STANDARDNI POLUTANTI U VODAMA

Water is life and thus the quality of water is an essential measure of the quality of life or

rather the existence of life. Consequently water quality management is (or should be) one of

the most important activities of mankind, so as to protect and save human life and the life of

other living things, which latter is a precondition of human life as well.

Voda je život, a time je i kvaliteta vode kljucna mjera kvalitete života ili

bolje kazano postojanja života. Upravljanje kvalitetom vode je (ili bi trebala biti) jedan od

najvažnijih aktivnosti čovječanstva u cilju zaštite i spasavanja ljudskog života i života

drugih živih bića, koja su preduvjet za opstojanost ljudskog života.

The management of water quality, or the protection of the aquatic ecosystem in a broader

sense, means the control of pollution. Water pollution originates from point and non-point

(diffuse) sources and it is always due to human action (the author strongly believes that no

such thing as “natural pollution” exists, as sometimes advocated by other people).

Upravljanje kvalitetom vode, ili zaštita vodenih ekosistema u širem

smislu, znači kontrolu zagađenja. Zagađenje vode potječe iz tačkastog i netačkastog

(difuznog) izvora i uzrok je uvijek zbog ljudskog djelovanja .

The control of water pollution, the protection of aquatic systems, is thus the control of human

activities that result in pollution.

Kontrola onečišćenja voda i zaštita vodenih sistema su stoga kontrola ljudskih

aktivnosti koje rezultiraju onečišćenjem voda.

A crucial element in the series of complex activities of planning and implementing water

pollution control actions is the quantitative determination and description of the cause-and-

eflect relationships between human activities and the state (the response) of the aquatic

system, its quantity and quality. These activities together can be termed the modelling of

aquatic systems (hydrological, hydraulic and water quality modelling). These activities are

aimed at calculating the joint effect (the impact) of natural and anthropogenic processes on

the state of water systems.

Ključni element u seriji složenih aktivnosti planiranja i provedbi kontrole zagađenja vode je

kvantitativno određivanje i opis uzrocno-posljedicnih odnosa između ljudskih aktivnosti i države

vodenog sistema . Ove aktivnosti zajedno možemo nazvati modeliranje vodenih sistema (hidrološko,

hidrauličko i modeliranje kvaliteta vode). Ove aktivnosti su usmjerene na izračunavanje zajedničkih

učinak a(utjecaja) prirodnih i antropogenih procesa na stanje vodovodnih sistema.

The subject of this teaching aid is to introduce the basics of water quality modelling to the

user. Although the qualitative and quantitative modelling of water systems (rivers, lakes and

reservoirs) should be done simultaneously we will have to separate them for the purpose of

this programme, always assuming that the quantitative state (the hydrological and hydraulic

parameters) of the water system is known and sufficiently well described. With this we can

focus on the quantitative, mathematical, description of processes that affect water quality.

Cilj ovog seminarskog rada je upoznati osnove modeliranja kvaliteta vode sa eventualnim

korisnicima. Iako bi kvalitativno i kvantitativno modeliranje vodovodnih sistema (rijeke, jezera i

akumulacije) trebalo biti sprovedeno istodobno, u cilju jednostavnijeg boljeg razumijevanja morat cemo

ih odvojiti jedno od drugog u seminarskom radu, uz pretpostavku da je kvantitativno stanje (hidrološki i

hidraulički parametri) vodenog sistema dobro opisano. Na taj nacin se možemo

usredotočiti na kvantitativni, matematički, opis procesa koji utječe na kvalitetu vode.

Consequently in the following sections of this programme all ,hydraulic

and hydrological river parameters (e.g rate of flow, flow velocity, stream depth and width,

etc) will be considered as given input data. Thus we will start with the introduction of the

basic mass transport and transformation processes, relying on continuity and conservation of

mass considerations.

U nastavku ce se svi hidraulični i hidrološki paramatri rijeke (npr. stopa protoka, brzina protoka,

dubina i širina protoka, itd) smatrati ulaznim podacima.

Polazna osnova modeliranja ce biti transport mase i procesi transformacije, oslanjajući se na zakon

kontinuitet i očuvanja mase.

Let us consider an elementary water body, a cube of dx, dy and dz dimensions as shown

in Figure 1. The quality of water within this elementary water body depends on the mass of

a polluting substance present there. Water quality models then should describe the change of

the mass of a polluting substance within this water body. The change of the mass of this

substance is calculated as the difference between mass-flows (mass fluxes) entering and

leaving this water body, considering also the effects of internal sources and sinks of the

substance, if any. The mechanism of mass transfer into and out of this water body includes

the following processes:

Posmatrajmo elementarni dio vodenog tijela, kocku elementarnih dimenzija dx, dy i dz kao što je

prikazano na slici 1.Kvaliteta vode unutar ovog elementarnog dijela vode ovisi o masi

onečišćujućih tvari koje su prisutne. Modeli kvaliteta vode bi zatim trebali opisati promjenu

mase zagađujucih tvari unutar ovog elementarnog vodenog tijela. Promjena mase ove

tvari se racuna kao razlika između masenih flukseva (masovni tokova) koji ulaze i napustaju

tijelo, pri cemu se uzimaju u obzir i učinci unutarnjih izvora i ponora materije, ako istih ima

.Mehanizam prenosa mase iz ovog vodnog tijela uključuje sljedeći procesa:

Mass transported by the flow, by the vX, vZ, and v, components of the flow velocity

vector. This process is termed the advective mass transfer. The transfer of mass, that

is the mass flux (in mass per time, M T-l, dimension) can be calculated in the

direction x as C*v,*dy*dz, where C is the concentration of the substance in the water

(in mass per volume dimension, M L”), see also Equation 1.1.

