Kreith F., Timmerhaus K., Lior N., Shaw H., Shah R.K ... · PDF fileFrank Kreith Boca Raton:...

Kreith F., Timmerhaus K., Lior N., Shaw H., Shah R.K., Bell K. J., etal..“Applications.” The CRC Handbook of Thermal Engineering. Ed. Frank Kreith Boca Raton: CRC Press LLC, 2000

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4.10 Heat Transfer in Manufacturing

Donald W. Radford and Timothy W. Tong

Introduction

In many manufacturing processes, thermal energy is either used to promote material transformations orgenerated as a byproduct of the process. In either case, the effects of heat transfer need to be understoodin order to achieve the desired product results. There is a rich body of literature related to heat transferin manufacturing. Presented in this section are only some highlights dealing with several commonlyused manufacturing methods. The aim is to provide sufficient information for practitioners to establishguidelines for designing manufacturing processes for their applications.

Casting

Effect of Heat Transfer in the Castings

Casting and solidification of metals are critically dependent upon temperature, rate of cooling, andthermal mass. Thus, heat transfer between the solidifying metal, the mold, and the surroundings is a keyfactor in the properties of the final solidified metal. Rates of heat extraction determine the form andshape of the solidification interface. Further, cooling rates also determine the subsequent grain size ofthe solidified metal. The direction of heat flow out of the solidifying metal determines the direction ofthe solidification interface and the resulting orientation of the grains in the final metal casting. Directionof heat flow out of a mold also impacts where the last metal freezes and where solidification shrinkagetakes place. Particularly in shape casting, it is critical to control the form and location of solidificationshrinkage to ensure a completely filled mold and therefore a completely formed part.

When we discuss the effects of heat transfer during solidification of a pure metal the primary concernsoften center around grain size, grain orientation, and shrinkage. As depicted in Figure 4.10.1, a roughlyplanar solidification interface progresses from the mold wall along the thermal gradients to the center

FIGURE 4.10.1 Planar solidification interface.

© 2000 by CRC Press LLC

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of the casting. By adjusting the thermal conductivity of localized areas of the mold wall, preferentialheat transfer can be generated which allows the development of directionally solidified grain structure.Such areas of enhanced heat transfer in the mold wall are termed chills (see Figure 4.10.2). These chillscan be used, in addition to generating directional growth, to enhance mold filling and ensure thatsolidification shrinkage is concentrated away from shape-critical regions. However, the effects of heattransfer become much more complicated during the freezing of an alloy.

Freezing of an Alloy

The freezing of an alloy is complicated by the segregation of the alloy constituents. Since in real castings,solidification of molten metal takes place under nonequilibrium conditions, diffusion in the solid stateis not fast enough to equilibrate the composition. Cooling at rates faster than the equilibrium coolingrate leads to composition gradients in the casting and influences the way that solid crystals grow fromthe liquid. These concentration gradients can exist over short or long distances within the casting.Concentration gradients over short distance result in microsegregation, while gradients over large dis-tances are termed macrosegregation. One approach for describing this phenomenon is based on theconcepts of constitutional undercooling (∆Tc), which is a result of liquid temperature gradients that leadto liquid temperatures that are lower than the equilibrium freezing temperature.

Figure 4.10.3 illustrates that ∆Tc occurs ahead of the solidification interface. Therefore, it can be usedto predict the form of the solidification interface. Changes to the heat transfer characteristics of theprocess can then be made to adjust the form of solidification and develop a grain structure that isoptimized for a specific application. The concentration gradients in the liquid can extend over distancesof a few millimeters. Since diffusion is negligible in the solid and incomplete mixing occurs in theliquid, the liquid adjacent to the solid-liquid interface has a different composition than the bulk melt.The first solid to form is solvent rich, with the subsequent solid being less solvent rich until the steady-state composition is reached. This steady-state composition is the same composition as the original metalmelt. The liquid adjacent to the solidification interface, therefore, is solute rich and the last material to

FIGURE 4.10.2 Different mold configurations produce different grain growth.


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solidify may be highly enriched in solute. This solute-rich material has a lower melting point and poorermechanical properties, which can lead to hot shortness as well as intergranular melting in the cast part.

Changes in the temperature gradient within the liquid can have a significant effect on the form anddegree of segregation in the cast part. By adjusting the heat transfer from the mold, the degree ofconstitutional undercooling (∆Tc) can also be changed, with a direct effect on the form of the solidificationinterface and on the microstructure of the final cast part. Figure 4.10.4 shows how segregation could beaffected by the cooling rate. A higher cooling rate results in less segregation due to a shorter mixingtime. The converse is true for a lower cooling rate.

Small ∆Tc, which can be related to rapid cooling from enhanced heat transfer, results in cellulargrowth with small ridges being formed on the leading edge of the planar solidification interface(Figure 4.10.5). A moderate ∆Tc results in dendritic growth and, subsequently, in a columnar grainstructure (Figure 4.10.6), while large ∆Tc can lead to finer dendrites that may result in a transition fromcolumnar to equiaxed grains (Figure 4.10.7). At very large levels of ∆Tc, independent nucleation resultsand equiaxed grains grow, imparting more uniform properties on the casting (Figure 4.10.8). Alloys withwide freezing temperature ranges and slow freezing favor large ∆Tc. Thus, by adjusting the heat transferof the process, the growing grain structure can be modified. Unfortunately, as the melt solidifies againstthe mold wall, the heat transfer characteristics of the mold are affected. In a real metal alloy casting,grains are often of mixed form due to changing ∆Tc. Consequently, the properties of the casting changefrom the mold wall toward the center of the casting.

In addition to the variations seen in the as-cast grain structure, changes in the amount of ∆Tc relatedto variations in heat transfer also result in varying degrees of segregation within the casting. Segregation

FIGURE 4.10.3 Constitutional undercooling, ∆Tc.

FIGURE 4.10.4 Effect of growth rate on segregation: (a) shorter mixing time, less solute segregation, (b) longermixing time, more solute segregation.


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FIGURE 4.10.5 Small ∆Tc results in cellular growth.

FIGURE 4.10.6 Moderate ∆Tc leads to dendritic growth.

FIGURE 4.10.7 Large ∆Tc results in transition to independent nucleation.


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across the dimension of a grain, or microsegregation, can usually be eliminated using a post-castinghomogenization heat treatment. However, if a homogenizing heat treatment is not performed, problemssuch as in-service galvanic corrosion, embrittlement, or hot shortness may result. A composition gradientover large distances is termed macrosegregation and leads to nonuniform properties throughout the castsection. These nonuniform properties can lead to variations in the response to heat treatment and cancarry over manufacturing problems to the wrought products. If macrosegregation exists, then changesto the casting alloy, or a reduction in cast section size is required.

Residual stresses can also result from thermal gradients within the casting. Materials of high thermalconductivity will show lower thermal gradients, resulting in a lower susceptibility to the generation ofharmful residual stresses. Unaccounted-for residual stresses can lead to cold cracking, or if less severe,to the buildup of internal stresses which may later lead to component distortion. Typical solutions torelieve the effects of residual stresses involve slow cooling rates or potentially a stress relief anneal. Ineither case, low heating and cooling rates are necessary.

Primary Processes

Primary casting processes are used to produce simple shapes and cast billets and ingots, which can thenbe reformed into other shapes for final use. The shapes may be remelted or may be formed to final shapeby other means, such as deformation processing. Primary casting processes have evolved during the pastseveral decades from a batch mode to continuous casting operations. Due to the high volume of castmaterial produced via continuous casting, quality issues have become very important. To improve thequality of continuous-cast materials, there has been significant modeling during the past decade. Thesenumerical models generally account for both the heat transfer and fluid flow within the solidifyingmaterial.

During solidification thermal gradients play a critical role in the generation of the cast microstructure.Thus, by adjusting the heat transfer of the molds, and the process, the microstructure can be readilyaffected. While this is true in all castings, it becomes very important in continuous casting processesbecause of the short periods of time available for solidification. Researchers have developed relativelycomplex numerical models which predict the temperatures and temperature gradients throughout thesolidifying material. Heat transfer models, which include the mold material, the air gap, flux, thesolidifying shell, and the molten metal, are used to improve the quality and reproducibility of continuous-cast sections. Quality is important at this stage of processing because defects that are introduced duringsolidification may cause major problems throughout the post-processing operations and can lead tosignificant lost production.

Secondary Processes (Shape Casting)

There are many forms of shape casting practiced today. However, for the purposes of this section, shapecasting may be separated into gravity-fed vs. pressure-fed molding. Pressure-fed processes are often

FIGURE 4.10.8 Very large ∆Tc leads to independent nucleation.


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used in the molding of parts with relatively thin sections which would be difficult to fill adequately bygravity. Even though cooling rates of small pressure-fed, die cast components can be very high, thesolidification front often takes on a dendritic nature. Yet, rather than acting as impediments to the inflowof molten metal, these dendrites are broken free by the pressure and act as independent nuclei, resultingin fine-grain, as-cast structures. Also, because fresh liquid metal is continually forced into the die inthese pressure-fed castings, shrinkage and shrinkage porosity become less of an issue.

In gravity-fed shape casting, mold filling and shrinkage porosity become greater potential problems.Shrinkage porosity generally results when ∆Tc is high and the mold design forces shrinkage to occur ina location which is not adjacent to fresh liquid metal. To overcome these problems, changes in the moldmaterial, additions of chills or insulated regions, or design changes to the size and shape of feederswhich supply fresh liquid metal may be necessary.

Corrective Measures for Shrinkage Porosity

One approach to overcoming shrinkage porosity is to increase the freezing rate of the metal. This isdone by adjusting the heat transfer of the mold, or of localized regions of the mold, to reduce the degreeof ∆Tc. This results in a localized shrinkage, which can then be dealt with by other means.

Another solution for solidification shrinkage is the use of risers, or feeders, such as that shown inFigure 4.10.9(a). The riser provides added hydrostatic head during the freezing of a casting and is thelast location to freeze. In this way, the final material to freeze remains completely in the riser and theassociated shrinkage cavity is also contained in the riser. The riser is subsequently cut from the castingand remelted. The design of a riser is based on the simple principle that the freezing time of a castingin a homogeneous mold is proportional to the square of the ratio of the volume of metal to the totalmold/casting interface area [(V/A)2]. This relationship is readily derived from heat transfer modelingand is verified experimentally.

Modifying the mold using a special insulated sleeve around the riser region to delay its solidificationcan reduce riser size. For complex shapes, or large shapes, multiple risers as shown in Figure 4.10.9(b)may be required to overcome “center line” shrinkage porosity if ∆Tc is large. The larger ∆Tc, the greaterthe number of risers that will be necessary. For castings with large section changes, and thick sectionsseparated by thinner sections, each of the heavy sections will require a riser. In general, casting designis based on the ability to solidify in a specified manner, and since solidification is highly dependentupon heat extraction, large section changes can pose severe difficulties. In certain cases of mold andpart design, a chill can effectively replace a riser. A chill such as that illustrated in Figure 4.10.9(c) canbe used in localized hot spots. It can also be applied to generate directional grain structures duringsolidification.

