A. James Department of Civil Engineering, University of Newcastle upon Tyne, UK

Transcription

1 FRESH SURFACE WATER - Vol. II - Chemcal Transport n Rvers - A. James CHEMICAL TRANSPORT IN RIVERS A. James Department of Cvl Engneerng, Unversty of Newcastle upon Tyne, UK Keywords: Mathematcal modelng, pollutant fate, reactor knetcs, advecton, dsperson, chemcal decay Contents 1. Introducton. Hydraulc Mechansms 3. Physcal, Chemcal and Bologcal Transformatons 4. Reactor Knetcs 5. Rver Models 6. Trends n Rver Modelng Glossary Bblography Bographcal Sketch Summary Due to human actvtes water polluton has become a wdespread phenomenon. An understandng of the behavor and fate of chemcals, whch are dscharged to the aquatc envronment as a result of these actvtes, s essental to the control of water polluton. In rvers the basc physcal movement of pollutant molecules s the result of advecton, but supermposed upon ths are the effects of dsperson and mxng wth trbutares and other dscharges. Some of the chemcals dscharged are relatvely nert, so ther concentraton changes only due to advecton, dsperson and mxng. However many substances are not conservatve n ther behavor and undergo changes due to chemcal or bochemcal processes lke oxdaton, photolyss, etc. Rver models are mathematcal representatons of the pattern of concentratons n space and tme. A varety of technques are employed, especally fnte dfference, to segment the movement of the chemcals through a spatal grd n steps -dmensonal grd n space and tme. Such basc models have been extended to deal wth partcular problems. For example polluton control legslaton s generally framed n a probablstc manner (e.g. n terms of a 90 percentle concentraton), so the correspondng models contan a stochastc element to generate frequency dstrbutons of concentraton. Rver models have also been formulated to smulate dffuse nputs, or deal wth lateral varaton of concentraton n wde rvers. The lower reaches of rvers are generally subject to tdal nfluence. Such estuarne reaches are hydraulcally much more complex, and requre specalzed models. Encyclopeda of Lfe Support Systems (EOLSS)

2 FRESH SURFACE WATER - Vol. II - Chemcal Transport n Rvers - A. James 1. Introducton Water qualty models attempt to smulate changes n the concentraton of pollutants as they move through the aquatc envronment. There are some pollutants that are suffcently nert for ther concentraton to be regarded as unchangng, except by hydraulc processes lke advecton and dsperson. These are referred to as conservatve substances and are often employed n the calbraton/valdaton of water qualty models. The basc mechansm nvolved n advecton and dsperson s dscussed n Secton snce ths affects both conservatve and non-conservatve substances. Supermposed upon these mass transfer mechansms, for the majorty of pollutants, are physcal, chemcal and bologcal processes whch also cause changes n concentraton. The knetc processes responsble for pollutant decay are dscussed n Secton 3. The fate of a pollutant s the resultant of the nteracton between mass transfer and knetc processes. The prncpal factors determnng the fate of a chemcal after dscharge, are the nature of the chemcal and the nature of the envronment. Even n a relatvely self contaned system lke a rver there are nteractons wth the atmosphere, the ground water and at the rver mouth, the sea. Idealzed reactors are often used to represent the fate of chemcals as they pass through a rver system. Two types of reactor CSTR and Plug Flow are descrbed n Secton 4. Secton 5 dscusses the ways n whch mathematcal models of rver water qualty have been formulated. It ncludes a bref menton of models for partcular types of stuaton but does not extend to estuares, as the pattern of water movements are so complex as to requre specalzed models. Secton 6 dscusses the trends n rver modelng. In modelng the fate of chemcals n the envronment, t s essental to defne a specfc control volume for the model whch must have a clearly defned boundary. The nputs and outputs that move across the boundares should be known as estmated by numercal or emprcal formulaton. Besdes these, the characterstcs of transport wthn the controlled volume and across the boundares are necessary for modelng. Furthermore, the reacton knetcs and rate constants of the model wthn the controlled volume play mportant roles n the models. A controlled volume can be as small as nfntesmally thn slce of water n a rapdly flowng stream or as a large as an ocean. No matter how large t s, the mportant pont s that the boundary of t must be clearly defned so that the volume s known and mass transport flux across the boundares can be determned. Generally speakng, at least four elements are necessary to successfully formulate a mathematcal model of pollutng chemcals: 1. relable feld data on chemcal concentraton and mass fluxes nformaton, Encyclopeda of Lfe Support Systems (EOLSS)