The other means of mass transfer is termed the dispersion or dispersive transport.

Here one has to explain this term because there is usually considerable confusion with

the terms diffusion and dispersion; -in short: dispersion is a term used for the

combined effect of molecular diffusion and turbulent diffusion, and both of these latter

processes is caused by pulsating motion, that is

Prenos mase protokom preko VX, VZ, i V, komponentih strujnog vektora. Ovaj proces je nazvan

advektivnim masenim prenosom. Prenos mase, odnosno fluks mase (jedinica mase u jedinici vremena,

M TL, dimenzija) se može izračunati u x-smjeru kao C * v, * dy * dz, gdje je C koncentracija tvari u vodi

(jedinica mase po jedinici volumena ML ").

Drugi aspekti prenosa mase nazivaju se disperzija ili disperzivni transport.

Ovdje treba detaljnije objasniti taj pojam jer obično dolazi do mijesanja pojma difuzije i disperzije;-u k

ratko: disperzija je termin koji se koristi za kombinovani učinak molekularne difuzije i turbulentne

difuzije , a oba ova spomenuta procesa su uzrokovana pulsirajucim kretanjem , odnosno

- “Brown”ovom toplotno induced motion of the molecule (molecular

diffusion), and

-- by the pulsation of the flow velocity around its mean value, caused by

turbulence (called the turbulent diffusion).

The dispersive mass transfer (E,, E,, E,) has the dimension of mass per time per area (M T-’

Le2) and it is usually expressed by the law of Fick which states that the transport of the

substance in a space direction is proportional to the gradient of the concentration of this

substance in that direction the proportionality factor being the coefficient of dispersion, as

shown in equation 1.1.

-"Brownim" toplinsko induciranim kretanjem molekula (molekularna

difuzija), i

- Po pulzaciji brzine strujanja oko svoje srednje vrijednosti, uzrokovane

turbulencijom (tzv. turbulentna difuzija).

Disperzivni prenos mase (E, E, E,) ima dimenziju mase po jedinici vremenu po području (M T-'

Le2) i obično se izražava po Fick-ovom zakonu po kojem je prenos materije u prostornom smjeru

proporcionalan gradijentu koncentracije materije u tom smjeru. Faktor proporcionalnosti se zove

koeficijent disperzije, kao prikazano u sljedecoj jednacini

Mass transport terms for deriving the basic model

These equations describe the dispersive and advective transport of a polluting substance from

the x direction into an elementary water body. The first term is actually the law of Fick

which states that the diffusive (dispersive) transport of the substance in a space direction is

proportional to the gradient of the concentration of this substance in that direction the

proportionality factor being the coefficient of dispersion. The user finds more information on

dispersion in the “general” part of this basic theory chapter and on the programme part on

“dispersion river models”. The second term is the advective transport term, which states that

the specific (per unit area) transfer of mass to a spatial direction is the product of the

concentration of a substance and the velocity of flow in that spatial direction. These are the

terms used in writing the overall mass balance (that is Eq. 1.2) of an elementary water body

as shown in Figure 1.

Uslovi za izvođenje osnovnog modela prenosa mase

Ove jednacine opisuju disperzivni i advektivni prenos zagađujuce tvare iz

x-smjera u elementarno vodeno tijelo . Prvi izraz predstavlja zapravo prvi Fick-ov zakon

u kojem se navodi da je difuzni (disperzivi) prenos materije u prostornom smjeru

proporcionalan gradijentu koncentracije ove materije u istom smjeru

Faktor proporcionalnosti se koeficijent disperzije.

Drugi clan predstavlja advektivni prenos, u kojem se navodi da je

specifični (po jedinici površine) prenos mase u prostornom smjeru proizvod

koncentracija tvari i brzine protoka u tom prostornom smjeru.

Legend

c - is the concentration, the mass of the quality constituent in a unit volume of

water (mass per volume, M Le3);

LE,,E, - are the dispersive mass fluxes in the spatial directions x, y, and z (in M L-2 T-l

dimension), with the assumption that the law of Fick holds for the joint effect

of molecular diffusion and turbulent diffusion, that is for dispersion;

v,,vy,vz - are the components of the flow velocity in spatial directions x, y , and z,

(length per time, L T-l);

dx,dy,dz - are the side lengths of an elementary cube, an elementary water body.

egenda

c - je koncentracija, masa zagadjujuce tvari po jedinici volumena

vode (masa po volumenu, M Le3);

LE,, E, - su disperzivni maseni fluksevi u prostornim smjerovima x, y, z (u M L-2 Tl

dimenzija), sa pretpostavkom da Fick-ov zakon zajednicki obuhvata molekularnu

difuziju i turbulentnu difuziju, odnosno za disperziju;

v,, VY, vz. - su komponente strujanja u prostornim smjerovima x, y i z,

(dužina po vremenu, L T-l);

dx, dy, dz - su bočne duzine elementarne kocke, elementarnog tijela vode.

Derivation of simple practical models from the basic model equation

The most simple water quality model (1)

The basic three dimensional water quality model is seldom used in its original complex way

(Eq. 1.3), mostly because three dimensional problems occur rarely. For example river

problems can be frequently reduced to one-dimensional (linear) or two dimensional

(longitudinal-transversal) problems, as it will be demonstrated in the programme. Another

reason of using simplified models is that transversal or vertical velocity measurement data are

seldom available.

