Ind. Eng. Chem. Res. 2007, 46, 1959-1967
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Using Computational Fluid Dynamics Modeling To Improve the Performance of a Solar CO2 Converter Ralph J. Price and Thomas H. Fletcher* Department of Chemical Engineering, 350 CB, Brigham Young UniVersity, ProVo, Utah 84602
Reed J. Jensen Los Alamos Renewable Energy, LLC, 19 Industrial Park Road, Pojoaque, New Mexico 87506
A solar collector to convert CO2 to CO at high temperature was previously developed, achieving a product with 4-6 mol % CO from pure CO2. Modeling results showed that reactions occurred in the thermal boundary layer of the heated zirconia rod at temperatures greater than 2300 K. This paper describes results of computer modeling of advanced designs meant to increase the conversion of CO from CO2. Several design modifications were tested using the model, including changing the cool-down region configuration, increasing the zirconia rod diameter, and changing the zirconia rod shape. Several operational adjustments were also modeled, including reducing the flow rate, dilution of CO2 with helium, and increasing the prototype operating pressure. Modeling results predicted that all of the proposed design modifications improved the CO conversion. Increasing the operating pressure and decreasing the flow rate were beneficial, but dilution of CO2 with He was predicted to decrease the amount of product CO. Several design modifications and operational adjustments have already been implemented experimentally and have increased the conversion of CO from CO2. Introduction CO2 is known to thermally dissociate to CO and O at high temperatures (greater than 2300 K). A solar concentrator to convert CO2 to CO at high temperature was previously developed, achieving 4-6 mol % CO in the product stream from an inlet stream of pure CO2.1 This CO can then be separated and (a) used as a fuel or (b) converted to H2 through the water-gas shift reaction.2 The flow, heat transfer, and reaction chemistry in this device were modeled previously using a computational fluid dynamics (CFD) model (FLUENT).3 The FLUENT model accurately predicted an outlet product stream with a CO concentration of 4.7 mol %. In addition, parametric studies were performed by varying two parameters: the inlet flow rate and the zirconia rod temperature profile. For this technology to be viable, the total energy obtained from this process (usable heat + chemical energy) must be much greater than the energy necessary to run the process (pumps, separation equipment, etc.). The economic success of the solar CO2 converter depends on maximizing conversion to CO with minimal cost. Maximizing conversion to CO also enables more cost-effective separation of product CO and O2 from CO2. Rough estimates show that this process would be economically sound if 12% CO conversion were achieved. To increase the conversion of the prototype, new design methods and operational modes were postulated. It seemed reasonable to test the ideas with CFD models before expensive design changes were made to the prototype converter. Improvement was determined based on (1) increased overall conversion of CO and (2) increased flow rate of outlet CO with similar overall conversion. Prototype improvements were classified as either (a) design modifications or (b) operational adjustments. Examples of design modifications include altering the shape, diameter, and location of the zirconia rod and altering the cool-down region. Examples of operational adjustments include altering the inlet flow rate, adjusting the * To whom correspondence should be addressed. Tel.: (801) 4226236. E-mail:
[email protected]. Fax: (801) 422-0151.
operating pressure, and diluting the CO2 with helium. Each of these adjustments was suggested based on improving conversion by positively affecting heat transfer, reaction kinetics, and/or reactor residence time. CFD modeling was necessary to compute the net effect of these three factors. Experimental Apparatus Traynor and Jensen1 built a first-generation solar CO2 converter that consisted of solar mirrors and a converter device. All or part of a 6 m2 bank of solar mirrors was used to reflect and magnify sunlight into a 6 in. long converter device. The converter device consists of a conical solar collection section lined with silver, with the solar flux focused on a zirconia rod located at the throat of the conical section. The zirconia rod is 8.07 cm long and has a diameter of 0.63 cm. Downstream of the rod, the product gas is cooled and monitored. This exhaust section rapidly cools the product gases to quench any reverse reactions of CO. The front end of the converter is sealed with a quartz window, which permits sunlight to pass through but contains the CO2 stream. A simple schematic for the solar CO2 converter is shown in Figure 1. The original prototype converter operated with an inlet flow rate of 10.0 standard liters per minute (slpm) of pure CO2. This flow rate corresponds to a Reynolds number (Re) in the throat of 91.4 using the properties of CO2 at 2200 K. A maximum Re of 340 was calculated for this prototype, occurring just upstream of the zirconia rod. This Re was calculated using the properties of CO2 at 548 K. These values are far below the transition Re for internal flow, so the prototype operates in the laminar regime.4 The solar flux on the zirconia rod heated the rod to a peak temperature of 2623 K. Under these operating conditions, the prototype converter achieved 4-6 mol % CO in the cooled product stream. Theoretical Development In an attempt to improve the performance of the prototype, several design and operational adjustments were suggested. The
10.1021/ie061035w CCC: $37.00 © 2007 American Chemical Society Published on Web 03/06/2007
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Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 Table 1. Kinetic Parameters for the Three Reversible Reactions
Figure 1. Schematic of the original solar CO2 converter prototype.
