Vorlesung 5 – Principles of Natural Gas Economics
Prof. Dr. Christian von Hirschhausen
Technische Universität Dresden Lehrstuhl für Energiewirtschaft und Public Sector Management
Energiewirtschaft 1 Vorlesung 5 (Erdgas) 14.11.2006
EE² -1- Agenda
1. Supply and Demand
2. Technical Aspects
3. Globalization of Natural Gas Markets
4. Natural Monopoly, Regulation, and Competition
5. Infrastructure Investments – the GASMOD Model
Backup
EE² -2- Erdgasreserven
BP Statistical Review of World Energy 2006
EE² -3- Erdgasförderung
BP Statistical Review of World Energy 2006
EE² -4- Reserves-to-Production Ratio
BP Statistical Review of World Energy 2006
EE² -5- Erdgasverbrauch
BP Statistical Review of World Energy 2006
EE² -6- Pro Kopf Verbrauch nach Regionen
BP Statistical Review of World Energy 2006
EE² -7- Erdgaslagerstätten Deutschland
• Hamburg Erdgasführende Becken •• •• N o r d d e u t s c h • • •• e s B e c k e n • Erdgasfeld ••• • •••••• • • •••••• •• ••• •••••••• • • • • Berlin ••• • •••••• • •••• ••• • • • •• • • • • •
••• 3 •• Reserven (2005): 190 Mrd. m Thüringer B ecken Förderung (2005): 16 Mrd. m3 Statische Reichweite : 11,8 Jahre
n e b a r G - in n e ecke h se-B rr olas e M b O • • Quellen: Verlag Glückauf: Jahrbuch 1999; BP Statistical Review of • • World Energy 2006
EE² -8- Agenda
1. Supply and Demand
2. Technical Aspects
3. Globalization of Natural Gas Markets
4. Natural Monopoly, Regulation, and Competition
5. Infrastructure Investments – the GASMOD Model
Backup
EE² -9- Wertschöpfungskette der Erdgaswirtschaft
Gewinnung Ferntransport / Handel Endkunden- Verteilung Endkunden (Hochdruck) FGG Vertrieb / (Niederdruck) - Langfristverträge Groß- Inter- Deutsch- - Spot-/Terminmarkt - Börsen/OTC abnehmer national land
Wellhead Processing Stadtwerk Plant Mainline Transmission System
Raw Gas Gathering System Kraftwerk Down- Down- Natural Gas Upstream stream stream Reservoir Storage Storage Storage LNG +
EE² -10- 2. Natural Gas Markets
a) Production d) LNG- Regasification Distribution
b) Liquefaction
e) Pipeline
c) Shipping
„DOWNSTREAM“
„UPSTREAM“ f) Storage
EE² -11- Natural Gas Production
Natural gas: - Mixture of hydrocarbon and non-hydrocarbon gases Æ Consists to about 90% of methane - Found in porous geologic formations Æ associated versus non-associated; onshore versus offshore production
Dry versus wet natural gas: - Dry gas: water content has been reduced by a dehydration process - Wet gas: unprocessed natural gas or partially processed natural gas produced containing condensable hydrocarbons
Sour versus sweet natural gas: - Sour gas: natural gas containing too much sulfur Æ impractical to use, without purifying, ( corrosive effect on piping and equipment) - Sweet gas: natural gas containing small amounts of sulfur that it can be used without purifying (no deleterious effect on piping and equipment)
EE² -12- Liquefaction
- LNG is an odorless, colorless, non-corrosive, and non-toxic cryogenic liquid - pre-treatment before liquefaction: natural gas liquids and components that would freeze under cryogenic temperatures (propane, butane, ethane, CO2, and water) have to be removed - under atmospheric pressure the gas is cooled down to 111 K (-161°C) - becomes a liquid - shrinking to about 1/600th of its volume - size of liquefaction units (“trains”) limited to compressor size - two technologies dominate the industry: - Air Products’ pre-cooled mixed refrigerant process (propane used for pre- cooling, liquefaction using a mixture of nitrogen, methane, ethane, and propane) - Philips’ optimized cascade process (natural gas passes through a cascade of three cooling processes using propane, ethylene, and methane as refrigerants)
EE² -13- LNG Supply Situation
