R. Balasubramaniam

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

S.A. Gokoglu

Glenn Research Center, Cleveland, Ohio

U. Hegde

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

The Reduction of Lunar Regolith by

Carbothermal Processing Using Methane

NASA/TM—2010-216927

November 2010
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R. Balasubramaniam

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

S.A. Gokoglu

Glenn Research Center, Cleveland, Ohio

U. Hegde

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

The Reduction of Lunar Regolith by

Carbothermal Processing Using Methane

NASA/TM—2010-216927

November 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors would like to thank K. Sacksteder and D. Linne of NASA Glenn Research Center and R. Gustafson and B. White 

of Orbitec, Madison, Wisconsin, for discussions and comments during the course of the investigation. Support for this work 

was obtained from the In-Situ Resource Utilization (ISRU) project which is a part of the NASA Exploration Technology 

Development Program, for which we are grateful.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

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

Level of Review: This material has been technically reviewed by technical management. 
Abstract. The processing of lunar regolith for the production of oxygen is a key component of

the In-Situ Resource Utilization plans currently being developed by NASA. In the carbothermal

process, a portion of the surface of the regolith in a container is heated by exposure to a heat source

so that a small zone of molten regolith is established. A continuous flow of methane is maintained

over the molten regolith zone. In this paper, we discuss the development of a chemical conversion

model of the carbothermal process to predict the rate of production of carbon monoxide. Our model

is based on a mechanism where methane pyrolyzes when it comes in contact with the surface of the

hot molten regolith to form solid carbon and hydrogen gas. Carbon is deposited on the surface of

the melt, and hydrogen is released into the gas stream above the melt surface. We assume that the

deposited carbon mixes in the molten regolith and reacts with metal oxides in a reduction reaction

by which gaseous carbon monoxide is liberated. Carbon monoxide bubbles through the melt and

is released into the gas stream. It is further processed downstream to ultimately produce oxygen.

Keywords: Carbothermal processing, lunar regolith, pyrolysis, kinetics

PACS: 47.70.Fw, 82.40.-g

The Reduction of Lunar Regolith by 

Carbothermal Processing Using Methane 

R. Balasubramaniam 

National Center for Space Exploration Research 

Glenn Research Center 

Cleveland, Ohio 44135 

S.A. Gokoglu 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

U. Hegde 

National Center for Space Exploration Research 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2010-216927 1
NOMENCLATURE

a = stoichiometric coefficient in chemical reaction in Eq (1)

A = melt surface area

Cm = concentration of methane (mole/m3)

k = reaction rate constant (m3/(mole · s))

p = variable proportional to the square root of time, p = (2kβ0t

∗

)

1/2

pi = value of p when methane flow is initiated, pi = (2kβ0ti)

1/2

rp = flux of carbon from pyrolysis (mole/(m2· s))

t, t∗ = scaled and physical (s) time, respectively

tc = scaled time at which CO production rate is a maximum

ti = time when methane flow is initiated (s)

tm = scaled time beyond which methane flow rate is turned off

t0 = reference time for a growing melt (s)

V = melt volume (m3)

V0 = reference melt volume for a growing melt (m3)

XCO = number of moles of carbon monoxide (mole)

α, α∗ = scaled and physical (mole/m3) concentration of carbon in the melt, respectively

β, β∗ = scaled and physical (mole/m3) concentration of metal oxide in the melt, respectively

β0 = initial concentration of metal oxide in the melt (mole/m3)

γ = rate constant for the pyrolysis of methane (m/s)

δ = scaled excess moles of carbon in the melt, δ = λtm − 1

λ = dimensionless parameter, λ =

aAγCm

kV β2

0

λ

0 = dimensionless parameter, λ0 = (2kβ0t0)1/2λ

1 Introduction

NASA’s plans for lunar exploration involves the production of oxygen for life support and use

as a propellant. Oxygen is available in the lunar regolith as oxides of various materials. The

extraction of gaseous oxygen from the oxides by reduction using hydrogen (Taylor and Carrier,

1992), molten salt electrolysis (Tripuraneni-Kilby et al., 2006) and carbothermal processing of

NASA/TM—2010-216927 2
regolith (ORBITEC, 2006) are currently being pursued by NASA (Sanders et al., 2008), and is a

prime candidate for In-Situ Resource Utilization.

Carbothermal processing refers to the use of carbon in some form, together with high processing

temperature, to reduce the oxides. Examples of carbothermal processes on Earth are the production

of silicon from silica using wood, charcoal or coal (a standard process), and the production of

titanium-rich materials by refining low-grade ilmenites using graphite (Wang and Yuan, 2006).