following adjustments were studied: (1) decreasing the inlet flow rate from 10.0 to 6.0 slpm, (2) decreasing the diameter of the pipe in the cool-down region, (3) changing the diameter and/or shape of the zirconia rod, (4) changing the cool-down section, (5) increasing the operating pressure of the prototype, and (6) diluting the CO2 with helium. The theoretical effects of these individual alterations are discussed in this section, based on how they may affect heat transfer, reaction kinetics, equilibrium, and reactor residence time. The effects of some of these adjustments can be illustrated with simple calculations, showing trends between conditions. CFD modeling is necessary to calculate the combined effects of multiple competitive phenomena. The CFD calculations are discussed in the next section. Flow Rate. Reducing the flow rate increases conversion by increasing residence time in the high-temperature region, defined as the space in the apparatus from the beginning of the zirconia rod to the beginning of the throat. This high-temperature region corresponds to the hottest portion of the rod. While reducing the flow rate increases conversion to CO from CO2, it may also decrease the outlet amount of CO produced because of a lower inlet flow rate. To approximate the effects of residence time, one-dimensional premixed laminar reacting flow calculations were performed using CHEMKIN.5,6 These premixed calculations were based on the three reversible reaction mechanism listed below as reactions 1-3. In this mechanism, M represents a third body that is needed for the reaction to occur, meaning any gas species.
CO2 + M T CO + O + M
(R1)
CO2 + O T CO + O2
(R2)
O2 + M T O + O + M
(R3)
These reactions have rate expressions that follow an extended Arrhenius expression:
k ) ATb exp
( ) -Ea RT
(1)
The pre-exponential factors (A), temperature exponents (b), and activation energies (Ea) used for all six reactions are found in Table 1, with the forward and reverse reactions designated with an F or R. The reaction rate constants for reactions 2 and 3, as well as the reverse reaction of Reaction 1, were taken from Tsang and Hampson.7 The kinetic parameters for the forward reaction of reaction 1 were calculated from thermodynamic equilibrium.
reaction
pre-exponential factor (A)
b
activation energy (Ea/R)
F1 R1 F2 R2 F3 R3
6.445 × 1010 m3 mol-1 s-1 6.167 × 102 m6 mol-2 s-1 1.686 × 107 m3 mol-1 s-1 2.530 × 106 m3 mol-1 s-1 1.807 × 1012 m3 mol-1 s-1 K1 1.886 × 101 m6 mol-2 s-1
0 0 0 0 -1 0
62 600 K 1510 K 26 500 K 24 000 K 59 380 K -900 K
Premixed calculations were performed to determine the minimum residence time at which the high-temperature equilibrium could be reached, as well as the theoretical maximum conversion to expect at various residence times. The results show that decreasing the flow rate leads to increased conversion of CO in the high-temperature region. Near-equilibrium conversion of 17.0 mol % CO can be reached at a flow rate of 2.5 splm, assuming a constant temperature of 2623 K. Decreasing the flow rate also changes the residence time in the cool-down section. An increase in the residence time in the cool-down region with the same cooling profile results in less effective CO quenching for lower flow rates, meaning that more of the CO is converted back into CO2 at these lower flow rates. As a result of this competition between formation and quenching and the radial temperature gradients in the high-temperature region, the exact amount of CO after the quench must be determined from CFD calculations. Pipe Diameter. Decreasing the diameter of the cool-down pipe from the original diameter (Dexit in Figure 1) to that of the throat diameter causes the convective heat transfer coefficient in the cool-down section to increase by a factor of almost 2. The heat transfer coefficients were calculated using an internal laminar flow correlation assuming a constant wall temperature.4 This correlation is shown in eq 2.
NuD )
hD ) 3.66 k
(2)
The two designs have the same cooling heat transfer rate because the surface area in the quench region of the base calculation (as in Figure 1) is a factor of 2 larger than when the quench region is at the throat diameter, which compensates for the difference in heat transfer coefficients. The real benefit of decreasing the exhaust pipe diameter is therefore to reduce the residence time in the cooling region, which results in more effective quenching for similar cooling rates. Adiabatic expansion effects in the quench region with the original configuration were calculated to cause an insignificant increase in both pressure and temperature (less than 1%) under the operating conditions studied. The expansion would be more beneficial if a large pressure drop occurred over it, causing rapid cooling behind a shock wave. Rod Shape and Diameter. From the original modeling of this converter,3 it was concluded that a “thermal boundary layer”, defined as a thin region of high-temperature gas (>2000 K) located directly around the zirconia rod, was the location where all significant CO-forming reactions occurred. These modeling results also showed that this thermal boundary layer only changes slightly as the flow is increased or decreased, since the majority of the thermal boundary layer is located in a low velocity region upstream of the throat. One way to increase the effect of this thermal boundary layer is to increase the hightemperature surface area of the zirconia rod. A larger hightemperature rod surface area corresponds to a larger thermal boundary layer area. This can possibly be achieved by increasing the diameter of the zirconia rod, changing its shape, or adding
Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 1961 Table 2. Summary of CFD Cases and Results
geometric configuration (Figure 2) CO2 flow rate (slpm) apparatus operating pressure (atm) inlet composition (% CO2/He) peak T_avg (K) peak CO_avg (mol %) peak conversion to CO (%) outlet T_avg (K) outlet CO_avg (mol %) overall conversion to CO (%) quenching efficiency (%) m˘ CO,out (mg/s)
base case
case 1
case 2
case 3
case 4
case 5
case 6
case 7
1 10.0 1.0 100 1480 8.53 9.32 1130 4.79 5.03 53.9 10.47
1 6.0 1.0 100 1590 10.4 11.6 1030 5.85 6.22 53.5 7.77
2 6.0 1.0 100 1590 10.4 11.6 970 6.47 6.91 59.5 8.64
