Methodology for determining the design parameters of combined type plasma-chemical reactor for gasification of carbon-containing raw materials

The paper shows the advantages of combined type reactors for plasma-chemical allothermic processes of carbon-containing raw materials gasification. The methodology for determining the design parameters of combined type plasma-chemical reactor for gasification of carbon-containing raw materials is developed. Analytical dependences for determination of time and constructive parameters of the combined type plasma-chemical reactor are established. Dependences contain interrelation between the main technological parameters of the process of thermo-conversion of carbon-containing raw materials taking into account thermochemical reactions. Dependences of constructive parameters of reaction zone of combined type plasma-chemical reactor for steam plasma gasification of carbon-containing media are obtained. It is established that at steam gasification of carbon-containing raw materials with the maximum particle size of 150 microns and the temperature in the reaction zone of 5000 K the volume of the reaction zone depends on the productivity of carbon-containing raw materials, which has a significant effect on the design parameters of the reaction zone.


Introduction
In recent years, there has been a growing interest in plasma-chemical allothermic processes, in which the initial carbon-containing raw materials in the form of finely dispersed phase enter the plasma.As a result of the plasma chemical process, the gaseous products and a solid inert residue are produced.The resulting gas can be used in the production of methanol, motor fuel and other types of chemical compounds, as an energy carrier in the technologies of heat and electricity generation, as protective atmospheres in the technologies of direct reduction of iron oxides and as a feedstock for hydrogen production [1,2].
Plasma-chemical allothermic technologies are characterized by universality to composition and properties of initial substances, selectivity of components of useful product, environmental safety, rational use of initial raw materials, high rates of chemical reactions, productivity of the process and low metal intensity of equipment.
Plasma-chemical reactors of separated and combined types are used for realization of allothermic processes.In the combined type reactors, unlike the separated type reactors, heating processes and chemical transformations occur in one and the same reaction zone, therefore the combined type reactors have a number of advantages, in particular higher intensity of heat exchange, because the oxidizer and carbon-containing raw materials (CCRM) are fed into the reaction chamber simultaneously, where they are heated by convective and radiation heat exchange with gas and electric arc, which leads to a more complete conversion of carbon from the CCRM.
The analysis of literature sources has shown that the works [3,4] contain methods of calculation of separated-type reactors design parameters.These methods do not take into account thermochemical transformations during gasification; at the same time, there are no methods of calculation of design parameters of combined type plasma-chemical reactors, which take into account the energy of transformation reactions.
The key parameter of thermal transformations of heterogeneous media is the residence time of a dispersed particle in the reaction zone of the reactor from the moment of its entering to the complete transformation of the carbon into carbon oxides.Since the CCRM is a polydisperse material, to ensure complete gasification of all particles, the calculation of process parameters should be carried out at the maximum particle size contained in the CCRM.This affects the quality and yield of the target product during gasification and has a significant impact on the geometric parameters of the reaction chamber.In this connection, it is necessary to take into account the conditions of heat exchange, to establish rational time indicators of the thermochemical transformations of the CCRM and their influence on the main geometric and operating parameters of the reaction chamber of combined type plasma-chemical reactors.
The purpose of this paper is to develop a methodology for calculating the design parameters of combined type plasma-chemical reactor for gasification of carbon-containing raw materials and to establish dependencies for the time and design parameters of combined type plasma-chemical reactor.These dependences should contain the relationship between the main technological parameters of the thermal conversion of carbon-containing raw materials, taking into account the thermochemical reactions occurring during their gasification.

