Modeling of a Transpiring Wall Reactor for the Supercritical Water

A mathematical model of the transpiring wall reactor (TWR) for supercritical water oxidation (SCWO) of the University of Valladolid, Spain, has been d...
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Ind. Eng. Chem. Res. 2005, 44, 3835-3845

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APPLIED CHEMISTRY Modeling of a Transpiring Wall Reactor for the Supercritical Water Oxidation Using Simple Flow Patterns: Comparison to Experimental Results M. Dolores Bermejo, Fernando Ferna´ ndez-Polanco, and M. Jose´ Cocero* High Pressure Process Research Group, Department of Chemical Engineering and Environmental Technology, University of Valladolid, 47011 Valladolid, Spain

A mathematical model of the transpiring wall reactor (TWR) for supercritical water oxidation (SCWO) of the University of Valladolid, Spain, has been developed, and the results calculated have been compared to experimental data of the reactor. This model divides the reactor into three main areas of different flow patterns: mixer (plug flow (PF)), upper part (CSTR), and cooling zone (PF). The comparisons of the calculated temperature profile to the experimental one and the calculated total organic carbon (TOC) removal to the experimental one are favorable. Thus, a theoretical study of the main operation parameters has been carried out. It is convenient working with the reactor using a feed of 16.5 kg/h, a transpiring flow relation of 0.5, a transpiring flow temperature of 200 °C, an air inlet temperature of 300 °C, and an isopropyl alcohol (IPA) concentration of 8% ww. Working with higher concentrations of IPA is possible to reduce feed and transpiring flow temperature and to work without preheating air and transpiring flow, obtaining TOC removals near 100%. Introduction Supercritical water oxidation (SCWO) is a process that consists of the oxidation of organic solutes in an aqueous medium using oxygen or hydrogen peroxide as an oxidizing agent, at temperatures and pressures above the critical point of water (647.3 K and 22.12 MPa). The main application of SCWO is the destruction of organic wastes. Conversion rates higher than 99% can be achieved with residence times shorter than 1 min. At the University of Valladolid (UVa), Spain, the High Pressure Process Group has been working with the SCWO process since 1993, developing the cool wall reactor for low salt concentration wastes in a pilot plant1,2 and in a demonstration plant.3 The advantage of the cool wall reactor consists of separating spatially pressure load and temperature effects. This is achieved using a reaction chamber that withstands high temperatures and corrosion effects and a pressure vessel where the wall is cooled by the feed keeping the wall temperature below 400 °C. The two main challenges of SCWO are corrosion and salt deposition. To overcome these two problems, a number of reactor designs have been developed. One of the more recent ones is the transpiring wall reactor (TWR), that consists of a reaction chamber limited by a wall through which clean water circulates, forming a cool protecting film against corrosive agents, salt deposition and scaling, and high temperature. The concept of the TWR splits the pressure effect and the corrosion and temperature effects. In the last years, a number of TWRs have been developed,4-8 and computational models have been * To whom correspondence should be addressed. Fax: +34983423013. E-mail: [email protected].

developed to explain the behavior of the reactor. Fauvel et al.9 modeled their reactor considering it as a cascade of ideally mixed tanks with a stage radial feed, after carrying out a residence time distribution study to investigate the flow pattern. The proposed hydrodynamic model was validated by experiments of ethanol oxidation in supercritical water. Other groups developed computational fluids models (CFD)5,6,10 to get an insight into local flow conditions and species concentrations inside the reactor and around the transpiring wall, because this information is hardly accessible for measurements. In these cases, to validate the computational results, local temperatures and destruction efficiency are used. In this paper, a simple flow pattern model has been developed in order to explain in an easy and intuitive way the behavior of the TWR of the University of Valladolid (UVa). This model is useful to prove different ways of operation and for essaying modifications in the reactor, as a previous step to install it in the demonstration scale pilot plant of the University of Valladolid situated in Santovenia de Pisuerga (Valladolid, Spain).3 Experimental Device The reactor modeled is the transpiring wall reactor situated in the supercritical water oxidation pilot plant of the University of Valladolid. The transpiring wall reactor consists of a stainless steel pressure shell with a volume of 10 L. It contains a reaction chamber limited by a porous alloy 600 wall through which clean water circulates. The main dimensions are shown in Scheme 1. The feed and the air are introduced in the reactor by its lower part, and they pass through the static mixer up to the upper part of the reaction chamber; the

