Characteristics of Methanol Hydrothermal Combustion: Detailed

Article pubs.acs.org/IECR

Characteristics of Methanol Hydrothermal Combustion: Detailed Chemical Kinetics Coupled with Simple Flow Modeling Study Mengmeng Ren,† Shuzhong Wang,*,† Jie Zhang,‡ Yang Guo,†,§ Donghai Xu,† and Yulong Wang† †

Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering of Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China ‡ State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an, Shaanxi 710048, China § Xi’an Jiaotong University Suzhou Academy, Suzhou, Jiangsu 215123, China S Supporting Information *

ABSTRACT: Hydrothermal flame is a promising solution for problems in the preheating process of supercritical water oxidation (SCWO) technology. A detailed chemical kinetics coupled with a simple flow model is developed and validated to reflect the characteristic of hydrothermal flame. Analysis of free radicals accumulation show that the high quantity of free radicals induced by high methanol concentration leads to ignition. A method to approach the ignition temperature through ignition delay time calculation with a specific reactor model is proposed, which shows good agreement with the existing experimental data and directs further design quantitatively. Extinction limits are discussed by laminar flame speed and the perfect stirred reactor (PSR) model comparatively. Ultimate extinction temperatures of different methanol concentrations are approached and suggest the possible improvement of hydrothermal flame stability at higher methanol concentration through flow field optimization.

1. INTRODUCTION Supercritical water oxidation (SCWO) is an innovative organic wet waste treatment technology benefited by the unique properties of water above its critical point (P = 22.1 MPa, T = 374 °C). Nonpolar compounds, such as oxygen, nitrogen, and carbon dioxide, and almost all organics are miscible with supercritical water so that oxidation of hazardous organic compounds can process quickly.1 However, corrosion and saltplugging are the two biggest challenges for SCWO.2 Hydrothermal flame regime is a promising solution for corrosion and plugging occurring at the preheating stage.3 It utilizes the hydrothermal flame as an inner heat source in the reactor to heat the cold feedstock. Thus, the preheated temperature can be decreased, and problems in the preheating stage can be relieved. Moreover, lower preheated temperature can decrease the investment of preheaters and increase the energy output from the SCWO system. Ignition temperature and extinction temperature are two of the most important parameters concerned in a hydrothermal flame system, which are the minimum preheated temperature to ignite and maintain the flame, respectively.4 Steeper et al.5 investigated methane and methanol hydrothermal flame in a © XXXX American Chemical Society

semibatch inverse diffusion reactor, showing the negative correlation between ignition temperature and fuel concentration. Wellig et al.6 studied methanol hydrothermal flame in a continuous diffusion reactor, which is the WCHB (wall cooled hydrothermal burner) in ETH. They found that the ignition temperatures were 50−60 °C higher than that in semibatch reactors, and the dependence of ignition temperatures on methanol concentration was weak in the continuous reactor. Meanwhile, Sobhy et al.7 observed interesting ignition delay phenomena during the semibatch methanol hydrothermal flame experiments. Research on the ignition mechanism of hydrothermal flame is insufficient yet. There has not been a calculation method for the ignition temperature of a specific methanol concentration so far. Studies on extinction temperatures were mainly conducted on continuous apparatus.6,8 It has been proved that the extinction temperature is largely dependent on the configReceived: Revised: Accepted: Published: A

March 1, 2017 April 17, 2017 April 20, 2017 April 20, 2017 DOI: 10.1021/acs.iecr.7b00886 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

are affected by a nonreactive collision body (M), and the effect of M varies with the reaction pressure.21 Since the reaction pressure of hydrothermal flame is much higher than that of gasphase combustion, the rate of the pressure-dependent reaction should be calculated considering their high-pressure limit. Through checking the pressure-dependent reactions listed by Brock et al.,19 four reactions are identified as lacking the highpressure limit expression in the original model adopted in this paper:

uration of reactors. Generations of WCHBs with different injection nozzles lead to different extinction temperature curves, which have been ascribed to the dependence of flow field on the nozzle configuration and size.9 Bermejo et al.8 also observed that extinction temperature in a premixed reactor increases with the feed flow rate. Lower extinction temperatures would be preferred in practical utilizations, which mean higher stability of the flame and lower energy consumed in preheating. What is the quantitative relationship between the extinction temperature and methanol concentration in different reactors? What is the lowest extinction temperature that can be reached through configuration optimization for a specific methanol concentration? These questions remain to be answered. Several modeling researches10−13 have been conducted to investigate hydrothermal flame, but the ignition and extinction conditions were seldom reproduced. This mainly ascribes to the absence of sufficient chemical kinetic models since the ignition and extinction phenomena are highly kinetic-concerned processes. A radical elementary reaction model developed from gas-phase combustion had been validated to reproduce the species profile during the SCWO process.14−16 Superiority of the detailed radical reaction model in reflecting the initiation, propagation, and termination reaction stages make it promising to model the ignition and extinction conditions. However, the thermodynamic properties of species, especially of supercritical water, need to be considered carefully. It is because the heat released during hydrothermal combustion is much more than that during low-concentration SCWO. Then, the temperature rise will be much larger, and the reaction temperature will be very sensitive to the thermodynamic properties such as specific heat capacity and enthalpy. In this paper, a detailed chemical kinetics coupled with a simple flow model and method is developed to explore the ignition and extinction characteristics of methanol hydrothermal flame. The ignition mechanism is illustrated from the view of radical accumulation, and the ignition temperatures at different reactors are approached through the calculation of ignition delay time. The extinction limits are also discussed by the laminar flame speed model and perfectly stirred reactor (PSR) model, respectively. In the end, the ultimate extinction temperature is predicted, which is the lowest extinction temperature that can be reached through flow field optimization. This work will help us understand hydrothermal flames better, and the proposed quantitative calculation method could be used in further reactor and process design.

H + OH( +M) = H 2O( +M)

(1)

CH3O(+ M) = CH 2O + H( +M)

(2)

CH 2O(+ M) = HCO + H( +M)

(3)

CO + OH( +M) = CO2 + H( +M)

(4)

20

With reaction 1, Burke et al. had compared the model predictions using the low-pressure limit expression of Srinivasan et al.22 and the falloff expression of Sellvage et al.,23 which are listed in Table 1. Burke et al. said that the Table 1. Arrhenius Parameters for Reaction Ratea of H + OH (+M) = H2O (+M) reference

Ab

17

× × × × ×

Li et al. Srinivasan et al.22 Sellevag et al.23 low

3.80 6.06 1.01 2.51 4.53

n 22

10 1027 1026 1013 1021

−2 −3.322 −2.44 0.234 −1.81 Fcent = 0.73g

Ec 0 1.21 × 1005d 1.20 × 1005e 1.14 × 1002f −4.99 × 1002

a

For the low-pressure limit only, the reaction rate r = k0[M][H][OH], in which k0 = ATn exp(−E/RT), is calculated by the parameters of lower-pressure limit. When considering the high-pressure limit, the reaction rate r = k0k∞[M]/(k0[M] + k∞)F[H][OH], where k∞ = ATn exp(−E/RT), is calculated by the parameters of the high-pressure limit, and F is the blending factor. bUnits of mol, cm3, and s. The unit of A and k is coordinated to ensure the unit of r is mol/(cm3 s) cUnits of cal/mol. dProvided as the reverse reaction with Ar as the main bath gas: H2O + M  H + OH + M. eProvided as the reverse reaction with H2O as the main bath gas: H2O + H2O  H + OH + H2O. fHighpressure limit, besides which all in the table are the low-pressure limit. g Parameter used to calculate F through the Troe form.21

differences are negligible in predictions against the validation set they conducted, of which the highest pressure is 8.7 MPa. However, the data from Sellevag et al. show that the rate curve of reaction 1 begins to fall off when pressure approaches 10 MPa, which is lower than the pressure of hydrothermal flames. We compared the two expressions on the hydrothermal conditions, and the results show negligible differences, which may due to the low sensitivity (Figure 1) of reaction 1 to the methanol oxidation process. When considering using H2O as the main bath gas which is more suitable for hydrothermal conditions, the expression of Srinivasan et al. is chosen for reaction 1. Furthermore, the whole H2/O2 mechanism revised by Burke et al. is also taken as the submechanism of the present model for consistency. Like reaction 1, reactions 2 and 3 also show negligible sensitivity to the methanol SCWO (Figure 1). However, they are important reactions concerning formaldehyde formation and consumption. We use the falloff expression advised by Baulch et al.24 for reaction 2 and add the high-pressure limit

2. MODEL AND METHOD A recent methanol gas-phase combustion mechanism from Li et al.17 is adopted in this work. Initial calculations with this mechanism show three problems to be solved to make the model suitable for hydrothermal flame: (1) Conversion rate of carbon monoxide to carbon dioxide is underpredicted. (2) Induction time at lower temperatures is underpredicted. (3) Flame temperature is overpredicted. These are are shown in Figures 3−6. The revisions we made to the original model are introduced in the following sections, including revisions of pressure-dependent reactions and hydrothermal sensitive reactions in the kinetic mechanism and the revision of thermodynamic parameters in the thermodynamic data set. 2.1. Chemical Kinetic Model. Pressure-dependent reactions were the main modifications made in literatures for the detailed chemical kinetic model of SCWO.14,18,19 The pressuredependent reactions refer to those elementary reactions which B