Alaska Norway
Russia
Middle East North Africa
Latin America West Africa Asia Oceania
Australia mtpa in 2005 mtpa in 2010 Sources: IEA (2004), Cedigaz (2004)
EE² -14- Shipping: Increasing Capacities
35,00
30,00
13,05 25,00
20,00 Ordered
bcm Active 15,00 4,45
8,60 10,00 19,52
12,65 5,00 6,87
0,00 Pacific Basin Atlantic Basin Total Source: Colton Company, 2005
EE² -15- Regasification: European LNG Import Capacities
Sources: IEA (2003), Cedigaz (2004)
bcm/a in 2005 bcm/a in 2010
(nominal values)
Rotterdam Wilhelmshaven Dansk Miford Haven Isle of Grain Zeebrugge Montoir
El Ferrol Rovigo Bilbao Panigaglia KrK Fos Cavaou Fos sur Mer Marmara Barcelona Sines Sagunto Brindisi
Huelva Cartagena Revithoussa
EE² -16- Existing and Proposed North American LNG Terminals
Existing Source: FERC (2006) Under EE² construction -17- Freeport, Texas – Construction is under Way
EE² -18- Pipelines
EE² -19- Kostenstruktur Ferngastransportleitungen
- Hohe Fixkosten (Infrastrukturinvestition & zugehörige Anlagen wie Verdichter- stationen) Æ versunkene Kosten - Geringe variable Kosten (Betrieb, Wartung, etc. sowie Antriebskosten für Verdichter) - Verdichterstationen alle 100 bis 150 km erforderlich - Verbrauch pro Verdichter (einstufig, Druckerhöhung um 15 bar): etwa 0,3% des durchgeleiteten Erdgases (IEA, 1994); für russische Pipelines etwa 0,5 - 0,8% ⎡ κ −1 ⎤ m κ RT Z ⎛ P ⎞ κ VC = c ∗ & SCη ∗ ∗ S S ∗8.64∗10−2 ⎢⎜ 1 ⎟ −1⎥ - Dahl (2001): η ⎢⎜ ⎟ ⎥ GCV ∗ gt ∗ κ −1 M gas ⎝ PS ⎠ ⎣⎢ ⎦⎥
VC Variable Kosten der Verdichtung (einstufig, isentrop) c Brennstoffkosten m& Massenstrom (Standardbedingungen) GVC Heizwert η Wirkungsgrade κ Isentropenexponent R Gaskonstante T Umgebungstemperatur Z Kompressibilitätsfaktor M Molare Masse Erdgas P1 Ausgangsdruck Eingangsdruck PS
EE² -20- Does Competition Phase-out Regulation? Europe: No major internal investment for many years
EE²Source: IEA (2005) Natural Gas Information -21- Erdgas aus Russland für Europa (einschließlich potenzieller Erdgasquellen aus der GUS)
NEGP
Quelle: Ruhrgas AG, Grundzüge der Erdgaswirtschaft, 2002
EE² -22- Russia-Ukrainian Gas Crisis (Jan 2006): So What?; or: „Storm in the Samowar“
Source: AP www.mosnews.com
EE² -23- Main Large Investment Projects
Recently finished: Green Stream (Libya-Italy, 8 bcm) Blue Stream (Russia-Turkey, 16 bcm) Interconnector (NL-UK, 16.5 bcm following enhancement) Euskador (France-Spain, 0.5 bcm)
Four main projects on the agenda: BBL (NL-UK, 16 bcm, 2007) Ormen Lange (NOR-UK, 25-30 bcm, 2008) NEGP (RU-Germany, 55 bcm, 2015) Nabucco (from Iran/Caspian from Turkey-SE Europe, 8 bcm, ???) + a number of small scale projects
EE² -24- Überregionale Erdgasleitungen
Europäischer Erdgasverbund: - Hochdruckebene (> 1 bis 80 bar) - grenzüberschreitender Verbund von der Nordsee bis zum Mittelmeer, von West- europa bis zu den Leitungssystemen Osteuropas - wirtschaftliche Optimierung der Erdgasströme - Erhöhung der Versorgungssicherheit
Quelle Karte: International Energy Agency (2006)
EE² -25- Storage
EE² -26- Natural Gas Storage: Competition and/or Regulation? (seasonal storage vs. peak storage)
Kavernenspeicher, Aquifere: unterirdische Hohlräume, die im Salzgestein durch Aussolen geschaffen wurden Porenspeicher (ehemalige Erdgaslagerstätten): Erdgasspeicherung in den Poren eines Speichergesteins, nach oben durch gasundurchlässige Gesteinsschicht abgedichtet
EE² -27- Technical and Economic Characteristics
Fee Salt Cavern DGF Fixed Fees (based on MMBtu of capacity reserved): Annual Demand Charge, $ MMBtu 1,00 0,40 Variable Costs (based on volume of throughput): Injection Fee, $/MMBtu 0,02 0,02 Withdrawal Fee, $/MMBtu 0,02 0,02 Fuel Expense, % 1 1 Injection Days To Fill 20 180 Withdrawal Days To Deplete 10 120 Typical Number of Cycles Per Year 4 to 5 1 to 1.5 Source: Simmons (2005, 8)
