Development Of Mathematical Model To Predict The

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ABSTRACT. Mathematical models were developed to simulate the microbial growth rate of bacteria .... This equation is the usual, form of Henry Michael's equation. ..... line – weaver Burk plot. .... At the maximum point slope = 0 therefore µp. = µ.
ISSN 0976-111X

INTERNATIONAL JOURNAL OF PHARMA WORLD RESEARCH

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Title: Development of Mathematical Model for the Prediction of Microbial Growth Rate of Bacteria and Fungi in BTX Contaminants Degradation in Soil Environment C.P. Ukpaka Department of Chemical/Petrochemical Engineering Rivers State University of Science and Technology Nkpolu, P.M.B 5080, Port Harcourt, Nigeria E-mail; chukwuemeka 24 @yahoo.com. ABSTRACT Mathematical models were developed to simulate the microbial growth rate of bacteria and fungi upon the degradation of benzene, toluene and xylene contaminated soil obtained in Omuigwe Aluu in Ikwerre Local Government area of Rivers State. Analysis was carried out to determine soil pH, electrical conductivity, available phosphorous, total nitrogen, organic carbon, organic, porosity, sandy, silt and clay and textural class was sandy clay. Because of the fact that level 0 -1 has significant available phosphorous of 8.52 mg/kg, organic carbon percentage of 0.90 higher them other level was chosen as the best for the remediation of benzene, toluene and xylene (BTX) contaminants. Microbial population of growth test was carried out to determine the total heterotrophic bacteria (THB) and total heterotrophic fungi (THF) of the contaminants with time. Toluene shows a significant value of bacteria population of 8.6 x 105cfu/g, benzene (4. 1 x 105 cfu/g) and xylene (3.5 x 105 cfu/g) at 28days. Benzene shows a significant value of (3.6 x 103 cfu/g) and toluene (3.2 x 103 cfu/g) for 28days. A conclusion was reached that the microorganisms in the soil were effective in toluene degradation. Keywords: Model, Prediction, Microbial, contaminants, BTX, Degradation. IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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1.

INTRODUCTION Various studies with benzene, toluene and xylene (BTX) contaminants degradation have shown that this organism is suitable for the testing of degradation characteristics of BTX mixture to ascertain substance that are environmental friendly. The main advantages of using bioremediation processes are that they (i) produced substances that are environmental friendly at the disassociation of enzyme- substrate complex to form enzyme and product, (ii) are easy and cheap to culture in the laboratory, (iii) are sensitive to pollutants, (iv) have a short/ long life- cycle based on the nature in time of toxicity of contaminants as well as the process conditions, (v) are model organisms for a widespread species on soil environment several monitoring studies were preformed for the assessment of the aromatic compounds degradation in both batch and continuous stirred tank reactor (CSTR) (Joner et al; 2001; Fismes et al; 2002; Benincasa et al; 2004; Kaiser & Guggenberger, 2003; Mohapatra et al 2006; Ghosh et al. 2006; Ukpaka, 2006; Kumar, 2007 & Meenu et al. 2007). Furthermore, two guidelines were developed for the routine testing of bacteria and fungi activity on benzene, toluene and xylene (BTX) contaminants degradation in a batch reactor. Assessment of degradation rate of BTX contaminants upon the activity of microbes were carried out. These guidelines are well established in microbiological research and standard testing, because various characteristics, properties and kinetic parameters can be observed to detect possible impacts of substances on the development of mathematical model to predict the microbial growth rate of bacteria and fungi in BTX contaminants degradation in soil environment (ASTM, 1986 & APHA, 1995). Therefore, we used batch reactor as a model procedure to predict the relation between pollutants and their effect on the microbial growth rate of bacteria and fungi (population) is investigated (Wick et al. 2003 & Straube et al. 2003; Hansen et al. 2004; Raza. et al. 2006; Newman et al. 1997; Bhabjit & Sarma, 2007; Utpal, & Sarma, 2007). The aim of the baseline experiments reported here was to determine the effect of benzene, toluene and xylene degradation on bacteria and fungi growth rate characteristics. In this paper the concentration- response curve for BTX and time as well as microbial concentration - response curve with time was also established. 2. MATERIALS and METHODS 2.1 The Model A chemical’s transformation rate will vary with differing aquifer redox conditions. Aerobic redox conditions will tend to occur in oxygenated (high levels of oxygen) shallow groundwater. Therefore, the advection dispersion equation can be written as: ∂ 2c ∂c ∂c − λc + DL = −V R ∂x 2 ∂x ∂t ……………………………………………….(1)

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2.2

Biodegradation of Petroleum Hydrocarbon Mixture without Activator Single Enzyme Catalyzed Reaction Generally an enzyme catalysed reaction of a given substrate such as petroleum hydrocarbon can be presented. Ukpaka, (2006) reveal that the rate of product formation depends on the dissociation of enzyme- substrate complex, the rate of reaction can be s written as V = Kp [EH ]…………………………………..………………………(2)