DOI: 10.1021/acs.iecr.7b00886 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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range 0.1−70 MPa, showing high pressure dependence. They provided the rate expression of OH disappearance and the partitioning of pathways into CO2 + H or HOCO. Nevertheless, the subsequent reaction rates of HOCO was not given. In the present model, we adopt the rate expression used by Brock et al.19 which is proposed by Larson et al.26 This expression considers the formation and decomposition of HOCO and can reproduce the CO concentration profile in the SCWO process quite well, in which reaction 4 is treated irreversible and two reversible reactions associated with HOCO are added: HOCO( +M) = H + CO2 ( +M)

(5)

HOCO( +M) = OH + CO( +M)

(6)

The Arrhenius parameters of all these revised reactions are listed in Table 2. Besides those pressure-dependent reactions, some reactions which turn sensitive at hydrothermal conditions also need to be evaluated. As shown in Figure 1, the reactions involving HO2 and H2O2 are highly sensitive to the reaction process under hydrothermal conditions. This is probably due to the important role of HO2 at low-to-intermediate temperature and the arising pathway of HO2 to H2O2 and next to OH caused by the higher reaction rate of reaction H2O2(+M) = 2OH(+M) at high pressure. Most reactions involving HO2 and H2O2 had been evaluated by Burke et al.20 in the H2/O2 submechanism which we adopt. Next, we evaluate the reaction which would significantly influence the induction time of methanol oxidation in supercritical water:

Figure 1. Reaction sensitivities for temperature and concentrations of CO, CH2O, and CH3OH at hydrothermal conditions in closed 0-D reactor. T = 490 °C, P = 24.1 MPa, fuel = 0.846 mol % methanol; oxidant = 1.485 mol % O2. Each species is analyzed at the time it is most consumed, and the sensitive coefficients are multiplied by a proper value for a better view.

used by Brock et al.19 to the expression of reaction 3. These revisions result in slight variations to the formaldehyde and carbon monoxide concentration profiles. Reaction 4 is the main pathway of carbon monoxide conversion to carbon dioxide. The sensitivity analysis also shows high sensitivity of this reaction to temperature and CO concentration (Figure 1). However, the original mechanism underpredicts the CO conversion rate in which the rate constant of reaction 4 is fitted by the method of weighted leastsquares with the literature data. Referring to the experimental data reviewed by Baluch et al.,24 we find that the data fitted by Li et al. are only those at pressures below 1 MPa. Fulle et al.25 measured the rate constant of reaction 4 over the pressure

CH3OH + HO2 = CH 2OH + H 2O2

(7)

Rate expressions of this reaction from literatures are listed in Table 3. Those from Brock et al.,19 Dagaut et al.,28 and Alkam et al.29 all had been used to model the SCWO of methanol. Compared with the expression of Li et al.,17 these three expressions have either a lower pre-exponential factor or higher activation energy, which all result in a lower reaction rate at specific temperature. Concerning the initial calculation result, in which the induction time is underpredicted more at lower temperatures, temperature-dependent modifications such as higher activation energy is preferred. Recently, Skodje et al.30

Table 2. Arrhenius Parameters for Reaction Ratesa reaction (2) CH3O (+M) = CH2O + H (+M) low (3) CH2O (+M) = HCO + H (+M) low (4) CO + OH (+M) → CO2 + H (+M)d high SRIe (5) HOCO(+M) = H + CO2(+M) low SRI (6) HOCO(+M) = OH + CO(+M) low SRI

Ab

Ec

n

6.80 × 10 1.87 × 1025 3.59 × 1014 3.30 × 1039 1.17 × 1007 2.45 × 10−03 1.391 1.74 × 1012 2.29 × 1026 2.49 5.89 × 1012 2.19 × 1023 1.37 13

0.0 −3.0 0.0 −6.3 1.354 3.684 2365 0.307 −3.02 5755 0.53 −1.89 4110

Reference

2.43 2.62 8.97 9.99 −7.25 −1.23 3.29 3.51 3.40 3.53

× × × × × ×

1004 1004 1004 1004 1002 1003 2020 × 1004 × 1004 1601 × 1004 × 1004 2676

Baulch et al.24 Brock et al.19 Larson et al.26

Larson et al.26

Larson et al.26

a

For unimolecular reactions 2, 3, 5, and 6, the reaction rate r = k0k∞[M]/(k0[M] + k∞)F[H][OH], where k0 = ATn exp(−E/RT) and k∞=ATn exp(−E/RT), is calculated by the parameters of low-pressure limit and high-pressure limit, respectively, and F is the blending factor. For the chemically activated bimolecular reaction 4, the reaction rate is r = k0k∞/(k0[M] + k∞)F[H][OH]. bUnits of mol, cm3, and s. The units of A and k are coordinated to ensure the unit of r is mol/(cm3 s). cUnits of cal/mol. dIrreversible reaction. eParameters used to calculate F through SRI form.27 C


