Numerical modeling of tidal modulated dispersion of brine discharges from a desalination plant in singapore coastal waters

NUMERICAL MODELING OF TIDAL-MODULATED DISPERSION OF BRINE DISCHARGES FROM A DESALINATION PLANT IN SINGAPORE COASTAL WATERS SINAPAH SWAMI DIDIER NATIONAL UNIVERSITY OF SINGAPORE 2003 NUMERICAL MODELING OF TIDAL-MODULATED DISPERSION OF BRINE DISCHARGES FROM A DESALINATION PLANT IN SINGAPORE COASTAL WATERS SINAPAH SWAMI DIDIER (B Sc Eng, Ecole Nationale des Ponts et Chaussées, France) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGMENT This Research would not have been possible without help and support from many people and organizations I wish particularly to express my greatest gratitude to the following: - My supervisor, Dr Lin Pengzhi, for his invaluable advice and support throughout the whole research - Post-Doctoral Dr Wu Yonsheng for his guidance and his expertise in numerical modelling - Staffs of National University of Singapore and Ecole Nationale des Ponts et Chaussées for making this agreement between France and Singapore possible - Finally, my family, who has supported me during this whole period away from home, and my friends, both in France and in Singapore, for their patience, encouragement, understanding and continuous support throughout my research TABLE OF CONTENTS ACKNOWLEDGMENT TABLE OF CONTENTS SUMMARY NOMENCLATURE 10 LIST OF FIGURES 14 LIST OF TABLES 17 CHAPTER – INTRODUCTION 18 1.1 GLOBAL CONCERN AND PROBLEMATIC 18 1.2 SINGAPORE CONTEXT 19 1.3 EFFLUENT DISCHARGE AT SEA OUTFALL .20 1.4 AIM OF STUDY 21 1.5 THESIS ORGANIZATION 22 CHAPTER – LITERATURE REVIEW 23 2.1 INTRODUCTION 23 2.2 THREE-DIMENSIONAL HYDRODYNAMIC MODELS 24 2.2.1 Theory-Hydrodynamic equations 24 2.2.1.1 Basic approximations 25 2.2.1.2 General basic equations 26 2.2.2 2.2.2.1 z-coordinate models 28 2.2.2.2 ρ-coordinate models 28 2.2.2.3 σ-coordinate models 29 2.2.3 Horizontal coordinate and discretisation 31 2.2.3.1 Horizontal coordinate 31 2.2.3.2 Horizontal discretisation 32 2.2.4 Boundaries conditions 33 2.2.4.1 Open boundary conditions 33 2.2.4.2 Coastal boundaries conditions 34 2.2.5 2.3 Vertical discretisation .28 Turbulence 34 THREE-DIMENSIONAL WATER QUALITY MODELS 36 2.3.1 Classifications of water quality model 36 2.3.2 Conceptual approach of coastal water quality applications 40 2.3.3 Three-dimensional water quality model in tropical coastal waters 42 2.3.4 Plumes dispersion and brine discharge modelling 43 2.4 2.3.4.1 Typical behavior of sea outfall discharge .43 2.3.4.2 Review of studies 45 SUMMARY OF RESEARCH GAPS ADDRESSED BY THE STUDY 46 CHAPTER - THREE-DIMENSIONAL HYDRODYNAMIC MODEL 47 3.1 OUTLINE 47 3.2 GOVERNING EQUATIONS 47 3.2.1 Turbulent flow: Reynolds Averaged Navier Stokes Equations 47 3.2.2 Eddy viscosity concept 49 3.2.3 Turbulence schemes 50 3.2.3.1 Parameterization of vertical processes: k − ε model .51 3.2.3.2 Parameterization of horizontal diffusion 52 3.2.4 Governing equations summary 52 3.3 BOUNDARIES CONDITIONS 54 3.4 NUMERICAL MODEL .55 3.4.1 Introduction .55 3.4.2 Model grid and spatial discretisation 55 3.4.3 Time discretisation 58 3.4.4 User-defined resolution 59 3.4.5 Solution Procedure .60 CHAPTER - VALIDATION OF LARGE-SCALE MODEL 61 4.1 OUTLINE 61 4.2 MODEL SET-UP 61 4.2.1 Study Area 61 4.2.1.1 Geographic and bathymetric conditions 61 4.2.1.2 Tidal conditions 62 4.2.1.3 Climatologic conditions 63 4.2.2 Numerical computation .63 4.2.2.1 Computational domain 63 4.2.2.2 Boundary conditions .64 4.2.2.3 Model input parameters 65 4.2.3 4.3 Validation procedure 66 RESULTS AND DISCUSSION 68 4.3.1 Results 68 4.3.2 Discussion 68 CHAPTER 5.1 – LOCAL MODEL .77 PRESENTATION OF THE CASE STUDY 77 5.1.1 Introduction .77 5.1.2 Objective of the study 78 5.1.3 Condition of discharge 78 5.2 5.1.3.1 Geographical situation of desalination plant and discharges 78 5.1.3.2 Bathymetry of the discharge area 80 5.1.3.3 Hydrodynamic conditions .80 5.1.3.4 Characteristics of brine discharge 81 5.1.3.5 Outfall design 