110

MATHEMATICAL MODEL FOR THE PREDICTION OF DISSOLVED OXYGEN KINETICS FOR DRY SEASON DEGRADATION OF PETROLEUM HYDROCARBON IN

POND SYSTEM

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

Abstract

Mathematical models were developed and formulated to correlate the effect of momentum transfer in dissolved oxygen distribution in a dry season biodegradation of hydrocarbon in a pond system. The dissolved oxygen concentrations were measured as shown in experimental data and the influence of the momentum transfer due to continuous discharge of contaminants was observed in surface displacement, vertical depth and inclined depth displacement (subsurface displacement) and their effect on substrate and biomass concentration were determined theoretical models were also developed to predict the relationship between the effect of momentum transfer on dissolved oxygen concentration at different depth, surface distance and inclined depth of the pond system. The effect of momentum transfer on the dissolved oxygen concentration was attributed to changes substrate and biomass concentrations. Finally comparisons of experimental results with theoretically computed model results presented. The comparison shows good match, meaning that, the developed models will be useful in monitoring and predicting the effect of momentum transfer on dissolved oxygen concentration and their effect on substrate and biomass concentration on biodegradation of hydrocarbon in a pond system.

Introduction

Although bioremediation is already in use in many countries for solving problems of wastewater treatment (Brow, 1990; Bradley & Chapelle, 1996; 1998; Ooni, 2001 & Ukpaka 2005); an increase in the application of this process is foreseen in the near future with the aim of reducing the degree of effect of these contaminants and their physicochemical properties, which influence biodegradation of petroleum hydrocarbon before and after treatment of the wastewater, to comply with increasingly restrictive environmental regulations (Ukpaka 2005, 2006). In biodegradation of petroleum hydrocarbon, knowledge of the biochemical rate constants of the reactions involved is very important for reactor design Ukpaka (2006) & Brown (1990) have published an extensive compilation of biokinetic data showing that biodegradation of petroleum hydrocarbon is a very selective process of solving environmental problems with an influencing factor of dissolved oxygen distribution due to momentum transfer.

Another important feature to be considered in the biodegradation of petroleum hydrocarbon is the occurrence of competitive reactions of individual hydrocarbon due to change in dissolved oxygen concentration at particular point in the oxidation pond due to continuous discharge of wastewater (Momentum transfer). Biodegradation of these petroleum hydrocarbon yields carbon dioxide, gases, biomass, heat released and before the formation of products intermediate product is first achieved which enzyme-substrate complex (Vogt et al. 2004; Yeager et al. 2004; Ukpaka, 2006, & Ukpaka et al. 2005). These circumstances make the study of biodegradation of petroleum hydrocarbon under the influence of momentum transfer on the concentration of dissolved oxygen in the pond system very difficult to carry out. However, in cases where the velocity of wind at surface is greater then the

Multidisciplinary Journal of Research Development Volume 14 No. 1 April, 2010

111

velocity of the inflow wastewater, the concentration of dissolved oxygen in surface can lead in the determination of spreading rate of the contaminant. This model is based on hydrodynamic theory and assumes that the rate of momentum transfer was experienced in subsurface and surface with continuous change in dissolved oxygen concentration. The mathematical application known as separation of variables was used as presented in this paper.

Pollutants in the environment have been studied generally, (water, air, soil and even the subsurface system) and their effect seems to be very significant (Hong-gyu & Richard, 1990; Brow, 1990; Leahy & Colwell, 1990; Bradley & Chapelle, 1996; 1998; Bryniok et al. 1998; Sujit, 2000; Odigure et al. 20001; Ogoni, 2001; Ogulu and Omubo-Pepple, 2000; Ahmed et al. 2003; Ahmed 2004; Ubaezue & Egereonu, 2004). The conclusion of their works lack the effect of momentum transfer or continuous discharge of effluent in such process and above all biokinetic model was required to simulate the stability of process upon the action of momentum transfer on the concentration of dissolved oxygen in the pond system. The main objective of this study is for the development of models for the prediction of dissolved oxygen concentration upon the action of momentum transfer as well as the rate of biodegradation. The objective of this study is to carry out a detailed investigation on the influence of momentum transfer on the functional parameters that attribute to the biodegradation of petroleum hydrocarbons in a continuous discharge of wastewater in pond system. Materials and Method Sampling

