Impact of a Natural Gas Cooler Design on the Cooling Performance

. This article describes a methodology for the identification of cooling performance of a natural gas cooler relative to the shape of its heat - transfer surface and presents the outputs of numerical solutions for four different shapes of heat - transfer surfaces in coolers designated as C _A, C _ B, C _ C and C _ D. Calculations were carried out for a cooler with a single row of tubes , and for coolers with two through six rows of tubes that were positioned above one another with an alternating arrangement. In all of the surface shapes, the boundary conditions were respected in order to facilitate the identification of the shape of the heat - transfer surface which is the most appropriate for achieving maximum cooling performance. Out of these four shapes, the best results were observed with the heat - transfer surface of the cooler designated as C _A . The cooling performance of a 1 m long tube with such a surface was 1, 650 W .


Introduction
Determination of cooling performance of natural gas coolers by applying an analytical method is a rather difficult and time-consuming task. The complexity consists primarily in the determination of individual parameters in the equations that characterise heat transmission or transfer through heat-transfer surfaces of various shapes. An optimal way how to identify the cooling performance is to apply numerical methods with clearly defined boundary conditions. This article presents results of the investigation into intensity of natural gas cooling with four different types of heat-transfer surfaces of the coolers used at a compressor station (CS) of a gas transit pipeline. The output of the investigation was the evaluation of individual cooling surfaces in terms of cooling intensity with forced convection of the cooling air.

Problem analysis
A shape of an external heat-transfer surface of a natural gas cooler is determined by the finned tubes, i.e., the fins with circular cross-sections that are installed along the entire length of the cooler tubes. These fins may be of various thicknesses sr (Fig. 1), various outer diameters dr, and various pitches b. The total cooling performance of such a device greatly depends on the overall heat transfer coefficient (k) that expresses the heat transfer from the gas through the cooler tube wall into the cooling air. If this overall heat transfer coefficient may be regarded as a constant parameter across the entire heat-transfer surface, the equation for calculating the cooling performance P is as follows [1][2][3]: wherein k is the overall heat transfer coefficient (W·m -2 ·K -1 ); S is the external surface area of the tubes, which was identified as a sum of the surface areas of the fins Sf and of the smooth sections of the tubes between the fins Sb (m 2 ); and t ∆ is the mean temperature difference between the heat-transfer media (K). Overall heat transfer coefficient k for a clean (without any sediments) heat-transfer surface of a finned tube is calculated using the following equation [2]: wherein sw is the tube wall thickness (m); λw is the thermal conductivity coefficient of the tube material (W·m -1 ·K -1 ); S1 is the internal surface area of the tubes that corresponds to a diameter d1 (m 2 ); α1 is the heat transfer coefficient for the inner side of the tubes (W·m -2 ·K -1 ); α2 is the heat transfer coefficient for the heat transfer from the external finned surface into the surrounding environment (W·m -2 ·K -1 ); and the f(ηf) formula is a function that depends on, inter alia, the fin efficiency ηf.

Thermal balance of the cooler
In the gas cooling process, a certain portion of the heat is not conducted directly into the cooling air but into the cooler structure itself. These losses are expressed by the loss coefficient ηz. The losses identified in the investigated coolers represented 0.5 -3 %; i.e., the value of the ηz coefficient ranged from 0.995 to 0.97. The real cooling performance P2 may then be calculated as follows [1]: The Qm1·c1 product contained in equation (4) represents the performance capacity of the gas C1, while the Qm2·c2 product represents the performance capacity of the air C2. The mean temperature difference t ∆ contained in equation (1) for cross-flows of heattransfer media was calculated using the following equation [1]: The first figure in the temperature index represents the heat transfer medium (1 -gas; 2air) while the second figure after a comma means either the entry (1) or the exit (2). The correction coefficient ψ is expressed using the P and R criteria as follows: n is the number of heat exchanger runs, as shown in Fig. 2.

Fig. 2.
A scheme of natural gas coolers with the media cross-flow.
Heat transfer coefficient inside a tube α1 was calculated using the following equation: wherein Tw is the temperature of a tube wall (K) and T1,mean is the mean value of the gas temperature (K). A characteristic length in Nu and Re criteria in equation (7) is the inner diameter of the tube d1. The calculation of heat transfer coefficient on the external side of a bundle of finned tubes was made using the following equation: The value of the constant parameter C, relative to the tube arrangement and a number of tube rows in the bundle, ranged from 0.20 to 0.38.
Coefficient Kf was identified using the following equation: wherein S2 is the external surface area of the smooth tubes (m 2 ).
Circular fins are subject to the following equation: A characteristic length in Nu and Re criteria in equation (8) is the outer diameter of the tube d2.