10.1021/ie0487742 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/27/2005

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Scheme 1. Scheme of the Reactor Indicating Its Main Dimensions in Millimeters

(2) Air stream supplied by a four-staged air alternative compressor (INGERSOLL-RAND, model H15T4) with a 36 kg/h air flow that can be regulated before entering into the reactor. (3) Transpiring flow that consists of tap water pumped by a DOSAPRO MILTON ROY, model MILROYAL C-MC 61 S(Q) 20 N, metering pump which supplies flows from 7 to 72 L/h. The three streams can be preheated electrically up to the desired inlet temperature. The products of the reactor are cooled in the intercoolers after leaving the reactor, and after depressurization, samples of the liquid and gas effluents can be taken. Model Description This model follows the main assumptions of other SCWO reactor modeling done by the High Pressure Process Group of the University of Valladolid:11-13 (1) Runge-Kutta, fourth order with a fixed step numerical integration method. (2) The pressure along the reactor is considered constant and equal to 23 MPa. The momentum equation may be neglected. (3) The physical properties of isopropyl alcohol and acetic acid are taken as those of the water at the same pressure and temperature. (4) The properties of the mixture are calculated as shown in eq 1

Prop(T,P) )

reagents flow down, mixing with the clean water that enters into the reactor by the transpiring wall, and purified water leaves the reactor by its lower part. A scheme of the reactor is shown in Scheme 4. Scheme 2 shows the flow diagram of the plant. Three streams are introduced in the reactor: (1) Feed steam containing the waste and the fuel in water, pumped by a DOSAPRO MILTON ROY, model M6-140 L-14 M 300/JVV1, metering pump which supplies flows from 4 to 40 L/h. Scheme 2. Flow Diagram of the SCWO Plant

∑xi‚Prop(T,P)i

(1)

where xi is the molar fraction of each component. The thermodynamic properties are taken from the literature.14-16 (5) The kinetics pathways used are those reported by Li et al.17 They suggest that the oxidation kinetics involve the formation and destruction of rate controlling intermediates: some organic compounds are destroyed into the final oxidation products, while others are transformed into stable intermediates. In this case, the organic matter (in our case, only isopropyl alcohol is considered because all the experiments were done using it as fuel and reagents) degrades fast into acetic acid, which is the only intermediate reagent considered for

Ind. Eng. Chem. Res., Vol. 44, No. 11, 2005 3837 Scheme 3. Kinetic Model Scheme

Scheme 5. Top Part of the Reaction Chamber

Scheme 4. Scheme of the Flow Patterns Used in the Model

The new items in this model are the following: The heats of reaction have been calculated for different temperatures using the Peng-Robinson equation of state (EOS) with Boston-Mathias alpha functions21 and then correlated with a polynomial equation shown in eqs 3-5.

∆HrA ) -0.9709T2 + 1174T - 2 133 215

(3)

∆HrB ) 269T - 901 590

(4)

∆HrAB ) -0.8182T2 + 625T - 752 517

Table 1. Kinetic Parameters in the Arrhenius Equation Used to Simulate the IPA Oxidation k1 (IPA to CO2) k2 (IPA to HAc) k3 (HAc to CO2)

A (s-1)

Ea (J/mol)

2.61 × 105 2.61 × 105 2.55 × 1011

64 000 64 000 1 727 000

the simulation of the SCWO process, since this compound presents the lowest kinetics under these conditions. In Scheme 3, the general reaction pathway considered is shown. The values of k1 and k3 are given by Chen et al.18 and Meyer et al.19 k2 depends on the chemical compound to be hydrolyzed into acetic acid, taken as the only stable intermediate. On the basis of a probabilistic approach, Li et al.17 have suggested that k2 can be derived from k1 and the number of carbon atoms which contains the pollutant, as shown in eq 2.

k2 1 ) k1 nc - 2

(2)

Values of the kinetic constants are given in Table 1. The oxidation kinetics is assumed to be first order to the concentration of each organic compound, as there is enough excess of oxidant and the change in oxidant concentration is negligible, regardless of the order of reaction with respect to the oxidizer Rice et al.20 The reactions considered are then the following: KA 9 (1) C3H7OH + O2 98 3CO2 + 4H2O 2 KAB 3 3 (2) C3H7OH + O2 98 CH3COOH + H2O 2 2 KB

(3) CH3COOH + 2O2 98 2CO2 + 2H2O where A is isopropyl alcohol (IPA) and B is acetic acid.