A material balance equation for the distribution of the total enzymes in the reacting system can be expressed as Et = [E ] + [EH ]…………………………..…………..(3) Combining equation (1) and (2) E Ep [EH ] = [Et ] [E ] + [EH ] The dissociation constants Ks can be expressed as the ratio of the rate constant K -1 and K1. K K H = −1 = [E ] / [EH ] ……………….…………………………………..……………(4) K1

[EH ]

=

[E ] [H ] KH

Combining equations (2), (3) and (4) we have [E ] [H ] ……………………………….(5) [E ] [H ] Kp S Kp KH V KH = [Et ] [E ] + [E ][H ] [E ] + [E ][H ] KH The reaction rate will be maximum when the total enzymes form a complex, hence S V max = Kp [Et ]......................................................................................................(6) Combining equation (1) and equation (1), we have [E ] VS ………………………….…………………………………..(7) = S [ ] + K H H V max

Hence, V S = V max S

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This equation is the usual, form of Henry Michael’s equation. With petroleum hydrocarbon mixture as growth limiting substrate, assuming H 1 , H 2 , H 3 …..H n as the hydrocarbons present, equation (1) can be expressed thus;  [H1 ] [H 2 ] • [H 3 ] • • • [Hn] .................................(7a) S • V S = V max   K H +[H1 ] K H + [H 2 ] K H + [H 3 ] K H + [Hn]   But the rate of hydrocarbon degradation is dH S V 1 = dt …………………………………………………………………….(7b) Hence combining equation (7a) and (7b) and on rearrangement we have  [H1 ] [H 2 ] • + [H 3 ] • • • + [Hn] dH ………………….(8) • V S dt =  + K Hn [Hn]   K H S 1 [H1 ] K H 2 + [H 2 ] K H 3 [H 3 ] Equation (8) can be expressed as n n  K Hn + H i  K   S S V max dt = π  [Hi] dH or V max dt = π 1 + [HiHi] dH ...........................(8a)    i = 1 i =1 For a single enzyme system

[ ]

n

V

S max

 K dt = π  Hi + 1dH ..............................................................(8b) [H ]  i = 1 i

On integrating equation (8b) yields H S V max dt = K H in H + (H 0 − H ) ....................................................................................(8c) 0

V max t = K H Inγ S

+ (1 − y )...............................................................................................(8d )

Equation (8d) represent the model equation for a single enzyme catalysed reaction and can be applied in the computation of maximum reaction rate ( Ukpaka, 2006). 2.3 Reaction Catalyzed by Multiple Enzyme Occasionally, multiple enzymes have been found to catalyse a given substrate particularly in biodegradation of petroleum hydrocarbon. Consequently, the velocity at any given time is the sum of the velocities contributed by each enzyme. Thus, for petroleum mixture we have H 1 , H 2 , H 3 , H n , the rate can be presented as; IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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[H ] m m m V = V max 1 K +1[H ] + V max 2 H 1 where Vm =

[H 2 ] + .... + m [H n ] V max n K + [H ] ………………………….(9) K H + [H 2 ] H n

dH ……………………………………………………..……………..(9a) dt

Substituting equation (9a) into equation (9) thus, equation (9a) becomes

[H1 ] + dH m = V max 1 dt K H 1 + [H1 ]

V

m max 2

[H 2 ] + .... + m V max K H 2 + [H 2 ]

Equation (9b) can be re-written as n m dH [Hi] dH = = ∑V dt dt K H + [Hi ] i =1 max i

V Where

m max

=

n

∑V

i = 1

n

V ∑ m

max

i =1

n

[H n ] ……….(9b) K H 3 + [H n ]

[Hi] iK H + [Hi ]

…………….(9c)

m max

…………………………………………………….……(10)

Equation (9c) can be written as n [H ] m V max dt = ∑ iK H +i [Hi] ........................................................................................(11) i i =1 Separating the variable and integrating equation (11) we have n n n H  m H − H V max t = ∑ K H ∑ In i  H 0  + ∑  0 H i …………………………….(12) i =1 i =1 i =1 n n n

t = ∑ K Hi ∑ In yi + ∑ yi ……………………………………………..(13) i =1 i =1 i =1 Equation (13) represents the model equation for the rate of a reaction being catalysed by multiple enzymes (Ukpaka, 2006).

V

m

max

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2.4

Kinetic Model for Biodegradation of Petroleum Hydrocarbon Mixture using Activator. Kinetic models for biodegradation of petroleum hydrocarbon mixture in the presence of activator have been developed. The developed models were for the evaluation of specific and maximum specific rates of biodegradation reaction in the presence of activator. The kinetic models formulated were tested using experimentally generated data. Both the theoretical and experimental results were comparable. The experimental results underpin the usefulness and practical application of the developed model in bioclean-up of petroleum- polluted environment and for designing treatment reactions for petroleum hydrocarbon based effluents. (Ukpaka, 2006). 2.5

Multiple Enzyme Catalysed Reaction with Activator E   +  + (H )  

βKs

Ka

[E ]

+ [H ]

Ks

Kp

[EH ]

Kp

[E ] + [P]

+

[EH]

Kp

[H] + [P]

