Numerical Modelling of Heavy Metal Dynamics in a River-Lagoon System

Hindawi Mathematical Problems in Engineering Volume 2019, Article ID 8485031, 24 pages https://doi.org/10.1155/2019/8485031 Research Article Numerical Modelling of Heavy Metal Dynamics in a River-Lagoon System F. Torres-Bejarano,1 C. Couder-Castañeda ,2 H. Ram-rez-León,3 J. J. Hernández-Gómez ,2 C. Rodr-guez-Cuevas ,4 I. E. Herrera-D-az,5 and H. Barrios-Piña6 1 Departamento de Ingenierı́a Ambiental, Universidad de Córdoba, Monterı́a, Colombia Centro de Desarrollo Aeroespacial, Instituto Politécnico Nacional, Mexico 3 PIMAS Proyectos de Ingenierı́a y Medio Ambiente S.C., Ciudad de México, Mexico 4 Facultad de Ingenierı́a, Universidad Autónoma de San Luis Potosı́, San Luis Potosı́, Mexico 5 Departmento de Ingenierı́a Agroindustrial, Universidad de Guanajuato, Campus Celaya-Salvatierra, Celaya, Guanajuato, Mexico 6 Tecnologico de Monterrey, Campus Guadalajara, 45138 Zapopan, Jalisco, Mexico 2 Correspondence should be addressed to C. Couder-Castañeda; Received 10 January 2019; Revised 1 April 2019; Accepted 18 April 2019; Published 6 May 2019 Academic Editor: Luis Cea Copyright © 2019 F. Torres-Bejarano et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction The concern for water environmental pollution by heavy metals has recently increased due to the negative effects it might have in human beings [1, 2]. Some heavy metals as Cadmium (Cd), Chromium (Cr), and Lead (Pb) may transform into persistent metallic compounds with high toxicity [3]. Due to their damaging effects on the ecological environment and on human health [4, 5], it is necessary to study heavy metal contamination in aquatic ecosystems [6]. Metals are naturally present in small concentrations or traces in earth’s crust; many of them are essential for the growth and development of plants, animals, and human beings. The geo-available origin of these metals occurs from the mother rock to the soils after being released by weathering. In contrast, the presence of high concentrations of metals with respect to the ecological norms is an indicator of anthropogenic activities, such as hazardous wastes derived from industrial activities, mining, and agriculture. 2 As rivers serve as a medium for transport of dissolved and particulate matter from continents to the ocean, nowadays, interest in the pollution of rivers by metals has increased along with the exponential increment of industrialisation, urbanisation, and agriculturisation of coastal areas. This has substantially increased the concern and level of awareness in this problem [7]. For this reason, heavy metal concentrations in waters have been analysed worldwide, particularly by proposing new numerical approaches [8]. In coastal waters, heavy metals are distributed through the water column (particulate and dissolved) and the bottom sediments. This occurs during the mixing of fresh and marine water, which causes flocculation and sedimentation of organic matter, nutrients, and trace elements from rivers. Actually, dissolved metals come into the particulate phase due to processes as flocculation, water pH, sediment mineralogy, and others during estuarine mixing [9]. Thus, heavy metals get bound to these elements and precipitate to the bottom. In this work, it is assumed that the partition coefficient does not depend on the concentration of the sorbing solids, according to Thomann and Mueller [10], in which the hypothesis is that the partition coefficient of metal in water is different from the partition coefficient of that metal in the bottom sediment and it is assumed that the decay in the sediment is approximately zero. This analysis applies to rivers where solids are not suffering a net resuspension in the water column; thus, this model was used to evaluate the concentrations of Cd, Cr, Pb, and Ni in the water column. On the other hand, according to Shimazu et al. [11], the sedimentwater partition of the chemical mainly depends on sorption to sediment organic matter, sediment inorganic matter, and reaction group. Flocculation plays a key role in the dynamics of estuarine and coastal environments, controlling the transport of finegrained cohesive sediments and particulate contaminants throughout these systems [12–14] (usually characterised by muddy bottoms [15]). Nevertheless, it should be pointed out, that during natural estuarine mixing, flocculation process may not occur; actually, salinity plays an important role in the process, depending on the reaction mechanism of a particular metal. For instance, flocculation starts at 10% of salinity during estuarine mixing for Cd [16, 17]. Moreover, other metals are known for their nutrient-like behaviour [18]. Thus, flocculation process constitutes an arduous task to model [19], which is not the aim of this work. For the above reasons, strategies and tools to mitigate the pollution of heavy metals are required [20]. A huge number of mathematical models that intend to predict the transport of heavy metals in flows exist, for example, the statistical models based on exponential functions (analytic models), which al (...truncated)