Welding

Welding processes can be subdivided into categories dependent upon whether the base metal melts andbecomes part of the joint material, or is joined without melting by the addition of a filler material. Ifthe base metal does melt, the joint is considered a fusion weld and the parent materials, plus any fillermaterial, mix and solidify in the “fusion zone.” In this case many of the same concerns related to heattransfer which were considered in the discussion of casting, also apply. However, in addition to theeffects in the fusion zone, it is also important to realize that a broader region of the parent material isexposed to high temperatures and to significant thermal gradients. This region outside the fusion zone,but still affected by the thermal processing, is called the heat-affected zone (HAZ). To better understandthe role of heat transfer in the welding of metals it is necessary to discuss the effects in both the fusionzone and the HAZ.

Heat Input

Unlike the solidification of castings which start out with a relatively uniform material temperature,welding processes transfer the heat into the material in a localized fashion. Therefore, heat is transferred,in a welding process, from the weld region into the remainder of the part, or parts, being welded. This


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means that relatively large thermal gradients can occur over a single component. The resulting thermalgradients can be extremely steep depending upon the rate of heat energy input and the thermal mass ofthe complete component.

Fusion Zone

Many welding processes are considered fusion processes. Fusion welding processes include stick weld-ing, torch welding, TIG, MIG, electron beam, laser beam, and others. For each of these processes theheat source is sufficient to melt a region of parent material, which must then resolidify in a way verysimilar to that of a casting. During the solidification of the fusion zone an as-cast microstructure isdeveloped which follows the same trends as discussed in the previous subsection on casting. Grainsonce again grow along the direction of heat flow and, in general, are relatively large and columnar. Thefusion zone microstructure can be adjusted through changes in the cooling rate; however, this is a moredifficult variable to control in welding processes than in casting. Approaches to controlling the thermalgradients include pre- and post-heating of the parent materials.

FIGURE 4.10.9 Different mold geometries for controlling porosity and grain growth: (a) incorporation of a riser,(b) use of multiple risers, and (c) combination of a riser and a chill.


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Details affecting the size and shape of the fusion zone are strongly dependent upon the type of weldingprocess and its inherent energy transfer capability. Very high-energy processes such as electron beamwelding enable relatively narrow and deep fusion zones. In such high-energy processes, the thermalenergy is highly focused. Both the fusion zone and the HAZ are relatively small. However, the thermalgradients introduced can be quite large. For these high-energy processes the microstructure in the fusionzone represents a more rapidly cooled as-solidified structure, with the potential of finer grain size. Open-flame welding, or torch welding, employs a much lower energy source. As a result, temperature gradientsare smaller but the ultimate temperatures at a distance from the fusion zone are higher. It follows thatthe extent of the HAZ and the region of affected parent microstructure become large.

Heat-Affected Zone

In all fusion welds there is a region around the weld zone where the parent metal has been heated, inthe solid state, to temperatures sufficient to cause structural and property changes. This region is calledthe HAZ. Heat transfer in the HAZ of a welded component determines the temperature profile andcooling rates. Based on the knowledge, or prediction, of the temperature profiles and cooling rates,microstructural variation can be estimated. Prediction of the form of the changing microstructure canthen be used to determine if metallurgical problems are to be expected, and whether welding processmodifications must be made. The extent of the HAZ is dependent upon many factors, including the heatsource energy, the thermal mass of parent material, the thermal conductivity of the parent, and theworkpiece geometry.

The impact that the varying temperatures and cooling rates of the HAZ have upon the materialmicrostructure is dependent upon the parent material and its pre-weld condition. For instance, two purealuminum plates might be joined by MIG welding. The resulting microstructural variation across theweld zone and the HAZ is shown schematically in Figure 4.10.10.

As indicated in the Figure 4.10.11, the microstructural variation can be quite severe, with yieldstrengths dropping to levels below half that of the unaffected parent. While this microstructure is highlyaffected by the welding process, the performance change is relatively uniform from the center of thefusion zone outward, not showing any localized regions of severely degraded properties. However, theresulting microstructure is directly related to the type of strengthening mechanisms available in thematerial and, therefore, to the material itself. Thus, it is useful to discuss some specific cases in whichthe effects in the HAZ can become quite deleterious, with the potential for localized failure. In additionto cold working, other common strengthening mechanisms should be discussed. Many aluminum alloys

FIGURE 4.10.9 (continued).


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are strengthened via precipitation hardening. The majority of steels are strengthened by phase transfor-mation effects related to quenching and the resulting variations on a Martensite structure.

For a material such as aluminum, which is precipitation hardened, mechanical property variationbecomes more complicated. Property degradation in precipitation-hardened alloys generally results fromexcessive exposure to elevated temperatures, leading to over-aging and the loss of strength. Since bothtime and temperature play an important role in the resulting mechanical properties, knowledge of thethermal history is critical. The minimum strength is seen in the HAZ, due to an optimal combination ofboth peak temperature and the time at that temperature. In this case the over-aging is most severe andit is not uncommon to see weld failures in the HAZ. Figure 4.10.12 indicates the variation of strengthand ductility moving from the center the fusion zone toward the affected precipitation-hardened parent.It should be noted that the low strength in the fusion zone could often be combated through the selectionof suitable filler metal.

Low-alloy carbon steel responds somewhat differently to the temperature profile within the weld zone(Figure 4.10.13). Again, choosing a higher-performance alloy as a filler metal can often enhance thefusion zone performance; however, effects in the HAZ are more difficult to control. The most basiceffect noted is similar to that of the cold-worked case where the grain size is quite large in the HAZnear the fusion zone resulting in relatively low strength. However, since no cold work was included, thegrain size variation is relatively uniform, ranging from large grains at the fusion interface to relativelyfine grain as the unaffected parent is approached. The secondary effect for this low-alloy carbon steelis related to the onset of the Martensite transformation, due to high cooling rates in HAZ. Since thecooling rate is highly dependent upon the relative ease of heat transfer, the extent of the transition toMartensite will be determined by many factors including parent thickness, thermal conductivity, andgeometry. If cooling rates within the HAZ are sufficiently high and cause Martensite to form, this regionwill be highly embrittled and very susceptible to weld failure. Thus, it becomes obvious that knowledge

FIGURE 4.10.10 Variation of microstructure in heat-affected zone (cold-worked aluminum).


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of the peak temperatures, thermal response time, cooling rate, and material composition throughout theHAZ is necessary.

Thermal History

To predict the deleterious effects of welding heat on the parent material microstructure, and, therefore,performance, it is necessary to investigate the thermal history. Specifically, the important componentsof the thermal history are maximum temperature attained, thermal response time, and the heating andcooling rates. Since heat input is highly localized, heat transfer into the parent material is affected bythe rate and direction of the welding operation. Conceptually, Figure 4.10.14 indicates an instantaneoustemperature distribution in a thin metal plate during fusion welding. The “F” refers to the fusion zone.It is important to realize that the isotherms are not centered on the fusion zone due to the travelingvelocity along the welding direction. This also means that the temperature gradients are steepest at theleading edge of the weld. On the trailing edge of the weld the solidified weld bead is still a source ofheat, flowing outward into the parent material.

Heat transfer theory permits a prediction of thermal history through use of appropriate models of thewelding process, starting from the equation for 3-D heat conduction in a homogeneous, isotropic solid:

(4.10.1)

where α = thermal diffusivity = .

FIGURE 4.10.11 Mechanical property variation in the heat-affected zone (cold-worked parent).

∂∂

+ ∂∂

+ ∂∂

= ∂∂

2

2

2

2

2

2

1Tx

Ty

Tz

Ttα

k thermal conductivity

c specific heat density( )

( ) ( )ρ


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FIGURE 4.10.12 Mechanical property variation in the heat-affected zone (precipitation-hardened parent).

FIGURE 4.10.13 Mechanical property variation in the heat-affected zone (low-alloy carbon steel).


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Solutions of this equation are available for a variety of models assuming infinite or semi-infiniteplates. Two cases of interest are the moving point source of heat and the moving line source of heatdiscussed next.

Moving Point Source of Heat

The moving point source is a reasonable description of welding thick sections, or for depositing a weldbead on a plate (see Figure 4.10.15). Relative motion between the source and the plate, in the x-direction,at a velocity, v, is assumed. By applying symmetry to the steady-state solution for a constant rate of

FIGURE 4.10.14 Temperature distribution in a metal plate during fusion welding.

FIGURE 4.10.15 Moving point heat source.


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heat input, q, and an infinite medium (Carslaw and Jaeger, 1959), one can obtain the following steady-state solution for a semi-infinite medium bounded by the plane z = 0

(4.10.2)

where r = and To is the initial temperature. In arc welding processes,

where E = the welding voltage and I = the welding current. Values of vary based on the process andthe heat source. For stick welding, ranges from approximately 1 to 3 kJ/mm, while for a weldingprocess such as electroslag welding, the value can exceed 100 kJ/mm.

Moving Line Source of Heat

For modeling thin sections, a line source of heat is much more appropriate because the heat input isuniform throughout the thickness. This approach would model a single-pass butt weld in thin sheet. Inthis case, the problem is 2-D heat flow with substantial heat transfer only in the x and y directions(Figure 4.10.16). Again, the steady-state solution can be generated (Carslaw and Jaeger, 1959) as

(4.10.3)

where K0(z) is the modified Bessel function of the second kind of order zero.

Solutions are also available for intermediate geometries, and for stationary heat sources that mightbe used in modeling spot-welding. The solutions are limited by the fact that the heat source is not trulya point or a line, requiring an offset of the origin. They are also limited by the thermal properties of thematerial (k, ρ, c) that vary with temperature, and that the workpieces are not semi-infinite. Yet, theexpressions still result in reasonably good agreement with experimental data. Computer solutions canovercome most of these limitations and generate quite complex models, allowing improved accuracy,particularly in modeling complex geometries.

FIGURE 4.10.16 Moving line heat source.

T Tqkr

v r x−( ) = π− −( )

0 2 2

expα

x y z2 2 2+ +

qEIv

∝

EIνEI

ν

T Tq

kK

vr vx−( ) = π

0 02 2 2α α

exp


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Summary of Thermal Effects

Heating and Cooling RatesAs indicated previously by the closer spacing of the temperature isotherms, heating and cooling ratesare at their maximum at the downstream edge of the fusion zone. Heating and cooling rates increasewith welding speed, ν, and with higher heat input and a correspondingly smaller fusion zone. Forinstance, in arc welding, the cooling rate is inversely proportional to heat input, ΕΙ/ν. In addition, materialswith high thermal conductivity also show increased rates of heat dissipation in the parent material. Thisresults in the need for higher-energy heat sources. Furthermore, higher thermal conductivity results ina larger HAZ. Heat-affected zones in conductive materials such as copper can extend four to five timesbeyond that of typical HAZ in steel.

Other material properties such as the coefficient of thermal expansion can also have a significanteffect on the success of welding operations. Higher thermal expansion coefficients result in the generationof high stresses that are conducive to distortion and to cracking in crack-sensitive alloys.

Distance from Weld AxisThe peak temperature, as well as heating and cooling rates, decrease with increasing distance from theweld axis. For any given location, the peak temperature increases with the rate of heat input, q, but thecooling rate decreases with increasing heat input.

