Showing papers on "Countercurrent exchange published in 2012"

Modeling of Air Flow in an Industrial Countercurrent Spray-Drying Tower

Abstract: This article presents both theoretical and experimental determination of the hydrodynamics of drying air in an industrial countercurrent spray dryer. Air velocity measurements were performed in selected areas of the tower to determine the flow pattern in the dryer and to collect data to validate the computational fluid dynamics (CFD) modeling and verify the results. For no-swirl operation mode, 3D CFD calculations showed high instability of the air flow in the dryer. A bent, pillow-shaped flow above the drying air inlet, which promotes deposition of particles in this area of the wall, was detected. CFD calculations also proved that when drying air was introduced to the tower tangentially; from 20° to 30° in relation to the initial air flow configuration in the spray-drying tower, the air flow was stabilized and air velocity near the wall increased, which might reduce wall deposition of particles. Comparison of experimental and theoretical results showed that the CFD model of countercurrent spray-drying pr...

Modeling of Microwave Drying of Fruits. Part II: Effect of Osmotic Pretreatment on the Microwave Dehydration Process

Abstract: The heat and mass transfer during the combined process of osmotic–microwave drying (OD-MWD) of fruits was studied theoretically and experimentally through modeling and numerical simulation. With the aim of describing the transport phenomena involved in the combined dehydration process, the mass and energy microscopic balances were set out. For the first step (OD), two models with different levels of complexity were proposed, an osmotic–diffusive and a countercurrent flow diffusive model. For MWD, the energy and mass balances were solved, using moisture- and temperature-dependent properties; inner heat generation due to transformation of the electromagnetic energy was accounted for by using the approximation of Lambert's law. The numerical solution obtained from OD was incorporated as initial values for the simulation of MWD. The model validation was satisfactorily carried out in pears, both fresh and osmodehydrated for 2 h in sucrose solutions and then irradiated in a microwave oven at 500 W. From the res...

Correlation for countercurrent flow limitation in a PWR hot leg

Abstract: Numerical simulations were done to evaluate countercurrent flow limitation (CCFL) characteristics in a pressurized water reactor (PWR) hot leg with the diameter of 750 mm by using a volume of fluid (VOF) method implemented in the CFD software, FLUENT6.3.26. The calculated CCFL characteristics agreed well with known values including the UPTF data at 1.5 MPa. Sensitivity analyses for system pressures up to 8 MPa showed that the calculated CCFL characteristics in the Wallis diagram were slightly mitigated from 0.1 MPa to 1.5 MPa with increasing system pressure, but they did not change from 1.5 MPa to 8MPa. Using the CCFLs calculated in this study and values measured under air–water and steam–water conditions, a CCFL correlation and its uncertainty were derived.

Heat and Mass Transfer in Agitated, Co-, or Countercurrent Conductive–Convective Heated Drum Dryer

Abstract: Agitating drum dryers are often used to dry granular solids with high moisture contents Moisture reduction and thermal treatment can be enhanced by a contact heating jacket or heated agitators A mathematical model was created to investigate the influence of operating parameters for the description of simultaneous heat and mass transfer in a dryer The model contains volumetric heat and mass transfer coefficients that are functions of temperature, velocity, etc To investigate the drying process and to determine the volumetric heat transfer coefficients, a pilot-plant agitating dryer was built Measurement and evaluation methods were developed to determine the volumetric heat transfer coefficients of granulated products The volumetric heat transfer coefficients were plotted with dimensionless Nu′-Re′ numbers The mathematical model and the transfer coefficients make it possible to calculate the moisture content and temperature of the drying product as well as the humidity and temperature of the drying g

Multi-effect plate type rising film countercurrent evaporation concentration device and method thereof

