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Applied Surface Science 253 (2006) 2327–2335

Theoretical analysis for the heterogeneous decomposition of

hydrogen sulfide to hydrogen on an iron-metallic plate in

a laminar stagnation-point flow

J.C. Martınez a, F. Mendez b,*, C. Trevino c

a Facultad de Ingenierıa, Universidad Autonoma de Campeche, 24030 Campeche, Mexicob Facultad de Ingenierıa, Universidad Nacional Autonoma de Mexico, 04510 Mexico DF, Mexicoc Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, 04510 Mexico DF, Mexico

Received 4 August 2005; received in revised form 11 January 2006; accepted 21 April 2006

Available online 8 June 2006

Abstract

In this work, we have theoretically analyzed the conversion process of hydrogen sulfide, H2S, to atomic hydrogen, H0, in a planar stagnation-

point flow over an iron-metallic surface. We assume that a binary mixture of hydrogen sulfide and methane composes the laminar stagnation flow.

In order to characterize this complex phenomenon with very specific chemical activities on the surface of the metallic plate, we propose a

heterogeneous reaction scheme based on four reactions: two electrochemical, one adsorption and an additional exothermic reaction needed to

complete the direct conversion of hydrogen sulfide to hydrogen on the surface of the iron. The nondimensional governing equations, which include

the mass species and momentum conservation of the mixture and the molecular diffusion of hydrogen into the iron plate, are numerically solved by

conventional finite-difference methods. The numerical results show the critical conditions of the H2S decomposition as functions of the involved

nondimensional parameters of the present model. In particular, we show parametrically the influence that has the initial concentration of H2S on the

surface coverage of the chemical products HS� H+ and H0 derived from the chemical and electrochemical reactions.

# 2006 Elsevier B.V. All rights reserved.

PACS: 82.30.Lp; 82.40.-g

Keywords: Hydrogen sulfide; Stagnation flow; Heterogeneous reactions; Iron plate; Hydrogen diffusion

1. Introduction

Nowadays, the analysis of hydrogen sulfide decomposition

is a multidisciplinary field of fundamental importance due to

that numerous examples and applications can modify severely

the operation and performance of different industrial devices.

For instance, in the petroleum industry, the so-called sour

corrosion originated by the presence of hydrogen sulfide in oil–

gas mixtures, can either accelerate or inhibit corrosion of iron

tubes under different conditions. In these chemical and physical

interactions between sour mixtures and metallic surfaces, the

component H2S generates atomic hydrogen, H0, at the iron

surface and this chemical specie penetrates into the metallic

body, which yields cracking and multiple fractures as a clear

* Corresponding author. Tel.: +52 55 56228103; fax: +52 55 56228106.

E-mail address: fmendez@servidor.unam.mx (F. Mendez).

0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2006.04.044

evidence of the corrosive process. In fact, the hydrogen in the

form of proton, H+, behaves as an ultra-fast diffuser in many

metals and alloys and different effects like electrolysis,

electroplating, aqueous corrosion, welding, etc. have a

profound influence to control the above diffusive process.

Therefore, the simultaneous presence of these combined effects

affects drastically the mechanical properties of metals and

alloys, reducing the average lifetime of metallic or dilute binary

alloy structures. A basic discussion of the above and related

aspects can be found in Glicksman [1]. The specialized

literature offers abundant experimental evidence to show this

corrosion type, including also sour solutions with the presence

of carbon dioxide CO2. In this direction, the recent work of Ren

et al. [2] clarifies as the simultaneous influence of H2S and CO2

can accelerate or inhibit the corrosion mechanism in circular

steel tubes. Similar experimental studies were reported by

Garcıa et al. [3] and Houyi et al. [4], showing the corrosive

effects caused by the decomposition of H2S. In general, the

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–23352328

most popular experimental techniques traditionally used to

explore the corrosion process in metallic bodies are based on

electrochemical, X-ray diffraction method and the above works

offer useful information about the use of these techniques.