3 6.0 1.0 100 1650 11.9 13.5 940 7.20 7.76 57.3 9.70
1 6.0 2.0 100 1530 11.0 12.3 970 4.47 4.68 38.0 5.85
1 12.0 2.0 100 1490 9.69 10.7 930 5.05 5.32 49.6 13.29
1 6.0 1.0 75/25 1640 8.22 11.9 970 4.66 6.52 54.6 6.11
4 10.0 1.0 100 1610 9.50 10.5 1170 5.15 5.44 51.7 12.2
features on the rod that increase its surface area (such as fins). This could also be accomplished by making the zirconia into a porous material. Increasing the zirconia rod diameter would increase the hightemperature boundary layer area proportionally to the rod diameter increase. Adding features to the zirconia rod would possibly have the added impact of increasing the mixing in the high-temperature region. Increased mixing would increase CO conversion due to increased CO2 that comes in contact with the thermal boundary layer. However, it was shown experimentally that fine features on the rod break during the rapid heating experienced during startup. Changing the rod diameter impacts multiple variables, including velocity and temperature, requiring CFD modeling. Cool-Down Section Modifications. One proposed modification to the cool-down section is to have the hot product gases impact a cold plate, bending the flow. This cold plate would be located directly past the high-temperature region, shielded from high solar flux, and cooled with water or cold gas. This proposed modification is intended to reduce the backward reactions of CO to CO2 by immediately contacting the high-temperature product gases with a cold environment. This design change also increases the heat transfer by causing the flow to become more turbulent through multiple changes of direction. The turbulent heat transfer coefficient is usually 2 to 3 times greater than the laminar heat transfer coefficient for developed internal flow.4 In addition to increasing the heat transfer, turbulent flow provides for better mixing. Better mixing and greater cooling heat transfer would result in more effective quenching of the product mixture. One side effect of this modification is a greater pressure drop through the apparatus as a result of several bends in the flow,8 although this should not cause any problems. Another way to increase heat transfer in the cool-down region is the addition of fins to the cooling heat transfer surface. These proposed design changes will alter both the flow and the heat transfer, and no simple calculations will show the comparative impact of these design modifications without CFD modeling. Operating Pressure. A change in the total pressure of the apparatus will impact the conversion by affecting heat transfer, equilibrium, reaction kinetics, and reactor residence time. Increasing the pressure from 1.0 to 2.0 atm, while keeping the volumetric flow rate constant, increased the average convective heat transfer coefficient between the zirconia rod and the CO2 by 41%. These heat transfer coefficients were calculated using an external laminar flow flat plate correlation (due to a lack of correlations for longitudinal flow over a cylinder). This correlation (shown in eq 3) is appropriate because it most accurately represents the flow of CO2 over the high-temperature portion of the zirconia rod.
NuL )
hL ) 0.66Re1/2 Pr1/3 k
(3)
Increasing the pressure to 2.0 atm, while keeping the mass flow rate constant, has little effect on the convective heat transfer coefficient. Increasing the pressure has little or no effect on the heat transfer between the high-temperature gas mixture and the cool pipe walls. This occurs because the laminar convective heat transfer coefficient for developed internal flow with a constant wall temperature is only a function of the pipe diameter and gas thermal conductivity. Increasing the pressure changes the thermodynamic equilibrium mole fractions of the CO2/CO/O2/O mixture at high temperatures. This effect follows LeChatelier’s Principle, which states that as pressure increases, gas-phase equilibrium favors the state with fewer total gas-phase moles.9 In other words, for the overall reaction CO2(g) f CO(g) + 1/2O2(g), a pressure increase would cause an equilibrium shift toward the reactant CO2. A pressure increase from 1.0 to 2.0 atm causes the equilibrium at 2623 K to shift from 17.3 to 14.3 mol % CO.10 Increasing the pressure also impacts the reaction kinetics in the prototype converter. Increasing the pressure increases the kinetic rates of the mixture and causes it to approach equilibrium more quickly. This is beneficial in the high-temperature region but a drawback in the cool-down region. The last effect of increasing the pressure, if the total mass flow rate of gas is held constant, is a corresponding increase in the reactor residence time due to increased density. An increase in reactor residence time will increase conversion in the high-temperature region but reduce the quenching effectiveness of the cool-down section. In summary, increasing the pressure causes changes in heat transfer, equilibrium, reaction kinetics, and reactor residence time, with competing effects on the amount of CO in the quenched exhaust stream. CFD modeling is therefore necessary to determine the combined effects of increasing the pressure. Helium Addition. The thermal conductivity of He is 5.5 times higher than that of CO2, which could increase the heat transfer from the hot zirconia rod to the surrounding gas and also from the hot gas to the cool pipe walls.4 Pure helium has a 53% higher convective heat transfer coefficient than pure CO2 in the heating section of the apparatus, based on an external flat plate laminar flow correlation, assuming the same volumetric flow rate in both cases. Mixtures of 50:50 mol % CO2/He and 75:25 mol % CO2/He have 30% and 13% greater heat transfer coefficients in the heating region than pure CO2. In the cooling region, helium has a 550% greater convective heat transfer coefficient than pure CO2, based on an internal laminar flow correlation with constant wall temperature. Mixtures of 50:50 mol % CO2/He and 75:25 mol % CO2/He mixtures have 340% and 220% greater convective heat transfer coefficients in the cooling region, respectively, than pure CO2 using the same
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Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007
Figure 2. Simple model configurations for the cases studied.
