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Methanol Conversion to Light Olefins over SAPO-34: Reaction Network and Deactivation Kinetics D. Chen,*,† A. Grønvold,‡,§ K. Moljord,‡,⊥ and A. Holmen† Department of Chemical Engineering, Norwegian UniVersity of Science and Technology (NTNU), N-7034 Trondheim, and SINTEF Applied Chemistry, N-7034 Trondheim, Norway
The kinetics of the reactions involved in the conversion of methanol to light olefins over SAPO-34, including deactivation caused by coke deposition, has been studied in an oscillating microbalance reactor between 673 and 823 K, space velocities from 50 to 2000 g/gcat,h and methanol partial pressures from 7 to 83 kPa. The proposed reaction network involves dimethyl ether as an unstable primary product, all the olefins formed in parallel as secondary products, and the paraffins formed from further reactions of olefins as stable tertiary products. The selectivity to ethene increased with increasing coke content and temperature. A kinetic model including the deactivating effect due to coke deposition has been developed to properly simulate the changes in activity and selectivity with the coke content. A linear dependency between the coke content and the reaction rate gave the best representation of the experimental data. Introduction From synthesis gas, which can be obtained by gasification, partial oxidation, or steam reforming from raw materials, such as biomass, coal and natural gas, methanol is synthesized using a proven technology. The catalytic conversion of methanol to olefins (MTO) was originally an intermediate step in Mobil’s process to convert methanol to synthetic gasoline using HZSM-5 as catalyst.1 However, interest has recently shifted toward the MTO process following the increased demand for olefins.2 As a consequence of the discovery of aluminophosphate molecular sieves, especially SAPO-34,3 it is possible to selectively produce ethene and propene at high methanol conversions, due to the narrow pores (0.43 nm) extending in three dimensions and the mild acidity of SAPO-34.4 However, fast deactivation of the catalyst due to coke formation has been reported.5-7 Most kinetic studies on methanol conversion have been made on HZSM-5 catalysts, and a number of simplified kinetic models have been developed. The complexity of the model varies according to the degree of lumping proposed.8-12 A very detailed analysis has been performed by Mihail et al.13-14 in which 33 reactions were used. Single-event kinetic modeling of MTO on H-ZSM-5 has been performed by Park and Froment15-16 on the basis of a detailed mechanistic description of the MTO reaction. Sedran et al.11 tested several alternative kinetic models for conversion of methanol to hydrocarbons, including an exponential activity function to account for the deactivation of the catalyst. A common characteristic of the kinetic models is the autocatalytic effect in the reaction network. However, to our knowledge, autocatalytic behavior has not been reported for conversion of methanol to light olefins over SAPO-34. A kinetic model for MTO over SAPO-34 based on results obtained in a plug flow fixed-bed reactor at 723 K has been * To whom correspondence should be addressed. Tel: +47 73593149. E-mail:
[email protected]. † NTNU. ‡ SINTEF Applied Chemistry. § Present address: Hydro Oil & Energy Research Center, Box 2561, N-3907 Porsgrunn, Norway. ⊥ Present address: Statoil, Postuttak, N-7005 Trondheim, Norway.
developed by Bos and Tromp.17 The conversion and the selectivities were studied as a function of the coke content of the catalyst. An exponential dependency was found to give the best representation of the effect of coke on the reaction rate. Unfortunately, direct measurements of coke formation in situ are not possible in a fixed-bed reactor. The determination of coke in this case must be done either by burning off the coke in the reactor or by taking the catalyst out of the reactor for weighing. Such measurements of coke content in a fixed-bed reactor may, therefore, introduce additional errors, and it is also a time-consuming process. The parameters in the model were, thus, estimated from a limited amount of data. Gayubo et al.18 performed a kinetic study of MTO in SAPO-34-based catalysts in a fixed-bed reactor, in which the catalysts were prepared by agglomerating the SAPO-34 (25 wt %) with bentonite (30 wt %), using fused alumina as the inert charge (45 wt %). The MTO reaction was studied as a function of time on-stream, and the initial reaction rates at different conditions were obtained by extrapolating ration rates to zero time. The authors have proposed a reaction network of MTO taking into account four individual steps for the production of ethene, propene, butanes, and other hydrocarbons (pentenes + paraffins). A kinetic model for the reaction network was developed; however, kinetics of coke deposition and deactivation during MTO were not included. Alwahabi and Froment19 have recently developed a single-event kinetic model of the MTO reaction on SAPO-34 based on the experimental data in a fixed-bed reactor. The deactivation caused by coke formation was modeled by fitting the conversion changes with time on-stream in the fixed-bed reactor. However, experimental data of coke formation and the deactivating effects of the coke formed are missing. An oscillating microbalance reactor (TEOM) provides an opportunity to achieve a better quantitative understanding of the activity and the selectivity changes with the coke formation.20 The mechanism and kinetics of the coking process have been investigated in detail in our previous work.21 The present work will focus on the selectivity to olefins and its changes with coke formation. A reaction network is proposed, and a kinetic model for this reaction network is developed, including the deactivation due to coke deposition.
