MATHEMATICAL MODELLING FOR
THE CONVERSION OF ANIMAL
WASTE TO METHANE IN BATCH BIO-
REACTOR
O.A. AWORANTI,
Department of chemical Engineering,
Ladoke Akintola University of Technology , Ogbomoso Oyo State, +234, Nigeria
funmi_ oyebanji@yahoo.com
S.E. AGARRY,
Department of chemical Engineering,
Ladoke Akintola University of Technology , Ogbomoso Oyo State, +234, Nigeria
sam_agarry@yahoo.com
A.O. ARINKOOLA
Department of chemical Engineering,
Ladoke Akintola University of Technology , Ogbomoso Oyo State, +234, Nigeria
moranroolaakeem@yahoo.com
V.ADENIYI
University of Lagos,Akoka Yaba Lagos State, +234,Nigeria
Abstract
An investigation was conducted to predict the behaviour of microbial processes leading to the production of biogas from animal waste. Mathematical model were developed for the prediction of the behaviour of microbial processes. The development of the models was based upon a material balance analysis of the digester operation, substrate utilization, cell growth and product formation. The model was solved using Runge kutta numerical technique embedded in polymath software. The digesters’ operations simulated with a starting valve of 300g/dm3 as the concentration of the substrate and 1.5g/dm3 as the concentration of the cell, within a period of 13days. The results of the simulation show that the substrate concentration shows exponential decline from (300g/dm3 to 6.88g/dm3), the cells growth shows exponential trend from (1.5g/dm3to 39g/dm3) The rate of growth of cell was increased from (0.5g/dm3-2.53g/dm3), death increased from (0.015g/dm3 to 0.161g/dm3) over the 13days and the biogas production which is the product also follow the exponential trend from (zero concentration to 219g/dm3). In all the model does the prediction well on all the parameters simulated, so it was can be used to predict the product formation rate as well as the design of reactor or digester.
Keys words: Batch, anaerobic, digesters, biogas, Animal wastes, Nigeria
Nomenclature
Volume of reactor
Q=flow rate (volume/time)
=concentration of micro organism in influent, (mass/unit volume)
=concentration of micro organism in reactor (mass/unit volume)
= specific growth
=rate of cell growth
rd = rate of death growth
Kd = decay rate coefficient (lysis constant)
rs = rate of substrate utilization
= a maximum specific growth reaction rate
=a parameter analysis to the michaelis constant g/ 3
= substrate concentration g/ 3
Cs(o)= Influent substrate concentration g/dm3
Cp = product concentration
Y=yield coefficient g/dm3.
1 Introduction
Many organic matters except mineral oil can be used as feedstock for anaerobic digestion to produce biogas. The main available substrates for anaerobic digestion include polysaccharide, protein, and lipids that usually exist in manure, plants, industrial wastewater, and municipal waste (Van Velsen et al, 1997).Manure of human beings, animals and poultry are easily biodegradable which serves as source of nutrients for microorganism. Manure with high protein content especially from chicken and pigs are good sources of substrate for anaerobic digester. Fresh state is digested as feedstock for biogas production.
This fermentation type involves biomass bacterial decomposition in absence of atmospheric oxygen which consequently produced biogas (gaseous mixture of methane (CH4) and carbon dioxide CO2). The anaerobic digestion of organic materials is biochemically a very complicated process involving hundreds of possible intermediate compounds and reactions each of which is catalyzed by specific enzymes. However, the chemical reaction is simplified as follows:
Anaerobic CH4
Biomass + CO2 + H2 + NH3 Digestion
Biogas is clear combustible non – polluting gas which is produced when insoluble organic matters such as animal dung’s are anaerobically fermented on air and water – tight containers called bioreactor. Biogas is a biomass conversion and has been considered as an alternative source of energy.(Fadalla et al.;2002) In biogas production, concentration of the digestible substrate is difficult to measure but the nearest measurable parameters are the Total Volatile Solids (TVS), Total Solids (TS), Biological Oxygen Demand (BOD) and Chemical Oxygen Demand (COD). These parameters are essentially used to determine the volume of the biogas digester and also the gas production rate since the volatile solid are the components being converted to biogas, hence the rate of its disappearance should be proportional to the rate of production of biogas (Zuru et al.;2003). Biogas Production is a microbial process and therefore requires the maintenance of suitable growth conditions for biogas — producing bacteria. The provision of nutrient, an optimum temperature, pH, adequate water medium, frequent agitation and other environmental factors are vital for the maximum activity of the bacteria (Omer et al.; 2002).
microorganism. Manure with high protein content especially from chicken and pigs are good sources of substrate for anaerobic digester. Fresh state is digested as feedstock for biogas production. The daily production of gas from pig manure depends on the feed given and body weight of animals. For example, the total solid content (TS) of fresh pig manure is about 20% and volatile solids (VS) content about 75 % of total solid. For feedstock of digester, the manure is subjected to ammonia inhibition due to high nitrogen content. The gas yield of conventional process ranges from 0.040-0.059m3/kg total solids (TS) and methane content ranges from 50-70 percent (Asia-Pacific Research and Training Center, 1995).
