MATHEMATICAL MODELING AND SIMULATION OF WATERCOURSES CONSIDERING FLOWRATE AND TEMPERATURE DYNAMICS

MATHEMATICAL MODELING AND SIMULATION OF WATERCOURSES CONSIDERING FLOWRATE AND TEMPERATURE DYNAMICS

DELFRATTE, E. S.; SCENNA, N. J.; CRUZ, A. S. M. SANTA

Artigo:

Due to the importance of the natural watercourses preservation, a mathematical model of heat and mass transfer dynamics of a fixed-geometry watercourse is fully developed. The mathematical model is derived from first principles and consists of both partial differential and algebraic equations. Semi empirical equations are applied to calculate the physicochemical properties, heat loads and mass transfer coefficients. The model is implemented and solved using gPROMS (General Process Modeling System). In this context, the proposed dynamic mathematical model predicts the temperature profile of the watercourse under study, as well as the waterbed one, while considering every major heat flux which impacts on the system (including radiation and non-radiation terms). The obtained results are compared against a well-known river and stream water quality modeling implementation, which allows concluding that a good calibration of the watercourse dynamics mathematical model is here achieved. 1. INTRODUCTION Nowadays, preservation and purgation of rivers is considered by national and international organizations which are responsible of quality control and preservation of water resources. Water pollution from human activities, either industrial or domestic, and accidental spillages, is a major problem in many countries (Tchobanoglous and Burton, 1991). So it is clear that estimation and simulation of flow and contaminant in river and water systems have more significance in water resources management in order to control and predict water quality. In addition, water resource temperature is a very important variable in ecological studies. Changes in its temperature can significantly impact its inherent resources dynamics (Caissie, 2006). It is therefore important to understand the thermal regime of rivers for an effective management of aquatic resources. Deterministic models are efficient tools to understand the dynamics and contribution of the heat and flow rate components (Maheu et al., 2013). This modeling approach consists of both partial Área temática: Engenharia Ambiental e Tecnologias Limpas 1differential and algebraic equations of heat and mass transfer processes into a fixed-geometry. Such models can be extremely complicated to solve, involving a large number of parameters and variables, but their main advantage is their closely approximation of reality. In this context, the primary objective of the present work is to introduce a complete mathematical model to describe temperature profiles of water resources taking into account mass and heat transfer equations, while considering a comprehensive description of the radiation and non-radiation heat transfer terms. Radiation terms including solar shortwave radiation, atmospheric longwave radiation and water longwave radiation are considered. On the non-radiation terms side, the model considers convection, evaporation and condensation. Real measurements of the heat fluxes of a watercourse are used to calibrate the model performance. 2. MATHEMATICAL MODEL 2.1. Watercourse Flowrate Dynamics The mass balance for the watercourse is expressed in Equation (1), which represents a one-dimensional model for the flowrate dynamics of the system, as represented in Figure 1, with no chemical reaction neither substances addition.

Due to the importance of the natural watercourses preservation, a mathematical model of heat and mass transfer dynamics of a fixed-geometry watercourse is fully developed. The mathematical model is derived from first principles and consists of both partial differential and algebraic equations. Semi empirical equations are applied to calculate the physicochemical properties, heat loads and mass transfer coefficients. The model is implemented and solved using gPROMS (General Process Modeling System). In this context, the proposed dynamic mathematical model predicts the temperature profile of the watercourse under study, as well as the waterbed one, while considering every major heat flux which impacts on the system (including radiation and non-radiation terms). The obtained results are compared against a well-known river and stream water quality modeling implementation, which allows concluding that a good calibration of the watercourse dynamics mathematical model is here achieved. 1. INTRODUCTION Nowadays, preservation and purgation of rivers is considered by national and international organizations which are responsible of quality control and preservation of water resources. Water pollution from human activities, either industrial or domestic, and accidental spillages, is a major problem in many countries (Tchobanoglous and Burton, 1991). So it is clear that estimation and simulation of flow and contaminant in river and water systems have more significance in water resources management in order to control and predict water quality. In addition, water resource temperature is a very important variable in ecological studies. Changes in its temperature can significantly impact its inherent resources dynamics (Caissie, 2006). It is therefore important to understand the thermal regime of rivers for an effective management of aquatic resources. Deterministic models are efficient tools to understand the dynamics and contribution of the heat and flow rate components (Maheu et al., 2013). This modeling approach consists of both partial Área temática: Engenharia Ambiental e Tecnologias Limpas 1differential and algebraic equations of heat and mass transfer processes into a fixed-geometry. Such models can be extremely complicated to solve, involving a large number of parameters and variables, but their main advantage is their closely approximation of reality. In this context, the primary objective of the present work is to introduce a complete mathematical model to describe temperature profiles of water resources taking into account mass and heat transfer equations, while considering a comprehensive description of the radiation and non-radiation heat transfer terms. Radiation terms including solar shortwave radiation, atmospheric longwave radiation and water longwave radiation are considered. On the non-radiation terms side, the model considers convection, evaporation and condensation. Real measurements of the heat fluxes of a watercourse are used to calibrate the model performance. 2. MATHEMATICAL MODEL 2.1. Watercourse Flowrate Dynamics The mass balance for the watercourse is expressed in Equation (1), which represents a one-dimensional model for the flowrate dynamics of the system, as represented in Figure 1, with no chemical reaction neither substances addition.

Palavras-chave:

DOI: 10.5151/chemeng-cobeq2014-0925-22391-159308

Referências bibliográficas

• [1] CAISSIE, D. The thermal regime of rivers: a review. Freshwater Biology, 51, 1389-1406, 2006.
• [2] GPROMS. gPROMS V2.0 Introductory User Guide. Process Systems Enterprise Ltd., London, 2001.
• [3] MAHUE, A.; CAISSIE, D.; ST-HILAIRE, A.; EL-JABI, N. River Evaporation and Corresponding Heat Fluxes in Forested Catchments. Hydrological Processes, doi: 10.1002/hyp.10071, In Press, 2013.
• [4] PELLETIER, G.; CHAPRA, S. QUAL2Kw theory and documentation - A modeling framework for simulating river and stream water quality. Washington State Department of Ecology, Washington, 2004.
• [5] TCHOBANOGLOUS, G.; BURTON, F.L. Wastewater Engineering: Treatment, Disposal and Reuse, 3 ed. McGraw-Hill, New York, 1991.

Como citar:

DELFRATTE, E. S.; SCENNA, N. J.; CRUZ, A. S. M. SANTA; "MATHEMATICAL MODELING AND SIMULATION OF WATERCOURSES CONSIDERING FLOWRATE AND TEMPERATURE DYNAMICS", p-7939-7946. In: Anais do XX Congresso Brasileiro de Engenharia Química - COBEQ 2014 [= Blucher Chemical Engineering Proceedings, v.1, n.2]. São Paulo: Blucher, 2015.
ISSN 23591757, DOI 10.5151/chemeng-cobeq2014-0925-22391-159308