Simulation of a Transpiring Wall Reactor for Supercritical Water

Jan 19, 2018 - Reactor corrosion and plugging problems severely hinder commercial application of supercritical water oxidation. ... Although there is ...
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Simulation of a Transpiring Wall Reactor for Supercritical Water Oxidation: Characteristics of Water Film Donghai Xu,* Shuwei Guo, Zhen He, Chuanbao Huang, Zefeng Jing, and Shuzhong Wang Key Laboratory of Thermo-Fluid Science & Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, China ABSTRACT: Reactor corrosion and plugging problems severely hinder commercial application of supercritical water oxidation. A transpiring wall reactor can overcome these two problems by forming a protective water film on the inner surface of a porous transpiring wall to isolate corrosive substances and inorganic salt. This work proposed water film coverage rate and inorganic salt concentration in water film as evaluation indexes of water film characteristics. A computational fluid dynamics model of a new transpiring wall reactor was built to explore the characteristics of water film under key operating parameter conditions by numerical simulation together with experiment validations. The results show that water film coverage rate raised either with transpiration intensity and transpiration water temperature increasing or with feedstock flow rate and feedstock preheating temperature decreasing. Inorganic salt concentration in water film declined as transpiration intensity and transpiration length increased. Two equations were proposed to guide the optimization of reactor operating parameters. organic wastes, such as corrosive solvent,6 painting effluent,7 landfill leachate,10 salt-containing wastewater,11 industrial wastewater,12 and sewage sludge.13,14 Experimental investigations on operating characteristics of TWR have been documented widely.6,14−18 Proper TWR configuration and operating parameters are crucial, otherwise corrosion and salt deposition problems will probably occur.6,10,11 Nonetheless, due to harsh reaction conditions (e.g., high temperature and high pressure), it is hardly accessible to get an information measurement in a TWR in real time. Thus, it is difficult to obtain fluid information in water film, which significantly affects TWR performance. As a cost-effective means, computational fluid dynamics (CFD) simulation can gain the details of TWR inside (e.g., temperature and substance concentration distributions), therefore becoming more favorable in TWR research.17−22 The traditional ideal fluid model faces difficulties to describe a complex SCWO process,23 and thus several various models have been developed for TWR simulation in SCWO.3 Abeln et al.20 performed 2D and 3D steady-state calculations to get insight into local flow conditions and substance concentrations in a TWR and in the gap between its pressure-bearing wall and transpiring wall. Bermejo et al.21 investigated the effects of different operating parameters (e.g., transpiration water temperature and flow rate) on reactor temperature, substance composition contours, and effluent compositions in their TWR. Presently, Zhang and Ma22 studied the influences of key operating parameters (such as transpiring water temperature and transpiration intensity) on the

1. INTRODUCTION Supercritical water oxidation (SCWO) can take advantage of supercritical water unique properties (e.g., high diffusion and mass transfer performance) to realize efficiently harmless treatment of biorefractory organic wastes, such as wastewater and sewage sludge, therefore, it has drawn increasing attention worldwide. Unfortunately, its extensively commercial utilization has been severely limited by reactor corrosion and salt deposition problems. Marrone et al.1,2 had comprehensively reviewed specific reactor configurations and operation approaches for the reactor corrosion and salt deposition control in SCWO. Although there is no one reactor design or operation mean that is clearly superior to the others in all aspects,3 proper reactor configuration design is considered as a key of SCWO commercialization.4 Present reactor types include a reverse flow tank reactor with a brine pool, a transpiring wall reactor, a reversible flow tubular reactor, a centrifuge reactor, a cool wall reactor, a downflow type reactor, a fluidized bed reactor, a double wall stirred reactor, a deep shaft reactor, and a transpiring wall reverse flow tank reactor, etc.1,3,5 Particularly, the transpiring wall reactor (TWR) is basically composed of a pressure-bearing wall and a porous nonloadbearing transpiring wall. Clean water permanently flows through the porous transpiring wall and forms a protective film on its inner wall, therefore, it prevents precipitated salt particles and corrosive matters from contacting the reactor inner wall via dissolving, diluting, and/or sweeping them away. This type of reactor exhibits a good performance in simultaneously overcoming reactor corrosion and salt deposition problems.6,7 It is regarded as a promising reactor construction in SCWO8,9 and has drawn much attention.3 Now, there have been many studies on SCWO in the TWR of © XXXX American Chemical Society

