Mathematical Solution for Selection of LNGC Propulsion Systems

MAN B&W DieselMAN B&W Diesel AG

LNGMathematical Solution for Selection of

LNG Carrier Propulsion Systems

MAN B&W Diesel

2

Introduction

The multi-billion dollar investment intensive LNG business is

generally governed by risk sharing consortia as well as by

20–30 years long-term supply and ship charter contracts.

A predictable and stable LNG supply from producing to con-

suming country is an essential requirement in this business

but also the strive for increased profitability in the transport

chain. A variety of modern propulsion technologies for LNG

carriers with potential for increased profits have emerged

recently and are offered in the market today (see fig. 1).

With it’s new 51/60DF engine MAN B&W Diesel is the only

company now which can provide all types of modern diesel

propulsion systems for LNG carriers. The customers can

be given expert advice in finding the most suitable transport

solution for their project specific needs.

Figure 1: Overview LNG Carrier Propulsion Systems

Natural Boil-Off Gas (NBOG)

Category I: GAS / HFO fuel flexibility>> 51/60DF diesel-electric system

>> slow-speed dual-fuel diesel engines

>> steam turbine system

Category II: Pure HFO Burning System>> slow-speed diesel engines with

NBOG reliquefaction on board

Category III: Pure GAS Burning System*>> gas turbine combined cycle electric

* expensive marine gas oil (MGO) as backup fuel only

A lot of studies on the economical benefits of modern LNG

carrier propulsion systems have already been published.

Their results, however, are usually based on certain assump-

tions regarding oil and gas prices (HFO, LNG purchasing

and selling price). In fact, by an appropriate choice of oil-

and gas price combination one can produce almost any

result needed – either in favour towards the one or the other

propulsion solution. It is not without any reason, therefore,

that such kind of studies are acknowledged with reserva-

tions and caution by the specialized readers.

To better support its customers in their investment decision,

MAN B&W Diesel has developed a method, which permits

to compare the profitability of two different LNG propulsion

systems “A” and “B” for all possible oil- & gas price combina-

tions in just one chart. A method, which reduces an appar-

ently complex problem to its main parameters of influence

and illustrates the basic trends in a simple and accessible

way – the charterer nomogram.

3

MAN B&W Diesel – LNG

This nomogram answers the question under which conditions

an LNG carrier propulsion system “A” is more profitable then

another LNG carrier propulsion system “B” from the char-

terers view, who plays a decisive role in the LNG transport

chain. It will be shown that the solution to this question can

be derived by a purely mathematical consideration. The re-

sulting formula (“Charterer Profit Criterion”) is represented at

the bottom of fig. 3 and was described for the first time in a

MAN B&W Diesel document [1]. The equation is of a very

general form and can be used for profit comparison of all

kind of LNG carrier propulsion systems.

The quantitative results of the analytical formula comparing

two modern propulsion concepts for a 200,000 m3 LNG

carrier class are visualized in fig. 4 and fig. 5. These charterer

nomograms can be calculated by means of the specifically

developed MAN B&W Diesel 3P analysis tool (3P = Propulsion

Profit Performance) based on purely technical input data

from the customer.

With the nomogram the charterer then can decide on his

own which propulsion solution will be the more profitable

option for his business depending on the oil & gas prices

that he assumes or expects for his individual LNG project

in the future.

Abbreviations

C1, C2 Constants

CIFLNG CIF Price of LNG at Discharge Terminal

CRE Charter Rate Expenses

FOBHFO HFO Price

FOBLNG FOB Price of LNG at Loading Terminal

FOE Fuel Oil Expenses (HFO, MDO)

FVG Forced Vaporized Gas

HFO Heavy Fuel Oil

HFOBurnt Amount of HFO Consumed

LNG Liquefied Natural Gas

LNGBurnt Amount of LNG Consumed

LNGDel Delivered Quantity of LNG

LNGLoad Loaded Quantity of LNG

NBOG Natural Boil Off Gas

PPF Port & Passage Fees

4

The ship charterer (mostly oil & gas or energy companies)

plays a key role in the LNG supply chain. He buys the LNG

cargo at the export terminal at a certain FOB price (or pro-

duces the LNG at certain FOB costs) and sells the LNG at

the import terminal at a higher CIF price. Furthermore, the

charterer pays for the fuel costs of the ship and compen-

sates the shipowner according to a contractually agreed

charter rate (see fig. 2).

