A Mathematical Model Development for Simulating Nitrate Pollutant Transport along a River

Abstract:

Contamination of surface water bodies by a wide range of organic and inorganic pollutants has been a serious problem in the recent time, these have an effect on human and aquatic animals. The water quality deterioration calls for regular monitoring of the water quality in order to maintain the health and sustainability of the aquatic ecosystems. Accurate monitoring of discharged pollutants into the rivers may be time taking and labour intensive. Water quality models are significant tools for simulating water quality and controlling the surface water pollution. The purpose of this study is to develop a simplified mathematical model which is hybrid cells in series model (HCIS) to simulate the spatial and temporal variation of nitrate concentration in natural rivers. The HCIS model was formulated to serve as an alternative method to the Fickian based models. Analytical solutions for the first order reaction kinetics of nitrate with the advection and dispersion process were derived using Laplace transformation technique. The model considered the effect of nitrate concentration at several points along the river downstream by considering the transformation of nitrite to nitrate through nitrification process. In addition, the uptake of nitrate by algae for its growth and conversion of nitrate to nitrogen gas due to denitrification process were considered. The HCIS-NO₃ model was applied to uMgeni River, South Africa to investigate the nitrate concentration along the river. Furthermore, the quantitative measures based on the coefficient of determination (R²) and standard errors (SE) were used to evaluate the performance of the model. The result shows that the simulated values agreed with the measured values of nitrate concentration in the river which resulted in a R² value of 0.72 and a low standard error. Analytical solutions of HCIS - NO₃ model were compared with the numerical solutions of the Fickian based ADE model for hypothetical problems. Comparison of the responses indicates that the HCIS - NO₃ and ADE- NO₃ models were in good agreement. The study shows that the hybrid model is a simple and effective tool for simulating pollutant transport in natural rivers.

• Periodical: International Journal of Engineering Research in Africa (Volume 57)
• Pages: 149-168
• DOI: https://doi.org/10.4028/www.scientific.net/JERA.57.149
• Online since: November 2021
• Authors: Kayode O. Olowe*, Muthukrishnavellaisamy Kumarasamy
• Keywords: Analytical Solution, Hybrid Cells in Series Model, Nitrate Nutrients, Water Quality Model

References

[1] Atashgahi S, Aydin R, Dimitrov MR, Sipkema D, Hamonts K, Lahti L, Maphosa F, Kruse T, Saccenti E, Springael D, Dejonghe W (2015) Impact of a wastewater treatment plant on microbial community composition and function in a hyporheic zone of a eutrophic river. Scientific reports 5:17284.

DOI: 10.1038/srep17284

[2] Rusanov AG, Khromov VM (2016) Longitudinal distribution of periphyton algae in the Moskva River under eutrophication. Water resources 43:513-521.

DOI: 10.1134/s0097807816030131

[3] Tyagi B, Kapoor R, Sinha D, Bhargava DS (2012) Mathematical Modeling and Simulation for Predicting DO Condition in Rivers. International Journal of Environmental Protection 2:29-34.

[4] Xia R, Zhang Y, Critto A, Wu J, Fan J, Zheng Z, Zhang Y (2016). The potential impacts of climate change factors on freshwater eutrophication: implications for research and countermeasures of water management in China. Sustainability, 8(3): 229.

DOI: 10.3390/su8030229

[5] Bailey RT, Ahmadi M (2014) Spatial and temporal variability of in-stream water quality parameter influence on dissolved oxygen and nitrate within a regional stream network. Ecological modelling 277:87-96.

DOI: 10.1016/j.ecolmodel.2014.01.015

[6] Temkin A, Evans S, Manidis T, Campbell C, Naidenko O. V (2019). Exposure-based assessment and economic valuation of adverse birth outcomes and cancer risk due to nitrate in United States drinking water. Environmental research, 176: 108442.

DOI: 10.1016/j.envres.2019.04.009

[7] Kannel PR, Lee S, Lee YS, Kanel SR, Pelletier GJ (2007) Application of automated QUAL2Kw for water quality modeling and management in the Bagmati River, Nepal. ecological modelling 202:503-517.

DOI: 10.1016/j.ecolmodel.2006.12.033

[8] Aissa-Grouz N, Garnier J, Billen G, Mercier B, Martinez A (2015) The response of river nitrification to changes in wastewater treatment (The case of the lower Seine River downstream from Paris). In Annales de Limnologie-International Journal of Limnology 51:351-364.

DOI: 10.1051/limn/2015031

[9] Nowka B., Daims H, Spieck, E (2015). Comparison of oxidation kinetics of nitrite-oxidizing bacteria: nitrite availability as a key factor in niche differentiation. Applied and environmental microbiology, 81(2): 745-753.