Figure 3. Experimentally determined zirconia rod temperature profile.
internal flow correlation. There is a clear incentive to use helium to increase heat transfer. The addition of helium also impacts the reaction kinetics, since the helium dilutes the CO2, causing a decrease in the rate of all reactions involving CO2. Premixed calculations show that reaction kinetic rates are only slightly lowered as a result of dilution.6 The addition of helium decreases the density, which decreases the residence time for the same mass flow rate. CFD modeling is needed to evaluate the overall impact of He addition to the CO2 in the converter. Details of Fluid Dynamic Calculations The theoretical analysis in the previous section showed that each suggested improvement entails competing factors that might increase or decrease CO production. FLUENT calculations were performed using the computational grid used previously by Price et al.3 for the fluid dynamic modeling where operational adjustments were the only factor. These calculations used an axi-symmetric two-dimensional (2-D) model using quadrilateral grid cells. The grid was constructed in a way where cells were packed preferentially into the hightemperature throat area and in the cool-down section. In all, four modeling grids were used for predictions: (1) the original geometry; (2) a geometry with no expansion following the rod; (3) a geometry with a larger diameter rod and no expansion following the rod; and (4) a geometry with a conic zirconia surface and an impaction plate directly after the zirconia cone. Simple schematics of these four configurations are shown in Figure 2. Grid independence studies were performed on each case by comparison of three parameters: zirconia rod heat flux, outlet temperature profile, and outlet CO mole fraction profile. For each case three grids were constructed, a course grid, a 1/2 size grid, and a 1/4 size grid. Predictions showed that the 1/2 size and 1/4 size grids gave similar results (within 2%) for the heat
flux off the zirconia rod, as well as the outlet profiles of temperature and CO mole fraction. The results from the 1/4 size grid are used in the results section. This grid had 18 256 grid cells for the original geometry, with grid cells packed preferentially into the high-temperature region and cool-down section. For the other three designs, the grid size and number of grid cells remained roughly the same. Eight model simulations were performed to examine the effectiveness of all suggested improvements. The input parameters that vary from case to case are shown in Table 2, along with overall modeling results. The inlet volumetric flow rate was typically 10.0 slpm or 6.0 slpm. The zirconia rod temperature profile was taken from the experimentally determined temperature profile shown in Figure 3. This temperature profile was programmed as a user-defined function. Previous modeling involving detailed radiation heat transfer predicted a zirconia rod temperature profile similar to the one determined experimentally.11 This radiation modeling determined that solar radiation heats the zirconia rod to the temperatures shown in Figure 3 and does not heat the gas to any significant extent nor cause significant photon-induced chemical reactions. This means that neglecting radiation does not impact the overall modeling results. While design modifications and operational adjustments undoubtedly will influence this temperature profile, standard experimental operation of the prototype dictates that the portion of the zirconia rod that extends into the silver funnel be heated to the softening temperature of the zirconia. This is achieved by varying the area of solar mirrors focused on the rod and thus the incoming radiation energy. With the experimental operation of the prototype known, it was assumed for all cases that all zirconia exposed to incoming radiation (any portion of zirconia upstream of the throat) have the same temperature as the original. The original prototype assumed a conservative approximation of the softening temperature of zirconia (2623 K) for the temperature of the rod upstream of the throat. The original downstream zirconia rod temperature profile versus distance was also used for all cases. This downstream temperature profile was based on the detailed radiation modeling efforts discussed previously which predicted similar rapid axial cooling of the zirconia rod downstream of the throat for various incoming radiation fluxes, in line with the experimentally determined rod temperature profile. The converging silver walls were modeled using adiabatic boundary conditions, and the throat and exhaust pipe walls were modeled as a constant temperature of 548 K. This is in contrast to earlier models which modeled the throat section as adiabatic. This change was made because the throat was kept at a constant temperature experimentally. For the cone and impaction plate case, the temperature of the zirconia cone exposed to the solar flux was assumed to be 2623 K. The unexposed side of the zirconia cone was assumed to be adiabatic, and the impaction plate was a constant temperature of 800 K.
Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 1963
Figure 5. Predicted radially averaged CO mole fraction profiles for the base case and Case 1. Figure 4. Predicted radially averaged temperature profiles for the base case and Case 1.