Section Size and Weld GeometryAs the parent material section increases in size the effective heat sink is also increased. Therefore, highertemperature gradients result, but the time at peak temperature is reduced. For more complex geometries,such as fillet welds (T or L joints), there are additional paths for heat flow, and the part is a more effectiveheat sink due to the geometry. Finally, it should be noted that the geometry changes from a 2-D to a3-D heat flow with increasing thickness.

To account for the changing section and geometry the concept of a thermal severity number (TSN)is often introduced, where TSN = combined thickness of heat flow paths (inches) × 4. To visualize theeffect of section size and weld geometry using the TSN, consider that a butt weld joining two 0.25-in.-thick plates results in a TSN of 2, while a fillet weld joining a 1-in.-thick plate to a 2-in.-thick plateresults in a TSN value of 20. Obviously, the temperature gradients for the fillet-welded joint of thethicker plates would make the joining operation more challenging. It should also be noted that joininga thin plate to a thick plate is a more difficult problem due to the greater “heat sink” effect of the thickplate. Consequently, increased heat input is required and it has the negative effect of rapidly meltingthrough the thinner material. This can be a difficult welding operation, but preheating the thick platecan alleviate the problem.

Pre- and Post-Heat Treatment of WeldsAs has been discussed, thermal gradients introduced by the welding operation can have significant effectson the parent material, and ultimately on the product success. To ensure acceptable performance of thecompleted joints additional operations can be performed, either in preparation for welding or after thewelding process is complete. Post-welding heat treatments can be used for practically sized fabricationsto readjust the microstructure of the component. This can be quite a good approach, particularly forsteels, where the performance can be modified through phase transformation.

Another often-used technique to reduce thermal gradients is to preheat the parent metal prior towelding. By increasing the base temperature, thermal gradients are reduced and the thermal severity islessened. This approach can be very effective for materials that are sensitive to rapid cooling, but arenot significantly affected by extended times at temperature. Again, for steels this can be an effectivesolution to welding problems. Multipass welds can often result in microstructures resembling those ofpreheated materials.


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Heat Treatment

The term heat treatment is used to describe a variety of processes that are applied to modify the propertiesof metals with the goal of generating improvements in hardness, strength, ductility, or toughness. Onething that all heat treatments have in common is that they all rely on the transfer of heat to or from theworkpiece material. Heat treatments can be subdivided into two categories, nonhardening thermalprocesses and hardening processes (Mangonon, 1999). Depending upon the specific heat treatment,different aspects of thermal processing must be controlled. Nonhardening processes generally rely onrelatively long times at temperature and are often considered isothermal processes, while it is morecommon that the control of thermal gradients is critical in the application of the principles of heat transferfor hardening processes.

Nonhardening Thermal Processes

Nonhardening thermal processes include processes such as thermal stress relief, annealing, and normal-izing. Residual stresses can be generated by many manufacturing processes, ranging from casting andwelding to mechanical deformation. Such stresses can lead to component distortion, cracking, stresscorrosion, and in some cases delayed failure. By holding the workpiece at an elevated temperature theinternal stresses diminish. Thermal stress relief consists of uniformly heating the workpiece to a tem-perature below the recrystallization temperature, in the recovery range, holding it for a predeterminedperiod of time related to the severity of the stress state, and then uniformly cooling it. As in allnonhardening thermal processes, temperature gradients are to be minimized and the processes aretypically considered isothermal.

An annealing heat treatment is performed to soften a material after significant amounts of cold workhave been performed. This softening may be desired to enable further mechanical working, or to adjustthe metallurgical properties for a specific application. Annealing is performed at temperatures above therecrystallization temperature and results in a softer, more equiaxed grain structure. The process, likethermal stress relief, involves relatively slow heating and cooling, with the time at optimum temperatureused to control the final grain structure and size. Long periods of time at high temperature lead to thefully annealed condition, while shorter times at the same temperature can be said to yield subcriticalannealing. The temperatures required for such a heat treatment are often given based on equilibriumheating and cooling rates. Since real processes do require finite heating and cooling rates, it must benoted that the critical temperatures will be shifted up with increasing heating rates and down withincreased cooling rates.

Normalizing is a term generally reserved for discussions regarding steels. In this nonhardening heattreatment, the cooling rate is specified as natural or air cooled. A normalized steel generally exhibits auniform fine-grained microstructure which enhances its homogeneity and the machinability; the normal-ization process is often applied after a shape has been generated by casting or forging. The strength andhardness of a normalized steel may either increase or decrease, depending upon the prior state of theworkpiece material.

Hardening Heat-Treating Processes

Hardening heat treatment processes are only applicable to materials which show multiple phases at lowtemperature, can be locked into a nonequilibrium microstructure by rapid cooling, and can be driventoward a desirable microstructural state during subsequent heating. The results of such a sequence aregenerally considered the principal strengthening approaches for metals. For steels, the Martensitictransformation is critical and is driven by the ability to rapidly cool the workpiece, generating thenonequilibrium structure, Martensite. Other materials, such as aluminum, are strengthened through amechanism described as precipitation hardening, and still others grow stronger by solid solution strength-ening. However, the ability to lock in the nonequilibrium structure and then subsequently adjust thematerial microstructure via thermally induced diffusion is shared among these hardening heat-treatmentprocesses.


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For carbon steels it is critical to be able to generate high cooling rates to inhibit equilibrium phasetransformation. Rapid cooling results in the generation of Martensite, an exceedingly hard and brittlenonequilibrium structure. A subsequent tempering heat treatment yields performance and microstructureswhich are otherwise unobtainable. This approach enables a combination of high strength and toughnesswhich are not possible through equilibrium processes and is the basis for the application of steel as theprincipal structural material in modern engineering design.

Since high cooling rates are critical in quench and temper processes, the transfer of heat from theworkpiece to the surroundings is important. Continuous cooling transformation (CCT) diagrams, suchas that shown in Figure 4.10.17, are used to determine necessary cooling rates. While attaining criticalcooling rates in thin sections is reasonably easy, the actual cooling rate in thicker sections varies withposition within the workpiece material. Changes in the cooling medium, and, therefore, the surfacecooling rate, can only be used to accomplish a certain degree of improvement in the depth of hardening.To ultimately improve the hardenability, it is generally necessary to choose an alloy developed to havea high hardenability, or in other words, a material that can be fully hardened at relatively slow coolingrates. Steels with increased carbon content, such as 1080 vs. 1034, and for even thicker sections of high-alloy contents such as 5140 and 9261, result in CCT curves that are shifted to the right, thus allowingslower cooling rates to still attain Martensite (see Figure 4.10.18). Tempering of this Martensite, underthermal conditions that are again often modeled as isothermal, results in a fine distribution of carbides

FIGURE 4.10.17 Continuous cooling transformation for 8630 steel. (From ASTM Handbook, Vol. 4, AmericanSociety for Testing and Materials, West Conshohocken, PA, 1991. With permission.)


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© 2000 by C

RC

Press LL

C

eel. (From ASTM Handbook, Vol. 4, American
FIGURE 4.10.18 Comparison of continuous cooling transformation showing the effect of increasing carbon content stSociety for Testing and Materials, West Conshohocken, PA, 1991. With permission.)

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which, by interfering with dislocation motion, increase the toughness and serviceability of the materialwithout sacrificing the strength.

Aluminum alloys are often heat-treated in a fashion similar to that of steel; however, the specifics ofthe microstructural changes are quite different. In precipitation-hardened aluminum alloys, the workpieceis quenched from the single-phase region in the same way as during the heat treatment of steel to lockin a nonequilibrium microstructure. However, the resulting nonequilibrium aluminum structure is a softand supersaturated solid solution, unlike the hard and brittle Martensite formed during the thermalprocessing of steel. Yet, it is still critical that this nonequilibrium structure be obtained throughout thecomplete workpiece section. In this case, the enhanced thermal conductivity of aluminum aids in allowinglarger sections to achieve satisfactory cooling rates. The supersaturated solid solution of Al-Cu and Al-Si alloys is then heated to an elevated temperature within the two phase region and held isothermallyfor a period of time to allow the development of a fine, coherent precipitate. These hard precipitatesinterfere with dislocation motion and result in substantial strengthening of the aluminum. This is thebasis of modern high-performance aerospace aluminum alloys, first developed in the early 1900s andwhich contributed to the success of the lighter-than-air rigid airships, the dirigibles.

In both the steel and aluminum cases described, increased times of heat treatment for the quenchedmaterial results in undue microstructural change and diminished mechanical properties. This is consid-ered over-aging in the precipitation-hardened aluminum alloys and leads to reduced strength and ductility.Since aging temperatures for aluminum alloys are relatively low, usually in the range of 200°C, theuseful upper temperature of these alloys is also limited. Extended use at temperatures even just above135°C can lead to substantial performance drops in a matter of weeks for an aluminum alloy such as2014 (see Figure 4.10.19).

Considerable information about heat treatment is available through many sources, including theAmerican Society for Testing and Materials (ASTM, 1991), that can be consulted to determine thespecific parameters required to generate final material properties and to understand the hardenability ofindividual materials. These sources typically include CCT diagrams for common materials and discussheat treatment trends for specialized materials not typical of larger material families.

FIGURE 4.10.19 Thermal history of a precipitation-hardened aluminum alloy. (From Mangonon, P.L., The Prin-ciples of Materials Selection for Engineering Design, Prentice-Hall, Englewood Cliffs, NJ, 1999. With permission.)


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Machining

Machining to shape and cutting can both be considered material removal processes. Traditional machiningprocesses remove material through mechanical processes. In these conventional material removal pro-cedures, heating and heat transfer is introduced at the tool/workpiece interface and is the result of thechip generation process. Nontraditional machining processes such as electrical discharge machining(EDM) or laser beam machining (LBM) also result in workpiece heating. For these noncontact processes,material is either eroded away by electric discharge or vaporized using LBM. Since very high heat fluxescan be present, high heating and cooling rates often result, and with them come metallurgical problemssuch as quench cracking (Kalpakjian, 1995). Thus, process parameters, including rates and power, mustbe determined based on the thermal properties of the workpiece to minimize the impact of such rapidheating and cooling.

In traditional metal removal operations localized heating of the workpiece and subsequent rapidcooling due to the thermal mass of the material can also result in surface character modification. Ingeneral, the surface is hardened by rapid cooling which can lead to surface cracking and spalling, or atleast to increased hardness and difficulty in further material removal. In steels, this surface hardening isoften referred to as a “white layer,” indicating the generation of Martensite due to the rapid cool-downafter the cutting tool has passed by. However, the effects of temperature on traditional machiningprocesses are probably often associated with decreased cutting tool life and associated cost increase.

