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    Achemical executive once notedthat his firm derives one-thirdof its income from products thatare less than ten years old. In-

    deed, existing companies thrive andnew ones proliferate through innova-tion and product improvement. Theydepend on scientists and engineersworking in the trenches or at thebench to drive development. Yet, mostpotential innovations never succeed.Engineers who can separate lucrative

    concepts from duds early on are worththeir weight in gold. Mastery of the in-formation in this article can help youbecome one of those engineers.

    Its important to define promisingprojects quickly so that money is notwasted on dead ends. Economic evalu-ation should begin at conception andcontinue in parallel with research andpilot studies before design and devel-opment expenses begin to balloon.Costs of prolonging a project and se-curing more detail increase exponen-

    tially with time. Clearly, if the projectis a loser, the sooner it is abandoned,the better. Any engineer with practi-cal experience can cite projects thatwere supported far beyond the pointof viability.

    One can construct the economic pro-file for a manufacturing process froma few basic data, such as raw materialprices, labor, and other costs. Detailson how to put these together are ex-plained in Chapter 6 of Ref. [1]. Sev-eral vital manufacturing expenseshinge on capital.

    This article describes how to esti-mate that capital quickly and with an

    accuracy of about +30 to 20%. Thisrange is good enough to define feasi-bility before a lot of money is spent onadvanced development activities.

    The sticker price of a process is tech-nically known as fixed capital, whatone would pay if a manufacturing linecould be bought in the same way that ahouse, automobile, or washing machineis purchased. It is fixed because (a) itrepresents real equipment that cannotbe converted easily to another asset,

    and (b) once built, it must be paidwhether the plant operates or not.

    Unlike consumer goods and appli-ances that are bought directly andput into service immediately, processequipment is usually custom designedin advance, then built and installedby specialists. Thus, a developmentteam is faced with predicting the fu-ture price of a process that doesntexist. Fortunately, through the ef-forts of generations of cost engineers,translation of technical specifications

    into future expenses can be done withamazing accuracy.

    With a process flow diagram andusing short-cut design techniques, anengineer can size major equipment,draw purchase prices from graphssuch as Figure 2, and build a capitalcost estimate.

    Purchase prices are, by necessityfrom the past. To estimate for the fu-ture, engineers must scale from onesize or capacity to another and fromone time to another. Then, to assesstotal capital, they must add costs forinstallation. How to go from flow sheetto final capital is described below.

    Variation of cost with sizeRelationships between cost and capac-ity are part of everyday experience. If,for example, one were transportingpeople in taxicabs and one cab held

    four persons (excluding driver), thecapital cost to convey eight people istwice that of carrying four. For 20 to30 people, a bus or van could be usedwhere equipment cost is no longer di-rectly proportional to number of peo-ple. This can be expressed mathemati-cally as follows:

    (1)

    where CP,v,r

    is the purchase price ofthe equipment in question, which hasa size or capacity of v in the year r,and CP,u,ris the purchase price of the

    Feature Report

    46 CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2009

    Feature Report

    Estimating capital costs early can prevent

    unnecessary expenditures on dead-end projects

    Gael D. Ulrich and Palligarnai T. VasudevanUniversity of New Hampshire

    Capital CostsQuickly Calculated

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    same type of equipment in the sameyear but of capacity or size u. In thetwin taxicab example, uis 4, vis 8, andthe size exponent ais unity. Althoughais 1 for multiple taxicabs, it is usu-ally less than unity when relating costto size in a bus or van.

