ESTIMATION OF BIOGAS REACTOR CONSTANTS USING … DAHIRU KIDA.pdf · The biogas reactor constants...
Transcript of ESTIMATION OF BIOGAS REACTOR CONSTANTS USING … DAHIRU KIDA.pdf · The biogas reactor constants...
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ESTIMATION OF BIOGAS REACTOR CONSTANTS USING MULTIPLE REGRESSION ANALYSIS
BY
SHUAIBU DAHIRU KIDA PG/M.ENG/08/48278
IN PARTIAL FULFILLMENT OF THE REQUIREMENT OF MASTER OF ENGINEERING IN CIVIL ENGINEERING (WATER RESOURCES AND
ENVIRONMENTAL ENGINEERING)
DEPARTMENT OF CIVIL ENGINEERING, FACULTY OF ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA
MARCH, 2011
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CERTIFICATION
SHUAIBU, DAHIRU KIDA, a postgraduate student in the Department of
Civil Engineering with Reg. No. PG/M.Eng/08/48278 has satisfactorily
complete the requirement of the research work for the degree of Masters in
Engineering in Civil Engineering. The work embodied in this thesis is the
original and has not been submitted in full for any other diploma or degree in
this or any other University.
Shuaibu, Dahiru Kida
(Student)
Engr. Prof. J.C Agunwamba Engr. J.C Ezeokonkwo
(SUPERVISOR) (HEAD OF DEPARTMENT)
(DEAN, FACULTY OF ENGINEERING) (EXTERNAL EXAMINER)
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DEDICATION
This work is dedicated to Almighty ALLAH.
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ACKNOWLEDGEMENT
I express my gratitude to my supervisor professor J.C Agunwamba who
engaged all his time for the successful completion of the programme.
I finally extended my thanks to all the lecturers of the department and
other staff for their contribution in one way or the other during the course of
study. May Allah reward them abundantly.
The programme can be suffered without the effort of wife, parents and
partners of Civil Engineering department of Kaduna polytechnic especially
Engr. Atta and Al Hassan, May Allah reward them also abundantly.
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ABSTRACT
Biogas generation is accomplished by anaerobic digestion of
biodegradable material in a biogas digester. Anaerobic digestion as a process
requires dynamic model for predicting process performance. Mathematical
model for biogas production from anaerobic digesters described in this study
was used to predict biogas generation using experimental data. Multiple
regression analysis was used in analyzing two sets of data, the first sets of
data contains four different experimental results of biogas yield in which the
biogas production rate was determined weekly. The second sets of data
containing four different experimental results had biogas production rate
determined daily, while the first data sets were used as a curve fitting model,
the second sets were used for the verification of the model derived. The
predicted values of biogas yield were close to the measured values with a
maximum correlation coefficient, R = 0.91.
It was further showed that the regression constants were dependent on
temperature only. Hence, the predictive capability of the model can be
improved by making those regression constants dependent on temperature.
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TABLE OF CONTENTS
Certification --------------------------------------------------------------------- i
Dedication ----------------------------------------------------------------------- ii
Acknowledgement -------------------------------------------------------------- iii
Abstract -------------------------------------------------------------------------- iv
Table of contents ---------------------------------------------------------------- v
CHAPTER ONE: INTRODUCTION -------------------------------------- 1
1.1 Background of study ---------------------------------------------------- 3
1.2 Research Problem -------------------------------------------------------- 3
1.3 Significant of study ------------------------------------------------------ 4
1.4 Research Objectives ---------------------------------------------------- 4
CHAPTER TWO: LITERATURE REVIEW
2.1 The history of biogas technology ----------------------------------------- 6
2.2 The need for a biogas system ---------------------------------------------- 8
2.3 Biogas production using Biogradable substances ----------------------- 10
2.3.1 Pretreatment of water Hyacinth to accelerate its Biodigestivity into
biogas ---------------------------------------------------------------------- 10
2.3.2 Biogas production using water hyacinth ------------------------------- 11
2.3.3 Biogas production from blends of cassava (MANIHOT UTILISSIMA)
peels with some animal wastes ---------------------------------------- 12
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2.3.4 Biogas production from waste using biofilm reactor:
Factor analysis in two stages system ---------------------------------- 13
2.3.5 Biodegradation of distillery spent wash in anaerobic
Hybrid reactor ----------------------------------------------------------- 14
2.4 Anaerobic digestion --------------------------------------------------------- 15
2.4.1 Substrate qualities for anaerobic digestion ---------------------------- 16
2.4.2 Digestion environment --------------------------------------------------- 17
2.4.3 Batch digesters ------------------------------------------------------------ 18
2.4.4 Continuous digester ------------------------------------------------------ 18
2.4.5 Semi-batch digester ------------------------------------------------------- 19
2.5 Biogas digester feed stocks ------------------------------------------------ 19
2.5.1 Feeding the digester ------------------------------------------------------ 21
2.5.2 Types of biogas digester ------------------------------------------------- 23
2.5.2.1 Complete mix digester ------------------------------------------------- 23
2.5.2.2 Plug flow digester ------------------------------------------------------ 24
2.5.2.3 Lagoon ------------------------------------------------------------------- 24
2.6 The law of Biogas production --------------------------------------------- 25
2.7 Factors that affect biogas production ------------------------------------- 28
2.7.1 Digester operating parameters ------------------------------------------ 28
2.7.2 Seeding and start-up procedure ----------------------------------------- 28
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2.7.3 Nutrient balance ----------------------------------------------------------- 29
2.7.4 Solid contents ------------------------------------------------------------- 31
2.7.5 Organic loading ----------------------------------------------------------- 31
2.7.6 Retention time ------------------------------------------------------------- 33
2.7.7 Volatile acid concentration ---------------------------------------------- 36
2.7.8 Stirring or Mixing of Digester content --------------------------------- 37
2.7.9 Inhibition and toxicity ---------------------------------------------------- 38
2.7.10 Temperature -------------------------------------------------------------- 39
2.7.11 pH and Alkalinity ------------------------------------------------------- 42
2.7.12 Solid-water ratio --------------------------------------------------------- 44
2.7.13 Quality and characteristics of waste material ------------------------ 44
2.7.14 Loading rate -------------------------------------------------------------- 44
2.7.15 Carbon nitrogen ratio --------------------------------------------------- 45
2.8 Kinetics of biogas production --------------------------------------------- 45
2.8.1 Design models ------------------------------------------------------------- 47
2.8.2 Stoichiometric models --------------------------------------------------- 51
2.8.3 Model trend ---------------------------------------------------------------- 57
2.9 Maximum likelihood ------------------------------------------------------- 60
2.10 Method of moments estimation ------------------------------------------ 63
2.11 Regression ------------------------------------------------------------------ 64
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2.11.1 Multiple linear regression ---------------------------------------------- 64
CHAPTER THREE: METHODOLOGY
3.1 Source of data --------------------------------------------------------------- 68
3.2 Use of statistical tools for analysis ---------------------------------------- 68
3.2.1 Multiple regression analysis --------------------------------------------- 68
3.2.2 Relationship between regression constants and design variables --- 70
3.3 Importance to design ------------------------------------------------------- 71
3.4 Model performance --------------------------------------------------------- 71
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Analysis ---------------------------------------------------------------------- 73
4.2 Verification of the relationships ------------------------------------------- 79
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION
5.1 Conclusion ------------------------------------------------------------------- 81
5.2 Recommendation ------------------------------------------------------------ 81
References ------------------------------------------------------------------------ 82-89
Appendix-------------------------------------------------------------------------90-103
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CHAPTER ONE
INTRODUCTION
1.0 BACKGROUND
Nature does not produce any wastes. All by – products and final
products of natural processes are used in a continuous cycle of the
composition and mineralization of organic substances. The biosphere has a
high buffer potential giving it a wide tolerance range for all natural products
and processes.
Only with the growth of human population and its economical
activities that wastes become a serious danger to the steady – state of the
natural metabolic processes. With the continuous growth of the cities and the
concentration of an increasing part of the population in municipal areas, a
solution of the waste problem becomes more and more inevitable. While a
big part of the inorganic wastes – like glass, plastics, metals etc – meanwhile
are recycled, the biggest part of the organic waste fraction is still simply put
on waste disposal sites. The uncontrolled decomposition of these materials
adds another stress factor to our endangered environment. The partially
anaerobic conditions cause gaseous emissions of carbon dioxide, ammonia
and methane to the atmosphere, while the products of the mineralization
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processes contaminate the ground water with phosphates, nitrates and other
mineral salts, thus poisoning the basic resources of human life.
On the other hand, organic wastes – contain significant energy
potentials as well as valuable plant nutrients and the capability of improving
and conserving agricultural soils. For these reasons, efforts have been taken
during the last decades on the development of waste processing technologies
which are ecologically safe and, at the same time, make use of the valuable
components and characteristics of the material. Technologies which have
been developed for the large-scale processing of organic wastes are the
composting and the anaerobic fermentation. Both methods have their
specific advantages and disadvantages. The decision for one of these
technologies can only be taken with regard to infrastructural technical, and
environmental conditions of the particular area.
The method employed by the developing countries like Nigeria in
disposing or treatment of their waste have brought more harm than good in
their environment and the world at large. Apart from the global warming and
harmful toxins that are being released by man made machinery, the
dependence on wood as a source of energy is on the increase and is really
affecting the natural reserves of forest and desert encroachment.
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Biogas has many advantages as a replacement for petrol, diesel and
the generation of light. Biogas gives the smallest emissions of carbon
dioxide and particulate matter of all vehicle fuels in the market today. The
methane molecule is the simplest of hydrocarbons, which means that the
exhaust produced by combustion is very clean.
The biogas reactor constants can be estimated using the multiple
regression analysis. The estimated yield of gas can be calculated and
compared with the measured yield of gas.
1.1 BACKGROUND OF THE STUDY
Biogas process has been used for long in some part of the country, but
only in small quantity. Though the development technology is still in its
embryonic stage, there were few large scale biogas plant of 1800m3 capacity
in 1996 at the energy research centre of Nigeria (ECN)(Sambo, 1992).
However, its potential is promising, is the energy research centre
Sokoto in Nigeria putting more effort to create awareness to our local farmer
on the construction and use of Biogas.
1.2 RESEARCH PROBLEM
Around the world, pollution of the air, water and soil from municipal,
industrial and agricultural operations continues to grow. Government,
industries, organizations and individuals are constantly searching for
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technologies that will allow for more efficient and cost-effective waste
treatment and disposal.
One technology that can successfully treat the organic fraction of wastes
(biogenic wastes) is indeed anaerobic digestion through fermentation. The
fermentation provides pollution prevention and also allows for sustainable
energy, water, fertilizer and nutrient recovery. Thus, this technology can
convert a disposal problem into a profit centre, and provides a realistic
solution to environmental, social and economical problems for developed and
developing nations.