The carbothermal processing of lunar regolith using methane as the source for carbon was first

performed by Rosenberg and co-workers at Aerojet in the 1960’s (Rosenberg et al., 1991). It

has been revisited by researchers at Orbital Technologies Corporation (ORBITEC) since the early

1990’s. An excellent reference and resource for the application of the carbothermal process for the

conversion of lunar regolith to ultimately produce oxygen is a report by ORBITEC (ORBITEC,

2006; see also Gustafson, White and Fidler, 2009). ORBITEC used lunar regolith simulants in

their processing experiments.

Figure 1 shows a schematic sketch of the carbothermal reactor. Lunar regolith is contained in a

suitable container. A portion of the surface of the regolith is heated by exposure to a heat source

such as a laser beam or a concentrated solar heat flux, so that a small zone of molten regolith is

established within the container. The unmelted regolith surrounding the molten zone thermally

insulates it from the container. A heat shield is used above the molten zone to minimize radiative

heat loss. A continuous flow of methane is maintained over the molten regolith zone. Since

the molten regolith is very hot (temperature will exceed 1650◦C), methane will pyrolyze when it

contacts the molten zone. Carbon is deposited on the surface of the melt, and hydrogen is released

into the gas phase above the melt surface. The deposited carbon reacts with metal oxides (chiefly

SiO2) in the molten regolith in a reduction reaction in which carbon monoxide is liberated. CO

bubbles through the melt and is released in the gas phase above the melt. It is carried downstream

for further chemical processing to ultimately yield oxygen, which is liquified and stored. Our

objective is to model the production of carbon monoxide in the carbothermal reactor, and predict

the rate at which CO is liberated as a function of the various physicochemical parameters of the

system. We also pursue simple strategies to control the buildup of carbon in the melt.

NASA/TM—2010-216927 3
Flow of

methane

Heat flux

Regolith

Molten 

regolith

Flow of

exit gases

Heat

shield

FIGURE 1: Sketch of the Carbothermal Reduction of Lunar Regolith.

2 Model formulation and assumptions

We assume that carbon deposition occurs on the hot molten surface via a surface reaction. This

surface reaction is regarded as first order with respect to a gaseous carbon-containing species and

produces solid carbon and gaseous hydrogen. This carbon-containing species need not necessarily

be methane; it can be some other carboneous species which may be produced by the gas-phase

pyrolysis of methane. In reality, depending on the operating pressure, flow conditions and temperature profiles above the hot molten surface, there would be a distribution of carbon-containing

species (e.g., methane, ethylene, acetylene, methyl radical, etc.,) and each of them would react

on the surface to deposit carbon at their own rates. Our model, however, “lumps” all of these

possibilities into a “single” species and describes the deposition process by a first-order surface reaction of this “predominant” species. For sake of simplicity, we call this “lumped” species methane

throughout the paper. Thus, the flux of carbon deposited on the surface of the melt is assumed to

be proportional to the concentration of methane in the gas phase adjacent to the melt surface.

We assume that the rate of transport of gaseous species from the bulk flow to the melt surface

is not limiting the surface reaction rate. This is expected to be valid in the practical application,

where the goal would be to maximize the carbon deposition rate so that the CO production rate

NASA/TM—2010-216927 4
is maximized. This can be accomplished by an ample and continuous supply of methane in the

bulk flow so that its rate of diffusion through the boundary layer above the melt surface is sufficiently fast to replenish its consumption at the surface. Under these conditions, the concentration

of methane at the surface can be assumed to be constant and approximated by its value at the flow

inlet. The surface reaction rate constant needs to be extracted by direct comparison of model predictions with experimental data. The analysis can easily be extended to situations where gas-phase

transport effects are significant.

The deposited carbon is assumed to be ‘well-mixed’ in the melt such that there are no spatial

gradients of the concentration of carbon or the metal oxide within the melt. This would be the

case when the zone is sufficiently small such that diffusion of carbon within the melt is rapid relative to the time of its reaction with the metal oxide. Mixing is more likely caused by temperature

gradients in the melt that generate a flow due to natural convection and thermocapillary forces.

Besides, the reaction in the melt liberates gaseous carbon monoxide in it, and the gravity-induced

bubble motion is likely to render the melt to be well-mixed. The melt viscosity is expected to play

a significant role in determining the relative rates of carbon advection and diffusion. Heiken et al.

(1991) mention that a synthetic liquid with the composition of a lunar basalt sampled by Apollo 11

has a viscosity in the range 4.5 poise (1495◦C) to 10 poise (1395◦C) and that terrestrial lavas are

ten times more viscous. The viscosity of melts typically depends on the processing temperature

and composition, in particular the proportion of MgO, CaO, FeO and Fe3O4, etc., in comparison

with those of SiO2 and Al2O3 (Themelis, 1995).