The dissociation constant of enzyme can be expressed as a ratio of the rate constants of the backward (K -1 ) and forward (K 1 ) reaction. Since (EH) and (EAH) are both product forming enzyme complexes and therefore rate determining. The reaction rate can be expressed as the sum of the two product forming rate complexes. Hence. = Kp (EH) + bK p (EAH) ……………………………………….……..…….(16) At any stage of the reaction the total enzyme present is (E t ) = (E) + (EH) + (EAH) Expressing each of enzyme complexes in terms of free enzyme, (E) we have (EH) =

[E ] [H ] [EAH ] KH

=

[A] [H ] [E ] ………………….…………(17) αK A

Substituting these expressions into equation (16) and combining it with equation (17), 2 have;

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K p [H ]

+ βK P

S

[H ][H ]

αK H K A KH [ ] [ ] [A][EH ] H A Et + + 1 + KH KA K AKH Assuming, V S Amax = K p [K ]

V

A

=

bV S Amax Hence

= bK p [E ] (H )

V

S A max

=

KH 1 +

+ βV S Amax

[H ]

[A]

[A] [H ] αK A K H

[A] [H ] …………………………………………….(19)

+ + KH K A αK A K H Equation (19) can be presented in the form of Henri-monten equation. S [H ] VA = V S Amax t

KS

[A]    [A]   [H ] 1 + 1 + K K A  A     β [ A]  β [ A]   1 +  1 + K α K A  A   

If we let  [A] , X = 1 + αK A  

 β [A]  , Y = 1 + K α A  

 A   ……………………………(20) Z = 1 + K A  

The equation (20) into equation (19) and it takes the form [H ] VS = S V Amax t K H z / y + [H ] X / Y The rate V A can also be expressed in terms of substrate [H ] VS = …………………………………………………………(22) K H z / y + [H ]X / Y The rate V A can also be expressed in terms of substrate dH VS = dtt IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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Combining equation (22) and (23) obtain, for multiple component.

α

dH dtt

= V S A max

[H1 ] K H z / y + [H1 ] XIY

[H 2 ] K H 1 z / y + [H 2 ]Z / Y

[Hn] K H 2 z / y + [H 2 ] z / y

On rearranging equation (2.33)

α

V

S A max

dt =

α

K S 1 ( z / y )1 + [H1 ]( X / Y )1 [H1 ]

K S 2 ( z / y ) 2 + [H 2 ] ( X / Y ) 2 H2

K Hn ( z / y ) n + [H n ] ( XIY ) n dH …………………………………..(23) [H n ]

Equation (23) can be expressed as: n  K ( z / y ) n + [H ii ] ( XIY )i  S  dH α V A max dt = π  Si [ ] H n  i =1 For a mono component

α V S A max dt =

K Si z / y + HX / Y H

On integrating S α V A max t = K S z / yInH / H 0 + XIY ( H 0 − H )

α V

S A max

t = K S z / yIny + XIY (1 − y )

where y = H / H 0

α V A max t = 1 y [ZK H Iny + x (1− y )] ………………………………………………………………………….. (23) S

Equation (23) represent the developed kinetic model for a single enzyme catalysed reaction with a catalyst and can be used in the computation of maximum specific rate. Multiple enzyme catalyzing the reaction with an activator. IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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  [A]  [H1 ] [H ] 1 + [A]   K H 1 1 + 1  K A  K A  m    + α V A max 1   β [A]   β [A]   1 +  1 +   K A  α α K A    

+ V A max 2 m

      

+

[H 2 ]

[A]   1 + [H 2 ]1 +  KA   KA  KH2  +   β [A]  β [A]   1 +  1 + αK A    αK A  [A] 

+ − − − − +V

m A max n

KH n

     [H n ]   [ A]     1 + [H n ]1 + [A]    KA  KA     +   β [ A]  β [ A]      1 + α K  1 + α K   A  A   

    ………………….……..(24)         

Combining equation (32) and equation (37) and substituting equation (30) into the resulting equation, we obtain. [H1 ] [H 2 ] dH m m = V A max 1 + V A max 2 dt K H 1 ( z / y )1 + [ H 1 ] ( XIY )1 K H 2 ( z / y) 2 + [ H 2 ] (Z / Y ) 2

+ V Aamx n m

[H n ] K Hn ( z / y ) n + [ H n ] ( XIY ) n

Rearranging equation (37), we have

dH m = V A max dtt Where

V

m A max

n

∑ KH i i =1

[H i ] K Si ( z / y ) i + [ H i ] ( XIY ) i

…………………….(39)

= V A max 1 + V A max 2 + V A max n m

m

m

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Hence

V A max dt = m

n

∑ KH

i =1

i

( ZIY )i + [ H ] ( XIY )i dt ………………………………..(40)

On integrating, we have;

V A max t = m

n

n

∑ KH i n∑ (ZIY ) i

i =1

i =1

n

∑ Iny i + i =1

n



i =1

n

( XIY ) i

∑ (1 − y) i =1

i

……..…(41)

Formulated equation (41) represents the model equation for multiple enzyme catalysed reaction with an activator. (Ukpaka, 2006). Determination of the Kinetic Constant The maximum specific rate in presence of activator is given as a

V K

Max a H

+ βV max   = KH 

The limiting maximum velocity depends on the concentration of the activator.



