Modeling Sulfur Poisoning of Palladium Membranes Used for Hydrogen Separation

Hydrocarbons are the most important source for hydrogen production. A combined reaction-separation process using inorganic membranes can significantly increase the reaction conversion by shifting the equilibrium toward product formation. Sulfur poisoning is a significant problem as it deactivates the most commonly used metallic membranes. -e relationship of the membrane activity and surface coverage with the surface structure has been recognized in the literature. A theoretical model to simulate hydrogen transport in the presence of sulfur compounds is presented. -is model accounts for active site deactivation and permanent structural damage to the membrane. Transport and reaction rate parameters used in the model have been estimated from experimental data. Qualitatively, the model represents well the behavior of inorganic membranes, including partial membrane activity regeneration after the sulfur source is removed.


Introduction
Hydrogen is a very important gas in many industrial areas [1].Currently, hydrocarbons are the main source for largescale production of hydrogen [2].Several processes produce a mixture containing mainly hydrogen and carbon monoxide, known as synthesis gas or syngas.e water-gas shift (WGS) process is used to adjust the syngas composition for further chemical synthesis routes or to increase the amount of hydrogen produced [3,4].In the WGS reaction, carbon monoxide, together with steam, is converted to carbon dioxide and hydrogen.
e attainable equilibrium with the WGS reaction depends on how the chemical equilibrium is controlled.
e most effective strategy involves forcing equilibrium displacement to the product side.
is is achieved by continuous removal of either hydrogen or carbon dioxide from the reaction zone [2].
e development of combined reaction and separation processes is a process intensification strategy that allows better yield in the case of reversible thermodynamic chemical reactions.Cost-effective inorganic membranes for gas separations open the door to substantial process improvements [5][6][7].Inorganic gas separation membranes can be used to selectively remove hydrogen and thus increase its production in a membrane reactor.
Palladium-based membranes are viable candidates for use in hydrogen separation because for their high hydrogen permeability and catalytic activity with respect to hydrogen dissociation.A significant technical barrier, however, impeding the development of a suitable hydrogen-separation membrane, is the susceptibility of palladium membranes to poisoning or deactivation by contaminants present in gaseous effluent streams, such as hydrogen sulfide [8].It has been reported that even the presence of small amounts of sulfur compounds in the feed can lead to deactivation of these materials after prolonged operation [9,10].It is well known that the catalytic activity of platinum and of most transition metals is drastically reduced when the reagents contain even small quantities of sulfur.Poisoning of the catalyst is an important industrial problem because it reduces the catalytic activity of many reactions [10].Catalytic poisoning by adsorbed sulfur compounds and corrosive decay produced by surface sulfidation have been reported as the two main mechanisms that reduce membrane performance [11].
is problem applies to a wide range of industrial processes.A review of experimental and theoretical information published in the open literature on the mechanism of sulfur poisoning of palladium membranes was provided by Gabitto and Tsouris [12].e authors also included studies based upon the reduction mechanism of transition metals because of the relevance of this mechanism on catalyst poisoning.
In the presence of hydrogen, palladium forms a continuous solid solution, exhibiting a fcc (face-centered cubic) crystal structure.At temperatures below 573 K, however, the phase diagram illustrates the formation of two distinctly different phases (α and β), a hydrogen-rich phase, and a palladium-rich phase.Although the two low temperature phases are both fcc in the crystal structure, they exhibit different crystal lattice parameters.
e temperatureinduced transition between the two hydride phases significantly deteriorates the mechanical properties of the membrane.Alloying with other metals (for example, Ag, Au, Cu, Ru, Rh, Ni, and Pt [13,14]) tends to lower the phase transition temperature and, under some circumstances, improve the hydrogen permeability [15].Typically, Ag is deposited on a Pd film.An alloy containing 73 wt.% Pd and 27 wt.%Ag (Pd 73 Ag 27 ) is the most commonly used one commercially due to its high hydrogen permeability [16].Pd-Ag membranes, however, show significant performance deterioration when exposed to even trace amounts of H 2 S (2-20 ppm).Peters et al. [17] reported that a 10 min exposure to 20 ppm H 2 S inhibits the H 2 flux by more than 80%.
Conde et al. [18] presented a review of palladium alloy membranes for hydrogen purification, including permeability data and other relevant characteristics of the alloys.
e authors reported the use of ternary alloys with enhanced physical and chemical properties and the use of computational methods to allow screening of promising alloys.In the case of alloys with a similar structure to the constitutive pure metals, fcc, for example, Vegard's law [19] predicts that the alloy lattice constant (a alloy ) is a linear function of the metal atomic fractions (x i,metal ) and metal lattice constants (a i,metal ), a alloy � Σa i,metal x i,metal . is law has been experimentally verified [20].
Cost is a major concern in wide-scale industrial applications.Pd-Au membranes show the highest H 2 S resistance of all binary Pd alloys due to smaller H 2 S binding energy and slow rate of sulfide formation but are cost-effective only for very thin membranes (∼1-10 μm) [12].In the case of Pd-Cu alloys, the hydrogen permeability increases through a maximum of around 40 wt.%Cu (Pd 60 Cu 40 ).