(5)

For the modeling, the reactor has been divided into three parts, with different flow patterns, as can be seen in Scheme 4. (1) The mixer consists of a tube filled with alumina. It is modeled using plug flow and considering a porosity of 0.6. (2) Upper part of the reaction chamber. The reagents leave the mixer flowing upward, and then, they have to change the direction of flow downward, as shown in Scheme 5. That is the reason this part of the reactor is considered as a perfect mixing stage, so it is modeled as a CSTR. (3) Reaction chamber. In this part, the reagent flow in the annular gap between the mixer and the porous wall and the transpiring water is joined to the product flow. Plug flow is considered. The global heat transmission coefficients, U, have been calculated from the individual heat transfer coefficients, h. For calculating the internal heat transfer in the mixer, the Kramer equation is used.22 The physical properties have been calculated for a stoichiometric mixture of air and water at the average temperature of the mixture. For calculating the external individual heat transfer coefficients equations from the literature23 are used. For the fluid that is circulating in the reaction chamber, water at a constant temperature of 500 °C is considered. The flow increase due to the inlet of transpiring flow is considered. A study of the influence of flow, inlet temperature, and length of the mixer has been carried out. The inlet temperature and length influence are negligible, but there is a strong linear dependence with the inlet flow. The global coefficients have been correlated in eq 6 as a function of the inlet flow

Um ) 1.96m0 + 6.09

(6)

where m0 is the reagent inlet flow in kg/h and Um is

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the global heat transmission between the mixer and the reaction chamber in W/m2 K. For the calculation of the heat transmission between the reaction chamber and the flow outside the transpiring wall, the same considerations employed for calculating the coefficient h0 for the reaction chamber are now used for hi. A study of the influence of flow, transpiring flow temperature, and position in the reactor has been carried out. The temperature of the transpiring flow has no influence on U, but the inlet flow and the position in the reactor have a notable linear influence. Thus, the parameters taken into account to fix the equation are inlet flow and position. The final equation is presented in eq 7 W m2 °C 4 kg/h e m0 > 12 kg/h f -3.04 + 1.11z + 2.67m0 12 kg/h e m0 > 20 kg/h f -15.6 + 16.80z + 2.67m0 m0 g 20 kg/h f -17.13 + 21.61z + 2.67m0

U |)|

{

(7)

where z is the longitudinal position in m. The global coefficient of the heat loses to the ambient, Uext, has been calculated, obtaining 0.55 W/m2 K. An excess of 20% has been considered. Mass and Energy Balances. Mixer. The mass balance for the isopropyl alcohol (A) and for the acetic acid (B) is shown in eqs 8 and 9

dXi ) Sm(Riri + βiriB) -Fi0 dz dFB ) Sm(ΣβiBriB - γBrB) dz

(8)

FCSTR + CBMP )

(9)

( )

dTm ) SmΣRij(-∆Hrij)rij - UπD(Tm - TR) dz (10)

where cp is the specific heat of the mixture, m0 is the inlet mass flow, D is the outside diameter of the mixer, ∆Hrij is the heat of reaction, TR is the temperature in the reaction chamber, and Tm is the temperature in the mixer. As the temperature profile should be calculated iteratively, for the first iteration, TR is considered as 400 °C, and for the second iteration, this value is taken as the calculated temperature in the previous iteration for each z. Top of the Reactor (CSTR). The mass balance for the isopropyl alcohol (A) and for the acetic acid (B) is shown in eqs 11-13

(11)

