Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology

ISSN No:-2456-2165

Prediction of Piggery Wastewater Nutrient

Attenuation by Constructed Wetland in a Humid
Environment
I. J. Udom1, E. S. Udofia2, S. A. Nta1, G. A. Usoh 1, E. O. Sam1
1
Department of Agricultural Engineering, Akwa Ibom State University, Ikot Akpaden
2
Department of Mathematics, Akwa Ibom State University, Ikot Akpaden

Abstract:- A mathematical model for predicting the or treat it before discharge to the surroundings instead of
reduction of nitrogen and phosphorus concentrations in stockpiling them in drains and pond where it decomposes
horizontal subsurface flow constructed wetlands was and becomes part of the soil as is the case in Nigeria
developed. The model considered the piggery wastewater (Kadurumba and Kadurumber. 2019, Ewuziem et al., 2009)
input, storage, plant use and nutrient output to the Nutrients (nitrogen and phosphorus) are the pollutants of
environment is predominantly through nitrogen concern in pig wastewater to safeguard infants’ health and
denitrification. Nutrient release from plant litter was not nutrient enrichment of water because oxidation of
considered an influence on the constructed wetland ammonium to nitrate take as much as 4.3 g for each gram of
because the young plants were picked for fodder and, ammonium (Henze et al., (1995).
contamination from rainfall and groundwater was
considered insignificant. The adjustment and Similarly, Phosphorus modifies freshwater plant and
authentication of the model was carried out by separate algae development (EPA, 2000) and substantially regulate
data sets. Nutrient attenuation followed exponential downstream water quality (Wallace and Knight, 2006) and
trend during the period followed by stability contingent use (Gouriveau, (2009).
on the decay coefficient. Simulated parameters
correlated highly with the observed values with R= Satisfactory wastewater management in developing
0.8940 for nitrogen and 0.9518 for phosphorus countries is impeded by financial requirement (Muga and
respectively. ME of 0.211 and 0.139, RMSE of 0.32 and Mihelcic, 2008), for construction, maintenance and
0.18, RE of 24 and 12%, model efficiencies of 64 and upgrading and ignorance of cheap but effective and
37% and index of agreements of 0.6527 and 0.8676 for sustainable wastewater management due to the huge
nitrogen and phosphorus respectively. The linear investments necessary to construct, maintain and improve
regression coefficients appear good for a natural system wastewater treatment amenities, but it is also due to lack of
under environmental influences. information on developments in wastewater treatment
technologies and the use of low cost wastewater treatment
Keywords:- Piggery Wastewater, Horizontal-Subsurface- know-hows (Mburu et al., 2012).
Flow-Constructed-Wetlands, Pollution, Water Quality,
Nutrients. Treatment or constructed wetlands (CW) systems
deliberately attenuate nutrients by receiving, retaining and
I. INTRODUCTION processing nutrients by physico-chemical and biological
paths (Abbasi et al., 2019; Nandakumar et al., 2019) as
Pork is highly consumed and accounts for over 30% of wastewater gradually passes through the wetland. The above
world-wide meat demand (Modern technologies for raising paths account for an assortment of nutrient attenuation
pigs, 2015). In 2016, (Soare and Chiurciu, 2017), pork’s per through disintegration, uptake and transformation of
capita consumption was the highest in the world accounting nitrogenous composites. There are qualitative evidences to
for over 39% of meat consumed from all sources. Pig show that the wastewater depuration efficiency of
production is an important aspect of the livestock enterprise constructed wetlands but quantitative confirmations are
in Nigeria’s agriculture (Uddin and Osasogie, 2016). required for ecological conditions and system design
(Kadlec and Wallace 2009) necessary for appropriate
Nutrient pollution from large scale pig farms is the design, operation, feedbacks and improvement of CW
main concern in managing pig waste (Udom et al., 2018). systems in different situations. CW design has evolved from
Pig waste contains excessive nutrient that can negatively input-output empirical relationships to complex
impact on land, water and aquatic environments (Mason, relationships (Kadlec and Wallace, 2009) but, the problem
2002); and breeds pathogens, bacteria and heavy metals of approximating the numerous parameter interactions
which are harmful to human health (Wendee, 2017, Horton involved in pollutant removal process justify the rising
et al., 2009). Good waste control is inevitable to secure utilization of prediction models for the design of CW
sustainable environmental quality (ECC, 1999; EPA, 2000). (Kadaverugu, 2016). A prediction model describes the
The best approach to managing waste is to recycle the waste physical processes and boundaries of a system using one or

