Influence of water-methanol solution additives on hydrocarbon fuel combustion in burner

Mathematical model of burning disposal a water-methanol solution by the gas fuel is presented. Two-dimensional model in the ANSYS Fluent Software is made. Thermal distribution of the flare and distribution of methane concentration are derived. We analysed the results of mathematical modelling.


Introduction
Ecological aspects of human life are becoming more important every year.Disposal of waste without harm to the environment is costly; therefore, the economic efficiency in choosing methods of utilization is tFhe important factor for the any industry [1].
In this paper, we consider the disposal of the water-methanol solution.This solution is a waste of the technological cycle of extraction and preparation for transportation by pipeline transport of natural gas.Most of the methanol is separated in the distillation column, but the residue contains a small volume of methanol in water, which is harmful to the environment.Currently, disposal of water-methanol solution is produced by incineration.About 60 commercial companies in Russia use the GFU-5.

Research method and data
The processes accompanying disposal by the example of burning a water-methanol solution is simulated.This is the basis for developing a methodology for calculating the considerate process.A water-methanol solution is the following volumetric composition: Н2O-99.67%,CH3OH-0.33 and the fuel is a natural gas of the following volumetric composition: CH4-98.9%;С2H6-0.12%;C3H8-0.01%;C4H10-0.01%;CO2-0.06%;N2-0.9%.

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Fuel gas consumption for atomization of industrial effluents is 0.1478 m 3 /s.Flow rate of combustible gas to Coanda's surface (Fig. 1) is 0.0739 m 3 /s.Consumption of water watermethanol is 0.278 kg/s.
The dimensions of the droplets formed at a given ratio of the gas and liquid phases were 55 μm.
The stationary model of the flame propagation in a two-dimensional setting is consider.Part of the fuel, aimed at spraying industrial effluents, moves inside the cylindrical pipeline.The industrial effluents comes from a coaxially located pipeline, smaller diameter, into the fuel flow through the nozzle.
Part of the gaseous fuel that passes through the nozzle forms a gas-droplet mixture with a water-methanol solution.Another part of the gaseous fuel flowing around the Coanda's surface comes to the periphery of the torch, where there is a mutual diffusion of the two streams and the environmental air to form a fuel mixture.
We model the diffusion process of a multicomponent mixture in accordance with the Maxwell-Stefan equations.Diffusion pressure is low [4]: where X imole fraction of component i;  diffusion velocity of component i, m²/s;  binary mass diffusion coefficient, m²/s;  thermal diffusion coefficient, m²/s; Ttemperature, K; d i -particle diameter, m.
The Maxwell diffusion coefficient is considered equal to the binary diffusion coefficient for an ideal gas.The barodiffusion effect, excluding the gravitational effect, is written by the following expression: In order to find the diffusion flux of a chemical species use Fick's law: where  the mass fraction of species i;  turbulent Schmidt number;   =  µ  2 /eddy viscosity, Pa•s;  µ =0.09constant [5]; dissipation rate, m 2 /s 3 ; keddy kinetic energy, m 2 /s 2 ;  , = (1 −   )/ ∑ (  /  ) ≠ the mass diffusion coefficient for species i, m²/s.
The equation of the diffusion flux vector of the mass component through the generalized diffusion coefficients A and B is consider.The following expression determin the diffusion coefficient of the component i in j: In the matrix of generalized diffusion coefficients according to the Fick's law, the coefficients A and B are determined by the following expression, according to [6]: where  the molecular weight, kg/kmol.The coefficients of thermal diffusion is determined in accordance to [7]  ] , The turbulence effects are determined in according by standard  −  model.This model are includes the transport of turbulent kinetic energy and the dissipation rate of turbulent kinetic energy equations [8] where   = −  ′   ′ ̅̅̅̅̅̅   /  -the production of turbulence kinetic energy, kg/(m•s 3 ); k turbulence kinetic energy, m 2 /s 2 ; turbulent dissipation rate, m 2 /s 3 ;  1 =1.44empirical constant;  2 =1.92empirical constant;   = 0.09empirical constant;   = 1.0empirical constant;   = 1.3empirical constant [5].
The chemical reactions are simulated in according by the mass conservation law of components i.
where R ithe net rate of production of species i by chemical reaction, kg/(s•m 3 );  rate of creation by addition from the dispersed phase, kg/(s•m 3 );  the mass fraction of species i.
The combustion model from a single gross reaction for each fuel component is considered.The reaction rate is calculated in according by the vortex dissipation model.Turbulent mixing affects the rate of chemical reactions.The lower value from the speed of the diffusion process and the rate of chemical reactions in according by the Arrhenius law is taken to determine the reaction rate [10].
where А = 4.0empirical constant; B = 0.5empirical constant; Y P the mass fraction of product P; Y Rthe mass fraction of reagent R; Nnumber of reactions;  , ′stoichiometric coefficient of reagent i in reaction r;  , ′′stoichiometric coefficient of product i in reaction r;  ,the molecular weight of species i, kg/mol.The chemical substance i formation rate is determined as the sum of the its formation rates according by Arrhenius law for each reaction: The fuel reaction heat is determined in according by the known calorific value: The heat transfer equation is solved in order to determine the thermal state: where  = /(  • )coefficient of thermal diffusivity, m²/s.Heat and mass transfer in the thermal control system of technical and technological energy equipment The specific heat capacity of each component does not depend on temperature.The specific heat capacity of the mixture is determined as the sum of the mass fractions of each component: The used boundary condition for the boundary G3 (Fig. 2) mean, that gas fuel flow enters through the pipeline dy80 with defined mass flow and the velocity profile according by the turbulent regime:∂υ/∂n=const.
The boundary condition for the boundary G4 describes admission the flow of the watermethanol solution with defined mass flow rate:/ = .
The boundary condition for the boundary G2 describes admission the flow of air with temperature equal to 0С.
The soil profile including the hill limits the burning area of the torch.This is described in according the boundary conditions G5.The lower boundary describes a wall, with the condition of adhesion, according by fallowing equations: / = 0; / = 0; / = 0.
The boundary condition for the boundary G1 is described by soft boundary conditions.

Results and discussion
These differential equations are solved in the software module ANSYS Fluent in a twodimensional flat formulation.The results of the mathematical experiments are presented as a distribution of temperature and component composition (Fig. 2).The facility is shown in Fig. 3 with flare geometric parameters when combusted defined mass flow the gas fuel and the water-methanol solution.The mathematical model may be the basis for further study of waste disposal in burner facilities.

Fig. 2 .
Fig. 2. Thermal distribution of the flare and distribution of methane concentration.

Fig. 3 .
Fig. 3.The facility with flare geometric parameters.The results of mathematical experiments satisfactorily correspond to the real dimensions of the facility flame.The formation of carcinogenic substances does not occur.The average temperature at the periphery of spraying the solution is about 1000 °C.The mathematical model allows us to determine the heat flux in the necessary direction.The mathematical model may be the basis for further study of waste disposal in burner facilities.