Water quality constituents
The items simulated by QUAL 2K
General mass balance
Mass balance for water quality constituents in each reach (except bottom algae)
Bottom algae,
Simulation processes for the model constituents
CO2
N2
JNH4+
JNO3-
JPO43-
Detritus (mo, mgD/L)
Non-living particulate organic matter composed of particulate carbon, nitrogen, and phosphorus
Results from death of plants (phytoplankton and bottom algae)
Lost via dissolution and settling
dmo
 rda PhytoDeath  BotAlgDeat h  DetrDiss  DetrSettl
dt
PhytoDeath  k dp (T )a p
BotAlgDeat h  kdb (T )ab
DetrDiss  kdt (T )mo
v
DetrSettl  dt mo
H
kdp(T) = temp-dependent phytoplankton death rate constant (/d)
kdb(T) = temp-dependent bottom algae death rate constant (/d)
kdt(T) = temp-dependent detritus dissolution rate constant (/d)
vdt = detritus settling velocity (m/d)
Inorganic suspended solids (mi, mgD/L)
dmi
v
 InorgSettl  i mi
dt
H
vi = inorganic SS settling velocity (m/d)
CBOD (mgO2/L)
Slowly reacting CBOD (Cs)
Results from detritus dissolution, lost via hydrolysis
dcs
 rod DetrDiss  SlowCBODHy dro
dt
SlowCBODHy dro  khc(T)c s
khc(T) = temp-dependent slow CBOD hydrolysis rate constant (/d)
Fast reacting CBOD (Cf)
Results from hydrolysis of slowly reacting CBOD, lost via oxidation and denitrification
dc f
 SlowCBODHy dro  FastCBODOxid  rondnDenitri
dt
kdc(T) = temp-dependent fast CBOD hydrolysis rate constant (/d)
FastCBODOxid  Foxcf k dc(T)c f
Denitri  (1  Foxdn )k dn(T)nn
kdn(T) = temp-dependent denitrification rate constant (/d)
Foxcf, Foxdn = attenuation factor due to low oxygen
Denitrification using fast CBOD (CH2O) as a carbon source
5CH2O + 4NO3- + 4H+ → 5CO2 + 2N2 + 7H2O
12 gC
5mol 
gO2
gO2
1mol  1gN
rondn  2.67
 0.00286
gC 4mol  14 gN 1000mgN
mgN
1mol
Low oxygen attenuation
Results in decreasing rates of fast CBOC oxidation, nitrification, and denitrification
Three models that characterize the low oxygen attenuation are available in QUAL 2K
1. Half-saturation
2. Exponential
3. 2nd-order half saturation
Note that low oxygen attenuations for nitrification and denitrification (Foxna, 1－Foxdn) can be
modeled in the same way
DO (o, mgO2/L)
Supplied by reaeration and plant photosynthesis
Consumed by fast CBOD oxidation, nitrification, and plant respiration
do
 roa PhytoGrowt h  rod BotAlgGrow th  roc FastCBODOxid  ron NH 4 Nitr
dt
 roa PhytoResp  rod BotAlgResp  OxReaer
Os (T, elev) - calculated using eqns 19.32 and 19.39 of textbook
ka – determined by one of three models; O’Connor-Dobbins, Owens-Gibbs, and Churchill
depending on depth and velocity of a stream
Nitrogen
Nitrogen problems in water quality
Cause of problems –
nitrification: oxygen depletion
denitrification: loss of nitrogen
eutrofication: oxygen depletion, scums, clogging of waterways, etc…
Problem itself (toxic effects) –
nitrate: blue baby symptom (methemoglobinemia, ~10mg/L of nitrate)
ammonia (NH3): at high pH (>9) and moderate temp (~ 20oC), toxic to fish
Nitrogen
Nitrogen processes
Nitrogen fixation –elemental nitrogen → org. N, blue-green algae
Ammonification – org. N → ammonia, bacterial decomposition, zooplankton excretion, cell death
Nitrification – oxidation of ammonia to nitrate via nitrite (1st order reaction)
Ammonia and nitrate assimilation – uptake of ammonia and nitrate by phytoplankton
Denitrification – dissimilative reduction of nitrate to free nitrogen under anaerobic conditions
Nitrification
Oxidation of ammonia to nitrite, to nitrate
Nitrogen in sewage = organic N (proteins, urea, etc.) + ammonia N
Sewage N → org. N → ammonia N → nitrite → nitrate
NH4+ + 1.5O2 → 2H+ + H2O + NO2-
NO2- + 0.5O2 → NO3NH4+ + 2O2 → NO3- + H2O + 2H+
1.5  32
 3.43 gO / gN
1 14
0.5  32
roi 
 1.14 gO / gN
1 14
2  32
ron 
 4.57 gO / gN
1 14
roa 
Slow growth of nitrifying bacteria, less competitive than OC oxidizing microbes for the substrate
and DO utilization
→ Takes place usually farther downstream than the discharge point where OC is decomposed
→ tc moves to further downstream (between tc for OC oxidation and tc for nitrification)
→ Dc increases
Nitrogen modeling (NBOD approach)
NBOD approach – simplify all nitrogen oxidation processes as a single reaction
NBOD (LN) – oxygen demand for the oxidation of nitrogen compounds
LN = 4.57 TKN
TKN (Total Kjeldahl nitrogen) = oxidizable N = org. N + ammonia N
Mass balances for NBOD and deficit in a stream at steady state
dLN
 k N LN
dx
dL
0  U N  k a D  k N L
dx
0  U
LN  L N 0 e
D  D0 e


