U. Hegde and R. Balasubramaniam

National Center for Space Exploration Research, Glenn Research Center, Cleveland, Ohio

S. Gokoglu

Glenn Research Center, Cleveland, Ohio

Analysis of Thermal and Reaction Times

for Hydrogen Reduction of Lunar Regolith

NASA/TM—2009-215623

April 2009
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U. Hegde and R. Balasubramaniam

National Center for Space Exploration Research, Glenn Research Center, Cleveland, Ohio

S. Gokoglu

Glenn Research Center, Cleveland, Ohio

Analysis of Thermal and Reaction Times

for Hydrogen Reduction of Lunar Regolith

NASA/TM—2009-215623

April 2009

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Space Technology and Applications International Forum (STAIF–2008)

sponsored by the Institute for Space and Nuclear Power Studies at the University of New Mexico

Albuquerque, New Mexico, February 10–14, 2008
Acknowledgments

U. Hegde and R. Balasubramaniam were supported under NASA Cooperative Agreement NCC3–975 with the National Center 

for Space Exploration Research. The authors greatly appreciate the encouragement and insights offered by K. Sacksteder and

D. Linne of the NASA Glenn Research Center, and useful discussions with E. Santiago-Maldonado of the NASA

Kennedy Space Center during the course of this work.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5285 Port Royal Road

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Available electronically at http://gltrs.grc.nasa.gov

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2009-215623 1

Analysis of Thermal and Reaction Times for 

Hydrogen Reduction of Lunar Regolith 

U. Hegde and R. Balasubramaniam 

National Center for Space Exploration Research 

Glenn Research Center 

Cleveland, Ohio 44135 

S. Gokoglu 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

System analysis of oxygen production by hydrogen reduction of lunar regolith has shown the 

importance of the relative time scales for regolith heating and chemical reaction to overall performance. 

These values determine the sizing and power requirements of the system and also impact the number and 

operational phasing of reaction chambers. In this paper, a Nusselt number correlation analysis is 

performed to determine the heat transfer rates and regolith heat up times in a fluidized bed reactor heated 

by a central heating element (e.g., a resistively heated rod, or a solar concentrator heat pipe). A coupled 

chemical and transport model has also been developed for the chemical reduction of regolith by a 

continuous flow of hydrogen. The regolith conversion occurs on the surfaces of and within the regolith 

particles. Several important quantities are identified as a result of the above analyses. Reactor scale 

parameters include the void fraction (i.e., the fraction of the reactor volume not occupied by the regolith 

particles) and the residence time of hydrogen in the reactor. Particle scale quantities include the particle 

Reynolds number, the Archimedes number, and the time needed for hydrogen to diffuse into the pores of 

the regolith particles. The analysis is used to determine the heat up and reaction times and its application 

to NASA’s oxygen production system modeling tool is noted. 

Nomenclature 

A reactor cross section area (m2) 

Aeff effective surface area of heater (m2

) 

Ar Archimedes number 

c molar concentration of hydrogen in particle (moles/m3

) 

cs molar concentration of hydrogen at reaction surface (moles/m3

) 

cx molar concentration of hydrogen at location x in reactor (moles/m3

) 

c0 molar concentration of hydrogen at upstream end of regolith bed (moles/m3

) 

Ceff effective specific heat (J/kg/K) 

Cpg specific heat of gas (J/kg/K) 

Cps specific heat of regolith (J/kg/K) 

D effective gas diffusion coefficient (m2

/s) 

E energy required to heat bed 

h heat transfer coefficient 

g gravitational acceleration (m/s2

) 

k equilibrium constant 

L length of regolith bed (m) 

Meff effective mass (kg) 
NASA/TM—2009-215623 2

Mtotal total molar water yield (mol) 

N number of regolith particles in the bed 

Nu Nusselt number 

Pr Prandtl number 

rp regolith particle radius (m) 

Re Reynolds number 

t time (s) 

tc chemical time (s) 

tD intra-particle diffusion time (s) 

tDLimit chemical time in diffusion limit (s) 

tR reactor residence time (s) 

tResLimit chemical time in equilibrium limit (s) 

T temperature (K) 

Th heater temperature (K) 

T1, T2 initial and final temperature of bed (K) 

u velocity through reactor (m/s) 

Vbed volume of regolith bed (m3

) 

x axial coordinate (m) 