    The same is true for chemical processequipment. This is easily demonstratedby comparing costs of two storagetanks. Assume they are spherical, madeof identical materials, but of different

    capacity. The volume of tank uis

    (2)

    The volume of tank vcan be similarlyexpressed. Dividing Equation (2) byits analog for tank v, the volume or ca-pacity ratio is

    (3)

    Costs of tanks are proportional not tothe volume, however, but to surfacearea or the quantity of metal plate usedin fabrication. The area of tank uis

    (4)

    The area ratio of vversus uis

    (5

    )

    At Csdollars per square meter of tank

    CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2009 47

    SCALING BY THE SIX-TENTHS RULE

    This photo shows a Portland cement plant in Devils Slide,Utah. The first operation on this site began production in1907. Its capacity of 110,000 metric tons per year (m.t./

    yr) was tripled with an expansion in 1948. A third factory, theone shown here, was completed in 1997 (635,000 m.t./yr

    capacity). According to a 1909 letterhead, company capitalat the time was $2.5 million. Using that as a basis, assum-ing a size-capacity exponent equal to 0.8, and escalating forinflation [Equation (11)], the 1948 estimated grass-roots fixedcapital would have been $2.5 million 30.8 x (80/12) =$40 million. Similarly, the 2004 value extrapolated from these

    numbers would be $40 million 20.8 (400/80) = $350million. According to local tax records, the 2004 evaluationis slightly greater than $100 million. This reveals the dangerof extrapolating over large time periods with no correction forimproved technology. For a more realistic estimate, a 2 million

    m.t./yr cement plant in the northeastern U.S. was reported tocost $300 million in 1998. Based on this number, the calculatedgrass-roots value of the Utah plant would be $300 million (0.635/2)0.8 (400/390) = $120 million. (Photo courtesy

    John Sommers of Holcim [U.S.], a wholly owned subsidiary ofHolcim Ltd., Switzerland. Used with permission.)

    EXPONENTIAL

    SIZE-CAPACITY RELATIONS

    E

    xponential size-capacity relationships are useful forindividual equipment items and for entire processing

    plants. The fixed capital of a component or plant hav-ing one capacity is scaled to that of another capacity byusing Equation (1). This practice is known popularly asthe sixth-tenths rulebecause 0.6 is a common expo-nent. Although quick and easy to use, this rule has limita-tions. One must know, at least, the capital cost of a plantor component at one capacity. The range in exponents isquite large, so one should have experience or know costestimates for at least two capacities to go on.

    The six-tenths rule is valuable for rapid order-of-magni-tude plant cost estimates where inaccuracy can be toler-ated. It is also useful for predicting product price as afunction of capacity when a capital estimate is availableat only one rate.

    There is a danger of extrapolating with the six-tenthsrule beyond its range of validity. For example, accord-ing to Equation (1), prices decrease with equipment size.This is reasonable and logical. But, with precision items,costs level off when a certain minimum sizeis reached.Savings in materials are offset by more labor required tomake miniature equipment. Prices might even go up assize decreases further, changing ato a negative number.

    Extrapolation to larger capacities is risky when predic-tions createequipment that is too large to be fabricatedor shipped. When any maximum size is exceeded, mul-tiple equipment items become necessary and the scalingexponent abecomes unity. Holland and Wilkinson avoidthis problem by specifying the size range (Ref. [2], Table950) for which Equation (1) is valid. You are safe usinggraphs such as Figure 2 if you stick with existing curvesand dont extrapolate.

    TABLE 1.TYPICAL EXPONENTS FOR EQUIPMENT COSTAS A FUNCTION OF CAPACITY*

    Sizerange

    Capacityunit

    Exponenta

    Agitators 1200 kW 0.7

    Blowers, centrifugal 508,000 kW 0.9

    Centrifugal pumps 0.01270 kW 0.3

    Compressors, reciprocating 102,000 kW 1.0

    Belt conveyors 1050 m 0.8

    Crushers 101,000 kg/s 0.8

    Drum dryers 2100 m2 0.6

    Dust collectors Bag filter Multicyclone

    21,1000.140

    m3/sm3/s

    0.90.6

    Electrostatic precipitators 51,200 m3/s 0.8

    Evaporators, falling-film 30320 m2

    1.0Filters, plate and frame 1170 m2 0.75

    Heat exchangers, floatinghead

    10900 m2 0.6

    Jacketed vessels 1800 m3 0.6

    Electric motors 108,000 kW 0.9

    Refrigeration units 510,000 kJ/s 0.6

    Vibratory screens 1130 kW 0.6

    Tanks Floating roof Spherical, 05 barg

    20070,000505,000

    m3

    m30.60.7

    *Exponents were determined from slopes of the curves in our collection of datafound in Figures 361 of Chapter 5, Ref. [1]. Results are included here primar-

    ily for illustration. It is much better to use the curves themselves in a costestimate.

