Research Article Volume 7 Issue 1
^{1}Department of Civil Engineering, College of Engineering, Gregory University, Nigeria
^{2}Rivers State University NkpoluOroworukwo, Department of Civil Engineering, Faculty of Engineering, Nigeria
Correspondence: Eluozo Solomon, Department of Civil Engineering, College of Engineering, Gregory University, Uturu, Nigeria
Received: May 29, 2023  Published: June 7, 2023
Citation: Eluozo SN, Arimieari LW. Modeling the transport of fecal coliform in ntanwaogba creek, influenced by variations in micronutrient deposition, velocity and dispersion coefficient. MOJ App Bio Biomech. 2023;7(1):6470. DOI: 10.15406/mojabb.2023.07.00176
The study of Micronutrients in Ntanwaogba Creek were thoroughly carried out to monitor its rates of deposition at different numerous discharge location sites in the study environment, this was imperative because the rates of biological waste discharge at regular interval, based on this factor, it was necessary to conduct a comprehensive investigation of their rate of concentration at different station point of discharge. This implies that the rate of dispersions from the contaminant influenced constant discharge of waste in the creek, and based on these factors, it was determined that such comprehensive research was required. Micronutrients act as a substrate for microbial growth, but the speed at which they are injected into the rill affects how quickly they move through the system. In order to determine the effects of these two parameters on the migration rate of faecal coliform at different point sources of discharge, the study observed different growth rate at different station point in the study location. This observed condition indicates that the pollutants had a range of development speeds, including both slow and fast, which was enabled by these considerations. The system discovered that lower velocities have an effect on velocity rates with higher concentrations, and that accumulation with micronutrients increased their concentration. However, the concentration rates varied depending on the dominant characteristics of the transport under pressure at various points of discharge. In the simulation, these two parameters were used to determine the various pressure rates at different station points. Unquestionably, the study has depicted the effects of these two parameters' pressures on the movement of faecal coliform in a range of figures that correspond to the several point sources of discharge looked at. The speeds recorded at various station locations represented the pressure rates at various rates of concentration in the research environment. It has established the scope of the influence of rill flow velocity and the variance in micronutrient deposition at various point sources. On the basis of model simulation prediction results, also, the dispersions at various point sources were evaluated. Both parameters showed correlations for the best fits when the predicted and experimental values were compared for model validation.
Keywords: modeling, transport, fecal coliform, micronutrients and dispersion coefficient
Many studies have shown that waterborne infections are extremely dangerous to human health. These facts make it clear that, if pollution rates are not controlled, there will always be significant hazards to the overall health of the ecosystem. Total Maximum Daily Load (TMDL) implementation costs were assessed by experts, and they range from $0.9 to $4.3 billion annually.^{1,2} The main factor causing stream impairments is pathogen influxes from landbased agricultural activities.^{2,3} Controlling pathogen contamination caused by cattle, meantime, is a difficult task. Riparian buffers can be fenced off to prevent pathogen contamination; however it is not apparent how broad the buffers need to be to be effective in preventing pathogen contamination of stream water.^{4} The research that has thoroughly evaluated studies in this field has elaborated on the pathogen contamination of stream water ^{4–8} (Jamieson. More research has concentrated on understanding pathogen transmission in stream water using mathematical models.^{5,6,9,10} Also, the principal source of drinking water is typically a surface reservoir, indicating that these bodies of surface water are frequently subjected to pathogen pollution.^{9,11–13 }There has been a considerable improvement in knowledge of water quality and water treatment for pathogen pollution in industrialized nations because specialists tracked the occurrences of 26 waterborne illnesses through public water sources, which were done by experts.^{12–21 }Also, the inflow of contaminated stream water into lakes and reservoirs during the rainy seasons might result in a significant rise in pathogen rates.^{4,22–24} For purposes of measuring the quantity of pathogen uptake from torrents running into lakes and reservoirs during wet seasons it also involved monitoring pathogen movement including its dispersion.^{2,3,25}