The properties of the reacting CO2 mixture throughout the reactor were calculated using the ideal-gas-mixing law. All individual heat capacities were defined using the piecewise polynomial equation available in FLUENT. The individual viscosities and thermal conductivities were defined using the kinetic theory of gases. The reactions were modeled by enabling the species transport model and selecting the carbon monoxide/ air mixture. Because the prototype operates in the laminar flow regime, the reaction rates were modeled using the laminar finite chemistry option with the rate coefficients listed previously in Table 1. In order to model all the reactions, the O radical species was included, with its properties taken from the JANAF Thermochemical Tables.12 The SIMPLE algorithm was used to model the pressurevelocity coupling.13 The momentum, energy, and all species equations were solved by the first-order upwind method. After significant convergence was achieved, the solution method for solving the momentum, energy, and species continuity equations was switched to the QUICK scheme, and the model cases were fully converged using this scheme. Nonreacting flow was modeled to obtain a first approximation of the temperature and velocity profiles for each case by running only the continuity, momentum, and energy equations for 10002000 iterations. The chemistry was then activated, and the model was run until it converged. All under-relaxation factors were reduced to 0.1 to avoid problems with convergence. Most models required 80 000-150 000 iterations to converge because of the low under-relaxation factors. Results and Discussion This section presents results from the eight representative simulations that illustrate the proposed changes to the solar converter. Additional details are provided by Price.11 Flow Rate. The theoretical analysis presented above indicated that lowering the CO2 flow rate could increase the conversion of CO2 to CO. A comparison of the base case with Case 1 (see Table 2) was made to illustrate how temperature, velocity, and CO concentration profiles changed when the CO2 flow rate changed from 10.0 slpm to 6.0 slpm. The temperature predictions for the two cases showed peak local gas temperatures of 2623 K, corresponding to the hottest portion of the zirconia rod. Figure 4 shows the predicted radially averaged temperature profiles for both cases. The radially averaged temperature profiles are area-weighted values. The temperature profiles are similar in both shape and relative magnitude. The peak average
temperature was predicted to be 1480 K for the base case and 1590 K for Case 1. The average outlet temperatures predicted were 1130 K for the base case and 1030 K for Case 1. Overall heat transfer from the rod to the gas and from the gas to the exhaust pipe was predicted to decrease from the base case to Case 1, but this was counteracted by lower velocities and longer residence times. The overall impact of both these phenomena is a higher average peak temperature and a lower average outlet temperature predicted for Case 1 versus the base case. Peak local CO concentrations of up to 21.4 mol % were predicted in both cases. Figure 5 shows the predicted radially averaged CO concentration profiles for both cases; a peak average CO conversion of 9.32% was predicted for the base case, and 11.6% was predicted for Case 1. Conversion is defined as the moles of CO produced per mole of CO2 entering the prototype. An outlet CO concentration of 4.79 mol % was predicted for the base case, with 5.85 mol % in Case 1. These predictions show that peak CO conversion was increased in the high-temperature region of Case 1 by 24.4%. Outlet conversion of CO was increased by 23.7% to 6.22% for Case 1. The quenching efficiencies, defined as the outlet amount of CO divided by the peak amount of CO, were similar for the two cases: 53.8% for the base case versus 53.5% for Case 1. Although the outlet conversion increased for Case 1, the total outlet amount of CO produced was 25.8% less (i.e., 7.77 mg/s for Case 1 versus 10.47 mg/s for the base case). These predictions agree with experimental results of between 5.5 and 7.0 mol % CO in the product stream when operated at 6.0 slpm. CO mole fraction profiles, CO flow rates, CO conversions, and quenching efficiencies were calculated using the mass-weighted values from the converged CFD simulation. These predictions show that decreasing the flow rate to 6.0 slpm caused the prototype converter to be more effective in the high-temperature region while only slightly reducing the effectiveness of the quenching. These effects are directly related to the residence times in both these regions. While this reduced flow increases the outlet conversion, it decreases the overall amount of CO produced. Pipe Diameter. A comparison of Case 2 with Case 1 (see Table 2) illustrates the effect of changing the exhaust pipe diameter from 2.50 to 1.27 cm. The throat diameter was 1.27 cm, so Case 1 had an expansion in the cool-down region while Case 2 had a straight pipe in this region. Both of these cases used an inlet flow rate of 6.0 slpm. Predicted radially averaged temperature and CO concentration profiles for Cases 1 and 2 are shown in Figures 6 and 7. Both temperature and CO concentration predictions showed no significant differences between the two cases upstream of the diameter change. Both
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Figure 6. Predicted radially averaged temperature profiles for Cases 1 and 2.