The internal source-sink terms, that were only denoted in Eq. 1.3 should be specified for each

problem explicitly and they vary with the components considered.

Here it will be briefly demonstrated how can one derive the most simple (river) models

version of Eq. 1.3, which can be used in the practice. In order to arrive to the possible most

simple water quality model we have to make first series of assumptions and approximations:

Derivacija jednostavnih praktičnih modela iz osnovnog modela jednacine

Najjednostavniji model kvaliteta vode (1)

Osnovni trodimenzionalni model kvaliteta vode se rijetko koristi u svom izvornom

kompleksnom obliku(Eq. 1,3), uglavnom zato sto se trodimenzionalni problemi javljaju rijetko. Na

primjer problemi rijeka se često mogu svesti na jednodimenzionalne (linearne) ili dvodimenzionalne

(uzdužno-poprečne) probleme . Drugi Razlog korištenja pojednostavljenih modela je sto su mjerni

podaci poprečne ili vertikalne brzine rijetko dostupni.

Pojmovi unutrasnjeg izvora-ponora, koji su naznačeni u jed. 1,3 treba navesti za svaki

problem eksplicitno i oni se razlikuju od prijasnjih komponenti.

Ovdje će se ukratko pokazati kako se moze derivirati najednostavniji (rijecni) oblik modela

jednacine. 1.3, koji se može koristiti u praksi. U cilju pronalazenja

najednostavnijeg modela kvaliteta vode mora se napraviti niz pretpostavkih i aproksimacija:

a, Neglect, for the time being, all terms accounting for dispersion. With this we assume

that the system is fully mixed, which means that any external material input (load) to

the river will be instantaneously and fully mixed with the water. This is a very rough

approximation and its consequences will be discussed in a subsequent sections

dealing with dispersion and mixing problems. However, this approximation holds with

long linear systems, e.g in the case of smaller rivers with continuous steady input

loads (waste water discharges).

b, Considering a river and a sewage discharge of steady state conditions (with flow not

varying in time) the initial concentration Co downstream of an effluent outfall can be

described by the general dilution equation (see Equation 1.4).

a)za nemarivanje svih uslova koji se ticu disperzije. Uz to možemo pretpostaviti

da se sistem u potpunosti miješa, što znači da ce se bilo koji vanjski materijalni ulaz (opterećenje)

u rijeku odmah i potpuno miješa sa vodom. Ova pretpostavka važi za sve

duge linearne sisteme, npr. manje rijeke sa kontinuiranim ulazom

opterećenja (otpadne vode).

B Posmatrajuci rijeku i kanalizaciju otpadnih voda pri stacionarnim uslovima (sa tokom koji se ne mijenja

u vremenu) početna koncentracije Co nekog rukavca rijeke koji tece nizvodno može biti

opisana općom jednacinom razrjedjivanja (vidi jednacinu 1,4).

The general dilution equation

Considering a river and an effluent discharge of steady state conditions (with flows and

concentrations not varying in time) and assuming instantaneous full cross-sectional mixing of

the sewage water with the river water the initial concentration Co downstream of an effluent

outfall can be calculated by the dilution equation (Eq. 1.4), which stems from the balance

equation of in- and outflowing fluxes written for the section of the discharge point (e.g. back-

ground river mass flux plus pollutant discharge mass flux equals the combined mass flow

downstream of the point of discharge). This equation is used very frequently in simple

analytical water quality models for calculating the initial concentration of pollutants.

OPCA JEDNACINA RAZRJEDJIVANJA

Posmatrajuci rijeku i odvod otpadne vode pri stacionarnim uvjetima I pod pretpostavkom instantnog

miješanja otpadne vode po punom prjesjeku sa vodom rijeke početna koncentracije Co

odvoda otpadnih voda koji tece nizvodno se mogu izračunati preko jednacine za razrjedivanje

(Eq. 1.4), koja proizlazi iz jednacine ravnoteže za flukseve dotoka I odvoda napisanog za podrucje tacke

ispustanja (npr. osnovni maseni fluks rijeke plus maseni fluks zagadjujucih tvari koji se ispustaju u rijeku

su jednaki kombiniranom maseni protoku nizvodno od točke ispuštanja). Ova jednacina se koristi vrlo

često u jednostavnim analitičkim modelima kvaliteta vode za izračunavanje početne koncentracije

onečišćujućih tvari.

Legend

CtJ - background concentration of the polluting substance in concern in the river, (MLe3);

cs - concentration of the pollutant in the waste water, (MLe3);

Q- discharge (rate of flow) of the river upstream of the effluent outfall, (L3 T-l);

q-

the effluent discharge, (L3 T-l);

The most simple water quality model (2)

Averaging flow and concentration over the cross section Equation 1.3 simplifies into Equation

1.5 where v is the average flow velocity along the stream.

Introducing the “time of travel” t = x/v and assuming first order reaction kinetics for a single

decay or decomposition process, as the only internal process (sink) one obtains the possible

most simple river water quality model in the form of Equation 1.6

This equation (the principle of first order reaction kinetics) states that the decay/decomposition

of a pollutant is proportional to the concentration of the pollutant and the factor of

proportionality is K, the decay rate coefficient (T-l).