The carbon in the melt is assumed to undergo a single-step, first-order chemical reaction with the

metal oxide present in the molten regolith. This reaction rate constant also needs to be determined

by comparison of the model predictions with experimental data. We assume that the deposited

carbon does not form a crust on the surface of the melt, shielding the melt surface from the heat

flux and the methane flow. While crusting has been observed under some conditions (ORBITEC

2006), rapid mixing due to bubble evolution and controlled rate of deposition of carbon greatly

diminishes the likelihood of crust formation.

NASA/TM—2010-216927 5
We assume that the molten zone is established and maintained by heating the regolith by suitable means, in a batch-processing mode. The heat transfer aspects of the problem are not analyzed

here. The processes of chemical conversion and heat transfer within the molten regolith are assumed to be uncoupled. Let V and A denote the volume and the surface area of the molten zone

of regolith. A is assumed to be constant and independent of time during the chemical conversion

process. We will analyze cases where the melt volume V is (i) a constant independent of time, and

(ii) increases as the square root of time. A constant melt volume implies that the molten regolith

fully occupies a fixed volume of its container (the regolith shown in Figure 1 is fully molten and

the container is in contact with the melt). It might also be applied for a case where the heat transfer

process is such that V and A are slowly varying in time compared to the time scale for chemical

conversion. When there is contact between the melt and the solid regolith particles, we assume

that there is a well-defined interface demarcating the melt and the solid regolith particles. Thus

no trickling of the melt into the regolith bed is considered. This assumption appears to be true in

the experiments of Gustafson et al. (2009) where they report their post-experiment observation of

only loose binding of the regolith particles to a solidified molten mass.

The analysis is organized as follows. We first consider V to be constant, and determine the evolution of the concentration of carbon and metal oxide in the melt. This is followed by an analysis of

a possible strategy to minimize the amount of leftover carbon in the melt. Finally, a growing melt

where V increases as the square root of time, for constant A, is also analyzed.

Let α

∗

and β

∗ denote the molar concentration (moles/m3

) of carbon and metal oxide, respectively, within the melt. At time t

∗ = 0, the initial concentrations are α∗ = 0 and β∗ = β0. The

chemical reaction between carbon and the metal oxide in the regolith is

a MOx + C ⇔ CO + a M. (1)

The stoichiometric coefficient of the oxide term in the above reaction is a = 1/x. We assume

that the chemical reaction is first order with respect to carbon and the metal oxide, with a rate

constant k (m3/(moles · s)). The flux of carbon due to pyrolysis of methane is denoted by rp,

and is assumed to be linearly proportional to the molar concentration of methane Cm in the gas

NASA/TM—2010-216927 6
phase adjacent to the melt surface, with the constant of proportionality denoted by γ (m/s). The

equations for the evolution of α

∗

and β

∗

in the melt can be obtained from mass conservation to be:

dα∗

dt∗

=

AγCm

V

− k α∗ β

∗

, (2)

dβ∗

dt∗

= −a k α∗ β

∗

. (3)

The instantaneous rate of production of carbon monoxide is

dXCO

dt∗

= −

V

a

dβ∗

dt∗

(4)

3 Results and Discussion

3.1 Constant melt volume

We assume that the melt area and volume are constant. The methane concentration Cm in the gas

phase is also assumed to be constant. Dimensionless variables are defined as follows.

α =

α

∗

β0/a, β =

β

∗

β0

, t =

t

∗

1/(kβ0)

. (5)

The scaled equations and boundary conditions are

dα

dt = λ − α β (6)

dβ

dt = −α β (7)

α(0) = 0, β(0) = 1 (8)

where λ =

aAγCm

kV β2

0

is a dimensionless parameter. λ is a measure of the relative importance of the

rate of production of carbon by the surface pyrolysis of methane to its rate of consumption by

reaction with the metal oxide. The former rate is constant for typical operating conditions of fixed

temperature, pressure, and sufficient flow rate to maintain a constant methane concentration. The

latter rate varies depending on the accumulation or depletion of carbon and the availability of the

NASA/TM—2010-216927 7
metal oxide in the melt. So, the magnitude of λ indicates the relative dominance of the two rates in

a competitive process; i.e., small lambda means relatively small carbon deposition rates, and vice

versa.

Equation (4) for the instantaneous rate of production of carbon monoxide can be expressed as

dXCO

dt∗

=

V kβ2

0

a

α β. (9)

Thus the instantaneous rate of production of carbon monoxide is proportional to the product of α

and β. The solution can be determined to be

α = β − 1 + λ t (10)

β =

2

√

λ Exp t −

λ

2

t

2



2

√

λ + Exp 

1

2λ

 √

2π

h

Erf 

√

1

2λ



+ Erf 

tλ

√−1

2λ

i (11)

The following expression is an asymptotic expansion for β that is especially useful for small values

of λ.