Methods
The sequence of the methodology for calculating the design parameters of the combined type plasmachemical reactor, presented in the paper, consists in the following: determining the heat for gasification of the CCRM; determining the heat transferred from the plasmotron to the CCRM particles; determining the residence time of particles in the reaction zone of the plasma-chemical reactor from the moment of its entering to complete gasification; determining the basic design parameters of combined type plasma-chemical reactor.
The volume (m 3 ) of the reaction zone of the plasma-chemical reactor is determined by the following formula [5]: where  -residence time of the carbon-containing particle in the reactor (i.e., the time from its entering into the reactor from the initial temperature to complete gasification), s; Mass flow rate of the generated gas is equal to (kg/s): where ox m -oxidizer mass flow rate, kg/s; c mmass flow rate of the CCRM, kg/s;  -mass stoichiometric ratio of oxidizer to the CCMR, kg/kg.Since the power supplied by the plasmotron to the CCRM particles, taking into account the efficiency of the plasmotron, is equal to the energy required for CCRM gasification, then: where  -efficiency of the plasmotron; N -plasmotron power, kW; s.m q specific mass energy consumption of the gasification process, kWh/kg.When Then, taking into account formulas ( 1) and ( 3), we obtain: To determine the residence time ( ) of a single CCRM particle in the reactor from the moment of its entering into the reactor to the gasification temperature, let us draw up a heat balance of a single CCRM particle, taking into account that the heat from an external source depends on time p.g ext () where p.g q heat required for gasification of a single CCRM particle, J; ext () qf  -heat, which is supplied to a single CCRM particle from an external source, J.
The heat for gasification of a single CCRM particle is determined from the formula: where f q  -total heat contained in the gasification products of a single particle, J; in q  -total heat contained in the initial single particle, J; ch.r q  heat input (or generated) during chemical reactions, J.
When considering the amount of heat supplied to the particle from an external source, we neglect the amount of heat going to the thermal conductivity of the particle, since the particle is a thermally thin body, and the radiation heat exchange between particles, due to their low concentration in the flow.
Since the heat supply from an external source to particle in combined type plasma-chemical reactor occurs due to convective and radiant heat exchanges, then p.g conv rad conv q heat supplied to the CCRM by convection, J; rad qheat supplied to the CCRM by radiation, J. Substituting formulas (7) and (8) into formula (6), we obtain: Let's consider the components of formula (9).The total heat in the gasification products of a single particle is: where f,i m mass of the i-th component of the process product, kg; f,i Ienthalpy of the i -th component of the process product, J/kg; f,i Cheat capacity of the i -th component of the process product, J/(kg•K); f T -final temperature (gasification temperature) of the particle, K.
Total heat contained in the initial particle: The heat introduced (or generated) during chemical reactions: where s.ch.r q  total specific heat effect of chemical reactions, J/kg: where C х -mass carbon content in the CCRM particle, (kg C)/(kg CCRM);  H -total heat effect of chemical reactions, J/mol; C М -molecular mass of carbon, kg/mol.Then Substituting formulas (12), ( 13) and ( 16) into the left side (9), we obtain: Taking into account that the particle has a spherical shape, mass of the particle is equal to: The heat supplied to the CCRM particle by convection [6]: where  -heat transfer coefficient, W/(m 2 •K); g Tgas temperature, K; in T -initial temperature of the particle, K; Fparticle surface, m 2 : Heat transfer coefficient is determined from Nusselt criterion [6]: where Nu -Nusselt criterion; since the particle has a spherical shape, at small values of the Reynolds criterion (Re), according to [6] Nu = 2;  -thermal conductivity coefficient of the environment, W/(m•K); l -geometric size, m, p ld = .Then The heat supplied to the CCRM due to radiant heat transfer [6]: Substituting formulas (19), (23), and (25) into (9), we obtain IOP Publishing doi:10.1088/1755-1315/1348/1/0120786