10.1021/ie0610748 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/10/2006
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Experimental Section The setup of the TEOM reactor, the catalysts, and the experimental methods are identical to those described in our previous work.22 A more detailed description of the TEOM reactor can be found in a recent review.23 Calcined SAPO-34 with a unit cell composition of (Si2.88Al18P15.12)O72 was obtained from SINTEF Applied Chemistry. SAPO-34 catalysts are typically cubic crystals with sizes of ∼2 µm. The SAPO34 particles (52-140 mesh) were dried in situ at 773 K in flowing He for more than 3 h. The MTO reaction was performed at WHSV ranging from 57 to 2558 g (g of cat)-1 h-1, methanol partial pressure ranging from 7.2 to 83 kPa, and temperatures between 673 and 823 K. The runs with different space velocities were carried out at 698 K and a methanol partial pressure of 7.2 kPa to obtain a relatively low coking rate. The runs with different methanol partial pressures were also performed at 698 K. The space velocity was adjusted to ensure an identical conversion when the partial pressure of methanol was increased. For high methanol partial pressures, very high space velocities were required as a result of very rapid coke formation. The conversion and selectivities were calculated on a CH2 basis (CH3OH f CH2 + H2O). The isomers of C4, C5, and C6 were lumped according to their respective carbon numbers, and the selectivities of C1-C6 hydrocarbons were calculated by normalization exclusive coke. The yield-conversion plots were presented on a weight basis, and the formation of DME, hydrocarbons (C1-C6), and water was included. The water fraction was calculated from the mass balance. Due to the fast coke deposition on the catalyst, pulse experiments were used to study the changes in activity and selectivity with coke content. Pulses of 3-min duration were used for PmeOH < 30 kPa, whereas 1-min pulses were used at high temperatures (773-823 K). It has been shown previously that the conversion and selectivity were not affected by the pulse size.21 Reaction Network As discussed previously,20 the yield-conversion plot is a powerful tool for distinguishing the type of product (stable or unstable, primary or secondary) and the type of deactivation (selective or nonselective). Selective deactivation has been illustrated for the MTO reaction over SAPO-34. However, only a simple reaction model was used previously,20 in which all the hydrocarbons were lumped together; dimethyl ether (DME) was treated as a primary product; and the olefins, as secondary products. The present work differentiates the individual hydrocarbons according to product types and determines the effect of coke formation on the distribution of olefins. In Figure 1, the product yields at different space velocities are plotted against the conversion at 698 K and a methanol partial pressure of 7.2 kPa. Initial conversions are obtained by varying the space velocity, and the different symbols in Figure 1 illustrate different space velocities. For a certain space velocity, the conversion decreased with increasing coke content. The solid lines enclosing such loops are OPEs (optimum performance envelopes20,24), which are obtained from approximately the first pulse (TOS ) 2 min). Although this treatment is not very rigorous due to deactivation during the first pulse, it is expected not to lead to large errors with respect to the selectivity plot in this case, since the selectivity change with coke content is small at low coke contents (as shown later in Figure 5). However, it should be noted that the ethene selectivity changes significantly at very low coke content, and the uncertainty in determining
the OPE of ethene formation is, thus, relatively large. From the OPEs, the types of products can be identified. The OPE curves for the yield of C2-C6 are almost straight lines, indicating that the selectivities to olefins are almost constant on the fresh catalyst, regardless of the conversion. In other words, the gas-phase olefins formed over SAPO-34 are quite stable, and the secondary reactions of olefins do not seem to be very important. It has to be noted that the linear OPE curves do not pass through zero conversion, which is a characteristic of secondary products. The hydrocarbons, including ethene, propene, C4, C5, and C6, can thus be considered as stable secondary products formed in parallel from DME at a methanol conversion less than 100%. Light paraffins (ethane and propane) are formed only at high conversions, meaning that paraffins are stable tertiary products. The OPE curve for coke went through 0 at an almost identical conversion as for the olefins (10%), and it increased with increasing conversion. Coke may, therefore, be considered as a secondary plus stable tertiary product. The detailed mechanism of coke deposition has been discussed previously.21 Reaction intermediates such as carbenium ions inside the pores of SAPO-34 were considered as the major coke precursors. Equilibrium between olefins formed during methanol to gasoline over ZSM-5 is achieved.25 This is different for SAPO34, in which the olefin distribution is far from