kN
x
U
ka
x
U
k
k
 Nx
 ax
k L
 N No (e U  e U )
ka  k N
Shortcomings
No considerations of org. N → ammonia N
No considerations of the sequential reaction from ammonia N to nitrate
No considerations of inhibitory cofactors (the number of nitrifying bacteria, pH, level of
oxygen)
 result in unrealistic simulation (tc is too close to the effluent point and Dc is exacerbated)
Nitrogen modeling (alternative approach)
Each of nitrogen oxidation processes handled as a single component comprising the
sequential reactions
dN o
 koa N o (org. N  ammonia N),
dt
dN i
 k ai N a  kin N i
(nitrite  nitrate),
dt
dN a
 koa N o  k ai N a
(ammonia N  nitrite)
dt
dN n
 kin N i (nitrate accumulati on)
dt
Mass balances for the deficit in a stream at steady state
dD
r oa k ai N a  roi kin N i  k a D
dt
Nitrification inhibition
Inhibitory cofactor (oxygen) – correction for the nitrification rate constants
(k ai or kin )  f nitr
where f nitr  1  e  ( knitr DO)
knitri = 1st order nitrification inhibition coeff. ( 0.6 L/mg)
fnitr ~ 1 at DO > 3 mg/L
 result in more realistic simulation (sag curve becomes more spread and the DO recovery
delays)
Mass stoichiometric coefficients for CBOD and NBOD
Decomposition of organic matter (algae)
C106H263O110N16P + 106O2 + 14H+ → 106CO2 + 16NH4+ + HPO42-+ 106H2O
Due to the oxidation of carbonaceous organic matter
roc 
106  32
 2.67 gO / gC
106 12
Due to the nitrification of ammonia decomposed from organic matter
16 14
 0.176 gN / gC
106 12
ron anc  4.57 gO / gN  0.176 gN / gC  0.804 gO / gC
anc 
Modeling of nitrate and ammonia
Separately simulated as target pollutants
Nitrate
Sources – nitrification, nonpoint sources
Sinks – denitrification, plant use, microbial assimilation
Ammonia
Conc. = f (pH, temp)
NH4+ = NH3 +H+
NH3 T  NH4   NH3 

NH3 H  
K
NH 

4
pK  0.09018 
2729.92
Ta
NH3   Fu NH3 T
Fu 
1
1  ( H  /K)
 