β =

1 − λt

(λ − 3λ

2 + . . .)(1 − λt)Exp(−t +

λ

2

t

2

) + 1 −

λ

(1−λt)

2 +

3λ2

(1−λt)

4 + . . . (12)

Plots of the scaled concentrations of carbon (α) and metal oxide (β), and the scaled rate of production of carbon monoxide (which is proportional to the product α β, see Equation 9) from the

solution given above are shown in Figure 2 for various values of λ. It is worthy of note that, in the

simplified model that we have developed, the only parameter that determines the behavior of the

reactor is λ. This parameter captures the effects of melt size relative to its surface area, reaction

rate constant, pyrolysis rate constant, and the concentrations of methane and metal oxide on the

rate at which chemical conversion takes place in the reactor.

Figure 2 shows that the metal oxide concentration in the melt decreases monotonically with time,

and the amount of carbon in the melt increases monotonically with time. The rate of production

of carbon monoxide is initially zero and increases with time as the reaction between the deposited

NASA/TM—2010-216927 8
0 20 40 60 80 100 120 140

0.0 t

0.2

0.4

0.6

0.8

1.0

Α

Β

0 20 40 60 80 100 120 140

0.000 t

0.002

0.004

0.006

0.008

0.010

ΑΒ

(a) λ = 0.01

0 5 10 15 20

0.0 t

0.2

0.4

0.6

0.8

1.0 Α

Β

ΑΒ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 t

0.5

1.0

1.5

2.0 Α

Β

ΑΒ

(b) λ = 0.1 (c) λ = 1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 t

1

2

3

4

5

6 Α

Β

ΑΒ

(d) λ = 10

FIGURE 2: Plot of the scaled concentrations of carbon (α) and metal oxide (β) in the melt and

the scaled rate of production of carbon monoxide (αβ) versus scaled time (t) for various values of

λ.

NASA/TM—2010-216927 9
0.01 0.1 1 10

0 Λ

2

4

6

8

10

12

tc

0.01 0.1 1 10

0.0 Λ

0.5

1.0

1.5

2.0

ΑHtcLΒHtcL

(a) (b)

FIGURE 3: (a) the scaled time tc at which the carbon monoxide production rate is a maximum and

(b) the corresponding scaled maximum rate of production of CO (α(tc)β(tc)), both as a function

of λ.

carbon and the metal oxide progresses, and finally decreases to zero as the reaction is completed.

The exact shape of the curves in Figure 2, especially that for the the rate of production of CO, is

quite sensitive to the value of λ.

As the metal oxide is depleted, the reaction finally slows down and stops. Figure 2 shows that

the rate of production of CO attains a maximum before it eventually decreases to zero. From

Equations (10) and (11), it can be shown that the maximum is attained at a time t = tc which

satisfies the following equation.

β(tc) = 3

4

(1 − λtc) + 

1

16

(1 − λtc)

2 +

λ

2

1/2

(13)

tc represents the time for which there is an optimal balance between the accumulation of carbon in

the melt due to deposition at the melt surface and its consumption by reaction with the metal oxide.

The dependence of tc and the scaled maximum CO production rate α(tc)β(tc) on λ are shown in

Figure 3. tc monotonically decreases with increasing λ, while the scaled maximum CO production

rate is a monotonically increasing function of λ. The results for tc would be useful in design and

operation of the reactor to ensure that requirements on the amount and rate of production of CO

are met, and identify times beyond which there is diminishing returns in operating the reactor.

NASA/TM—2010-216927 10
Since the amount of carbon in the melt increases with time, there is unreacted carbon that is left

behind in the melt after the reaction is completed. A useful strategy to minimize the amount of

unreacted carbon is to turn the supply of methane off at an appropriate time before the reaction is

completed, such that the residual amount of carbon present in the melt at that time is sufficient to

react with the remaining amount of the metal oxide. This scenario is addressed below.

3.2 Control of carbon in the melt

It can be seen from Figure 2 that towards the end of the conversion process (for large t), α is

quite large. This represents the large amount of carbon that has been deposited on the surface of

the melt. On the other hand, the concentration of metal oxide in the melt is quite low, showing

that much of the metal oxide has been converted. Therefore, much of the carbon that has been

deposited remains unreacted in the melt. Once the chemical conversion process is terminated after

a sufficient amount of the metal oxide in the regolith is converted, the unreacted carbon remains

in the spent regolith. It is wasted, unless the spent regolith is specifically processed to recover the

carbon. Since carbon (in the form of methane) is envisioned to be transported from Earth to the

moon, it is desirable to minimize the carbon loss by minimizing the unreacted carbon in the melt.

