دوماه نامه

نوع مقاله : مقالات پژوهشی

نویسندگان

دانشگاه لرستان

چکیده

مدل‌سازی انتشار آلودگی در رودخانه یکی از مهم‌ترین مسائل بخش مهندسی محیط زیست است. معادله حاکم بر انتشار آلودگی در رودخانه‌ها، معادله انتقال و پخش است. در توسعه مدل‌های کامپیوتری جهت شبیه‌سازی انتشار آلودگی در آبراهه‌ها علاوه بر حل عددی معادله حرکت، نیاز به تخمین ضریب پخشیدگی نیز است. در این مقاله برای توسعه مدل کامپیوتری، معادله حرکت با استفاده از روش حجم محدود گسسته و برای تخمین ضریب پخش آلودگی نیز از روش روندیابی غلظت و فرمول‌های تجربی فراوانی بکار گرفته شده است. نتایج ارزیابی فرمول‌های تجربی نشان داد که این فرمول‌ها به خاطر اینکه پدیدآورندگان آن‌ها به خاطر ساده‌سازی که در مرحله مدل‌سازی صورت می‌گیرد دارای دقت مناسب نیستند. به جهت صحت سنجی عملکرد مدل عددی توسعه داده شده، انتشار آلودگی در دو رودخانه سورن و ناریو انگلستان مدل‌سازی شد. انتخاب این دو رودخانه به دلیل در دسترس بودن اطلاعات هندسی، هیدرولیکی و همچنین پروفیل غلظت اندازه‌گیری شده در ایستگاه‌های مختلف بوده است. نتایج نشان می‌دهد که مدل توسعه داده برای شبیه‌سازی انتشار آلودگی در رودخانه‌ سورن دارای دقتی برابر با (R2=0.86) و برای رودخانه ناریو (R2=0.91) می‌باشد و ارزیابی کلی نتایج مدل عددی دقت مناسب آن را تأیید می‌نماید.

کلیدواژه‌ها

عنوان مقاله [English]

Calculation of Longitudinal Dispersion Coefficient and Modeling the Pollution Transmission in Rivers (Case studies: Severn and Narew Rivers)

نویسندگان [English]

  • A. Parsaie
  • A.H. Haghiabi

Lorestan University

چکیده [English]

Introduction: The study of rivers’ water quality is extremely important. This issue is more important when the rivers are one of the main sources of water supply for drinking, agriculture and industry. Unfortunately, river pollution has become one of the most important problems in the environment. When a source of pollution is transfused into the river, due to molecular motion, turbulence, and non-uniform velocity in cross-section of flow, it quickly spreads and covers all around the cross section and moves along the river with the flow. The governing equation of pollutant transmission in river is Advection Dispersion Equation (ADE). Computer simulation of pollution transmission in rives needs to solve the ADE by analytical or numerical approaches. The ADE has analytical solution under simple boundary and initial conditions but when the flow geometry and hydraulic conditions becomes more complex such as practical engineering problems, the analytical solutions are not applicable. Therefore, to solve this equation several numerical methods have been proposed. In this paper by getting the pollution transmission in the Severn River and Narew River was simulated.
Materials and Methods: The longitudinal dispersion coefficient is proportional of properties of Fluid, hydraulic condition and the river geometry characteristics. For fluid properties the density and dynamic viscosity and for hydraulic condition, the velocity, flow depth, velocity and energy gradient slope and for river geometry the width of cross section and longitudinal slope can be mentioned. Several other parameters are influencive, but cannot be clearly measured such as sinuosity path and bed form of river. To derive the governed equation of pollution transmission in river, it is enough to consider an element of river and by using the continuity equation and Fick laws to balancing the inputs and outputs the pollution discharge. To calculate the dispersion coefficient several ways as empirical formulas and artificial intelligent techniques have been proposed. In this study LDC is calculated for the Severn River and Narew River and some selected empirical formulas have been assessed to calculate the LDC.
Dispersion Routing Method: As mentioned previously, calculating the LDC is more important, so firstly, the longitudinal dispersion was calculated from the concentration profile by Dispersion Routing Method (DRM). Using the DRM included the four stage.1-considering of initial value for LDC .2-calculating the concentration profile at the downstream station by using the upstream concentration profile and LDC.3- Performing a comparison between the calculated profile and measured profile.4- if the calculating profile is not a suitable cover, the measured profile of the process will be repeated until the calculated profile shows a good covering on the measured profile.
Numerical Method: The ADE includes two different parts advection and dispersion. The pure advection term is related to transmission modeling without any dispersing and the dispersion term is related to the dispersion without any transmission. To discrete the ADE the finite volume method was used. According to physical properties of these two terms and the recommendation of researchers a suitable scheme should be considered for numerical solution of ADE terms. Among the finite volume schemes, the quickest scheme was selected to discrete the advection term, because of this scheme has suitable ability to model the pure advection term. The quickest scheme is an explicit scheme and the stability condition should be considered. To discrete the dispersion term, the central implicit scheme was selected. This scheme is unconditionally stable.
Results and Discussion: The results of longitudinal dispersion coefficient for the Severn River and Narew River were calculated using the DRM method and empirical formulas. The results of LDC calculation showed that the minimum and maximum values for the Severn River was equal to the 12.5 and 41.5 respectively and for the Narew River were reported as 18.0 and 56.0 respectively. The value of the LDC derived using the DRM was used as one of the input parameters for developing the computer program. For validation of numerical model, a comparison was conducted with results of analytical solution. This comparison showed that the performance of numerical method is quite suitable. For assessing the performance of numerical model the pollution transmission in the both mentioned rivers was simulated. The calculated LDC and time steps and distance steps was considered as 4m and 2s. The results of simulation showed that the performance of developed computer model is suitable for practical purposes.
Conclusion: In this paper the Finite volume method such as numerical model for Discretization the ADE and also estimating the LDS the Dispersion routing method has been used. To primary evaluating of the model the compression between the model result and analytical solution of ADE has been done. To assess the accuracy of the model in engineering work the results of the model compared with two rivers data observations (Severn and Narew). Final result showed that the performance of model is suitable.