Since the cutting tool must be harder than the workpiece under all conditions if workpiece materialremoval is to be successful, any thermal conditioning of the cutting tool which reduces its hardness willcompromise its useful life. The energy involved in the cutting process is highly localized at the cuttingtool tip and is primarily converted to heat. The heat generation rises rapidly as the cutting speed isincreased. Because of this, excess speed is always considered the biggest factor in decreased tool life.The heat generated is concentrated in the forming chip, especially at high cutting speeds. Since this chipis in direct contact with the rake face of the cutting tool as the material is removed, the adjacent toolmaterial temperature increases. The temperature increase of the rake face of the cutting tool can beapproximated by

(4.10.4)

where E = cutting energy and h is undeformed chip thickness.While cutting fluids can be used as a coolant to help increase tool life, the high pressures at the rake

face make the introduction of fluids as lubricants difficult. However, the introduction of cutting fluidsto cool the forming chip can be effective in maintaining lower tool temperatures. In many cases the onlysolutions to tool life maintenance are decreased speeds and enhanced cutting tool materials. Enhancedcutting tool materials are generally defined as materials that retain hardness at higher use temperatures.These can be steels with alloying ingredients which form more stable carbides, or may in fact benonmetallic cutting tool materials such as cermets and ceramics.

Tool life prediction is based on the speed, feed, and depth of cut, but changes in tool life are oftengiven as a power law relationship based strictly on speed due to much greater heating from speedincreases.

ut n = C (4.10.5)

where

u = cutting speed (m/min)t = tool life (min)C = cutting speed for 1 min of lifen is a characteristic of the tool material

T Evhk cT ≅

ρ

1 2


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In general terms the tool life relationship can include the effects of speed, feed, and depth of cut, as follows

(4.10.6)

where

n1 < n2 < n3

u = cutting speed (m/min)f = feed rate (m/min)w = depth of cut (m/rev)K = material-dependent constant

However, since n1 is generally significantly smaller than n2 and n3, speed is the controlling factor.Therefore, changes to cutting processes that reduce tool heating will increase cutting tool life.Figure 4.10.20 illustrates the relationship between the unit cost and cutting speed. There is a base costassociated with handling. Machining cost decreases with an increase in cutting speed because cuttingtime is reduced. Tool costs and tool changing costs are greater for higher cutting speed due to increasedwear. When all these costs are accounted for, there exist an optimum speed for minimizing the unit cost,as shown in the diagram.

Deformation Processing

Bulk deformation processes such as forging, extrusion, and rolling can be carried out at either cold-workor hot-work temperatures. However, in the majority of cases the processes are considered isothermal

FIGURE 4.10.20 Dependency of unit cost on cutting speed. (From DeGarmo, E.P., Black, J.T., and Kosher, R.A.,Materials and Processes in Manufacturing, 8th ed., Prentice-Hall, Englewood Cliffs, NJ, 1997. With permission.)

tK

u f wn n n= 1 1 11 2 3


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and heat transfer is not a primary issue. In hot-work processing, the heat is used to lower the flow stressof the workpiece and to reduce the amount of force required to generate the necessary deformation.Under hot-work conditions attention does have to be paid to the temperature increase in the equipmentperforming the mechanical deformation. If the tooling temperature is the same as the workpiece tem-perature, the process is considered isothermal.

One concern related to heat transfer in deformation is the efficiency of working and the heat rise thatcorrespond to low process efficiencies. To reshape a material, plastic deformation must be accomplished.Therefore, the work going to plastic deformation is desirable. However, elastic work, redundant work,and work to overcome friction also exist. Thus, efficiency of working can be described in terms of thedesired work vs. the total work performed. Efficiency is then

(4.10.7)

where

UPL = plastic workUEL = elastic workUf = work to overcome frictionUφ = redundant workUT = total work

Processes range in efficiency from roughly 20% for extrusion, which exhibits large amounts of redundantwork and frictional work, to 90% for cold rolling. Of these work contributions, the sum of the plasticwork, the frictional work, and the redundant work primarily result in heat generation. It is usual practiceto consider that the work expended to overcome friction leads to heating of the tooling, while adiabaticheating of the workpiece is related to the plastic and redundant work contributions. Based on theseassumptions, the maximum theoretical temperature rise of the workpiece can be computed as

(4.10.8)

where J = 4.18 Nm/cal. From this equation, a maximum theoretical temperature rise of as much as280°C can be generated in an aluminum workpiece and as much as 570°C in titanium. Such temperaturerises are of greatest concern during hot work operations because they can lead to localized melting ofthe workpiece. Finally, it should be noted that as the working velocities and strain rates increase, lesstime will be available for heat transfer away from the working zone and localized melting will becomemore of a concern.

Plastics Molding

Processing of plastics generally involves thermal energy. Unlike metallic materials, plastics have poorthermal conductivities. This can result in a large heat buildup in the material and can lead to problemsof excessive localized shrinkage and possible material degradation. The specific effects of heat buildupdepend on whether the plastic is a thermoset or a thermoplastic.

Thermoplastics Processing

Thermoplastics are polymers that do not cross-link and, therefore, can be reheated and remelted manytimes. Polymers, including polyethylenes and polyetherimides, are thermoplastics. Heating reduces theviscosity of these materials and allows them to be molded at elevated temperatures and then cooled tolock in the new shape. The primary heat-induced problems that can be encountered in processing

ηφ

=+ + +

=U

U U U U

U

UPL

EL PL f

PL

T

∆TU U

cJPL=+ φ

ρ


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thermoplastics are related to regions within the parts that have significant differential volumes. Theregions of greater volume cool more slowly and thus, as in casting metals, results in localized shrinkageand even fracture. Typical solutions revolve around mold redesign to reduce the section variation.

In general, cooling rates are not of great consequence in the processing of thermoplastics as long asthe molds and part shape are correctly designed. However, some thermoplastics are semicrystalline innature. For these thermoplastics, cooling rates define the degree of crystallinity, which in turn determinesmany of the mechanical and physical properties of the resulting polymer component. Enhanced crystal-linity often leads to improved chemical resistance, enhanced mechanical property retention at elevatedtemperatures, and even higher absolute mechanical performance. Unfortunately, generating controllableamounts of crystallinity is often difficult in practice and as a result many semicrystalline polymers aremodified to change the kinetics of the reaction and decrease the likelihood of crystalline transformation.

Thermoset Processing

Thermosets are polymers that are cross-linked during processing. The cross-linking results in a materialthat cannot be remelted and reprocessed and, as a result, must be molded to final shape. Polymers suchas phenolics, epoxies, and vinylesters are examples of thermosets. Thermosets may be processed at roomtemperature or at elevated temperatures, depending on the specific material and the form of the reactionthat leads to cross-linking. During cross-linking, heat is evolved. Since these polymers have inherentlypoor thermal conductivity, the temperature rise due to cross-linking, particularly in a large volume ofthe material, can lead to thermal degradation. To slow such rapid exothermic reactions, cures are in somecases carried out at reduced temperature. However, as the materials are spread over larger areas, suchas thinner films or as matrix materials in composites, heat transfer out of the material is more rapid andthe peak temperatures drop to manageable levels.

Again for thermosets, increased temperatures generally lead to added shrinkage. For a specific polymer,the degree of shrinkage is generally enhanced with increased cure (cross-link) rates. Thus, cure ratesare generally controlled to minimize shrinkage and property degradation, while still keeping processtimes to a reasonable duration. Much research has been performed on thermoset curing as these materialsform the basis for the vast majority of polymer matrix composites in service today.

Thermal Spray Deposition

Thermal spray is a method to create protective surface coatings or alter surface properties. Near net-shape manufacturing can also be accomplished using this technique. Typically, liquid droplets are sprayedonto a substrate. Solidification of the droplets could take place partially during flight or entirely afterthey have arrived at the substrate. Due to the momentum of the droplets, splats are formed upon impactof the droplets. The shape of the splat is affected by the properties of the droplet, surface roughness,and substrate temperature. There is experimental evidence that low substrate temperatures result in star-shaped splats, whereas high substrate temperatures (400°C) produce disc-shape splats (Dykhuizen, 1994).The size of the splat directly impacts the coating thickness as well as the coating properties. Dykhuizen(1994) reviewed splat size models developed before 1994. Madejski (1976, 1983) presented models thataccounted for surface tension and solidification. Recently, Zhang (1999) developed a model that accountsfor the effects of thermal contact resistance as well. Zhang’s model can be summarized as follows

(4.10.9)

where ξm is the flattening ratio defined as the splat radius compared to the droplet initial radius (Ro).The Reynolds number is defined as Re = with vo and µ being the initial droplet velocity andviscosity, respectively. The Weber number is defined as We = where σl is the surface tension ofthe melt. In Equation 4.10.9, ω is a constant that assumes values between 0.6 and 1.0 and S is given as

11 18

3 1 1

1 151 0

5 2 2 5

Re . ..

.ξ ξω ξm m m

m

WeS

+−( ) −( )

+

=

2ρνo oRµ 2

1

ρνσo oR


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where ks and kl are the thermal conductivities of the deposited layer and the melt, respectively. The Jacobnumber, Ja, is defined as

where Tf and Tsi are the fusion temperature and the initial substrate temperature, respectively, and hfg isthe latent heat of vaporization. The Prandtl number, Pr, is defined as Pr = with νl and αl being thekinematic viscosity and thermal diffusivity, respectively, for the melt. The coating thickness is given by

(4.10.10)

where R″t,c is the thermal contact resistance, and t is time. Equations 4.10.9 and 4.10.10 are the twoequations that can be used to estimate the splat size and the coating thickness.

References

Heat Treating, in American Society of Testing and Materials Handbook, Vol. 4, West Conshohocken,PA, 1991.

Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, 2nd ed., Oxford University Press, Oxford,1959.

DeGarmo, E.P., Black, J.T., and Kosher, R.A., Materials and Processes in Manufacturing, 8th ed.,Prentice-Hall, Englewood Cliffs, NJ, 1997.

Dykhuizen, R.C., Review of impact and solidification of molten thermal spray droplets, J. Thermal SprayTechnol., 3, 351-361, 1994.

Kalpakjian, S., Manufacturing Engineering and Technology, 3rd ed., Addison-Wesley, Reading, MA,1995.

Mangonon, P.L., The Principles of Materials Selection for Engineering Design, Prentice-Hall, EnglewoodCliffs, NJ, 1999.

Madejski, J., Solidification of droplets on a cold surface, Int. J. Heat Mass Transfer, 19, 1009-1013, 1976.Madejski, J., Droplets on impact with a solid surface, Int. J. Heat Mass Transfer, 26, 1095-1098, 1983.Zhang, H., Theoretical analysis of spreading and solidification of molten droplet during thermal spray

deposition, Int. J. Heat Mass Transfer, 42, 2499-2508, 1999.

SJa k

ks

l

=

2RePr

Jac T T

hf se

fg

=−( )

να

l

l

sk R

R

k R

RS ts t c

o

s t c

o

= −′′

+

′′

+, ,

2

2


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4.11 Pinch Point Analysis

Kirtan K. Trivedi

Introduction

Many industrial processes require addition and removal of heat to streams within the process. This isnotably the case in the chemical process industry and power generation. In the chemical process industry,raw materials are heated or cooled to the appropriate reaction temperature. Heat may be added or removedto carry out the reaction at the specified condition of temperature and pressure. Heat addition and removalachieve product separation. The products may be heated or cooled to the correct temperature for storageand transportation. Normally, for a large petrochemical complex cogeneration scheme with a condensingcycle or a combined cycle is used to provide external heat and power required for the site. In the utilityplant, air, demineralized water, and boiler feed water streams need to be heated and the flue gas andcondensate streams need to be cooled. Thus, at all times heat is either added or removed in a variety ofprocess streams by utilities or by heat exchange between process streams. In an integrated plant this isnormally achieved with a heat exchanger network (HEN). A large fraction of the capital cost of manyprocess plants is attributed to heat recovery networks.

