U. Hegde and R. Balasubramaniam

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

S. Gokoglu

Glenn Research Center, Cleveland, Ohio

Development of a Reactor Model for

Chemical Conversion of Lunar Regolith

NASA/TM—2009-215626

April 2009
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U. Hegde and R. Balasubramaniam

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

S. Gokoglu

Glenn Research Center, Cleveland, Ohio

Development of a Reactor Model for

Chemical Conversion of Lunar Regolith

NASA/TM—2009-215626

April 2009

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Space Technology and Applications International Forum (STAIF–2007)

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

Albuquerque, New Mexico, February 11–14, 2007
Acknowledgments

U. Hegde and R. Balasubramaniam were supported under NASA Cooperative Agreement NCC3–973 with the National Center 

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

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

 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

Springfi eld, VA 22161

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

Level of Review: This material has been technically reviewed by technical management. 
Abstract. Lunar regolith will be used for a variety of purposes such as oxygen and propellant production and 

manufacture of various materials. The design and development of chemical conversion reactors for processing lunar 

regolith will require an understanding of the coupling among the chemical, mass and energy transport processes 

occurring at the length and time scales of the overall reactor with those occurring at the corresponding scales of the 

regolith particles. To this end, a coupled transport model is developed using, as an example, the reduction of ilmenitecontaining regolith by a continuous flow of hydrogen in a flow-through reactor. The ilmenite conversion occurs on the 

surface and within the regolith particles. As the ilmenite reduction proceeds, the hydrogen in the reactor is consumed, and 

this, in turn, affects the conversion rate of the ilmenite in the particles. Several important quantities are identified as a 

result of the analysis. 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 

time for hydrogen to diffuse into the pores of the regolith particles and the chemical reaction time. The paper investigates 

the relationships between these quantities and their impact on the regolith conversion. Application of the model to 

various chemical reactor types, such as fluidized-bed, packed-bed, and rotary-bed configurations, are discussed. 

INTRODUCTION 

Lunar mare basalts containing oxygen include olivine, ilmenite, and pyroxene (Heiken et al., 1991). Energy has to 

be supplied to remove the oxygen, i.e., the associated chemical reactions are endothermic. Free energy 

considerations show that the iron containing minerals require the least energy input for this purpose (Taylor and 

Carrier, 1992). Various technologies have been proposed for the chemical conversion such as ilmenite reduction by 

hydrogen, molten electrolysis, and carbothermal reduction using methane (McKay and Allen, 1996, Rice et al., 

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 extraction 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. A need exists, 

therefore, to establish an analytical framework to couple these sub-systems together. The building blocks of this 

framework are the individual sub-system models. This paper discusses the development of a generalized analytical 

model of the chemical reactor sub-system. 

While the developed methodology should be applicable to different gas-solid reactors, only the reduction of ilmenite 

by hydrogen will be considered here. Ilmenite is a major component of titanium-rich mare basalts. The overall gassolid reaction considered is given by: 

. + 22 ⇔ + + 22 OHTiOFeHTiOFeO . (1) 

NASA/TM—2009-215626 1

Development of a Reactor Model for 

Chemical Conversion of Lunar Regolith 

U. Hegde and R. Balasubramaniam 

The 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 
The formed water is electrolyzed in the electrolyzer subsystem to produce oxygen. This electrolysis process is not 

considered in the model development here. 

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 non-ilmenite 

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 1370-1670 K (Chambers, 1995, McKay and Allen, 1996). 

However, hydrogen reduction has been found to be effective at lower temperatures also, e.g., in the range of 970-

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. 

The equilibrium characteristics of the reduction reaction have been studied to some extent. An expression for the 

equilibrium constant as a function of the reaction temperature alone has been provided (William and Erstfeld, 1979): 

)6439.0/1.2126( 10 − + = T k . (2) 

More recently, computational studies have suggested a pressure dependence of the equilibrium constant (Altenberg 

et al., 1993), but the pressure sensitivity has been found to be much less than the temperature sensitivity. This is 

reasonable since gas phase moles are conserved in the reaction. The reaction rate and chemical kinetics of the 

reduction process appear to be much less studied. There is consensus that the reaction rate is of Arrhenius type and 

an activation energy for the forward reaction has been estimated (Butler et al., 2001) as 18.8 kcal/mole. As noted 

earlier, the conversion is endothermic and energy needed for conversion, ∆H, has been estimated to be 11kJ/mol 

(Yoshida et al., 2000). 