equilibrium.26 Additionally, equilibrium cannot explain the constant olefin distribution at different space velocities, since the partial pressure of olefins (related to the level of oxygenates conversion) has a profound influence on the equilibrium between olefins.25 Instead, we believe that the constant olefin distribution is caused by the low reactivity of olefin and the lower adsorption capacity for olefins relative to methanol.27 The low olefin reactivity over SAPO-34 has been demonstrated from the observation that the reaction rate of propene conversion was almost 100× lower than the MTO reaction.27 The low reactivity of olefins was also observed by Dahl et al.28 during ethanol and propanol conversion over SAPO-34. Salehirad and Anderson29 reported that ethene conversion was faster on the methylated SAPO-34 than on the bare catalyst, but the reaction rate of propene was still much lower than for methanol. It should be noted that the conversion of methanol was C5 > C4, C3 Changes in the product selectivities for a complex reaction due to coke formation on a zeolite-type catalyst can be caused by changes in conversion, acidity (including density and strength distribution), and shape selectivity.20 The linear OPE pattern in the yield-conversion plots for all the hydrocarbons (Figure 1) shows constant selectivities at different conversions on the fresh catalyst. In other words, the change in the conversion level itself due to the coke deposition should not influence the selectivity to the hydrocarbons. The heat of adsorption as function of the site coverage of methanol measured by methanol adsorption on SAPO-34 indicated a uniform distribution of acid strength,27 which is in good agreement with the result obtained from ammonia TPD experiments.35 In addition, the number of active
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sites per cage was estimated to be 0.8,36 indicating that a maximum of 80% of the cages are active for reaction. Each cage can be considered as a microreactor, and coke deposition reduces the number of microreactors. The number of active sites in each accessible microreactor is close to 1; therefore, it is not expected that the change in the number of total active sites due to coking influences the product distribution. The change in acidic properties is, therefore, unlikely to be the main reason, and shape selectivity is a more likely reason for the selectivity change. The MTO reaction on differently sized crystals has demonstrated the importance of the shape selectivity on the selectivity changes due to coke deposition.37 The results showed almost no effect of crystal size on the selectivity, but a significant effect of coke deposition. Therefore, the transition-state shape selectivity was considered to be dominant at relatively high coke contents. The formation of larger molecules via a larger-sized reaction intermediate was significantly suppressed by the reduced free space in the cavities by coke deposition, hence, enhancing the ethene formation. The much lower ethene selectivity at the low coke content (Figure 3) can be explained by a weak or no effect of the transition-state shape selectivity.37 However, a possible effect of the changes in the reaction mechanism with coke content cannot be excluded. Deactivation Due to Coke Deposition The coke deposition and deactivation of the MTO reaction at 698 K and PMeOH ) 7.2 kPa for different space velocities have been discussed in detail in our previous work.21 Deactivation of zeolites due to coke deposition is normally very complicated, since intracrystalline diffusion often influences both activity and selectivity. Coke deposition can reduce the number of active sites by site coverage or by pore blockage. Coke deposition can also increase the effective diffusion length and, thus, decrease the effective diffusivity and the effectiveness factor. It has been demonstrated that intracrystalline diffusion plays a key role in determining the activity and the coke deposition during MTO on SAPO-34 with the crystal size used in the present work.27,38-40 The role of the intracrystalline diffusion in MTO has recently been reviewed by Ruthven41 and Chen et al.;23 however, no attempts have been made to distinguish between different causes of deactivation in the modeling in the present work. Our previous work21 has shown that coke deposition increases significantly with increasing temperature. Figure 7A shows that the conversion of the oxygenates decreases more significantly with time on-stream at the higher temperature; however, Figure 7B indicates a rather similar deactivating effect of coke molecules formed during MTO at different temperatures. It means that the rapid deactivation of oxygenates at high temperatures is a main result of the rapid coke deposition. A small difference in the initial conversion of oxygenates with temperature can be observed at lower coke content (Figure 7B). This is mainly due to the high conversions, in which the conversion is not very sensitive to the change in the activity at such conditions. In addition, it can partly be a result of diffusion limitation. It is well-known that diffusion limitations reduce the observed activation energy.