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    Feature Report

    48 CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2009

    surface, purchase prices of the tanksare given by the following:

    (6)

    (7)

    Their relative cost, found by combin-ing Equations (6) and (7), is

    (8)

    Radius ratio can be replaced with ca-pacity ratio via Equation (3):

    (9)

    and substituted into Equation (8) toyield

    (10)

    Comparing Equations (1) and (10),we see that the size exponent ais 2/3.In other words, doubling the size of aspherical storage tank increases itsprice by about 60%.

    Exponents for various individualequipment items are listed in Table 1.

    For our purposes, the form of Equa-

    tion (1) is more important than the ex-pression itself. It tells us that plottingcapacity versus cost on log-log coordi-nates will yield a straight line of slopea. That is the basis for the format ofFigure 2. Plots such as this one haveseveral advantages over equations.1. The range of valid sizes is defined by

    lengths of curves.2. Exponent a can be estimated by a

    quick glance at the curves (45 deg.slope represents an exponent of 1.0,for example; 30 deg. an exponent of

    about 0.6, and so on).3. Changes in a are visually obvious

    through curvature of a line.(Fee-based software, such as that de-scribed in Ref. [3] can be used whenmachine computation is preferredover reading from a chart.)

    Adjusting for inflation/deflationPredesign estimates are usually madefor products of the future but mustbe assembled from prices of the past.Because of inflation or deflation, theprice of a pump or filter will change asit sits on a warehouse shelf. The Con-sumer Price Index, Wholesale Price

    Index, and Salary Survey Index areindicators of inflationary trends in thegeneral economy. Similar indices areavailable for chemical engineers toscale equipment capital from one timeperiod to another.

    To use an inflation index, I, sim-ply include its ratio in Equation (1).

    For example, if the purchase price ofequipment of capacity v in year r isCP,v,r, its price in year sis:

    (11)

    A predicted cost index for year s is

    1970 1980 1990Year

    2000 2010 2020100

    1,000

    200

    300

    400

    500

    600Costindex,

    I

    700

    800900

    2,000

    3,000

    4,000

    5,000

    1970 1980 1990 2000 2010 2020

    0%

    2%

    5%

    10%20%

    Slopes correspond to

    inflation rates as indicated

    Nelson-Farrar Index

    Marshall & Swift

    Chemical Engineering

    Plant Cost Index

    (CEIndex = 400 is the

    basis for cost data

    in Figure 2)

    US Bureau of Labor Statistics-Hourly Earning Index

    (Chemical & Allied Products)

    FIGURE 1. A history of selected cost indices pertinent to chemical processing

    TABLE 2. TYPICAL COSTS ASSOCIATED WITH PURCHASE ANDINSTALLATION OF A HEAT EXCHANGER* IN A PROCESS MODULE

    Direct Project Expenses Cost Fraction of f.o.b. **equipment

    Direct materials Equipment f.o.b. price,CP $10,000 1.0CP

    Materials used for installation 7,100 0.71CP

    Direct labor 6,300 0.63CP

    Total direct materials and labor $23,400 2.34CP

    Indirect Project Expenses

    Freight, insurance, taxes 1,400 0.14CP

    Construction overhead 4,400 0.44CP

    Contractor engineering expenses 2,600 0.26CP

    Total indirect project costs $ 8,400 0.84CP

    Bare module capital,CBM $31,800 3.18CP

    Contingency and Fee

    Contingency 4,800 0.48CP

    Fee 1,000 0.10CP

    Total contingency and fee $ 5,800 0.58CP

    Total module capital $37,600 3.76CP*Purchase price, $10,000; ** f.o.b. = free on board

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    divided by its historic value for year rto form the escalation ratio.