Modeling of nitrogen in QUAL2K
Dissolved organic nitrogen (no, mgN/L)
Supplied by dissolution of detritus
Lost via hydrolysis
dno
 rnd DetrDiss  DONHydr
dt
Ammonia nitrogen (na, mgN/L)
Supplied by hydrolysis of dissolved organic nitrogen and plant respiration
Lost via nitrification and plant photosynthesis
dna
 DONHydr  rna PhytoResp  rnd BotAlgResp  NH4Nitrif
dt
 rna Pap PhytoPhoto  rnd Pab BotAlgPhot o
Preference for ammonium in the photosynthesis
Preference for ammonium in the photosynthesis
Nitrate nitrogen (nn, mgN/L)
Supplied by nitrification
Lost via denitrification and plant photosynthesis
dnn
 NH4Nitrif  Denitri  rna (1  Pap )PhytoPhot o  rnd (1  Pab )BotAlgPht o
dt
Preference for ammonium in the photosynthesis
Phosphorus
Critical role in genetic systems and in the storage and transfer of cell energy
Naturally scarce – present in insoluble form, easily settles
Human activities stimulates a large quantity of P discharges – wastewaters, agricultural land use
(fertilizer), urban runoffs, soil erosion, etc.
Usually, serves as a growth limiting factor for algal growth – critical factor for eutrophication
Types of phosphorus in modeling
1. Soluble reactive phosphorus (SRP) – inorganic orthophosphate (H2PO4-, HPO42-, PO43-)
2. Particulate organic P (POP) – living plants, animals, bacteria, organic detritus
3. Dissolved organic P (DOP) – dissolved compounds containing P, decomposed from
particulate org. P
4. Particulate inorganic P – phosphate minerals, sorbed orthophosphate, phosphate complexed
compounds
5. Nonparticulate inorganic P – condensed phosphate such as in detergent, available for plant
growth
The level of total phosphorus (TP) has been used for the indication of eutrophication.
Modeling of phosphorus in QUAL 2K
Dissolved organic phosphorus (po, mgP/L)
Supplied by dissolution of detritus
Converted to inorganic P by hydrolysis
dpo
 rpd DetrDiss  DOPHydr
dt
Dissolved inorganic phosphorus (pi, mgP/L)
Supplied by hydrolysis of dissolved organic P and plant respiration
Consumed for plant photosysthesis
dpi
 DOPHydr  rpa PhytoResp  rpd BotAlgResp  rpa PhytoPhoto  rpd BotAlgResp
dt
Phytoplankton and plants (photosynthesis and respiration)
Impacts on the level of DO via photosynthesis and respiration
- Photosynthesis (P) contributes to DO recovery
- Respiration (R) consumes DO
- Impacts on N, P, and SOD
Photosynthesis = f (light)
Upstream – heterotrophic oxidation (oxygen depletion, turbidity increase, light decrease)