Figure 7. Changes in conversion of oxygenates with the time on-stream (A) and the coke content (B) at 425 °C (O), 500 °C (4), and 550 °C (0). Partial pressure of methane of 14 kPa, WHSV ) 263 g (g of cat)-1 h-1
in the present work. Coke deposition can significantly change the intracrystalline diffusion resistance, increasing the complexity in modeling of the formation and consumption of DME. Therefore, methanol and DME are lumped together as oxygenates in our model. The kinetic models for coke deposition and the conversion of oxygenates were developed in our previous work,21 in which the conversion of oxygenates was treated as a first-order reaction. In the present work, the model is explored to predict the selectivity change with coke formation. The TEOM reactor is treated as an ideal isothermal plug flow reactor containing 5-10 mg of catalyst. The integral model for methanol conversion is used in the present work, but an approximation has been made to assume uniform distribution of coke in the catalyst bed. The experimental coke contents were used to fit the parameters in the deactivation functions. In the model, all mole fractions are calculated on a dry basis, that is, on the basis of CH2 equivalents. The reactor models can be expressed as
dx b )b r d(W/FMeOH)
(3)
The kinetic model for the reaction network presented in Figure 2 is expressed as follows,
Kinetic Model of the MTO Reaction Network It was found that it is difficult to model the formation and consumption of DME properly. It is expected that the formation and conversion of DME are influenced by intracrystalline diffusion, due to the large crystals (∼2 µm) of SAPO-34 used
ri ) k0i φiy6P0 for i ) 1-5 5
k0i φi)y6P0 ∑ i)1
r6 ) (
(5)
Ind. Eng. Chem. Res., Vol. 46, No. 12, 2007 4121 Table 1. Reaction Rate Constants, k0i ; Deactivation Rate Constants, ri, at Different Temperatures and Parameters for Arrhenius Equation ki0 ) Ai exp(-Ei/RT) T, °C 400 k01 k02 k03 k04 k05 k07 R1
R2 R3 R4 R5 R7
425 10-2
0.22 ( 1 × 0.35 ( 1 × 10-2 0.13 ( 1 × 10-2 0.038 ( 2 × 10-2 0.008 ( 9 × 10-3 0 0.038 ( 1 × 10-3 0.041 ( 1 × 10-3 0.040 ( 2 × 10-3 0.050 ( 8 × 10-3 0.115 ( 4 × 10-2 0.066 ( 3 × 10-2
500 10-2
0.25 ( 1 × 0.31 ( 1 × 10-2 0.11 ( 1 × 10-2 0.035 ( 2 × 10-3 0.011 ( 6 × 10-3 0.006 ( 5 × 10-3 0.049 ( 3 × 10-4 0.052 ( 3 × 10-4 0.052 ( 8 × 10-4 0.060 ( 6 × 10-4 0.114 ( 3 × 10-2 0.066 ( 2 × 10-2
0.55 ( 5 × 0.67 ( 5 × 10-2 0.23 ( 5 × 10-2 0.087 ( 1 × 10-2 0.017 ( 1 × 10-2 0.020 ( 1 × 10-2 0.054 ( 3 × 10-3 0.059 ( 2 × 10-3 0.054 ( 4 × 10-3 0.060 ( 1 × 10-2 0.059 ( 1 × 10-2 0.057 ( 3 × 10-2
where i ) [ethene, propene, butenes (C4), C5, C6, oxygenates, ethane + propane]. The formation of paraffins (ethane and propane) was treated as a secondary reaction of all hydrocarbons. The rate of formation is described by eq 6,
r7 ) k07φ7(1 - y6)P0
(6)
where k0i is the initial rate constant, φi is the deactivation function, P0 is the initial methanol partial pressure, and yi is the mole fraction on a CH2 basis. All rate constants are assumed to depend on the catalyst coke content, which is taken into account by the deactivation functions, φi. Different deactivation functions42,43 have been tried to describe the change in reaction rates with coke content. The linear function (eq 7) was found to give the best fit to the experimental data.