is high percentage of Cu significantly reduces the membrane cost relative to pure Pd, and the Pd 60 Cu 40 alloy exhibits increased resistance to hydrogen sulfide poisoning.Furthermore, a Pd 60 Cu 40 membrane can withstand repeated temperature cycling with less distortion than pure Pd because at 40 wt.%Cu, the critical temperature for ß-hydride phase formation is below room temperature [21].Palladium-copper alloys having between 30 and 60 wt.%Cu form the body-centered cubic (bcc) phase, which has higher hydrogen permeability, however, is less resistant to sulfur compounds than the facecentered cubic (fcc) structure of other Pd-Cu alloys [21][22][23].Kulprathipanja et al. [24] found that low concentrations of H 2 S decreased hydrogen permeation through Pd and Pd-Cu alloy membranes by blocking hydrogen dissociation sites.At high H 2 S concentrations, a sulfur surface layer did not allow hydrogen even to penetrate the Pd-Cu surface.Sulfidation of Pd and Cu formed micron-size pores and caused the membrane to fail.For membranes with bulk Cu concentration above 60 wt.%, a phase change occurs, from bcc to fcc, and this process decreases hydrogen permeation.e introduction of S into the Pd layer creates structural distortions that are responsible for the appearance of defects, such as cracks and pinholes [8].
Studies of sulfur adsorption on surfaces of Pd and Pd alloys, using density functional theory, show that sulfur forms strong bonds with pure Pd, Cu, and Ag surfaces.e bond strength decreases from pure Pd surfaces to pure Cu to pure Ag.On the alloy surfaces, the adsorption energies are in general weaker in comparison to adsorption on the pure Pd (1 1 1) surface, but the reduction in binding energy is not large [25].
Experiments have shown that Pd membranes exposed to H 2 S for long periods of time, under certain conditions, develop thick Pd 4 S scales.Morreale et al. [11] used computational methods to quantify the influence of Pd 4 S layers on the hydrogen permeation rate.e authors' results were in good agreement when predicting the activation energy of the hydrogen permeation, but the permeability values were seven times greater than the computational predictions [11].
oen et al. [26] prepared P-Cu and Pd-Au composite membranes depositing the Pd alloy on stainless steel tubes.
ey used an intermediate layer of ZnO 2 to prevent intermetallic diffusion.For their Pd-Cu and Pd-Au membranes, they reported hydrogen fluxes exceeding the DOE Fossil Energy 2010 target [26].
Pomerantz and Ma [27] used corrosion-scale growth experiments to study the interactions of H 2 S with Pd and Pd-Cu membranes in the presence of H 2 S. e authors plated with Pd coupons of 316L PSS, previously oxidized to form an intermetallic diffusion barrier, by an electroless deposition method.e authors reported that the exposure of the Pd coupons to the 50 ppm H 2 S/H 2 mixture resulted in sulfur adsorption on the Pd surface and formation of a Pd 4 S scale on top of the Pd layer.e morphology of the deposited Pd changed from a granular structure to a coral-like structure upon the Pd 4 S scale formation.
Cheng and Ma [28] investigated the effect of temperature on sulfur poisoning of Pd-Au alloys.
eir experimental results confirmed the presence of Pd 4 S on pure Pd surfaces.For the Pd-Au alloy coupons, no surface morphology changes were observed throughout the entire temperature range studied (350-500 °C).e authors concluded that the Pd-Au alloy showed high resistance to sulfur adsorption and sulfide formation.
Khatib et al. [29] prepared ultra-thin Pd and Pd alloy (Pd-Ag and Pd-Cu) membranes with a phosphorus component on a porous hollow fiber α-alumina support.e authors concluded that, even though the presence of phosphorus lowered the hydrogen permeance and H 2 /N 2 2 International Journal of Chemical Engineering selectivity, it drastically improved the Pd alloy membrane's capacity of recovery in H 2 after H 2 S poisoning.e presence of P also produced more homogeneous surfaces and less segregation, conferring a structural integrity to the membrane by suppressing the formation of cracks and pinholes.e simplest membrane is a single, uniformly structured wall of a certain material, the so-called symmetric, standalone membranes.In order to achieve sufficient mechanical strength, single-walled symmetric systems have a considerable thickness.
is is a disadvantage with respect to obtaining large fluxes, which require thin separation layers.Use of asymmetric structures can solve this problem.ese systems consist of a supporting layer with large pores (low flow resistance) of sufficient mechanical strength on top of which layers of gradually decreasing pore size are deposited [30].Self-supporting, mechanically resistant Pd or Pd alloy dense membranes must be typically a few hundred μm thick.e cost of these membranes is not trivial because Pd is an expensive metal.In recent years, several groups have focused their attention on the development of composite metal membranes whereby a thin (few μm) metallic film is deposited on (or in) the pores of an underlying porous support [31,32]. is kind of membrane aims to have the mechanical resistance of the support and the high selectivity of a dense membrane with better permeabilities.Porous glass, ceramic, and metal supports have been utilized [33].Sometimes an oxide layer is added between the metallic layer and the support in order to prevent intermetallic diffusion.Intermetallic diffusion between the layers leads to rapid flux decline and shortened membrane lifetime [34].
Gabitto and Tsouris [35] proposed a theoretical model to simulate hydrogen transport through composite inorganic membranes.is model simulates operation of membranes made of three or more porous or metallic layers.Transport through Pd alloy metal layers is simulated using a comprehensive model proposed by Ward and Dao [36].e model accounts for external mass transfer, surface adsorption and desorption, transitions to and from the bulk metal, and diffusion within the metal.Transport through porous ceramic layers is simulated following Burggraaf [30].
e main objective of this work is to study the mechanism of sulfur poisoning in metal-ceramic membranes for hydrogen separation.e authors will modify the theoretical model presented by Gabitto and Tsouris [35] to simulate hydrogen flow in multilayer, asymmetric hydrogen-separation membranes in the presence of H 2 S. A sulfur poisoning mechanism will be proposed and added to the model.e model will allow us to simulate hydrogen transport in Pd and Pd alloy membranes in the presence of sulfur compounds.