Downstream – autotrophic recovery (solids settling, light increase, nutrients increase)
106CO2 + 16NH4+ + HPO42-+ 106H2O  C106H263O110N16P + 106O2 + 14H+
106CO2 + 16NO3- + HPO42-+ 122H2O + 18H+  C106H263O110N16P + 138O2
Mass ratio of C:N:P = 40%:7.2%:1%
Unit of phytoplankton (algae) = mgChl/L (chlorophyll a, mgA/L), the chlorophyll to carbon ratio =
10 – 50 mgA/mgC
 Stoichiometric mass ratio – 100 mgD(organic matter):40mgC:7.2mgN:1mgP:1mgA
Simulation – zero order distributed sources
Deficit
D
PR
(1  e  k at )
ka
녹조류 (green algae)
 녹색을 띠며 엽록소 a와 b를 이용하여 광합성 산물인 전분을 생산 (Chlorophyta)
 담수와 해수 모두에 서식
 호수의 조류 중에는 계절적으로 크게 번식하여 물의 색을 변화시키는 종도 존재
구멍갈파래
잎파래
납작파래
참깃털말
청각
남조류 (blue green algae)
 체세포 분열로 번식하며, 원핵생물(prokaryote)인 세균류처럼 핵막이 결여된
구조
 남조세균 (Cyanobacteria)
 인이 풍부한 호소 등 정체 수역에서는 남조류의 성장속도 증가하여 수화
(agal bloom) 현상 발생
 일부 남조류의 경우 독소를 생산하여 포유동물이나 어패류를 폐사 시킴
규조류 (diatom)
 단세포, 규산질의 단단한 외피 (규조류 : Thalassionsira rotula)
 외피는 상각과 하각으로 구성, 두 피각이 비누곽처럼 끼워져 각 개체를 구성
 다양한 수역에서 그 수환경에 적응한 종류가 출현, 수질판정
 화석화된 종류 조사, 과거의 수환경 파악
 연안에 많이 분포, 수온이 낮은 곳
 다른 규조류와 함께 혼합 적조를 일으키는 경우가 많음
10~60 mm
녹조현상
 부영양화된 호수나 유속이 느린 하천에서 부유성의 조류 (식물성 플랑크톤) 가
대량 증식하여 수면에 집적하여 물색을 현저하게 녹색으로 변화시키는 현상
 수화현상의 한 종류로 남조류의 대량 증식으로 인해 물색이 녹색으로 변하는 현상
 적조현상과 비교되어 메스컴으로부터 명명된 이름
c.f.) 적조현상 : 봄철 규조토의 대량 증식으로 황갈색으로 물색이 변하는 경우
녹조현상이 생태계에 미치는 영향
 시각적 영향
착색 또는 스컴으로 인한 시각적 불쾌감
 공중위생상의 문제점
남조류 독소에 의한 인체 및 가축에의 영향, 이취미 발생으로 인한 불쾌감 유발
 생태학적인 영향
생태계 파괴로 인한 개체군 변화 서식처 이동
 동물의 건강에 미치는 영향
남조류 독소에 의한 가축이나 야생동물의 폐사,
산소 부족에 의한 물고기 및 수중생물 폐사
 경제적 손실
레크리에이션 활동 저해로 인한 지역 경제적 손실
 상수원에 미치는 영향
남조류 독소발생, 이취미 생성, 여과지폐쇄등
팔당댐의 월별 조류 발생 현황
팔당호의 월별 식물 플랑크톤 우점종 및 개체수 현황
월별
우점조류종
세포수 (cell/ml)
총세포수 (cell/ml)
5월
Coleasterum
3,840
20,250
6월
Coleasterum
27,720
62,160
7월
Microcystis
92,560
150,895
8월
Aulacoseira
3,490
18,140
9월
Cyclotella
2,960
7,300
10월
Aulacoseira
13,620
22,040
11월
Aulacoseira
4,610
13,223
 조류의 천이현상 : 남조류 (7월)  규조류 (10월)
 남조류 증식의 제한인자 : 수온
Effect of light on photosynthesis
Photosynthesis = f (light intensity)  DO level varies seasonally and diurnally
P(t )  I (t ) where  available light (langleys/ d)
P(t )  Pm sin  (t  t r )
1 langley  1 cal/cm 2
P(t )  0
tr  t  ts
otherwise
where
Pm = max rate (g m-3 d-1)
 = angular frequency (=/(fTp))
tr = time of sunrise (d)
tp = time of sunset (d)
f = fraction of day having sunlight (photoperiod)
Tp = daily period (typically 1 d = 24 hrs)
Photoperiod fraction (f) and time for solar noon (tn)
f 
t s  tr
Tp
tn 
t s  tr
2
Pm
Average daily photosynthesis rate (g
Tp
P

