MATHEMATICAL MODELLING OF DEPOSIT FORMATION PROCESSES ON HEAT-EXCHANGE SURFACES OF PISTON COMPRESSOR AIR COOLERS

ABSTRACT

When operating mine compressor equipment, its efficiency and productivity are affected by a number of factors, which leads to a decrease in the standard technical characteristics of the compressor. One of the main factors reducing compressor performance is poor cooling of the compressed air due to soot formation in the intermediate and final air coolers.

The article examines and mathematically models the processes of soot formation on the heat exchange surfaces of air coolers of piston compressors.

АННОТАЦИЯ

При эксплуатации шахтного компрессорного оборудования на его эффективность и производительность влияет ряд факторов, что приводит к снижению нормативных технических характеристик компрессора. Одним из основных факторов снижения производительности компрессора является плохое охлаждение сжатого воздуха из-за образования накипи в промежуточном и концевом охладителях.

В статье приводится исследование и математическое моделирование процесса образования накипи на теплообменных поверхностях охладителей поршневых компрессоров.

Keywords: compressor, air cooler, unit, heat exchange, capacity, power consumption, heat capacity, air pressure.

Ключевые слова: компрессор, охладитель воздуха, оборудование, теплообмен, мощность, потребляемая мощность, теплоемкость, давление воздуха.

Introduction

Compressed air cooling has a major impact on the key performance indicators of compressor equipment. It is known that an increase in the temperature of the compressed air in the intercooler leads to an increase in the work required in the next stage. Therefore, on the one hand, it is necessary to cool the air compressed in the intercooler as much as possible, and on the other hand, as a result of the increase in heat exchange surfaces, there is a further decrease in the temperature of the air leaving the intercooler. For example, to cool compressed air to a level that differs from the temperature of the water entering the cooler by 5 °C, 18-20 % more heat exchanger surface area is required compared to a difference of 8 °C, which means that the hydraulic resistance also increases [2; p.41-52].

Thus, the efficiency of the cooling system depends on the energy costs of the compressor equipment. In addition, since only a small part of the heat can be cooled in the compressor stages during the compression process, the technical and economic performance of a compressor station is mainly influenced by the efficiency of the intermediate and pre-cooling.

Such phenomenon as the appearance of soot on heat exchanger surfaces significantly reduces the heat transfer intensity and negatively affects the efficient operation of the compressor equipment cooling system due to the appearance of additional thermal resistance of the soot layer. In addition, the flow area of the tubes is reduced, which can lead to a significant increase in pressure in the heat exchanger. The use of tube coolers is one of the energy efficient types of coolers that transfer heat well to water [2; p.41-52].

Soot formation on heat exchanger surfaces is determined by a number of factors, one of the most important being water temperature and hardness. The rate of soot formation is strongly influenced by the water temperature and the temperature of the surface on which the soot layer is formed. This results in significant differences in the rate of formation on the heat transfer surface and significantly affects the distribution of overall heat transfer coefficients and pressure loss characteristics in the pipe. Another important factor affecting deposition is the shear stress at the heat transfer surface, and increasing this stress can significantly reduce soot formation and provide cost effective solutions in cooler design. The temperature of the fluid varies along the heat transfer surface with changes in the thermal resistance of the body. This results in significant differences in the rate of soot formation on the heat transfer surface and its thickness.

The formation of fouling on the heat exchanger surface depends significantly on the temperature and properties of the cooling water. At the same time, the growing body layer causes various flow changes due to the reduction of the pipe area for free passage of water and changes in the gravel at the flow boundary. the body layer also creates additional thermal resistance affecting the surface temperature. All these features are taken into account in the mathematical modelling of the compressor equipment cooling system.

The heat removed from the air in the intermediate or final cooler is defined as follows [1; p.104-107]꞉

                             (1)

where t₁ is the temperature of air entering the cooler, ⁰С;

- the air temperature leaving the cooler, ⁰С;

 – heat capacity of air, .

Crystallisation and precipitation of precipitates as particles, the rate of solids formation is expressed as the difference between the rate of solids formation  and the rate of solids removal, ie.

,                                         (2)

where  – the thickness of the plaque formation layer, mm;

  – time, sec;

 – wall shear stress, Pa;

 – empirical coefficient, .

Thermal resistance of the body

                                                               (3)

where  – heat transfer coefficient of the body, .

The rate of plaque formation is expressed as follows:

                                   (4)

,                                           (5)

where  – surface temperature, К;

 – current density, kg/m³;

 – dynamic viscosity of liquid, Pa·sec;

 – universal gas constant,  ;

and  – empirical dimensions that depend on the physical nature of the coolant.

The change in the temperature of the cooling water along the length of the pipe is expressed as follows

,                                                 (6)

where  – specific heat flux, ;       

 – weight consumption of water, ;

 – specific heat capacity of water,  ;

 – pipe perimeter, m.

,                                                   (7)

where  – cooling compressed air weight consumption, ;

specific heat capacity of the cooled compressed air, .

Specific heat flow on the heat transfer surface:

,                                                (8)

where  – overall heat transfer coefficient, .

,                                           (9)

where  – the thickness of the metal of the pipe, m;

 – thermal conductivity of the heat transfer pipe, 

 and  – heat transfer of compressed air and cooling water, respectively,.

Plaque formation surface temperature ꞉

                                         (10)

Heat transfer coefficients are calculated from correlation equations for pressure drop and heat transfer at the heat exchanger surface from tube geometry and fluid thermophysical properties. These correlations are usually expressed as follows:

,                               (11)

where  – flow rate in the pipe, m/s;

 – equivalent pipe diameter.

Taking into account fouling on the heat exchanger surfaces, the flow rate and equivalent diameter are determined as follows:

;                               (12)

.                               (13)

Considering the above equations, the thermal resistance of the case and its heat transfer coefficient is lower than that of the cooling water, the heat transferred from the compressed air is determined by the following equation:

                                    (14)

Using the above expressions, it is difficult to determine the thickness of the body in the cooling tube during the operation of the cooling system. For this purpose, due to the impossibility of determining the change of liquid temperature in the refrigerant tube and taking into account the concentration of solids in the liquid, we propose the following expression for theoretical calculation of soot formation thickness in tubes: taking into account the influence of these parameters

δ_f = R-                                                     (15)

where,  R- pipe radius (m), t- water flow time (s), ρ_о- initial density of liquid (kg\m³),  𝛾- temperature dependence of the density factor (1\С^о), T₀- initial water temperature (С^о), G- concentration of solids in liquid (mg/kg), l- pipe length (m)

Based on the above expression (15), a Delphi programming language programme was created to determine the thickness of bodies formed in the intermediate and final cooler tubes of a reciprocating compressor. In this case, it is possible to determine in advance the optimum cleaning period of soot formed in the cooling tube, if we know the formation of soot from the main parameters, i.e. temperature, initial water temperature, water hardness value.

In the table 1 below, we have presented the variation of body thickness formed in the intercooler and intercooler tubes of a reciprocating compressor over time.

Table 1.

The variation of body thickness formed in the intercooler and intercooler tubes of a reciprocating compressor over time.

References:

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