2D Materials as Protective Coating against Low and Middle Temperature (100˚C - 300˚C) Corrosion-Erosion in Waste to Energy Plant: Case of Graphene

The combustion of MSW contains several species which if liberated into the flue gas will participate in erosion-corrosion reactions with the alloy surface and with the oxide layers. Actually with the evolution of material science and the discovery of 2D materials, we can handle that situation as well as possible. The graphene as 2D material presents a lot of advantage due to it physical properties such: melting point, boiling point and thermal conductivity, which can help to manage the problem of low and middle temperature (100˚C -300˚C) erosion-corrosion into the boiler wall of waste to energy. The aim of the study was focused on analyzing the resistance at low and middle temperature (100˚C - 300˚C) in the enclosed environment and the corrosion-erosion resistance abilities of the graphene sheet as the 2D protective coating material. This paper analyzed the possibility of using the graphene in the aggressive environment which is waste to energy boiler. The results obtained from this study after simulation using ANSYS software which is one of the best software for simulations showed that Graphene protects the furnace walls against corrosion-erosion for temperatures lower than 400˚C and that in the presence of certain impurities such as: sodium (Na), sulfur (S), chloride (Cl) and Phosphorous (P), Sodium Chloride (NaCl), Hydrogen Chloride Dioxide Carbone 2 ) of Sulfur 2


Introduction
Municipal Solid Waste (MSW) becomes a point of focus globally due to its harmful effects on the environment and human health if it is not managed properly. MSW was proved globally to be used as a resource, and it has a major opportunity in the realm of conversion technologies [1]. The combustion of Municipal Solids Wastes (MSW) contains several species which if liberated into the flue gas can participate in corrosion reactions and erosion with the alloy surface and with the oxide layers. Other than the significant concentration of chlorine, there is a large concentration of ash, which can contain alkali metals such as sodium and potassium or heavy metals, such as zinc and lead (Table 1). There is also an appreciable amount of sulfur in waste streams like textiles. There is roughly 5 -10 times more chlorine in MSW than sulfur [2].
When we observe the combustion of MSW we can see quickly there is a different than that of any other fuels because of its heterogeneous nature. The corrosion mechanism can be indicated by: metal oxides (oxidation) [3], metal sulfides (sulfidation), mixtures sulfides (sulfidation) and oxides (oxidation), metal carbides (carburization) and metal chlorides (chlorination) [2].
By the way, Graphene consists of a single layer of carbon atoms arranged in a hexagonal lattice is a 2D materials which present a lot of advantages due to its physical properties [5] [6] (Table 2) which make it a good candidate as a protective solution against low and middle temperature corrosion-erosion into boiler walls.

Effect of Temperature on Graphene
Understanding the effect of thermally driven metal degradation is essential because of the temperatures present in industrial processes such as in: heat exchangers, boiler, and gas turbines.
The graphene has been employed as anti-oxidation coatings because of their ambient thermal stability [7] [8] [9]. Thermal oxidation stimulates exothermic chemical reaction for graphene as follows [10]: Table 1. Impurities which influence corrosion-erosion damage of boiler combustion gas environment in WTE plant [4].

Kind of MSW MSW
Contaminants of fuel (wet base) Graphene Graphene : C O CO With ΔHf = −393 kJ/mole. The activation energy required to form an initial vacancy in graphene is ~7.5 eV and the formation energy of subsequent vacancies decreases when adjacent atoms are sequentially detached [11]. Thus, subsequent removal of the carbon from the initial vacancy requires minimal energy.
Analyzing the Raman spectroscopy performed at different locations under a range of temperatures (up to 1000˚C) elucidated the stability of corresponding 2D materials. By analyzing Figure 1, we can see that after 600˚C, the absence of characteristics Raman peak means that for such temperatures the graphene starts to deteriorate. Meaning, under 600˚C graphene coatings is acceptable.
Therefore, we will focus our study on medium and low temperatures in a closed and aggressive environment. Then, we will analyze the erosion corrosion resistance of Graphene as a 2D material in order to highlight its ability to protect the materials behind it. To achieve this objective we will run simulations using ANSYS software.