Received: October 28, 2017 Revised: December 29, 2017 Accepted: January 5, 2018

A

DOI: 10.1021/acs.iecr.7b04479 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research formation of water film and feed degradation, and paid special attention to the temperature profile near the inner surface of porous wall. Apparently, TWR performance against corrosion and salt deposition is substantially dependent on water film characteristics. However, current research mainly focuses on the contours of temperature, velocity, and substance concentrations inside the TWR. To the best of our knowledge, now the investigation on water film characteristics is very scarce and there is no any report about water film coverage rate and substance concentrations in water film. Recently, a new TWR was constructed in our lab. Two quantitative correlations involving water film thickness and main operating parameters are put forward through theoretical analysis and mathematical deduction on heat and mass transfer between water film and bulk fluid in our latest publication.24 This work further expands our previous research by numerical simulation and experimental validation. Apart from water film temperature, water film coverage rate and substance concentration in water film are proposed as evaluation indexes of water film characteristics. The influences of operating parameters of transpiration water and feedstock on water film characteristics above were explored for the first time. This information is valuable for guiding the optimization of TWR structure and operating parameters.

forming on the inner surface of the transpiring wall is expected to avoid reactor corrosion and salt deposition problems. Organic feedstock and oxidant were introduced from reactor top inlets (2 mm ID) and rapid exothermic oxidation reactions took place, so leading to the formation of a supercritical region in the reactor upside. Subcritical transpiration water flowed downward along the porous transpiring wall by gravity, and simultaneously cooled the reaction fluid to form a subcritical region at the reactor bottom. Ideally, a uniform and continuous protective water film was formed on the inner surface of the transpiring wall to prevent inorganic salts and corrosive substances in bulk fluid (organic feedstock and oxidant) from contacting the reactor inner wall. Salt particles precipitating in the supercritical region fell to and redissolved in the subcritical region, and then they were discharged from the reactor bottom outlet (4 mm ID) continuously. In this study, methanol (purity >99.9%) added to deionized water was adopted as artificial organic wastewater feedstock, and oxygen (purity >99.9%) and deionized water were separately oxidant and transpiration water. The volumetric flow rate (Qme) and methanol mass concentration (wme) of organic feedstock, the preheating temperature of bulk fluid (Tbulk), and the transpiration water temperature (Ttw) varied in the ranges of 0.6 to 1.4 L·h−1, 15 to 25 wt%, 673 to 873 K, and 473 to 623 K, respectively. Sodium chloride was added to the initial feedstock to form 1 or 3 wt% of salt concentration in salt deposition investigations. 2.2. Analysis Methods. As shown in Figure 1, in fact, some temperature measurement points were set in the two cross sections at the transpiration lengths of 41 mm and 123 mm to determine radial temperature distribution of fluid in the TWR. Herein, transpiration length (L) refers to the distance from the underside surface of the reactor top cover along gravitation direction. Three extra temperature measurement points were placed at L = 20, 70, and 120 mm with the distance of 1.5 mm from the inner surface of transpiring wall to monitor water film temperatures. Moreover, two pipelines (1 mm ID) were inserted into the TWR nearly 1 mm from the inner surface of the transpiring wall at L = 45 mm and L = 102 mm, and each sampling inlet faced water film in parallel. Thus, we could sample the fluid in water film (within about 2 mm thickness) at the location above for water film properties analysis. Salt content was measured by a professional meter (Model PP-50). Corrosion and salt deposition morphologies of the inner surface of the transpiring wall were observed by a scanning electron microscope (SEM, Model JSM-6390A). Oxidation coefficient γ is calculated as the actual added amount of oxidant divided by the theoretical demand amount of oxidant

2. EXPERIMENTAL SECTION 2.1. Experimental Procedures. As shown in Figure 1, the pressure-bearing wall (60 mm ID) and the porous transpiring

Figure 1. Basic configuration of our TWR.

