FILE COPY

NBSIR 77-862 IX) NOT REMO\^

STUDIES OF HYDROGEN LIQUEFIER EFFICIENCY AND THE

RECOVERY OF THE LIQUEFACTION ENERGY

R.O. Voth

W.R. Parrish

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

August 1977

IMBSIR 77-8 62

STUDIES OF HYDROGEN LIQUEFIER EFFICIENCY AND THE

RECOVERY OF THE LIQUEFACTION ENERGY

R.O. Voth

W.R. Parrish

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

August 1977

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director

CONTENTS

Page

CHAPTER 1. HYDROGEN LIQUEFIER EFFICIENCY 1

R. 0. Voth

1. SUMMARY 1 1.1. Introduction 1 1.2. Derivation of the Defined Cycle 2 1.2.1. Losses due to expander and compressor

inefficiency 6 1.2.2. Losses due to heat exchanger temperature

difference 8 1.2.3. Losses due to pressure drop 11

1.2.4. Multipressure liquefaction cycles 11

1.3. The Real Hydrogen Liquefier 11

1.3.1. Efficiency and losses of real liquefier

components 15

1.3.1.1. Compressor 15

1.3.1.2. Expanders 16

1.3.1.3. Joule-Thomson expansion valve ... 17

1.3.1.4. Expansion ejector valve 17

1.3.1.5. Heat exchangers 19

1.3.2. Real hydrogen liquefier cycle 19

1.3.2.1. The design of a practical

hydrogen liquefier 32

1.4. Comparison Between Defined Cycle and Real Gas

Cycle 35

1.5. Conclusions 35

1.6. Nomenclature 39

1.7. References 41

1.8. APPENDIX - Hydride Compressors 4 2 1.8.1. Introduction 42

1.8.2. Properties of metal hydrides 42

1.8.3. Hydride compressor system 42

CHAPTER 2. RECOVERY OF HYDROGEN LIQUEFACTION ENERGY 4 5 W. R. Parrish

2. SUMMARY 4 5 2.1. Introduction 4 5 2.2. Electrical Utility Applications 46

2.2.1. Liquefaction energy recovery factor 46

2.2.2. Liquefaction energy recovery systems .... 47

2.3. Recovery of Rare Gases 51

2.3.1. Helium recovery process 52

2.3.2. Work limitations 52

2.3.3. Refrigeration limitations 53

2.4. Conclusions 53

2.4.1. Utility application 53

2.4.2. Rare gas recovery 53

2.5. References 54

2.6. APPENDIX - Air Plant Design 55

2.6.1. Design using an atmospheric column 55

2.6.2. Subatmospheric column 57

iii

ABSTRACT

Liquid hydrogen is a potential synthetic fuel. It is nonfossil, its production and storage technology is well developed,

and it is inherently nonpolluting . However, the economics of

liquefying hydrogen are costly both in the energy required to

produce the liquid and in the capital costs of the liquefier.

These costs could be reduced by increasing the liquefier efficiency and/or by recovering a portion of the liquefaction energy

at the use site. This paper provides the maximum hydrogen liquefier efficiency based on the efficiency of available components and the fraction of original liquefaction energy that can

be recovered at the use site. Since the inefficient compressors

and expanders are the major cause of liquefier inefficiency, no increase in liquefier efficiency above the current 30 to 35

percent is probable without a corresponding increase in compressor and expander efficiency --a difficult task since both the

compressors and expanders have a long and stable history of

development. However, roughly one-third to one-half of the

actual energy required to liquefy hydrogen can be recovered at

the use site and this represents a cost credit for liquid hydrogen.

Key words: Component efficiency; cryogenics; efficiency; energy

recovery; hydrogen; liquefier.

iv

CHAPTER 1

HYDROGEN LIQUEFIER EFFICIENCY

R. 0. Voth

1. SUMMARY

The efficiency of current hydrogen liquefiers lies in the range of 30 to

35 percent of Carnot. Since this efficiency appears low when it is compared

to other thermodynamic cycles, this study was undertaken to determine the

maximum possible efficiency for large capacity mechanical liquefiers using

state-of-the-art compressors, expanders, and heat exchangers. Two approaches

were used to determine the maximum efficiency. The first approach employs a defined liquefaction cycle that uses an ideal gas working fluid. Although

the working fluid is ideal, the real effects on liquefier efficiency of heat

exchanger temperature difference, system pressure drop, and component efficiency can be determined. The second approach uses hydrogen properties in

practical cycles to determine maximum liquefier efficiency. With a real gas

working fluid the final expansion device could be a Joule Thomson valve, an expansion ejector or a wet expander (the exhaust of the expander contains

liquid) instead of the theoretical isothermal expander of the defined cycle.

The maximum liquefier efficiency found from the two approaches agreed

closely and they were in the range of 30 to 3 5 percent. Because the com- pressors and expanders were the major sources of inefficiency, no increase

in liquefier efficiency is probable without a corresponding increase in the

compressor or expander efficiency -- a difficult task since both the com- pressors and expanders have a long and stable history of development. Consequently, higher liquefier efficiencies are not probable in the near future.

Because of the large dependence of the liquefier efficiency on compressor

efficiency, a metal hydride compressor was investigated. The heat required by

the hydride compressor was obtained from the waste heat of a parallel mechanical compressor. However, because of the low quality of this heat, the hydride

compressor did not contribute significantly to an increase in the overall

efficiency of the compressor system.

1.1. Introduction

The cost of producing liquid from gaseous hydrogen is an economic barrier

to the early adoption of liquid hydrogen as an "energy carrier". Decreasing

the liquefaction costs is partially dependent on increasing the efficiency of

the liquefaction process above the current 30 to 35 percent [1] . This study

investigates the efficiency of hydrogen liquefiers in the following manner:

1) By using a defined cycle with a perfect gas working fluid, the

maximum efficiency of the liquefier as a function of the efficiency

of the liquefier components is established. The defined cycle

efficiency — the cycle is reversible for reversible components —

includes the effects of component inefficiency, system pressure drop,

and heat exchanger temperature difference.

2) The efficiencies of practical cycles with a real-gas (hydrogen)

working fluid are determined and compared to the defined cycle

efficiencies. The practical liquefier is designed for maximum

efficiency using a Joule Thomson expansion valve, an expansion ejector,

or a wet expander as the final expansion device. The comparable

efficiencies found by the defined cycle and the practical liquefier,

shows that the penalty in efficiency associated with the use of a real gas can be made small with appropriate cycle selection.
As a result of these calculations, the inefficiency of the compressors and ex- panders are shown to have the most influence on the overall liquefier efficiency.

An unsuccessful attempt to increase the efficiency of the compressor by

the use of a metal hydride is shovm in Appendix A. Without an increase in

compressor or expander efficiency, the current hydrogen liquefier efficiencies

of 30 to 35 percent of Carnot will not be increased significantly in the

future

.

1.2. Derivation of the Defined Cycle

The analysis of a hydrogen liquefaction cycle is a complex thermodynamic

and economic problem. The thermodynamic complexity results from the nonideal properties of hydrogen. For example, simple first law analysis does not

\incover negative heat exchanger temperature differences dictated by the variable specific heats in the real gas when invalid boundary conditions are chosen

Therefore, it is necessary to perform a more complex numerical analysis of

the system heat exchangers. Variable properties also require optimization of

pressure ratios and temperature inlets for the expanders used in the system.

The analysis must also include economics. For example, a heat exchanger

designed for small temperature differences will increase the overall cycle

efficiency but require an increased capital expenditure. The usual approach

to cycle studies is to make a parametric study of the liquefaction cycle

using a computer and then to choose one of the calculated cycles that is com- patible with available components. Although this approach gives exact results, one is never quite sure that a different (and unconsidered) cycle

might not yield a superior efficiency.

By using a simple defined cycle which is reversible for reversible components, we are able to easily evaluate the effect of various system components, and to make a reasonably accurate estimate of the maximum possible

cycle efficiency with components of given efficiencies.

Liquefier efficiency is based on the equation:

•' ' _ Ideal power requirements ,^ 2 ^ ^cy Actual net power requirements

The net power required by the cycle is the required compressor power less the

recoverable power from the expanders. The cycle efficiency should be 100

percent when the components in the cycle are ideal and the effect of com- ponent losses in the cycle on cycle efficiency should be realistic.

By extending the earier work of Collins [2] for an ideal liquefaction

cycle, the defined cycle shown schematically in figure 1.1 is derived. The

cycle uses a refrigeration loop to precool and condense a separate product

stream. The refrigeration loop bypass turbines are situated so the inlet

temperature of each expander is higher than the discharge temperature of the

preceding expander by the temperature difference of the heat exchanger. The

heat exchanger temperature difference is proportional to the absolute temperature as defined by a constant C = AT/T. The final expander in the refrigeration loop is a theoretical isothermal expander used to condense the product

stream. Both the refrigerant and the product streams are perfect gases with

constant specific heats. The product stream condenses at T^ with a latent

heat 28.988 K times the specific heat (i.e., the same ratio as for hydrogen).

Changing the latent heat ratio and the value of T^ would make the defined

cycle applicable to other fluids. The high temperature (heat rejection) end

of the cycle (T„ figure 1.1) is taken as 300 K in the calculations, while the

n cold end temperature (T ) was taken as 20.268 K, the normal boiling point

of liquid parahydrogen

.

2
d

Isothermall

Compressorh p^Q^ . ^

Product (i)

Figure 1.1. Schematic of the defined cycle.

3
The arrangement of the expanders in the precooling portion of the cycle

(figure 1.1)/ is the most efficient arrangement because the refrigeration

required by the product stream is exactly matched at each temperature by the

refrigeration produced by the expanders. For reversible expanders and heat

exchangers, this arrangement is reversible. For finite size heat exchangers,

balanced flow maintains a constant heat exchanger temperature difference,

and the flow through each expander is the same as the product stream flow,

03. In order to maintain AT T in the heat exchanger (which minimizes the

heat exchanger losses [3]), a slight imbalance in the flow is required, re- sulting in a slightly greater expander flow.

Returning to the definition of cycle efficiency (equation 1.2.1), the

cycle efficiency can be written as

the overall cycle efficiency based on W^j^r

ideal liquefier power requirements,

actual total compressor power, and

the recoverable expander power.

The expander output can be recovered by using it to drive either a booster

compressor stage or an electrical generator to provide part of the power re- quired by the main compressor. In either case, the power required by the

liquefier is reduced by part of the expander output. In the first case the

required compressor power is reduced by an amount equal to the expander power

assuming an equal efficiency for both compressors. In the second case the

recoverable expander power is less than the expander output due to the

inefficiency of gear trains and the electrical generator. In the calculations

presented here the total compressor power requirements were reduced by the

total calculated expander power.

where

n cy

W . ci

W

ca

The ideal work of liquefaction is determined from the availability function of the product.

where

^ = ^1 - ^o - ^o (^1 - =0^

y = availability associated with the minimum work of formation,

also the maximum work recoverable from a fluid at the defined

state,

T = absolute temperature,

h = specific enthalpy,

s = specific entropy and,

subscripts

1 = defined state — liquid hydrogen at 1 atmosphere,

0 = ambient conditions -- 1 atmosphere pressure, 300 K temperature.

For a perfect gas system the ideal liquefaction power can be defined as the sum of: 1) the ideal power required to precool the product stream (W^^) , and

2) the ideal power required to condense the product (^2''' Precooling the product stream occurs over a variable temperature, and the ideal work for this

process is given by Jacobs [4] as.

4
T - T. ^1 = -^T (1.2.4)

Im

where

T = ambient temperature also equal to T„ for the liquefier, O ri

"^im = - ^c)/l^ (V^C^'

= lowest refrigeration temperature,

Q = heat load equal to the product stream flow rate ((L) times

Cp(T^ - , and

C = constant pressure specific heat.

