Modeling of Solute Transfer in a River with Transient Storage Zones Using a Network of Equivalent Electrical Circuits

Document Type : Research Article

Authors

1 Ph.D. Student of Water Structures, Department of Water Structures Engineering, Tarbiat Modares University, Tehran, Iran.

2 Professor in Sediment and River Engineering, Water Structures Engineering Department, Tarbiat Modares University

3 Professor in Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran.

4 Professor in Department of Applied Physics, Polytechnic University of Cartagena, Cartagena, Spain.

Abstract

Human activities everyday release a huge amount of domestic, industrial and agricultural waste into water bodies and continuously change the ecosystem conditions in the world. Considering the harmful effects of these pollutants entering water resources, study about pollution transfer in streams and predicting the pollutant concentration at downstream points seem to be important. For this purpose, the well-known classical advection-dispersion equation (ADE) was presented as the first attempt for describing mass transfer and energy transfer in physical systems. This equation is useful for channels with relatively prismatic and uniform cross-sections.
Experimental studies carried out in rivers show that ADE is no longer applicable for natural streams, especially mountain pool and riffle streams because of their irregular cross-sections. Afterward, some more accurate models, referred dead zone models or transient storage models, were suggested by several researchers for predicting solute concentration in natural rivers and calibrated using tracer approach. Such models cause more realistic concentration-time distributions which have lower picks and longer residence time. Solving such models, for which in most cases the analytical solution doesn’t exist, needs numerical methods –methods which usually deal with complexity and is time-consuming.
In this study, we have applied Network Simulation Method (NSM) –a powerful and efficient computational method for simulating systems governed by differential equations based on the electric circuit concepts and the analogy between the governing differential equations of hydrodynamic and electrical phenomena– which according to the previous studies simulates desirably the transport of mass in natural streams, to solve two transient storage models. The method consists of two phases of designing and simulating. In designing phase, the system of differential equations corresponding to the prototype must be discretized spatially over the studied domain and then, for each term of the discretized equations the equivalent electrical devices are chosen. These electrical elements are connected based on the algebraic sign of the terms to satisfy Kirchhoff’s current low. Regarding the mathematical models, in most studies, electric potential and electric current are equivalent to the value of the unknown variable and its flux, respectively. The last step of designing the electro-analogical model is the implementation of initial conditions and boundary conditions of unknown variables using appropriate dependent and/or independent, voltage and/or current sources. Simulating this equivalent electrical network is performed through an appropriate electrical-computational circuit code, such as PSpice code. PSpice, which is a powerful circuit analysis software, uses the Newton-Raphson iterative algorithm to solve this set of nonlinear equations and performing the transient analysis.
In this paper, NSM is firstly verified by simulating a transient storage transport model developed by Bencala and Walters (1983) for unsteady conservative solute transfer in pool and riffle streams. This model includes two equations for solute concentration in the main channel and in the storage zone and involves one storage zone. The analytical solution for this model has been presented in Laplace domain by Kazezyılmaz-Alhan (2008) considering a hypothetical channel with a constant cross-sectional area, flow velocity, and dispersion coefficient and for two types of upstream boundary conditions including a continuous injection and a pulsating solute injection. The results of this verification were desirable.
Then, the accuracy and efficiency of NSM were compared with Finite Volume Method (FVM) –a widely used numerical method in computational fluid dynamics- through simulating an unsteady reactive solute transport using a nested two-storage zone transport model developed by Kerr et al. (2013). This model consists of three equations and involves two storage zones including the surface and hyporheic storage zones interacting together. The results of simulating a hypothetical solute transport problem with this nested model indicate a good match between these two methods with near-zero error indices. The computational time needed for NSM and FVM were 117 seconds and 505 seconds, respectively. So, NSM is much faster. Furthermore, the implementation of boundary conditions in NSM is direct, easier and more flexible.
Therefore, NSM is proposed as a precise and efficient alternative for numerical methods in solving one-dimensional coupled differential equations of unsteady transport, simultaneously and providing benchmarks without complex mathematical calculations. Because of its analogical based concept, it can be used as a predicting and monitoring tool for transport phenomena instead of using troublesome physical hydraulic models to perform the water quality studies with less time, low expense and higher accuracy. Hence, in critical conditions, including a sudden spill of a high-hazardous contaminant in a specified point of the river or increasing the concentration of a chemical element to its maximum level, the monitoring and controlling measures at different parts of the river can be carried out with an acceptable accuracy and speed to improve the water quality.

