. On the basis of these results the availability of biogas CHP units has been calculated. The results have been compared with the values of availability of small cogeneration systems based on a combustion engine or gas turbine fed on the nonrenewable energy source -natural gas. The histograms of biogas CHP units have been presented. The function of occurrence of a specified time of disconnections has been obtained as a lognormal function

F Wolańczyk

J Wilk

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Int. J. of Applied Mechanics and Engineering, 2006, vol.11, No.3, pp.671-678 
 
 
AVAILABILITY OF SMALL COMBINED HEAT AND POWER UNIT FED 
ON BIOGAS 
 
J. WILK* and F. WOLAŃCZYK 
Rzeszów University of Technology, Department of Thermodynamics 
ul. W. Pola 2, 35-959 Rzeszów, POLAND 
e-mail: joanwilk@prz.rzeszow.pl 
 
 
The paper addresses the calculations of the availability of the CHP unit fed on biogas. In the paper the authors 
present the results of exploitation investigations of two small biogas CHP units working in the waste-water 
treatment plant in Rzeszów. The investigation period is from January 2002 to December 2003. On the basis of 
these results the availability of biogas CHP units has been calculated. The results have been compared with the 
values of availability of small cogeneration systems based on a combustion engine or gas turbine fed on the non-
renewable energy source - natural gas. The histograms of biogas CHP units have been presented. The function of 
occurrence of a specified time of disconnections has been obtained as a lognormal function. 
 
 Key words: CHP unit, biogas fuel, availability, disconnections time. 
 
1. Introduction  
 
 A small CHP (combined heat and power) unit as a cogenerator based on a combustion engine or gas 
turbine can be an alternative energy source for a large energetic system. This system may be applied 
wherever the requirement for thermal and electric energy exists in relatively small amounts. Biogas fuel 
feeding presents an attractive option in applications for small CHP unit systems. 
 The exploitation of a small biogas CHP unit is related to its operating time. The system availability is 
a parameter which represents the possibilities of system worktime. It is a ratio of the real system worktime to 
the possible system worktime. It is an important quantity in the economic analysis of the work of a biogas 
CHP unit. Literature regarding CHP system availability refers to small cogeneration systems based on a 
combustion engine or gas turbine fed on the non-renewable energy source-natural gas. Example values of 
availabilities of small gas CHP systems are presented in Tab.1. 
 
Table 1. Availability of small gas CHP systems (Skorek, 2002). 
 
 Piston combustion engines Gas turbines 
N kW60<  kW80080 −  kW800>  MW55.0 −  MW255 −  >25 MW 
A 0.958 0.945 0.912 0.927 0.900 0.933 
 
 
 The results of the exploitation investigations of two small biogas CHP units are presented in this 
work. Each CHP unit consisted of a Diesel engine type SW680, driving the asynchronous generator. 
Technical parameters of the unit are characterized by Nowak and Wolańczyk (2002) and Wilk et al. (2004) 
− rated electric power output  – kW9795 − ; 
− rated thermal power output – kW130128 − ; 
− lower heating value of biogas – 3nmkJ36.24LHV =  (Wilk and Wolańczyk, 2004); 
                                               
* To whom correspondence should be addressed 
J.Wilk and F.Wolańczyk 672 
− biogas consumption – hm50V 3nbg = ; 
− maximum exhaust gas temperature – C480o . 
 
 Figure 1 presents the simplified scheme of electricity and heat production for the single cogeneration 
system based on the biogas in the waste-water treatment plant in Rzeszów. The graph of the monthly 
worktime of the units in the considered time interval is shown in Fig.2. The investigations concerned the 
time interval from January 2002 to December 2003.  
 
3
2
1 7
7
4
5 5
6
8
910
 
 
1- CHP unit 
2- heat exchanger coolant/water 
3- coolant fan cooler 
4- heat exchanger exhaust gas/water 
5- water heater 
6- emergency heat exchanger 
7- water divider 
8- sludge heat exchanger 
9- sludge digester 
10- biogas container 
     ––––   biogas 
     – –          exhaust gas 
 
Fig.1. Scheme of biogas cogeneration system. 
 
 
 
 
Availability of small combined heat and power unit FED on biogas 673
0
200
400
600
800
1000
1200
1400
1600
Ja
nu
ary
 20
02
Fe
bru
ary
 20
02
Ma
rch
 20
02
Ap
ril 
20
02
Ma
y 2
00
2
Ju
ne
 20
02
Ju
ly 
20
02
Au
gu
st 
20
02
Se
pte
mb
er 
20
02
Oc
tob
er 
20
02
No
ve
mb
er 
20
02
De
ce
mb
er 
20
02
Ja
nu
ary
 20
03
Fe
bru
ary
 .2
00
3
Ma
rch
 20
03
Ap
ril 
20
03
Ma
y 2
00
3
Ju
ne
 20
03
Ju
ly 
20
03
Au
gu
st 
20
03
Se
pte
mb
er 
20
03
Oc
tob
er 
20
03
No
ve
mb
er 
20
03
De
ce
mb
er 
20
03
h/
m
on
th CHP I
CHP II
 
 
Fig.2. Monthly worktime of CHP units. 
 
