SPE 165898

Optimization of Compressed Natural Gas Marine Transportation with Composite-Material Containers Michael Nikolaou, University of Houston, Xiuli Wang, XGas, and Michael J. Economides, University of Houston

Copyright 2013, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Asia Pacific Oil & Gas Conference and Exhibition held in Jakarta,

Indonesia, 22–24 October 2013.

This paper was selected for presentation by an SPE program committee following review of information contained in an

abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and

are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum

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consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not

more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE

copyright.

Abstract Marine transportation of natural gas is critical for its monetization. Pipelines and liquefied natural gas (LNG) are the

established technologies for offshore natural gas transportation, with compressed natural gas (CNG) recently proposed as an

economically preferable alternative under certain conditions.

In previous work, we have delineated areas in a transportation-distance/gas-volume diagram, where each of the three

transportation means mentioned above is economically most attractive. In general, once offshore pipelines are excluded

because of water depth and sea-floor terrain limitations, CNG transportation is considered attractive compared to LNG for

relatively small volumes and short distances. Until recently, the preferred material for proposed CNG containers has been

metal, for reasons of simplicity, robustness, and development cost. However, metal CNG containers have a number of

disadvantages, the most obvious of which is that the container itself may be several times heavier than the contained gas, and,

consequently, such gas may be only a small fraction of the cargo carried by a loaded CNG ship.

Composite containers are an alternative to metal, with a number of advantages. First, composites are significantly lighter

than metal. Second, composite containers can reach considerably higher containment pressures (hence capacity), while still

maintaining lower weight compared to metal. Finally, composite containers are much less prone to corrosion, and as a result

can contain gas that has not been fully treated. These facts make composite containers an attractive proposition and greatly

increase the overall attractiveness of using CNG to monetize stranded gas.

We present here a thorough study using both metal and composite containers and optimized operating conditions, such as

pressure and temperature, to explore the applicability of CNG for marine stranded gas transportation. A new map of the

economic attractiveness of LNG and CNG as a function of transportation distance and gas volume is presented, showing a

considerably expanded area of CNG preference over LNG.

Introduction Marine transportation of natural gas is critical for its monetization. Pipelines and liquefied natural gas (LNG) are the

established technologies for offshore natural gas transportation. The technical feasibility of a third alternative, namely

marine transportation of natural gas as compressed natural gas (CNG), was briefly demonstrated in the sixties, but without

commercial success [1]. Interest in marine CNG transportation has been rekindled recently, as a result of development of

new CNG containers suitable for marine transportation of natural gas [2-3], supported by economic feasibility studies (e.g.

[1]) that broadly delineated general conditions for which marine CNG transportation is favored. In general, once offshore

pipelines are excluded because of water depth and sea-floor terrain limitations, CNG transportation is considered attractive

compared to LNG for relatively small volumes and short distances. Until recently, the preferred material for proposed CNG

containers has been metal, for reasons of simplicity, robustness, and development cost. However, metal CNG containers

have a number of disadvantages, the most obvious of which is that the container itself may be several times heavier than the

contained gas, and, consequently, such gas may be only a small fraction of the cargo carried by a loaded CNG ship.

2 SPE 165898

Composite containers are an alternative to metal, with a number of advantages [4]. First, composites are significantly

lighter than metal. Second, composite containers can reach considerably higher containment pressures (hence capacity),

while still maintaining lower weight compared to metal. Finally, composite containers are much less prone to corrosion, and

as a result can contain gas that has not been fully treated. These facts make composite containers an attractive proposition

and greatly increase the overall attractiveness of using CNG to monetize stranded gas.

We present here a thorough study using both metal and composite containers and optimized operating conditions, such as

pressure and temperature, to explore the applicability of marine CNG for marine stranded gas transportation. In addition to

specific numbers, we uncover general principles and associated factors that govern the relative advantages and disadvantages

of LNG vis as vis CNG. A new map of the economic attractiveness of LNG and CNG as a function of transportation distance

and gas volume is presented, showing a considerably expanded area of CNG preference over LNG.

Formulas for NPV calculation To assess the economic merit of a CNG project using metal or composite CNG containers and to compare it to LNG

alternatives, we calculate the net present value (NPV) of each project over a finite time period.

The NPV is defined in a standard way as

Gas SalesNPV PV CAPEX (1)

where CAPEX refers to project-related capital expenditure; and Gas SalesPV refers to the present value (PV) of net cash from

gas sales over a time period of N years, equal to

After Taxes,

Gas Sales After Taxes,

1 1

ACFPV DCF

(1 )

N Nk

k kk k i

(2)

where After Taxes,ACF k is annual cash flow after taxes in year k ; i is the discounting interest rate; and DCF is discounted cash

flow.

Total CAPEX is assumed to be incurred instantly at zero time, and to comprise expenditures on terminals and on the gas

transportation fleet, i.e.

Terminals Fleet fleetCAPEX CAPEX ( ) CAPEX ( , ) q G L q (3)

where TerminalsCAPEX ( )q depends on the natural gas transportation rate that meets consumption, q ; and

Fleet fleetCAPEX ( )G

depends on the natural gas carrying capacity of the fleet of natural gas transportation vessels, fleetG , which in turn depends on

q and the transportation distance, L , from natural gas source to delivery destination.

Details on calculation of each of the above terms are provided below. Numerical values for all parameters that appear in

corresponding formulas are shown in Table 3. Additional details on data sources and derivations are provided in Appendices.

General trends for NPV of LNG and CNG projects

Before executing specific numerical calculations for NPV differences between LNG and CNG projects, important insights

can be obtained by identifying general trends that point to orders of magnitude of related quantities as well as to the effect of

various factors on these quantities. To derive our results, we make the following simplifying assumptions:

- The transportationed gas is consumed at a uniform rate, q , which does not change over time.

- As stated in Eq. (3), total CAPEX is the sum of two terms: CAPEX for terminals (liquefaction/regasification for

LNG, compression/decompression for CNG) assumed to be proportional to q ; and CAPEX for gas transportation,

assumed to be proportional to the capacity (volume) of the gas transportation fleet, which in turn is proportional to

the product L q (as further elaborated in subsequent sections), i.e.

Terminals FleetCAPEX C q C L q , (4)

- Annual operating expenditure (OPEX) is the sum of two terms: OPEX for gas volume change

(liquefaction/regasification for LNG, compression/decompression for CNG) assumed to be proportional to q ; and

OPEX for gas transportation (voyage costs), assumed to be proportional to the product L q , i.e.

Transport VolumeChangeOPEX C L q C q , (5)

- Asset depreciation is linear down to zero over N years, i.e. annual depreciation, D , is constant as

CAPEXD

N, (6)

- Annual cash flow from gas sales is constant each year, i.e.