Model Development.
e goal of the project is to accurately model the poisoning mechanism.
e poisoning process comprises two sequential steps: sulfur adsorption and chemical reaction on the surface.e occurrence of the chemical reaction is limited by the value of the reaction rate constant [37].We will study first the adsorption mechanism of hydrogen sulfide on Pd(111) surfaces.Our conclusions, however, will also be applicable to homogeneous Pd alloys with a similar crystal structure.e adsorption of hydrogen sulfide on Pd(111) is a complex process involving several steps [38].e process starts with H 2 S binding preferentially on top of Pd sites, followed by H 2 S dissociation into adsorbed SH and S. e final result is one S atom preferentially binding at the threefold fcc site.
Figure 1(a) depicts the top view of the unit cell for the surface plus one S atom on a threefold site.e S atom blocks the three contiguous adsorption sites for hydrogen adsorption (depicted by the triangle surrounding the S atom).Approaching hydrogen molecules will interact with the S atoms.ese interactions are repulsive in nature.Figure 1(b) shows a p(2 × 2) surface; in this case, the S atom blocks four contiguous sites for hydrogen adsorption.
In Figure 2, we show a schematic of a 0.33 ml covered Pd surface with the atoms close to scale.Speller et al. [45] determined that S adsorbs on Pd (1 1 1) from the gas phase forming several structures at low temperatures.High coverage leads to a (√3 × √3) R 30 °LEED pattern.Using scanning tunneling microscopy (STM), the authors also reported coexisting structures of (√3 e adsorbed S atoms will block a sizable area of the surface, thus decreasing the hydrogen flux.e maximum coverage measured was 33% of a monolayer, where one monolayer is a S layer with the Pd (1 1 1) surface lattice constant [45].e schematics in Figure 2 show that the size of the S atom will block three neighboring Pd threefold sites mainly by the size difference between the two atoms.It has been reported that sulfur desorption is a slow process due to the strong binding of S atoms on the Pd surface [46].Speller et al. [45] stated that full coverage is unlikely because S is electronegative on metals and, hence, the presence of shortterm repulsion forces between S atoms will produce potential barriers which prevent S atoms from jumping into vacant sites close to neighboring S atoms.
Pd 4 S is the most common corrosion product of reaction between H 2 S and a Pd/Pd alloy surface [21,27,37,[47][48][49].Metallic Pd has a fcc structure with a lattice parameter of 3.9 Å, while Pd4S has a tetragonal structure with lattice parameters of 5.1 Å and 5.6 Å. e lattice reordering due to the formation of the bulk Pd sulfide causes a drastic change in the morphology, which leads to irreparable damage.
Figure 3 depicts the formation of Pd 4 S by combination of the S atom with the three Pd atoms in the fcc hollow site plus a neighboring Pd atom.Partial recovery of the membrane functionality can be achieved [50][51][52].
e inability to completely recover hydrogen permeability, however, suggests that part of the sulfide poisoning is irreversible by scale formation [11,51,53].
Sulfur incorporation into the membrane can be described through a two-step process: It should be remembered that S adsorption, in equation ( 1), blocks three extra neighboring sites as previously discussed, while in equation ( 2), the formation of Pd 4 S reduces an extra hydrogen adsorption site.One of the main problems in this research is the determination of the values of the transport parameters associated with the adsorption step and the surface reaction step.
Formation of Pd 4 S can be also considered through equation (3).In this case, Pd 4 S reduction is a function of the partial pressure ratio between H 2 S and H 2 (P H 2 S /P H 2 ) [11]: In this work, we did not consider reaction when the P H 2 S /P H 2 value was below the equilibrium values reported by Iyoha et al. [37].e value of the equilibrium constant for the reaction given by equation ( 2) has been determined experimentally [21,28,37]; however, there is not complete agreement among the published values for the change of Gibbs free energy for the reaction shown in equation ( 1) [27,47,53]. is issue creates uncertainty on the equilibrium values to be used.In this work, we used the values reported by Iyoha et al. [37].
