MODELLING DESIGN OF CONTINUOUS ANAEROBIC DIGESTERS …€¦ · According to Eckenfelder (2000) the...
Transcript of MODELLING DESIGN OF CONTINUOUS ANAEROBIC DIGESTERS …€¦ · According to Eckenfelder (2000) the...
International Journal of Energy and Environmental Research
Vol.5, No.3, pp.42-67, November 2017
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42 ISSN 2055-0197(Print), ISSN 2055-0200(Online)
MODELLING DESIGN OF CONTINUOUS ANAEROBIC DIGESTERS FOR
MUNICIPAL SOLID WASTE IN BIOGAS PRODUCTION
Asinyetogha Hilkiah Igoni* and Ibiye Sepiribo Kingnana Harry
Department of Agricultural & Environmental Engineering, Faculty of Engineering, Rivers
State University of Science and Technology, PMB 5080, Port Harcourt, Nigeria
ABSTRACT: Mathematical models have been developed for the design of anaerobic
continuous digesters for the production of biogas from municipal solid waste (MSW) in Port
Harcourt metropolis, Nigeria. Field and laboratory investigations were conducted and used to
determine the physical, chemical and bio-kinetic properties of the MSW relevant to the digester
design. The design models were simulated for total solids (TS) concentration of 4-10% and
fractional conversion of 0.2-0.8 using Microsoft Visual Basic Version 6.0 program. The
simulation results were analyzed with Microsoft Chart Editor; and mathematical relationships
established between TS concentration and volume of digester; residence time; volume of biogas
produced; net heat required; and cost of digester. It was found that, at maximum fractional
conversion of 0.8, whereas the TS concentration varied directly as the volume of digester, it
was inversely proportional to the time of digestion for the same levels of percentage
stabilization. This is indicative of an accelerated growth rate of microbes with increasing TS
concentration.
KEYWORDS: Continuous Anaerobic Digester; Biogas Production; Municipal Solid Waste;
Waste Management
INTRODUCTION
Municipal Solid Waste Management
The load of municipal solid waste (MSW) in Port Harcourt metropolis, Nigeria has been
estimated at 1,947,134.25kg with a projected population of 1,754,175 persons; and despite this
magnitude of waste the management has been grossly ineffective and inefficient (Igoni, 2016a).
The current MSW management practice in Port Harcourt involves collection, transportation
and disposal of the waste at a dumpsite. Despite the inadequacy of the MSW management
functional elements, the ones that are implemented are also improperly done, as the rate of
generation is always higher than the rate of collection. The absence of a treatment process for
the waste before disposal exacerbates the already debilitating adverse consequences of its
improper collection, transportation and disposal. A treatment option that has become very
attractive is the anaerobic digestion of the waste to generate biogas (Igoni, 2006).
Solid waste is a non-fluid type of waste and this makes its handling and management relatively
difficult, compared to the types of waste that can flow from one location to another, or even
vaporize (Ogunbiyi, 2001). So, MSW, according to Bailie et al (1996) comprises small and
moderately sized solid waste items from houses, businesses, and institutions. It is described as
waste collected by private and public authorities from domestic, commercial and some
industrial (non-hazardous) sources is referred to as municipal solid waste (Kiely, 1998). For
Byrne (1997) MSW is generated from urban areas, particularly houses and shops.
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Following the apparent mismanagement of the MSW in Port Harcourt and the concomitant
adverse impacts on the people and environment, an alternative management procedure that
would consider the reduction of the waste volume and its pollution load would be required.
Igoni et al (2005) investigated the potential of generating biogas from MSW in Port Harcourt
and found that the waste has rich organic content of about 68%, which predisposes it as a
veritable material for the generation of biogas in anaerobic digestion. Therefore, treating the
waste using anaerobic digestion process will not only reduce the waste volume and pollution
load, but also yield an energy source that would mitigate the energy quest of the people.
Processes in Biogas Generation
Biogas is gas given off when organic materials decompose in an anaerobic environment. This
decomposition is either physical or chemical processes at high temperature and/or pressure, or
biological processes using microorganisms at low temperature and atmospheric pressure.
These methods impact on the environment differently, especially in terms of their ability to
reduce waste load. Gas is produce in all the processes, but referred to as biogas when derived
from the biological system (Hobson et al, 1981). Biogas is a colorless, relatively odorless and
inflammable gas, with the following composition (Madu and Sodeinde, 2001), shown in Table
1, that burns with a blue flame and has a heat value of 4500 – 5000 kcal/m2 when its methane
content is in the range of 60 – 70%. It is also stable and non-toxic.