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Industrial & Engineering Chemistry Research Table 3. Arrhenius Parameters for Reaction Ratea of CH3OH + HO2 = CH2OH + H2O2 source Li et al.17 Skodje et al.30 Brock et al.19 Dagaut et al.28 Alkam et al.29

3.98 2.28 3.34 9.64 1.10 5.40

Ab

n

× × × × × ×

0 5.06 4.12 0 0 0

1013 10−05 10−02 1010 1013 1011

thermodynamic model from the Chemkin database. Consequently, we fit the specific heat capacity values at supercritical pressure from the NIST database by piecewise polynomial upon seven temperature ranges. Considering that enthalpy and entropy are also used to determine the chemical reaction equilibria, we retain the enthalpy value at 298.15 K, and the entropy values at all temperatures are the same as those in the Chemkin database. The fitting coefficients upon different temperature ranges are listed in Table 4. With this expression, the calculated specific heat capacity and enthalpy are able to represent the sharp change in the transcritical region quite well (Figure 2).

Ec 1.94 1.02 1.62 1.26 2.22 1.78

× × × × × ×

1004 1004 1004d 1004 1004 1004

a

Reaction rate is r = k[CH3OH][HO2] with k = ATn exp(−E/RT). Units of mol, cm3, and s. The units of A and k are coordinated to ensure the unit of r is mol/(cm3 s) cUnits of cal/mol. dAnother pathway: CH3OH+HO2 CH3O+H2O2. b

conducted a theoretical calculation on this reaction and gave a three parameters expression which contains a temperature exponent. At the same time, another pathway to produce CH3O and H2O2 was also provided, as presented in Table 3. Consequently, the expression from Skodje et al. for reaction 7 and the addition of reaction CH3OH + HO2 = CH3O + H2O2 are adopted in this study. 2.2. Thermodynamic Properties. The thermodynamic properties including specific heat capacity (Cp), enthalpy (H), and entropy (S) are evaluated in this section. Using the Chemkin-II package,31 these properties at standard state are calculated as a function of temperature only and given in terms of polynomial fits with seven coefficients in each temperature range as follows: Cp0 R

= a1 + a 2T + a3T 2 + a4T 3 + a5T 4

Figure 2. Piecewise polynomial fitting result (with coefficients listed in Table 4) of specific heat capacity (Cp) and enthalpy (H) of water at 25 MPa. Scatter points are data from NIST database, and solid lines are fitting results by piecewise polynomial.

(8)

a a a a a H° = a1 2 T + 3 T 2 + 4 T 3 + 5 T 4 + 6 RT 2 3 4 5 T

2.3. Numerical Method. The Chemkin-II program31 is used to solve the detailed species equations with different flow patterns. The SENKIN code32 is adopted to model the species profile at plug flow reactors and the ignition delay time at closed-0D reactors. The PSR code33 is applied to model the ignition delay time at transient perfectly stirred reactors (PSRs) and the ultimate extinction temperature at steady PSRs. The PREMIX code34 is used to calculate the laminar flame speed by the freely propagating model.

(9)

a a a S° = a1 ln T + a 2T + 3 T 2 + 4 T 3 + 5 T 4 + a 7 R 2 3 4 (10)

Starting from the standard-state value, the entropy at a specific pressure is calculated as S = S ° − R ln(P /Psta)

3. MODEL VALIDATION WITH SPECIES AND TEMPERATURE PROFILES 3.1. Species Concentrations Profiles during Methanol SCWO. Species concentration profiles during methanol SCWO reactions are effective indicators to validate the applicability of the detailed kinetic models for hydrothermal conditions. In this section, we illustrate the improvement of the present model on the first two matters proposed in the beginning of the Model and Method section, which are the underpredicted induction times and conversion rates of CO to CO2.

