Abstract
Recent years have seen considerable advancement in cryogenic technology. Air separation devices have used the cold box with heat exchanger plate-fin (PFHE) in numerous applications. Cryogenic technologies are used in many industrial processes to recover heat and reduce energy consumption. The multistream plate-fin heat exchanger (MSPFHE) is heavily utilized in the air separation plant’s (ASU) design. The plate-fin heat exchanger, one of the most important applications in the cryogenic industry, is the focus of the current investigation. The air entering this operation has been cooled by utilizing energy from streams originating from the distillation tower in the air separation unit (ASU) to reduce energy usage. The project aims to develop and create a multistream plate-fin heat exchanger (MSPFHE) that may be used in the cold box of an air separation unit practically and without limitations. The pinch technique, a method based on the usage of composite curves, was used in the creation of MSPFHE. With pinch technology, it is possible to divide a multistream exchanger into block portions that represent enthalpy intervals and identify the entry and departure sites for the streams. The correlations used in the MSPFHE thermal design model were first modeled and compared to earlier models as part of this effort. This model has been turned into MATLAB code and utilized in two case studies to yield acceptable results during the sizing step. Calculations of thermodynamic properties, heat transfer, pressure drop, choice of fin type, and final heat exchanger size were all part of the design of the MSPFHE. Finally, based on the software’s ability to reproduce the identical environmental conditions nature produces, the case study results have been validated using Aspen EDR. These findings were matched to findings from the literature and determined to be reliable and consistent.
1. Introduction
The sector of the cryogenic industry has expanded significantly since the turn of the century. One of the crucial processes in this sector is the distillation-based separation and liquefaction of air, which occurs at cryogenic temperatures below 120 K. The success of these techniques is highly dependent on the heat exchangers (HEXs) utilized, as evidenced by previous experience with cryogenic systems [1]. In reality, cryogenic heat exchangers are important components in the air separation industry in terms of up-front costs and technological challenges [2]. The project’s overall success hinges on the equipment’s description being correct. The energy needed for these methods to achieve cooling below 120 K is significant. In order to reduce energy waste, cryogenic activities must therefore become more thermally efficient, making energy conservation a top priority in this situation. Thus, as depicted in Figure 1, recent population growth and industrial development have increased energy demand. Therefore, energy recovery is one of the most cutting-edge methods for reducing energy use.
Two of the most essential strategies for reducing energy consumption (heat recovery processes) are the development of heat exchangers and the utilization of the energy associated with numerous industrial process byproducts in order to use it in new processes. To transfer heat between two or more fluid streams operating at different temperatures, devices known as heat exchangers are used. They are found in all industrial plants and are frequently among the most crucial elements. A heat exchanger’s primary purpose is effectively transferring heat from a hot to a cold side. The temperature distribution is influenced by the temperature difference between the two fluids, the area to which heat is transferred, the conductive and convective properties of the fluids, and the flow situation. The governor correlation of this condition is given by Newton’s law of cooling [3], illustrated in the following equation:
Therefore, a heat exchanger’s ability to convey the necessary amount of heat determines its efficiency. If the heat transfer coefficient cannot be raised, the best ways to improve heat transmission are to expand the heat transfer area or modify the temperature. The heat exchanger needs a hotter fluid or one that can transfer heat to a colder fluid, neither of which are commonly accessible, so even if increasing the temperature difference makes sense, doing so would not be very advantageous. It takes more effort in both cases to administer the hot fluid at a high temperature or the cold fluid at a low temperature. There will also be unwanted thermal strains on surfaces if the temperature differential between the two fluids is large enough. Those as mentioned earlier often cause deflections and reduce material life. These variables make increasing the heat transfer area the best approach of action, which is frequently the preferred and most acceptable choice, as shown in Figure 2. The use of expanded metal interface surfaces between flowing fluids is one of the most common methods for increasing the surface area available for heat transmission. Fins are the usual name for these enlarged metal connections.
Plate-fin heat exchangers (PFHE) are the most compact and economical heat exchangers for a variety of applications. They might have two or more streams. PFHEs are well renowned for their great thermal efficiency, mobility, lightweight, and little maintenance requirements. Their inexpensive initial investment, installation costs, and operational costs make them advantageous for both cryogenic and noncryogenic applications. In contrast to a shell-and-tube unit, which has a surface area per unit volume of 40–70 m2/m3, these units often have a total surface area of 1000–1500 m2/m3 of volume [5].