Salt caverns are more expensive, but also more flexible In a competitive natural gas markets, salt caverns play a critical role in risk management „Merchant storage“ are mostly salt caverns
EE² -28- U.S. Natural Gas Storage
Storage Type N° Storage Sites
Depleted Gas/Oil 316 Aquifer 38 Salt Cavern 21
EE² -29- U.S. Natural Gas Storage
316 Depleted Gas/Oil; 38 Aquifer; 21 Salt Cavern 14 storage facilities regulated by FERC Change of paradigm: from cost-based to market-based rates Firm and interruptible storage services State: mainly cost-of-service regulation
EE² -30- Storage Investment Requirements U.S.
Incremental Working Gas Capacity 450 bcf 400
350
300
250
200
150
100
50
0 Total Other Midwest New York Gulf Coast West Coast
Eastern 2004-2008 West Virginia West Pennsylvania/ 2009-2020 Western Canada Canada/Michigan
EE² Source: FERC (2004) Current State of and issues concerning Underground-31- Natural Gas Storage (p.15), Docket AD04-11-000 Change of Regulation Paradigm?
Currently 14 storage facilities regulated by FERC, for the time being on a cost- based level
Need for additional capacity: from cost-based to market-based rates? More generous interpretation of market power by FERC
A “missing money” problem in favour of market-based rates?
Emergence of independent merchant storage operators (e.g. Falcon Gas Storage)
EE² -32- Storage Projects (bcf), 2005
Source: Ferc (2006)
EE² -33- 20 18 Europe: Capacity Expanding Recently … 16 bcm14 12
10 8
6 4
2 0 UK Italy Spain Latvia Turkey France Austria Poland Croatia Belgium Bulgaria Hungary Romani a Denmark Germany Netherlands Czech Republic 1994 2005 Slovak Republic - 40 storage system operators (SSO) own approx. 68.3 bcm working capacity in Europe -15 bcm new storage projects in Europe (UK, Germany, NL, F, etc.)
EE²Source: IEA Natural Gas Information (2005), IEA (1994) Natural-34- Gas Transportation, and ERGEG Ref. E05-STO-06-03 … and More Storage Necessary in the Future Net Surplus/Deficit of Storage Capacity (in bcm)
EE²Source: Höffler and Kübler (2006) -35- Untertage-Erdgasspeicher in Deutschland
Erdgas Porenspeicher in Betrieb
in Planung oder Bau
267 3 max. Arbeitsgaskapazität in Mill. M (Vn)
Kavernenspeicher in Betrieb
in Planung oder Bau Rohöl, Mineralölprodukte, Flüssiggas Kavernenspeicher in Betrieb
in Planung oder Bau
2 Anzahl der Einzelspeicher
Quelle: Niedersächsisches Landesamt für Bodenforschung, 2005
EE² -36- Case Study „Merchant Storage“ in Germany: Trianel Project in Epe
Kennzahlen: 150 Millionen EUR 1.5 Milliarden KWh (120 mcm) 3 Kavernen, H-Gas Ausspeiseleistung 300.000 cbm/h Einspeiseleistung 150.000cbm/h Anschluss an Ferngasnetze von Eon Ruhrgas und RWE Erstes kommunales Erdgasspeicherprojekt Beteiligung von kommunalen Unternehmen und Stadtwerken
EE² Bildquelle: Epe Erdgasspeicher (bereits existierend, Essent-37- ) Distribution
EE² -38- Agenda
1. Supply and Demand
2. Technical Aspects
3. Globalization of Natural Gas Markets
4. Natural Monopoly, Regulation, and Competition
5. Infrastructure Investments – The GASMOD Model
Backup
EE² -39- More Competition through a „Globalization of Natural Gas Markets“ (trade in 2002 and 2030, billion cubic meters)
189 22 112112 19 11 6363 139 13 66 184 66 2727 57 11 52
EE² -40- Source: IEA, 2004 EU-15 Natural Gas Supply Costs (2010-2020)
US $/MBTU
Gulf LNG Source: OME, 2001
EE² -41- Liquefaction Capacities Worldwide 2005 vs. 2010
Alaska Norway
Russia
Middle East North Africa
Latin America West Africa Asia Oceania
Australia bcm/a in 2005 bcm/a in 2010 Sources: IEA (2003), IEA (2004), Cedigaz (2004)
EE² -42- Convergence of Trans-Atlantic Natural Gas Prices?
