Fuel Reformation and Hydrogen Generation with Direct Droplet

ARTICLE pubs.acs.org/IECR

Fuel Reformation and Hydrogen Generation with Direct Droplet Impingement Reactors: Model Formulation and Validation Mark J. Varady and Andrei G. Fedorov* Multiscale Integrated Thermofluidics Research Laboratory, GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, United States

bS Supporting Information ABSTRACT: Onboard fuel reforming to produce hydrogen for portable fuel cell applications has been widely studied because the liquid has a high volumetric density as an energy storage medium. Several portable fuel reforming devices presented in the literature attempt to scale down the designs of traditional large-scale unit operations, an approach that becomes suboptimal as the size of the application is reduced. Unique reactor designs in which the various unit operations are combined in a synergistic manner are required to achieve higher energy densities and more compact reactors. Spraying a finely atomized liquid directly onto a hot catalyst is one such method that has been experimentally demonstrated. This work focuses on developing a fundamental understanding of this approach and optimizing it by utilizing a droplet generator array with precise control over the droplet spacing, diameter, velocity, and trajectory, thus providing ultimate control over the reactor performance. The regular nature of the droplet generator array also enables modeling on a reactor-unit-cell basis with minimal empiricism, which can be used to optimize the reactor performance. The steady-state unit-cell model developed in this work accounts for the transport and evaporation of the droplet stream, impingement and subsequent film accumulation and vaporization, and gas-phase transport and reaction. The key components of the model were validated using relevant results from the literature to establish confidence in applying the complete model to predict reactor performance. Further, a reactor prototype mimicking the reactor unit cell used in the simulations was constructed and used to experimentally validate the comprehensive transportreaction model for the specific case of methanol steam reforming. In a companion article, this complete model was used to study the effects of reactor operating parameters on conversion, selectivity, and power density, aiming at an optimal reactor design.

’ INTRODUCTION Hydrogen fuel cells have been proposed as a promising, highefficiency energy conversion technology for portable applications.1 However, because even highly compressed hydrogen exhibits a low volumetric energy density2 and because compressed hydrogen presents potential safety issues, this method becomes less feasible as the scale of the device decreases. To address this problem, the hydrogen can be stored as a high-energy-density liquid hydrocarbon fuel and converted into hydrogen onboard as demanded by the fuel cell. Development of such portable fuel reformers has been widely studied over the past decade, particularly for battery replacement, as power demands on electronic devices have increased for military3,4 and consumer5,6 electronics applications, and has also been proposed to power automobiles.7 The basic design of a fuel reformer is shown schematically in Figure 1, in which the fuel is pumped from the storage tank, vaporized, mixed with any other gaseous reagents, and converted to hydrogen over a fixed catalyst bed. Options are also available for separating the hydrogen through a selectively permeable membrane8 or removing the CO using a preferential oxidation reactor stage.9 In large-scale applications, the approach taken is to accomplish each of these functions in a dedicated component individually optimized for efficiency, which is also called the unit-operations design approach. However, Mitsos et al.10 argued that power/energy density is the more critical design goal and that this often conflicts with the efficiency maximization achieved by the unit-operation reactors. This discrepancy calls for a search for alternative reactor r 2011 American Chemical Society

configurations in which judicious integration of the various components is utilized to maximize power or energy density. One fruitful approach is multifunctional reactor design in which two or more unit operations are combined in a single component, possibly enhancing performance and reducing size.

’ DEVICE CONCEPT A promising concept of an ultracompact reactor for hydrogen generation from liquid fuels is one that takes advantage of directly spraying a finely atomized liquid onto a fixed heated catalyst bed where the droplets vaporize and react. Deluga et al.11 and Salge et al.12 described such a reactor utilizing an automotive fuel injector to atomize ethanol, soy oil, and glucose/water solutions, which were sprayed onto a heated RhCe catalyst on an Al2O3 support, generating hydrogen by partial oxidation and autothermal reforming. This design offers some distinct advantages over the more commonly studied microchannel reactor configurations for portable fuel reforming. Two-phase flow in the vaporizer section of microchannel reactors results in extremely high pressure drops and corresponding demands on pumping power, as well as large temporal variations in flow rate due to the formation of stabilized vapor slugs in the microchannels.13 Received: March 20, 2011 Accepted: May 26, 2011 Revised: May 19, 2011 Published: May 26, 2011 9502

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Industrial & Engineering Chemistry Research

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Figure 1. Schematic of the unit operations of a fuel reforming plant for generating hydrogen from a liquid hydrocarbon fuel in which each function is carried out in a separate dedicated component.

Figure 3. Schematic of the DDIR unit cell used for model development showing geometric parameters, different zones of the unit-cell domain, droplet transit to the catalyst and corresponding variables, and possible film growth at the catalyst interface. Figure 2. Schematic of the direct droplet impingement reactor (DDIR) showing the regular spacing of the droplet array and the uniform frequency of droplet generation. Additionally, the breakdown of the DDIR into additive unit cells is shown, as a route to system scaleup.

Spraying the liquid directly onto the catalyst does not confine the vapor, avoiding these problems. However, the variations in droplet size, velocity, and impingement location and angle cause some unpredictability in reactor performance and, moreover, complicate the formulation of a rational mathematical model that would be required to carry out reactor design and optimization studies. This work focuses on eliminating these uncertainties in the droplet delivery method by using a regularly spaced array of droplet generators, each of which periodically releases a single droplet of controlled diameter and velocity. A piezoelectrically actuated ultrasonic droplet generator developed by our laboratory has been shown to achieve these goals.1416 This reactor design could also use any other droplet generation method that results in equivalent control of reagent delivery. A schematic of the basic embodiment of this reactor design is shown in Figure 2, and this design is called a direct droplet impingement reactor (DDIR) from this point forward.17 This is a simple layered reactor design consisting of a droplet generator array and a catalyst layer separated by a space in which droplets travel while being heated and partially vaporized. The key idea is that the DDIR can be conceptualized as an array of identical unit cells, each of which contributes equally to the reactor output. Scalability to a desired reagent throughput is achieved by utilizing the requisite number of preoptimized unit cells depending on the overall throughput demanded by the specific application. Furthermore, model development is reduced

to the case of a single unit cell, simplifying the design procedure considerably. This model predicts the influence of critical reactor operating parameters such as droplet size, velocity, and spacing; catalyst bed size; and heat input and spatial distribution, as substantiated below, and can be used to optimize the reactor design and operation using unit-cell simulations.

