TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

A simple mathematical model for assessing water quality in a closed-system shrimp farm

, *

* Corresponding author · click or hover a name for details

pp. 2031–2043Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2265XML
Received:
12 Feb 2025
Published Online:
27 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2265
Pages:
2031–2043

Abstract

The problem of wastewater from shrimp farming affects the environment, both in terms of wastewater discharge and soil deterioration. Wastewater management is also quite expensive for the production costs of shrimp farmers. Therefore, the approach to using shrimp farming technology in closed-system farms is proposed, which reduces wastewater discharge into the environment and reduces the cost of wastewater treatment for farmers. This research presents a simple mathematical model for assessing water quality in such closed-system shrimp farms. The method for determining various parameters for determining the mathematical model is presented. The model solution is estimated by the Runge-Kutta method of the fourth order. This research simulates the situation to compare the different parameter values in each situation, which affect the level of water quality in closed-system shrimp farms at different times. The research found that the initial water quality, the rate of chemical reaction of pollutants, the rate of pollution formation, the rate of pollution decomposition, the rate of decrease in pollution concentration due to water circulation between the farm and the water treatment pond, and time all affect water quality. The results from the calculation can help closed-system shrimp farmers know the trend of pollution concentration changes in closed-system shrimp farms in order to find ways to develop techniques for improving water quality.

Keywords

Subject Classifications

65L05

References

[1] S. C. Chapra, Surface Water-Quality Modeling. Long Grove, IL: Waveland Press Inc. (2008).
[2] S. Tookwinas, Closed-recirculating Shrimp Farming System. Southeast Asian Fisheries Development Center (2000).
[3] W. Kraychang, S. Meechowna, W. Welamas, and N. Pochai, “A simple mathematical model of water quality control for recirculating pond on a shrimp farm,” Engineering Letters, vol. 29, no. 4, pp. 1470–1477 (2021).
[4] P. Unyapoti and N. Pochai, “A shoreline evolution model with a twin groins structure using unconditionally stable explicit finite difference techniques,” Engineering Letters, vol. 29, no. 1, pp. 288–296 (2021).
[5] S. Khatbanjong and N. Pochai, “Numerical groundwater quality assessment model using two-level explicit methods,” Engineering Letters, vol. 29, no. 1, pp. 183–190 (2021).
[6] P. Othata and N. Pochai, “Irrigation water management strategies for salinity control in the Chao Phraya River using Sualyev finite difference method with Lagrange interpolation technique,” Engineering Letters, vol. 29, no. 2, pp. 332–338 (2021).
[7] P. Othata and N. Pochai, “A mathematical model of salinity control in a river with an effect of internal waves using two explicit finite difference methods,” Engineering Letters, vol. 29, no. 2, pp. 689–696 (2021).
[8] P. Phosri and N. Pochai, “Numerical computation of a water-quality model with advection-diffusion-reaction equation using an upwind implicit scheme,” Thai Journal of Mathematics, vol. 19, no. 1, pp. 187–196 (2021).
[9] P. Unyapoti and N. Pochai, “A shoreline evolution model with a groin structure under non-uniform breaking wave crest impact,” Computation, vol. 9, no. 4 (2021).
[10] N. Pongnoo and N. Pochai, “A numerical treatment of a couple mathematical models of ground water flow in rice field near marine shrimp aquaculture farm,” Applied Mathematical Sciences, vol. 6, pp. 283–289 (2012).
[11] S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, 6th ed. New York, NY: McGraw-Hill (2010).
[12] J. C. Butcher, Numerical Methods for Ordinary Differential Equations. Chichester, UK: John Wiley and Sons (2003).
[13] R. England, “Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations,” Comput. J., vol. 12, pp. 166–170 (1969).
[14] N. Pochai and P. Phosri, “A couple mathematical models of the water quality measurement in a stream using upwind implicit methods,” IAENG International Journal of Applied Mathematics, vol. 51, no. 1 (2021).
[15] N. Sittijinda and N. Pochai, “Numerical simulation of water quality in a couple of ponds of shrimp farming,” in Proc. 26th Annu. Meeting in Mathematics (AMM 2022), School of Mathematics, Institute of Science, Suranaree University of Technology, Thailand, pp. 70–80 (2022).

Views: 129Downloads: 7Citations: 1