B φ)1-R bC
(7)
C is the weight percent of coke on the catalyst (gcoke/gcat %). It should be noted that the experimental relationship between the deactivation and the coke content is not perfectly linear, as shown in Figure 7B. It follows a curve of a decrease in effectiveness factor with increasing Thiele modulus. A rigorous modeling, including intracrystalline diffusion and changes with coke deposition, will be necessary in the future to perfectly simulate the deactivation function of this system. As mentioned above, selective deactivation for the MTO reaction over SAPO-34 was found. The different reaction steps have different deactivation rates, that is, different Ri values. The effect of coke on the selectivity, that is, the ratio of the reaction rates, can now be modeled by using different values for the empirical Ri constants. A fourth-order Rung-Kutta method was used to integrate the ordinary differential equations. The estimation of the parameters of the kinetic model has been carried out by the nonlinear least-squares routine in MATLAB using the Levenberg-Marquardt method. The optimum function is given in eq 8, n
S)
550 10-2
10-2
0.755 ( 6 × 0.76 ( 6 × 10-2 0.28 ( 5 × 10-2 0.104 ( 2 × 10-2 0.030 ( 9 × 10-3 0.028 ( 9 × 10-2 0.063 ( 1 × 10-3 0.066 ( 1 × 10-3 0.058 ( 3 × 10-3 0.062 ( 6 × 10-3 0.065 ( 1 × 10-2 0.072 ( 2 × 10-2
Ai (kmol/gcat, kPa, h)
E (kJ/mol)
7210 40 15 17 5 181
38.4 27.0 26.9 49.8 32.4 59.6
individual parameters was tested by t-test, and the standard deviation of each parameter was also calculated in a 95% confidence interval.42 All the parameters in the model have been estimated separately at different temperatures. Reaction and deactivation rate constants together with their standard deviations are listed in Table 1. Statistical analysis indicated that the overall regression is meaningful. The empirical deactivation rate constant R follows the order of the molecular size. Larger molecules have larger changes in selectivity with coke content and, thus, a higher deactivation rate. This may point out the importance of the effect of transition-state shape selectivity on the product selectivity.37 The standard deviation for R5 and R7 is relatively large. It is mainly due to the relatively large experimental error for the analysis, since the mole fractions of C6, ethane, and propane are very low in most of the experiments. Figure 8 shows an Arrhenius plot of the initial kinetic rate constants for the formation of the various products. The rate constants fitted Arrhenius law well. The estimated apparent activation energies and pre-exponential factors are presented in Table 1. Figure 9 shows the comparison between experimental and predicted mole fractions for each component. The rate constants were calculated from the Arrhenius equation using the parameters presented in Table 1. The model fitted the experimental results generally well at all temperatures, except for C6. The reason for the deviation in predicting the C6 mole fraction is at least partly due to the relatively large experimental error in the GC analysis, since the mole fraction of C6 is very low, especially at relatively high coke contents. The same argument also holds for methane. The mole fraction of methane is very low at the conditions used in the present work. In addition, a very small fraction of methane was founded in a few blank experiments, possibly caused by decomposition of methanol on the metal
m
∑ ∑ wij[(yiPR) - (yiEXP)] i)1 j)1
(8)
where index i indicates the component considered; index j, the kinetic run; yiPR and yiEXP are the predicted and experimental molar fraction for component i; and wij is a weighting factor. After the parameters was estimated, an extensive statistical analysis was performed. The significance of the overall regression was tested by means of an F-test. The significance of the
Figure 8. Arrhenius plot for reaction rate constants. 9, Ethene; 2, propene; ×, butenes; [, C5; b, C6.