One strategy to minimize the carbon loss is by turning the flow of methane off at some point in

time before the end of the conversion process. The idea is that the amount of carbon present in the

melt at the time the methane flow is turned off is sufficient to react with the residual metal oxide

in the melt. Since there is no fresh carbon that is deposited to the melt after the flow of methane

is turned off, the steep increase in the amount of carbon in the melt depicted in Figure 2 will be

avoided.

By turning the methane flow off, we mean that the concentration of methane in the inlet gas stream

is zero. Since there are other sub-systems present downstream of the carbothermal reactor to

process the carbon monoxide produced, there must still be gases flowing through the entire system.

We anticipate that even with the concentration of methane in the inlet stream to the carbothermal

reactor being zero, the gas flow rate through the entire system is maintained by employing other

‘sweep’ gases (such as hydrogen, carbon monoxide, inert gas, etc.).

NASA/TM—2010-216927 11
We assume that the methane flow is turned off at t = t0. For t ≤ t0, the solution given in Equations

(10) and (11) applies. The chemical conversion for t > t0 can be modeled as

dα

dt = −α β (14)

dβ

dt = −α β (15)

α(t0) = αt0, β(t0) = βt0(16)

where

βt0 =

2

√

λ Exp t0 −

λ

2

t

2

0



2

√

λ + Exp 

1

2λ

 √

2π

h

Erf 

√

1

2λ



+ Erf 

t0√λ−1

2λ

i (17)

Note that αt0 = βt0 − 1 + λt0. Let αt0 − βt0 = λt0 − 1 = δ. δ represents the moles of carbon in

the melt in excess of stoichiometry at the time that the methane flow is turned off. The solution to

Equations (14) - (16) is

β =

βt0δ eδ(t0−t)

βt0 + δ − βt0e

δ(t0−t)

t ≥ t0 (18)

α = δ +

βt0δ eδ(t0−t)

βt0 + δ − βt0e

δ(t0−t)

t ≥ t0 (19)

When δ = 0 the number of moles of carbon and metal oxide are in stoichiometric balance. The

above results may be specialized for δ = 0 to

β = α =

βt0

1 + βt0(t − t0)

t ≥ t0 (20)

It can be shown that as t → ∞

β → 0, α → δ for δ > 0 (21)

β → −δ, α → 0 for δ < 0 (22)

β → 0, α → 0 for δ = 0 (23)

NASA/TM—2010-216927 12
0 20 40 60 80 100 120 140

0.0 t

0.2

0.4

0.6

0.8

1.0

Α

Β Α,Β

0 20 40 60 80 100 120 140

0.000 t

0.002

0.004

0.006

0.008

0.010

ΑΒ

(a) λ = 0.01

0 10 20 30 40 50

0.0 t

0.2

0.4

0.6

0.8

1.0

Α

Β

ΑΒ Α, Β

0 2 4 6 8 10 12 14

0.0 t

0.2

0.4

0.6

0.8

1.0 Α

Β

Α, Β ΑΒ

(b) λ = 0.1 (c) λ = 1

0 2 4 6 8 10

0.0 t

0.2

0.4

0.6

0.8

1.0

Α, Β ΑΒ

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0 t

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Α

Β Α, Β

ΑΒ

(d) λ = 10

FIGURE 4: Plot of the scaled concentrations of carbon (α) and metal oxide (β) in the melt and

the scaled rate of production of carbon monoxide (αβ) for various values of λ, with carbon loss

control (solid curves), for a case with δ = 0. Methane flow is turned off beyond the time at which

the curves for α and β intersect. Dashed curves correspond to a case where the methane flow is

not turned off (same as in Figure 2).

NASA/TM—2010-216927 13
0.01 0.1 1 10

0 Λ

2

4

6

8

10

12

tc

0.01 0.1 1 10

0.0 Λ

0.5

1.0

1.5

2.0

ΑHtcLΒHtcL

(a) (b)

FIGURE 5: (a) the scaled time tc at which the carbon monoxide production rate is a maximum and

(b) the corresponding scaled maximum rate of production of CO (α(tc)β(tc)), both as a function

of λ, with carbon loss control employed. The dashed curve corresponds to a case where methane

flow is not turned off (same as in Figure 3).

Therefore, when δ ≤ 0, there is potential for zero carbon loss in the melt, if the chemical conversion is carried out for a sufficiently long time.