SPE 165898 3

Gas Sales,ACF k q T for all 1,...,k N (7)

where T is the gas transportation tariff.

- The tax rate, Taxf , is constant.

- The annual interest rate, i , is constant over N years.

Based on the above assumptions, Eq. (1) yields

NPV ( ) L LA B L q (8)

where

Tax

Tax

Terminals

Tax Volume Change

1ˆ

1

1

L N

N

N

A f I T

fI C

N

f I C

(9)

Tax Transport

Tax

Fleet

1ˆ

1

L N

N

B f I C

fI C

N

(10)

with

(1 ) 1ˆ

(1 )

N

N N

iI

i i (11)

(see Appendix A).

NPV difference between LNG and CNG

Inspection of Eq. (8) provides the following important insights regarding the NPV difference between CNG and LNG

projects.

First, the value of the gas tariff, T , has no effect on LNG CNGNPV NPV NPVˆ , because Eqs. (8)-(11) imply

NPV L LA B L

q (12)

where

Tax

Terminals Tax VolumeChange1 1ˆ

L N N

fA I C f I C

N (13)

Tax

Tax Transport Fleet1 1ˆ

L N N

fB f I C I C

N (14)

This realization is independent of whether economies of scale are considered or not, because the term Tax1 Nf I T in

Eq. (9) is independent of CAPEX or OPEX assumptions. Of course, the value of T has a significant effect on the actural

NPV of either CNG or LNG projects, e.g. it affects whether that NPV is positive or negative.

Second, Eq. (12) implies that, to the extent that economies of scale are negligible and the factors Terminals ,C

Volume Change ,C Fleet ,C and TransportC are constant, the sign of NPV depends solely on the transportation distance, L .

While this assumption is removed in the next section, where scale effects are examined in detail, the conclusion remains that

L is the key driver for the sign of NPV.

Third, it is clear that longer distances will favor LNG over CNG, due to the positive sign of the coefficient LB of L in

Eq. (12). This is because Terminals 0 C , Volume Change 0 C ,

Fleet 0 C , and Transport 0 C , reflecting the fact that CNG

requires relatively lower CAPEX for gas terminals and OPEX for compression as well as higher CAPEX and OPEX for

building and operating a transportation fleet, whereas the reverse is true for LNG.

4 SPE 165898

Selecting between LNG and CNG: Crossover distance

The crossover distance CrossoverL , at which the relative NPV ranking for LNG and CNG is reversed, is where NPV 0 .

Equation (12), implies

Terminals Volume Change

Crossover

Fleet Transport

h C CL

h C C (15)

where the parameter

Tax

Tax Tax

1 1ˆ

1 1

NI f N ih

f N f (16)

(see Appendix B) is of the order of magnitude of 110 1/y for typical values of NI and

Taxf (e.g. as in Table 1).

Equation (15) offers a simple criterion for assessing the relative merits of CNG and LNG, in that this equation relies on

very few assumptions, and describes explicitly the effect of relative costs on CrossoverL . As such, it offers a quick assessment

of the magnitude of CrossoverL , what affects it, and in what way, rather than a single number. Furthermore, Eq. (15) suggests

that what will alter the specific value of CrossoverL over a range of gas rate values, q , is differences between LNG and CNG in

economies of scale reflected in each of the terms TerminalsC , VolumeChange ,C

FleetC , and TransportC . Nevertheless, a nominal value

of CrossoverL offers an order of magnitude expected for CrossoverL . This claim will be supported in more detail in the next

section, where economies of scale and their effect on CrossoverL are quantified.

Note that Crossover 0L according to Eq. (15).

Note also that that CrossoverL is not a function of the gas transportation tariff, T . This makes conclusions about the relative

economic attractiveness of CNG and LNG projects fairly robust in terms of gas price fluctuations.

Table 1. Typical values for parameters affecting NPV for LNG and CNG projects

Parameter Value

[%]i , , 10

[y]N 10

Tax [%]f 35

$million

Bcf/y

T 5

[miles/h]v 23

For typical values of 0.10i , Tax 0.35f , 10 yN (Table 1) it follows from Eq. (16) that 0.2 1/yh . For sample

values of TerminalsC , VolumeChange ,C

FleetC , and TransportC based on Table 2, Eq. (15) yields

Crossover 3.7 kmilesL (17)

for CNG with metal containers, and

Crossover 5.2 kmilesL (18)

for CNG with composite containers.

SPE 165898 5

Table 2. Sample values for process factors affecting CrossoverL , Eq. (15).

LNG CNG Metal CNG Composite

Terminals

$million

Bcf/y

C 27 0.5 0.5

Fleet

$million

kmile Bcf/y

C 1 7.5 5.3

VolumeChange

$million

Bcf

C 1.0 0.1 0.1

Transport

$million

kmile Bcf

C 0.1 0.5 0.45

Values of i and N other than these in Table 1 have a very small effect on the value of CrossoverL , as shown in Fig. 1,

obtained for the nominal value of Taxf in Table 1 and for the nominal values of parameters in Table 2. Therefore, the same

values of i and N will be held throughout this study.

Fig. 1. Effect of i and N on CrossoverL . The dot represents the nominal point according to Eqs. (17) (left) and (18) (right).

Variability in the four factors TerminalsC , VolumeChangeC , FleetC , and TransportC that determine the NPV difference between

LNG and CNG has a significant effect on the value of CrossoverL , as shown in Fig. 2. Nevertheless, the general trend is that

CNG remains competitive in comparison to LNG for relatively short distances even for large quantities of transportationed

natural gas. This claim will be examined in more detail in the next section, where economies of scale are explicitly included

in the calculations.

6 SPE 165898

Fig. 2. Comparison of NPV of LNG and CNG (metal and composite) projects for parameter values in Table 1 and Table 2. The

shaded bands correspond to 50% variability in the coefficients TerminalsC , VolumeChangeC ,

FleetC , and TransportC for LNG and CNG.

Note that the nominal NPV for LNG is negative because of the low gas transportation tariff of 5 $/MscfT ; however the relative

position and variability bands of the two NPV lines are independent of T .

An assessment of how each of the four factors TerminalsC , VolumeChangeC ,

FleetC , and TransportC affects CrossoverL is

provided by series expansion of CrossoverL around the nominal parameter values shown in Table 1 and Table 2, resulting in

VolumeChange TransportCrossover Terminals Fleet

Crossover Terminals VolumeChange Fleet Transport

0.85 0.15 0.76 0.24

C CL C C

L C C C C (19)

and

VolumeChange TransportCrossover Terminals Fleet

Crossover Terminals VolumeChange Fleet Transport

0.85 0.15 0.70 0.30

C CL C C

L C C C C (20)

for metal or composite CNG containers, respectively. Eqs. (19) and (20) imply that relative variability in TerminalsC ,

VolumeChangeC , FleetC , and TransportC can have significant effect on the variability of

CrossoverL , as confirmed in Fig. 2.