(ki(TR) + kiB(TR) 3600V) 1000

FBm + 3600V(ΣβikiB(TR)CiCSTR) 2000[(mCSTR/FCSTR) + 3600VkB(TR)] (12) Fi0 - CiCSTR

XiCSTR )

mCSTR FCSTR

Fi0

(13)

where C is the concentration in mol/L, the subindex CSTR refers to the values inside the top part of the reactor, τ is the residence time in the CSTR in s, Fi0 is the molar flow of i (A) in the inlet of the reactor in mol/ h, Xim is the conversion of i (A) at the outlet of the mixer, FCSRT is the density inside the CSTR, FBm is the molar flow of acetic acid in the outlet of the mixer in mol/h, and V is the volume of the CSTR in m3. It can be calculated by eq 14

V ) SLCSTR

(14)

where S is the section of the reactor and LCSTR is the length of the top part of the reactor considered as a CSTR. Experimentally, the CSTR length has been fixed at 40 mm. mCSTR is the mass flow at the outlet of the CSTR in kg/h. It is the addition of the reagent flow, m0, and the transpiring flow that enters in the CSTR, as shown in eq 15

mCSTR ) m0 + mTranspTACSTR/AT

where i ) A (isopropyl alcohol), R, β, and γ are the stoichiometric coefficients of reactions 1, 2, and 3, respectively, rij is the reaction rate,  is the porosity of the bed inside the mixer, Sm is the section of the mixer, Fi0 is the initial molar flow of each component, X is the conversion, and z is the longitudinal position of the reactor. The energy balance of the mixer is calculated as shown in eq 10

c pm 0

Fi0(1 - Xim) mCSTR

CiCSTR )

(15)

where mTranspT is the total flow that enters into the reactor through the porous wall in kg/h and ACSTR/AT is the fraction of transpiring wall in the CSTR. The energy balance of the CSTR is shown in eq 16

[m0(∆HT)in + q + V(Σkij(TR)CiCSTR(-∆HR)ij)] ) [mCSTR(∆HT)out + qT] (16) where ∆HT is the enthalpy of the total mixing at the inlet conditions (in) and at the outlet conditions (out) in J/kg and q is the heat flow that goes into the CSTR with the transpiring flow in J/h. It is calculated by eq 17

q)

∫∆hH O(T) dm 2

(17)

where ∆hH2O is the enthalpy of water at the temperature T that crosses the transpiring wall at every element, dm, and qT is the heat flow transmitted by convection through the transpiring wall in J/h. It is the addition of the heat transmitted through the roof, qTroof, and that transmitted through the wall, qTwall. This calculation is shown in eqs 18-20.

∫2Uπr(TR - TTransp) dr qTwall ) ∫UπD(TR - TTransp) dz

qTroof )

qT ) qTroof + qTwall

(18) (19) (20)

Ind. Eng. Chem. Res., Vol. 44, No. 11, 2005 3839 Table 2. Experimental Results from the TWR of the University of Valladolid a b c d

CIPA (%)

feed (kg/h)

exc air (%)

R

TOC (ppm)

conversion (%)

tR (s)

TFT (°C)

Tfeed (°C)

Tair (°C)

8.0 8.0 8.0 8.0

7.6 12.0 13.9 19.3

4.4 2.8 2.6 3.5

1.67 1.44 1.04 0.45

5.1 62.5 7.2 23.6

100.00 99.50 99.96 99.90

75.5 52.5 53.3 49.3

150 117 132 193

419 367 331 261

429 467 470 259

Heat Transmission in the Roof. The radial temperature profile in the roof of the transpiring wall was calculated. For this purpose, for every radial step, dr, the flow between walls, mbw, temperature of the transpiring flow, TTransp, heat transmitted to the top part of the reactor by convection, qTroof, and heat introduced in the CSTR with the transpiring flow, q, are calculated with eqs 21-24, respectively.

dm ˘ bw ) -2πrmTranspT/ATransp dr ˘ bw cp(H2O)(TTransp)m

(21)

dTTransp ) 2Uπr(TCSTR - TTransp) dr 2Uextπr(TTransp - Tamb) (22)

dqTroof ) 2Uπr(TCSTR - TTransp) dr

(23)

dq ) 2πrmTranspT/ATransphH2O(TTransp) dr

(24)