Samples were carried out at specific points in the pond using automatic pipette, attached on a slide rule to determine the various depths and the wastewater samples were collected in one of the pond in Niger Delta area of Nigeria, at various sampling point in the pond system. The collected samples were transferred into sample bottles and stored in cool container before transfer to the laboratory for analysis. Similarly, samples were collected at various distance (surface) inclined and vertical depth (subsurface). Analysis

The analysis for each of the parameters was carried out according to the international standard as specified by American Society for Testing and materials (ASTM). Although there are several standardized test to measure the concentration of dissolved oxygen in any given substance as well as microbial concentration, individual hydrocarbon concentration. The British Standard Institution (BSI), the International Organization for Standardization (ISO), these various tests method and their reporting requirements are not completely defined. The American Public Health Association (APHA) method also establishes procedures of evaluating dissolved oxygen concentration and the individual microbial concentration in the system. And the various APHA standard used were APHA 5230D for dissolved oxygen concentration, APHA 92228 for pseudomonas sp. (cfu/100ml) and Bacillus (cfu/100ml), ASTM D5392-93 for E-coli (cfu/100ml), ASTM D5295-92 for Enterroccci (cfu/100ml) and APHA 9215C for total plate count (cfu/ml). Experimental Procedure

Figure 1 shows the main experimental set-up of pond system as presented in this paper. Samples were collected at different surface distance, incline and vertical depth (subsurface) every week for laboratory analyses to be carried on the following parameters.

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

112

(i) Microbial activity was determined at different points of the pond system to ascertain the effect of momentum transfer due to continuous discharge of wastewater in the pond system.

(ii) Dissolved oxygen concentration of the wastewater was determined at different points of the

pond system to ascertain the distribution due to momentum transfer. (iii) Individual hydrocarbon concentration of the wastewater was determined at different points

of the pond system to ascertain the rate of degradation as a result of momentum transfer.

Before starting the experiments, the initial composition of the pond system was measured to determine the concentration of dissolved oxygen, microbial concentration and individual hydrocarbon concentration at different point in the pond system for dry season.

The wastewater contaminants velocity was determined at various sampling point A1, A2, A3, A4, C1, C2, C3, C4, B1, B2, B3 and B4. Since momentum is defined as a product of mass and its velocity. The specific rate (velocity) on the substrate concentration, microbial concentration and dissolved oxygen concentration were measured at these various sampling points. From Figure 1, 0 is hydrocarbon, ~ is wave formation created as a result of disturbance, is direction of flow.

Figure 1: The Main Experimental set-up of Pond System

oooo oooo oooo oooo oooo oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo

oooo oooo oooo oooo oooo oooo oooo oooo oooo

oooo oooo

oooo

oooo

oooo oooo

A0 A1 A2 A3 A4

B0 B1 B2 B3 B4

Sampling point

C0 C1 C2 C3 C4

Immersed object in

water

Soil

Soil

Soil

Surface land

Surface land

Discharged pointed

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

113

Modelling the Flow Process of the Contaminants at Surface and Subsurface of Pond System The flow process model of contaminants in the aqueous media are governed by several phenomena, such as fluid flow and transport pattern, concentration of substrate (mixture content) diffusion, and other microscope movement through fractures and pores. These phenomena are governed by the principles of conservation of mass and of momentum. The conservation of mass for fluid is expressed as the equation of continuity and the conservation of momentum is expressed in the Navier-Stokes equations for flow of a viscous compressible fluid. Dissolved Oxygen and Biochemical Oxygen Demand Model Relationship In idealized BOD(t) the oxygen demand by microbes in the process of stabilization of organic content of wastewater samples is given as

tKotBOD 11

(1) Similarly, considering the time and distance of the occurrence of the minimum DO or the maximum dissolved oxygen deficit DOc is given as

tc =

oK

KKDoKK 1

12

1

2

12 KKIn 1

(2)

and

DOc = tKoK

K1

2

1 (3)

From equation (1) making o the subject of the formula and substituting it into equation (2) and (3) yields

tKt

o

BODK

KKDOKK

t

11KKIn1

1

12

1

2

121

(4) and

tKtKt

C

BODDO 1

11KK

2

1

(5) Equation (5) is useful in correlating the relationship between dissolved oxygen with biochemical oxygen demand.