0
P(t )dt
Tp
m-3d-1)
Pa
 Pm
2f

P
Average daylight photosynthesis rate (g m-3d-1)
Tp
Pa


0
P(t )dt
fTp
tr
 Pm
2

tn
fTp
ts
Tp
Modeling of algal growth and loss (phytoplankton) in QUAL 2K
Governing equation
da p
dt
da p
dt
 PhytoGrowt h  PhytoLoss
 k g a p  klossa p
Growth of phytoplankton
Growth rate = f (temp, nutrient, light)
N , L – attenuation factors for nutrients and
k g (T , N , I )  k g (T ) N L
light limitation (0~1)
Temperature effect
k g (T )  k g , 20 T 20
  1.066
Nutrient limitation (nitrogen and phosphorus)
– Liebig’s law of the minimum

n( na  nn )
pi 
,

 k sn  n( na  nn ) k sp  pi 
 N  min 
Half-saturation constants for nutrient
limitation of phytoplankton growth
Nutrient
ks
Nitrogen
5~20 mgN/L
Phosphorus
1~5 mgP/L
Growth of phytoplankton
Light limitation
Light variation along the depth of a stream (Beer-Lambert law)
I ( z )  0.47 I 0 e  ke z
I0: solar radiation at the surface
The extinction coefficient (ke, m-1)
ke  keb  0.052mi  0.174mo  0.0088a p  0.054a p
ke : background extinction coeff. due to
2/ 3
particle-free water and color
mi: inorganic SS
mo: detritus
1. Half-saturation light model
Phytoplankton growth attenuation due to light as a function of depth,
FLP 
I ( z)
K L P  I ( z)
KLP = half-saturation coefficient for light (ly/d)
The depth-averaged light attenuation factor – combined with the Beer-Lambert law
and integrated over the depth, H
L 
1
ke H
 KL P  I0 

 ke H 
 K L P  I 0e

Growth of phytoplankton
2. Smith’s function
FLP 
I ( z)
KLP = the Smith parameter, light intensity at which the growth rate is
70.7% of the maximum (ly/d)
K L P  I ( z)2
2
The depth-averaged light attenuation factor


I o / K L P  1  (I o / K L P )2
1

L 
ln 
ke H  ( I o / K L )e  ke H  1  (( I o / K L )e  ke H ) 2 
P
P


3. Steele’s function
I (z)
I ( z ) 1 K L P
FLP 
e
KLP
KLP = light intensity at which the growth rate is optimal (ly/d)
The depth-averaged light attenuation factor
2.718282   K L P e
L 
e
ke H 

Io
 ke H
e

Io
KLP



Growth of phytoplankton
Growth Attenuation Factor for Light
1
Saturation
3
2
0.8
1
0.6
Half Saturation
0.4
1 = Half Saturation
2 = Smith's Function
3 = Steele's Equation
0.2
0
0
100
200
Light Intensity, I (ly/d)
300
400
Modeling of algal growth and loss (phytoplankton) in QUAL 2K
Loss of phytoplankton
1. Respiration (excretion) – oxygen consumption, release of nutrients (N, P) and
organic carbon
PhytoResp  k rp(T) a p
krp(T) = temp-dependent respiration rate constant (/d)
2. Death
PhytoDeath  k dp (T )a p
kdp(T) = temp-dependent death rate constant (/d)
3. Settling
PhytoSettl 
va
ap
H
va = settling velocity (m/d)
The complete model for phytoplankton
da p
dt
 k g (T )N L a p  (krp  kdp 
va
)a p
H
Modeling of bottom algae
Governing equation
da p
dt
 BotAlgPhot o  BotAlgResp  BotAlgDeat h
Growth of bottom algae (zero order rate)
BotAlgPhot o  C gb (T ) NbLb
Cgb(T) = temp-dependent max. bottom algae photosynthesis
rate (gD m-2d-1)
Temperature effect
Cgb (T )  Cgb, 20 T 20
  1.066
Nutrient limitation (nitrogen and phosphorus)
– Liebig’s law of the minimum