β V A max = V A max 1 + m

m



KA   [ A] 

1 1 + K A I [ A] Equation (43) can be rearranged to take the form.

β =

K A = ([A] – β [A]I β or K A = ([A] – [1 – β])I β The kinetic constants involved in these models can be determined experimentally using line – weaver Burk plot.

2.6

Kinetics of the Reaction Kf KP (E ) + (H ) (EH ) → (E ) + P Kr Separating the reaction (45) into single reactions we shall have. K (E ) + (H ) f (EH )..................................................................................................(46)

(EH ) (EH )

Kr (E ) + (H )............................................................................................(47) → p (E ) + P................................................................................................(48) →

K

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The reaction kinetics of the above reaction can be presented or represented as: From equation (46), we have µf = K f [E] [H] ……….…………………………………………………..(49) From equation(47), we have µr = K r [EH] ……………………………………………..……………….(50) From equation (48), we have µp = K p [EH] ………………………………………………………………(51) µ K [ EH ] Dividing equation (50) by (49) r = r ……………………………………(52) µf K f [ EIH ] The rate of reaction of the forward and reversible are equal meaning that µ f = µ t

Kr Kf

= K H ......................................................................................(53)

K r [ EH ] = K f [ E ] [ H ] .......................................................................(54) Dividing both sides of (55) by K r [ EH ] = K s Since Kr /K f =K s thus,

Kf Kr

= 1

Ks

Kr

[ EIH ] ………………………….…(55)

………………………………………………..(56)

Substituting equation (56) into (55) we shall have [EIH ] …………………………………………………….………(57) [EH] = Ks Substituting equation (57) into (51) [ EIH ] ……………………………………………………(58) µp = Kp Ks But Et = [E ] + [EH ] ………………………………………………………………..(59) Dividing equation (58) by (59)

µp Et

=

K p [EIH ] KH

÷ [E ] + [EH ]……………………..…………………………….(60)

Substituting (57) into (59) IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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µr

=

Et

µr

=

Et

µr

K p [EIH ] KH K p [EIH ] KH

×

[EIH ] K Ht

=

K p [EIH ] KH

÷

K S [E ] + [EIH ] K Ht

KH ………………………………………………..(61) K H [E ] + [EIH ]

K H [EIH ] K H [E ] + [EIH ]

=

Et

÷ [E ] +

Multiplying both sides of equation (61) by E t

µr Et

• Et =

µp =

K p K t [EIH ]

K H [E ] + [EΙH ]

K p Et [EΙH ]

K H [E ]+ [EΙH ] But µ max = Kp E t

…………………………………………………..(62)

………………………………………………………………..(63)

Substituting (63) into (62) µ max [EΙH ] ………………………………………………………………..(64) µp = K H [E ]+ [EΙH ] Dividing both the numerator and denominator of the right-hand side of equation (64) by [E]. (µmax [EΙH ]) /[E ] µ max [H ] = µp = (K H [E ] + [E ] [H ]/[E ]) K H + [H ]

µp =

µ max [H ]

K H + [H ]

………………………………………………………………….….(65)

Equation (65) is monod equation of Henry Michael’s form of equation. Taking the inverse of equation (65) KH

+ 1

Where K H µ max

= slope

1

µp

=

µ max [H ]

µ max

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1 µ max

= Intercep

At the maximum point slope = 0 therefore µ p

= µ max

2.7 Reaction Kinetics The mathematical formulations for the following conditions were developed. 1. A reaction catalysed by single enzyme 2. A reaction catalysed by multiple enzyme 2.7.1 Single Enzyme Catalysed Reaction Generally an enzyme catalysed reaction of a given substrate such as monoaromatic hudrocarbon (BTX) can be presented since the rate of product formation depends on the dissociation of product forming complex. Applying equation (65) [H ] ……………………………………………………………(67) µ s = µ H max K H + [H ] The equation (65) is monod equation the usual, form of Henry Michael’s equation with monoaromatic, hydrocarbon mixture as growth limiting substrate. The monoaromatic hydrocarbon substarate concentrations present are S B , S T , and S X . where B = Benzene T = Toluene E = Ethyl benzene X = Xylene  [H B ] [H X ]  …………………………(68) [H T ] µ s = µ H max    K HB + [H B ] K HT + [H ] K HX + [H X ] But the rate of momoaromatic degradation is µ s = dH

dt

…………………….….(69)

Substituting equation (69) into  [H B ] [H T ] [H E ] [H X ]  ………..(70) − dH = µ H max   dt  K HB + [H H ] K HT + [H T ] K HE + [H H ] K HX + [H X ]



µ

 K + [H B ] K HT + [H T ] K HX + [H X ] dt =  SB dH ……………………….(71) ⋅ max [H T ] [H X ]   [H B ] S

Let B = 1, T = 2,



µ

H max

X = 3 equation (71) can be written as

 K + [H1 ] K H 2 + [H H 2 ] K H 3 + [H 3 ] ⋅ dt =  H 1 dH ……………………….(72) [H 2 ] [H 3 ]   [H1 ]

Equation (72) can be expressed as IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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−µ