α particle conversion 

α0 particle conversion at x = 0 

β regolith thermal diffusivity (m2

/s) 

δ thermal conduction length scale (m) 

ε void fraction in regolith bed 

ρa molar concentration of ilmenite in regolith (mol/m3

) 

ρg gas density (kg/m3

) 

ρs regolith density (kg/m3

) 

μ gas viscosity (Ns/m2

) 

λ gas thermal conductivity 

Ψ molar outflow of water (mol/s) 

Introduction 

Hydrogen reduction of lunar regolith has been proposed as a viable technology for oxygen production 

on the Moon. (Taylor and Carrier 1992, McKay and Allen 1996, Rice, Hermes and Musbah 1997). The 

reduction processes involve solid-gas reactions. Such systems are well developed for earth applications 

but mainly for the purpose of metal extraction as opposed to water vapor and oxygen production for lunar 

applications. In addition, in the lunar context, the reactor must interface with the other sub-system 

processes such as upstream regolith extraction and beneficiation, and downstream electrolysis and phase 

separation in a way that establishes the most favorable balance between efficiency, robustness, and 

equivalent system mass. For example, the reduction of ilmenite may be represented as: 

FeO.TiO2 + H2 ⇔ Fe + TiO2 + H2O (1)

It is carried out in the reactor sub-system. The formed water may be electrolyzed in the electrolyzer 

subsystem to produce oxygen and hydrogen. 

From upmass and cost considerations, it is essential to operate these systems on the lunar surface in as 

nearly a closed-loop manner as possible for the hydrogen. It is in this context that knowledge of 

processing times in the various sub-systems becomes important. For example, a mismatch between the 

flux of water exiting the reactor and the amount of water that may be processed by the electrolyzer must 
NASA/TM—2009-215623 3

be mitigated by design such as sizing the appropriate buffer tank. This paper investigates the factors that 

influence the overall processing time in the reactor sub-system. 

The temperature of the reaction is one of the important parameters of the process. Ilmenite is just one 

constituent of mare basalt and it cannot be assumed that regolith beneficiation (e.g., in this case, removal 

of the nonilmenite components) will be carried out prior to the reactor processes. The sintering and 

melting temperature of the unbeneficiated regolith is noted to be in the range of 1370 to 1670 K 

(Chambers 1995, McKay and Allen 1996). However, hydrogen reduction has been found to be effective 

also at lower temperatures, e.g., in the range of 970 to 1270 K (Yoshida et al., 2000). Therefore, while 

three-phase (gas-liquid-solid) reactors for hydrogen reduction may be applicable at post-melt 

temperatures, these are not considered here and attention is restricted to gas-solid interactions. In order to 

provide a basis for discussion, it is assumed that the chemical reduction of the regolith occurs in a gassolid fluidized bed reactor. 

The conversion process in the reactor consists of the following overall steps (1) transfer of regolith 

into the reactor, (2) fluidization and heating of the regolith, (3) reaction of hydrogen with the ilmenite 

portion of the regolith, (4) outflow of left-over hydrogen and produced water vapor, and (5) removal of 

the spent regolith from the reactor. In this paper, attention is focused on steps (2) to (4). 

The reported values for the thermal diffusivity, β, of lunar regolith are very low (Heiken, Vaniman 

and French 1991). In the absence of a gas flow, the time to heat the regolith bed over a distance δ is 

proportional the ratio δ2

/β, which results in unacceptably large values. On the other hand, hydrogen has a 

relatively high thermal conductivity and helps to stir the bed so that having hydrogen flow through the 

bed decreases the heating time appreciably. Thus, it is advantageous to fluidize the bed during the regolith 

heating step. There are also advantages related to reducing regolith particle agglomeration and sintering 

which can adversely impact reaction times and water production rates. 

The objectives of this paper are (1) to develop analytical models for regolith heating and for chemical 

reduction by hydrogen in order to identify parameters influencing the heating and reaction times, (2) to 

identify the parameters that govern these times, and (3) to obtain relationships for the reaction time in the 

two limits of diffusion (i.e., mass transfer) control and chemical equilibrium control. As noted earlier, 

these times are important from the overall oxygen production system perspective. The thermal analysis is 

based upon a Nusselt number correlation. The reaction model considered is based upon a “shrinking core” 

diffusion-reaction model for the gas-solid reduction process (Levenspiel 1998) which is coupled with the 

inflow/outflow of gases. The methodology has been discussed in our earlier work (Hegde, 

Balasubramaniam and Gokoglu 2007). It appears consistent with results of regolith particulate analysis 

conducted on Apollo-returned samples (McKay and Allen 1996) which suggest that the ilmenite particles 

are not completely solid but have some porosity that would enable gases to diffuse into the particles, i.e., 

the FeO portion can be essentially completely converted leaving behind the reduced iron. 

