# Anaerobic Digestion Of Waste Biomass Biology Essay

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Various kinetic model have been advanced for anaerobic digestion of waste biomass and methane production .early models were based on a single-culture system and used the Monod equation (1-3).More recently, several dynamic simulation models have been developed based on a continuous multicultural system; these correspond to the major bioconversion steps in anaerobic digestion but again makes assumption that culture growth obeys Monod-type kinetics.

4.2 Development of the model

The flowing points were taken into consideration in the development of the kinetic model:

1. Complex polymeric compounds can't be taken by the microorganisms without initial hydrolysis into soluble (consumable) compounds. The direct substrate (intake food) for cell growth and methane production is the hydrolysis assimilable compounds which are the product of hydrolysis.

2. The transport of hydrolyzed assimilable compounds which into the cell is not rate limiting.

The digestion process is assumed to take place in three stages.

Stage 1) extracellular hydrolysis of complex compounds into soluble substrates.

Stage 2) Transport of soluble assimilable substrates into the cell of the microorganisms.

Stage 3) utilization of assimilable substrates for growth and methane formation.

Stage 1:

Hydrolysis is assumed to be a first-order reaction with respect to the concentration of hydrolyzable substrate S (mass/volume):

Let S-denotes the hydrolyzable substrate concentration (it doesn't include non-

hydrolyzable substrate).

Sh-denotes concentration of hydrolyzed substrate (g/L)

Kh-denotes hydrolysis rate coefficient, L/day

Then)……………………………………………… (1)

To clarify more ,how equation 1 is derived .Assume we have a digester shown below with initial concentration of hydrolyzable substrate ,S and outlet concentration after some product are hydrolyzed represented by Cs.

CS

STo (S+Sr )

The rate of change of the concentration of S can be written using the rate law, mathematically as

, where denoted the transfer coefficient or rate constant. The negative sign indicates there is degradation. But if the amount of hydrolyzed substrate is represented by Sh, then =S - Sh.

Therefore substituting the value of to the above rate equation) can be written. The validity of the assumption was experimentally proved by pavlostathis and Gossett (6).

Stage 2:

Internalization or transport of the hydrolyzed substrate into the cell is accomplished by diffusion. Therefore the transport of the hydrolyzed substrate into the cell of the microorganism is dependent and related to the following factors.

The difference in concentration of the hydrolyzed substrate ( ) outside and inside the cells of the microorganisms.(this is called the diffusion gradient ).

The concentration of the active cell biomass (the amount of microorganism actively growing by feeding the soluble hydrolyzed substrate).

Let X- denotes the active biomass of cell concentration.

Su- denotes the intercellular (inside cell) concentration of hydrolyzed substrate.

K- denotes hydrolyzed substrate transport rate coefficient, time-1

Then the rate change of hydrolyzable substrate, S can be written in terms of the above parameters as follows:

………………………………………………. (2)

It is assumed that hydrolyzed substrate entering into the cell is metabolized very fast so the intercellular concentration ≈0.

Therefore equation 2 becomes

…………………………………………………….(3)

The concentration of the hydrolyzed substrate outside the cell () can be derived by combining equation 1 and 3.

## )=

## )=

Therefore, ……………………………………… (4)

Stage 3:

Microorganisms' cell growth on hydrolyzed (assimilable) substrate is assumed to follow Monod kinetics as discussed earlier and is expressed as

………………………………………………………… (5)

Where -denotes the specific growth rate of the microorganism, time -1.

-denotes maximum specific growth rate of microorganism, time -1.

-denotes half saturation constant for hydrolyzed substrate, g/L.

Substituting the value of the hydrolyzed substrate concentration from equation 4 into equation 5, equation 5 becomes

……………………………………………………… (6)

Under steady state condition of continuous digestion in a completely mixed reactor without recycling, the flowing relationship holds.