81 MODEL SETUP 82 5.2.1 Computational domain 82 5.2.2 Coherens-based Local Model .82 5.2.3 Bathymetry recovery 82 5.2.4 Near field approximations 85 5.2.5 Boundary, meteorological and wave conditions .86 5.2.6 Model input parameters 87 5.3 RESULTS AND DISCUSSION 89 5.3.1 Monitoring and Analysis Plan 89 5.3.2 Hydrodynamic stage for the discharge .91 5.3.3 Dispersion at the vicinity of the discharge and time variations 92 5.3.4 Horizontal distribution 92 5.3.5 Environmental aspects 94 5.3.6 Effect of assumptions 95 CHAPTER CONCLUSION 106 6.1 SUMMARY OF RESEARCH CONTRIBUTIONS 106 6.2 LIMITATIONS AND FUTURE RESEARCH 107 REFERENCES: 108 APPENDIX A 121 A MATHEMATICAL REPRESENTATION: GENERAL FORM OF A SCALAR ADVECTION- DIFFUSION EQUATION .122 APPENDIX B 124 B TIDAL PREDICTION MODEL: HARMONIC METHOD AND HYDRODYNAMIC CONSIDERATIONS 125 B.1 Traditional full harmonic methods .125 B.2 Limitations: hydrodynamic considerations 127 B.3 Tidal Constituents Table: Example .128 SUMMARY Simulations of coastal processes in Singapore’s waters have been carried out, in the past, using two-dimensional or multi level models A better understanding of these processes, which is essential for a sustainable economic development in the coastal area, requires more accurate analysis and modeling tools such as full three-dimensional models The purpose of this study was to develop a full three-dimensional model for Singapore’s coastal waters, based of the latest developments of the art, and to apply it to simulation of tidal motions and salinity distribution for two different length-scales First, a full three-dimensional large-scale model, covering Singapore and its surrounding, have been developed to simulate tides and tidal currents The model is derived from COHERENS, a recently coupled hydrodynamic-ecological model for regional and shelf seas originally developed for the North Sea The governing equations are solved using a conservative finite difference analysis, an Arakawa “C” grid system and a σ-coordinate system in the vertical direction A mode-splitting technique coupled with a predictorcorrector algorithm is applied to save of computational time The equations are discretised in explicit, semi-implicit and implicit schemes As far as parameterization of vertical processes is concerned, a k − ε model is selected A recent form of stability function derived in Luyten et al (1996) insures the stability of the scheme The numerical model is validated against a range of observed parameters such as tidal elevations and applied for the simulation of tides and tidal currents As a result, the accuracy of the model is proven and the numerical stability that had limited the implementation of full 3D model is achieved Another full three-dimensional model, also derived from COHERENS, covering a local domain in the southwest coast of Singapore is developed The model was developed for purpose of numerical modeling of tidally modulated dispersion of brine waste discharges from a coastal desalination plant, and was inspired by the Desalination Plant Programme of Singapore’s authorities Due to the lack of data, a bathymetry recovery of the domain is performed using interpolation techniques Since the study focuses on the mixing processes in the far field, a near field mixing approximation is achieved The simulation is carried out for sea and weather conditions favorable for this type of study (critical conditions): absence of wind and no wave-current interaction The open boundaries conditions are generated, implementing harmonic constituents method Eventually, the horizontal and vertical distribution profiles of the brine in dilution are simulated As expected, the dispersion of the brine mass is governed by the joint effects of negative buoyancy and hydrodynamics the tidal currents The dilution rate is very high and the salinity level drops rapidly as one moves away from the source Indeed, at distance from the discharge, along the coast in particular, the salinity does not exceed PSU above the ambient seawater salinity As a result, this numerical model demonstrates the applicability of full three-dimensional model for this type of study, as well as the feasibility of this desalination plant for Singapore, from an environmental point of view and as the first approximation 17, pp.363–385 53 Jensen, T.G (1998) Open boundary conditions in stratified ocean models, Journal of Marine Systems, 16, pp 297–322 54 Jia, Z.