With the charter rate the shipowner has to cover all his

expenses related to the purchase, operation, maintenance,

and manning of an LNG carrier.

Since the charterer owns the cargo and has to pay for the

fuel costs, the correct selection of propulsion system can

generate significant additional profits in his favour. By the

choice of his preferred fuel(s) the charterer indirectly (or very

often even directly) specifies the type of LNG carrier propul-

sion concept that has to be used.

The Business Model for LNG Transport

Figure 2: Charterer’s Profit Consideration

Natural Boil-Off Gas (NBOG)Expenses:

Loaded LNG (= LNGDelivered + LNGFuel ) @ FOB price

+ Fuel Oil Expenses (HFO, MDO)

+ Charter Rate Expenses

+ Port & Passage Fees

Income:Delivered LNG @ CIF price

HFO Fuel HFO FuelLNG Fuel

PROFIT = INCOME minus EXPENSES

5


Mathematical Analysis

Based on the charterer’s business model for LNG transport illustrated in fig. 2,

it is possible to perform a non-quantitative, purely mathematical analysis,

which as a matter of fact has the inherent advantage of obtaining a strictly

logical and unambiguous result.

(a) LNG is purchased by the charterer at FOB price (or produced at FOB costs)

and sold at a higher CIF price.

(b) PROFIT = Income – Expenses

(c) From the charterer’s point of view we can write

Income = LNGDel · CIFLNG

Expenses = LNGLoad · FOBLNG + FOE + CRE + PPF

Once we accept the statements (a), (b), and (c) as “axioms” we obligatorily obtain

(1) PROFIT = LNGDel · CIFLNG – LNGLoad · FOBLNG + FOE + CRE + PPF

Equation (1) describes the charterer’s profit problem in its full complexity without any simplification.

Simplification Step 1:

We can certainly assume that for a given class of LNG

carrier tonnage (or ship cargo capacity) we will have the

same amount of passage & port fees for a fixed trans-

port route.

Simplification Step 2:

Charter rates will be primarily dictated by the general

situation in the LNG charter market at a given point

of time, the ship size, transport route and type of the

charter contract (long-term trade, spot trade). The

influence of the ship propulsion system on the charter

rate can be assumed to be negligible.

Then, using equation (1), the difference in charterer profits that are generated by different LNG carrier

propulsion technologies A and B for a given ship size can be written as

PROFITA – PROFIT B > 0 if

(2) LNG ADel

· CIFLNG

– LNG BDel · CIFLNG – LNG A

Load – FOBLNG – LNG BLoad FOBLNG + FOEA – FOEB

– CREA – CREB + PPFA – PPFB > 0

The liquid fuel oil expenses (neglection of 1% MDO pilot fuel consumption in the case of 51/60DF