The aim of a designer is to synthesize a near-optimal configuration for a process. This indicates thata proper trade-off between the capital invested and the operating cost of the plant should be achieved.The capital cost depends on the type, number, and size of units utilized to satisfy the design objectives.A substantial part of the operating cost usually depends upon the utilities consumed. To reduce thesecosts, the process designer should aim for an economic combination having a nearly theoretical minimumnumber of heat exchanger units and aim to recover the maximum possible heat with them. An obviousway to recover heat is by exchanging it between hot process streams that need to be cooled, and coldprocess streams that need to be heated, in addition to the heating and cooling utilities. Furthermore, thedesigner should also investigate the operability of the final design.

The above objectives can be achieved by synthesizing a good heat exchanger network. However, avery large number of alternatives exist. Because of this, it will be highly rewarding to synthesize quicklyand systematically the best possible alternatives. It is now possible to do this with the aid of PinchTechnology.

Pinch technology refers to a large and growing set of methods for analyzing process energy require-ments in order to find economically optimal and controllable designs. Considerable development hastaken place in pinch technology during the past 2 decades, mainly due to the efforts of Linnhoff andcoworkers.1 Pinch technology has proved to be effective and is successfully applied to process integrationthat encompasses overall plant integration including heat exchanger networks and heat and powerintegration or cogeneration. To date, there are 65 concepts used by this technology. However, due to thelimited scope of this section, only the fundamental concepts are discussed here.

Industrial applications of this technology include capital cost reduction, energy cost reduction, emis-sions reduction, operability improvement, and yield improvement for both new process design andrevamped process design. Imperial Chemical Industries (ICI) where this technology was first developed,reported an averaged energy saving of about $11,000,000 per year (about 30%) in processes previouslythought optimized. The payback time was typically in the order of 12 months. Union Carbide showedeven better results. Studies conducted by Union Carbide on nine projects showed average savings of50% with an average payback period of 6 months. Savings in energy cost of about $8,000,000 per yearwas achieved by Union Carbide on these nine projects. BASF reports energy savings of 25% obtainedby application of pinch technology to their Ludwigshafen site in Germany. Over a period of 3 yearsabout 150 projects were undertaken by BASF. Energy saving of 10% with a payback period of 2 yearsis reported by applying pinch technology to the Caltex Refinery situated in Milnerton, Cape, SouthAfrica. The energy consumption before the study was 100 MW for the whole refinery. A newsfront


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article in Chemical Engineering2 gives more details about the experience of various companies in usingpinch technology and the benefits obtained.

Fundamental Principles and Basic Concepts

Pinch technology is based on thermodynamic principles. Hence, in this section we will review theimportant thermodynamic principles and some basic concepts.

Temperature-Enthalpy Diagram

Whenever there is a temperature change occurring in a system, the enthalpy of the system will change.If a stream is heated or cooled, then the amount of heat absorbed or liberated can be measured by theamount of the enthalpy change. Thus, Q = ∆H. For sensible heating or cooling at constant pressurewhere CP = mcp,

(4.11.1)

For latent heating or cooling, ∆H = mλ (specific latent heat of condensation or evaporation). If weassume that the temperature change for latent heating or cooling is 1°C, then CP = mλ .

Equation (4.11.1) enables us to represent a heating or cooling process on a temperature-enthalpydiagram. The abscissa is the enthalpy and the ordinate is the temperature. The slope of the line is (1/CP).Figure 4.11.1a shows a cold stream being heated from a temperature of 20°C to 80°C with CP =2.0 kW/°C.

FIGURE 4.11.1 The temperature enthalpy diagram.

∆ ∆H CP T=


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As enthalpy is a relative function, the stream can be drawn anywhere on the enthalpy scale as longas it is between its starting and target temperatures and has the same enthalpy change. Figure 4.11.1bshows such a case. Thus, one of the important advantages of representing a stream on the temperatureenthalpy plot is that the stream can be moved horizontally between the same temperature interval.Figure 4.11.1c shows two different streams in the same temperature interval.

Two streams can be easily added on the temperature-enthalpy plot to represent a composite of thetwo streams. Figure 4.11.2 shows how to obtain the composite of two streams on this plot. This featurewill be used in later sections to predict the minimum utility requirement for multistream problems.

A heat exchanger is represented by two heat curves on the temperature-enthalpy diagram, as shownin Figure 4.11.3a. This figure also shows how we will represent heat exchangers in a grid diagram formFigure 4.11.3b and the conventional form Figure 4.11.3c. In the grid diagram form, the hot stream goesfrom left to right and the cold stream goes from right to left. If the flow is countercurrent in the exchangerthen the temperature will decrease from left to right. Two circles connected by a vertical line representthe exchanger. The advantages of the grid diagram will become apparent when we discuss the designof heat exchanger networks. The exchanger has a temperature difference at the hot end and another atthe cold end. The smaller of these two temperature differences is called ∆tmin.

Some Definitions

A match between a hot and a cold stream indicates that heat transfer is taking place between the twostreams. A match between two streams is physically achieved via a heat exchanger unit. The number ofheat exchanger units impacts the plot plan and determines the piping and the foundation cost.

For reasons of fouling, mechanical expansion, size limitation, cleaning, improved heat transfer coef-ficients, etc., many process heat exchangers are the shell-and-tube type with 1 shell pass and 2 tubepasses. Often what appears as a single match between two streams in a heat exchanger networkrepresentation is actually installed as several 1-2 exchangers in series or parallel. The term shell will beused to represent a single 1-2 shell-and-tube heat exchanger. Please refer to Section 4.3 for morediscussion on 1-2 shell-and-tube heat exchangers.

Software

Pinch technology is a state-of-the-art technology for process integration and design. Different researchersat various universities have written programs, but only a handful of commercial programs are available.Table 4.11.1 shows the commercially available programs for process integration.

FIGURE 4.11.2 Composite stream obtained from two different streams in the same temperature interval.


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At the Department of Process Integration, University of Manchester Institute of Science and Tech-nology (UMIST), a consortium funded by various companies conducts research and develops the majorityof the concepts of pinch technology. The software developed by the consortium is available to its membersonly. The consortium is called the Process Integration Research Consortium (PIRC).

Optimization Variables and Heat Exchanger Network Design Philosophy

The objective of the heat exchanger network synthesis problem is to design a network that meets aneconomic criterion such as minimum total annualized cost. The total annualized cost is the sum of theannual operating cost (which consists mainly of energy costs) and annualized capital cost.

The capital cost of a network primarily depends on the total surface area, the number of shells, andthe number of units that will be installed. The capital cost also depends on the individual type of heatexchangers and their design temperature, pressure, and material of construction.

If we include the pressure drop incurred in a heat exchanger, then the capital and operating cost ofthe pumps will also have to be taken into account. We will limit the scope of this section by not includingstream pressure drop constraints.

Figure 4.11.4 shows some of the variables that affect the optimization of a heat exchanger network.To make the network operable or flexible, extra cost may be incurred. This cost may be in the form ofadded equipment or use of extra utilities or use of additional area for some of the exchangers in the network.

From the above discussion, it is clear that the synthesis of heat exchanger networks is a multivariableoptimization problem.

FIGURE 4.11.3 Heat exchanger representation.


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TABLE 4.11.1 Commercially Available Computer Programs for Pinch Technology

Software name Marketed by

Supertarget Linnhoff-March Limited, Targeting House, Gadbrook ParkNorthwich Cheshire, CW 9742, U.K.Phone: (44) 1606 815100Fax: (44) 1606 815151

Aspen Pinch Aspen Technology Inc., Ten Canal Park, Cambridge, MA 02141Phone: (617) 577 0100Fax: (617) 577 0303

Heatnet Britain’s National Engineering Laboratory, East Kilbride, ScotlandHEXTRAN Simulation Sciences Inc., 601 S. Valencia Ave., Brea, CA 92621

Phone: (714) 579 0354Fax: (714) 579 0412

DPI Software Department of Process Integration, UMIST, Manchester, U.K.Phone: (44) 161 200 4382Fax: (44)161 236 7439

HX-Net Hyprotech Ltd., 300 Hyprotech Center, 1110 Center Street North, Calgary T2E 2R2, Alberta, Canada

Phone: (403) 520 6122, Fax: (403) 520 6060

FIGURE 4.11.4 Optimization variables in the design of heat exchanger networks.


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To better understand the design process, consider a simple problem consisting of two streams. Thefirst stream needs to be cooled from 160 to 40°C with a mass heat flow capacity, CP, of 1 kW/°C. Thesecond stream needs to be heated from 50 to 180°C with a CP of 2 kW/°C. The economic basis for thisdesign is given in Table 4.11.2. The objective is to design an optimal heat exchanger network. The directheat recovered between the two streams and the external utilities required to achieve the target temper-ature will determine the optimal solution. It is assumed that all process streams as well as utility streamshave a film heat transfer coefficient of 1 kW/°C m2.

An intuitive approach for designing the heat exchanger network is to assume a value for the minimumapproach temperature, ∆tmin, for all the process-process exchangers within the network, i.e., no exchangerin the network will have an approach temperature less than the assumed value of ∆tmin. For the firstiteration, let ∆tmin = 10. The network for this ∆tmin is shown in Figure 4.11.5. For the network structureshown in Figure 4.11.5, Table 4.11.3 shows the details of the network design at different values of ∆tmin.Figure 4.11.6 shows the optimization curve for this problem.

The design procedure used is summarized in Figure 4.11.7. It is an iterative procedure and can takea long time to find the optimal solution. For multiple stream problems, at a given value of ∆tmin, a numberof different designs can be feasible. Hence, a better approach is needed.

TABLE 4.11.2 Economic Data for the Design Problem

Heat Exchangers

Installed cost per shell ($) = 10,000 A0.6 (m2)

Utility Data

Cost of using hot oil = 68 ($/kW.yr), ($2.36/MMBtu)Cooling water = 2.5 ($/kW.yr), ($0.09/MMBtu)Temperature range of hot oil = 320–310°C Temperature range of cooling water = 10–20°C

Plant Data

Interest rate = 10%/yrLifetime = 5 yrOperation time = 8000 h/yrCalculated capital recovery factor (CRF) = 0.2638/yr

FIGURE 4.11.5 Network for the two stream problem, ∆tmin = 10°C.


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The design can never violate the laws of thermodynamics. The philosophy adopted in pinch technologyis to establish targets for the various optimization variables based on thermodynamic principles. Thesetargets set the boundaries and constraints for the design problem. Further, targets help us identify the varioustrade-offs between the optimization parameters. They help us in obtaining a “birds-eye view” of the solutionspace and identify the optimal values of the optimization parameters. Once the optimal values are identified,design the network at these values. This approach will always lead to an optimal design. This approach issummarized in Figure 4.11.8. Setting targets ahead of design eliminates the iterations required. Based onthe stream data and using thermodynamic principles, targets can be easily set as discussed below.