Other interesting application directly related with the

petroleum industry is the use of metal oxides in reactors. In

these systems, we find that the metal oxides can operate as non-

catalyst and catalyst substrates for the processes of desulfur-

ization and denitrogenation of oil–gas mixtures with high

content of H2S. For instance, Wu et al. [5] studied

experimentally the adsorption and desorption mechanisms of

H2S on a polycrystalline UO2 catalytic sample, operating under

non-isothermal conditions. They used an ultrahigh vacuum X-

ray chamber containing instrumentation to collect experimental

data with photoelectron spectroscopy, low energy ion scattering

and temperature programmed desorption techniques. The

experimental results obtained for different temperatures of

the catalyst show the dissociative character of the component

H2S. Other experimental studies have also been performed with

different metal oxides and similar results were reported by

Reshetenko et al. [6]. They investigated experimentally the

reaction of heterogeneous decomposition of the hydrogen

sulfide on bulk oxides g-A12O3, a-Fe2O3 and V2O5 in the

interval of temperature 500–900 8C. In these studies, the main

objective is focused on the design of membrane reactors, which

offer evident advantages for the hydrogen production by means

of the direct decomposition of H2S. Chan et al. [7] used a

catalytic-membrane reactor containing a packed bed of Ru-Mo

sulfide catalyst to investigate the H2S decomposition. In order

to validate their experimental results, they developed also a

one-dimensional analytical model under non-isothermal con-

ditions, examining in detail the effect of some hydrodynamic

and transport properties on the decomposition of H2S to H0.

They showed that the nondimensional Reynolds and Peclet

numbers (which define the hydrodynamic and transport

conditions of the acid mixtures), affect dramatically the

conversion of H2S. A practical advantage of this type of

catalytic reactors, among others, is that the recovery of H0 from

H2S is a plausible economical alternative to the conventional

Claus process widely used in petroleum and minerals

processing industries, Chan et al. (op. cit.).

Recognizing that the study of the H2S conversion is very vast

and complex, we have included some additional references [8–

13] that offer sufficient details to appreciate correctly the

fundamental and practical importance of these processes.

However, apart from the work of Chan et al., the majority of

the above works together with the references [2–6] only give

experimental evidence of this decomposition for different

applications. To our knowledge, new theoretical methodologies

and predictions in the specialized literature are missing. There-

fore, in the present work we study theoretically the conversion

process of hydrogen sulfide into atomic hydrogen, using a simple

analytical model that takes into account the following fact:

In order to accelerate the corrosive process under laboratory

conditions is indispensable to elevate gradually the temperature

of the catalytic surface to control, among other factors, the

simultaneous adsorption–desorption reactions. However, the

corrosion in typical cases, particularly in petroleum industry is

not manifested immediately. Therefore, it should be accepted

that at room temperature (as normally are operating some

equipments of the petroleum industry), the chemical and

electrochemical interactions between oil–gas mixtures (with a

given percentage of H2S) and metallic structures are, in general,

very slow processes, and in a first approximation, the desorption

reactions are negligible. Then, we have not considered necessary

the use of a catalytic surface to accelerate the conversion of H2S.

Instead; we choose a simple iron plate immersed in a sour

environment composed by a binary mixture of methane and

hydrogen sulfide. The mixture as well as the iron plate is found at

room temperature. In this sense, the present physical config-

uration is in accordance with real prototypes frequently used in

laboratory conditions. In fact, in the previously cited works non-

isothermal catalytic surfaces or electrochemical cells are

exposed to very strong acid ambient to promote rapidly the

corrosive effect. Therefore, the present physical model is

visualized as an isothermal mixture of methane and hydrogen

sulfide flowing perpendicularly to an iron horizontal plate. In the

following sections, we derive the mathematical model and

showing the corresponding numerical results that are obtained

with conventional finite-difference methods. However, we

anticipate that the mass transport of hydrogen sulfide from the

mixture to the iron plate, the heterogeneous conversion of H2S to

H0 on the surface of the metal and the diffusive transport of it

through the iron plate, represents a conjugate mass transfer

problem, because the corresponding mathematical formulation

reflects just this simultaneous mixture-metallic surface interac-

tion. Therefore, the present work is organized following this

structure: first, we derive theoretically the conjugate mass

transfer-conversion problem, which is required to solve the

heterogeneous decomposition of hydrogen sulfide on an iron-

metallic plate in a laminar stagnation-point flow and second, we

include other sections to show specifically numerical results,

discussion and conclusions.

However, we must emphasize that the present theoretical

predictions must be completed and compared with experimental

results. To our knowledge, this particular mechanism of

heterogeneous decomposition of the specie H2S in a sour-gas

mixture on a iron-metallic plate subject to a laminar stagnation

flow has still not been previously treated with some measurement

techniques in order to show experimental evidence. In this

direction, we consider that novel techniques like cross-sectional

scanning electron microscopy (SEM) images and scanning

electrochemical microscope (SECM) used to estimate the

surface coverage of metallic vapor deposition and catalytic

activity on surfaces can be preliminarily used to obtain

experimental data.