γ=

wall (47 mm ID, 146 mm of total effective transpiration length (L), and 3.5 mm thickness) of our TWR (410 mL net capacity) were made from stainless steel 316. The transpiring wall possessed about 20 μm filtering precision and 20% surface density (i.e., 0.2 of porous wall porosity). In order to realize uniform distribution of water film, three branches of transpiration waters (i.e., tw1, tw2, and tw3) separately entered into the upper, middle, and lower annular spaces between the pressure-bearing wall and the transpiring wall simultaneously, and each branch had two inlets (4 mm ID) at the same height with the same flow rate of transpiration water. The water film

Fox 1.5Fmewme

(1)

where wme is methanol mass concentration (wt%). Typically, excess oxidant is provided in SCWO to guarantee effective removal of organic matters, and so γ was maintained at 1.2 in this work. Moreover, transpiration intensity, κ, is calculated as the mass flux of transpiration water relative to that of bulk fluid, which is expressed by the following equation,16,22 κ= B

Ftw Fme + Fox

(2) DOI: 10.1021/acs.iecr.7b04479 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research where Fox is the oxidant mass flux (kg·s−1), Fme is the mass flux of methanol solution (kg·s−1), and Ftw is the mass flux of transpiration water (kg·s−1). Experiments were conducted three times at the same conditions to determine the uncertainties of data. Results plotted are average values and their uncertainties are the sample standard deviations.

The momentum equation is expressed by ∂τij ∂(ρuiuj) ∂(ρui) ∂p + ρgi + Sm =− + + ∂xj ∂xj ∂xi ∂τ

(4)

where p is static pressure, τij is stress tensor, gi is the gravity acceleration in the i-direction, and Sm is momentum source. The energy equation is given by

3. TWR CALCULATION MODEL DESCRIPTION 3.1. Simplification of Physical Model and Boundary Conditions. Figure 2 indicates a simplified two-dimensional

∂(ujτij) ∂(ρujh) ∂p ∂(ρh) ∂ ⎛⎜ ∂T ⎞⎟ + Sh = + + λ ⎟+ ⎜ ∂xi ∂xj ∂xj ⎝ ∂xj ⎠ ∂t ∂τ (5) N

h=

∑ Yhi i + i=1

(6)

where h is total enthalpy, λ is effective thermal conductivity, p and τij are the same as those in eq 4, Sh is energy source, and Yi is the mass fraction of the component i. Component transportation equation is described by

Figure 2. Simplified physical model of the TWR.

∂(ρujYi ) μ ⎞ ∂Y ⎞ ∂(ρYi ) ∂ ⎛⎜⎛ = + ⎜ρDi ,m + t ⎟ i ⎟⎟ + Si ⎜ ∂xj ∂xj ⎝⎝ Sct ⎠ ∂xj ⎠ ∂τ

calculation model established on the following assumptions. Calculation area was started from the inner surface of pressurebearing wall, of which boundary conditions were regarded as adiabatic boundary conditions at steady state conditions. The influence of inlet momentum of transpiration water (at its inlet pipeline locations on the reactor) on its even distribution in the annular gap between the transpiring wall and the pressurebearing wall was ignored. Apart from the thermal conductivity of the transpiring wall, other wall surfaces were considered as adiabatic boundaries. Full preheating and mixing of the twophase flows (feedstock and oxidant) had been achieved before the reactor top inlet (i.e., nozzle). The heat capacity of the fluid mixture was calculated as the mass average of the pure component heat capacities. Additionally, reactor pressure p was maintained at 24 MPa, and gravity (g = 9.81 m·s−1) was considered due to its significant effect on fluid flow and water film formation. CFD calculation and grid partition were carried out by the commercial softwares Fluent 6.3.26 and Gambit 2.4.6, respectively. A regular quadrilateral element was used for the reactor grid partition and the total grid number was 115080. Due to large variation gradients of physical properties (e.g., velocity, temperature) near the inner surface of the transpiring wall, the boundary layer grids encryption at the location was implemented to improve calculation accuracy, and meanwhile the grid independence validation was performed to guarantee the rationality and accuracy of the grids form and size. 3.2. Control Equation and Turbulence Model. 3.2.1. Control Equation. Organic matter SCWO in a TWR is a very complex process involving fluid flow, heat and mass transfer, and chemical reactions. This is required to solve the equations of mass, momentum, energy, and component transportation at steady state conditions.25 Mass equation is described by ∂(ρui) ∂ρ + =0 ∂τ ∂xi