To understand the interaction between the different optimization variables, consider the heat curveswith ∆tmin = 10 as shown in Figure 4.11.9a, for the simple two stream system discussed above. Threedifferent sections can be easily identified on this diagram. Section 1 represents the cold utility require-ment, Section 2 represents the process-process heat exchange, and Section 3 represents the hot utilityrequirement. So from this set of heat curves we can calculate the utility requirements for the system.Again for each section we can calculate the area required, as we know the duty for each section and theterminal temperatures. Further, we can deduce that each section will require one unit. We can use Bell’smethod3 to estimate number of shells required for each unit that represents the different sections. InSection 2, three shells will be required. The heat curves for the hot and cold streams establish targets

TABLE 4.11.3 Network Design Details for the Two Stream Problem

∆tmin

Total Annualized Cost ($/yr) Design Parameter E-1 E-2 E-3

10 32,388 Duty, kW 160 100 20Number of shells 1 3 1Area, m2 1.98 8.29 1.18Capital cost $/yr 3974 14,566 2919Operating cost $/yr 10,879 50

20 28,808 Duty, kW 170 90 30Number of shells 1 2 1Area, m2 2.08 5.43 1.59Capital cost $/yr 4089 9606 3479Operating cost $/yr 11,559 75






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for energy, area, units, and shells. These are the major components that contribute towards the annualizedcost of the network.

Now for the same system, let us increase the ∆tmin to 40°C. The new set of heat curves is shown inFigure 4.11.9b. The above exercise can now be repeated to obtain targets for energy, area, units, andshells. When we increase the value of ∆tmin the utility requirement will increase and the total networkarea required will be decreased. The number of units for this system remains the same, but the numberof shells required will decrease. Section 2 now only requires one shell. Thus, as the value of ∆tmin

increases, the utility cost increases and the capital cost decreases. This indicates that ∆tmin is the singlevariable that fixes the major optimization variables shown in Figure 4.11.4. Hence, we can reduce themultivariable optimization problem to a single-variable optimization problem. This single variable is∆tmin. At the optimum value of ∆tmin, the other optimization variables, viz., number of shells, number ofunits, total network area requirement, and the hot and cold utility requirements will also be optimal. For

FIGURE 4.11.6 Optimization curve for the two stream problem.

FIGURE 4.11.7 Intuitive procedure for heatexchanger network design.


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a multistream problem the same conclusion can be easily derived. Hence, for the multistream problemoptimization discussed in the next subsections we will develop methods to optimize the value of ∆tmin.

The targets obtained by the above procedure are based on thermodynamics. Further, they are estab-lished ahead of design using stream data only and, hence, help us identify where to initialize our design.This is a very powerful concept as it eliminates the need to develop a number of different designs tofind the optimal design. The targeting procedure identifies the optimal region ahead of design. A designcan be easily developed based on the design principles discussed later. Some local optimization can beconducted to account for other factors such as operability, flexibility and constructability.

FIGURE 4.11.8 Pinch technology approachfor heat exchanger network design.

FIGURE 4.11.9a Effect of ∆tmin on the energy, area, units, and shells required for a heat exchange system.


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Multistream Design Problem

Consider a four-stream problem. Table 4.11.4 lists the starting and target temperatures of all the streamsinvolved in the flowsheet. It also shows the CP values. While pressure drop constraints on the individualstreams determine the film heat transfer coefficients, we shall not take into account this constraint.Instead, we use (unrealistically) the same heat transfer coefficient value of 1 kW/m2 K for all streams.Our objective is to design an optimum heat exchanger network for this process using the economicsoutlined in Table 4.11.2. Further, let ∆tmin denote the minimum temperature difference between any hotprocess stream and any cold process stream in any exchanger in the network. We shall use this problemto illustrate the concepts of pinch technology.

Targets for Optimization Parameters

Energy Targets

Composite CurvesLet us plot the heat curves for all the hot streams on the T-H diagram (see Figure 4.11.10). We candivide the diagram into a number of temperature intervals, defined by the starting and target temperaturesfor all the streams. Between two adjacent temperatures we can calculate the total heat content of all thestreams that are present in this temperature interval. For example, between 180°C and 60°C the sumtotal of the heat available is calculated as:

FIGURE 4.11.9b Effect of ∆tmin on the energy, area, units, and shells required for a heat exchange system.

TABLE 4.11.4 Stream Data for a Design Problem

Stream Number

Stream Name Ts (°C) Tt (°C) CP (kW/°C)

1 C1 20 160 402 C2 120 260 603 H1 180 20 454 H2 280 60 30


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A composite curve that represents the heat content of all the hot streams is obtained by summing theheat available in each of these temperature intervals, as shown in Figure 4.11.10. Similarly, a compositecurve for all the cold streams can be obtained. These two composite curves can be used as the heatcurves for the whole process.

To obtain the energy target, fix the hot composite curve and move the cold composite curve horizontallytill the shortest vertical distance between the two curves is equal to the value of ∆tmin. The “overshoot”of the cold composite curve is the minimum hot utility requirement and the “overshoot” of the hotcomposite curve is the minimum cold utility requirement.4 For ∆tmin = 30°C, the minimum hot utilityrequirement is 4750 kW and the cold utility requirement is 4550 kW (see Figure 4.11.11).

The Problem TableThe above procedure for obtaining the energy targets using composite curves is time-consuming andclumsy. An alternative method based on thermodynamic principles was developed. Hohmann4 called itthe feasibility table. Linnhoff and Flower5 independently developed the problem table. The problemtable algorithm is easy and involves no trial and error.

The algorithm consist of the following steps:

1. Select a value of ∆tmin. Since we have already established the targets using composite curves for∆tmin = 30°C, we shall use that value here.

2. Convert the actual terminal temperatures into interval temperatures as follows:

for the hot streams: Tint = Tact – ∆tmin /2for the cold streams: Tint = Tact + ∆tmin /2

where Tint = interval temperature and Tact = actual stream temperature.

FIGURE 4.11.10 Construction of the hot composite curve.

∆

∆

H T T CP

H kW

j

j

2 3 2

2 180 60 45 30 9000

= −( )

= −( ) +( ) =

∑


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The interval temperatures now have the allowance for ∆tmin. This modification guarantees that fora given Tint, the actual temperature difference between the hot and cold stream will always begreater than or equal to ∆tmin.

3. All the interval temperatures for both the hot and cold streams are sorted in descending order andthe duplicate intervals are removed (see Table 4.11.5).

4. For each interval, an enthalpy balance is made. The enthalpy balance for interval i is calculatedusing the following equation:

where ∆Hi = net heat surplus or deficit in interval iCPc = mass specific heat of a cold streamCPh = mass specific heat of a hot stream

For the example problem, this calculation is shown in Table 4.11.6. Within each interval the enthalpybalance will indicate that there is either a heat deficit or surplus or the interval is in heat balance. A heatsurplus is negative and a heat deficit is positive.

The second law of thermodynamics only allows us to cascade heat from a higher temperature to alower temperature. Thus, a heat deficit from any interval can be satisfied in two possible ways — byusing an external utility or by cascading the surplus heat from a higher temperature interval. If no externalutility is used, the heat cascade column of Table 4.11.6 can be constructed. All intervals in this heatcascade have negative heat flows. This is thermodynamically impossible in any interval (it would meanheat is flowing from a lower to a higher temperature). To correct this situation, we take the largestnegative flow in the cascade and supply that amount of external hot utility at the highest temperatureinterval. This modification will make the heat cascade feasible, i.e., none of the intervals will have

FIGURE 4.11.11 Composite curves for the design problem.

∆H T T CP CPi i i c

j

N

h

j

N

j

streams

j

streams

= −( ) −

+ ∑ ∑int, int, 1


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negative heat flows. The amount of external heat supplied to the first interval is the minimum amountof hot utility required. The surplus heat in the last interval is the minimum amount of cold utility required.

For the example under consideration, the minimum hot utility required is 4750 kW and minimumcold utility required is 4550 kW. These are the same targets obtained from the composite curves. It isclear, however, that the problem table algorithm is an easier, quicker, and more exact method for settingthe energy targets. One can easily set up a spreadsheet to implement the problem table algorithm. Further,once the energy targets are obtained, the composite curves can be easily drawn to visualize the heatflows in the system. It should be noted that the absolute minimum utility targets for a fixed flowsheetare determined by the case of ∆tmin = 0.

Capital Cost Targets

To find the optimal value of ∆tmin ahead of design, we need to set the targets for the capital and energycosts. As seen before, the capital cost target for a given ∆tmin depends on the total area of the network,number of shells required in the network, and the number of units required in the network. We will nowestablish these targets.

Target for Minimum Total Area for the NetworkThe composite curves can be divided into different enthalpy intervals at the discontinuities in the hotand cold composite curves. Between any two adjacent enthalpy intervals, if the hot streams in thatinterval transfer heat only to the cold streams in that interval and vice versa, then we say that verticalheat transfer takes place along the composite curves.6 This mode of heat transfer models the purecountercurrent heat exchange.

The equation for establishing the minimum area target is based on a complex network called the“spaghetti” network. This network models the vertical heat transfer on the composite curves. In this

TABLE 4.11.5 Generation of Temperature Intervals for ∆tmin = 30°C

Stream No.

Actual Temperature (°C) Interval Temperature (°C) Interval Number

Ordered Interval Temperatures (°C)Ts Tt Ts Tt

1 20 160 35 175 1 2752 120 260 135 275 2 2653 180 20 165 5 3 1754 280 60 265 45 4 165

5 1356 457 358 5

TABLE 4.11.6 The Problem Table

Stream No. 1 2 3 4

CP40

60

45

30

Temperature Interval

Interval Number ∆Tint ΣCPcj – ΣCPhj ∆Hint

Heat Cascade

Corrected Heat Cascade

Hot Utility–275 0 0 4750275–265 1 10 60 600 –600 4150265–175 2 90 30 2700 –3300 1450175–165 3 10 70 700 –4000 750165–135 4 30 25 750 –4750 0135–45 5 90 –35 –3150 –1600 315045–35 6 10 –5 –50 –1550 320035–5 7 30 –45 –1350 –200 45505–Cold Utility 8 4550


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network, for any enthalpy interval defined by the discontinuities in the composite curves, each hot streamis split into the number of cold streams in that enthalpy interval. Each cold stream in the enthalpy intervalis also split into the number of hot streams in that interval. A match is made between each hot streamand each cold stream. Figure 4.11.12 shows this network. The area target is obtained by the followingequation:

where Amin = total minimum area for the network∆TLMTDi = ∆TLMTD for enthalpy interval iqj = heat content of stream j in enthalpy interval ihj = film plus fouling heat transfer coefficient of stream j in enthalpy interval i

The above equation gives a minimum total surface area for any system where the process streamshave uniform heat transfer coefficients. Townsend and Linnhoff6 claim that for nonuniform heat transfercoefficients the above equation gives an useful approximation of the minimum area, with errors beingtypically within 10%.