e crystalline structure resulting from the formation reaction of Pd 4 S has a lattice constant roughly twice that of palladium, 0.39 to 0.65 nm, thus creating structural stresses which are relieved by the formation of pinholes and cracks in the membrane [48].
e proposed theoretical model simulated the poisoning mechanism based upon the comprehensive model proposed by Ward and Dao [36].Hydrogen permeation through a Pd alloy layer is a complex process that involves several steps: (1) Reversible dissociative adsorption of hydrogen on the high-pressure surface, given by equations ( 7) and (8) (2) Reversible dissolution of surface atomic hydrogen in the bulk layer of the metal, given by equations ( 9) and (10) (3) Reversible dissociative adsorption of hydrogen sulfide on the high-pressure surface, given by equations ( 11) and (12) (4) Chemical reaction of sulfur atoms on the highpressure surface, given by equation (13) (5) Diffusion of atomic hydrogen inside the metallic bulk, given by equation ( 14) (6) Reversible movement of atomic hydrogen on the bulk metallic layer to the surface, given by equations ( 15) and (16) (7) Reversible recombinative desorption of hydrogen at the low-pressure surface, given by equations ( 17) and ( 18) Steps 1, 2, 5, 6, and 7 apply to hydrogen transport through the membrane, while steps 3 and 4 describe the fate of hydrogen sulfide.Every step is represented by its corresponding flux equations: where J j H 2 is the hydrogen flux in the step j, J j H 2 S is the hydrogen sulfide flux in the step j, θ H 2,1 is the fractional surface coverage (surface H/Pd ratio) on the high-pressure (i � 1) or low-pressure side (i � 2) of the metallic layer, θ ads is the fractional surface coverage (surface S/Pd ratio) on the high-pressure side of the membrane, and θ irrevS is the fractional surface coverage (surface Pd 4 S/Pd ratio) on the high-pressure side of the membrane.X s,i is the H/Pd volumetric ratio in the bulk metal adjacent to the surface i, ] d is the activated rate constant for the surface-to-bulk transition, β d is the activated rate constant for the bulk-to-surface transition, N b is the bulk concentration of Pd atoms (Pd atoms/m 3 ), N s is the surface concentration of Pd atoms (Pd atoms/m 2 ), and L M is the metallic layer thickness.e gas phase fluxes, Γ S and Γ i , are given as follows: where i � 1 represents the high-pressure and i � 2 represents the low-pressure sides of the Pd layer.P 1 and P 2 are the pressure values in the bulk of the gas phase on the highpressure and low-pressure sides of the metallic layer, T is the temperature, and R g is the ideal gas constant.e transport parameters k d and D, the sulfidation adsorption rate constant k dS , and the sulfidation reaction rate constant k RS are calculated using the estimation procedure described below.
In the derivation of equations ( 11) and (12), it has been assumed that the adsorption of hydrogen sulfide on the membrane surface is controlled by the initial step: H 2 S (g) ⟶ H 2 S (ad). is process depends linearly upon the free metallic surface calculated as shown before.e chemical reaction on the surface is complex and depends upon the activity of Pd on the surface.We have assumed this activity International Journal of Chemical Engineering to be constant, and the value is included inside the reaction coefficient k RS ; therefore, the reaction rate depends solely on the value of adsorbed sulfur atoms fractional surface coverage.
e equations representing the poisoning model are obtained from mass balances for hydrogen, in both sides of the membrane, in a thin layer inside the metal, and for hydrogen sulfide, on the high-pressure side (Figure 4).
Mass balance points for hydrogen are set on the highand low-pressure sides of the membrane and on the two boundary layers adjacent to the membrane's sides.A mass balance for sulfur is set on the high-pressure side of the membrane.
e five mass balances plus the irreversible sulfur reaction lead to a system of ordinary differential equations (ODEs) on the fractional surface coverage values of hydrogen, θ H 2,1 and θ H 2,2 , the values of the H/Pd ratio in the bulk metal (X s,1 and X s,2 ), and sulfur coverage on the high-pressure side of the membrane (θ adS ): e calculation of the transport parameters appearing in equations ( 21)-( 26) is not a trivial matter because data for adsorption-desorption of H 2 S on metallic surfaces are lacking.e same problem has been found with respect to the kinetic parameters of the surface reaction.is issue will be addressed below.

Calculation of Parameter Values.
e goal of the project is to accurately model the poisoning mechanism; therefore, the two kinetic parameters, k ads and k rs , have to be estimated.
e work of Morreale et al. [11] reports experimental data that can be used for this task.Unfortunately, close examination of this work shows growth in depth of the Pd 4 S scale.
is multilayer process is incompatible with the model based on surface phenomena we have proposed here.Some of Morreale et al. observations show that the multilayer growth of the Pd 4 S scale is controlled by diffusion of Pd atoms through the surface of the scale.ese observations do not explain either the process of partial recovery of membrane functionality, when the input sulfur stream is removed or predict accurately hydrogen permeation rates [11].erefore, we proposed to study Morreale et al. experimental data at short times when the thickness of the scale is small.Using the assumption of constant hydrogen adsorption at short times, we can represent the process using only ( 1) and ( 2).In this case, sulfur adsorption is represented by the following differential equations: We ran several simulations to obtain the parameters of the model described by equations ( 26) and ( 27). e kinetic parameters k adS and k RS are determined by an error minimization procedure.In Table 1, we show the results of this procedure.e values of k adS were taken from experimental results reported by Pomerantz [52]. is author stated that the amount of sulfur increased with decreasing temperature.Sulfur adsorption is an exothermic reaction, and higher temperatures would cause less sulfur to adsorb [54].A similar trend was seen with bulk Pd sulfides in previous works [37,48], indicating that bulk sulfides would only form at lower temperatures.Indeed, at 623 K, the S/Pd atomic ratio was close to 0.25, which corresponds to the atomic ratio of Pd 4 S.At 673, 723, and 773 K, only surface sulfides formed from the dissociative chemisorption of H 2 S [51].e last statement is contradicted by the work of Morreale et al. [11], who reported high-scale thickness for temperatures in the range 623-908 K.
We also proposed the following equation for calculation of the poisoning reaction activation energy (E rs ) using the values of k rs appearing in Table 1: e calculated results are shown In Figure 5. e aforementioned process yields the following values: k rso � 3.95•10 −3 •s −1 and E rs � 18.46 kJ/mol.
We tested the values of these parameters using a computer code developed to implement our model.Some results are shown in Figure 6, where the fractions of adsorbed and reacted sulfur are plotted versus time.It can be seen that the amount of adsorbed sulfur decreases as time increases.e converse is true for the reacted sulfur fraction.is is the expected result as the irreversible surface reaction decreases the adsorbed sulfur ratio and increases the surface fraction covered by the Pd 4 S scale.Morreale et al. [11] reported that the presence of the scale significantly reduces the hydrogen flow through the membrane.
e authors' experimental results showed a reduction of more than 90% of the original value.
We can conclude that the calculated values used in conjunction with our developed model qualitatively predict the expected transient behavior in membrane processes.

Numerical Solution.
e system of ordinary differential equations (ODEs) ( 21)-( 26) was solved using a Runge-Kutta implicit 5 th order routine [55,56] with variable integration step.In this work, we used the Fortran solver RADAU5 downloaded from [57]. is program solves the initial value problem for stiff or non-stiff systems of ordinary differential equations (ODE) of the form: where, p is a vector of constant parameters and y is the vector of dependent variables to be determined.e computer code was validated by comparing calculated results for hydrogen flow without the presence of sulfur against reported values by Ward and Dao [36].e results are presented in the section below.

Results and Discussion
Table 2 lists the values of the parameters used in the numerical calculations.e hydrogen transport parameters, k d , β d , ] d , and D, have been taken from the literature [36] or estimated by the authors using the following: e hydrogen diffusivity through Pd has been estimated from the values reported by Ward and Dao [36].e driving force used in this work is the difference between H/Pd volumetric density inside a thin layer close to both surfaces.
To validate our results, we run our computer code without sulfur in the input stream.Under this condition, our results should be similar to the ones predicted by Ward and Dao [36]. is comparison is shown in Figure 7.We can see that very similar results are obtained for the data calculated for both temperatures using our computer code and Ward We ran simulations at two different temperatures: 643 K and 943 K. e low temperature value is located within the surface transport control parameter area, while the higher temperature value is located within the diffusion control regime.
In Table 3, the range of standard values used in calculating simulation results are shown.
In Figure 8, we plot typical variations of the adsorbed hydrogen, adsorbed S, and irreversible Pd 4 S fractions on the high-pressure side of the membrane at 643 K. Figure 8 shows that, at short times, hydrogen and S atoms compete for adsorption on the membrane surface.S atoms initially adsorbed faster due to the higher value of the adsorption constant (k ds ); however, S atoms also compete with the irreversible reaction that leads to Pd 4 S formation.erefore, the adsorbed sulfur fraction decreases as time increases, while the reacted fraction of the Pd surface increases continuously.We can also observe in Figure 8 that the surface hydrogen coverage is about 44% of the total surface instead of 97% when there is no S present in the high-pressure stream.
Typical results for the effect of withdrawing the contaminant from the input stream after a given period of time (T � 643 K) are shown in Figure 9.We can see in Figure 9 that the effect of removing the contaminant from the feed is to significantly increase the hydrogen surface fraction and reduce the S adsorbed fraction; however, the palladium sulfide surface fraction remains constant.is effect recovers more than 90% of the membrane functionality before sulfur contamination.e surface fraction that is free for hydrogen adsorption increases very fast after removing the S contaminant because the adsorbed sulfur atoms not only preclude surface adsorption on the Pd sites they occupy but also repel hydrogen adsorption in three contiguous sites.e results presented in Figure 9 prove that the membrane function recovery is produced mostly because adsorbed sulfur atoms are removed from the high-pressure side of the membrane.
e hydrogen-absorbed fraction on the lowpressure side remains practically constant.
Ward and Dao [36] reported that, at low temperatures (643 K), the flux through the membrane is controlled by the value of the adsorbed hydrogen fraction on both sides of the membrane.e results presented in this work confirm that the adsorbed hydrogen concentration determines the flux through the membrane.We can see typical results for the variation of flux with time in Figure 10.
e results presented in Figure 10 show that, in the presence of H 2 S, the hydrogen flux increases up to a fraction of the value without contaminant (∼24%) in a short period of time and remains constant until the contaminant in the feed is removed (1300 s). e introduction of the pure hydrogen feed immediately increases the hydrogen flux until a constant value, that is, 90% of the initial hydrogen flux value, is reached.
Typical results for high temperature (943 K) are shown in Figure 11.
e time evolution of the different components adsorbed fractions is similar to the previous case; however, in this case, the hydrogen flux value is determined by the diffusion flux and not by the values of the adsorbed species fractions.e results shown in Figure 12 prove that the process at 943 K is controlled by the diffusion step.In this case, the flux is calculated using the following equation: Equation (31) shows that the flux is directly proportional to the difference in hydrogen volumetric concentration at both sides of the membrane and inversely proportional to the membrane thickness.
A way to confirm this behavior is to calculate the flux through the membrane thickness for several membrane thickness values.In the diffusion limited regime, the flux should increase as the membrane thickness decreases.In Figure 12, we show results for two different membrane thickness values.e results presented in Figure 12 confirm that the transport process is diffusion controlled.
Figure 13 shows the hydrogen volumetric fraction values used to calculate the hydrogen flux through the membrane in Figure 12 for L � 1e − 3 m.We can see that, at short times, the hydrogen volumetric fraction increases until becoming constant at longer times.e value of the flux is proportional to the difference in hydrogen volumetric ratios on both sides of the membrane.e model presented in this work is based upon the strong interaction between hydrogen transport and surface coverage and structure.Caution should be used, however, because the real mechanism is very complex and includes, for example, di usion through the scale as reported by Iyoha et al. [37].e lack of precise data to calculate the transport and reaction parameters is also a problem.e values of the model parameters used in the calculations were based upon pure Pd membranes [11,36,52]; however, the model can be applied to homogeneous Pd alloys with similar crystal structure using modi ed values of the model parameters.Modi cations should be introduced in the proposed model if signi cant segregation of the alloy components is present on the surface [12] e assumption of surface segregation occurring only a monolayer deep has been used successfully for experimental determinations of segregation in Pd-Cu and Pd-Au alloys [58].However, there is a lack of experimental data to determine the extent of atomic segregation on the Pd surface.

Conclusions
e model proposed in this work describes qualitatively well the transport process under di erent operating conditions.Competitive adsorption between H 2 S and H 2 and surface reaction on the membrane surface are accounted for.A porous scale that only blocks part of the membrane surface is assumed.
e model provides useful insights into the transport mechanism through calculation of the change in coverage of the relevant chemical species.

International Journal of Chemical Engineering
Modeling results from simulations without sulfur contamination are similar to equivalent ones calculated using Ward and Dao's model [36].e hydrogen flux is strongly related to hydrogen coverage of the high-pressure side of the membrane at low temperatures.Increase in sulfur coverage produces a decrease in hydrogen coverage of the membrane surface.Under diffusion control conditions, at higher temperatures, the hydrogen flux depends upon the hydrogen coverage on both sides of the membrane.e rate of the sulfidation reaction seems to be higher than the net rate of S adsorption; therefore, the Pd sulfide growth reduces irreversibly the S coverage on the surface.Bulk concentration of Pd atoms (Pd atom g/m 3 ) N s :

Nomenclature
Surface concentration of Pd atoms (Pd atom g/m 2 ) P i : Pressure value in the bulk of the gas phase on the high-or low-pressure side of the membrane (Pa) R g : Ideal gas constant (J mol −1 •K −1 ) T: Temperature (K) X s,i : H/Pd volumetric ratio in the bulk metal adjacent to the i surface (dimensionless)

Data Availability
All data used in the preparation of the manuscript are stored in Excel worksheets, and they can be made available upon request as necessary.
triangles, and disordered S structures.e adsorption site of the S atom was the (√3 × √3) R 30 °threefold site as mentioned previously.Both the S and the Pd metallic structures are fcc close-packed; however, the Pd unit cells are rotated 30 °, as shown in Figure 2(b).

Figure 1 :
Figure 1: (a) Sulfur adsorption on fcc surfaces; (b) sulfur adsorption on a p(2 × 2) surface.Pd atoms are depicted in grey and S atoms in white.

Figure 2 :
Figure 2: Model of the (√3 × √3) R 30 °structure: (a) high coverage structure; (b) 30 °angle between S and Pd unit cells main directions.Yellow and blue circles represent sulfur and palladium atoms, respectively.

2 Figure
Figure Schematic of the poisoning model.

Figure 9 :Figure 10 :Figure 11 :
Figure 9: Time evolution of adsorbed species before and after switching feeds with and without S contamination.

Figure 13 :Figure 12 :
Figure 13: Time evolution of the volumetric H/Pd ratios on both sides of the membrane.

Table 1 :
Summary of calculated hydrogen sulfide parameter values.

Table 2 :
Summary of hydrogen transport parameter values used in model calculations.

Table 3 :
Standard operating data used in the simulations.