Abstract: The present invention relates to the technical fields of a multi-effect evaporation concentration process and equipment, and specifically to a multi-effect plate type rising film countercurrent evaporation concentration device and a method thereof. The device comprises a plate type heat exchanger structure and a flash evaporation tank structure. The device is characterized in that the device comprises five groups of plate type rising film countercurrent evaporation devices, wherein the five groups of the plate type rising film countercurrent evaporation devices form a series connection; each group of the plate type rising film countercurrent evaporation device comprises a plate type heat exchanger, a flash evaporation tank, and a pump; each group of the plate type rising film countercurrent evaporation device is in the sealed negative pressure system condition; the pressure inside each group of the device is increased along with the increase of the raw material liquid concentration. The raw materials are subjected to heat exchange through the plate type heat exchanger, and then are separated from the solvent through the flash evaporation separator. The heat exchange treatments are sequentially performed until the material enters the fifth group of the flash evaporation tank. The heat-exchanged steam and the steam discharged from the outlet of the fifth group of the flash evaporation tank are introduced into the outlet pipe. With the present invention, the heat energy of the secondary steam after separation is completely utilized; the reverse heat exchange of the heat exchanger and the designed negative pressure and temperature condition limit the generation of the vaporization phenomenon of the material liquid in the heating process so as to reduce the scaling possibility.

Transport analysis in reverse electrodialysis with pulsatile flows for enhanced power generation

Abstract: Time-dependent velocity profile and concentration distributions formed in a single reverse electrodialysis (RED) unit have been successfully pursued using simulation framework for evaluating performance of the unit, i.e., open circuit voltage and short circuit current. The single RED unit consists of two adjunct fluid channels, separated by the semi-permeable membrane. Through one of the channels, sea water flows, and the other is occupied by fresh water, flowing in the opposite direction (countercurrent operation). The diffusion-convection transport of the rate-limiting ion, Na+ in this study, for both channels is treated. The diffusive transport of cation across the membrane is expressed as boundary conditions for the bi-mechanism model. Our simulations conducted using an orthogonal collocation on finite element scheme show that the concentration difference of 35 g/L between sea water and fresh water results in the open circuit voltage of 63 mV and the short circuit current density of 11.5 A/m2. These values are close to ones that were obtained from the experiments.

Method for extracting capsorubin and capsaicine by utilizing continuous countercurrent ultrasonic extracting machine

Abstract: The invention provides a technical scheme of a method for extracting capsorubin and capsaicine by utilizing a continuous countercurrent ultrasonic extracting machine. The scheme comprises the following processes: 1, inputting well crushed capsicum powder into an extraction tube from the material inlet of the continuous countercurrent ultrasonic extracting machine by a quantitative feeder, and simultaneously inputting an extraction solvent which is heated into the extraction tube from the slag discharging end of the continuous countercurrent ultrasonic extracting machine; 2, carrying out countercurrent ultrasonic extraction on the capsicum powder in the extraction tube of the continuous countercurrent ultrasonic extractor by the extraction solvent under normal pressure for 30-40min; 3, discharging capsicum slag from the slag discharging port of the continuous countercurrent ultrasonic extracting machine after completing the countercurrent ultrasonic extraction, processing the capsicum slag to recover the solvent, and discharging the obtained extract from the liquid outlet of the continuous countercurrent ultrasonic extracting; and 4, carrying out slag-liquid separation on the extract, inputting the extract to a liquid separation tank, uniformly inputting a separation agent to the separation tank, allowing them to be statically layered, carrying out concentration and solvent removal processing on the obtained lower layer extract to obtain finished capsorubin, and concentrating and drying the obtained upper layer extract to obtain finished capsaicine.

Effects of Gravity and Inlet Location on a Two-Phase Countercurrent Imbibition in Porous Media

Abstract: We introduce a numerical investigation of the effect of gravity on the problem of two-phase countercurrent imbibition in porous media. We consider three cases of inlet location, namely, from, side, top, and bottom. A 2D rectangular domain is considered for numerical simulation. The results indicate that gravity has a significant effect depending on open-boundary location.

Controlling the column spacing in isothermal magnetic advection to enable tunable heat and mass transfer

Abstract: Isothermal magnetic advection (IMA) is a recently discovered method of inducing highly organized, non-contact flow lattices in suspensions of magnetic particles, using only uniform ac magnetic fields of modest strength. The initiation of these vigorous flows requires neither a thermal gradient nor a gravitational field, and so can be used to transfer heat and mass in circumstances where natural convection does not occur. These advection lattices are comprised of a square lattice of antiparallel flow columns. If the column spacing is sufficiently large compared to the column length and the flow rate within the columns is sufficiently large, then one would expect efficient transfer of both heat and mass. Otherwise, the flow lattice could act as a countercurrent heat exchanger and only mass will be efficiently transferred. Although this latter case might be useful for feeding a reaction front without extracting heat, it is likely that most interest will be focused on using IMA for heat transfer. In this paper, we explore the various experimental parameters of IMA to determine which of these can be used to control the column spacing. These parameters include the field frequency, strength, and phase relation between the two field components, the liquid viscosity, and particle volume fraction. We find that the column spacing can easily be tuned over a wide range to enable the careful control of heat and mass transfer.

COPROX Fixed Bed Reactor – Temperature Control Schemes

Abstract: Different temperature control schemes for the COPROX stage of a 5-kW fuel cell system were analyzed. It was found that, among the schemes proposed, i.e., co- and countercurrent heat exchange, single adiabatic reactor and series of adiabatic reactors with interstage heat exchange, the best choice for temperature control was the series of adiabatic reactors with interstage heat exchange. This scheme represented the best way to keep the average temperature around 443 K, which was found to be the most suitable temperature for selectivity towards CO oxidation. If hydrogen is produced from ethanol steam reforming, the heat withdrawal can be carried out by the water/ethanol reformer feed mixture, thus contributing to the energy integration of the overall system.

A practical countercurrent fluid catalytic cracking regenerator model for in situ operation optimization

Abstract: A practical countercurrent fluid catalytic cracking (FCC) regenerator model with improved descriptions of gas and solid flow patterns is proposed. A three-zone and two-phase gas model was utilized to describe the gas flow through the regenerator, addressing the different phase mass-transfer properties in the different zones. A new two-continuously stirred-tank reactor-with-interchange model was used to describe the solid flow and to address the effect of freeboard on catalyst regeneration. Otherwise, this model also considered the usually adopted expanding section for reducing solid carryover. The model was programmed in Matlab language with coupled hydrodynamics and reaction kinetics models and tested and validated by the data from an industrial FCC regenerator operated under both partial and full CO combustion modes. After fitting a single model parameter, the interchange solid flux between the dense bed and freeboard, the model predictions were in reasonable agreement with the commercial data for both modes. © 2011 American Institute of Chemical Engineers AIChE J, 2012

On Bubble Rising in Countercurrent Flow

Abstract: A single bubble of typical volume 20 mm³ ≤ VB ≤ 400 mm³ was placed in downward conically diverging flow of low and moderate viscous liquids (aqueous solutions of glycerine and of electrolytes (NaCl, Na3PO4, MgSO4), and butanol). Experiments were performed over a range of Reynolds number 60≤Re≤2200, Weber number 1≤We≤14, Tadaki number 1≤Ta≤10, Eötvös number 1≤Eo≤22, and bubble aspect ratio 0.4≤b/a≤0.9. The bubble shape, bubble position and motion were investigated by direct observation of two plane projection of bubble by high speed camera. Typical sampling frequency was 150 fps. Relatively long records, (approximately 9000 frames per one bubble observation) allow us to get relevant statistics of treated data. Bubble aspect ratio has been determined from both projection planes. Dimensionless front area of observed bubble has been introduced as suitable parameter for correlation with Eötvös number. Model of static bubble and classical Wellek correlation were employed as asymptotes. Bubble rising velocity has been determined and tested for each single bubble with respect to liquid properties. Velocity data are plotted within the frame given by several theoretical predictions for pure and contaminated liquids. Dimensional analysis is used considering viscosity and surface tension effect. New simple correlation of bubble rising velocity separating the effects of viscosity and surface tension is presented.

Countercurrent prevention system

Abstract: The utility model relates to a countercurrent prevention system. The countercurrent prevention system comprises grid-connected inverted power supplies. The grid-connected inverted power supplies are connected with an electrical network. The grid-connected inverted power supplies and the electrical network are respectively connected with a local load. The countercurrent prevention system further comprises a detection device for detecting whether countercurrent happens, a countercurrent prevention controller, and an energy storage system. The energy storage system is respectively connected with the grid-connected inverted power supplies, the local load, and the electrical network. The countercurrent prevention controller controls the charging and discharging of the energy storage system to prevent the countercurrent based on the detection result of the detection device. When the countercurrent happens or is about to happen, the energy storage system is controlled by the countercurrent prevention controller to start charging. That the countercurrent happens because excess electric energy flows to the electrical network is avoided, frequent cutting off and accessing of the grid-connected inverted power supplies in the prior art is avoided, shock to the electrical network is decreased, and the service life of the grid-connected inverted power supplies is extended. The using of the energy storage system can further play an active role in load shifting, and can smooth the output of the grid-connected inverted power supplies.

A Study of Slender Bluff-Body Reacting Wakes Formed by Concurrent or Countercurrent Fuel Injection

Abstract: The work presents an investigation of turbulent propane flames stabilized by planar injection across the span of a square cylinder, either from its leading face against the approach flow or directly into its vortex formation region. The non-premixed or partially premixed reacting wakes were studied by regulating the fuel injection level and position. Turbulent velocities, temperatures, CH*, flame images, and exhaust emissions were measured using laser velocimetry, digitally compensated thermocouples, chemiluminescence imaging, and gas analysis. Lean and ultra-lean fuel/air velocity ratios of 0.36 and 0.23 were investigated under concurrent and countercurrent injection at a Reynolds number, based on the square burner diameter, of 5700. Large eddy simulations were undertaken using the dynamic Smagorinsky model, the eddy dissipation concept, and an 11-step global mechanism for propane combustion and NOx. The methodology helped to elucidate some aspects regarding the interaction of the flame front with the vo...

Method and press tool for fabricating a plate heat exchanger

Abstract: The method involves producing individual plates (1) from a non-pressed plate blank by converting a tool with exchangeable mold elements to a converted tool that produces cross flow plates or countercurrent flow plates. The plate blank is pressed with the converted tool into the cross flow plate or countercurrent flow plate. Corresponding edges (12) and/or contact surfaces (13) and inflow cross-sections (Z1, Z2) and outflow cross-sections (A1, A2) are formed in main flow directions of two respective mediums. Distance between adjacent individual plates is determined. Independent claims are also included for the following: (1) a pressing tool for pressing individual plates for plate heat exchangers (2) a system for manufacturing individual plates for plate heat exchangers.

Multi-effect evaporation and concentration device

Abstract: The utility model relates to the technical field of a multi-effect evaporation and concentration process and equipment, in particular to a multi-effect evaporation and concentration device. The multi-effect evaporation and concentration device comprises plate type heat exchanger structures and flash tank structures. The multi-effect evaporation and concentration device is characterized by comprising five groups of serial plate type rising film countercurrent evaporation devices, and each group of serial plate type rising film countercurrent evaporation device comprises a plate type heat exchanger, a flash tank and a pump; the devices are all under a closed negative pressure system condition, and pressure in each group of device is improved along with the improvement of the concentration of raw material liquid; raw materials are subjected to heat exchange through the plate type heat exchangers and then separated from solvents through a flash separator, and step-by-step heat exchange is carried out until the flash tank of the fifth group; and steam subjected to heat exchange and steam out of the outlet of the fifth group of flash tank are both introduced into an outlet pipeline. According to the multi-effect evaporation and concentration device, heat energy of secondary steam after separation is sufficiently utilized, and vaporizing phenomena of liquid materials, which are generated in a heating process, are limited by the reverse heat exchange of the heat exchangers and designed negative pressure and temperature conditions, thereby reducing scaling possibility.

A Critical Review on the Numerical Methods of Two-Phase Flows

Abstract: The two-phase flow processes play a significant role in the heat transfer processes in the chemical and power industry, including in nuclear power plants. This study is a critical review on the determination of the heat transfer characteristics of pure refrigerants flowing in vertical and horizontal tubes. The authors’ previous publications on this issue, including the numerical analyses, are summarized here. The lengths of the vertical and horizontal test sections varied between 0.5 m and 4 m countercurrent flow double-tube heat exchangers with refrigerant flowing in the inner tube and cooling water flowing in the annulus. The measured data are compared to numerical predictions based on the solution of the artificial intelligence methods and CFD analyses for the condensation and evaporation processes in the smooth and enhanced tubes. The theoretical solutions are related to the design of passive containment cooling systems (PCCS) in simplified water boiling reactors (SWBR). A genetic algorithm (GA), various artificial neural network models (ANN) such as multilayer perceptron (MLP), radial basis networks (RBFN), generalized regression neural network (GRNN), and adaptive neuro-fuzzy inference system (ANFIS), and various optimization techniques such as unconstrained nonlinear minimization algorithm-Nelder-Mead method (NM), non-linear least squares error method (NLS), and Fluent CFD program are used in the numerical solution. It is shown that the heat transfer characteristics of laminar and turbulent condensing and evaporating film flows such as heat transfer coefficient and pressure drop can be predicted by means of numerical analyses reasonably well if there is a sufficient amount of reliable experimental data. Regression analysis gave convincing correlations, and the most suitable coefficients of the proposed correlations are depicted as compatible with the large number of experimental data by means of the computational numerical methods. Dependency of the output of the ANNs from various numbers of input values is also shown for condensing and evaporating flows.Copyright © 2012 by ASME

Method for purifying reverse osmosis concentrated water with active carbon-membrane separation countercurrent absorption

Abstract: The invention discloses a method for purifying reverse osmosis concentrated water with an active carbon-membrane separation accumulation countercurrent absorption technology. The method comprises the following steps of: extracting concentrated drain water produced in the running process of a reverse osmosis device, and adding into a membrane reactor for undergoing an adsorption reaction; dissolving powder active carbon (PAC) into the membrane reactor for continually adsorbing, wherein the adding amount of the PAC is determined according to the content of organic matters in the reverse osmosis concentrated water, and the adding amount of the PAC can be added appropriately if a treatment effect is poor; and performing aerated stirring and circulating reflux, adsorbing for 10-15 minutes, uniformly dispersing the PAC, fully mixing with reverse osmosis concentrated water, and discharging purified water with a hollow fiber membrane assembly. PAC accumulation countercurrent absorption and membrane separation are used together, so that cost is low, operation is easy and convenient, and automatic degree is high. Due to the adoption of the method for purifying reverse osmosis concentrated water, the requirements of the Discharge Standard of Pollutants for Municipal Wastewater Treatment Plant are met, and the potential hazard of direct discharge on a water environment is reduced; and the method plays an important role in maintaining the balance of a water ecological system.

Modeling of Non-equilibrium Effects in the Gravity Driven Countercurrent Imbibition

Abstract: One of the main mechanisms in the secondary enhanced oil recovery is countercurrent imbibition(1). Many math- ematical models describe countercurrent imbibition considering local equilibrium. However, Barenblatt proposed a model to describe the effect of nonequilibrium con- stitutive relations in oil water displace- ment. This paper implements this model for a gravity driven countercurrent imbibi- tion process. Firstly Darcy's equation was written for vertical displacement of the oil phase and the water phase. In addition, us- ing mass conservation it is possible to for- mulate Barenblatt's model for two phase gravity driven countercurrent process. This model allows to simulate counter- current displacement in a core initially sat- urated with an oil phase and water phase. The initial condition satisfies gravity - cap- illary equilibrium in a tube of 1 m length. Moreover, we assume no flow boundary at both ends. After establishing initial and boundary conditions, initial distribution of local ef- fective saturation, � = Sw + � @S w

Multistage countercurrent flow heat exchange-evaporation-refrigeration device

Abstract: The invention discloses a multistage countercurrent flow heat exchange-evaporation-refrigeration device, comprising direct devaporizers, an air outlet, an air inlet, a water tank, heat exchanging chambers and fan drifts, wherein the direct devaporizer the upper part of which is provided with a spray system is arranged in the heat exchanging chamber; the air outlet is arranged on the upper part ofthe spray system; the air inlet is arranged on the lower part of the direct devaporizer; the water tank is mounted at the bottom of the heat exchanging chamber; the heat exchanging chambers mutually separated are evenly distributed in a machine case; the fan drift is arranged between the adjacent heat exchanging chambers; the upper port of the fan drift is communicated with the air outlet of the last stage heat exchanging chamber; the lower port of the fan drift is communicated with the air inlet of the next stage heat exchanging chamber; the air outlet of the final stage heat exchanging chamber leads outdoor, the water discharging pipe of a water pump of the water tank of the next stage heat exchanging chamber is connected with the spraying system of the last stage heat exchanging chamber; and the cool water in the water tank of the final stage heat exchanging chamber is output through the water pump. The invention not only can reduce the irreversible loss of the heat and moisture exchange of the cool water in the process of heat and moisture exchange of inlet air and improve heat exchanger efficiency, but also can achieve single cool water supply, or single cool air supply, or simultaneous cool water and cool air supply according to different conditions and demands.

Simulation of Countercurrent Multi-Effect Drying System

Abstract: The paper bulids a countercurrent multi-effect drying process model which can be expressed as a linear programming(LP) problem with the minimum total energy consumption as target function. Based on the model it can be conventient to solve the heat load , degree of drying and other drying parameters of each effect. And it realizes the mathematical simulation an analysis of multi-effect drying process. Such process not only reuses the secondary steam but also utilizes the high energy grade. Drying silica sand using 1-effect drying to 5-effect drying is presented as an example. The energy consumption and energy saving rate are compared by using co-current multi-effect drying and countercurrent multi-effect drying. As a summary, the countercurrent multi-effect drying is better than co-current drying. Considered the equipment investment and energy conservation, the study also concluded that the countercurrent 4-effect drying is the optimum selection, and it can save 57.6% energy compared to countercurrent 1-effect drying.

A laboratory exercise using a physical model for demonstrating countercurrent heat exchange

Abstract: A physical model was used in a laboratory exercise to teach students about countercurrent exchange mechanisms. Countercurrent exchange is the transport of heat or chemicals between fluids moving in opposite directions separated by a permeable barrier (such as blood within adjacent blood vessels flowing in opposite directions). Greater exchange of heat or chemicals between the fluids occurs when the flows are in opposite directions (countercurrent) than in the same direction (concurrent). When a vessel loops back on itself, countercurrent exchange can occur between the two arms of the loop, minimizing loss or uptake at the bend of the loop. Comprehension of the physical principles underlying countercurrent exchange helps students to understand how kidneys work and how modifications of a circulatory system can influence the movement of heat or chemicals to promote or minimize exchange and reinforces the concept that heat and chemicals move down their temperature or concentration gradients, respectively. One example of a well-documented countercurrent exchanger is the close arrangement of veins and arteries inside bird legs; therefore, the setup was arranged to mimic blood vessels inside a bird leg, using water flowing inside tubing as a physical proxy for blood flow within blood vessels.

Tail gas heat utilization method for low-concentration gas heat countercurrent catalytic oxidation apparatus

Abstract: The invention discloses a tail gas heat utilization method for a low-concentration gas heat countercurrent catalytic oxidation apparatus. The method adopts a gas catalytic oxidation reactor to treat low-concentration gas exhaust gas, high-temperature exhaust gas exhausted by the gas catalytic oxidation reactor sequentially passes through a high-temperature exhaust gas heat exchanger and a low-temperature exhaust gas heat exchanger which are connected in series, so that the heat of the exhaust gas can be conducted to water flowing through the heat exchangers to increase the temperature of the water, and thereby high-temperature hot water and low-temperature hot water can be respectively provided for users; a regenerator connected with an intake tube of the gas catalytic oxidation reactor is then utilized to transfer the waste heat of the cooled exhaust gas to the low-concentration gas exhaust gas, so that the low-concentration gas exhaust gas can be preheated before entering the gas catalytic oxidation reactor, and finally, the exhaust gas which is further cooled is exhausted into the atmosphere by a relay fan connected with an exhaust tube of the regenerator. Through the method, energy resources are saved, the waste of energy is reduced, the grade of exhaust gas heat energy is increased, and the service life of the apparatus is prolonged.

Modified correction-factor analysis on membrane extraction in multipass countercurrent-flow external-recycle rectangular modules

Abstract: In the present study the modified correction-factor analysis is introduced to investigate the Performances in multipass countercurrent-flow recycled membrane extractors, in which the unknown solute outlet concentrations are neither in the estimating equation for mass-transfer rate nor in the modified correction-factor charts, and thus the calculation is easy and direct without using the try-and-error method, which should be employed in the conventional correction-factor analysis. Experimental results confirm the prediction values for the extraction of acetic acid from aqueous solution by methyl isobutyl ketone in the double-pass device.

Minimum temperature difference analysis and pinch technology of multi-tube heat exchanger networks

Abstract: In industrial practice,multi-tube heat exchangers,which involve both countercurrent and co-current flows are commonly used.Pinch technology is proposed for heat exchanger networks(HEN) with countercurrent flow,but cannot be applied to multi-tube HEN directly.Thus,it is necessary to analyze the relationship among minimum temperature difference,pinch characteristics and total cost quantitatively for multi-tube HEN.Considering the selection of tubes number and total cost of HEN,minimum temperature difference was optimized to minimize total annual cost.Then,it was used to synthesize multi-tube HENs based on pinch technology.Meanwhile,the correction factor for log mean temperature difference(LMTD) was calculated and the results were analyzed.Two case studies demonstrated the effectiveness and application prospect of the presented method.