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

114

Determination of Dissolved Oxygen at Distance

The times (and also the distance downstream) of the occurrence of the minimum DO or the maximum dissolved oxygen deficit DOc is obtained by different rating equation (4) with respect to time. Then,

O

o

KKKDO

KKt

112

1

2

121 K

KIn1

(6) and

DOc = tKo

1

2

1

KK

(7)

2.4.3. Force Balance Model on a Fluid Element in a Pond The conservation of the moment equation can be expressed in a linear or angular momentum form. The energy slope line, the water surface slope and below the water surface slope are assumed not to be the same in this paper. For this investigation it is assumed, the energy line has a slope of Sf and below the surface level has a slope of So. Then, the conservation of momentum equation is given as

element volume on the acting forces

theofresultant The

element volumefor the momentum

of damage of rate The

(8) The mathematical representation of equation (8) is givens as

fg FFFFdt

dU 21

(9) where Fg = g A x So gravity force (10) Ff = gA xSf friction force

F1-F2 = ½ g Ayx

2

hydrostatic force (12)

Substituting equation (10), (11) and (12) into equation (9) yields

fo xSgAAyx

xSAgdt

dU

2

21.

(13) Since

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

115

XuV

tuxAg

dtdU .

(14) Therefore, substituting equation (14) into equation (13) and rearranging the equation obtained yields

Ayx

gSSxgAxuV

tuXA fo

2

21

(15) The investigation was conducted under the following condition, a constant cross-section and one-dimensional flow, thus equation (15) becomes

fo SSgtuV

tu

(16) Methodical Application

The momentum transfer process for the pond system can be described as a simple batch phenomenon under conditions where organic sedimentation, sediment reactions and loss of organic volatiles component of petroleum hydrocarbon are negligible. Therefore equation (16) can be resolved by the application of separation of variables.

oSgtuV

tu

Equation (16) is expressed by considering the following boundary condition such as at x = 0; t = 0; U = Cu (17) at x = L, t = t (18) Equation (16) can be further be expressed by using the necessary mathematical approach, such as Let U = TX (19) where T is a function of (t) and X is a function of x only. The use of equation (19) called the method of separation of variable may enable one to reduce a partial differential equation to several ordinary differential equation. To this end I have

XTtu '

(20)

and

'TXtu

(21)

Substituting equation (20) and (21) into equation (19) yields

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

116

T’X + VTX’ = g(So-Sf) (22) Equation (22) can be expressed by considering both sides to be constant. In practice, it is convenient to write this real constant at either 2 or --2. Therefore equation (22) becomes

2''' TX

SgXXTV

TT o (23)

The general solution from equation (23) is given as follows:

(i) teCT2

1 (24)

(ii) X

VeCX2

2

(25)

(iii) C1 = 2e

Cn (26)

(iv) VSg o2 (27)

(v) tLV (28)

(vi) UL =

V

LSgVSg oo

eCeC 21 (29)

(vii) UL =

V

LSgV

Sgn

oo

eCeCC 1

2

22

(30)

(viii) UL =

V

LSgV

LSg

n

oo

eeC 21

(31)

(ix) 1

n2 CIn11 UVV

(32)

(x) So = L

n

CCIn

1 VLV

(33)

(xi) L

n2

UCIn

1LSg

VV

o

(34)

Model for Correlation of Momentum Transfer and Dissolved Oxygen for Dry Season

Recalling equation (2) which states that

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

117

o

o

ic K

KKDOKK

KKt

1

122

12

In 1

Making DOo the subject of the equation

o

o

ic K

KKDOKKKKt

1122

2 In 1

(35) Taking the log of both sides and on rearranging the equation will yield

12c1

122 In t KKK

KKDOKK

o

o

i

12c1

122 In t KKK

KDOKDOKK

o

oo

i

(36)

12c1

12

1

2 tIn KKK

KKKKDO

oO

o

O

KKK

KK

KKDO

1

12

1

2

12ctIn

(37)

Similarly, to determine the effect of momentum transfer due to continuous discharge of wastewater on the DO concentration; let assume that Cn = DOo concentration at the discharge point (Receiving point) therefore equation (37) into equation (31) yields.