Keywords


Ataieyan, A., Ayyoubzadeh, S. A. and Nabavi, A. (2016). Introduction of Network Simulation Method and investigation of its feasibility in simulation of contaminant transfer in a river. 15th National Conference of Hydraulics, Qazvin, Iran. (In Persian)
Bellver, F. G., Garratón, M. C., Meca, A. S., López, J. A. V., Guirao, J. L. and Fernández-Martínez, M. (2017). Applying the Network Simulation Method for testing chaos in a resistively and capacitively shunted Josephson junction model. Results in physics, 7, 813-822.
Bencala, K. E., McKnight, D. M. and Zellweger, G. W. (1990). Characterization of transport in an acidic and metal‐rich mountain stream based on a lithium tracer injection and simulations of transient storage. Water Resources Research, 26(5), 989-1000.
Bencala, K. E. and Walters, R. A. (1983). Simulation of solute transport in a mountain pool‐and‐riffle stream: A transient storage model. Water Resources Research, 19(3), 718-724.
Bottacin-Busolin, A., Marion, A., Musner, T., Tregnaghi, M. and Zaramella, M. (2011). Evidence of distinct contaminant transport patterns in rivers using tracer tests and a multiple domain retention model. Advances in water resources, 34(6), 737-746.
Briggs, M. A., Gooseff, M. N., Arp, C. D. and Baker, M. A. (2009). A method for estimating surface transient storage parameters for streams with concurrent hyporheic storage. Water Resources Research, 45(4).
Cánovas, M., Alhama, I., Trigueros, E. and Alhama, F. (2015). Numerical simulation of Nusselt-Rayleigh correlation in Bénard cells. A solution based on the network simulation method. International Journal of Numerical Methods for Heat & Fluid Flow, 25(5), 986-997.
Caravaca, M., Sanchez-Andrada, P., Soto, A. and Alajarin, M. (2014). The network simulation method: a useful tool for locating the kinetic–thermodynamic switching point in complex kinetic schemes. Physical Chemistry Chemical Physics, 16(46), 25409-25420.
Chabokpour, J., Minaei, O. and Daneshfaraz, R. (2017). Investigation of longitudinal dispersion coefficients of nonreactive contaminants in porous media. Iranian Journal of Hydraulics, 12(2), 1-12. (In Persian)
Choi, J., Harvey, J. W. and Conklin, M. H. (2000). Characterizing multiple timescales of stream and storage zone interaction that affect solute fate and transport in streams. Water Resources Research, 36(6), 1511-1518.
Del Cerro Velázquez, F., Gómez‐Lopera, S. A. and Alhama, F. (2008). A powerful and versatile educational software to simulate transient heat transfer processes in simple fins. Computer Applications in Engineering Education, 16(1), 72-82.
Elder, J. W. (1959). The dispersion of marked fluid in turbulent shear flow. Journal of fluid mechanics, 5(4), 544-560. Abbott, M. B., Price, W. A. (Eds.). (1993). Coastal, estuarial and harbour engineer's reference book. CRC Press.
Garcia-Hernandez, M. T., Castilla, J., González-Fernández, C. F. and Horno, J. (1997). Application of the network method to simulation of a square scheme with Butler-Volmer charge transfer. Journal of Electroanalytical Chemistry, 424(1-2), 207-212.
González-Fernández, C. F., García-Hernández, M. T. and Horno, J. (1995). Computer simulation of a square scheme with reversible and irreversible charge transfer by the network method. Journal of Electroanalytical Chemistry, 395(1-2), 39-44.
Horno Montijano, J. (2002). Network simulation method. Research Signpost.
Kazezyılmaz-Alhan, C. M. (2008). Analytical solutions for contaminant transport in streams. Journal of hydrology, 348(3-4), 524-534.