Interpretation of Eqs. (19) and (20) suggests that an uncertainty percentage in the cost coefficients of gas terminals or ships

results in an about equal percentage uncertainty in CrossoverL , whereas an uncertainty percentage in the cost coefficients of gas

volume change and transportation has a significantly smaller effect.

When economies of scale are considered, the four factors TerminalsC , VolumeChangeC ,

FleetC , and TransportC in Eq. (15) are

not constant. Rather, TerminalsC , VolumeChangeC are functions of q , and FleetC , TransportC are functions of L and q . It is

differences in scaling among these four factors, rather than scaling itself, that result in different values of CrossoverL for

different q , as will be quantified in the following sections.

Breakeven value of gas transportation tariff as function of transportationati on distance

The breakeven value of gas transportation tariff, BreakevenT , is where NPV 0 . Equations (8)-(11) imply

NPV T TA B T

q (21)

where

Tax

Transport Tax Fleet

Tax

Volume Change Tax Terminals

(1 ) 1

1 1

ˆ

( )

N

N

N

T

N

f IC f I C L

N

f IC f I C

N

A

(22)

Tax(1 )ˆ NT f IB (23)

Therefore, by Eq. (21),

CNG Metal LNG CNG Composite LNG

SPE 165898 7

Volume Change Terminals Transport

Breakeven

Fleet)( ( )

T

T

AT

C

B

C C h C h L

(24)

where h is as in Eq. (16). For typical values of 0.10i , Tax 0.35f , 10 yearsN (Table 1) and for sample values of

TerminalsC , VolumeChange ,C FleetC ,

TransportC shown in Table 2, Eq. (24) yields the BreakevenT lines in Fig. 3.

Fig. 3. Breakeven value of gas transportation tariff as function of transportation distance for LNG, CNG-Metal, and CNG-Composite

projects for parameter values in Table 1 and Table 2. The shaded bands correspond to 50% variability in the coefficients

TerminalsC , VolumeChangeC , FleetC , and TransportC for LNG and CNG.

An assessment of how each of the four factors TerminalsC , VolumeChangeC , FleetC , and TransportC affects BreakevenT is

provided by series expansion of BreakevenT around the nominal parameter values shown in Table 1 and Table 2, resulting in

Breakeven Terminals

Breakeven TerminalsCNG Metal

VolumeChange

VolumeChange

Fleet

Fleet

Transport

Transport

0.40

0.80 7.9

0.40

0.80 7.9

5.9

0.80 7.9

2.0

0.80 7.9

L

L

L

T C

T C

C

L

C

L

C

C

C

L

C

(25)

Breakeven Terminals

Breakeven TerminalsCNG Composite

VolumeChange

VolumeChange

Fleet

Fleet

Transport

Transport

0.40

0.80 5.9

0.40

0.80 5.9

4.1

0.80 5.9

1.8

0.80 5.9

L

L

T C

T C

C

C

CL

L C

L

C

C

L

(26)

and

CNG Metal LNG CNG Composite LNG

8 SPE 165898

Breakeven Terminals

Breakeven TerminalsLNG

VolumeChange

VolumeChange

Fleet

Fleet

Transport

Transport

21.1

25.2 1.2

4.0

25.2 1.2

0.78

25.2 1.2

0.40

25.2 1.2

T C

T C

C

C

C

C

C

C

L

L

L

L

L

L

(27)

for CNG-metal, CNG-composite, and LNG containers, respectively.

Equations (25)-(27) allow a quick assessment of the effect of CAPEX or OPEX variability on the break-even tariff value

for gas transporation over a certain distance. They point to what are important factors to consider improving for each

technology, such as terminals and liquefaction/regasification for LNG and transportation fleets for CNG. For example, these

equations imply that a 10% reduction in the transportation OPEX factor, TransportC , results in relative reduction of about 2%,

3%, and 0.1% on gas tariff for transportation over 1000 miles via CNG-metal, CNG-composite, and LNG ships, respectively.

By contrast, 10% reduction in the terminals CAPEX factor, TerminalsC , results in corresponding relative reductions of about

0.5%, 0.6%, and 8%.

Economies of scale and power laws

Power laws describing economies of scale are widely applicable [5].

For an activity whose cost (e.g. CAPEX, OPEX) depends on capacity, Q (e.g., natural gas processing rate, natural gas

storage volume, natural gas carrying volume, etc.), the resulting cost, F is assumed to follow economies of scale, namely to

depend on capacity through the standard power law

1

0

0

  ( ) ˆ

a

a QF Q c Q c Q

Q (28)

where any combination of nominal capacity, 0Q , and nominal CAPEX per capacity,

0c , that satisfies

0 0 0 0ˆ ˆ a ac c Q c c Q (29)

can be selected for representation of the constant c in Eq. (28).

Equivalently, cost per capacity is assumed to drop as capacity increases, following economies of scale, as

0

0

( )ˆ

a

aF Q Qc Q c

Q Q (30)

It is widely accepted that for economies of scale related to chemical process facilities the exponent a is of the order of

0.3 1 0.7 a a , (31)

reflecting the decrease in cost per capacity as capacity increases [5]. Values of 1a closer to 0 or 1 indicate more or less

pronounced economies of scale, respectively. We substantiate these claims below with specific numbers for liquefaction and

regasification terminals, compression stations, and gas transportation ships.

Of course, economies of scale can easily be excluded from the calculations, if desirable for simplicity, by setting

1 1 0 a a in Eqs. (28)-(30).

CAPEX for LNG

The cost of LNG terminals and ships has varied widely in recent years [6]. While there are efficiency improvements due

to technological advances, prevailing market conditions continue to drive price volatility. Recent developments such as

floating LNG (FLNG), mini LNG (mLNG) and others offer more data points to the price mix. Nevertheless, we assess the

required CAPEX for LNG projects below, using average scenarios. We incorporate economies of scale, to be able to

characterize price trends over a wide enough range for comparison purposes.

CAPEX for LNG liquefaction and regasification terminals

For LNG, the CAPEX for terminals, Terminals, LNGCAPEX ( )q , is assumed to be a function of the gas rate, q , and entails two

terms, referring to fixed costs for liquefaction and for regasification terminals, i.e.

