Thermo-hydraulic rating of a shell and tube heat exchanger for methanol condensation Evaluación térmico-hidráulica de un intercambiador de calor de tubo y coraza para la condensación de metanol

Shell and tube heat exchangers are the most common type of heat exchangers, and are applicable for a wide range of operating temperatures and pressures. In the present work the thermo-hydraulic rating of a shell and tube heat exchanger was carried out, in order to perform the condensation of a methanol stream using water as coolant. The overall heat transfer coefficient for both the sensible-heat and latent-heat zone had values of 166.41 W/m 2 .K and 1,198.39 W/m 2 .K, respectively; while the required total heat transfer area and percent excess area had values of 38.08 m 2 and 3.05 %, respectively. The pressure drops of methanol and water streams reached the values of 51,490.84 Pa and 2,890.50 Pa, respectively. The proposed shell and tube heat exchanger can be employed satisfactorily for the demanded heat transfer service, since the calculated percent excess area does not exceed 25%, and the pressure drop of the water stream does not exceed the value of 80,000 Pa.


INTRODUCTION
In most industrial fields, cooling and heating fluids are needed. The device utilized to implement the heat transfer between the fluids is termed as heat exchanger (Yousufuddin, 2018).
Heat exchanger is a universal device in many industrial applications and energy conversion systems (Rao and Raju, 2016). A heat exchanger is an apparatus or equipment built for efficient heat transfer between two or more fluid streams at different temperatures (Nigusse et al., 2014). Usually, heat exchangers remove the heat of a particular medium by allowing it to absorb into another heat transfer medium such as water, oil, air, etc. Currently, numerous heat exchanging techniques are available and are widely used in the applications such as refrigeration, air conditioning, automobiles, process industry, solar water heater systems, thermal power plants, and so forth (Abeykoon, 2014).
Various heat exchangers for industrial processes and systems have been designed. Among them, the shell-andtube heat exchanger is the most common type (Arani et al., 2016).
Shell-and-tube heat exchangers (STHXs) are widely used in many industrial areas, and more than 35-40% of heat exchangers are of this type due to their robust geometry construction, easy maintenance, and possible upgrades (Zhang et al., 2010). According to (Abeykoon, 2014), STHXs are widely popular in petrochemical industry, power generation, energy conservation and manufacturing industry (Rao and Raju, 2016) due to their simplicity in design/manufacture, great sustainability to meet requirements, efficient thermal performance, structural simplicity, low costs, design flexibility and also the capability of adapting to different operating conditions.
In STHXs, one of the fluids flows inside the tubes while other fluid is forced through the shell and over the outside surfaces of the tubes (Fig. 1). Baffles are placed inside the shell to ensure a good circulation of the fluid within the shell across the tubes and hence they help to induce a high rate of heat transfer. Also, the heat transfer performance of the heat exchangers may reduce as they become older particularly due to fouling and scaling. Figure 1. A two pass tube, baffled single pass shell, shell-and-tube heat exchanger.
Source: Adapted from (Kakaç et al., 2012) Two important problems in heat exchanger analysis are (1) rating existing heat exchangers and (2) sizing heat exchangers for a particular application. Rating involves the determination of the rate of heat transfer, the 717 change in temperature of the two fluids and the pressure drop across the heat exchanger (Ebieto & Eke, 2012),as well as the percent excess area (Cao, 2010).
Condensation heat transfer occurs in many engineering applications, such as in power condensers, boilers, and steam generators, which are all important components in conventional and nuclear power stations (Kakaç et al., 2012).
Condensation is the process by which a vapor transforms into a liquid. For condensation to take place, it is necessary to remove heat from the condensing fluid by means of a cooling medium. If the vapor is a pure substance, as long as the pressure remains constant, condensation takes place isothermally. The temperature of the process is the saturation temperature of the vapor at the prevailing pressure. A condenser is a piece of equipment in which a vapor is condensed by heat extraction with a cooling medium (Cao, 2010).
A condenser is a two-phase flow heat exchanger in which heat is generated from the conversion of vapor into liquid (condensation) and the heat generated is removed from the system by a coolant. Condensers may be classified into two main types: those in which the coolant and condensate stream are separated by a solid surface, usually a tube wall, and those in which the coolant and condensing vapor are brought into direct contact. Condensers in which the streams are separated may be subdivided into three main types: air-cooled, shell-and-tube, and plate. In shell-and-tube condensers, the condensation may occur inside or outside the tubes. The orientation of the unit may be vertical or horizontal (Kakaç et al., 2012). The most used cooling medium in condensers is water (Cao, 2010).