Solving Eq. 1.6 for the initial conditions defined above (C = C, at x=x,, that is t = tJ the simple

exponential decay equation (Equation 1.7) is obtained, which is at the same time the most

simple water quality model used in the practice. Equation 1.7 will be subsequently referred

to also as the “Decay Equation”. This equation can be used for a number of water quality

‘modelling purposes (such as the “decay” of BOD, COD, etc, see also at the description of ’

BOD-DO models), and forms an essential part in developing coupled reaction models (see

under this heading for more details).

legenda

CtJ - koncentracija zagađujucih tvari koji postoje rijeci prije mijesanja sa otpadnim vodama, (MLe3);

CS - koncentracija zagađujucih tvari u otpadnim vodama, (MLe3);

Q- brzina toka rijeke uzvodno od tacke izlijevanja otpadnih voda, (L3 Tl);

Q- brzina toka otpadnih voda, (L3 T-l);

Najjednostavniji model kvaliteta vode (2)

Usrednjavanje protoka koncentracije po poprecnom presjeku jednacina 1.3. se pojednostavljuje u

Jednacinu 1.5. gdje je v je prosječna brzina toka rijeke duz cijele duzine.

Uvodjenje pojma "vrijeme putovanja" t = x / v, a pod predpostavkom kinetike reakcije prvog reda

za process propadanja ili raspadanja , kao jedini unutrasnji procesu (ponor) dobiva se

najjednostavnijiji oblik modela kvaliteta vode rijeke u obliku jednacine 1.6.

Ova jednacina (pravilo kinetike reakcije prvog reda) pokazuje da je propadanje / raspadanje

štetnih tvari proporcionalno koncentraciji onečišćujućih tvari i faktor

proporcionalnosti je K, koeficijent brzine propadanja (TL).

Rješavanje jednacine. 1.6 sa početnim uslovima utvrdjenim iznad (C = C, u x = x,, da je t = TJ )

dobiva se jednostavna jednacina eksponencijalnog raspada (jednacina 1.7.), koji je istovremeno

model kvaliteta vode koji senajvise koristi u praksi. Jednacina 1.7 se takodjer naziva Jednacina

raspada . Ova jednacina se može koristiti za razne svrhe modeliranja kvaliteta vode i

čini bitnu osnovu za razvoj slozenijih modela kvaliteta vode.

Legenda

Legend

C- is the concentration, the mass of the quality constituent in a unit volume of water

(mass per volume, M Lm3);

C, - is the initial concentration of the pollutant downstream of a point source of pollution

(see also Eq. 1.4)

V- is the mean flow velocity of a river reach investigated (L T-l)

denotes the internal sources and sinks of the substance, (M Lm3 T-l);

K- is the reaction rate coefficient for first order kinetics (T“)

t- is the time of travel interpreted as t =x/v

X- the distance downstream (L)

pri cemu je :

C-je koncentracija, masa sastojka kvalitete koja se mjeri po jedinici volumena vode

(masa po volumenu, M Lm3);

C - je početna koncentracija zagadujucih tvari nizvodno od točke izvora zagađenja

(vidi također Jed. 1.4)

V-je srednja brzina protoka rijeke (L Tl)

i označava unutarnje izvore i ponore tvari, (M Lm3 Tl);

K-je koeficijent brzine promjene reakcije prvog reda kinetike (T ")

t-je vrijeme putovanja te se tumači kao t = X / V

X- udaljenost nizvodno (L)

Derivation of coupled reaction models

Chemical, biological or biochemical processes to which water quality constituents are

subjected seldom occur alone but in a coupled way. If we consider such a coupled process

situation, still in a generalizable way, assuming that the product of a decomposition/decay

process of a water quality component (C,) is another water quality constituent (C,) which

latter is subjected to further decay/decomposition then we can derive a simple set of coupled

reaction models in the form of Equations 1.8 and 1.9, where K, and K, are the respective

reaction rate coefficients of the not yet named water quality processes. With this we have

actually derived the still most frequently used basic river model, the oxygen sag curve model

(Streeter and Phelps, 1925). Assuming that the parameter C, is the biologically decomposable

organic matter content of the water (expressed in Biochemical Oxygen Demand, BOD which

is the amount of oxygen utilized by microorganisms from a unit volume of water for the

decomposition of organic matter during a selected period of time) and assuming that the other

parameter C, is the oxygen deficit compared to saturation level Eq 1.8 and 1.9 are the basic

equations of the traditional oxygen sag curve model which states that the oxygen consumed

by microorganisms adds to the oxygen deficit, while the process of aeration (or reaeration;

the uptake of oxygen across the water surface due to turbulence and molecular diffusion)

reduces this deficit.

Derivacija modela kombinovanih reakcija

Hemijski, biološki ili biokemijski procesi kojima su sastojci kvalitete vode podvrgnuti se rijetko odvijaju odvojeni, vec u kombinaciji jedan sa drugim. Ako razmatramo takvu situaciju kombinacije procesa

,još uvijek po poopćenim pravilima, uz pretpostavku da je proizvod procesa razgradnje / propadanja

komponente kvalitete vode (C,) je neki drugi kvalitete vode (C,) koji

je kasnije isto podvrgnut daljnjim procesima propadanja / razgradnje onda možemo izvući jednostavan

niz kombinovanih modela reakcije u obliku jednacina 1.8 i 1.9, gdje su K i K, odgovarajući

koeficijenti brzine reakcije procesa kvalitete vode koji jos nisu imenovani. Na ovaj nacin je zapravo izvrseno izvodjenje najčešće uportrebljenog osnovnog modela rijeke tzv. Model krivulje pada kisika