Using mechanistic approach and suitable differential mass balance equations, a comprehensive simulation work has been carried out to describe the response of the bio digester. A unified approach has been made to develop a set of model equations that are general in nature and are capable of predicting the desired response simply by selecting suitable kinetic parameters. In the present investigation a systematic and programme bio-reaction engineering studies have been carried out using animal wastes as the raw material in a batch digester. An attempt here has been made to develop kinetic model equation to predict dynamic response of the behaviour of microbial processes leading to the production of biogas from animal waste, to determine mathematically the rate of growth of micro organism involved in biogas and to utilize experimental parameters in determining the prediction of various microbial activities. (Biswas. J et al.; 2006)
It is observed that the simulated data obtained from the proposed model equation does the prediction well on all the parameters. It s thus expected that such studies would lead to a better concept of anaerobic biodegradation of animal wastes, to predict the product formation rate and can also be utilized for design and scale up purposes.
2 Methodology
Design models for batch digester were developed using the fundamental principle of material balance analysis (Igboni, 2006) with the kinetic parameters of the animal wastes determined by (R.Miller et al 1987) and the established relationship between microbial and substrate concentration in monod kinetic ( Reynolds and Richards,1996).The system were then simulated over a range of time interval, concentration of substrate and initial concentration of cell with a computer programme using polymath.
Assumption
Assume a constant volume process
The volatile solids are the components being converted to biogas
The rate of their disappearance is proportional to the rate of production of biogas Assume the rate of growth of the organism followed Monod kinetics.
Reaction Mechanism of biogas production under anaerobic condition requires the following pathway cellulose→butyric acid→acetic acid→methane
The equations involved are:
2 2 .
2 4
2 2 2 .
The model formulation for the anaerobic digestion of dung’s is achieved with the following material balance expression.
Rate of Accumulation= (Rate of material flow into reactor) + (Rate of appearance or disappearance of material in the reaction) – (Rate of material flow out of reactor)
This expression can be symbolically represented as
] (1)
= Rate of change of micro organism concentration in the reactor measured in terms of mass (mixed liquor volatile suspended solids), mass/unit volume time.
Rate Laws
Cells +substrate →more cells +product
Monod equation
= (2)
=cell growth g/ 3
=cell concentration g/ 3
=specific growth rate
The specific growth rate can be expressed as µ=µmax cs/ks+cs (s-1) (3)
Where the specific death growth rate can be expressed as = a maximum specific growth reaction rate
=a parameter analysis to the michaelis constant g/ 3
= substrate concentration g/ 3
kobs (4)
Application of the model to batch reactor processes.
In batch reactor there is no flow and out flow. i.e Q=0 Q[( =0
Material Balance For Mass Of Micro –Organism in the Batch Digester.
[Rate of accumulation of cells (g/s)]= [Rate of cells entering (g/s)] - [Rate of cells Leaving (g/s)] + [Net rate of generation of live cells (g/s)]
(5)
For Batch system the entering micro organism concentration is zero So therefore equation (5) becomes
(6)
kobs ] (7)
Eliminating in equation (8) and so therefore it becomes this
kobs ] (8)
Material Balance For Substrate utilization in the Batch Digester
[Rate of accumulation of substrate (mol/s)]= [Rate of substrate entering (mol/s)] - [Rate of substrate Leaving (mol/s)] + [Rate of substrate generation (mol/s)]
= (9)
= = (10)
→The rate of substrate consumption for maintenance whether or not the cells are growing. m= maintenance utilization
m= mass of substrate consumed for maintenance/mass of cells time
When product is only produced during the growth phase We can write in this way
/ (11)
Yp/c = mass of product formed/mass of cells formed
Solution to themodel (Formulae used for the model are as follow)
Mass Balances
Cell
kobs (12)
Substrate
= = (13)
Product
/ v (14)
Rate laws
1
.
(15)
rd=kdCc (16)
=mCc (17)
1
.
⁄ 1
.
(18)
/ (19)
Parameter needed for the model 0 =300g/dm3
0 =1.5g/dm3
Constant Parameter
= 1.7g/dm3 =0.01hr-1
/ =0.45g/g(est)
=0.33hr-1
=1/0.8g/g
n =0.5
The above model is to be solved using polymath software. The software employs the numerical method Runge Kutta of order 5. Additional data (partial source: Modelling Bioreactor R. Miller and M.Melick, Chemical Engineering feb.16 p.113 (1987)
3. Result and Discussion
The summary of the results of the simulation is presented in Table 1 and analysed graphically using Figures 1-4
Variable initial value minimal value maximal value final value
t 0 0 13 13
Cc 1.5 1.5 39.14903 39.14903
Cs 300 248.82835 300 6.88
Cp 0 0 291.0019 291.0019
rd 0.015 0.015 0.38358 0.38358
Ysc 12.5 12.5 12.5 12.5
Ypc 5.6 5.6 5.6 5.6
Ks 1.7 1.7 1.7 1.7
m 0.03 0.03 0.03 0.03
umax 0.33 0.33 0.33 0.33
rsm 0.045 0.045 1.15074 1.15074
Kobs 0.33 0.0857033 0.33 0.0857033
rg 0.4922108 0.4922108 2.2614522 1.66
Variation of Substrate Concentration with Time
Fig 1 Concentration of substrates (Cs) against Time.