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
more governing equations. Prediction models define the In this paper, we develop a prediction model for
connection among the model parameters and connect them piggery wastewater nutrient attenuation using a sub-surface
with between the model components and link them together horizontal flow CW. This study will be useful for CW
using precise mathematical balances (Jorgensen and development and application in pollution control.
Bendoricchio, (2001). FITOVERT (Giraldi et al., 2010),
HYDRUS 2D/3D (Simunek et al. 2008), PHWAT (Brovelli II. MATERIALS AND METHOD
et al. 2009) are examples of CW models with prediction
capabilities for intermittently inundated soils and pollutant A. Study Area and Project Location
fate but they are not freely available. STELLA is a dynamic The location of the horizontal subsurface flow
software program with wide application but is expensive for constructed wetland (HSSFCW) at the Obio Akpa campus
rural applications (Allen 2019). of Akwa Ibom State University (AKSU) is highlighted in
Figure 1. Obio Akpa is situated between longitudes 07o 3”E
and 07o 3”E and latitude 04o 45”N and 04o 55”N.

Fig 1 Location of Piggery and Constructed Wetlands.

Mean lowest and highest temperatures are between wetland basins were packed to 0.60 m depth with sharp-
18OC -27OC and 24OC - 36OC. A perennial stream is the sand and Pennisetum clandestinum (PC) was planted in two
main channel in the watershed with a population of over cells while the third cell was the control.
150,000 people (NPC, 2006). Relative humidity ranges
between 55-86% and average rainfall is between 2050 mm C. Sample Collection and Monitoring
to 2450 mm. Estimated untreated wastewater volume of 9.46 The wetland was monitored after three month's
m3/day is released on the floodplain. stabilization. Wastewater samples were collected at the inlet
before loading the CW and three days after at the outlet of
B. Experimental Setup the CW. The status of total nitrogen (TN) and total
The study was carried out at the Akwa Ibom State phosphorus (TP) were investigated (AOAC, 2007).
University. A (7 m x 1.75 m x 0.60 m) concrete CW having Destructive and systematic sampling techniques were
three wetland cells were created. A 2.5 mm thick Texclear adopted for the plants and the soil respectively. Nutrient
plastic liner covered the entire wetland floor. Both the attenuation was calculated from the differences in
wastewater inlet and outlet regions of the wetland basin wastewater concentrations before and after residence in the
were jam-packed up to 0.60 m depth with 30 mm crushed CW.
granite rock at a distance of one meter from each end. The

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
E. Model Derivation
Equations derived based on the above assumptions
were:

 Nitrogen

𝑑𝑁
= −𝜌 𝑁(𝑡) + 𝑓(𝑡) [2.1]
𝑑𝑡

𝑁(0) = 𝑁0 Where,
Fig 2 Theoretical Model of Nutrient Attenuation Process in N = nitrogen concentration (mg/l)
CW
𝜌 = CW nitrogen removal rate (mgd-1)
In Figure 2 the theoretical model of the nutrient
attenuation pathways for conversion of organic matter to 𝑑𝑁
ammonia and phosphate and consequent transportation, + 𝜌 𝑁(𝑡) = 𝑓(𝑡) [2.2]
retaining, use by plants and discharge (denitrification, 𝑑𝑡
volatilization, and burial) from the CW. The model divides By using integrating factor,
the CW into three simple partitions: (1) wastewater pool (2)
CW soil, and (3) CW plant. The CW water pool comprise 𝐼. 𝐹 = 𝑃(𝑡) = 𝜌
pig excess flow, organic nitrogen and phosphorus deposit.
Impact of pollutant input from the atmosphere is negligible
𝑒 ∫ 𝑃(𝑡)𝑑𝑡 = 𝑒 ∫ 𝜌𝑑𝑡 = 𝑒 𝜌𝑡
in CW. The site for nitrification of ammonium nitrogen is in
the aerobic part of the CW media and the water pool, while
Multiplying both sides of (2.2) by the integrating
nitrate attenuation is restricted to the anaerobic region in the
dynamic CW media and the root zone of CW macrophytes. factor, we have
Nitrogen is mainly lost to the atmosphere in conditions
𝑑𝑁
where the alkalinity is high (Reddy and Delaune, 2008). 𝑒 𝜌𝑡 ( + 𝜌 𝑁(𝑡)) = 𝑒 𝜌𝑡 𝑓(𝑡)
Ammonium ion oxidation in the water pool and oxidized 𝑑𝑡
media also produces nitrate.
𝑑
(𝑁𝑒 𝜌𝑡 ) = 𝑒 𝜌𝑡 𝑓(𝑡)
Phosphorus attenuation derives from deposition of 𝑑𝑡
suspended organic matter residue but then does not result in
𝑑(𝑁𝑒 𝜌𝑡 ) = 𝑒 𝜌𝑡 𝑓(𝑡)dt
gaseous losses. The physical routes of advection (inflow,
outflow), deposition, resuspension, and dispersion is also 𝑡 𝑡
applicable to phosphorus transportation and destiny in the ∫ 𝑑(𝑁𝑒 𝜌𝑠 ) = ∫ 𝑒 𝜌𝑠 𝑓(𝑠)𝑑𝑠
CW. Biologically available inorganic phosphorus (typically 0 0
orthophosphate) alone is easily reached by CW
𝑡
macrophytes. Phosphorus introduced to the CW from
𝑁(𝑡)𝑒 𝜌𝑡 − 𝑁0 = ∫ 𝑒 𝜌𝑠 𝑓(𝑠)𝑑𝑠
groundwater, sediment and runoff and breakdown of organic 0
matter are the main sources of inorganic phosphorus in CW
media and water pool. Apart from plant gathering, burial is 𝑡
nearly the single means for the attenuation of phosphorus in 𝑁(𝑡)𝑒 𝜌𝑡 = 𝑁0 + ∫ 𝑒 𝜌𝑠 𝑓(𝑠)𝑑𝑠
0
CW (Kadlec and Wallace, 2009).
Dividing through by 𝑒 𝜌𝑡
D. Model Assumptions
Assumptions considered in the derivation of the first 𝑡
order equations to describe the rate of nutrient attenuation in 𝑁(𝑡) = 𝑁0 𝑒−𝜌𝑡 + 𝑒 −𝜌𝑡 ∫ 𝑒 𝜌𝑠 𝑓(𝑠)𝑑𝑠 [2.3]
the CW were: 0

 CW contains no initial nutrients. 𝑁(0) = 𝑁0 Suppose 𝑓(𝑡) ≡ 0, 𝑤ℎ𝑒𝑟𝑒 𝑓(𝑡) 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑓𝑙𝑢𝑒𝑛𝑡, then
 Nutrient introduction is periodical at the 𝑓(𝑡).
 Nutrient concentration at time 𝑡 > 0 𝑖𝑠 𝑁(𝑡) 𝑁(𝑡) = 𝑁0𝑒 −𝜌𝑡 [2.4]
 Plant use, retention in CW media, biogeochemical
process creates the nutrient attenuation avenues from the This is a first order differential equation with the initial
CW at the rate 𝜌 proportional to the quantity present. condition (background concentration) 𝑁(0) = 𝑁0
 Nitrogen supply rate to the CW from precipitation is
The quantity of N nutrient in the CW is represented by
insignificant.
 Supply to and from groundwater is zero..