The fundamental parts of a fin-plate heat exchanger are depicted in Figure 3, including a stub pipe, header tank, distributed fin, heat transfer fin, partition plate, sidebar, and cover plate. Its ability to manage several streams of up to 12 or more at times in some industrial activities, such as pulp mills, steelworks, and the CO2 separation and liquefaction industry, solidifies its dominance in air separation and other cryogenic systems. A large surface area per unit volume is beneficial for low-temperature changes. For instance, the temperature differential affects cryogenic compressor power and hydrocarbon dew point management systems.
This heat exchanger passages type comprises layers that alternate between corrugated fin layers. Parting sheets are used to divide the layers, and sidebars surround them to seal the margins and provide ports for stream inlets and outflows. Cap sheets specify the top and bottom of the block. Figure 4 shows a stack of fins between the separating sheets. The parting sheets, fins, sidebars, and top plates are assembled in a fixture as part of the primary method for producing plate-fin heat exchangers, and the assembly is then brazed to create the heat exchanger core. The premade thin-walled fins (with a thickness of 0.1 mm) are cut using electro-discharge machining (EDM), while the sidebars and parting sheets are milled and sheared to size.
Plate-fin heat exchangers can be made from a variety of materials (aluminum or stainless steel alloys are examples of common materials); however, this standard only applies to brazed aluminum plate-fin heat exchangers. Either vacuum brazing or dip brazing is used to attach fins to separate sheets. Most metals, including stainless steel, copper, and nickel alloys, may be successfully brazed using a vacuum brazing furnace. The stubborn oxide coating on the aluminum surface can be removed by either placing it in a molten salt bath or a very high vacuum.
There are two possible classes of multistream heat exchangers (MSHE). One type is a multichannel heat exchanger without thermal contact between the walls separating the fluids, such as a plate or shell and tube heat exchanger. The other is the multistream plate-fin heat exchanger. The design incorporates the tiny heat exchanger’s fins because of the following reasons:(1)The fin, which acted as a secondary surface, could heat fluid streams by causing sheets of material to separate.(2)Heat transfer is considerably more effective when the fin’s thermal conductivity is high.(3)By increasing fluid turbulence, fins can increase the local coefficient of convective heat transfer.
Heat exchangers are used in a number of cryogenic applications to transmit heat, but high-performance heat exchangers are required in air separation systems that produce liquid nitrogen, liquid oxygen, and liquid argon. Recuperative heat exchangers eliminate the need for external refrigeration by precooling the incoming warm air stream with the product’s cold gas stream. For the system to be profitable, it must operate at least 95% effectively. In order to get the system to function appropriately overall in terms of energy, cryogenic heat exchangers should be designed to operate at just a small range of temperature differences. Large heat transfer surfaces are required for this, necessitating the use of heavy, expensive equipment. Such heat exchangers must be very efficient in order to be cost-effective. It has been established that a cryogenic heat exchanger utilized in an air separation plant can boost efficiency by 1% while cutting power consumption by 5%.
A plate-fin heat exchanger’s fins aid in heat transfer in a number of different ways. Initially, they serve as secondary surfaces that help a certain plate’s heat transfer to the fluid stream (the primary surface). Second, as the fins join two neighboring plates, a parallel path of heat transmission by conduction develops. Last but not least, common fin features may disrupt the boundary layer and raise the local convective coefficient of heat transmission. The most typical fin sheets used in plate-fin heat exchangers are depicted in Figure 5 [9].
The design of a multistream plate-fin heat exchanger (MSPFHE) is a complex problem since it can support many streams (up to 12), has a large surface area per volume, and has a high heat transfer coefficient. Together with the availability of about sixty standardized fin pieces (plain fin, louvered fin, offset strip fin, wavy fin, etc.) with different heat transfer and pressure drop capabilities, all of these characteristics pose significant technological application limits. The primary problem, however, is the absence of a general design process that can simultaneously consider alternatives for combining different fin types and limitations placed on using different fin features.