H max

dt =

3   K + [H ]  H K  i   si  1 + Hi dH ……………(73) − = dH or dt µ π π max   [H ii ]  Hi i = 1 i =1   3

[ ]

Integrating both sides of equation (73) t

− µ max ∫ dt = H

H

0 t

H

 + 1dH 

H K Hi ∫ dt = ∫ [H ] ds + ∫ dH H0 H0 0 i

− µ max H

t

H H

− µ max ∫ dt = K i s

 K Hi

∫  [H ] H0 i

0

s

s H t H dH H dH t K InH H H H + ⇒ − = + µ si 0 0− ∫ ∫ max 0 H0 H H0

H µ max (t − 0) = K H (InH − InH 0 ) + H − H 0 i

H  + H − H ……………………………………………….…(74) − µ max t = K H In  H  0  H0 

Dividing both sides of equation (74) by – 1 H µ max t = K H In  H H 0  + H − H 0 ……………………………………….….(75)  + H0 = K H In  H −H .  H H0 H0 0  where β = H …………………………………………………..………………..(76) H0 Substituting (74) into (78)

µ max t H

µ max t H

= − K Hi Inβ i + 1 − β i .......................................................................................(77)

Equation (75) represent the model equation for a single enzyme catalysed reaction and can be applied in the computation of maximum reaction rate. 2.7.2 Reaction Catalyzed by Multiple Enzyme Occasionally multiple enzymes have been found to catalyze a given substrate particularly in biodegradation or bioremediation of monoaromatic hydrocarbon. Consequently the

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velocity at any given time is the sum of the velocities contributed by each enzyme. Thus for a monoaromatic hydrocarbon mixture S 1, , S 2 , and S 3 , the rate can be represented as:

µm =

[H 1 ]

µ max i m

K H + [H i i ]

+

[H 2 ] K H 2 + [H 2 ]

µ max 2 m

[H 3 ] K H 3 + [H 3 ]

µ max 3 m

+

.............(78)

Combining (77) and (78) we obtain the expression −

µ

dH = dt

[H1 ]

m

K H1 +

max 1

[H ] µ +

1

[H 2 ] K H 2 + [H 2 ]

m max 2

+

µ

m max 3

[H 3 ] K S 3 + [H 3 ]

Equation (78) can be re-written as



dH = dt

3

∑ µ max i

[H1 ]

m

i −1

+

K Hi

or −

[H i ]

dH = dt

3

µ max i ∑ µ max i m

m

i −1

……(79)

[H i ] K Hi + [H i ]

……………………………………………………………………………………………(8 0) Separating the variables −

− µ max dt = m

µ

m max

dt =

 K Hi + [H i ]  dH ………………….(81) [ ] H i −1  i  3

∑ 

  K Hi  1 + ∑  [H ]  dH ……………………………….……………..(82) i −1  i  3

Integrating both sides of equation (80)

−µ

t

m max

∫ dt = 0

H   H K Si   dH dH + ∑ ∫ ∫   i −1  H 0 H i H0  3

 H − µ (t − 0) = ∑  K Hi InH +H max H i −1  0 3

m

∑  K 3

i −1

Hi

InH H

H0

∑  K

H H0

 3  = ∑ [K Hi (InH − InH ) + (H − H 0 )]  i −1 

+ (H − H 0 ) 

+ (H − H 0 ) …………………………..……………(83)  i −1 Dividing both sides of equation (83) by - 1 −µ

m

max

t =

3

Hi

In H

H0

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µ

m max

t=

∑ − K 3

i −1

In H

+ H 0 

H0

H0

−H

 H 0 

H  +  0 −H H0  H0 H 00  max i −1 Substituting equation (79) into (86)

µ

m

µ

t=

m max

∑ − K

Hi

t=

3

Hi

In H

3

∑ [− K

i −1

Si

Inβ i + (1 − β i ) ]

………………………..(84)

……………………………….(85)

3. MATERIALS AND METHODS 3.1 Sample Collection The benzene, toluene and xylene samples were collected from the Department of Chemical/Petrochemical Engineering Laboratory in Rivers State University of Science and Technology Port Harcourt and their concentrations measured in g/ml. The soil samples were collected from the Omuigwe Aluu in Ikwerre Local Government Area of Rivers State and then transported to the Rivers State University of Science and Technology Laboratory for purpose of Isolation and identification of possible microorganisms present in the soil. 3.2 Microbiological Analysis Microbiological Analysis of the samples involved enumeration and isolation of bacterial was carried out in the laboratory using the international standard equipment recommended. Ten fold serial dilution methods (Ofunne, 1999) were employed for the enumeration and isolation of bacteria. In this method, 1.0ml of sample teacheate was added to 9.0me of sterile normal saline (dilute) to give 10-1 dilution. Further serial dilutions were made by transferring 1.0ml of 10-1 dilution to another 9.0ml of diluents up to 10-6 dilution. From the 10 -1 dilution to another 9.0ml of diluents up to 10-6 dilution. From the 10 -1 dilution, 0.1ml aliquots of samples were introduced on to the surface of the sterile solid nutrient agar medium in Petric dishes. The inocula were spread plated using a sterile bent glass rod. The inoculated plates were inoculated at 270C for twenty four (24) hours, and the colonies that developed were courted and recorded and taken as the population of bacteria in colony forming unit per millilitre (Ofulme) leacheate of the samples. For the purpose of fungi pure cultures were obtained by sub-culturing discrete colonies on to fresh sterile solid nutrient agar medium, which were incubated at 370C for twenty four (24) hours identification of fungi isolates was done by reference to Buchanan and Gibbons, (1994).