According to Eq. (2), the equilibrium constant for the temperature range of interest is of the order of 0.1. This 

suggests that substantial excess hydrogen beyond the stoichiometric value is needed to completely reduce the 

regolith. Therefore, a closed system where a batch of regolith and a fixed amount of hydrogen are placed in a vessel 

and allowed to react is not practical because of the large volume of hydrogen required to provide the needed oxygen 

for realistic regolith batch amounts. Thus, an open system where a batch of regolith is treated with flowing hydrogen 

is considered here. 

The conversion process may be modeled in terms of the following overall steps: (i) inflow of hydrogen into the 

regolith containing reactor, (ii) reaction of hydrogen with the ilmenite portion of the regolith, and (iii) outflow of 

left-over hydrogen and produced water vapor. Step (ii) is the gas-solid reaction step which is the key to the 

conversion. Results of regolith particulate analysis conducted on Apollo-returned samples (McKay and Allen, 1996) 

suggest that the 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 with the reduced iron remaining behind in the 

particulates. These observations support utilization of a “shrinking core” diffusion-reaction model for the gas-solid 

reduction process (Levenspiel, 1998). This model must then be coupled with the inflow/outflow of gases to 

complete the reactor sub-system model. The chemical reactor analysis is carried out in the next section which is 

followed by a discussion of the obtained results. 

MODEL DEVELOPMENT 

In the first sub-section below, the shrinking core model for the hydrogen-regolith reaction is obtained. Shrinking 

core analyses in the literature generally assume an irreversible (forward only) reaction proceeding to completion. 

This assumption is mostly valid for cases where the equilibrium constant is large so that the gaseous reactant is 

almost all consumed at the reaction site. Here, the equilibrium constant according to Eq. (1) is of the order of 0.1 so 

that the amount of hydrogen must be well in excess of stoichiometric values for complete conversion of the regolith. 

Therefore, in general, both the forward and backward reactions must be considered. The regolith will also have a 

particle size distribution. Here, for simplicity, the regolith will be assumed to be comprised of identical spherical 

particles. Relaxation of this assumption is straightforward at the expense of increased book-keeping, but it does not 

change the qualitative features of the analysis. As the hydrogen flows through the regolith bed, because of depletion 

due to reaction, the concentration of hydrogen at the exterior surface of a particle will depend upon its location in the 

NASA/TM—2009-215626 2
reactor. This essentially is the coupling between the reactor flow and the gas-regolith reaction and is considered in 

the second sub-section below. Finally, the obtained solutions are assessed for applicability to different reactor types 

such as fluidized bed, packed bed, and rotary bed. 

Intra-Particle Gas-Regolith Reaction Analysis 

The shrinking core model as envisioned here is schematically depicted in Fig. 1. Conversion proceeds from the 

exterior particle surface inward. As the reaction progresses into the interior of the particle, the reactant and product 

gases must diffuse through the particle matrix structure formed after the conversion. 

 

FIGURE 1. Shrinking Core Model Configuration 

The diffusion of hydrogen in the particle interior between rp and rs is considered. Assuming quasi-steady behavior, 

and an effective diffusion coefficient, D, for the gases in the interior particle matrix, the concentration, c, of 

hydrogen varies according to: 

 0)( 2 = ∂

∂

∂

∂

r

c Dr

r

 . (3) 

Boundary conditions for c have to be provided at the core (reaction) surface radius, rs, and at the exterior particle 

radius, rp. Note that the particle typically preserves its original (unreacted) size even during the reaction process as 

the main constituents (i.e., the non-ilmenite portion) are largely unaffected. 