(Streeter i Phelps, 1925). Uz pretpostavku da je parametar C, biološki rastvorljiva

organska tvar iz vode (izražen u Biohemijskoj Potrošnja Kisika, gdje BPO

količina kisika koju koriste mikroorganizami u jedinici volumena vode za

razgradnju organske tvari u toku nekog odredenog vremena) i uz pretpostavku da je drugi

parametar C, je nedostatak kisika u odnosu na razinu zasićenosti Jednacine 1.8 i 1.9 su osnovne

jednacine tradicionalne modela krivulje pada kisika SAG po kojoj se kisik koji konzumiraju

mikroorganizami nadoknaduje nedostatak (manjak) kisika, dok se proces aeracije (ili rearacije;

unos kisika po cijeloj površini vode uslijed turbulencije i molekularne difuzije)

smanjuje taj nedostatak.

Here the reaction rate coefficients gain specific meaning, that is

K1-

is the rate coefficient of biochemical decomposition of organic matter (T-l)

K, - is the reaeration rate coefficient (T-l)

t- is the time, that is the time of travel in the river interpreted as t=x/v, where

x is the distance downstream of the point of effluent discharge

The set of differential equations (Eqs 1.8, and 1.9) can be solved for initial conditions

C, =C1,O and C2=C2,0 at x=0; (t=t& (to be calculated with the dilution equation (Eq 1.4) in

a similar way as shown there), obtaining Equations 1.10 and 1.11.

Ovdje koeficijenti brzine reakcije dobivaju specifična značenja, a to je

K1-je koeficijent biohemijske razgradnje organske materije (TL)

K - je koeficijent brzine promjene rearacije (TL)

t-je vrijeme, odnosno vrijeme putovanja tumačeno kao t = X / V, gdje je

x je udaljenost nizvodno od točke ispusta otpadnih voda.

Skup diferencijalnih jednadžbi (1.8 i 1.9) može se riješiti za početne uvjete

C, = C1, O i C2 = C2, 0 na x = 0, (t = t & se racuna pomocu jednacina za razrjeđivanje (Eq 1.4) )

za dobivanje jednacina 1.10 i 1.11.

Cl, c2 - Are concentrations of interacting water quality constituents (the product of the

“decomposition” process of C1 is C,, which latter is also a decaying od

decomposing constituent (MLe3)

G&20 - are initial concentrations of the above two water quality constituents (see also

Eq. 1.4) (ML-3)

K,& - are the reaction rate coefficients of the above processes, (T-l)

t- is the time of travel interpreted as t =x/v, (T)

X- the distance downstream (L)

Cl, c2 - su koncentracije interativnih sastojaka kvalitete vode (proizvod

procesa “dekompozicije” C1 je C, pri cemu je potonji također proizvod procesa propadanja

(MLe3)

G & 20 - su početne koncentracije navedena dva sastojka kvaliteta vode (vidi također

Jed. 1.4) (ML-3)

K & - su koeficijenti brzine reakcije navedenih procesa, (TL)

t-je vrijeme putovanja tumačeno kao t = X / V, (T)

X-je udaljenost nizvodno (L)

The main process that affect (deplete) the oxygen content of water is the oxygen consumption

of microorganisms, living in the water, while they decompose biodegradable organic matter.

This means that the presence of biodegradable organic matter is the one that mostly affect the

fate of oxygen in the water. There are internal and external.sources of such biodegradable

organic matter. Internal sources include organic matter that stem from the decay (death) of

living organisms, aquatic plants and animals (also termed “detritus”, or dead organic matter).

Among external sources anthropogenic ones are of major concern and this includes waste

water (sewage) discharges and runoff induced non-point source or diffuse loads of organic

matter.

Glavni proces koji utječe na promjenu kolicine kisika u vodi je potrošnja kisika od strane

mikroorganizama, koji žive u vodi, dok razgrađuju biorazgradive organske tvari.

To znači da prisutnost biorazgradive organske materije najviše utječe na

sadrzaj kisika u vodi. Postoje unutrasnji i vanjski izvori biorazgradive

organska materije. Unutrasnji izvori uključuju organske tvari koje potječu od propadanja (smrti)

živih organizama, vodenih biljaka i životinja (tzv. mrtva organska materija).

Među vanjskim izvorima od velike vaznosti su antropogeni izvori, a to uključuje otpadnu

vodu (kanalizacija) i ispuštanje i otjecanje vode izazvano nestacionarnim izvorima ili nagomilanom

difuznom organskom materijom.

In the models biodegradable organic matter is taken into consideration by a parameter termed

“Biochemical oxygen demand, BOD”. BOD is defined as the quantity (mass) of oxygen

consumed from a unit volume of water by microorganisms, while they decompose organic

matter, during a specified period of time. Thus BOD, is the five day biochemical oxygen

demand, that is the amount of oxygen that was used up by micro-organisms in a unit volume

of water during five days “incubation” time in the respective laboratory experiment. Thus the

unit of BOD is mass per volume (e.g g0,/m3, which equals mgO,/l).

Pri modeliranju biorazgradive organske materije, uzima se u obzir parametar nazvan

"Biohemijska potrošnja kisika, BPK". BPK se definira kao količina (masa) kisika

potrosena od jedinice volumena vode od strane mikroorganizama, dok razgrađuju organsku materiju ,

tijekom određenog vremenskog intervala. Tako BPK, je petodnevna biohemijska potrosnja kisika,

odnosno ona količina kisika koja se konzumira od strane mikroorganizama u jedinici volumena

vode tijekom pet dana "inkubacije" u odgovarajućem laboratorijskom eksperimentu. Tako je

jedinica BPK masa po jedinici volumena (npr. G0, / m3, što iznosi MgO, / l).