medium-speed diesel engines) are

(3) FOE = HFOBurnt · FOBHFO

6

In general, LNG carrier propulsion systems may consume

a part of the loaded LNG, see fig. 2, so we can write

(4) LNGLoad = LNGDel + LNGBurnt

Using above expressions, the simplified charterer’s

profit equation (2) then becomes

PROFITA – PROFIT B > 0 if

LNG ADel · CIFLNG – LNG B

Del · CIFLNG – LNG ADel + LNG A

Burnt · FOBLNG – LNG BDel + LNG B

Burnt · FOBLNG – HFO A

Burnt · FOBHFO – HFO B

Burnt · FOBHFO > 0

(5) Û < · + +CIFLNG

FOBLNG

FOBHFO

FOBLNG

LNG ADel – LNG B

Del

HFO ABurnt

– HFO BBurnt

LNG BDel – LNG A

Del HFO A

Burnt – HFO B

Burnt

LNG BBurnt – LNG A

Burnt

HFO ABurnt

– HFO BBurnt

FOBHFO

FOBLNGÛ · HFO A

Burnt – HFO B

Burnt < LNG ADel – LNG B

Del · CIFLNG

FOBLNG

FOBHFO

FOBLNG

– HFO ABurnt

– HFO BBurnt · > 0

CIFLNG

FOBLNG

Û LNG ADel – LNG B

Del · – LNG ADel – LNG B

Del – LNG ABurnt – LNG B

Burnt

+ LNG BDel – LNG A

Del + LNG BBurnt – LNG A

Burnt

For a given class of LNG carrier design (cargo capacity) and transport distance the amount of

consumed fuels and delivered cargos for two different LNG carrier propulsion technologies

A and B (or two different fuel operation modes for a given propulsion system) is fixed and, hence,

we can write

(5') Û < C1 · – C1 + C2

CIFLNG

FOBLNG

FOBHFO

FOBLNG

“Charterer Profit Criterion”

7


The result shall briefly be described:

C1 and C2 are constants the value of which is determined by purely technical aspects (amount of

consumed and delivered LNG, amount of HFO burnt). The term on the left hand side represents the

fuel price ratio of purchased LNG (FOB price) and HFO. The remaining term on the right hand side

denotes the ratio of LNG selling price (CIF) to LNG purchasing price (FOB).

According to equation (5') the limiting case (i.e. PROFITA = PROFIT B) represents a straight line of

the form

Y = c1 · X – c1 + c2

It must be emphasized that the mathematical approach performed and the resulting equation

(“Charterer Profit Criterion”) are of a very general form and can be used for profit comparison of all

kind of LNG carrier propulsion systems. The same formula can also be applied to compare the

profitability of two different fuel operation modes (e.g. pure gas operation versus NBOG + HFO add

up operation) for a given propulsion system.

A summary of the mathematical approach described above and of the resulting solution is given

in fig. 3.

Figure 3: Mathematical Solution for Profit Comparison from the Charterer’s View

Charterer PROFIT = LNGDel · CIFLNG – LNGLoad · FOBLNG + FOE + CRE + PPF A... LNG carrier with propulsion system A

B... LNG carrier with propulsion system B

< · + +CIFLNG

FOBLNG

FOBHFO

FOBLNG

LNG ADel – LNG B

Del

HFO ABurnt

– HFO BBurnt

LNG BDel – LNG A

Del HFO A

Burnt – HFO B

Burnt

LNG BBurnt – LNG A

Burnt

HFO ABurnt

– HFO BBurnt

PROFITA > PROFIT B if

< C1 · – C1 + C2 ÛCIFLNG

FOBLNG

FOBHFO

FOBLNG

“Pure” Mathematics

“Charterer Profit Criterion” System A vs. System B

For given transport distance and ship design

8

Illustration of the Formula – The Charterer Nomogram

To illustrate the mathematical solution, fig. 4 compares the

charterer’s annual profitability for two different types of

modern propulsion systems that have entered the orderbook

at several yards. In the diagram (“charterer nomogram”)

there are limiting lines for various transport distances. In the

field below the limiting line we have higher annual profitabil-

ity for the HFO burning propulsion concept and in the field

above the limiting line there is higher annual profitability for

the gas burning propulsion concept (in this chart calculated

with NBOG + FVG operation mode).

It can be clearly seen that the answer as to which solution is

more profitable depends very much on the prevailing prices

of oil (HFO), the LNG purchasing (FOB) and LNG selling (CIF)

price but also on the position of the limiting line. The latter

depends from the value of the constants C1 and C2, which

apart from the transport distance are determined by purely

technical aspects of the propulsion system (overall efficiency,

type of fuel used), ship design (cargo capacity), and logistics

(time loss due to fuel oil bunkering, waiting etc).