V

LSgV

LSg

o

L

oo

ee

KKK

KK

KKU

2

1

12

1

2

12cIn t

(38) Equation (38) can be written as

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

118

oSg

VV

o

L e

KKK

KK

KKU

21

1

12

1

2

12cIn t

(39) where

o

o

KKK

KK

KKDO

1

12

1

2

12cIn t (40)

Therefore equation (39) becomes

LSg

VV

L

o

eDoU

21

(41) Rearranging and taking the log of both side yields

LSg o

2

o

L

VV-1

DOUIn

(42) Similarly, equation (42) can be written as

LSgV

Vo

o

L2

DOUIn

1

(43) Equation (42) can be used in correlating and predicting the dissolved oxygen characteristics,

as well as degradation process in pond system under the influence of momentum and mass transfer due to continuous discharge of wastewater in the pond system. The correlation model has been developed using equation of momentum transfer and application of separation of variable at different distance, time and depth. The experimental data was used in examining the reliability of this model. Results and Discussion

The results obtained from the investigation are presented in figures as shown below

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

119

The dry season theoretical concentration of BOD, DOodl and dodl versus vertical depth is

shown in Figure 2. From Figure 2, it is seen that the BOD concentration decreases with increase in vertical depth whereas the concentrations of DOodl and Dodl increases with increase in vertical depth. From Figure 2, it is observed that equal momentum transfer on BOD, DOodl and Dodl concentration at a vertical depth of 0.85m and 0.9m respectively.

Figure 4.27: Dry season theoretical concentration of BOD, DOodI and DodI versus vertical depth

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

vertical depth (m)

Con

cent

ratio

n of

BO

D, D

Ood

I and

Dod

I (m

g/l)

BODDOodIDodI

Figure 4.28: Dry season theoretical concentration of BOD, DOoLI and DOLI versus surface distance

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60

Surface distance (m)

Con

cent

ratio

n of

BO

D, D

OoL

I and

DO

LI (m

g/l) BOD

DOoLIDOLI

Figure 2:

Figure 3:

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

120

The dry season theoretical concentration of BOD, DOodl and Dodl versus surface distance is shown in Figures 3. From Figure 3, it is seen that the BOD, DOodl and DOdl concentrations decreases with increase in surface distance. The decrease in BOD, DOodl and DOdl concentration can be attributed to microbial activity, momentum transfer, the composition of the wastewater in pond system and concentration of the individual hydrocarbon and the effect of negative velocity (-VI) generated on the system.

Figure 4 illustrates the dry season theoretical concentration of BOD and DOtl versus time. The result obtained from Figure 4 showed that the BOD and Dotl concentration decreases with time. The decrease in BOD and DoLI can be attributed to effect of momentum transfer, microbial activity and the characteristics of the wastewater in pond system.

Figure 4.29: Dry season theoretical concentration of BOD and DOtI versus time

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6 7 8 9

time (week)

Con

cent

ratio

n of

BO

D a

nd D

OtI

(mg/

l) BODDOoLI

Figure 4:

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

121

Figure 5 illustrate the dry season comparison of theoretical BODT, DodlT and experimental

BODE, DodIE versus vertical depth. The result obtained from Figure 4.30 for DodT and DodE shows good match. Similarly, comparison of the BODT concentration with BODE shows a fair match, these variations can be attributed to lack of degradation, lack of displacement, over displacement of BOD, DO and individual hydrocarbon in pond system and the effect of negative velocity (-VI) generated by the system.