    A number of different indices are

    used by cost engineers. Three of them,developed specifically for chemical andpetroleum plants, are illustrated inFigure 1. The Nelson-Farrar index ap-plies particularly to petroleum refineryconstruction, whereas the Marshall &Swift (M&S) and Chemical Engineer-ing (CE) indices are overall chemi-cal industry averages. Up-to-dateM&S and CE values are publishedmonthly on the Economic Indicatorspage of Chemical Engineering (seep. 72), where trends, historic values,

    and other economic data are also dis-played. That page is reprinted as thelast of each issue, changing as newerdata accumulate. Because of its acces-sibility and accuracy, the Chemical En-

    gineeringPlant Cost Index (CEPCI) isfavored by us. (Further information onthe CEPCI can be found in Ref. [48].)

    Installation costsFrom plots such as Figure 2, one candetermine purchase prices, CP,v,r, formajor equipment items that appearon a process flow diagram. But, eachitem must be transported to the siteand placed on a foundation where it

    becomes shrouded with piping, struc-tural steel, insulation, instruments,and other paraphernalia to form a pro-

    cess module. Because of these addedsteps, installed cost is several timesgreater than purchase price.

    To obtain overall plant capital costs,one can sum purchase prices for allthe equipment items on the flowsheetand multiply the total by a so-calledLang factor. In a paper mill, where theprecise, high-speed machinery is ex-pensive, a larger fraction of total costis invested in the original purchase.Installation, though costly, is a smallerfraction of purchase price than for

    pumps and heat exchangers. Thus, theLang factor itself is relatively smallfor a paper mill, about 2.5.

    In an oil refinery, process vessels andequipment themselves are somewhatsimpler, but installation of piping, in-sulation, and instruments is more ex-pensive, creating a larger Lang factor.Holland and Wilkinson (pp. 968 ofRef. [2]) recommend values of 3.8 fora plant that processes primarily solids(for instance, a cement plant); 4.1 for aprocess containing both solid and fluidstreams (a fertilizer plant, perhaps),and 4.8 for a fluid processing plantsuch as an oil refinery.

    0.1 1 10 100 1,000 10,000

    10

    102

    103

    104

    105

    106

    All Except Teflon Tube Teflon TubeShell /Tube F

    MShell F

    M

    cs/cs 1.00 cs 1.0cs/Cu 1.25 Cu 1.2Cu/Cu 1.60 ss 1.3cs/ss 1.70 Ni 1.4ss/ss 3.00 Ti 3.3

    cs/Ni 2.80 Max. pressure,Ni/Ni 3.80 7 baracs/Ti 7.20 F

    p= 1.0

    Ti/Ti 12.0

    t

    CBM=CPx FBMa

    Purchasedequipmentcost,C

    p($)

    Exchanger surface area,A(m2)

    Shell and Tube Heat Exchangers

    CEPlant Cost Index = 400 (Jan - 2004)

    Hairpin

    multitube

    Bayonet

    Double-pipe

    Scraped-wall

    Multiple double-pipe

    Teflon tube

    Floating head

    Fixed tube sheet

    and U-tube

    Kettle reboiler

    FIGURE 2. Purchased equipment costs for shell-and-tube and double-pipe heat ex-changers. Bare module factors FBM

    a are obtained from Figure 4 using material factorsgiven here and pressure factor F

    pfrom Figure 3 (cs = carbon steel, ss = stainless steel)

    Circle 44 on p. 70 or go to adlinks.che.com/23013-44

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    Feature Report

    50 CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2009

    Guthrie [9, 10] proposed individ-ual module factors, unique to eachequipment type. We like this tech-nique because it is accurate, direct,

    and relatively easy to use. In essence,Guthries approach is an efficient andaccurate way to synthesize a Lang fac-tor for any process.

    For estimates of pre-design accu-racy, one merely needs appropriateinstallation factors. Cost charts thatinclude prices and installation factorsfor any equipment likely to be foundon a chemical engineering flow sheetare provided in Figures 361 of Ch. 5,Ref. [1].

