Modeling of heat exchange processes in a condenser of a pyrolysis bioenergy plant

. The article presents the results of mathematical modeling of heat exchange processes in the condenser of a pyrolysis plant, in order to identify the optimal parameters for cooling the biomass pyrolysis steam. A mathematical model of the thermal balance of the condenser of a pyrolysis plant has been developed for the calculation, selection and thermal analysis of the working cycle of the condenser, which allows to obtain the values of the optimal parameters of the temperature regime. The technological scheme of a pyrolysis bioenergy plant with a recuperative heat exchanger, which simultaneously provides hot water, gaseous and liquid biofuels to the consumer, is presented. The analysis of the obtained results shows that the water temperature at the outlet of the condenser of the pyrolysis plant is on average in the range of 60-70 o C and suitable for heat supply systems of an autonomous consumer.


Introduction
In the In the developed countries of the world, small bioenergy is intensively developing, especially the direction of processing biomass in order to obtain alternative fuels [1][2][3][4].Among modern technologies for processing hydrocarbon waste and plant biomass, the most effective is thermochemical processing by pyrolysis [5][6][7].
In pyrolysis plants, in order to obtain the maximum amount of high-quality biofuels (solid, liquid and gaseous) from biomass, it is necessary to create a heat exchanger-cooler, i.e. a condenser with optimal parameters of the cooling medium [8][9][10].
The steam-gas mixture from the pyrolysis plant (PP) reactor enters the condenser, where, after condensation and cooling, pyrogas and liquid fuel are obtained.The amount of liquid biofuel and pyrolysis gas obtained largely depends on the heat exchange processes between the steam-gas mixture and the cooling water, the thermal parameters of the condenser.
Many researchers from different countries have carried out work on optimizing technological parameters and intensifying heat exchange in PP [11][12][13][14][15].However, the thermal engineering calculation and modeling of heat transfer processes in order to optimize the parameters in PP capacitors have not been studied enough.
The conducted studies show that the vapor-gas mixture obtained by the evaporation of biomass and various hydrocarbon wastes differs in composition and in thermodynamic, physical properties from the properties of simple water vapor.In this regard, in order to select rational parameters of the condenser PP, in this work, modeling of heat exchange processes in non-stationary temperature conditions was carried out.

Materials and methods
The purpose of the work is to simulate heat exchange processes and analyse the thermal parameters of a pyrolysis BEP condenser with a recuperator.A schematic thermal diagram of a pyrolysis bioenergy plant (PBEP) with a recuperative heat exchanger is shown in figure 1.Heat exchange occurs when the vapor-gas mixture condenses on the surface of the cooling pipes of cold water.In this case, heat is transferred from the hot coolant (steam) through the wall of the tubes to the cooling cold coolant.In our case, cold water from artesian with an initial temperature  1 = 16 ÷ 18 0 C is used as a cold coolant.When steam condenses in the PP condenser, the steam temperature, which is equal to the condensation temperature tk, is considered constant and is determined by the pressure in the condenser Pk.
According to the calculation scheme, a mathematical model of the thermal balance of the PP capacitor is compiled in the following form of a differential equation: Where,   -the specific heat capacity of the circulating water of the condenser, kJ /(kg* s);  cooling water consumption in the condenser, kg/s;   -water temperature, 0 C; K -heat transfer coefficient, W/(m 2 * 0 C);   -temperature of steam during condensation in the condenser, 0 C; F -heat exchange area, m 2 .
We introduce the following notation: Then equation ( 2) has the following form: To solve the differential equation ( 4), we make up the initial conditions in the following form: for F=0;   = 0 = 1 , then the solution of equation ( 4) with respect to the temperature of the cooling water takes the form: If we equate the heat of water heating     ( 2 −  1 ) to the heat of steam condensation     (  −   ), after some transformations, the thermal balance of the condenser through the enthalpy of steam: Where,  к ,  к -enthalpy of steam and condensate in the PU condenser, kJ/kg;  =  heat exchange area, m 2 ; ddiameter of cooling water pipes, m; l -length of the pipe in the condenser, m.The material balance of the capacitor is PP: Where,   -steam consumption, kg/s;   -pyrolysis gas consumption, kg/s;  pyrolysis liquid consumption, kg/s.The speed of the cooling water in the PP condenser is determined by the formula [16][17][18]: Where,   -heat given off by the condensing steam of the cooling water, W;   -water density, kg/m 3 ; ∆  -water heating in the condenser, 0 C. The average temperature of the cooling water in the condenser, o C: , 02 Where,  1 ,  2 -temperatures of the cooling water at the inlet and outlet of the condenser, 0 C. The total heat flow through the heat exchange surface is determined by the heat transfer equation: Heat transfer coefficient: Temperature difference:

Discussions
The work carried out studies on modeling heat exchange processes in the condenser of a pyrolysis bioenergy plant, which used pipelines made of different materials (steel and brass) with diameters of 10 mm, 15 mm and 20 mm, cooling water flow rate from 0.01 kg /s to 0.05 kg / s, within the water temperature from 16 0 C to 20 0 C. The obtained results of mathematical modeling can be seen in figure 3 and figure 4. From the results of studies carried out on the basis of steel pipelines (figure 3), it was found that at d = 10, with a flow rate of 0.01 kg/s of cooling water, the water temperature is reached 64 0 C, with a thermal power of 2 kW.At d = 15, with a flow rate of 0.025 kg/s of cooling water, the water temperature is reached 47 0 C, with a thermal power of 3.2 kW.At d = 20, with a flow rate of 0.05 kg/s of cooling water, the water temperature is reached 38 0 C, with a heat output of 4.3 kW.
According to the results of mathematical modeling produced on the basis of brass pipes (figure 4), it was found that at d = 10, with a flow rate of 0.01 kg / s of cooling water, the water temperature is reached 68 0 C, with a heat output of 2.1 kW.At d = 15, with a flow rate of 0.025 kg/s of cooling water, the water temperature is reached 49 0 C, with a thermal power of 3.5 kW.At d = 20, with a flow rate of 0.05 kg/ s of cooling water, the water temperature is reached 39 0 C, with a thermal power of 4.8 kW.
Analysis of the obtained research results show that in the condenser pipes with diameters of 15-20 mm, it is possible to obtain hot water temperatures at the condenser outlet in the range of 60-70 0 C. Analyzing the results obtained, which are presented in figure 3 and figure 4 it can be concluded that when modeling heat exchange processes in a PBEP condenser, the type of pipeline material does`t matter significantly.

Conclusions
According to the theoretical studies carried out by the method of mathematical modeling of heat exchange processes of the PBEP condenser, the following conclusions can be drawn:  It has been established that when cooling water moves with a flow rate of 0.01 kg/s in steel pipelines with a diameter of d=10÷20 mm, the water temperature at the condenser outlet changes accordingly tw2=63÷98 0 С.  With the movement of cooling water with a flow rate of 0.01 kg / s in brass pipelines with a diameter of d=10÷20 mm, the water temperature at the condenser outlet changes accordingly tw2=68÷100 0 С.  With an increase in the flow rate of cooling water from 0.01 kg/s to 0.05 kg/s, the temperature of the water at the condenser outlet is from 98 0 С to 35 0 С for the steel version at d=20 mm, and for the brass version from 100 0 С to 39 0 С . The results of modeling the thermal regime of the PBEP condenser shows that the temperature at the condenser outlet is on average in the range of 60÷70 0 С, which can be used in hot water supply and heat supply systems for autonomous consumers. Thus, with the movement of cooling water in pipelines with a diameter of d=20 mm, an average thermal power of 2.6÷4.8kW was obtained with a change in the flow rate of cooling water in the range of 0.01÷0.05kg/s.

For
the development of a mathematical model based on the schematic diagram of the PBEP, we present the design scheme of the PBEP capacitor model in figure 2.

4 .Fig. 3 .
Fig. 3. Graph of cooling water temperature changes depending on water flow and pipe diameter (material -steel).

Fig. 4 .
Fig. 4. Graph of cooling water temperature changes depending on water flow and pipe diameter (material -brass).

Table 1 .
) Initial data for the calculation