1.3 SIGNIFICANT OF THE STUDY
The importance of the study are:
To provide the best method for estimation of yield;
Several existing models do not predict measured values well, therefore
the need for better predictive modes; and
No kinetic equations available for design will help to generate the
equations for design of this particular design.
1.4 OBJECTIVES OF THE STUDY
Determine the equation for yield estimation using multiple regression
analysis;
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Investigate relationships between regression constants and design
parameters;
Compare the results using data in the literature;
Apply the derived relationships in design; and
Compare the predicted design parameters from the relationship with
measured data.
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CHAPTER TWO
LITERATURE REVIEW
2.1 THE HISTORY OF BIOGAS TECHNOLOGY
Biogas was first observed from decaying vegetation that produced a
combustible gas by Alessandro Volta. In 1776 he wrote that combustible air
was being produced continuously in lakes and ponds in the vicinity of como
in Italy. Volta had noted that when he disturbed the bottom sediment of the
lake, bubbles of gas would rise to the surface. He noticed that when the
sediment contained more plant materials, more bubbles came up. In 1806
William Henry showed that Volta’s gas was identical with methane gas.
Humphery Daung in the early 1800s noticed that methane was present in
farm yard manure pices. In 1868 Bechamp demonstrated that methane was
formed from carbon compounds by action of micro – organisms.
Tappeiner (1882-4), showed conclusively that methane was of
microbiological origin, the first plant of biogas was set in a leper asylum in
India in 1990 (Vaclav et al., 1980). According to (Kerekezi et al., 1997),
biogas technology has been in use since the late 1940s. Although its original
purpose was not the reproduction of fuel gas. Initially biogas digester were
used for treating waste and producing fertilizer, particularly in India and
China.
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In Denmark more than 15 large scale biogas plants producing 2,000 to
15,000m3 of biogas per day has been built by 1993 and plans were underway
to construct 100 more digester for production of biogas.
In 1978 Cornell University built the first plug digester that was able to
digest the manure from sixty cows. The development of biogas has been
extended in Sweden where about 227 biogas plants have been built in the
country today producing energy, fuel and fertilizer. In mid 1950s, the
ministry of energy in Kenya, officially launched biogas training body and
plant construction programme which was launched in 1993 to 1994 in mere
district, with the assistance of German technical cooperation organization
(GTZ) in the early stage of the programme, (until late 1986) all gas activities
concentrated in Meru. To date the national biogas figure in Kenya is
estimated to be about 500 units (Kekezi et al, 1997).
In Nigeria, the development of biogas technology is still in its
embryonic stage, there were few large scale biogas plants of 1800m3 capacity
in 1996 at the energy research centre of Nigeria (ECN) (Sambo, 1992).
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2.2 THE NEED FOR A BIOGAS SYSTEM.
Biogas is an aspect of renewable source of energy produced from organic
material cow dung, human waste, sheep and goat droppings, pig and poultry
excreta, cassava, yam, banana and other peels, corn cob and stalk rice husk,
groundnut shell, water hyacinth and other different types of biomass. As a
time of growing global awareness of the need to conserve both energy and
environment the use of biogas plant as a waste treatment system and source
of energy offers many benefits. These benefits can be considered from two
aspects, the immediate primary benefits of the gas and manure, and the
secondary benefits related to the inputs-human animal and crop waste.
1. Use of the gas as fuel saves such as items as kerosene, coal and
eliminates the need to burn other valuable natural resources. Thus, by
using biogas instead of firewood, deforestation and hence soil erosion in
reduced.
2. The gas provides a convenient and cheap source of power not only for
cooking, but also for lighting, heating and running farm machinery.
3. The effluent and sludge remaining after digestion has taken place, is rich
and effective manure. All objectionable odors can be removed and
harmful microorganisms
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4. Due to the removal of carbon digestion, the organic materials remaining
is richer in nitrogen and phosphorus than the original materials and are
thus a superior fertilizer to normal compost. Also use of the residue as
manure saves mineral fertilizer and their expenses on them.
5. It generates many other social benefits such as control of environmental
pollution, an ideal method of waste disposal, reduction in incidence of
eye and lung diseases and greater availability of time for the other
productive employment.
6. It is also a valuable method of treating sanitation thereby reducing their
harmful bacteria and parasitic content because the cow dung that are
sometimes washed into the streams during rainfall are cleared from
production, it can thus help to prevent the water fetch from the stream
being infected with bacteria from cow dung thereby preventing infection
from drinking water, which in many rural areas are untreated and also
reduces the degradation of the ecosystem.
7. To data, the main interest in the third world in biogas technology has
come from countries of Asia and pacific region. Despite the numerous
advantages of using biogas as a source of energy and source of nitrogen-
rich fertilizer, it has made only little impact in Africa and Latin America.
Attitude of biogas technology varies from region to region. While the
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west often sees new and renewable energy sources as morally superior,
green or soft or appropriate, the third world suspects that they are second-
class technology.
2.3 BIOGAS PRODUCTION USING BIOGRADABLE SUBSTANCES
Generation of biogas using biomethanation process from various bio-
wastes is well known. Biomethanation is an important biological conversion
process which converts biomass in the absence of oxygen to methane and
carbon dioxide, popularly known as biogas and leaves a stabilized residue
which makes excellent organic manure. Biomethanation process is gaining
wider acceptance presently due to production of biogas, which can be further
used for augmenting the energy demand. Energy has a major economical
and political role as an important resource traded world wide.
Biomethanation technology may be perceived as potential alternative as it
provides not only renewable source of energy but also utilizes recycling
potential of dedgradable organic portion of wastes on materials. The activity
of methanogenic bacteria depends on several factors such as Degister
temperature, PH etc.
2.3.1 Pre-treatment of Water Hyacinth to Accelerate its Biodigestivity
Biogas is a medium grade fuel, is produced from the anaerobic
digestion of water hyacinth, this being undertaken with input measures to
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accelerate the rate of biogas production. One set of water hyacinth samples
was chopped to about 6mm by 10mm pieces, the second set was ground, the
third set was chopped and blenched while the fourth set was simple
blenched.
Each of the four sets of sample was placed inside a sample biodigester
plant and left to biodigest at temperature kept within the range 280C 37
0C
from the chopped sample, 3.95dm3 of biogas was produced from every
kilogram of total solids of feedstock, after 15 to 28 days detention period.
With ground water hyacinth as feedstock, biogas yield commenced after 5
days and produced 4.01dm3/kg of total solid for samples subjected to
chopping and blenching for biogas production yield commenced after
14days and biogas production was 3.31dm3/kg.
The results show that biogas production rate during anaerobic
digestion of water hyacinth is substantially affected by the pre-treatment
given to the substrate.
2.3.2 Biogas Production Using Water Hyacinth
Water hyacinth is a fast growing plant that has been used as raw
materials for a few purposes (Pieterse, 1978; Decter and others, 1985). The
Water hyacinth has been used for water purification (Sinha and Sinha,
1969). Water hyacinth absorbs some pollution agents in the waters. The
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polluting materials becomes incorporated into the structure of the plant and
are thus removed. The water hyacinth that has been so used for water
purification may further be utilized as a feedstock materials to be
biodigested to yield biogas. The chemical constituents of water hyacinth
include cellulose, hemi-cellulose and lignin, (Tsao, 1978) and is found to be
59-66% anaerobically biodegradable with methane production ranging from
0.24-0.34m3/kg of volatile solid added (Moeller et al, 1984).
2.3.3. Biogas Production From Blends of Cassava (Manihot Utilissima)
Peels with Animal Wastes
Cassava peels obtained after peeling cassava roots were anaerobically
digested using 50litre capacity fermentor and in blends with some animal
wastes. The peels were blended with cow dung, poultry droppings and swine
dung, in the ratio of 1:1. The mean flammable biogas yield of the cassava
peels alone was 2.29 to 0.97 litres/total mass of slurry. When blended with
the cow dung, poultry droppings and swine dung, mean flammable biogas
yield was increased to 4.88 ± 1.73, 5.55± 2.17 and 5.65± 2.62 litres/total
mass of slurry, respectively. Flammable biogas was produced by cassava
peels and cow dung and cassava peels plus poultry dung produced
flammable gas from the 9th day whereas cassava peels and swine dung
started flammable gas production from the 11th day. While cassava and
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swine had the highest cumulative gas yield of 169.601/total mass of slurry,
the cassava peels and cow dung experienced fastest or set of flammable gas
production. Overall results indicate that the relatively low flammable biogas
production and slow on set of gas flammability of cassava peels can be
significantly enhanced when combined with the animal wastes in defined
portions (Ofoefule and Uzodinma, 2009).
2.3.4 Biogas production from waste using biofilm Reactor: factor
analysis in two stage system.
Factor analysis was applied in two states of biogas production from
banana stem waste allowing a screening of the experimental variables:
temperature (T), organic loading rates (OLR) and hydraulic retention times
(HRT). Biogas production was found to be strongly influenced by the three
experimental variables. Results from factorial analysis have shown that all
variables: HRT, OLR and T have significant effects on biogas production.
Increase HRT and OLR could increase the biogas yield. The performance
was tested under the conditions of various T (30oC - 60
oC), OLR (0.3g Ts/.d),
and HRT (3 -15d) (N. zainol, J. Salihon and R. Abdul-Rahman, 2009).
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2.3.5 Biodegradation of Distillery spend wash in Anaerobic hybrid
Reactor.
A lab-scale anaerobic hybrid (combining sludge blanket and filter)
rector was operated in a continuous mode to study anaerobic biodegradation
of distillery – spent wash. The study demonstrated that at optimum hydraulic
retention time (HRT) of 5 days and organic loading rate (OLR), 8.7kg
COD/m3d, the COD removal efficiency of the reactor was 79%. The
anaerobic reduction of sulfate increases sulfide concentration, which
inhibited the metabolism of methanogens and reduced the performance of the
reactors. The kinetics of biomass growth, that is, yield coefficient (Y =
0.0532) and decay coefficient (kd = 0.0041d-1
) was obtained using Lawrence
and McCarty model. However, this model failed in determining the kinetics
of substrate utilization. Bhatia others (2006) model having inbuilt provision
of process inhibition described the kinetics of substrate utilization, maximum
rate of substrate utilization (R = 1.945d-1
) and inhibition coefficient values
(ki = 0.0321/mg). Modeling of the reactor demonstrated that Parkin (2006)
and Speece, and Bhatia (2006) models, both, could be used to predicts the
effluent substrate concentration. However, Parkin and Speece (2006) model
predicts effluent COD more precisely (within 2%) than Bhatia
(within 5 – 20%) of the experimental value. (Kumar, & others (2006).