1 2 (u1 + u 22 + u32) 2

(7)

where Di,m is the diffusion coefficient of the component i, μt is turbulent eddy viscosity coefficient, Sct is turbulence Schmidt number, and Si is the production or consumption of the component i due to reactions. 3.2.2. Turbulence Model. Proper transpiration water parameters can lead to a supercritical region and a subcritical region in a TWR, and fluid flow in the supercritical region belongs to turbulent flow. Physical properties near the critical point of water change drastically, so high temperature and velocity gradient easily induce fluid eddies. The RNG k−ε model26 is confirmed to be more accurate to describe the flow field with recirculation zones and eddies in contrast to the standard k−ε model,22 and the low-Reynolds number model is more suitable for the supercritical region.27 Thus, the lowReynolds number RNG k−ε model was used as the turbulence model in this research. The second order numerical schemes were chosen to improve calculation accuracy and get good flow field distribution. The pressure−velocity coupling scheme was a pressure-based calculation model, which is implicit, 2D, and steady. 3.3. Turbulence-Chemical Reaction Model. Supercritical water oxidation and turbulent flow have a strong correlation and interaction in the TWR. On the one hand, a large amount of heat released due to rapid SCWO reactions leads to the drastic variations of density, viscosity, diffusion coefficient, and other physical parameters, so affecting fluid velocity and flow state. On the other hand, turbulent flow remarkably influenced SCWO reactions by enhancing the mixing of reactants and products. Apparently, in the supercritical zone homogeneous oxidation reactions take place without interface mass transfer resistance. However, in the trans-critical region, reactions are likely affected by the reactants mixing rate, especially in the region of adding low temperature transpiration water. Thus, this work selected the currently most proper finite rate/eddy dissipation model as the turbulent−chemical reaction model in numerical simulation. The model calculates Arrhenius reaction rate and eddy diffusion rate, and the smaller one was adopted as the calculation result of net reaction rate.

(3)

where ρ is fluid density, τ is time, xi (i = 1, 2, 3) is the icoordinate axis direction, and ui (i = 1, 2, 3) is the velocity in the i-direction. C

DOI: 10.1021/acs.iecr.7b04479 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research ⎛μ ⎞ 1 Si′ = −⎜ vi + C2ρ|vi|vi⎟ ⎝α ⎠ 2

As shown below, a single-step oxidation reaction (without intermediate products formation) between methanol and oxygen in supercritical water was used as the reaction model CH3OH + 1.5O2 = CO2 + 2H 2O

where μ is the dynamic viscosity (Pa·s), α is the permeability (m2), vi is the flow rate in the i-direction (m·s−1), C2 is the internal resistance coefficient (m−1), and ρ is the fluid density (kg·m−3). Based on eqs 11−13, eqs 14 and 15 can be obtained as follows,

(8)

The reaction rate is expressed by Arrhenius law ⎛ E ⎞ n m −r = cme coxA exp⎜ − a ⎟ ⎝ RT ⎠

(9)

C2 =

where A is the pre-exponential factor, Ea is the activation energy (kJ·mol−1), R is the gas constant (J·K−1·mol−1), cme is the methanol concentration (mol·L−1), cox is the oxygen concentration (mol·L−1), and n or m is the reaction order. Corresponding kinetics parameters of methanol SCWO are A = 1 × 1026.2, Ea = 408.8 kJ·mol−1, n = 1, and m = 0.28 3.4. Porous Media Model. Compared with reactor operating pressure, the pressure drop of transpiration water flowing across the transpiring wall is negligible, so its effect on the variations of physical properties was not considered. Numerical calculation also ignored the influence of the twophase flow so as to obtain steady-state temperature distribution. A momentum loss term was added to the momentum equation of the porous media model, which is required to determine the internal resistance coefficient and permeability of the porous media. Herein, the two were calculated via the relationship between pressure drop and velocity obtained by the experimental method. The fitting equation between the experimental pressure drop and velocity of the fluid flowing across the porous transpiring wall is expressed as follows, 2 Δp = a1vtw + a 2vtw

(15)

Table 1. Internal Resistance Coefficient (C2) and Permeability (α) of the Porous Wall at Various Porosity (β) Conditions item

β = 0.2

β = 0.3

β = 0.4

β = 0.5

C2/m−1 α/m2

1.46 × 1007 2.4 × 10−13

3.78 × 1006 7.05 × 10−13

1.37 × 1006 1.71 × 10−12

5.83 × 1005 3.84 × 10−12

3.5. Physical Properties of Stainless Steel 316. The temperature gradient near the porous transpiring wall in the TWR is large, and the thermal conductivity and specific heat of the wall material are sensitive to the temperature change, so the variation of material physical properties should be taken into account in the calculation of heat transfer of the porous wall. The correlation equations for accurately calculating the thermal conductivity and specific heat of 316 material are proposed as follows,29