(11)

accounting for the effect of pressure departure from standardstate pressure (Psta). However, due to the ideal gas conception, the specific heat capacity and enthalpy at different pressures are regarded as equal to the standard-state values, which cannot represent the values at supercritical conditions especially in the large specific heat region. This may be the reason for the abnormal high temperature results in the initial calculations with the

Table 4. Polynomial Coefficients Fitting Different Temperature Ranges temperature range 1000−2000 K 680−1000 K 670−680 K 660−670 K 650−660 K 640−650 K 298−640 K

a1 3.47 1.45 3.07 −8.68 8.05 −2.47 1.76

× × × × × × ×

a2 1001 1003 1006 1006 1006 1006 1002

−7.62 −6.00 −8.98 2.60 −2.47 7.76 −1.62

× × × × × × ×

a3 10−02 1000 1003 1004 1004 1003 1000

7.35 9.37 −2.29 1.18 1.58 −2.60 5.79

× × × × × × ×

a4 10−05 10−03 10−01 10−01 10−01 10−01 10−03

−3.09 −6.50 1.99 −5.88 5.75 −1.84 −9.09 D

× × × × × × ×

a5 10−08 10−06 10−02 10−02 10−02 10−02 10−06

4.82 1.69 −1.45 4.40 −4.41 1.45 5.29

× × × × × × ×

a6 10−12 10−09 10−05 10−05 10−05 10−05 10−09

−3.54 −3.04 −6.28 1.74 −1.58 4.72 −4.53

× × × × × × ×

a7 1004 1005 1008 1009 1009 1008 1004

−1.55 −6.89 −1.52 4.27 −3.94 1.20 −6.85

× × × × × × ×

1002 1003 1007 1007 1007 1007 1002


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original model, are predicted much better with the present model, which is reflected by the lower variation rates of methanol yields. A slight deviation is shown at 550 °C, at which the experimental conversion rate of methanol is higher than the calculated result. This situation was also encountered by Brock et al.16 when modeling with their own elementary model. They ascribed it to the possible residual oxygen in preheating lines that accelerates the reaction rate. Besides, it seems that only condition 3 is well-predicted in Figure 5. Actually, conditions 1 and 2 are reproducibility experiments conducted by Vogel et al.35 to be consistent with condition 3 by Rice et al.36 But deviations were not eliminated, which can be considered as experimental error. Anyway, the present model is improved much in the reproducibility of induction time at different temperatures. Moreover, yield profiles of CH2O, CO, and CO2 are also presented in Figures 3 and 4. This shows that the conversion rate of CO to CO2 is largely underpredicted by the original model, while with the present model the curve of CO2 yield become steeper and can reflect the variation tendency of experimental data quite well. 3.2. Flame Temperatures. Figure 6 shows the calculated adiabatic flame temperatures of different methanol concen-

Figures 3, 4, and 5 show the comparison of experimental and calculated species concentration profiles at three different

Figure 3. Product yield of methanol oxidation in supercritical water at 550 °C. Solid line: calculated by present model; dashed line: calculated by original model of Li; scatter point: experimental data from Brock et al.16 P = 246 atm, [CH3OH]0 = 0.7 mmol/L, [O2]0 = 3.8 mmol/L, [H2O]0 = 4.34 mol/L.

Figure 4. Product yield of methanol oxidation in supercritical water at 525 °C. Solid line: calculated by present model; dashed line: calculated by original model of Li; scatter point: experimental data from Brock et al.16 P = 246 atm, [CH3OH]0 = 0.7 mmol/L, [O2]0 = 4 mmol/L, [H2O]0 = 4.6 mol/L.

Figure 6. Adiabatic flame temperature of different preheated temperatures. Line and symbol: calculated value, if not declared in parentheses. The line with a symbol is calculated by the present model at conditions with pure oxygen as oxidant. Scatter point: experimental data (13.5, 9, and 4.5 mol % data from ref 6; copyright 2009 Elsevier); 10 mol % data from ref 7; copyright 2007 Elsevier).

trations varying with preheated temperatures. The adiabatic flame temperatures of 9 mol % calculated by the original model are also plotted. It is shown that the present model can modify the abnormal high temperature calculated by the original model. The calculated results can also reflect the rapid increase in adiabatic flame temperature when the preheated temperature is near the critical point. It is attributed to the large specific heat capacity of water near the critical point (Figure. 2). For a fixed concentration methanol solution, the released heat when completed combustion is a constant. If the preheated temperature is below the critical temperature, much heat is demanded to overcome the critical region, resulting in a smaller temperature increase than that with a preheated temperature above the critical temperature. The temperatures of continuous diffusion flame detected by Wellig et al.6 are also plotted in Figure 6. It is shown that all the detected flame temperatures are lower than the calculated adiabatic flame temperature which would be the highest temperature with an ideal adiabatic condition. The variation trend of the flame temperature with preheated temperature is

Figure 5. Methanol yield during supercritical water oxidation. Solid line: calculated by present model; dashed line: calculated by original model; scatter point: experimental data.35,36 No. 1: 483 °C, [CH3OH]0 = 1.89 mmol/L, [O2]0 = 4.2 mmol/L;35 No. 2: 483 °C, [CH3OH]0 = 2.1 mmol/L, [O2]0 = 2.16 mmol/L;35 No. 3: 480 °C, [CH3OH]0 = 1.91 mmol/L, [O2]0 = 4.34 mmol/L.36

temperatures. Both the original and present model results are plotted. The induction times, which are underpredicted by the E


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Figure 7. Temperature and free radicals profiles of methanol oxidation in supercritical water at different methanol concentrations: (a) 2 mol % and (b) 10 mol %.