In the next section, the regolith heating is considered first and a model for the heating time and 

required power is developed. Pertinent results from the shrinking core analysis are also presented. 

Subsequently, in the Results section, factors impacting these processes are evaluated and discussed and 

applications of the model to NASA’s oxygen production system modeling tool are noted. 

Model Development 

In the first sub-section below, the time taken to heat the regolith is calculated using a Nusselt number 

correlation for fluidized bed heat transfer. This is followed by a summary of the particle conversion 

analysis and the coupling between the particle conversion and the bulk reactor flow. 

Heat Transfer Analysis 

It is assumed that the regolith is heated by a cylindrical rod located centrally in the cylindrical reactor. 

The surface temperature of the heater rod can be controlled e.g., by adjusting the current through it as in 

an electrical heater or by controlling the energy flux as in a solar concentrator heat pipe. The different 
NASA/TM—2009-215623 4

pathways for heat transfer in the bed are gas convection and conduction, particle motions, and possibly, 

radiative transfer. 

Fluidized bed heat transfer correlations developed in the literature under convective-conductive 

conditions suggest that the controlling step is the heat transfer from the heater surface to the gas film next 

to it. Direct transfer of heat to the bed particles adjoining the heater is not efficient because the contact 

area between particles and the heater surface is small. If the bed is well stirred by fluidization, its 

temperature is nearly uniform. In such a case, a Nusselt number may be defined which relates the heat 

transfer to the bed through the gas film in contact with the heater, i.e., the regolith bed is taken to be a 

uniform entity. The reactor wall is not usually insulated from the bed, so in general, there will also be heat 

transfer from the bed to the reactor wall. If the reactor wall is not too thick and its thermal conductivity is 

high, the wall may be assumed to be at a uniform temperature. Furthermore, if the reactor’s thermal mass 

(i.e., the product of its mass and specific heat) is small compared to that of the bed, it is reasonable to 

assume that the temperature of the reactor is the same as that of the bed. 

The heating rate with the above scenario is given by: 

hA ( ) T T

dt

dT MeffCeff = eff h − , (2) 

where the thin film heat transfer coefficient, h, is related to the Nusselt number, Nu, by: 

Nu = 2hrp /λ . (3) 

In Equation (2), MeffCeff is the effective value of the product of the mass and specific heat and is a 

weighted average of the values for the gas, regolith, and reactor. Aeff is the effective or active surface area 

of the heater rod in contact with the bed. 

The solution of Equation (2) for the instantaneous bed temperature T is given by: 

( ) ( ( )) 1 eff eff eff T = Th − Th −T exp − hA t / M C . (4)

Conversely, the time to raise the bed temperature from T1, to a temperature T2 is given by: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

− = −

1

2

eff

eff eff ln

T T

T T

hA

M C

t

h

h

h . (5) 

Various fluidized bed heat transfer Nusselt number correlations are available in the literature. For 

example, the following one (Borodulya et al. 1991) appears to describe the situation adequately: 

( ) ( )

ε

− ε − ε + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

ρ =

2.3

2.3

0.14 0.24

0.1 1 Nu 0.74Ar 1 0.46RePr

pg

ps

g

s

C

C . (6) 

The Archimedes number, Ar, the Reynolds number, Re, and the Prandtl number, Pr, are defined as 

follows: 

3 2 Ar = 8grpρg (ρs − ρg )/μ , (7)

Re = 2urpρg /μ , (8) 
NASA/TM—2009-215623 5

= Cpgμ λg Pr / . (9) 

The energy, E, required to heat the bed and reactor from T1 to T2, in the absence of other losses (e.g., 

radiative), is given by: 

( ) E = MeffCeff T2 −T1 . (10) 

An average power required is obtained by dividing E by the time, Th. Note that the instantaneous power, 

MeffCeffDT/dt, can be obtained by substituting the solution for T (Eq. (4)) into Equation (2). 