3 FRESH SURFACE WATER - Vol. II - Chemcal Transport n Rvers - A. James. a mathematcal model formulaton that can adequately reflect the real dynamc and transport condton, 3. approprate rate constants and knetc coeffcents for the model, and 4. the crtera wth whch to assess the model performance.. Hydraulc Mechansms It s mportant to apprecate that not all pollutants mx freely wth water. There are some chemcals whch are mmscble and others whch may have partcle szes and densty dfferences whch cause them to rse or snk. However the majorty of pollutants whch are n true soluton, collodal soluton or n fne suspenson, are carred along and mxed by the movement of the water. The processes nvolved are advecton and dsperson, respectvely. Advecton may be defned as mass transport n the aquatc envronment at the velocty of the bulk lqud. Any factors that nfluence flow would also affect the advectve transport. Dsperson refers to the spreadng of a pollutant from a regon of hgh concentraton to other regons of lower concentraton. It s brought about at the molecular level, over long tme scales by Brownan Moton (.e. random movement of solute and solvent molecules), but at the macroscopc level and n much smaller tme scales t s due to eddy dffuson (.e. transport due to random varatons n the advectve velocty). Chemcal transport due to advecton and dsperson can be descrbed by the prncple of mass conservaton and Fck s law as followng t = U X + X K X R Where C = concentraton, U = average velocty n the -th drecton, X = dstance n the -th drecton and R = reacton transformaton rate. K s the dffuson coeffcent n the -th drecton, and t s assumed to be constant. The three dmensonal advecton-dffuson equaton can be wrtten as = U V W + K t x y z x C + K x y C + K y z C R z Where U, V, W = average n x, y, z drecton, respectvely, and K z, K y, K z = dffuson coeffcent n x, y, z drecton, respectvely. (1) () The modelng of chemcal transport, based on (1) and () may be from zero-dmensonal to three-dmensonal, as detaled n the followng. Some lakes or reservors n whch strong turbulence exsts and concentraton of chemcals s consdered unform, zero dmensonal models are approprate for such lakes and reservors. Encyclopeda of Lfe Support Systems (EOLSS)

4 FRESH SURFACE WATER - Vol. II - Chemcal Transport n Rvers - A. James Most rvers n practce are consdered as horzontal lnear networks of segments or volume elements, especally for long, narrow and shallow rvers. A one dmensonal transport model s approprate to these rvers. A one dmensonal model can be appled to narrow estuares whle some estuares are conceptually composed of multple nter-connectng one-dmensonal channels. In modelng the hydrodynamcs and water qualty of relatvely shallow estuares, the crucal assumpton nvolves vertcally well-mxed layers that allows for vertcal ntegraton of the contnuty, momentum, and mass transport equatons (Benelmouffok and Yu, 1989). The two dmensonal laterally average models requre the hypothess of unform lateral mxng n the cross channel drecton. These models are the standard smulaton technques for reservors or estuares whch have consderable varatons of densty and water qualty condton n the vertcal and lateral drectons. For those lakes and estuares n whch chemcal transport s caused not only by advecton but also by dsperson n the whole envronment, three dmensonal models are normally used Bblography TO ACCESS ALL THE 15 PAGES OF THIS CHAPTER, Vst: Bencala, K.E. (1984) Interactons of Solutes and Streambed Sedment. Water Resources Research 0(1), pp Bennel Mouffok, D.E. and Yu, S.L. (1989) Two Dmensonal Modellng of Hydrodynamcs and Pollutants Transport n a Wet Detenton Pond. Water Scence and Technology, 1(8/9), pp Clfforde, I. (1991) Urban Polluton Management. Water and Waste Treatment 35(), pp -40. Czernuszenko, W. (1987) Dsperson of Pollutants n Rvers. Hydrologcal Journal 3(1), pp Danel, T.M. and Wundke, A.D. (1993) Neural Network Assstng n Water Qualty Modelng. nd Australasan Conference on Computng for the Water Industry, Melbourne, Australa. NATL CONF PUBL INST ENG AUST., No. 93, part, pp Dtoro, D.M. (1969) Stream Equatons and Methods of Characterstcs. Proc. ASCE Santary Eng. Dv. Journal, 95, SA4, pp Ellott, D.J. (1993) Rver Models. Chapter 6 n An Introducton to Water Qualty Modellng, edted by A. James. Wley, Chchester. EPA (1987) Rates, Constants and Knetcs: Formulatons n Surface Water Qualty Modellng. nd edton, U.S. Envronmental Protecton Agency Report No. EPA/600/3-85/040. Athens, Georga, U.S.A. Falconer, R.A., Lu, S.W. and Chen, Y. (199) Applcaton of Hgh Order Accurate Schemes for Encyclopeda of Lfe Support Systems (EOLSS)