Figure 7. Predicted radially averaged CO mole fraction profiles for Cases 1 and 2.
cases have identical peak temperature and CO concentration that occur upstream of this diameter change. The gases cooled down more quickly in the reduced exhaust diameter case (Case 2). The predicted average outlet gas temperature also decreased from 1030 K for Case 1 to 970 K for Case 2. From the highest temperature region to the outlet, Case 2 dissipated 10.7% more heat than Case 1. This increased cooling also led to a greater predicted outlet CO concentration, 6.47 mol % in Case 2 versus 5.85 mol % in Case 1. This change corresponds to an 11.2% greater CO conversion, with a quenching efficiency of 59.5% for Case 2. These modeling results show that narrowing the exhaust pipe diameter increases the heat transfer from the CO2/CO/O2 product mixture. In addition, the narrowed pipe diameter decreased the residence time in the quenching region. Both these factors combine to provide better quenching that leads to increased CO concentrations in the product. The increased radial dispersion of CO into colder environments caused by the expansion in the original converter does not significantly affect quenching, since Case 2 predicted an 11.2% increase in the amount of CO in the outlet stream from a 10.7% increase in cooling heat transfer. Zirconia Rod Diameter. The effects of increasing the zirconia rod diameter and, hence, narrowing the annulus for the gas passage are shown by comparing Cases 2 and 3. The increase in rod diameter causes an increase in the thermal boundary layer area. The original zirconia rod had a diameter of 0.724 cm, while the thicker modeled rod had a diameter of 1.143 cm. Both Case 2 and Case 3 had a narrow exhaust pipe (with a diameter of 1.27 cm). To achieve accurate radial profiles of temperature and CO concentration, the grid size through this narrow annulus was decreased by a factor of 5 in the radial
Figure 8. Predicted radially averaged temperature and CO mole fraction profiles for Case 3.
direction. This model was run with an inlet flow rate of 6.0 slpm, corresponding to the proposed operation of this new prototype design. The predicted temperature profile and the CO mole fraction profile for Case 3 have local maxima of 2623 K and 21.6 mol %, respectively. The high-temperature thermal boundary layer is only slightly less thick, 0.62 mm, than the annular gap, 0.63 mm, as it approaches the throat section. Also, there is still a steep thermal gradient in the throat section. Predicted radially averaged temperature and CO concentration profiles for Case 3 are shown in Figure 8. Both these profiles have similar shapes and relative maxima to the base case, as well as the other cases previously discussed. Both the average temperature and CO mole fraction profiles predicted for Case 3 showed higher maxima than any other case (1650 K and 11.9 mol %, respectively). The profiles also show that quenching starts at a slightly earlier axial rod location for this case versus other cases. This was due to the decreased annular distance between the zirconia rod and the cool throat walls providing more immediate cooling. The model predicted an average outlet temperature of 940 K, with an average outlet CO concentration of 7.20 mol %. The outlet CO represents a conversion of 7.76%, with a quenching efficiency of 57.3%. The conversion of CO from CO2 increased by 12.3% compared to Case 2. The quenching efficiency for Case 3 is slightly lower than for Case 2. This is due to increased reverse reaction kinetics during the initial stages of quenching that result from the increased CO concentrations. The quenching efficiency is positively impacted by higher velocities in the narrow annulus which correspond to an increased convective heat transfer coefficient and a reduced residence time. Experimental results verify the modeling predictions for this case as well. Outlet CO mole fractions between 7.0 and 8.5 mol % were observed experimentally using a largerdiameter zirconia rod in the prototype while operating at 6.0 slpm. Several factors led to increased conversion for Case 3 versus Case 2. First, the larger diameter rod led to a greater thermal boundary layer area. This increased both the average temperature and CO mole fractions. Second, the larger-diameter rod caused higher velocities in the annular section of the device which led to higher heat transfer and lower residence time in that section. Both the higher heat transfer and the reduced residence time positively impacted quenching. These modeling predictions agree with the experimental results for this case. Operating Pressure. Two cases were run to show how changing the pressure affects converter performance. The operating pressure was set to 2.0 atm for both of these cases. The first higher pressure case (Case 4) had the same mass flow as Case 1 (6 slpm). The second higher pressure case (Case 5)
Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 1965
Figure 9. Predicted radially averaged temperature profiles for the three pressure cases.
Figure 10. Predicted radially averaged CO mole fraction profiles for the three pressure cases.
had a volumetric flow rate of 12 slpm to have similar velocities and residence times as Case 1. The radially averaged temperature profiles for Cases 4 and 5 are compared with those from Case 1 in Figure 9. The predicted temperature profiles for all three cases are quite similar in shape. The temperature profiles for Cases 1 and 4 were expected to be quite similar, based on the theoretical analysis that shows that increasing the pressure while maintaining the same mass flow rate should have no effect on the overall heat transfer. However, radially averaged maximum temperatures predicted in Cases 4 and 5 were lower than that in Case 1 (1590 K for Case 1, 1530 K for Case 4, and 1490 K for Case 5), which is most likely due to faster reaction kinetics at higher pressures. This means more energy is driving the endothermic reaction of CO2 to form CO and less energy is heating the gas. This same phenomenon in reverse causes the higher pressure cases to cool less quickly in the post-rod region. The predicted temperatures for Case 5 are lower than those of Case 4 throughout the reactor. This was also expected as the increase in heat transfer due to increased velocity is more than counteracted by the higher mass flow rate. Predictions from Cases 4 and 5 emphasize that heating and cooling alone are not strong functions of residence time. The CO mole fraction predictions for all three cases were also compared to analyze the impacts of pressure on the reaction kinetics and equilibrium. The predicted radially averaged CO mole fraction profiles are shown in Figure 10. An outlet CO mole fraction of 5.85 mol % was predicted for Case 1, with 4.47 mol % for Case 4 and 5.05 mol % for Case 5. These outlet CO mole fractions correspond to outlet CO mass flows of 7.77 mg/s CO for Case 1, 5.85 mg/s CO for Case 4, and 13.29 mg/s CO for Case 5. A higher peak radially averaged CO conversion was predicted for Case 4 than for Case 1 (12.3% versus 11.6%).