’ MODEL FORMULATION The model considers the coupled processes of droplet transport and evaporation, impingement of the droplets on the catalyst surface and liquid film growth, and vapor-phase transport and reaction in a single unit cell of the DDIR. The schematic of the unit cell in Figure 3 defines the geometric and droplet parameters, as referenced throughout the model formulation. The unit cell is approximated as a two-dimensional axisymmetric domain of constant radius, Rcell, and is divided into a droplet transit zone (0 e z e Hcell) and a catalyst zone (Hcell e z e Hcell þ Hcat) with the possibility of liquid film formation, which is described in more detail below. In reality, each unit cell has a rectangular cross section, but approximating it as circular reduces the dimensionality of the problem, thereby increasing computational efficiency and enabling a detailed parametric study while still capturing the underlying physics of the problem. Droplet Transport Model. Droplets of radius Rd,0 are released at the position z = 0 at velocity Vd,0 and temperature Td,0 with a frequency f. The trajectory of a single droplet is tracked with the following set of first-order ordinary differential equations, assuming that the droplet remains along the center line of the unit cell, that the droplet remains spherical, and that the droplet temperature is spatially uniform, a simplification that is met in the limit of 9503

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low-Biot-number transport

md

dZd ¼ Vd dt

ð1Þ

dVd Dp ¼ 6πf1 μg Rd ðVd uÞ ð2Rd ÞπRd 2 Dz dt

ð2Þ

dmd ¼ m_ ev;d dt

ð3Þ

md cp;l

dTd ¼ f2 hð4πRd 2 ÞðTg Td Þ þ dt

∑i m_ ev;d, i hfg, i

ð4Þ

Here, md = 4/3πFlRd3 is the droplet mass; m_ ev,d is the rate of evaporation from the droplet; and m_ ev,d,i and hfg,i are the evaporation rate and heat of vaporization, respectively, of species i in the binary droplet. Correction factors f1 and f2 account for departure from Stokes flow and flow normal to the droplet surface during evaporation, respectively, and are available from Miller and Bellan.18 This closely follows the analysis presented by Varanasi et al.19 for tracking a binary droplet with evaporation. Of most importance is the dependence of the droplet transport equations on the surrounding gas-phase conditions through the local axial gas velocity, u; gas pressure gradient, ∂p/∂z; convective heat-transfer coefficient, h; and gas temperature, Tg. A modified D2 law incorporating convective effects is used to evaluate m_ ev,d, which also depends on the surrounding gas-phase conditions. Either mass-transfer- or heat-transfer-controlled evaporation is possible. The mass-transfer-limited case is given by ! 1 yf, ¥ m_ ev;d ¼ 2πRd Fg Dg Shd ln ð5Þ 1 yf ;s where Dg is the average mass diffusion coefficient and yf,¥ and yf,s are the mass fractions of fuel at the surface and far from the droplet in the surrounding gas phase, respectively. The heattransfer-limited case is given by " # kg cp;g ðTg Td Þ Nud ln þ1 ð6Þ m_ ev;d ¼ 2πRd cp;g hfg In both cases, the dimensionless mass- and heat-transfer coefficients are estimated from the correlations of Ranz and Marshall,20 Shd = 2 þ 0.552Red1/2Scg1/3 and Nud = 2 þ 0.552Red1/2Prg1/3. The rate of evaporation for each species in the droplet depends on the relative rate of liquid diffusion as described by Sirignano.21 When liquid diffusion is slow compared to droplet evaporation, the species evaporate in proportion to their initial composition throughout the droplet lifetime, because the composition in the bulk of the droplet remains unchanged. If liquid diffusion is relatively fast, then m_ ev,d,i changes throughout the droplet lifetime and is given by yi, s ð7Þ m_ ev;d, i ¼ m_ ev;d yj, s

∑j

The surface mole fraction (and thus the mass fraction) of each species is calculated by using the ClausiusClapeyron equation to find the mole fraction if the droplet consisted of a single

species, χ*i,s, and then using Raoult’s law to find the mole fraction * . Nonideal of the species in the vapor mixture χi,s = γiχi,lχi,s solution effects are considered by using the activity coefficient of the species, γi.22 Gas-Phase Conservation Equations. Steady-state solutions of the species concentration, temperature, and velocity fields in the gas phase are desired for a certain set of operating conditions, requiring the solution of the following conservation equations in each domain. In reality, these are time-averaged equations, as the process is naturally transient because of the periodic nature of droplet introduction into the reactor. The applicability of the time-averaged equations presented below is limited to the case when the relaxation times for the various transport processes are greater than the process time scale defined by the frequency, f, of droplet introduction. r 3 ðvCi Þ ¼ r 3 ðDe, i rCi Þ þ Si ðz, rÞ

ð8Þ

r 3 ðFcp vTÞ ¼ r 3 ðke rTÞ þ Sh ðz, rÞ

ð9Þ

μg v 3 rðFg vÞ ¼ ε rp þ v þ r 3 ðμg rvÞ þ Sm ðz, rÞ K

ð10Þ

Here, the velocity, v, is the vector sum of axial, u, and radial, w, components, and it must be remembered that r is the gradient operator in the two-dimensional cylindrical coordinate system. For eq 8 De,i represents the effective diffusion coefficient of species i in the gaseous mixture, which is assumed to be given by the multicomponent mixture rule23 De, i ¼

