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, Slovaia NAVRHNUTIE A OVERENIE MATEMATICKÉHO MODELU PRE ZISTENIE PRIEPUSTNOSTI KOMPRESOROVEJ STANICE Vaszi ZS., Varga A. Katedra pecí a teplotechniy, Hutníca faulta, Technicá univerzita Košice, Slovenso Abstrat V čase hospodársej rízy sa dostáva do popredia úspora plynu aj pri jeho preprave. KS1 Veľé Kapušany je hlavnou preberacou stanicou, de rusý plyn vstupuje do Slovensej republiy, a preto jeho priepustnosť je veľmi dôležitý pre celý tranzit. V uplynulom rou EUSTREAM a.s. prepravilo viac ao 76, 2 miliard metrov ubicých zemného plynu. Aj eď táto spoločnosť udržuje dôležitú pozíciu v rámci európsych prepravných systémov je veľmi dôležitá efetívna preprava taéhoto množstva zemného plynu. V čase eď už dodáva zemného plynu z východného smeru nie je viac samozrejmosťou ešte viac vstupuje do popredia úspora deného plynu či už pri preprave, alebo pri distribúcii. Príspevo sa zaoberá priepustnosťou jednotlivých ompresorových agregátov v závislosti od vstupných parametrov, ao aj návrhom matematiceho modelu, a prepisom daného modelu do programu. Výstupy z programu sa dajú využiť pre vytváranie ombinácie prevádzovaných ompresorových agregátov. Pomocou tohto programu je možné zistiť aj vplyv teploty plynu na prepravné parametre jednotlivých agregátov. Výsledom riešenia je analýza priepustnosti vybraných druhov strojov pri zabezpečovaní požiadavy na dopravu denného objemového množstva plynu v rozsahu od 110 do 230 mil.m 3 v závislosti od vstupného tlau, ompresného pomeru, teploty oolia ao aj sledovanie vplyvu teploty plynu na prepravu plynu. Riešenie danej problematiy sa napíšu do troch bodov: Analýza pracovných charateristí všetých strojov, toré sú predmetom vzájomnej spolupráce a ich spracovanie do matematicých 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 taing over station is KS1 Veľé Kapušany, where Russian gas enters the Slova 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 woring characteristics of all machines that are the subject of mutual cooperation, and their incorporation into mathematical terms. Defining the optimal woring 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 wor 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 m in the transit pipeline on the territory of the Slova 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 Veľé Kapušany equipments Jablonov nad Turňou Veľé Zlievce Ivana 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 taing over points. Compression station KS1 - Veľé Kapušany is the most important point in the transit system in Slovaia and therefore its throughput determines the performance of the transit system of the Slova 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 M T = f P1 1, n M T T n η = f 1, (1) 1 P1 T1 and to determine the basic parameters of the drives. η = f ( P, n ) P f ( P,η, t ) t t t = (2) 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 = f ( q) P t = f ( q) e = f ( q) f ( q) t o 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 o 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, η, n tt, η tt, P t e, e tt for the given input parameters p 1, t 1 ε, based on the polynomial equations for : ε, P, P t,max, η, n tt, e, 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, q 20,, P,, η,, n tt,, η t,t, P tmax,, e,, 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 P 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 P = a q + b q + c q + d 3 2 ; t, max t t t t tt ; e =P/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 - 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 and capacity of turbine P t. Obtained results are given in Fig 1.
Acta Metallurgica Slovaca, 15, 2009, 2 (117-125) 122
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, P t = f(q) (8) for the corresponding input parameters p 1, ε and t o, 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 o,, in essentially affected by the energy consumption e t or e. 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 Veľé 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 turboompresory. Bratislava : 1988, 393 s., str. 231-234 [2] Stanovenie priepustnosti KS1 Veľé 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 požiadavy nízych prepravných množstiev, Správa HF a SjF TUKE, máj 2009 [5] Andrejčíová M.: Energia pre planétu nie je zadarmo. In.: Výsumnovedecé ativity atedier zameraných na mareting a obchod s dôrazom na _Obnoviteľné_ zdroje energie. Zborní z medzinárodnej vedecej onferencie, Vysoé Tatry 7.-8.5.2008. Košice: EU PHF Košice, 2008. ISBN 978-80-225-2580-0 [6] Jandača J., Malcho M.: Analýza merania objemového množstva zemného plynu bez prepočítavania na obchodnú jednotu; SLOVGAS 3/2007, str.17, ISSN1335-3853