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
𝑡 𝐷
𝑁(𝑡) = 𝑁0 𝑒 −𝜌𝑡 + 𝑒 −𝜌𝑡 ∫ 𝑒 𝜌𝑠 𝑓(𝑠)𝑑𝑠 , 𝑎𝑡 𝑡 > 0 [2.5] 𝑁(𝑡) = 𝑁0𝑒 −𝜌𝑡 + ⌈1 − 𝑒 −𝜌𝑡 ⌉ (2.9)
0
𝜌

This decay exponential function tells us that as 𝑡 → ∞ This demonstrates that though the amount of nitrogen
the quantity of 𝑁(𝑡) decreases to zero (0) but not rapidly will decline in the CW, it will not be completely eradicated
because of the presence of the influent 𝑓(𝑡) from the CW but, there will still be some background
concentration within the CW. In practice, piggery
Assuming 𝑓(𝑡) ≡ 0, , wastewater is released into the CW at a given time period T.
Presuming that the initial influent is at a time = 0+ , then the
Then the attenuation of the nitrogen will be fast. From initial concentration is 𝑁(0+ ) = 𝐷.
experimental observation, we discover that the above
statement and reason does not represent reality. Hence, we Such that,
assume further that the introduction of nitrogen 𝑓(𝑡) = 𝐷
into the CW is at a constant quantity over a period of time, 𝑑𝑁
− 𝜌 𝑁(𝑡), 0 < 𝑡 < 𝑇, 𝑡ℎ𝑎𝑡 𝑖𝑠, 𝑡 ∈ (0, 𝑇) [2.10]
and then the model equation becomes 𝑑𝑡

𝑑𝑁 𝑁(0+ ) = 𝐷
= −𝜌 𝑁(𝑡) + 𝐷 [2.6]
𝑑𝑡
Then solving this, we have,
𝑁(0) = 𝑁0
𝑁(𝑡) = 𝐷𝑒 −𝜌𝑡 [2.11]
𝑑𝑁
+ 𝜌 𝑁(𝑡) = 𝐷 [2.7] Which means that, the concentration before the second
𝑑𝑡
influent is,
𝑁(0) = 𝑁0
𝑁(𝑇 −) = 𝐷𝑒 −𝜌𝑇 [2.12]
By still using the method of integrating factor to find the
solution of the above problem, The model for next influent, that is, 𝑇 ≤ 𝑡 ≤ 2𝑇 is

𝐼. 𝐹 = 𝑒 ∫ 𝑓𝑑𝑡 = 𝑒 𝜌𝑡 𝑑𝑁
= −𝜌 𝑁(𝑡), [2.13]
𝑑𝑡
Multiplying both sides of Equation (2.7) by the integrating
factor, we have 𝑁(0+ ) = 𝑁(𝑇 −) + 𝐷 = 𝐷 + 𝐷𝑒 −𝜌𝑟 ,

𝑑𝑁 𝑤ℎ𝑒𝑟𝑒,
𝑒 𝜌𝑡 ( + 𝜌 𝑁(𝑡)) = 𝑒 𝜌𝑡 𝐷
𝑑𝑡
𝑟 = 𝑡 − 𝑇, 𝑡 = 𝑇 + 𝑟
𝑑
(𝑁𝑒 𝜌𝑡 ) = 𝑒 𝜌𝑡 𝐷 𝑇 = loading interval (d)
𝑑𝑡

𝑑(𝑁𝑒 𝜌𝑡 ) = 𝑒 𝜌𝑡 𝐷dt 𝑡 = CW retention time (d)

𝑡 𝑡 Solving the above equation, we have

∫ 𝑑(𝑁𝑒 𝜌𝑠 ) = 𝐷 ∫ 𝑒 𝜌𝑠 𝑑𝑠
0 0
𝑁(𝑡) = (𝐷 + 𝐷𝑒 −𝜌𝑇 )𝑒 −𝜌(𝑡−𝑇) [2.14]
𝐷 𝜌𝑡
𝑁(𝑡)𝑒 𝜌𝑡 − 𝑁0 = ⌈𝑒 − 𝑒0⌉ 𝑁(2𝑇 −) = 𝐷(1 + 𝑒 −𝜌𝑇 )𝑒 −𝜌𝑇
𝜌