Minimum Number of Units TargetThe minimum number of units is given by:7

u = N + L – s

where u = number of units including heaters and coolersN = number of streams including utilitiesL = number of loopss = number of separate networks

FIGURE 4.11.12 Enthalpy intervals for area targeting and the spaghetti network that mimics vertical heat transfer.

AT

q

hLMTDii

j

jj

N

i

streams

min =

∑ ∑1

∆

Nintervals


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A loop is a closed path through the network and its effect is to increase the number of units. For anetwork to have a minimum number of units, the number of loops should be zero. Figure 4.11.13 showsa loop on the gird diagram. Normally for a given stream system, only a single network exists and if thenumber of loops is assumed to be zero, then the above equation can be reduced4 to u = N – 1.

Figure 4.11.13 illustrates the occurrence of independent networks. The total network consists of twoindependent subnetworks. Thus, for the system shown in this figure, N = 5, L = 1, s = 2, and u = 4.

Target for Minimum Number of ShellsTrivedi et al.8 have developed a method for estimating the total number of shells required for the heatexchanger network. The method starts by setting the energy targets for the selected value of ∆tmin. Thehot and cold utilities are added to the process stream system and the composite curves for the processand the utility streams are constructed. No external utility requirement will be needed for these sets ofcomposite curves. Hence, these are called the balanced composite curves. The method estimates thenumber of shells based on the balanced composite curves. The method involves two steps:

Step 1: Estimate the total number of shells required by the cold process streams and the cold utilitystreams (see Figure 4.11.14a).

• Commencing with a cold stream target temperature, a horizontal line is drawn until it interceptsthe hot composite curve. From that point a vertical line is dropped to the cold composite curve.This section, defined by the horizontal line, represents a single exchanger shell in which the coldstream under consideration gets heated without the possibility of a temperature cross. In thissection, the cold stream will have at least one match with a hot stream. Thus, this section impliesthat the cold stream will require at least one shell. Further, it ensures that log mean temperature(LMTD) correction factor, Ft ≥ 0.8.

• Repeat the procedure until a vertical line intercepts the cold composite curve at or below thestarting temperature of that particular stream.

• The number of horizontal lines will be the number of shells the cold stream is likely to requireto reach its target temperature.

• Repeat the procedure for all the cold streams including the cold utility streams.• The sum of the number of shells for all the cold streams is the total number of shells required

by the cold streams to reach their respective target temperatures.

FIGURE 4.11.13 Loops and independent subnetworks in a heat exchanger network.


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Step 2: Estimate the total number of shells required by the hot process streams and the hot utilitystreams (see Figure 4.11.14b).

• Starting from the hot stream initial temperature, drop a vertical line on the balanced compositecurve until it intercepts the cold composite curve. From this point, construct the horizontal and

FIGURE 4.11.14a Shell targeting for cold streams on the balanced composite curves. Cold streams will requireeight shells.

FIGURE 4.11.14b Shell targeting for hot streams on the balanced composite curves. Hot streams will require nineshells.


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vertical lines until a horizontal line intercepts the hot composite curve at or below the hot streamtarget temperature.

• The number of horizontal lines will be the number of shells required by the hot streams for heatexchange in the network.

• Repeat the procedure for all the hot streams including the hot utility streams.• The sum of the number of shells required by the hot streams would be the total number of shells

required by the hot streams to reach their respective target temperatures.

The quasi-minimum number of shells required in the network would be the larger of either the totalnumber of shells required by the hot streams or the total number of shells required by the cold streams.

Optimum ∆Tmin Value

The above procedures establish, for a selected ∆tmin value, targets for minimum energy, minimum area,minimum number of units, and minimum number of shells. These targets, along with the cost data, can betranslated into capital and energy cost for the network. The targets can be evaluated at different values of∆tmin to obtain a birds-eye view of the solution space and the optimal value of ∆tmin ahead of design. Thisphilosophy was first proposed by Hohmann4 and later developed by Linnhoff and Ahmad9 as Supertargeting.

For the design problem data discussed above, the different targeting curves are shown inFigure 4.11.15a-f . It is seen from the total annualized cost curve, Figure 4.11.15f, that the optimal regionis very flat. While selecting a value of ∆tmin from the optimal region, a couple of points should be keptin mind. Different values of ∆tmin lead to different topologies. Hence, we should take into account differentfactors that can affect the final cost. These factors include the nature of the composite curves and theproblem constraints that have significance in the network synthesis and refinement. The optimal valueof ∆tmin selected for this problem is 40°C and the target values for energy, area, units, shells, andannualized total cost are given in Table 4.11.7.

The Pinch Point

On the composite curves, there is one or more enthalpy value for which the two composite curves are∆tmin apart. For the example under consideration (see Figure 4.11.11), this occurs at a hot streamtemperature of 150°C and cold stream temperature of 120°C. This is also the fourth temperature intervalin the problem table. In this interval, the heat cascade has zero heat flow, i.e., no heat is transferredacross this interval when minimum hot utility is used. This interval, identified by a zero in the correctedheat cascade column, is referred to as the pinch point.7,10 The significance of the pinch point is nowclear — for the minimum external utility requirements do not transfer heat across the pinch point. Anyextra amount of external heat that is put into the system above the minimum will be transferred acrossthe pinch point and will be removed by the cold utility.11

Cross Pinch Principle11

For a given value of ∆tmin, if the network is using Qh units of hot utility and if Qhmin is the minimumenergy target then,

Qh = Qh min+α

If the network uses Qc units of cold utility and if Qcmin is the minimum energy target then,

Qc = Qc min + α

where α = the amount of cross pinch heat transfer

Significance of the Pinch Point

The pinch point divides the stream system into two independent subsystems. The subsystem above thepinch point is a net heat sink and the subsystem below the pinch point is a net heat source. Thus, for a


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system of hot and cold streams, to design a network that meets the minimum utility targets the followingrules set by the pinch principle should be followed:11

• Do not transfer heat across the pinch point• Do not use hot utility below the pinch point• Do not use cold utility above the pinch point

We shall use these principles to design the network for the optimal value of ∆tmin.

FIGURE 4.11.15a Minimum energy targeting plot.

FIGURE 4.11.15b Minimum network area targeting plot.


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Network Design

Network Representation on the Grid Diagram

If we attempt to design the network using the conventional flowsheet format, any changes in the designmay lead to redrawing the flowsheet. Hence, we shall use the grid diagram to represent and design thenetwork. Figure 4.11.16 shows the grid diagram for the design problem assuming all hot streams are

FIGURE 4.11.15c Targeting plot for minimum number of shells.

FIGURE 4.11.15d Minimum energy cost targeting plot.


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cooled with cooling utility and all cold streams are heated with hot utility. On this grid diagram we canplace a heat exchanger match between two streams without redrawing the whole stream system. Thegrid representation reflects the countercurrent nature of heat transfer that makes it easier to checktemperature feasibility of the match that is placed. Furthermore, we can easily represent the pinch pointon the grid diagram, as shown in Figure 4.11.16.

FIGURE 4.11.15e Minimum annualized capital cost targeting plot. (From The Chemical Engineer, the Instituteof Chemical Engineers, 30, 1987. With permission.)

FIGURE 4.11.15f Targeting plot for total annualized cost. (From Linnhoff, B. With permission.)


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Pinch Point and Network Design

We will now continue with the design of the example problem. Figure 4.11.11 shows the compositecurves with ∆tmin = 30°C for the process flowsheet. It also shows the pinch point. The pinch point is themost constrained region of the composite curves. From optimization principles, we know that for aconstrained problem, the optimal solution is located at the point formed by the intersection of multipleconstraints. Hence, if we can satisfy the constraints at that point then we are guaranteed an optimaldesign. Thus, we should start the design where the problem is most constrained viz. the pinch point.11

The pinch point divides the problem into two independent subnetworks — above the pinch subnetworkthat requires only hot utility and below the pinch subnetwork that requires only cold utility.

Pinch Design Rules and Maximum Energy RecoveryLet us make some observations at the pinch point. Immediately above the pinch point11

and immediately below the pinch point,

This condition defines the pinch point that is the constraint that the designer has to satisfy. Thus, eachand every match in the sink subnetwork, at the pinch point, should be placed such that CPh ≤ CPc.Similarly, each and every match in the source subnetwork, at the pinch point should be placed such thatCPc ≤ CPh. Figure 4.11.17 shows these conditions on the T-H diagram.

Sometimes the above condition may not be satisfied. Stream splitting should be undertaken in sucha situation.

Figure 4.11.1812 shows the algorithms that are developed for placing matches immediately at the pinchpoint for both the above and below pinch subnetworks. Nh and Nc denote the number of hot and coldstreams at the pinch point.

FIGURE 4.11.16 Grid diagram representation of the stream in the design problem. (From Linnhoff, B. Withpermission.)

CP CPh c∑ ∑≤

CP CPh c∑ ∑≥


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The matches and stream splitting can be easily identified with the “CP table.”11 Consider the streamsystem shown in Figure 4.11.19. The CP table is shown in the same figure. The two rows in this tablecontains the condition that needs to be satisfied for the subnetwork under consideration. The CP valuesof the hot and cold streams are arranged in a descending order in the columns. The stream numbers areshown in brackets adjacent to the CP values. For the sink subnetwork under consideration, the CP valuefor the hot streams is listed in the left column and the CP value for the cold stream is listed in the rightcolumn. There is no feasible match for hot stream 1. Hence, it will have to be split. The hot stream 2can match with either stream 3 or 4. Once we split hot stream 1, we violate the stream populationconstraint. To satisfy this constraint we will have to split a cold stream. Either stream 3 or 4 can be split.The designer can use his judgment and decide which stream should be split depending on controllability

FIGURE 4.11.17 CP matching rules at the pinch point.

FIGURE 4.11.18a Algorithm for sink subnetwork design at the pinch point.


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FIGURE 4.11.18b Algorithm for source subnetwork design at the pinch point.

FIGURE 4.11.19 Identifying matches and stream splitting using the CP table.


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and other physical constraints. For example, it is not advisable to split a stream that may have a two-phase flow.

Two different designs will be obtained depending on which stream is split. The hot stream is splitinto two streams having CP values of X and 7-X. In the first alternative, we split stream 4 into streamshaving CP values of Y and 6-Y. In the second option we split stream 3 into streams having CP valuesof Z and 5-Z. To find the initial values of X, Y, and Z it is recommended that all matches except for oneare set for CP equality. Thus, for the first option set, X = 5 and Y = 2. For the second option set, X = 6and Z = 1. This is an initial solution. The values of X, Y, and Z can be adjusted to obtain an optimal design.

Once the matches are identified at the pinch, the heat loads for these matches are fixed to maximizethe heat exchange to the limit of heat load of either the hot stream or the cold stream. This will eliminate(or “tick-off”) that stream from the analysis. Fixing the heat loads for match with this heuristic will alsohelp us to minimize the number of units and thus the installation cost.11

Matches away from the pinch point do not have to satisfy the conditions outlined above as the systemis not constrained in this region. Matches are easily identified away from the pinch point.