1 χi χj =Dij

∑ j6¼ i

ð11Þ

where Dij is the binary diffusion coefficient of dilute species i in j, which is obtained from the relation of Chapman and Enskog.23 Further, the effective diffusion coefficient in eq 11 is multiplied by the factor ε/τ in the porous catalyst zone, where τ is the tortuosity. The species source term Si(z,r) arises from droplet evaporation in the droplet transit zone and from reaction in the catalyst zone, where it has been assumed that, at steady state, each successive droplet undergoes the exact same trajectory; integrates the effects of all droplets traveling through a given point per unit time; and assumes that the droplet radius is small compared to the radial extent of the unit cell. These basic assumptions are used in deriving the source terms due to droplets for heat and momentum, as well. Details of the derivation are provided in the Supporting Information, as well as in ref 8 m_ ev;d, i ðzÞf δðrÞ > > > < MW i Vd ðzÞ 2πr 0 e z < Hcell Si ðz, rÞ ¼ Nrxn > > νik R k Hcell e z e Hcell þ Hcat > :

∑

k¼1

ð12Þ Here, MWi is the molecular weight of species i and νik is the stoichiometric coefficient of species i in reaction k, which proceeds at a rate Rk. In eq 9, the effective thermal conductivity, ke, in the droplet transit zone is simply that of the gas-phase mixture, whereas in the catalyst zone, it is the geometric mean of the thermal conductivities of the catalyst, ks, and gas, kg: ke = ks1εkgε.25 This also assumes local thermal equilibrium between the catalyst and the gas, allowing a single energy conservation equation to be used in the 9504



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Figure 4. Geometric idealization of the accumulating liquid film, showing the division of the liquid film domain along the catalyst interface. Inside the catalyst layer, the film takes a cylindrical shape defined by a sharp boundary with z = Hcell þ hf,c and r = Rf. Outside the catalyst layer, the film assumes the form of a spherical cap.

catalyst zone. Droplet vaporization tends to cool the surrounding medium in the droplet transit zone, whereas in the catalyst zone, heat consumption or release with enthalpy change ΔHi due to chemical reaction contributes to the heat sink or source term. 8 qc ðzÞf δðrÞ > > > < Vd ðzÞ 2πr 0 e z < Hcell Sh ðz, rÞ ¼ Nrxn > > > Hcell e z e Hcell þ Hcat : ΔHi R i

∑

i¼1

ð13Þ In eq 10, the factor K is the permeability of the porous catalyst and is calculated using the CarmanKozeny equation.25 In the droplet transit zone, ε = 1 and K = ¥, so that the Darcy friction term disappears here. In the catalyst zone, the Darcy friction term balances the pressure gradient term, as expected. Further, there are no explicit momentum source terms in the catalyst zone, although reactions resulting from a changing number of moles have an indirect influence on velocity through the continuity equation. The momentum source term in eq 10 arises from viscous drag from the droplets traveling in the axial direction in addition to vapor generation at the droplet surface. 6πμg f1 Rd ðVd uÞf δðrÞ 2πr δðrÞ Vd 2πr m_ f Sm, r ðz, rÞ ¼ 16Fev;d R d 2 Vd

Sm, z ðz, rÞ ¼

ð14Þ

g

if Rcell were made larger than the length scales for disturbance for each of the transport equations in the gas phase, defined as follows Lspecies

pffiffiffiffiffiffiffiffi Dg τ ,

Lheat

pffiffiffiffiffiffiffi Rg τ ,

Lmom

pffiffiffiffiffiffiffi νg τ

ð16Þ

The characteristic time scale, τ, is defined as the transit time of the droplet from the ejection point to the impingement point, τ ≈ Hcell/Vd,0. There is also the possibility of supplying external heat along the boundary of the unit cell (e.g., by an electric heater) DT ke Dr

¼ q00w ðzÞ

ð17Þ

r ¼ Rcell

At the boundary of the droplet generator (z = 0), an adiabatic impermeable boundary is assumed DCi uð0, rÞ ¼ wð0, rÞ ¼ Dz

z¼0

DT ¼ Dz

¼0

ð18Þ

z¼0

At the reactor outlet, the pressure is specified as pout, a heat-fluxmatching boundary condition is enforced where convective heat transfer to ambient at Tout occurs with heat-transfer coefficient h, and the molar flux is unchanging (weak boundary condition) pðHcell þ Hcat , rÞ ¼ pout

The gas-phase conservation equations are subject to boundary conditions. First, along the axis of the unit cell and at its boundary, symmetry conditions are enforced

ð15Þ

DT h½TðHcell þ Hcat , rÞ Tout ¼ ke Dz z ¼ Hcell þ Hcat DðuCi Þ ¼0 ð19Þ Dz

These conditions are satisfied when the unit cell under consideration is surrounded by exactly identical unit cells (i.e., a large number of unit cells constitute the overall reactor). It should be noted that the case of a single droplet stream could also be studied

Film Accumulation Model. At the interface of the catalyst zone, accumulation of a liquid film is possible when a droplet does not completely vaporize upon impact before arrival of the next droplet. Additionally, the accumulated liquid can

wðz, 0Þ ¼ wðz, Rcell Þ Du DCi ¼ ¼ Dr Dr r ¼ 0, Rcell

r ¼ 0, Rcell

Dp ¼ Dr

¼0

z ¼ Hcell þ Hcat

r¼0

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penetrate the catalyst layer through capillary forces if the surface is wetting. Eventually a steady state is achieved in which the film boundary remains stationary and the vaporization rate from the liquid film matches the rate at which droplets arrive at the catalyst interface. (If the vaporization rate is sufficiently low, then flooding occurs where the liquid film completely covers the catalyst surface and quenches the reaction. The other extreme is flash evaporation upon droplet impingement.) Vaporization from the film interface results in additional sources for species, heat, and momentum. The geometric idealization of the film is depicted in Figure 4, where the portion of the film above the catalyst interface is a hemispherical cap with thickness hf,g, and the depth of penetration, hf,c, is constant along the radial extent of the film, Rf, such that the shape of the penetrated liquid is a cylinder. The outer boundaries of the portions of the film imbibed in the catalyst bed and supported above it are given by Γf,c and Γf,g, respectively. Energy conservation in the accumulated liquid film at steady state satisfies 0

DT 0 ¼ @ ke Dn Γf Z

int

!

