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Solar reforming of methane in a direct absorption catalytic reactor on a parabolic dish: II—Modeling and analysis
SolarEnergy, Vol. 52, No. 6, pp. 479-490, 1994 1994JZlsevier SciinceLtd
Printedin the USA. All rightsreserved 0038a2X/94 $6.00 + .OO
0038-092x(94)30016-6
SOLAR REFORMING OF METHANE IN A DIRECT ABSORPTION CATALYTIC REACTOR ON A PARABOLIC DISH: II-MODELING AND ANALYSIS RUSSELLD. SKOCYPEC, ROY E. HOGAN, JR., and JAMES F. MUIR SandiaNational Laboratories, Albuquerque, NM 87 185, U.S.A.
Abstract-The CAtalytically Enhanced Solar Absorption Receiver (CAESAR) test was conducted to de termine the thermal, chemical, and mechanical performance of a commercial-scale, dish-mounted, direct cat&tic absorption receiver (DCAR) reactor over a range of steady state and transient (cloud) operating conditions. The focus of the test was to demonstrate “proof-of-concept” and determine global performance such as reactor efficiencies and overall methane conversion. A numerical model was previously developed to provide guidance in the design of the absorber. The one-dimensional, planar, and steady-state model incorporates the following energy transfermechanisms: solar and intkued radiation, heterogeneouschemkal reaction, conduction in the solid phase, and convection behveen the fluid and solid phases. Improvements to the model and improved property values are presented here. In particular, the solar radiative transfer model is improved by using a three-thtx technique to more accurately representthe typically conical incident flux. A spatklly varying catalyst loading is incorporated, convective and radiative properties for each layer in the multilayer absorber are determined, and more real&ticboundary conditions are applied. Considering that this test was not intended to provide data for code validation, model predictions are shown to generally bound the test axial thermocouple data when test uncertainties are included. Global predictions are made using a technique in which the incident solar flux distribution is subdivided into flux contour bands. Reactor pm-l&ions for anticipatedoperatingconditions w that a finther decreas in optical density (i.e., extinction coefkcient) at the fkont of the absorber inner disk may improve absorber conditions. Code-validation experiments are needed to improve the confidence in the simulation of large-scale reactor operation.
1. INTRODUCTION solar reforming of methane with carbon dioxide was demon&rated in the CAtalytically Enhanced Solar Absorption Receiver (CAESAR) test, which was a joint project between Sandia National Laboratories (SNL) and DLR (Stuttgart, Germany). The test reactor, designed to produce approximately 100 kW_, was instaRedandteatedona150kW, 17mparabolicdish at the DLR PAN facility. The CAESAR reactor (see Fig. 1) is an integrated solar receiver and chemical reactor uniquely suited to high-temperature /high-flux environments. This type of chemical reactor volume@icaRy absorbs concentrated solar energy throughout a cat&tic porous absorber matrix volume, promoting -0~s reactions with fluid-phase reactant species flowing through the absorber. In this particular reactor, the porous absorber consists of a reticulated alumina ceramic impregnated with rhodium catalyst. A numerical model was previously developed to provide guidance in the design of the absorber and it . . dtscwmdindetailbyHoganandSkocypec(1992). &Iping&culati ons for the thermal and chemical p$&f of the reactor were presented for a range pammeMs and operating conditions by Skocypec and Hogan ( 1992). Predicted performance
This w& pertbmrti at Sam&a National Laboratories, suppoln#ibp~U.s. Dapemmnt 0fEnergytmdercomract DE-ACXW-7gInruq789. 479
was based on a prototype absorber and anticipated op crating conditions. These predictions were used to assist the final absorber design for CAESAR. At that time, however, some inibrmation (such as abao&er radiative, convective, and catalytic proper&) mcemary to model and evaluate the final design was not availabk. The objectives of this paper are to: (a) discuss improvements of the numerical modeI deacfibcd by HoganandSkocypec(l992);(b)comparemodof’predio tions with test data; (c) indicate the predicted performance potential of these types of mactors under more ideal conditions; and (d) identify research needed to advance the simulation of these reactors.
2. TEST DIBCRDWON
TheobiectiveoftheCAFSARtestwastode&rmine the thermal, chemical, and mechanical pe&mtance of a commercial-scale, dish-mounted direct a&&& absorption receiver (DCAR) reactor over a nmgge of steadystateandtmnsient(cLoud)ope&ngcond&ns The focus of the test was to m “proof-of-
of the reactor in detail. As shown schematicaby in Fii. 2, the absorber disks (64 cm diameter, 5 cm thick) were fabricated in nine pieces: a 30 cm &aweter inner diskandeightouterringpiecm.TwovoLumetricab sorbersweretes@&bothhadsma&xopti&&n&ies
R. D. SKOCYPEC
480
ABSORBER-CATALYST COATED POROUS ALUMINA I
CERAMIC INSULATION
/
CERAMIC BACKWALL
----
PRODUCT GAS
A
f&r
CYLM&?MXL~EEL
Fig.
co,co,,
CH,,
+
W)
P REACTANT GAS (COP, CH,)
1. Schematic
(i.e., extinction coefficients) at the front (sunlit) side of the absorbers; the second was designed to also tailor the gas maas flux with the incident solar flux distribution. The first absorber had three axial layers (51 10 /20 pores-per-inch ( ppi ) front to back) and was radially uniform, providing a radially uniform flow resistance. The second absorber was radially nommiform, having the same inner disk but with an outer ring having smaller pore sixes ( lo/30 ppi front to back), providing increased 5ow maiatance through the outer ring0 thereby inducing more mass flow through regions of higher incident solar flux (the inner disk). The test temperatures were measured with unshielded thermocouples installed in holes drilled from the rear of the absorber. Due to the reticulated nature of the absorber and large radiative fluxes, data from thermocouples located within the absorber require interpretation, which is discussed below. A cross-array of thermocouples immediately behind the absorber provide the temperature distribution of the gas leaving the absorber. product gas composition was determined by on-line analyxers and by post&& gas chromatography analysis of collected gas samples. An accmate knowledge of the solar flux distribution and solar power incident to the reactor is mzesmry to evaI~temactorperformanceandtoconductmodeling analyses. The incident solar flux distribution was charact&edinatiofpoatWt susins for conthe DLB HEWl dltions&n&trtoteatsofintemat[aaeMuiret~I. egtis (I%)]. A regmm?mWve EHSBMES shown in Fig. 3.
of CAESAR reactor.
3. MODEL DEXRWIION
Hogan and Skocypec ( 1992) describe the numerical model and solution procedure used to predict reactor performance in detail. Improvements of the model and improved properties are presented here. In particular, the radiative transfer model has been improved, a spatially varying catalyst loading has been incorporated, convective and radiative properties for each layer in the multilayer absorber have been determined, and more reahstic boundary conditions have been applied. The model, in general, remains the same as presented byHoganandSkocypec(1992). Briefly, the one-dimensional, planar and steadystate model of the absorber incorporates the folknving energy transfer mechanist solar and infrared radiation, heterogeneous chemical reaction, conduction in the solid phase, convection between the fluid and solid phases, and interaction with the quartz reactor window. Energy transfer at the microscale is not explicitly modeled. A continuum (rather than a discrete) approach has been taken. To account for radial variations in incident solar flux and mass flux, several one-dimensional and radially uncoupled problems am solved independently. For each problem, the model provides axialdi&butions(throughtheahaorber)of:solid,5uid and thermocouple temperature, fluid compo&ion, and energy f&es. These are used to determine reactor (global) e&iencie loams, and eonversion. 3.1 Radiative transfer The tbtcatlux technique, as developed by Incropera and Houf ( 1979) to more accurately account for the
Solar reforming of m&we-Part
II
481
I
SECTION A-A I,
CENTRAL DISK 1st h 2nd ABSORBERS FRONT
b15.0 ;
-
OUTER RING 1st ABSORBER 2nd ABSOBER
l/8 In. AL4iMtNA S99J I, ,; ,LRAWtC flBER GABKU
*ALL “v” TONGUE 6 GROOVE JOINTS TRIANGULAR IN CROSS SECTION: 1.099 BASE x 0.953 HEIGHT
DIMENSIONS IN CM Fig. 2. Schematic of CAESAR absorbers.
Fig. 3. Measured solar incident flux distribution for Test lLB34.
R.D.