    Installation expenses for a heat

    exchanger are listed in Table 2. Inthis case, the bare module value of a$10,000 heat exchanger is $31,800. Itsbare module installation factorFBMistherefore 3.18.

    It should be emphasized that oneneed not go through the process de-scribed in Table 2 to use cost data from

    sources such as Ref. [1] where installa-tion factors are provided. Look, for ex-ample, at Figures 2, 3 and 4. Assumewe need to estimate what a floatinghead heat exchanger having 50 m2

    heat transfer surface area contributesto capital cost. We find the January2004 purchase price, CP,to be $10,000from Figure 2. If shell and tubes aremade of carbon steel, FM is 1.0 from

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    10 100

    1.0

    1.5

    Pressure

    factor,

    Fp

    Pressure, p(barg)

    High pressure on shell side alone

    or both tube and shell side

    High pressure

    on tube side only

    FIGURE 3. Pressure factors (ratio of purchase price of a high pressure heat ex-changer to one designed for conventional pressures)

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    the list in the lower right from Figure2. If service pressure is below 10 barg,the pressure factor, FP, is also 1.0,and, of course, their productFPFMis unity. For this value of the abcissa,one reads a bare module installationfactor F

    BM

    csof 3.18 from the ordinate of

    Figure 4. Thus, the heat exchangerscontribution to the cost of its processmodule is $10,000 3.18 = $31,800(the value derived in Table 2.)

    Contingency and feeTo obtain total module cost, that is, thetotal expense required to procure andinstall the heat exchanger in the bat-tery limits and to make it ready for op-eration, contingency and fee must beadded. These, according to Guthriesdata, are 15% and 3% of bare modulecapital, respectively. Thus, as illus-trated in Table 2, the cost of a $10,000heat exchanger, after installation, is$37,600 (3.18 1.18 = 3.76 times thepurchase price).

    Auxiliary facilitiesTo derive the contribution of a heatexchanger to a grass-roots plant, itsshare of site development, auxiliarybuilding, and offsite capital must beconsidered. Guthrie recommends anadded 30% above total module capi-tal for auxiliaries. Thus, the capitalcost associated with a $10,000 heatexchanger in a grass-root plant is es-timated to be approximately $49,000.The appropriate Lang factor is thus4.9, near the number recommendedin Perry (pp. 968, Ref. [2]) for a fluidprocessing plant.

    Severe or extreme serviceWith compatible process streams,carbon steel is normally the most eco-nomical material from which to makechemical equipment. But, corrosion,erosion, and other harsh conditions,often demand more expensive alloys.Extreme temperatures and pressuressometimes require extra-heavy vesselwalls or special materials.

    To reflect demanding service condi-tions, we developed special correction

    factors (denoted FBMa

    ) that are listed inour cost charts. The purchase price ofan equipment item fabricated from themost common or base material (usuallycarbon steel) is multiplied by this spe-cial bare module factor to yield the in-stalled price of equipment constructedfrom the material in question.

    We describe how special bare mod-ule factors are derived for piping inRef. [11]. Figures 3 and 4 were devel-oped for heat exchangers in a similarway. By following the path described

    in Figures 2, 3 and 4, one finds that

    FBM

    ss for a stainless-steel shell-and-

    tube exchanger is 5.8 (below 10 bargservice pressure). Thus, the 2004 baremodule cost of a 50 m2 floating headexchanger is $10,000 5.8 = $58,000if constructed of stainless steel. Witha current CEPlant Cost Index in therange of 550, the bare module capitalof that heat exchanger today will beapproximately $58,000 (550/400) =$80,000.