P

By replacing Q, the ideal work for the variable temperature process be- comes , T - T,

W = -Afi ^(LC (T -T). (1.2.5)

1 p H C

The ideal power required to condense the fluid at a constant temperature

is

T , - T

W = Q {-^ ^) , (1.2.6)

C

where

Q = A X (i), and

A = Latent heat.

Thus, the total ideal power required is,

T - T T - T

W^. = Ar^ — (I) C (T - T ) + (L (A) (-^ ^) (1.2.7) ci T^^ p H C

or since A = 28.988 x C^,

T - T T — T

W^. = — (I) C„(T„ - T ) + 28.988 C (L ^) . (1.2.8) ci . T^^ p H C p

Since the minimum compressor power is a result of a reversible isothermal

process, compressor efficiencies used in the calculations are based on the

ideal isothermal work of compression. For a perfect gas the isothermal com- pressor power is given by, m RT iln Pr

W. = ^ (1.2.9)

where

= isothermal compression power,

m = mass flow through the compressor!

R = gas constant.

5
T„ = compression temperature (T = T )

,

H ri U

Pr = pressure ratio (high pressure/low pressure) , and

' - isothermal efficiency of the compressor.

The total flow through the compressor is the sum of the flows through the ex- panders, and the total expander flow is a function of losses in the cycle.

These losses are a result of the inefficiency of the expanders, of heat ex- changer temperature differences and of system pressure drop. Each of these

loss effects will be covered separately.

1.2.1. Losses due to expander and compressor inefficiency

In this section only the losses from inefficient expanders and compressors

will be considered. The heat exchangers have zero temperature differences

and there is no system pressure drop.

The losses incurred by inefficient precooling expanders are a result of

a less than ideal temperature drop across the expanders. This decreased temperature drop increases the number of expanders required in the precooling

portion of the liquefier thereby increasing the compressor flow rate. Flow

through the isothermal expander also increases with decreasing efficiency.

With zero temperature difference in the heat exchanger, the flow through each

precooling expander is equal to the product stream flow. Thus, the compressor

flow due to the precooling expanders becomes

ra = N X 0) (1.2.10) pre exp ^

' where

m^^^ = total mass flow rate through the precooling expanders, and

^exp ~ number of precooling expanders.

The temperature drop across an expander operating with a perfect gas is

^in - Tout = Ve '^in " ^^''^ (I-^'ID

where

= the expander inlet temperature,

T^^^ = the expander outlet temperature,

rip^g = isentropic efficiency of the precooling expanders,

Pr = pressure ratio across the expander,

a = (k - l)/k, and

k = ratio of specific heats (1.404 for hydrogen at ambient temperature and zero pressure)

.

From figure 1.1, expressions for T^, T^, T , can be written based on the

expander efficiencies as follows ^

^2 (1 -

n pre

+ n pre

Pr"") (1.2.12)

= T2 (1 -

n pre

+ n pre

Pr"") (1.2.13)

1 n+1 = T

n

(1 -

n pre

+ n pre

Pr"^). (1.2.14)
Assioming the same efficiency for all the precooling expanders and substituting to maintain T„ in the equation yields,

n N

Solving for the number of expanders (N^^^) results in

In (^)

N = . (1.2.16)

In (1 - n + n Pr~^) pre pre

If the expanders are reversible, the equation reduces to

In (^)

^exp = ^ ' (1.2.17)

In (Pr ^)

The recoverable power from each precooling expander becomes,

= ^ C (T.^ - T^^^), (1.2.18)

pre

or summing from T„ down to T_, the total recoverable power becomes

n C

Wj^ = ^ C {T^ - T^). (1.2.19)

pre ^

The mass flow through the isothermal expander is related to the expander

efficiency and the flow and latent heat of the product stream as,

28.988 (Cp) (o)) "'iso " ~. T^R In Pr ' (1.2.20)

ISO C

where

28.988 Cp = latent heat of the product stream, J/mol,

n- = isothermal efficiency of the expander, ISO

and R = gas constant.

The recoverable power from the isothermal expander is equal to

W„ = 28. 988 (C„) ((L) . (1.2. 21)

t\ • p ISO

An equation for the overall cycle efficiency can now be written by substituting into the general cycle efficiency expression, equation (1.2.2).

= :

^ (1.2.22)

(m + m. ) R T„ Im Pr ^re ^2 H

, , „^ , c pre ISO

7
minimum ideal-cycle power, equation (1.2.8) '

total mass flow through the precooling expanders, equations

(1.2.10) and 1.2.16) mass flow through the isothermal expander, equation (1.2.20)

recoverable work from the precooling expanders, equation

(1.2.19)

recoverable work from the isothermal expander, equation

(1.2.21)

.

The specific heat (C^) cancels in equation 1.2.22 when the results of the

previous equations are substituted. This leaves the condensing temperature

(T^) , the ratio of latent heat to specific heat, and the ratio of specifc

heats (k) as the only parameters relating the equation to a hydrogen liquefier. Although the specific heat ratio, k, varies over a broad range as the

temperature of hydrogen is reduced, it was found that this variation affected

the optimum pressure ratio for the cycle but had little effect on the maximum cycle efficiency shown in the results. The ratio of latent heat to

specific heat (28.988 K) was determined for the case of equilibrium conversion

from normal to parahydrogen as the temperature of the product stream is reduced. The effect of conversion at temperatures lower than equilibrium can

be determined by varying the latent heat to specific heat ratio.

Cycle efficiencies as a function of expander and compressor efficiencies

are shown on figure 1.2. In this figure the precooling expanders and the

isothermal expander were assumed to have the same numerical efficiency. The

plotted results are for a liquefier with six precooling expanders.

The results show that without considering any losses from heat exchanger

temperature differences or pressure drop, the maximum cycle efficiency obtainable with 80 percent of adiabatic precooling expanders, an 80 percent isothermal

expander, and a 60 percent isothermal compressor is approximately 40 percent

of Carnot.

1.2.2. Losses due to heat exchanger temperature difference

Calculation of the effect of heat exchanger temperature difference on overall liquefier efficiency greatly complicates the simple equation used in

the previous section. This complication results because losses in the colder

portion of the cycle compound the losses due to heat exchanger temperature

differences in the warmer portion of the cycle. The cycle efficiency calculation must therefore become more specific about flow rates in each heat

exchanger and through each expander. In the previous cycle efficiency calculation, the number of expanders could be non-integer without affecting the

validity of the results. However, in considering the heat exchanger temperature differences losses, the number of expanders must be integer.

When heat exchanger temperature differences are considered, the number

of precooling expanders required in the cycle is increased because of the

overlaps between the discharge temperature of a previous expander and the

inlet temperature of the following expander. Also, the flow through each

expander must be higher than the product stream flow rate because the temperature difference in each heat exchanger decreases with absolute temperature.

The procedure followed was to select a number of precooling expanders,

solve for the required pressure ratio and determine the flow through the isothermal expander. Using this flow as the inlet and discharge flow to the

bottom or coldest portion of the n*^^ heat exchanger (figure 1.1), the required

flow to the top or warm end of the same heat exchanger was determined from an

where

W

ci

m . pre

m

.

ISO

pre

and = iso

8
LUQ

n l I I I I

\ \ \ \ \ \ I I 40 50 60 70 80 90 100

EXPANDER EFFICIENCY, %

Isothermal Condensinq Expander has the same Numerical

Efficiency as the Adiabatic Precooling Expanders

Figure 1.2. Defined cycle efficiency without pressure drop and heat exchanger

temperature difference losses.

9
energy balance around the heat exchanger. The product flow stream maintains

its flow of 0) throughout the procedure. The flow at the top of the nth heat

exchanger now becomes the inlet and discharge flow for the cold end of the

(n - 1) heat exchanger. The summing procedure continues to the compressor

end of the cycle when the total compressor flow is determined.

The pressure ratio determination is made by deriving an equation similar

to equation (1.2.15) except that C (where C = AT/T, used to define heat ex- change temperature difference) is included in the derivation. Equation

(1.2.15) now becomes

(1.2.23)

pre

L[(l - C)(T^/T^) + Hp^^ - 1]

(1.2.24)

By selecting the number of expanders, a required pressure ratio can be calculated.

Performing an energy balance around each heat exchanger, the following

equations were derived and used to calculate the overall cycle efficiency.

1. m = m . + m

ISO pre

where

n=l

Z n=Nm

exp

n=l

I n=N

(jj + m

n+1

1 - C (1.2.25)

exp

m

m. exp+1

the total mass flow through the expanders

mass flow through the isothermal expander or

m. from equation (1.2.20). ISO ^ V /

n=l

2- W^ = "r ^ = Wr. £ ^-.l^Cpf^n - ^n^l (1-^)1 (^•2-26)

pre ISO iso n=N

where

exp

"Nexp+1

total recoverable expander power,

T^

ISO

recoverable power from the isothermal expander

equation (1.2.21).

pre

and

recoverable power from the precooling expanders,

T = T ^,/[l - n + n Pr~°')/(1 -c)]

n n+1 pre pre

10
w . 3. n = ^ . (1.2.27)

^ m RT„ In Pr

« W

The results of the calculated cycle efficiency including losses due to

heat exchanger temperature difference will be presented in the next section.

1.2.3. Losses due to pressure drop

The pressure drop losses were included in the cycle efficiency calculation in a rather inexact method. Since it was difficult to calculate the

losses when the pressure drop was distributed throughout the system, cycle

efficiencies were calculated with the entire pressure drop occurring at two

locations. The minimum losses due to system pressure drop were calculated

by taking the entire pressure drop immediately before and after the isothermal

expander. The maximum loss was determined by taking the entire pressure drop

immediately before and after the main compressor. In the calculations the

reduced pressure ratio for either the isothermal expander or the entire cycle

was found by

:

P^r =

''^ a I AP/p! •

Figures 1.3 and 1.4 show the final results of the cycle efficiency analysis. All losses are included in the plots with the double line denoting the

maximum and minimum pressure drop effect. The cycle efficiency varied with

the number of expanders and if the maximum efficiency occurred with less than

six expanders that point was plotted, otherwise the cycle efficiency for six

precooling expanders was plotted.

1.2.4. Multipressure liquefaction cycles

Losses in the cold end of the liquefaction cycle increase the flow in the

warm end of the cycle. This increased warm end flow results in increased warm

end losses. To minimize these losses, a three pressure cycle (employed in most

state-of-the-art hydrogen liquefiers) can be simulated with the defined cycle

by increasing the pressure ratio across the isothermal expander while maintaining the pressure ratio across the precooling expanders. Although the

three pressure cycle requires an additional compressor and more complex heat

exchangers, an increase in the cycle efficiency of one to two percentage points

can be attained as shown by figure 1.5. The results shown on figure 1.5 are for a fixed pressure ratio of 9.6 across the precooling expander while the

pressure ratio across the isothermal expander was varied from 9.6 to 100.

1.3. The Real Hydrogen Liquefier

A more practical liquefier has many similarities to the defined cycle

but real properties of hydrogen must be used instead of the ideal fluid equations. Hydrogen with variable specific heats and a positive Joule-Thomson

coefficient at low temperatures introduces many variables not considered in

the defined cycle study. Whereas the defined cycle was' limited to the use

of an isothermal expander, the real cycle allowed the use of either a JouleThomson valve, a wet expander (which contains liquid in its discharge) , or an expansion ejector as the final expansion device in the liquefier. The variable specific heats and the heat of converting normal to parahydrogen introduce the possibility of heat exchanger temperature pinches.