To date several authors have evaluated the performance of condensers. In this sense, (Botsch & Stephan, 1997) presented a model to describe the behaviour of an industrial scale shell-and-tube condenser. The model can be used under steady-state as well as under transient conditions, and is able to predict vapour and condensate flow rates, pressure drop and the temperatures of the vapour, condensate, wall and coolant. The results of several simulations were compared with experimental data to achieve a validation of the model. Similarly (Soltan et al., 2004) studied the effect of baffle spacing on heat transfer area and pressure drop for shell side condensation in the most common types of segmentally baffled shell and tube condensers, (TEMA E and J types with conventional tube bundles). As a result of this research a set of correlation were presented to calculate the optimum baffle spacing for segmentally baffled shell and tube condensers. Likewise, (Hajabdollahi et al., 2011) carried out the thermo-economic optimization of a shell and tube condenser, based on two new optimization methods, namely genetic and particle swarm (PS) algorithms. The procedure is selected to find the optimal total cost, including investment and operation cost of the condenser. Initial cost included condenser surface area and operational cost included pump output power to overcome the pressure loss. The design parameters considered were tube number, number of tube pass, inlet and outlet tube diameters, tube pitch ratio and tube arrangements (30, 45, 60 and 90º). In other study, (Pačíska et al., 2013) performed the thermalhydraulic simulation of an unconventional horizontal cross-flow shell-and-tube steam condenser using three commercial software packages, that is: Chemstations CHEMCAD, Aspen Shell & Tube Exchanger and HTRI Xchanger Suite, where the operating parameters at the inlet of the apparatus, thermophysical properties of streams, and the geometry of the apparatus were taken from the operator of the condenser. The results obtained were then compared to experimental data, while the observed differences between acquired data (heat duty and outlet temperature, pressure, and vapour mass fraction) and data from the operator were the principal markers of suitability of each individual software package. Also, (Singh and Sarkar, 2018) accomplished the energy, exergy and economic assessments of a shell and tube condenser of 580-MW nuclear power plant out using different water-based hybrid nanofluids. The effect of nanoparticle concentration on reductions of coolant requirement, pumping power and operating cost were also investigated. (Isah et al., 2019) assessed the performance of a stripper/gas overhead shell and tube condenser operating under steady state conditions in two stages in an ammonia plant. Two different methods were employed in monitoring the heat exchanger fouling, namely dirt factor trend method and a statistical control technique where a Cumulative Sum (CuSum) chart is used to check the stability of the process. Data were obtained through steady state monitoring and direct measurements from the plant. The data were analyzed using various energy equations and a computer program to determine the overall heat transfer coefficient, heat duty, capacity ratio, corrected log-mean-temperature difference, fouling factor, temperature range of both fluids and effectiveness. Finally, (Pattanayak et al., 2019) developed the correlation for heat transfer coefficient, condenser pressure, cooling water flow rate and velocity towards assessment of thermal performance of a shell and tube steam condenser using the data of actual operating condition of a typical Indian coal fired power plant with nominal generation capacity of 210000 kW. The characteristics of various parameters affecting the thermal performance of the steam condenser are presented for different operating conditions. The analysis includes development of correlation for the heat transfer coefficient, system effectiveness, condenser heat load and cooling water flow rate through a simulation model. The relationship proposed can be used for thermal performance evaluation of a steam surface condenser in actual running condition with basic measured operating data like cooling water inlet temperature and flow rate. The correlations for condenser thermal performance provided in this study contain no constant coefficients and are function of inlet condition of condenser.
In the present study the thermo-hydraulic rating of a proposed shell and tube heat exchanger is carried out, in order to perform the condensation of a methanol stream using water as coolant. Several evaluation parameters are calculated, being the most important the percent excess area and the pressure drop of both fluid streams. The results obtained of these parameters are compared with the maximum allowable values established by the process, to determine if the proposed heat exchanger is feasible to use for this heat transfer service.