Table 1. Composition of biogas
Constituents % Composition
Methane (CH4) 55 – 75%
Carbon dioxide (CO2) 30 – 45%
Hydrogen Sulphide (H2S) 1 – 2%
Nitrogen (N2) 0 – 1%
Hydrogen (H2) 0 – 1%
Carbon Monoxide (CO) Traces
Oxygen (O2) Traces
The basis of organic waste decomposition
The design of anaerobic digesters is based on the inherent ability of organic materials to
decompose when acted upon by microorganisms in the absence of oxygen. The digester
provides the controlled conditions where the interaction between the waste and microbes
occurs. The bio-kinetic behavior of the MWS influences the pattern of decomposition, and aid
the determination of digester physical parameters. Anaerobic digestion (AD) had been widely
used for the treatment and stabilization of industrial, agricultural and municipal waters and
sludge (Hobson et al, 1981), but Kiely (1998) states that recently anaerobic digestion is also
being applied to the treatment of MSW, with biogas generated only as a “waste product”
Research objective
There are different types of anaerobic digesters for the processing of MSW. To develop an
appropriate bio-digester for MSW in Port Harcourt would require the consideration of the
properties of the MSW. Igoni et al (2006, 2007) have reported on the properties of MSW in
Port Harcourt and relevant to digester designs. There are different types of applicable anaerobic
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bioreactors for MSW processing, including batch, plug-flow and continuously stirred tank
reactors. The objective of this paper is to ease the design of continuously stirred tank reactors
in anaerobic digestion of MSW in Port Harcourt for biogas production, by providing design
models formulated for that purpose.
THEORETICAL FORMULATION
The processes of anaerobic digestion
In anaerobic digestion, facultative anaerobes, described as obligate anaerobes during
methanogenesis decompose the organic material in using it as a food source. Reynolds and
Richards (1996) classified them as (i) liquefaction of solids, (ii) digestion of soluble solids, and
(iii) gas production; and Kiely (1998) identified four different trophic microbiological bacterial
groups operational in AD, and that it is the cumulative effect of all these groups that ensures
process continuity and stability in the three processing stages of i) hydrolysis, ii) acidogenesis
and iii) methanogenesis. Complex organic substrates such as carbohydrates, proteins, fats and
lipids will be hydrolyzed into simpler soluble products, which are further converted into acetic
acid, hydrogen and carbon dioxide.
According to Eckenfelder (2000) the breakdown of carbohydrates, nitrogenous compounds and
fats can be expressed using chemical formula as follows:
𝐶6𝐻12𝑂6 + 2𝐻2𝑂 → 2𝐶2𝐻4𝑂2 + 2𝐶𝑂2 + 4𝐻2 (1)
From the acetic acid and hydrogen products of the above reaction, methane would be produced
thus:
2𝐶2𝐻4𝑂2 → 2𝐶𝐻4 + 2𝐶𝑂2 (2)
4𝐻2 + 2𝐶𝑂2 → 𝐶𝐻4 + 2𝐻2𝑂 (3)
When these expressions are combined, the generalized equation for the anaerobic digestion
process is obtained as follows:
𝑂𝑟𝑔𝑎𝑛𝑖𝑐𝑚𝑎𝑡𝑡𝑒𝑟
+𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑
𝑤𝑎𝑡𝑒𝑟
𝐴𝑛𝑎𝑒𝑟𝑜𝑏𝑖𝑐
𝑚𝑖𝑐𝑟𝑜𝑏𝑒𝑠⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ 𝑁𝑒𝑤𝑐𝑒𝑙𝑙𝑠
+𝐸𝑛𝑒𝑟𝑔𝑦𝑓𝑜𝑟 𝑐𝑒𝑙𝑙𝑠
+ 𝐶𝐻4 + 𝐶𝑂2 +𝑂𝑡ℎ𝑒𝑟 𝑒𝑛𝑑𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠
(4)
Anaerobic digestion reaction mechanism
Anaerobic digestion is modelled as a first order process, where the rate of increase in biomass
is proportional to the initial biomass concentration and described by the rate equation (5).
Xdt
Xdrx (5)
rx - growth rate of biomass, mg/l/day
X - initial concentration of biomass, mg/l
- specific growth rate of the mixed population
(days-1)
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= mass of cells produced / mass of cells present per unit time
t - time, days
METHODOLOGY
Laboratory experimentation
The kinetic behavior of the MSW in anaerobic processing was investigated using five batch-
wise anaerobic digesters, each of 5 liters volume. Igoni (2016b) has reported the successful
adaptation of batch experiment data for the design of anaerobic continuous digesters, after the
procedure outlined by Bailey and Ollis (1986). The schematic diagram of the experimental
design layout for a single batch reactor set-up is shown in Figure 1.
The full view of the reactor experimentation set-up is shown in Figure 2.
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The digesters were improvised with large cans because of the limitation of the unavailability
of model digesters, but deriving substantial impetus from Hobson et al. (1981), who said “with
a batch digester a smaller experimental system may be suitable as the digester has only to be
loaded once and may not even need to be stirred. One or two liters could be big enough”. The
containers were properly lagged with wool material of about 25 mm thickness, to minimize the
interaction between the temperatures inside and outside of the digesters.
Two perforations were made on the cover of the digester through which the gas hose and
thermometer were fitted. The hose extending from the digester top was connected to the tail of
a burette, which in turn was then partly immersed in water in a graduated cylinder. The waste
materials were processed (shredded and mashed), and the digesters were then loaded with 2 kg
of organic MSW, which was diluted to a 26.7% total solids (TS) concentration after metals,
glass and other non-biodegradable materials had been removed.
The properties of MSW relevant to its anaerobic biodegradation was investigated and presented
by Igoni et al. (2007). The TS concentration was determined by adopting the procedure for the
determination of TS outlined in 2540 G of Standard Methods for the Examination of Water and
Waste Water (APHA, 1995); and the moisture content was determined by the oven–drying
method.