Numerical calculations
Identification of a cooler's performance by applying an analytical procedure does not facilitate an adequate comparison of heat-transfer surfaces in terms of heat removal intensity since different coolers have different designs of their heat-transfer surface (tube diameter, fin diameter, fin thickness and fin pitch). The key parameters that affect the cooling performance of a cooler during its utilisation are as follows:  Gas flow rate (an amount of the cooled natural gas);  Gas temperature at the entry into the cooler;  Air flow rate (determined by a number of fans and their performance);  Shape and size of the heat-transfer surface;  Tube arrangement in the cooler's block (above one another, alternating);  Cooler blocks arrangement (cross-flow, multi-cross flow).

Characteristics of the heat-transfer surface of the examined coolers
The heat-transfer surface of the investigated natural gas coolers was determined by the parameters listed in Table 1 and by the geometry presented in Fig. 1. Numerical calculations were made separately for the case of forced convection with a single row of tubes in the cooler, and then for two through six rows. In a simulation, natural gas with a mean temperature of 65 °C was flowing through the cooler tubes. At this temperature, a numerical solution was made for the cooling intensity of finned tubes in all types of cooling surfaces.
The numerical solution was made with a symmetrical section of one tube fin in each row of tubes. The input boundary conditions were a gas pressure of 7.45 MPa and a gas temperature of 65 °C, while the heat-transfer surface was assumed to be clean.

Physical properties of the used media
The numerical solution was made with two different gases-natural gas and air. The properties of the gas with a temperature of 65°C and the air with a temperature of 20°C are listed in Table 2. The air flow was in the transit section; that is why the Shear-Stress Transport (SST) turbulence model was selected for the numerical calculation. Air velocity at the outlet from the fan 4.7 m·s -1

Calculation area
The modelled area was investigated at a mean temperature of natural gas on the inner side of the tube. The calculation area represented the point on the heat-transfer surface located in the middle of the tube length and the width of the cooling surface. The model of the symmetrical part of one fin and one tube for the cooling surface with a single row of tubes is shown in Fig. 3. For this model of the heat-transfer surface, the cooling performance of all of the coolers was plotted by applying the following command areaInt(Heat Flux)@Domain Interface1 Side2. The results are shown in Fig. 4.  The cooling performance for the six-row arrangement of the heat-transfer surface is shown in Fig. 5. The evaluation of changes in the temperature along the height of the cooling surface that was formed of a single row of a finned tube, up to the six-row arrangement, was made using a section where several fins were located in the middle of the tube length. Thermal fields were plotted using the following command: areaAve(Temperature)@Domain Interface1 Side2. For a single row of fins, a 3D image of the thermal field is shown in (Fig. 6). The temperatures on the fins in individual coolers ranged from approximately 30 to 41°C. The correlations between the cooling performance and the number of rows of tubes in forced convection, for 1 row of tubes (Pf) and for 1 through 6 rows of tubes arranged above one another with an alternating arrangement, are graphically represented in Fig. 7. The cooling performance of a 1 meter long finned tube for the individual types of the examined heat-transfer surfaces was identified for 1 through 6 rows of tubes in the heattransfer surface based on the identified cooling performance. This required knowing the fin pitch, which was calculated as follows: The tf values for all four heat-transfer surfaces are listed in Table. 3. For the C_A cooler with the single-row arrangement of the cooling surface (Fig. 4), the cooling performance of a 1 m long tube (Pl1) was calculated as follows: Calculated values of cooling performance Pl1 for the individual types of heat-transfer surfaces applicable to 1 meter of the finned tube are listed in Table 4.

Conclusion
An analysis of the results of numerical solutions that were made for all four types of heattransfer surfaces with 1 through 6 rows of tubes has brought the following conclusions:  Cooling performance increased with a higher number of rows of tubes positioned above one another with an alternating arrangement. With forced convection, the best cooling performance was observed with the heat-transfer surfaces of C_A and C_D coolers. This may be attributed to the dimensions of the tubes and fins and the consequent value of Kf coefficient. The Kf value for the C_A cooler was 14. This paper has been written with the financial support from the VEGA granting agency within the project no. 1/0626/20, VEGA 1/0532/22 and from FMT VŠB-TUO within the project no. SP 2022/13.