Sanitary and industrial wastewater discharged into rivers, is a general problem that occurs in most of the world and Mexico is not the exception, the main goal of this research is to determine based on simulations of pollutants concentrations, the assimilation capacity of the Gallinas River against discharges of agricultural and industrial wastewater from the cultivation and processing of sugar cane under two different hypothetical simulation scenarios, based on reproducing two well know scenarios. In sugarcane cultivation, large quantities of fertilizers are used whose main active components are based on nitrogen or phosphorus compounds, therefore, the wastewater resulting from sugarcane processing contains a high organic content from 20 to 40% of inorganic compounds, such as nitrogenous substances, organic acids, and phosphorous sulfates. For this reason, the physical–chemical variables of interest analyzed in this work are the PO $$_4$$4 (phosphate), NO $$_3$$3 (nitrate), and DO (dissolved oxygen). With the simulation results according to each scenery, it can be determined, that despite the continuous discharge of polluting elements, the Gallinas River has a good assimilation capacity thanks to reaeration processes that permit efficient recovery of the dissolved oxygen in the water column. Gallinas River is located in the region known as the Huasteca Potosina, this investigation is relevant for the region due to the River is of vital importance being the main tributary that allows socioeconomic development activities in this zone. To carry out the simulations, was used the Explorer Modeling System 8.4 (EFCD) model and was performed two samplings campaign along 15 km in the water body to calibrate the numerical model to represent the dry and wet seasons during May and September respectively named as calibration scenarios.

This paper describes the development of a two‐dimensional water quality model that solves hydrodynamic equations tied to transport equations with reactions mechanisms inherent in the processes. This enables us to perform an accurate assessment of the pollution in a coastal ecosystem. The model was developed with data drawn from the ecosystem found in Mexico’s southeast state of Tabasco. The coastal ecosystem consists of the interaction of El Yucateco lagoon with Chicozapote and Tonalá rivers that connect the lagoon with the Gulf of Mexico. The results of pollutants transport simulation in the coastal ecosystem are presented, focusing on toxic parameters for two hydrodynamic scenarios: wet and dry seasons. As it is of interest in the zone, the transport of four metals is studied: Cadmium, Chromium, Nickel, and Lead. In order to address these objectives, a self‐posed mathematical problem is solved numerically, which is based on the measured data. The performed simulations show how to characterise metals transport with an acceptable accuracy, agreeing well with measured data in total concentrations in four control points along the water body. Although for the accurate implementation of the hydrodynamic‐based water quality model herein presented boundary (geometry, tides, wind, etc.) and initial (concentrations measurements) conditions are required, it poses an excellent option when the distribution of solutes with high accuracy is required, easing environmental, economic, and social management of coastal ecosystems. It ought to be remarked that this constitutes a robust differential equation‐based water quality model for the transport of heavy metals. Models with these characteristics are not common to be found elsewhere.