∑i

m00ev;f , i hfg, i

dA þ q00i πRf 2

ð20Þ

where the heat input by conduction/convection from the surroundings and heat generated by an embedded heater at the catalyst interface, q00i , completely go into vaporization of the liquid. This assumes that, at steady state, the liquid temperature is spatially uniform at its saturation point. Mass and momentum conservation in the liquid are also satisfied and are written in integral form. This approach does not allow for all of the local details of the film interface to be resolved, but it is able to approximately predict the lateral extent and penetration depth of the liquid film, as demonstrated in the section Validation of Model Components with Literature Results. The liquid film domain is split along the catalyst interface, and separate mass conservation equations are written for each subset of the domain. For the liquid domain subset outside the catalyst, the equation is Fl

d"f ;g 4 ¼ πFl Rd 3 f 3 dt

Z

∑ m00ev;f, i dA m_ p

Γf ;g i

ð21Þ

dhf ;c þ dt

Z

Rf

2πr 0

∑i m00ev;f , i dr ð1 RÞm_ p ¼ 0

ε2πRf hf ;c Fl

dRf þ dt

Z

ð22Þ

Hcell þ hf ;c

2πRf Hcell

∑i m00ev;f , i dz Rm_ p ¼ 0

ð23Þ

Here, the factor R is the fraction of the penetrated liquid that contributes to increasing the film radius. Although the steadystate solution is desired where the film is stationary, the transient forms of the mass conservation equations enable an iterative solution to minimize the interface velocities, thereby approximating the location of the liquid film boundaries, which is elaborated in the Model Implementation section. The steady-state momentum equations in integral form are similarly split into radial and axial components, where the only forces on the liquid film are capillary suction and Darcy friction, which balance with the rate of momentum leaving the film interface due to vaporization Z Z Rf 1 Rf μ ð1 RÞm_ p 2πr m00ev;f , i 2 dr ¼ 2πrPc ε dr hf ;c Fg 0 K Fl 0 i

∑

ð24Þ 1 Fg

Z

Hcell þ hf ;c

2πRf Hcell

∑i

m00ev;f , i 2

Z dz ¼

Hcell þ hf ;c

2πRf Pc ε dz

Hcell

μ Rm_ p Rf K 2Fl

ð25Þ

To close the model, conditions at the film interface for the gasphase species and momentum must be specified (thermal conditions are specified in eq 20) Ci ¼ CT χi, s ,

where "f,g is the volume of this liquid domain subset; m 00ev,f,i is the local evaporation rate of species i along the subset boundary, Γf,g; and m_ p is the capillary penetration rate of the liquid. Also, the time-averaged rate of droplet delivery is m_ p = 4/3 πFlRd 3f. Mass conservation for the film domain subset on the catalyst side takes a similar form, but instead, the imbibed liquid volume is written as "f,c = ε2πRfhf,c and split into two equations such that the film interface velocities, dhf,c/dt and dRf/dt, appear explicitly επRf 2 Fl

Figure 5. Meshed two-dimensional axisymmetric DDIR unit-cell domain obtained using Gambit v. 2.2.30 and triangular elements. The mesh was graded so that the cell density was highest around the film interface and droplet transit axis to resolve high gradients in these regions.

vn ¼

1 Fg

∑i m00ev;f , i ,

ðz, rÞ ∈ Γf ;g ∪ Γf ;c

vt ¼ 0 ð26Þ

Here, the species mole fraction at the interface of the film, χi,s, is calculated in an identical manner to that described above for the surface of a droplet; CT is the total molar concentration of the gas phase; and vn and vt are the normal and tangential components, respectively, of the gas-phase velocity.

’ MODEL IMPLEMENTATION The domain of the unit cell was meshed in the geometry and mesh-generation software Gambit v.2.2.30 using triangular elements where the mesh density was greatest around the film interface and axis, as shown in Figure 5, because the temperature and concentration gradients are highest in these regions. 9506



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Figure 6. Flowchart showing the three-level iteration procedure employed to solve for the steady-state conditions of the DDIR for a particular set of operating conditions.