Previous research has looked at several parts of the procedure, including the mechanical design of PFHEs, novel exchanger surfaces, banking configurations, and flow compensation approaches that have been suggested to boost efficiency. Most design methods in the literature are generally based on the effectiveness-NTU method, which considers the exchanger as a whole and requests data such as bulk mean temperature and midpoint properties. Gaseous streams exhibit fluctuating thermohydraulic properties, particularly close to their dew points; therefore, they use an integral rather than a differential approach. The design created using these methods is, therefore, probably approximative.
Heat transfer of heat exchangers has already been improved in a number of ways. Early experimental studies on different fin geometries were done by Kays and London [10] to improve heat transfer in heat exchangers. The experimental research on OSFs was broadened by Kays [11], Briggs and London [12], London and Shah [13], Mochizuki and Yagi [14], Shah et al. [15], and Manglik and Bergles [16]. They examined the impacts of fin shapes as nondimensional forms on heat transfer and pressure drop using 18 different OSFs. After inspecting, they found two correlations: one for pressure drop and the other for heat transmission. When contrasting the expressions’ outcomes with the experimental information from Kays and London [17], their correlations may be satisfactory. Perhaps, the most complete design guide was Kays and London’s monograph. Later, theoretical and numerical investigations were based on the experimental results.
Morley looked at the transfer of heat across three fluids at the beginning of 1933 [18]. Using integration, Morley devised an analytical answer to a differential third-order equation whose solution was the fluid stream temperature. Since then, many similar evaluations have been conducted; however, this inquiry may be the first to focus on multistream heat exchangers (MSHEs). The initial uses of MSHE for the simultaneous transfer of heat between more than two streams were in cryogenic processes [19]. Numerous articles and publications that examine the design of multistream plate-fin heat exchangers (MSPFHE) may be found in earlier literature. Kays and London [17], Kern and Kraus [20], Shah et al. [21], and Haseler [22] are some of the most well-known investigations. Bentwich [23] modeled an idealized multistream heat exchanger with constant fluid characteristics using a finite-difference approach. Chato et al. [24] proposed a multiflow heat exchanger and multiple models for parallel design and simulation.
In an air separation unit, where five fluid streams exchange heat with six fluid streams in parallel and counterflow, Boehme et al. [25] have simulated reversible heat exchangers. When using a numerical approach, the fluid properties, capacity rates, and heat transfer coefficients are considered constants, and the HEX is separated into many sections. One phase’s streams are taken into account. Field data are compared to the model’s results. Morantes et al. [26] have published a design technique that addresses the flaws of preceding methodologies, where the PFHE is represented as a network of two-stream heat exchangers. For the simulation of PFHEs, two different approaches are put forth: one model uses precise geometry data to perform thermal-hydraulic calculations and the other model regresses a number of parameters based on available operational data to estimate the heat exchange between streams.
In subsequent papers [27, 28], the thermal design of plate and fin multistream heat exchangers using pinch technology is provided. The PFHEs are divided into sections according to the composite curves of the process, where the stream characteristics are assumed to remain constant, and the pressure drops per stream are distributed according to their corresponding heat duties. The length of a two-stream heat exchanger is first calculated for each section, and then the fin types for the other streams are selected to maintain the heat duty per layer. Finally, the heights of the various portions are uniformized by reducing the allowed pressure drops of the streams. One of the fundamental issues with this methodology is that the number of passes acquired for each stream is not an integer. The lengths of the passes do not have to be the same, and if the heat duty is low, some of the portions of the PFHEs may be pretty small (short in length), which makes the designs challenging to implement.
To verify that the total number of passes for all the streams in the PFHE is an integer, an additional step is taken in this study in contrast to the bulk of the previously described ways. A cryogenic case study involving air separation was also conducted using the novel model at temperatures below zero.
Studies in the past have shown numerous ways to design MSPFHE. At first, MSPFHE was frequently built as a two-stream exchanger extension [22]. This method applies to plate-fin heat exchangers that only handle two different fluids, even with several layers, since the half-fin idealization is valid in this case. The validity of the half-fin idealization is typically questioned because heat exchangers typically handle more than two numbers of fluids. In previous investigations [29], a multistream heat exchanger was also created as a monolithic block to evaluate the thermophysical properties at the typical temperature between the entry and exit. This method has substantial drawbacks since a specific fluid stream may be thermally communicating with more than one stream and because uncommon phenomena like temperature crossover may occur. This calculation can also lead to inaccurate exchanger sizing due to the fluids’ temperature-dependent thermohydraulic characteristics. This is true, particularly when the fluid temperature is near the dew point.
