Sensitivity Analysis of Variables Related to Bacterial Hydrolysis

A Study to Help Optimize Anaerobic Digestion of Recalcitrant Wastes

Anaerobic Digestion

• Bio-waste stabilization/energy production process

• Complex and often unstable process

• Common Reactor Geometries

– Complete mix

– Plug flow

– Batch

– Fixed Film

Proposed Solution

Mathematical Modeling

• Simulation of parameter influence on anaerobic hydrolysis. • Parameters in study:

• Substrate Concentration • Surface Area / Particle Size • Microbial Concentration • Leachate Flow Rate • pH • Temperature

`

StvaK

StvaK

dt

dSm

StvaK

StvaK

SvdsK

SvdsK

dt

dStva

SvdsK

SvdsKSvssK

dt

dSvds

SvssKdt

dSvss

7

6

7

6

5

4

3

21

1

•This Kinetic model studies : 1.Hydrolysis 2. Acidogenesis 3. Methanogenic Steps •Mesophilic temperature = 35 C •HRT = 10 to 50 days • Hydrolysis & Acidogenesis prevailed at HRT lower than 20 days •Methanogenic steps are prevailed at higher HRT •Kinetic Constants are found experimentally & equations are used to simulate the process. Borja

Borja-Three stages of Anaerobic Digestion

Borja

• Kinetic Constants : • K1 = Kinetic constant for non-soluble organics 0.054 0.003 /day • K2 = Max. rate of soluble organic matter degradation = 4.2 0.3 gm soluble COD /l. day • K3 = saturation constant = 9.8 0.5 gm SCOD /l

• K4 = Max. rate of soluble organics = 3.6 0.2 gm SCOD /l. day • K5 = saturation constant = 10.2 0.5 gm SCOD /l

• K6= Max. rate of TVA consumption = 4.3 0.2 gm TVA-COD /l. day • K7 = saturation constant = 3.1 0.2 gm TVA-COD /l

• Svds0=variable • Svss0=76 g NSCOD/l • Stva0=0.64 g COD /l • Sm0=0 g COD /l

Concentration COD vs. Time (days) to 90% Degradation

Concentration of COD vs. Time (days) to 90%

Degradation

0

10

20

30

40

50

60

70

0 50 100 150 200

Tim

e (

day

s) f

or

90

% H

ydro

lysi

s

g SCOD/L

riivi

r VrCQdt

dCV

Veeken et all- Solution Transport

Vr = Reactor Volume

Qv = leachate effluent rate

Ci =Concentration of 'i'

Ri = production rate of C

i

Prdt

dP

rmrPv VrVrMQdt

dMVr rmv VrFQ

dt

dFVr

Hydrolysis Dependence on Sufficient Leachate Flow

Rate

Leachate flow rate vs. Time (days) to Reach 90%

degradation

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

Tim

e (

day

s) f

or

90

% H

ydro

lysi

s

Reactor Volume/ Leachate Flow Rate (h)

Sanders

tk

RRsbk

t

0

= density of substrate (kg/m3)

Rt = average particle radius at time t (m)

R0 = average particle radius at time t =0 (m)

ksbk = surface based hydrolysis constant kg /m2.day

This model considers directly the particle radius as a function of

rate of hydrolysis.

Sanders- Particle Radius

Sanders

Efficiency of degradation hydrolysis (using starch) :

%1000

0

M

MM t

M0 = Initial mass of substrate at t =0

M0-Mt = Total mass hydrolyzed

= Cumulative CH4(t) + (VFA(t) * total volume) + (Glucose(t)*total volume)

= conversion factor

%100

)(

30

30

R

tkR

sbk

%100)

)(

1(0 0

0

30

30

n

particle

sbk

M

M

R

tkR

M0particle = Mass of separate substrate particle at t =0

Hydrolysis Depending on the Substrate Particle Size

Radius of Particle vs. Time (days) to 90% Degradation

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1 1.2

Tim

e (

day

s) f

or

90

% H

ydro

lysi

s

Radius of Particle (mm)

h

h

sx

h

s

hs

X

X

XK

X

X

Kdt

dX

Dimock

Xs = SBCOD

Xh = heterotrophic organisms concentration

Kh = hydrolysis rate constant

Kx = hydrolysis saturation constant

•SBOD is hydrolyzed using surface limited process.

Dimock-Particle Break Up Model/Microorganism Concentration

Dimock

)(max

H

sHNAA

sNA

X

XbXXK

dt

dX

dt

dX

Concentration based hydrolysis model :

KA = adsorption rate constant [M-1L3T-1]

bmax = (Xs/XH)maximum …….assume bmax = 1

Surface - area based hydrolysis model :

Akdt

dXsbk

s

Ksbk = surface based

hydrolysis constant [ML-5T-1]

Dimock-Particle Break Up Model

Hydrolysis Rate Dependent on the Surface Area

& Concentration of Heterotrophic Bacteria

Concentration of Heterotrophic Bacteria as COD vs. Time (days)

For 90% Degradation

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Tim

e (

day

s) f

or

90

% H

ydro

lysi

s

Heterotrophic Bacteria (g COD/L)

Han Yu- Influence of pH on Hydrolysis

r = overall acidogenic activity mg COD /g VSS .day

Rmax= 400 mg COD/gVSS d

Kh=1.395 x 10^-4 M

Koh=8.327 x 10^-9 M

Han Qing Yu

Hydrolysis Rate Dependent on pH

Temperature Dependence

Han Qing Yu

r = reaction rate

A= frequency factor=7480

Ea=apparent activation energy kcal/mol=1.83 kcal/mol

R=universal gas constant = 0.001987 kcal/mol.Kelvin

T=Temperature in Kelvin

Efficiency of Hydrolysis dependent on Temperature

Temperature Dependence

CONCLUSION

•Mathematical modeling helps explaining influence of

parameters on hydrolysis

•Hydrolysis Rate is maximized with:

• Minimization of COD in leachate

• Maximization of Leachate flow rate

• Minimization particle diameter

• Maximization of microbial concentration

• pH near 6

• Higher temperatures (bounded)

•Future progress can be guided by these findings