Since radiative losses vary as the fourth power of temperature, they can become important as the 

reactor is heated to higher temperatures. It is expected that there would be insulation around the reactor 

that would reduce this loss. This loss can be accounted for by including it in the energy required. 

Chemical Conversion Analysis 

The chemical conversion analysis couples the “shrinking core” model with the inflow and outflow of 

the gases and has been discussed in earlier work (Hegde, Balasubramaniam and Gokoglu, 2007). Here, 

some results are presented to highlight the findings from the model and to show how the characteristic 

times of the process are obtained. 

Defining the conversion α by: 

3

3

1

p

s

r

r

α = − , (11) 

the shrinking core analysis of a single particle yields a relationship between α and the associated 

conversion time, t: 

[] [] [ ]

2

2 / 3 6 31 21 1

a p

x s

r

D c c t

ρ

− − α − − α − = − . (12) 

Further, assuming equilibrium conditions at the reaction surface, the above equation reduces to: 

[] [] 2

2 / 3 0

(1 )

6 31 21 1

a p k r

Dkc t

+ ρ − α − − α − = − . (13)

Note that an expression for the equilibrium constant, k, as a function of only the reaction temperature has 

been provided (William and Erstfeld, 1979): 

( 2126.1/ 0.6439) 10 − + = T k . (14) 

The time for complete conversion is given by setting α to unity. 
NASA/TM—2009-215623 6

Coupling Particle Analysis With the Reactor Bulk Flow 

Assuming that the gas velocity, concentration of hydrogen and the associated conversion α are 

functions of axial distance along the reactor, and the inlet hydrogen concentration is constant in time, the 

following equation has been obtained: 

( )

( )

( )

( ) ( ) x

r u

D

p

1/ 3 2

0

1/ 3

1/ 3

0

1/ 3

3 1

2 1 1

2 1 1 ln

1 1

1 1 4ln = − ε ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

− α +

− α +

+

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

− − α

− − α − , (15) 

where α0 is the value of α at x = 0 and is given by Equation (13). 

In certain cases, closed form solutions may be obtained for the concentration of hydrogen and extent 

of conversion in the reactor. An example is when the regolith and gases are sufficiently stirred or wellmixed so that gradients in conversion and gas concentration are smeared out. In this well-stirred limit, the 

concentration of hydrogen exiting the reactor is also the average concentration in the reactor and is given 

by: 

( )

( ) [ ]

( ) ⎪

⎪

⎪

⎪

⎪

⎭

⎪

⎪

⎪

⎪

⎪

⎬

⎫

⎪

⎪

⎪

⎪

⎪

⎩

⎪

⎪

⎪

⎪

⎪

⎨

⎧

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

⎥

⎦

⎤ ⎢

⎣

⎡ − − α

− α

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ − ε

+

+ =

u

L

r

D

k

k

c

c L

p 1/ 3

1/ 3

2

0

1 1

1 1 3 1

1

1 . (16) 

Results 

Regolith batch sizing will depend upon the oxygen production required and the processing time per 

batch. In general, the processing time per batch is the sum of the heating and chemical conversion times. 

This section considers factors influencing these times based upon the analysis presented earlier. 

Heating Time 

Equation (5) indicates that the heating time is related directly to the Nusselt number and batch size 

(i.e., regolith mass) and inversely related to the active surface area of the heater. The Nusselt number 

depends upon the Reynolds number of the gas flow relative to the regolith particles, the Archimedes 

number, and the Prandtl number of the fluidizing gas. The Prandtl number is practically constant with 

temperature. The Reynolds number is related to the fluidizing velocity and particle size. The particle size 

is fixed by the regolith characteristics and there may be some flexibility in this regard depending upon the 

preprocessing facilities available. The fluidizing velocity is also related to the particle size. The 

Archimedes number is mainly dependent upon the regolith density (which is much greater than the gas 

density). The most flexible way of changing the heating time seems to be by changing the regolith batch 

size, active heater area, and/or power input to the heater. 

The active heater surface area may be increased by increasing the heater diameter. For a fixed reactor 

diameter, this also increases the height, L, of the regolith bed which is also conducive to heat transfer. 

However, this may have implications for the reaction time as will be discussed later. The regolith batch 
NASA/TM—2009-215623 7

size may be reduced to decrease the heating time but this may be restricted from overall oxygen 

production considerations. 