Heat Transmission in the Transpiring Wall. For calculating the temperature profile in the transpiring wall, for every step, dz, the flow between walls, mbw, temperature of the transpiring flow, TTransp, heat transmitted to the top part of the reactor by convection, qTwall, and heat introduced in the CSTR with the transpiring flow, q, are calculated with eqs 25-28, respectively. Initial values of the parameters are taken for the profile calculation in the roof.

dm ˘ bw ) -πDimTranspT/ATransp dr cp(H2O)(TTransp)m ˘ bw

(25)

dTTransp ) UπDi(TR - TTransp) dz UextπDext(TTransp - Tamb) (26)

dqT ) UπDi(TR - TTransp) dz

(27)

dq ) πDimTranspT/ATransphH2O(TTransp) dz

(28)

Equations 27 and 28 are only used for the top part of the reactor (the CSTR) and then TR ) TCSTR. Reaction Chamber. The mass balance of the total mass flow in the reaction chamber, m, the reagent i (A), and the acetic acid molar flows are calculated in every step using eqs 29-31.

dm ˘ ) πDimTranspT/ATransp dz dXi -Fi0 ) S(RiCriC + βiBriB) dz dFB ) S(Σ βiBriB - γBCrBC) dz

(29) (30) (31)

The energy balance is expressed in eq 32.

(

cp m ˘

)

dTR dm ˘ + TR ) πDmTranspT/ dz dz ATransphH2O(TTransp) + SΣ(-∆Hrij)rij UπDi(TR - TTransp) + UπD(Tm - TR) (32)

Results Comparison to Experimental Data. The reactor has been working in the pilot plant of the University of Valladolid for two periods of 6 months. From all the experimental data, four of them, under different operation conditions, have been selected to be reproduced using the model, to see how accurately the real behavior of the reactor is represented. The data are listed in Table 2. The parameter R is the relation of the transpiring flow divided by the flow of reagents (the addition of feed flow and air flow). In Figure 1, the temperature profiles (upper plot) and concentration profiles (lower plot) are represented for the data in parts a-d, respectively. It can be seen that in all cases the mixture of feed and air enters into the mixer, and, because the reaction is proceeding, the temperature TM is increasing (the lines TM, XAM, and FBM should be read in the opposite sense, because the flow in the mixer is countercurrent to the rest of the reactor, so the beginning of the mixer is 1270 mm and the end is 70 mm). As the temperature is increasing, the conversion of IPA increases too, and the acetic acid flow, FB, is first increasing, because part of IPA is turning into acetic acid, and then decreasing, as it is turning into CO2. Then, the reagents enter into the reaction chamber (TR, FB, and XA lines). The temperature, conversion, and acetic acid flow have a constant value at the beginning of the reactor, because this top part is considered as a CSTR. In the top, the higher temperature of the reaction chamber is registered. It can be seen that the temperature then decreases along the reactor chamber, because of the mixing with the transpiring water. The temperature of the transpiring water is considered in line TFT. It can be seen that it is increasing along the reactor. Now, the behavior of the reactor is described, so the results in the four plots are studied carefully. In Figure 1a, it can be seen that the temperature in the mixer is increasing very fast, reaching nearly 1000 °C, and then, it is cooled in the mixer by heat transmission, and the reaction temperature in the top of the reactor is 700 °C. The reaction is complete in the first 250 mm of the mixer, and the total organic carbon (TOC) removal is 100%, but it has the disadvantage that the reaction temperature in the mixer results as being very high so the materials can be damaged. In plot b, the same thing happens, but the temperature TM grows only to 800 °C and the reaction needs 700 mm of mixer to be finished. This temperature is still too high. In plot c, the temperature does not reach a maximum in the mixer and the reaction is completed in the top of the reaction chamber. It could be convenient because the highest temperature reached in the

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Figure 1. Temperature, conversion, and acetic acid flow profiles simulated in the reactor for different feeds and feed temperatures. Comparison to experimental data.

mixer is only 600 °C. In plot d, the temperature in the mixer only reaches 400 °C and the reaction begins in the mixer but takes place also in the reaction chamber. At the end of the reactor, not all of the acetic acid has been removed. As can be seen in all of the plots, the experimental temperatures fit well with the experimental data, so it can be assumed that the temperatures calculated in the mixer and in the transpiring flow are consistent with the real ones. In respect to TOC removal, it can be seen that for sample d the TOC predicted by the model is around 300 ppm and the experimental one is 23 ppm, so the model overpredicts the TOC in the outlet of the reactor.