2. Theoretical formulation

2.1. Governing equations for the gas-phase mixture and for

the iron plate

In Fig. 1, we show the physical model, coordinate system

and a sketch of the stagnation-point flow configuration.

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–2335 2329

Fig. 1. Schematic diagram of the physical model.

The system of coordinates is located on the vertical axis of

symmetry of the plate. Also in this figure, x and y denote the

horizontal and vertical axis, respectively. A binary mixture of

methane and hydrogen sulfide with mass concentrations

denoted by YCH4and YH2S, respectively, flows permanently

with a gradient velocity a and ambient temperature T1,

perpendicular to the iron horizontal plate of finite thickness h.

We assume that the iron plate is found also at ambient

temperature T1 and in the lower surface of the plate, the

presence of hydrogen is absent. Due to heterogeneous

electrochemical and chemical reactions on the surface of the

iron plate (the detailed reaction mechanism will be providing in

the following subsection), continuously is carried out the

decomposition of H2S to H0. Therefore, for the binary mixture

zone (we assume that in this region, no exist homogeneous

reactions of any type), the stagnation-point boundary layer

governing equations are the following: mass and momentum

equations,

@u

@xþ @v

@y¼ 0; (1)

ru@u

@xþ rv

@u

@y¼ m

@2u

@y2þ ra2x; (2)

the term—ra2x represents the pressure gradient that is easily

obtained by using the boundary layer theory, Schlichting [14].

Here, u and v are the longitudinal and transversal components

of the velocity vector and a is a constant related with the

velocity. r and m represent the density and dynamic viscosity of

the mixture, respectively. During the decomposition process of

H2S to H0, we assume uniform values for the properties of the

mixture. On the other hand, the mass conservation equation by

specie can be written as,

u@Yi

@xþ v

@Yi

@y¼ Di

@2Yi

@y2(3)

where i = CH4 or H2S and Di is the molecular diffusion coeffi-

cient of the specie i. Furthermore, we accept a global mass

conservation between both species, given by the relationshipPYi ¼ 1. Therefore, we require only considering the mass

conservation equation of the hydrogen sulfide H2S. In addition,

in order to solve the system of Eqs. (1)–(3); we need appropriate

boundary conditions. Far from the iron plate, we have that,

y!1 : u ¼ ax; YH2S ¼ YH2S1 ; (4)

where YH2S1 and u represent the mass concentration of H2S and

the longitudinal component of the velocity u = ax evaluated

both at infinity, respectively. This last condition is easily

derived from the potential theory of a stagnation laminar flow.

Other relevant boundary conditions are directly related to the

heterogeneous reactions at the upper surface of the iron. At

room temperature, the methane gas is inert and therefore cannot

react with the iron surface. However, due to the presence of H2S

into the mixture, the contact of this specie with the metal can

induce a dissociative adsorption. Nelen et al. [11] and Lai et al.

[15] have supported spectroscopic experimental evidence of

this chemical dissociation, using metals in contact with a sour

ambient composed basically by H2S and operating at room

temperature or lower than it. In addition, Wilhelm and Abayar-

athna [16] using electrochemical cells showed that the hydro-

gen permeation could be utilized to investigate hydrogen

sulfide adsorption in refinery environments. In the past, the

concept of dissociative adsorption has been widely studied and

we suggest the work of Somorjai [17] to see details that are

more specific. Therefore, we accept the existence of this

molecular dissociation (together with the chemical kinetic

given in the next section), destroys the hydrogen sulfide and

inversely, atomic hydrogen is created at the surface of the iron.