𝐷 𝜌𝑡 The concentration before the third influent is

𝑁(𝑡)𝑒 𝜌𝑡 = 𝑁0 + ⌈𝑒 − 1⌉
𝜌 𝑁(2𝑇 −) = 𝐷(1 + 𝑒 −𝜌𝑇 )𝑒 −𝜌𝑇
Dividing through by 𝑒 𝜌𝑡 The model for next influent, that is, 2𝑇 ≤ 𝑡 ≤ 3𝑇 is
𝐷 𝑑𝑁
𝑁(𝑡) = 𝑁0𝑒 −𝜌𝑡 + ⌈1 − 𝑒 −𝜌𝑡 ⌉ (2.8) = −𝜌 𝑁(𝑡),
𝜌 𝑑𝑡
The quantity of nitrogen that will remain in the system 𝑁(0+ ) = 𝑁(2𝑇 −) + 𝐷 [2.15]
at 𝑡 > 0 after a constant quantity 𝐷 has been introduced
into the system is represented by, = 𝐷(1 + 𝑒 −𝜌𝑇 + 𝑒 −2𝜌𝑇 ),

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
𝑊ℎ𝑒𝑟𝑒,

𝑟 = 𝑡 − 2𝑇

𝑡 = 2𝑇 + 𝑟

Solving, we have
Fig 3 Nitrogen Sharing in Constructed CW
𝑁(𝑡) = 𝐷(1 + 𝑒 −𝜌𝑇 + 𝑒 −2𝜌𝑇 )𝑒 −𝜌(𝑡−2𝑇) [2.16] By applying the assumptions above, we get the
resulting mass balance equation
The concentration before the 4th influent is
𝒅𝑵
𝑁(3𝑇 −) = 𝐷(1 + 𝑒 −𝜌𝑇 + 𝑒 −2𝜌𝑇 )𝑒 −𝜌𝑇 = 𝑫 − 𝜹𝟐 𝑵(𝒕) − 𝜹𝟏 𝑵(𝒕) − 𝜶 𝑵(𝒕) − 𝜷𝑵(𝒕)
𝒅𝒕
− 𝜺𝑵(𝒕) [𝟐. 𝟐𝟎]
The general concentration before the nth influent is
From Equation (2.15), we collect all the constants
𝑁((𝑛 − 1)𝑇) = 𝐷(1 + 𝑒 −𝜌𝑇 + 𝑒 −2𝜌𝑇 together
+ 𝑒 −3𝜌𝑇 + . . . + 𝑒 −(𝑛−1)𝜌𝑇 )𝑒 −𝜌𝑇 [2.17]
𝑑𝑁
When making the nth influent, = 𝐷 − (𝛿2 + 𝛿1 + 𝛼 + 𝛽 + 𝜀)𝑁(𝑡) [2.21]
𝑑𝑡