    Summary and applicationWith more than 30 years experienceteaching process design and econom-

    Please visit us at ACHEMA 2009, Hall 8.0 Stand S41 - S45

    0 5 10 15 20

    0

    5

    10

    15

    20

    25

    30

    Baremodu

    lefactor,F

    Pressure factor-material factor product, Fpx FM

    aBM

    FIGURE 4.Bare module factors are a function of material and pressure factors forheat exchangers

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    Feature Report

    52 CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2009

    ics, we find that of the time and effortrequired by students to estimate amanufacturing cost, about 90% is con-sumed preparing a PFD and defining

    capital cost. Now that you have readthis article, we suggest that you applyyour learning to a project near at hand.Define the capital and go the extra10% to estimate manufacturing eco-nomics for the product or process thatpays your salary. If you do research,

    your path is likely to become more di-rect and efficient. Even people in tech-nical service or sales will do their jobsbetter when they understand the key

    factors that control expenses in theirbusiness. In doing this exercise youmay discover you have been spendingtime on a worthless project and moveon to generating some of that gold youare worth.

    Edited by Gerald Ondrey

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    AuthorsGael D. Ulrich (34R Prent-iss St., Cambridge, MA02140-2241; Email: [email protected]) is professoremeritus of chemical engi-neering at the University ofNew Hampshire, where hejoined the faculty in 1970.He worked at Atomics Inter-

    national Div. of North Ameri-can Aviation and Cabot Corp.prior to entering teaching. He

    holds a B.S.Ch.E. and an M.S.Ch.E. from theUniversity of Utah and an Sc.D. from the Mas-sachusetts Institute of Technology. For the pastforty years, he has consulted for a number ofcorporations and presided over a small contractresearch firm for ten. Material in this article wasextracted from Ref. [1] published with coauthorP. T. Vasudevan in 2004.

    Palligarnai T. Vasudevanis Robert C. Davison profes-sor of chemical and environ-mental engineering at theUniversity of New Hamp-shire (Chemical EngineeringDepartment, Kingsbury Hall,Rm W301, 33 College Road,Durham, NH 03824; Phone:603-862-2298; Email: [email protected]) where he joined thefaculty in 1988. He worked

    for a large petrochemical company for sevenyears prior to entering teaching. For the past 26years, he has worked in the areas of catalysisand biocatalysis. He is currently collaboratingwith researchers in Spain in the areas of hy-drodesulfurization and enzyme catalysis. Va-sudevan holds a B.S.Ch.E. from Madras, India,a M.S.Ch. E. from SUNY at Buffalo and a Ph.D.Ch.E. from Clarkson University.

    References1. Ulrich, G.D. and Vasudevan, P.T., Chemical

    Engineering Process Design and Economics,A Practical Guide, 2nd edition, Process Pub-lishing (ulrichvasudesign.com), 2004.

    2. Perry, J. H., Green, D.W. and Maloney, J.O.,Chemical Engineers Handbook, 7th Edi-tion, McGraw-Hill, New York, 1997.

    3. Vasudevan, P.T., and Agrawal, D., A SoftwarePackage for Capital Cost Estimation, Chem.

    Eng. Educ., 33, pp. 254256, 1999.

    4. Hall, R.S., Matley, J., and McNaughton, K.J.,Current Costs of Process Equipment, Chem.

    Eng., pp. 80116, April 5, 1982.

    5. Kohn, P.M., CE Cost Indexes Maintain13-Year Ascent, Chem. Eng., pp. 189190,May 8, 1978.

    6. Matley, J., CE Plant Cost Index Revised,Chem. Eng.,pp. 153156, April 19, 1982.

    7. Matley, J. (1985), CE Cost Indexes Set SlowerPace, Chem. Eng., pp. 75-76 (April 29, 1985.

    8. Vatavuk, W.M., Updating the CE Plant

    Cost Index, Chem. Eng., pp. 6270, January,2002.

    9. Guthrie, K.M., Data and Techniques for Pre-liminary Capital Cost Estimation, Chem.

    Eng., pp. 114142, March 24, 1969.

    10. Guthrie, K.M., Process Plant Estimating,Evaluation and Control, Craftsman, SolanoBeach, California, 1974.

    11. Ulrich, G.D. and Vasudevan, P.T., Short-cutPiping Costs, Chem. Eng., pp. 4449, March2006.

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