Figure 6 illustrates the dry season comparison of theoretical BoDT, DOdlT and experimental

BoDE, DOLiE versus surface distance. The result obtained from Figure 6 for DodT and DodE shows good match. Similarly, comparison of the BoDT concentration with BoDE shows fair match, these variations can be attributed to lack of degradation, lack of displacement, over displacement of BOD, DOdI, composition of individual hydrocarbon in pond system and the effect of negative velocity (-VI) generated on the system.

Figure 4.30: Dry season comparison of theoretical BODT, DodIT, and experimental BODE, DOdIE versus vertical depth

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1 1.2 1.4

vertical depth (m)

Con

cent

ratio

n of

BO

D, D

odI (

mg/

l)

BODT

DodIT

BODE

DOdIE

Figure 4.31: Dry season comparison of theoretical BODT, DoLIT, and experimental BODE, DOLIE versus vertical depth

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Surface distance

Con

cent

ratio

n of

BO

D, D

oLI (

mg/

l)

BODTDoLITBODEDOLIE

Figure 5:

Figure 6:

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

122

The effect of momentum transfer on the biochemical oxygen demand (BOD) and dissolved

oxygen (DO) concentration was investigated at different depths. The momentum transfer of the BOD decreases with increase in depth, as shown in Figure 7. Similarly, the momentum transfer of the dissolved oxygen (DO) increases with increase in depth. From Figure 7, it is seen that equal momentum transfer was observed on UBOD and UDodl at a depth of 0.85m, UDOodl and UDodl at a depth of 0.95m, where the close region is a visible region of equal momentum transfer in the pond system (ranging from 0.68 to 0.95m).

Figure 8 illustrates the actual velocity distribution of BOD concentration in pond system. The

momentum transfer due to positive velocity (+V) is higher than the opposing velocity (-V). Since the negative velocity creates friction opposing the positive velocity, one can say that actual velocity of

Figure 4.32: Dry season momentum transfer values versus depth for UBOD, UDOodI and UDodI

-0.6-0.4-0.2

00.20.4

0.60.8

11.21.41.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Depth (m)

Mom

entu

m tr

ansf

er (m

g) (m

day

-1) UBOD

UDOodIUDodI

Figure 4.32a: Dry season momentum transfer versus distnce for BOD upon the influence of (+V) and (-V)

0

1

2

3

4

5

6

0 10 20 30 40 50 60

Dis tance (m)

Dry

sea

son

mom

entm

tran

sfer

of B

OD

co

ncen

tratio

n (m

g/l)

BOD+V

BOD-VBOD AV

Figure 7:

Figure 8:

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

123

BOD distribution in the pond system is computed as [VI = (+VI)-(-VI)] velocity value with respect to distance for dry season.

Figure 9 illustrates the actual velocity distribution of DO concentration in pond system. The

momentum transfer due to positive velocity (+V) is higher than the opposing velocity (-V). Since the negative velocity creates friction opposing the positive velocity, one can say that actual velocity of DO distribution in the pond system is computed as [VI=(-VI)-(-VI)] velocity value with respect to distance for dry season.

Figure 10 illustrates the actual velocity distribution of DO concentration in pond system. The

momentum transfer due to positive velocity (+V) is higher than the opposing velocity (-V). Since the

Figure 4.32b: Dry season momentum transfer versus distance for DO upon the influence of (+V) and (-V)

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60Distance (m)

Dry

sea

son

mom

entu

m tr

ansf

er o

f D

O c

once

ntra

tion

(mg/

l)DO+VDO-VDO AV

Figure 4.32c: Dry season momnetum transfer versus depth for DO upon the infleuence of (+V) and -(V)

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60

Depth (m)

Dry

sea

son

mom

entu

m tr

ansf

er o

f DO

co

ncen

tratio

n (m

g/l)

DO+VDO-VDO AV

Figure 9:

Figure 10:

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

124

negative velocity creates friction opposing the positive velocity, one can say that actual velocity of DO distribution in the pond system is computed [VI=(-VI)-(-VI)] velocity value with respect to depth for dry season.