Hence, we propose the following mass-transfer boundary con-

ditions, together with the classical hydrodynamic conditions for

the velocity’s components,

y ¼ 0 :@YH2S

@y� v9GWH2S

rDH2S

¼ @YH0

@y� v11G

DH0

¼ 0 and

u ¼ v ¼ 0:

(5)

Here, WH2S is the molecular weight of specie H2S. v9 and v11

are the surface reaction rates in units of mol of H2S and H0

destructed and created by unit time and unit surface of the plate,

respectively. The parameter G and appropriate laws for the

reaction rates vj (here j denotes the equation number corre-

sponding to the heterogeneous reaction model defined by

Eqs. (8)–(11), given lines below), are defined in the following

section. The above mass transportation boundary conditions

represent the compatibility conditions needed to solve the

conjugate mass transfer problem. Because the mass concentra-

tion YH2S and molar concentration YH0 at the upper surface of

the iron metal are unknowns, we need additional information

provided by the molecular diffusion of the hydrogen into the

iron metal. In the present work, we adopt a simple model for the

molecular diffusion of hydrogen, taking into account the crea-

tion of this specie at the iron surface. However, it is important to

mention that in the present model, we avoid to consider

sophisticated diffusion models, which take into account unsa-

turable traps. Physically, the appearance of these traps is similar

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–23352330

to fissures or voids where hydrogen as proton, H+, remains

trapped into the metals in large concentrations causing poten-

tially the corrosion phenomenon [1]. Considering stationary

conditions, we propose

@2YH0

@y2¼ 0; (6)

together with,

y ¼ �h : YH0 ¼ 0; (7)

2.2. Heterogeneous reaction model

We assume a surface reaction model to describe the

simultaneous reactions of the dissociative adsorption of H2S

and the oxidation of iron metal. In general, Nelen et al. [11] and

Lai et al. [15] showed that this dissociative adsorption is

selective, depending strongly on surface and temperature

conditions. On the other hand, the first step to yield corrosion in

metals comes from the anodic reaction of the metal with the

sour environment. This result has been widely confirmed

experimentally in the above works [11,15,16]. In this

electrochemical reaction, there is an electronic interchange

between the sour ambient and the iron metal, which easily

conducts to the formation of Fe2+. Thus, we follow the above

works together with recent experimental evidence of Cabrera

et al. [18] to propose the following reaction model:

Fe ! Fe2þ þ 2e�; (8)

H2S ! HS� þHþ; (9)

Fe2þ þHS� ! FeS þ Hþ; (10)

Hþ þ e� ! H0; (11)

thus, electrochemically, when the iron metal is in contact with

the sour mixture, the HS� ion is reduced to hydrogen atomic

H0, reacting with Fe2+ and in this form, ferrous sulfide, FeS, is

formed at the metal surface. However, it is very important to

note that this mechanism does not contain the adsorption–

desorption of the film product FeS, as well as the adsorption

of methane gas CH4. Surface films of FeS can retard the

corrosion process. However, we assume moderate generation

rates for this component. In this reactive scheme, we have

assumed that the specie HS� reacts necessarily with Fe2+;

otherwise, the generation of ions H+ would be drastically

reduced. On the other hand, the adsorption kinetic is given

by a sticking probability, Si or accommodation coefficient,

which represents the portion of the collisions with the surface

that successfully leads to adsorption, [17]. Since we have only

one adsorption reaction given by Eq. (9), in the following lines

we denote this coefficient as Si = k9. In addition, the rate of

collisions, Zw, can be computed by using the classical kinetic

theory and the specie concentrations at the surface can be

represented by the surface coverages ui. This is defined as

the ratio of the number of sites occupied by surface species i to

the total number of available sites. Considering the stationary

case, then the steady-state governing equations can be written

as

uv þ uHS� þ uHþ þ uH0 ¼ 1; (12)

duHS�

dt¼ v9 � v10 ¼ 0; (13)

duHþ

dt¼ v9 þ v10 � v11 ¼ 0 (14)

and since the mechanism of surface coverage of the hydrogen is

affected by the presence of diffusion of this specie into the

metal; then the corresponding reaction rate can be written as

duH0

dt¼ v11 �

DH0

G

���� @CH0

@y

����y¼0

¼ 0: (15)

In the above relationships, uv denotes the surface coverage of

empty sites. All the reaction rates, vj, in above equations are in

s�1 units and are defined by,

v9 ¼ k9u2v; v10 ¼ k10uvuHS� ; v11 ¼ k11uHþ (16)

and the kinetic factors kj as

k9 ¼S2

0PM

G ð2pWH2SRTÞ1=2exp

�� DE9

RT

�; (17)

k10 ¼ A10exp

�DE10

RT

�; (18)

k11 ¼kBT

hP

exp

�� ne11FDV11

RT

�: (19)

In the above relationships, S20 is the pre-exponential factor of the

sticking coefficient between the hydrogen sulfide and the iron

and is of order of 0.02, [19]. The superscript ‘‘2’’ on S20

represents the dissociative character of this reaction.