The pH was measured from a digital pH meter, and the substrate and biomass concentrations,
were respectively determined in terms of the chemical oxygen demand (COD), and the mixed
liquor volatile suspended solids (MLVSS) using the respective procedures in 5220 b.4b and
2540 G of Standard Methods for the Examination of Water and Waste Water. The carbon and
nitrogen contents were determined, from where the carbon to nitrogen (C:N) ratio was
computed. The carbon was determined by adapting the Walkley-Black method for determining
soil organic matter (Walkley and Black, 1934); and the nitrogen was determined with the usual
macro-Kjedahl method. The thermometer, was passed into the headspace of the digester, and
measured the temperature of the headspace inside of the digester. The ambient temperature was
measured from maximum and minimum thermometers at the same time. These temperature
measurements were taken at 0800 hours and 1400 hours, and aimed at determining temperature
variation within and outside the digester, to ensure proper digester insulation with respect to
digester construction materials. After these initial measurements from the waste replications,
the digesters were made airtight with glue and other adhesives, and the set-up allowed running.
Each of the digesters was dismantled at intervals of 5 days, which gave the experimentation a
total lifespan of 25 days. At each dismantling, substrate (COD) and microbial (MLVSS)
concentration measurements were repeated.
Design Models Formulation
The general form of material balance expression, which has been variously described
[Andrews, 1978; Kiely, 1998; 1Reynolds and Richards, 1996; Tchobanoglous et al, 2003] as
in equation (6a), was used for the formulation of models for MSW in the continuous digester.
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𝑅𝑎𝑡𝑒 𝑜𝑓𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑖𝑛
𝑅𝑒𝑎𝑐𝑡𝑜𝑟
=𝑅𝑎𝑡𝑒 𝑜𝑓
𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑓𝑙𝑜𝑤𝑖𝑛𝑡𝑜 𝑅𝑒𝑎𝑐𝑡𝑜𝑟
±
𝑅𝑎𝑡𝑒 𝑜𝑓𝑎𝑝𝑝𝑒𝑎𝑟𝑎𝑛𝑐𝑒 𝑜𝑟𝑑𝑖𝑠𝑎𝑝𝑝𝑒𝑎𝑟𝑎𝑛𝑐𝑒𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑑𝑢𝑒
𝑡𝑜 𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛
−𝑅𝑎𝑡𝑒 𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝑓𝑙𝑜𝑤 𝑜𝑢𝑡 𝑜𝑓𝑅𝑒𝑎𝑐𝑡𝑜𝑟
(6a)
A simplified form is:
Accumulation = Inflow + Net growth - Outflow
(6b)
For the anaerobic digestion process, this expression is symbolically represented as:
][][][
XQVXQVdt
Xdnetror
(7)
dt
Xd ][ - rate of change of microorganism concentration in the reactor measured in terms
of mass (mixed liquor volatile suspended solids), mass MLVSS/unit volume.
time
Vr - volume of reactor, m3
Q - flow rate, volume / time
Xo - concentration of microorganisms in influent, mass MLVSS/unit volume
X - concentration of microorganism in reactor, mass MLVSS/unit volume
net - net rate of microorganisms growth, mass MLVSS/unit volume time
Monod (1949) described the kinetics of substrate decomposition by the following empirical
relationship.
SK
S
s max (8)
max - maximum growth rate, days-1
S - concentration of limiting substrate, mg/l
Ks - half saturation constant (i.e. concentration of S when 𝜇 =𝜇𝑚𝑎𝑥
2), mg/l
and net = ][][][
][max XkX
SK
Sd
s
(9)
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then, ][][][][
][][
][max XQXkX
SK
SVXQV
dt
Xdd
s
ror
(10a)
or
][][
][
][][][
][max XkX
SK
SVXXQV
dt
Xdd
s
ror (10b)
and 𝑘𝑑 =𝜇𝑚𝑎𝑥
𝑌 (10c)
This is the general model for the anaerobic digestion process.
RESULTS/FINDINGS
The results from the batch experimentation for the anaerobic digestion of the MSW and the
deduced data for the CSTR are presented in Tables 2-4.
Table 2. Experimental batch digesters' data
Digester
no.
Duration
of
digestion,
t (days)
Initial MSW
concentration,
So (mg/l)
Effluent MSW
concentration,
Se (mg/l)
Initial
microbial
concentration,
Xo (mg/l)
Effluent
microbial
concentration,
Xe (mg/l)
- 0 462.12 - 32.05 -
1 5 462.12 328.77 32.05 114.31
2 10 462.12 78.71 32.05 206.45
3 15 462.12 26.49 32.05 137.45
4 20 462.12 13.19 32.05 127.89
5 25 462.12 5.43 32.05 12.87
Table 3. Reduced data from batch experimentation for the determination of process
kinetic parameters
Digester
no.