Variation of Concentration of Cells with Time
The increasing concentration of cell was observed as the time increases while the substrate declines in value. The cell growth experienced the initial lag phase while this was followed by the exponential rise in cell concentration before it finally peak at a value of 39 g/dm3 reaching stationary stage or state of constant concentration or stagnant activities. This was attained at about ten days of microbial activities culminating in maximum cell yield. The diagrammatical representation is as shown in figure 2. This model result is consistent with the experimental result as reported by (R. Miller and Melick.)
Fig 2 concentration of cells against Time
Variation of Product Concentration with Time.
The product, biogas, follows an interesting trend in concentration with time as shown in figure.3. Starting from the origin of zero concentration, it rises in value exponentially to about 219 g/dm3 within the same length of time. The value peaks at this time tending to stationary value. Again, the model predicted well the experimental observation as reported by (R. Miller and Melick.)
0 100 200 300 400
0 2 4 6 8 10 12 14
Cs
(g
subst
ra
tes/
d
m3
tota
l
feed)
Time (days)
0 5 10 15 20 25 30 35 40 45
0 2 4 6 8 10 12 14
Cc
(g
cell
s/dm3
feed)
Fig. 3 Concentration of products(Cp) against Time.
Variation of Rates of Growth and Death with Time
The rates of growth and death also show interesting trend. The organisms grow exponentially from the initial value of 0.5 g/dm3.h to 2.33g/dm3.h. From this point, the growth experiences stationary stage for about a day or two before declining further till the tenth day of the experiment. Simultaneously, the rate of death begins, though at lower rate, as the growth commences. The rate of death continues and peaks at about 0.35 g/dm3.h. This gives a good net rate of growth of the organisms for the process time. The diagrammatical representation of the whole process is as presented in figure 4. The model predicts accurately the experimental report as presented by (R Miller et. al.)
Fig 4 Rates of growth and Death against Time.
4.0 Conclusion
The behaviors of the process had been accurately predicted with the aid of the mathematical simulation tools employed in research.The substrate consumption follows the expected profile which initially experienced a lag time of stationary value before experiencing exponential decline reaching maximum conversion at about ten days.The model predicted well the cells concentration growth which rises exponentially and peak at about ten days. The model also predicted well the biogas production rate as reported in the literature. The value peaks at the tenth day of the process which gives the maximum conversion of the substrate to product.Finally, the rates of growth and death follow the expected trend conforming well to the literature report. The development of design parameters from these animal wastes and kinetic model for batch anaerobic digester would greatly facilitate and encourage fabrication of digesters of various sizes.
References
[1] Ame ,Catherine .V and Scott F. H 1992. Element of chemical reaction engineering, 2nd ed.,Prentice-Hall, Inc. Pg 675-683
[2] Asia-Pacific Research and Training Center, 1995). Improving Soil Fertility through Organic Recycling, FAO/UNDP Regional Project RAS/75/004, Project Field Document No. 10.
[3] Biswas. J Chowdhury.R and Bhattacharya P (2006) Mathematical modelling for the prediction of biogas generation of an anaerobic digester based on food/ vegetable residues
[4] Calestons. (1983)., Essel, B. and Hagan (1996) Biomass Conversion and Technology. Elservier Applied Science, London. [5] Miller.R and Melick, M (partial source: Modelling Bioreactor Chemical Engineering feb.16 p.113 (1987)
[6] Olorunnisola A. 2007. Production of fuel briquettes from waste paper and coconut husk admixtures. Agricultural Engineering International: the CIGR Ejournal Vol. IX, Manuscript EE 06 006.
0 50 100 150 200 250
0 2 4 6 8 10 12 14
Cp (g p rod uct /dm3 feed) Time 0 1 2 3
0 5 10 15
[7] Omer, T.O.,and Fadalla, L.O. (2002). Engineering design and Economic Evaluation of a family — sized biogas project in Nigeria. Technovation.
[8] Reynolds, T. D. and P. A. Richards. 1996. Unit operations and processes in Environmental Engineering, 2nd ed., Boston: PWS Publishing Company. 798p.
[9] Igoni, A. H., C. L. Eze, M. J. Ayotamuno and M. F. N. Abowei. 2005. Potentials of biogas generation from municipal solid-waste in the Port Harcourt metropolis. In Proc. 1st Annual Conference of Science and Technology Forum, 1(2): 67 – 72. Uyo, Nigeria [10] Zuru, A.J.B and Dangoggo(2003) Ecology of methane formation. In: R. Mitchell(ed), Journal of water Pollution Microbiology. Vol. 2,