5 FRESH SURFACE WATER - Vol. II - Chemcal Transport n Rvers - A. James Advectve Transportaton n a -D Model. Ashgate Publshng Ltd., Unversty Press, Cambrdge. Fscher, H.B. (1981) Transport Models for Inland and Coastal Waters. Academc Press, London. James, A. (1984) An Introducton to Water Qualty Modellng. Wley, Chchester. Leonard, P.B.A. (1979) A Stable and Accurate Convectve Modellng Procedure Based on Quadratc Upstream Interpolaton. Computer Methods n Appled Mechancs and Engneerng, 19, pp Luk, G.K.Y., Lau, Y.L. and Watt, W.E. (1990) Two-Dmensonal Modellng n Rvers wth Unsteady Pollutant Source. Journal of Envronmental Engneerng, 116(1), pp Manson, J.R. and Walls, S.G. (000) Conservatve, Sem-Lagrangan fate of transport model for fluval systems. Water Research, 34(15), pp McBrde, G.B. (198) Modellng Advecton and Longtudnal Dsperson. Proceedngs of Rver and Estuarne Mxng Workshop, edted by J.C. Rutherford, New Zealand Water and Sol Organzaton, Wellngton, New Zealand. McBrde, G.B. and Rutherford, J.C. (1984) Accurate Modellng of Rver Pollutant Transport. Journal of Envronmental Engneerng 110(4), pp McDonnell, R.A. (000) Herarchcal modellng of envronmental mpacts of rver mpoundment based on GIS. Hydrol. Processes, 14(11), pp Orlob, G.T. and Beck, M.B. (1983) Mathematcal Modellng of Water Qualty. Wley, Chchester. Rajar, R. and Cetna, M. (1995) Hydrodynamc models as a bass for water qualty modellng. 3 rd Internatonal Conference on Water Polluton. Computatonal Mechancs Inc., Bllerca, MA 0181 (USA), pp Raunch, W., Henze, M., Koncos, L., Rechert, P., Shanahan, P., Somlyody, L. and Vanrolleghem. P. (1998) Rver Water Qualty Modellng. The State of the Art. Water Scence & Technology 38(11), pp Rechert, P. and Wanner, O. (1991) Enhanced One-Dmensonal Modellng of Transport n Rvers. Journal of Hydraulc Engneerng, 117(9), pp Rodda, H.J.E., Shankar, U. and Demuth, S. (1999) Applcaton of GIS to Water Qualty Modellng n New Zealand. Internatonal Assocaton of Hydrologcal Scences, Publcaton No. 54, pp Scarlatos, P.D. (1996) Estuarne Hydraulcs. Chapter 9 n Envronmental Hydraulcs, edted by Sngh, V.P. and Hagar, W.H. Publshed by Kluwer Academc Publshers, London. Streeter, V.L. and Phelps, (195) A study of the polluton and natural purfcaton of the Oho Rver Bulletn No. 146, U.S. Publc Health Servce. Thomann, R.V. (197) Systems Analyss and Water Qualty Management. Envronmental Research and Applcatons Inc., New York. Valentne, E.M. and Wood, I.R. (1977) Longtudnal Dsperson. Journal of Hydraulcs Dv., ASCE 93, HY9, pp Ven der Perk, M. (1998) Calbraton and dentfablty analyss of a water qualty model to evaluate the contrbuton of dfferent processes to the short term dynamcs of suspended solds and dssolved nutrents n the surface water of a rural catchment. Hydrologcal Processes 1(5), pp Van Rjn, L.C. (1896) Mathematcal Modellng of Suspended Sedment n Non-Unform Flows. Journal of Hydraulc Engneerng 11(6), pp Warn, A.E. (198) Calculatng Consent Condtons to Acheve Rver Qualty Objectves. Effluent and Water Treatment Journal, pp Young, P. and Whtehead, P.G. (1975) A Recursve Approach to Tme Seres Analyss for Multvarate Systems n G.C. Vansteenkste (ed) Computer Smulaton of Water Resource Systems. Yoshda, K. (1989) Mathematcal Models for Evaluaton of the Fate of Chemcals n the Envronment. Ese Kagakn 35(5), pp Encyclopeda of Lfe Support Systems (EOLSS)

6 FRESH SURFACE WATER - Vol. II - Chemcal Transport n Rvers - A. James Bographcal Sketch Sam James worked n the Cvl Engneerng Department of The Unversty of Newcastle Upon Tyne from 1958 to 1989, where he was successvely Lecturer, Senor Lecturer and Reader n Envronmental Engneerng. He was also a partner n Envronmental Software Ltd and responsble for a number of rverne, estuarne, and marne models of water qualty n varous countres. Encyclopeda of Lfe Support Systems (EOLSS)