With decreasing transport distance, the field of possible oil

and gas price combinations which lead to a higher annual

profitability of the gas burning 51/60DF electric propulsion

concept becomes larger and larger.

Figure 4: Charterer Nomogram for Constant Cargo Capacity Ship Design

Propulsion System Profit ComparisonShip: 200,000 m3 Class, Service Speed = 20 kn, Twin-Screw

Logistics: 10 hours HFO bunkering time per 10,000 nm

1.0 1.5 2.0 3.0

Fuel

Pric

e Ra

tio H

FO /

LNG

(FOB

)

Ratio LNG Selling Price (CIF) / LNG Purchasing Price (FOB)

0.0

2.0

2.5

0.5

1.0

1.5

2.5

3.5 4.0

Transport Distance 10,000 nm




Oil / Gas Price Situation 09-2004(Prices all based on USD/t, Henry Hub CIF)


Higher profit for GAS propulsion with the 51/60DF electric concept

Higher profit for HFO propulsion with slow-speed engines and NBOG reliquefaction

9


Additional valuable information can be gained from the charterer nomogram:

A horizontal line (C1 = 0), see 2,000 nm line in fig. 4, means

that both solutions deliver the same amount of LNG

(LNG ADel = LNG B

Del). In such a case the criterion as to which

propulsion concept is more profitable becomes independent

of the LNG selling price (CIF) and is influenced only by the

operating expenses (fuel price ratio).

A negative inclination of the limiting line (C1 < 0), see fig. 5,

represents a case where the gas burning 51/60DF electric

propulsion concept delivers more LNG than the HFO pro-

pulsion with slow-speed engines and NBOG reliquefaction

in spite of the fact that it has been calculated to be running

on pure gas operation mode (NBOG + FVG) throughout the

whole year! The reason for this originates from the aspect

that the profit comparison in figure 5 is based on ships

having all the same displacement (constant displacement

ship design). On such a basis of comparison the pure gas

burning 51/60DF electric propulsion concept allows an LNG

carrier design with about 3% more cargo capacity. This

advantage is primarily due to the resulting HFO fuel weight

savings, which can partly be replaced by additional LNG

cargo weight, see [2].

Figure 5: Charterer Nomogram for Constant Displacement Ship Design* (* 3% higher cargo capacity for ship with 51/60DF electric propulsion)

Propulsion System Profit ComparisonShip: 134,000 t (200,000 m3 Class), Service Speed = 20 kn, Twin-Screw

Logistics: 10 hours HFO bunkering time per 10,000 nm

1.0 1.5 2.0 3.0

Fuel

Pric

e Ra

tio H

FO /

LNG

(FOB

)

Ratio LNG Selling Price (CIF) / LNG Purchasing Price (FOB)

0.0

2.0

2.5

0.5

1.0

1.5

2.5

3.5 4.0







Higher profit for GAS propulsion with the 51/60DF electric concept

Higher profit for HFO propulsion with slow-speed engines and NBOG reliquefaction

10

The decisive advantage of the charterer nomogram is that it

can be calculated by MAN B&W Diesel without any need for

confidential or sensitive customer data like projected oil &

gas prices (FOB, CIF)! For determination of the position of

the limiting line(s) only a minimum of technical customer in-

put is required:

>> Cargo capacities of the ship designs for the

respective propulsion options

>> Ship service speed and corresponding power

at propeller

>> Transport distance(s)

>> Logistics input (data per round trip): time needed

for loading / unloading of the LNG cargo, extra time

needed for manoeuvring, waiting, etc.

>> Hotel electric load, required electrical power for

LNG cargo loading / unloading.

Based on this minimum technical input MAN B&W Diesel

can generate for its customer a project specific charterer

nomogram by means of its 3P analysis tool (3P = Propulsion

Profit Performance), which was developed inhouse specific-

ally for the economic evaluation of LNG carrier propulsion

systems.

With the nomogram the charterer then can decide on his

own which propulsion solution will be the more profitable

option for his business depending on the oil & gas prices

that he assumes or expects for his individual LNG project

in the future.