The network obtained will satisfy the energy targets set. Such a network is called maximum energyrecovery (MER) network.11

Local Optimization — Energy Relaxation

The optimal region is generally very flat and the optimal value of ∆tmin is not a single point but a region.The targeting exercise helps identify this region. Once a value of ∆tmin is selected and the network isdesigned using the methodology outlined above, there is still some scope for further optimization. Thisis achieved by a process called energy relaxation.11

The number of units in the design obtained using the above procedure will generally be greater thanthe target value. This is due to the presence of loops. If we can eliminate the loops in a network thenthe heat transfer area is concentrated on fewer matches and, hence, will decrease the piping andfoundation requirements. This will tend to decrease the capital cost of the network. However, the someenergy penalty may be incurred.

Identifying loops in a large network cannot be done visually. Trivedi et al.13 have proposed LAPIT,Loop And Path Identification Tree, for identifying loops and paths present in the network. A path is theconnection between a heater and a cooler via process-process matches.

Loops can be broken by removal of a unit in a loop and redistributing the load of the unit among theremaining units of the loop. Some exchangers may result having a very small ∆tmin when a loop is broken.The ∆tmin across such exchangers can be increased by increasing the utility consumption along a paththat consists of a heater, the unit having a small value of ∆tmin, and a cooler.

Loop-breaking is a very complex optimization process. Trivedi et al.13,14 have proposed a detail methodthat systematically breaks loop and identifies options available at each step of the process. The methodis based on LOop Network Interaction and load Transfer Analysis (LONITA)14 and on a best-first-searchprocedure.13

Summary of the Design Procedure

The pinch design procedure can now be summarized. Establish a value of the optimum ∆tmin using thetargeting techniques. This identifies the region in which the design should be initialized. Using the pinchdesign procedure, design the network. Reduce the number of units using the loop-breaking and energy-relaxation techniques outlined above.

Example

The above principles and procedures are used for the design of the network for the multisteam designproblem. The value of optimum ∆tmin is 40°C. The final network MER design is shown in Figure 4.11.20.Note that the annualized capital cost of this network is only about 4% higher than the target value of$692,700. This design is in the neighborhood of the predicted optimum.


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The design after energy relaxation is shown in Figure 4.11.21. This design has one less unit than theMER design in Figure 4.11.20. Hence, this will decrease the piping, installation, and maintenance cost.The cost of the new design is about 2% higher than the MER design. Since we are using simplifiedmodels for costing, the cost of the design in Figure 4.11.21 is within the errors of cost estimating.However, this design will be cheaper when the detail cost is evaluated as it has fewer number of units.

Table 4.11.7 compares the target values of the various optimization parameters with actual designvalues for Figures 4.11.20 and 4.11.21.

Selection of Utility Loads and Levels

The annual operating cost depends on the amount and type of utilities used. In a complex process suchas an ethylene plant, there would be about four to five steam levels and about seven to eight refrigeration

FIGURE 4.11.20 Pinch design for the design problem. Total annualized cost: $720,800.

FIGURE 4.11.21 Energy relaxation of the pinch design in Figure 4.11.20. Total annualized cost: $733,700.


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levels. High-pressure steam is generated within the process and is let down to other steam levels viasteam turbines that generate power. Steam from these levels is used for heating the process. The powergenerated from the turbines is used by the compressors and pumps and to generate various levels ofrefrigeration needed. The question faced is what pressure levels of steam to use and what is the load oneach level. Also, what are the best temperature levels of the refrigeration and what will be their respectiveloads.

Pinch technology helps us answer these questions in a very simple manner using the grand compositecurves (GRCC).15 The GRCC is the curve that shows the heat demand and supply within each temperatureinterval. This curve is derived from the problem table (refer to Table 4.11.6). In the problem table, wehad modified the stream starting and target temperatures depending on the value of ∆tmin. From now onwe shall refer these modified temperatures as shifted temperature. The heat flows between two adjacentshifted temperature intervals can be plotted on the shifted-temperature-enthalpy plot. Figure 4.11.22shows the heat cascade and how the GRCC is developed for the design problem. The GRCC gives usa graphical representation of heat flows taking place in the system. At the pinch point the heat flow is zero.

TABLE 4.11.7 Comparison of Target and Design Values for Different Network Optimization Variables at ∆tmin = 40°C

Target Value

Figure 4.11.20 MER Design Figure 4.11.21 Design

Design Value% Deviation from Target Design Value

% Deviation from Target

Total network area, m2 687 779 13 708 3Total hot utility consumption, kW 5500 5500 6400 16Total cold utility consumption, kW 5300 5300 6200 17Number of units 7 7 6Number of shells 8 9 7Energy cost, $/yr 387,250 387,250 450,700 16Annualized capital cost $/yr 305,407 333,576 9 282,996 -7Total annualized cost, $/yr 692,657 720,826 4 733,696 6

FIGURE 4.11.22 Grand composite curve for the design problem.


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The GRCC is piecewise linear. The slope of this curve also changes from interval to interval. A linewith a positive slope indicates that the system in that region needs external heat. A line with a negativeslope indicates that there is surplus heat available within that temperature interval that can be cascadeddown within the system and used at a lower temperature interval. It is very clear from the GRCC thatabove the pinch region is a heat sink and below the pinch region is a heat source.

To further explain the importance of the grand composite curve and the kind of information that canbe extracted from it, consider the curve shown in Figure 4.11.23. Consider the section AB that is betweenthe shifted temperature interval of 395°C and 380°C. This section demands external heat of 2000 kW.Hence, we should place a hot utility such as high-pressure steam or hot oil to supply it.

Next, consider the section BC of the GRCC between the shifted temperature intervals of 380°C and350°C. This section has a heat surplus and so we can use it elsewhere in the system. We can drop avertical line from B to meet the GRCC at point D. The section CD of the GRCC that is a heat deficitregion of the system can now be satisfied by the heat surplus from the BC section. This section of theGRCC is called a “pocket” and the process is self-sufficient with respect to energy in this region. Thesection DE now needs external heat. This heat can be supplied at any temperature ranging from thehighest available temperature to a minimum temperature corresponding to point D.

Following the same logic, EFG will be a “pocket.” In section GHI one hot utility level can be usedat a shifted temperature level of point G with a total duty of 3000 kW, or two levels can be used — oneat 260°C with a duty of 1500 kW and the other at the shifted temperature level of point H, i.e., 240°Cwith a duty of 1500 kW. The choice is dictated by the trade-off between the power requirement, capitalinvestment, and complexity of the design. Using only one level will make the design of the utility systemsimpler and the capital cost of the heat exchanger smaller due to higher temperature approaches. On theother hand, if there is demand for power then using two levels will produce more power.

A similar economic trade-off will be required for supplying the external heating requirement in sectionKL of the composite curve. Point L is the pinch point. Below point L, heat needs to be rejected into acooling utility such as an air cooler or cooling water. Also, in the below pinch section of the processwe can address the question, “Is it possible to raise steam at some temperature? If so, how much?”

FIGURE 4.11.23 Selection of utility loads and levels.


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For example, for the process GRCC shown in Figure 4.11.23, we want to find out how much low-pressure superheated steam can be generated. The saturation temperature of the low-pressure steam is170°C and boiler feed water is available at 130°C. The superheat is 10°C. Using a simple trial and errorprocedure, we can find out how much steam will be generated.

• Assume the amount of steam that is generated.

• Develop a heat curve for the low-pressure steam generation on the shifted temperature scale.

• As generation of low-pressure steam will be a cold stream, the temperature of the stream will beincreased by ∆tmin /2.

• Keep on increasing the amount of steam generated till the steam generation heat curve touchesthe process GRCC at any point.

Once the utility levels are decided, introduce them into the stream data and obtain the balancedcomposite curves. The number of pinch points will increase. In addition to the original process pinchpoint, each utility level will introduce at least one pinch point. A balanced grid diagram that includesall the utility streams and all the pinch points identified on the balanced composite curve can now beused along with the network design algorithms to develop a network that achieves the target set.

Data Extraction

Process integration studies start from a base case flowsheet. This flowsheet may be existing or may bedeveloped from the designer’s experience. To conduct pinch analysis properly it is important to extractthe flowrate, temperature, and heat duty data correctly.

The stream target and starting temperatures should be chosen so that we do not generate the originalflowsheet.12 To illustrate this, consider the flowsheet shown in Figure 4.11.24. If we extract the data astwo streams then we might end up with the original flowsheet. If the drum temperature is not importantthen we can consider it to be one stream and we stand a chance for finding new matches. The drum andthe pump can then be kept at a natural break point in the system if the process allows.

While extracting data extra care should be taken when streams are mixing nonisothermally.12 Considerthe system shown in Figure 4.11.25. Stream A is being cooled to the mixed temperature and stream Bis being heated to the mixed temperature. This happens due to mixing the streams. The mixed streamis then heated to a higher temperature. If we extract the data as shown in Figure 4.11.25a and if the

FIGURE 4.11.24 Flowsheet for data extraction example.


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pinch temperature is 70°C, then we are inherently transferring heat across the pinch point by mixingthe two streams. In the process of mixing we are cooling stream A and then subsequently heating it upagain. The correct way to extract the data is shown in Figure 4.11.25b.

When a stream is split and the split streams have two different target temperatures then each streamis considered as two separate streams.

Process Integration and Recent Developments

Until now, we have discussed the design and optimization of heat exchanger networks. But heat exchangernetworks are a part of a whole process. For the process to be optimally designed, all the unit operationsshould be properly integrated. Generally, each unit operation is individually optimized. It is a miscon-ception that if each individual unit is individually optimized then the resulting process is also optimized.Each unit operation interacts with others in the process. Hence, for the process to be optimized, eachunit operation should be properly integrated.

Pinch technology has developed systematic ways to integrate complex processes. Methods are avail-able for appropriate placement and integration of heat engines, heat pumps, and various other unitoperations within the process. This technology has also established guidelines for process modifications,developing shaftwork targets, total site-wide integration, revamping existing processes, and much more.Trivedi16 discusses the details of these methods and procedures.

References

1. Linnhoff B., Use Pinch Analysis to Knock Down Capital Costs and Emissions, Chem. Eng. Prog.,33, August, 1994.

2. Samdaniust, G. and Moore, S., Pinch Technology: Doing More With Less, Chem. Eng., 43, July 1993.3. Bell, K.J., Estimate S & T Exchanger Design Fast, Oil Gas J., 59, Dec. 4, 1978.4. Hohmann, E.C., Optimum Networks for Heat Exchange, Ph. D. dissertation, University of Southern

California, Los Angeles, 1971.5. Linnhoff, B. and Flower, J. R., Synthesis of Heat Exchanger Networks, AIChE J., 633, July 1978.6. Townsend, D.W. and Linnhoff, B., Surface Area Targets for Heat Exchanger Networks, IChemE

11th Annu. Res. Meet., Bath University, U.K., April 1984.

FIGURE 4.11.25 Data extraction for streams that are mixing.


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7. Linnhoff, B., Mason, D.R., and Wardle, I., Understanding Heat Exchanger Networks, Comp. Chem.Eng., 3, 295, 1979.

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