PHYSICAL-MATHEMATICAL MODEL FOR FIXED-BED SOLID FUEL GASIFICATION PROCESS SIMULATION

Phycial-mathmatical model for fixed-bed coal gasification process simulation is proposed. The heterogeneous carbon oxidation chemical reactions were simulated via Arrhenius equation while homogeneous reactions in gas phase were calculated using Gibbs free energy minimization procedure. The syngas component concentration field and fuel conversion distribution as well as syngas final temperature and composition were defined for fixed bed gasification of T-grade coal of Kuznetskiy deposit. The optimal fuel residence time and gasifyer specific productivity were defined. The prevail reactions in oxidizing and reduction zones together with its height were defined.


Introduction
Solid fuel is one of major sources of primary energy in the world nowadays according to BP data [1] and provides nearly 30 % of world generation.While energy consumption is expected to increase by 35 % to 2035 year the share of coal generation is expected to be significant and has a value close to 25 % [1].Such decrease is seem to appear due to economic and ecological issues connected to coal usage like carbon, sulfur and nitrogen oxide emissions, lower efficiency compared to combined cycle for natural gas and solid particles in flue gases [2].
The solid fuel gasification may solve both these problems.Syngas may be used in combined cycle.Gasification process features allow to decrease nitrogen oxide formation intensity and apply modern gas-cleaning technics [3] which are inefficient with existing direct combustion technology.
Gasificationprocess of turning fixed carbon from coal into combustible gasinclude many chemical reactions and physical processes.That makes it quite difficult to define process outcome at different expoitational conditions.To resolve this problem the physicalmathematical model with macrokinetic limitations was proposed.Based on it the gasification process characteristics were calculated for T-grade bituminous coal of Kuznetskiy deposit.

Material characterization
The T-grade bituminous coal was used to simulate fixed bed coal gasification process.The fuel proximate analysis was carried out using ISO 17246:2010 [4].The moisture, ash, volatile matter and fixed carbon content values were defined.Ultimate analysis was carried out via Euro EA 3000 CHNOS analyzer.Results presented in Table 1.

Model statement
The fixed bed counter-flow gasification process was modeled.Reactor chamber was presented as a set of consequently connected cylindrical domains with equal height and fuel residence time.The temperature distribution in each domain was considered to be uniform.The rate of heterogeneous chemical reactions were simulated via Arrhenius equation.
Considering fuel residence time in each domain to be marked as W , the total amount of turned into gas phase carbon could be calculated as: there Rgas constant, J/(mole K); i T -temperature in domain i, K; i X -fuel conversion value; W -fuel residence time, s; > @ OX -oxidizer molar concentration.Conversion value could be calculated as: here i m -fuel mass after i th domain, kg; a m -ash mass, kg; 0 m -initial fuel mass, kg.Because next conversion value depends on previous, to increase calculation preciseness the equation 1 was integrated by time: there t is time moment, s.Considering 1 i i t t W analytical solution of equation 3 will take the following form: Smart Grids 2016 The gas-phase composition was defined by Gibbs free energy minimization procedure with assumption that gaseous mixture in each domain exists in equilibrium by following equation [6]: there i n -molar amount of i th substance, mole; i P -molar potential of i th substance, J/mole, which could be defined as follows: there , i i h s -enthalpy and entropy of formation of i th substance at temperature T , J/mole, J/(mole K); 0 p and p -ambient and current pressure in system, Pa.To follow material balance of system with N substances and M types of atoms the possible solution domain was limited by following set of equations: , , 0, there ij a -stoichiometric coefficient (number of j-type atoms in molecule i); j b -total amount of j-type atom in system, mole.The Gibbs free energy minimization procedure was realized using Lagrange multipliers via steepest descent methods.As long as presence of components with close to zero content has a negative impact on calculation preciseness the number of taken into account substances was decreased to six following: H 2 O, CO, CO 2 , H 2 , CH 4 and O 2 .Nitrogen content in air and inorganic matter content in fuel were considered to be chemically passive and were taken into account only in equation of thermal balance.
To define thermal effect of turning system from initial condition into final the Hess law was used: , there fi H -enthalpy of formation of i th substance, J/mole; «pr» and «f» indexes refer to reaction products and feed, respectively .Thermal effect of process could be defined as follows: , there i H -i th substance heat of formation, J/kg; i m -mass of i th substance, kg.

Simulation results
Using proposed model the fixed bed gasification process characteristics were defined for Tgrade bituminous coal.The initial conditions were 400 °C for gaseous feed and 20 °C for fuel.The coal/steam/air ratio was 1/1/1.5 according to [7].The residence time of fuel in Smart Grids 2016 gasifyer was chosen to supply final conversion 0.9 and was defined to equal to 0.15 min.The temperature and conversion fields were obtained (fig. 1) as well as substance concentration distribution (fig.2) over reactor height.
This resulted into more intense temperature drop and calorific value increasing.The methane content values over the reaction zone was small and could be not taken into account in further calculations.

Conclusion
Equilibrium thermodynamics and heterogeneous chemical kinetics combination were used to simulate counter-flow fixed bed gasification process for T-grade bituminous coal of Kuznetskiy deposit.The optimal fuel residence time was defined as well as syngas composition and final temperature.Based on temperature distribution and syngas concentration fields over the reactor height the oxidation and reduction zones were distinguished.Prevailing chemical reaction on each step were defined.

Table 1 .
Proximate and ultimate analysis results for T-grade bituminous coal.

Table 2 .
Kinetic constant values for heterogeneous chemical reactions.