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

___Published by European Centre for Research Training and Development UK (www.eajournals.org)

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






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)






= 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.






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.






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)






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)






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)






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)






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)






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)






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)






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






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:






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






= 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






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)






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.






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






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






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






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






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.

REFERENCES

American Public Health Association (APHA). (1995). Standard methods for the examination

of water and wastewater, 19th Edition; Greenberg A. E. (Ed). Byrd Springfield,

Washington D. C. 1100pp

Andrews, J. F. (1978): The development of a dynamic model and control strategies for the

anaerobic digestion process. In James, A (Ed.) Mathematical Models in Water Pollution

Control; John Wiley & Sons, Chichester. 420p

Bailey, J. E. and Ollis, D.F. (1986): Biochemical engineering fundamentals; McGraw-Hill

Book Publishers, New York, 753p.

Bailie, R. C., Everett, J. W., Liptak, B. G., Liu, D. H. F., Rugg, F. M. and Switzenbaum, M.

S. (1996). Solid waste, In Environmental Engineers Handbook. (Eds) Liu, D. H. F.,

Liptak, B. G. and Bouis, P. A., Lewis Publishers, New York. 1148–1248.

Bushwell, A. M. and Mueller, H. F. (1952). Mechanics of methane fermentation. Journal of

Industrial Engineering Chemistry, 44(3), 550.

Byrne, K. (1997): Environmental science, Thomas Nelson & Sons Ltd, UK. 206 p

Eckenfelder, W. W. Jr (2000). Industrial water pollution control. McGraw-Hill Higher

Education, Boston Burr Ridge, pp394-411.

Graef, S. P. and Andrews, J. F. (1973). Mathematical modelling and control of anaerobic

digestion, in C. F. Bennett (Ed), Water, Chemical Engineering Progress Symposium

Series, No. 136, Vol. 79, p 101.

Hobson, P. N., Bousfield, S. and Summers, R. (1981). Methane production from agricultural

and domestic wastes, Applied Science Publishers Ltd., London. 269p

Igoni, A. H. (2006). Design of anaerobic bioreactors for simulation of biogas production

from municipal solid waste. PhD Thesis, Rivers State University of Science and

Technology, Nigeria. 261pp

Igoni, A. H. (2016a). Analyses of anaerobic batch digestion of municipal solid waste in the

production of biogas using mathematical models; Energy and Environment Research;

Vol. 6, No. 1; pp44-56. URL: http://dx.doi.org/10.5539/eer.v6n1p44

Igoni, A. H. (2016b). Adaptation of batch experiment data to the design of an anaerobic

continuous digesters. Agricultural Engineering International, CIGR Journal 18(2):378-

387. http://www.cigrjournal.org

Igoni, A. H., Abowei, M. F. N., Ayotamuno, M. J. and Eze, C. L. (2006). Bio-kinetics of

anaerobic digestion of municipal solid waste. Newviews Engineering Analysis and

Modelling, Vol. 1, No. 1, 98-112.

Igoni, A. H., Ayotamuno M. J., Ogaji, S. T., & Probert, S. D. (2007). Municipal solid waste

in Port Harcourt, Nigeria. Applied Energy, 84(6), 664-670


http://dx.doi.org/10.5539/eer.v6n1p44





Igoni, A. H., Eze, C. L., Ayotamuno, M. J., and Abowei, M. F. N. (2005). Potentials of

biogas generation from municipal solid waste in Port Harcourt metropolis. Proceedings

of the 1st Annual Conference of Science and Technology Forum, Uyo, Nigeria. Vol. 1,

No. 2, pp67-72.

Kiely, G. (1998). Environmental engineering, International Edition, Irwin McGraw-Hill,

Boston. 979p

Levenspiel, O. (1999). Chemical reaction engineering, (3rd Edition). John Wiley and Sons,

Inc; New York. 668p.

Madu, C. and Sodeinde, O. A. (2001). Relevance of biomass in the sustainable energy

development in Nigeria. Proceedings of the National Engineering Conference and

Annual General Meeting of the Nigerian Society of Engineers. Pp220-227.

Monod, J. (1949). The growth of bacterial cultures. Annual Review of Microbiology, Vol

111.

Ogunbiyi, A. (2001). Local technology in solid waste management in Nigeria. Proceedings of

the National Engineering Conference and Annual General Meeting of the Nigerian

Society of Engineers. Pp. 73-79.

Perry, H. R. and Green, W. D. (1997): Perry’s Chemical Engineering Handbook. 7th Edition.

McGraw-Hill Publishers, New York. P21 – 8.

Peter, M. S. and Timmerhaus, K. D. (1981). Plant design and economics. McGraw-Hill Book

Company, Tokyo. P537.

Reynolds, T. D. and Richards, P. A. (1996): Units operations and processes in environmental

engineering, Second Edition, PWS Publishing Company, Boston. 798p

Stafford, O. A., Hawks, O. L. and Horton, R. (1980). Methane production from Waste

organic matter, CRC Press Inc. London. 306p

Tchobanoglous, G., Burton, F. L. and Stensel, H. D (2003). Wastewater engineering:

Treatment and Reuse. Tata McGraw-Hill Publishing Company Limited, New Delhi.

1819p

Viessman, W. (Jr) and Hammer, M. J. (1993): Water supply and pollution control. Harper

Collins College Publishers New York, pp513-679.

Walkley, A. and Black, I. A. (1934). An examination of the Degtjareff method for

determining soil organic matter and a proposed modification of the chromic acid

titration method. Soil Science. 37: 29-37

Whitesides, R. W. (2001): Process equipment cost estimating by ratio and proportion – a

PDH online Course. www.PDHcenter.com. 8p






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



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



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






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



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


modelling design of continuous anaerobic digesters …€¦ · according to eckenfelder (2000) the...

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