TYPES OF MODELS THAT APPLY TO THE STUDY OF WATER QUALITY - ENVIRONMENT - 2025

Models for water quality are mathematical formulations that simulate the behavior and effects of pollutants in water. In this sense, possible scenarios of the impact of pollutants are presented, using various formulas that start from certain parameters and variables.

There are different models of water quality depending on the source of contamination and the body of water to be evaluated. These models consist of computer programs based on mathematical algorithms.

Evaluation of water quality. Source: CSIRO

The models integrate field data from various variables and factors, plus certain input conditions. From this data, the models generate the possible scenarios, extrapolating data in time and space based on probabilities.

The most informative parameter to evaluate the contamination of a water body is the biochemical oxygen demand (BOD). Most of the models include the estimation of the variation of the BOD as a criterion to generate their scenarios.

Governments have established water quality regulations that must be met in order to obtain permits to carry out potentially polluting activities. In this sense, models are a useful tool to understand the possible impact on water quality of a given activity.

Mathematical foundation

The models used to forecast the behavior of water quality are based on differential equations. These equations relate the amount of change in one function to the magnitude of the change in another.

Nonlinear differential equations are used in water quality models, because water pollution processes are complex (they do not respond to a linear cause-effect relationship).

Parameters

When applying a certain model it is necessary to take into account a series of parameters.

In general, basic parameters such as Biological Oxygen Demand (BOD), Chemical Oxygen Demand (COD), nitrogen and phosphorus present are estimated.

BOD is one of the most important contamination indicators, since high values ​​indicate a large number of microorganisms. For its part, COD indicates the amount of oxygen necessary to oxidize organic matter by chemical means.

The parameters to be evaluated depend on the type of body of water, either lentic (lakes, ponds, swamps) or lotic (rivers, streams). The flow, area covered, volume of water, temperature and climate must also be taken into account.

It is also necessary to consider the source of contamination to be evaluated, since each contaminant has a different behavior and effect.

In the case of discharges to the water body, the type of discharge, pollutants it contains and its volume are considered.

Classification

There are numerous mathematical models to simulate the behavior of pollutants in bodies of water. They can be classified depending on the type of process they consider (physical, chemical, biological) or the type of solution method (empirical, approximate, simplified).

The factors that are taken into account to classify these models are dynamics and dimensionality.

Dynamic

Stationary models consider that it is sufficient to establish the probability distribution of the state of the pollutant at a given instant or space. Subsequently, he extrapolates that probability distribution considering it the same in all time and space of that body of water.

In dynamic models, it is assumed that the probability of pollutant behavior can change in time and space. Quasi-dynamic models perform the analysis in parts and generate a partial approximation to the dynamics of the system.

There are programs that can work in both a dynamic and a quasi-dynamic model.

Dimensionality

Depending on the spatial dimensions that the model considers, there are dimensionless, one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D).

A dimensionless model considers the medium to be homogeneous in all directions. A 1D model can describe the spatial variation along a river, but not in its vertical or cross section. A 2D model will consider two of these dimensions, while a 3D model will include all of them.

Examples

The type of model to be used depends on the body of water to be studied and the objective of the study, and must be calibrated for each particular condition. In addition, the availability of information and the processes to be modeled must be taken into consideration.

Some examples of models for studies of water quality in rivers, streams and lakes are described below:

QUAL2K and QUAL2Kw (Water Quality Model)

Simulates all the water quality variables under a simulated constant flow. Simulates two levels of BOD to develop scenarios of the river or stream's ability to degrade organic pollutants.

This model also allows simulating the resulting amount of carbon, phosphorus, nitrogen, inorganic solids, phytoplankton, and detritus. Likewise, it simulates the amount of dissolved oxygen, which predicts possible eutrophication problems.

Other variables such as pH or the ability to eliminate pathogens are also projected indirectly.

STREETER-PHELPS model

It is a very useful model to evaluate the behavior of the concentration of a specific pollutant in the area of ​​influence of a discharge into a river.

One of the pollutants that produces the most significant effect is organic matter, so the most informative variable in this model is the dissolved oxygen demand. Therefore, it includes a mathematical formulation of the main processes associated with dissolved oxygen in a river.

Model MIKE11

It simulates various processes such as the degradation of organic matter, photosynthesis and respiration of aquatic plants, nitrification and oxygen exchange. It is characterized by simulating the processes of transformation and dispersion of pollutants.

RIOS model

This model was designed in the context of watershed management and combines biophysical, social and economic data.

It generates useful information to plan remediation measures and includes parameters such as dissolved oxygen, BOD, coliforms and analysis of toxic substances.

QUASAR model (Quality Simulation Along River Systems)

The river is modeled separated into sections, defined by the tributaries, spillways and public intakes that arrive or depart from it.

Among other parameters, it considers the flow, temperature, pH, BOD and concentration of ammonia, nitrates, Escherichia coli, and dissolved oxygen.

WASP (Water Quality Analysis Simulation Program)

You can approach the study of the body of water in different dimensions (1D, 2D or 3D). When using it, the user can choose to enter constant or time-varying kinetic transport processes.

Point and non-point waste discharges can be included and their applications include various physical, chemical and biological modeling frameworks. Here different aspects such as eutrophication and toxic substances can be included.

AQUASIM model

This model is used to study the quality of water in both rivers and lakes. It works like a flow chart, allowing to simulate a large number of parameters.

References

1. Castro-Huertas MA (2015) Application of QUAL2KW in the modeling of the water quality of the Guacaica River, department of Caldas, Colombia. Degree work. Faculty of Engineering and Architecture, Department of Chemical Engineering, National University of Colombia. Colombia. 100 p.
2. Di Toro DM, JJ Fitzpatrick and RV Thomann (1981) Water Quality Analysis Simulation Program (WASP) and Model Verification Program (MVP) - Documentation. Hydroscience, Inc., Westwood, NY, for US EPA, Duluth, MN, Contract No. 68-01-3872.
3. López-Vázquez CM, G Buitrón-Méndez, HA García and FJ Cervantes-Carrillo (Eds.) (2017). Biological wastewater treatment. Principles, modeling and design. IWA Publishing. 580 p.
4. Matovelle C (2017) Mathematical model of water quality applied in the Tabacay river micro-basin. Killkana Technical Magazine 1: 39-48.
5. Ordoñez-Moncada J and M Palacios-Quevedo (2017) Water quality model. Concesionaria Vial Unión del Sur. SH Consortium. Double carriageway. Rumichaca-Pasto. Nariño Department. HSE, Asesoría e Ingeniería Ambiental SAS 45 p.
6. Reichert P (1998) AQUASIM 2.0 - User Manual, computer program for the identification and simulation of aquatic systems, Swiss Federal Institute for Environmental Science and Technology (EAWAG), Switzerland.
7. Rendón-Velázquez CM (2013) Mathematical models of water quality in lakes and reservoirs. Thesis. Faculty of Engineering. National Autonomous University of Mexico. Mexico, DF 95 p.