The power input to the heater is related to the heater temperature Th. From Equation (5), it is clear that 

increasing the heater temperature will decrease the time to heat the regolith to a given temperature T2. 

However, there are limitations to raising Th substantially over T2 e.g., the presence of hot spots or regions 

in the regolith bed which are at higher than desired temperature. 

Chemical Time 

The shrinking core analysis provides an expression for the conversion time of a single particle. In 

many instances it is assumed that the conversion time of the regolith bed is the same as the single particle 

conversion time. Equation (15) provides a means for determining the conditions under which this holds. 

Choosing x = L (i.e., the height of the regolith bed), it is clear that the right hand side of Equation (15) is 

related to the ratio of the gas residence time in the bed, L/u, to its diffusion time in a particle, rp

2

/D. This 

time factor ratio plays an important role in determining the extent of conversion in the bed. For example, 

the upstream end (entrance region) of the bed is always exposed to fresh hydrogen and would be the first 

to get converted. The time ratio factor gives a measure of the conversion in the remaining portions of the 

bed. Figure 1 plots the conversion, α(L), at the downstream end (exit region) as a function of the time 

ratio factor for the case where α0 is equal to unity, i.e., when the particles at the entrance are already 

completely converted. As the time ratio factor becomes small (i.e., the intra-particle diffusion time is 

much greater than the gas residence time in the regolith bed) it can be seen from Figure 1 that the 

conversion, α(L), also approaches unity, i.e., the particles at the downstream end of the bed (and more 

generally, at any location in the bed) are also consumed fully. This indicates that the time rate of chemical 

conversion for all particles in the bed is given by Equation (13). The corresponding time for complete 

conversion may be termed the chemical time in the diffusion controlled limit. Setting α to one in 

Equation (13) yields: 

( )

0

2

Limit 6

1

Dkc

k r

t a p

D

+ ρ = . (17) 

 

Figure 1.—Dependence of the Regolith Conversion at the Downstream End of the Reactor 

Bed Upon the Time Ratio Factor 3(1-ε) DL/rp

2

u.

Time Ratio Factor, 

3(1-ε)DL/(rp

2

u) 

α (L) 
NASA/TM—2009-215623 8

On the other hand, as the residence time becomes much larger compared to the diffusion time, i.e., the 

time ratio factor becomes large, it can be seen from Figure 1 that the conversion occurs first primarily 

near the upstream end of the bed and not much conversion occurs downstream since α(L) is small for this 

condition. This is referred to as the chemical equilibrium limit, i.e., the residence time in the bed is long 

enough so that the water concentration reaches its chemical equilibrium value in the gas phase. At this 

point no further conversion takes place. In this limiting case, the chemical time may be estimated by 

assuming equilibrium concentration of water in the outflow. Then, the molar outflow of water is given by: 

( ) 0 1

uAc

k

k

+

ψ = , (18) 

and the total molar water yield is: 

total ResLimit M = ψt . (19) 

Equating this to the available molar water yield in the regolith provides the chemical time in the residence 

time limit or equilibrium limit: 

tResLimit = ρa (1− ε)Vbed /ψ . (20) 

Since the conversion time in the diffusion limit depends inherently upon the particle characteristics such 

as its size and the intra-particle gas diffusivity, it is clear that this is a lower limit to the conversion time. 

The equilibrium limiting conversion time is variable however, depending upon the flow velocity and bed 

height. Varying these quantities is a way to slow down the conversion rate. This may be useful from an 

overall system design perspective. 

Application to System Design 

The analysis of heating and chemical times presented here may be applied to sizing and design of the 

reactor assembly. It has been noted in earlier studies that the regolith reduction rate increases directly with 

the temperature, (McKay and Allen 1996) presumably due to increase in the effective diffusion 

coefficient (Hegde, Balasubramaniam and Gokoglu 2007). This implies that most of the conversion 

occurs at the operating temperature. In other words, the heating and chemical reductions are essentially 

serial operations for a given batch of regolith. Thus, a system comprising two reactors may be used for 

increased throughput. Ignoring for current purposes, the regolith loading and unloading times into the 

reactor chamber, it is clear that designing for equal heating and reaction times will ensure continuous 

production of oxygen, i.e., as one batch of regolith is being heated the other batch is being chemically 

reduced. 