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2.4 ANAEROBIC DIGESTION
Anaerobic digestion is a purely natural process and has been employed
by humans for centries to treat waste and improve sanitation in living
communities. For centuries it has been used to provide some exciting
possibilities, handling human, animal, municipal and industrial wastes safely,
and providing fertilizer substitutes for farmers (Marchaim, 1992). In the face
of global energy crises, many none oil producing societies like Germany see
the employment of anaerobic digestion as a means to convert waste and
energy crops into methane which can then reduce their dependency on
imported petroleum and natural gas.
Anaerobic digestion is a process that takes place in the presence of
biodegradable biomass (substrate), anaerobic micro-organisms (facultative as
well as obligatory), and a milieu (digester) free of molecular oxygen (O2).
The process converts the energy in biomass into energy in a gaseous mixture
otherwise known as biogas. The principal gases in biogas are methane (CH4)
and carbon dioxide (CO2) together with small to minute concentrations of
other gases. This composition depends on substrate quality, conditions of
digestion, environment and the type of micro organisms involved. The
process of gasification that is a thermal transformation process can also be
used. Biogas is also produced at sewage disposal locations and many
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countries still tapping this have potentials to increase their home made energy
methane. The qualities of biogas produced however vary according to
method used. Table 2.1 shows average composition and energy value of
biogas usually associated with anaerobic digestion processes.
Table 2.1: Average composition and energy value of biogas
Composition Formulae Contents %
Methane
Carbon dioxide
Hydrogen
Nitrogen
Hydrogen sulphide
CH4
CO2
H2
N2
H2S traces
50 -60
30 -40
5 – 10
1 - 2
Calorific value 4700 – 6000Kcal/m3 or 20 -24 MJ/ m
3
Source: Tandon and Roy(2004)
2.4.1 Substrate qualities for anaerobic digestion
In a study on the biochemistry of anaerobic digestion Bushwell (1962)
found a relationship between the biogas productivity and the substrate
digested. He summarized this into a formula generally referred to as the
theoretical gas equation.
CnHaOb + (n-a/4-b/2) H20 = (n/2-a/8+b/4)Co2+(n.2+a/8-b/4) CH4
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Though the calculated results of this formula do not agree always with
practical yields potentials of different biomass types. The cultivation of oil
crops like sunflower and maize in mix cropping system for biogas production
is aimed at maximizing biogas and methane productivity based on knowledge
of theoretical gas equations. The theoretical gas equation only considers the
biogas productivity of the major cell contents (fats, proteins and
carbohydrates) and makes no mention of cell wall and digestibility problems
(Honemeier, 2008).
2.4.2 Digestion environment
Anaerobic digestion as the name suggest takes place in a molecular
oxygen free environments. Such environments can be natural as in swamps,
they can be man made as in landfills, and commercial anaerobic digesters.
Commercial anaerobic digesters are created to trap biogas for further
processing (scrubbing) into commercially useful methane.
They can be of any shape and can be made form any available material
provided the reaction milieu (temperature, pH, moisture, etc) is conducive to
the proper activity of the micro-organism consortium involved. Biogas
digesters are classified based on loading OK, follow pattern and temperature
requirements during the digestion process. Base on loading Ok three types of
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biogas digesters are usually distinguished; Batch digesters, and semi batch
digesters (Honemeier, 2008).
2.4.3 Batch digesters
There are digesters that can take biomass with a wide range of
moisture contents. The most important thing is to calculate the retention time
and the appropriate digester volume. The digester is operated by repeatedly
feeding and emptying after the calculated retention time. The concept of
loading rate is hence very appropriate to batch digesters than any other types.
Batch digesters are disadvantageous in that the gas productivity is either not
enough or is erratically produced.
2.4.4 Continuous digesters
Continuous digesters as the name implies are fed and emptied
continuously. They can be fed automatically as well as manually but the
emptying occurs automatically due to the ability to push out the effluents by
the pressure that develops within the digester. Unlike batch digesters biomass
for continuous digestion must be of high moisture content (very low DMC)
and homogenous. Gas production is continuous and more in volume than in
the batch digestion system. For this reason nearly all biogas digesters today
are operated in the continuous mode.
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2.4.5 Semi batch digesters
Semi batch digesters are those that do digest substrate with normal
retention time with cellulosic or lignified biomass having extreme the
retention time of about six months. The one with normal retention time can
be fed and emptied as allowed by the retention time without disturbing the
other. All types of digesters must function at a constant temperature that
depends on the microorganisms used. Basically, microorganisms in the
digester fall into groups requiring temperatures in the ranges <20oC, 25 -
40oC, and >45
oC. Those requiring 25 -40
oC are termed mesophilic, those
requiring <20oC are pscyhrophilic.
Temperature requirements of digesters are usually used in combination
with the name of the digester type in the classification of digesters. A
mesophilic batch digester for instant is one that is fed in batch and operated at
a constant temperature in the range 25 -40oC. The majority of modern biogas
are operated at the mesophilic range and at optimum pH of 7 -8.
2.5 BIOGAS DIGESTER FEED STOCK
A digestion is a process carried out by bacteria. The “medium” in
which the bacteria grow must contain an energy source, and sources of
carbon and nitrogen for cell synthesis, as well as the trace elements for
bacterial metabolism. These are usually provided in the animals excretes,
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vegetable matter and factory wastes used as feed. Although most waste
contain all the nutrients required by the bacteria, generally the main
constituents, the energy and nitrogen sources will not be in correct ratio for
optium utilization of each. Faecal waste, for instance are generally too high in
nitrogen content and same factory waste (Eg starch, sugar solutions) may
have too little nitrogen. The carbon to nitrogen ratio (C/N) of the former
might adjusted by the addition of a carbon sources (eg potatoes or straw).
Table 1 Gas production from animal excreta.
Piggery waste, slurry from fattening pigs on dry barley feed.
Detention time Gas production Temperature
10 - 15days 0.300m3/kg
30o - 35
oC
10 days 0.39m3/kg
40o
20 days 0.38m3/kg
45o
7 days 0.284m3/kg
Below 25o
3 days 0.170m3/kg
Below 25o
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Poultry waste, from caged layers.
Total solids in
slurry
Detention time Gas production Temperature
2 – 6.5% 20 days 0.380m3/kg
35oC
5% 10 days 0.195m3/kg
35oC
10% 0.189m3/kg
8% 0.258m3/kg
Diary cattle waste: slurry from cows on silage concentrate
Total solid Detention time Gas production Temperature
21 days 0.206m3/kg
35oC
20 days 0.172m3/kg
35oC
2.5.1 Feeding the digester
Digesters are usually fed based upon three criteria: volatile solids, hydranlic
retention time, and carbon and nitrogen ratio.
i. Volatile solids (VS) are a measure of the amount of organic matter in
material. If too much organic matter is added, the acid forming bacteria
can convert the organic matter to acids before the methanigens can use
the acid. The resulting acid accumulation will cause the digester to fail
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because the methanogenic bacteria cannot survive in highly acidic
conditions.
ii. Hydraulic retention time (HRT) is a measure of the amount or period
of time the digester liquid remains in digester. If 10 liters of a 200
litres reactor is added and removal each day, it would take 20 days to
completely replace the reactor contents. Hydraulic retention time is
very crucial because if the feed does not stay in the reactor long
enough for the entire digestion process to take place, biogas will not be
produced. Because the digester will only be working for relatively
short period of time, hydraulic retention will not play a large role in
designing a digester (www.ce.ufe.Edu/activities/waste/wddstu.html).
iii. Carbon and nitrogen ration (C: N) just as balance diet contributes to
healthy bacteria population so it does, anaerobic bacteria commonly
use carbon as a energy sources for growth and nitrogen to build cell
structure. Generally, 25 -30 times more carbon is required by the
bacteria than nitrogen. The bacteria most efficiently utilize feeds which
have a carbon and nitrogen ratio of approximately 30:1. In developing
countries, the primary substrate is cattle dung due to large cattle
populations. This is a good substrate, because it is moderately
23
degradable, and is well balanced nutritionally (C/N = 25:1)
(www.fao.org/docrep/To541E06.htm).
2.5.2 Types of biogas Digester
There are three main types of biogas anaerobic digester: complete mix
digester, plug flow digester and lagoon digester
2.5.2.1 Complete mix digester:
This may be the most feasible one for poultry farms. This digester is
common in warmer climate where they flush manure out of barns or pens
with water, making it more diluted and having concentration of total solid
between 3 and 11%. The manure accumulates, allowing foreign undesirable
materials to settle out before entering the digester. The complete mix digester
makes use of gravity and pump to move the influent and effluent. It is often
in the shape of a vertical cylinder and constructed of steel or concrete. (See
Fig 2.1) The floor may be flat or conical and a mixer maybe used to ensure
that the manure is fully digested by the bacteria. The complete mix digester
has a hydraulic retention time of 10 to 20 days and tends to be the most
expensive of the three types.
Fig 2.1 Complete mix digester
Out flow In flow
V C Q
C O
Q
24
2.5.2.2 Plug flow digester
The plug flow digester uses manure with a higher solid concentration
between 11 and 14%. This system is used primarily at diary farms where
manure is collected from scraping systems. Plug flow digesters are typically
and constant volume, long linear, concrete rectangular below ground for
insulation. The length to width ratio is roughly 5:1 and has a depth of 2.44m.
(See Fig 2.2) it is called plug flow because each day a “plug” of manure is
added pushing manure currently in the digester further down the trough like
an assembly line. The hydraulic retention time (HRT) for plug flow digester
is about 20 -30 days. Both the complete-mix digester and plug flow are often
heated so that they operate at a constant temperature year round increasing
the efficiency.
Fig 2.2 Plug flow digester
2.5.2.3 Lagoon:
The lagoon is the simplest and is also the least expensive. Gas is
collected by covering part or the entire lagoon where manure is held and
C + dC Q
C
dx x
Q C C
25
stored with a floating cover. The gas can be reached by a long perforated pipe
with slight vaccum. The influent is often from hydraulic flushing with a total
solid concentration much less than 3%. Though the lagoon is a cheap and
straight forward method of biogas digestion. It takes longer to produce gas
and fluctuates more with the temperature and seasons.
Precautions must also be taken so that the ground water is not contaminated
from the manure. (Cary, 2003).
