Weight and size characteristics modelling of the power plants contact condensers

The article presents the fundamental principles of mixing condensers calculation. The design calculation flow chart of apparatuses of this type is proposed. A good convergence of the droplet motion hydromechanics with the other authors works results is identified. The operating conditions calculation results of the contact condenser as a part of the chemical energy unit with hydrocarbon raw material partial oxidation showed that mass transfer impact on the heat exchange is quite significant (the Gukhman criterion is 0.0076), which affects the high process intensity (heat transfer coefficient is ∼179 W/(m2·°C)). However, as expected, the device is characterized by the low resistance of ∼6 Pa.


Introduction
Modern heat and power complexes include gas-turbine plants with steam supply to the combustion chamber (STIG scheme) [1,2]. In this case, steam injection into the combustion chamber substantially increases the turbine specific capacity due to the working body increase; blades and flame tube walls air cooling changing into the steam cooling makes it possible to grow the working body temperature; steam inlet into the oxidation zone helps to reduce the nitrogen oxides emission [3]. The exhausted combustion products deep heat recovery system based on the traditional waste heat boiler and contact condenser is a key element of the mentioned complexes. A similar system is proposed for application in the complex chemical energy use schemes of the hydrocarbon raw materials with air-steam gasification [4], since under the certain operating modes, water vapour content in the reaction products is from 33 to 47 vol. % and it must be returned to the main energy cycle. However, if the waste heat boilers design calculation is a traditional task and has already been carried out taking into account the synthesis gas thermal and physical characteristics [5], a small number of works is devoted to modelling the contact heat exchangers and particularly packless ones.

Problem statement
Taking into consideration the foregoing, performing the contact condenser volume processes modelling and defining the condenser weight and size characteristics determining the apparatus cost seems to be relevant. The apparatus scheme and working bodies flows are represented in figure 1. The apparatus packless design was chosen on the basis of the gas path aerodynamic resistance minimizing considerations, although in this case the heat exchange intensity decreases as compared to the packless apparatuses. The scrubbing liquid (water) can serve as an absorbent for extracting the undesirable components from the total or partial oxidation products, and the contact condenser is in fact the upstream first purification stage before the absorber, where the dead weight impurities content of the synthesis gas is  [6], one can expect the predominant absorption of carbon dioxide. In the hollow condenser, when absorption phenomena occur in the spray opposite direction of the gas phase motion, counter flow is theoretically carried out. Nevertheless, as a result of gases circulation and mixing, such devices are similar to the complete mixing devices by the phases interaction type and they have lower mass exchange effective driving force than the packless devices have under the proper counterflow [7].

Figure 1.
Mixing packless condenser: 1 is the synthesis gas inlet from the waste heat boiler; 2 is the synthesis gas outlet; 3 is the cooling water inlet; 4 is the heated water and condensate outlet.
The contact condenser organization according to this scheme will make it possible: • to conduct flexible temperature control and CO 2 content by changing the spray water flow; • to exclude or minimize the moisture separators volumes, since the main part of the water vapour condensate is removed with irrigation water into the storage tank; • to have the mixing apparatuses smaller metal consumption in comparison with the recuperative heat exchangers one, this causes the capital costs reduction and provides ease of operation and scheme high reliability. Thus, the calculation task is to define the diameter and height of the apparatus cylindrical section, as well as CO 2 content of the exhaust synthesis gas. Besides, it is necessary to consider that the steel grade and the thickness of the construction elements determining the apparatus cost should be chosen on the assumption of the corrosion activity and synthesis gas pressure.

Theory
For achieving the objective, the contact condenser calculation flow chart was developed (figure 2). The calculation is based on the heat balance equation and gas and liquid temperatures logarithmic mean difference as the simplest and most reliable method of defining the process driving force [8]. Gas phase thermal and physical properties are calculated according to the recommendations set forth provided in paper [9]. where d is the liquid droplet diameter, m; g is the gravitational acceleration of the gravity field, 9.81 m/s 2 ; d ρ , g ρ are the densities of the sprayed liquid droplets and gas phase, kg/m 3 ;ν is the gas kinematic viscosity coefficient at the gas average temperature in the apparatus, m 2 /s. For atomization the liquid in scrubbers, the mechanicalatomizers through which the liquid is sprayed owing to its increased pressure (for water in scrubbers from 3 to 5 at.) are most widely used. The apparatus droplets size due to breaking varies in a wide range from 1 to 150 μm. Determining the drops average diameter is difficult, since their formation depends on many factors. The droplets diameter d when sprayed by the mechanical atomizers is possible to be determined in the first approximation by the formula [8], m: (2) whereσ is the surface tension, kg/m;υ is the outflow velocity, m/s; k is the coefficient depending on the liquid surface tension, for example, for waterσ =0.00745 kg/m, and k =2.5.
Since defining the droplet calculated diameter depending on the atomizer type and liquid pressure before the atomizer is particularly difficult, for approximate calculations the droplet average diameter can be determined according to the following formula [10], m: where p is the liquid pressure before the atomizer, Pa. Furthermore, Archimedes criterion is defined according to the ratio: (4) where w is the gas phase velocity, it is accepted according to [8] at the level of 1 m/s. The presented above ratios characterize the solid particles motion. Liquid drops, unlike the solids can deform and grow or fragment during motion, which results in the resistance coefficient and floating velocity change. It was shown in [7] that the surface tension and sprayed liquid viscosity at Re fl. > 500 impact the resistance coefficient value. Paper [11] shows that the liquid droplets fragmenting probability is high when the Weber numbers exceed 10. In the conducted calculations the Weber number varies from 0.002 to 8.689 at the droplets diameter from 0.6 to 5.5 mm, correspondingly and therefore droplets do not fragment. It should be noted that in the experiments described in [11] the droplets initial characteristic dimensions of the examined liquids range from 3 to 6 mm and the droplets motion initial velocity is from 0 to 3 m/s, which corresponds to the obtained droplets diameters from 0.6 to 5.5 mm at the droplets motion initial velocity from 8 to 24 m/s. The active volume of the packless condenser is defined by the following equation, m 3 : (5) where Q is the amount of heat transferred in the scrubber, kW;α is the heat-transfer coefficient,