i

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

i

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)

ii

DEDICATION

This work is dedicated to Almighty ALLAH.

iii

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.

iv

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.

v

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

vi

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

vii

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

viii

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

1

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

2

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.

3

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

4

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;

5

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.

6

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.

7

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).

8

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

9

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

10

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

11

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

12

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

13

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).

14

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).

15

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

16

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

17

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

18

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.

19

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,

20

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

21

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

22

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

REFERENCES

Ahmed T. Sulaiman: (2001). Focusing on Renewable Energy Sources in Nigeria’s Developmental Strategy. Keynote Address at a National Workshop on Creating Demand and Removing Barriers to Renewable Energy Market Development in Nigeria, Sheraton Hotels and Towers Abuja, N.c. 13-14.

Aliyu, M.; Dangoggo, S. M. and Atiku (1995). Biogas Production from Pigeon

Droppings. Nigeria Journal of Solar Energy. 13,45. Amon, Th., V. Kryvosrucko, B. Amon, G. Moitzi, D. Lyson, E. Hackl, D Jeremic,

W. Zollitsch, and Milk Yield by Dairy Cows. J. Dairy Sci. 84:2217-2226. Anaerobic Digestion: Making Energy and Solving Modern Wastes Problem. Anaerobic Digestion: Making Energy Solving and Solving Modern Wastes

Problems Edited by Henrik. Andara, A. R. and J. M. L. Esteban. 1999. Kinetic Study of the Anaerobic

Digestion of the Solid Fraction of Piggery Slurry. Biomass and Bioenergy. 17.435-443

Andrew, J. K (1975), Dynamic Models for the Anaerobic Digestion Process. J.

San. Engineering Dic. Asce 25 (SAI): 95-116. Angelidaki, I., L. Ellegard and B. K. Ahring (1999). “A Comprehensive Model

of Anaerobic System. Biotechnology and Bioengineering. 63.363 AOAC (1990). Official Methods of Analysis of Assoc. Office Anal. Chemistry,

14th Edu. Arlinton, Virginia 22209. APHA (1992). Standard Methods for Examination of Water and Wastes

Water. ASAE Standard (1986) American Association of Agic. Eng’ng Livestock

Wastes Management. 4th Internatioal Symposum on livestock Wastes, Michigan. U. S. A. 150-166.

83

Axaopulos, P., P. Panagakis, A. Tsavdaris, and D. Georgakakis, (2001). Simulation and Experimental Performance of a Solar-Heated Anaerobic Digester. Solar Energy 7092) 155-164.

Balch W.E, Fox G. E, Magrum LJ, Woese CR, Wolfe RS (1979). Methanogens:

Re-evaluation. Barlet, H. D. 91978). Nutrient Change During Storage of Anaerobic Digester

Effluent. Asae No. 78-4563 AM. Soc, Agric Eng’ng. Michigan, U. S. A. Batstone, D. J. et al. (2001). The IWA Anaerobic Digestion Model No 1

(ADM), the World Congress “Anaerobic Digestion, Antwerpen, Sept 2-6.

Beccari, M., Bonemazzi, F., Majone, M. and Ricarddi, C. (1996) Interaction

Between Acidogenesis and Methanogenesis in the Anaerobic Treatment. Prentice- Hall Inc. Englewood, Cliffs, N. J. pp.124.

Ben-Hassan, R.C. (1986). Continuous production of biogas from design

manure using a No-mix innovative anaerobic digester. Unpublished M. Sc Thesis TUNS, Halifax Biochem. 32:509-513.

Blanchard, J. P. (1987). Methane production by continuous digestion of

wastes. In: D. I. (ed.). Global Bioconversion Vol. 1 CRC Press Inc. Florida.

Blumensaat, F. and J. Keller 2005. Modeling of two-stage anaerobic

digestion using the IWA Anaerobic Digestion Model No. 1 (ADMI). Water Research. 39.171-183.

Bockhorst, R.H. and Pos, J. (1980). Livestock Wastes: A Renewable Resource.

Proceedings of the 4th International Symposium on Livestock Wastes. Michigan, 81-121.

84

Boone, D. R. & Bryant, M. P. (1989). Diffusion of the Interspecies Electron Carriers 11 Ion and Formate in Methanogenic Ecosystems and its Implications in the Measurement of Km for H Ion or Formate Uptake. Appl Environ Microbio 55,1735-1741.

Brodman John, (2001) U. S. Energy Challenges and Opportunities. A Paper

Presented at a National Workshop on Creating Demand and Removing Barriers to Renewable Energy Market Development in Nigeria, Sheraton Hotels and Towers Abuja, Nov. 13-14.

BRTC (1994) Biogas Research and Training Centre, Chengdu, China. Unpubl.

Training manual on Biogas Technology. Bryant, M.P (1976). Nutritional Requirements of Methanogenic Bacteria. In:

R. F. Gould (ed). Anaerobic Biol. Proc., Advanced Chem. Series 105. Am. Chem. Soc. Washington.

Bushwell, A. M. and Mueller, M. F. (1962). Mechanism of Methane

Fermentation Industrial and Engineering Chemistry 44:450. Cary. F. (2003) Possible solution to Project: Anaerobic Digester. www.