Lagoon Digester and Biogas Handling
2.6 THE LAW OF BIOGAS PRODUCTION
Fermentation materials require different fermentation techniques
because they have different chemical components and structures and produce
biogas at different speeds. (See Table 2.2). The more anaerobically
degradable matter a fermentation contains, the more rapidly it produces
26
biogas. Conversely, the less anaerobically degradable matter it contains, the
more slowly it produces biogas (BRTC, 1994)
Table 2.2: Biogas-producing rates of some fermentation materials
Material Yield of biogas is
(m3/kg/)
Methane contents (%)
Animal born (yard
manure)
0.260 – 0.280 50 -60
Pig manure 0.516 -
Horse dropping 0.200 – 0.300 -
Green grass 0.630 70
Wheat straw 0.432 59
Leaves 0.210 – 0.294 58
Sludge 0.640 50
Brewery liquid waste 0.300 – 0.600 58
Carbohydrate 0.750 49
Lipid 1.440 72
Protein 0.980 50
Source: BRTC (1994)
27
In the process of wastes fermentation, biogas is produced at an increasing
speed at first; after period of time, the speed reaches its peak and remains
steady for some time, then it begins to drop remarkably. Materials of
excrement type with high nitrogen content produce biogas rapidly, and the
amount of biogas they produce in the first 20 days of fermentation, accounts
for more than three quarters of the total amount of biogas they produce in
60days. Those materials with high carbon content produce biogas rather
slowly and they gain the highest speed of biogas production very late, the
amount of biogas they produce in the first 40 days of fermentation accounts
for more than three quarters of the total biogas they produce in 60 days
(Yongfu, 1989).
Generally speaking, materials with high content in nitrogen produce
biogas rapidly; the anaerobically degradable matter they contain can be
converted into methane within a rather short period of time. On the contrary,
materials with a high carbon content produce biogas rather slowly. However,
not all materials with high carbon content decompose slowly. In fact, some of
these materials decompose very fast, for example materials (contained in
grains and potatoes), glucose, and sucrose etc. if the digester is fed with too
much of them, fermentation system is likely to be acidified.
28
2.7 FACTORS THAT AFFECT BIOGAS PRODUCTION
2.7.1 Digester operating parameters
The performance of anaerobic digester system is affected by a number
of parameters ranging from environmental conditions to the operation and
maintenance of the system. The conditions and practices necessary for
optimum performance of anaerobic digesters include: seeding and proper
start –up procedures, nutrient balance, solids concentration, loading rate,
retention time, temperature, pH and alkalinity and volatile organic acid
concentration.
2.7.2 Seeding and start – up procedure
Seeding is recommended as a start-up procedure for anaerobic
digestion. It consists of the addition of actively digesting materials to a new
digester to ensure that good cultures of all species of anaerobic bacteria are
present for start-up (Singh, 1977). The time required for start-up is inversely
proportional to the amount of seeding materials provided; thus increasing the
quantity, seeding materials as observed by Andrew (1975), results in the
acceleration of start-up process of both the batch and the continuous flow
digesters. In the absence of adequate seeding materials, digester failure may
occur.
29
It is suggested that the recommended loading rate be reduced by 90%
at the start-up, increasing gradually to full loading as the digestion process is
established. Performance can be monitored by monitoring the gas production,
volatile acid content, pH, alkalinity, and temperature and gas composition of
the digester regularly (Kugleman and Jeris, 1981). Any imbalance will
usually be indicated by sudden changes in the parameters. Also, to be
monitored periodically are the total solid, volatile solids, ammonia and
organic nitrogen and the Chemical Oxygen Demand (COD) of the digester
mixed liquor, the supernatant and the sludge.
2.7.3 Nutrient balance
In the metabolism of any organic structure, various organic and
inorganic substances play a role. Such as role may be stimulatory, in which
the growth rate of the organism increases with increase in the concentration
of the substance, or inhibitory in which the growth rate declines with
concentration. Generally, most substance plays an active role at high
concentration. Substances which at normal concentration produced
stimulatory effect on micro-organisms are considered as nutrients. They
include carbon, nitrogen, sodium, potassium, calcium and magnesium. Trace
amount of iron, cobalt, phosphorus and sulphur, are also necessary for the
maintenance of optimum growth of anaerobes (Kugleman and Jeris, 1981)
30
The organic nutrients provide the carbon component that is converted to
methane and also serve as source of energy while the nitrogen component
serves as the food source.
The relative proportions of the various nutrients are very important in
determining the amount of biogas yield. Hills (1979), reported a 60 to 70%
increase in methane yield when the C/N ratio was decreased from 60 to 25.
Methane as well as biomass yield also vary in relation to the proportion of
carbohydrate, protein and lipids that comprises the degradable fraction of the
volatile solids content of the wastes (Jeris and McCarty, 1964; Cowly and
Woese, 1984). Carbohydrate yields the highest quantity of anaerobic
bacterial cell mass per unit mass of ultimate Biochemical Oxygen Demand
(BOD) as well as the least quantity of methane per kilogram of dry substrate;
lipids yield the lowest and highest quantity of methane per kilogram of dry
substrate; lipids yield the lowest and highest quantities of biomass and
methane, respectively.
Maximum methane yield occurs in mesophilic digesters when the non
lignin C/N ratio is between 2 and 32 (Hills and Roborts, 1981). Because most
animal manures have a C/N ratio of 10 (Hashimoto et al, 1981), the potential
to increase the methane yield by the addition of carbonaceous materials such
as crop residues is apparent. The practical limitation of this concept,
31
however, is that most of the crop residues are necessary to pre-treat residues
to increase biodegradability (Millet et al., 1994). A.C.N ratio of 30:1 is
generally recommended.
2.7.4 Solid contents
The concentration of solids in the substrate determines to a large
extent, the amount, and rate of biogas production. The amount of methane
that can be generated during anaerobic digestion is a function of the fraction
of biodegradable component of that total solid, soluble, volatile solids are
commonly used to estimate the amount of biodegradable portion of the
wastes. It is therefore, an important parameter in estimating potential
methane production. Total solids concentration of fresh wastes range from
12.7% for dairy to 25.5% for poultry (Smith, 1981).
2.7.5 Organic loading
Organic loading refers to the mass of organic matter added per unit
volume of digester per unit time. It is usually expressed as kilogram volatile
solids per unit volume of digester per day (kg VS/m3
day), although it may
also be expressed as kg (TOD/ m3
day) if the wastes is soluble (Grandy and
Lim, 1980). Organic loading is a function of influent substrate concentration
as well as the hydraulic retention time. For any given retention time, the
higher the substrate concentration, the higher the organic loading rate.
32
Conversely, at any given influent substrate concentration, the lower the
retention time, the higher the organic loading rate. High loading rate makes
for a more effective utilization of digester capacity, that is, it minimizes
digester volume requirement at any overall hydraulic retention time. High
loading rate also results in higher daily rate of biogas production, higher rate
of volatile solids reduction and faster rate of wastes stabilization (Ben-
Hassan, 1986). Using a mesophilic farm size digester operated at a retention
time of 36 to 38 days, Converse et al. (1981) established the following
relationship between gas production and loading rate:
Y = 0.282LR – 0.139
Where: Y = gas yield (cubic metre = m3/kg VS added)
LR = loading rate (kg VS/ m3day)
Typical range of loading rates as given by Hashimoto et al. (1979) are shown
in Table 2.3. To maintain a uniform gas production and to minimize the
possibility of upsetting the balance between acidogenesis and
methanogenesis, loading rate should be maintained as uniformly as possible.
33
Table 2.3: A typical loading rate for mesophilic anaerobic digesters
Type of manure Loading rate (kg Vs/m3day)
Beef cattle
Dairy cattle
Poultry
Swine
1.6 - 8.0
1.6 – 8.0
1.6 – 5.0
1.1 – 5.0
Source: Hashimoto et al. (1979a)
2.7.6 Retention time
The number of days the organic material stays in the digester is called
the retention time. There are two significant retention times in an anaerobic
digester. Solids retention and hydraulic retention time (HRT). The SRT is the
average time the bacteria (solids) are in the anaerobic digester. The HRT is
the time the liquid is in the anaerobic digester. SRT is the most important
retention time, and should be determined correctly because it indicates the
potential of bacteria wash out. If a significant wash out of bacteria occurs, the
digester can fail.
Solid Retention Time (SRT) is a fundamental design parameter used in
process control of anaerobic digestion (Table 2.4). SRT is the theoretical time
that microbial cell are retained in a biological system. It is determined as the
34
ratio of mass of biomass in the system to the amount of biomass leaving this
system per given time.
SRT = Mass of Microorganisms in the system (mg)
Mass of microorganism leaving the system per time (mg/day)
Table 2.4: Optimum retention time and gas production at different
temperature
Biomas Operating
Temp. (oC)
Optimum retention
time (days)
Gas production
(L/L - day)
Volatile Solid
Destroyed (%)
Poultry
manure
15
25
35
55
30
20
0.48
1.38
1.45
50.8
61.1
75.0
Cattle
Manure
15
25
35
60
35
30
0.25
0.48
0.66
40.0
60.0
65.0
Source: Hawkes (1979).
Preliminary tests must be undertaken on the particular wastes at various
retention times to obtain a loading rate versus gas yield relationship. A study
carried out in Korea (Hawkes, 1979) investigated the optimum retention
times for optimum gas production for different temperatures with poultry
manure and cattle manure fed to 20 laboratory digesters. Results obtained
showed that the optimum retention time fails rapidly at higher temperatures.
35
Fundamentally, SRT which is also known as Mean Cell Residence
Time (MCRT), or Sludge Age in the case of municipal wastes, should be
determined using quantity of active biomass in the system. In a continuous
stirred tank reactor with no recycle, SRT, equals the Hydraulic Retention
Time (HRT) which is the mean theoretical time that the liquor spends in the
system. HRT is determined as the ratio of the reactor volume to the effluent
flow rate that is
HRT = Reactor volume (m3)
Out flow rate of effluent (m3/d.)
The minimum SRT is the minimum microbial reproduction time. Long
SRT results in a more complete destruction of volatile solids and hence,
higher methane Yield per unit organic matter metabolized at any given
temperature (Hashimoto and Cheng, 1981).
Long retention time also maximizes the potential for acclimation to
toxic environment as well as minimizing the severity of response to toxicity
(Speece and Parkin, 1983). In other words, long retention time provides
sufficient capacity to cope with temporary fluctuations in temperature, pH,
alkalinity or overloading. Kinetic studies show that 90% or more of the
biologically available solids was mesophilically (35oC) biodegraded within
12 days (Smith, 1981). At a retention period of 20 days, methane production
from dairy cattle is essentially complete (Loehr, 1984) implying that
36
designing a system with longer retention time would only result in increased
digester size and system cost without appreciably more methane per unit
mass of biodegraded solids. Patelunas (1976) and Patelunas and Regan
(1977) reported that the gas production from a laboratory scale digester per
unit volume of digester was maximum at a detention time of 7 to 10 days,
while Bartlet (1978) reported at optimum detention period of 12 to 14 days
for a full size anaerobic digester.