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3.3 Analysis of physicochemical properties of soil sample. The physicochemical parameters of soil samples were analysis using International Standard method as recommended by world Health Organization. 4. RESULTS AND DISCUSSION The results obtained from the investigation are presented in tables as shown below The percentage organic carbon, and organic matter were greater in the first level compare to other levels. From table 1 level ( 6-1) has 0.52% organic carbon, 0.90% organic matter, level (1-2) has 0.26% organic carbon, 0.45% organic carbon, level (2-3) has 0.06% organic carbon, 0.10% organic carbon, level (3 -4) has 0.24% organic carbon, 0.41% organic matter, level (4-5) has 0.11% organic carbon, and 0.19% organic matter. This implies that first level is preferred to others because of the fact that the microorganisms in the soil were used for the remediation process. Table 1: Results of laboratory analysis of five (5) Ngara Soil Samples Omuigwe Aluu. Parameters Soil Depths (m) 0-1 1-2 2-3 3-4 4-5 Soil pH (1:25) 5.10 4.80 5.20 4.80 5.00 93 141 60 90 59 Electrical conductivity (µs/Cm) Available ρ (mg/kg) Total N. (%) Organic C. (%) Organic M (%) Moisture Content (%) Particle Density (g/cm3) Bulk Density (g/cm3) Porosity (%) Sand (%) Silt (%) Clay (%) Textural Class

8.52 0.04 0.52 0.90 13.88 2.60 1.68 35 57 1 42 SC

5.46 0.05 0.26 0.45 13.82 2.56 1.69 34 55 3 42 SC

3.18 0.04 0.06 0.10 14.92 2.60 1.71 34 57 1 42 SC

3.42 0.04 0.24 0.41 15.12 2.64 1.78 33 57 1 42 SC

1.68 0.03 0.11 0.19 16.49 2.56 1.69 34 55 2 43 SC

4.2 Contaminants Concentration The results of the concentration of the contaminants with respect to time are presented in table 2.

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Table 2: Concentration of the various contaminants with time Time (Day) 0.00 7.00 14.00 21.00 28.00 35.00

Concentration of benzene (S b )g/ml 39.06 36 .42 33.96 31.66 29.52 27.53

Concentration toluene (S t ) 46.07 40.05 34.82 30.27 26.32 22.88

of

Concentration xylene (S x )g/ml 53.09 52.72 52.35 51.99 51.62 51.26

of

Benzene Concentration: The variation of concentration of benzene with time is shown in Fig. 1a. The concentration of benzene in benzene samples has optimum value of 36.06g/ml at 0 day, and then decrease in descending order as the days increases for 36.42g/ml at 7 days, 33.96 at 14 days, 31.66g/ml at 21days, 29.52g/ml at 28 days then 27.53g/ml at 35 days. Toluene Concentration: The variation of concentration of Toluene with time is depicted in Fig 1b. The concentration of Toluene in Toluene samples has optimum value of 46.07g/ml at 0 day, and then decreases to 40.05g/ml at 7 days, 34.82g/ml at 14 days, 30.27g/ml at 21 days, 26.32g/ml at 28 days, and 22.88g/ml at 35 days. Xylene Concentration: The variation of concentration of xylene with time is depicted in gig 52.the concentration of xylene samples has its optimum value of 53.09g/ml at 0 day, and then decreases to 52.72g/ml at 7 days, 52.35g/ml at 14 days, 51.99g/ml at 21 days, 51.62g/ml at 28 days, and 51.26g/ml at 35 days. The result microbial population and differentiating the microbes present are presented in table 3. Table 3: Microbial Population of Contaminated soil with Respect to Time Time Bacterial Population (Cfu/G) /Fungi Population (Cfu/G) (in days) (THB) B (THB) T (THB) X (THB) B (THB) T (THB) X

0.00 7.00 14.00 21.00 28.00 35.00

1.0 x 103 1.0 x 103 6.0 x 103 1.0 x 104 4.1 x 105 4.0 x 105

1.0 x 103 2.0 x 103 1.8 x 104 4.0 x 104 8.6 x 105 8.0 x 105

1.0 x 103 5.0 x 104 8.0 x 104 9.0 x 104 3.4 x 105 9.0 x 104

1.0 x 103 1.0 x 103 2.6 x 103 3. 1 x 103 5.3 x 103 5.0 x 103

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1.0 x 103 1.8 x 103 3.2 x 103 4. 7 x 103 3. 2 x 103 1. 1 x 103