SPE 165898 9

Terminals, LNG Liquefaction RegasificationCAPEX ( ) CAPEX ( ) CAPEX ( ) q q q (32)

Following Eq. (28), the dependence of LiquefactionCAPEX ( )q on q is considered to be

Liquefaction

Liquefaction1

Liquefaction Liquefaction 0, Liquefaction

0, Liquefaction

 CAPEX ( )

a

a qq c q l q

q (33)

with

Liquefaction 0.20a (34)

and

0, Liquefaction

0, Liquefaction

1,937 Bcf/y

$14 million/(Bcf/y)

q

l (35)

as shown in Fig. 4 (see Appendix C for justification and details). Note the wide confidence bands, particularly for CAPEX

per gas rate at very low gas rates and CAPEX at very high gas rates.

Fig. 4. CAPEX per gas rate (left) and CAPEX (right) for LNG liquefaction terminals as a function of gas rate. The dots correspond to

actual data (see Appendix C). The continuous lines are based on Eq. (33) (left) and Eq. (30) (right) with a from Eq. (71). The shaded

areas are 80% confidence bands for the averages at each q .

Similarly, the regasification contribution to TerminalsCAPEX ( )q is considered to be dependent on q as

Regasification

Regasification1

Regasification Regasification 0, Regasification

0, Regasification

 CAPEX ( )

a

a qq c q l q

q (36)

with

Regasification 0.17a (37)

and

0, Regasification

0, Regasification

730 Bcf/y

$2 million/(Bcf/y)

q

l (38)

as shown in Fig. 5 (see Appendix D for justification and details). Note again the wide confidence bands, particularly for

CAPEX per gas rate at very low gas rates and CAPEX at very high gas rates.

10 SPE 165898

Fig. 5. CAPEX per gas rate (left) and CAPEX (right)for LNG regasification terminals as a function of capacity. The data points are from [7]. The continuous lines are based on Eq. (36) and the shaded areas are 80% confidence band for the averages.

CAPEX for LNG ships

The CAPEX for an LNG fleet is the sum of CAPEX for all LNG ships, namely

Fleet, LNG Ships, LNG Ship, LNGCAPEX CAPEX n (39)

The number of LNG ships in the fleet is

Ships, LNG

Ship, max, LNG

(2 )

L v qn

G, (40)

where the ceiling function, x , denotes the smallest integer larger than x , and Ship, max, LNGG is the maximum size of an LNG

ship that is reasonably available with today's technology (Fig. 6).

Fig. 6. Number of LNG ships for transportation of gas at rate q over a distance L .

The capacity of each LNG ship in the fleet is

Ship, LNG

Ships, LNG

(2 )

L v qG

n, (41)

as shown in Fig. 7.

SPE 165898 11

Fig. 7. Size of each LNG ship, Ship, LNGG , in a fleet for transportation of gas at rate q over a distance L .

The CAPEX for each LNG ship, Ship, LNG Ship, LNGCAPEX ( )G , is a function of the gas carrying capacity (volume) of a ship,

Ship, LNGG following economies of scale, as in Eq. (28), i.e.

Ship, LNG

Ship, LNG1 Ship, LNG

Ship, LNG Ship, LNG Ship, LNG Ship, LNG 0, LNG Ship, LNG

Ship 0, LNG

CAPEX ( )

a

a GG c G s G

G (42)

with

Ship, LNG 0.47a (43)

and

3

0, LNG

3

Ship 0, LNG

1.0 $million/(1000 m LNG) 46 $million/(Bcf NG)

266,000 m LNG 5.6 Bcf NG

s

G

(44)

3

Ship, max, LNG 266,000 m LNG 5.6 Bcf NG G , (45)

(see Appendix E and Fig. 8).

Fig. 8. CAPEX and CAPEX per gas capacity (volume) for LNG ships (tankers). The data points are averages for LNG tankers of capacities 155, 210 (Q-Flex) and 266 (Q-Max) thousand m3, (3.3, 4.4, and 5.6 Bcf NG, respectively) reported in [8] based on data from [9]. The continuous lines are based on Eq. (42).

Combining Eqs. (42) and (41) yields the total CAPEX for LNG shown in Fig. 9.

0 1 2 3 4 5 6

0

50

100

150

200

250

0 50 100 150 200 250

GShip , LNG Bcf NG

CA

PE

XShi

p,L

NG

$m

illio

n

GShip , LNG 1000 m3 LNG

0 1 2 3 4 5 6

60

80

100

120

140

160

1800 50 100 150 200 250

1

2

3

GShip , LNG Bcf NG

CA

PE

XS

hip

,LN

G

GS

hip

,LN

G

$m

illion

Bcf

NG

GShip , LNG 1000 m3 LNGC

APE

XS

hip

,LN

G

GS

hip

,LN

G

$m

illion

1000

m3

LN

G

12 SPE 165898

Fig. 9. CAPEX and CAPEX per gas capacity (volume) for LNG fleets.

CAPEX for CNG

CAPEX for CNG terminals

The main contributor to CAPEX for CNG terminals is gas compression, and secondarily decompression. For simplicity,

we assume that the CAPEX for a decompression station is half of the CAPEX of a compression station, which we discuss

next.

The cost of a gas compression station [10], is a function of the required compressor horsepower (HP), which, in turn, is a

function of the CNG compression ratio, r , and gas rate, q [1]. Assuming a compression ratio 4r , the CAPEX for

compression stations as a function of q is represented as

Compression

Compression1

Compression Compression 0, Compression

0, Compression

CAPEX ( ) HP( )

a

a qq c q l q

q (46)

with

Compression 0.36a (47)

and

0, Compression

0, Compression

365 Bcf/y

$million0.2

Bcf/y

q

l

, (48)

(see Appendix F and Fig. 10).

Fig. 10. CAPEX for CNG compression stations. The continuous line is Eq. (46), based on data collected in [11] (see Appendix F).

0 100 200 300 4000

20

40

60

q Bcf y

CA

PE

XC

ompr

ession

$m

illio

n

0 100 200 300 400

0.20

0.25

0.30

0.35

0.40

0.45

0.50

q Bcf y

CA

PE

XC

ompr

ession

q$m

illio

nB

cfy

SPE 165898 13

CAPEX for CNG ships

The CAPEX for a CNG fleet is the sum of CAPEX for all CNG ships, namely

Fleet, CNG Ships, CNG Ship, CNGCAPEX CAPEXn (49)

The situation with Ships, CNGn and Ship, CNGCAPEX is somewhat more complicated with CNG than with LNG [12], since the

CNG ships themselves provide temporary storage during loading and offloading of transportationed gas at a finite rate,

offload,maxq (of the order of up to 0.2 Bcf/d with current technology [2-3]). Because CAPEX on CNG ships constitutes most

(over 80%) of the total CAPEX of CNG projects [1], we discuss below how to keep that expenditure low by designing a

sensible CNG fleet through proper selection of the number and size of CNG ships.

To account for economies of scale, we use again Eq. (28) for the CAPEX of each CNG ship, i.e.

Ship, CNG

Ship, CNG1 Ship, CNG

Ship, CNG Fleet, CNG Ship, CNG Ship, CNG 0, CNG Ship, CNG

Ship 0, CNG

CAPEX ( )

a

a GG c G s G

G (50)

Because no commercial CNG project has materialized to date, the values of the parameters in the above Eq. (50) cannot be

based on actual data. However, estimates have been provided by developers of CNG containers [1], based on which it can be

inferred that

Ship, CNG 0.24a (51)

and

Ship 0, CNG

0, CNG

1 Bcf

$million300

Bcf

G

s, (52)

as shown in Fig. 11 (see Appendix H).

Fig. 11. CAPEX and CAPEX per gas capacity (volume) for CNG ships. The data points are from [1]. The continuous lines are based on Eq. (50).

The total number of CNG ships is

Ships, CNG Cycles n n n (53)

where

Cycles

offload, max

1q

nq

(54)

is the number of concurrent delivery cycles of CNG transportation ships required to meet demand of gas rate q ; and n is

the number of ships in each cycle delivering gas in succession, one after another, each ship having capacity [12]

Ship, CNG Ship, max, CNG

Cycles

offload, max

(2 )min{ , }

( 1)

L v qG G

qn n

q

(55)

0.0 0.2 0.4 0.6 0.8 1.0

0

50

100

150

200

250

300

GShip , CNG Metal Bcf

CA

PE

X$m

illio

n

0.2 0.4 0.6 0.8 1.0

300

350

400

450

500

550

600

GShip , CNG Metal Bcf

CA

PE

X

GS

hip

,CN

GM

etal

$m

illion

Bcf

14 SPE 165898

Selecting a value for n has a significant effect on the total capacity of the CNG fleet, with higher values of n resulting in

lower values of Fleet, CNGG as shown in Fig. 12, adapted from [12]. Following the analysis in Appendix G, we select

min 4 n n and

Ship, m ax, CNG offload, max

min

Cycles

(2 )

max{ , 1 }

L v q q

G qn n

n (56)

Fig. 12. Total capacity of a CNG fleet that contains n ships for each of cyclesn gas deliverly cycles, as a function of dimensionless

gas consumption rate, offload,maxq q . The number of delivery cycles, cyclesn , depends on the gas consumption rate, q , and

maximum gas offloading rate, offload,maxq , as cycles offload,max n q q . The shaded areas are conic bounds, with the upper bound

being offload,max

1 2

q q

n [12]. Note, that the required fleet capacity fleet, CNGG is fairly well approximated by its upper bound

CNG

2

Lf q

v in Eq. (84) when 1n .

The dependence of Fleet, CNG Metaln and Fleet, CNG Metaln on q and L resulting from combination of Eqs. (56), (53), and (54) is

shown in Fig. 13, and corresponding ship sizes are shown in Fig. 14.

SPE 165898 15

Fig. 13. Number of ships for transportation of gas at rate q over a distance L using metal or composite CNG containers. The

apparent discontinuities when crossing values of q equal to multiples of offload, max 73 Bcf/yq are due to the change of Cyclesn by

1. The two graphs are identical.

Fig. 14. Size of ships for transportation of gas at rate q over a distance L using metal or composite CNG containers. The two

graphs are identical.

Combining Eqs. (50), (56), (53), and (54) yields the results in Fig. 15.

16 SPE 165898

Fig. 15. CAPEX and CAPEX per gas capacity (volume) for CNG-Metal or CNG-Composite fleets.

Note that economies of scale for CNG ships are much less pronounced than for LNG ships, as manifest by the fact that

Ship, CNG Ship, LNG0.24 0.47 a a (c.f. Fig. 11 and Fig. 8). This was expected with current technology, since increased CNG

ship capacity is created not by increasing CNG container size but by adding more CNG containers, in a modular fashion [2-

3]. Note also that the potential exists for reduced CAPEX on CNG vessels in the future as experience on CNG ships

accumulates and placement of CNG containers on barges, which are less expensive, becomes a possibility.

OPEX for LNG

OPEX for LNG terminals

The cost of gas liquefaction and regasification is set at [13]

0,LNG

$million1

Bcfl (57)

OPEX for LNG ships

Shipping costs consist of operating costs (mainly staffing, insurance, and repairs & maintenance) and voyage costs [6].

Such costs are proportional to travel distance times the amount of gas transportationed, but the proportionality constant

follows economies of scale, as LNG tanker size increases, i.e.

SPE 165898 17

Transport, LNG

Ship, LNG

Transport, LNG 0, Transport, LNG Transport, LNG Ship, LNG

0, Transport, LNG

OPEX ( )ˆ

a

Gc L q C G L q

G (58)

with

Ship, LNG 0.30a (59)

0, Transport, LNG

$million0.07

kmile Bcf

c (60)

Ship, 0, Transport 4.5 BcfG (61)

(see Appendix I and Fig. 16).

Fig. 16. Transportation cost per gas unit per source-destination distancefor for LNG ships.

OPEX for CNG

OPEX for CNG terminals

0,LNG

$million0.1

Bcfl (62)

OPEX for CNG ships

Because CNG reduces gas volume 200 times, as opposed to 600 by LNG, we set

Transport, CNG Ship, LNG Transport, LNG Ship, LNG( ) 3 ( ) C G C G (63)

Results Use of the formulas in the preceding section along with the data in Table 3 produces the NPV results shown in Fig. 17.

0 1 2 3 4 5 6

0.08

0.10

0.12

0.14

GShip , LNG Bcf

CT

rans

port

$m

illio

n

km

ile

Bcf

18 SPE 165898

Table 3. Parameter values in formulas used to calculate NPV

LNG CNG

Metal Containers

CNG

Composite Containers

TerminalsCAPEX

a 0.20 (Liquefaction)

0.17 (Regasification)

0.36 (Compression)

0.36 (Decompression)

0.36 (Compression)

0.36 (Decompression)

0 [Bcf/y]q 1937 (Liquefaction)

730 (Regasification)

365 (Compression)

365 (Decompression)

365 (Compression)

365 (Decompression)

0

$million

Bcf/yl

14 (Liquefaction)

2 (Regasification)

0.2 (Compression)

0.1 (Decompression)

0.2 (Compression)

0.1 (Decompression)

r NA 4 4

FleetCAPEX

Shipa 0.47 0.24 0.24

0

$million

Bcfs

46 300 210

Ship 0 [Bcf]G 5.6 1 1

TerminalsOPEX

Volume Change

$million

BcfC

1 0.1 0.1

FleetOPEX

Transporta 0.30 0.30 0.30

0, Transport

$million

kmile Bcf

c 0.07 0.21 0.21

Ship, 0, Transport [Bcf]G 4.5 4.5 4.5

SPE 165898 19

20 SPE 165898

Fig. 17. NPV per natural gas rate for LNG, CNG Metal and CNG Composite. The white lines correspond to NPV=0.

Comparison between LNG and CNG Metal or CNG Composite is shown in Fig. 18.

SPE 165898 21

Fig. 18. Difference in NPV/q between LNG and CNG Metal and between LNG and CNG Composite. The intersection between the

plotted surface and the 0-plane is the line indicating the value of CrossoverL for each corresponding q .

The break-even value of the gas transportation tariff as a function of L and q for LNG and CNG Metal and CNG

Composite is shown in , and the difference between corresponding values between LNG and CNG (Metal and Composite) is

shown in

22 SPE 165898

Fig. 19. Break-even value of gas transportation tariff as a function of transportation distance and gas rate for LNG, CNG Metal, and CNG Composite.

SPE 165898 23

Fig. 20. Difference in BreakevenT between LNG and CNG Metal (left) and between LNG and CNG Composite (right). The white lines in

each contour plot indicate the value of CrossoverL for each corresponding q (shorter distances favor CNG).

It is interesting to compare the fraction of CAPEX allocated to the transportation fleet for each of the three options

studied, as shown in Fig. 21.

5

5

555

5

5

5

5

4

444

44

44

3

333 33

3

22

21

0

1

23

4

5

678

0 2 4 6 8 100

100

200

300

400

500

Distance, L kmiles

Gas

rate

,q

Bcf

yTBreakeven , LNG TBreakeven , CNG Metal

2

222

2

22

22

1

1

11

0

0

0

0

1

1

2

2

3

4

5

678

0 2 4 6 8 100

100

200

300

400

500

Distance, L kmiles

Gas

rate

,q

Bcf

y

TBreakeven , LNG TBreakeven , CNG Composite

24 SPE 165898

Fig. 21. Fraction of CAPEX allocated to the transportation fleet for LNG, CNG Metal, and CNG Composite.

Discussion and conclusions The relative advantages and disadvantages of LNV vis a vis CNG for marine transportation of stranded natural gas were

examined for both metal and composite CNG containers. Fundamental analysis combined with actual data revealed the

following general principles that underlie the marine LNG/CNG comparison.

- The key factor for determining whether marine LNG or CNG is economically preferable is the distance between

natural gas source and delivery destination, with shorter distances favoring CNG.

- A secondary factor for determining whether marine LNG or CNG is economically preferable is the quantity of

natural gas transported, to the extent that it influences differences in economies of scale for LNG and CNG systems.

Smaller quantities of gas generally can be transported more economically using CNG, rather than LNG, for larger

distances than larger quantities can.

- The price of natural gas has no effect on whether CNG or LNG is preferable. However, price obviously has a strong

effect on the overall economic feasibility of whichever of CNG or LNG is chosen.

- Composite CNG containers have significantly better economics than metal CNG containers.

The above findings offer a strong incentive towards undertaking a pioneering commercial effort for proof-of-concept of

marine transportation of stranded gas using CNG, with potentially important implications well into the future.

Nomenclature

NPV Net present value ($million)

PV Present value ($million)

CAPEX Capital expenditures ($million)

SPE 165898 25

N Total number of years (#)

k Year number (#)

CF Cash flow ($million/y)

DCF Discounted cash flow ($million/y)

ACF Annual cash flow ($million/y)

i Interest rate (% or fraction)

q Gas transportation rate (Bcf/y)

L Gas transportation distance (one-way, from origin to destination) (kmiles)

Fleet G Fleet capacity (gas volume) (Bcf)

Ship G Ship capacity (gas volume) (Bcf)

Terminals C Terminals cost per gas rate (compression and expansion for CNG, liquefaction and regasification for LNG)

($million/(Bcf/y))

Fleet C Gas transportation fleet cost per gas rate per distance between gas origin and destination

($million/kmiles/(Bcf/y))

OPEX Operating expenditures ($million/y)

VolumeChange C Gas volume adjustment cost per gas volum (compression and expansion for CNG, liquefaction and

regasification for LNG) ($million/Bcf)

Transport C Gas transportation cost per gas volume per distance between gas origin and destination

($million/kmiles/Bcf)

D Annual depreciation in linear scheme ($million/y)

, L LA B NPV factors, Eq. (8)

NI Time factor for NPV calculation, Eq. (11)

taxf Tax rate (% or fraction)

x LNG CNGx x for the variable x

Crossover L Upper bound on distance for which CNG is economically favored over LNG

h Factor for calculation of CrossoverL , Eq. (16)

T Gas transportation tariff = Gas sales price – Gas purchase price ($million/Bcf)

, T TA B NPV factors, Eq. (21)

Breakeven T Lower bound on gas price for which gas transportation is economically feasible

Q Capacity (e.g., natural gas processing rate, natural gas storage volume, natural gas carrying volume, etc.)

( ) F Q Cost as a function of capacity ($ million)

a Exponent in power law for economies-of-scale, e.g. Eq. (28)

( ) l q Land facilities cost per gas consumption rate unit ($/(Bcf/year))

n Number of ships

x Ceiling of x = smallest integer greater than or equal to x

MTPA Million tones LNG per annum

s Ship cost per gas volume ($million/Bcf)

v Voyage speed (mph or kmiles/y)

travelt One-way travel time from gas source to delivery destination

r CNG compression ratio

HP Compression power (hp)

References 1. Economides, M.J., K. Sun, and G. Subero, Compressed Natural Gas (CNG): An Alternative to Liquefied Natural Gas. SPE

Production & Operations, 2006. 21(2): p. 318-324.

2. EnerSea Transport LLC. 2013; Available from: http://www.enersea.com/.

3. Sea NG Corporation. 2013; Available from: http://www.coselle.com/.

4. Neptune Gas Technologies, L. Neptune CNG System. 2013; Available from: http://neptunegas.ca/technology/index.html.

5. Peters, M.S., K. Timmerhaus, and R.E. West, Plant Design and Economics for Chemical Engineers. 5th ed. 2003: McGraw-Hill.

6. Thakur, N. (2011) LNG shipping economics on the rebound. Petroleum Economist, http://www.petroleum-

economist.com/Article.aspx?ArticleId=2801286.

7. Griffin, K., et al., The Global Liquefied Natural Gas Market: Status & Outlook. 2003, US Energy Information Administration.

8. Capman Consulting (2012) LNG Report 2012.

26 SPE 165898

9. Drewry Maritime Research. 2012.

10. Rui, Z., et al., Regressions allow development of compressor cost estimation models, in Oil & Gas Journal. 2012, PennWell

Corporation: Tulsa, United States, Tulsa. p. 110-115.

11. Miscellaneous, Oil & Gas Journal Databook. 2010, Tulsa, OK: PennWell.

12. Nikolaou, M., Optimizing the Logistics of Compressed Natural Gas Transportation by Marine Vessels. Journal of Natural Gas

Science and Engineering, 2010. 2(1): p. 1-20.

13. Shively, B., J. Ferrare, and B. Petty, Understanding Today's Global LNG Business. 2010: Enerdynamics.

14. Cornot-Gandolphe, S., et al. THE CHALLENGES OF FURTHER COST REDUCTIONS FOR NEW SUPPLY OPTIONS

(PIPELINE, LNG, GTL). in 22nd World Gas Conference. 2003. Tokyo, Japan.

15. Cheniere Energy, I., November 2011 Investor Presentation. 2011:

http://www.plsx.com/finder/viewer.aspx?doc=11502&slide=263892#doc=11502&slide=263892&.

Appendix A. Derivation of NPV formula, Eq. (8) Assuming constant annual cash flow after taxes, i.e.

After Taxes, After TaxesACF ACF constant k (64)

we have

After Taxes

Tax

ACF ACF (ACF )

ACF (1 )

Tax

Tax

D f

f D f (65)

where the annual cash flow is

Gas SalesACF ACF OPEX . (66)

It follows that

Gas Sales After Taxes,

1

After Taxes,

1

After Taxes

Tax

Gas Sales Tax Tax

PV DCF

ACF

(1 )

(1 ) 1ACF

(1 )

ACF (1 )

(ACF OPEX) (1 )

N

k

k

Nk

kk

N

N

N

Tax N

N

i

i

i i

I

f D f I

f D f I

(67)

Substitution of Gas SalesPV from the above Eq. (67), CAPEX from Eq. (4) and OPEX from Eq. (5) into Eq. (1) yields

Terminals Fleet

Transport Volume Change Tax Tax

Terminals Fleet

NPV 1

N

C C L qT C L C q f f I

N

C C L q

(68)

which immediately implies Eq. (8).

Appendix B. Derivation of approximation in Eq. (16)

Using the approximation (1 ) 1 Ni N i and substituting NI from Eq. (11) into Eq. (16) yields

Tax

Tax

Tax

Tax

Tax

(1 )

(1 ) 1

1

(1 )

(1 ) 1

1

1

1

N

N

fi i

Nih

f

fN i i

N i N

f

i

N f

(69)

SPE 165898 27

Appendix C. CAPEX for LNG liquefaction terminals, Eq. (33) According to [14], p. 11, doubling the capacity of an LNG liquefaction terminal reduces the CAPEX per gas flow rate by

about 25%. This reduction in specific cost is due to economies of scale, usually due to utility sharing among liquefaction

trains (e.g. see [15]). Consequently, the term Terminals( ) CAPEX ( ) /̂l q q q must satisfy the equation

(2 )1 0.25

( )

l q

l q (70)

The function in Eq. (33) satisfies Eq. (70) if

Liquefaction

ln 0.750.42

ln 2

a (71)

However, available data indicate that economies of scale may be less pronounced, as can be claimed based on example data

shown in Table 4. One instance is ALNGT1-3 (9.6 MTPA), resulting from expansion of ALNGT1 (3 MPTA) with two

additional liquefaction trains and with specific cost reduction from 270 to 200 $/MTPA, corresponding to

Liquefaction

ln(200 / 270)0.26

ln(9.6 / 3)

a (72)

However, the instance of ELNGT1-2/ ELNGT1 implies

Liquefaction

ln(200 / 270)0.43

ln(7.2 / 3.6)

a (73)

Therefore, we choose to fit the entire data set in Table 4 using Eq. (30) with results shown in Eqs. (34) and (35) and Fig. 4.

Table 4. Data on specific costs of liquefaction terminals

Project Capacity

(MTPA)

Capacity

(Bcf/y)

Specific cost

($/MTPA)

ALNGT1 3 138 270

Gladstone 3.5 161 2000

ELNGT1 3.6 166 270

Snohvit 4.3 198 1200

Angola 5.2 240 1650

ELNGT1-2 7.2 332 200

Curtis 8.5 392 1700

Sakhalin 9.6 443 1000

ALNGT1-3 9.6 443 200

Oman 10.4 480 270

Gorgon 15 692 2100

Nigeria 22 1015 390

RasGas 36.3 1675 350

Qatargas 42 1937 420

Fig. 22. Specific cost of liquefaction projects (data points) and fit by Eq. (30) with a from Eq. (71) (continuous line) along with 95%

confidence interval for averages (shaded area).

Appendix D. CAPEX for LNG regasification terminals, Eq. (36) According to [7], p. 46, "In the United States, most new terminals are estimated to cost US$200 to US$300 million for a

sendout capacity from 183 to 365 Bcf/y (3.8 to 7.7 million tons/y) of natural gas". Using these data points with Eq. (36)

yields

28 SPE 165898

Regasification

365ln

1831 0.4

300ln

200

a

(74)

Using the same data for calibration yields the values in Eq. (38).

Table 5. Data on specific costs of regasification terminals

Regasification Terminal Capacity (Bcf/y) Cost ($million)

EcoElectrica, Puerto Rico 34 150

AES, Dominican Republic 46 70

Fujian LNG, PRC 128 250

GNL Quintero, Chile 146 775

Golden Pass LNG, Sabine Pass, LA 730 1100

Dragon LNG, Milford Haven, Wales 730 1300

Appendix E. CAPEX for LNG fleet, Eq. (42)

The required gas carrying capacity for each ship, Ship, LNGG , depends on the gas consumption rate, q , and travel distance, L ,

as follows: The total capacity of an entire LNG fleet is

Fleet, LNG

2

LG q

v, (75)

This capacity is distributed over as few ships as possible, to ensure the smallest possible CAPEX and OPEX. Because there

is an upper bound, Ship, max, LNGG , on the maximum capacity of an LNG ship (as shown in Fig. 8) the number of required LNG

ships is

Ships, LNG

Ship, max, LNG

(2 )

L v qn

G (76)

Consequently,

Ship, LNG

Ship, m ax, LNG

(2 )

(2 )

L v qG

L v q

G

, (77)

According to [8], based on data from [9], new LNG tankers of capacity 155,000 m3 cost $180-190 million, and Q-Flex

(200,000 m3) and Q-Max (266,000 m

3) tankers cost $200-300 million. Using average values of $185 and $250 million,

respectively, the preceding three data points can be approximated by an equation similar to Eq. (28), with

Ship, LNG Ship, LNG1 0.53 0.47 a a , as shown in Fig. 8.