2.7.7 Volatile and concentration
Related to the parameter of pH are alkalinity is volatile acid
concentration. Volatile acids are produced as the end products of
acidogenesis and are the primary metabolic substrate of the methoanogens. In
a well maintained anaerobic system, high volatile acid concentration does not
arise because the acids are utilized at the same rate as they are produced.
Under such a system, the volatile acid concentration remains fairly constant
with any sudden change in volatile acid concentration usually indicating a
disruption in the equilibrium of the system. Volatile acid concentration less
than 200mg/L as acetic acid is usually considered satisfactory.
37
2.7.8 Stirring or Mixing of Digester content
Stirring of the slurry improves the gas production. About 11.8%
additional gas was produced with stirred slurry than no stirring (Sambo,
1992).
Stirring or mixing of the digester content enhances the gas production
by improving the anaerobic digestion process. Mixing ensures that the solids
retention time equals the hydraulic retention time and enables the three
phases of gas formation to take place throughout the digester. Biological
activities are increased when digester fluid are mixed to provide
homogenous temperature and nutrient conditions throughout the digester and
to allow for optimal interaction between micro-organism and wastes
constituents.
Generally, mixing is carried out to achieve the following objectives:
a. Maintenance of uniform temperature through out the system;
b. Dispersion of potential metabolic inhibitors such as high
concentrations of volatile acid, ammonia or sulphide;
c. Disintegration of coarse organic particle and bioflocs to make for
greater net surface area available for bacterial attack;
d. Distribution of influent substrate uniformly throughout the digester;
thereby preventing the creating of tank volume;
38
e. Allowing the use of higher loading rate with faster rate of BOD
reduction;
f. Provision of good fluid consistency for reliable effluent outflow;
g. Prevention of scum and crust formation at the liquid surface;
h. Assisting gas release and removal from the liquid-solid-gas system
(Kugleman and Jeris, 1981; Loehr, 1983; Ben-Hassan, 1986).
Mixing is achieved either through sludge recirculation or gas recirculation or
by mechanical means such as mechanical draft tube, turbine or propeller
produced gases but is generally not sufficient to achieve mixing conditions
necessary for process optimization (Overcash et al., 1983) Kugleman and
Jeris (1981) indicated that 3 to 6 periods of mixing per day, each lasting one
to 3 hours is generally satisfactory.
2.7.9 Inhibition and toxicity
Digester treating municipal waste have failed on occasion because of
the presence of copper, zinc, chromium and nickel. High concentrations of
alkali metals like magnesium, calcium, sodium, and potassium can be toxic to
anaerobic bacteria. The digestion of livestock waste containing high nitrogen
to carbon ratios is more likely to result in toxic conditions for bacteria arising
from the concentration of free ammonia.
39
Methanogenic bacteria appear to be very sensitive to certain materials
and environmental conditions. Being obligate anaerobes, a small amount of
oxygen or oxidized products such as nitrate are inhibitory to these bacteria. It
is essential that a highly controlled environment be maintained to promote
the growth of these microbes.
Some alkali and alkaline earth-metal salts above certain concentrations
exhibits toxicity. Ammonia is inhibitory when present in high concentration.
At concentrations between 1500 and 3000mg/ l and pH greater than 7.4,
ammonia can become inhibitory. At concentrations above 3000mg/ l, the
ammonium ion itself becomes inhibitory regardless of pH (Singh, 1977).
2.7.10 Temperature
Micro organisms display a wide variety of responses to temperature
and therefore, are classified into three groups according to the temperature
range in which they function best. Generally, bacteria that grow best at lower
than 20oC are identified as psychrophiles; those that prefer temperature
higher than 45oC are called thermophiles while those that grow best at
temperature between 20oC to 35
oC are referred to as mesophiles (Stanley
Associates, 1979).
40
Anaerobic bacteria are believed to be extremely sensitive to
fluctuations in temperature or temperature changes of only a few centigrade
could lead to catastrophic failure, implying that thermal stability is very
important. Although the response of species of microbes to changes in
temperature may be qualitatively similar, they differ quantitatively. For
examples, while all species of anaerobes, such as have been mentioned, are
known to be extremely sensitive to temperature fluctuations, relatively
modest reduction in temperature below the optimum does slow down
methane fermentation more than acid formation (Kugleman and Jeris,1981)
leading to imbalanced conditions. Similarly slight increase in temperature
above the mesophilic optimum of 35oC have been reported to stimulate
methane production to a greater extent than did acid formation (Speece and
Parkin, 1983).
It is also possible to operate anaerobic digesters at thermophilic
temperature ranges although a different microbial specie would be involved
(McCarty, 1964). Thermophilic digestion results in a more rapid reaction rate
and better degradation of the organic (including lipids) at any specific
retention time. It is estimated that 5 to 10% more volatile solids are
degradable at thermophilic range than at other ranges of temperature
(Kugleman and Jeris, 1981). Thus, noted by Pfeffer (1974), and Pfeffer and
41
Liebman (1976), thermophilic temperature is more efficient for effective and
efficient methane fermentation than other temperature ranges. Thermophilic
digestion is also more effective in the destruction of pathogens especially
parasitic works and their ova (Pyle, 1978).
Temperature plays an important role in the rate of digestion, and the
overall running temperature of the digester should be fixed early in the design
stage. The general range of temperature can be mesophilic or thermophilic,
and most digesters run in the mesophilic range, at about 30 - 40oC, below
about 25oC digestion is very slow. In any temperature range what is most
important is to ensure that the temperature is kept uniform, in actual value
and over the digester contents. Sudden change in digester temperature of
even 5oC can cause drastic oscillations, in bacterial metabolism and gas
production and the bacteria can take days to recover (Subba, 1998).
In a number of papers published recently, the “psychrolidic digestion”
in temperature of 10o
- 25oC is reported (Wellinger, Fao 1989) using the
UASB – reactor, it could be demonstrated that, at temperature as low as
10oC, digestion was successful. The start up temperature digestion is one of
the major constraints for the application of this technic (Wellinger, 1989).
Furthermore, gas yield tends to increase with temperature. Below 40oC the
mesophilic bacteria are more active and best yield are for temperature in the
42
range of 30 -40oC. To maintain this temperature in cold whether, part of the
gas produced in utilized for slurry heating. Above (40 - 60oC) the
thermophilic bacteria are more active. The bacteria can be very sensitive to
changes in their environment. Temperature is a prime example, it has been
determined that 35oC is an ideal temperature for anaerobic digestion. As the
temperature falls, bacteria activity decreases, and production decreases. As
the temperature increases some bacteria begin to die, once again biogas
production decreases (www.ce.uf.edu/activities/waste/weddsty.hfml)
2.7.11 pH and Alkalinity
Anaerobic bacteria are quite sensitive to changes in pH. In particular,
the methane formers, especially the hydrogen-utilizing species show a very
low degree of tolerance of pH changes. The optimum pH range is 7.0 to 7.2
(Blanchard and Gills, 1987). However, a pH range of 6.5 to 7.7 is generally
within the satisfactory range (Singh, 1977; Grandy and Lim, 1980). A pH of
less than 6.0 or greater than 8.0 rapidly inhibits ethanogenesis under most
operating condition (Blanchard and Gills, 1987).
Rapid changes in pH can result due to fluctuation in temperature or
loading rate which may result in rapid production of volatile acid with the
resultant inhibition of methanogens. It may also occur as a result of
temporary presence of inhibitor and toxicants. Fluctuation in pH can be
43
accommodated through proper control of temperature and/or loading rate and
adequate mixing. However, effective and tight control of pH required the
availability of sufficient alkalinity to form buffer in the system.
Alkalinity is a measure of the buffering capacity of the digester
content and consists of bicarbonate, carbonate and hydroxide components
(Hashimoto et al., 1979). Buffers usually form naturally in anaerobic systems
through the production of CO2 and through the release of positively charged
ions such as ammonium ions and cations of acids into the solution. If wastes
contain carbohydrate only, buffer formation may not take place because
cations are not released in the decomposition of carbohydrates (Kugleman
and Jeris, 1981). It is important to have sufficient buffer to maintain the pH
as close to 7.0 as possible because organic acids are always formed during
anaerobic decomposition of organics.
On pH, three laboratory digesters were used in ratio 1:1 cow dung to
water then buffered with pH of 4, 7and 9 and digesters firmly sealed to obtain
anaerobic condition pH of 4 is toxic to bacteria. Gas production was low and
latter stopped. Optional gas production is by pH of 7 followed by pH of 9
additives such as ash could be added to reduces the toxicity in waste (Sambo,
1992).
44
2.7.12 Solid – water ratio. The solid – water ratio has great effect on gas
production. The ratio of 1:20 (solid to water) gives higher gas production
than the lower and higher solid – water ratio (Barnett, 1978).
2.7.13 Quality and Characteristics of waste material
Anaerobic digestion is applicable to solid waste collected as fresh or
generally less than seven days old. The solid waste should be free from soil,
and stones and fibrous bedding materials. The quality of solid waste is
affected by the sources of collection. Materials with high cellulose do not
digest well. In most cases materials with high cellulose content act as fitter
and reduce the capacity of the digester to produce gas. Materials that float, to
the top of the digester or sink to the bottom of the digester are undesirable.
Floating materials form scum, and those that sink may clog the bottom of the
reactor. In short, materials that are highly degradable produce more biogas.
2.7.14 Loading Rate
The ability of a digester to convert organic materials into methane is
related to its loading rate. Loading rate is commonly defined as the amount of
volatile solids fed to the digester per day per unit volume of the digester.
Volatile solids are a measure of the amount of digestible organic material in a
feed stock. The loading rate depends on the characteristics of the solids added
45
to the probable biogas yield. In general, materials with high volatile matter
produce more biogas of digester properly.
2.7.15 Carbon nitrogen ratio
The bacteria responsible for the anaerobic process require both
elements, as do all living organisms, but they consume carbon roughly 30
times faster than nitrogen. For favourable conditions of biogas production, a
carbon to nitrogen ratio of about 30:1 is ideal for the raw material fed into a
biogas plant. If the ratio is less than this, losses of nitrogen due to
ammonification may result while the values in excess of 50:1 may slow down
the process of degradation as the micro organisms may go through increasing
number of life cycles before biodegradation may be initiated (Agunwamba,
2001).
2.8 KINETICS OF BIOGAS PRODUCTION
The structural kinetic models for dynamic simulation of the anaerobic
degradation on the different degradation matrix with kinetic constants for
different degradation steps or organic materials in completely stirred tank
reactions (CSTR) is used to predict real process response to specific
operating conditions. However, organic loading rate (OLR) and hydraulic
retention time (HRT) are the parameters applied most frequently in practice.