Problem definition
It's desired to condense 5,800 kg/h of a gaseous methanol stream with a feed temperature and pressure of 95 ºC and 134,000 Pa, respectively. A shell and tube heat exchanger is available with the following design parameters: The cooling agent will be water at an inlet temperature of 2 ºC, while the outlet temperature of this fluid must not exceed 15 ºC due to energetic safety reasons. The fluids will flow at countercurrent configuration inside the equipment, circulating the water inside the tubes and the methanol through the shell, and the heat exchanger will be located horizontally. The pressure drop of the chilled water should not exceed the value of 80,000 Pa, while the calculated percent excess area must not exceed 25%. It's necessary to know, from the thermo-hydraulic viewpoint, if this proposed heat exchanger is feasible to use for the intended heat transfer service.

Calculation methodology 719
To carry out the thermo-hydraulic evaluation of the proposed shell and tube heat exchanger, several correlation and equations published in (Cao, 2010) (Flynn et al., 2019) were used, by means of which it was determined some important evaluation parameters such as the percent excess area of the suggested equipment and the pressure drop of chilled water. Each of the steps used to carry out the evaluation of the proposed heat exchanger are presented next.

Percent excess area:
Step 1. Definition of the main initial parameters for both streams: Table 1 shows the main initial parameters that must be defined for both streams. In this case, the outlet temperature of the hot fluid (condensate) will be equal to the saturation temperature under the working pressure of this stream (Ph), that is: T2 = Tsat.
Step 2. Main initial parameters of the proposed shell and tube heat exchanger: Table 2 displays the main initial parameters that must be known for the proposed shell and tube heat exchanger (condenser). Step 3. Determination of the saturation (condensing) temperature (Tsat) of the hot stream at the working pressure Ph.
Step 4. Mean temperature of the cold fluid ( t ): 720 2 2 1 t t t   (1) Step 5. Physical properties of the hot fluid both in the vapor and liquid state at the saturation temperature (Tsat): Table 3 presents the main physical properties that must be determined for the hot fluid both in the vapor and liquid states. Step 6. Physical properties of the cold fluid at the mean temperature determined in Step 4.  Step 7. Heat exchanged in the condensation zone ( Step 8. Heat exchanged in the sensible-heat zone ( Step 9. Total heat exchanged or heat load ( Step 11. Temperature of the cold fluid at the fictitious transition point ( 3 Step 12. Logarithmic Mean Temperature Difference (LMTD):  Desuperheating (sensible-heat) zone (LMTDS): Step 13. Coefficient R: Step 14. Coefficient S: Step 15. Parameter PX: Step 16. LMTD correction factor (Ft): Step 17. Effective mean temperature difference: Step 18. Tube-side flow area ( Step 19. Velocity of the tube-side fluid ( c v ): According to the problem definition (Section 2.1), the cold fluid (water) will flow inside the tubes, while the hot condensing fluid (methanol) will circulate through the shell, thus: Step 20. Internal film heat transfer coefficient for the tube-side fluid ( i h ): According to (Cao, 2010) the film heat transfer coefficient for water flowing inside tubes can be calculated using the following equation: Step 21. Internal film heat transfer coefficient for the tube-side fluid referred to the external area ( io h ): 723

Sensible-heat zone calculations
Step 22. Clearance between tubes (c): Step 23. Shell-side flow area ( s a ): Step 24. Shell equivalent diameter ( eq D ):  For a square pattern of the tubes: Step 28. Overall heat transfer coefficient for the sensible-heat zone ( S U ): Step 29. Required heat transfer area for the sensible-heat zone ( S