G = (NV)/(NA) � 3 � 10�27 mol/cm2 is the surface molar con-

centration and corresponds to the surface site density divided by

the Avogadro’s number. Here, NV ¼ Naexpð�Qv=kBTÞ (in

units of sites/cm2) and represents the total number of vacancies

formed by thermal agitation per unit surface; Na is the total

number of atoms in the solid, is the energy required to form a

vacancy, which Qv depends on the material and is of order of

�1.08 eV (see references [20,21] for more details) and NA is the

Avogadro’s number (=6.0225 � 1023 molecules/mol). R is the

universal gas constant (=8.3143 J/K mol), ne11 = 1 and repre-

sents, in general, the number of participating electrons in the

electrochemical reaction [Eq. (11)], F is the constant of Fara-

day (=9.6487 � 104C/mol), kB is the Boltzmann’s constant

(=1.3805 � 10�23 J/K) and hP is the constant of Planck

(=6.6256 � 10�34 J s). Furthermore, T is the temperature in

Kelvin and PM is the pressure of the mixture of H2S and CH4;

we assume in the numerical calculations that both are fixed

parameters, which means that the mixture during the stationary

reactive process is subject to isobaric and isothermal condi-

tions. The reactant concentrations, YH2Sw, YH0w

, etc. are the

surface concentrations and are obtained after solving the

YH2Swcoupled gas-phase equations with the governing

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–2335 2331

equations for the surface coverage of the adsorbed species,

together with hydrogen diffusion into the metal. We can

anticipate that at room temperature conditions, the surface

coverages corresponding to the species HS� and H0 are pre-

dominant, indicating a rich generation of hydrogen.

It is important to mention that the contact of the metal with

the sour mixture yields spontaneously a cell-electrochemical

potential of magnitude DV8. Because at room conditions this

electrochemical potential is of order of 0.44 V [22], with the aid

of the Faraday’s law, the corresponding electrochemical energy

associated with this reaction is DE8 = ne8FDV8 with ne8 = 2

(reciprocally, the electrochemical energy associated with

reaction (11) is zero, because DV11 = 0). Therefore, we assume

that this electrochemical energy is used to initiate the

adsorption reaction, Eq. (11), which is equivalent to write

DE8 = ne8FDV8 � DE9. Finally, the stationary condition is used

in Eqs. (12)–(16) to derive, after some simple algebraic

manipulations, that surface coverage of the products are

directly related to uV by means of the following relationships,

uHS� ¼k9

k10

uv; uHþ ¼2k9

k11

u2v and

uH0 ¼ 1� uv �k9

k10

uv �2k9

k11

u2v;

(20)

3. Nondimensional governing equations

The set of coupled governing Eqs. (1)–(20) can considerably

simplify by introducing appropriate nondimensional variables.

The main advantage is to reduce the number of involved

physical parameters. In particular, for the gas phase we

introduce a stream function c to satisfy the global mass

conservation, Eq. (1): u = @c/@y and v ¼ �@c=@x. In this case,

the governing equations for the gas-mixture region have a

similarity solution. Therefore, we define the following

nondimensional variables

h ¼ y

d¼�

ra

m

�1=2

y; j ¼ � y

h; f ¼ c

xðam=rÞ1=2;

YH2S ¼YH2S

YH2S1

and CH0 ¼ YH0

ðYH2S1Þm:

(21)

In the above change of variables, we use (YH2S1 )m to denote

molar concentration of H2S at infinity. The resulting nondimen-

sional governing equations now take the form

d3 f

dh3þ f

d2 f

dh2��

d f

dh

�2

þ 1 ¼ 0; (22)

d2YH2S

dh2þ ScH2S f

dYH2S

dh¼ 0; (23)

where ScH2S is the Schmidt number of H2S, given by

ScH2S ¼ m=ðrDH2SÞ. The nondimensional boundary conditions

are then given by

h!1 :d f

dh� 1 ¼ YH2S � 1 ¼ 0; (24)

h ¼ 0 : f ¼ d f

dh¼ 0; (25)

and the compatibility conditions at the upper surface of the iron

plate as

dYH2S

dh

����h¼0

¼�

n1a

�1=2k9GWH2S

rDH2SYH2S1

u2v;

@CH0

@j

����j¼0

¼ � hk9GWH2S

rDH0 YH2S1

u2v;