At the core radius, let the concentration of hydrogen be cs. The value of c at the particle radius is denoted by cx

where x refers to the location of the particle along the flow direction in the reactor. In terms of cs and cx, the 

solution of Eq. (3) yields: 

 p x

sp

xs Dcrr

rr

ccD Dc +− −− = ]/1/1[]/1/1[][ . (4) 

The flux of hydrogen at the reaction surface may be obtained from the above equation to be: 

 Radius of reaction surface, rs(t) 

 Particle radius, rp

Unreacted core 

NASA/TM—2009-215626 3
 ]/1/1[

1 ][ ] 2

sp

xs

s

r rr

cc D

r r

c D s −

− = ∂

∂

 . (5) 

This hydrogen flux is related to the conversion of FeO at the reaction surface. With ρa being the molar concentration 

of FeO in the unreacted particle, the conversion of FeO by the flux of hydrogen is given by: 

s sa s r r

c Drr

dt

d ]4 34 3 2

∂

∂ −= ππρ . (6) 

Using the value of D(dc/dr)rs from Eq. (5) and solving for rs yields: 

 2

3/2 ][6 1]1[2]1[3

pa

sx

r

tccD

ρ

α α − −=−−−− , (7) 

where α is defined as: 

 3

3

1

p

s

r

r

α −= . (8) 

Equation (7) is the shrinking core result in terms of the hydrogen concentration at the reaction surface and the 

overall particle surface. For the classical case of an irreversible reaction with all of the hydrogen being consumed at 

the reaction surface, the value of cs above would be zero, while this is not the case here. In the next section, a 

description for cx is provided and the connection between cx and cs is discussed. 

Reactor Bulk Flow Analysis 

It is assumed that the regolith particles form a bed in the reactor. The packing of the particles is characterized by the 

linear loading, N/L, of the particles. For example, the loading for a packed bed will be greater than that for a 

fluidized bed. It is assumed that the gas flow through the bed is characterized by a bulk flow velocity, u and the 

species (i.e., hydrogen or water) concentration is a function of only the distance along the bed length, x. The 

hydrogen concentration, cx, is a function of x due to depletion by the reaction. Neglecting inter-particle gas 

diffusion in the bulk flow, the convection of hydrogen is related to its depletion by reaction in the following manner: 

 L

N

r

c Dr

x

c

uR s s r

x

r )(4 2 2

∂

∂ = ∂

∂

π π . (9) 

Upon using the results from the previous section for (dc/dr)rs and incorporating the shrinking core result from Eq. 

(7), the following equation is obtained for cx: 

 ])1(1[

]1[ ][4 3/1

3/1

2

α

α

−−

− −−= ∂

∂

psx

x

r r

L

N ccD

x

c

uR . (10) 

This may be rewritten in the following form: 

 u

x

r

D

V

V

cc

c

bed p

void

sx

∂

−−

− −−= −

∂

])1(1[

]1[ ))(1(3 ][ 3/1

3/1

2 α

α

. (11) 

NASA/TM—2009-215626 4
The required boundary value for cx at the inlet is: 

 0 )0( cxcx = = , (12) 

where c0 is the concentration of hydrogen at the reactor inlet, i.e., the value of cx at x =0. 

It may be noted that the factor D/rp

2 is the inverse of the intra-particle diffusion time, tD, and the factor Vvoid/Vbed

is the void fraction in the bed (i.e., the volume not occupied by particles). The factor dx/u represents the residence 

time of the gases in an axial slice dx of the regolith bed. Correspondingly, a bed residence time, tR, may be 

identified by the factor L/u where L is the length of the regolith bed. 

The factor [cx –cs] appears in both the shrinking core result and the bulk flow analysis. For an inwardly directed 

diffusive flux of hydrogen to exist within the reacted portion of the particle matrix, [cx –cs] must be greater than 

zero. The form of this factor will depend upon the relationship between the diffusion time tD and a chemical 

reaction time, tc.This reaction time is related to the instantaneous forward and backward reaction rates of the 

hydrogen reduction reaction (Eq. (1)). Different cases may be envisioned such as: 

(i) tD >> tc : The rate of gas diffusion in the particles is much slower than the chemical reaction. In this case, the 

processes are intra-particle diffusion controlled, and the chemical reaction may be assumed to be in equilibrium. 