Representing HRT with the symbol ÆŸ,

…………………………………………………………………….. (7)

That means the specific growth rate of the bacteria is equal to the time duration starting the time the microorganism get fed of biodegradable substrate until the remaining is washed out with the product formed. In other terms equation 7 implies the growth rate of the bacteria is proportional to the time they get continuous feed of assimilable substrate, and this time is equal to the hydraulic retention time.

The other relationship that holds for steady state condition is as follows:

Let F -denotes volumetric substrate removal rate, g/L.

So-denotes input biodegradable substrate concentration, g/L.

S-as used above denotes the hydrolysable substrate concentration in the digester, g/L.

Then ……………………………………………………….. (8)

To achieve simplification on the model, the following assumption are taken into consideration.

1) Maintenance energy is assumed to be small. That means the energy consumed for functions other than production of new cell material is neglected.

2) Microbial decay is also assumed to be small.

This assumption makes the biomass yield coefficient, represented by Y, constant.

The biomass yield coefficient (Y) is the ratio of the rate of new cell development to rate of substrate consumption (cell mass /substrate mass).

Then the active call biomass can be expressed as

………………………………………… (9)

Since, .

Substituting equation 9 into equation 6 for the value of X, equation 6 becomes

………………………………… (10)

Equation 10 is the basic equation for substrate utilization in the anaerobic digestion of complex organic substances.

4.3 Adjustment of the basic model equation to more realistic conditions.

The half saturation constant with respect to the hydrolyzed substrate (KS, mass/volume) is expected to be small value. KS for sugar in methane fermentation was reported to be 0.24g/L(6).When S>> KS ,which may be the case in practical anaerobic digestion of complex feeds, the second term on the right hand side of equation 10 becomes negligible (KS/S≈0) and the equation degenerates to

……………………………………….. (11)

In the case of easily hydrolysable substrates, may be very large in relation to the other values. The extreme case of soluble and assimilable substrates eg.glucose, =∞.In such cases the first term of equation 10 becomes negligible and the equation is reduced to

…………………………………………. (13)

To show the effluent substrate concentration (S), is dependent on the influent substrate concentration (), the flowing arrangement can be done.

If can be represented by A and , then substituting this values in equation 10,it can be written as

………………………………………………….(14)

At washout ,S0=S ,and equation 10 can be written as

………………………………………………(15)

Equation 15 also shows that if S>>K, ≈at critical retention time.

Equation 10 can also be arranged as

…………………………………………………(16)

to show that as S approaches zero , approaches zero. That means ,growth is possible only when there is enough hydrolysable substrate.

4.4 Incorporating refractory coefficient to the model equation.

As it is discussed earlier ,the volatile solid (VS) content of the feed is the one that has the main potential to yield methane gas ,as it is combustible /degradable in the digester .But there is non-biodegradable part always in the feed no matter how long the process runs. The non-biodegradable part from the volatile solids is called Refractory material .

Let us first ,restate the terms again to avoid confusion before proceeding to the next step .

Let -denotes the input biodegradable substrate concentration, g/L at time t=0.

Sr -denotes is the refractory ( non-biodegradable) concentration , g/L.

STO-denotes total feed concentration ,g/L .( STO=So+Sr).

S-denotes biodegradable substrate concentration in the effluent or in the digester ,g/L.

ST-denotes total substrate concentration in the effluent ,or digester ,g/L.( ST=S+Sr).

ST=(Sr+S)

ST=(Sr+S)

STO=(S0+Sr)

Note that Sr does not show any change from feed to product since it is biodegradable )

Now ,refractory coefficient can be defined based on the above illustration.

Refractory coefficient (R) is the decimal fraction representing the proportion of substrate that is non-biodegradable at infinite digestion time.

Mathematically , R=……………………………………………(17)

The flowing relationship can be then written

S0 =STO -Sr= STO -R STO= STO(1-R),

S0= STO(1-R)………………………………………………………………..(18)

And ,

S=ST -Sr= ST-RSTO,

S=ST -RSTO………………………………………………………………….(19)

By using equation 7,18 and 19 equation 10 can be written as

……………………..(20)