DOI: 10.1128/aem.02734-14

[10] Donner SD, Coe MT, Lenters JD, Twine TE, Foley, JA (2002) Modeling the impact of hydrological changes on nitrate transport in the Mississippi River Basin from 1955 to 1994. Global biogeochemical cycles 16:16-22.

DOI: 10.1029/2001gb001396

[11] Tisseuil C, Wade, AJ, Tudesque L, Lek S (2008) Modeling the stream water nitrate dynamics in a 60,000-km European catchment, the Garonne, southwest France. Journal of environmental quality 37:2155-2169.

DOI: 10.2134/jeq2007.0507

[12] Pohlert T, Huisman JA, Breuer L, Frede HG (2005) Modelling of point and non-point source pollution of nitrate with SWAT in the river Dill, Germany. Advances in Geosciences 5:7-12.

DOI: 10.5194/adgeo-5-7-2005

[13] Sui Y, Frankenberger JR (2008) Nitrate loss from subsurface drains in an agricultural watershed using SWAT2005. Transactions of the ASABE 51:1263-1272.

DOI: 10.13031/2013.25243

[14] Oeurng C, Cochrane TA, Arias ME, Shrestha B, Piman T (2016) Assessment of changes in riverine nitrate in the Sesan, Srepok and Sekong tributaries of the Lower Mekong River Basin. Journal of Hydrology: Regional Studies 8:95-111.

DOI: 10.1016/j.ejrh.2016.07.004

[15] Yin Y, Jiang S, Pers C, Yang X, Liu Q, Yuan J, Yao M, He Y, Luo X, Zheng Z (2016) Assessment of the spatial and temporal variations of water quality for agricultural lands with crop rotation in China by using a HYPE Model. International journal of environmental research and public health, 13:336-342.

DOI: 10.3390/ijerph13030336

[16] Lam QD, Schmalz, B, Fohrer N (2010) Modelling point and diffuse source pollution of nitrate in a rural lowland catchment using the SWAT model. Agricultural Water Management, 97: 317-325.

DOI: 10.1016/j.agwat.2009.10.004

[17] Wadi AS, Dimian MF, Ibrahim FN (2014) Analytical solutions for one-dimensional advection–dispersion equation of the pollutant concentration. Journal of earth system science 123:1317-1324.

DOI: 10.1007/s12040-014-0468-2

[18] Kumarasamy MV (2015) Deoxygenation andReaeration Coupled hybridMixing cells Based Pollutant Transport Model to Assess Water Quality Status of a River. International Journal of Environmental Research, 9:341-350.

[19] Olowe KO, Kumarasamy M (2017) Development of the hybrid cells in series model to simulate ammonia nutrient pollutant transport along the Umgeni River. Environmental Science and Pollution Research 24:22967-22979.

DOI: 10.1007/s11356-017-9916-2

[20] Ghosh N (2001) Study of solute transport in a river. Ph. D thesis, Dept of Civ. Eng., IIT. Roorkee, INDIA.

[21] Saggar S, Jha N, Deslippe J, Bolan N. S, Luo J, Giltrap D. L, Tillman R. W (2013). Denitrification and N2O: N2 production in temperate grasslands: Processes, measurements, modelling and mitigating negative impacts. Science of the Total Environment, 465, 173-195.

DOI: 10.1016/j.scitotenv.2012.11.050

[22] Kumarasamy M, Ghosh NC, Mishra GC, Kansal ML (2013) Hybrid model development for the decaying pollutant transport in streams. International Journal of Environment and Waste Management, 12:130-145.

DOI: 10.1504/ijewm.2013.055589

[23] Kinnunen K, Nyholm B, Niemi J, Frisk T, Kylä-Harakka T, Kauranne T (1982) Water quality modelling of Finnish water bodies. Vesihallitus. National Board of Waters.

[24] Brown LC, Barnwell TO (1987) The enhanced stream water quality models QUAL2E and QUAL2E-UNCAS: Documentation and user manual (p.189). US Environmental Protection Agency. Office of Research and Development. Environmental Research Laboratory.

[25] Ghosh NC, Mishra GC, Kumarasamy M (2008) Hybrid-cells-in-series model for solute transport in streams and relation of its parameters with bulk flow characteristics. Journal of Hydraulic Engineering, 134:497-502.

DOI: 10.1061/(asce)0733-9429(2008)134:4(497)

[26] Etemad-Shahidi A, Taghipour M (2012) Predicting longitudinal dispersion coefficient in natural streams using M5' model tree. Journal of hydraulic engineering 138:542-554.

DOI: 10.1061/(asce)hy.1943-7900.0000550

[27] Hill AR, Kemp WA, Buttle JM, Goodyear D (1999) Nitrogen chemistry of subsurface storm runoff on forested Canadian Shield hillslopes. Water Resources Research 35:811-821.

DOI: 10.1029/1998wr900083