(ii) tc >> tD: The rate of chemical conversion is much slower than the intra-particle gas diffusion. In this case, the 

processes are reaction controlled. 

(iii) tc ~ tD: Both the gas diffusion rate and chemical reaction rates are of similar magnitude, and need to be 

accounted for. 

In this paper, attention is primarily focused on the methodology for case (i). The methodology for the other two 

cases is somewhat more complex and will be considered in future work. 

Chemical equilibrium at the reaction surface implies that the local number of moles of water and hydrogen are 

related according to: 

 ss = kcc1 , (13) 

where c1s represents the molar concentration of water at the reaction surface. The sum of the molar concentrations 

of hydrogen and water (i.e., the overall molar concentration) at the reaction surface is, therefore, (1+k)cs. The 

reduction reaction (1) results in no changes to the number of moles in the gas phase. It is therefore assumed that the 

overall molar concentration at all points in the flow/reaction domain is constant. This is a reasonable assumption 

when the variation of the thermodynamic pressure in the reactor bed is negligible. With the understanding that the 

inlet flow to the reactor is entirely composed of hydrogen at concentration c0, the following relationship is obtained: 

 )1(

0

k

c

cs + = . (14) 

Thus, Equations (7) and (11) provide two simultaneous equations for cx and α as functions of time, t. After 

considerable manipulation, the solution for α may be written in the following form: 

 x

ur

D

p

3/1 2

0

3/1

3/1

0

3/1

)1(3] 1)1(2

1)1(2 ln[] )1(1

)1(1 ln[4 ε

α

α

α

α −= +−

+−

+ −−

−− − , (15) 

NASA/TM—2009-215626 5
where the void fraction is denoted by ε, and α0 is the value of α at x=0 and is given from Eq.(7) by: 

2

0

0

3/2

0

][6 1]1[2]1[3

pa

s

r

tccD

ρ

α α − −=−−−− . (16) 

Since k is of the order of 0.1 as noted earlier, only about 10% of the incoming hydrogen can, at most, be converted 

to water. As a reasonable first approximation, therefore, it may be assumed that α is independent of x, i.e., all 

particles in the reactor are being consumed at the same rate. In this case, a closed form solution for cx at the end of 

the reactor bed can be readily obtained by integrating Eq. (11) between x =0 to x = L. The solution may be shown 

to be: 

]} ])1(1[

]1[ ))(1(3exp[1{)1( )( 3/1

3/1

2

0

u

L

r

D k

k

c

Lc

p α

α

ε −−

− −−+

+ = . (17) 

Correspondingly, the molar water concentration at the outlet is: 

 ]} ])1(1[

]1[ ))(1(3exp[1{) 1

()( 3/1

3/1

1 0 2 u

L

r

D kc

k

k Lc

p α

α

ε −−

− −−− + = . (18) 

Application to Different Reactor Types 

The developed model may be applied to different reactor types and, as examples, three common types of 

configurations are considered below. It may be noted that the main reason the model is applicable to these reactors is 

that the regolith conversion is determined largely by diffusional processes occurring within individual particles 

which are largely independent of the bulk flow. 

Fluidized-Bed Reactor 

In a fluidized bed, the void fraction and flow velocity are coupled. The coupling is described in terms of 

experimental and/or analytical correlations (McCabe et al 2001). For example, for incipient fluidization in the 

viscous flow regime, the fluid velocity is related to the void fraction by: 

ε

ε

μ

ρ ρ

−

− = 15.37

)( 3

2

p

gs

f u gr . (19) 

Generally, the flow velocity, u, is chosen to be between the incipient fluidization velocity and the particle settling 

velocity, us: 

2

5.4

)(

p

gs

s u gr

μ

ρ − ρ = . (20) 

Equations (17) and (18) may be utilized once u and ε are fixed. 