-G., Morton, M R and Hamrick, J M (2001) Wetting and Drying Simulation of Estuarine Processes, Estuarine, Coastal and Shelf Science, 53, pp 683-700 55 Kourafalou, V.H., Oey, L.-Y., Wang, J.D and Lee, T.N (1996) The fate of river discharge on the continental shelf - Modeling the river plume and the inner shelf coastal current, Journal of Geophysical Research, 101, pp.3415–3434 56 Lin, B and Falconer, R.A (1997) Three-dimensional layer-integrated modeling of estuarine flows with flooding and drying Estuarine, Coastal and Shelf Science, 44, pp.737–751 57 Lopez, F C Jr., 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science and management, Ocean and Coastal Management, Volume 43, pp 725-748 119 120 APPENDIX A 121 A Mathematical representation: general form of a scalar advection- diffusion equation As mentioned, there is less consensus on the basic equations describing the water quality model -especially for the biological part- than the physical model which is precisely powered by the Navier Stokes equations Similarly to the temperature and salinity equations in the physical model, the biological and contamination processes can be represented using scalar transport equations of advection-diffusion type The transport equation has been widely implemented, and its general form for a quantity ψ can be written as follows (Luyten et al., 1999): (I + Ah + Av + As − Dv − Dh )ψ = P(ψ ) − S (ψ ) (2.11) where ψ may represent temperature, salinity, turbulence variables, biological state variables, sediment or contaminant concentrations The meaning of the different operators is explained below I is the time derivative operator defined by : I (ψ ) = ∂ (ψ ) ∂t (2.12) Ah is the horizontal derivative operator given by : Ah (ψ ) = ∂ (uψ ) + ∂ (vψ ) ∂x1 ∂x (2.13) 122 Av is the vertical advection operator defined by : Av (ψ ) = ∂ (w ψ ) ∂x3 (2.14) As is the vertical sinking operator : As (ψ ) = wψs ∂ψ ∂x3 (2.15) where wψs is a non-physical sinking (or swimming) rate specific for the quantity ψ The value is negative (positive) in the case of sinking (swimming) Dv is the vertical diffusion operator defined by Dv (ψ ) = ∂ ∂x3  ψ ∂ψ   λT  ∂ x   (2.16) ψ where λT is the vertical diffusion coefficient appropriate for the quantity ψ The definition is similar to the diffusion in the physical model Dh is the horizontal diffusion operator defined by: Dh (ψ ) = ∂  ψ ∂ψ  ∂  λH + ∂x1  ∂x1  ∂x  ψ ∂ψ  λ H ∂x     (2.17) where λψH is the (uniform) horizontal diffusion coefficient for the quantity ψ P(ψ ), S (ψ ) represent respectively all other positive source terms and all other negative sink terms in the transport equation 123 APPENDIX B 124 B Tidal prediction model: Harmonic method and hydrodynamic considerations “Tidal prediction is probably the oldest form of coastal ocean prediction, and certainly the most accurate” (Parker et al., 1999) Scientists and seamen have been aware of the correlation between the tide and the changing phases of the moon for centuries Basically, there are traditional methods that were developed and sophisticated during the 19th century (Kelvin L and Darwin G) and other methods including hydrodynamic considerations (Parker et al., 1999) Three-dimensional tidal modelling is part of the latter one B.1 Traditional full harmonic methods They are only based on the knowledge of the astronomical frequencies The tidegenerating force varies with time according to the changing relative positions of the earth, moon, and sun, as the earth rotates, the earth revolves around the sun, and the moon revolves around the