Figure 11. Predicted radially averaged temperature and CO mole fraction profiles for Case 6.
This increase is due to the increased reaction kinetics at higher pressure that causes higher initial production of CO. This increased production of CO also corresponds to the lower average temperatures seen in Figure 9 for Case 4. The increased residence time at high temperatures also enables increased production of CO. Unfortunately the peak production of CO is not preserved because of inefficient quenching due to increased kinetics of the reverse reactions of CO to CO2 and increased residence time in the cooling region. Case 4 has a quenching effectiveness factor of 38.0% versus 53.5% for Case 1. A higher peak radially averaged CO conversion was predicted in Case 4 than in Case 5 (12.3% versus 10.7%). This is due to the increased residence time in the heating region in Case 4 that enables higher conversion of CO from CO2. The increased peak CO production is not preserved because of increased residence time in the cooling region allowing for reverse reactions of CO to CO2. The quenching effectiveness factor for Case 5 is 49.6% compared to 38.0% for Case 4. These predictions show that increasing the flow rate and the internal pressure can result in a higher outlet amount of CO. A 71.0% increase was predicted in the outlet mass flow rate of CO for Case 5 compared to Case 1. In summary, these predictions show that increasing the pressure can increase the amount of CO produced, depending on the flow conditions. This increased CO production comes as the result of faster overall reaction kinetics and increased heat transfer due to higher pressure. Higher pressure also causes faster reverse reaction kinetics and lowered equilibrium conversion which, in some cases, may counteract the increased reaction rates and heat transfer and result in lower overall CO yield. These predictions did not include the possibility of cooling the hot gases by quickly reducing the pressure using a sudden expansion or a shock. This could be an effective way to increase the amount of CO preserved, especially at higher pressures. Helium Addition. The addition of helium was modeled in Case 6, with 25 mol % He in the inlet stream. This addition of helium corresponded to a lower overall mass flow rate to maintain the same volumetric flow rate of 6.0 slpm. The predicted peak local temperature for Case 6 was 2623 K, and the peak local CO mole fraction was 17.1 mol %. The predicted radially averaged temperature and CO mole fraction profiles are shown in Figure 11. These profiles are similar in shape and relative magnitudes to the other cases. The predicted maximum average temperature was higher than that in Case 1 (1640 K versus 1590 K), while the predicted outlet temperature was lower than in Case 1 (970 K versus 1030 K). These temperature predictions correspond to greater heat transfer for both heating and cooling, as expected with helium. The peak radially averaged CO conversion of 11.9% was 2.6% higher than that
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Figure 12. Predicted temperature and CO mole fraction profiles for Case 7.
predicted for Case 1, and the 6.52% outlet CO conversion was 4.8% higher than for Case 1. The quenching efficiency increased to 54.2% versus 53.5% for Case 1, meaning more effective quenching of the product mixture. The lower predicted CO mole fractions and lower outlet CO flow rate are the result of dilution. The predictions show that helium increased heat transfer in the prototype, causing improved heating and cooling. This increase in heat transfer increased the conversion of CO2 to CO but decreased the exit flow rate of CO, due to dilution of the CO2 by the He. Conical Rod and Impaction Plate. A completely new geometry was modeled in Case 7. The idea behind this geometry was to increase the hot surface area in order to convert more CO2 in the thermal boundary layer. A second-generation prototype converter was built with a honeycomb type zirconia section exposed to the same high solar flux as the original prototype. The honeycomb section was built from different conelike surfaces drilled into a cylinder of zirconia, with exit holes at the tip of the cone-like void spaces. All zirconia surfaces exposed to the solar flux were assumed to be heated to 2623 K. Just behind this honeycomb zirconia, a cold impaction plate maintained at 800 K quenched the product mixture. Model predictions for this geometry were performed with a flow rate of 10 slpm. For this flow rate, the Reynolds number in the throat was estimated to reach 2500, using the properties of CO2 at 2200 K. This is close to the critical Reynolds number for an internal flow of 2300, so this prototype was assumed to operate in the turbulent flow regime. Laminar kinetic rates were still assumed because of the nature of the reaction scheme. Sensitivity analysis of the kinetic parameters showed that the forward reaction of Reaction 1 is the dominant reaction under the prototype operating conditions. Because this reaction is essentially uni-molecular, it is independent of turbulence and mixing. The k- turbulence model was used to model the turbulent flow. Figure 12 shows both the temperature and the CO mole fraction profiles for this geometry. Because of the more complex geometry, average profiles are not shown. The peak gas temperature was predicted to be 2623 K, with a peak CO mole fraction that was 21.6 mol %. An average outlet temperature of 1170 K was predicted, with an average outlet CO mole fraction of 5.15 mol %. This outlet CO mole fraction corresponds to 12.2 mg/s, a 16.5% increase in the outlet amount of CO versus the base case. The outlet temperature was greater than in all other cases because the impaction plate wall was modeled as 800 K. The predicted radially averaged gas temperature and