Simulation Methodology
To solve our problem we use ANSYS software which is a good one for analysis of possibility of using the graphene single layer to protect the boiler walls into waste to energy plant against erosion-corrosion. For that, we have used ANSYS software.

Flow Simulation
A transient computational fluent dynamic (CFD) simulation applying a pressure-based solver was employed to solve the density weighted Reynolds-averaged Navier-Stokes (RANS) equations, as follows [12]: ρ: Density (kg/m 3 ) u i : Favre-averaged velocity in tensor notation x, y, z: Direction of coordinate axes i, j, k: Tensorial indices ': Fluctuations with respect to a Reynolds averaging '': Fluctuations with respect to a Favre averaging g = Gravity (m/s 2 ) u i , u j : Reynolds stress (kg/m•s 2 ) u i : Favre-averaged velocity in tensor notation u i : Resolved fluctuating velocity components p: Pressure (Pa) With: h: Enthalpy (j/kg) Z i J : Diffusive flux of chemical species q i , q r : The generic source term and reaction heat term Y: Mass fraction of species R z : Production rate of zth component Where, the stress tensor, ij τ , is given by [12]: The species product by diffusive flux of combustion is defined by the Fick's law: u t : Turbulent eddy viscosity (kg•m/s). Sc: Schmidt number.

Radiation Modeling
To solve the problem in the present work, we use the discrete ordinates (DO) model of the radiative transfer Equation (RTE), considering the absorption and emission effects [12]: The S2S model assumes any absorption, emission, or scattering of radiation by the medium can be ignored; as a result, reducing the computational cost by only considering the surface-to-surface radiation. In this model, the radiation heat transfer to a surface from another surface is a direct function of the surfaceto-surface view factor. Therefore, the radiation energy balance for each surface follows the equation below [12] kj F : The view factor between surface k and surface j.

Combustion Modeling
Combustion inside the burner and furnace domains was modeled using the eddy-dissipation model (EDM). It should be noted that, because in the gas-fired furnace the burners create high velocity combustion products, the Arrhenius chemical kinetic calculations were not considered thereby the computational cost is significantly reduced. In EDM, the species transport formulation for the local mass fraction species (Y z ), for the zth species, was solved assuming that the reaction rates were dominated by turbulence. Therefore, the species transport equation becomes as follows [13]: z S : Source term of zth component.

Turbulence Model
The standard k-ε model uses model transport equations to obtain dissipation rate k and turbulence kinetic energy k. Hence, the model transport equation for k can be obtained by applying the precise equation, whereas the model transport equation for k can be determined through the application of physical reasoning. Thus, to derive the k-ε model, assuming a complete turbulent flow with an insignificant molecular viscosity, making this k-ε model only applicable in flows which are fully turbulent. Hence, alterations are needed to improve both the model's applicability and its performance. Two model variants that use ANSYS Fluent are the k-e model and realizable k-e model, as formulated below [14] ( ) ( ) where: k G = production of turbulence kinetic energy due to velocity gradients.

Erosion Model
Here, we will present the erosion model using the experimental formula below [15]: C(d p ) = function of particle α = impact angle of the particle path with the wall face f(α) = function of impact angle ω = relative velocity of particle b(ω) = function of relative particle velocity A face = area of the cell face at the wall Default values are: C = 1.8 × 10 −9 , f = 1 and b = 0 Using the Tulsa Angle Dependent Model, Equation (30), can be rewrite as describe below: The Equation (13) will rewrite by making substitutions as follows:

Assumptions and Boundary Conditions
To make these simulations, some assumptions and boundary conditions are required, such as: The boiler is considered as a cube box; We consider the a single layer graphene sheet with the size: 500 mm (long) and 250 mm (large); The temperature into the boiler is considered variable; We considered the pressure into boiler at 4 Mpa; The graphene sheet is applied inside of wall of rectangular cube, meaning it already coated; For our research we consider mechanical exfoliation as the production method of graphene and Chemical Vapor Deposition as method for coating and The substrate is the steel.