earth In addition, distances between the moon and earth and between the earth and sun vary with time Moreover, Orbital planes are at angles relative to the earth’s equatorial plane and these angles also vary with time All these motions modulate the tidal forces, so that the tidal energy is distributed into many frequencies For more details see Doodson (1921), Cartwright and Eden (1973) and Pugh (1987) The following tables show the fundamental periods in the motions of the earth, moon and sun and the key tidal constituents (Parker et al., 1999) 125 Practically, in the harmonic method the tide is represented by a sum of various tidal constituents The height of the tide at any time is represented by a formula such as (Schureman, 1958): h = H + ∑ fH cos[at + (V0 + u ) − κ ] (2.10) where h= height of the tide at any time t H = mean height of water level above datum used for prediction H= mean amplitude of any constituents A f = node factor a= speed of constituent A t= time, reckoned from some initial epoch (V0 + u ) = value of equilibrium argument of constituent A at t=0 κ= epoch (phase) of constituent A To resolve these tidal constituents, data time series as long as possible is required (e.g 15 days to resolve M2, but 29 days for N2) The harmonic analysis was traditionally performed with a least square solution technique (Foreman, 1978), or Fourier analysis solution technique (Schureman, 1958) Nevertheless, to accurately predict the tide height and the tidal currents, hydrodynamic effects must be considered 126 B.2 Limitations: hydrodynamic considerations Traditional tide and tidal currents predictions are affected in shallow-water area such as bays, estuaries The problems in the prediction accuracy can be explained by hydrodynamics In this part, we briefly review these considerations In terms of harmonic analysis and prediction, although most of the tidal frequencies are still due to astronomical relations, amplitudes and phases variations result from hydrodynamics Phenomena such as full or partial reflections of the very long tidal waves, discharges, storm surges, nearness of basin lengths or shelf widths to resonance for particular tidal frequencies, continuity effects, frictional damping and advective\inertial effects all affect the tide and tidal currents In addition, in shallow-water areas, several non linear mechanisms cause a modulation and distortion of the tide that lead to the transfer of tidal energy to other frequencies, which are represented by new tidal constituents called overtides and compound tides More details are given in Parker et al (1999) For some effects like overtides and compound tides, theoretical and physical explanations have been proposed and have derived correction techniques (e.g Parker, 1991) But, for phenomena like wind, storm surges, river discharge, no matter how good the harmonic constants are, the statistical methods have failed In some cases, real-time water level and current information that are provided to the maritime community are more helpful Another mean is three-dimensional tidal model that is able to reproduce the propagation wave from ocean to shelf, and quite accurately reproduce the observed tidal data (e.g Xing and Davies 1996) 127 B.3 Tidal Constituents Table: Example 128 [...]... characteristics of Singapore s coastal waters have been also studied in the past In 1979, a tides and tidal currents studies in the Straits of Malacca and Singapore were jointly carried out by Indonesian, Malaysian, Singaporean and Japanese teams Several numerical hydrodynamic models also have been developed (Koh et al, 1997; Cheong et al., 1992; Shankar et al., 1997; Zhang 2000) Although the complexity of the... the east In past four decades, Singapore coast has experienced rapid and huge transformations such as land reclamation and portal infrastructure construction The continuous economic development of the island has led and is leading to an inevitable and increasing degradation of the coastal strips