Packed-Bed Reactor 

In this type of reactor, the particle bed is generally constrained physically within a given volume. In conjunction 

with the regolith volume, this provides the void fraction. The flow velocity may be picked independently of the void 

fraction; however, excessive pressure drop may limit its value. 

NASA/TM—2009-215626 6
Rotary-Bed Reactor

In rotary-bed reactors, the regolith bed undergoes a rotational motion. This may be implemented, for example, by 

rotor vanes within the reactor or by rotating the reactor vessel about its axis. Depending upon the intensity of the 

mixing, the reactor may be characterized as “weakly-stirred”, “moderately-stirred”, or “well-stirred”. These 

characterizations refer to how well the mixing smears out the average spatial gradients in the gas species 

concentrations and the particle conversion, α. The weakly-stirred case maintains the spatial gradients and may be 

described by the procedure considered earlier, i.e., by Eqs. (15) - (18). In the well-stirred reactor, both the gas 

species concentrations and α are independent of location. The value of cx may then be identified with c(L) and the 

solution of Eq. (11) in conjunction with Eqs. (12) and (14) yields: 

}

] ])1(1[

]1[ ))(1(31[

1{ 1 )(

3/1

3/1

2

0

u

L

r

D

k

k

c Lc

p α

α

ε −−

− −+

+

+ = , (21) 

and, correspondingly, 

}

] ])1(1[

]1[ ))(1(31[

1 1{ 1 )(

3/1

3/1

2

0

1

u

L

r

k D

kc Lc

p α

α

ε −−

− −+

− + = . (22) 

The equation for α is obtained by substituting Eq. (21) for cx in Eq. (7). 

In the “moderately-stirred” case, spatial gradients exist in the gas phase concentration but are relatively weak in the 

particle conversion α. In this case, utilizing a spatial average between x = 0 and x = L for cx yields the following 

equation for the spatial average of α, <α>: 

}.1]])1(1[

)1( )1(3{exp[

)1(

])1(1[

)1(

1

)1(

2 1)1()1(3

3/1

3/1

2

3/1

3/1

3/2

− ><−−

><− −−

><−

><−−

−+

=−><−−><−

α

α

ε

α

α

ρ ε

α α

u

L

r

D

X

L

u

k

kt

p

a (23) 

 

RESULTS 

The equations developed above serve to clarify several features of reactor performance. Important parameters in the 

solution are the diffusion time tD, reactor residence time tR, void fraction ε, and regolith particle conversion α. The 

relationships between these parameters determine the output stream of the reactor. 

Diffusion Time-Residence Time Interaction 

The ratio of the residence time to diffusion time is: 

 ))(( 2

D p

R

r

D

u

L

t

t = . (24) 

As this ratio becomes large, Eq. (18) or (22) implies: 

NASA/TM—2009-215626 7
)1( )( 0

1 k

kc

Lc

+

→ . (25) 

The above value of c1(L) corresponds exactly to the equilibrium conversion for a batch system which is reasonable 

in this limit of large residence time. This value also represents the maximum possible molar conversion of hydrogen 

to water. 

On the other hand as the ratio of residence time to diffusion time becomes small, i.e., 

 → 0

D

R

t

t

, (26) 

then, Eq. (18) or (22) implies: 

0)(1 Lc → (27) 

which indicates that no conversion takes place since the hydrogen rapidly sweeps past the regolith without time for 

intra-particle diffusion to occur. 

Regolith Particle Conversion α

It may be shown that as α tends to zero, the value of c1(L) approaches the equilibrium conversion amount. This may 

be expected since this case represents the early stages of the conversion process where the reaction occurs on the 

surfaces of the regolith particles (i.e., there is no intra-particle diffusion involved). On the other hand, as α tends to 

unity, the conversion is complete and consequently: 

0)(1 Lc → . (28) 

Thus, molar conversion of hydrogen to water is highest during the early stages of the conversion and then decreases 

with decrease in the size of the unreacted particle core. Equivalently, the conversion decreases with time. 