The effect of momentum transfer on the Biochemical oxygen demand (BOD) and dissolved

oxygen (Do) concentration was investigated at different velocity. The momentum of BOD decreases with increase in velocity as shown in Figure 11. Similarly, the momentum transfer of the dissolved oxygen (DO) increases with increase in velocity as shown in Figure 11. From Figure 11, it is seen that equal momentum transfer was observed on UBOD and UDodl at a velocity of 0.45m/day, UDOodl and UDOodl at a velocity of 0.41m/day and UBOD and UDodI illustrates equal momentum transfer on UBOD and UDOodl at a velocity of 0.47m/day, where the close region is a visible region of equal momentum transfer in pond system (ranging from 0.41 to 0.47m/day).

Figure 4.33: Dry season momentum transfer values versus velocity for UBOD, UDOodI and UDodI

-0.6

-0.4

-0.20

0.2

0.4

0.6

0.8

11.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5

Velocity (m/day)

Mom

entu

m tr

ansf

er (m

g) (m

day

-1)

UBODUDOodIUDodI

Figure 4.22: Dry season microbial population versus distance

0

10000

20000

30000

40000

50000

60000

0 10 20 30 40 50 60

distance (m)

mic

robi

al p

opul

atio

n (c

fu/m

l)

E-ColiEnterrococci

Figure 11:

Figure 12:

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

125

The result of the microbial analysis presented in Figure 12 clearly showed the activities of two micro-organisms (E-coli and enterrococci). The enterrococci survive reasonably compared to E-coli. The result presented graphically in Figure 12, depicts the various stages of microbial growth in pond system with incremental step of exponential and decline phases. This is possible due to the influence of momentum transfer in the pond system or due to the long intervals at which the samples were taken. From the Figure 12, it is seen that all the micro-organisms experienced a decline phase and is likely, due to experimental condition and the momentum transfer effect on the physiochemical parameters in pond system due to continuous discharge of wastewater.

The dry season microbial population versus distance for pseudomonas sp and Bacillus were shown in Figure 13. The result obtained showed that the pseudomonas sp posses the highest population compared to Bacillus type of microorganism. The effect of momentum transfer in pond system created several lag, exponential, stationary and death or decline phase with increase in distance. The change in the microbial growth can be attributed to changes in the physicochemical parameters of the pond system and the component of inflow wastewater into the pond system.

Figure 4.23 : Dry season microbial population versus distance

0500

1000150020002500300035004000

0 10 20 30 40 50 60

distance (m)

mic

robi

al p

opul

atio

n (c

fu/m

l)

PseudomonasBacillus

Figure 13:

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

126

The dry season microbial population versus time for E-coli and Enterrococci were showed in

Figure 14. The result presented in Figure 14 showed that Enterrococci posses the highest population compared to E-coli type of microorganisms. The microbial growth as illustrated in Figure 14 shows different lag, progressive, stationary and death phase experienced by the E-coli and Enterrococci microorganisms presented in pond system. These phases achieved by the microorganisms in pond system can be attributed to the effect of momentum transfer and the changes in the physicochemical parameters of the wastewater in the pond system and the effect of negative velocity (-VI) generated on the system.

From Figure 15, it is seen that the microbial population of pseudomonas sp and Bacillus sp

encounter different lag, progressive, stationary and death phase, this can be attributed to the effect of

Figure 4.24 : Dry season microbial population versus time

0

10000

20000

30000

40000

50000

60000

0 2 4 6 8 10

time (week)

mic

robi

al p

opul

atio

n (c

fu/m

l)

E-ColiEnterrococci

Figure 4.25 : Dry season microbial population versus time

0

500

1000

1500

2000

2500

3000

3500

4000

0 2 4 6 8 10

time (week)

mic

robi

al p

opul

atio

n (c

fu/m

l)

Pseudomonas

Bacillus

Figure 14:

Figure 15:

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

127

physicochemical parameters on velocity distribution characteristics and the effect of momentum transfer due to continuous discharge of wastewater in the pond system for dry season. Conclusion

The above study brings out the following conclusions on the velocity, momentum transfer due to continuous discharge of wastewater, microbial growth rate, and dissolved oxygen concentration distribution upon the influence of momentum transfer for pond system of dry season.