H2O2 → 2OH, many more OH radicals are produced, which would largely promote methanol conversion through CH3OH + OH → (CH3O or CH2OH) + H2O. In this way, a sudden temperature increase or a flame surface would be induced at higher methanol concentration. As shown in Figure 7, there is a period of time when the temperature seems not to change, which is at about 16 and 7 s for methanol concentrations of 2 and 10 mol %, respectively. Actually, the time before the OH radical concentration or temperature increase rate reaches its peak is often defined as the ignition delay time in gas-phase combustion research, which is treated as an important indicator of the ignition process. The ignition delay phenomenon observed by Sobhy et al.7 may be partly ascribed to this radical accumulation time. We calculate the ignition delay times at different preheated temperatures for different methanol concentrations, as shown in Figure 8. The

not so consistent with the calculated result, which may because the flame position varies with the preheated temperature while the thermocouple was fixed.37 The experimental data from Sohby et al.7 are also plotted, which are detected in a semibatch inverse diffusion flame apparatus. The lowest methanol concentration among these experimental data is 10.2 mol %, while the detected temperatures are all much lower than the calculated adiabatic flame temperature of the 10 mol % condition. This can be explained by the configuration of the apparatus. The semibatch inverse diffusion means that the methanol solution is preinjected into the reactor, and there is no supplement during reaction. Therefore, the unburned methanol solution is heated by the flame, and its temperature could not be strictly treated as the preheated temperature as calculating the adiabatic flame temperature.

4. CHARACTERISTICS OF METHANOL HYDROTHERMAL COMBUSTION 4.1. Free Radical Accumulation and Ignition. Hydrothermal flame is usually characterized by a sharp temperature increase, which is different from the low-concentration oxidation process. To investigate the ignition mechanism, we calculate the temperature and main radical concentration profile (Figure 7) of two different methanol concentrations, 2 and 10 mol %, which are typical feed concentrations of SCWO and hydrothermal flame, respectively. It shows that the radical concentrations at 10 mol % are several magnitudes higher than that at 2 mol %. The increase in rate of temperature is proportional to the radical concentration. At higher methanol concentration, the initiation reaction CH3OH + O2 → (CH3O or CH2OH) + HO2 and propagation reaction CH3OH + HO2 → (CH3O or CH2OH) + H2O2 are both accelerated, and hence, more HO2 and H2O2 radicals are produced and accumulated. As a result, through the branching reaction

Figure 8. Ignition delay time modeled by closed 0-D model with stoichiometric air as oxidant, combining with the ignition conditions detected by Wellig et al.6 and Sobhy et al.7 F


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Industrial & Engineering Chemistry Research experimental concentration and preheated temperature range conducted by Sobhy et al. is marked by a pink region, showing that the calculated ignition delay time is 4−11s. Considering the mixing time for reactants, the calculated results can approach the experimental data at 10−15 s well. The calculation also shows that the ignition delay time decreases with methanol concentration and the logarithm of ignition delay time decreases linearly with the increase in temperature at a specific methanol concentration. Bermejo et al.38 had tested the “starting residence time” that isopropanol spent in the tubular reactor before the ignition, which showed the same variation trends as the calculated ignition delay time in this work. Tubular reactors are commonly treated as plug flow, so the ignition delay time calculated by the 0-D closed reactor model would approach the “starting residence time”. The agreement of the variation trend validates the ignition mechanism of radical accumulation further. 4.2. Critical Ignition Temperature. Other than the ignition delay time, ignition temperature is the commonly used indicator in hydrothermal flame research. We hypothesize the lowest temperature at which the ignition delay time is equal to the residence time in the combustor to be the ignition temperature. In continuous reactors, the residence times τ are related to the combustion chamber volume V, inlet mass flow rate ṁ , and density ρ at ignition temperature with the equation τ = ρV/ṁ . The residence times in continuous reactors are shorter than those in semibatch reactors, which would be the reason why the ignition temperature detected by Wellig et al.6 in WCHB is 50−60 °C higher than that detected by Steeper et al.5 in a semibatch reactor. For the methanol concentration of 9−12 mol %, the detected ignition temperature from Wellig et al. is 470−480 °C, and the corresponding residence time is 0.15−0.16 s with an experimental flow rate (2g/s) and combustor volume (3.2 cm3). We use the 0-D closed model to calculate the ignition delay times at this concentration and preheated temperature range, among which the shortest ignition delay time is 0.26 s as marked in the red region in Figure 8. The calculated ignition delay time is longer than the residence time at the actual ignition temperature, illustrating that the ignition is actually promoted in the continuous WCHB. The promotion factor might be the recirculation of radicals in the reactor. Then, we use the transient perfectly stirred reactor (PSR) model to approach the ignition process in continuous reactors. In these calculations, the initial temperature in the reactor is set the same as the inlet temperature, and the initial species is full of water. Figure 9 shows the calculated temperature and species profiles at different preheated temperatures. It shows that the water in the reactor is displaced by methanol and oxygen as time goes on. For lower preheated temperatures of 420 and 450 °C, the concentrations of species in the reactor become equal to the inlet values at about 1 s and stay constant, and the temperatures stay still until 1000s, which means that the ignition would not happen. With the increase in preheated temperature, it can be observed that there is a sudden variation in temperature and species concentration, which indicates the ignition. The higher the preheated temperature is, the faster the ignition happens. Hence, the lowest preheated temperature that could induce the ignition is the critical ignition temperature in PSR, which considers totally recirculation of species and radicals. Furthermore, we plot the ignition times calculated by the transient PSR model varying with preheated temperature for