2. Causes of CHP system failures  
 
 Small CHP systems are liable to different failures during the worktime. The most often occurring 
causes of incidental disconnections of small CHP systems based on combustion engine or gas turbine are 
failures of: the control system, ignition system, lubrication system, heat system, heat exchanger, generator, 
exhaust system, engine, electric system, feed system and cooling system. 
 The failures time and the time to repair the system are the time of incidental disconnections. The 
time of planned disconnections is the time predicted mostly for routine maintenance.  
 The most frequent causes of incidental and planned disconnections of small cogenerated CHP 
systems are presented in Tab.2. The results of the investigated biogas CHP I unit refers to 135 cases of 
disconnections, the results of CHP II refers to 115 cases of disconnections and the literature results refer to 
618 cases of disconnections of the CHP systems fed on natural gas. 
 
Table 2. Main causes of disconnections of the small cogenerated CHP units. 
 
The cause of 
disconnection 
CHP I % 
(135 cases) 
CHP II % 
(115 cases) 
Skorek (2002) % 
(618 cases) 
Engine 39.4 37.5 9 
Electric system 4.7 9.9 5 
Cooling engine system 5.8 6.4 9 
Control system 8.0 5.2 24 
Ignition system 6.7 - 10 
Lubrication system 2.2 17.5 9 
Routine maintenance 16.1 11.3 10 
Heat system - 0.7 5 
Heat exchanger - 6.0 6 
Generator - 2.9 3 
Exhaust system 3.7 0.3 2 
Feed system 0.5 - - 
Others 12.8 2.2 8 
 
 
J.Wilk and F.Wolańczyk 674 
 The time of disconnections of the investigated CHP systems is presented in Fig.3. The graph in Fig.3 
refers to total worktime (2002 and 2003). It can be seen that the time of engine failures has the largest value 
in the case of both CHP systems.  
 
0 25 50 75 100 125 150 175 200 225 250
Engine
Electric system
Cooling engine system
Control system
Ignition system
Lubrication system
Routine maintenance
Others
Heat system
Heat exchanger
Generator
Exhaust system
Feed system
time, h
CHP I
CHP II
 
 
Fig.3. Disconnections time of biogas CHP units working in the waste-water treatment plant in Rzeszów 
(Wilk et al., 2004). Investigation period is from January 2002 to December 2003. 
 
3. Availability of small biogas chp unit system 
 
3.1. Steady state availability 
 
 The steady state availability is a measure in determining the long term performance of a system 
which is to be operated continuously. The small biogas CHP unit is an example of this system. The steady 
state availability of a system is defined as Ananda and Gamage (2004) 
 
  
xy
yA
τ+τ
τ
=    (3.1) 
 
where xτ  is the mean time to repair the system and yτ  is the mean time between failures. The possible 
worktime of the system 0τ  is the sum of xτ  and yτ . The mean time to repair the system xτ  is the sum of 
the time of planned disconnections pτ  and the time of incidental disconnections npτ . The definition of the 
system availability can be formulated as a ratio of the real system worktime to the possible system worktime  
 
  
( )
0
npp0A
τ
τ+τ−τ
= .   (3.2)  
 
 It is known that the disconnection time of many repairable systems is well characterized by a normal 
distribution 
 
Availability of small combined heat and power unit FED on biogas 675
  ( )
( ) σπ














σ
µ−
−
=σµ 21
2
2
2
x
2
1
xf
exp
,, ,          0x > ,  (3.3) 
 
or lognormal distribution (Ananda and Gamage, 2004; Kumar and Knezevic, 1998) 
 
  ( )
( ) x2
x
2
1
xf 21
2
2
σπ














σ
µ−
−
=σµ
lnexp
,, ,          0x > .  (3.4) 
 
 Ananda and Gamage (2004) in their paper present the example with simulated data. It deals with 
lognormal distribution of xτ  with the following population parameter configurations: 0.5=α , 1.0=β , 
0.1=µ , 5.0=σ , where α  and β  are the parameters in the equations to the availability calculation  
 
  ( ) ( )
122
2
1A
−















 β−σ
+α−µ+= exp .  (3.5) 
 
In this case, the actual availability of the system is 0.9798. 
 
3.2. Results of the investigation 
 
 The exploitation investigation of two small biogas CHP units made it possible to make a histograms 
of disconnection time duration observation. The histograms presented in Fig.4 reveal that the most durable 
observed disconnections time is 2 hours and was observed nearly 10 times in the case of CHP I, and 15 times 
in the case of CHP II. 
 
2.5 5.0 7.5 12.5 15.00.0 10.0
disconnections time, h
5
15
0
10
nu
m
be
r 
of
 o
bs
er
va
tio
n
CHP I
2002
2003
 
 
J.Wilk and F.Wolańczyk 676 
 
 
Fig.4. Histograms of disconnections time of biogas CHP units. 
 