The effect of momentum transfer (U) resulted to increase in velocity distribution of the following, biochemical oxygen demand and dissolved oxygen concentration in pond system for dry season. The overall theoretical velocity for dry season is given as 0.31(m/day) and -0.45(m/day), whereas the overall theoretical momentum transfer rates (U) is within the range of 0.005 to 0.1762(mg)(m/day).

The effect of momentum transfer (U) on the physicochemical parameters reduces the degradation rate of the BOD concentration as well as the microbial growth rate in pond system for dry season. The results of the theoretical models were compared with the experimental data obtained from the investigation and the result shows good match, meaning that the developed models will be useful in predicting and monitoring the effect of momentum transfer on the BOD and DO concentration of pond system. The effect of momentum transfer (U) slightly enhances the physicochemical parameters distribution of BOD and DO concentration in pond system, thereby increasing or reducing the BOD and DO concentration, which enhance theoretical data for predicting the behaviour of the microbial growth, microbial decay and substrate concentration. The variation in the results may be attributed to experimental error during transportation, sampling and laboratory analysis and the necessary mathematical assumption considered during the model development.

Similarly, for dry season the BOD concentration is given as 7.143 or BODUIn LII = 7.143. Heavier

individual hydrocarbon suffers a decrease in momentum transfer and substrate concentration distribution throughout the flow field in pond system for dry season. The rate of momentum transfer of substrate increases with increase in distance. The variation in the behaviour of the system for dry season momentum transfer rate can be attributed to friction, gravitation and hydrostatic forces acting on the individual hydrocarbon and other external influence and environmental factors.

The substrate concentration of the flow field in terms of depth, decreases in magnitude as momentum transfer (U) increases almost up to the bottom of pond depth, that is, momentum transfer between the surface and the sub-surface. Similarly, the BOD and DO concentration of the flow field in terms of depth decreases in magnitude as momentum transfer (U) increases.

Finally, the developed models will be useful in the following areas of application: (a) Monitoring and predicting the biokinetics study of individual hydrocarbon concentration upon

the influence of momentum transfer due to continuous discharge of wastewater in pond system. (b) To quantify and characterize the biomass built up in a bioreactor upon the influence of

momentum transfer due to continuous discharge of wastewater in pond system. (c) Monitoring and predicting the effect of momentum transfer on the performance of individual

hydrocarbon degraders in pond system. (d) Monitoring and predicting the effect of the physicochemical parameters in pond system upon

the influence of momentum transfer for continuous discharge of wastewater. Predicting the best period of biodegradation, the lag, progressive, stationary and decline phase

upon the influence of momentum transfer due to continuous discharge of wastewater in pond system. And predicting the best period and conditions for carrying out bioremediation programme.

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

128

Nomenclature BOD(t) = Biochemical oxygen demand concentration (mg/l) o = Initial DO concentration of the influence diluted water (mg/l) K1 = Initial BOD deoxygenation rate coefficient (day-) t = time (sec) K2 = final BOD deoxygenation rate coefficient (day-1) DO = initial concentration of dissolved oxygen (mg/l) DOc = critical concentration of dissolved oxygen (mg/l)

dtdu

= the rate of change of momentum (gm/s2)

Fg = gravity force (N) F1 = initial hydrostatic force (N) F2 = final hydostatic force (N) Ff = frictional force (N) g = acceleration due to gravity (m/s2) A = average cross-section area (m2) X = length of fluid element (m) So = below the surface water slope ’ = density (g/cm3) Sf = slope of the energy time V = velocity (m/s) T = time (separation of variable parameter) X = biomass concentration (cfu/ml) tc = critical time of dissolved oxygen (sec) J = centroid height of the hydrostatic force (m) U = momentum of system (mg/s) Cn = individual petroleum hydrocarbon concentration (mol %) References Hong-gyu, S. & Richard, B. (1990). Effect of jet fuel spills on the microbial community of soil

Journal of applied and environmental Microbial 14, 72-76. Brow, R.A. (1990). Oxygen sources in-situ Bioremediation of ground water and contaminated soil

water pollution control federation 63, annual conferences Washington, 99-118. Leahy, J. & Colwell, R. (1990). Microbial degradation of hydrocarbon in the environment. Microbial

Reviews. 55, 305-315. Bradley, P.M. & Chapelle, F.H. (1996). Anaerobic mineralization of Vinyl chloride in Fe(III)

reducing aquifer sediments. Environ. Sci. Technol. 32, 533-557. Bradley, P.M. &Chapelle, F.H. (1998). Effect of contaminant concnetraiton on aerobic microbial

mineralization of DEC and Vc in stream-bed sediment. Environ. Sc. Techno. 32, 553-557.