482
SKOCYPEC
refractive effect at air-water interfaces, is used in this analysis to model radiative transfer in the solar band. It more accurately accounts for the typically conical solar flux distribution from dish concentrators. Volumetric absorption and radiative flux predictions from the three-flux technique compare well to those obtained from both the more detailed discrete ordinate method and experiments [ Incropera and Houf ( 1979)], particularly for conical incidence and anisotropic scattering. The three-flux technique offers a good compromise between accuracy, operational convenience, and computation time. The two-flux technique is used for the infrared radiative transfer, which is typically diffuse. The porous absorber matrix is modeled as a quasicontinuous, nonisothermal, homogeneous medium with transparent boundaries. It is assumed to be an absorbing, emitting, and isotropically scattering medium. Isotropic scattering is assumed because there is a lack of phase function information for radiative transfer within the reticulated material. (Anisotropic phase functions can be incorporated in both techniques.) As discussed below, any actual anisotropy is accounted for when radiative properties are determined. The fluid phase is assumed to be radiatively nonparticipating. The three-flux technique approximates radiative transfer by grouping the noncollimated radiant energy into three isotropic components in the three regions indicated in Fig. 4. The positive-directed hemispherical flux is comprised of two fluxes, qzl and qiz, with the boundary between each isotropic region specified by pc( cos( 0,)). The negative-directed hemispherical flux is represented by q;. Additionally, a collimated flux ( qs,mll)can be included, which is used primarily when analyzing reflectance/transmittance experimental data. For the solar band, the radiative transfer is represented by,
4,: dz
+ A%( 1 - bdqs + A
7 (1-
+ /%(2 - %)G
-
Pc)qs.coll,( 1)
& 2 4Wli,
(3)
For the infrared band, dq: = -P,(2
- W)q: + B&WI;
dz
+ 2aiMl dq; - -/hbq: dz-
- 4c,
(5)
+ 8,(2 - wbl; - 2&(
1 - w,)Z-f.
(6)
At the absorber inlet (sunlit side), the solar and infrared fluxes are specified by considering the interaction with the quartz window. The solar flux from the concentrator [having a rim angle of 32’ (rc = 0.848)] that exits the quartz window and is incident on the absorber is defined as q:,,inc. For these simuand qs+z,inc are zero. The incident lations, both qs,coil,inc solar flux is assumed uniform over the frontal area being modeled. The boundary conditions at the absorber inlet are S,:(O) =
4S:,inc
+
Ps.w(
l
-
P(e)4;(0)9
(7)
qs+z(O) = Ps,w/M;(o).
(8)
q:(O)
(9)
= p,wq;(O)
+ ~,w&..
Because the reactor (absorber and housing) is expected to be reasonably uniform in temperature near the rear of the absorber, and because no additional radiative data is available, adiabatic radiative boundary conditions are specified at the absorber exit: G(L)
+ 4 ,'2 (L) = q,(L), q:(L)
= q;(L).
(10)
(11)
Radiative properties for this reticulated material are not well known. The scattering environment requires phase function and scattering cfoss-section information that, if the absorber was comprised of spheres or cylinders, could be determined using Mie Theory. HOWever, the reticulated nature of the absorber precludes the use of Mie Theory. Additionally, dependent scattering may occur within the absorber, for which the standard radiative transfer equations do not directly apply. Consequently, an empirical approach is used to determine the effective solar and infrared properties for the porous absorber matrix. Spectrally weighted data from both hemispherical and specular reflectance andtransmittance experiments [see Skocypec and Hogan ( 1992)] were obtained for various thicknesses of the rhodium-coated absorber illuminated with collimated incident Ilux. Predictions from the three-flux model with a collimated incident ~W&ng were made using &?&rent tXdE&nBandw6mcotnlxued to ho& fhe &Fuse and specular measured data. The albedo and extinction coefficients for the best fit are taken as the &ective radiative properties. These prop-
II
Solar reforming of methane-Part
483
Noncollimated
n
z=L
it=0
Fig. 4. Coordinate system for three-flux radiative transfer technique.
erties include any effects of anisotropic scattering.
and dependent
3.2 Heterogeneous chemistry and mass conservation The reactionrateexpessio~ and mass conservation equations are presented by Hogan and Skocypec ( 1992 ) and Skocypec and Hogan ( 1992 ) . The carbon dioxide reforming reaction is, CH, + CO1 w 2C0 + 2H2,
the boundary
conditions
4
T
_k
dC(L)-
are,
=h,( T,(O) -
TAO)),
0
t 16)
’
dz
(15)
An energy balance on the fluid at z = 0 gives the additional boundary condition,
(12)
(~IA)CpmtT/(O)- T/,in) and the associated water-shift reaction is, CO2 + H2 Q CO + H20.
- (1 - +)h,(T,(O) (13)
The reaction rates in Skocypec and Hogan ( 1992) are presented in terms of variable weight percent rhodium. Predictions in that re&rence were presented for an anticipated catalyst loading of 0.2%. Analyses of the absorbers ins&lied in the CAESAR tests indicated higher average loadings that were not uniform. The pretest rhodium loadings are presented in Table 1.
d2T
Table I. Pretest parameter values Absorber
Pores/inch Thickness (cm) % Rh loading Radiation 8, (m-l) i’: (m-l) w, Convection dm”/m’)
-#$)-&L_
-k(l
hc(W/mZK) & stole + ds: +cloolldz dz -
(RI~RI
+ &~Rz)
dq; dz -
ah,(T, - T’),
(14)
(17)
where Tf,i, is the fluid temperature at the reactor inlet. These boundary conditions include only surface tmnsfer mechanisms, similar to the approach taken in semitransparent media [Viskanta and A ( 1975 )] . Roundary conditions for the
Layer
3.3 Energy conservation Energy conservation for the solid phase depends on the effective radiative properties, chemical reaction rates, entMpies of reaction, porosity of the alumina matrix, specific heat transfer area for the alumina matrix, and convective heat transfer coeihcient between the solid and fluid phases. For the solid phase,
- ?‘A@) = 0,
Radially uniform
I
Nonuniform*
1
2
3
5 2.0 0.6
10 1.73 0.3
20 1.27 0.4
10 2.0 0.6
?I 014
232.5 0.331 298.5 0.537
280.5 0.286 359.7 0.540
403.5 0.319 561.5 0.644
280.5 0.286 359.7 0.540
564.5 0.524 807.0 0.771
600 74
900 79
1400 100
900 79
1800 120
2
k = 4.327 W/mK, 4 = 0.85. Inlet: P,,,ti = 1.0 atm, T,. = 300 K. Window: paw= 0.1, P,,~= 0.05, c,,~ = 0.7, T, = 800 K. ??Outer ring (inner disk same aa uniform abaorbr).