Another main process in the oxygen household of streams is the process of reaeration, the

uptake of oxygen across the water surface due to the turbulent motion of water and to

molecular diffusion. This process reduces the “oxygen deficit” (D) of water, which is defined

as the difference between saturation oxygen content and the actual dissolved oxygen level.

Drugi glavni proces kisika toku rijeke je proces rearacije,

unos kisika preko površine vode zbog turbulentnog strujanja vode i

molekularne difuzije. Ovaj proces smanjuje "deficit kisika" (D) vode, što je definirano

kao razlika između zasićenog sadrzaja kisika i stvarne otopljene kolicine kisike.

General description of the traditional oxygen sag curve

In this model the decomposition of biodegradable organic matter is expressed as the “first

order” decay of BOD (termed here L) in function of the time

The oxygen line, the oxygen sag curve, is written for the oxygen deficit D is such a way that

oxygen consumed by microorganisms adds to the oxygen deficit, while the process of aeration

(or reaeration; the uptake of oxygen across the water surface due to turbulence and molecular

diffusion) reduces this deficit (Equations 2.3 and 2.4).

In these equations the initial conditions, e.g L = I+ and D = D, at x =0 (t =t,,) should be

calculated using the “Dilution equation” (Eq 1.4). The substitution of waste water and river

parameter values is relatively straight forward in the case of calculating L, (Eq. 2.5), while

for calculating D, first the initial oxygen concentration should be calculated (Eq. 2.6) and the

result of this should be subtracted from the saturation DO concentration to achieve D, (Eq.

2.7).

The saturation dissolved oxygen concentration of the water is temperature dependent, and the

respective values can be obtained either from tables published in the relevant literature or

from experimental expressions. In this teaching aid we will use the latter method in the form

of Equation 2.8 (Wang et. al, ref. Gromiec, 1983):

Opći opis tradicionalnog modela krivulje pada kisika

U ovom modelu raspadanje biorazgradive organske materije se izražava kao

raspad “prvog stepena” BPK u funkciji vremena

Linija kisika, odnosna krivulja pada kisika, je nacrtana za deficit D kisika na takav način da

se kisik konzumiran od strane mikroorganizama dodaje deficitu (manjku) kisika, dok proces aeracije

(ili rearacije; upijanje kisika preko površine vode uslijed turbulencije i molekularne

difuzija) smanjuje taj deficit (Jednadžbe 2,3 i 2,4).

U spomenutim jednacinama početni uvjeti, npr. L = I + i D = D, pri x = 0 (t = t,,) se

racunaju pomocu "jednacine razrijedjivanja (dilution equation)" (EQ 1.4).Zamjenom vrijednosti

parametara otpadnih voda i rijeke se dobiva vrijednost

parametara L, (Eq. 2.5), dok se

za izračunavanje D, prvo treba izračunati pocetna kolicina kisika(J. 2,6) i

rezultat toga treba oduzeti od koncentracije zasićenja DO kako bi se izracunala vrijednost D, (J.

2.7).

Koncentracija zasićenog otopljenog kisika u vodi zavisi od temperature i

odgovarajućih vrijednosti mogu se dobiti iz tablica objavljenih u literaturi ili

iz eksperimentalnih izraza. U ovom nastavku ćemo koristiti metodu pomocu jednacine u obliku2,8 (Wang i sur, ref Gromiec, 1983.).

The oxygen sag curve (which the user can see in the “Graph window” when in the respective

menu item) has a critical point where the dissolved oxygen content of water is the lowest, that

is when the oxygen deficit is the highest. The time of travel (or the corresponding

downstream distance) can be expressed by finding the minimum of the sag curve. It is

obtained in the form of Eq. 2.9 for tcrit,, Eq. 2.10 for x Crit, and Eq. 2.11 for Dcrit. Thus the

critical dissolved oxygen concentration is obtained as the difference between saturation oxygen

concentration and the critical oxygen deficit (Eq. 2.12).

For the practical use of the above simple model equations one should find, estimate, the

values of the two model parameters K, and K,.

There are two basic ways of estimating values of the reaction rate parameters:

1. If one has in-stream measurement data of DO and BOD then one can calibrate the

model, by fitting the calculated curves to the measured ones. This can be easily done

for BOD (for K,), expressing K, from Eq. 2.2; but the value of reaeration coefficient

K, can be found only by trial-error model

2. If you do not have access to measurement data then you can estimate model

parameters using formulae and tables published in the relevant literature.

Krivulja pada kisika ima kritičnu tačku na mjestu gdje kolicina otopljenog kisika u void najniža, odnosno

kada je kisik deficit najviši. Vrijeme putovanja (ili odgovarajuća udaljenost nizvodno)

može se izraziti pronalažeci minimalnu vrijednost krivulje. To je

dobiveno u obliku jed. 2,9 za t krit, J. 2,10 x za krit, I J. 2,11 za Dcrit. Tako

se kritična vrijednost koncentracije otopljenog kisika dobiva kao razlika između zasićene koncentracije kisika i

kritičnog deficita kisika(J. 2,12).

Za praktičnu primjenu navedenih jednostavnih modela jednacina treba pronaći o procijeniti,

vrijednosti dva parametra modela K i K,.