Results and discussion
In order to establish the influence of thermal effect of chemical reactions on the residence time of particles in the reaction zone, consider the following endothermic chemical processes of carbon gasification [4]: -without chemical reactions, i.e. 0 H  = -steam-oxygen (at 80% H2O, 20%O2) gasification  For example, for particles of 150 microns in the absence of chemical reactions the residence time is 0.0018 s, at steam-oxygen gasification -0.0036 s, and at steam-plasma gasification -0.0057 s, i.e. the residence time increases more than 3 times, which leads to corresponding increase in the design parameters of the reactor.
Consider the process of steam gasification of CCRM due to two main reactions at a temperature of 1800-2000 K [4]: The first reaction occurs when the oxygen in the CCRM interacts, and the second reaction occurs when the injected water interacts with the residual carbon.
Material and energy balances of chemical reactions are (29): When performing thermodynamic calculations, the masses of components of gasification products are established, which are necessary to determine the heat effects of chemical reactions.In order to determine the heat generated during chemical reactions (29a), we express the heat of each reaction through the unit mass of the formed product.At known value of mass of formed hydrogen (G k H2), which is established on the basis of thermodynamic calculations, the material balance of the second reaction is as follows: Based on this, the mass of carbon monoxide G 2 CO formed by the second reaction from (29a) is At known mass of formed carbon monoxide ( f CO G ) (according to thermodynamic calculations), the mass of carbon monoxide 1 CO G formed by the first reaction is equal to: Material balance of the first chemical reaction (29a): The heat that is released as a result of the first reaction (MJ/kg): The heat that is absorbed as a result of the second reaction (MJ/kg): Then the total specific heat effect of chemical reactions occurring at steam gasification of carboncontaining media (in J/kg): Based on equation (37), the dependence of the particle residence time in the plasma-chemical reactor on the particle size and gas temperature was obtained for the process of vapor-plasma thermal conversion of the CCRM (figure 2).The dependence shows that an increase in particle size and a decrease in gas temperature lead to an increase in the residence time of the CCRM particles in the reaction zone.
Substituting the formula (37) into (5), we obtain the dependence for determining the volume of the reaction zone of the plasma-chemical reactor at steam plasma gasification of the CCRM: . 3600 Based on equation (38), the dependence of the reaction zone volume on the mass productivity and gas temperature was obtained for the process of steam-plasma thermal conversion of CCRM with a maximum particle size of 150μm (figure 3).The dependence shows that the reaction zone volume increases with increasing CCRM productivity, and increasing gas temperature leads to a decrease in the reaction zone volume.Based on equation (39), for the process of steam-plasma thermal conversion of the CCRM with a maximum particle size of 150 μm at gas temperature of 5000 K, the dependence of the reaction zone length on the reactor diameter and mass productivity was obtained (figure 4), which allows the selection of rational values of the reaction zone length and reactor diameter depending on the mass productivity of CCRM.

Conclusions
A methodology for calculating the main design parameters of the reaction zone of the combined type plasma-chemical reactor for gasification of the CСRM has been developed.
Analytical dependences for determining the residence time of particles before their complete gasification in the combined type plasma-chemical reactor have been established.Analytical dependences contain the relationship between the main technological parameters of the process of thermal conversions of the CCRM and take into account the thermal effect of thermochemical reactions.
Dependences of design parameters of the plasma-chemical reactor reaction zone on the mass productivity of the CCRM at steam plasma gasification with the maximum particle size of 150 μm and temperature in the reaction zone of 5000 K have been obtained.
gas generated during gasification of the CCRM, m 3 /s; g mmass flow rate of gas generated during gasification of the CCRM, kg/s; g  -gas density, kg/m 3 .
where in,i m mass of the i -th component in the initial particle, kg; in,i I enthalpy of the i -th component in the initial particle at initial temperature, J/kg; in,i C heat capacity of the i -th component in the initial particle at the initial temperature, J/(kg•K); in Tinitial temperature, K.We assume that heat capacity of the i-th component of the product at the final temperature f T is equal to heat capacity of carbon at the final temperature f T , i.e., f , f,C i CC = , and heat capacity of the i-th component in the initial particle at the initial temperature н T is equal to the heat capacity of carbon at the initial temperature in T , i.e., in, in,C i CC = , and assume that the mass of the CCRM particle ( p m ) does not change during heating from the initial in T to the process temperature f

C
reduced radiation coefficient, W/(m 2 •K 4 ); pl Tplasma arc temperature, K.Then, taking into account the formula (21): 27, 28a, 28b), the dependence (figure1) of the particle residence time in the combined type plasma-chemical reactor on the particle size and thermal effect of endothermic chemical reactions was obtained, which shows a significant influence of the thermal effect of chemical reactions on the residence time of the CCRM particle in the reaction zone.

Figure 1 .
Figure 1.Dependence of CCRM particle residence time in the combined type plasma-chemical reactor on the maximum particle size and thermal effect of endothermic chemical reactions.

Figure 2 .
Figure 2. Dependence of particle residence time in plasma-chemical reactor on the maximum particle size and gas temperature in the reaction zone under steam plasma gasification of CCRM.

Figure 3 .
Figure 3. Dependence of the reaction zone volume on the mass productivity and temperature in the reaction zone under vapor plasma gasification of particles with a maximum size of 150 μm.The length of the reaction zone L (m) at a certain value of the reactor diameter D:

Figure 4 .
Figure 4. Dependence of the reaction zone length on the reactor diameter and mass productivity under steam plasma gasification at the temperature in the reaction zone 5000 K of particles 150 μm.