 On the basis of the histograms the function of probability density of occurrence of specified 
disconnection time has been obtained as a lognormal function. The results are presented in Fig.5. The black 
points on the graph refer to the first system (CHP I) which has been working from the 1st of January 2002 to 
the 18th of December 2003. The white points refer to the second system (CHP II) which was started on the 
11th of February 2002 and it was working to the end of December 2003. The solid line on the graph in Fig.5 
represents lognormal distribution according to Eq.(3.4) with parameters: 0.1=µ , 5.0=σ . 
 
2 4 6 8 120 10
x, h
0.1
0.3
0.0
0.2
0.4
f(x
)
CHP I
CHP II
 
 
Fig.5. The time to repair the biogas CHP unit characterized by a lognormal distribution. 
 
3.3. Calculations of availability 
 
 The availability of two small biogas CHP units working in the waste-water treatment plant in 
Rzeszów from January 2002 to December 2003 has been calculated according to Eq.(3.2) on the basis of the 
Availability of small combined heat and power unit FED on biogas 677
exploitation investigation results. The calculated values of availability and the values of possible worktime, 
times of planned and incidental disconnections are shown in Tab.3.  
 
Table 3. Availability of small biogas CHP unit system. 
 
Biogas CHP 
unit system Worktime 0τ , h p
τ , h npτ , h A  
 
CHP I 
2002 8760 154 160 0.964 
2003 8448 85 291 0.955 
2002&2003 17208 239 451 0.960 
 
CHP II 
2002 7783 143 160 0.961 
2003 8760 56 356 0.953 
2002&2003 16543 199 516 0.957 
 
4. Final remarks 
 
 The work presents the results of exploitation investigations of the small biogas cogeneration system 
working in the waste-water treatment plant. The availability of the CHP unit has been obtained on the basis 
of the investigations. 
 As a result of the exploitation investigations of the CHP units fed on biogas the following 
conclusions can be formulated: 
ß disconnection of the CHP unit caused by engine disconnection (planned and incidental) has the 
greatest influence on the CHP unit availability; 
ß the most often appearing disconnection time is similar for both the units and it is equal to about 2 
hours; 
ß the probability density of occurrence of specified disconnection time has a lognormal function form; 
ß the availability of the investigated CHP units fed on biogas has a comparable value to the values of 
availability of conventional systems working under similar conditions. 
 
Nomenclature  
 
 A  – availability 
 CHP – combined heat and power 
 f – function of probability density 
 N – power, kW, MW 
 βα,  – parameters in Eq.(3.5) 
 µ  – location parameter 
 σ  – scale parameter 
 τ  – time, h 
 0τ  – possible worktime, h 
 pτ  – time of planned disconnections, h 
 npτ  – time of incidental disconnections, h 
 
Subscripts  
 
 yx,  –  variables representing the time to repair the system and the time between failures of the system 
 
References  
 
Ananda M.A. and Gamage J. (2004): On steady state availability of a system with lognormal repair time. – Applied 
Mathematics and Computation, vol.150, pp.409-416. 
J.Wilk and F.Wolańczyk 678 
Kumar U.D. and Knezevic J. (1998): Availability based spare optimization using renewal process. – Reliability 
Engineering and System Safety, vol.59, pp.217-223. 
Nowak A. and Wolańczyk F. (2002): Economic and technical aspects of using the biogas on example of Sewage 
Treatment Plant in Rzeszów City. – Politechnika Szczecińska, Ninth International Symposium on Heat Transfer and 
Renewable Sources of Energy, pp.355-360. 
Skorek J. (2002): Ocena efektywności energetycznej i ekonomicznej gazowych układów kogeneracyjnych małej mocy. – 
Gliwice: Wydawnictwo Politechniki Śląskiej. 
Wilk J., Wolańczyk F. and Malkiewicz A. (2004): Availability of small biogas CHP unit. – Wydawnictwo Politechniki 
Szczecińskiej, Ten International Symposium on Heat Transfer and Renewable Sources of Energy, pp.163-168. 
Wilk J., Wolańczyk F., Malkiewicz A. and Nowak A. (2004): Energy aspects of biogas fuel disposal and energy system 
modernization in the waste-water treatment plant. – Wydawnictwo Politechniki Szczecińskiej, Ten International 
Symposium on Heat Transfer and Renewable Sources of Energy, pp.157-162. 
Wilk J. and Wolańczyk F. (2004): Higher and lower values of biogas. – Wydawnictwo Politechniki Szczecińskiej, Ten 
International Symposium on Heat Transfer and Renewable Sources of Energy, pp.169-174. 
 
 
Received: March 24, 2005 
Revised:   March 2, 2006 
 
 
 
 
 
 
 


AVAILABILITY OF SMALL COMBINED HEAT AND POWER UNIT FED ON BIOGAS

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AVAILABILITY OF SMALL COMBINED HEAT AND POWER UNIT FED ON BIOGAS

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