Methane yield decreases approximately in a straight line with the increase in
46
OLR and decrease in temperature. Methane yield at any hydraulic retention
time as a function of a critical HRT at which the reactor fails, the maximum
methane yield and temperature term calculated from Arrhenius equation. The
Arrhenius equation was based on the production rate of CH4 and H2S as the
products of methanogenic and sulfactor reducing reactions, respectively. For
finding the constants in the Arrhenius equation, first the reaction order was
evaluated from the experimental data gathered in the vials experiments
(Alejandar Castro-Gonzalez, 2002). Results rendered a first order kinetics
equation. Drury (1999) did a work on the modeling of sulfatoreduction on
anaerobic reactor for the treatment of mine waste. He did it an equivalent to
the equation 1 for the sulfareduction. Thus, the equation used for
methanogenesis and sulfareduction were.
CH4 (t) = CH4 max (1 – exp(-k CH4) ------------------(2.1)
Where: CH4 (t) is the cumulative methane production during time t (in ml at
NTP)
CH4 max is the maximum methane production (in ml at NTP);
KCH4 is the first order reaction rate constant for methanogenesis (d-1
);
T is the time (d); and
H2S(t) = H2S max (1-exp (-KH2ST) --------------------------- (2.2)
Where:
47
H2S (t) represent the H2S cumulative production during time t (in ml at NTP)
H2S max is the maximum H2S production (in ml at NTP)
KH2S is the first order reaction rate constant for sulfato –reduction (-d-1
)
t is the time (d).
The rate of methanogensis and sulfacto-reduction are presented as a
function of temperature by the Arrhenius equation:
KV = Ko exp-Ea/RT
---------------------------------------------------- (2.3)
Where:
Ea = reaction activation energy, cal/mol
R = gases universal constant rate constant for methanogases of sulfacto-
reduction, respectively (-d-1
)
The parameters values for CH4 max and k were estimated by the minimum
square using the methane cumulative production (Doucety Sloop, 1992).
Linearizing Equation (2.3) renders a simple way for calculating the constants
as shown in Equation (2.4).
In KV = KoInRT
Eal ---------------------------------------------------- (2.4)
2. 8.1 Design models
For a completely mixed continuous system, Hasimoto el al (1978),
Chem (1983) and Hill (1985) observed that variations of the concentration of
48
active microbial biomass and the rate-limiting substrate can be describes by
Equation (2.5) and (2.6) respectively:
5.2*1
X
SRTu
dt
dx
6.20
Y
xv
HRT
SS
dt
ds
Where:
X = the concentration of active microbial biomass (kgX/m3r)
µ = the specific microbial growth rate, (1/d)
So = The influent concentration of rate limiting substrate (kg VSo/m3r)
HRT = The mean hydraulic retention time, HRT, (d)
SRT = The mean biological solid retention time (d)
S = The concentration of rate-limiting substrate, (kg VS/ m3r)
Y = The microorganism growth yield coefficient, (kgX/Kg VSo)
t = Time (d)
Micro-organism and substrate concentrations do not change under steady
state conditions. That is:
0;0 dt
ds
dt
dx
Eq. (2.5) reduces to Eq. (2.7);
µ = 7.21
SRT
49
and Eq. (2.6) reduces to Eq (2.8)
8.2......................................................................................0
Y
X
HRT
SS
The relationship between the microbial growth rate, µ and the
concentration of the rate limiting substrate, S are given in Eq (2.9).
9.2......................................................................................SXb
Sm
Where:
µm = Maximum growth rate, (1/d)
b = Kinetic parameter; (kg VS/kgX)
by combining the above equations, it can be formulated that
10.2......................................................................................0 K
SRT
HRTHRT
K
S
S
m
With K = Y. b; K = kinetic parameter (dimensionless)
Hashimoto et al (1983) and Chem (1983) have shown that high values
of the K parameter are an indicator of inhibition of microbial activity. The K
parameter is a function of substrate concentration S0 for a high solid
digestion process, the hydraulic retention time, HRT is equal to the solid’
retention time SRT ie. HRT = SRT. Now Eq (2.10) can be re-formulated and
becomes Eq. (2.11).
50
11.2......................................................................................10 KHRT
K
S
S
m
In the above equations, the death rate of micro-organisms is not
included. In the case of high solids digestion process with high HRT, the
death rate should be considered.
Equation (2.1) becomes Eq. (2.8) (Tentcher, 1994)
With KD (specific death rate) (1/d), and Eq. (2.12) becomes Eq (2.13)
KHRTKHRT
HRTKK
S
S
HRTK
dt
dx
Dm
D
D
11
1
12.2......................................................................................1
0
`
Andrews (1975) and Hill et al., (1977), have shown that the maximum
value of KD is equal to 0.1 of the value µm (Hill, 1982). Hence Eq (2.13) can be
reformulated as given in Eq. (2.14):
14.2.............................................................11.01
1.01
0 KHRTHRT
HRTK
S
S
m
m
It is clear that if B is the methane yield (Nm3 CH4/KgVS0 and Bo is the
ultimate methane yield, (Nm3CH4/KgVS0), the relationship between B, Bo, S
and So can be formulated as given in Eq. (2.14).
16.2.......................)1()1.01(
1.01(1
15.2.......................................................................................
0
0
0
0
kxHRTxMHRTx
xHRTxKBB
S
SS
BB
mm
51
The steady-state volumetric methane production rate (Nm3CH4/M3r/d) is
given in Eq. (2.17)
Equation (2.17) is the considered basic equation to describe the
methane production kinetics of a digester.
17.2...................1**1.01*
**1.01*1
*, 00
4
KHRTHRT
HRTK
HRT
BSCHr
mm
mr
2.8.2 Stoichiometric Models
The amount of biogas (methane and carbon dioxide) produceable
from a waste of sample of known chemical composition can be estimated
from the stoichiometry of the overall anaerobic reaction involved. Bushwell
and Muchler (1962) presented a simplified general formula for anaerobic
conversion of typical substrate of the form CnHaOb to methane and carbon
dioxide.
18.2.................................................................................482
4820
24 OHC
4
22baa
CHban
COban
Hba
n
Where:
n = the number of carbon atoms contained in a molecule of organic
substance.
52
a = hydrogen
b = oxygen
Bushwell’s formula can be used to calculate the theoretical yield of
methane by an organic compound composed of carbon, hydrogen and
oxygen and with know molecular formula. To find out the theoretical yield
of biogas by a gram of an organic substance, one must first calculate the
number of gram molecules contained in a gram of this organic substance. to
calculate the theoretical yield of biogas by a gram of an organic substance,
one can simplify Bushwell’s formula as follows:
M
x1
4.22 19.2............................................................................482
ban
In this formula, M = molecular weight of the organic substance.
Under standard temperature and pressure (00C, 101,325Pa), the volume of
methane produced by a gram of an organic substance equals:
20.2..................................482
4.22
482
14.22
ban
M
ban
Mx
Also, volume of carbon dioxide can be deduced from the following
example:
21.2.........................................................................482
4.22litres
ban
M
53
The theoretical yield of CH4 and CO2 form a gram of acetic acid
(CH3COOH) as shown in Eq. (2.18) given that the mol. Weight of CH3COOH is
60 and the volume of CO2
23.2..........................................373.04
2
8
4
2
2
60
4.220
22.2.........................................................373..04
2
8
4
2
2
60
4.22
2
C
In practice, besides the organic substances composed of the
elements, carbon dioxide, hydrogen and oxygen, other substances like
sodium acetate (NaAc), and calcium acetate (Ca (AC)2) are also used to
produce biogas through fermentation. However, Bushwel’s formula cannot
be used directly to calculate the theoretical yield of biogas. But NaAc and
Ca(Ac)2 can ionize completely in water. NaAc ionizes completely in water to
give: Na+ and Ac in its water solution; water ionizes weakly into H+ and OH.
NaAc → Na+Ac-
H2O → OH-+H++
The chemical equation is expressed as follows:
NaAc + H2O → NaOH + HAc
With this chemical equation, Bushwell’s formula to calculate the theoretical
yield of biogas by HAc and then NaAc, can be used. For example, the
54
theoretical yield of methane by a gram of NaAc is calculated by noting that
the molecular weight of NaAc = 82.
The chemical equation of the hydrolysis of a gram of NaAc is:
NaAc + H2O → NaOH + HAC
82 60
1 x
732.082
60x
The theoretical yields of biogas by some common organic substances are
shown in Table 2.5.
Table 2.5: The theoretical yields of biogas by some common organic
substances
Organic substance Molecular formula Molecular
weight
Yield CH4per
gram (1/g)
Yield of CO2 per
gram (1/g)
Formic acid
Acetic acid
Propionic acid
Butyric acid
Sodium formate
Sodium acetate
Sodium
propionate
Sodium butyrate
HCOOH
CH3COOH
CH3CH2COOH
CH3(CH2)COOH
HCOONa
CH3COONa
CH3CH2COONa
CH3(CH2)2COONa
CH3OH
46
60
74
88
68
82
96
110
32
0.122
0.373
0.530
0.636
0.83
0.273
0.409
0.509
0.525
0.365
0.373
0.378
0.382
0.247
0.273
0.291
0.306
0.175
55
Methanol
Ethanol
Glucose
Sucrose
CH3CH2O6
C6H12O6
C12H2O11
46
180
342
0.730
0.373
0.393
0.244
0.373
0.393
Source: Yongfu (1989). The biogas technology in China, Chengdu
Biogas Research and training centre, Chenghu China Pp. 45-48.
Bushwell’s formula can be applied to calculate the theoretical yield of biogas
by the simple organic substances and that of the complex organic
substances as well. The theoretical yields of biogas by carbohydrate, protein
and lipid are shown in Table 2.6.
Table 2.6: Theoretical yields of biogas by carbohydrate, protein and lipid
Component Methane yield of CH4/g (1/g) C02 Yield of CO2/g (1/g)
Carbohydrate
Protein
Lipid
0.37
0.49
1.04
0.37
0.47
0.36
Source: Yongfu (1989): Biogas Tech: the Asian-Pacific Examples. Agric
Publishing house, Belgin, China, Pp. 22.
For wastes of the form CnHaObNc such as protein, Peavy et al. (1988)
gave the following formula:
56
19.28
3482482
04
324
2242 NCOdcba
CHcba
Hdcb
nNOHC eban
The above stoichiometric relationship do n’ot take into account the fact that
a portion of the substrate is converted into cells. It therefore, gives the
theoretical maximum yield. The rate of methane production can also be
estimated by calculating the methane equivalent of the net COD reduction.
i.e. total COD reduced minus COD converted to biomass. The relevant
equation is given by Kugleman and Jeris (1981) and Benefield and Randfall
(1980) as follow:
Y = Y0 *∆S – 1.4∆x+……………………………………(2.24)
Where:
Y = methane production rate (1/day);
Y0 = litres of methane produced per gram COD at STP = 0.351/g
(COD at STP);
∆S = ultimate COD removal rate (g/d) = Q (S0 – S);
S0-S = COD reduction (g/1);
∆X = daily biomass production (g cell/ultimate BOD; and
1.42 = ultimate BOD per gram of cell).