1.0 x 103 1.0 x 103 2.8 x 103 3.8 x 103 3.6 x 103 3.5 x 103

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From table 1, the first 28 days toluene sample has the highest population of 8.6 x 105cfu/g, followed by benzene sample of 4.1 x 105 cfu/g before xylene sample 3.4 x 105cfu/g. The microbial population of bacterial and fungi decreases as days increases. The decrease in population may be as a result of the decrease in the concentration of the contaminants and the microbial organisms involved may not have enough to feed and some will die, which implies that the microorganisms are remediating the affected aquifer. 4.3 Maximum Specific Rate of Reaction For Multiple Enzyme Catalysed Reaction Recalling the Monod’s Equation thus:

µ max (t )= ∑ [− K si Inβi 3

S

i −1

+ (1 − β i )]

The following computed results were obtained as shown in table 4. Table 4: Shows the specific rate of reaction for multiple enzyme catalysed reaction with time. m Time /Day µ max 0.00 7.00 14.00 21.00 28.00 35.00

0.0000 57.3643 114.9927 229.1312 229.9086 287.3145

The values of maximum specific rate of reaction for multiple enzyme catalyzed reaction µ were determined using the data in Table 3 and presented in table 4. m

max

5. CONCLUSION The investigation illustrates the microbial activities on gradating benzene, toluene and xylene contaminants in soil environment obtained in Niger Delta areas of Nigeria. Rapid growth was experienced on the bioreactor containing toluene and the physicochemical parameters of the soil environment favours the degradation as well the microorganisms. The following conclusion can be drawn from the research work such as; 1. Estimating the degradation period. 2. The effect of physiochemical parameters of soil environment on the degradation rate of benzene, toluene and xylene contaminants. IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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3. 4.

The usefulness of batch reactor for effective remediation mechanisms. The effective of phosphorus as nutrient for improving degradation rate as well as enhancing microbial growth rate. Product formation which is environmentally friendly by the mechanism of bioremediation of benzene, toluene and xylene was studied.

5.

Nomenclature C = Contaminant concentration as a function of x , y, z, t H = Substrate concentration (mol%) Kp = Equilibrium constant of product formation (mol %) VS = Velocity of single enzyme (mls) K KH = Equilibrium constant ( r ) Kf E EH Ho

V

S max

I n β Kf Kr

µ

S max

t

µ

m

µ

m

= = = = = = = = = =

Enzyme concentration (cfu/g) Enzyme- substrate complex (cfu/g) initial substrate concentration (mol%) Maximum specific rate of reaction for single enzyme (mol %/day) Inhibitor concentration (mol%) Integral value ie 1, 2, 3, 4, Constant Rate of forward reaction (mol%)-1 Rate of backward reaction (mol%)-1 Maximum specific rate of reaction for single enzyme catalysed reaction

=

(cfu/ml/day). Time (day)

=

Specific rate of reaction for multiple enzyme catalysed reaction (cfu/ml/day).

max

KS Km

µ

F V

max

=

Maximum specific rate of reaction for multiple enzyme catalysed reaction

= =

(cfu/ml/day). First order constant (mol%)-1 Monod constant or dissociation constant (cfu/ml)-1

=

Maximum specific rate (cfu/ml/day)

= =

Flow rate (am3/day) Rate reactor volume (Am3)

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REFERENCES APHA. 1995. Standard methods for the Examination of water and Wastewater. 19th edition. American Publication Health Association, Wallington Dc, p 18. ASTM 1986. Standard Practice for algae growth potential testing with selenastrum capricornutum. In American Society for Testing and Materials. Annual Book of ASTM Standards. Water and Environmental Technology. Section 11, pp.27-32. Benincasa, M. Abalos, A; Oliveira, I & Manresa, A. 2004. Chemical Structure Surface properties and biological activities of the biosurfacant produced by pseudomonas aeruginosa LBI from Soapstock. Antonic Van Leeuwenhock. 85, pp. 1-8. Bhabajit, B. & Sarma, H.P. (2007). Soil acidity and its effect on exchangeable Al, Ca, mg, mn and lime requirement of tea garden soils of lakhimpur district, Assam, Poll. Res (2692), pp.203-206. Fismes, J; Perrin -Ganier, C; Empereur- Bissonnet, P; Morel, J. L. 2002. Soil - to - root transfer and translocation of polycyclic aromatic hydrocarbon by vegetables grown on industrial contaminated soils. J. Environ. Qual. 31 (5), pp. 1649-1656. Ghosh, A; Saez, A.E; Ela, W. 2006 Effect of pH, Competitive anions and Nom on the Leaching of arsenic from solid residuals. Sci. Total Environ. 363, pp.46 -59 Hansen, L. D; Nestler, C; Ringelberg, D & Bajpai, R, 2004. Extended bioremediation of PAH/PCP contaminated soils from the POPILE wood treatment facility. Chemosphere, 54 (10) pp. 1481 -1493. Joner, E. J; Johnson, A; Loibner, S. P; Cruz, D; Szolar, M.A; Portal. O. H. J & Leyval, J. M.C. 2001. Rhizosphere effects on microbial community structure and dissipation and toxicity of polycyclic aromatic hydrocarbons (PAHs) in spiked soil. Environ. Sci. Technol. 35, pp. 2773-2777. Kaiser, K; Guggenberger, G. 2003. Mineral Surfaces and soil organic matter. Eur. J. Soil Sci, 54, pp. 219-236. Kumar, N. (2007): Net primary production and relative growth rate of planted tree species oncoal overburden dump. Poll. Res. 26(2), pp.189-192.