Figure 9. Temperature and species profile of 10 mol % methanol ignition in transient PSR model at different preheated temperatures.

different inlet methanol concentrations, feed flow rates, and combustion chamber volumes (Figure 10). The critical ignition

Figure 10. Ignition time in transient PSR model of different methanol concentrations and reactor flow conditions.

temperature of each condition is labeled. At the condition of 3.2 cm3 and 2g/s, which is equal to the experimental condition of Wellig et al.,6 the critical ignition temperature is 467−471 °C. It agrees well with the experimental data (470−480 °C) and the phenomena that ignition temperature is weekly independent of methanol concentration. The modeling results also show that the combustion chamber volume and feed flow rate play more important roles in the critical ignition temperature. As the combustor chamber volume increases or the feed flow rate decreases, the critical temperature will decrease. This can be generally ascribed to the increase in residence time. For further design of experimental or up-scale apparatus, the volume of the combustion chamber should be decided with considering the feed flow rate, and an expectant ignition temperature can be calculated with the model and method developed in this work. G


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Industrial & Engineering Chemistry Research 4.3. Laminar Flame Speed. Laminar flame speed is an important indicator that relates to the stability of hydrothermal flame.8 We calculate the laminar flame speeds of different methanol concentration with varied preheated temperatures, as shown in Figure 11. The calculated laminar flame speed is

12. The ultimate extinction temperature decreases with the increase in methanol concentration. The adiabatic flame

Figure 12. Ultimate extinction temperatures (PSR model) and adiabatic flame temperatures at ultimate extinction conditions, comparing with experimental extinction temperatures (Coaxial, Wellig data from ref 6; copyright 2009 Elsevier. Coaxial, Prikopsky data from ref 9; Radial, Weber data from ref 42; copyright 1996 Elsevier).

Figure 11. Laminar flame speeds of methanol hydrothermal flame with different preheated temperatures.

about 0.2−10 cm/s, much lower than the common value of gasphase combustion which is about 50 cm/s at room temperature.39 This is partly due to the higher density at high-pressure conditions40 and partly due to the water-dilution effect. It also shows that the laminar flame speed increases with preheated temperature especially at the transcritical region, which may result from the transform of condensed water from liquid-like to gas-like behavior. Calculated data near the critical temperature are relatively sparse since a converged solution is difficult to get, mainly due to the sharply varied properties of water at this region. None of the available experimental data concerns methanol hydrothermal flame speed so far. The flow rate of the 4 wt % isopropanol hydrothermal flame in a tubular reactor conducted by Bermejo et al.8 is about 10−30 cm/s at an extinction temperature of 370−380 °C. This could be a reference for the calculated methanol hydrothermal flame speed, considering the differences between fuels. According to the laminar flame propagating theory, the extinction temperature is the temperature at which the laminar flame speed is equal to the fluid flow rate. For a higher fluid flow rate, a higher extinction temperature results. Additionally, this is based on the one-dimensional flow hypothesis, where the axial diffusion is the only way of heat and radicals transfer from flame to unburned fluid. In many flow cases, the hydrothermal flame is not only stabilized by axial diffusion but also by the turbulent mixing or back-flow mixing. For example, the extinction temperature of 10 mol % methanol in WCHB6 is 263 °C, and the corresponding flow velocity is about 4 cm/s. In this condition, the laminar flame speed is lower than 1 cm/s, which means that the flame stability is enhanced by the flow regime. This can be the reason that the extinction temperature in the vessel reactor is lower than that in the tubular reactor.41 4.4. Ultimate Extinction Temperature. In this section, we explored the lowest extinction temperature that can be reached by flow field optimization. The steady PSR model is used to meet the ideal perfect back-mixing flow condition. In each case, the initial iterative value of the reactor temperature is set as the estimated flame temperature. The ultimate extinction temperatures of different methanol concentrations, which are obtained by decreasing the inlet temperature until no temperature increases occur in the PSR, are plotted in Figure