Computing the efficiency of many different optimized hydrogen liquefier

cycles using the properties of hydrogen, shows that the majority of the

hydrogen liquefier losses are due to the inefficiencies of the compressors

and expanders. In comparison the remaining losses are so small that only

11
40 50 60 70 80 90 100

EXPANDER EFFICIENCY, %

Isothermal Condensing Expander has the same Numerical

Efficiency as the Adiabatic Precooling Expanders

Figure 1.3. Defined cycle efficiency including losses from pressure drop

and heat exchanger temperature differences.

12
EXPANDER EFFICIENCY,?

Isothermal Condensing Expander has the sane Numerical

Efficiency as the Adiabatic Precooling Expanders

Figure 1.4. Defined cycle efficiency including losses from pressure drop

and heat exchanger temperature differences.

13
10 +Jc

•r-O

a.

(U

<u

>-

o>-

<

— Ti^ = 60% of isothermal

n. = 80% of isothennal

'iso n = 80% of adiabatic

'pre

T—

r

T—

r

1—

r

1 —

0 20 40 60 80 100

PRESSURE RATIO ACROSS THE ISOTHERMAL EXPANDER

The Isothermal Condensing Expander and the Adiabatic

Precooling Expanders are 80 Percent Efficient

Figure 1.5. Increase in defined cycle efficiency resulting from the use of a three pressure cycle.

14
slight gains in liquefier efficiency can be achieved by using unreasonably

large heat exchangers, and/or by substituting the more thermodynamically

efficient expansion ejector or wet expander for the Joule-Thomson expansion

valve as the final expansion device. Maximum liquefier efficiency is achieved

by removing the heat of converting normal hydrogen to parahydrogen at the

highest temperature possible and by locating the expanders to minimize heat

exchanger temperature differences. Choosing between a Claude cycle, Brayton

cycle, or cascade cycle is primarily a matter of providing the best pressure

ratios and inlet temperatures for the available compressors and expanders

rather than a matter of changing the hydrogen liquefier efficiency.

1.3.1. Efficiency and losses of teal liquefier components

Efficiency is defined as the rario of ideal work to actual work for a particular process. Losses for all components were determined using an availability balance around the component. The sum of the losses and the

ideal power required to produce a unit of liquid divided by the isothermal

compressor efficiency minus the power output of the expanders resulted in

the actual power required to produce the liquid. Expressed in equation form

the actual power required to produce the liquid is

=

, - (1.3.1)

c where

actual power required to produce liquid,

total liquefier losses,

ideal power required to produce liquid,

isothermal efficiency of the compressor,

recoverable power from the expanders.

Overall liquefier efficiency becomes,

W

Cl

and

W

n =

p

Cl

a

w . Cl

+ W . T Cl

(1.3.2)

The liquefier is 100 percent efficient when the efficiency of the compressor

is 100 percent of isothermal, and the total losses in the liquefier are equal

to the expander output power. In this equation (equation 1.3.2) the expander

output power is treated as a loss because the room temperature compressor

must be large enough to supply the total expander output power plus the ideal

power required to produce the liquid.

In the following sections the methods used to calculate the losses for

the various liquefier components are defined. Also, the state-of-the-art

efficiencies are assigned to the components used in the practical liquefier,

1.3.1.1. Compressor

For a real gas, the ideal power required to compress a fluid is;

^ci = -

'^in^ '

15
where

P^^ = isothermal compressor power,

m = mass flow rate,

lb ^ = availability of the outlet fluid, ^out

and = availability of the inlet fluid.

The compressor efficiency is then defined as;

= , where

ac

P is the actual compressor power required by the liquefier. Compressor

ac losses are determined bv;

''l-n.

L = A

c n ^out ^in

c (1.3.4)

where

= compressor losses.

and = isothermal compressor efficiency.

Compressor efficiencies are usually given in terms of the adiabatic work.

Depending on the compression ratio, the isothermal efficiency of most com- pressors is 60 percent while very large compressors may approach 70 percent [8].

A compressor efficiency of 60 percent of isothermal was used throughout this

study.

1.3.1.2. Expanders

Expander efficiency is expressed by;

Ah

n = TvT- ' (1.3.5) pre Ah

s where

ripj.g = isentropic expander efficiency.

Ah = actual specific enthalpy change across the expander,

and Ahg = isentropic specific enthalpy change across the expander.

Expander losses are determined by the difference in availability across

the expander or;

L = m (4^ . - ij^ ^) . (1.3.6)

e ^out

Although this expander loss includes the power output of the expander, it is

appropriate because room temperature compression power is required to supply

the energy (see equation (1.3.2) and its discussion). The expander power

was recovered by reducing the actual isothermal compressor power by the total

power from the expanders.

Expander efficiencies of 80 percent of isentropic were used for the

majority of the calculations. Efficiencies of 60 and 100 percent were also

used to determine the effect of expander efficiency on overall liquefier

16
efficiency. The 80 percent efficiency is reasonable [5] if care is taken to

match operating pressure ratios and inlet temperatures to the characteristics

of the expander.

1.3.1.3. Joule-Thomson expansion valve

The Joule-Thomson (JT) expansion valve has an efficiency equivalent to

a zero expander efficiency. Ignoring m.inor velocity effects, the zero efficiency results in no change in enthalpy across the valve during an expansion

process

.

The Joule-Thom.son valve losses tend to be high because of the zero efficiency; however, they can be minimized by carefully selecting the operating

conditions. Losses are determined by;

'JT = m out ) . (1.3.7)

1.3.1.4. Expansion ejector valve

The expansion ejector valve was originally proposed to produce refrigeration at temperatures below the normal boiling temperature of the refrigerant [5] . Instead of using room temperature vacuum pumps to reduce the pressure

of the liquid bath, the expansion ejector uses some of the energy of the high

pressure, cold gas refrigerant to pum.p a second liquid bath to a lower pressure. Figure 1.6 shows an expansion ejector and its location in the cold end

of a liquefier.

The expansion ejector efficiency is given by;

ih_Ah -, 2 s 3 , 2 m, Lh , ^ 1 s 1 , 3 (1. 3. 8)

where

subscripts

and

by;

m

Ah^

1

2

mass flow,

isentropic specific enthalpy change,

primary supply stream,

secondary or pumped stream,

discharge stream.

Expansion ejector losses are determined from the availability functions

L . = m,4^, + m-jii)-, - (m. + m-,) ^r, • (1.3.9)

ej 11 2 2 1 2 3

Expansion ejector efficiencies have not been measured using hydrogen;

however, they have been measured using nitrogen [6] . Since the primary and

secondary flows are the same gas, the ejector efficiency should be nearly

the same using hydrogen or nitrogen. The efficiencies reported in the

nitrogen experiment are a function of the primary to secondary mass flow

ratio, and they range from zero to nearly 20 percent. The efficiencies used

in the hydrogen liquefier calculations were varied accordingly.

17
EXPANSION EJECTOR

Figure 1.6. An expansion ejector and a cold end using the ejector.

18
1.3.1.5. Heat elxchangers

Selecting the proper counterflow heat exchanger involves a balance between the cost of energy to produce the liquid and the capital cost of the

exchanger. Decreasing the heat exchanger temperature difference improves

the liquefier efficiency but may result in a large and overly expensive

exchanger. Thus, the size of each exchanger was calculated based on assigned

end point temperatures. If any heat exchanger in the liquefier was unreasonably

small or large, the end point temperatures were reassigned and the liquefier

efficiency recalculated.

Heat exchanger size was determined using a method described by Daney [7].

He based the heat exchanger size on the numerical value of AU/m found from;

where

AU dh W =

(AT,) da ' (1.3.10)

A = heat transfer area on one side of the counterflow heat ex- changer,

U = overall heat transfer coefficient,

A = mass flow rate on one side of the exchanger,

dh = change in specific enthalpy on one side of the exchanger,

AT = local heat exchanger temperature difference.

and

da = dA/A.

The local heat exchanger temperature differences for 20 points along the

length of the exchanger were used to numerically integrate the right side of

the above equation.

The heat exchanger size was varied from 300 to 1000 J/ (mol K) in the

study. These sizes provided a good balance between the capital cost and

losses for the heat exchangers.

1.3.2, Real hydrogen liquefier cycle

A schematic for a representative hydrogen liquefier is shown in figure

1.7 and the corresponding fluid states are given in table 1.1. Many other

combinations and numbers of Claude and Brayton modules were investigated,

but this liquefier (with six precooling expanders in Claude modules and a Joule-Thomson (JT) valve as the final expansion device) is taken as typical.

The fluid states shown in table 1.1 show the heat exchanger temperature differences and pressure drops. The product stream (4, 8, 12, etc.) is at a sufficient pressure to condense in the normal hydrogen liquid bath and it is

maintained at equilibrium ortho-para concentration as it is cooled. The primary JT expansion valve is supplied by a separate compressor with the pressure

and temperature at point 25 adjusted for maximum liquefier efficiency. The

refrigerant supply pressure (point 2) is selected to eliminate the intermediate

heat exchangers between the modules, i,e, the inlet temperature of a following

expander is nearly the same as the discharge temperature of a preceding ex- pander. Eliminating the intermediate heat exchangers increases liquefier

efficiency since the temperature differences of the remaining exchangers are influenced less by unbalanced flows, variable specific heats, etc.

The precooler refrigerant is normal hydrogen (streams 1, 2 and 3) except

for the small amount of parahydrogen mixed into the returning low pressure

refrigerant (point 29). The increased parahydrogen content is accounted for

in the precooler return flow but is converted back to normal hydrogen in the room temperature compressor. Because of the relatively low parahydrogen flow

at point 32, the back conversion assumption has an insignificant effect on the overall liquefier efficiency.

19
COMPRESSORS

LIQUID

PARAHYDROGEN

Figure 1.7. Representative hydrogen liquefier.

20
Table 1.1 Fluid states for example hydrogen llquefier (figure 1.2).

PT P T

K

H

J/ Cp

S

* nio 1

)

J/(g-raol-k)

m Para

Content

°//o

1 15.923 300 8534.483 119,,2315 6926,.237 1,.0 25

2 6.171 300 8525.816 127.,1327 4547,.207 10..2954 25

3 1.130 294.985 8521.895 140.,7698 306,. 964 11,.3205 25.16

4 1.740 300 8521.895 137.,667 1383,. 097 ,9107 25

5 15.765 209.603 5961.912 109.,126 7385,. 382 1..0 25

6 6.109 209.603 5960.620 117.,057 5004,.652 9..1791 25

7 1.142 206.099 5863.111 130.561 855

,

. 996 10..2040 25.18

8 1.723 209.603 5957.341 127.,591 1841.. 142 ,9107 equil.

9 15.609 143.360 4190.847 99.,077 8628,.977 1,,0 25

10 6.048 143.360 4201.616 107.,079 oZ3o

,

. 929 6.,7339 25

11 1.153 140.964 4145.566 120. 493 2158..972 9.,0545 25.21

12 1,706 143.360 4166.843 117. 419 3102

.

, 158 ,9107 equil.

13 15.455 94.272 2993.868 88. 973 10463., 103 1.,0 25

14 5.988 94.272 3025.948 97. 165 8037

.

, 805 6.,7339 25

15 1.165 92.696 3004.547 110. 542 4003.,066 7.,7588 25.24

16 1.689 94.272 2829.978 106. 051 5175., 835 9107 equil.

17 15.302 59.686 2183.928 78. 335 12844., 752 1.,0 25

18 5.928 59.686 2258.297 87. 112 10285

.

, 832 5. 0460 25

19 1.176 58.688 2269.863 ICQ. 611 6247

.

,654 6. 0709 25.31

20 1.672 59.686 1713.571 91. 243 8501.,981 9107 equil

.

21 15.150 38.352 1565.074 65. 318 16130., 801 1. 0 25 22 5.869 38.352 1767.462 76. 972 12838.,948 3. 0932 25 23 1.188 36.525 1797.070 90. 437 . 8827

.

,278 4. 1181 25.45

24 1.656 38.352 908.545 74. 647 12675

.

, 599 9107 equil

.

25 15.0 24.066 651.222 37. 344 23609

.

, 245 1. 0 25

26 1.2 22.970 1476.127 79. 753 11711

.

305 1. 0248 26.82

27 1.639 24.066 460.745 60. 265 1 £ c / o 16542

.

322 9107 equil.

28 1.212 20.944 651.222 39. 455 22975. 845 1. 0 25

29 1.212 20.944 1451.586 77. 671 12311. 629 1. 0 25

30 1.623 22.030 404.123 57. 881 17201. 106 9107 equil

.

31 1.607 21.991 -474.703 17. 992 28288. 859 9107 equil

.

32 1.212 20.962 389.344 59. 313 16756. 521 0248 100

33 1.218 20.962 -498.958 16. 918 28586. 829 8858 100

21
The calculated compressor work per unit of product required to overcome

the losses of other types of precoolers considered is shown on table 1.2.

This compressor work is a function of the temperature and pressure at the

interface between the precooler and the cold end (P^, T^, point 25, figure

1.7), the number and efficiency of the expanders, the pressure drop and size

of the heat exchangers and the ratio of the refrigerant stream mass flow to

the product stream mass flow (m^/ih^ , figure 1.7). The compressor work, , shown per gm mole of product stream flow (point 27) , is based on a compressor

efficiency of 60 percent of isothermal and the recovery of the total expander

output. The pressure of the returning refrigerant (pt 3, figure 1.7) was 1.0

atm for all precoolers considered. Each precooler was assembled from Brayton

and Claude modules as designated by the cycle type shown on table 1.2 where

the warmest module is listed first proceeding to the coldest module listed

last. The Claude modules were always used without the intermediate heat

exchanger as explained previously. Figure 1.8 is a plot of compressor work

required to overcome losses in the precooler versus the interface temperature between the precooler and cold end.

Similar plots of compressor work to overcome losses in the JT expansion

valve, the expansion ejector, and the wet expander cold ends are shown on figures 1.9 and 1.10. The compressor work shown was minimized by choosing

the optimum interface pressure for each cold end and each interface temperature and it is again expressed as the work per gram mole of product stream

flow. Figure 1.9 shows a performance band for the expansion ejector cold

end. The band is bounded by a zero efficiency curve (also used to define the

performance of the JT valve cold end) , and a 20 percent efficiency curve. Two performance curves are also shown for the wet expander cold end (figure

1.10). One curve is for a wet expander with 80 percent liquid in its exhaust, and the other curve is for a wet expander with the liquid in its

exhaust limited to 24 percent by mass. By using the performance information on figures 1.8, 1.9 and 1.10, the

optimum interface temperature and pressure can be found for the various cold

ends. In order to find the overall liquefier efficiency using the various

cold ends, an estimated precooler performance is defined by the hand-drawn

curve on figure 1.8. The total work required by a liquefier can be found by

summing the ideal work of liquefaction divided by the 60 percent isothermal

compressor efficiency to the compressor work to overcome losses in the precooler (figure 1.8) and the chosen cold end (figure 1.9 and 1.10). In

equation form this is

= W./.6+W +W T ci pre c where

and

= total liquefier work,

W^^ = ideal liquefier work,

^pre ~ compressor work to overcome losses in precooler,

= compressor work to overcome losses in cold end.

From the total work, the liquefier efficiency can be found and a plot of this

liquefier efficiency versus interface temperature is shown on figure 1.11.

The most efficient liquefier results when a wet expander with 80 percent

liquid in its exhaust is used as the final expansion device. A reciprocating

expander is able to operate at these conditions; however, a turbo-expander is

limited to 24 percent or less liquid in its exhaust and the liquefier efficiency suffers. The expansion ejector requires a raised inlet temperature to

recover any pumping power from the primary stream. At low inlet temperatures

the expansion ejector becomes a JT valve with no pumping ability while at

higher temperatures pumping energy is recovered from the primary stream.

22
Table 1.2 Compressor work required to overcome losses for various types of precoolers.

Run

I atm

I K

No. Exp's/Eff

,

Cycle

Type* DPOP 1 HX2 Size

3 Parameter4 5 6 Ratio

m./m,

3 4

Comp . Wi for Los

J/(g- mol'K^ J/ (g'mo

1 30 34. 03 6/80 CCCCCC 0.01 511 513 532 617 394 157 . 7302 31774

2 30 34 6/80 CCCCCC 0.01 517 519 541 637 422 122 . 6578 31824

6 25 30 4/80 CCCC 0.01 668 482 437 225 34209

7 20 30. 25 4/80 CCCC 0. 01 672 484 438 348 .7769 34262

8 10 32.

5

6/80 ^ f> ^ CCCCCC 0. 01 587 585 607 690 572 89 . 2358 31187

9 10 32.5 6/80 CCCCCC 0. 01 593 591 611 684 528 108 . 2436 33273

11 15 30 6/80 CCCCCC 0. 01 563 560 572 622 354 380 .6982 34362

13 15 24 6/80 CCCCCC 0.01 599 597 585 704 414 113 . 8858 35825

20 30 34.1 6/80 CCCCCC 0.01 510 512 531 615 392 158 . 7270 31360

25 30 34 6/80 CCCCCC 0.01 510 511 530 613 401 165 .5889 33702

26 30 34 6/80 CCCCCC 0. 01 510 511 529 612 399 163 .5910 33684

27 30 34 4/80 CCCC 0.01 775 851 645 806 . 5889 31693

28 30 34 4/80 CCCC 0.01 775 857 646 805 . 5867 31712

29 20 30.2 4/80 BBBC 0.01 317 223 171 101 . 7769 35845

32 7 35.3 4/80 BBBC 0.01 680 587 441 627 .2204 28859

33 7 35.3 4/80 BBBC 0.02 680 587 441 575 .2173 32527

34 5 36 4/80 BBBB 0.01 615 522 382 297 .1631 29001

35 5 36 5/80 BBBBB 0.01 586 524 421 324 277 .1631 27186

36 5 36 6/80 BBBBBB 0.01 561 516 442 355 289 263 .1631 26291

37 30 34 4/80 CCCC 0.01 775 859 646 456 .5359 3088S

38 30 34 4/60 CCCC 0.01 686 621 716 538 .5384 67707

41 15 24 6/60 CCCCCC 0.01 572 568 587 683 442 173 .8858 71485

* C designates a Claude module and a B designates a Bray ton module.
38.000 1—

36.000 —

- 34.000 o

£

a 32J0OO

o

0£Oto

(/i la 30JOOO

o

28.000

26.000

Compressor Efficiency = 60 % of Isothermal

Expander Efficiency = 80 % of Adiabatic

V 029

11 ,\ 09

**26

O33

28>^2

27

08 A2O

37\

034

O32

0 35

1

1

1 0 36 1

1 20 25 30 35 40

INTERFACE TEMPERATURE, K

45

Figure 1.8. Compressor work required to overcome losses in the precooler for various cycles and interface temperatures.

24
10,000 r—

8000

oE

6000

WORK,

:ssoR 4000

COMPRf

2000

24

COht'RESSOR EFFIC1ENCY=60% of ISOTHERMAL

0 % Efficient Ejector

and JT Valve

20 % Efficient Ejector

26 28

INTERFACE TEMPERATURE, K

25
30 35 40 45 50

INTERFACE TEMPERATURE, K

Figure 1.10. Compressor work required to overcome losses in

a wet expander cold end for various interface

temperatures.

26
36

Compressor Efficiency = 60 % of isothermal

Expander Efficiency = 80 X of isentropic

35

3

34 u

a.

>-zUJ

C3 33

»—

u.u.

tu

32

Wet expander; Liquid in

discharge is 80 % of total

di scharge flow.

Expansion ejector

Efficiency = 20%

Joule Thomson expansion valve

Wet expander; Liquid in

discharge limited to 24 % of total

di scharge f 1 ow.

31

30

20 25 30 35

INTERFACE TEMPERATURE, K

40 45

Figure 1.11. Hydrogen liquefler efficiency using a wet expander, expansion

ejector or a Joule Thomson valve final expansion device versus

the interface temperature.

27
Because the losses in the cold end are a small percentage of the total

liquefier losses, only a small advantage is gained by substituting a wet

expander or expansion ejector for a JT valve in a properly optimized cycle.

Tables 1.3 and 1.4 show the losses for the representative liquefier.

The liquefier efficiency is 33.24 percent of Carnot with the majority of the

losses occurring in the compressors and expanders. The JT valve losses are

low because its inlet temperature is low. Replacing the JT valve with a reversible expander would increase the liquefier efficiency to 33.72 percent

of Carnot.

All liquefiers which were investigated used from four to six Claude or Brayton modules in different combinations in the precooler and had nearly the same efficiency and loss distribution as the representative liquefier.

The choice of the type of precooler did not affect efficiency but it did

change the precooler pressure ratio. Since an increased refrigeration load on a Brayton module is absorbed by increased expander pressure ratio, the

compressor pressure ratio for the precooler of a liquefier employing mostly

Brayton modules tended to be high. On the other hand, the Claude module

absorbs the refrigeration load by increased expander flow and the compressor

pressure ratio is determined solely by the number of expanders (when the

expanders are placed so the discharge temperature of a preceding expander is

nearly the same as a following expander). Thus, the compressor pressure

ratio for the precooler of a liquefier using six or more Claude modules

tended to be low.

Besides the Claude and Brayton modules, a separate nitrogen refrigerator

can be used to precool the product stream (cascade cycle) . A liquid nitrogen

module using a JT valve as the final expansion device was compared to an all

hydrogen Claude module precooling the same product stream. Figure 1.12 shows

the schematics of the two modules. Identical losses above the inlet temperature of the two modules were assumed. The losses in the Joule-Thomson

nitrogen module were determined and then the expander efficiency required to

produce the same losses in the Claude module was determined. If expander

power is not recovered, the expander efficiency required to achieve identical

losses between the two modules is 85.8 percent.

Figure 1.13 shows the room temperature compressor work required to cool

the product stream for the two systems if the expander power is recovered.

These results show that when expanders with efficiencies below about 75

percent are available, the best overall liquefier efficiency would be

achieved with a cascade cycle. This conclusion must be qualified, however,

because sufficient fluids are not available to provide the close precooling

temperatures assumed in the example. This is especially true for temperatures below the normal boiling temperature of liquid nitrogen where expanders

are required in the hydrogen liquefier to achieve high efficiencies. Other

more practical reasons may suggest the use of liquid nitrogen precooling: 1)

it may be possible to obtain higher efficiency expanders and compressors for

nitrogen than hydrogen. Consequently, even though the warm temperature

portions of the nitrogen precooling cycle are identical with an all-expander

hydrogen cycle, lower losses will result from the higher component efficiencies; 2) liquid nitrogen may be required to purify the gaseous hydrogen

supply. Since a nitrogen liquefier is required anyway, it can be increased

in size to provide precooling to the hydrogen liquefier. Other than these two

reasons, no particular gain in efficiency is provided by using liquid nitrogen precooling.

28
Table 1.3 Individual component losses and turbine work

for the representative liquefier.

HX No.

1

2

3

4

5

6

7 Totals

E^ander No.

1

2

3

4

5

6 Totals

JT Valves

Other Cold End

Totals

Size Parameter

J/ (g'mol'k)

599.25

597.61

621.19

704.61

414.12

113.73

43.93

Efficiency

Z

80

80

80

80

80

80

HEAT EXCHANGERS

Losses

J/ (g'mol* liquid)

1286.628

1120.766

972.130

746.017

770.293

989. 732

142.045

Total Losses

J/ (g'mol'liquid)

6027.610 6027.610

EXPANDERS

Work Produced

J/ (g'nol* liquid)

3355.308

2355.252

1750. 861

1440.650

1016.764

1017.328

10936.163

COLD END

Losses

J/ (g'Eol* liquid)

4651.460

3692.622

3270.314

3410.956

3215.289

3930.506

22171.147

740.816

640.107

1380.923

TOTAL LOSSES

22171.147

1380.923

29579.680

Table 1.4 Work requirements for the representative liquefier.

Work Required Percent of

J/ (g'mol'liquid) Total

Compressor Losses (60 percent isothermal compressor) 38777.673 45.09

Expander Losses (80 percent of isentropic efficiency) 22171.147 25.78

Heat Exchanger Losses 6027.610 7.01

Cold End Losses 1380.923 1.60

Ideal Power Requirements 28586.830 33. 24*

Total 96944.183 112.72

- Expander Power - 10936.163 - 12.72

Total Liquefier Power Requirements 86008.020 100.00
Pt P T atm K

1 51 130

2 1 128

3 1 130

4 1 78.76

Pt

12

34

Patm

Varies

1

1

1

T

K 130.00

128.00

130.00

78.76

Pressure at point 1 varies from 6.8 to 34 atm depending

on the efficiency of the expander.

Figure 1.12. A nitrogen module with a JT valve and an all hydrogen Claude

module cooling the same product stream.

30
3000

2500

o

E

o

2000 — JT System

o

^ 1500

oo

o

UJ

0£

or

UJ

1000

500

60 % Isothermal

Compressor

— JT System

80 % Isothermal

Compressor

Expander

System

0 20 40 60 80 100

EXPANDER EFFICIENCY IN CLAUDE CYCLE, percent

Figure 1.13. The Claude module expander efficeincy required to provide equal

performance between the Claude module and the nitrogen module

using a JT valve.

31
1.3.2.1. The aesign of a practical hydrogen Liquefier

Of the many cycles shown on table 1.2, some are not suited for use with real expanders and compressors because of the high operating pressure

ratios assumed for the components. Many of the problems associated with

compressing hydrogen at room temperature using rotary compressors also apply

to turbo-expanders, i.e\ low pressure ratio capability per stage. These

pressure ratio problems become less severe as the operating temperature of

the turbo-expanders decreases. One possible solution to the high temperature

expander problem is to replace all the hydrogen expanders above the condensing

temperature of liquid nitrogen with a nitrogen precooler refrigerator since

nitrogen is much more amenable to expansion and compression in turbo-machinery.

A theoretical study of such a cycle [8] indicates an overall hydrogen liquefier efficiency of 36 percent which resulted from the assumed expander and

compressor efficiencies shown in table 1.5. The compressor efficiencies shown

in table 1.5 are adiabatic instead of the isothermal efficiency used in this

study. The theoretical study of the hydrogen liquefier using nitrogen precooling yielded liquefier efficiencies comparable to those determined in this

study for an all hydrogen liquefier.

Table 1.5 Assumed compressor and expander efficiency used to determine

a hydrogen liquefier efficiency by Linde [8]

.

Efficiency

Percent Adiabatic

Nitrogen Compressor

N2 Recycle , 80

N2 Booster 65

N2 Makeup 75

Hydrogen Compressors (all) 80

Hydrogen Expanders (all) 79

Nitrogen Expanders (all) 84

A possible theoretical cycle successfully using high temperature turboexpanders instead of nitrogen precooling in an all-hydrogen liquefier is shown

in figure 1.14. This cycle would use four Brayton modules in the precooler

together with a wet expander cold end. The interface fluid state conditions

at points 4, 5 and 6 are shown on table 1.6. These inlet conditions of the

wet expander cold end result in only a slight precooler flow imbalance

(mg/m^) . The low flow imbalance allows a relatively low pressure ratio across

each expander. Increasing the number of expanders decreases the pressure

ratio across each expander further as shown in figure 1.15.

Table 1.6 Interface fluid state points for the

all Brayton module liquefier.

PT P

(figure 1.14) atm

H

J/ (g • mol

)

J/ (g«mol«K) m

5

1.2

1.28

1.23

36.00

35. 51

36. 00

21.00

1724. 69

1781. 36

831.84

-498.15

77.008

89.783

74.663

16.955

1. 00000

1.00015

0.16329

0.16314

32
33

Figure 1.16 shows the variation in liquefier efficiency as a function of

the number of expanders. Again the liquefier efficiency is based on 80 percent

isentropic expanders, 60 percent isothermal compressors, and a heat exchanger

size parameter of around 500 J/(mol'K). By judicious choice of the temperature level between each Brayton cycle module, the pressure ratio of each

expander could be adjusted to exactly match its optimum operating requirements.

1.4. Comparison Between Defined Cycle and Real Gas Cycle

The calculated efficiencies of the hydrogen liquefier compare well with

the efficiencies found earlier for a defined cycle as shown on figure 1.17.

Two bands are shown for the defined cycle efficiency; one band is for a constant

isothermal expander efficiency of 80 percent, while the other is for a constant

isothermal expander efficiency of 100 percent. The band width shows the

maximum and minimum effect of pressure drop on the defined cycle efficiency.

Several points show comparable calculated efficiencies for the real gas

liquefier

.

The efficiencies of the theoretical defined cycle and the theoretical

real cycle compare well even though the final expansion devices of the two

cycles are quite different. The defined cycle uses a theoretical isothermal

expander as the final expansion device while the real cycle can use a JouleThomson expansion valve, a wet expander, or an expansion ejector. The defined

cycle interface temperature - the temperature between the final expansion

device and the precooler - is fixed at the normal boiling tem.perature of

parahydrogen . On the other hand the interface temperature for the real cycle

is chosen for each final expansion device to maximize liquefier efficiency.

The interface temperature of the real cycle is always greater than the normal

boiling temperature of parahydrogen. Because the interface temperature is

higher for the real cycle than for the defined cycle, changing the precooling

expander efficiencies can affect the overall efficiency of the two cycles

differently. When the real cycles uses a Joule-Thomson valve the interface

temperatures are nearly the same as the defined cycle and this difference does

not appear (see figure 1.17). But the interface temperature for a real cycle

using a wet expander or an expansion ejector is higher. In this case changing

the precooling expander efficiencies changes the liquefier efficiency

differently which leads to a mismatch at the 60 percent precooler expander

efficiency point. However, the variance is within the bands shown on figure 1.17.

1.5. Conclusions

The efficiency of hydrogen liquefiers is dependent upon expander efficiency, compressor efficiency, and to a much lesser extent on the heat ex- changer size and pressure drop. The cold end losses account for about one to

two percent .of the total compressor power, so substituting the more reversible

wet expander or expansion ejector for the Joule-Thom.son valve has little

effect on the liquefier efficiency. The cycle efficiencies obtained in a hydrogen gas system compare favorably with the ultimate efficiencies derived

for a defined cycle using an ideal gas. This direct comparison reinforces

the validity of the hydrogen gas calculations, and shows no particular

penalty due to the non-ideal characteristics of the hydrogen gas.

The type of cycle (Brayton, Claude, or Cascade) used in the liquefier

has a minimal effect on the efficiency of a hydrogen liquefier. The liquefier

cycle chosen should be based primarily on using available expanders and com- pressors in their most efficient operating situations and on the economics

of using large heat exchangers with resulting low AT's and pressure drops.

The Claude cycle arrangement of precooling m.odules is most amenable for use

in a low pressure ratio cycle because the precooling load is absorbed by increasing the expander flow instead of increasing the expander pressure ratio

as in the brayton cycle module. On the other hand the most efficient use of

35
31

5 6 7 8

NUMBER OF EXPANDERS IN PRECOOLER

Figure 1,16. Liquefier efficiency as a function of the number of Brayton

modules.

36
60 TYPE OF COLD END FOR REAL LIQUEFIER

A Wet expander 80% liquid in exhaust

PRECOOLER EXPANDER EFFICIENCY, percent

Figure 1.17. Comparison of real liquefier efficiency with the defined cycle

efficiency.

37
the Claude modules (placing the expanders such that the inlet temperature of

a following expander is nearly the same as the discharge temperature of a preceding expander) requires the use of many low pressure ratio expanders to

cover the temperature span required in the liquefier. For low precooling

loads (low product stream flow rates) the Brayton cycle module is particularly

suitable for centrifugal expanders because the expanders operate at raised

pressure levels with relatively low pressure ratios.

Actual liquefiers could not achieve the efficiencies determined from

any of the theoretical cycles. Among the reasons for the lower actual

efficiencies are:

1. losses due to heat leak to the cold portions of the liquefier are

not included in the theoretical cycles.

2. Any input power required to purify the hydrogen supply to the

liquefier has not been included.

3. A continuous equilibrium conversion from normal to parahydrogen

was assumed. In an actual liquefier the conversion would probably be nonideal requiring removal of some of the conversion energy at temperatures

lower than equilibrium. This conversion at lower temperatures would also reduce

the actual liquefier efficiency.

4. Hydrogen leakage from low temperature components such as expanders

would significantly reduce overall liquefier efficiency. No leakage was allowed in the theoretical cycles.

5. The theoretical calculations assumed the recovery of the total

expander output power. In an actual liquefier recovery of the total expander

power is not possible due to inefficiencies in the mechanical or electrical

interface between the expanders and the liquefier compressor.

The results of these studies indicate that with a 60 percent efficient

isothermal compressor, 80 percent adiabatic precooling expanders, and an

80 percent isothermal expander, the maximum liquefier efficiency attainable

is 40 percent (figure 1.2). Losses due to system pressure drops and heat

exchanger temperature differences reduces the defined cycle efficiency to

34 percent (figure 1.3) and 30 percent (figure 1.4). A reasonable efficiency

for a practical liquefier may lie somewhere between 30 and 34 percent without

considering other losses such as heat leak to the cold components. One

would expect that an efficiency of 30 percent may be the practical limit for

liquefiers using state-of-the-art components. Very large compressors may

exhibit isothermal efficiencies approaching 70 percent; the practical limit

of liquefier efficiency would then be 35 percent. Based on this analysis,

the currently reported efficiencies of 30-35 percent for industrial hydrogen

liquefiers show good design and optimization. Increasing the compressor

and/or expander efficiency has the highest potential for increasing the

overall liquefier efficiency.

Because of the large dependence of the liquefier efficiency on compressor

efficiency, a hydride compressor was investigated. The hydride compressor

using the waste heat from a primary compressor is discussed fully in the Appendix. The hydride compressor proved to be no more efficient than conventional compressors.

Since hydrogen liquefier efficiency is primarily dependent upon the efficiency of the expanders and compressors, no large increase in liquefier

efficiency can be expected in the near future. Both expanders and com- presrors have had a long development history, and the probability of step

increases in their efficiency is quite remote.

38
A

1.6. Nomenclature

Heat transfer area on one side of a counterflow heat exchanger.

C Constant used to define heat exchanger temperature difference

C = AT/T.

Cp Constant pressure specific heat.

h Specific enthalpy.

Ah^ Actual specific enthalpy change.

Ah Isentropic specific enthalpy change,

s k Ratio of specific heat, 1.404 was used in the calculations for

hydrogen.

Compressor loss.

Expander loss.

Expansion ejector loss.

Lj^ Joule Thomson valve loss.

ih Mass flow rate refers to to^.al mass flow rate.

A^g^ Mass flow rate through the isothermal expander.

Ap^g Total mass flow rate through the precooling expanders.

^exp Number of precooling expanders.

P Absolute pressure.

P Actual isothermal compressor power.

cLC P . Ideal isothermal compressor power , real gas

.

Pr Pressure ratio, high pressure/low pressure.

Q Heat flow.

R Gas constant.

s Specific entropy.

T Absolute temperature.

Absolute temperature of the cold end of the liquefier, 20. 268 I< was used in the hydrogen calculation.

Absolute temperature of the high temperature end of the hydrogen

liquefier; 300 K was used.

AT^ Local heat exchanger temperature difference.

T^^ Absolute inlet temperature.

T ^ Absolute outlet temperature, out

39
T Absolute ambient temperature T = T„ in the derivation and calculation,

o o H _ H C T^^ Log mean temperature difference T^^ = ~— . In (/)

C

U Overall heat transfer coefficient.

Ideal power requirements for precooling the product stream.

W2 Ideal power requirements to condense the produce stream.

W Compressor work required to overcome losses in the cold end,

^ * J/(g-mol),

W Actual total compressor power,

ca W^^ Ideal liquefier power requirements.

W„ Recoverable expander power, total.

Isothermal compression power.

Wp^^ Compressor work to overcome losses in precooler.

W„ Recoverable expander power from the precooling expanders,

pre

W„ Recoverable power from the isothermal expander W = 28.988 x ISO C X U. ISO

p

Total liquefier work.

Greek

V

a (k - l)/k

\l) Availability function of h and s.

n Isothermal efficiency used for the compressor.

^ r n Overall cycle efficiency based on minimum compressor power,

rigj Isentropic ejector efficiency.

n • Isothermal efficiency of the isothermal or coldest expander. ISO

n Isentropic efficiency of the precooling expanders.

u) Mass flow rate of the product stream, defined cycle.

X Latent heat, 28.988 K x C was used in the calculations for

hydrogen. ^

40
1.7. References

[1] Parrish, W. R. and Voth, R. 0., Cost and availability of hydrogen, Nat.

Bur. Stand. (U.S.) Special Publication 419, (J. Hord, Ed.) (May 1975).

[2] Collins, S. C. and Cannaday, R. L., Expansion machines for low temperature processes (Oxford Univ. Press, 1966).

[3] Grassmann, Von P. and Kopp, J., On the choice of temperature difference

and heat transfer coefficient in heat exchangers, Kalletechnik 9^, No.

10, 306-308 (1957).

[4] Jacobs, R. B., The efficiency of an ideal refrigerator. Advances in

Cryogenic Engineering , 7_' ^- ^- Timmerhaus, pp. 567-571 (Plenum

Press, Inc., New York, NY, 1962).

[5] Rietdijk, J. A., The expansion-ejector, a new device for liquefaction

and refrigeration at 4 K and lower. Commission 1, International Institute

of Refrigeration (1966)

.

[6] Daney, D. E . , McConnell , P. M. and Strobridge, T. R. , Low temperature

nitrogen ejector performance. Advances in Cryogenic Engineering , 18 , Ed. K. D. Timmerhaus, pp. 476-485 (Plenum Press, Inc., New York, N.Y.,

1973)

.

[7] Daney, D. E., Refrigeration for an 8 K to 14 K superconducting transmission line, Nat. Bur. Stand. vU.S.) NBSIR 74-375, (Oct. 1974).

[8] Survey study of the efficiency and economics of hydrogen liquefaction,

NASA CR-132631, prepared by the Linde Division of Union Carbide Corporation,

70 pages (1975)

.

[9] Cummings, D. L. and Powers, G. J., Storage of hydrogen as metal hydrides,

Ind. Eng. Chem. Process Des. Develop. 13_ (2), 182 (1974).

[10] Wiswall, R. H. and Reilly, J. J., Metal hydrides for energy storage,

Proc. of the 7th Intersociety Energy Conversion Engineering Conf., 1342

(1972)

.

41
1.8. APPENDIX

Hydride Compressors

W. R. Parrish

1.8.1. Introduction

As pointed out in section 1.5, one way to significantly improve the

liquefaction cycle efficiency is to increase compressor efficiency. This

appendix considers the feasibility of using the waste heat generated by a conventional compressor to drive a metal hydride "compressor." Calculations

show that there is too little high quality heat to make this hybrid compressor

system worthwhile.

1.8.2. Properties of metal hydrides

This section gives a terse explanation of the properties of metal hydrides; more complete details are presented elsewhere [9,10]. If certain

metals are exposed to gaseous hydrogen the following reaction takes place

M + IH2

^

MHj^ . (Al)

The extent of this reversible reaction depends upon the pressure of

hydrogen. However, over the major portion of the reaction the equilibrium

pressure remains nearly constant. This "plateau" pressure varies with temperature according to

In P = a + AH/RT (A2

)

where P is the pressure, a is a constant, AH is the heat of formation, i.e.

hydration for eq. (Al) , R is the gas constant and T is the absolute temperature. For the hydride of interest here, AH is negative. This means that

the plateau pressure increases with increasing temperature. It also implies

that, if a constant temperature is required, heat must be removed during

hydride formation (charging) and heat must be added during dissociation (discharging) . 1.8.3. Hydride compressor system

Figure 1.18 shows a schematic of the compressor system considered here.

Hydrogen enters the system at pressure P, and ambient temperature, part of the

hydrogen (1-f) goes through a conventional compressor while the remainder, f,

goes to the hydride beds. If necessary, the flows are recombined and sent

through another compression stage. Heat removed from the compressor is used

to heat the hydride beds. Three parallel beds are needed; while one bed is

discharging, another bed is charging. The third bed is being cooled or heated, depending upon what portion of the cycle it is in. The cold bed is

being charged at pressure P, as the warm bed is being discharged at pressure

Assuming that no external heat is added, the maximum value of f depends

upon how much of the heat produced by the compressors can be added to the warm

bed as it discharges. Table I.l shows this dependence for three different

systems; it also shows the possible increase in efficiency of this type of

system. The heat duty of the compressor is calculated by assuming that all of

the work going into the compressors is converted to heat. The compressor

efficiency for estimating the heat duty is assumed to be 80 percent of adiabatic. (The heat duty calculated here for system II was five percent less

42

than that given by a more detailed compressor design for the same inlet and

outlet pressures [9]).

The fraction of heat utilized depends upon the operating temperature

range of the compressor cooling fluid. If water is used at temperatures

between 80 and 200 °F, less than half of the heat could be used to keep the

discharging bed warm. Based on table A.l it is unlikely that the hydride compressor concept

could ever become a useful system, at least at the pressures considered here.

This conclusion is independent of the type of hydride considered because of

the chemical nature of hydrides. Ideally, one would desire the hydride to

have a low value of AH and a rapid change in pressure with temperature.

However, as eq. (A2) shows, these two conditions are contradictory since they

would require the value of AH to be small and large simultaneously.

Table A.l. Results of feasibility of using hydride compressors.

Hydride Material I NbH-^NbH,

System

II

VH VH

III

^2 FeTi "trii. FeTiH

AH- kJ/a-mol H [2] -39 -40 -23

Pj^, atm. 1.0 2.8 4.7

V ^, atm. 6.8 16.7 30. 0

P^, atm. 6.8 40.0 66.7

Maximum Hydride

Temperature

Bed

°C ,; 71 63 64

Fraction of Flow

Through Hydride Bed, f

Apparent Overall

Adiabatic Compressor Efficiency

Percent

Fraction of Compressor Heat Put

Into Discharging

Hydride Bed

I

System

II III I

System

II III

0.00

0.25

0. 38

0. 50

1.00

0

0. 036

0.053

0. 069

0.129

0 0

0.050 0.087

0.074 0.129

0.097 0.169

0.182 0.317

80

83

84

86

92

80 80

83 83

84 84

85 86

90 92

44
CHAPTER 2 RECOVERY OF HYDROGEN LIQUEFACTION ENERGY

W. R. Parrish

2 . SUMMARY

This chapter considers the technical feasibility of recovering a portion

of the energy which goes into liquefying hydrogen. Three possible recovery

systems are analyzed; two of which could have direct application in the

electrical utility industry. The first system uses a liquid hydrogen pump, a heat exchanger and a room temperature expander for shaft work recovery.

Depending upon the desired outlet pressure it is possible to recover over 60

percent of the ideal work of liquefaction. This is the additional amount of

work available at the use point from the use of liquid hydrogen instead of

gaseous hydrogen at 1.0 atm. Burning a fraction of the hydrogen to heat the

expander inlet gas is an unattractive option.

If the refrigerating capacity of liquid hydrogen can be utilized in an air separation plant, the energy recovery can be even greater. For example,

if such a system is used to feed a hydrogen-oxygen MHD power generator, there

would be an effective energy savings of 105 percent of the ideal work of

liquefaction. However, if the system feeds a hydrogen-oxygen fuel cell only

about 20 percent could be recovered.

The third energy recovery system involves using hydrogen as the refrigerant for extracting rare gases from the atmosphere. Because of the anticipated supply and demand picture, helium is probably the only rare gas for

which there will be a large future demand. However, calculations show that

a helium recovery unit could produce at best only 10"^ moles of helium for

each mole of liquid hydrogen vaporized.

Thus, it is technically feasible to recover an appreciable fraction of

the energy of liquefaction if energy is the desired product. This energy

recovery has the net effect of reducing the energy cost of producing liquid

hydrogen; this, in turn, makes the storage of hydrogen as a liquid more attractive. However, the concept of using liquid as the refrigerant for

recovering rare gases from the atmosphere is much less attractive.

2.1. Introduction

In the future the most probable means of storing large quantities of

energy derived from solar and/or nuclear sources will be synthetic fuels.

Based on availability, environmental and economic considerations, the most

promising synthetic fuel is hydrogen. Three options exist for storing large

quantities of molecular hydrogen: compressed gas, metal hydride and liquid.

Compressed gas might be an attractive option if depleted oil and gas fields

are available; metal hydride technology is advancing rapidly but both the

technical and economic feasibility still are unproven. Of the three options,

only liquid hydrogen offers proven storage technology which makes it a strong

contender in many potential applications.

However, a major drawback to storing hydrogen as a liquid is the amount

of energy required for liquefaction; the ideal work of liquefaction is 28.7

KJ/g-mol or roughly 10 percent of the lower heating value of hydrogen. Due to

liquefier inefficiencies, the actual work of liquefaction is roughly three

times greater than ideal [1] . Any liquefaction energy recovered would have the net effect of lowering

the energy cost of producing liquid hydrogen. This paper investigates the

feasibility of recovering a portion of the liquefaction energy as previously

45
suggested [2]. Three types of systems are considered. The first type utilizes the refrigeration capacity of liquid hydrogen for three electrical power

generators: gas turbines, fuel cells and MHD generators; the applications are directed toward (but not restricted to) the electrical utilities because they

represent a potentially large consumer of hydrogen. The feasibility of using

liquid hydrogen as the primary refrigerant for separating air and for re- covering rare gases from the atmosphere are also evaluated.

2.2. Electrical Utility Applications

2.2.1. Liquefaction energy recovery factor

To measure the benefit of recovering liquefaction energy we define the

Liquefaction Energy Recovery Factor (LERF) as LERF = (E^ - E^/^)/Elj (2.1)

where E^ is the electrical power output per g-mol of hydrogen with liquefaction energy recovery, E^/q is the power output without recovering liquefaction energy and E is the ideal work of liquefying one g-mol of hydrogen.

Ltd. The liquefaction energy recovery factor based on actual work of liquefaction

is obtained by multiplying eq. (2.1) by the efficiency of liquefaction plants

relative to the Carnot efficiency. The efficiency of large liquefaction

plants is expected to range from 33 to 40 percent.

To keep the calculations on a common basis the values in eq. (2.1) are calculated on the assumption that the fuel enters the system at 1.0 atm.

Therefore E.. is based on 1.0 atm suction pressure as is E likewise, the

LI w/o

values of E^ are based on 1.0 atm liquid entering the recovery system. If the

electrical power generator operates above 1.0 atm, the work of compressing

hydrogen to the Operating pressure is accounted for in E^^^ by assuming a hydrogen compressor operating at 60 percent efficiency based on isothermal

compression. If the recovery system is a net producer of shaft work it is

assumed that this work is converted to electrical energy at a 95 percent

efficiency.

2.2.2. Liquefaction energy recovery systems

This section considers two classes of liquefaction energy recovery systems. The first takes advantage of the difference in shaft work required to

compress a liquid as compared to a gas; however, the refrigeration capability

is wasted. The second type of recovery system makes direct use of net shaft

work and the refrigeration capacity of liquid hydrogen.

Figure 2.1 shows a schematic of the first kind of energy recovery system.

Liquid hydrogen is compressed to some intermediate pressure P^, warmed to

ambient temperature and then expanded to a given final pressure which is

equal to the inlet pressure of the power generator; both the liquid pump and

expander are assumed to operate at an efficiency of 80 percent of adiabatic.

The shaft work is converted to electricity and the hydrogen is sent to the

power generator. Also, it is possible to heat the high pressure hydrogen prior

to expansion by burning some fraction f of the hydrogen leaving the expander.

Figure 2.2 shows values of LERF for f = 0.0 as a function of expander

inlet and outlet pressure. The calculations are based on the thermodynamic

data of McCarty and Weber [3] . For the case when the expander inlet and

outlet pressures are equal (i.e., no expander is used) the value of LERF shows

the energy saved by compressing liquid instead of gaseous hydrogen. The

46
o D. CO 0-=> II —1

o

QJ

fO

III

o

>>

ai

i- QJ <u

eno

T

(J

<*- o;O" ^—c

Oio

s- T3

in o

>1

i.Oi>

o

(J

a>

s-

•t->

i-o

^-B

Oi __

t-> _

(/I >, n3

1/)

1+- o

o

U

ma "O

a> c

u

1/1

47
Expander efficiency = 80% of adiabatic

Pump efficiency = 80% of adiabatic

f = 0.0

Expander outlet pressure. 30 atm

20

10

Denotes LERF without expander

L

100 200

EXPANDER INLET PRESSURE, atm

300

LERF as a function of expander inlet and outlet Pressures for

the pump-expander system.

48
curves show an asymptotic behavior with increasing expander inlet pressure

and, as one would expect, the relative gain with increasing inlet pressure

decreases with increasing expander outlet pressure. There is little advantage

in an expander system if the outlet is greater than 20 atm; however, the

energy savings of compressing liquid instead of gas are significant at the

higher pressures. It is expected that ^2~'^2 generators will operate at

30 atm [9] while fuel cells will operate very close to ambient pressure.

If all of the hydrogen goes to the power generator (f = 0) the value of

LERF is independent of the power generator. However, if some hydrogen is

burned the relative efficiencies of the burner, expander, and the power

generator must be considered. Figure 2.3 shows how LERF varies with expander

inlet pressure and f if a gas turbine having an efficiency of 28 percent

(based on LHV) is used. (It is assumed that the burner has an efficiency of

70 percent based on LHV) . In this case the expander outlet pressure is 8 atm

which corresponds to present-day gas turbines [4]. For expander inlet pressures of less than 115 atm it is better not to burn any hydrogen; higher inlet

pressures make burning only a slightly beneficial option. Over the range of

values considered here, LERF is nearly a linear function of f. Therefore the

optimum value of f would be the value of f corresponding to the maximum temperature allowed in the burner. Even though there is little benefit in burning some of the hydrogen, figure 2.3 shows that it is possible to obtain a LERF of 40 percent by recovering shaft work only.

Similar calculations for two other power generators, MHD and fuel cells,

show that, at expander inlet pressures of 200 atm or less, it is better to

send all of the hydrogen to the power generator; this is because they are more

efficient than the burner-expander system. Therefore, it is apparent that

burning hydrogen is not generally an attractive option.

In the above calculations the refrigerating capacity of liquid hydrogen

was wasted. Liquid hydrogen could be put to the same uses as are being con- sidered for LNG "cold" [5]. However, liquid hydrogen is a more useful re- frigerant because of its lower temperature (liquid hydrogen boils at 20 K

while LNG boils at 112 K or higher) . One obvious application is to use liquid

hydrogen as a coolant in an air separation plant. The ability to produce

gaseous oxygen on-site could have energy, economic and environmental benefits.

Assuming an ideal, i.e. reversible, process it would be possible to produce a stoichiometric quantity of oxygen from air by recovering the ideal work of

liquefaction for hydrogen without any additional work. A more detailed, and

lengthy, analysis (more details are given in the Appendix) shows that at best,

only 40 percent of the stoichiometric could be produced without additional

work. Thus additional work is required if a stoichiometric amount of oxygen

is desired. Even so, the more realistic calculations point out the following

advantages for using liquid hydrogen as a refrigerant in an air plant:

1. Based on the ideal work of separation (6100 J/g-mol of gaseous 0^

product) , it is possible to obtain an efficiency of 18 percent for an air

plant using a single distillation column. This can be compared to the

efficiency of 10 to 12 percent reported by Bliss and Dodge [6] for con- ventional single column plants and 19 percent for large dual column air

plants as given by Springmann [7].

2. If the column could be operated at 0.33 atm, the efficiency could

increase tonearly 34 percent.

3. If high pressure gaseous oxygen is the desired product, using liquid

hydrogen as a coolant makes it attractive to compress liquid instead of

gaseous oxygen. Smith [8] has pointed out that it is normally unattractive to pump liquid oxygen to provide high pressure gaseous oxygen in a conventional air separation plant; however, liquid hydrogen cooling

provides enough refrigeration capacity at 90 K to permit the liquid

oxygen to be pumped and expanded to produce net shaft work as earlier

described for hydrogen.

49
0.5

0.4

0£o

C_)

>-Oo

>-

LU

0.3

0.2

o

UiCr

0.1

No advantage

to burn H

f = 0.00

Slight advantage

to burn

Expander outlet pressure = 8 atm

Burner efficiency = 70% (LHV)

Expander efficiency = 80% of adiabatic

Pump efficiency = 80% of adiabatic

Gas turbine efficiency = 28% (LHV)

100 200

EXPANDER INLET PRESSURE, atm

300

FIGURE 2.3 LERF as a function of expander inlet pressure and mass fraction

burned for a pump-expander system in conjuntion with a gas

turbine.

50
Table 2.1 shows the relative benefits of recovering hydrogen liquefaction

energy, with and without utilizing refrigeration, for the MHD generator and

fuel cell. The gas turbine option was omitted because gas turbines normally

use air. The values of LERF are based on an expander inlet pressure of 200

atm for both hydrogen and oxygen. The calculations for the MHD generator are based on data by Seikel, et.al. [9] for their "option 3" ^2~'^2 ^y^^^^' their

systems are based on using an air separation plant and on operating the

combustor at 30 atm. For this case substantial gains in overall efficiency can

be made by using just shaft work as well as shaft work plus refrigeration. In

the latter case a LERF value of 0.98 represents one-third of actual energy of

liquefaction and a substantial energy saving. There is little benefit from

pumping and expanding oxygen because the expander outlet pressure is so high.

From an economic standpoint, liquefaction energy recovery should be very

attractive since an air separation plant is already required.

The results are quite different in the case of fuel cells. Even after

considering the increased efficiency of the ^2~'^2 ^^^^ cell over the H2-air

fuel cell, there is an insufficient gain in LERF to justify using the liquid

hydrogen for separating air. Even so, to conserve energy it still would be

worthwhile to recover the available shaft work.

2.3. Recovery of Rare Gases

The atmosphere is the primary source of all the rare gases except helium,

which currently is extracted from natural gas. Table 2.2 gives the approximate atmospheric concentrations of the rare gases. The concentrations of

neon, krypton and xenon are quite low but the comnercial demand for these

gases is also low. Therefore, conventional air plants equipped with recovery

systems can produce a sufficient supply of these gases. However, the situation for helium is quite different. Helium is in greater demand than the

other rare gases and its demand could significantly increase if there is

large-scale implementation of high temperature gas reactors, superconducting

transmission lines and/or superconducting magnetic energy storage devices.

However, natural gas reserves are depleting rapidly which means that sometime

in the future, air will become the primary source of helium. Therefore, the

following section considers the feasibility of using liquid hydrogen as a refrigerant for recovering helium from the atmosphere.

Table 2.1. Estimated values of LERF (liquefaction energy recovery factors)

for MHD generator and fuel cell based on a 200 atm expander inlet pressure.

NO SHAFT WORK FROM OXYGEN

MHD"^ Fuel Cell^

Shaft Work Only 0.58 0.17

Shaft Work + Refrigeration

1 atm column 0.98 0.18

1/3 atm column 1.26 0.45

SHAFT WORK FROM OXYGEN

H2 Shaft v;ork Only 0.63

H2 Shaft Work + Refrigeration

1 atm column 1.04 0.34

1/3 atm column 1.31 0.61

^MHD Generator n = 0.65 based on LHV [9].

^Fuel Cell n = 0.51 for H2-air and 0.58 for H2-O2 [10].

51
Table 2.2. Atmospheric concentration of the rare gases [11]

•

Component Composition, ppm by volume

Neon

Helium

Krypton

Xenon

18

510.09

2.3.1. Helium recovery process

The most attractive way to recover helium from air is to condense air

under several atmospheres of pressure and at a temperature of 64 to 70 K. Under these conditions the vapor phase will contain roughly 25-40 percent

nitrogen, 46-55 percent neon, 15-20 percent helium and 1-4 percent hydrogen

[12]; depending upon the temperature and pressure, there could also be 1-4

percent oxygen. The hydrogen and oxygen are removed first using a deoxo

reactor. Then the enriched vapor goes to an adsorbant bed operating at 77 K

which removes the nitrogen and neon [11, 12].

To estimate the technical feasibility of recovering helium with the above

process the practical amount of air throughput per unit of hydrogen vaporized

must be considered. Two possible limitations exist. One is a work limitation, i.e. how much air that can be compressed using an expander system for

hydrogen as described in section 2.2.2. The other possible limitation is in

how much air can be processed for the given amount of refrigeration available.

It is assumed here that the helium recovery system will be self-sufficient in energy, i.e. all the necessary shaft work will be derived from gas

expanders. If liquid hydrogen is compressed to 200 atm, warmed to room temperature and expanded back to 1.0 atm, there is a net energy output of roughly

5040 J/g-mol H^. Then the amount of air compressed is given by

where P is the air compressor outlet pressure in atm. This equation assumes:

1. An air compressor efficiency of 60 percent of isothermal.

2. An expander efficiency of 60 percent of isothermal for the air being

discharged from the system; this recovers some of shaft work of the

compressor

.

3. Gas compression at 300 K. The air pressure is an operating variable but it should be as high as possible to minimize the nitrogen content of the vapor going to the absorption

bed; the lower nitrogen content lowers the hydrogen refrigeration load. The

lowest practical pressure would probably be about 1.5 atm. Equation (2.2)

then gives 4.7 moles of air per mole of hydrogen. For this case if all of the

helium was recovered there would be only 23 x 10"^ moles of helium produced

per mole of hydrogen vaporized.

However, the work limitation can, in principle, be eliminated by com- pressing the liquid air, warming and expanding it back to 1.0 atm. By using

the above assumptions and by assuming that: 1) air behaves like nitrogen, 2)

the pump and expander efficiencies are 80 percent of adiabatic and 3) the

expander inlet pressure is 200 atm, one obtains

2.3.2. Work limitations

Moles of air compressed

Moles of H- vaporized 1.9/ln P (2.2)

52
Moles of air compressed _ 5040

Moles of H2 vaporized 3837 In P-4100 U.i)

Thus, if the air pressure is 2.9 atm, the air expander system could provide

all of the compressor work.

2.3.3. Refrigeration limitations

There are three areas of the helium recovery system where the amount of

air processed could be limited by the available refrigeration. The first area

is in removing the heat of absorption for neon and nitrogen. Secondly, if the

air is to be compressed and expanded to provide shaft work the air stream will

be warmed by several degrees Kelvin; the hydrogen must then supply this lost

refrigeration. Lastly, the heat exchanger which cools the incoming air stream

will not be 100 percent effective and the hydrogen stream must make up the

difference

.

Considering first the heat of absorption, calculations show that the

ratio of helium to hydrogen throughput could be roughly 0.05; thus, this would

not be a limitation. Taking only the loss of refrigeration due to air com- pression into account, the maximum air throughput rationcould be only 1.5.

Also, if the heat exchanger has an effectiveness of 0.95, one again obtains a maximum throughput ratio of 1.5. Therefore, one must conclude that the maximum air to hydrogen throughput ratio is roughly 1.5; this implies that at best

it be possible to recover only about 7 x 10~6 moles of helium per mole of

hydrogen vaporized.

2.4. Conclusions

2.4.1. Utility application

Analysis of two types of recovery systems show that it is technically

feasible to recover roughly one-third to one-half of the actual energy re- quired for liquefying hydrogen; this, in effect, represents a cost credit for

liquid hydrogen. Using shaft work only (neglecting the refrigeration capacity

of liquid hydrogen) , 20 to 25 percent of actual liquefaction energy can be

recovered.

The biggest energy savings can be obtained if the power generating unit

is a MHD generator; recovery of shaft work is attractive for gas turbine

systems and, to a lesser extent, for fuel cells.

The results given here clearly show that economic analyses will be justified

when hydrogen becomes an important synthetic fuel.

2.4.2. Rare gas recovery

Based on supply and demand considerations the only rare gas which would

be worth recovering from the atmosphere is helium. However, refrigeration

capacity limits the ratio of helium recovered to hydrogen vaporized to the

order of 10~5. Therefore, this recovery system could not be feasible unless

the cost of helium becomes extremely expensive and the demand remains high.

53
2.5. References

[I] Strobridge, T. R. , Cryogenic refrigerators - an updated survey, Nat.

Bur. Stand. (U.S.) Tech. Note 655 (June 1974).

[2] Selected Topics on Hydrogen Fuel, Ed. J. Hord, Nat. Bur. Stand. (U.S.)

Special Publication 419 (May 1975).

[3] McCarty, R. D. and Weber, L. A., Thermophysical properties of parahydrogen from the freezing line to 5000 R for pressures to 10,000 PSIA,

Nat. Bur. Stand. (U.S.) Tech. Note 617 (April 1972).

[4] Griffin, L., Piiblic Service Company of Colorado, Denver, Colorado,

private communication (December 1974)

.

[5] Chansky, S. H. and Haley, H. E. , The utilization of LNG cold. Paper 68-D

31 presented at the 1968 American Gas Association Operating Section

Distribution Conf.

[6] Bliss, H. and Dodge, B. F. , Oxygen manufacture - thermodynamic analyses

of processes depending on low temperature distillation of air. Part II,

Chem. Eng. Prog. 45 (2), 129 (February 1949).

[7] Springmann, H. , Large air separation unit plants, ASME Paper 74-WAPID-8

(December 1974 )

.

[8] Smith, D. E. , Comparison of liquid pumping and gas compression in gasproducing oxygen plants. Book, Advances in Cryogenic Engineering 6^, Ed.

K. D. Timmerhaus, pp. 202-209, (Plenum Press, Inc., New York, N.Y.,

1961)

.

[9] Seikel, G. R. , Smith, J. N. and Nichols, L. D. , H2-O2 combustion powered

steam - MHD central power systems. Book, Hydrogen Energy, Part B, Ed. T.

N. Veziroglu, pp. 969-982, (Plehum Press, Inc., New York, N.Y., 1975).

[10] Federal Power Commission, National Power Survey, Energy Distribution

Research (to be published)

.

[II] Baron, R. , Cryogenic Systems, Book, (McGraw Hill Company, New York, N.Y.

1966) .

[12] Tompkins, J. F. and Geist, J. M. , Large-scale neon recovery and purification process. Book, Advances in Cryogenic Engineering 8_, Ed. K. D.

Timmerhaus, pp. 484-488 (Plenum Press, Inc., New York, N.Y., 1963).

[13] Ruhemann, M. , The Separation of Gases, Book, (Clarendon Press, Oxford,

(1949) .

[14] Bliss, H. and Dodge, B. F., Oxygen manufacture-thermodynamic analyses of

processes depending on low temperature distillation of air. Part I, Chem

Eng. Prog. 45 (1), 51 (1949).

54
2.6. APPENDIX

Air Plant Design

This appendix briefly describes the preliminary process design of an air

separation plant which uses the refrigerating capacity of liquid hydrogen.

The plant is designed to produce 8 kg of 99 percent pure gaseous oxygen for

every kg of liquid hydrogen vaporized. More complete details for designing

conventional air plants are given by Ruhemann [13] and by Bliss and Dodge

[14] .

2.6.1. Design using an atmospheric column

Figure 2.4 shows a flowsheet for an air plant which utilizes the liquefaction energy of liquid hydrogen. The plant has one distillation column

which operates at 1.0 atm and is very similar to a Linde single-column air

plant. Based on the results of calculations using the availability function

one would expect that air compression could be eliminated because no additional refrigeration is necessary. However, more realistic calculations show

that liquid hydrogen can condense only 10 percent of the stiochiometric

quantity of air. Also, heat is required in the reboiler to provide a vapor

flow. Therefore, a large fraction of the air must be condensed in the column

reboiler. Because air boils at a lower temperature than oxygen, the air must

be compressed to roughly 3.7 atm to provide a 2.5 K temperature difference in

the reboiler. Even so, this is lower than the 6.0 atm or higher required by

conventional plants which derive refrigeration from gas expansion. Also, up

to 40 percent of the compressor work can be obtained from the expander system

described in section 2.2.2.

After the air is compressed it goes through the main heat exchanger where

it is cooled by the product streams. Due to the hydrogen flow there is a 40

percent excess of refrigeration available in this exchanger; this is more than

enough to condense the water and carbon dioxide impurities in the air. The

air leaving the main heat exchanger contains 10 percent liquid; it contains

one percent vapor after going through the reboiler. (To make sure there was

an adequate reboiler duty for column operation, an enthalpy-composition

diagram was used [13]. Air was treated as a binary mixture of oxygen and

nitrogen. ) The remaining vapor is condensed in the precooler and the air is

expanded to 1.0 atm through a Joule-Thompson valve. It then enters the column

as a saturated liquid.

The nitrogen-rich - stream, which contains 7 percent oxygen, leaves the

column as a vapor, goes through the precooler and then through the main heat

exchanger (the heat duty of the precooler is based on a minimum temperature

difference of 2 K) . The oxygen comes off of the bottom of the column as a liquid and is compressed to the desired product pressure. It is possible to

compress the oxygen to a higher pressure and then expand the ambient temperature gas to the final pressure. However, the net work out of this expander

is probably too small to justify this system if the final oxygen pressure is

much greater than 1.0 atm. For these calculations, the pump was taken to be

80 percent efficient based on adiabatic compression.

The liquid hydrogen is first compressed to 200 atm before going to the

precooler. It enters the precooler at roughly 28 K because it has been warmed

by the compression (again assuming an 80 percent of adiabatic pump efficiency)

.

The hydrogen then goes through the main heat exchanger before it is expanded

to the desired outlet pressure. The net work from the expander is used in the

air compressor.

55
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2.6.2. Subatmospheric column

The primary attraction of using a subatmospheric column is the

reduction of inlet air pressure. If the column operates at 1/3 atm the inlet

air has to be compressed to roughly 1.6 atm to provide a 2 K temperature

difference across the reboiler. However, this advantage is somewhat offset by

the work required to compress the nitrogen-rich stream back to 1.0 atm. Since

the nitrogen stream should be compressed at low temperatures to minimize the

work, there will be some loss of refrigeration due to compression. In fact,

by assuming an 80 percent of adiabatic efficiency for the compressor, there is

very little excess refrigeration available in the main heat exchanger.

Also, it has been assumed that the air plant is leak tight; if vacuum

pumps are needed, the advantage of subatmospheric operation could disappear.

57
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. HUMl.lCA 1 ION OK HI- PORT NO. NBSIR 77-8622. Gov't .Accc-ssKin No.

3. Kei ipii'ni's .Accession No.

4. TlTl.F ANn SliBTITI.i; STUDIES OF HYDROGEN LIQUEFIER EFFICIENCY AND THE

RECOVERY OF THE LIQUEFACTION ENERGY

5. Publ icat ion Date

6. I'^t- r [ orm 1 n i: Orc.ini/.ition Oojc

275.05

7. AUTHORfSi 8. Pt rl^trr.ung t^rcan. Report N\'.

9. PKRKORMINC; ORC. AN I/.AT ION NA.MH ANP ADDRF-SS NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Prouct Task «ork t n,l No. 2750153

11. ' onir.iLi Ciraiu No.

12. Sponsoring Ort;.in izai u>n Nami- and Complete- AJdrcs> 'Sfreef. City. Siatc. ZIP)

Same as above

13. lypt ol Kt-pori PiTio-i C-OVl ftJ

M. "^pon s or m ^ Acrru * o

15. SLPPl.l- MI'NTAKV NO l h.--

16. ABSTRACT (A 200-word or less tactual summary ot most si^tticant information- U document includes a sif^nilicant bibliography or literature survey, mention it here.) Liquid hydrogen is a potential synthetic fuel. It is nonfossil,

its production and storage technology is well developed, and it is

inherently nonpolluting . However, the economics of liquefying hydrogen

are costly both in the energy required to produce the liquid and in the

capital costs of the liquefier. These costs could be reduced by increasing the liquefier efficiency and/or by recovering a portion of the

liquefaction energy at the use site. This paper provides the maximum

hydrogen liquefier efficiency based on the efficiency of available

components and the fraction of original liquefaction energy that can be

recovered at the use site. Since the inefficient compressors and ex- panders are the major cause of liquefier inefficiency, no increase in

liquefier efficiency above the current 30 to 35 percent is probable

without a corresponding increase in compressor and expander efficiency --

a difficult task since both the compressors and expanders have a long

and stable history of development. However, roughly one-third to onehalf of the actual energy required to liquefy hydrogen can be recovered

at the use site and this represents a cost credit for liquid hydrogen

.

17. KH"! 'I'ORHS (.SIX to twelve t-ntrifs, alphuhclicnl ardrr. . .ipi i.jI i z<' only the fir.-.l h-llrr i>l the lirst k'V uor./ unUss ./ /ro;>,r name, separated by semicolons ) Component efficiency; cryogenics; efficiency; energy recovery; hydrogen;

liquefier

.

18. A\ AI1.AHI1.1TV XX I'nlHniK-.l

[ l-or Oif.cl.il Oistnl^ution. Ho Not Release lo N l l.-^

[ Order |- rom Sup. of Hoc, U.S. (lovernment Printirij; Oince

Ma.shinv.ton, P.C . :o io:. SP < .ii. No. ( 1 ( XX "rder 1- rom National Trclniical Inlorni.il ion Service iN llsl

'^prinj;! leld, \'irj;iiii.i 1 S ]

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1 1 RPPORT'

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