CO conversion at the throat were 1610 K and 10.5%, respectively. If these are the peak values, the overall quenching efficiency was 51.7%. It is anticipated that this quenching efficiency would increase if the impaction plate temperature were decreased. This analysis shows that this conical design would increase conversion due to the greater high-temperature surface area of to the conic zirconia surface and better quenching by impaction with a cool wall. Predictions of this geometry should be extended to three dimensions to more fully represent the honeycomb structure of the zirconia actually used experimentally at Los Alamos Renewable Energy Corporation. Summary of CFD Calculations. A summary of the results of the CFD simulations is presented in Table 2. The outlet CO flow rate is a function of the heat transfer to the gas, the kinetic rates of formation in the hot boundary layer of the solar-heated surface, and the rapid quenching in the cooling region to minimize the reverse reactions. Lowering the flow rate increases conversion but lowers the outlet CO flow rate. The use of a smaller cooled exit tube increased conversion, as did the use of a larger rod diameter (and corresponding smaller annulus at the throat). The use of helium increased heat transfer but lowered the outlet CO mass flow rate due to dilution of the CO2. Increasing the pressure by a factor of 2 was beneficial as long as the input flow rate also increased by a factor of 2, although lower quenching efficiencies were predicted at increased pressure. The geometry change to increase heat transfer surface area using a conical-type honeycomb showed promise for increasing conversion as well. Conclusions Several process flow and geometrical design modifications were explored with both simple intuitive calculations and 2-D CFD models (FLUENT). The simple calculations were used to identify promising modifications, and the 2-D models were used to compute the competing effects of heat transfer, residence time, formation-reaction kinetics, and reverse-reaction kinetics. The 2-D CFD models were used to show that the following modifications would improve performance: reducing the diameter of the pipe in the cool-down region, increasing the zirconia rod diameter, and changing the zirconia rod shape and cool-down section. Decreasing the overall flow rate increased conversion but decreased the mass flow rate of CO produced. Increasing both the operating pressure and the overall flow rate was also shown to improve the conversion of CO from CO2, even though chemical equilibrium dictates lower CO at elevated pressures. Increasing the pressure at the same flow rate reduced both the amount and the conversion of CO. Dilution of CO2 with helium increased heat transfer but decreased the overall amount of CO due to the dilution of the CO2 as a reactant. Several of these design modifications and operational adjustments have already been implemented experimentally and have increased the conversion of CO from CO2, in agreement with predicted model trends. Continued efforts, both experimental and computational, are needed to achieve the CO conversion necessary to make this process economically viable. Literature Cited (1) Traynor, A.; Jensen, R. Direct Solar Reduction of CO2 to Fuel: First Prototype Results. Ind. Eng. Chem. Res. 2002, 41, 1935. (2) Foster, P. Continuous CO Separation by Liquid Absorption in Aqueous Cuprous Chloride (CuCl) and Magnesium Chloride (MgCl2) Solution. M.S. Thesis, Chemical Engineering Department, Brigham Young University, Provo, UT, 2006 (in progress).
Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 1967 (3) Price, R.; Morse, D.; Hardy, S.; Fletcher, T.; Hill, S.; Jensen, R. Modeling the Direct Solar Conversion of CO2 to CO and O2. Ind. Eng. Chem. Res. 2004, 43, 2446. (4) Incropera, F. P.; DeWitt, D. P. Fundamentals of Heat and Mass Transfer; Wiley: New York, 1996. (5) Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames; report UC-401; Sandia National Laboratories: 1992. (6) Kee, R. J.; Rupley, F. M.; Meeks, E.; Miller, J. A. CHEMKIN-111: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical and Plasma Kinetics; report UC-405; Sandia National Laboratories: 1996. (7) Tsang, W.; Hampson, R. F. Chemical Kinetic Data Base for Combustion Chemistry, Part I, Methane and Related Compounds. J. Phys. Chem. Ref. Data 1986, 15, 1087. (8) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 2002. (9) Sandler, S. I. Chemical and Engineering Thermodynamics; Wiley: New York, 1999.
(10) Gordon, S.; McBride, B. J. Computer Program for Computation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations; NASA SP-273; NASA: 1971. (11) Price, R. J. Modeling Three Reacting Flow Systems Using Modern Computational Fluid Dynamics. Ph.D. Dissertation, Chemical Engineering Department, Brigham Young University, Provo, UT, 2006 (in progress). (12) JANAF Thermochemical Tables, 2nd ed.; Dow Chemical Company: Midland, MI, 1971. (13) Patankar, S. V. Numerical heat Transfer and Fluid Flow; McGraw Hill: Boston, 1980.
ReceiVed for reView August 7, 2006 ReVised manuscript receiVed January 25, 2007 Accepted February 1, 2007 IE061035W
