Conventional Pollutants in Rivers and Estuaries

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Conventional Pollutants in Rivers and Estuaries
ORGANIC MATTER
OXYGEN
DECOMPOSITION (bacteria/animals)
PRODUCTION (plants)
Chemical energy
Solar energy
CARBON DIOXIDE
INORGANIC NUTRIENTS
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THE DISSOLVED OXYGEN SAG
WWTP
River
DO (mgL-1)
Critical concentration (decompositionreaeration)
Distance
Decomposition dominates
Rearetion dominates
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BIOCHEMICAL OXYGEN DEMAND

• Experiment
• decomposition of carbonaceous matter
• C6H12O66O2? 6CO26H2O
• Mass balance ?
• General solution gg0e -k1t
• Oxygen mass balance ?
• General solution for oxygen

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BIOCHEMICAL OXYGEN DEMAND(ctd.)

• Lrog g
• LL0 exp(-k1t)
• BODL0-L

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Streeter-Phelps equation

• Steady state for ultimate BOD ?
• Steady state for DO ?
• Deficit DCs-C ?
• Solutions
• BOD
• D

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Streeter-Phelps Equation (Example)

• L010 mg L-1
• ka2.0 d-1
• kd0.6 d-1
• D0 0 mgL-1
• U16.4 mi d-1

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Streeter-Phelps Equation (Code)

• xspan0100
• parameter definition
• global ka kd U
• ka2.0
• kd0.6
• U16.4
• y010 0'
• initial concentrations are given in mg/L
• x,y ODE45('dydx_sp',xspan,y0)
• plot(x, y(,1),'linewidth',1.25)
• hold on
• plot(x, y(,2),'r','linewidth',1.25)
• do_any0(2)exp(-kax/U)y0(1)...
• kr/(ka-kd)(exp(-kdx/U)-exp(-kax/U))
• ylabel('mg L-1')
• xlabel('Distance (mi)')
• legend('BOD', 'DO')
• plot(x,do_an,'r')

• function dydydx_sp(x, y)
• global ka kd U
• Ly(1)
• Dy(2)
• dyy
• dy(1)-kd/UL
• dy(2)kd/UL-ka/UD

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Critical Deficit and Distance

• Dc , xc ? dDc/dxc0

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DCS DEPENDENCE ON VARIOUS FACTORS

• Increases with WLQ
• Increases with T
• Increases with D0
• Decreases with Q

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Stream Re-aeration Formulas

• OConnor-Dobbins
• Owens-Edwards-Gibbs
• H1-2.5 U0.1-0.5 Q4-36
• USGS

• ka re-aeration constant, d-1
• U mean stream velocity, ft-1
• H mean stream depth, ft
• Q flow-rate, ft3s-1
• t travel time, d

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Sedimentation of BOD
kd
ka
L
D
0
ks

• Steady state for ultimate BOD ?
• Deficit DCs-C ?
• Solution

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Estimation of kr and kd in a stream
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Principle of Superposition

• Mass balance for DO deficit
• In terms of L and N

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Diurnal Variations
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Sensitivity Analysis

• First order analysis
• yf(x)
• y0f(x0)

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Sensitivity Analysis

• Monte Carlo Analysis
• 1. Generate dx0 N(0,?x)
• 2. Determine yf(x0dx0)
• 3. Save YY y
• 4. ii1
• 5. If i lt imax go to 1
• 6. Analyze statistically Y

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xspan0100 parameter definition Lrzeros(100,10
1) Drzeros(100,101) global ka kd
U U16.4 y010 0' initial concentrations are
given in mg/L for i1100, ka2.00.3randn
kd0.60.1randn while ka lt 0 kr lt 0,
ka2.00.3randn kd0.60.1randn end
x,y ODE45('dydx_sp',xspan,y0)
Lr(i,)y(,1)' Dr(i,)y(,2)'
end subplot 211 plot(x, mean(Lr,1),'linewidth',1.
25) hold on plot(x, mean(Lr,1)std(Lr,0,1),'--',
'linewidth',1.25) plot(x, mean(Lr,1)-std(Lr,0,1
),'--', 'linewidth',1.25) ylabel('mg
L-1') title('BOD vs. distance') subplot
212 plot(x, mean(Dr,1),'r','linewidth',1.25) hold
on plot(x, mean(Dr,1)std(Dr,0,1),'r--',
'linewidth',1.25) plot(x, mean(Dr,1)-std(Dr,0,
1),'r--', 'linewidth',1.25) xlabel('Distance
(mi)') title('DO Deficit vs. distance') print
-djpeg bod_mc.jpeg
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DYNAMIC APPROACH

• Routing water (St. Venant equations)
• Continuity equation
• Momentum equation (Local acceleration
  Convective accelerationpressure gravity
  friction 0

Kinematic wave
Diffusion wave
Dynamic wave
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KINEMATIC ROUTING

• Geometric slope Friction slope
• Mannings equation
• Express cross section area as a function of flow

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KINEMATIC ROUTING (ctd)

• Express the continuity equation exclusively as a
  function of Q
• Discretize continuity equation and solve it
  numerically

k1
?t
k
1
2
3
4
n
n-1
n
5
?x
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KINEMATIC ROUTING (ctd)

• Discretize continuity equation and solve it
  numerically
• Example
• Q2.5m3s-1 S00.004
• B15m n00.07
• Qe2.52.5sin(wt) w2pi(0.5d)-1

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S00.004 B15 n00.07 n80 Qzeros(2,n)2.5 d
x1000. meters dt700. seconds alpha(n0B(2.
/3.)/sqrt(S0))(3./5.) beta3./5. for it1150
if itdt/24/3600 lt 0.25 Q(2,1)2.52.5
sin(2.piitdt/(0.5243600)) else
Q(2,1)2.5 end for i2n
Q(2,i)(dt/dxQ(2,i-1) ((Q(1,i)Q(2,i-1))/2.)
(1-beta)... alphabetaQ(1,i))/ (dt/dx
((Q(1,i)Q(2,i-1))/2.)(1-beta)...
alphabeta) end Q(1,)Q(2,) if
floor(it/40)40it x1n
plot(x,Q(1,)) hold on end end
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ROUTING POLLUTANTS

• Mass conservation
• Discretized mass balance equation

k1
?t
k
1
2
3
4
n
n-1
n
5
?x
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ROUTING POLLUTANTS (ctd)

• Alternate formulation
• Example
• u 1 ms-1
• ?x 1000 m
• ?t 500 m

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ROUTING POLLUTANTSNumerical Example
u1. m/s dx1000 m dt500 s n100 x1100
yx-20 c0exp(-0.015y.y) c1c0 plot(x,c0) ho
ld on for it1120 for i2n-1
c1(i)c0(i)udt/dx (c0(i-1)-c0(i)) end
c0c1 if fix(it/40)40it
plot(x,c0) end end xlabel('x
(km)') ylabel('C mgL-1')
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ROUTING POLLUTANTS (ctd)

• More accurate (second order both time and space)
  formulation

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