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Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 117
DESIGN AND VERIFICATION OF THE MATHEMATICAL MODEL
FOR DETECTING THE THROUGHPUT OF THE COMPRESSOR STATIONS
Vaszi ZS. , Varga A.
Department of Furnaces and Thermal Technology, Faculty of Metallurgy, TechnicalUniversity
in Košice, Slovakia
NAVRHNUTIE A OVERENIE MATEMATICKÉHO MODELU PRE ZISTENIE
PRIEPUSTNOSTI KOMPRESOROVEJ STANICE
Vaszi ZS. , Varga A.
Katedra pecí a teplotechniky, Hutnícka fakulta, Technická univerzita Košice, Slovensko
Abstrakt
V čase hospodárskej krízy sa dostáva do popredia úspora plynu aj pri jeho preprave.
KS1 – Veľké Kapušany je hlavnou preberacou stanicou, kde ruský plyn vstupuje do Slovenskej
republiky, a preto jeho priepustnosť je veľmi dôležitý pre celý tranzit. V uplynulom roku
EUSTREAM a.s. prepravilo viac ako 76, 2 miliard metrov kubických zemného plynu. Aj keď
táto spoločnosť udržuje dôležitú pozíciu v rámci európskych prepravných systémov je veľmi
dôležitá efektívna preprava takéhoto množstva zemného plynu. V čase keď už dodávka zemného
plynu z východného smeru nie je viac samozrejmosťou ešte viac vstupuje do popredia úspora
deného plynu či už pri preprave, alebo pri distribúcii. Príspevok sa zaoberá priepustnosťou
jednotlivých kompresorových agregátov v závislosti od vstupných parametrov, ako aj návrhom
matematickeho modelu, a prepisom daného modelu do programu. Výstupy z programu sa dajú
využiť pre vytváranie kombinácie prevádzkovaných kompresorových agregátov. Pomocou
tohto programu je možné zistiť aj vplyv teploty plynu na prepravné parametre jednotlivých
agregátov. Výsledkom riešenia je analýza priepustnosti vybraných druhov strojov pri
zabezpečovaní požiadavky na dopravu denného objemového množstva plynu v rozsahu od 110
do 230 mil.m 3 v závislosti od vstupného tlaku, kompresného pomeru, teploty okolia ako aj
sledovanie vplyvu teploty plynu na prepravu plynu.
Riešenie danej problematiky sa napíšu do troch bodov:
• Analýza pracovných charakteristík všetkých strojov, ktoré sú predmetom vzájomnej
spolupráce a ich spracovanie do matematických vyjadrení.
• Definovanie optimálnych pracovných režimov jednotlivých strojov.
• Vyhodnotenie priepustnosti jednotlivých agregátov.
Abstract
In the time of the economic crisis the saving of gas in its transport had came to the
forefront. The main taking – over station is KS1 – Veľké Kapušany, where Russian gas enters
the Slovak Republic, and therefore the throughput is very important for the entire transit.
Eustream a.s. transported more than 76,2 billion cubic meters of natural gas in last year.
Although the company maintains an important position in European transport systems is a very
important the effective transport of this natural gas quantity. At a time when the natural gas is
not supplies from the eastern direction is more obvious to saving gas, whether in transport or
distribution. The paper describes the throughput of each compressor set, depending on the input

Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 118
parameters, as well as design of the algorithm and mathematical approach in form of software.
This software can be used for creating the combination of operating compressor aggregates.
With this software it is possible to detect the effect of temperature on gas transport parameters of
the individual aggregates. Results of the analysis is the permeability of certain types of
machinery to ensure the requirements for the transport of gas daily mass in the range from 110
to 230 mil.m 3 according to the input pressure, compression ratio, the ambient temperature as
well as monitoring the impact of temperature of gas in gas transport.
The solution of the problem is described in the following three points:
• Analysis of the working characteristics of all machines that are the subject of mutual
cooperation, and their incorporation into mathematical terms.
• Defining the optimal working regimes of the individual machines.
• Evaluation of the permeability of different aggregates
Key words: Compressor station, mathematical model, throughput, compressor set
1. Introduction
Turbo compressors are not work under the conditions for which they were designed,
i.e. under conditions, which are reflected in the design of the flow cross-section, blade angles
and so on. It is obvious that, depending on the factors that affect the operation of the compressor
changed will be the compression and efficiency. Compression, efficiency and input power vary
depending on the parameters of the inlet gas. The parameters of the inlet gas have major impact
on the overall throughput of compressor stations.
2. Characteristics of compressor stations
There are 4 compressor stations representing the major technological complexes in
the mutual distance of about 115 km in the transit pipeline on the territory of the Slovak
Republic. Characteristics of the individual stations with the number of aggregates are given in
Tab 1.
Table 1 Distribution and number of aggregates
Major technological
Veľké Kapušany
equipments
Jablonov nad
Turňou
Veľké Zlievce
Ivanka pri Nitre
TS 6 MW 23 21 22 22
ES 25 MW 3 3 3 -
T 23 MW 1 1 2 4
R 28 MW 3 2 - -
These technological devices provide the required transport by increasing the pressure
level to compensate the pressure loss in pipes and to ensure the contracted amount of pressure
and transport of the natural gas to the border taking over points.
Compression station KS1 - Veľké Kapušany is the most important point in the transit
system in Slovakia and therefore its throughput determines the performance of the transit system
of the Slovak Republic. Information about compressor aggregates are in Tab 2.

Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 119
Table 2 Compressor aggregates
Aggregates
Range speed
(sp.min -1 )
Max usable
speed.
(sp.min -1 )
Pursuit of
the
projected
(MW)
Max power
Summer
(MW)
Winter
(MW)
Number of
aggregates
max.
Immed
use
Maximum
compression
ratio
GT750-
6 MW
3800 - 5600 5300 6 5,5 6 19 16 1,22 3)
NP
PGT 25
3250 - 6500 6200 22,67 19 1) 20,5 1) 1 1 2) 1,46
Cooper –
Rolls
3120 - 5050 4700 27,426 25 28 3 3 2) 1,7
Electrical
drives 2600 - 3900 3700 25 25 25 3 2 1,45
GE ** 4250 - 6405 6300 34 3 1,75
1)
Restrictions on the quantity of emissions generated in the further improvement of performance exceed the limit sets
2)
Under operation may also be 3CR with 1NP, but in practice operate only 3 aggregates and one is left in reserve.
3)
In the two-stage operation the compression ratio is. 1.44 max.
**) New aggregates in KS1
3. Calculation of the throughput of different aggregates
The problem of the aggregate sets in operation, depending on the required volume of
gas transport through the compressor station, inlet gas pressure, the compression ratio and the
ambient temperature, must be solved as the throughput of gas through the individual aggregates
of KS and conditions of the operation of individual drives depending on the ambient
temperature.
To solute this problem, it is necessary to undergo subsequent steps:
• to revise the characteristics of the individual aggregates and drives based on a graphic
form according to the mathematical regression analysis using the software Fotofilter
and Excel to create universal characteristics of individual aggregates:
⎛
⎜
M ⋅ T
ε = f
⎜
⎝
P1
1 ,
n ⎞
⎟
T ⎟
1 ⎠
P k
⎛ M ⋅ T
= f ⎜
⎜
⎝
P1
1 ,
⎞ ⎛
n M ⋅ T
⎟
T ⎟
⎟ ⎞
⎜
n
η = f
1 ,
(1)
k
1 ⎠ ⎝ P1
T1
⎠
and to determine the basic parameters of the drives.
η = f ( P , n ) P f ( P ,η , t )
t
k
t
t
= (2)
k
• to design the mathematical model for the calculation of the throughput of the individual
aggregates under required output parameters at KS1, depending on the input
parameters, p 1 , t 1 , t a of the individual aggregates,
• to execute a simulations of the impact of the input parameters p 1 , T 1 , on the throughput
of the individual aggregates at KS1,
• to process data obtained from the simulations based on regression analysis into the
polynomial dependencies:
n = f ( q)
P k
= f ( q)
P t
= f ( q)
e k
= f ( q)
f ( q)
t
ok
e t
= (3)

Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 120
4. Algorithm of the program for calculation
• input parameters p 1 , t 1 , ε, t ok
• calculation of terms
M
x =
min
min
.
P
1
T
1
and
M max. T
1
x
max
= (4)
P1
and other parameters of compressors and drives - P k , η k , n tt , η tt , P t e k , e tt for the given input
parameters p 1 , t 1 ε, based on the polynomial equations for : ε, P k , P t,max , η k , n tt , e k , e tt .
• adjustment of the above calculated x to q 20 ( gas throughput adjusted for t = 20 o C)
• output data : data sets for the corresponding aggregates : i, n k , q 20, , P k, , η k, , n tt, , η t,t ,
P tmax ,, e k ,, e tt ,

Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 121
5. Acquisition of data sets in program EXCEL:
Obtained data sets related to the constants n and Pk for compressors for variety of
input pressures p 1 , compression ratios ε and ambient temperature ta are processed in
program„Excel“ into the polynomial dependencies for each aggregate :
3 2
n = a q + b q + c q + d
p
p
p
p
(5)
and for each turbine:
3 2
P = a q + b q + c q + d
k
k
k
P = a q + b q + c q + d
3 2
;
t, max t t t t tt
k
k
; e
k
=Pk/q (6)
e = Ptmax/q (7)
Verification of the mathematical approach
To be able to exploit the mathematical models for the simulations using the input
parameters, it is necessary to verify the above based on the practical measurements at KS1
provided in Tab.3.
Table 3 Throughput KS1
Measured data
KS1
Calculated data
Q 0 P 1 P 2 T 1 P+R+E ČKD 6MW Q 0 del KS1
(mil.m 3 /d)
(20°C)
(MPa) (°C) I II
(mil.m 3 /d)
(20°C)
258,45 4,9 6,51 17 0+2+1 5 4 255 1,33
248 4,5 6,19 17 0+2+1 5 4 248 0
(%)
Q 0
P 1
P 2
T 1
P p
P k
- natural gas volume related to the commercial conditions m3/d
- gas input pressure at KS1 resp.KS2
- gas output pressure at KS1 resp.KS2
- gas input temperature at KS1 resp.KS2
- output pressure from KS1
- input pressure to KS2
del_KS1 – difference between measured and calculated data of gas volume
P+R+E: number of machines under operation (Pignone, Cooper, electro-drive, CKD)
ČKD 6MW: number of machines under operation (CKD- 6MW) I – first level ; II – second level
6. Results
Gas transport and related energy consumption depend beside the parameters p 1 , ε and
ta also on the input gas temperature t 1 , which lays within the range of 17 – 23 °C.
Based on the above described procedures, executed were the calculations of
temperature t 1 effect on the transported gas volume q, compressor capacity P k and capacity of
turbine P t . Obtained results are given in Fig 1.

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Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 123
Fig.1 Effect of input gas temperature on the transporting parameters of the compressor for p 1=5 MPa; ε=1,4
Based on graphs analysis, it follows out that the input gas temperature does not effect
essentially the transport parameters of the individual aggregates and therefore this temperature is
not considered when calculated further the database and the calculations are executed for the
input gas temperature t 1 = 20 °C.
The described program provides the datasets as depending on p 1 , ε and t a..
These datasets from program EXCEL defined may be the limits of the gas throughput
for the individual aggregates operation (q min , q max ) and graphs :
n, P k , P t = f(q) (8)
for the corresponding input parameters p 1 , ε and t ok , expressed in form of the polynomial
equations.

Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 124
Fig.2 Energy nominal consumption of the compressor and turbine as depending on the natural gas throughput
Based on the above graphs, it follows out that the energy nominal consumption of
compressor or turbine, when defining the optimum combination of the co-operation of the
individual machines in the requested amount of gas transport under defined input parameters p 1 ,
ε and t ok, , in essentially affected by the energy consumption e t or e k . The most suitable variant
is the combination of the aggregates with the lowest nominal energy consumption.
Graph on the relationship e = f (q) provide the information that with the increased gas
throughput the nominal energy consumption for all considered aggregates falls.
7. Conclusion
The aim of this article is to analyse the throughput of the compressor station KS1 –
Veľké Kapušany and design of the suitable mathematical model. In the article described is the
algorithm of the program, based on the mathematical description of the process. The above
provided the tool by the aid of which determined could be the effect of the transported gas
temperature upon the transport parameters of the individual aggregates. Designed mathematical
model was verified and proved the inaccuracy up to 2 percent. Software Program based on the
mathematical description of the process enables also to define the optimal combinations of
aggregates for the daily transport of gas within the range of 110 to 230 mil.m 3 as depending on
the entry pressure, compression ration and ambient temperature. The suitable optimum
combinations of the aggregates in the compression station is necessary mainly due to the
reduction of the natural gas consumption in this station, needed for gas transport via transit
pipeline.
Literature
[1] Nohel J.: Tepelné turbíny a turbokompresory. Bratislava : 1988, 393 s., str. 231 - 234
[2] Stanovenie priepustnosti KS1 Veľké Kapušany. Správa SjF a HF TUKE, jún 2006
[3] Varga A.: Doprava a využitie plynov 1. Košice 2004

Acta Metallurgica Slovaca, 15, 2009, 2 (117 - 125) 125
[4] Optimalizácia spolupráce vybraných strojov pri zabezpečení požiadavky nízkych
prepravných množstiev, Správa HF a SjF TUKE, máj 2009
[5] Andrejčíková M .: Energia pre planétu nie je zadarmo. In.: Výskumnovedecké aktivity
katedier zameraných na marketing a obchod s dôrazom na _Obnoviteľné_ zdroje energie.
Zborník z medzinárodnej vedeckej konferencie, Vysoké Tatry 7.-8.5.2008. Košice: EU
PHF Košice, 2008. ISBN 978-80-225-2580-0
[6] Jandačka J., Malcho M.: Analýza merania objemového množstva zemného plynu bez
prepočítavania na obchodnú jednotku; SLOVGAS 3/2007, str.17, ISSN1335-3853