12 (daily data, USD/MBTU) Henry Hub NBP 10
8
6
4
2
0 1996 1997 1998 1999 2000 2001 2002 2003 2004
Neumann, Siliverstovs, and Hirschhausen (2005): - No cointegration between European and North American natural gas prices until recently - But: „something“ is happening (increasing convergence) - Future European natural gas prices may no longer be determined in Moscow or Oslo, but at Henry Hub
EE² -43- Agenda
1. Supply and Demand
2. Technical Aspects
3. Globalization of Natural Gas Markets
4. Natural Monopoly, Regulation, and Competition
5. Infrastructure Investments – The GASMOD Model
Backup
EE² -44- Wertschöpfungskette der Erdgaswirtschaft
Gewinnung Ferntransport / Handel Endkunden- Verteilung Endkunden (Hochdruck) FGG Vertrieb / (Niederdruck) - Langfristverträge Groß- Inter- Deutsch- - Spot-/Terminmarkt - Börsen/OTC abnehmer national land
Wellhead Processing Stadtwerk Plant Mainline Transmission System
Raw Gas Gathering System Kraftwerk Down- Down- Natural Gas Upstream stream stream Reservoir Storage Storage Storage LNG +
EE² -45- Funktionsweise des Entry-Exit Systems: Hypothetische Ein- und Ausspeisezonen für Deutschland (Riechmann, 2001, 777/778)
•• BriefmarkeBriefmarke für für die die Einspeisung Einspeisung ins ins Netz Netz undund Entnahme Entnahme aus aus dem dem Netz, Netz, geographischgeographisch differenziert differenziert •• ZusätzlichZusätzlich möglich: möglich: Versteigerung Versteigerung von von knapperknapper Entry-Kapazität Entry-Kapazität • Sekundärhandel der gebuchten Kapazität • Sekundärhandel der gebuchten Kapazität Emden möglichmöglich •• KostendeckungKostendeckung des des Netzbetreibers Netzbetreibers
Netzgebiet Einspeisetarif Ausspeisetarif € / (m³/h/a) € / (m³/h/a) Jena
A (Jena) 30 10 (St.Kathariny) B 30 10 St.
C 30 10 Kathariny
D 20 20
E 30 10
F (Emden) 30 10 G 20 20
EE² -46- Neue Rechtliche Rahmenbedingungen in Deutschland
EnWG 2005 - Teil 2 (§§6-10): Unbundling - Teil 3 (§§11-28a): Regulierung des Netzzuganges • Diskriminierungsfreier Netzzugange • Entfernungsunabhängige Entgelte Æ Entry-Exit-System für Erdgasfernleitung • Angemessen, diskriminierungsfrei, transparente Entgelte • Nur jeweils ein Einspeise- und ein Ausspeisevertrag pro Transaktion
GasNEV (2005) - Ein- und Ausspeise-Entgeltbestimmung laut GasNEV - i.d.R. kostenorientiert (Kostenarten-/Kostenstellen-/Kostenträgerrechung) - in Ausnahmefällen marktbasiert, §19 GasNEV
Æ Verbesserung hin zu mehr Wettbewerb im Erdgassektor
EE² -47- Marktgebiete in Deutschland
ERT: 4 (3 H-Gas/1 L-Gas) Ontras: 1 BEB: 2 (1 H-Gas/1 L-Gas) RWE: 3 (2 H-Gas/1 L-Gas) Wingas: 3 Regional Level: Bayerngas, Erdgas Münster, EWE, Gas-Union, GdF, GVS-ENI Total: 19
EE² -48- Agenda
1. Supply and Demand
2. Technical Aspects
3. Globalization of Natural Gas Markets
4. Natural Monopoly, Regulation, and Competition
5. Infrastructure Investments – The GASMOD Model
Backup
EE² -49- Need for Investments in Infrastructure
- Increasing natural gas demand Æ Environmental as well as security of supply issues
- Increasing importance of imports via liquefied natural gas Æ Diversification of suppliers, security of supply
- GASMOD: numerical model of the European Market Large number of European importing and exporting countries / regions (including indigenous production of each region) Preliminary assumption of one gas company per country/region Capacity data from GTE, European Commission Production and transport cost data (LRMC) to the EU by OME (2001) Trade data (flows, prices) by IEA and BP for 2003 Assumptions on price elasticities (differing between Western and Eastern Europe)
EE² -50- GASMOD Model Simulation Results for EMF 23
Franziska Holz, Christian von Hirschhausen and Claudia Kemfert
Dresden University of Technology Chair of EnergyEconomics and Public Sector Management (EE²), and German Institute of Economic Research (DIW Berlin)
EMF 23 Meeting Berlin, June 6-7, 2006
EE² -51- GASMOD Model Structure: 2-Stage Game of Exports and Intra-European Trade
Wholesale Trader r France exp-cap capf,r f imp-capr Final market f,r Upstream m France In p tra ca -E Producer U- ca f Russia p Final r,m imp-cap market r
m Germany
13 possible exporters (pipe and LNG) Wholesale Upstream Producer Trader Wholesale trade between 17 European regions f Algeria_LNG r Germany
EE² -52- Model Specification: Profit optimization of each player
- Profit maximization program of the exporter: Max.,Π=−( xf ,,,r p r) ( p r( X r) c fr) * x fr x fr, (similar for the domestic producer and the trader) s.t. xcapfr, ≤ - FOC (assuming Cournot competition): ∂pX∂XX pX( ) mc=+ p Xrr() ⋅⋅⋅⋅−rr rr x λ cap fr,, r() r() fr ∂∂xXXpXfr, r r r r
⎛⎞θ fr, cap mcfr, =+∗− p r() X r *1⎜⎟ 1 λ ⎝⎠σ r Variables: - f exporting firm, i.e. upstream producer - r importing firm, i.e. downstream trader (here: one firm per country) Oligopolistic Mark-up - m final consumer market, by assumption equivalent to the importing regions
- mcf,r marginal production cost of the producer f (incl. transport costs to trader r) - pe equilibrium import price for the trader r (border price) r Price elasticity of demand - p0m reference market price on final market m - d0m reference demand on final market m Cournot assumption - Θf,r market share of exporter f with trader r Market share - σr price elasticity of r - xf,r supply by exporter f to trader r - yr,m supply by trader r to end-market m - domprodr domestic production in European countries
EE² -53- Model Specification: Equilibrium program of the two-stage game
Linear demand function: ⎛⎞∑ yrm, 00⎜⎟r (with a constant elasticity of demand) pY()=+⋅ pσ p −1 mm m m m⎜⎟0 ⎜⎟Ym ⎝⎠ Equilibrium program of the two-stage game: θ - FOC Exporters: ⎛⎞fr, cap mcfr,,= p r() X r*1⎜⎟+−⊥≥ x fr 0 ⎝⎠σr λ ⎛⎞ - FOC domestic producers: domθ r cap dom mcrrr= p() X*1⎜⎟+−⊥≥ x r 0 ⎝⎠σr λ ⎛⎞ - FOC Traders: 0 ∑ yrm, ⎛⎞θrm, 0 pm ⎜⎟r cap pX()= 1*++ p * −−⊥≥ t y 0 (serving the final demand) rr⎜⎟ m⎜⎟0 rm, m ⎝⎠σσmmm⎜⎟Y ⎝⎠ - Capacity constraints: 00≤ cap−⊥ x λ cap ≥ (on transport and λ domestic production capacity) dom - Market Balance: ∑ xxf ,,rr+=∑ y rm fm
EE² -54- Results: Exports in the EMF Reference Scenario
Expected increase of natural gas exports over time comes with an increasing diversification of supplies, in favor of LNG LNG mainly comes from North Africa, Africa and the Caribbean, only little from the Middle East Russia is an important player but does not become dominant
700,00
Venezuela 600,00 Trinidad
Nigeria 500,00 UK
400,00 Netherlands Norw ay
300,00 Russia
Middle East 200,00 Iran
Iraq 100,00
Exports to Europe in bcm per year per bcm in Europe to Exports Egy pt
Lybia 0,00 2003 2010 2015 2020 2025 Algeria
EE² -55- Results: Endmarket Prices
Steady growth of prices, in line with the assumptions High demand scenario expectedly leads to higher prices than in the reference scenario
600,00 EMF_Reference 500,00 High Demand 400,00 Russian Exports 300,00 Middle East Exports 200,00 Middle East Russian 100,00 Exports
0,00 Liquefaction constraint 2003 2010 2015 2020 2025
EE² -56- Results: Capacity bottlenecks 2015
LNG
Belgium ↔ NL ↔ Germany Germany ↔ France Italy/ Switzerland ↔ Balkan Germany ↔ Poland France ↔ Italy / Switzerland Austria → Germany Austria → Czech/Slovak Rep.