Exposure Elements
Following elements will be used for the simulation: Chemical elements: sodium (Na), sulfur (S), chloride (Cl) and Phosphorous (P) Gases and composite elements: Sodium Chloride (NaCl), Hydrogen Chloride (HCl), Dioxide of Carbone (CO 2 ) and Dioxide of Sulfur (SO 2 ).
We choice to simulate the behavior of graphene in front of these elements because they are the dominants elements met into WTE.

ANSYS Input
See Table 3 and Table 4.

Results and Analysis
This chapter is devoted to simulation of erosion resistance of graphene sheet at certain temperature and the corrosion analysis because we cannot make the last one on ANSYS software. The simulation will be made such as: Step 1. Simulation of Temperature resistance of graphene sheet alone coated the boiler walls.
Step 2. Temperature resistance Simulation of the graphene sheet coated the boiler walls in presence of some chemical elements.
Step 3. Erosion Simulation of the ability of graphene sheet coated the boiler wall in presence of some chemical element and gases.
Step 4. Analysis of Corrosion barrier of graphene sheet.

Geometry
In order to have convincing results as mentioned in the hypotheses, we will coat Graphene sheets (one layer) on the walls of a closed box which represents the walls of an oven. Below Figure 2, the geometry used for our simulation.

Mesh
After defining our geometry, we need to define the appropriate mesh which is important for the calculations.
Below Figure 3 is the mesh.

Data Analysis
To exploit the data collect after running our simulation will be drop the data the table for further analysis.
We categorize the data obtained in three Classes such as:  Thereby, the graphene sheet resists well and can protect the wall of boiler against any attack due to the temperature between (148˚C -761.85˚C).

Data Analysis
We have simulated the behavior of graphene coated at some range of temperature and in presence some chemical selected elements, such as: Sodium, Chloride, Sulfur and Phosphor.
To analyze the data obtained from this simulation we will follow the approach used in point 3.1, the results of these simulations are synthetized on the following tables.

Results of Simulation of Graphene Coated the Boiler Wall
Containing Sodium (Na) After this simulation, we have categorized the behavior of the graphene sheet in three Classes, such as: Graphene

Results of Simulation of Graphene Coated the Boiler Wall
Containing of Sulfur (S) After this simulation, we have categorized the behavior of the graphene sheet in three classes, such as:

Average Comment
In the Table 5 and Figure 9, we compare the limit of all these simulation results. We observe a significant difference between data of simulation graphene working alone when it coat at the boiler walls and data of simulation of graphene in presence of some chemical elements which are considered as pollutants and dangerous for the boiler walls. Thus, these elements reduce the protective capacity of Graphene approximately by half but the graphene still good.
Considering the temperature values into the table above graphene can perfectly work without convenient with all selected chemical elements until a max of 400˚C.

Erosion Simulation of Graphene Sheet Coated the Boiler Walls
For this simulation we still using, the geometry and mesh at the point 4.1.1. We will simulate the erosion behavior of graphene coated the boiler walls in presence of gases and one simple chemical element such as: HCl, SO 2 , KCl, P and CO 2 .

Erosion Simulation of Graphene in Presence of SO 2 Analysis Comment
By analyzing the results presents above on the table and figure, we have: Class 1: ≤754.85˚C, represented by bleu and bleu bright on the Figure 12 Figure   12(b), meaning the graphene sheet cannot support and work.

Erosion Simulation of Graphene in Presence of Phosphorous Analysis
Comment By analyzing the results presents above on the table and figure, we have: Class 1: ≤756.85˚C, represented by bleu and bleu bright on the Figure 16(b), what means a graphene sheet work well without any problem; in the Figure 17, we can observe the erosion rate is approximately zero; Class 2: [800˚C -2584.85˚C], represented by green and yellow on the Figure  16(b), meaning graphene sheet still supporting and work with increases of temperature; Class 3: [2600˚C -5088.85˚C], represented yellow red and red on the Figure  16(b), meaning the graphene sheet cannot support and work.

Average
For all of those cases presented above, we will look the average what is presented in the Table 6 below.
Regarding to data of this table, graphene combined with chemical and some gases will ensure a good protection of boiler walls against erosion until at 460˚C.