57
In terms of volume per unit volume of the digester, CH4 production rate can
be estimated using the relationship developed by Chem and Hashimoto
(1979a); that is
25.2..............................................................1
100
Km
KSY
ny
This is the same as Equation (2.13)
Where:
Yy = volumetric methane yield (LCH4/1 of digester Vol/day)
= ultimate CH4 yield L/g vs added as retention time tends to 1
S0 = influent total vs concentration (g/1); and
µm = maximum specific growth rate d-1.
2.8.3 Model Trend
Buswell and Mueller (1962) developed a model that predicts methane
production from chemical composition of degradable waste. The model is
expressed as:
26.2.........................48248224
422 CHban
COban
OHba
nOHC ban
Where: CnHaOb is organic matter, H2O is water, CO2 is carbon dioxide, CH4 is
methane, a, b, and n are dimensionless coefficients.
58
Jewell (1978) developed an empirical model for biogas production for a
plug- flow digester and is expressed as:
BGmethrone = 05 (Sbo – Sb1 HRT………………………………….(2.27)
Where Sbo is influent biodegradable volatile solides (BVS) concentration
(g/L), Sb1 is effluent BVS concentration (g/L), HRT is hydraulic retention time
(days), and BGmethrone is the volumetric methane production rate: volume of
gas produced per digester volume per day (L/L*day).
Chen and Hashimoto (1978) developed a model that predicts methane
production rate and is expressed as:
28.2.........................................................1
1*
KHRT
K
HRT
SBY
m
ooy
Where: Yy is methane production rate (L of CH4 per L digester volume
per day), B0 is ultimate methane yield (LCH4/g VS added), S0 is influent
volatile solid concentration (g/L), K is kinetic parameter (dimensionless), and
µm is maximum specific growth rate (day-1). The K parameter was empirically
determined from:
K = 0.06 + 0.0206e 0.051.S0…………………………………….. (2.29)
The µm value was calculated from (Hashimoto et al., (1981):
µm = 0.013*T-0.129……………………………………… (2.30)
59
Where: T is digester temperature (oC)
Bryant (1979) studied microbial methane production. He investigated
the relationship of three general methabolic groups of bacteria or stages of
fermentation. The three metabolic groups of bacteria include: first-stage-
fermentative bacteria, second-stage-H2-producing acetogenic bacteria, and
stochiometry and kinetic of formation.
Hill (1982a, 1982b, and 1982c) performed computer analysis of
microbial kinetics of methane fermentation to show: (a) maximum
volumetric methane production, and (b) maximum total daily methane
production to design the continuous flow anaerobic digester. He analyzed
methane fermentation kinetic to produce a set of optimized design criteria
for steady-state digestion, and developed a dynamic computer model to
predict digester operating conditions (i.e., retention time, loading rate, and
temperature) for four major animal types (diary, poultry, swine, and beef).
Hashimoto (1983) studied the effects of temperature (350C and 550C),
influent volatile solid concentration and hydraulic retention time on
methane production from swine manure. Hashimoto (1984) experimentally
determined the K parameter specific for swine manure. Later, Hashimoto et
al. (1994) discussed about commercializing the technology of methane
60
production from animal waste, and described the design and construction of
a centralized anaerobic digestion facility that converts dairy manure into
electrical energy and fertilizer.
2.9 MAXIMUM LIKELIHOOD
Because biogas production is a time dependence, the stochastic
differential equations often provide a convenient way to describe the
dynamics of economic and financial data, and a great deal of effort has been
expended searching for efficient ways to estimate models based on them.
Maximum likelihood is typically the estimator of choice; however, because
the density is generally unknown, one is forced to approximate it. The
simulation – based approach suggested by Pederson (1995) has great
theoretical appeal, but previously available implementations have been
computationally costly. Burham and Gallant (2001) examine a variety of
numerical techniques to improve the design and performance of this
approach. Maximum likelihood estimation for size – biased distributions of
the form considered here also follows directly from the equal probability
case. In general, the log likelihood for the size – biased is distributions of the
form considered here also follows directly from the equal probability case.
61
In general, the log likelihood for the size – biased is
n
i
vnoxifIn1
n
1i
1 ln; xIn *yIn
As pointed out by Van Deusen (1986) the first term is a constant and
may be dropped if desired, the second term is the usual (equal probability)
log – likelihood, in s and the third term is a correction term accounting for
the fact that observations were not drawn with equal probability. Rather
than numerically maximizing in y* directly, it is often more useful to have
first and second – order derivative information for Newton-type algorithms
and for variance estimation via the Hessian.
Other maximum likelihood estimation by Wonnacott and Wonnacott
(1977), assume normally distributed error in order to derive the maximum
likelihood estimates of α and β. That is, those hypothetical population
values of α and β that generate the greatest probability for the sample
values observed. The maximum likelihood estimate (MLE) of α and β turn
out to be the least squares.
In order to specify how well is the maximum likelihood, assume for
now a set of three fixed x values (x1, x2, x3), which have generated a sample
of three observations (y1, y2, y3). The likelihood that such a population would
62
give rise to the sample observed is the joint probability density of the
particular set of three “e” values. Geometrically, by moving the regression
line and its surrounding e distribution through all possible positions in space,
each position involves a different set of trial values for α and β. In each case
the likelihood of observing y1, y2, y3 would be evaluated.
For generality, suppose a sample of size n, rather than just three, we
wish to know p (y1, y2---yn the likelihood or probability density of the sample
observed is expressed as a function of the possible population values of α, β
and δ2.
Consider the probability density of the value of y, which is 22 p(y1)
(1/2 δ2)(y1-(2+βα1)]2
For a given y, s or y1s or what the various values of α, β and δ2 can be
evaluated as:
31.2.........................................2
21
2
1( L
2
12/2xiye
n
The maximum likelihood estimates can be obtained by choosing α and β.
32.2.........................................2
1, L
2
12
1
2/221
2
xiyexxxpn
n
63
2.10 METHOD OF MOMENTS ESTIMATION
The moment equations under size – biased sampling require the raw
moments of the size – biased distribution. These moments are simple ratios
of the moments of the equal probability forms, define vα, as the yth raw
moment of the size biased distribution of order α.:
dxxLxfvv )(221
1
Modified moment equations can be developed using the first moment and
the coefficient of variation; this scheme may be preferable because there is
one equation to solve for one unknown, simplifying estimation as in the
equal probability case, Cohen (1965).
The variance of a size biased random variables of order is given as:
211)12(12)( vvXxVar
The coefficient of variation is defined as the square root of the
variance divided by the mean. In general, the coefficient of variation for the
size biased distribution of order α is T2* =
x
XxVar )(
.1
momentrthecalledN
xx th
rn
j
r
j
64
The first moment with r = 1 is the arithmetic mean x. the rth moment
about the mean x is defined as
)33.2..(..................................................)(
)(1
7
N
xxxxM
rr
n
j
r
jr
2.11 REGRESSION
Many engineering and scientific problems are concerned with
determining a relationship between a set of variables. For instance in a
chemical process one may be interested in the relationship between the
output of the process, the temperature at which it occurs and the amount of
catalyst employed. In many situations, there is a single response variable Y,
also called the dependent variables and independent variables x1- - - xr. The
simplest type of relationship between the dependent variable y and the
input variables x1, - - - xr is a linear relationship. That is, for some constants
β0, β1, - - - - βr the equation (Rose, 2004).
Y = β0, + β1x1 + - - - - + βrxr,
2.11.1 Multiple Linear Regression
The vector – matrix approach proposed in the preceding section
provides a smooth transition from simple linear regression to linear
65
regression involving more than one independent variables. In multiple linear
regression, the model takes the form E ,Y- = β0 + β1x1 + β2x2 + - - - - + βmxm.
Again, we assume that the variance of Y is δ and is independence of
x1, x2 - - - , and xm. As in simple linear regression, we are interested in
estimating (m + 1) regression coefficients β0, β1 - - - , and βm, obtaining
certain interval estimates, and testing hypotheses about these parameters
on the basis of a sample of Y values with their associated values of (x1, x2, - -
- , xm). Suppose our sample of size n in this case takes the form of arrays xii,
x21 - - - - xml, Y1), (X21, x22, - - - -, Xm2, Y2), - - - - (Xn1, Xn2- - - - xnm, yn, (X12, X22, - -
- -, Xm2, Ys), - - - - (X1n, X2n - - - - xmn, Yn). For each set of values X, k = 1,2, - - - -,
m, of xi, y is an independent observation from population Y defined by Y =
β0, + β1x1 + - - - - + βmxm. + E, Soong (2004).
Where E is the random error, with mean x and variance δ2
Multiple regression is one of the fussier of the statistical techniques. It
makes a number of assumptions about the data, and it is not that they are
violated. It is not the technique to use on small samples, where the
distribution of scorers is very sknewed, according to Tabachnick and Fidell,
(1996).
66
A regression equation for estimating a dependent variable, say x1,
from independent variables x2, x3, …. Is called a regression equation of x1 on
x2, x3… and like that; for three variables, it is given by
X1 = a + bx2 + cx3 …………………………………….(2.34)
The constants, a b and c can be determined by the method of lest
squares. The least square regression plane of x1 on x2 and x3 can be
determined by solving simultaneously the three normal equations.
2
332331
32
2
2221
321
xcxxbxaxx
xxcxbxaxx
xcxbanx
Where n is the set of data points (x1, x2, x3)
The coefficient of multiple correlation x1 with respect to x2 and x3 is
given by
)36.2(....................
3
2
1
23.1
n
xxS
lest
Where xlest = value of x1 for the given values of x2 and x3 is given by
)37.2(....................1
2
1
2
23.123.1
SR
Where: σ1 = standard deviation of x1 and r2 1.23 is called the coefficient of
multiple determination. The value of r2 1.23 lies between 0 and 1. Also
67
21
2121
12
2
13
2
12
2
23.1
2
23
231312
2
12
2
122
23.1
1:
39.2..............................1)(1(1
)38.2.........(....................1
2
n
xnxxxrwhere
rrr
r
rrrrrr
r12 = the linear correlation coefficient between he variables x1 and x2,
and ignoring the variable x3; and similarly r13 and r23, r12 r13, r23 are partial
correlation coefficients.
From Eq. (2.38), we have:
40.2..........................................11 2
23.123.1 rS
68
CHAPTER THREE
METHODOLOGY
3.1 SOURCES OF DATA
The data for the analysis of this study was obtained from unpublished
Ph.D dissertation by Ugwuishiwu (2009). The model obtained was verified
by data obtained from a published journal article by Bamgboye (1994) and
Abdul-Rahman (2009) of University of Ibadan, and World Academy of
science engineering and technology.
3.2 USE OF STATISTICAL TOOLS FOR ANALYSIS
The statistical tools that is going to be used for this analysis is the
regression analysis method for the purpose of establishing a formula that
will estimate the predicted yield of gas that will be compared with the
measured yield of gas.
3.2.1 Multiple Regression Analysis
Many engineering and scientific problems are concerned with
determining a relationship between a set of variables. The regression
method will describe the set of dependent variables of gas yield, y on
independent variable of time, x. The regression coefficients can be
69
estimated from the set of data to formulate the equations that can be used
to estimate the predicted yield of gas.
70
3.2.3 Relationships between regression constants and design variables
In C = Ina1 + In a - a2 2 -----------------------------------------------------(3.1)
C = eIna In - a2 2 --------------------------------------------------- -(3.2)
C = e 22 aIna -------------------------------------------------------(3.3)
C = 2
2
1
aaea --------------------------------------------------------- (3.4)
From Equation (3.1);
In C = 2
21 aaInIna ------------------------------------------------- (3.5)
Y = 22120 XX -------------------------------------------------- (3.6)
This implies that
Y = 110 ,, aInaInC
X1 = 2
2,22 XaandIn
Where:
C = Gas yield
a1 = Function of strength of waste, waste characteristics, rate of
biodegradation.
a2 = Function of size of reactor
Detention time
71
3.3 IMPORTANCE TO DESIGN
Because there are no kinetic equations available for design, it will help to
be necessary generate an equivalent design equation the equation for
design and
Provide the best method for estimation of yield.
Several existing models do not predict measured values well. Hence, the
need for better predictive models.
3.4 MODLE PERFORMANCE
The performances of the model developed in this study were assessed
using various standard statistical performance evaluation criteria. The
statistical measures considered were multiple correlation coefficients
(MCC), standard error of estimate (SEE), coefficient of correlation (CORR),
mean absolute percentage error (MAPE), and root mean square error
(RMSE). Statistical performance measures are listed in Table 3.1
Table 3:1: List of the performance measures
Statistical parameter Expression
Multiple correlation coefficient (MCC) MCC = yqyp rr 22 111
Standard error of estimate (SEE) SEE = 21 MCCY
72
Coefficient of correlation (CORR) CORR =
n
i
pp
i
n
i
n
i
p
o
yyy
oy
yyy
y
2
2
1
0
1
1
00
1
Mean absolute percentage error
(MAPE)
MAPE = 1001
1 1
11 xy
yy
n
n
io
op
Root means square error (RMSE)
RMSE =
N
yyn
I
po
1
2
11
Where ryp and ryq are the linear correlation coefficient between the
variables y and p as well as y and Q, respectively. σy is the standard
deviation of the dependent variables y. oy1 and oy1 are the observed and
predicted gas yield respectively, po
yandy
are the mean of the observed and
predicted gas yield and n is the number of data points.
73
CHAPTER FOUR
RESULTS AND DISCUSSION
4.1 ANALYSIS
From the design model, attempt was made to determine if the
constants relate to the parameters; like pressure, volatile solids, total viable
count, BOD, COD and Ph. It was observed that no meaningful relationship
could be established except for the temperature at which the yield was
determined; an almost linear relationship could be ascertained. As the
temperature decreases, the volume of the constant, a1 decreases and with
increase in temperature, a1 increases. The reverse was the case for the
constant a2. As temperature increases, a2 decreases and vice versa. The
verifications also show the same kind of relationships between the
constants and the measuring temperature of the resulting gas yield.
The curve-fitted model and the verifications are presented in the
figures below.
The curve fitted model: the single curve fitted model for 1 to iv is C =
17.46θ0.676e-0.0048θ2 ……………………………………………….(4.1)
74
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50
Temperature
a1
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 10 20 30 40 50
Temperature
a2
0
2
4
6
8
10
12
14
16
18
20
24 25 26 27 28
Temperature
a1
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
24 25 26 27 28
Temperature
a2
Fig. 4a and 4b: Relationships between Model Constants and Temperature for The Verification Data
Fig. 4c and 4d: Relationships between Model Constants and Temperature for The Curve Fitting Data
A
B
C
D
Fig. 4.1a Fig. 4.1b
Fig. 4.1c Fig. 4.1d
75
0
20
40
60
80
100
120
7 14 21 28 35 42 49 56 63
Time
Gas Y
ield
Gas Yield
(Measured)
Gas Yield
(Cal)
0
20
40
60
80
100
120
7 14 21 28 35 42 49 56 63
Time
Ga
s Y
ield
Gas Yield
(Measured)
Gas Yield
(Cal)
Fig.4.1: Comparison between Measured and calculated data for Biogas Plant 1
Fig.4.2: Comparison between Measured and Calculated Data for Biogas Plant 2
76
0
20
40
60
80
100
120
140
7 14 21 28 35 42 49 56
Time
Gas Y
ield
Gas Yield
Measured)
Gas Yield
(Cal)
0
20
40
60
80
100
120
7 14 21 28 35 42 49 56 63
Time
Gas Y
ield
Gas Yield
(measured)
Gas Yield
(Cal)
Fig.4.3: Comparison between Measured and Calculated Data for Biogas Plant 3
Fig.4.4: Comparison between Measured and Calculated Data for Biogas Plant 4
77
0
20
40
60
80
100
120
3 5.4 9 12.6 15
Time
Gas Y
ield
gas Yield(Measured)
Gas Yield(Cal)
0
20
40
60
80
100
120
6 7 8 9 10 11 12 13 14 15 16 17
Time
Gas Y
ield
Gas Yield(Measured)
Gas Yield(Cal)
Fig.4.5: Comparison between Measured and Calculated Data for Biogas Plant 5
Fig.4.6: Comparison between Measured and Calculated Data for Biogas Plant 6
78
0
20
40
60
80
100
120
3 5.4 9 12.6 15
Time
Gas Y
ield
gas Yield(Measured)
Gas Yield(Cal)
0
20
40
60
80
100
120
6 7 8 9 10 11 12 13 14 15 16 17
Time
Gas Y
ield
Gas Yield(Measured)
Gas Yield(Cal)
Fig.4.5: Comparison between Measured and Calculated Data for Biogas Plant 5
Fig.4.6: Comparison between Measured and Calculated Data for Biogas Plant 6
79
4.2 VERIFICATION OF THE RELATIONSHIPS
The relationship between the measured and the calculated yield of
gas using the data obtained from the literature (Bamgboye, 1994; and
Abdul-Rahman, 2009) can be compared in order to see whether a relation
exists or not (See Table 4.1)
Table 4.1: Models Performance
BIOGAS PLANT CORR MAPE RMSE SEE
I 0.72 2.58 4.21 0.33
II 0.74 2.19 3.21 0.30
III 0.89 2.10 2.62 0.21
IV 0.91 2.08 2.60 0.20
V 0.78 2.17 3.19 0.29
VI 0.71 2.56 4.10 0.31
VII 0.82 2.11 2.65 0.22
VIII 0.79 2.15 3.13 0.28
The model performance for the biogas yield is shown in Table 4.1.
Plants (I-IV) were used as a verification of the established model to check its
performance. The results of the Table 4.1 shows a maximum correlation
80
coefficient of 0.91 in plant IV and a minimum of 0.72 in plant I, all of the
curve fitting data with an average errors of estimates of 0.26, 3.16, and 2.24
for SEE, RMSE and MAPE, respectively. The verification data of plants (V-VIII)
gave significant comparison with a maximum correlation coefficient of 0.82
in plant VII and a minimum of 0.71 in plant VI. This is also followed with an
estimation errors average of 0.28, 3.27 and 2.25 for SEE, RMSE and MAPE,
respectively.
81
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
5.1 CONCLUSION
In general, the developed model was observed to give a fair
comparison judging from the fact that both the curve fitting model and the
verifications gave similar results from the statistical measuring tools of
performance even though the analytical data were of diverse sources. This
singular fact demonstrates that the yield of biogas is significantly affected by
the detention time in which the waste is subjected during biodegradation as
suggested by the model. The relationship between the measured and the
predicted biogas yield was good and approximate except for a few
outrageous diversions, notwithstanding, a good correlation coefficient
average of 0.80 was obtained in all.
5.2 RECOMEDNATION
No doubt, the model gave good estimation of biogas yield irrespective
of the data source. It is recommended for application in real design.
82
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90
APPENDIX
EXPERIMENTAL RESULTS
PLANT 1
Θ C measured C calculated
7 45.80 63.55
14 90.50 94.62
21 101.70 110.65
28 107.20 114.00
35 102.60 107.27
42 90.40 93.68
49 72.30 76.58
56 50.60 58.90
63 38.00 42.76
91
PLANT III
T C measured C calculated
7 26.2 63.55
14 54.5 94.63
21 84 110.65
28 116.2 114.00
35 95 107.27
42 49.6 93.68
49 28.8 76.58
56 20.5 58.90
92
PLANT VI
T C measured C calculated
7 20.3 63.55
14 48.7 94.62
21 66.3 110.65
28 97.6 114.00
35 70.8 107.27
42 48.4 93.68
49 39.7 76.58
56 25.3 58.90
63 16.9 42.76
93
PLANT V
Θ C measured C calculated
3.0 20.60 36.53
5.4 30.30 53.83
9.0 50.40 74.17
12.6 75.60 89.70
15.0 80.80 97.76
PLANT VI
Θ C measured C calculated
6 50.25 57.62
7 60.30 63.55
8 63.31 69.05
9 70.33 74.17
10 74.37 78.92
11 78.42 83.33
12 82.46 87.41
13 80.43 91.17
94
14 77.40 94.62
15 67.31 97.76
16 62.26 100.62
17 55.19 103.18
PLANT VII
Θ C measured C calculated
11 80.32 83.33
12 83.35 87.41
13 88.48 91.17
14 91.56 74.62
15 93.60 97.76
16 89.56 100.62
17 85.52 103.18
18 79.46 105.45
19 75.42 107.46
95
PLANT VIII
Θ C measured C calculated
15 92.28 97.76
16 96.32 100.62
17 100.36 103.18
18 102.40 105.45
19 104.46 107.46
20 98.40 109.18
21 98.40 110.65
22 94.36 11.85
23 91.33 11.80
[ ncYXnX 1&,1 22
1 ]
56.5874 = 19 210 68.17144621.40
120.3937 = 40.4621 2210 6759.40268.17140449.89
5083.4572 = 1714.68 210 1728.975,2136759.4026.89
00048.0,676.0,9085.2 210
96
C = 2
21 aea a
Ina1 = 9085.20 a1 = 17.46
= 676.01
- a2 = 00048.02
[C = 17.46 200048.0676.0 e ]