Abdu dullra llrahman hman Al Al-Muqb Muqbal ali Supervisor Dr. - PowerPoint PPT Presentation

Sultan Qaboos University College of Science Department Of Mathematics and ============================= Presentation on: Abdu dullra llrahman hman Al Al-Muqb Muqbal ali Supervisor Dr. Anton Purnama Model studies of sea outfall effluent discharge 1 5/19/2019

Sea outfall discharge 2 Model studies of sea outfall effluent discharge 5/19/2019

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Contents of the Presentation 1) Far field model ( Mathematical Model)  Single point source discharge  Two point sources discharges  Multiple point sources discharges 2) Near field model (3-D)  CORMIX  VISJET Desalination brine discharged plumes 5/19/2019 4 Model studies of sea outfall effluent discharge

Far field model (Mathematical model)    h y my U Shoreline Diagram of multiple point sources Uniformly sloping beach 5 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) In far field model we use a two – dimensional advection diffusion equation on   0        sloping beach for a point source where ,   x k k h y k k h x , y 0 k k      n c                k  hUc hD Q x x y y    k k k k  x y y  k 0    With boundary conditions , and c     k ii c ) x y , 0 , y i hD ) 0, y 0  y k y Where : C : Concentration (vertically well-mixed) 3 2 D : Coefficient of dispersivity (proportional to ) h 0 h : water depth Q : rate of discharge U : drift current (proportional to ) 1 2 h 0 δ: Dirac delta function (point source) 6 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model)   0 y y    y y k k Outfall Region A Region B Point source        c     k hUc hD 0   k      x y y There are two matching conditions :    ii ) hUc dy Q k k 0      i ) lim c x y , lim c x y , k k     y y y y k k 7 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) In terms of dimensionless quantities    2 y y , x x h , c ( x , y ) c ( x , y ) Q h U h 0 k k * * 0 0 * 0 * * 0 Equation is reduced to  2 *  *  * c 5 c c     0 0 0 y 0   *  2 2 y x y * * *   where h U D 0 0 0 8 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) By using Laplace transform    ___    px * c p y , e c ( x , y dx ) k * * k * * * * xk Equation is reduced a second – ordinary differential equation 2 d c dc 5     k * k * y p c 0 * * k 2 2 dy dy * * Which can be simplified further to the modified Bessel’s equation By writing     3 4   c p y , y u z with z ( ) 2 py k * * * * 2 d u du 9     2 2 z z ( z ) u 0 2 4 dz dz 9 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) the general solution in the two regions is given by       3 4     c p y , A p y ( ) I 2 py for 0 y y ,  k * * 3 2 * k *           3 4    c p y , B p y ( ) K 2 py for y y ,   k * * 3 2 * k * To obtain the particular solution, the functions and can be determined from the matching conditions      lim c p y , lim c p y ,      k * *  k * *       y k y k * * and    ( )  k q       3 2 3 2   k y c p y , dy y c p y , dy k * * * k * * * * * pm    0 ( k ) 10 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model)    It is found that 2 q     k A p ( ) K 2 p ( k ) 3 2   3 4 m ( k )    2 q and     k B p ( ) I 2 p ( k ) 3 2   3 4 m ( k ) the inversion of the Laplace transform we obtain the exact analytical solution in the form 3 4                2 ( k ) y 1 ( y k ) *  *       c ( x , y ) q exp I   k * * * k 3 2      m x ( k ) [  k ] y   x k  x k   * * * * c ( x , y ) After summing for all concentration from the n+1 multiport sources, the k * * * analytical solution of Equation is given by 3 4   n               2 ( k ) y 1 ( y k )  * *       c ( x , y ) q exp I   n * * * k 3 2          m x ( k ) [ k ] y x k x k   * * * *  k 0 11 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) One point source     3 4 Contours of concentration for single point source when and 12 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) Value of shoreline’s concentration y  In the limit as 0 * We obtain 5 2            4 q   ( k  k     c x ,0 exp   n * *       x k   x k  3 m * * 13 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) By differentiation Equation the maximum value of concentration is 5 2      4 5 5  m  5 2     c exp 0 m      2 2 3   which occurs at the position at x 2 5 * m This maximum value inversely  proportional to the point source 𝛽 Maximum value of concentration 3 1.96 The concentration at the beach for a single point source 4 0.95 14 Model studies of sea outfall effluent discharge 5/19/2019

Two point sources discharges Diagram of two sea outfalls 15 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) Two point sources Contours of concentration for two point sources when α =3 and ħ= 2 : left, ℓ = 3 and right, ℓ = 8 16 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model) Compounded concentration at the beach for two point sources 17 Model studies of sea outfall effluent discharge 5/19/2019

Far field model (Mathematical model)   Merging of contours of concentration for five points sources when 6 18 Model studies of sea outfall effluent discharge 5/19/2019

Near field model ( Computational model) CORMIX VISJET Scenario I Positively buoyant plume (heated brine discharges) for single Plume port and multiport discharges. Scenario II Plume Negatively buoyant plume (dense brine discharges) for single port and multiport discharges. 19 Model studies of sea outfall effluent discharge 5/19/2019

Near field model ( Computational model) Thanks for person Dr. Doneker for given me a permission to use CORMIX in this study . 20 Model studies of sea outfall effluent discharge 5/19/2019

Near field model ( CORMIX ) Table3.1: Input data for CORMIX simulations of single port discharges Parameter Heated brine discharge Dense brine discharge Outfall type Single Ambient (unbounded coastal environmental) Velocity of the currents (m/s) 0.3 Depth at discharge (m) 8.73 Wind speed (m/s) 2.5 Temperature (degree C ) 27 Salinity (ppt) 35 Manning or Darcy – Weisbach f 0.025 (Uniform) Density (kg/m 3 ) 1022.72 Brine effluent Flow rate (m 3 /s) 0.7 Temperature (degree C ) 40 30 Salinity (ppt) 37 50 (Uniform) density(kg/m 3 ) 1019.45 1032.64 Distance to shoreline ( m) 500 Number of ports 1 Port height (m) 1 Port diameter (m) 0.7 Shoreline location Right Vertical angle (degrees) 30 Horizontal angle (degrees) 90 Mixing zone Water Quality Standard (degree C ) 1 - Water Quality Standard (ppt) - 2 Regulatory Mixing Zone (m) 150 Region of Interest (m) 1000 Output steps per module 50 21 Model studies of sea outfall effluent discharge 5/19/2019

Near field model ( CORMIX ) 3.1.1 Scenario I: Heated brine discharges   500 m Density ( kg/m 3 ) Ambient 1022.72 Effluent 1019.45 The positively buoyant plume from single port discharges 22 Model studies of sea outfall effluent discharge 5/19/2019

Near field model ( CORMIX ) Side view of the positively plume in Figure 3.2 23 Model studies of sea outfall effluent discharge 5/19/2019

Near field model ( CORMIX ) 3.1.2 Scenario I I: Dense brine discharges   500 m Density ( kg/m 3 ) Ambient 1022.72 Effluent 1032.64 The negatively buoyant plume from single port discharges 24 Model studies of sea outfall effluent discharge 5/19/2019