Duration
of
digestion,
t (days)
�̅�
�̅�𝑡
ln (𝑆𝑜
𝑆𝑒)
So – Se
𝑆𝑜 − 𝑆𝑒
�̅�𝑡
ln (𝑆𝑜
𝑆𝑒)
�̅�𝑡⁄
- 0 - 0 0 - - -
1 5 73.18 365.9 0.340 133.35 0.364 0.000929
2 10 119.25 1192.50 1.770 383.41 0.322 0.00148
3 15 84.75 1271.25 2.859 435.63 0.343 0.00225
4 20 79.97 1599.4 3.556 448.93 0.281 0.00222
5 25 22.46 561.5 4.444 456.69 0.813 0.00791
�̅� = average cell mass concentration during the biochemical reaction - that is X = ½(Xo + Xt),
where Xo and Xt are the cell mass concentrations at the respective times t = 0 and t = t (Reynolds
and Richards, 1996)
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Table 4: Reduced data from batch experimentation for determination of CSTR
parameters
Rate of
MSW
utilization, ds/dt,
mg/l/day
Specific
rate of
MSW
utilization,
U, day-1
1/U
Rate of
growth of
microbes, dx/dt,
mg/l/day
Mean
cell
residence
time, ,
days
1/
1/Se
0 0 0 0 - - -
41.72 0.570 1.754 16.45 4.444 0.225 0.00304
25.58 0.215 4.662 17.44 6.849 0.146 0.0127
6.25 0.074 13.56 7.03 12.06 0.0829 0.0378
4.66 0.058 17.16 4.79 16.67 0.060 0.0758
0.56 0.025 40.11 -0.767 29.41 0.034 0.1842
Application of Material Balance to Continuous Reactor Processes
This is done in two stages, for the microorganisms and substrate.
Material Balance for Mass of Microorganism
The mass balance for the mass of microorganisms in a complete-mix reactor, will, therefore
be:
XkX
SK
SVXXQV
dt
Xdd
S
coc max (11)
For a steady state condition, where
0dt
Xd, assuming Xo is negligible at the
commencement of the process, equation (11) becomes:
XkX
SK
SVXQ d
S
c max (12a)
or (eliminating [X])
d
S
c kSK
SVQ max (12b)
But Q
Vc is defined as the mean cell residence time (c).
Therefore
d
SC
kSK
S
max
1
(13a)
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or
SK
SKkS
S
Sd
c
)(1 max
(13b)
Material balance for total substrate utilization
The mass balance for substrate utilization in a CSTR will be given as
SQVrSQdt
SdV cSoc (14a)
csoc VrSSQdt
SdV (14b)
rs - rate of substrate utilization, and defined mathematically as
XSK
Skr
S
s
(15)
So, substituting for ‘rs’ in equation (14b) from equation (15) and assuming steady – state
condition
0..
dt
Sdei gives:
0
c
S
O VXSK
SkSSQ (16a)
or
X
SK
Sk
Q
VSS
S
co ][][
(16b)
XSK
SkSS
S
ho
(16c)
h - hydraulic retention time, which is the same as the mean cell residence time (c) for no
cell recycle anaerobic system. This describes the digestion time for the CSTR, such that
]][[
][)(]([
XSk
SKSS
e
eseoh
(17)
From equation (13a)
d
CS
kSK
S
11
max
(18)
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And from equation (16c)
][
][][
Xk
SS
SK
S
h
eo
S
(19)
Combining equations (18) and (19) gives:
d
Ch
e kXk
SS
11
][
][
max
(20a)
Xkk
SS d
c
h
o
1
max
(20b)
or
hcd
co
kk
SSX
1
max (21a)
or hcd
co
k
SSYX
1 (21b)
Also, rearranging equation (19) and substituting for max from equation (10c)
1
1
dc
cdS
kYk
kKS
(22)
again from equation (20b)
c
cd
h
o k
YX
SS
11
(23a)
or Y
k
YX
SS d
ch
o
1 (23b)
and from combining equations (16c) and (23a), then
YkYkS
K
k
s
cd
c 1
1
(24) Considering the fractional conversion () of the substrate (S), defined as:
o
o
S
SS (25a)
then
1
SS
o (25b)
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Substituting for [So] in equation (16c) gives
XSK
SkS
S
s
h
1
(26a)
XSK
SkSS
s
h
1
1 (26b)
1
1
XSk
SSSKsh
(27a)
SXk
SSKSh
1
(27b)
or
Xk
SKsh
1 (27c)
Models for the Continuous digester design
The models for the CSTR is strictly based on the requirements of a high rate, low solids
processing, where there is “continuous mixing and continuous or intermittent sludge feeding
and sludge withdrawal, and the contents are in a homogenous state (Reynolds and Richards,
1996). The fixed cover variation was considered for the model development, because “high-
rate digesters usually have fixed covers” (Reynolds and Richards, 1996).
Volume
Continuous digester volume is described by the product of the flow rate of the medium and the
hydraulic retention time (Kiely, 1998; Reynolds and Richards, 1996); Tchobanoglous et al,
2003)
This is stated mathematically as:
Vc = Qh (28a)
Vc - overall volume of the continuous digester, m3
Q - influent sludge flow rate, m3/day
Substituting for h from equation (27c) in equation (28a) gives:
Xk
SKQV S
c
1 (28b)
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Dimensions and Configuration
The configuration of tanks for continuous-flow anaerobic processes, according to Kiely (1998),
tends to be ‘circular or square in shape and rarely rectangular’. For the development of the
CSTR dimensions in this work, a circular cross-sectional configuration is adapted to guarantee
effective and efficient mixing as Tchobanoglous et al (2003) state that “the conditions will
depend on the reactor geometry and the power input”.