In the past, studies to understand the coastal processes in Singapore such as erosion, tides and tidal currents,... three-dimensional plume dispersion model for a local domain on the west coast of Singapore (Local Model) 4 Apply the Local Model on the numerical modeling of tidally modulated dispersion of brine waste discharges from a coastal desalination plant 5 Estimate under the most critical pollution conditions, the environmental impact of such a discharge In order to achieve this study, a numerical model, called COHERENS,... state 18 1.2 Singapore context Due to its geographic and economic context, coastal issues particularly concern Singapore, a 690-km2 island, off the southern tip of the Malay Peninsula The coastal waters of Singapore comprise of the Johor Strait in the north and the Singapore Strait that stretches from the Malacca Straits to the northwest, to the Java Sea to the south and the South China Sea to the east... COHERENS, has been modified, validated against a wide range of observed physical parameters such as tidal elevations, temperature, and salinity The Large Scale Model is used to simulate tides and tidal currents in Singapore s coastal waters Besides the development and the validation of this model, the second objective of a largescale study consists of properly apprehending tidal phenomena those of which are... z-coordinate models seem to be disadvantageous in resolving equally efficiently the Navier-Stokes equations in both shallow water and deep areas of the domain (CSEP, 1996) This disadvantage is particularly detrimental to an accurate modeling of coastal waters behaviors 2.2.2.2 ρ-coordinate models Another type of vertical discretisation is used in ρ-coordinate models whereby interfaces between layers are... The coastal region comprises of only a narrow stretch of land and sea extending a few tens of kilometers on either side of the shoreline According to the Office of Naval Research International Field Office (ONRIFO) in its Ocean Science and Engineering Newsletter (Ali, B.H., 2000), the coastal area that occupies less than 10% of the surface and 1% of its volume accounts for nearly a quarter of oceanic... growing Countless examples of alarming pollution events exist in all coastal regions in the world It is gradually becoming understood that the design of remedial actions must rest on a clearer understanding of the physical, geomorphological and biological processes in the coastal zone As a matter of fact, a sustainable, demographic and economic development of the coastal regions of the world makes... use of full three-dimensional numerical, so far, few have been applied to Singapore s coastal waters The main reason was numerical limitations (Zhang, 1999) By employing 19 the latest developments of full three-dimensional models one can expect to overcome these numerical limitations; and therefore, end up with a more accurate and efficient tool to study coastal processes in Singapore s coastal waters. .. Introduction In the past decades, coastal areas have been suffering from major environmental degradations due to human economic activities In order to design remedial actions, the need for a better understanding of the hydrodynamic, bio-chemical processes has catalyzed the development of more efficient accurate, and reliable tools of analysis and modelling For the assessment of coastal processes many numerical .. .NUMERICAL MODELING OF TIDAL-MODULATED DISPERSION OF BRINE DISCHARGES FROM A DESALINATION PLANT IN SINGAPORE COASTAL WATERS SINAPAH SWAMI DIDIER (B Sc Eng, Ecole Nationale des Ponts et Chaussées,... accurately and efficiently Three-dimensional modeling of tidally modulated dispersion of brine waste discharges from a coastal desalination plant in Singapore s coastal waters: the question of. .. a coastal desalination plant, and was inspired by the Desalination Plant Programme of Singapore s authorities Due to the lack of data, a bathymetry recovery of the domain is performed using interpolation