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A mathematical model of water pollution measurement in a stream using a collocation method with a higher order Legendre polynomial
(2025-08-01)
Thongtha, Kaboon
;
Pochai, Nopparat
In environmental research, challenges with water contamination assessment are generally prevalent. Through data collection, pollution levels in a system may be determined. This is quite challenging and involved; the measurements of what was measured vary from one point to another in every location. The governing equations for a uniform flow pollution dispersion model are used in water quality modeling. The advection-diffusion-reaction equation used in water quality model-ing for a uniform flow stream is a stable pollution dispersion model. This study presents a one-dimensional mathematical model for measuring stream water quality by collocation higher order Legendre polynomial functions. A water pol-lutant concentration can be approximated using the collocation method. A related water quality quantification method may also be employed with the suggested mathematical simulation to approximate the solution.
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A simple mathematical model for assessing water quality in a closed-system shrimp farm
(2025-08-01)
Thongtha, Kaboon
;
Pochai, Nopparat
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.
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Irrigation water management strategies for salinity control in the chao phraya river using sualyev finite difference method with lagrange interpolation technique
(2021-01-01)
Othata, Pornpon
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Pochai, Nopparat
—The problem of salinity in tap water is a very important problem. Drinking water that is higher than the World Health Organization designation can greatly affect peo-ple’s health. In this research, a salinity management model is also applied in a river with a dam with an interpolation process for initial and boundary conditions. An unconditionally stable explicit finite difference scheme with the Lagrange interpolating polynomials for the initial and boundary conditions is utilized to estimate the saltiness level with a few conditions of a proposed model. The suggested computational technique allows for a clear consensus on the effects of realistic implementations for water supply processes.
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A simple mathematical model of water quality control for recirculating pond on a shrimp farm
(2021-01-01)
Kraychang, Witsarut
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Meechowna, Sompoom
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Welamas, Weerapol
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Pochai, Nopparat
— In many countries, shrimp is one of the most valuable export commodities. Shrimp farming raises a number of issues, including shrimp waste contamination, shrimp feed residues, and biochemical reactions in the shrimp pond. In this research, mathematical models were utilized to analyze the water quality in shrimp ponds and wastewater treatment ponds for circulation systems, with BOD serving as a significant indication of water quality. In the circulation system, two separate ponds were investigated: the shrimp pond and the wastewater treatment pond. The shrimp pond was tested for pollutant levels generated by shrimp excretion, shrimp feed residues, and biochemical reactions. A Chaipattana low-speed surface aerator was used to treat the shrimp pond pollutants, and some of the waste was drained to the next pond. The pollutant levels in the treatment pond were investigated. This pond is polluted by sewage from the shrimp pond as well as biological reactions. Lower-efficiency aerators treat the contaminants in the treatment pond, and part of the waste is transferred to the next pond. The advection equation is being used to describe the pollutant concentration in two ponds, and Runge-Kutta order 4 is also being used to determine the approximated solution to the problem. The results of the mathematical model are presented in graphs and tables comparing the pollutant concentrations in many cases. The last section shows an example of wastewater treatment by aerator in a shrimp pond. It was found to reduce the number of days needed for wastewater treatment. The water quality could generate shrimp in this condition, but the water quality could not grow shrimp if the aerator was not turned on the first day of shrimp farming and then turned on the next day. On the first day of shrimp farming, the aerator should not be turned off since the pollutant concentration would be high, making wastewater treatment difficult the next day. In addition, the research showed a maximum five-day reduction in wastewater treatment time (last days of the month). When wastewater is treated every other day, every three days, or every five days, the pollutant concentration must be lower than the minimum necessary for shrimp farming. It can also be used to reduce the cost of water treatment by saving energy.
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A simple numerical model for water quality assessment with constant absorption around nok phrao island of trang river
(2020-01-01)
Kraychang, Witsarut
;
Pochai, Nopparat
Nok Phrao Island is given to the island by the indigenous people. It is located near the Trang estuary with several rivers flowing through. Since this island is the assembly point of different river currents, it consequently causes problems with the quality of water. This island area accumulates different pollution such as municipal and industrial pollution. This problem affects today life of the local people such as their occupation, healthy, and ecosystem. However, there are some problems which are still unsolved because of many influential factors which cannot yet be identified. In order to overcome these obstacles, mathematical models could be useful before conducting operations on the Nok Phrao Island. In this research, mathematical models were applied to assess the water quality at Nok Phrao Island by assuming observation points in the models to get a pollutant concentration before and after the implementation of biological treatment from the wastewater treatment station. The mathematical models proposed in this research could be recommended for the assessment of the standard water quality at Nok Phrao Island to account for the increase in population or growth of industries around Nok Phrao Island in the future.
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A one-dimensional mathematical simulation to salinity control in a river with a barrage dam using an unconditionally stable explicit finite difference method
(2019-12-01)
Othata, Pornpon
;
Pochai, Nopparat
Salinity refers to the amount of salt in rivers, where the salt can be in many different forms. There are two main methods of defining the concentration of salt in water such as the total dissolved solid measurement (TDS) and the electrical conductivity measurement (EC). The salinity is measured by evaporating water to dryness and weighing the solid residue. The electrical conductivity measurement is measured by passing an electric current through the water and measuring how readily the current flows. The total amount of salt in the water can affect the taste of water. The World Health Organization’s guideline on water palatability is that water with a salinity level of less than about 0.50–0.60 g/L is generally considered to be of a standard level. The drinking-water becomes significantly and increasingly unpalatable at salinity levels greater than about 1.0 g/L. In this research, a one-dimensional mathematical model of salinity measurement in a river is proposed. A modified model of salinity control in a river with a barrage dam is also introduced. An unconditionally stable explicit finite difference technique is used to approximate the salinity level under several conditions from the proposed model. The proposed computational technique gives good agreement results in realistic scenarios for water supply processes.

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