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Makkar, R. S & Cameotra, S.S. 1999. Biosurfactant Production by Microorganisms on Unconventional Production. F. Am. Oil Chem. Soc. 71, pp. 61-64. Meenu, S; Hitendra, K.S. & Somesh, Y. (2007). Assessment of cytotoxic potential of brilliant blue FCF on vicia faba L. root meristems. Poll. Res. 26(2), pp.193-197. Mohapatra, D. Mishra, D. Roy-Chaydhury, G& Das, R.P. (2006). Effect of dissolved organic matter on the adosorption and stability of As(V) on manganese Wad. Sepa. Technol. 49, pp.223-229. Mohapatra, D; Mistra, D; Roy Chaydhury, G. & Das, R. P. 2006. Effect of dissolved organic matter on the adsorption and stability of As (V) on manganese Wad. Separ. Purif. Technol. 49, pp. 223 - 229. Newman, L.A., Strand, S.E; Chve, N; Duffy, J. & Ekuan, G. (1997). Uptake and biotransformation of trichloroethylene by hybrid poplars. Environ. Sci. Techno. 31, pp.1062-1067. Newman, L.A; Strand, S.E; Choe, N; Duffy, J & Ekuan, G. 1997. Up take and biotransformation of trichloroethylene by hybrid poplars. Enviro. Sci. 11 pp.10621067. Ofunne, J.I. (1999). Bacteriological Examination of clinical specimens. publications. Ama, J.K. Recration park, Owerri, Nigeria, pp.24-25.

Achugo

Raza, Z. A; Khan, M. S; Khalid, Z. M & Rehman, A. 2006. Production of Biosurfactant using different hydrocarbons by psendomon as aeruginosa EBN - 8 mutant. Z. Naturforsech. 61C, pp. 87 - 94. Raza, Z.A. Khan, M.S.; Khalid, Z.M. & Rehman, A. (2006). Production of biosurfactant using different hydrocarbons by pseudomonas aeruginosa EBN-8. Mutant, Z. Walurforsch. 61C., pp.87-94. Richard, T; Van de Wicle; Willy, V & Siciliano, S.D 2004. Polycyclic aromatic hydrocarbon. Release from a soil matrix in the in vitro gastrointestinal tract. J. Environ. Qual. 33, pp. 1343 -1353. Schmitz, R.P. Kretkowski, C; Eisentrager, A, & Dott, W. 1999. Ecotoxicological testing with new kinetic photorhabdus Iuminescens growth and luminescence inhibition assays in micro titration scale. Chemosphere 38, pp. 67-78 IJPWR VOL 2 ISSUE 2 (Mar-Jun) - 2011

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Shafeeq. M; Kokub, D; Khalid, Z. M & Malik, K.A 1993. Production of biosurfactant by Pseudomonas Aeruginosa Strain K-3 grown on Molasses. In proceedings of an International symposium on Biotechnology for sustainable Development. Dec. 15-20, held at NiBGE Faisalabad, Pakistan, pp.72-79. Straube, W.L. Nestler, C.C; Hansen, L.D; Ringleberg, D. Pritchand, P.H; & Jones0Mechan, J. (2003). Remediation of polyaroatic hydrocarbons (PAHS0 through land farming with biostimulation and bioaugmentation, Acta biotechnol. 23(2-3), pp.179-196. Straube, W.L; Nestler, C.C; Hansen, L.D; Ringleberg, D; Pritchard, P.H & JonesMechan, J. 2003. Remediation of Polyaromatic hydrocarbons (PAHs) through Landfarming with biosfimutation and bioaugmentation. Acta Biotechnol. 23(2-3), pp. 179 - 196. Ukpaka, C.P. 2006. Modelling Degradation kinetics of petroleum hydrocarbon mixture at specific concentration. Journal of Research in Engineering, 3(3), pp.47-54. Ukpaka, C.P. 2006. Modelling the Microbial Thermal Kinetics System in Biodegradation of n- Paraffins. Journal of Modeling. Simulation and Control (AMSE). 67 (1), pp. 44 – 61. Ukpaka, C.P. 2007. Biodegradation Kinetics for the production of carbon dioxide from natural aquatic Ecosystem Polluted with Crude Oil. Journal of Science and Technology Research, 4 (3), pp. 41- 49. Utpal, G. and Sarma, H.P. (2007). Study of ground water contamination due to municipal solid waste dumping in Guwahati city. Poll. Res. 26(2), pp.211-214. Wick, L.Y. Pasche, N. bernasconic, S.M. Pelz, O; Harms, H. (2003). Characterization of Multiple-substrate utilization by anthracene degrading mycobacterium frederiksbergense (B501). Appl. Environ. Microbiol. 69(10), pp.6133-6142. Wick, L.Y; Pasche, N; Bernasconi, S.M; Pelz, O. & Harms, H. 2003. Characterization of Multiple-Substrate Utilization by anthracite degrading mycobacterium frederiksbergense LB501T. Appl. Environ. Microbiol. 69 (10), pp. 6133- 6142.

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