$\frac{dc}{dx}+\beta (x)K=A(x)$ 1
Nomenclatures
C = Concentration
B = Micronutrients
K = Dispersions. Velocity of flow
A= Fluid Density
X = Distance
Multiplying the equation through by $C[x]$ , we have:
$C(x)\frac{dC}{dx}+C(x)\beta (x)K=C(x)A(x)$ 2
Let $P(x)=C(x)\beta (x)$ 3
Then Equation (2), we have:
$C(x)\frac{dC}{dx}+C(x)\beta (x)K=C(x)A(x)$ 4
$C(x)\frac{dC}{dx}+P(x)K=C(x)A(x)$ 5
$C(x){P}^{1}+P(x)K=C(x)A\left(x\right)$ 6
$C(x){P}^{1}=C(x)AP(x)K$ 7
Differentiate 2^{nd} term on the left hand side of (6) with respect to x, we have
$K\frac{dC}{dx}=C\left(x\right)A\left(x\right)C\left(x\right){P}^{1}$ 8
$\frac{dC}{dx}=\frac{1}{K}\left[C\left(x\right)A\left(x\right)C\left(x\right){P}^{1}\right]$ 9
$\frac{dC}{dx}=\frac{C\left(x\right)}{K}\left[A\left(x\right){P}^{1}\right]$ 10
Applying separation of variables, by dividing through by C(x) and cross multiply by dx, gives:
$\frac{dC}{C}=\frac{1}{K}\left[A\left(x\right){P}^{1}\right]dx$ 11
$\frac{1}{C\left(x\right)}dC=\frac{1}{K}\left[A\left(x\right){P}^{1}\right]dx$ 12
$\frac{1}{C\left(x\right)}dC=\left(\frac{A\left(x\right)}{K}\frac{{P}^{1}}{K}\right)dx$ 13
$\int \frac{1}{C\left(x\right)}}dC={\displaystyle \int \left(\frac{A\left(x\right)}{K}\frac{{P}^{1}}{K}\right)}dx+\eta $ 14
$\mathrm{ln}C\left(x\right)={\displaystyle \int A\left(x\right)}dx{\displaystyle \int \frac{{P}^{1}}{K}}dx+\eta $ 15
$\mathrm{ln}C\left(x\right)=\frac{1}{K}\left[Ax{P}^{1}\right]x+\eta $ 16
$\mathrm{ln}C\left(x\right)=\left(\frac{A(x)}{K}\frac{{P}^{1}}{K}\right)x+\eta $ 17
Taking exponent of the both side of the equation
$C\left(x\right)=\ell {}^{\left(\frac{A\left(x\right)}{K}\frac{{P}^{1}}{K}+\eta \right)}$ 18
$C\left(x\right)=D\ell {}^{\frac{1}{K}}{}^{\left(Ax{P}^{1}x\right)}$ 19
The water samples were taken sequentially according to the requirements set forth at various places. These samples were obtained at various locations, which resulted in fluctuations at various distances, resulting in variable faecal coliform concentrations, and the experimental results were compared. Using the conventional procedure for the experiment at several samples at various stations, a typical laboratory experiment was carried out to track faecal coliform.
(Table 16)(Figure 16) shows how the major influencing factors in the research environment affect the migration rate of faecal coliform. The variance of the contaminant's exponential growth rate in terms of quick and slow growth in relation to increase in distance was depicted in the figures. However, during the transport system's exponential phase. The observed fluctuations are primarily related to the pace of micronutrient depositions, including dispersion from the pollutant at several station locations, where the starting concentrations are recorded. The growth rate's behaviour did exhibit some degree of variability. Such a condition shows that the concentration change rate at different study locations was determined by the micronutrient's function as a substrate for any bacterium. The study looked at these pressures from transport and the impact that condition had on the flow dynamics that pushed the microorganisms at different station points of discharge. The many types of micronutrient depositions that have been seen in the rill and the fluctuations in those depositions as a whole have affected the growth rate of faecal coliform in the study region, as shown in graphical representation in all of the figures. The behaviour of faecal coliforms was monitored through the use of modeling and simulation by examining the variable effect of contaminant movement at distinct station points of discharge. The experimental and prediction values of each created figure expressed best fit correlations.
Distance [x] 
Predictive values conc.[Mg/L] variation of velocity and dispersion coefficient [0.0042/27.5] 
Experimental values conc.[Mg/l] variation of velocity and dispersion [0.0042/27.5] 

2 
0.126042926 
0.03112 

4 
0.137548218 
0.10196 

6 
0.150103721 
0.16624 

8 
0.1638053 
0.22468 

10 
0.17875757 
0.278 

12 
0.195074694 
0.32692 

14 
0.212881257 
0.37216 

16 
0.232313216 
0.41444 

18 
0.253518939 
0.45448 

20 
0.276660336 
0.493 

22 
0.301914097 
0.53072 

24 
0.32947304 
0.56836 

26 
0.359547584 
0.60664 

28 
0.392367355 
0.64628 

30 
0.428182938 
0.688 

32 
0.467267795 
0.73252 

34 
0.509920346 
0.78056 

38 
0.607260908 
0.89008 

40 
0.662692134 
0.953 

42 
0.723183165 
1.02232 

44 
0.789195861 
1.09876 

46 
0.861234246 
1.18304 

48 
0.939848348 
1.27588 

50 
1.025638403 
1.378 

54 
1.221426272 
1.61296 

56 
1.332918969 
1.74724 

58 
1.454588803 
1.89368 

60 
1.587364749 
2.053 

62 
1.732260583 
2.22592 

64 
1.890382616 
2.41316 

66 
2.062938146 
2.61544 

68 
2.251244672 
2.83348 

70 
2.456739959 
3.068 

72 
2.680993007 
3.31972 

74 
2.925716041 
3.58936 

76 
3.192777575 
3.87764 

78 
3.484216684 
4.18528 

80 
3.802258571 
4.513 

82 
4.149331558 
4.86152 

84 
4.528085626 
5.23156 

86 
4.941412646 
5.62384 

88 
5.392468463 
6.03908 

90 
5.884696991 
6.478 
Table 1 Shows the model's Prediction and Experimental Values for Faecal Coliform Concentrations at Various Distances
Distance [x] 
Predictive values conc.[Mg/L] variation of velocity and dispersion coefficient [0.0032/29.9] 
Experimental values conc.[Mg/l] variation of velocity and dispersion [0.0032/29.9] 
2 
0.102408622 
0.0387048 
4 
0.111096671 
0.1027384 
6 
0.12052179 
0.1668296 
8 
0.130746508 
0.2310072 
10 
0.141838662 
0.2953 
12 
0.153871841 
0.3597368 
14 
0.166925881 
0.4243464 
16 
0.181087387 
0.4891576 
18 
0.196450315 
0.5541992 
20 
0.213116588 
0.6195 
22 
0.23119678 
0.6850888 
24 
0.250810842 
0.7509944 
26 
0.272088905 
0.8172456 
28 
0.295172137 
0.8838712 
30 
0.320213683 
0.9509 
32 
0.34737968 
1.0183608 
34 
0.376850362 
1.0862824 
38 
0.443504458 
1.2236232 
40 
0.481130086 
1.2931 
42 
0.521947764 
1.3631528 
44 
0.566228295 
1.4338104 
46 
0.614265457 
1.5051016 
48 
0.666377952 
1.5770552 
50 
0.72291152 
1.6497 
54 
0.850773977 
1.7971784 
56 
0.922951168 
1.8720696 
58 
1.001251662 
1.9477672 
60 
1.086194941 
2.0243 
62 
1.178344562 
2.1016968 
64 
1.278311889 
2.1799864 
66 
1.386760152 
2.2591976 
68 
1.504408852 
2.3393592 
70 
1.632038525 
2.4205 
72 
1.770495928 
2.5026488 
74 
1.920699654 
2.5858344 
76 
2.083646229 
2.6700856 
78 
2.260416716 
2.7554312 
80 
2.452183898 
2.8419 
82 
2.66022005 
2.9295208 
84 
2.885905385 
3.0183224 
86 
3.130737206 
3.1083336 
88 
3.396339848 
3.1995832 
90 
3.684475446 
3.2921 
Table 2 Model Prediction and Experimental Values on Fecal Coliform Concentration at Various Distances
Distance [x] 
Predictive values conc.[Mg/L] variation of velocity and dispersion coefficient [0.0028/29.9] 
Experimental values conc.[Mg/l] variation of velocity and dispersion [0.0028/29.9] 
2 
0.071382281 
0.00900792 
4 
0.077438146 
0.04106336 
6 
0.084007773 
0.07321384 
8 
0.091134748 
0.10550688 
10 
0.098866355 
0.13799 
12 
0.107253889 
0.17071072 
14 
0.116352997 
0.20371656 
16 
0.126224047 
0.23705504 
18 
0.136932529 
0.27077368 
20 
0.148549486 
0.30492 
22 
0.161151993 
0.33954152 
24 
0.174823659 
0.37468576 
26 
0.18965519 
0.41040024 
28 
0.205744985 
0.44673248 
30 
0.223199791 
0.48373 
32 
0.242135413 
0.52144032 
34 
0.262677477 
0.55991096 
38 
0.309137641 
0.63932328 
40 
0.33536398 
0.68036 
42 
0.363815285 
0.72234712 
44 
0.394680316 
0.76533216 
46 
0.428163846 
0.80936264 
48 
0.464488022 
0.85448608 
50 
0.503893835 
0.90075 
54 
0.593018302 
0.99688936 
56 
0.643328251 
1.04685984 
58 
0.697906349 
1.09816088 
60 
0.757114694 
1.15084 
62 
0.821346104 
1.20494472 
64 
0.891026719 
1.26052256 
66 
0.966618835 
1.31762104 
68 
1.048623967 
1.37628768 
70 
1.137586175 
1.43657 
72 
1.234095678 
1.49851552 
74 
1.338792768 
1.56217176 
76 
1.452372053 
1.62758624 
78 
1.575587076 
1.69480648 
80 
1.709255302 
1.76388 
82 
1.854263552 
1.83485432 
84 
2.01157388 
1.90777696 
86 
2.18222996 
1.98269544 
88 
2.367364004 
2.05965728 
90 
2.568204283 
2.13871 
Table 3 Shows the model's Prediction and Experimental Values for Faecal Coliform Concentrations at Various Distances
Distance [x] 
Predictive values conc.[Mg/L] variation of velocity and dispersion coefficient [0.0011/17.5] 
Experimental values conc.[Mg/l] variation of velocity and dispersion [0.0011/17.5] 
2 
0.022082347 
0.03668 
4 
0.02533143 
0.11156 
6 
0.029058567 
0.23564 
8 
0.033334096 
0.33748 
10 
0.038238704 
0.419 
12 
0.043864952 
0.48212 
14 
0.050319016 
0.52876 
16 
0.057722699 
0.56084 
18 
0.066215721 
0.58028 
20 
0.075958364 
0.589 
22 
0.087134489 
0.58892 
24 
0.099955012 
0.58196 
26 
0.114661881 
0.57004 
28 
0.131532644 
0.55508 
30 
0.150885684 
0.539 
32 
0.173086231 
0.52372 
34 
0.198553254 
0.51116 
38 
0.261279889 
0.50188 
40 
0.299723275 
0.509 
42 
0.343823024 
0.52652 
44 
0.394411385 
0.55636 
46 
0.452443059 
0.60044 
48 
0.519013216 
0.66068 
50 
0.595378165 
0.739 
54 
0.783469107 
0.95756 
56 
0.898744744 
1.10164 
58 
1.030981448 
1.27148 
60 
1.182674783 
1.469 
62 
1.356687501 
1.69612 
64 
1.556303559 
1.95476 
66 
1.785290103 
2.24684 
68 
2.047968555 
2.57428 
70 
2.349296171 
2.939 
72 
2.694959591 
3.34292 
74 
3.091482159 
3.78796 
76 
3.546347028 
4.27604 
78 
4.068138387 
4.80908 
80 
4.666703457 
5.389 
82 
5.35333833 
6.01772 
84 
6.141001145 
6.69716 
86 
7.044556637 
7.42924 
88 
8.081056661 
8.21588 
90 
9.270061997 
9.059 
Table 4 Shows the model's Prediction and Experimental Values for Faecal Coliform Concentrations at Various Distances
Distance [x] 
Predictive values conc.[Mg/L] variation of velocity and dispersion coefficient [0.0021/17.5] 
Experimental values conc.[Mg/l] variation of velocity and dispersion [0.0021/15.5] 
2 
0.038006482 
0.469408 
4 
0.044377655 
0.421408 
6 
0.051816852 
0.341408 
8 
0.060503111 
0.229408 
10 
0.070645481 
0.085408 
12 
0.082488055 
0.090592 
14 
0.096315846 
0.298592 
16 
0.112461642 
0.538592 
18 
0.131314021 
0.810592 
20 
0.153326697 
1.114592 
22 
0.179029442 
1.450592 
24 
0.209040837 
1.818592 
26 
0.244083159 
2.218592 
28 
0.284999759 
2.650592 
30 
0.332775368 
3.114592 
32 
0.388559786 
3.610592 
34 
0.45369556 
4.138592 
38 
0.61855438 
5.290592 
40 
0.722245035 
5.914592 
42 
0.843317755 
6.570592 
44 
0.984686361 
7.258592 
46 
1.149753131 
7.978592 
48 
1.342490681 
8.730592 
50 
1.567537569 
9.514592 
54 
2.137131844 
11.178592 
56 
2.495387493 
12.058592 
58 
2.913698918 
12.970592 
60 
3.4021335 
13.914592 
62 
3.972446253 
14.890592 
64 
4.638362732 
15.898592 
66 
5.415909357 
16.938592 
68 
6.32379912 
18.010592 
70 
7.383881944 
19.114592 
72 
8.621670538 
20.250592 
74 
10.06695441 
21.418592 
76 
11.75451678 
22.618592 
78 
13.72497174 
23.850592 
80 
16.02574166 
25.114592 
82 
18.71219851 
26.410592 
84 
21.84899648 
27.738592 
86 
25.51162799 
29.098592 
88 
29.78824053 
30.490592 
90 
34.78175812 
31.914592 
Table 5 Model Prediction and Experimental Values on Fecal Coliform Concentration at Various Distances
Distance [x] 
Predictive values conc.[Mg/L] variation of velocity and dispersion coefficient [0.035/26.5] 
Experimental values conc.[Mg/l] variation of velocity and dispersion [0.035/26.5] 
2 
1.015504788 
3.651 
4 
1.111859812 
2.899 
6 
1.217357372 
2.235 
8 
1.33286495 
1.659 
10 
1.459332333 
1.171 
12 
1.597799431 
0.771 
14 
1.749404823 
0.459 
16 
1.915395121 
0.235 
18 
2.09713522 
0.099 
20 
2.296119523 
0.051 
22 
2.513984227 
0.091 
24 
2.752520777 
0.219 
26 
3.013690598 
0.435 
28 
3.299641222 
0.739 
30 
3.612723947 
1.131 
32 
3.955513173 
1.611 
34 
4.330827566 
2.179 
38 
5.191669134 
3.579 
40 
5.684274788 
4.411 
42 
6.223620772 
5.331 
44 
6.81414199 
6.339 
46 
7.460694146 
7.435 
48 
8.168593671 
8.619 
50 
8.943661443 
9.891 
54 
10.72139917 
12.699 
56 
11.738687 
14.235 
58 
12.85249904 
15.859 
60 
14.07199387 
17.571 
62 
15.4071991 
19.371 
64 
16.86909376 
21.259 
66 
18.46969864 
23.235 
68 
20.2221751 
25.299 
70 
22.14093331 
27.451 
72 
24.24175073 
29.691 
74 
26.54190183 
32.019 
76 
29.06030016 
34.435 
78 
31.81765388 
36.939 
80 
34.83663598 
39.531 
82 
38.14207078 
42.211 
84 
41.76113802 
44.979 
86 
45.72359637 
47.835 
88 
50.0620281 
50.779 
90 
54.81210701 
53.811 
Table 6 Model Prediction and Experimental Values on Fecal Coliform Concentration at Various Distances
Figure 1 Model Prediction and Experimental Values on Fecal Coliform Concentration at Various Distances.
Figure 2 Model Prediction and Experimental Values on Fecal Coliform Concentration at Various Distances.
Figure 3 Shows the model's Prediction and Experimental Values for Faecal Coliform Concentrations at Various Distances.
Figure 4 Shows the model's Prediction and Experimental Values for Faecal Coliform Concentrations at Various Distances.
The system keeps track of the contaminant's behaviour at several station points of discharge that are seen in the research environment. An experimental approach was used to monitor the station points, and it led to concentration variations at various stations spaced uniformly apart. The microorganisms' growthrelated behaviour was evaluated, thus, it was found that the concentration of faecal coliform in Ntanwaogba Creek increased gradually and quickly. To identify the variables influencing the faecal coliform's transport behaviour, the reaction of the organism in the rill was evaluated. The pollutant was observed to rise at various station sites in response to micronutrients identified in various stations that support the behaviour, demonstrating the contrast between their effects on the concentration's slow and fast stages of growth.
None.
None.
The authors declare that they have no competing interests.
©2023 Eluozo, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work noncommercially.