484
R. D. SKCCYPEC
have been specified in eqns (7-l 1). The fluid-phase energy balance, thermophysical properties, and enthalpic equations are given in Hogan and Skocypec ( 1992 ) . The specific heat transfer surface area and the convective heat transfer coefficient for each layer were determined from estimations based on optical image analysis [seeSkocypec and Hogan ( 1992 )] and physical data (porosity, web sizes, etc.). 3.4 Solution procedure The equations describing the thermal and chemical conditions in the volumetric solar absorption chemical reactor are formed as a system of fifteen coupled, nonlinear, first-order, ordinary differential equations. The radiative properties, specific heat transfer area, convective heat transfer coefficient, and rhodium loading vary for each absorber layer (having different ppi). Table 1 presents a summary of all property values for each layer in both absorbers. The radiative transfer and energy equations require the boundary conditions for this system of equations to be imposed at both the absorber inlet and the absorber exit. This nonlinear two-point boundary value problem is solved using the SUPQR Q computer code developed by Scott and Watts ( 1977 ) , which preserves relative accuracy by reorthonormalizing the solution vectors whenever they begin to lose their numerical linear independence, and by the use of an adaptive solution point scheme. The absolute and relative error criteria are 1 X 10m3. 4. COMPARISON
WITH TEST DATA
As mentioned above, the thermocouple data may not directly represent either the solid absorber temperature or the gas temperature. Assuming the thermocouples are not in direct contact with and are not directly shaded by an absorber web, the predicted thermocouple response (calculation of the thermocouple bead temperature in the predicted thermal environment) can be determined and can be compared with the measured data. If the thermocouple bead had identical radiative and chemical properties as the solid absorber, its temperature would be the same as the solid temperature. However, because no catalytic chemistry occurs on the thermocouple and its radiative properties are different, the predicted thermocouple response differs. Because this correction is determined with the predicted thermal conditions from a continuum analysis, discrete effects around each thermocouple that are unknown (e.g., contact with the solid, total shading by a web, etc.) are not accounted for. These discrete effects can significantly affect the actual thermocouple response. The thermocouple response is predicted by performing an energy balance on the thermocouple bead in the predicted thermal environment (local radiative, convective fluxes), assuming the thermocouples are not in direct contact with the absorber. The thermocouple temperature is given by the nonlinear tmnscendental equation:
~~TC&C + hc(TTC- T’)
=~(4:,+4:2+43+q:+Y;),
(18)
where trc is the thermocouple emissivity and is assumed equivalent to the absorptivity. The thermocouple temperature is calculated using a Newton-Raphson approach. 4.1 Comparison with axial temperature distributions
To compare model predictions with test thermocouple data, estimations of absorber properties during the test need to be specified. Because the posttest analysis of the uniform absorber indicated substantial changes in the rhodium activity and physical cracking [Muir et al. ( 1994)], steady state conditions during one of the earlier tests in the test sequence was chosen for comparison in the hope that pretest parameter estimates for the absorber were applicable. Test 1L-B34 was one of the earliest tests for which good (steadystate) data were obtained, although many tests had been conducted prior to this test (approximately 7.6 h of testing, out of a total of 11.5 h of testing on this absorber). Unfortunately, it is probable that the absorber had already been altered from pretest conditions. Three parameter values are believed to have large uncertainties: the solar flux level (recall the nonuniform flux distribution shown in Fig. 3), the fluid mass Bux (due to the annular ring flow entry technique indicated in Fig. I), and the rhodium activity (due to nonuniform loading and posttest indications of deactivation). The incident solar flux near the location of the axial thermocouples (center of the absorber) was determined by examining the HERMES flux data. For test lL-B34 (40 min), qZl,inc = 525 f. 15 kW /m 2. For the absorber with a radially uniform flow resistance, the annular fluid inlet with no mixing region may produce a radially nonuniform flow field, with decreased flow toward the absorber centerline. At the centerline, the maximum fluid mass flux is that for uniform flow (0.1075 kg/ m2s), with an estimation that the mass flux near the center could be decreased by up to 20%. The rhodium activity in each of the three layers in the absorber could range from the pretest values specified in Table I to the measured posttest values. The measured posttest decrease in reaction rates is accounted for in the model by decreasing the catalyst weight-percent loading levels to: 0.031 for the 5 ppi layer, 0.039 for the 10 ppi layer, and 0.084 for the 20 ppi layer (the degradation was not axially uniformcompare with Table 1) . The thermocouple emittance during these tests was taken to be 0.85 f 0.15 in eqn(l8). The effects of these parameter uncertainties are considered when comparing the predicted thermocouple response with the thermocouple data. Parameter values that provide an upper bound, a lower bound, and a best estimate fa the predi&d thermocouple response are listed in Table 2. Parameter values are chosen to bound the response of the thermocouples
Solar reforming of methane-Part
485
II
TabIe 2. Parameter values for test I L-B34 (40 min) Rhodium Loading (wt%) TX estimate
vc
Upper Best Lower
1.0 0.85 0.7
Layer I
Layer 2
Layer 3
0.031 0.075 0.6
0.039 0.0375 0.3
0.084 0.05 0.4
0.0863 0.1075 0.1075
540 525 510
* (kg/m2s); ** (kW/m2).
located toward the front of the absorber. As dkussed below, the parameter values tbat produce the lower temperature bound at the front of the absorber may not produce the lower temperature bound at the rear of the absorber. The upper-bound parameter values are: higher thermocouple emittance, lower 5uid mass flux, higher solar flux near the absorber center, and post&& rhodium loading. The lower-bound parameter values are: lower thermocouple emittance, uniform fluid mass flux, lower solar flux near the absorber center, and pretest rhodium loading The best-estimate parameter vahtes are: average thermocouple emittance, uniform fluid mass 511x, average solar 5ux near the absorber center, and a rhodium loading that gives a predicted exit temperatum equal to the measured exit fluid tempeMums,Tbislastconditionwasimpoaedbecausethe greatest co&ience lies in the thermocouple data near the rear of the absorber and in the fluid temperature data (recaiI the previous discussion regarding discrete etkcts on the absorber thermocouple data). For layers 2 and 3, the best-estimate rhodium loading is slightly lower than the measured postkst values. Figure 5 shows the comparison of the test data with the predict& dues. The thermocouple data is generallyboundedbythesepredictionsanddiscmtee5ects may be apparent (e.g., the data point at 3.7 cm). The
difference between the upper bound and lower bound is not constant with axial position in the aknber. Also, the thermocouple response for the best-estimate and lower-bound cases cross toward the rear ofthe absorkr, corresponding to the solid/fluid temperatures in both cases. Figure 6 shows the corresponding predktions for the solid and fluid temperature distributions There is a large di5krence between the predict& thermocouple response and the predicted solid and fluid temperatures toward the front of the absorber due to the solar flux. The predicted thermocouple, solid, and fluid temperatures all coalesce toward the mar of the ab sorber~wherethesolarfluxissmallandthe~ture is more uniform. For the lower-bound case, the temperature of the absorber toward the front results in decmased thermal losses and higher exit temperatures, relative to the best-estimate case. Consaqunrtty, the axial temperature distributions of the lower-bound and best-estimate cases cross. The effect of en: on the thermocouple temperature decreases astbeflukiandsolid temperatures equilibrate [see eqn ( 18)]. Figure 7 shows the corresponding methane mole fraction distributions, which are similar in magnitude. The volumetric power distributions for the terms in the energy equation are shown in Ftg. 8 for the bestestimate parameters. The e&et of decmasing the optical density toward the front (sunlit) side of the absorber
Fig. 5. Comparison of test thermocouple data (test lGB34,40 min) with pmdkted thermocouple reapowe.
R. D. SKOCYPEC
-
I
0
i
6 Lal
PoAicKl
(CA)
Fig. 6. Predictedaxial distributions of solid and fluid temperature for test ILB34, 40 min.
is evident by the deeper penetration into the absorber of the solar energy (i.e., it is more volumetric), relative to that shown in Skocypec and Hogan (1992). This effect is also shown by the solid temperature distributions (Fig. 6). The discrete layer locations in the absorber can be observed in the chemical power distributions. 4.2 Comparison with global reds To provide global results using the one-dimensional model predictions, the nonuniform solar flux distribution is subdivided into solar flux contour bands. Model predictions are made for each flux band (using the average incident flux), which are then spatially integrated over the absorber cross-section. Ama-averagmg the solar flux is inappropriate because the thermal and
chemical response is nonlinear with solar flux. The fluid mass flux is assumed uniform across the absorber. Once the fluid leaves the absorber, the fluid from each flux contour band mixes to produce a uni&m exit mixture (no heterogeneous chemistry occurs). Conservation of mass and energy are used to obtain the mixture composition and temperature. The thermal and chemical efficiencies and methane conversion are calculated from the exit mixture conditions. For test 1LB34, the three-dimensional incident solar flux distribution is shown in Fig. 3, indicating nonuniform illumination conditions. Figure 9 shows a grey-scale image of the 256 X 256 pixel HERME da* with outlines of the inner disk and outer ring of the absorber. A very sharp dropoff in flux values is ol%erved at the center of the image, which is believed to be caused
Fig. 7. Predicted axial distributions of methane mole &action for test lLB34,40 min. Upper bound, best estimate, and lower bound csscs rek to ~MuwcM~~~ rtaponse.
487
Solar reforming of methane-Part II
Fig. 8. predicted axial distributionsof volumetric power for test lLB34,40 min, with bestestimate pammetex values (see Table 2).
by a flux meter located in the reflective surface used to obtain HERMES data. The afkcted area is small, so that the effect on this analysis is negligible. Contours for specified flux levels are calculated and the contour tines &stored as polygon spiine-fit paths.
of the image is determined e center of the absorber. By *on, only the flux that ilhmCnates the 0.3 m rad&s absorber is analyzed. The polygon areas within all contour paths-‘&e determined, from which the appropriate area for each flux band is detamiaed.~~~usedWhe~in~tillg~
Table 3 shows the six flux bands, the area foF each asapercentageofthetotalabsorberarqaad*~ dieted results for each flux baad (the i fluxforeach&&ationistakentobethe
tween 250 and 450 kW/m’, which is re&&ed in the mixture values. Global reactor e@ciencies are inedfkom these data. Thermal cfbciency, V*, is tfic parcent of
to cakuhte exit conditions. The contour banda f&rthe flux ilh&nating the absorber are graphically i-ted in Fii 10 as shaded contours. the pboolt#
inTable 1 ofMuirad(l%M), = 79.396, q& = 50.7%, and 45.996
4.3 Pre&tiions for anticipated condjtiolls A&nag4 the rc4xhr was never opemted at the hipBGl incident flux conditions or+aUy a&&ated for*tesgitisinfbrmativetoassessthep&rnmmz of&eradia@taiiomdabsorber(innerdiskrrtldouter
-0.4
-0.2
-0.0
0.2
0.4
0.6
x (m> Fig. 9. Grcy-scale image of measured solar incident flux distribution for test ILB34.._ Inner .__ disk and outer ring areas identiticd.