Iran - pipe
Lybia
EE² -57- The UK Market
Rapidly decreasing production capacity with depleting North Sea fields BUT: Domestic demand can be served by imports in the next decades because enough import capacities will be constructed (LNG and pipe from Norway and the Continent)
100
90 Domes tic Production for domestic 80 consumption
70
60 Impor ts 50
40
30
20 Total Domes tic consumption Exports to Europe in bcm per year per bcm in Europe to Exports 10
0 2003 2010 2015 2020 2025
EE² -58- Russia: One Supplier in a Diversified Import Portfolio
Slightly increasing importance of Russian exports to Europe until 2025 to 30% of European imports, but far from reaching a dominant position Utilization only of capacities that already exist - NEGP comes in only towards the end of the observation period Diversion to US or Asia unlikely, and if so, there would sparse capacities
700 Venezuela
24% 23% 26% 28% 30% Trinidad 600 Nigeria
UK 500 Netherlands
400 Norw ay
Russia
300 Middle East
Iran 200 Iraq
Egy pt 100 Exports to Europe in bcm per year per in bcm to Europe Exports Lybia
0 Algeria 2003 2010 2015 2020 2025
EE² -59- Russian Gas Exports to Central and Western Europe: Options (Stern, 2006, 3)
EE² -60- Iran & The Nabucco Project
We assume: pipeline to Turkey (10 bcm), extended to 20 bcm in 2025 Æ Could feed in the Nabucco pipeline from Turkey to Austria via the Balkan We find positive and high shadow variables of the Iranian export capacity Æ Additional Iranian gas (via Nabucco) would find its customers in Europe at the relatively low costs assumed BUT: Nabucco is a long-standing project which lacks political support Æ Unlikely to come about with the complexity of the project
EE² -61- Middle East LNG
Middle East producers only export few to Europe because lower cost LNG suppliers are available for Europe „Residual“ LNG shipments can go to North America, etc. Contracted exports are higher but long term contracts do not reflect “market fundamentals” which are the driving factors in GASMOD
18 GASM 16 OD Result 14 (EMF
12 Refere nce 10 Scena
8 Publicl
6 y Known 4 Contra cted
Exports to Europe in bcm per year per in bcm to Europe Exports 2 Export Volum 0 2003 2010 2025
EE² -62- Agenda
1. Supply and Demand
2. Technical Aspects
3. Globalization of Natural Gas Markets
4. Natural Monopoly, Regulation, and Competition
5. Infrastructure Investments and Long-Term Contracts
Backup
EE² -63- Legende Übung
Variable Kosten der Verdichtung [€/a] kv c Brennstoffkosten [€/m³]
V& Volumenstrom [m³/a] Unterer Heizwert [J/kg] H u ρ Dichte [kg/m³] P Leistung [J/a] w Spezifische Verdichterarbeit [J/kg] κ Isentropenexponent [1,3] R Gaskonstante [8314,34 J/(kmol*K)] T Umgebungstemperatur [K] Z Kompressibilitätsfaktor [0,6 - 0,7]
M Gas Molare Masse Erdgas [19 – 21,5 kg/kmol] pD Ausgangsdruck (Druckseite) [bar] Eingangsdruck (Saugseite) [bar] pS η Wirkungsgrad
EE² -64-