By the study of the model results, it can be seen that the most convenient feed flow for working in the reactor is that between (c) 15 kg/h and (d) 18 kg/h. Thus, a feed flow of 16.5 kg/h is chosen. Theoretical Study of the Operation Parameters. A theoretical study of the main operation parameters was carried out in order to know the optimal operation parameters of the reactor: feed temperature, transpiring flow, transpiring flow temperature, air temperature, and IPA concentration. Feed Temperature. The feed temperature study was carried out with the operation parameters listed in Table 3. Despite of the fact that at these temperatures

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Figure 2. Temperature, conversion, and acetic acid flow profiles simulated for different feed temperatures. Table 3. Operation Conditions for the Feed Temperature Theoretical Study feed (kg/h) Tair (°C) R TFT (°C) air Tfeed (°C) % IPA

16.5 Tfeed 0.5 200 stoichiometric 300, 275, 250, and 200 8

two phases exist in the beginning of the mixer, only one phase has been considered in order to simplify the model, taking into account that air mass transfer to the liquid phase is favored by high temperatures and pressures and by the turbulence existing in the mixer. In Figure 2, the temperatures, conversions, and acetic acid flows calculated at four different feed temperatures

are represented: (a) 300 °C, (b) 275 °C, (c) 250 °C, and (d) 200 °C. It can be seen that TM, the temperature in the mixer, is higher when the feed temperature is higher and the reactor temperature is increasing too. In respect to the TOC removal, it can be seen that the IPA conversion is lower in the mixer when the temperature decreases and that all the IPA is removed in the reaction chamber, but for temperatures lower than 300 °C, the TOC removal is not complete. Table 4 shows the effluent TOC calculated for the different feed temperatures. A previous paper about cool wall reactor modeling11 studied the influence of the feed temperature with plug flow. In that work, the minimum feed temperature for oxidizing all of the acetic acid was 350 °C, with 6% IPA. For this new reactor, it is considered that the reaction

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Figure 3. Calculated temperature, conversion, and acetic acid flow profiles for different transpiring flow relations. Table 4. Effluent TOC Calculated for Different Feed Temperatures Tfeed

TOC

300 275 250 200

17 320 487 761

Table 5. Operation Condition Parameters for Studying the Influence of R feed (kg/h) Tair (°C) Tfeed (°C) TFT (°C) air R % IPA

16.5 Tfeed 300 200 stoichiometric 1, 0.5, and 0.25 8

takes place in the mixer and in a new CSTR area in the top of reactor, and the model is able to reproduce the experimental behavior of the reactor working at relatively low feed temperatures with nearly 100% TOC removal. Transpiring Flow Relation. Once 300 °C was selected as the feed temperature, the effect of the parameter R (transpiring flow divided by reagent flow (feed and air)) was studied. The operation parameters selected are listed in Table 5. In Figure 3, the temperature, conversion, and acetic acid flow calculated for different R values are shown: (a) R ) 0.5, (b) R ) 1, and (c) R ) 0.25. It can be seen that for all cases the main influence is in TR (temperature in the reaction chamber), that is lower for higher R, and the length of the reactor at a temperature higher than the critical temperature of water decreases too. These influences were also pointed out by Lieball et al.10 The TOC removal is affected by how the acetic acid is eliminated because for lower temperatures in the reaction chamber the kinetics is slower and it is not possible to eliminate all the acetic acid, as can be seen in part b. Another important point is that the products leave the reactor at a subcritical temperature in order to have the salts solved. Thus, it is not possible working with R ) 0.25 and R ) 0.5 is chosen. In Table 6, effluent TOCs calculated for different R values are shown. Transpiring Flow Temperature. In Table 7, the operation parameters for studying the influence of the

Table 6. Effluent TOC for Different Flow Relations R

TOC

0.25 0.5 1

17 856

Table 7. Operation Parameters for the Study of the Transpiring Flow Temperature Influence feed (kg/h) Tair (°C) Tfeed (°C) TFT (°C) air R % IPA

16.5 Tfeed 300 200, 100, and 25 stoichiometric 0.5 8

Table 8. Effluent TOC for Different Transpiring Flow Temperatures TFT (°C)

TOC

200 100 25

17 118 548

transpiring flow temperature in the behavior of the reactor are listed. The transpiring flow temperature does not seem to affect the mixer or reaction chamber temperature profiles, with the exception of the top temperature. The profiles calculated by the model are plotted in the Supporting Information. However, it affects enough the reaction so that TOC removal is not complete at 100 and 25 °C. In Table 8, effluent TOCs for different transpiring flow temperatures have been calculated. It can be seen that at 200 °C the TOC is almost 0, at 100 °C the TOC increases slightly, and at 25 °C the TOC increases considerably. Air Temperature. In Table 9, the operation parameters for studying the air inlet temperature influence are presented. The lower the air temperature is, the lower the temperatures inside the mixer and the reaction chamber and the higher the acetic acid flow in the reaction chamber. Thus, 300 °C would be the chosen as the air temperature because it is the only one that gives total TOC removal. The profiles calculated by the model are plotted in the Supporting Information.

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Figure 4. Temperature, conversion, and acetic acid flow profiles for different combinations of feed temperature and IPA concentration. Table 9. Operation Parameters for Studying the Air Temperature Influence feed (kg/h) Tair (°C) Tfeed (°C) TFT (°C) air R % IPA

16.5 300, 150, and 25 300 200 stoichiometric 0.5 8

Table 10. Effluent TOC for Different Air Temperatures Tair (°C)

TOC

300 150 25

17 304 488

Table 11. Operation Parameters for Studying the Combined Influence of Feed Temperature and IPA Concentration feed (kg/h) Tair (°C) Tfeed (°C) TFT (°C) air R % IPA TOC

16.5 25 250 25 stoichiometric 0.5 13 201

16.5 25 200 25 stoichiometric 0.5 14 65

16.5 25 150 25 stoichiometric 0.5 15 32

In Table 10, effluent TOCs calculated for different air inlet temperatures are listed. Combined Effect of IPA Concentration and Feed Temperature. In Table 11, operation parameters for studying the combined influence of feed temperature and IPA concentration are shown. With these simulations, we are studying the possibility of “changing” some heat given by preheating by some heat given by additional fuel. Thus, in this case, the air temperature and transpiring flow temperature are kept at 25 °C and the feed temperature is reduced. It could be very convenient for the plant operation working without transpiring flow and air preheaters because it reduces operating and capital costs. Introducing transpiring water as cold as possible also helps to keep the wall relatively cool and dissolve salts in solution.10 Reducing the inlet temperature to lower than 300 °C would decrease corrosion and salt precipitation problems in the preheaters.

In Figure 4, the temperature, conversion, and acetic acid flow calculated for different combinations of IPA concentration and feed temperature are calculated. In part a, with 13% IPA and a feed temperature of 250 °C, a TOC effluent of 201 ppm is obtained, in part b, with 14%, it is possible to reduce the inlet temperature to 200 °C and obtain a effluent TOC of 65 ppm, and in part c, a 32 ppm TOC effluent is obtained with a feed temperature of 150 °C and 15% IPA. In the three examples, the reaction temperature is around 500 °C in the top of the reactor, but we can see that both the temperatures in the mixer and in the reactor chamber are reduced when the inlet temperature is reduced. It reduces the length of the reactor under supercritical conditions when the inlet temperature is reduced. With respect to the reaction, it can be seen that, when lowering the inlet temperature, less IPA is consumed in the mixer, and all the reaction takes place in the top of the reactor, having better TOC removal with higher IPA concentration. This is quite convenient for the SCWO process because it is possible to introduce in the transpiring reaction chamber the feed under subcritical conditions, so if it has inorganic salts solved, these are going to precipitate in the reactor chamber, where they are not able to produce plugging or to scale the reactor wall. Conclusions In this paper, a modeling using simple flow patterns has been developed in order to reproduce and explain the behavior of the SCWO transpiring wall of the UVa. For this purpose, the reactor has been modeled as a series of zones with different flow patterns: plug flow and CSTR. For this model, the heat of reaction has been fitted to a polynomial as a function of reaction temperature and a study of the influence of operation parameters on the global heat transfer coefficients has been carried out in order to apply the model under very different operation conditions. The model has been compared with experimental data, of temperature and TOC removal, under very different operation parameters, and it can reproduce quite accurately the behavior of the reactor.

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Using the model, a theoretical study of the influence of the operation parameters has been made. High feed, air, and transpiring flow temperatures are favorable for TOC removals, but high transpiring flows can lead to high TOCs in the effluents. The ideal operating conditions for 8% IPA are the following: a 16.5 kg/h feed, a feed temperature and air temperature of 300 °C, and a transpiring flow relation of 0.5 at a transpiring flow temperature of 200 °C. If the IPA concentration is increased, the feed temperature can be reduced to 150 °C and the air and transpiring flow temperatures can be introduced at ambient temperature, with eliminations higher than 99% and TOC effluents up to 32 ppm TOC. Under these conditions, feed can enter into the reaction chamber under subcritical conditions, avoiding plugging and scaling problems in the mixer. Acknowledgment The authors wish to thank CETRANSA, CARBUROS META Ä LICOS, and EMGRISA for providing technical and financial support. This project has been partially financed by EU project “Supercritical Fluids and Materials Network”. SUPERMAT Interreg Atlantic III. M.D. Bernejo thanks the Ministerio de Educacio´n Ciencia for the FPU Grant. Supporting Information Available: Figures showing the temperature, conversion, and acetic acid flow calculated for different transpiring flow temperatures and for different air inlet temperatures. This material is available free of charge via the Internet at http:// pubs.acs.org. Symbols A ) surface (m2) ACSTR ) transpiring area in the CSTR (m2) ATransp ) total transpiring area (m2) C ) concentration (mol/L) cp ) specific heat capacity (J/kg K) D ) external diameter of the mixer (m) Di ) internal diameter of the transpiring wall (m) Dext ) external diameter of the pressure shell (m) de ) equivalent diameter (m) di ) internal diameter (m) F ) molar flow (mol/h) hi ) internal heat transfer coefficient (W/m2 K) h0 ) external heat transfer coefficient (W/m2 K) h ) specific enthalpy (J/kg) ∆Hr ) heat of reaction (J/mol) ∆HT ) total enthalpy of the mixture (J) k ) kinetic reaction constant kw ) conductivity of the wall (W/m K) L ) length (m) m ) reagent flow (kg/h) m0 ) inlet reagent flow (kg/h) mTransp ) transpiring flow in every position (kg/h) mTranspT ) total transpiring flow (kg/h) P ) pressure (MPa) q ) heat flow (W) r ) radius (m) ri ) reaction rate S ) reaction chamber section (m2) Sm ) mixer section (m2) T ) temperature (°C) U ) global heat transfer coefficient reactor chambertranspiring flow (W/m2 K) Um ) global heat transfer coefficient mixer-reactor chamber (W/m2 K)

Uext ) global heat transfer coefficient with the ambient (W/ m2 K) V ) volume (m3) x ) molar fraction X ) conversion z ) position (m) Subindex A ) refers to IPA B ) refers to acetic acid CSTR ) refers to the top of the reaction chamber (CSTR) H2O ) refers to water m ) refers to the mixer R ) refers to the reaction chamber Transp ) refers to the transpiring water Greeks R ) stoichiometric coefficient of reaction 1 β ) stoichiometric coefficient of reaction 2 γ ) stoichiometric coefficient of reaction 3  ) porosity F ) density (kg/m3) τ ) residence time (s)

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Received for review December 20, 2004 Revised manuscript received March 7, 2005 Accepted April 5, 2005 IE0487742