(26)

which can be combined in only one relationship,

� bdYH2S

dh

����h¼0

¼ @CH0

@j

����j¼0

; (27)

where the nondimensional parameter b is defined as

b ¼ DH2S=ðm=raÞ1=2

DH0=h; (28)

and represents the competition between the rate of molecular

diffusion of hydrogen sulfide into the momentum boundary

layer thickness of the mixture zone to the rate of hydrogen

diffusion along the thickness of the iron metal. In fact, an order

of magnitude analysis reveals that the momentum and mass

transfer boundary layers at the mixture zone are given by

d � (m/ra)1/2 and dDeðDH2S=aÞ1=2; respectively. Therefore,

the ratio of both thicknesses is related to the Schmidt number

through the relationship d=dD ¼ Sc1=2H2S. In addition, we use the

coordinate h defined in relationships (21) in order to avoid that

the momentum boundary layer, Eq. (22), depends on any

nondimensional parameter. This is an advantage from the

numerical point of view, because the numerical solution of

Eq. (22) will be universal and can be found elsewhere, [14].

However, our numerical calculations included the numerical

solution of this equation in order to solve necessarily Eq. (23).

The details are given in the next section.

On the other hand, the molecular diffusion of hydrogen into

the iron is governed by the following equation,

@2CH0

@j2¼ 0; (29)

and at j = 1 we have imposed for simplicity that,

CH0 ¼ 0: (30)

3.1. Numerical procedure

In this section, we describe briefly the iterative scheme to

solve the set of Eqs. (22)–(30), together with the surface

coverage relationships (20). The procedure is the following:

we assume an arbitrary or initial value for the nondimen-

sional concentration of hydrogen at the surface of the iron

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–23352332

Fig. 3. Surface coverage of the product H+, uHþ , as a function of the non-

dimensional parameter k9/k10 and different values of the nondimensional

concentration YH2S1 .

metal, ðCH0Þi, in order to know the right-hand side of

boundary condition (27). Thus, assuming a given value of the

nondimensional parameter b, we obtain the concentration

gradient of H2S at the surface of the iron plate and therefore,

the governing Eqs. (22)–(25) for the region of binary mixture

can be solved in a closed form. However, this initial value of

ðCH0Þi is not sufficient to guarantee that the boundary

condition (24), h!1: Y! 1 is fulfilled. Therefore, we

develop a simple iterative scheme on ðCH0Þi in order to satisfy

this condition. Hence, we solve the ordinary differential

Eqs. (22)–(25) with the Runge-Kutta’s technique of fourth-

order, together with an appropriate shooting method to obtain

the optimal number of iterations that guarantee the

satisfaction of the above boundary condition at infinity.

Once that we have correctly found the right-hand side of the

Eq. (27); we replace the concentration gradient of H2S into

Eq. (26) to estimate uv. The other surface coverages of the

products HS�, H+ and H0 are evaluated with the aid of the

relationship (20). In addition, the solution of the binary

mixture governing equations permits to know, among other

results, the value of the nondimensional concentration of H2S

at the surface.

4. Results

In this section, we show the numerical results obtained by

solving numerically the system of Eqs. (22)–(30), together with

the stationary coverage relationships (20). All numerical

calculations were performed with the following data: Schmidt

number ScH2S ¼ 1:8, b = 4.9922 � 10�2 and Figs. 2–11 were

plotted with a room temperature of T1 = 300 K, except Fig. 12,

for which we have analyzed the influence of the parameter G on

the nondimensional surface concentration of the hydrogen, CH0 ,

in the temperature interval 300 K < T < 500 K. Under these

conditions, k9 = 2.85 � 104 s�1 and k11 = 6.25 � 1012 s�1; how-

ever, we have not sufficient data to estimate k10. Therefore, we

Fig. 2. Surface coverage of the product HS�, uHS� ; as a function of the

nondimensional parameter k9/k10 and different values of the nondimensional

concentration YH2S1 .

assign arbitrary values to this parameter. In this sense, we present

the numerical predictions by using the nondimensional ratio k9/

k10 as a relevant parameter to understand the decomposition

process. In Figs. 2–5 we have plotted the surface coverages of the

product species HS�, H+, H0 and the vacancy surface coverage uv

as functions of the nondimensional parameter k9/k10 with four

different values of the hydrogen sulfide mass concentration at

infinity, YH2S1 ; respectively. Hence, in Fig. 2 we can appreciate

the surface coverage of HS�, uHS� as a function of the parameter

k9/k10. Here, the influence of this parameter is clear because for

increasing values of k9/k10, the surface coverage is also increased

and this behavior is amplified for increasing values of the initial

concentration of H2S. In the approximated interval 0.03 9 k9/

k10 9 70, we obtain the major sensitivity to this parameter. For

Fig. 4. Surface coverage of the product H0, uH0 , as a function of the non-

dimensional parameter k9/k10 and different values of the nondimensional

concentration YH2S1 .