Plots of the scaled concentrations of carbon, metal oxide, and the rate of production of carbon

monoxide are shown by the solid curves in Figure 4, where carbon loss control is implemented

with δ = 0. Note that δ = 0 ⇒ αt0 = βt0. Thus, the methane flow is turned off beyond the time

at which the curves for α and β intersect. For the dashed curves in Figure 4, the methane flow is

not turned off. These are the same as the curves shown in Figure 2. Comparing the solid and the

dashed curves, we see that with carbon loss control, the amount of carbon remaining in the melt (α)

is drastically reduced after the methane flow is turned off. As a consequence, the corresponding

metal oxide concentration (β) is larger than that without control of carbon loss, and it takes a

longer time for the conversion to be completed. When λ ≤ 1, however, the rate of production of

carbon monoxide in general (proportional to αβ), and in particular the peak CO production rate,

are not significantly affected. In contrast, when λ = 10, the carbon monoxide production rate

is significantly reduced when carbon loss control in implemented. The dependence of the time

NASA/TM—2010-216927 14
tc at which the CO production rate is a maximum, and the scaled maximum CO production rate

α(tc)β(tc) on λ are shown in Figure 5 when carbon loss control is implemented. In this figure, tc

satisfies Equation (13) for λ ≤ 0.842, and equals 1

λ

for λ > 0.842.

3.3 Growing melt

We now analyze a case where the melt volume increases with time. Specifically, we will permit

the volume to increase as the square root of time. This would be the case when the regolith (of unbounded extent), initially at a constant temperature below its melting temperature, is heated so that

its surface temperature is instantaneously raised and maintained above the melting temperature.

The rate of growth of the melt volume will depend on the latent heat and other thermal properties

of the regolith. In our analysis, we will assume that the melt volume V (t

∗

) = V0

qt

∗

t0

, where V0

and t0 are known reference values. We will assume that the surface area A of the melt surface is

a constant, which is valid when the heat transfer is predominantly one-dimensional. We retain all

other assumptions for the chemical process discussed before.

The conservation of mass yields the following equations for the molar concentration of carbon

and metal oxide in the melt.

d

dt∗

(

√

t

∗α

∗

) = AγCm

√

t0

V0

− k

√

t

∗ α

∗ β∗

(24)

d

dt∗

(

√

t

∗β

∗

) = β0

2

√

t

∗

− a k√t

∗ α

∗ β∗

(25)

We will permit a time delay between the start of melt growth (t

∗ = 0) and the initiation of methane

flow (t

∗ = ti). The initial conditions are α∗ = 0 and β∗ = β0 at t∗ = ti

. Dimensionless variables

are defined as follows.

α =

α

∗

β0/a, β =

β

∗

β0

, p = (2kβ0t

∗

)

1/2

, pi = (2kβ0ti)

1/2

(26)

The governing equations in terms of these variables are

d

dp(p α) = (2kβ0t0)

1/2λ p − p2α β (27)

NASA/TM—2010-216927 15
d

dp(p β) = 1 − p

2α β (28)

α(pi) = 0, β(pi) = 1 (29)

Equations (27) and (28) may be partially solved and written as

p α = p β +

λ

0

2

(p

2 − p2

i

) − p (30)

d

dp(p β) = 1 − p β 

p β +

λ

0

2

(p

2 − p2

i

) − p



(31)

where λ

0 = (2kβ0t0)1/2λ. λ is the same parameter defined earlier (with V0 used for the melt volume). The dimensionless parameter kβ0t0 is the ratio of the time scale for the growth of the melt

volume to the time scale for the reaction in the melt.

The instantaneous CO production rate is

dXCO

dt∗

= V k α∗ β

∗ =

V0 k β2

0

a(2kβ0t0)

1/2

p α β (32)

Thus, the CO production rate is proportional to p α β. Equation (31) for p β is a form of the

Riccati equation, but does not appear to have a closed-form solution. We have solved Equation

(31) numerically. Plots of the scaled concentrations of metal oxide (β), carbon (α), and the rate of

production of CO (p α β) are shown in Figure 6 for various values of λ

0 when the methane delay

time ti = 0. A log-log scale has been used in these plots to concisely capture the various features

of the curves shown. Many of the qualitative features of the curves in Figure 6 are the same as

those in Figure 2 for a constant volume melt. The metal oxide concentration decreases monotonically with time. For large times, the carbon concentration increases with time because there is no

carbon consumption once the metal oxide is depleted. The rate of production of CO is initially

zero, attains a maximum at some time, and finally falls off when the metal oxide is depleted. An

interesting feature in Figure 6 not present in Figure 2 is the behavior of carbon concentration with

time for small values of λ

0

, i.e., λ

0 = 0.01 and 0.1. The carbon concentration has a local maximum

and a local minimum before it increases monotonically for large values of time. This behavior

may be explained as follows. Initially the carbon concentration α is zero. Deposition at the surface