Kerr, P. C., Gooseff, M. N. and Bolster, D. (2013). The significance of model structure in one-dimensional stream solute transport models with multiple transient storage zones–competing vs. nested arrangements. Journal of hydrology, 497, 133-144.
Manteca, I. A., Meca, A. S. and López, F. A. (2014). FATSIM‐A: An educational tool based on electrical analogy and the code PSPICE to simulate fluid flow and solute transport processes. Computer Applications in Engineering Education, 22(3), 516-528.
Meddah, S., Saidane, A., Hadjel, M. and Hireche, O. (2015). Pollutant dispersion modeling in natural streams using the transmission line matrix method. Water, 7(9), 4932-4950.
Moya, A. A. and Horno, J. (1999). Application of the network simulation method to ionic transport in ion-exchange membranes including diffuse double-layer effects. The Journal of Physical Chemistry B, 103(49), 10791-10799.
Nordin, C. F. and Troutman, B. M. (1980). Longitudinal dispersion in rivers: The persistence of skewness in observed data. Water Resources Research, 16(1), 123-128.
O’Connor, B. L., Hondzo, M. and Harvey, J. W. (2009). Predictive modeling of transient storage and nutrient uptake: Implications for stream restoration. Journal of Hydraulic Eng., 136(12), 1018-1032.
Runkel, R. L. (1998). One-dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers.
Serna, J., Velasco, F. J. S., and Meca, A. S. (2014). Application of network simulation method to viscous flows: The nanofluid heated lid cavity under pulsating flow. Computers & Fluids, 91, 10-20.
Socolofsky, S. A. and Jirka, G. H. (2005). Special topics in mixing and transport processes in the environment. Engineering–Lectures. 5th Edition. Texas A&M University, 1-93.
Sofiev, M. (2002). Extended resistance analogy for construction of the vertical diffusion scheme for dispersion models. Journal of Geophysical Research: Atmospheres, 107(D12), ACH-10.
Thome, C. R. and Zevenbergen, L. W. (1985). Estimating mean velocity in mountain rivers. Journal of Hydraulic Engineering, 111(4), 612-624.
Trévisan, D. and Periáñez, R. (2016). Coupling catchment hydrology and transient storage to model the fate of solutes during low-flow conditions of an upland river. Journal of Hydrology, 534, 317-325.
Tuinenga, P. W. (1988). SPICE: a guide to circuit simulation and analysis using PSpice. Prentice Hall PTR.
Versteeg, H. K. and Malalasekera, W. (2007). An introduction to computational fluid dynamics: the finite volume method. Pearson Education.
Zueco, J., Bég, O. A. and Ghosh, S. K. (2010). Unsteady hydromagnetic natural convection of a short-memory viscoelastic fluid in a non-Darcian regime: network simulation. Chemical Engineering Communications, 198(2), 172-190.
Zueco, J. and Campo, A. (2006). Network model for the numerical simulation of transient radiative transfer process between the thick walls of enclosures. Applied Thermal Engineering, 26(7), 673-679.
Zueco, J. and López-Ochoa, L. M. (2013). Network numerical simulation of coupled heat and moisture transfer in capillary porous media. International Communications in Heat and Mass Transfer, 44, 1-6.
Borland C++ Builder, Version 6.0 [Build 10.155], Copyright © 1983-2002, Borland Software Corporation. Portions copyright 1996-2002 toolsfactory GmbH.
MATLAB, Version R2015a (8.5.0.197613), copyright © 1984-2015, MathWorks, Inc.
PSpice, Version 9.2, copyright © 1986-2000, Cadence Design Systems, Inc.
  • Receive Date: 10 February 2019
  • Revise Date: 09 June 2019
  • Accept Date: 29 July 2019
  • First Publish Date: 22 November 2019