(10)

λ = 9.2 + 0.0175 × T − 2 × 10−6T 2

(16) −1

−1

where λ is thermal conductivity (W·m ·K ) and T is temperature (K). 2.82 × 106 (17) T2 where cp is the specific heat at a constant pressure (J·kg−1·K−1). 3.6. Effective Thermal Conductivity of Porous Wall. The effective thermal conductivity of the transpiring wall is closely related to the porous wall structure and fluid physical properties, which can be calculated by the following equation, c p = 472 + 13.6 × 10−2T −

(11)

where Qtw is the volumetric flow rate of transpiration water (m3·s−1), β is the porosity of the porous wall, and S is the area of the porous wall. The S can be calculated by the reactor size mentioned in Section 2.1. Basic Qtw data were obtained from the display interface above directly as well, so vtw could be calculated by eq 11 if β is given. For the porous media with the same properties, the pressure drop of the source term in the momentum equation can be expressed as

Δp = −Si′δ

(14)

Thus, C2 and α of the porous wall under different porosity conditions can be calculated, and some results are listed in Table 1.

Q tw βS

2a 2 ρδ

a 1 = 1 α μδ

where Δp is the pressure drop (Pa) of fluid flowing across the transpiring wall, which can be directly obtained from the display interface of the experimental plant, because a differential pressure transducer was installed to determine the pressure drop above. a1 is the fitting coefficient (kg·m−2·s−1) of the linear term of flow velocity, a2 is the fitting coefficient (kg·m−3) of the quadratic term of flow velocity, and vtw is the flow velocity (m·s−1) of transpiration water in the porous transpiring wall. The flow velocity in the transpiring wall pores is calculated according to the flow rate and flow area of transpiration water, vtw =

(13)

λ′ = βλf + (1 − βλs)

(18) −1

−1

where λ′ is the effective thermal conductivity (W·m ·K ), β is the porosity of the porous wall, λf is the thermal conductivity of fluid (W·m−1·K−1), and λs is the thermal conductivity of the solid material of the porous wall (W·m−1·K−1). 3.7. Physical Property Parameters. At a constant pressure, physical property parameters of fluid vary with increasing temperature. For example, water physical properties change drastically near its critical point (Tc = 647.3 K, pc = 22.1 MPa), and a slight temperature variation may cause physical properties to change in an order of magnitude. Also, physical properties of other substances probably vary greatly during water state transition (e.g., from subcritical state to supercritical

(12)

where δ is the thickness of the porous wall, S′i is the source term of the momentum equation in the i-direction, and it can be calculated as D

DOI: 10.1021/acs.iecr.7b04479 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 3. Comparison of experimental and calculation temperatures in two cross sections at conditions of p = 24 MPa, Qme = 1.0 L·h−1, Tbulk = 723 K, wme = 15 wt%, κ = 0.3, Ttw = 573 K, and γ = 1.2. (a) L = 41 mm, (b) L = 123 mm.

Figure 4. Concentrations contours of (a) CH3OH, (b) O2, and (c) CO2, and (d) temperature distribution in the TWR at conditions of p = 24 MPa, Qme = 1.0 L·h−1, Tbulk = 723 K, wme = 15 wt%, κ = 0.30, Ttw = 573 K, and γ = 1.2.

state), therefore, substantially affecting the field distribution of the reactor. Thereby, the treatment of physical property parameters directly influences the calculation processes stability and the results accuracy. Density, specific heat, thermal conductivity, and viscosity of each pure component are able to be checked from the National Institute of Standards and Technology database.30 Additionally, the mass diffusion coefficient can be calculated according to the correlation formulas reported previously.31 3.8. Water Film Coverage Rate. Water film coverage rate, ω, is defined here for the first time, which is the ratio of the flow rate of the transpiration water at one location on the inner surface of the transpiring wall to the total flow rate of the fluid (including feedstock, oxidant, and transpiration water): ω=

Ftw,w Ftot,w

=

Herein, Ftw,w and Fbulk,w are able to be obtained by numerical simulation, and Ftw,w can also be calculated by the formula reported in our previous work.24 Water film coverage rate can characterize the continuity and uniformity of the water film formation and distribution. Obviously, the closer it is to 1.0 ω, the better the water film quality is.