Appendix F. CAPEX for CNG compression stations, Eq. (80) The cost of compression stations as a function of HP has been reported in [10], using US data from 1992 to 2008 collected in

[11]. The authors in [10] use a quadratic function of HP in the range 3,000 to 30,000, namely

2Compression 0 6 7

CAPEX HP HP

HP HP

a (78)

with 0 6,500,617 , 6 1,019.361a , 7 0.0041406 . To allow for better extrapolation in either direction, a power-law

(cf. Eq. (28)), in the form

CompressionCompression

Compression

CAPEXHP

HP

ac

(79)

is fit to the above Eq. (78), with Compression

Compr 1ession

$49,178

hpa

c

, Compression 0.36a (Fig. 23).

SPE 165898 29

Fig. 23. CAPEX for compression stations. The dashed line is based on [10]. The continuous line is from best fit of Eq. (79).

The total cost for a gas compression station [10], is a function of the required compressor horsepower (HP), which, in

turn, is a function of the CNG compression ratio, r , and gas flow rate, cq [1]. The CAPEX for compression stations as a

function of HP is represented as

Compression

Compression1

Compression Compression 0, Compression

0

HP( , )CAPEX (HP) HP( , ) HP( , )

HP

a

a r qc r q c r q (80)

with

2

2 1 0 hpHP( , ) (ln ) ln ( )ˆ c qr q h r h r h q F r q (81)

as reported in [1].

Therefore, for a given compression ratio, r , in Eq. (81), substitution of HP into Eq. (80) yields Eq. (46). For a

compression ratio 4r the required HP cq , by Eq. (81), is

hp

2HP hp hp21.933 (ln 4) 20.976 ln 4 14.275 85.5 234

MMscf/d Bc(

f/)

y4 qF

q. (82)

Therefore, substituting Eq. (82) into Eq. (79) yields

Compression

Compression

Compression

Compression

Compression

1

Compression

1

0, Compression

0, Compression

1

1

$ hp49,178 234

Bcf/yhp

$million1.63

(Bcf

CAPE

)

X

ˆ

/y

a

a

a

a

a

q

ql

q

qq

(83)

For a reference gas rate 0, Compression 365 Bcf/ycq , Eqs. (29) and (83) yield

Compression

Compression

0.36

0, Compression 0, Compression 1

$million1.63 36

$million( ) Bcf/y 0.2 5

(Bcf/y) Bcf/y

a

c al c q

.

Appendix G. Selecting the number and size of ships in a CNG transportation fleet It has been shown [12] that the capacity of CNG fleet is bounded as

Fleet, CNG CNG CNG Fleet, LNG

CNG

1 2 2ˆ

21

L LG q f q f G

v v

n

f

(84)

with

0HP 6 7 HP

c HP a

5000 10 000 15000 20000 25000 30 000

1500

2000

2500

3000

hp

$hp

30 SPE 165898

Fleet, CNG

CNG

Fleet, LNG

1ˆ

21

Gf

G

n

(85)

as shown in Fig. 12, adapted from [12]. The CNG capacity factor, CNGf , in Eq. (84) refers to how many times larger a real

CNG fleet is than a theoretically ideal (but physically unrealizable) CNG fleet of infinite ships ( n ), each of

infinitesimally small capacity (Fig. 12) – essentially an approximation of a two-way floating pipeline. As shown in Fig. 24,

opting for a relatively larger number of relatively smaller CNG ships results in significant reduction of Fleet, CNGG , entirely due

to better logistics [12]. Additional reduction of Fleet, CNGG could result from introducing temporary CNG storage capacity in

addition to that of CNG ships, but this possibility is not considered here, for the sake of simplicity.

Fig. 24. CNG fleet capacity factor as a function the number of CNG ships per delivery cycle (cf. Fig. 12).

Based on the preceding arguments, it is evident that a reasonable value of n must be selected to make Fleet, CNGG , and

consequently keep Fleet, CNGCAPEX low, without overly increasing the corresponding Fleet, CNGOPEX .

In reducing Fleet, CNGG , overly large values of n are to be avoided, since, in addition to higher Fleet, CNGOPEX , such values

will eventually increase Fleet, CNGCAPEX , due to reverse economies of scale associated with very small ships, as quantified in

Eq. (50). This claim can be quantified as follows.

Combination of Eqs. (49)-(55) yields

Ship, CNGFleet, CNG 1

offload, max

offload, max

CAPEX

1

a

n

q qn

q q

(86)

with Ship, CNG1 0.76 a (Eq. (51)). The optimal value of n can be computed from Eq. (86) in terms of offload, maxq q as

offload, max

offload, maxopt

Ship, CNG Ship, CNG

12

8.3

q q

q qn

a a (87)

(Fig. 25).

3 4 5 6 7 8 9 101.0

1.5

2.0

2.5

3.0

n

f CN

GG

Fle

et,C

NG

GF

leet

,LN

G

SPE 165898 31

Fig. 25. Approximation (continuous line) and exact values of optn .

Appendix H. CAPEX for CNG fleet, Eq. (50) According to [1], new CNG ships based on Votrans technology cost $150 and $300 million for gas carrying capacities of 0.4

and 1.0 Bcf, respectively. Fitting Eq. (28) to these data results in Eqs. (51) and (52).

Appendix I. OPEX for LNG fleet, Eq. (58) Data from Drewry Maritime Research reported in [6] implies the gas transportation costs shown in Fig. 26. Fitting the

slopes, 1 2, , of the two straight lines by the power law

Transport, LNG

0, Transport, LNG

0, Transport, LNG

a

Gc

G (88)

yields Eq. (60).

Fig. 26. LNG transportation cost as function of distance for LNG tankers of capacities 170,000 (linear fit: Cost 0.0733 L ,

2 0.99R ) and 215,000 m3 (linear fit: Cost 0.0683 L , 2 0.99R ).

0 1 2 3 4 50

1

2

3

4

5

6

7

8

9

q

qoffload, maxn

opt

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

Distance , L kmiles

Tra

nsp

ort

cost

$m

illio

n

Bcf 170,000 m3

215,000 m3