Diameter and Height
The diameter and height of the tank is related to the tank volume by the following equation;
Vc = Ac x Hc
(29)
Ac - cross-sectional area of the tank
Hc - height of the tank.
For a circular cross-section, the area of the cross-section is:
4
2
cc
DA
(30)
Substituting for Ac in equation (29) gives:
ccc HDV2
4
1 (31)
Using the ratio of 2:1 for the relationship between digester tank diameter and height so that
Dc = 2Hc or Hc = ,2
cD then
3
8
1cc DV (32)
or 38
c
c
VD
(33)
Substituting for Vc from equation (28b) gives:
Xk
SKQD S
c
1
83 (34)
and
Xk
SKQH S
c
1
23 (35)
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Gas diffusion Rates for CSTR Mixing
Stafford et al (1980) present the formula for the rate of gas diffusion as:
𝑄 = 𝐾𝑉𝑒3𝐷𝑐
(36a)
𝑄𝑔 = 𝐾𝑉𝑒3 {√
8
𝜋𝑄 [(
𝛼
1−𝛼) (
𝐾𝑠+[𝑆]
𝑘[𝑋])]
3}
(36b)
Qg - gas discharge rate (m3/s)
K - proportionality constant
Ve - representative velocity (m/s)
They reported a velocity value of 0.18 m/s as appropriate for effective mixing of digester
content and prevention of scum formation; and that K values between 10 and 13 gave
satisfactory mixing performance for conventional-size digesters.
Digester Heating
Ambient temperature in Port Harcourt ranges between 22oC and 30oC. To maintain the digester
at the design mesophillic temperature of 35oC external heaters are used, where “the sludge is
pumped at high velocity through the tubes, while water circulates at high velocity around the
outside of the tubes” (Tchobanoglous et al, 2003). The circulation of water promotes high
turbulence on both sides of the heat transfer surface and results in higher heat transfer
coefficients and better heat transfer. Reynolds and Richards (1996) say the use of an external
heater, which heats the pumped sludge outside the digester, controls the problem of caking
associated with internally heated digesters, since any sludge caking will occur in the pipes in
the heat exchanger. It enhances de-caking of the pipes, digester maintenance and high heat
transfer efficiency.
Heater Requirements
(i) Required Quantity of Water for Heating
The specific digester heat requirement is defined as:
odwwt
TTCMq (37)
Mw - mass flow rate of hot water, kg.s-1
Cw - specific heat of hot water, J.kg-1.oC
odw
t
wTTC
qM
(38)
(ii) Required Surface Area for Heat Exchange
The heat flow across the walls of a tube is described as
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QN = UAT (39)
QN - Net heat transfer into the digester. J.s-1
U - heat transfer coefficient, J.m-2.s.oC
T - temperature difference between digester and incoming sludge, oC
For the externally heated digester, ‘A’ in the above equation is the surface area with which heat
is exchanged with the incoming sludge stream to the digester; and U = Uw. Therefore,
A = Sd
N
TTU
Q
(40)
𝐴 = 2𝜋𝑟𝑙 (41)
r - radius of heat exchanger pipe, m
l - length of pipe in water bath, m
Cost Estimation
The cost of an anaerobic digester is estimated as a function of an existing digester with similar
characteristics. So to achieve adequate estimation is somewhat difficult, as there are very few
commercial digesters in operation. Peter and Timmerhaus (1981) presented the power factor
equation that gives a fairly accurate estimate.
6.0
1
2
C
CYX d
(42)
Xd - cost of proposed digester, N
Y - current cost of existing digester, N
C1 - capacity of existing digester with known cost
C2 - capacity of proposed digester
This empirical formulation considers the price index of the base year of manufacture of the
digester with known cost; and the actual capital cost of the proposed digester determined
relative to the price index of the current year. The first step is to use the relative price indices
of the respective years to determine what would have been the actual cost of the digester with
known cost and capacity in the current year. Whitesides (2001) said “cost indices must be used
when basing the approximated cost on other than current prices”. He states that the known cost
of the digester must be multiplied by the ratio of the cost index of the current year to that of the
base year. This translates mathematically thus:
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o
oI
ICY
(43)
Co - base cost of existing digester, N
I - current price index
Io - base price index
When this is related to the power factor equation, then, the estimated cost of the proposed
digester will be:
6.0
1
2
C
C
I
ICX
o
o
(44)
4.2.7 Models for Methane and Biogas Production
The basic stoichiometric equation (45) presented by Buswell and Mueller (1952) in Kiely
(1998) is used to determine the amount of methane (CH4).
42248248224
CHban
COban
OHba
nOHC ban
(45)
The volume of biogas produced is estimated by predicting the volume of methane gas and
applying the equation (45).
Considering an organic matter represented as C6H10O5, such that n = 6, a = 10 and b = 5, then
the following chemical relationship can be established.
C6H10O5 + H2O 3CO2 + 3CH4
(46)
Knowing that the molecular weights: C6H10O3 = 162, CO2 = 44, and CH4 = 16, then from
equation (46)
1 mole of C6H10O5 3 moles CH4
1 kg C6H10O5 1000g 1000g/162g/mole
= 6.173 moles
6.173 moles C6H10O5 will yield (6.173 x 3) = 18.519 moles CH4. Relying on Avogadro’s
postulation, then 1 mole of CH4 0.0224 m3. Therefore, 18.519 moles CH4 18.519 x 0.0224
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= 0.415 m3. This shows that 1 kg of the organic matter would yield 0.415 m3 of CH4, which
accounts for the difference in concentration of the MSW as it is digested from So to Se.