4. RESULTS AND DISCUSSION 4.1. Model Validation. Figure 3 compares calculation and experimental data of temperatures in two cross sections (L = 41 mm and L = 123 mm) of the TWR. Apparently, temperature had the maximum value in the reactor center and gradually dropped along either the radial direction or the transpiration length. Thus, temperature gradients existed in radial and axial directions of the TWR due to exothermal oxidation reactions and cooling effect of transpiration water. Overall, the cross sections of L = 41 mm and L = 123 mm were located in the supercritical region (>647.3 K) and the subcritical region (0.8 in tested cases) raised while water film temperature and concentrations of O2, CO2, and bulk fluid in water film reduced as transpiration length increased. Inorganic salt content in water film dropped with transpiration intensity, transpiration length, and water film coverage rate increasing. As transpiration intensity increased from 0.15 to 1.2, the sodium chloride content in water film at L = 0.045 m and L = 0.102 m reduced from 0.45 to 0.15 wt% and from 0.35 to 0.08 wt%, respectively. Salt deposition could be avoided in the TWR if the salt content in initial feedstock was controlled to be lower than the maximum Csalt, in in eq 21 along the whole transpiration length. Relatively low water film coverage rate, high water film temperature, and salt content in water film in the upper part of the TWR imply the necessity and significance to further optimize the reactor upper configuration and operating parameters in subsequent work.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-29-82665749; Fax: +86-29-8266-8703; E-mail: [email protected]. ORCID

Donghai Xu: 0000-0003-0076-3078 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 and 21206132), the Fundamental Research Funds for the Central Universities (xjj2016116), the National Key Research and Development Program of China (2017YFB0603604 and 2016YFC0801904), and the Special Financial Grant from the Shaanxi Province Postdoctoral Science Foundation.

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NOMENCLATURE Qme = volumetric flow rate of methanol solution (L·h−1) wme = methanol mass concentration (wt%) Tbulk = preheating temperature of bulk fluid (K) Ttw = transpiration water temperature (K) Fox = oxidant mass flux (kg·s−1) Fme = mass flux of methanol solution (kg·s−1) Ftw = mass flux of transpiration water (kg·s−1) xi = i-coordinate axis direction ui = velocity in the i-direction p = static pressure

■ K

τij = stress tensor gi = gravity acceleration in i-direction Sm = momentum source h = total enthalpy Sh = energy source Yi = mass fraction of component i Di,m = diffusion coefficient of component i ut = turbulent eddy viscosity coefficient Sct = turbulence Schmidt number Si = production or consumption of component i due to reactions A = pre-exponential factor Ea = activation energy (kJ·mol−1) R = gas constant (J·K−1·mol−1) cme = methanol concentration (mol·L−1) cox = oxygen concentration (mol·L−1) n or m = reaction order Δp = pressure drop of fluid flowing across porous wall (Pa) a1 = fitting coefficient of the linear term of flow velocity (kg· m−2·s−1) a2 = fitting coefficient of the quadratic term of flow velocity (kg·m−3) vtw = flow velocity of transpiration water in porous transpiring wall (m·s−1) Qtw = volumetric flow rate of transpiration water (m3·s−1) S = area of the porous wall (m2) Si′ = source term of the momentum equation in i direction vi = flow rate in i-direction (m·s−1) C2 = internal resistance coefficient (m−1) T = temperature (K) cp = specific heat at a constant pressure (J·kg−1·K−1) λ′ = effective thermal conductivity (W·m−1·K−1) λf = thermal conductivity of fluid (W·m−1·K−1) λs = thermal conductivity of solid material of porous wall (W·m−1·K−1) T r = fluid temperature in reactor center (K) Tc = water critical temperature (K) Pc = water critical pressure (MPa) Ftw,w = flow rate of transpiration water on the inner surface of porous transpiring wall (kg·s−1) Ftot,w = total flow rate of fluid on the inner surface of porous transpiring wall (kg·s−1) Fbulk,w = flow rate of bulk fluid on inner surface of porous transpiring wall (kg·s−1) L = transpiration length (from the underside surface of reactor top cover) (m) Csalt, film (L) = salt content in water film at L-location (g· kg−1) Csalt, in = salt content in initial feedstock (g·kg−1) ω(L) = water film coverage rate at L-location Kbulk (L) = mass ratio of bulk fluid to total fluid in water film at L-location Csol, film (L) = salt solubility in water film at L-location (g· kg−1)