&xlevelsspe&edfbrCaseZBinSkocypec (1992). Fortheinwdisk,q,l,iM:= 1912kW/m2,ti/ A = 0.2538 kg/m%; and for the outer ring, qsleinc=
488
R. D.
0.4
SKOCYPEC
1
250-350
150-250
-0.4
-0.2
-0.0
0.2
0.4
0.6
x 0-d Fig. 10. Contour bands for measured solar flux incident on absorber, test lLB34. 317 kW/m2, ni/A = 0.042 kg/m’s The pretest parameter values specified in Table 1 for the nonuniform absorber are used. Figure 11 shows the predicted axial temperature and methane mole traction distributions for both the inner disk and outer ring. Thermal and chemical conditions are more uniform between the inner disk and outer ring than predicted conditions for a nontailored abaorber[seeSkocypecandHogan(l!I92)].Theinner disk solid reaches an unacceptably high temperature, which is caused in part by the unexpectedly high rhodium loading for the first layer (indicated in Table 1). The high catatyst loading both decreases the front surface temperature due to the endothermic chemical activity and causes a thermal maxima within the absorber due to rapid reactant depletion. This effect of increased catalyst loading was also observed by Skocypec and Hogan (1992). The effect of decreasing the optical density toward the front of the absorber relative to that in the prototype absorber in Skocypec and Hogan ( 1992 ) is also evident in Fig. 11. To reduce the temperature of the inner disk, the optical density should be further decreased, if practical, and either the mass flux incmaaed or the rhodium loading decreased. Predicted reactor efhciencies are nti = 71.5%, &h = 46.796, and 99.1% of the methane is converted. Relative to the reactor e&iencies calculated
for test 1L-B34, a significant increase in methane conversion is obtained with similar thermal and chemical efficiencies. 5. DIRKCTION
FOR FUTURE WORK
The focus of this test was to demonstrate “proofofconcept” and determine global performance such as reactor efficiencies and overall methane conversion. That is, this test and previous tests [Skocypec et al. ( 1989)] were not intended to provide data for code validation. From a numerical modeling perspective, the most important need is to conduct laboratory-scale experiments under relatively well controlled conditions with sufficient diagnostics so that comparisons can be made with code predictions. That is, code-validation experiments need to be conducted, producing greater confidence in our predictive capability for larger-scale reactors. A&&io& but at thistimetheyam pment of these reactors. 6. SIJMMARY
Improvements ofthe previous numerical model and improved property vahres have been pmeented. In par-
Table 3. Pmdictec exit conditions for tast lLB34 (40 min) Plux &W/m’)
4bAlV.a
XC&
xc*
&U
X,,
50-150
1.2
0.446 0.329 0.230 0.154 0.092 0.047 0.177
0.485 0.354 0.248 0.163 0.096 0.045 0.188
0.037 0.165 0.270 0.352 0.418 0.468 0.328
0.028 0.139 0.234 0.310 0.370 0.412 0.287
1N-250 250-350 350-450 450-550 >550 Mixture values:
3E 39:o 18.6 0.9
X,, 0.004 0.013 0.018 0.021 0.024 0.028 0.020
481.7 533.0 578.2 622.7 670.5 743.7 610.0
Solar reforming of methane-Part
L-
II
489
Molehctton
I
i
&alPo&oIl (cI$
Fig II. Predicted axial distributions of temperature and methane mole fraction for inner disk and outer ring with anticipated operating conditions.
titular, the solar radiative transfer model has been improved by the application of a three4lux technique. A apatiaily varying catalyst loading has been incorporated, convective and radiative properties for each layer in the multilayer absorber have been determined, and more realistic boundary conditions have been applied. In general, model predictions bound the test axial thermocouple data when test uncertainties are include4l. Global predictions have been made using a technique in which the incident solar flux distribution is subdivided into flux contour bands. Global predictions such as reactor efficiencies and methane conversion compare! well with test data. Reactor predictions for anticipated operating conditions suggest that a further decrease in optical density at the front of the absorber inner disk may be beneficial. Code-validation experiments are needed to improve the confidence in the capability to simulate large-scale reactor operation.
Acknowledgments--The authorsgratefullyacknowledgethe assistanceof M. W. Glass (SNL) for image processing and contour quantification, R. Buck (DLR) for conducting the CAESAR teets and providing test data, A. R. Mahoney (SNL) for measuring absorber radiative properties, and M. S. Bohn (NREL) for providing specific heat transfer area estimations for the absorber.
NOMENCLATURE
reactorRontalarea(m2) constant-pressure specific heat of mixture (J/kg K) cortveetive beat transfer coefhcient ( W/m2K) enthalpy of reaction for reforming maction (J/kmol CH4) cnthalpy
COZ)
of reaction for water-shift reaction (J/ kmol
k thermal conductivity ( W/mK) L geometric thickness of absorber ( m) mixture mass flow rate (kg/s) P,“, reactor pressure (atm) q: positive- or negative-directed infrared hemispherical radiative flux (W/m*) positiveditected solar flux within region 1 positive-directed solar flux within region 2 negative-directed solar flux within region 3 reaction rate for reforming reaction (( kmol of CH, consumed)/(s m3)) reaction rate for water-shift reaction (( kmol of CO, R2 consumed)/(s m’)) T temperature (K) w% weight percent of rhodium catalyst Xi mole fraction of species i 2 geometric distance into the absorber (m)
Greek symbols matrix specific convective heat transfer area ( m2 /m 3, extinction coethcient (m-’ ) emittance chemical efficiency (5%) thermal efficiency (t ) angle from normal angle from normal defining regions for q:, and q& cas @, ~0s edI reflectance Stefan43oltzmannconstant (W/(m2 K’)) porosity, = (void volume)/( matrix volume) single scattering albedo
Subscripts TC thermocouple co11 collimated inc incident in inlet f fluid r infraredband s solar band, solid w window
490
R. D.
SKCXYPEC
REFERENCES
Hogan, R. E., Jr., and Skocypec, R. D., Analysis of catalyticahy enhanced solar absorption chemical reactors: I-Basic conm and numerical model description, Trans.ASME, J. ofsolar Energy Engineering, 114,. 106-I I I ( 1992). Incropera, F. P., and Houf, W. G., A three-flux method for predicting radiative transfer in aqueous suspensions, Trans. ASME, J. Heat Transfer, 101,496-501 ( 1979). Kleih, J., Beurteilung von konzentrierenden Spiegelsystemen mit Hilfe des MeBsystems HERMES und des Simuhationsprogrammes HELIOS, DLR-Forschungsbericht FB 89-51, in German (1989). Muir, J. F., Hogan, R. E., Skocypec, R. D., and Buck, R., Solar reforming of methane in a direct absorption catalytic reactor on a parabolic dish: I-Test and analysis, Solar Energy, 52,467-477 ( 1994).
Scott, M. R., and Watts, H. A., Computational solution of nonlinear two-point boundary-value problems, Proceedings of the Ft$h Symposium on Computers in Chemical Engineering, Czechoslovakia, 17-27 ( 1917 ) Skocypec, R. D., Boehm, R. F., and Chavez, J. M., Heat transfer modeling of the IEA/SSPS volumetric receiver, Trans. ASME, J. of Solar Energy Engineering, 111, 138143(1989).
Skocypec, R. D., and Hogan, R. E., Jr., Analysis of catalytically enhanced solar absorption chemical reactors: II-Predicted characteristics of a 100kWcbi,i reactor, Trans. ASME, J. of Solar Energy Engineering, 114, I 12- I 18 ( 1992). Viskanta, R., and Anderson, E. E., Heat transfer in semitransparent solids. In: Advancesin heat transfer,Irvine, T. F., and Hartnett, J. P. (eds), pp. 385-391 (1975).