کلیدواژه‌ها [English]

  • Transmission of Pollutant
  • Finite Volume Method
  • Severn River
  • Narew River
  • Dispersion Routing
1- Riahi-Madvar, H., et al., An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS. Expert Systems with Applications, 2009. 36(4): p. 8589-8596.
2- Mahmoudian Shooshtari, M., principles of open channel flow. Vol. 2. 2003, Ahvaz: Shahid Chamran University. 486.
3- Baghbanpour*, S. and S. M. Kashefipour, Numerical Modeling of Suspended Sediment Transport in Rivers (Case Study: Karkheh River). JWSS - Isfahan University of Technology, 2012. 16(61): p. 45-58.
4- Mirbagheri, S., M. Abaspour, and K. Zamani, Mathematical modeling of water quality in river systems. 2009.
5- Mahdavi, A., S.M. Kashefipour, and M.H. Omid, Effect of sorption process on cadmium transport. Proceedings of the Institution of Civil Engineers - Water Management, 2013. 166(3): p. 152-162.
6- Benedini, M. and G. Tsakiris, Water quality modelling for rivers and streams. 2013: Springer Science & Business Media.
7- Szymkiewicz, R., Numerical Solution of the Advection Equation, in Numerical Modeling in Open Channel Hydraulics. 2010, Springer Netherlands. p. 219-261.
8- Parsaie, A. and A. Haghiabi, The Effect of Predicting Discharge Coefficient by Neural Network on Increasing the Numerical Modeling Accuracy of Flow Over Side Weir. Water Resources Management, 2015. 29(4): p. 973-985.
9- Parsaie, A., A. Haghiabi, and A. Moradinejad, CFD modeling of flow pattern in spillway’s approach channel. Sustainable Water Resources Management, 2015. 1(3): p. 245-251.
10- Parsaie, A., H. Yonesi, and S. Najafian, Predictive modeling of discharge in compound open channel by support vector machine technique. Modeling Earth Systems and Environment, 2015. 1(2): p. 1-6.
11- Parsaie, A. and A. Haghiabi, Computational Modeling of Pollution Transmission in Rivers. Applied Water Science, 2015: p. 1-10.
12- Kashefipour, S.M. and A. Roshanfekr, Numerical modelling of heavy metals transport processes in riverine basins. 2012: INTECH Open Access Publisher.
13- Kashefipour, S.M., B. Lin, and R.A. Falconer, Dynamic modelling of bacterial concentrations in coastal waters: effects of solar radiation on decay. 2002.
14- Ataie-Ashtiani, B., D.A. Lockington, and R.E. Volker, Truncation errors in finite difference models for solute transport equation with first-order reaction. Journal of Contaminant Hydrology, 1999. 35(4): p. 409-428.
15- Ataie-Ashtiani, B. and S.A. Hosseini, Error analysis of finite difference methods for two-dimensional advection–dispersion–reaction equation. Advances in Water Resources, 2005. 28(8): p. 793-806.
16- Naseri Maleki, M. and S.M. Kashefipour, Application of Numerical Modeling for Solution of Flow Equations and Estimation of Water Quality Pollutants in Rivers (Case Study: Karkheh River). Civil and Environmental Engineering, 2012. 42.3(68): p. 51-60.
17- Givehchi, M., M. Faghfour Maghrebi, and J. Abrishami, Application of Depth-Averaged Velocity Profile for Estimation of Longitudinal Dispersion in Rivers. Ab va Fazilab Journal, 2009. 20(4): p. 91-96.