𝑁(𝑛𝑇 +) = 𝑁((𝑛 − 1)𝑇) + 𝐷 [2.18] 𝐿𝑒𝑡 𝛾 = 𝛿2 + 𝛿1 + 𝛼 + 𝛽 + 𝜀

= 𝐷(1 + 𝑒 −𝜌𝑇 + 𝑒 −2𝜌𝑇 + 𝑒 −3𝜌𝑇 + . . . + 𝑒 −(𝑛−1)𝜌𝑇 ) Then

𝑒 −𝜌𝑇 𝑁(𝑛𝑇 +) = 𝐷(𝑒 −𝜌𝑇 + 𝑒 −2𝜌𝑇 𝑑𝑁

= 𝐷 − 𝛾𝑁(𝑡)
+ 𝑒 −3𝜌𝑇 + . . . + 𝑒 −(𝑛−1)𝜌𝑇 + 𝑒 −𝑛𝜌𝑇 ) 𝑑𝑡
𝑑𝑁
𝑁(𝑛𝑇 +) − 𝑒 −𝜌𝑇 𝑁(𝑛𝑇 +) = 𝐷( 1 − 𝑒 −𝜌𝑇 ) + 𝛾𝑁(𝑡) = 𝐷 [2.22]
𝑑𝑡
(1 − 𝑒 −𝜌𝑇 )𝑁(𝑛𝑇 +) = 𝐷( 1 − 𝑒 −𝜌𝑇 )
𝑁(0) = 𝑁0
𝐷( 1 − 𝑒 −𝜌𝑇 )
𝑁(𝑛𝑇 +) = Solving, we have the nitrogen removal model as,
1 − 𝑒 −𝜌𝑇
𝐷
𝐷 𝑁(𝑡) = 𝑁0 𝑒−𝛾𝑡 + ⌈1 − 𝑒 −𝛾𝑡 ⌉ [2.23]
lim 𝑁(𝑛𝑇 +) = [2.19] 𝛾
𝑛 → ∞ 1 − 𝑒 −𝜌𝑇

F. Summation of Nutrient Removal Sites  Phosphorus

The above prediction model does divide nitrogen into Phosphorus attenuation model was obtained on the
the different partitions of the CW. To account for these same principles as nitrogen. The only difference the
partitions in the model, we assume further as below: partitioning of phosphorus which excludes loss to the
atmosphere as shown in the diagram below.
 The nitrogen supply rate into the CW from precipitation
is insignificant,
 Rate of nitrogen consumption by CW macrophyte is 𝛿2 ,
 No loss to groundwater,
 Rate of nitrogen discharge (effluent) from the system is
𝛼,
 The rate of nitrogen supply into the CW is 𝐷
 The rate of retention of nitrogen in the CW water pool is Fig 4 Phosphorus Partitioning in CW.
𝛿1
Based on the assumptions and the parameters above,
 The rate of retention of nitrogen in the CW media is 𝜀
the model equation becomes
 The rate of denitrification of nitrogen in the CW is 𝛽
𝑑𝑃
= 𝐷 − 𝑘𝑃; 𝑃(0) = 𝑃0
𝑑𝑡

Where 𝑘 = 𝛼1 + 𝛼2 + 𝛼3 + 𝛼4

D = input phosphorus concentration (mg/l)

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
𝛼1 = CWplant use (mg/l)  Root Mean Square Error (RMSE)
It quantifies the dispersion between simulated and
𝛼2 = accumulation in CW media and sediment (mg/l) measured data.

𝛼3 = retention in wetland water pool (mg/l) N

1
RMSE = √ ∑(Pi − Oi )2 [2.27]
𝛼4 = discharged phosphorus concentration (mg/l) N
i=1

Other variables are as defined for nitrogen.  Relative Error (RE):

Hence, RMSE
RE = × 100 [2.28]
y̅
𝑑𝑃
+ 𝑘𝑃 = 𝐷 [2.24]
𝑑𝑡 Where,

𝑃(0) = 𝑃0 y is the mean of observed values.

Solving, we have the phosphorus removal model as  Model Efficiency

Model efficiency (EF) was calculated as:
𝐷
𝑃(𝑡) = 𝑃0 𝑒 −𝑘𝑡 + ⌈1 − 𝑒 −𝑘𝑡 ⌉ [2.25]
𝑘 ̅ )2 − ∑(P − P
∑(O − O ̅)2
EF = ̅ )2 [2.29]
∑(O − O
G. Model Solutions
Solutions to the first order equations concerning the
Where,
nutrients attenuation in the CW were obtained by using
MATLAB approach. Consequently, standardization of ̅ = mean observed values;
O = observed values; O
model constants and verification of the model were carried
out using data obtained from the experiment. Finally, the
̅ = mean predicted values
P = predicted values and, P
model was validated by comparing field values with model
predictions.
 Index of Agreement (IA):
H. Evaluation of Model Performance
The model was evaluated statistically to indicate its ∑Ni=1(Oi − Pi )
2
d= 1− ,0 ≤ d ≤ 1 [2.30]
performance. evaluated (Fox, 1981). ∑N ′ ′ 2
i=1(O i + P i )