NASA/TM—2010-216927 16
Β Α

p Α Β

0.01 0.1 1 10 100 10 p

-4

0.001

0.01

0.1

1

Β

Α

p Α Β

0.01 0.1 1 10 100 10 p

-4

0.001

0.01

0.1

1

(a) λ

0 = 0.01 (b) λ0 = 0.1

Β

Α

p Α Β

0.01 0.1 1 10 100 10 p

-4

0.001

0.01

0.1

1

10

Β

Α

p Α Β

0.01 0.1 1 10 100 10 p

-4

0.001

0.01

0.1

1

10

(c) λ

0 = 1 (d) λ0 = 10

FIGURE 6: Case of a growing melt – Plot of the scaled concentrations of carbon (α) and metal

oxide (β) in the melt , and the scaled rate of production of carbon monoxide (p α β) for various

values of λ

0

, versus p (proportional to square root of time, Eq (26)).

NASA/TM—2010-216927 17
tends to increase α, while consumption due to the reaction and dilution due to increasing melt

volume both tend to decrease α. α would tend to increase linearly with time for a constant rate of

deposition without consumption or dilution. For small time, the reaction is slow, and the constant

rate of carbon deposition overpowers its dilution, as the melt volume increases at a slower rate

(growing as √

t). As time increases, the carbon consumption due to the reaction increases. Thus, α

attains a maximum and subsequently decreases for a period of time until the reaction slows down

due to metal oxide depletion. α thus attains a minimum. Thereafter, carbon deposition once again

overpowers dilution, and α increases with time. Between the maximum and minimum of α, Figure

6 shows that the rate of production of CO is practically constant.

When λ

0

is sufficiently large (λ

0 > 1), consumption and dilution of carbon are both weak compared to its deposition, and no local extrema in α are present in Figure 6. Control of carbon loss

in the melt, especially for large λ

0

, may be implemented along the lines discussed in the previous

section, if desired.

We explored the effect of delaying the initiation of methane flow, and the results are shown in

Figure 7 for λ

0 = 0.01 and 0.1. The maximum carbon concentration achieved after the methane

flow is turned on is lowered. The longer the delay in methane flow initiation, the lower is the peak

of carbon concentration. Analogous to the carbon loss strategy discussed earlier, manipulating the

methane flow initiation time can be used as a method of controlling carbon build-up in the melt

and possible carbon crust formation. The peak rate of production of CO is not affected by delaying

the initiation of methane flow.

In the models that we have described above for both constant and growing melt volume, the rate

constants k and γ are crucial physical properties that the model requires as input. These rate constants are not readily available in the literature and must be obtained by comparison of the model

predictions with experimental results. Results from well-controlled experiments, however, do not

seem to be available. Preliminary estimates k = 4.5 × 10−8 m3

mole·s

and γ = 0.04 m

s

have been obtained for a lunar regolith simulant (see Balasubramaniam et al., 2009 for details) that best fit the

test data obtained by ORBITEC. In these tests, however, the flow rate of methane in the gas phase

NASA/TM—2010-216927 18
Α

0 2 4 6 8 10

0.000 p

0.001

0.002

0.003

0.004

0.005

p Α Β

0 2 4 6 8 10

0.000 p

0.002

0.004

0.006

0.008

0.010

(a) λ

0 = 0.01

Α

0 2 4 6 8 10

0.00 p

0.01

0.02

0.03

0.04

0.05

p Α Β

0 2 4 6 8 10

0.00 p

0.02

0.04

0.06

0.08

0.10

(b) λ

0 = 0.1

FIGURE 7: Effect of delay of methane flow initiation for a growing melt – Plot of the scaled

concentrations of carbon (α) and the scaled rate of production of carbon monoxide (p α β) versus

p for pi = 0, 0.5, 1, 1.5, 2, 2.5, for (a) λ

0 = 0.01 and (b) λ0 = 0.1. For each curve, the value of pi

corresponds to the value of p at which the curve crosses the p axis.

NASA/TM—2010-216927 19
was sufficiently low that a substantial amount of the incoming methane was pyrolyzed. Thus, the

model assumption that gas phase concentration of methane at the surface can be assumed to be

constant and approximated by its value at the flow inlet is questionable in these tests. These values

for the rate constants must be used with caution and as preliminary estimates only.