Printedin the USA. All rightsreserved 0038a2X/94 $6.00 + .OO
0038-092x(94)30016-6
SOLAR REFORMING OF METHANE IN A DIRECT ABSORPTION CATALYTIC REACTOR ON A PARABOLIC DISH: II-MODELING AND ANALYSIS RUSSELLD. SKOCYPEC, ROY E. HOGAN, JR., and JAMES F. MUIR SandiaNational Laboratories, Albuquerque, NM 87 185, U.S.A.
Abstract-The CAtalytically Enhanced Solar Absorption Receiver (CAESAR) test was conducted to de termine the thermal, chemical, and mechanical performance of a commercial-scale, dish-mounted, direct cat&tic absorption receiver (DCAR) reactor over a range of steady state and transient (cloud) operating conditions. The focus of the test was to demonstrate “proof-of-concept” and determine global performance such as reactor efficiencies and overall methane conversion. A numerical model was previously developed to provide guidance in the design of the absorber. The one-dimensional, planar, and steady-state model incorporates the following energy transfermechanisms: solar and intkued radiation, heterogeneouschemkal reaction, conduction in the solid phase, and convection behveen the fluid and solid phases. Improvements to the model and improved property values are presented here. In particular, the solar radiative transfer model is improved by using a three-thtx technique to more accurately representthe typically conical incident flux. A spatklly varying catalyst loading is incorporated, convective and radiative properties for each layer in the multilayer absorber are determined, and more real&ticboundary conditions are applied. Considering that this test was not intended to provide data for code validation, model predictions are shown to generally bound the test axial thermocouple data when test uncertainties are included. Global predictions are made using a technique in which the incident solar flux distribution is subdivided into flux contour bands. Reactor pm-l&ions for anticipatedoperatingconditions w that a finther decreas in optical density (i.e., extinction coefkcient) at the fkont of the absorber inner disk may improve absorber conditions. Code-validation experiments are needed to improve the confidence in the simulation of large-scale reactor operation.
1. INTRODUCTION solar reforming of methane with carbon dioxide was demon&rated in the CAtalytically Enhanced Solar Absorption Receiver (CAESAR) test, which was a joint project between Sandia National Laboratories (SNL) and DLR (Stuttgart, Germany). The test reactor, designed to produce approximately 100 kW_, was instaRedandteatedona150kW, 17mparabolicdish at the DLR PAN facility. The CAESAR reactor (see Fig. 1) is an integrated solar receiver and chemical reactor uniquely suited to high-temperature /high-flux environments. This type of chemical reactor volume@icaRy absorbs concentrated solar energy throughout a cat&tic porous absorber matrix volume, promoting -0~s reactions with fluid-phase reactant species flowing through the absorber. In this particular reactor, the porous absorber consists of a reticulated alumina ceramic impregnated with rhodium catalyst. A numerical model was previously developed to provide guidance in the design of the absorber and it . . dtscwmdindetailbyHoganandSkocypec(1992). &Iping&culati ons for the thermal and chemical p$&f of the reactor were presented for a range pammeMs and operating conditions by Skocypec and Hogan ( 1992). Predicted performance
This w& pertbmrti at Sam&a National Laboratories, suppoln#ibp~U.s. Dapemmnt 0fEnergytmdercomract DE-ACXW-7gInruq789. 479
was based on a prototype absorber and anticipated op crating conditions. These predictions were used to assist the final absorber design for CAESAR. At that time, however, some inibrmation (such as abao&er radiative, convective, and catalytic proper&) mcemary to model and evaluate the final design was not availabk. The objectives of this paper are to: (a) discuss improvements of the numerical modeI deacfibcd by HoganandSkocypec(l992);(b)comparemodof’predio tions with test data; (c) indicate the predicted performance potential of these types of mactors under more ideal conditions; and (d) identify research needed to advance the simulation of these reactors.
2. TEST DIBCRDWON
TheobiectiveoftheCAFSARtestwastode&rmine the thermal, chemical, and mechanical pe&mtance of a commercial-scale, dish-mounted direct a&&& absorption receiver (DCAR) reactor over a nmgge of steadystateandtmnsient(cLoud)ope&ngcond&ns The focus of the test was to m “proof-of-
of the reactor in detail. As shown schematicaby in Fii. 2, the absorber disks (64 cm diameter, 5 cm thick) were fabricated in nine pieces: a 30 cm &aweter inner diskandeightouterringpiecm.TwovoLumetricab sorbersweretes@&bothhadsma&xopti&&n&ies
R. D. SKOCYPEC
480
ABSORBER-CATALYST COATED POROUS ALUMINA I
CERAMIC INSULATION
/
CERAMIC BACKWALL
----
PRODUCT GAS
A
f&r
CYLM&?MXL~EEL
Fig.
co,co,,
CH,,
+
W)
P REACTANT GAS (COP, CH,)
1. Schematic
(i.e., extinction coefficients) at the front (sunlit) side of the absorbers; the second was designed to also tailor the gas maas flux with the incident solar flux distribution. The first absorber had three axial layers (51 10 /20 pores-per-inch ( ppi ) front to back) and was radially uniform, providing a radially uniform flow resistance. The second absorber was radially nommiform, having the same inner disk but with an outer ring having smaller pore sixes ( lo/30 ppi front to back), providing increased 5ow maiatance through the outer ring0 thereby inducing more mass flow through regions of higher incident solar flux (the inner disk). The test temperatures were measured with unshielded thermocouples installed in holes drilled from the rear of the absorber. Due to the reticulated nature of the absorber and large radiative fluxes, data from thermocouples located within the absorber require interpretation, which is discussed below. A cross-array of thermocouples immediately behind the absorber provide the temperature distribution of the gas leaving the absorber. product gas composition was determined by on-line analyxers and by post&& gas chromatography analysis of collected gas samples. An accmate knowledge of the solar flux distribution and solar power incident to the reactor is mzesmry to evaI~temactorperformanceandtoconductmodeling analyses. The incident solar flux distribution was charact&edinatiofpoatWt susins for conthe DLB HEWl dltions&n&trtoteatsofintemat[aaeMuiret~I. egtis (I%)]. A regmm?mWve EHSBMES shown in Fig. 3.
of CAESAR reactor.
3. MODEL DEXRWIION
Hogan and Skocypec ( 1992) describe the numerical model and solution procedure used to predict reactor performance in detail. Improvements of the model and improved properties are presented here. In particular, the radiative transfer model has been improved, a spatially varying catalyst loading has been incorporated, convective and radiative properties for each layer in the multilayer absorber have been determined, and more reahstic boundary conditions have been applied. The model, in general, remains the same as presented byHoganandSkocypec(1992). Briefly, the one-dimensional, planar and steadystate model of the absorber incorporates the folknving energy transfer mechanist solar and infrared radiation, heterogeneous chemical reaction, conduction in the solid phase, convection between the fluid and solid phases, and interaction with the quartz reactor window. Energy transfer at the microscale is not explicitly modeled. A continuum (rather than a discrete) approach has been taken. To account for radial variations in incident solar flux and mass flux, several one-dimensional and radially uncoupled problems am solved independently. For each problem, the model provides axialdi&butions(throughtheahaorber)of:solid,5uid and thermocouple temperature, fluid compo&ion, and energy f&es. These are used to determine reactor (global) e&iencie loams, and eonversion. 3.1 Radiative transfer The tbtcatlux technique, as developed by Incropera and Houf ( 1979) to more accurately account for the
Solar reforming of m&we-Part
II
481
I
SECTION A-A I,
CENTRAL DISK 1st h 2nd ABSORBERS FRONT
b15.0 ;
-
OUTER RING 1st ABSORBER 2nd ABSOBER
l/8 In. AL4iMtNA S99J I, ,; ,LRAWtC flBER GABKU
*ALL “v” TONGUE 6 GROOVE JOINTS TRIANGULAR IN CROSS SECTION: 1.099 BASE x 0.953 HEIGHT
DIMENSIONS IN CM Fig. 2. Schematic of CAESAR absorbers.
Fig. 3. Measured solar incident flux distribution for Test lLB34.
R.D.