Therefore, the unit of CH4 generated will be represented as:
kg/m3 of CH4 produced = 0.415 (So – Se)
(47a)
Then with a conversion factor (M = 1.43) of COD to VS the equation becomes
Cm = 0.415M (So - Se)
(47b)
Cm - actual concentration of dissolved methane gas, kg.m-3
Volume of Methane Produced
The weight of gas transferred from a liquid to a gas region occurs across a liquid gas interface,
with the interfacial area equal to the cross-sectional area of the digester. Therefore, the rate of
diffusion in the gas-liquid contact system is described by the diffusion equation:
mst
L
L
gCC
V
AK
dt
dC
(48a)
integrating tCCV
AKC mst
L
Lg (48b)
𝑑𝐶
𝑑𝑡 -rate of diffusion, kg.m-2.day
KL - diffusion coefficient, m.day-1
A - interfacial gas transfer area, m2
VL - volume of liquid, m3
Cst - saturation concentration of gas in the liquid, kg.m-3
Cg - concentration of methane gas in gas collector, kg.m-3
The saturation concentration of the gas is given as:
c
mst
H
PC (49)
Pm - partial pressure of the methane gas
Hc - Henry’s constant
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Graef and Andrews (1973) said that for mesophillic digester, Henry’s constant has been found
as 3.25 x 10-5 mol/ (l/mmHg).
Mass of methane gas produced is 𝑀𝑚 = 𝐶𝑔 𝑥𝑉𝑔
(50)
And the volume is m
mm
MV
(51)
Mm - mass of methane gas, kg
Vg - volume of gas collector, m3
m - density of methane gas, kg/m3
Vm - volume of methane gas produced, m3
Perry and Green (1997) give the density of methane as 0.644kg/m3
4.2.7.2 Volume of biogas produced
Considering biogas composition as 60% methane and 40% other constituents, then total volume
of biogas produced would be:
60
100 mt VV
(52)
Characteristics of Waste Effluent Concentration
Effluent Volatile Solids Concentration
This is defined as:
𝑆𝑒 = 𝑆𝑒𝑏 + 𝑅𝑆𝑜 (53)
Se - effluent VS concentration, mg/l
Seb -effluent biodegradable substrate concentration mg/l
𝑅 − 𝑅𝑒𝑓𝑟𝑎𝑐𝑡𝑜𝑟𝑦 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑜𝑟𝑦 𝑉𝑆
𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑖𝑛𝑓𝑙𝑢𝑒𝑛𝑡 𝑉𝑆
(54)
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Effluent biodegradable substrate concentration
This is obtained as:
𝑆𝑒𝑏 = 𝑆𝑖𝑏(1 − 𝛼)
(55)
where: Sib - influent biodegradable substrate concentration, mg/l
- fractional conversion
Percentage Stabilization
The efficiency of the waste stabilization system for biogas generation has been presented by
Viessman and Hammer (1993) as:
o
eo
S
SSE
100 (56)
where: E - efficiency of removal of biodegradable waste load.
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DISCUSSION
Validation of design models
The models developed were used to design the continuous digester for MSW in Port Harcourt
and simulate its performance over a range of fractional conversion of 0.2 to 0.8 and percentage
total solids concentration of 10 to 30%, using Microsoft Visual Basic Version 6.0. The
simulation results are presented in Tables 5 to 9.
Digester volume and total solids concentration
Figure 4 shows the relationship between volume of digester and total solids concentration. It is
characterized by a linear equation (57) – an indication that any increase in total solids
concentration will result in a corresponding increase in volume of digester.
𝑉𝑑 = 0.0063(𝑇𝑆) + 4.161 (57)
Figure 4. Effect of total solids on volume of digester
Time of digestion and total solids concentration
The relationship between total solids concentration and time of digestion, Figure 5, is described
by the polynomial equation (58) of order 2, with a correlation percentage of 98.8.
y = 0.0063x + 4.1615
R² = 1
60
80
100
120
140
160
180
200
220
0 10 20 30 40
Vo
lum
e o
f d
iges
ter,
m3
Total solids concentration,Thousands
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Figure 5. Effect of total solids concentration on time of digestion
𝑡𝑑 = 1𝐸−09(𝑇𝑆)2 − 6𝐸−05𝑇𝑆 + 8.9081
(58)
The indication is that a geometric increase in TS concentration results in an arithmetic decrease
in the time of digestion. This may be connected with the multiplied increase in microbial
concentration with increasing TS concentration (Table 9); so that MSW decomposition took
less and less time. This corroborates the reports of earlier investigations reported by Bailey and
Ollis, 1986; and Levenspiel, 1999.