4 Conclusions

We have developed a model which describes the chemical conversion of lunar regolith in a carbothermal reactor to produce carbon monoxide, and eventually oxygen. Methane flows over a

molten regolith zone in the reactor continuously at a fixed temperature and pressure to maintain its

concentration. Our model assumes a two-step process for the chemical conversion. First, methane

is pyrolyzed as it comes in contact with the hot, molten regolith surface. The solid carbon formed

after pyrolysis is deposited on the melt, and mixes with it uniformly. The second step is the reaction which takes place between carbon and the metal oxide in the melt to yield carbon monoxide

that bubbles out of the melt. We considered both constant volume and growing melt cases. For

a constant volume melt, our model shows that a single parameter captures the effects of melt size

relative to its surface area, reaction rate constant, pyrolysis rate constant, and the concentrations of

methane and metal oxide on the rate at which chemical conversion takes place in the reactor. For

a growing melt, the ratio of the time scale for melt growth to the chemical time scale also appears

in the dimensionless parameter. Simple strategies to control the amount of unreacted carbon in the

melt by turning the flow of methane off at a suitably chosen time, and to control the build up of

carbon at the beginning of the process when the melt is growing are discussed. Rigorous validation

of the model predictions with experimental results needs to be performed.

NASA/TM—2010-216927 20
References

Balasubramaniam, R., Gokoglu, S., and Hegde, U., “Determination of Chemical Kinetic Rate

Constants of a Model for Carbothermal Processing of Lunar Regolith Simulant Using Methane,”

AIAA-2009-1390, 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, January, 2009.

Also NASA/TM-2009-215617, July 2009.

Gustafson, R.J., White, B.C., and Fidler, M.J., “Demonstrating Carbothermal Reduction of Lunar

Regolith Using Concentrated Solar Energy,” AIAA-2009-6476, AIAA SPACE 2009 Conference

& Exposition, Pasadena, California, September, 2009.

Heiken, G.H., Vaniman, D.T., and French, B.M., “Lunar sourcebook: a user’s guide to the moon,”

Cambridge University Press, 1991.

ORBITEC, “Carbothermal Reduction of Lunar Regolith,” Phase 1 Final Report OTC-GS0167-FR06-1, Orbital Technologies Corporation (ORBITEC), Madison, Wisconsin, USA, 29 September

2006.

Rosenberg, S.D., Beegle, R.L., Jr, Guter, G.A., Miller, F.E., Rothenberg, M., “The onsite manufacture of propellant oxygen from lunar resources,” In NASA. Johnson Space Center, Space

Resources, Volume 3: Materials, 162-185, 1991 (SEE N93-16875 05-91).

Sanders, G.B., Larson, W.E., and Sacksteder, K.R., Mclemore, C., Johnson, K., “NASA In-Situ

Resource Utilization (ISRU) Technology and Development Project Overview.” Space Technology and Applications International Forum (STAIF) Conference, Albuquerque, NM, February

2008. (200800100672: (April 2008) NTRS).

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).

Themelis, N.J., Transport and Chemical Rate Phenomena, Gordon & Breach Publishers, New

York, NY, 1995.

Tripuraneni-Kilby, K.C., Centeno, L., Doughty, G., Mucklejohn, S., and Fray, D.J., “The Electrochemical Production of Oxygen and Metal via the FFC-Cambridge Process,”SPace Resources

Roundtable VIII, Colorado School of Mines, 2006. http://www.isruinfo.com/docs/srr8/tripuraneni

kilby et al nov 1.zip

Wang, Y. and Yuan, Z., “Reductive kinetics of the reaction between a natural ilmenite and carbon,”

Int. J. Miner. Process. 81, 133-140 (2006).

NASA/TM—2010-216927 21
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The Reduction of Lunar Regolith by Carbothermal Processing Using Methane 

5a. CONTRACT NUMBER

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6. AUTHOR(S)

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

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13. SUPPLEMENTARY NOTES

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14. ABSTRACT

The processing of lunar regolith for the production of oxygen is a key component of the In-Situ Resource Utilization (ISRU) plans currently 

being developed by NASA. In the carbothermal process, a portion of the surface of the regolith in a container is heated by exposure to a heat 

source so that a small zone of molten regolith is established. A continuous flow of methane is maintained over the molten regolith zone. In 

this paper, we discuss the development of a chemical conversion model of the carbothermal process to predict the rate of production of 

carbon monoxide. Our model is based on a mechanism where methane pyrolyzes when it comes in contact with the surface of the hot molten 

regolith to form solid carbon hydrogen gas. Carbon is deposited on the surface of the melt, and hydrogen is released into the gas stream 

above the melt surface. We assume that the deposited carbon mixes in the molten regolith and reacts with metal oxides in a reduction 

reaction by which gaseous carbon monoxide is liberated. Carbon monoxide bubbles through the melt and is released into the gas stream. It is 

further processed downstream to ultimately produce oxygen.

15. SUBJECT TERMS

Carbothermal reduction; In-Situ Resource Utilization (ISRU); Chemical kinetics; Modeling; Lunar regolith simulant; Lunar regolith; 

Lunar simulant; Lunar exploration; Lunar science; Carbothermal processing; Pyrolysis; Kinetics 

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