Postoje dva osnovna načina procjene vrijednosti parametara brzine reakcije:

1. Ako netko ima umetnute mjerne podatke DO i BOD u rijeci, onda se može kalibrirati

model, uporedujuci izračunate krivulje izmjerenim. To može lako biti učinjeno

za BPK (za K,), izražavajući K, u jed. 2,2, ali vrijednost koeficijenta reaeracije

K, može se naći samo na osnovu gresaka pri pokusaju simulacije modela

2. Ako se nema pristup podacima mjerenja onda se može procijenit modela

pomoću parametara koristeci formule i tablice objavljene u literaturi.

The value of the reaeration coefficient K, depends, eventually, on the hydraulic parameters

of the stream and a large number of experimental formulae have been presented in the

literature along with reviews of these literature equations (Gromiec, 1983, Jolankai 1979,

1992). These expressions deviate from each other, sometimes substantially. For the purpose

of this CAL programme we have developed a special equation on the basis of a number of

literature published equations that give, the value of K2 in function of flow velocity v and

stream depth H, by simply averaging the coefficient values of different authors (when they

were relatively close to each other). The thus obtained formula is Equation 2.13.

Vrijednost koeficijenta K rearacije zavisi od hidrauličkih parametara

toka rijeke i od velikog broja eksperimentalnih formula prikazanih u

literaturi zajedno sa recenzijama tih literatura (Gromiec, 1983, Jolankai 1979,

1992). Ovi izrazi odstupaju jedan od drugih, ponekad bitno te je stoga

razvijena posebna jednacina na temelju velikog broja jednacina objavljenih u literaturi

koje daju, vrijednost K2 u funkciji brzine strujanja v i

dubine toka H, tako sto se uzimala prosjecna vrijednost koeficijenata različitih autora

Tako dobivena formula je jednacina 2.13.

Both the reaeration coefficient K, and especially the decomposition rate coefficient K, depend

on the ambient (water) temperature. For this latter the most widely accepted formula is Eq.

2.14

One should note that reported literature values of K, and K2 vary over wide ranges of which,

for this teaching aid programme, we will consider the following domain:

K, - 0.1 - 1.7 day-’

Kz - 0.2 - 1.2 day-’

If we discretize this domain at 0.1 day-’ steps we can obtain the Table 2 for the variation of

the f =K,/K, ratio. The table is not shown but is included in the programme. From this table

one should not adopt values of f lower than 0.5 or higher than 5 .O

Oba koeficijenta rearacije, a posebno koeficijent brzine raspadanj K, ovisi

o sobnoj (voda) temperaturi.

Obicno se za raspon vrijednosti koeficijenata koriste

sljedeći domeni:

K - 0,1 do 1,7 dana-'

Kž - 0,2 do 1,2 dana-'

The BOD decay model

The BOD decay model describes the decomposition of biodegradable organic matter is

expressed as the “first order” decay of BOD (termed here L) in function of the time (which

is the time of travel along the stream t =x/v).

In Equation 2.2 the initial conditions, e. g L = L, at x = 0 (t = t& should be calculated using the

“Dilution equation” (Equation 1.4 and 2.5).

For more details see the “Basic theory”, the “General description of BOD-DO river models”

and the “General description of the traditional oxygen sag curve”.

t

Legend

L- BOD in the water (M, usually g0,/m3)

Lo-

initial BOD in the stream (below waste water discharge), see also Eq. 2.5 (M, usually

g Q/m31

K*-

is the rate coefficient of biochemical decomposition of organic matter (T-l, usually

day-‘)

t- is the time, that is the time of travel in the river interpreted as t =x/v, where x is the

distance downstream of the point of effluent discharge (T, usually days)

Model propadanja BPK

Model propadanja BPK koji opisuje razgradnju biorazgradivog organske materije je

izražena kao propadanje "prvog reda" BPK u funkciji vremena (koje

je vrijeme putovanja uz tok rijeke t = x / v).

U jednacini 2,2 početni uvjeti, e. g L = L, u x = 0 (t = t & treba izračunati pomoću

" jednacine razrijedjivanja" (jednacine 1.4 i 2.5).

t

legenda

L-BPK u vodi (M, obično G0, / m3)

Lo-

Početne vrijednosti BPK u potoku, vidi također Jed. 2,5 (M, obično

g Q/m31

K * -

je brzina promjene koeficijenta biokemijske razgradnje organske materije (Tl, obično

dan-')

t-je vrijeme, odnosno vrijeme putovanja uz tok rijeke, te se tumači kao t = X / V, gdje je x

udaljenost nizvodno od točke ispusta (T, obično dana)

The dissolved oxygen model

The traditional dissolved oxygen model describes the fate, the “sag”, of the dissolved oxygen

in the river as influenced by the decay of biodegradable organic matter and the reaeration

process (across the water surface).

In Equation 2.4 the initial conditions, e.g D=D,, L=L, at x=0 (t=tJ should be calculated

using the “Dilution equation” (Equation 1.4, 2.5 and 2.6).

For more details see the “Basic theory”, the “General description of BOD-DO river models”

and the “General description of the traditional oxygen sag curve”.

Legend

D- is the oxygen deficit of water (g0,/m3), see also equations 2.7 and 2.8.