The commercial computational fluid dynamics (CFD) software Fluent v.6.3.26 was used to solve the gas-phase species, energy, and momentum conservation equations using the standard solver packages available with the options set to optimize the solution procedure. Custom code was integrated with the software using the available user-defined-function (UDF) capability to apply a multilevel iterative procedure for determining the droplet trajectory (lowest iteration level), vaporization rate from the film (middle iteration level), and steady-state film dimensions (highest iteration level), as summarized in Figure 6. The droplet trajectory was solved for a given solution of the gas-phase conservation equations using a fourth-order vector RungeKutta method to integrate eqs 14 with surrounding conditions obtained from the current gas-phase solution as predicted by Fluent. This, in turn, provided sources for the gas-phase conservation equations due to droplet heating, drag, and evaporation. These sources were applied in the computational cells adjacent to the unit-cell axis and depended on the droplet conditions at the corresponding point along its trajectory. The gas-phase conservation equations were solved again with these updated source terms, and the procedure was repeated until the solution was globally converged. Sources for the gas-phase conservation equations also arise from vaporization from the accumulated liquid film. These source terms were applied in the computational cells adjacent to the film interface, with the vaporization rate in each cell determined by the net local heat flux at the interface. As an initial guess, the total vaporization rate from the film was set equal to the droplet delivery rate with the sources uniformly distributed over the computational cells adjacent to the interface. At this level of iteration, the gas-phase equations were solved until convergence was achieved, the film interface sources were updated, and the procedure was repeated until the mass flow rate at the reactor outlet no longer changed within a specified tolerance. Once the solution had converged for a given guess of the steady-state film dimensions, the film interface velocities in eqs 22 and 23 were used along with a pseudo-time step to update the film dimensions. A new mesh was created with the updated film dimensions, and the gas-phase solution from the previous iteration for the film dimensions was mapped onto the new mesh to improve the rate of convergence of the solution for

Table 1. Operating Parameters for Grid Sensitivity Study for Methanol Steam Reforming by the DDIR parameter

description

value

Rd,0

initial droplet radius (μm)

10.0

Vd,0

initial droplet velocity (m/s)

5.0

Td,0

initial droplet temperature (K)

300

XM,d,0

initial droplet methanol mole fraction

0.5

q00int

heat flux at the catalyst interface (W/cm2)

1.97

q00w

heat flux at the unit-cell periphery (W/cm2)

0

Rcell Hcell

unit-cell radius (m) 0.004 distance from the droplet generator to the catalyst (m) 0.001

Hcat

length of the catalyst bed (m)

ε

catalyst porosity

0.3

dp

average catalyst particle size (mm)

0.1

ks

catalyst thermal conductivity [W/(m K)]

1.0

0.006

the new mesh. This process was repeated until the interface velocities were vanishingly small within a specified tolerance.

’ VALIDATION OF MODEL COMPONENTS WITH LITERATURE RESULTS Methanol steam reforming was used as a model problem for a grid-dependence study because the work in the companion article33 focuses on optimization of this reaction using the DDIR model developed here. The reaction mechanism consists of the methanol steam reforming reaction CH3 OH þ H2 O T 3H2 þ CO2

0 ΔH298 ¼ 49:5 kJ=mol

ð27Þ and the methanol decomposition and watergas shift reactions account for the minor presence of CO in the product stream, which is important because even concentrations as low as 100 ppm can poison the fuel cell anode26 CH3 OH T 2H2 þ CO 9507

0 ΔH298 ¼ 90 kJ=mol

ð28Þ



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Figure 7. Comparison of evaporating droplet surface area and temperature change for 50% heptane/50% decane mixture as a function of droplet lifetime using the DDIR model and that presented by Varanasi et al.19

H2 O þ CO T H2 þ CO2

0 ΔH298 ¼ 47 kJ=mol

ð29Þ 27,28

was employed The kinetic model developed by Peppley et al. to compute the reaction rates, as it has been shown to be applicable over a wide range of operating conditions. The conditions of the model problem are summarized in Table 1. The results show that at least 10 cells along the film radius or a cell size of 10 μm is required, whichever results in the highest mesh density. The cell size was varied smoothly to 40 μm at the unit-cell boundaries, which was sufficient to capture the variations in gas-phase-dependent variables. In addition, the droplet transit, gas-phase reaction, and film growth/penetration models were validated independently within the framework of the overall solution using appropriate results from the literature. To validate the droplet transit model, the numerical study of the evaporation of a binary droplet carried out by Varanasi et al.19 was used as a basis for comparison. In that study, a 50% molar heptane/decane droplet initially at 350 K evaporated in a quiescent environment of dry nitrogen at 375 K. To emulate this scenario using the general DDIR model, the gas phase in the droplet transit zone was set to match the abovestated conditions, and the source terms coupling the gas phase to the droplet transit were disabled. Also, the droplet was given a sufficiently low velocity that it did not impinge on the catalyst during the droplet lifetime. Comparison of the droplet temperature and normalized surface area for the two models demonstrated good agreement, as shown in Figure 7. Both models predict the rapid evaporation of the more volatile heptane component, resulting in a temperature drop until the wet bulb temperature of the mixture is attained, followed by a more gradual evaporation and temperature recovery once the heptanes are depleted from the droplet. For capillary penetration of a liquid into a wetting porous substrate, the bulk of the literature studies consider the sorption of a volume of liquid initially deposited on the substrate in the absence of evaporation to obtain the transient evolution of the

Figure 8. Comparison of capillary penetration model used in DDIR studies with numerical results of Alleborn and Raszillier29 for imbibition of a liquid film into a thick porous substrate. The liquidgas interface is shown for both methods at three time instances.

film interface (moving-surface problem). This is a significant departure from the DDIR, where a steady stream of droplets is supplied to the substrate with vaporization, resulting in a stationary liquid film (free-surface problem). However, the transient integral mass and momentum conservation equations (eqs 2125) can be used to study the typical moving-surface problem to gain confidence in its applicability to the free-surface problem in the steady-state DDIR. Here, the results of Alleborn and Raszillier29 involving the simultaneous spreading and sorption of a single liquid droplet on a thick porous substrate were considered in which momentum conservation in the liquid layer is a balance between pressure and Darcy friction with a constant capillary pressure acting at the liquid interface. The liquid front was tracked using a modified enthalpy method.30 Initially, the liquid was located completely above the surface and was imbibed into a substrate with a porosity of 0.25, a dimensionless permeability of Pm = 3KRe2/he4 = 105, and a dimensionless capillary suction of Su = PcRe2/σhe = 5 105, where he and Re are the equilibrium height and radius, respectively, of a given volume of liquid on a solid surface with a contact angle θc. Alleborn and Raszillier’s results showed that a dimensionless time of tσhe3/ 3μRe4 = 0.29 is required to imbibe 99% of the liquid volume with the profile of the liquid front presented graphically for intermediate times. For the DDIR capillary penetration model, an initial film radius of 5 mm was assumed, from which all other parameters were calculated using the dimensionless groups defined above and assuming equal initial dimensionless volumes. The location of the liquid interface is compared at three different times for both methods in Figure 8, demonstrating that the DDIR model effectively captures the radial spreading of the liquid as it enters the porous layer. Finally, the conversion of methanol by steam reforming over a porous Cu/ZnO/Al2O3 catalyst carried out by the experiments of Lee et al.31 was used to validate the gas-phase transport and reaction in the DDIR model. The DDIR model parameters of a unit-cell diameter of 0.25 in., packed with 1.0 g of catalyst with a particle size of 0.30.42 mm, for different 9508