 Bias or Mean Bias Where O’i = |Oi - P| , P’i = |Pi -P | , Oi is the observed
N
value, Pi is the simulated value and P is the simulated mean.
1 d = 1corresponds to a perfect match of predicted to observed
ME = ∑(Pi − Oi ) [2.26] data.
N
i=1

I. Model Calibration
Where P and O are the predicted and observed values and N Model calibration parameters for nitrogen and
is the number of observations. phosphorus removal respectively, are presented in Table 1
Table 1 Parameters for Calibration of Nitrogen and Phosphorus Removal.
Symbols Description N P Unit
𝑁0 Initial concentration of Nitrogen 6.00 mg/l
𝑃0 Initial concentration of Phosphorus 2.23 mg/l
𝑡 Retention time 3 3 Days
𝜌 Rate of Nutrient removal from the wetland system. 0.122 0.078 m3/day
𝐷 Input rate (mean) 29.2 11.52 m3/day
𝑇 Period time of introducing nutrient. 3 3 Days
𝛿1 Nutrient retention in wetland water column 1.48 mg/l
𝛿2 Plant Nutrient uptake 8.90 mg/l
𝛽 Denitrification (52% of net N input) 15.2 mg/l
𝜀 Nutrient retention in wetland sediment 5.05 mg/l
𝛼𝑁 Effluent rate or output 2.07 m3/day
𝛼1 Plant uptake 2.08 mg/l
𝛼2 Nutrient retention in wetland sediment 2.87 mg/l
𝛼3 Retention in wetland water column 2.01 mg/l
𝛼4 Effluent rate 1.24 mg/l

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
To calibrate the model, field data collected within February – April, 2018 were used. The procedure was to adjust the model
parameters and forcing within the boundaries of the uncertainties to get a model representation of the processes of interest that
satisfies pre-agreed conditions.

J. Model Validation
Input parameters for model simulation are shown in Table 2.

Table 2 Parameters for Model Simulation for Nitrogen and Phosphorus Attenuation.
Symbols Description N P Unit
𝑁0 Initial concentration of Nitrogen 6.06 mg/l
𝑃0 Initial concentration of Phosphorus 2.23 mg/l
𝑡 Retention time 3 3 Days
𝜌 Rate of Nutrient removal from the wetland system. 0.125 0.082 md-1
𝐷 Input rate (mean) 27.40 10.21 m3/day
𝑇 Period time of introducing nutrient. 3 3 Days
𝛿1 Nutrient retention in wetland water column 1.28 mg/l
𝛿2 Plant Nutrient uptake 8.76 mg/l
𝛽 Denitrification (52% of net N input) 5.82 mg/l
𝜀 Nutrient retention in wetland sediment 5.65 mg/l
𝛼𝑁 Effluent rate or output 1.28 m3/day
𝛼1 Plant uptake 2.43 mg/l
𝛼2 Nutrient retention in wetland sediment 2.81 mg/l
𝛼3 Retention in wetland water column 1.71 mg/l
𝛼4 Effluent rate 0.96 mg/l

The simulation of the prediction model was effected by CW are presented in Figures 6 and 9 respectively. There was
comparing the field data with the model prediction by a high degree of relationship between the simulated and
plotting the simulated and field data against time after observed values.
running a calibrated model with a new set of data
(independent data set) with physical parameters and the
derived functions to reflect new conditions and discover
how well the model simulations fit the new data set.

III. RESULTS AND FINDINGS

 Model simulation Results

Simulations of nutrient attenuation in the CW were
executed using the parameters shown in Table 2 to define
the overall relations and connections that influence the
attenuation of nitrogen and phosphorus in CW. The model
simulations after introducing mathematical equations,
parameters and initial conditions in the state variables are
presented in Figures 5 and 6.

Fig 6 Correlation of Observed and Simulated Attenuation of

Nitrogen in Constructed Wetland.

Fig 5 Simulated and Observed Nitrogen Attenuation in CW.