482
SKOCYPEC
refractive effect at air-water interfaces, is used in this analysis to model radiative transfer in the solar band. It more accurately accounts for the typically conical solar flux distribution from dish concentrators. Volumetric absorption and radiative flux predictions from the three-flux technique compare well to those obtained from both the more detailed discrete ordinate method and experiments [ Incropera and Houf ( 1979)], particularly for conical incidence and anisotropic scattering. The three-flux technique offers a good compromise between accuracy, operational convenience, and computation time. The two-flux technique is used for the infrared radiative transfer, which is typically diffuse. The porous absorber matrix is modeled as a quasicontinuous, nonisothermal, homogeneous medium with transparent boundaries. It is assumed to be an absorbing, emitting, and isotropically scattering medium. Isotropic scattering is assumed because there is a lack of phase function information for radiative transfer within the reticulated material. (Anisotropic phase functions can be incorporated in both techniques.) As discussed below, any actual anisotropy is accounted for when radiative properties are determined. The fluid phase is assumed to be radiatively nonparticipating. The three-flux technique approximates radiative transfer by grouping the noncollimated radiant energy into three isotropic components in the three regions indicated in Fig. 4. The positive-directed hemispherical flux is comprised of two fluxes, qzl and qiz, with the boundary between each isotropic region specified by pc( cos( 0,)). The negative-directed hemispherical flux is represented by q;. Additionally, a collimated flux ( qs,mll)can be included, which is used primarily when analyzing reflectance/transmittance experimental data. For the solar band, the radiative transfer is represented by,
4,: dz
+ A%( 1 - bdqs + A
7 (1-
+ /%(2 - %)G
-
Pc)qs.coll,( 1)
& 2 4Wli,
(3)
For the infrared band, dq: = -P,(2
- W)q: + B&WI;
dz
+ 2aiMl dq; - -/hbq: dz-
- 4c,
(5)
+ 8,(2 - wbl; - 2&(
1 - w,)Z-f.
(6)
At the absorber inlet (sunlit side), the solar and infrared fluxes are specified by considering the interaction with the quartz window. The solar flux from the concentrator [having a rim angle of 32’ (rc = 0.848)] that exits the quartz window and is incident on the absorber is defined as q:,,inc. For these simuand qs+z,inc are zero. The incident lations, both qs,coil,inc solar flux is assumed uniform over the frontal area being modeled. The boundary conditions at the absorber inlet are S,:(O) =
4S:,inc
+
Ps.w(
l
-
P(e)4;(0)9
(7)
qs+z(O) = Ps,w/M;(o).
(8)
q:(O)
(9)
= p,wq;(O)
+ ~,w&..
Because the reactor (absorber and housing) is expected to be reasonably uniform in temperature near the rear of the absorber, and because no additional radiative data is available, adiabatic radiative boundary conditions are specified at the absorber exit: G(L)
+ 4 ,'2 (L) = q,(L), q:(L)
= q;(L).
(10)
(11)
Radiative properties for this reticulated material are not well known. The scattering environment requires phase function and scattering cfoss-section information that, if the absorber was comprised of spheres or cylinders, could be determined using Mie Theory. HOWever, the reticulated nature of the absorber precludes the use of Mie Theory. Additionally, dependent scattering may occur within the absorber, for which the standard radiative transfer equations do not directly apply. Consequently, an empirical approach is used to determine the effective solar and infrared properties for the porous absorber matrix. Spectrally weighted data from both hemispherical and specular reflectance andtransmittance experiments [see Skocypec and Hogan ( 1992)] were obtained for various thicknesses of the rhodium-coated absorber illuminated with collimated incident Ilux. Predictions from the three-flux model with a collimated incident ~W&ng were made using &?&rent tXdE&nBandw6mcotnlxued to ho& fhe &Fuse and specular measured data. The albedo and extinction coefficients for the best fit are taken as the &ective radiative properties. These prop-
II
Solar reforming of methane-Part
483
Noncollimated
n
z=L
it=0
Fig. 4. Coordinate system for three-flux radiative transfer technique.
erties include any effects of anisotropic scattering.
and dependent
3.2 Heterogeneous chemistry and mass conservation The reactionrateexpessio~ and mass conservation equations are presented by Hogan and Skocypec ( 1992 ) and Skocypec and Hogan ( 1992 ) . The carbon dioxide reforming reaction is, CH, + CO1 w 2C0 + 2H2,
the boundary
conditions
4
T
_k
dC(L)-
are,
=h,( T,(O) -
TAO)),
0
t 16)
’
dz
(15)
An energy balance on the fluid at z = 0 gives the additional boundary condition,
(12)
(~IA)CpmtT/(O)- T/,in) and the associated water-shift reaction is, CO2 + H2 Q CO + H20.
- (1 - +)h,(T,(O) (13)
The reaction rates in Skocypec and Hogan ( 1992) are presented in terms of variable weight percent rhodium. Predictions in that re&rence were presented for an anticipated catalyst loading of 0.2%. Analyses of the absorbers ins&lied in the CAESAR tests indicated higher average loadings that were not uniform. The pretest rhodium loadings are presented in Table 1.
d2T
Table I. Pretest parameter values Absorber
Pores/inch Thickness (cm) % Rh loading Radiation 8, (m-l) i’: (m-l) w, Convection dm”/m’)
-#$)-&L_
-k(l
hc(W/mZK) & stole + ds: +cloolldz dz -
(RI~RI
+ &~Rz)
dq; dz -
ah,(T, - T’),
(14)
(17)
where Tf,i, is the fluid temperature at the reactor inlet. These boundary conditions include only surface tmnsfer mechanisms, similar to the approach taken in semitransparent media [Viskanta and A ( 1975 )] . Roundary conditions for the
Layer
3.3 Energy conservation Energy conservation for the solid phase depends on the effective radiative properties, chemical reaction rates, entMpies of reaction, porosity of the alumina matrix, specific heat transfer area for the alumina matrix, and convective heat transfer coeihcient between the solid and fluid phases. For the solid phase,
- ?‘A@) = 0,
Radially uniform
I
Nonuniform*
1
2
3
5 2.0 0.6
10 1.73 0.3
20 1.27 0.4
10 2.0 0.6
?I 014
232.5 0.331 298.5 0.537
280.5 0.286 359.7 0.540
403.5 0.319 561.5 0.644
280.5 0.286 359.7 0.540
564.5 0.524 807.0 0.771
600 74
900 79
1400 100
900 79
1800 120
2
k = 4.327 W/mK, 4 = 0.85. Inlet: P,,,ti = 1.0 atm, T,. = 300 K. Window: paw= 0.1, P,,~= 0.05, c,,~ = 0.7, T, = 800 K. ??Outer ring (inner disk same aa uniform abaorbr).