Figure 6: Charterer Nomogram, Additional Information

Additional Note on Charterer Nomogram (Fig. 4 and 5):

A negative inclination of the limiting line in figures 4

and 5 means

A... HFO propulsion with slow-speed engines and NBOG

reliquefaction

B... GAS propulsion (NBOG + FVG) with the 51/60DF

electric concept

and vice versa

C1 < 0 Û LNG ADel < LNG B

Del

11


Conclusion

From the mathematical solution for profit comparison of two

different propulsion systems (see fig.3) and the resulting

charterer nomograms (see fig. 4 and 5) we have to conclude

that there is a tendency towards

GAS burning concept with the 51/60DF electric system for

>> Short, medium, and long transport distances

>> High HFO / LNG (FOB) fuel price ratios

>> Low LNG selling to purchasing price ratios CIF / FOB

>> Optimised constant displacement ship designs

(i. e. more cargo capacity in case of vessel design for

pure gas operation with the 51/60DF)

HFO burning concept with slow-speed engines and NBOG reliquefaction for

>> Long to very long transport distances

>> Low HFO / LNG (FOB) fuel price ratios

>> High LNG selling to purchasing price ratios CIF / FOB

>> Constant cargo capacity ship designs (i. e. ship designs

with the same cargo capacity but in general of different

displacement)

It must be emphasized that above results have been obtained

through a very general approach applicable to all LNG carrier

sizes. The only restriction in the mathematical analysis was

that one has to compare similar ship sizes with each other.

Quantitative calculations at MAN B&W Diesel confirm that

the class of the LNG carrier as such (e. g. 150K, 200K, 250K)

has no influence on the validity of the trends and statements

above. Ship size is no decisive factor for determination of

the most suitable propulsion concept from the profit point of

view in the LNG transport chain.

Regardless of the customer’s final choice, MAN B&W Diesel

is the only company which can provide all types of modern

diesel propulsion solutions for LNG carriers, which are dis-

cussed in the market today. Upon request MAN B&W Diesel

scientifically calculates with a minimum of project-related in-

formation which propulsion concept suits best its customers’

individual demands.

MAN B&W Diesel supports the customer decides.

Sokrates Tolgos

MAN B&W Diesel AG

Augsburg, Germany

April 2006

REFERENCES

[1] Tolgos, S.: Mathematical-Analytical Consideration of HFO vs. Gas

Propulsion for LNG Carriers from the Charterer’s Point of View.

Memorandum, MAN B&W Diesel AG, Augsburg, 20th April 2005.

[2] Tolgos, S. and Bille, O.: Economic Evaluation of LNG Carrier

Propulsion Concepts. Technical Paper, MAN B&W Diesel AG, 2006.

About the Author

Born in 1966 in Greece, Sokrates Tolgos received his Dipl.-Ing. degree

in Aerospace Engineering from the University of Stuttgart, Germany,

in 1993. Having specialized during his studies in the field of aircraft

propulsion and turbomachinery he started his professional career at

BMW Rolls Royce Aeroengines as an R&D engineer in gasturbine aero-

dynamics. There he took part in the development of the BR710 and

BR715 aircraft engines. From 1998 he worked with the Sulzer Group in

various positions as a contract manager for industrial turbomachinery

projects and as a marine sales engineer. In 2003 he joined MAN B&W

Diesel, where he has presently been assigned the sales responsibility

of medium-speed marine engines for LNG carrier and cruise vessel

applications worldwide.

MAN B&W Diesel – a member of the MAN GroupMAN B&W Diesel – a member of the MAN Group

Copyright © MAN B&W Diesel AGReproduction permitted provided source is given.Subject to modification in the interest of technical progress.D2366338EN Printed in Germany KW9-05061

MAN B&W Diesel AGStadtbachstr. 186224 AugsburgGermanyPhone +49 821 322-0Fax +49 821 [email protected]

Mathematical Solution for Selection of LNGC Propulsion Systems

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