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–2335 2333

Fig. 5. Surface coverage of the vacancy sites, uv, as a function of the non-

dimensional parameter k9/k10 and different values of the nondimensional

concentration YH2S1 .

Fig. 7. Surface coverage of the product HS�, uHS� , as a function of the

nondimensional concentration YH2S1 and different values of the nondimen-

sional parameter k9/k10.

instance, for k9/k10 = 1, the increments in uHS� are very

pronounced and just for this value of the parameter k9/k10, the

surface coverage uHS� reaches maximum values. In Fig. 3, we

show similar results for the surface coverage of H+, uHþ . In this

case, we obtain the opposite behavior: for increasing values of the

parameter k9/k10, the surface coverage uHþ , decreases. However,

this effect is attenuated if the initial concentration of H2S is

increasing. This result is interesting because the presence in the

mixture of this specie reflects the incipient activity of the

heterogeneous surface reactions in order to yield this specie. In

the limit of small values of the nondimensional parameter k9/k10,

we found that for values of k9/k10 � 0.04 practically the surface

coverage uHþ has been stabilized in an asymptotic value, which

Fig. 6. All surface coverages, u, as functions of the nondimensional parameter

k9/k10 and YH2S1 ¼ 0:1.

depends on the assumed initial values of the H2S concentration.

In the opposite case of k9/k10� 1, the corresponding surface

coverage practically disappears for values of k9/k10 � 10.

Therefore, the approximate interval 0.04 9 k9/k10 9 10 defines

the major sensitivity of the reaction to this parameter. In Fig. 4,

the production of H0 diminishes rapidly for increasing values of

the parameter k9/k10 and is very sensible to the assumed values of

the initial concentration of H2S. In this case, the critical interval

corresponds to 0.01 9 k9/k10 9 100. In order to complete the

results related with the prediction of surface coverage, in Fig. 5

we also show the surface coverage of the vacancy sites, uv as a

function of the same parameter k9/k10 and different values of the

nondimensional concentration YH2S1 . Here, we obtain qualita-

Fig. 8. Surface coverage of the product H0, uH0 , as a function of the non-

dimensional concentration YH2S1 and different values of the nondimensional

parameter k9/k10.

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–23352334

Fig. 9. All surface coverages, u, as functions of the nondimensional concen-

tration YH2S1 and k9/k10 = 0.1.Fig. 11. Nondimensional hydrogen distribution, CH0 , as a function of the

nondimensional coordinate j, YH2S1 ¼ 0:1 and different values of the non-

dimensional parameter k9/k10.

tively the same results that those obtained by the surface coverage

of H+; in addition, the interval is practically the same. Also, in

Fig. 6 we have plotted together (for a representative value of

YH2S1 ¼ 0:1), the different surface coverage as functions of the

nondimensional parameter k9/k10. Complementary, in Figs. 7 and

8 we show only the surface coverage of the products HS� and H0

as functions of the nondimensional concentration YH2S1 . In

Fig. 7, the HS� surface coverage increases for increasing values

of YH2S1 and this increment is very sensible to increasing values

of the parameter k9/k10. Similarly in Fig. 8, the presence of a

major quantity of hydrogen sulfide in the mixture reflects a drop

of the surface coverage of H0, reaching smaller values if the ratio

k9/k10 is increased. This result confirms some experimental

predictions of that those mixtures with high content of hydrogen

sulfide can inhibit the corrosion effect.

Fig. 10. Nondimensional hydrogen distribution, CH0 , as a function of the

nondimensional coordinate j, k9/k10 = 0.1 and different values of the nondi-

mensional parameter YH2S1.

