the study area, this behaviour of E.coli in the study area
shows that the microbes in some condition maintained the physical process from high
concentration to low concentration, while in some condition the microbes are
subjected to lag phase condition, that can be attributed to the influence of some the
deposition variation of microelements in the soil, these condition are found in the
influence permeability on E.coli transport depositing very high concentration at
different days between ten to hundred days, at different velocity, the model were
compared with experimental values and both values compared faviourably well, the
model can be applied to determine the rate of E.coli in a homogenous soil.

9. Modeling of E. Coli Transport on Homogeneous Clay Formation Influenced by Permeability
in Ahaoda East Rivers State of Nigeria
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