Total solids concentration and volume of gas produced
In Figure 6, the increase in TS concentration results in an increase of the volumes of biogas
and methane produced. The relationship is also described by a polynomial function as in
equations (59) and (60)
𝑉𝑡 = 2𝐸−07(𝑇𝑆)2 − 0.0009𝑇𝑆 + 3.1555
(59)
𝑉𝑚 = 1𝐸−07(𝑇𝑆)2 − 0.0005𝑇𝑆 + 1.8869
(60)
The similarity in the curves in Figure 6 and the ensuing equations are indicative of the direct
proportionality relationship between volumes of biogas and methane for the same TS
concentration.
y = 1E-09x2 - 6E-05x + 8.9081
R² = 0.9881
8
8.1
8.2
8.3
8.4
8.5
5 10 15 20 25 30 35
Tim
e o
f d
iges
tio
n,
day
s
Total solids concentrationThousands
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Figure 6. Effect of TS concentration on volumes of biogas and methane
Digester volume and net heat required
Figure 7 shows the effect of digester volume on the net heat required by the digester,
described by equation (61), which is a perfect polynomial function of order 2.
𝑄𝑛 = −0.006𝑉𝑐2 + 0.5667𝑉𝑐 + 182.88
(61)
It shows that successive increases in the net heat required for increasing digester volume is a
constant.
Figure 7. Effect of volume of digester on the net heat required by digester
y = 2E-07x2 - 0.0009x + 3.1555
R² = 1
y = 1E-07x2 - 0.0005x + 1.8869
R² = 10
20
40
60
80
100
120
140
0.00 10.00 20.00 30.00 40.00
Vo
lum
e o
f gas
Total solids concentration, m3Thousands
Vol of
biogas
Vol of
methane
y = -0.0006x2 + 0.5667x + 182.88
R² = 1
200
210
220
230
240
250
260
270
280
0 50 100 150 200 250
Net
hea
t re
quir
ed, J.
s-1
Volume of digester, m3
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Digester volume and cost
The curve of Figure 8 describes the variation of cost of digester with its volume. A power
function expressed by equation (62) perfectly fits the relationship.
𝑋𝑑𝑐 = 2𝐸 + 06𝑉𝑐0.6 (62)
Equation (62) shows that a continual increase in the volume of digester will result in increasing
costs, with declining marginal difference between successive cost amounts. When this is
related to Figure 4, given the relationship between volume of digester and TS concentration, it
would show that the cost of the digester would be optimal for the maximum TS concentration,
usually 10% (Hobson et al, 1981), desired for low-solids digesters of which the CSTR is suited.
Figure 8. Variation of digester cost with its volume
Implications to Research and Practice
The development of models for the design of a CSTR for anaerobic digestion of MSW will
ease the construction of different scales of bioreactors for both laboratory and field operations.
The tedium associated with the processing of MSW will be drastically reduced, thus making
MSW management relatively easy. The production of biogas will relieve energy demand,
especially for a developing country, like Nigeria, with dire energy constraints.
CONCLUSION
The crises of municipal solid waste management of Port Harcourt, Nigeria have attained critical
dimensions, such that a treatment component must necessarily be incorporated into its
hierarchy. The treatment method that would offer optimal advantage would involve reduction
of pollution load and conversion of the waste to useful end product. The anaerobic continuous
digester is one such facility that would process the waste and produce biogas as an energy
source. The models developed in this work have shown the possibility of developing a CSTR
y = 2E+06x0.6
R² = 1
20
25
30
35
40
45
50
55
60
0 50 100 150 200 250
Co
st o
f d
iges
ter,
NM
illi
ons
Volume of digester, m3
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for varying amounts of total solids concentration and desired fractional conversion for the
MSW type in Port Harcourt, Nigeria. The maximum TS concentration would be 10% for ease
of flow and optimal digester cost relative to volume of biogas produced.
Future Research
This paper provides a basis for the investigation of the efficacy of using the CSTR for MSW
processing, in relation to other types of reactors. It would also further research into co-digestion
of MSW and other organic substrates, for optimum production of biogas.
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Byrne, K. (1997): Environmental science, Thomas Nelson & Sons Ltd, UK. 206 p
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Igoni, A. H. (2006). Design of anaerobic bioreactors for simulation of biogas production
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in Port Harcourt, Nigeria. Applied Energy, 84(6), 664-670
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APPENDIX
Simulation results for the continuous digester
Table 5. Summary of CSTR Parameters at 4% TS (TS = 9,971.44, VS = 6,640.98)
Se Xe tc Vcd Ec Vmc Vtc Vmcs Qnc Xdc
0.2 0.90
1
0.08
9
5.53 44.0
9
16.1
3
0.7
5
1.25 0.017
0
218.1
3
20,900,646.9
1
0.3 0.81
4
0.11
8
6.34 50.5
3
24.2
0
1.4
4
2.40 0.028
5
218.1
3
22,681,554.1
8
0.4 0.72
8
0.14
6
6.87 54.7
9
32.2
7
2.2
2
3.70 0.040
5
218.1
3
23,811,008.6
9
0.5 0.64
1
0.17
5
7.28
5
58.0
6
40.3
4
3.0
7
5.12 0.052
9
218.1
2
24,653,148.6
9
0.6 0.55
4
0.20
3
7.64 60.9
1
48.4
0
4.0
1
6.68 0.065
8
218.1
2
25,372,677.5
3
0.7 0.46
8
0.23
2
7.99 63.7
4
56.4
7
5.0
6
8.43 0.079
3
218.1
2
26,074,410.7
1
0.8 0.38
1
0.26
0
8.40 66.9
8
64.5
4
6.2
9
10.4
8
0.093
9
218.1
2
26,860,958.0
8
Table 6. Summary of CSTR Parameters at 6% TS (TS = 16,208.81, VS = 10,795.07)
Se Xe tc Vcd Ec Vmc Vtc Vmcs Qnc Xdc
0.