Latent-heat zone calculations
Step 30 Step 32. Reynolds number of the shell-side fluid in the latent-heat zone [ Step 33. Coefficient P: Step 34. Liquid Prandtl number of the shell-side fluid in the latent-heat zone [  h Pr ]: Step 35. Assumption of the wall temperature ( w T ).
Step 36. Parameter H: Step 37. Parameter X: Step 38. Flow per unit length on a horizontal condensate layer ( ' ' G ): Step 39. Film heat transfer coefficient of the shell-side fluid for the condensation of a vapor on a film without considering the effect of vapor velocity ( f h ): Step 40. Nusselt number of the shell-side fluid in the latent-heat zone without considering the influence of the vapor velocity ( f Nu ): Step 41. Nusselt number of the shell-side fluid in the latent-heat zone corrected for the vapor velocity ( Step 43. Overall heat transfer coefficient for the latent-heat zone (  Step 44. Average temperature of the cold fluid in the condensation zone (  t ): Step 45. Verification of the wall temperature ( w The calculated value of w T is accepted if it is within the range of ± 1.0 ºC with respect to the value assumed in step 35. In the case that this condition is not fulfilled, the w T value calculated by the equation (41) is substituted in the equation (32), and the calculation is repeated until the previous requisite is achieved.
Step 46. Required heat transfer area for the latent-heat zone (  Step 47. Total heat transfer area required by the heat exchange system ( T A ): Step 48. Condenser heat transfer area ( cond Step 49. Percent excess area ( exc A % ):

Pressure drop:
Step 50. Mass velocity of the tube-side fluid ( c Step 51. Reynolds number of the tube-side fluid ( c Re ): Step 57. Pressure drop of the hot fluid in the shell-side for the inlet mass flow ( s p  ):

RESULTS AND DISCUSSION
The results obtained when evaluating the proposed shell and tube heat exchanger are presented hereafter, specifically with respect to the determination of the percent excess area and the pressure drop of both streams.

Percent excess area
Step 1. Definition of the main initial parameters for both streams: Table 5 shows the available initial data defined of both streams.  (Sinnott, 2005). Source: Own elaboration.
Step 2. Main initial parameters of the proposed shell and tube heat exchanger: Table 6 exposes the main initial design parameters of the proposed shell and tube heat exchanger: Step 3. Determination of the saturation (condensing) temperature (Tsat) of methanol at the working pressure Ph:
Step 4. Mean temperature of water ( t ): Step 5. Physical properties of methanol both in the vapor and liquid state at the saturation temperature (Tsat): Table 7 presents the main physical properties for methanol both in the vapor and liquid states, as referred by (Green & Southard, 2019). Step 6. Physical properties of chilled water at the mean temperature determined in Step 4.
According to (Green & Southard, 2019) the chilled water will have the physical property values presented in Table 8 at the mean temperature calculated in Step 4.  Table 9 shows the results of the parameters determined in steps 7-21.       Step 35. Assumption of the wall temperature ( w T ): It's assumed a wall temperature of 60ºC, which will be checked later in Step 45. Table 12 indicates the results of the parameters calculated in steps 36-44.
Since the calculated value of Tw is within the range of ± 1.0 ºC with respect to the assumed value of Tw in step 35 (60 ºC), there is no need of correct this value and repeat the calculation procedure.
Step 46. Required heat transfer area for the latent-heat zone (   Table 13 exposes the results of the parameters considered in steps 50-57, corresponding to the pressure drop of both fluids.  (Cao, 2010) the factor (μc/μcw) -0.14 is taken as 1.0. † As recommended by (Cao, 2010) the factor (μh(v)w/μh(v)) 0.14 is taken as 1.0.
Taking into account the results obtained in the calculation methodology, the heat exchanged in the condensation zone (  Q ) is 10.3 times higher than the heat exchanged in the sensible heat zone ( S Q ), which is mainly due to the high value that presents the heat of condensation of methanol at the saturation temperature (1,085,768.39 J/kg).
Also, the internal film heat transfer coefficient for water referred to the external area had a value of 6,026.05 W/m 2 .K, while the value of the film heat transfer coefficient of methanol in the latent-heat corrected by vapor velocity (  h h ) is 31.7 times higher than the film heat transfer coefficient of methanol in the sensible-heat zone ( hs h ). This is because the high value that presents the Reynolds number of methanol in the latent-heat zone, which increases the Nusselt number of methanol in the latent-heat zone corrected for the vapor velocity (  Nu ), therefore increasing proportionally the value of  h h . It's worth to mention that the Reynolds number of methanol in the latent-heat zone (447,392.14) is 6.4 times superior to the Reynolds number of methanol in the sensible-heat zone (69,909.91).
Moreover, the overall heat transfer coefficient for the latent-heat zone (1,198.39 W/m 2 .K) is 7.2 times higher than the overall heat transfer coefficient for the sensible-heat zone (166.41), which occurred basically because the high value of 