Epa.Gov/agstar, pp4. Chen, R.C. (1979). Up to Date Status of Anaerobic Technology in China.

Proceedings 3rd Int’l Symp. Anaerobic Digestion. Boston Massachusetts. 415.

Chen, Y.R. and Hashimoto, A.G. (1979a). Kinetics of Methane production. Proceedings of Symposium. Biotechnology in Energy Production and Conversation. Scott C.D (ed.). John Willley, New York, PP. 267

Chen, Y.R. and Hashimoto, A.G. (1989) Energy Requirement for Anaerobic

fermentation. Proc. Symp. Biotech. In Energy Production and Conservation. Scott. C.D Scot (ed.). John Willey, New York.

Cherenmisinoff, P.N and Morresi, A.C (1976), Energy from solid wastes.

Mercel Inc. New York.

85

Chynoweth, D.P., Turick, C.E., Owens, J.M., Jerger, D.E & Peck, M.W. 1993. Combs. D.K. (1998). Comparison of Corn Silage Hybrids for Yield, Nutrient Composition. In Vitro Digestibility, Concentrations in Methonogenic Soils and sediments. FEMS Microbiology.

Converse, J.C; Evans, G.W and Robinson, K.L (1981). Production from Large –

size on farm digester for poultry manure. Proc. 4th Int’l Conf. Livestock Wastes. ASAE Publ. No. 2 -81. Am. Soc. Agric. Engr. St Joseph’s Michigan, U.S.A.

Converti, A., A.D. Borghi, S. Arni, and F. Molinari, (1999). Linearized Kinetic

Models for the simulation of the mesophilic Anaerobic Digestion of pre-Hydrolyzed Woody Waste. Chemical Engineering Technology.

Costello, D.J., P.F. Grenfield, and P.L. Lee. 1991a. Dynamics modeling of a

single-stage high-rate anaerobic reactor-II. Model verification. Water Research. 35(7):859-871.

Cowly, I.D and Wase, D.J. (1984). Anaerobic digestion of farm wastes. A

review of part 1. Proc. Biochem. 6(5):28-83. CRC (1980). Canadian Research Council. Anaerobic Digestion: Principles and

Practices for biogas systems, World Bank, New York. 2-9. Dilwyn E. and Mike, H. (1989). Guide to Mathematical Modeling, School of

Mathematics and Computing, Thames polytechnic, London SE18GPF. Dioha, J.I, Umar, M.K; Eboaty, A.N and Okoye, P.A.C. (2005). Comparative

Studies of the Yield of Biogas from cow Dung and Poultry Droppings. Nigeria Journal of Solar Energy. Vol. 15 pp 60-66 Solar Energy Society of Nigeria.

Dubrovskis, V, Viesturs, U., (1998) “Anaerobic Digestion of Agricultural

Waste.” Zinathe Publishing House, Riga, (in Russian). EEA (2003) European Environmental Assessment Report no. 10, European

Environment Agency, Copenhagen 2003 – ISBN 92-9167-574-1.

86

EEG (2000). Gesetz fur den vorragen Erneuerbarer Energien Erneuerbare-Energien-Gesetz (29.03.2000), BGBI. I 2000, 305 ff. Energiepflanzen Mais and Kleegras. Forstwirtschaft, Umwelt und Wasserwirtschaft. Forschungsprojek Nr. 1249 GZ 24.002/59-HAI/01.

EPA (1987). Environmental Protection Agency, biogas Technology- a Relief to

Forest Destruction. A Bulletin of the EPA, Washington, U.S.A. P.3 – 9. Eze J.I, (2003). Some Factors Affecting Biogas Production. Nigeria Journal of

Solar Energy. Solar Energy Society of Nigeria. ISSN:0794-9537. FAO, (1997). Renewable Biological Systems for Alternative Sustainable

Energy Production, (FAO Agricultural Services Bulletin - 128). FAO/CMS A (1996) System Approach to Biogas Technology from “Biogas

Farming System: a sustainable Alternative for the Benefit of the small scale Farmers and the Environment workshop-seminar on Making Better use of Local Feed Resources SAREC-UAF. Fatty Acids in Anaerobic Digestion Process. Biotechnol. Bioeng. 23(7), 157-166.

Fischer, J.R., E.C and Wolfe, and J.H Porter. (1984). Anaerobic Digestion of

Swine Manure at Various Influent solids Concentrations. Agricultural Wastes. 11:157-166

Frazier, E.C and Wolfe, M.N (1978). Biotechnology and Energy Consumption.

TATA McGraw-Hill Publishers. New York, p. 144-149. Fry, L.J., (1973), Methane Gas from Animal droppings. Mimcogr. P.O

Booysens, Johnansburgh. Fuel Gas production from Biomass, pp.19 – 46. Edited by D.L. Wise. Boca Raton, FL: CRC Press.

Grandy, C.P and Lim, C.L (1980). Biological Wastes Water Treatment: Theory

and Applications. Mercei Aekker Inc. New York. Harikishan, J., and S. Sung. (2003). Cattle Waste Treatment and Class a

Biosolid Production Using Temperature-Phased Anaerobic Digester. Advances in Environmental Research. 7:701-706.

87

Harikishian J., and S. Sung. (2003). Cattle Waste Treatment and Class a Biosolid Production Using Temperature-phased Anaerobic Digester. Advances in Environmental Research. 7:701-706.

Hashimoto A. G. (1983). Thermophilic and Mesophilic Anaerobic

Fermentation of Swine Manure. Agricultural Waste. 6:175-191. Hashimoto A. G. (1984). Methane from Swine Manure: Effect of

Temperature and Influent Substrate Concentration on Kinetic Parameter (K). Agricultural Waste. 9:299-308.

Hashimoto A. G., T. G. Edgar, and H. Nakano. (1994). Methane Production

from Animal Wastes. Journal of Soil and Water Conservation. 49 92): 62-68.

Hashimoto, A. G. (1979). Two-Phase System to convert Straw and Manure

Methane ASAE paper No. 84-4092. AM. Soc. Agric. Engr. St. Joseph’s Michigan.

Hashimoto, A. G. Varel, V. H and Prior, R. L (1979). Theoretical Aspect of

Methane Production: Stat-of-the-Art. Proc 4th Int’I conff. Livestock Wastes. ASAE Publ. No. 2-81. AM. Soc. Agric. Engr. Michigan.

Hashimoto, A. G. Varel, V. H. and Cheng, Y. R. (1981). Methane and Protein

Production from Animal Feedstock Wastes. J. Soil and Water Conserv. 3491):16-19.

Hashimoto, A. G; Robinson, S. A. and Cheng, Y. R. (1983). Some Mechanical

Aspects of Anaerobic Digestion of beef manure. Asae Paper No. 82-4052. AM. Soc. Agric. Engr. Michigan.

Hawkes, D. I. (1979). Factors Affecting net Energy production from

Mesophilic Anaerobic Digestion: Proc. At International Conference on Anaerobic Digestion venue of conf. St. Joseph’s …. At Michigan, U. S.A.

88

Heeroo H. R. (2001). International Development Funding Programs for Renewable Energy. A Paper Presented at a National Workshop on Creating Demand and Removing Barriers to Renewable Energy Market Development in Nigeria, Sheraton Holtels and Towers Abuja. Nov. 13-14.

Honemeier, B. (2008). The Impact of Genotype and Harvest Time on Dry

Matter, Biogas and Methane Yields on Maze (Zea maysl). A thesis Submitted in Partial fulfillment of the Requirement for the Degree of Doctor of Agricultural Science (Dr. Agr.0 to the faculty of Agricultural Sciences, Nutritional and Environmental Management, Justus-Liebig-University Geiessen.

IEA (2004). International Energy Agency (Ed.): World Energy Outlook 2004,

International Energy. Karime, K., K. T. Klasson, R. Hoffmann, S.R. Drescher, D.W. Depaoli, and M.H.

Al-Dahhan (2005). Anaerobic digestion of animal waste: effect of mixing. Bioresource Technology. 96: 1607-1612.

Kerezi. S. and Ranja, T (1997) Renewable Energy Technologies in Africa.

Briddles Publisher. Masse D. I., and R.L. Droste (2000). Comprehensive model of anaerobic

digestion of swine manure slurry in a sequencing batch reactor. Waste Research. 34 (12): 3087-3106.

McGrarth, R.J. and I.G Mason (2004). An observational method for the

assessment of biogas production from anaerobic waste stabilization pond treating farm dairy wastewater Biosystems Engineering. 87(4) 471-478.

McGrath R.J., and I.G. Mason. (2004). An observational method for the

assessment of biogas production from an anaerobic waste stabilization pond treating farm dairy wastewater. Biosystems Engineering. 87 (4). 471-478.

89

Metcalf, L. and Eddy, H.P. (2003). Wastes Water Engineering: Treatment, Disposal and Reuse. McGraw-Hill book Co. New York.

Okeke, C. E. (2001), Renewable Energy Technology Development in Nigeria.

Paper presented at a National Workshop on Creating Demand and Removing Barriers to Renewable Energy Market Development in Nigeria, Sheraton Hotels and Towers Abuja, Nov. 13-14.

Sambo A.S (1992) Effect of Operating on Biogas production Rate. Sokoto

Energy Research centre Usman Danfodio University Sokoto PP36 -40. Shoemaker A.M and Visser A. (2000) Treatment of Biogas. AD-NETT-A

Network on anaerobic digestion of Agro-industrial wastes. P: 8-21. Subba N.S (1998) Advance in Agricultural Micro biology Mohan Primtani

Publisher Ltd, New Delhi PP205 – 208. Uzodinma E. O, (2004). Methane production from cow dung. Seminar

presented at National Centre for Energy Research and Development (unpublished).

Vaclav S and Williams E (1990) Energy in the Developing World Oxford press

London PP208. WHO (2005) World Health Organization (Ed.): Energy, Sustainable

development and health. Yougfu (1989) Biogas Tech: the Asian –Pacific Examples. Agric Publishing

House, Belgin, China, PP.22.

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 ]