Corrosion Analysis
Corrosion is a chemical phenomenon which ANSYS cannot do. Therefore, we will proceed by analytic method to solve this issue. That method is a microscopic analysis aspect of graphene:    Firstly, we analyze the pore diameter (Table 7) of the carbon ring in terms of the electron density is smaller than the kinetic diameter of various gases and chemicals elements, such as: He, H 2 , CO 2 , O 2 , N 2 , and CH 4 . For that we can take an example of the pore diameter of an octagon ring (considering electron density) is only 1.5 Å. Only large vacancies with a size above 5Å, that is, two lattice parameters, can be penetrated by the gas molecule.  Secondly, we refer to the relation (1), the initial energy to form vacancy in the graphene structure is approximately to 7.5 eV [16] and according to the Raman Spectra of temperature evolution ( Figure 5), and graphene conserve that energy for the temperature under 700˚C. Graphene   The hexagonal pore lattice diameter of graphene is 0.246 nm of and with a measured C-C bond length of 0.14 nm, the Graphene is considering the nuclei of the carbon atoms. When the Van der Waals radii (0.11 nm) pore diameter is reduced to 0.064 nm the carbon atoms are considered. The graphene ensures minimal permeability when the pore lattice present a small geometric and that even for smaller atoms such as helium. Moreover, the dense and delocalized electron cloud of π-conjugated carbon network in Graphene blocks the Class within its close packed aromatic rings and poses a repelling field to the reactive atom or molecule, consequently providing a physical separation between the refined metal surface and environmental reactants.
This energy barrier for a single layer coating of graphene is high enough to block the diffusion of oxygen to the underlying metal interface. The energy barrier magnitude of varies with molecular permission through the graphene lattice and the path of the atomic, suggesting that graphene can be the thinnest ever known corrosion barrier.

Conclusions and Suggestions
The arrival of new materials such as 2D materials (Graphene), a new door opens to mitigate or combat corrosion-erosion due to temperature by using the thermal properties of these materials (graphene).
Analyzing the graphene sheet at some range of temperature, also at the pressure of 4 MPa and in presence of some chemical elements, such as: Na, Cl, S and P. Thus, the results of simulation revealed a perfect protection of boiler walls by the graphene sheet, such as:  With Na: the graphene sheet will ensure a good protection for the temperature ≤ 412.85˚C;  With Cl: the graphene sheet will ensure a good protection for the temperature ≤ 412.85˚C;  With S: the graphene sheet will ensure a good protection for the temperature ≤ 411.85˚C and  With P: the graphene sheet will ensure a good protection for the temperature ≤ 700˚C; With all these elements combined in the boiler, Graphene sheet provides good wall protection for temperatures ≤ 415.6˚C.
After that, we analyzed the erosion caused by the contaminating elements contained in the boiler, such as: hydrogen chloride, sulfur dioxide, phosphorus, potassium chloride and carbon dioxide. It turns out that the graphene sheet coating the walls of the boiler protects these perfectly for temperatures ≤ 700˚C.
Comparing the results of the simulation of the empty boiler and the one filled with impurities represented by some chemical elements, we note a reduction of approximately half of the resistive capacity of Graphene, that is to say 1067˚C to 415.85˚C. In spite of this, it continues to protect the coated wall.
The graphene can handle well the problem of corrosion-erosion in general and the problem of corrosion-erosion due to temperature. It is excellent candidate as anticorrosion-erosion coatings because of the great impermeability to all gases and salts (what is one of the responsible of corrosion into boiler in WTE) [17]. The Graphene-coated steel exhibits outstanding anti-corrosion-erosion properties.
Finally, graphene as a 2D material used in this study offers a great protection against corrosion-erosion for temperatures below 400˚C, which will increase the life of the wall of the WTE boiler operating under temperatures lower than the above mentioned, this directly implies the life of the WTE.
Furthermore, our objective was to test and prove the use of Graphene in an aggressive and closed environment. Being able to work in an aggressive environment, Graphene can certainly be applied to other scales and environments as protection against corrosion-erosion.