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Figure 11. Thermal resistance network for calculating the heat input into the reactor from the applied heat to the electrical heater. Figure 9. Validation of methanol steam reforming reaction kinetics and porous medium model used in the steady-state DDIR model. Simulation conditions correspond to the experiments of Lee et al.,31 which are the basis for comparison.

Figure 10. Schematic of the experimental apparatus used to approximate the behavior of a unit cell of the DDIR, along with the instrumentation used to actuate the devices and collect data.

catalyst temperatures between 433 and 533 K, were used to closely match the experimental conditions. The DDIR model was additionally modified so that the boundary condition at z = 0 was set to a velocity inlet condition consisting of 15% methanol/15% steam/balance nitrogen with a total flow rate of 200 sccm, with no droplet delivery. The comparison of methanol conversion at the reactor outlet as a function of reactor temperature showed good agreement between the DDIR model and the experimental results, as shown in Figure 9. Possible differences are variations in the specific surface area of the catalyst used and in the catalyst formulation used.

’ EXPERIMENTAL VALIDATION OF UNIT-CELL MODEL In an effort to both develop further confidence in the predictive capabilities of the DDIR model and demonstrate the device concept, an experimental apparatus mimicking the conditions of the unit-cell reactor was developed and used to evaluate the reactor performance. Experimental Apparatus. The unit-cell experimental reactor shown in schematic form in Figure 10, was designed to meet the following requirements: • The droplet generator produces a single stream of droplets with a uniform size operating continuously without interruption. Droplet size, flow rate, and delivery frequency can be easily adjusted by a change of atomizer components. • Impingement of droplets on the catalyst surface is clearly visible by an external camera, and resulting images can be recorded on demand. • Two independent heaters are employed (1) at the impingement interface and (2) along the periphery of the reaction chamber to control the film growth and catalyst bed temperature, respectively. • The electrical heater at the impingement interface has sufficient power capacity to prevent flooding of the catalyst with droplets of 40-μm diameter impinging at a frequency of 100 kHz. • Instrumentation is provided to monitor the temperatures at the catalyst interface and reactor outlet, as well as the species composition at the reactor outlet. In this apparatus, droplets are generated by forcing the liquid fuel through the nozzle at elevated pressure and breaking up the resulting jet using an attached ultrasonic actuator. A sinusoidal signal generated by function generator 1 is amplified to power the ultrasonic actuator. Also, the sync signal from function generator 1 is used to trigger a light-emitting diode (LED) powered by function generator 2 such that the period pulse sent to the LED is at most 1/10th of that driving the actuator. This stroboscopic illumination method has been described in detail elsewhere.15 To analyze the composition of the product stream, inert Ar is swept across the reactor outlet and into a Hiden HPR 20 mass spectrometer. The applied voltage to each NiCr heater is independently controlled manually by a Variac plugged into 9509



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Figure 12. (a) Impingement of droplet stream and accumulation of liquid film on stainless steel mesh (25-μm opening) holding a packed bed of catalyst particles (100-μm average particle diameter). Illumination of the interface with a red LED clearly shows the extent of the liquid film. (b) Magnified stroboscopic image of droplets in transit (f = 30 kHz).

the available 120 V ac outlet. Further details of the experimental setup including calibrations and measurement error estimates are provided in the Supporting Information and in ref 24. Estimate of Heat Losses. Proper comparison of the experimental results to the simulations requires a good estimate of the heat losses at the edge of the unit-cell apparatus to incorporate into the model. Heat losses at the edge of the unit cell are by combined natural convection and radiation, which have associated thermal resistances R0c = 1/2πRcellhc and R0r = 1/2πRcellhr, respectively. Here, the natural convective heat transfer coefficient, hc, is given by the correlation of Churchill and Chu,20 and the radiative heat transfer coefficient is approximated by hr = εσ(Ts þ T¥)(Ts2 þ T¥2).20 Ignoring the thermal resistances of the reactor walls, which are much smaller than the air-side resistances, the equivalent resistance network in Figure 11 was used to calculate the local heat flux entering the reactor, q00w, compared to the local heat flux applied by the heater, q00h q00w ¼

0 q00h Req;out ðTs T¥ Þ 0 Req;out

ð30Þ

where, R0eq,out is the effective parallel thermal resistance of the convective and radiative resistances. Variation of Film Size with Applied Heat Flux. Using the unit-cell experimental apparatus, a steady stream of droplets impinged on the catalyst interface, and the variation in the lateral extent of the accumulated liquid film was observed with power applied to the interface heater. For all cases, Rd,0 = 31 μm, f = 30 kHz, and Vd,0 = 5.1 m/s, as depicted in Figure 12b, verifying the regular, well-controlled nature of droplet delivery to the catalyst interface. The error associated with length measurement ((1 pixel) was 1.5 μm at this magnification. For the observed droplet conditions, the Weber number We = FVd2Rd/σ = 43, which is below the splashing threshold (We > 80),32 which was also visually confirmed. A wider view is shown in Figure 12a, clearly demonstrating the growth of a liquid film on the catalyst interface, which is highlighted by illuminating the interface with a red LED. The total heat supplied at the interface was varied between 6 and 20 W, and the image was recorded at each setting. Approximately 5 min was allowed to elapse after the interface heater

Figure 13. Comparison of accumulated liquid film radius observed experimentally with simulation results under identical conditions.

voltage had been changed to ensure that steady state had been achieved. The measurement error for the film size ((1 pixel) was (0.1 mm for each case because the same magnification was used for each image. Simulations were performed for the same range of applied interface heat, and the resulting radial extent of the film was compared with the experimental results, as shown in Figure 13. If the heat input to the reactor were insufficient to completely vaporize the impinging droplet stream, flooding would occur, and this is shown in the hatched region. Decrease in the film size with increasing supplied heat was observed for both the experimental and simulation results, as expected, and the results correspond with exceptional accuracy. Capillary Penetration Depth. If the maximum capillary penetration rate is larger than the droplet delivery rate, then each droplet is completely imbibed into the catalyst layer, and none of the accumulated liquid film protrudes from the catalyst surface. The transition from a completely imbibed liquid film to one that is partially supported above the catalyst interface was observed experimentally by comparing the results for average catalyst particle sizes of 100 and 10 μm. In both cases, a stream of 15-μm droplets was delivered at 1 MHz with 3.6 W applied to the interface heater. In Figure 14a, the film thickness above the catalyst interface is not measurable, although the wetted portion of the interface is clearly visible by the reflected light from the stroboscopic source. With the smaller catalyst particles, the film thickness is clearly not vanishing, as seen in Figure 14b. It is impossible to compute the capillary penetration rate from the visualization results because of its dependence on the penetration depth, which is not optically accessible. For this reason, simulations were carried out under identical conditions to ensure that the relative rates of droplet delivery and capillary penetration were commensurate with the observed experimental results. For both simulations, 15-μm-diameter droplets were delivered at a rate of 1 MHz with an initial velocity of 15 m/s. Also, for both cases, Rcell = 1.5 mm, with a total of Qint = 3.6 W applied uniformly along the catalyst interface. Note that, in the experiments, the overall lateral extent of the reactor is larger because of the encasing material, but the inner diameter is the same as in the simulations. Figure 15 shows the accumulated liquid at the catalyst interface for both (a) the 100-μm particles and (b) the 10-μm particles. In this figure, the heavy vertical line 9510



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Figure 14. Visualization of accumulated liquid film at the catalyst interface with a 3.6-W interface heater power and an impinging stream of 15-μm droplets at 1 MHz: Average catalyst particle diameter = (a) 100 and (b) 10 μm.

Figure 15. Simulation results accompanying visualization of liquid accumulation at the catalyst interface. For both cases, Rd,0 = 7.5 μm, f = 1 MHz, Rcell = 1.5 mm, Qint = 3.6 W, and dp = (a) 100 and (b) 10 μm.

denotes the catalyst interface, with the catalyst bed lying to the left (corresponding to the experimental visualization results). The results show that the liquid penetrates deeper into the catalyst layer but does not spread as much for the larger catalyst particles. Also, more liquid is supported above the catalyst interface for the smaller catalyst particles. These results qualitatively agree with the experimental results presented above, but there is some disagreement between the experimental and simulation results, with each case displaying an approximately 40% difference between the observed and simulated film sizes.

However, it should also be noted that the ratios of the observed to the simulated film radius are approximately the same, with values of 0.63 for the 100-μm particles and 0.65 for the 10-μm particles. One possible reason for the numerical discrepancy is overestimation of the heat losses used in the simulations, which would cause the size of the accumulated liquid film to be greater than expected. Another feature observed in the simulation results is a factor of 100 increase in gas-phase pressure at the catalyst interface with the factor of 10 decrease in the catalyst particle size, due to the 9511



Figure 16. Transient response of hydrogen output from the DDIR unitcell experimental apparatus after activation of the atomizer. The interface heater supplied 2 W under dry conditions and increased to 4 W after activation of the atomizer.

Figure 17. Comparison of experimental and model results for the hydrogen generation rate from a stream of 27.5-μm droplets delivered at a frequency of 100 kHz impinging on a catalyst bed of 150 mg with applied interface heat varying between 1.5 and 11 W.

increased Darcy friction. In the experiments, this pressure increase was not realized because the space between the atomizer and catalyst was not enclosed. Hydrogen Production Rate. Here, the methanol steam reforming reaction was carried out at varying heater power input to observe the transition from flooding to stable film formation while monitoring the product composition with the mass spectrometer. Argon was introduced at the reactor inlet at a rate of 250 sccm, as well as being swept across the reactor outlet at the same rate. The average catalyst particle size used was 100 μm, and catalyst was filled to a height of 15 mm in the inner tube of the reactor, with the remainder of the tube filled with inert alumina particles of approximately the same average size. Droplets with a diameter of 56 μm were introduced into the reactor at a rate of 24 kHz, with approximately 10 mm of space separating the surface of the droplet generator and the catalyst interface. The voltage of the periphery heater was kept constant throughout the entire test at 50 Vrms, whereas the interface heater voltage was varied between 3.5 and 10 Vrms. At each interface heater voltage setting, a dwell time of at least 10 min was used to allow the catalyst bed temperature and species composition to reach steady

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state. The transient response of the hydrogen partial pressure read at the mass spectrometer shown in Figure 16 justified waiting 10 min before taking measurements. When droplet impingement commenced, the catalyst surface was hot, so the conversion was high, and the interface cooled quickly as the liquid film accumulated at the catalyst interface. The heater was adjusted manually from its low baseline value after impingement occurred, at which point the hydrogen flux partially recovered and approached its steady-state value. This manual adjustment was necessary because supplying the interface heat rate necessary to achieve a steady-state film would cause burnout under dry conditions. Once steady impingement occurred, the change in heater input required less time to adjust to steady state. The steady-state results for these experiments are shown in Figure 17 in the form of hydrogen flow rates and are compared with model results. The simulation results roughly follow the observed experimental results for applied interface heat above 5 W. However, the simulations slightly overpredict the hydrogen generation rate at higher applied interface heat, even with an artificially high value of 25 W/(m2 K) used for the convective heat transfer coefficient compared to the baseline value of 15 W/(m2 K) calculated from the experimental conditions. There are a few plausible explanations for this: (1) The heat losses in the simulations might be underpredicted, (2) hotspots in the catalyst bed in the vicinity of the interface heater might cause local catalyst deactivation and reduced conversion in the experiments, and (3) the specific surface area of the catalyst used in the experiments might be lower than the manufacturer reported value used in the simulations. Given of all these possible sources of error, the results are in satisfactory agreement. Most interesting are the experimental results observed below an applied interface heat of 5 W. Below this point, the simulations predict flooding of the catalyst interface and no hydrogen production. However, the simulations do not account for axial heat transfer from the periphery heater to the interface, so that the actual heat supplied to the interface is higher than that in the simulations. Because the power supplied to the periphery heater is constant throughout all experiments, the hydrogen production rate approaches a constant value at low values of applied interface heat. This is estimated by the isothermal catalyst condition at 505 K, also shown in Figure 17.

’ CONCLUSIONS A novel reactor concept, the direct droplet impingement reactor (DDIR), for converting liquid fuels through vaporization of droplets and subsequent chemical conversion on a fixed catalyst bed has been introduced, as an extension of the reactive flash volatilization technique pioneered by Schmidt’s group at the University of Minnesota. The DDIR reactor design provides significant advantages by offering unparalleled capabilities in management of the droplet parameters, leading to precise control over the reactor performance. More importantly, the development of a tractable reactiontransport model is enabled using a repeatable unit-cell approach, which allows one to undertake a comprehensive study of the influence of the important reactor operating parameters, leading to a rational design of the DDIR class of reactors. Validation of the key components of the reactor model against relevant literature results provides confidence in applying the complete DDIR model to study various reacting systems. Of particular importance is the steam reforming of methanol, which has been widely studied as a method for distributed hydrogen generation for fuel cells. An 9512


Industrial & Engineering Chemistry Research experimental prototype of the DDIR unit cell for methanol steam reforming was built and characterized to provide further support for the validity of the model developed here by comparing the experimental results for film growth, capillary penetration, and hydrogen production rate with simulation results under approximately identical conditions. The model developed and validated in this article was applied in the companion article33 to provide recommendations for optimal operation of the DDIR for methanol steam reforming.

’ ASSOCIATED CONTENT

bS

Supporting Information. Complete transient model development with reduction to steady-state case. Details of implementation of the model in Fluent CFD software. Details of the construction, equipment, and procedures used in DDIR unit-cell experimental studies. This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ1 404 385 1356. Fax: þ1 404 894 8496. E-mail: AGF@ gatech.edu.

’ ACKNOWLEDGMENT The authors acknowledge financial support of this work through NSF CBET Grant 0928716, which was funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). ’ REFERENCES (1) Dyer, C. K. Fuel cells for portable applications. J. Power Sources 2002, 106 (12), 31–34. (2) Conte, M.; Iacobazzi, A.; Ronchetti, M.; Vellone, R. Hydrogen economy for a sustainable development: State-of-the-art and technological perspectives. J. Power Sources 2001, 100 (12), 171–187. (3) Patil, A. S.; Dubois, T. G.; Sifer, N.; Bostic, E.; Gradner, K.; Quah, M.; Bolton, C. Portable fuel cell systems for America’s army: Technology transition to the field. J. Power Sources 2004, 136, 220–225. (4) Palo, D. R.; Holladay, J. D.; Rozmiarek, R. T.; Guzman-Leong, C. E.; Wang, Y.; Hu, J. L.; Chin, Y. H.; Dagle, R. A.; Baker, E. G. Development of a soldier-portable fuel cell power system: Part I: A breadboard methanol fuel processor. J. Power Sources 2002, 108 (12), 28–34. (5) Flipsen, S. F. J. Power sources compared: The ultimate truth? J. Power Sources 2006, 162 (2), 927–934. (6) Muller, M.; Muller, C.; Gromball, F.; Wolfle, M.; Menz, W. Micro-structured flow fields for small fuel cells. Microsyst. Technol. 2003, 9 (3), 159–162. (7) Thomas, C. E.; James, B. D.; Lomax, F. D.; Kuhn, I. F. Fuel options for the fuel cell vehicle: Hydrogen, methanol or gasoline? Int. J. Hydrogen Energy 2000, 25 (6), 551–567. (8) Wilhite, B. A.; Schmidt, M. A.; Jensen, K. F. Palladium-based micromembranes for hydrogen separation: Device performance and chemical stability. Ind. Eng. Chem. Res. 2004, 43 (22), 7083–7091. (9) Pan, L.; Wang, S. A compact integrated fuel-processing system for proton exchange membrane fuel cells. Int. J. Hydrogen Energy 2006, 31, 447–454. (10) Mitsos, A.; Chachuat, B.; Barton, P. I. What is the design objective for portable power generation: Efficiency or energy density? J. Power Sources 2007, 164 (2), 678–687. (11) Deluga, G. A.; Salge, J. R.; Schmidt, L. D.; Verykios, X. E. Renewable hydrogen from ethanol by autothermal reforming. Science 2004, 303 (5660), 993–997.

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