The relationship amongst the simulated and observed Fig 7 Simulated and Observed Variations for Phosphorus
attenuation of nitrogen and phosphorus contaminants in the Removal in CW

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
The correlation between the simulated and observed pigs. Nitrogen release to the atmosphere is primarily through
attenuation of phosphorus in the CW is presented in Figure denitrification of nitrogen. Contamination from rainfall and
9. There was high correlation among the simulated and interchange with subsurface are insignificant matched with
observed values. other processes.

In the research, nitrogen and phosphorus attenuation

was exponential in the first three days of detention of the
wastewater in the CW and thereafter the attenuation was
constant at greater detention periods contingent on the decay
constant. The CW design was centered on first order plug
flow reaction that is characterized by decay response
indicating a weakening in contaminant strength along the
CW basin as long as the strength of the entering wastewater
exceed that of the CW. This remark is compatible with that
of Kadlec and Wallace (2009) for a number of CW. The
relationship among the observed and simulated attenuation
rates removal for N and P in Figures 6 and 8 indicated good
agreement as presented by regression equations in Figures 6
for N (R = 0.9537) and Figure 8 for P (R = 0.9912)
separately.

Fig 8 Correlation of Observed and Simulated Removal of The linear regression coefficients are very good agreed
Phosphorus in CW that the CW was a natural system sited in the field, where
unrestrained impelling influences might wane optimum
IV. DISCUSSION ON FINDINGS efficiency according to Jørgensen and Bendoricchio, (2001).

A. Process Model Assumptions and Development B. Statistical Indicators of Model Performance

In this model, nutrient discharge due to plant die-off The statistical pointers of model performance are
was not considered to have an input into the wetland since shown in Table 3.
the macrophytes are likely to be mowed fresh to feed the

Table 3 Statistical Pointers of Model Performance

Nutrient R2 R Mean bias Root Mean Square Relative Model efficiency Index of
error (mm) Error (mm) Error (%) (%) Agreement
Nitrogen 0.9537 0.9766 0.211 0.32 24 84 0.6527
Phosphorus 0.9912 0.9956 0.139 0.18 12 77 0.8676

The statistical pointers of simulation performance are and also in the field data. For instance, the model adopts the
summarized in Table 3. The rate of coefficient of steady-state situation but in reality, this may not be true (as
determination (R2, 0.9537, 0.9912) indication that a good the flux can vary with the change in moisture level and
relationship exists between observed and simulated values atmospheric demand). Overload of phosphorus in the
for both Nitrogen and Phosphorus separately. The wetland bed and /or low bed porousness of the parent
proportion of mean bias error (MBE) is equivalent to 0.21 material used for bed construction could prejudice
and 0.14 mm for both nitrogen and phosphorus separately. A phosphorus attenuation efficiency as observed by
positive rate of MBE shows excessive estimation and vice- Karczmarczyk (2004).
versa. The mean root square errors are 0.32 and 0.18 mm for
both nitrogen and phosphorus. The extent of root mean C. Model Applications and Limitations
square error (RMSE) is a suitable parameter of model The models developed in this study are suitable for
performance. In an ideal situation, the rate of relative error performance analysis of horizontal subsurface flow
(RE) and the model efficiency (EF) will be 0% and 100%, constructed wetlands getting secondary piggery wastewater.
separately. So the RE value of about 24 and 12 % and EF Their application requires information on inflow wastewater
value of about 64 and 37 % obtained in this study show that concentrations (mg/l) of organic nitrogen and phosphorus in
the strength of model in predicting real life attenuation of the wetland and the inflow rate. The initial values of
the nutrients was good for nitrogen and reasonable for nitrogen and phosphorus in the soil and in the wastewater
phosphorus. The limit of index of agreement (d) value is are also required (Udom, 2023).
from 0 to 1. A higher value indicates a better agreement
between the simulated and observed values. In this study,
the value of d (0.6527 and 0.8676) indication a good
performance of the model in attenuating the nutrients.
However, much departure from the ideal value for the model
may be owing to in-built assumptions in the model code,

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Volume 8, Issue 9, September – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
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