L- BOD in the water (g0,/m3)

PJ-

is the initial oxygen deficit in the water (downstream of effluent outfall) (g0,/m3), see

also equations 2.6 and 2.7

Lo-

is the initial BOD concentration in the water (g0,/m3), (downstream of effluent

discharge), see also Eq 2.5

K-

is the rate coefficient of biochemical decomposition of organic matter (T-l, usually

day-‘)

K, - is the reaeration rate coefficient (T-l, usually day-‘)

t- is the time, that is the time of travel in the river interpreted as t=x/v, where x is the

distance downstream of the point of effluent discharge; and v - is the mean flow

velocity of the river reach in concern. (T)

Model otopljenog kisika

Tradicionalni model otopljenog kisika opisuje pad otopljenog kisika

u rijeci kao posljedicu utjecaja propadanja biorazgradive organske materije i procesa reaeracije.

U jednacini 2,4 početne uvjete,. D = D, L = L, u x = 0 (t = TJ treba izračunati

pomoću " jedacine za razrjeđivanje " (jednacina 1.4, 2.5 i 2.6).

legenda

D- deficit kisika u vodi (G0, / m3), vidi također jednacine 2,7 i 2,8.

L-BPK u vodi (G0, / m3)

PJ-

je početni deficit kisika u vodi (nizvodno od ispusta otpadnih voda) (G0, / m3), vidi

također jednadžbe 2,6 i 2,7

Lo-

je početna BPK koncentracija u vodi (G0, / m3), (nizvodno od tacke ispustanja otpadne vode

), vidi također Eq 2,5

K-

je brzina promjene koeficijent biohemijske razgradnje organske materije (Tl, obično

dan-')

K - je brzina promjene koeficijenta rearacije (Tl, obično dan-')

t-je vrijeme, odnosno vrijeme putovanja uz tok rijeke, te se tumači kao t = X / V, gdje je x

udaljenost nizvodno od točke ispusta (T, obično dana)

TThe “dilution equations” for BOD and DO

Considering a river and an effluent discharge of steady state conditions (with flows and

concentrations not varying in time) and assuming instantaneous full cross-sectional mixing of

the sewage water with the river water the initial concentration C, downstream of an effluent

outfall can be calculated by the dilution equation (Eq. 1.4), which stems from the balance

equation of in- and outflowing fluxes written for the section of the discharge point (e.g.

back-ground river mass flux plus pollutant discharge mass flux equals the combined mass

flow downstream of the point of discharge). This equation is used very frequently in simple

analytical water quality models for calculating the initial concentration of pollutants.

This two dilution equations compute the initial concentration of BOD and DO in the river

downstream of a point source sewage discharge, with the assumption of instantaneous mixing.

For more details see the “Basic theory”, the “General description of BOD-DO river models”

and the “General description of the traditional oxygen sag curve”.

Legend

L, - is the initial concentration of BOD in the river, downstream of the effluent discharge

point (MLm3, e.g. mgO,/l);

Lb-

is the background concentration of BOD in the river, (ML3, e.g. mgO,/l);

L, - is the BOD content of the waste water, (MLm3, e.g. mgO,/l);

DO0 - is the initial concentration of dissolved oxygen in the river, downstream of the effluent

discharge point (MLm3, e.g. mgO,/l);

DO, - is the background concentration of dissolved oxygen in the river, (MLe3, e.g. mgO,/l);

DO, - is the dissolved oxygen content of the waste water, (MLe3, e.g. mgO,/l);

Qb - discharge (rate of flow) of the river upstream of the effluent outfall, (L3 T-l, e.g.

m3/s);

9s -

the effluent discharge, (L3 T-l, e.g. m3/s);

Jednacine razrjeđivanje za BPK i DO

Posmatrajuci rijeku i odlijevanje vode u stacionarnim uvjetima (tok i

koncentracija ne variraju u vremenu), i pod pretpostavkom da se otpadna voda trenutna puna presjeka miješa sa vodom rijeke preko citavog presjeka

spočetna koncentracija C, nizvodno od ispusta otpadnih voda

se moze izračunati jednacine za razrjedjivanje (J. 1.4), koja proizlazi iz jednacine ravnoteže

za ulijevanje i izlijevanje masenih tokova rijeke pisane za dionicu ispusta (npr.

maseni tok nadolazece rijeke plus maseni tok otpadnih voda jednak je kombiniranom masenom

toku nizvodno od točke ispuštanja otpadnih voda). Ova jednacina se koristi vrlo često u jednostavnim

analitičkim obradama modela kvaliteta voda za izračunavanje početne koncentracije onečišćujućih tvari.

Ove dvije jednacine za razrjeđivanje racunaju početnu koncentraciju BPK i DO u rijeci

nizvodno od kanalizacijske tačke izvora ispuštanja, s pretpostavkom trenutnog miješanja.

Legenda

L, - je početna koncentracija BPK u rijeci, nizvodno od tacke ispusta

(MLm3, npr. MgO, / l);

Lb-

je koncentracija BPK nadolazece rijeke, (ML3, npr. MgO, / l);

L, - je BPK sadržaj otpadnih voda, (MLm3, npr. MgO, / l);

DO0 - je početna koncentracija otopljenog kisika u rijeci, nizvodno od tacke

ispuštanja otpadnih voda(MLm3, npr. MgO, / l);

DO, - je koncentracija otopljenog kisika nadolazece rijeke, (MLe3, npr. MgO, / l);

DO, - je količina otopljenog kisika otpadnih voda, (MLe3, npr. MgO, / l);

QB - protok rijeke uzvodno od ispusta otpadnih voda, (L3 Tl, npr.

m3 / s);/

qs- kolicina ispusta