2
2.03
5
0.16
1
6.6
1
85.66 16.1
3
3.26 5.43 0.038
0
236.3
8
31,134,422.2
3
0.
3
1.83
9
0.22
6
7.1
1
92.12 24.2
0
5.56 9.27 0.060
4
236.3
7
33,333,839.4
3
0.
4
1.64
4
0.29
0
7.4
1
95.99 32.2
7
7.97 13.2
9
0.083
1
236.3
6
33,333,839.4
3
0.
5
1.44
9
0.35
4
7.6
2
98.76 40.3
4
10.4
8
17.4
6
0.106
1
236.3
6
33,908,964.1
8
0.
6
1.25
2
0.41
9
7.8
0
101.0
8
48.4
0
13.0
9
21.8
2
0.129
5
236.3
5
34,837,637.6
8
0.
7
1.05
6
0.48
3
7.9
7
103.3
1
56.4
7
15.8
6
26.4
3
0.153
5
236.3
4
34,837,637.6
8
0.
8
0.86
1
0.54
8
8.1
6
105.8
1
64.5
4
18.8
8
31.4
6
0.178
4
236.3
3
35,340,686.4
0
Table 7. Summary of CSTR Parameters at 8% TS (TS = 23,280.61, VS = 15,504.89)
Se Xe tc Vcd Ec Vmc Vtc Vmcs Qnc Xdc
0.
2
3.63
3
0.26
2
7.1
3
132.6
7
16.1
3
8.49 14.1
4
0.064
0
254.6
1
40.477,926.3
0
0.
3
3.28
3
0.37
7
7.4
5
138.6
2
24.2
0
13.7
6
22.9
3
0.099
2
254.5
9
41,558,169.2
1
International Journal of Energy and Environmental Research
Vol.5, No.3, pp.42-67, November 2017
___Published by European Centre for Research Training and Development UK (www.eajournals.org)
67 ISSN 2055-0197(Print), ISSN 2055-0200(Online)
0.
4
2.93
4
0.49
2
7.6
3
142.0
2
32.2
7
19.1
4
31.9
1
0.134
8
254.5
7
42,167,611.9
6
0.
5
2.58
5
0.60
7
7.7
6
144.4
0
40.3
4
24.6
4
41.0
6
0.170
6
254.5
5
42,590,407.9
6
0.
6
2.23
5
0.72
3
7.8
6
146.3
6
48.4
0
30.2
6
50.4
4
0.206
8
254.5
3
42,934,912.9
8
0.
7
1.88
6
0.83
8
7.9
6
148.2
1
56.4
7
36.0
8
60.1
3
0.243
4
254.5
1
43,261,049.1
6
0.
8
1.53
6
0.95
3
8.0
7
150.2
8
64.5
4
42.2
2
70.3
6
0.280
9
254.4
9
43,621,260.0
4
Table 8. Summary of CSTR Parameters at 10% TS (TS = 31,186.84, VS = 20,770.43)
Se Xe tc Vcd Ec Vmc Vtc Vmcs Qnc Xdc
0.
2
5.70
0
0.39
3
7.4
0
184.5
5
16.1
3
17.3
1
28.86 0.093
8
272.8
2
49,344,119.5
5
0.
3
5.15
1
0.57
4
7.6
2
189.9
9
24.2
0
27.3
4
45.57 0.143
9
272.7
7
50,211,118.8
1
0.
4
4.60
3
0.75
4
7.7
4
193.0
3
32.2
7
37.4
9
62.48 0.194
2
272.7
3
50,691,375.4
0
0.
5
4.05
5
0.93
5
7.8
2
195.1
2
40.3
4
47.7
5
79.58 0.244
7
272.6
8
51,021,044.3
3
0.
6
3.50
7
1.11
5
7.8
9
196.8
3
48.4
0
58.1
7
96.95 0.295
5
272.6
4
51,287,867.4
1
0.
7
2.95
8
1.29
6
7.9
6
148.4
4
56.4
7
68.8
2
114.7
1
0.346
8
272.5
9
51,539,422.9
2
0.
8
2.41
0
1.47
6
8.0
3
200.2
2
64.5
4
79.8
6
133.1
0
0.398
9
272.5
4
51,816,708.2
0
Table 9. CSTR Results for Various Percentage Total Solids (PTS) Concentrations
PTS TS VS Sc Xe tdc Vd Vmc Vtc Qnc Xdc
4 9,971.44 6,640.98 0.381 0.2604 8.40 66.98 6.29 10.48 218.12 26,860,958.08
6 16,208.81 10,795.07 0.861 0.5479 8.16 105.81 18.88 31.46 236.33 35,340,686.40
8 23,280.61 15,504.89 1.536 0.9527 8.07 150.28 42.22 70.36 254.49 43,621,260.04
10 31,186.84 20,770.43 2.410 1.4765 8.03 200.22 79.86 133.10 272.54 51,816,708.20