In order to complete the numerical results related with the

diffusive process of hydrogen; in Fig. 10, we show the hydrogen

distribution into the iron metal as a function of the

nondimensional transversal coordinate j, different values of

the concentration YH2S1 and k9/k10 = 0.1. Following this

numerical prediction for the hydrogen profile, we can see that

an increment of the H2S fraction in the mixture yields a minor

fraction of the hydrogen specie at the surface, inhibiting the

diffusive process. Reciprocally, in Fig. 11, we can appreciate

the same hydrogen distribution into the metal as a function of

the nondimensional transversal coordinate j, YH2S1 ¼ 0:1 and

different values of k9/k10. The sensitivity of the reactions, which

is measured through the values of the parameter k9/k10, shows

that the diffusive process of the atomic hydrogen H0 can be

accelerated or inhibited for moderate or high values of this

Fig. 12. Nondimensional hydrogen concentration at the surface (j = 0), CH0 , as

a function of the parameter G and YH2S1 ¼ k9=k10 ¼ 0:1.

J.C. Martınez et al. / Applied Surface Science 253 (2006) 2327–2335 2335

parameter, respectively. Finally, in Fig. 12, we have plotted the

surface concentration of hydrogen as a function of the

parameter G and YH2S1 ¼ k9=k10 ¼ 0:1. Here, the hydrogen

concentration increases very sensibly to increasing values of G.

We anticipate in Section 2.2 to G as an exponential function of

the temperature; then for increasing values of the room

temperature, the hydrogen concentration also increases.

However, for large increments of the temperature we can

active the desorption reactions at the upper surface of the iron

metal. Therefore, the present results must take with care: in

order to analyze the physical influence of temperature effects

with large deviations of the room temperature, it is

indispensable to include the energy equations for the mixture

and for the iron metal. Hence, this last figure shows that for

moderate deviations of the room temperature, we can obtain a

more vigorous hydrogen generation at the metal surface.

5. Conclusions

In the present work, we have developed an analytical model

to understand the mechanism of adsorption and decomposition

of hydrogen sulfide to hydrogen into an iron–metal plate. The

physical model used is very simple: a binary mixture of

methane and hydrogen sulfide, flows perpendicularly to an iron

horizontal plate. At room temperature the metal reacts easily

with this sour mixture, yielding Fe2+, which is recombined with

HS� to conduct the process of generation of atomic hydrogen

H0. The specie HS� comes directly from the dissociative

adsorption of H2S and operates as a control to drive the reaction

Fe2+ + HS� ! FeS + H+. We follow the well-known sticking

surface coverage concept to predict as the available sites of the

surface metal are occupied with the different products, due to

the proposed heterogeneous kinetic mechanism. Since a finite

fraction of the generated hydrogen is conducted to the metal,

we have included a simple process of diffusion of this specie. In

this sense, the mathematical model is based on a conjugate

mass transfer analysis, where the simultaneous interaction

between the stagnation-point flow and the iron metal

determines the heterogeneous surface reactions of the iron.

The numerical results of the present work determine clearly

the surface coverage of the involved products. However, we

have not found directly in the specialized literature, experi-

mental data to support these theoretical predictions. Probably,

the main reason is due to that the sour corrosion in metallic

pieces under laboratory conditions, always is carried out in

short times, by increasing the temperature of the system. On the

other hand, in the Section 1 we cited the references

[3,4,9,11,15,18] where indirectly the theoretical predictions

of the present work are confirmed. For instance, it is well known

and documented in some of these references that a major

content of hydrogen sulfide in the mixture yields a drop of the

surface coverage of H0. This result was showed in Fig. 8, which

predicts theoretically that those mixtures with high content of

hydrogen sulfide can inhibit the corrosion effect.

On the other hand, the numerical predictions show that the

electrochemical reactions (8) and (11) are, in general faster than

other reactions (9) and (10), because the surface coverage of the

transition specie H+ is smaller than the surface coverage of the

other products. This result can be well appreciated in Fig. 6.

Finally, it is important to note that the present model which is

evaluated at room temperature only explains the decomposition

of the specie H2S and the corresponding generation and

molecular diffusion of atomic hydrogen H0 into the metal. The

trapping and cracking mechanisms that spread hydrogen in the

form of protons, H+, through the surrounding lattice of the

metal, accumulating internally H0 molecules in specific voids

or traps to conduct the sour corrosion is outside of the main

objectives of the present work.

Acknowledgements

This work has been supported by a research grant no. 43010-

Y of Consejo Nacional de Ciencia y Tecnologıa at Mexico.

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