A three-stream heat exchanger was the most basic multistream device. According to studies, the currently known analytical solutions for three-fluid heat exchangers are only relevant to a certain design and flow configuration [30–32]. They found that adding three-stream heat exchangers and multistream units in general dramatically increases the complexity of the analysis when using the conventional effectiveness-NTU method. Later researchers [33–35] divided the heat exchanger to solve size issues in many tests. Instead of using the entire stream, a tiny portion was used to analyze the fluid properties.
The pinch technique addressed all of these limitations and recommended the division of the exchanger into a number of small parts by composite curves to accurately account for the local interactions between the fluid streams and the variation in fluid properties. The suggested methodology ensures a converged solution with the fewest number of iterations while handling the transverse heat transport via the fins. Each element in a stream has had its fluid properties evaluated. Consequently, using this technique, also known as a differential technique, reduces the error margin for the sizing of multistream plate-fin heat exchangers. The method has been successfully demonstrated for a range of streams with balanced heat capacity. This strategy could be utilized for entry and departure points that are intermediate. The pinch technique has replaced the common wall temperature assumption with a more thorough analysis that accounts for all potential heat transfer paths within a multistream unit, including heat conduction through fins of nonadjacent layers and the independent design of block sections per stream. The flow lengths produced by this design are suitable for each stream’s heat duty and pressure drop. One can make a single flow length where the end dimensions match to an acceptable degree by selecting a typical length and gradually changing the fin type on the other streams. Furthermore, it showed that it could manage more than two fluids and determine the temperatures in every heat exchanger area.
Although past studies have discussed the design of MSPFHE, many more investigations are still required to determine the ideal design. The study aims to model and design an MSPFHE that can be used in the cold box of an air separation unit practically and without restrictions. The MSPFHE was designed using the pinch approach, a methodology based on the utilization of composite curves. Pinch technology can be used to separate a multistream exchanger into block parts that correspond to enthalpy intervals and pinpoint the locations of the streams’ entry and exit points.
This study first modeled the correlations used in the MSPFHE thermal design model as part of this effort. This model has been turned into MATLAB code and used in two case studies to produce good results during sizing. This model contributes to an increased reliability in dealing with MSPFHE design and heat load calculations using pinch technology and contributes to designing heat exchangers. Calculations of thermodynamic properties, heat transfer, pressure drop, choice of fin type, and final heat exchanger size were all part of the design of the MSPFHE. Finally, based on the software’s ability to reproduce the same environmental conditions that nature creates, the case study results have been validated using Aspen EDR. These findings were evaluated for quality and compatibility with findings from the literature. The outline for the current study is given in Sections 2 (a mathematical model), 3 (the design methodology being validated), and 4 (the discussion and conclusion).
2. Mathematical Model
2.1. Assumptions
The heat exchanger’s fluids have no phase change. Moreover, the following working hypotheses limit the potential for heat transfer:(1)The heat exchanger operates under steady-state circumstances(2)Neither flow maldistribution nor longitudinal heat conduction through walls is taken into account(3)The fluid’s characteristics are unaffected by temperature(4)It is assumed that the hot side fin layer () and the cold side fin layer () are equivalent(5)The resistance to fouling and the resistance to thermal walls have been taken into account
The justifications that prompted to make these assumptions in this study are as follows:(1)Since the boundary conditions for temperature and flow rate at the entrance are set, and the exchangers operate for a more extended time period, adopting the steady flow condition does not impact the outcomes and makes the problem easier to solve(2)The longitudinal axial transfer of heat is negligible and does not affect the results(3)The solution is made easier by assuming that properties are constant with temperature since the change in properties with temperature is negligible(4)Assuming the same number of fins for both fluids easily applies to the heat exchange surface calculations(5)The addition of fouling factors to both sides improves accuracy
2.2. Thermal Modeling of Plate-Fin Heat Exchanger
A typical parallel and countercurrent flow plate-fin heat exchanger circulates both hot and cold fluid in the opposite direction, as shown schematically in Figure 6. In order to maximize the pressure that can be applied, a design method for plate and fin exchangers in a countercurrent configuration is expanded here. Only one fluid in a countercurrent configuration may use up all its allowed pressure drop. Due to the known overall heat duty and the permissible pressure loss in each stream, it is possible to accurately anticipate the outlet temperatures of each stream to begin the computations.
The lengths (length, breadth, and height), the number of passes per stream, and the kind of fins used by each stream are all determined by the design of MSPFHEs for a certain heat duty and allowable pressure drop. One of PFHE’s most crucial properties is volume, particularly if the streams it processes have different fin types and, consequently, different area densities (i.e., heat transfer surface per unit volume of the exchanger). As a result, rather than the area, the PFHEs’ volume is frequently used in various ways as a design parameter.
Composite curves are used to describe the thermal balance of an entire heat transfer process [36]. They are made by merging composite curves that are both hot and cold. The hot composite curve, made by thermally collecting all hot streams present in the practicability, illustrates the overall amount of heat that must be eliminated from the process. Instead, the cold composite curve, which is created by the thermal collection of all cold streams present in operation, represents the entire quantity of heat that must be given to the process. The quantity of heat that may be recovered inside the system is represented by the superposition through both curves, and the overshoot on both edges represents the amount of additional heating and cooling required to achieve thermal balance.
The supply and goal temperatures of the process streams were used to segment the temperature axis into intervals, and the enthalpy contributions (from hot streams) and needs (from cold streams) for each interval were combined to produce the composite curves. The final step is to cumulatively plot these enthalpies against the corresponding temperatures to create two curves for hot streams and cool streams. Then, the cold composite curve, which is always greater (the heating curve), is positioned in proportion to the hot composite curve (the cooling curve). In the region where the composite curves overlap, heat can be recovered in this manner. The positioning of the T-H diagram is the outcome of the two curves’ horizontal adjustment. The thermodynamic limit is reached when this vertical distance equals zero, whereas the economic limit is reached when the shortest vertical distance between the curves equals . Increased heat recovery results from bringing the curves closer together. The heat integration bottleneck is also known as the heat recovery pinch because it is the point in the heat integration process where the vertical distance between the composite curves is minimum (equal ).
Using composite curves, which are made up of two independent lines, the process can be demonstrated when the smallest temperature difference, , is known. The composite curves’ overlap shows how much heat can be recovered from the process at its greatest possible level. , or the lowest permitted temperature differential in heat exchanger units, has a significant impact on both the size of the heat exchanger and the need for external utilities. The location where the two lines are closest together is referred to as the pinch. The best option for the procedure can be discovered by adjusting the value of .
The hot and cold streams enter an MSPFHE at different temperatures, where they are heated or cooled to various temperatures. This suggests that various locations throughout the exchanger’s length must have streams flowing into and out of them. These points show the composite curves’ varying slopes. The enthalpy intervals are calculated along a vertical line drawn at each location where the slope changes. Enthalpy intervals are used to determine the total number of sections in a multistream exchanger. As a result, the design of a multistream exchanger is divided into a number of smaller issues. The major issue with the design is to physically measure each of the different components so that their measurements are uniform. For example, all components must have the same width and height. The proportion of hot to cold channels within each section must be the same.
In order to break down the PFHE into its constituent parts for the generation of MSPFHEs, composite curves have been used in the appropriate model. The location of a stream’s entry or exit at each segment along the length of the exchanger ensures that each section has the same number of streams and heat duty. The composite curves are a useful tool for determining the number of sections and their corresponding number of streams and heat duty since it can be assumed that a stream is either entering or exiting when there is a change in slope. As a result, this study models MSPFHE using the four fundamental phases listed as follows:(1)Divide the temperature field, heat load, and stream population of the multistream plate-fin heat exchanger into portions (intervals) using the composite curves. Each stream in the stream population per enthalpy period has a set flow rate, allowable pressure drop, and heat load. The permitted pressure drop per stream, which corresponds to a specific enthalpy interval, is assumed in this study to be linearly distributed according to the percentage of heat load [26]. Thus,(i)Using equation (3), we calculate the number of passes of the two-stream exchanger.(ii)Each stream’s heat burden should be consistent, and the streams must split in such a way that the sum of the hot and cold branches is equal, determining the number of passes for rest streams according to the equations (4)–(6).(2)For each section (each section represents a heat exchanger),(i)Choose the reference stream and the critical stream. The reference stream is the sort of stream that is opposite of the critical stream but has the lowest permitted pressure (the critical stream is a stream with the lowest allowable pressure drop).(ii)Create a two-stream heat exchanger utilizing the streams chosen in step (2-i) and calculate the volume of two-stream exchanger by solving equations in Table 1. Use equations (7) and (8) to calculate the length of the two-stream exchanger (L) and pressure drop (). where is density of stream which calculated as .(i)We only have one degree of freedom in this situation. The height of the exchanger (H) is determined by fixing the exchanger’s width (W).(ii)The length of each stream’s passes is calculated using the following equations:(iii)Modify the fin type for each stream until the lengths fall within a reasonable range, at which point equation (11) is used to determine the pressure drop for the remaining streams. With this modification, the HE length rather than the exchanger volume can be used to calculate the pressure drop.(3)Calculate the height of each section using the following equation: where N is total number of streams in this section (summation of both hot and cold streams).(4)If the heights of the sections are not same, then(i)Select the greatest height as the target value for the height of all the sections(ii)Vary the Reynolds number of the critical stream of each section, except the one chosen as target value until HT matched with tolerance
According to the suggested technique, the full design methodology has been carried out using computer code, with the design being completed in MATLAB [38]. This code was used to build a plate-fin multistream heat exchanger (MSPFHE) based on the techniques stated in the parts that came before it. It contains a mainline and nine subroutines. The work’s flowchart (a description of the MSPFHE design approach) is shown in Figure 7, and it explains how to calculate the ideal required area of heat transfer, choose the right fin geometry, determine its size, and size the entire exchanger. The benefit of using code during the sizing stage is that it can handle each stream in an exchanger separately and provide profiles of temperature, pressure, Reynolds number, heat transfer coefficients, etc.
3. Validation of the Design Methodology
The primary goal of this work is to develop MSPFHE using the given model and validate the results using two separate techniques: first, by code and then by Aspen EDR.
3.1. Implementation and Validation of Methodology by Code
In this part, two case studies were used to evaluate and test the reliability of the MSPFHE design code technique.
3.1.1. Hypothetical Case Example
Two cold and two hot streams make up a hypothetical heat exchanger instance [34] with four streams total. The four streams, operating circumstances, and physical characteristics of a technique for designing a multistream plate-fin heat exchanger (MSPFHE) are shown in Tables 2 and 3. The minimum temperature difference in this situation is 20°C.
The composite curves are constructed at a minimum temperature of 20°C, as shown in Figure 8(a). Using the present methodology, this example is divided into six pieces, with the design of a multistream plate-fin heat exchanger (MSPFHE) being carried out in each phase independently. In this case, the design only considers the “balanced” process-to-process intervals and disregards the process-to-process intervals that use external utilities. As a result, only parts II, III, and IV experience heat exchange. The allowable pressure drops in a heat recovery network are thought to be distributed linearly. The stream population for each time period is shown in Figure 8(b) (stream intake and outlet).
(a)
(b)
The heat load, input, and exit temperatures are displayed for each interval in Table 4. According to the amount of heat produced during each period, the permissible pressure drop for each stream is distributed, as shown in Table 5.
The current study’s results of the final block design of the heat exchanger (length, width, height, and volume), along with the results of the final block design of the heat exchanger from a previous study [34], are shown in Tables 6 and 7. The results demonstrate that there is good consistency between the current study’s output and the output of previous studies. Additional final design details for sections in the current study are provided in Tables 8–10.
3.1.2. Case Study
This case study focuses on the multistream plate-fin heat exchanger (MSPFHE) used in an air separation unit. The heat exchanger has two hot streams (HP air and LP air) and three cold streams (LP nitrogen, waste nitrogen, and LP oxygen). There is no phase-change heat transfer process with this MSPFHE. The minimum temperature difference in this instance is 15 (°C), and the MSPFHE design parameters are displayed in Tables 11 and 12.
The composite curves with enthalpy intervals are shown in Figure 9. The five enthalpy intervals in this diagram correspond to utility exchangers (intervals 1 and 5) and process heat recovery (intervals II, III, and IV).
Figure 10 shows each era’s stream population and entrance and exit places.
The intake and output temperatures, heat loads per segment, and maximum allowed pressure drop per stream are shown in Tables 13 and 14, respectively.
Table 15 displays the findings of the final design case study and the heat exchanger’s capacity, width, and length. Tables 16 to 18 offer further final design information for the sections.
3.2. Validation Procedures for Heat Exchangers by Aspen EDR
The case study results are compared with those from the simulation software program in this section. Aspen EDR is the precise simulation program used for comparisons in this work. Aspen EDR runs in-depth simulations of plate-fin heat exchangers (PFHEs) based on the MIT-developed thermal-hydraulic correlations, which are not reported in the open literature. The Aspen EDR program has been given input parameters for the dimensions of the various sections, process information, the number of passes per stream, and the thermal-hydraulic behavior of the fins.
The multistream plate-fin heat exchanger (MSPFHE) in this process contains five streams, two hot (HP air and LP air) and three cold (LP nitrogen, waste nitrogen, and LP oxygen), as was shown in the preceding section through a case study. Phase-change heat transfer is not used in this multistream plate-fin heat exchanger (MSPFHE). The various PFHE parts are modeled as distinct exchangers in ASPEN EDR. The EDR menu begins by stating the computing method, the number of streams, the project title, and the process data. Figures 11 and 12 display every single one of these inputs.
After the input data have been assembled, the program is run with the display of errors and warnings (if any), and Table 19 for section III provides a detailed comparison of the outcomes and error percentage. Table 19 shows that the results of adopting the suggested design approach are very similar to those of the comprehensive simulation program.
4. Discussion and Conclusion
The sizing stage, which calculates the block sizes of the various streams and scales the entire exchanger to develop a modeling methodology, is part of the process design of the MSPFHE proposed in this work. Several thermal process design components have been studied to increase efficiency through the use of new banking arrangements, exchanger surfaces, and flow compensation techniques. All of the heat exchanger measurements have been established, and the design’s sizing components are completely covered. Here, a “differential” approach was utilized to divide the heat exchanger block into multiple segments using composite curves, taking into account the consistency of the fluid’s properties as mentioned in the preceding sections. This method allows the designer to see each stream’s temperature and pressure profiles even when they are still in the conceptual stage. Only a tiny portion of an exchanger’s stream is utilized if the midpoint value for a property is used rather than the stream in its entirety. Using this technique, decisions can be made that are more precise and efficient, such as altering the fin type for a specific stream at a critical point or lowering the block section after a certain stage. The case studies that are offered provide examples of some of these components.
The height and width values of sections should be surprisingly identical throughout the entire MSPFHE. This is due to the uncomplicated distribution strategy and the demands of manufacturing. Components in the original design with lower heights must be changed to meet this requirement. The flow channels that link the components can be made wider to achieve this. A smaller pressure drop results from this modification’s lower Reynolds numbers. Because of this, not all of the allowed pressure drops are applied. This is a relatively conservative decision because the design does not fully utilize pressure reductions. Only one stream can fully utilize the pressure drop in any particular stretch of the pipeline because the hot and cold streams are typically configured in counterflow. Important streams may be included in several components. However, only the entire flow channel is subject to the overall pressure drop constraints, not the individual parts. Therefore, when seen from the perspective of the entire exchanger, the total pressure drops of all streams may be fewer than the permitted pressure drops. The channel numbers of various sections are loosened to achieve nearly identical heights between sections. The real pressure applied decreases as a result. Pressure decreases in all streams may therefore be much smaller than permitted. This indicates that some of the permitted pressure decreases may be wasted.
The method’s design objective is to increase the allowable pressure drop of significant streams. The pressure reduction of crucial streams in intervals II, III, and IV is shown in Table 12. The pressure decrease of these streams was the largest throughout each time, according to preliminary calculations. Unfortunately, this results in erratic block dimensions, which are undesirable for the unit’s construction. These issues are resolved by implementing a fitting stage where pressure drop is minimized to achieve consistent block heights (Tables 14–16). As a result, MSPFHE rarely uses the pressure drop to its full potential.
The multistream exchanger used in this case study has the following primary measurements: 2.33 m long, 1 m wide, and 0.21 m height. The height of the heat exchanger can be changed by adjusting the width, which can also be changed to vary the block height. When the exchanger’s width is decreased to 0.5 m, its height becomes equivalent to 0.42 m, and vice versa. Additionally, the preliminary calculations of a case study (total external hot duty is 1070 kW and the external cold duty is 405 kW extracted through the process) show that using this heat exchanger reduces energy consumption.
Designating a fin type for critical and reference streams is one area that needs more study. The designer can access many fin types because the final block dimensions depend on the fins used. As a result, numerous designs are possible. Anyhow, the choice of the fin will depend on the required block size, price, and accessibility. The study’s technique made it possible to specify heat exchanger dimensions as a design objective and achieve them by choosing the type of fin, where block size, pressure drop, and heat duty are all factors integrated with the proper choice. The range of applicability of the generalized formulas for the friction factor and heat transmission is one of the disadvantages of this method. This is true for fluids with very low viscosities, frequently displaying high Reynolds numbers outside the formulas’ permitted range.
The findings of the suggested design approach are compared to those of Aspen EDR, a rigorous simulation program chosen for comparison purposes. The results and error percentage are compared in detail in Table 17 for Section III. Since all streams are not present in all sections, Sections II and IV of the exchanger are not included in the analysis, resulting in a thermal imbalance in the program.
The design approach used in this work was based on the fundamental tenet that the size of heat exchangers depends on the heat transfer coefficient, which affects the stream’s ability to transmit heat in the HE unit. In the case of plate and fin exchangers, choosing the proper secondary surfaces might be done, as shown in the paper. The theoretical method outlined in the paper could not be used in practice due to a few problems. For instance, it was thought that there were no restrictions on producing any fin density, which may be the biggest limitation at the moment. It utilized the availability of precise generalized correlations for pressure drop and heat transfer as a function of fin geometry and also applied it to single-phase heat transfer.
Symbols
| A: | Area (m2) |
| : | Free-flow area (m2) |
| : | Coefficient in friction factor |
| : | Coefficient in Colburn factor |
| : | Exponent in friction factor |
| : | Exponent in Colburn factor |
| : | Specific heat capacity (J·kg−1 K−1) |
| : | Heat capacity flow rate (W K−1) |
| : | Cold stream heat capacity flow rate per passage (W·K−1) |
| : | Hydraulic diameter (m) |
| : | Friction factor |
| : | Fin frequency (fins·m−1) |
| : | Ratio of fin area to total area |
| H: | Enthalpy (Kw) |
| HT: | Exchanger height (m) |
| : | Temperature (K) |
| : | Wall temperature (K) |
| : | Ratio of heat transfer area on one side of the exchanger to total volume of the exchanger (m2·m−3) |
| : | Ratio of heat transfer area on one side of the exchanger to volume between plates on that side (m2·m−3) |
| : | Fin efficiency |
| : | Viscosity (Pa·s) |
| : | Colburn factor |
| k: | Thermal conductivity of the fin (W·m−1·K−1) |
| L: | Stream length (m) |
| : | Mass flow rate (kg·s−1) |
| : | Number of streams |
| : | Number of passes per stream |
| : | Prandtl number |
| : | Thickness of separating sheet (m) |
| : | Heat duty (W) |
| : | Fouling resistance (m2·K·W−1) |
| : | Ratio of heat capacity flow rates of hot streams to cold streams |
| : | Reynolds number |
| : | Wall thermal resistance (m2·K·W−1) |
| : | Heat transfer coefficient (W·m−2·K−1) |
| : | Volume (m3) |
| W: | Exchanger width (m) |
| : | Pressure drop (Pa) |
| : | Logarithmic mean temperature difference (K) |
| : | Fin spacing (m) |
| : | Density (kg·m−3) |
| : | Fin thickness (m). |
Data Availability
The data used in this study are included in the article.
Disclosure
Our previous manuscript, “Design of the Multi-stream Plate-Fin Heat Exchanger in the Air Separation Units,” could not cover all types of multiflow heat exchangers, as it was able to design a heat exchanger with one hot flow and several cold flows, or vice versa. The current manuscript addresses this problem and uses a different approach to construct a heat exchanger (MSPFHE) in air separation units with multiple hot and cold streams operating simultaneously.
Conflicts of Interest
The authors declare that they have no conflicts of interest.