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the induction period depended on the crystal size, temperature, and concentration of oxygenates.37 For SAPO-34 used in the present work, the effect of intracrystalline diffusion cannot be avoided,27 and thus, the induction period is very short. For example, the induction period measured at 698 K and 30 kPa methanol partial pressure was about 15-30 s. Hence, ignoring the induction period should not create a large error. Conclusions A reaction network for the MTO reaction has been established, DME is a nonstable primary product, all the hydrocarbons are formed in parallel from oxygenates, and ethane and propane are considered to be stable tertiary products. A relatively simple kinetic model, in which methanol and DME were lumped, was developed to describe the change in selectivities with the coke content. Catalyst deactivation was well-described by a linear relation between the coke content and the reaction rate. The experimental data fitted the model generally well in the temperature range of 673-823 K. The secondary reactions of olefins were not included in this kinetic model, because their reactivity was low. The distribution of olefins was not affected by the partial pressure of methanol and the space velocity, but increasing temperature and coke deposition increased the ethene selectivity significantly during MTO over SAPO-34. The effect of coke on the selectivities is proposed to be a result of transition-state shape selectivity, favoring the formation of smaller molecules as the void volume in the cavities is reduced by coke. Acknowledgment The support of this work by the Norwegian Research Council and Norsk Hydro ASA is gratefully acknowledged. Figure 9. Parity plot for mole fraction of olefins. 698 K, methanol partial pressure of 7.2 kPa and WHSV. 0, 385; ∆, 113; / , 82; ], 57 g (g of cat)-1 h-1; 773 K, 12 kPa and 266 g (g of cat)-1 h-1, 2; 823 K, 8 kPa bar, and 268 g (g of cat)-1 h-1, [; 673 K, 7.2 kPa and 385 g (g of cat)-1 h-1, b.
part in the setup. The reproducibility of the methane mole fraction is relatively poor. It is expected that the experimental uncertainty is larger at low conversions, such as high coke contents and low temperatures. Therefore, kinetic modeling of methane formation is not reported in the present work. The apparent activation energies for the olefin formation are relatively low, as shown in Table 1. As discussed previously,27,37 this is due in part to the intracrystalline diffusion limitation. The intrinsic activation energy can be estimated by accounting for the effect of diffusion.42 If we assume that MTO was controlled completely by intracrystalline diffusion, the activation energy should be 2× the activation energy measured, namely, 76 kJ/mol. The apparent activation energy for ethene formation is then expected to be between 38 and 76 kJ/mol. However, for zeolite-catalyzed reactions, the apparent activation energy also involves the heat of adsorption.43 The real intrinsic activation energy for the surface reaction is then estimated43 to be between 68 and 106 kJ/mol, taking into account the measured adsorption heat of 30 kJ/mol for methanol.27 The presence of intracrystalline diffusion limitation makes it difficult to compare the activation energy directly with the literature data. In addition, it is worth mentioning that the estimated initial rate constant is only an approximation, and the induction period during which conversion increased with time on-stream or coke content is ignored in the present work. Induction periods have been observed during MTO over SAPO-34, and the length of
Nomenclature Ai ) pre-exponential factor for the reaction rate, k0i , kmol (g of cat, kPa,h)-1 C ) weight percent of coke on the catalyst (g of coke/100 g of cat) E ) activation energy, kJ/mol FMeOH ) molar flow rate of methanol (mol/h) i ) 1, 2, 3, 4, 5, 6, 7 represents ethene, propene, butenes (C4), C5, C6, oxygenates, and ethane + propane, respectively. j ) number of kinetic run k0i ) initial rate constant for the formation of component i, kmol (g of cat, kPa,h)-1 P0: initial methanol partial pressure, kPa b r ) [r1, r2, r3, r4, r5, r6, r7]; matrix of reaction rate, kmol (g of cat, h)-1 ri ) rate of formation of I, kmol (g of cat,h)-1 S ) objective function W ) catalyst loading, g of cat wij ) weighting factor. b x ) [x1, x2, x3, x4, x5, x6, x7]; matrix of conversion xi ) conversion to i yi ) mole fraction of component i on a CH2 basis yiEXP ) experimental molar fraction for component i yiPR ) predicted molar fraction for component i Ri ) empirical deactivation constant for the reaction corresponding the formation of i defined by eq 7 φi ) deactivation function for the formation of component i Literature Cited (1) Chang, C. D. Methanol Conversion to Light Olefins. Cat. ReV. Sci. Eng. 1984, 26, 323.
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ReceiVed for reView August 15, 2006 ReVised manuscript receiVed October 19, 2006 Accepted October 20, 2006 IE0610748