n( na  nn )
pi 
,

 k sNb  n( na  nn ) k sPb  pi 
Nb  min 
Growth of bottom algae
Light limitation
Light variation along the depth of a stream (Beer-Lambert law)
I ( H )  I 0 e  ke H
I0: solar radiation at the surface
Combining the above equation with each of three models used for the impact of light
on phytoplankton photosynthesis
1. Half-saturation light model
Lb 
I0
K L b  I 0 e  ke H
2. Smith’s function
Lb 
I o e  ke H
K L b  ( I o e  ke H ) 2
2
3. Steele’s function
I o e  ke H 1
Lb 
e
K Lb
I o e  ke H
k Lb
Loss of bottom algae (1st order rate)
1. Respiration
BotAlgResp  krb (T )ab
2. Death
BotAlgDeat h  kdb (T )ab
krb(T) and kdb(T) = temp-dependent respiration and death rates,
respectively (/d)
The complete model for bottom algae
dab
 C gb (T ) N L  (k rb  k db )ab
dt
Sediment oxygen demand (SOD)
Oxygen demand for the oxidation of organic matter in bottom sediment
Organic matter in sediment – settlement of wastewater particulates, allochthonous
particulates, plants, phytoplankton, detritus, etc.
Sediment oxygen demand (SOD)
Modeling of the conversion of sediment organic matter – computation of the
fluxes of ammonium, nitrate, methane, and phosphate
Fundamental assumption – sediment consists of two layers (thin aerobic top layer
and underlying anaerobic layer)
1. Settling of particulate organic matter (phytoplankton and detritus) – transport of
organic carbon, nitrogen, and phosphorus to the sediment (anaerobic layer)
2. Decomposition (mineralization) of the delivered organic matter in the anaerobic
layer – generation of soluble methane, ammonium, and inorganic phosphorus
(phosphate) - diagenesis
3. Transport (diffusion) to the aerobic layer and subsequent oxidation of methane
and ammonium
→ The flux of oxygen from the overlying water required for the oxidation of
methane (CSOD) and nitrification of ammonium (NSOD), SB’ (areal oxygen
demand, gO2m-2d-1)
Diagenesis of organic matter in sediments
Carbon
In anaerobic layer
CH2O → 1/2CO2 + 1/2CH4 (diffuses upward to the aerobic layer)
In aerobic layer
1/2CH4 + O2 → 1/2CO2 + H2O  1/2g of methane consumes 2.67 g of oxygen (CSOD).
Nitrogen
In aerobic layer (nitrification of ammonium diffused from the anaerobic layer)
NH3 + 2O2 → NHO3 + H2O  1g of nitrogen consumes 4.57 g of oxygen (NSOD).
In anaerobic layer (denitrification of nitrate using methane as a carbon source)
5/8CH4 + NHO3 → 5/8CO2 + 1/2N2 + 7/4H2O
The entire process (conversion of ammonium to inorganic nitrogen via nitrification/denitrification)
NH3 + 3/4O2 → 1/2N2 + 3/2H2O  1 g of nitrogen consumes 1.714 g of oxygen (NSOD’, the ratio
of O to N consumed during nitrification and denitrification)
SOD (SB’ gO2m-2d-1) = CSOD + NSOD
Diagenesis of organic matter in sediments (in QUAL 2K)
The total downward flux of particulate organic matter (POM, phytoplankton + detritus)
J POM  rdava a p  vdt mo
Diagenesis of organic matter in sediments (in QUAL 2K)
POM flux (JPOM, gDm-2d-1) =
1. particulate organic carbon (POC) flux (JPOC, gO2m-2d-1) +
2. particulate organic nitrogen (PON) flux (JPON, gNm-2d-1) +
3. particulate organic phosphorus (POP) flux (JPOP, gPm-2d-1)
Each flux is divided into: labile (fast reactive, G1), slowly reactive (G2), and non-reactive (G3)
fractions
For the fluxes of dissolved nutrients (dissolved carbon, nitrogen, and phosphorus) produced via
diagenesis in the anaerobic layer
JC (gO2m-2d-1) = JC,G1+ JC,G2
JN (gNm-2d-1) = JN,G1+ JN,G2
JP (gPm-2d-1) = JP,G1+ JP,G2
The fluxes of methane, ammonia, nitrate, and phosphate from the aerobic layer to the overlying
water – obtained from the mass balances in the aerobic and anaerobic layers
JCH4 =SB’/o(CH4, aerobic – cf)
cf: fast reacting CBOC in the overlying water (gO2/m3)
JNH4 =SB’/o(NH4, aerobic-dissolved – na/1000) na: ammonia conc. in the overlying water (mgN/m3)
JNO3 =SB’/o(NO3, aerobic-dissolved – nn/1000) nn: nitrate conc. in the overlying water (mgN/m3)
JPO4 =SB’/o(PO4, aerobic-dissolved – Pi/1000) na: phosphorus conc. in the overlying water (mgP/m3)
o: DO in the overlying water (gO2/m3)