The equations provided here provide a framework for achieving the proper design parameters. The 

diffusion limited chemical time (Eq. (17)) provides the minimum time for conversion. Equations (5) and 

(10) in conjunction provide the power and heater rod characteristics (e.g., effective area) for a given 

heating time, e.g., the minimum reaction time. If the power available is less than the heating power 

required, the heating time has to be increased. In such a case, the reaction time needs to be modified e.g., 

by driving the reactor dimensions toward the residence limited conversion time (Eq. (20)). Clearly, this is 

an iterative process. Currently, NASA is developing an overall system model incorporating these ideas 

(Santiago-Maldonado 2007). 
NASA/TM—2009-215623 9

Conclusions 

Analytical models for regolith heating and for chemical reduction by hydrogen have been developed 

to identify parameters influencing the heating and reaction times. These times are important from the 

overall oxygen production system perspective. The regolith heating model is based upon a Nusselt 

number correlation for fluidized bed heat transfer. While particle size and parameters such as the particle 

Reynolds and Archimedes numbers play a role in the heating time determination, it appears that the most 

feasible way of controlling this time is by adjusting the active heater surface area and mass of the regolith 

per batch. The chemical reduction model results from coupling a shrinking core type of analysis with the 

overall regolith bed flow characteristics. It is shown that the chemical time in the diffusion limit is also 

the lower limit for the conversion time. However, by adjusting the residence time of the gases in the 

regolith bed, the conversion time can be increased. 

References 

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Between a Surface and a Fluidized Bed: Consideration of Pressure and Temperature Effects,” 

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Chambers, J.G., “Quantitative Mineralogical Characterization of Lunar High-Ti Mare Basalts and Soils 

for Oxygen Production,” Journal of Geophysical Research, 100, 14391–14401, (1995). 

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Conversion of Lunar Regolith, Space Technologies and Applications International Forum, 

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Heiken, G.H. Vaniman, D.T., and French, B.M., Lunar Sourcebook, Cambridge University Press, New 

York, NY, 1991, pp. 285–300. 

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DC, 1996. 

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Production, AIAA Paper No. 97–0890, American Institute of Aeronautics and Astronautics, 

Washington, DC, 1997. 

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Resources Roundtable Inc., Golden, CO, 2007. 

Taylor, L.A., and Carrier, W.D. III, “Production of Oxygen on the Moon: Which Processes are Best and 

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on Water Production by Hydrogen Reduction of Lunar Soil Simulant in a Fixed-Bed Reactor, Space 

Resources Roundtable Inc., Golden, CO, 2000. 
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01-04-2009 

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Technical Memorandum 

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4. TITLE AND SUBTITLE

Analysis of Thermal and Reaction Times for Hydrogen Reduction of Lunar Regolith 

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6. AUTHOR(S)

Hegde, U.; Balasubramaniam, R.; Gokoglu, S. 

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WBS 387498.04.01.04.03 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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This publication is available from the NASA Center for AeroSpace Information, 301-621-0390

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14. ABSTRACT

System analysis of oxygen production by hydrogen reduction of lunar regolith has shown the importance of the relative time scales for 

regolith heating and chemical reaction to overall performance. These values determine the sizing and power requirements of the system and 

also impact the number and operational phasing of reaction chambers. In this paper, a Nusselt number correlation analysis is performed to 

determine the heat transfer rates and regolith heat up times in a fluidized bed reactor heated by a central heating element (e.g., a resistively 

heated rod, or a solar concentrator heat pipe). A coupled chemical and transport model has also been developed for the chemical reduction of 

regolith by a continuous flow of hydrogen. The regolith conversion occurs on the surfaces of and within the regolith particles. Several 

important quantities are identified as a result of the above analyses. Reactor scale parameters include the void fraction (i.e., the fraction of 

the reactor volume not occupied by the regolith particles) and the residence time of hydrogen in the reactor. Particle scale quantities include 

the particle Reynolds number, the Archimedes number, and the time needed for hydrogen to diffuse into the pores of the regolith particles. 

The analysis is used to determine the heat up and reaction times and its application to NASA’s oxygen production system modeling tool is 

noted. 

15. SUBJECT TERMS

Hydrogen reduction; ISRU; Lunar regolith; Ilmenite; Shrinking core 

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