Bed Void Fraction ε

The factor (1-ε) appearing in Eqs. (15) – (22) can be expressed as: 

bed

regolith

V

V

1 ε =− . (29) 

For fixed regolith volume, the above factor is changed by changing the volume of the bed. The relationship between 

bed volume, flow velocity, and residence time can become complex. However, for the special case of a cylindrical 

reactor of fixed radius, the effect of changing bed length while keeping velocity constant is cancelled by the 

corresponding change in residence time (see, for example, Eq. (18)). 

Temperature and Pressure 

Temperature and pressure impact the conversion due to their influence on the equilibrium constant k and effective 

diffusion coefficient D. Equation (2) provides the dependence of the equilibrium constant on temperature. As 

temperature increases, the equilibrium conversion amount is increased. However, the temperature cannot be 

increased indefinitely and 1250-1300 K appears to be the maximum allowable feasible temperature range in order to 

avoid sintering of the regolith as noted in the introduction section. 

NASA/TM—2009-215626 8
The effective diffusion coefficient for the regolith has not been well characterized to date. However, one may expect 

that its temperature and pressure dependence will be similar to that of gas phase diffusion which is inversely 

proportional to pressure and directly proportional to temperature via typically a power law: 

 ba

T

T

P

P

DD )()(

0

0 = 0 . (30) 

Thus, as pressure increases, the effective diffusion coefficient decreases implying an increase in the diffusion time 

t

D. On the other hand, as temperature increases, the diffusion coefficient also increases resulting in a decrease in the 

diffusion time. 

Endothermicity Effects 

As noted in the introduction section, the conversion process is endothermic. Therefore, it is of interest to estimate 

the temperature drop of the regolith particles due to reaction. Let the regolith be heated up initially to temperature Ti 

and assume that gas and regolith are at the same temperature during the process. The temperature of the regolith as 

a function of the particle conversion α, neglecting the gas phase effects, may be written from energy conservation 

as: 

 α

ρ

ρ α

pss

a

i C

H

TT

∆ )( −= . (31) 

Typical values of ρa, ρs, Cps, and ∆H are 5400 mol/m3, 3000 kg/m3, 750 J/(kgK), and 11000 J/mol. Using these 

values indicates a temperature drop of approximately 25 K for the regolith particles as a result of the chemical 

reaction. This is a negligible drop compared to an initial temperature of approximately 1300 K. Of course, this does 

not include possible temperature drop due to heat loss to the surroundings. 

 CONCLUSIONS 

An analytical model for a reactor for hydrogen reduction of ilmenite has been developed. The reactor outflow 

composition is derived by coupling a shrinking core regolith particle model with the bulk flow in the reactor. As a 

result, the interactions among the chemical, mass and energy transport processes occurring at the length and time 

scales of the overall reactor with those occurring at the corresponding scales of the regolith particles are obtained. 

For the case where gas diffusion inside the regolith particles is the controlling step, important parameters identified 

are the regolith bed void fraction, intra-particle gas diffusion time, and reactor residence time. These parameters are, 

in turn, related to flow velocities, reaction temperatures and pressures, as well as to the type of reactor. The 

maximum molar conversion of hydrogen to water is given by the equilibrium ratio and occurs when residence time 

is much greater than intra-particle diffusion time. Application of the model to fluidized bed, packed bed, and rotary 

bed configurations have been indicated. 

NOMENCLATURE 

α particle conversion 

<α> spatial average of α 

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) 

a,b numerical constants in effective diffusion 

coefficient expression in Eq. (19) 

c molar concentration of hydrogen in particle 

(moles/m3) 

c1 molar concentration of water (moles/m3) 

c1s molar concentration of water at reaction 

surface (moles/m3) 

NASA/TM—2009-215626 9
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) 

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

D effective gas diffusion coefficient (m2/s) 

D0 effective gas diffusion coefficient at 

reference temperature and pressure (m2/s) 

∆H endothermic heat of reaction (Joules/mole) 

g gravitational acceleration (m/s2) 

k equilibrium constant 

L length of regolith bed (m) 

N number of regolith particles in the bed 

P gas pressure (Pa) 