18- Riahi Modvar, H. and S.A. Ayyoubzadeh, Estimating Longitudinal Dispersion Coefficient of Pollutants Using Adaptive Neuro-Fuzzy Inference System. Ab va Fazilab Journal, 2008. 19(3): p. 34-46.
19- IZADINIA, E. and K.J. ABEDI, INVESTIGATION OF LONGITUDINAL DISPERSION COEFFICIENT IN RIVERS. 2011.
20- Banejad, H., et al., Numerical Simulation of the Flow and Contaminant Transport in Groundwater, Case Study: Nahavand Plain Aquifer. Water and Soil Science, 2013. 23(2): p. 43-57.
21- Shen, C., et al., Estimating longitudinal dispersion in rivers using Acoustic Doppler Current Profilers. Advances in Water Resources, 2010. 33(6): p. 615-623.
22- Seo, I.W. and T.S. Cheong, Predicting Longitudinal Dispersion Coefficient in Natural Streams. Journal of Hydraulic Engineering, 1998. 124(1): p. 25-32.
23- Atkinson, T. and P. Davis, Longitudinal dispersion in natural channels: l. Experimental results from the River Severn, UK. Hydrology and Earth System Sciences Discussions, 2000. 4(3): p. 345-353.
24- Davis, P. and T. Atkinson, Longitudinal dispersion in natural channels: 3. An aggregated dead zone model applied to the River Severn, UK. HYDROL EARTH SYST SC, 2000. 4(3): p. 373-381.
25- Davis, P., T. Atkinson, and T. Wigley, Longitudinal dispersion in natural channels: 2. The roles of shear flow dispersion and dead zones in the River Severn, UK. Hydrology and Earth System Sciences Discussions, 2000. 4(3): p. 355-371.
26- Zeng, Y. and W. Huai, Estimation of longitudinal dispersion coefficient in rivers. Journal of Hydro-environment Research, 2014. 8(1): p. 2-8.
27- Najafzadeh, M. and A.A. Sattar, Neuro-Fuzzy GMDH Approach to Predict Longitudinal Dispersion in Water Networks. Water Resources Management, 2015. 29(7): p. 2205-2219.
28- Sattar, A.M.A. and B. Gharabaghi, Gene expression models for prediction of longitudinal dispersion coefficient in streams. Journal of Hydrology, 2015. 524(0): p. 587-596.
29- Azamathulla, H. and A. Ghani, Genetic Programming for Predicting Longitudinal Dispersion Coefficients in Streams. Water Resources Management, 2011. 25(6): p. 1537-1544.
30- Azamathulla, H.M. and F.-C. Wu, Support vector machine approach for longitudinal dispersion coefficients in natural streams. Applied Soft Computing, 2011. 11(2): p. 2902-2905.
31- Noori, R., et al., How Reliable Are ANN, ANFIS, and SVM Techniques for Predicting Longitudinal Dispersion Coefficient in Natural Rivers? Journal of Hydraulic Engineering, 2015. 0(0): p. 04015039.
32- Noori, R., et al., Predicting the Longitudinal Dispersion Coefficient Using Support Vector Machine and Adaptive Neuro-Fuzzy Inference System Techniques. Environmental Engineering Science, 2009. 26(10): p. 1503-1510.
33- Noori, R., et al., A framework development for predicting the longitudinal dispersion coefficient in natural streams using an artificial neural network. Environmental Progress & Sustainable Energy, 2011. 30(3): p. 439-449.
34- Kashefipour, S.M. and R.A. Falconer, Longitudinal dispersion coefficients in natural channels. Water Research, 2002. 36(6): p. 1596-1608.
CAPTCHA Image