484
R. D. SKCCYPEC
have been specified in eqns (7-l 1). The fluid-phase energy balance, thermophysical properties, and enthalpic equations are given in Hogan and Skocypec ( 1992 ) . The specific heat transfer surface area and the convective heat transfer coefficient for each layer were determined from estimations based on optical image analysis [seeSkocypec and Hogan ( 1992 )] and physical data (porosity, web sizes, etc.). 3.4 Solution procedure The equations describing the thermal and chemical conditions in the volumetric solar absorption chemical reactor are formed as a system of fifteen coupled, nonlinear, first-order, ordinary differential equations. The radiative properties, specific heat transfer area, convective heat transfer coefficient, and rhodium loading vary for each absorber layer (having different ppi). Table 1 presents a summary of all property values for each layer in both absorbers. The radiative transfer and energy equations require the boundary conditions for this system of equations to be imposed at both the absorber inlet and the absorber exit. This nonlinear two-point boundary value problem is solved using the SUPQR Q computer code developed by Scott and Watts ( 1977 ) , which preserves relative accuracy by reorthonormalizing the solution vectors whenever they begin to lose their numerical linear independence, and by the use of an adaptive solution point scheme. The absolute and relative error criteria are 1 X 10m3. 4. COMPARISON
WITH TEST DATA
As mentioned above, the thermocouple data may not directly represent either the solid absorber temperature or the gas temperature. Assuming the thermocouples are not in direct contact with and are not directly shaded by an absorber web, the predicted thermocouple response (calculation of the thermocouple bead temperature in the predicted thermal environment) can be determined and can be compared with the measured data. If the thermocouple bead had identical radiative and chemical properties as the solid absorber, its temperature would be the same as the solid temperature. However, because no catalytic chemistry occurs on the thermocouple and its radiative properties are different, the predicted thermocouple response differs. Because this correction is determined with the predicted thermal conditions from a continuum analysis, discrete effects around each thermocouple that are unknown (e.g., contact with the solid, total shading by a web, etc.) are not accounted for. These discrete effects can significantly affect the actual thermocouple response. The thermocouple response is predicted by performing an energy balance on the thermocouple bead in the predicted thermal environment (local radiative, convective fluxes), assuming the thermocouples are not in direct contact with the absorber. The thermocouple temperature is given by the nonlinear tmnscendental equation:
~~TC&C + hc(TTC- T’)
=~(4:,+4:2+43+q:+Y;),
(18)
where trc is the thermocouple emissivity and is assumed equivalent to the absorptivity. The thermocouple temperature is calculated using a Newton-Raphson approach. 4.1 Comparison with axial temperature distributions
To compare model predictions with test thermocouple data, estimations of absorber properties during the test need to be specified. Because the posttest analysis of the uniform absorber indicated substantial changes in the rhodium activity and physical cracking [Muir et al. ( 1994)], steady state conditions during one of the earlier tests in the test sequence was chosen for comparison in the hope that pretest parameter estimates for the absorber were applicable. Test 1L-B34 was one of the earliest tests for which good (steadystate) data were obtained, although many tests had been conducted prior to this test (approximately 7.6 h of testing, out of a total of 11.5 h of testing on this absorber). Unfortunately, it is probable that the absorber had already been altered from pretest conditions. Three parameter values are believed to have large uncertainties: the solar flux level (recall the nonuniform flux distribution shown in Fig. 3), the fluid mass Bux (due to the annular ring flow entry technique indicated in Fig. I), and the rhodium activity (due to nonuniform loading and posttest indications of deactivation). The incident solar flux near the location of the axial thermocouples (center of the absorber) was determined by examining the HERMES flux data. For test lL-B34 (40 min), qZl,inc = 525 f. 15 kW /m 2. For the absorber with a radially uniform flow resistance, the annular fluid inlet with no mixing region may produce a radially nonuniform flow field, with decreased flow toward the absorber centerline. At the centerline, the maximum fluid mass flux is that for uniform flow (0.1075 kg/ m2s), with an estimation that the mass flux near the center could be decreased by up to 20%. The rhodium activity in each of the three layers in the absorber could range from the pretest values specified in Table I to the measured posttest values. The measured posttest decrease in reaction rates is accounted for in the model by decreasing the catalyst weight-percent loading levels to: 0.031 for the 5 ppi layer, 0.039 for the 10 ppi layer, and 0.084 for the 20 ppi layer (the degradation was not axially uniformcompare with Table 1) . The thermocouple emittance during these tests was taken to be 0.85 f 0.15 in eqn(l8). The effects of these parameter uncertainties are considered when comparing the predicted thermocouple response with the thermocouple data. Parameter values that provide an upper bound, a lower bound, and a best estimate fa the predi&d thermocouple response are listed in Table 2. Parameter values are chosen to bound the response of the thermocouples
Solar reforming of methane-Part
485
II
TabIe 2. Parameter values for test I L-B34 (40 min) Rhodium Loading (wt%) TX estimate
vc
Upper Best Lower
1.0 0.85 0.7
Layer I
Layer 2
Layer 3
0.031 0.075 0.6
0.039 0.0375 0.3
0.084 0.05 0.4
0.0863 0.1075 0.1075
540 525 510
* (kg/m2s); ** (kW/m2).
located toward the front of the absorber. As dkussed below, the parameter values tbat produce the lower temperature bound at the front of the absorber may not produce the lower temperature bound at the rear of the absorber. The upper-bound parameter values are: higher thermocouple emittance, lower 5uid mass flux, higher solar flux near the absorber center, and post&& rhodium loading. The lower-bound parameter values are: lower thermocouple emittance, uniform fluid mass flux, lower solar flux near the absorber center, and pretest rhodium loading The best-estimate parameter vahtes are: average thermocouple emittance, uniform fluid mass 511x, average solar 5ux near the absorber center, and a rhodium loading that gives a predicted exit temperatum equal to the measured exit fluid tempeMums,Tbislastconditionwasimpoaedbecausethe greatest co&ience lies in the thermocouple data near the rear of the absorber and in the fluid temperature data (recaiI the previous discussion regarding discrete etkcts on the absorber thermocouple data). For layers 2 and 3, the best-estimate rhodium loading is slightly lower than the measured postkst values. Figure 5 shows the comparison of the test data with the predict& dues. The thermocouple data is generallyboundedbythesepredictionsanddiscmtee5ects may be apparent (e.g., the data point at 3.7 cm). The
difference between the upper bound and lower bound is not constant with axial position in the aknber. Also, the thermocouple response for the best-estimate and lower-bound cases cross toward the rear ofthe absorkr, corresponding to the solid/fluid temperatures in both cases. Figure 6 shows the corresponding predktions for the solid and fluid temperature distributions There is a large di5krence between the predict& thermocouple response and the predicted solid and fluid temperatures toward the front of the absorber due to the solar flux. The predicted thermocouple, solid, and fluid temperatures all coalesce toward the mar of the ab sorber~wherethesolarfluxissmallandthe~ture is more uniform. For the lower-bound case, the temperature of the absorber toward the front results in decmased thermal losses and higher exit temperatures, relative to the best-estimate case. Consaqunrtty, the axial temperature distributions of the lower-bound and best-estimate cases cross. The effect of en: on the thermocouple temperature decreases astbeflukiandsolid temperatures equilibrate [see eqn ( 18)]. Figure 7 shows the corresponding methane mole fraction distributions, which are similar in magnitude. The volumetric power distributions for the terms in the energy equation are shown in Ftg. 8 for the bestestimate parameters. The e&et of decmasing the optical density toward the front (sunlit) side of the absorber
Fig. 5. Comparison of test thermocouple data (test lGB34,40 min) with pmdkted thermocouple reapowe.
R. D. SKOCYPEC
-
I
0
i
6 Lal
PoAicKl
(CA)
Fig. 6. Predictedaxial distributions of solid and fluid temperature for test ILB34, 40 min.
is evident by the deeper penetration into the absorber of the solar energy (i.e., it is more volumetric), relative to that shown in Skocypec and Hogan (1992). This effect is also shown by the solid temperature distributions (Fig. 6). The discrete layer locations in the absorber can be observed in the chemical power distributions. 4.2 Comparison with global reds To provide global results using the one-dimensional model predictions, the nonuniform solar flux distribution is subdivided into solar flux contour bands. Model predictions are made for each flux band (using the average incident flux), which are then spatially integrated over the absorber cross-section. Ama-averagmg the solar flux is inappropriate because the thermal and
chemical response is nonlinear with solar flux. The fluid mass flux is assumed uniform across the absorber. Once the fluid leaves the absorber, the fluid from each flux contour band mixes to produce a uni&m exit mixture (no heterogeneous chemistry occurs). Conservation of mass and energy are used to obtain the mixture composition and temperature. The thermal and chemical efficiencies and methane conversion are calculated from the exit mixture conditions. For test 1LB34, the three-dimensional incident solar flux distribution is shown in Fig. 3, indicating nonuniform illumination conditions. Figure 9 shows a grey-scale image of the 256 X 256 pixel HERME da* with outlines of the inner disk and outer ring of the absorber. A very sharp dropoff in flux values is ol%erved at the center of the image, which is believed to be caused
Fig. 7. Predicted axial distributions of methane mole &action for test lLB34,40 min. Upper bound, best estimate, and lower bound csscs rek to ~MuwcM~~~ rtaponse.
487
Solar reforming of methane-Part II
Fig. 8. predicted axial distributionsof volumetric power for test lLB34,40 min, with bestestimate pammetex values (see Table 2).
by a flux meter located in the reflective surface used to obtain HERMES data. The afkcted area is small, so that the effect on this analysis is negligible. Contours for specified flux levels are calculated and the contour tines &stored as polygon spiine-fit paths.
of the image is determined e center of the absorber. By *on, only the flux that ilhmCnates the 0.3 m rad&s absorber is analyzed. The polygon areas within all contour paths-‘&e determined, from which the appropriate area for each flux band is detamiaed.~~~usedWhe~in~tillg~
Table 3 shows the six flux bands, the area foF each asapercentageofthetotalabsorberarqaad*~ dieted results for each flux baad (the i fluxforeach&&ationistakentobethe
tween 250 and 450 kW/m’, which is re&&ed in the mixture values. Global reactor e@ciencies are inedfkom these data. Thermal cfbciency, V*, is tfic parcent of
to cakuhte exit conditions. The contour banda f&rthe flux ilh&nating the absorber are graphically i-ted in Fii 10 as shaded contours. the pboolt#
inTable 1 ofMuirad(l%M), = 79.396, q& = 50.7%, and 45.996
4.3 Pre&tiions for anticipated condjtiolls A&nag4 the rc4xhr was never opemted at the hipBGl incident flux conditions or+aUy a&&ated for*tesgitisinfbrmativetoassessthep&rnmmz of&eradia@taiiomdabsorber(innerdiskrrtldouter
-0.4
-0.2
-0.0
0.2
0.4
0.6
x (m> Fig. 9. Grcy-scale image of measured solar incident flux distribution for test ILB34.._ Inner .__ disk and outer ring areas identiticd.
&xlevelsspe&edfbrCaseZBinSkocypec (1992). Fortheinwdisk,q,l,iM:= 1912kW/m2,ti/ A = 0.2538 kg/m%; and for the outer ring, qsleinc=
488
R. D.
0.4
SKOCYPEC
1
250-350
150-250
-0.4
-0.2
-0.0
0.2
0.4
0.6
x 0-d Fig. 10. Contour bands for measured solar flux incident on absorber, test lLB34. 317 kW/m2, ni/A = 0.042 kg/m’s The pretest parameter values specified in Table 1 for the nonuniform absorber are used. Figure 11 shows the predicted axial temperature and methane mole traction distributions for both the inner disk and outer ring. Thermal and chemical conditions are more uniform between the inner disk and outer ring than predicted conditions for a nontailored abaorber[seeSkocypecandHogan(l!I92)].Theinner disk solid reaches an unacceptably high temperature, which is caused in part by the unexpectedly high rhodium loading for the first layer (indicated in Table 1). The high catatyst loading both decreases the front surface temperature due to the endothermic chemical activity and causes a thermal maxima within the absorber due to rapid reactant depletion. This effect of increased catalyst loading was also observed by Skocypec and Hogan (1992). The effect of decreasing the optical density toward the front of the absorber relative to that in the prototype absorber in Skocypec and Hogan ( 1992 ) is also evident in Fig. 11. To reduce the temperature of the inner disk, the optical density should be further decreased, if practical, and either the mass flux incmaaed or the rhodium loading decreased. Predicted reactor efhciencies are nti = 71.5%, &h = 46.796, and 99.1% of the methane is converted. Relative to the reactor e&iencies calculated
for test 1L-B34, a significant increase in methane conversion is obtained with similar thermal and chemical efficiencies. 5. DIRKCTION
FOR FUTURE WORK
The focus of this test was to demonstrate “proofofconcept” and determine global performance such as reactor efficiencies and overall methane conversion. That is, this test and previous tests [Skocypec et al. ( 1989)] were not intended to provide data for code validation. From a numerical modeling perspective, the most important need is to conduct laboratory-scale experiments under relatively well controlled conditions with sufficient diagnostics so that comparisons can be made with code predictions. That is, code-validation experiments need to be conducted, producing greater confidence in our predictive capability for larger-scale reactors. A&&io& but at thistimetheyam pment of these reactors. 6. SIJMMARY
Improvements ofthe previous numerical model and improved property vahres have been pmeented. In par-
Table 3. Pmdictec exit conditions for tast lLB34 (40 min) Plux &W/m’)
4bAlV.a
XC&
xc*
&U
X,,
50-150
1.2
0.446 0.329 0.230 0.154 0.092 0.047 0.177
0.485 0.354 0.248 0.163 0.096 0.045 0.188
0.037 0.165 0.270 0.352 0.418 0.468 0.328
0.028 0.139 0.234 0.310 0.370 0.412 0.287
1N-250 250-350 350-450 450-550 >550 Mixture values:
3E 39:o 18.6 0.9
X,, 0.004 0.013 0.018 0.021 0.024 0.028 0.020
481.7 533.0 578.2 622.7 670.5 743.7 610.0
Solar reforming of methane-Part
L-
II
489
Molehctton
I
i
&alPo&oIl (cI$
Fig II. Predicted axial distributions of temperature and methane mole fraction for inner disk and outer ring with anticipated operating conditions.
titular, the solar radiative transfer model has been improved by the application of a three4lux technique. A apatiaily varying catalyst loading has been incorporated, convective and radiative properties for each layer in the multilayer absorber have been determined, and more realistic boundary conditions have been applied. In general, model predictions bound the test axial thermocouple data when test uncertainties are include4l. Global predictions have been made using a technique in which the incident solar flux distribution is subdivided into flux contour bands. Global predictions such as reactor efficiencies and methane conversion compare! well with test data. Reactor predictions for anticipated operating conditions suggest that a further decrease in optical density at the front of the absorber inner disk may be beneficial. Code-validation experiments are needed to improve the confidence in the capability to simulate large-scale reactor operation.
Acknowledgments--The authorsgratefullyacknowledgethe assistanceof M. W. Glass (SNL) for image processing and contour quantification, R. Buck (DLR) for conducting the CAESAR teets and providing test data, A. R. Mahoney (SNL) for measuring absorber radiative properties, and M. S. Bohn (NREL) for providing specific heat transfer area estimations for the absorber.
NOMENCLATURE
reactorRontalarea(m2) constant-pressure specific heat of mixture (J/kg K) cortveetive beat transfer coefhcient ( W/m2K) enthalpy of reaction for reforming maction (J/kmol CH4) cnthalpy
COZ)
of reaction for water-shift reaction (J/ kmol
k thermal conductivity ( W/mK) L geometric thickness of absorber ( m) mixture mass flow rate (kg/s) P,“, reactor pressure (atm) q: positive- or negative-directed infrared hemispherical radiative flux (W/m*) positiveditected solar flux within region 1 positive-directed solar flux within region 2 negative-directed solar flux within region 3 reaction rate for reforming reaction (( kmol of CH, consumed)/(s m3)) reaction rate for water-shift reaction (( kmol of CO, R2 consumed)/(s m’)) T temperature (K) w% weight percent of rhodium catalyst Xi mole fraction of species i 2 geometric distance into the absorber (m)
Greek symbols matrix specific convective heat transfer area ( m2 /m 3, extinction coethcient (m-’ ) emittance chemical efficiency (5%) thermal efficiency (t ) angle from normal angle from normal defining regions for q:, and q& cas @, ~0s edI reflectance Stefan43oltzmannconstant (W/(m2 K’)) porosity, = (void volume)/( matrix volume) single scattering albedo
Subscripts TC thermocouple co11 collimated inc incident in inlet f fluid r infraredband s solar band, solid w window
490
R. D.
SKCXYPEC
REFERENCES
Hogan, R. E., Jr., and Skocypec, R. D., Analysis of catalyticahy enhanced solar absorption chemical reactors: I-Basic conm and numerical model description, Trans.ASME, J. ofsolar Energy Engineering, 114,. 106-I I I ( 1992). Incropera, F. P., and Houf, W. G., A three-flux method for predicting radiative transfer in aqueous suspensions, Trans. ASME, J. Heat Transfer, 101,496-501 ( 1979). Kleih, J., Beurteilung von konzentrierenden Spiegelsystemen mit Hilfe des MeBsystems HERMES und des Simuhationsprogrammes HELIOS, DLR-Forschungsbericht FB 89-51, in German (1989). Muir, J. F., Hogan, R. E., Skocypec, R. D., and Buck, R., Solar reforming of methane in a direct absorption catalytic reactor on a parabolic dish: I-Test and analysis, Solar Energy, 52,467-477 ( 1994).
Scott, M. R., and Watts, H. A., Computational solution of nonlinear two-point boundary-value problems, Proceedings of the Ft$h Symposium on Computers in Chemical Engineering, Czechoslovakia, 17-27 ( 1917 ) Skocypec, R. D., Boehm, R. F., and Chavez, J. M., Heat transfer modeling of the IEA/SSPS volumetric receiver, Trans. ASME, J. of Solar Energy Engineering, 111, 138143(1989).
Skocypec, R. D., and Hogan, R. E., Jr., Analysis of catalytically enhanced solar absorption chemical reactors: II-Predicted characteristics of a 100kWcbi,i reactor, Trans. ASME, J. of Solar Energy Engineering, 114, I 12- I 18 ( 1992). Viskanta, R., and Anderson, E. E., Heat transfer in semitransparent solids. In: Advancesin heat transfer,Irvine, T. F., and Hartnett, J. P. (eds), pp. 385-391 (1975).