P0 reference gas pressure (Pa) 

r regolith particle radial coordinate (m) 

rp regolith particle radius (m) 

rs radius of reaction surface (m) 

Rr internal radius of reactor (m) 

t time (s) 

t

c chemical time (s) 

t

D intra-particle diffusion time (s) 

t

R reactor residence time (s) 

T temperature (K) 

Ti initial temperature of regolith at start of 

conversion (K) 

T0 reference gas temperature (K) 

u velocity through reactor (m/s) 

us incipient fluidization velocity (m/s) 

Vbed volume of regolith bed (m3) 

Vvoid void volume in regolith bed (m3) 

x axial coordinate (m) 

REFERENCES 

Altenberg, B. H., Franklin, H. A., and Jones, C. H.,“Thermodynamics of Lunar Ilmenite Reduction,” in Proceedings of the XXIV

Lunar and Planetary Science Conference, Lunar and Planetary Institute, Houston, TX, 1993, pp. 27-28. 

Butler,E. E., Debelak, K. A., and Roth, J. A., Kinetics of Ilmenite (FeTiO3) Reduction with Hydrogen, Space Resources 

Roundtable Inc., Golden, CO, 2001. 

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). 

Heiken, G. H. Vaniman, D. T., and French, B. M., Lunar Sourcebook, Cambridge University Press, New York, NY, 1991, pp. 

285-300. 

Levenspiel, O.,ChemicalReaction Engineering, John Wiley & Sons, New York, NY, 1998, pp. 424-498. 

McCabe, W. E., Smith, J. C., and Harriott, P., Unit Operations of Chemical Engineering, McGraw Hill, NY, 2001, pp.173-195. 

McKay, D. S., and Allen, C. C., Hydrogen Reduction of Lunar Materials for Oxygen Extraction on the Moon, AIAA Paper No. 

96-0488, American Institute of Aeronautics and Astronautics, Washington, DC, 1996. 

Rice, E.E., Hermes, P. A., and Musbah, O. A., Carbon Based Reduction of Lunar Oxides for Oxygen Production, AIAA Paper 

No. 97-0890, American Institute of Aeronautics and Astronautics, Washington, DC, 1997. 

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

30, (12), 2858-2863, (1992). 

Williams, R. J., and Erstfeld, T. E., High Temperature Electrolyte Recovery of Oxygen from Gaseous Effluents from the 

Carbochlorination of Lunar Anthracite and the Hydrogenation of Ilmenite: A Theoretical Study, NASA TM 58214, NASA, 

Washington, DC, 1979. 

Yoshida, H., Watanabe, T., Kanamon, H., Yoshida, T., Ogiwara, S., and Eguchi, K., Experimental Study 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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4. TITLE AND SUBTITLE

Development of a Reactor Model for Chemical Conversion of Lunar Regolith 

5a. CONTRACT NUMBER

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5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

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

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WBS 387498.04.01.05.01.03 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

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

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Lunar regolith will be used for a variety of purposes such as oxygen and propellant production and manufacture of various materials. The 

design and development of chemical conversion reactors for processing lunar regolith will require an understanding of the coupling among 

the chemical, mass and energy transport processes occurring at the length and time scales of the overall reactor with those occurring at the 

corresponding scales of the regolith particles. To this end, a coupled transport model is developed using, as an example, the reduction of 

ilmenite containing regolith by a continuous flow of hydrogen in a flow-through reactor. The ilmenite conversion occurs on the surface and 

within the regolith particles. As the ilmenite reduction proceeds, the hydrogen in the reactor is consumed, and this, in turn, affects the 

conversion rate of the ilmenite in the particles. Several important quantities are identified as a result of the analysis. 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 time for hydrogen to diffuse into the pores of the regolith particles and the 

chemical reaction time. The paper investigates the relationships between these quantities and their impact on the regolith conversion. 

Application of the model to various chemical reactor types, such as fluidized-bed, packed-bed, and rotary-bed configurations, are discussed.

15. SUBJECT TERMS

Hydrogen reduction; Ilmenite; Lunar regolith; Shrinking core 

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