temperatures of each methanol concentration at the ultimate extinction conditions are also plotted. It shows that the adiabatic flame temperature seems to be a constant around 600 ± 20 °C at the ultimate extinction conditions. Hence, maintaining the adiabatic flame temperature higher than 620 °C would be a crude criterion in estimating the ultimate extinction temperature. Three experimental extinction temperature curves of WCHB with different nozzles6,9,42 are also plotted in Figure 12. All the experimental extinction temperatures are higher than the ultimate extinction temperature. The radial nozzle tested by Weber et al.42 produces a more stable flame than that of coaxial nozzles, and the modified coaxial nozzle tested by Wellig et al.6 are better than the simple one tested by Prikopsky et al.9 At a methanol concentration of about 6 mol %, the experimental values are very close to the ultimate value, which is 376 °C and just near the pseudocritical temperature. This may because the sharp variation of physical properties near the critical point promotes the back mixing and enhances the flame stability. Beyond the critical point, the experimental extinction temperatures are gradually higher than the ultimate value. The largest discrepancy is as high as 150 °C

5. CONCLUSIONS With the modification of pressure-dependent reactions, hydrothermal sensitive reactions, and thermodynamic properties, the developed model can reflect the species and temperature variation at hydrothermal conditions reliably. The high quantity of free radicals induced at high methanol concentration is proved to be the main factor that causes the rapid reaction and flame formation. Retaining the ignition delay time, which varies with preheated temperature and methanol concentration, is a criterion for hydrothermal flame ignition. A quantitative method to determine the ignition temperature through ignition delay time calculation with a specific reactor model is validated, which would direct further design of the hydrothermal process. On the extinction limits, the ultimate extinction temperatures of different methanol concentration, which are the lowest extinction temperatures that can be achieved through flow field optimization, are predicted by the PSR model. Referring to the H


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Industrial & Engineering Chemistry Research ultimate extinction temperatures, the existed experimental apparatus shows good stability near the critical point, while the stability of higher methanol concentrations can be promoted further. In further research, this developed detailed chemical kinetic model can be imported into a CFD code to investigate the detailed flow−reaction characteristic of hydrothermal flame. A refined flow pattern induced by different injectors and its subsequent influence on ignition and extinction conditions will be illustrated.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b00886. Definition of sensitivity coefficients. (PDF)

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Psta = standard-state pressure τ = residence time (s) V = volume of combustor chamber (cm3) ρ = density (g/cm3) ṁ = mass flow rate (g/s)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 29 82665157. Fax: +86 29 82668703. ORCID

Shuzhong Wang: 0000-0002-0384-8993 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Projects from National Natural Science Foundation of China (21576219, 51406146), Special Financial Grant from the China Postdoctoral Science Foundation (2014T70922), and Fundamental Research Funds for the Central Universities and Jiangsu Province Natural Science Foundation of China (BK20140406).

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NOMENCLATURE SCWO = supercritical water oxidation T = temperature (°C) P = pressure (MPa) WCHB = wall cooled hydrothermal burner M = nonreactive collision body [M] = mole concentration of M (mol/cm3) PSR = perfectly stirred reactor A = pre-exponential factor (compatible unit with reaction rate) n = temperature exponent E = activation energy (cal/mol) r = reaction rate (mol/(cm3 s) k = reaction rate constant (coordinated unit with reaction rate) k0 = reaction rate constant at low-pressure limit (coordinated unit with reaction rate) k ∞ = reaction rate constant at high-pressure limit (coordinated unit with reaction rate) F = blending factor of pressure-dependent reactions Fcent = coefficient used to calculate F through Troe form R = gas constant (cal/(mol K)) Cp = heat capacity (cal/(mol K)) H = enthalpy (cal/mol) S = entropy (cal/(mol K)) ai = polynomial fitting coefficients for thermodynamic properties, i = 1−7 I


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Characteristics of Methanol Hydrothermal Combustion: Detailed

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