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System

129

Bryniok, D.; Koziollek, P. Baner, S. & Knackmuss, H.J. (1998). Cometabolic biodegradation of Cis-1-2-dichlorethene by ethane utilizing bacteria In: Wickrammanayake GB, Hinchec RE, eds. Bioremediation and Phytoremediation; Chlorinated and Recalcitrant Compounds. Columbus OH: Battelle press. 181-186.

Sujit, K.K. (2000). Time dependent mathematical model of secondary air pollutant with instantaneous

and delay removal. Journal of modeling simulation and control, 61(2), 30-40. Odigure, J.O. & Abdulkareem, A.S. (2001). Modelling of pollutants migration from gas flaring in the

Niger Delta area. Journal of modeling, simulation and control, 62(3), 57-63. Ogoni, H.A. (2001). Development of a mathematical model for the optimum biomass formation in a

batch fermentator. Journal of modeling simulation and control, 62(4), 11-20. Ogulu, A. & Omubo-Pepple, V.B. (2000). Mathematical model for the rheological effect of sludging

blood flow 2. Journal of modeling, simulation and control, 62(4), 43-45. Ahmed, A.M.; Mohamed, A.A.; & Gamal-Mostafa, A.E. (2003). Environmental impacts on waste

and sediment of the river Nile ingreater cairo (near Helwavecity). Journal of modeling, simulation and control, 63(3), 30-36.

Ahmed A.M. (2004). Biogeochemical monitoring of major cations approach to the understanding of

sodication problem in a small catchment in Eygpt. Journal of modeling, simulation and control, 65(1), 35-48.

Ubaezue, U. & Egeronu, K.I. (2004). Investigation on nitrate pollution in groundwater of Owerri and

environs. South Easter Nigeria. Journal of modeling, simulation and control, 65(1), 57-76. Vogt, C; Simon, D.; Alfreider, A; & Babel, W. (2004). Microbial degradation of chlorobenzene

under oxygen-limited conditions leads to accumulation of 3-dichlorocatechol. Environmental Toxiology and chemistry, 23. 265-270.

Yeager, C.M. Arthur, K.M. Bottomley, P.J. & Arp., D.J. (2004). Trichloroethylene degradation by

toluene-oxidizing bacteria grow on non-aromatic substrates. Biodegradation, microbial chlorination & dechlorination, 31(15), 19-28.

C.P. Ukpaka ; H. A. Ogoni; S.A. Amadi and A. J. Akor

130

Ukpaka, C.P. (2006). Modelling microbial growth rate kinetics in spherical coordinate of aqueous medium. Journal of Science and Technology Research, 5(1), 1-9.

Ukpaka, C.P. (2006a). Modeling degradation kinetics of petroleum hydrocarbon mixture at specific

concentration. Journal of Research in Engineering, 3(3), .47-56. Ukpaka, C.P. (2006b). Factors Affecting Biodegradation reaction of petroleum hydrocarbon at

various concentration International. Journal of Physical Science. 1(1), 27-37. Ukpaka, C.P. (2005). Biodegradation kinetics for the production of carbon dioxide from natural

aquatic ecosystem polluted with crude oil. Journal of science and technology research, 4(3), 41-49.

Ukpaka, C.P. Ogoni, H.A; Amadi, S.A.; & Adelayo, T.A. (2005). Mathematical modeling of the

microbial growth and decay rate of pseudomonas species on biodegradation of Bonny light crude oil. Global journal of Pure and applied science, 11(3),.423-431.

Mathematical Model For The Prediction Of Dissolved Oxygen Kinetics For Dry Season Degradation Of Petroleum Hydrocarbon In Pond System