GREEK SYMBOLS κ = transpiration intensity γ = oxidation coefficient ρ = fluid density (kg·m−3) τ = time λ = effective thermal conductivity (W·m−1·K−1) β = porosity of porous wall δ = thickness of porous wall DOI: 10.1021/acs.iecr.7b04479 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research μ = dynamic viscosity (Pa·s) α = permeability (m2) ω = water film coverage rate

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SUBSCRIPTS tw = transpiration water me = methanol solution bulk = bulk fluid ox = oxidant c = water critical point

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ABBREVIATIONS SCWO = supercritical water oxidation TWR = transpiring wall reactor CFD = computational fluid dynamics ID = inner diameter tw1 = upper branch of transpiration water tw2 = middle branch of transpiration water tw3 = lower branch of transpiration water

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REFERENCES

(1) Marrone, P. A.; Hodes, M.; Smith, K. A.; Tester, J. W. Salt precipitation and scale control in supercritical water oxidationpart B: commercial/full-scale applications. J. Supercrit. Fluids 2004, 29, 289−312. (2) Marrone, P. A.; Hong, G. T. Corrosion control methods in supercritical water oxidation and gasification processes. J. Supercrit. Fluids 2009, 51, 83−103. (3) Xu, D. H.; Wang, S. Z.; Huang, C. B.; Tang, X. Y.; Guo, Y. Transpiring wall reactor in supercritical water oxidation: a technical review. Chem. Eng. Res. Des. 2014, 92, 2626−2639. (4) Brunner, G. Near and supercritical water. Part II: Oxidative processes. J. Supercrit. Fluids 2009, 47, 382−390. (5) Cocero, M. J.; Martinez, J. L. Cool wall reactor for supercritical water oxidation: Modelling and operation results. J. Supercrit. Fluids 2004, 31, 41−55. (6) Fauvel, E.; Joussot-Dubien, C.; Tanneur, V.; Moussiere, S.; Guichardon, P.; Charbit, G.; Charbit, F. A porous reactor for supercritical water oxidation: experimental results on salty compounds and corrosive solvents oxidation. Ind. Eng. Chem. Res. 2005, 44, 8968− 8971. (7) Abeln, J.; Kluth, M.; Pagel, M. Results and rough cost estimation for SCWO of painting effluents using a transpiring wall and a pipe reactor. J. Adv. Oxid. Technol. 2007, 10, 169−176. (8) Kritzer, P.; Dinjus, E. An assessment of supercritical water oxidation (SCWO) existing problems, possible solutions and new reactor concepts. Chem. Eng. J. 2001, 83, 207−214. (9) Bermejo, M. D.; Cocero, M. J. Supercritical water oxidation: a technical review. AIChE J. 2006, 52, 3933−3951. (10) Gong, W. J.; Duan, X. J. Degradation of landfill leachate using transpiring-wall supercritical water oxidation (SCWO) reactor. Waste Manage. 2010, 30, 2103−2107. (11) Fauvel, E.; Joussot-Dubien, C.; Guichardon, P.; Charbit, G.; Charbit, F.; Sarrade, S. A double-wall reactor for hydrothermal oxidation with supercritical water flow across the inner porous tube. J. Supercrit. Fluids 2004, 28, 47−56. (12) Bermejo, M. D.; Cocero, M. J. Destruction of an industrial wastewater by supercritical water oxidation in a transpiring wall reactor. J. Hazard. Mater. 2006, 137, 965−971. (13) Xu, D. H.; Wang, S. Z.; Gong, Y. M.; Guo, Y.; Tang, X. Y.; Ma, H. H. A novel concept reactor design for preventing salt deposition in supercritical water. Chem. Eng. Res. Des. 2010, 88, 1515−1522. (14) Xu, D. H.; Wang, S. Z.; Tang, X. Y.; Gong, Y. M.; Guo, Y.; Wang, Y. Z.; Zhang, J. Design of the first pilot scale plant of China for supercritical water oxidation of sewage sludge. Chem. Eng. Res. Des. 2012, 90, 288−297. L

DOI: 10.1021/acs.iecr.7b04479 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX