Multi-stream Heat Exchanger Research Articles

Experimental Performance Evaluation of a Multi-stream Heat Exchanger for Integration of High-Temperature Steam Electrolysis with Nuclear Reactor Systems

Experimental Performance Evaluation of a Multi-stream Heat Exchanger for Integration of High-Temperature Steam Electrolysis with Nuclear Reactor Systems

Energy transfer and conversion in the Allam cycle with a multi-stream heat exchanger

The Allam cycle is renowned for its high efficiency and low emissions in power generation, utilizing supercritical carbon dioxide as the working fluid. The regenerator, one of the key heat exchangers, plays a crucial role in the system. However, modeling the regenerator is challenging due to the presence of multiple pinch points. This study proposes a regenerator model that employs three multi-stream heat exchanger modules in Aspen Plus. A thermodynamic and economic analysis of the system was conducted and compared with a conventional system utilizing the two multi-stream heat exchanger modules. Simulation results show that the combustion chamber has the highest exergy loss in the system, accounting for 46.9 % of the total exergy loss. The turbine is identified as the most capital-intensive component, representing 44.9 % of the total equipment investment. Furthermore, a sensitivity analysis was conducted on key parameters. The results indicate that under certain operating conditions, the heat provided by the air separation unit is insufficient to reduce the temperature difference at the hot outlet of the regenerator. Compared to the conventional Allam cycle system using the 2R model, the 2R model predicts deviations of up to 28.9 %. This proposed model provides a new approach for the efficient allocation of energy utilization in the multi-stream heat exchange process within the Allam cycle system.

Multivariate multi-objective collaborative optimization of pumped thermal-liquid air energy storage

Pumped thermal-liquid air energy storage (PTLAES) is a novel energy storage system with high efficiency and energy density that eliminates large volumes of cold storage. In this study, three different configurations of PTLAES systems with direct and indirect thermal energy storage were proposed. The “adaptive segmentation-based temperature transfer matrix” method was developed to capture the heat transfer characteristics of multi-stream plate-fin heat exchangers (MPFHEs), which is the key component of the system. To determine the upper limit of the techno-economic performance of the system, single/multi-objective optimization was performed with up to 35 decision variables. Additionally, the “Pareto efficiency” concept was defined to quantify the goodness of a point compared to the Pareto front. The results showed that the irreversible heat transfer and pressure drop in MPFHEs contribute 20.6 %–44.3 % of the total exergy destruction. Therefore, the design of MPFHEs significantly impacts the system performance. Multivariate multi-objective collaborative optimization can significantly improve the optimization results. PTLAES with closed loop indirect thermal energy storage was determined to have the best overall performance, achieving round-trip efficiency of 63.3–70.1 %, levelized cost of storage (LCOS) of 0.162–0.181 $/kWh, and energy density of 122–161 kWh/m3. The optimized PTLAES system can achieve lower LCOS than lithium-ion batteries when the discharge duration exceeds 3.5 h. Furthermore, it was shown that key criteria including round-trip efficiency, LCOS, and energy density can be traded off over a broad design space of different system configurations, parameter combinations, and material choices. This research demonstrated that PTLAES is a promising choice for long-duration energy storage and provided guidance for the design and techno-economic optimization of PTLAES systems.

Modeling and Design of a Multistream Plate-Fin Heat Exchanger in the Air Separation Units by Pinch Technology

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.

Pinch and exergy assessment of an innovative hydrogen and methane purification process configuration based on solar renewable energy

Energy recovery from waste sources and developing new high-performance systems are essential to minimize energy consumption. A novel purification structure is developed to produce hydrogen and liquid natural gas (LNG) using exhaust gases from various industries, mixed refrigeration system, organic Rankine cycle (ORC), and solar energy sources. Solar parabolic trough collectors are used to supply energy in the low-temperature ORC. The proposed system produces 1.922 kg/s hydrogen with purity of 94.25 mol% and 1.777 kg/s LNG as the main product by consuming 10.56 kg/s crude hydrogen feed gas. The LNG and pure hydrogen specific power consumption (SPC) are 0.4111 and 0.3803 kWh/kg, respectively. The SPC of the sum of both products is obtained at 0.1975 kWh/kg. The methane and hydrogen recovery factors are 94.80% and 98%, respectively, indicating maximum methane and hydrogen absorption of the crude hydrogen feed gas. The exergy analysis indicates that the total exergy destruction of the integrated system is calculated at 5561 kW, and its exergy efficiency is obtained as 28.56%. The heat exchanger networks for the HE1, HE2, HE3, HE4, and HE6 multi-stream heat exchangers are extracted through the pinch strategy. The multi-stream heat exchangers have 8, 13, 6, 8, and 2 simple heat exchangers. The outcome results obtained from the parametric study is a 25.88% increase in the production rate of the main products (LNG and pure hydrogen). In addition, when the ratio of LNG to fuel gas increases by 48.08%, the ratio of main product to by-product increases from 54 to 62 mol%. By performing parametric analysis, it can be concluded that increasing the hydrogen content of the crude feed improves the performance of the system.

Optimization of inserted coiled tube three-fluid heat exchanger using genetic algorithms

The three-fluid heat exchanger is a multi-stream heat exchanger that provides three streams at different temperatures for certain usage objectives. Recently, optimizing heat exchangers generally and three-fluid heat exchangers especially have received great attention in the energy field. The current study objective is to get the optimal mass flow rate of the three streams to minimize the entropy generation number and maximize effectiveness. Optimization is performed on the inserted coiled tube type for 24 cases with different usage objectives and different mass flow rate constraints. The optimization is done using an analytical approach for the temperature profiles and a regressed model for the overall heat transfer coefficients. Single-objective and multi-objective genetic algorithms are the optimization algorithms. The result shows that cooling the hot fluid is the most efficient usage objective; however, heating the intermediate-temperature fluid is the less efficient usage objective. Also, the study shows that the entropy generation number is dependent on the mass flow rate constraint. The maximum effectiveness of 0.693 occurs when the usage objective is cooling the hot fluid. In this case, the mass flow rate of the cold and the intermediate-temperature fluids are maxima while the mass flow rate of the hot fluid is minimum. The minimum entropy generation number 0.0486 occurs when the mass flow rate of the cold fluid is maximum while the mass flow rate of the hot fluid and intermediate-temperature fluid are minimal.

Study on strengthening power generation by using LNG cold energy with multi-stream heat exchange

The utilization of cold energy released during the liquefied natural gas vaporization to enhance power generation is an efficient method for energy conservation and emission reduction. In this study, a novel multi-stream cascade combined cycle (MS-CCC) is proposed, which integrates multi-stream heat exchange into the power generation system. In contrast to the cycles of the previous research, MS-CCC improves the utilization efficiency of cold exergy while simultaneously recovering the cold exergy of the working fluid without the need for additional heat exchangers in the system. The thermodynamic performance and economic benefits of MS-CCC were evaluated by comparing them with traditional combined cycle (CC), parallel combined cycle (PCC) and cascade combined cycle (CCC) by genetic algorithm, and the study also investigated the influence of operating parameters and cycle structure on the performance of MS-CCC. Compared to the CC, PCC and CCC, the exergy efficiency of MS-CCC can be higher by 88.6 %, 63.1 % and 12.4 % respectively when the same working fluid is employed. Additionally, the net annual income with the optimal working fluids can be increased by 1.039, 1.036 and 0.405 M$, respectively. The maximum net annual income of MS-CCC reaches 1.225 M$ with an exergy efficiency of 17.46 % when employing the optimum working fluid group of ethane + R32. The exergy efficiency of MS-CCC can be maximized at certain condensing temperatures, and it increases with the decline of the natural gas exhaust pressure of the system. Furthermore, the removal of direct expansion has minimal effect on the system efficiency, and by adding one stage of Rankine cycle, the exergy efficiency can be increased by more than 24.4 %.

Hydrogen Purification through a Membrane–Cryogenic Integrated Process: A 3 E’s (Energy, Exergy, and Economic) Assessment

Hydrogen (H2) is known for its clean energy characteristics. Its separation and purification to produce high-purity H2 is becoming essential to promoting a H2 economy. There are several technologies, such as pressure swing adsorption, membrane, and cryogenic, which can be adopted to produce high-purity H2; however, each standalone technology has its own pros and cons. Unlike standalone technology, the integration of technologies has shown significant potential for achieving high purity with a high recovery. In this study, a membrane–cryogenic process was integrated to separate H2 via the desublimation of carbon dioxide. The proposed process was designed, simulated, and optimized in Aspen Hysys. The results showed that the H2 was separated with a 99.99% purity. The energy analysis revealed a net-specific energy consumption of 2.37 kWh/kg. The exergy analysis showed that the membranes and multi-stream heat exchangers were major contributors to the exergy destruction. Furthermore, the calculated total capital investment of the proposed process was 816.2 m$. This proposed process could be beneficial for the development of a H2 economy.

An investigation of multistream plate-fin heat exchanger modelling and design: a review

Abstract In line with population expansion and industrial development, the world’s energy consumption has been rising gradually over the past three decades. As a result, methods for energy conservation have been sought. One of the most common strategies is heat recovery, which is efficient and cost-effective to the extent possible. Heat recovery is not just about saving energy for primary consumption; it is also about lowering emissions and protecting the environment. In this respect, one of the most important strategies for heat recovery is to develop heat exchangers and exploit the energy associated with many of the processes’ output products in order to use it in new processes. Many researchers working in the field of heat engineering are now looking into novel heat transfer techniques. Use of the heat exchanger as a compact is one of these ways that might be considered. The current review therefore concentrates on the design of plate-fin heat exchangers (PFHE) and multi-stream plate-fin heat exchangers (MSPFHE) based on various models. The current review offers some suggestions for upcoming studies on improving heat transfer and minimizing power use.

Experimental investigation on RORC system performance for recovering LNG cold energy under heating and cooling capacities variations

A large amount of available cold energy exists in Liquid Natural Gas (LNG). While it is not efficiently utilized and is released into the ocean. To efficiently utilize LNG cold energy, a power generation test bench based on the organic Rankine cycle has been established with R290 as the working fluid, a scroll expander as the thermal conversion device, and a multi-stream heat exchanger as the high-efficiency heat exchange device. The low-grade heat source and LNG are simulated by electrically heated hot water and −198 °C liquid nitrogen. The following are the main conclusions: (1) Heating and cooling capacities have different degrees of influence on system performance, and there is a matching relationship between the two capacities; (2) system maximum thermal efficiency and cold energy utilization rate are 6.13% and 12.04%, respectively. The comprehensive performance reaches the highest when the ratio of heating-to-cooling capacity is 1.96; (3) among the main components in the system, the increasing proportion of expander exergy destruction plays a positive role in improving the total system exergy efficiency. While the increasing proportion of heat exchangers exergy destruction has a negative influence in system exergy efficiency.

Study on multi-stream plate fin heat exchanger coupled with ortho-para hydrogen conversion based on distributed parameter model

The distributed parameter model is used to simulate full domain of multi-stream CFPFHE (catalyst filled plate fin heat exchanger). The heat transfer due to the extended catalyst surface area, the ortho-para hydrogen conversion heat and the flow resistance in porous catalyst are integrated in the model. The results show that increasing the mass flow of fluid channel filled with catalyst not only decreases HEPUP (heat exchange amount per unit pump power), but also weakens efficiency of o-p conversion. For example, when the mass flow of fluid A (in which catalyst is filled) increases from 0.06 kg/s to 0.084 kg/s, the pump power increases by 34.6%, and the HEPUP and the average outlet para-hydrogen decreases by 30.9% and 7.0% respectively. In addition, A deviation parameter ϕ is defined to qualitatively describe the degree of inlet maldistribution. Although no catalyst filled in fluid C channel, the effect of ϕC on the outlet para-hydrogen mass fraction is obvious. With ϕC increasing from 0 to 1.5, the outlet para-hydrogen mass fraction in the layer numbered by 42 (middle layer of fluid A) increases by 6.8%, decreases by 11.9% and 11.9% respectively, in the layer numbered by 6 (upmost layer of fluid A) and 76 (downmost layer of fluid A). The increase of inlet maldistribution of fluid C prevents the potential of catalyst filled in up and down layers of fluid A from being fully utilized.

Key factors affecting the performance of the multi-stream heat exchanger for CO2 condensation

The multi-stream heat exchanger (MS-HEX) is an important equipment in CO2 capture processes, especially for CO2 condensation. By now, little attention has been paid to thoroughly investigating its performance. To provide insights for optimizing the design and operation of the MS-HEX, this paper evaluated the impacts of some key factors, such as the flow arrangement and the content of non-condensable (NC) gases, on the performances of the MS-HEX, including the exit vapor fraction, the pressure drop, the heat transfer coefficient (HTC), and the sub-cooling degree. A 3D CFD model was developed and validated. Based on simulations, it was found that the flow arrangement can clearly affect the performance of the MS-HEX, and there existed an optimal one, which can give the highest sub-cooling degree. Moreover, increasing the volume fraction of NC gases can lead to a decrease of the HTC and the sub-cooling degree; and Ar showed the biggest impact, followed by O2 and N2. For instance, compared to condensing a stream containing 5 vol % N2, condensing a stream containing 5 vol % Ar led to a lower HTC and a lower sub-cooling degree, which can be up to 27.3% and 4 K, respectively.

Numerical investigation of turbulent nanofluid flow behavior in a multi-stream plate-fin heat exchanger with a novel design of fractal fins

Plate heat exchangers are widely used in various industries. This study considers using a novel design of fractal shape fins with a new structure on the performance of multi-stream plate-fin heat exchangers for the first time, which has not been studied by researchers before. The numerical study is done with a 3D finite volume method. The effect of using Oil/MWCNT nanofluid and using various configurations of fractal fins with different attack angles ranging from 30 degrees to 100 degrees with the range of Reynolds number of 10,000–40,000, have been studied in the current research. These changing parameters have a significant impact on the flow field and heat transfer in the heat exchanger. The results of this study show that increasing the angle of attack of fractal fins creates more flow deflection and higher fluid mixing. The rise of the Reynolds number creates stronger vortexes as the flow passes over the fins, thereby it can augment the fluid mixing in the areas which are close to the finned. As the Reynolds number rises, the growth of the thermal boundary layer diminished. It can also be seen that as the fluid impacts the fractal fins at higher angles of attack, the temperature distribution becomes more uniform in the heat exchanger. Increasing the Reynolds number from 10,000 to 40,000 increases the heat transfers up to 63 %. At the constant Reynolds numbers, increasing the fraction of solid nanoparticle volume up to 4 % in the cooling fluid augment the heat transfer rate by 48 % compared to the base fluid. Increasing the fluid velocity results the amplification of longitudinal vortex formation. Therefore, the pressure loss is higher at the increased Reynolds numbers. At the lower Reynolds numbers, the pumping power has a weaker dependency on the nanofluids concentration. Increasing the angle of attack of fractal fins increases the pumping power by 50 % compared with the angle of attack of 30 degrees. Increasing the fractal fin angle of attack compared with 30 degrees increases friction by 45–85 %. Changes in the Colburn factor show that considering all parameters that increase heat transfer, the Colburn factor increases by 23–42 % compared with the base scenario with Re = 10,000 and angle of attack = 30 degrees.

Design and optimisation of novel cascade mixed refrigerant cycles for LNG production – Part II: Novel cascade configurations

Large scale production of liquefied natural gas (LNG) typically employs energy-intensive cascade refrigeration cycles. Three well-established cascade cycles in the LNG industry are the Propane Pre-cooled Mixed Refrigerant (C3MR), Dual Mixed Refrigerant (DMR) and Phillips Cascade cycles. Previous work has focused on improving the energy efficiency of these cascade cycles with various methods (e.g. exergy analysis), as this can bring significant economic benefits. However, potential benefits associated with changes in the configuration of a cascade cycle are usually neglected. This work develops three cascade cycle options, based on structural modifications, to be competitive with the commercial processes. The novel configurations are the CryoMan Cascade cycle, the Bypass Cascade cycle and the Double CryoMan Cascade cycle. The performance of these novel cascade cycles is evaluated with a case study previously used to assess the commercial processes. The optimisation strategy consists of a genetic algorithm with regeneration of the population followed by a nonlinear optimisation. The results obtained demonstrate that the structural changes enable the novel cascade cycles to achieve energy savings of up to 15.6% compared to the C3MR cycle, and up to 5.9% compared to the DMR cycle. Moreover, these energy savings come at the expense of only minor added process complexity, as the number of compression stages and multi-stream heat exchangers are kept the same as in the commercial processes.

Numerical Simulation and Comparative Analysis of Three Boil-Off Gas Reliquefaction Systems

Abstract In view of the problem that the boil-off gas (BOG) generated by small liquefied natural gas (LNG) ships affects the transportation safety, three BOG reliquefaction systems are improved, which are as follows: case 1: serial nitrogen expansion reliquefaction system (N2-BOG); case 2: single mixed refrigerant reliquefaction system (SMR-BOG); and case 3: propane precooled mixed refrigerant reliquefaction system (C3MR-BOG). The basic process is simulated in aspen plus and combined with the mathematical model built up in matlab where the three cycles are optimized with the specific power consumption (SPC) as the objective function. The results show that the SPC of three cases are 0.8021 kWh/kg (LNG), 0.4150 kWh/kg (LNG), and 0.5063 kWh/kg (LNG); the coefficient of performance (COP) of cases 1, 2, and 3 are 0.20, 0.39, and 0.30; the exergy efficiency of 36.56%, 70.66%, and 57.93% along with the total product cost of 89.00 $/h, 55.73 $/h, and 77.54 $/h are achieved in Cases 1–3, respectively. In addition, the overall exergy destruction of the cycles and each equipment are discussed, and the matching of the cold and heat sources of the multistream heat exchanger in the three systems is analyzed. In conclusion, under the condition that the BOG mass flowrate is 350 kg/h, the improved SMR-BOG has advantages on thermodynamic performance and economic analysis, which makes it a better choice.

A hybrid batch distillation/membrane process for high purification part 2: Removing of heavy impurities from xenon extracted from natural gas

High-purity xenon of 6 N purity grade and higher is widely used in electronics, space, and medicine. A hybrid distillation/membrane process for the purification of xenon extracted from natural gas by gas hydrate crystallization is studied experimentally and via simulations. Membrane gas separation data for xenon-containing mixtures is measured for polysulfone membrane and polyetherimide/polyimide blend membrane. Parametric analysis and process optimization are performed in Aspen Plus Dynamics™ for a middle-vessel batch distillation column with an integrated hollow fiber membrane unit implemented via Aspen Custom Modeler™. Removal of higher- and lower-boiling impurities such as ethane, carbon dioxide, propane, methane, and krypton is considered to achieve 6 N and 9 N target purity grades. Hybrid distillation/membrane process flowsheets built with a multi-stream passive heat exchanger with either retentate or permeate being returned to the column are analysed. It is shown that the operating conditions and the configuration of the hybrid process with a membrane separation treatment of heavy impurities fraction can be tailored to achieve up to 30% increase in batch productivity for the considered case studies and improve xenon recovery reaching above 99.8% as compared to standalone batch distillation, which is especially critical for higher purity grades.

Geometric optimization of thermo-hydraulic performance of multistream plate fin heat exchangers in two-stage condensation cycle: Thermodynamic and operating cost analyses

LNG is an energy carrier with growing importance, but LNG cryogenic cycles are energy-intensive. Because the thermo-hydraulic performance of heat exchangers affects the operation and energy consumption of a compressor. The optimization of heat exchangers is key to improving the energy efficiency of a cryogenic plant. In this work, the screening analysis and optimization procedures are performed for a two-stage condensation plant to enhance the Coefficient of Performance (COP) as the operating performance criterion. Five geometric design categories of applied fins, such as fin type, fin height, fin thickness, fin frequency, and the number of layers of MPFHEs (Multistream Plate Fin Heat Exchanger) are selected as input parameters for the optimization process. Then, a thermodynamic analysis including the second law analysis and capital and operating costs assessment are carried out to show the improvements of applied optimization in the mentioned objectives. The results of the optimization procedure have indicated a considerable improvement in the COP of up to 13.7% and significant mitigation in total power consumption of up to 11.8 MW. Furthermore, the optimal configuration of heat exchangers presents an increase in exergy efficiency of up to 4.1%, a saving in exergy destruction of 10.2 MW and up to 8.6 M USD/year in the operating cost when compared with conventional cases.

Passage Arrangement Optimization of Plate-Fin Heat Exchanger under Uncertain Operating Conditions

As the total flow rate and passage number increase, the quality of the passage arrangement has an important influence on the thermal efficiency of a multi-stream plate-fin heat exchanger (PFHE). The operating conditions are uncertain due to changes in environmental and product requirements, which affect the design of passage arrangements. If this influence is not considered enough in design, it will lead to the loss of heat transfer efficiency of the PFHE. Therefore, an optimization design method for passage arrangement is developed considering the influences of uncertain operating conditions. First, the uncertain operating conditions of the PFHE are represented using probability density functions of mass flow rates and temperature. Next, the optimization goals are chosen through the correlation calculation between the passage arrangement and the heat transfer indexes by the integral-mean temperature difference method. The particle swarm optimization algorithm is adaptively improved for the passage arrangement calculation. Then, the result under uncertain operating conditions is compared with the result under a single condition. The total heat transfer rate is increased, and the dimensionless mean square error of the cumulative heat load is decreased, so the method of designing the passage arrangement under uncertain operating conditions is effective.

Performance enhancement of hydrogen liquefaction process via absorption refrigeration and organic Rankine cycle-assisted liquid air energy system

This study focuses on the design and analysis of a liquid hydrogen production process integrated with an absorption refrigeration system, a liquid air energy storage system, and an organic Rankine cycle for designing an energy-efficient integrated process. The absorption refrigeration system and liquid air energy storage system facilitate hydrogen pre-cooling, whereas the organic Rankine cycle helps to recover the waste heat generated after air combustion. An ammonia/water-based absorption refrigeration system accompanied by liquid air precools the hydrogen to −180 °C, and the vapor compression refrigeration system liquifies the hydrogen. In this study, an energy-efficient process integration scheme was designed to reduce the overall energy consumption and recover waste heat. The net specific energy consumption of the process was 6.71 kWh/kg. The design variables and composite curve analyses indicate that the most energy-intensive part of the process is the liquefaction section. Moreover, exergy analysis indicates that multi-stream heat exchangers primarily contribute towards exergy destruction. The exergy efficiency of the process was 35.7%. Environmental analysis shows that the refrigeration cycles mainly contribute towards carbon dioxide emissions. Furthermore, according to the economic analysis, compressors and multi-stream heat exchangers accounted for 88.5% of the total capital investment. Overall, these analyses report energy efficient integration and indicate the potential for further improvements, particularly in the refrigeration cycle. This study is expected to provide insights into the design of energy-efficient integrated hydrogen liquefaction processes that exploit the benefits of the absorption refrigeration system, liquid air energy storage system, and organic Rankine cycle.

An improved Levenberg–Marquardt method for nonsmooth equations with application to multi-stream heat exchangers

Systems of nonsmooth equations are very useful in the study of nonlinear complementarity problems, variational inequality problems, bilevel programming problems, and arise in the mathematical modeling of many problems in chemical processing, mechanics and engineering. In this paper, we introduce a hybrid method for solving systems of nonsmooth equations, which combines the idea of Levenberg–Marquardt–type methods with bundle techniques, while avoiding the hypothesis of differentiability of the least squares merit function. Some numerical results comparing the proposed method with LP-Newton method indicate that the improved Levenberg–Marquardt algorithm works quite well in practice. As an application of the proposed algorithm, we consider the multi-stream heat exchanger network problem, where a heat exchange network must be designed to meet a specified exit temperature for a given set of streams.