utility cost estimation.pdf

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Typical process utilities includeelectricity, process steam, refrig-erants, compressed air, coolingwater, heated water, hot oil, pro-

cess water, demineralized water, mu-nicipal water, and river, lake, or oceanwater. For preliminary cost estimates,waste disposal cost can also be treatedlike a utility expense.

Unlike capital, labor, and other ex-penses, utility prices do not correlatesimply with conventional inflationaryindexes, because basic energy costs

vary erratically, independent of capi-tal and labor.

In essence, utility priceis linked to two separate variables inflation and energy cost.

Elementsof manufacturing expense that dependon labor and capital follow inflationarymetrics like the CE Plant Cost Index(CEPCI).

Energy cost, such as that forfuel in an electrical or steam generat-ing plant, is like a raw material whoseprice can vary widely and erratically.

To reflect this dual dependence, weneed a two-factor utility cost equationsuch as the following:

CS,u= a(CEPCI) + b(CS,f) (1)where CS,uis the price of the utility, aand bare utility cost coefficients, CS,fis the price of fuel in $/GJ, and CEPCIis an inflation parameter for projectsin the U.S.1

Deriving the coefficientsTo derive Coefficients a and b, amanufacturing cost analysis must beprepared for a given utility.2 Electricpower price, for instance, includes

raw material costs, labor, supervision,maintenance, overhead, and a numberof other items that determine totalmanufacturing expense and, ulti-mately, selling price. In such a list, in-dividual cost items can be divided intotwo categories, those dependent onnormal inflation and those dependent

Feature Report

How to EstimateUtility CostsUtility estimates are often complicated because

they depend on both inflation and energy costs.

This simplified approach offers a two-factor utility-

cost equation and the relevant coefficients

for a number of utilities

Engineering Practice

66 CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2006

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

NOMENCLATURE a The first utility cost coefficient in Equa-

tion [1], which reflects inflation-depen-dent cost elements

AAnnual utility cost, $(U.S.)/yr b The second utility cost coefficient in

Equation [1], which reflects energy-dependent cost elements

CS,f Fuel price for use in Equation [1],$(U.S.)/GJ

CS,u Utility price ($ per unit designatedin Table 1)

foOperating or online factor(dimensionless)

HHV Higher heating value(see Note h to Table 1)

LHV Lower heating value(see Note i to Table 1)

mMass flowrate, kg/s p Pressure: barg (bar gage) for steam;

bara (bar absolute) for compressed air PPower consumption, kW qVolumetric flowrate, m3/s for liquids

or N m3/s for gases QCCooling capacity in a refrigeration

system, kJ/s QH Heating capacity of a heat source, kJ/s

Subscripts c Cooling cw Cooling water e Electricity H Heating refrig Refrigerant S Price waste treat Waste treatment

FIGURE 1. Prices for fuels on an energy-equivalent basis. Numbers are U.S. aver-ages, delivered. [From U.S. Dept. of Energy (www.eia.doe.gov). The Oil and Gas Jour-nal (www.ogjonline.com), and informal sources. Values for gasoline do not includetaxes, which may add from 30 to 50%, depending on the location.]

1. Evaluated monthly by the staff of ChemicalEngineering and printed along with historicalvalues of this and other indexes on the last pageof each issue.

2. See Vatavuk [1] or Chapter 6 of Reference [2]for information on how manufacturing costs areevaluated.


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CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2006 67

TABLE 1.UTILITY COST COEFFICIENTSa

Cost coefficients

a b

Electricity, $/kWh

Purchased from

outside

1.3 104 0.010

Onsite power charged

to process module

1.4 104 0.011

Onsite power charged

to grass-roots plant

1.1 104 0.011

Compressed and Dried Airb, $/Nm3 (0.1 < q< 100 Nm3/s; 2 < p< 35 bara)

Process module 5.0105q0.30(ln p) 9.0 104(ln p)

Grass-roots plant 4.5105q0.30(ln p) 9.0 104(ln p)

Instrument Airb, $/std m3

Process module 1.25104 1.25103

Grass-roots plant 1.15104 1.25103

Process Steamc, $/kg (1 < p< 46 barg; 0.06 < ms< 40 kg/s)

Process module 2.7105ms0.9 0.0034p0.05

Grass-roots plant 2.3105ms0.9 0.0034p0.05

Cooling Waterd

, $/m3

(0.01 < q< 10 m3

/s )Process module 0.0001 + 3.0105q1 0.003

Grass-roots plant 0.00007 + 2.5105q1 0.003

Demineralized (boiler feed) Waterd, $/m3 (0.001 < q< 1.0 m3/s)

Process module 0.007 + 2.5104q0.6 0.04

Grass-roots plant 0.005 + 2.0104q0.6 0.04

Drinking Waterd, $/m3 (0.001 < q< 10 m3/s)

Process module 7.0104+ 3.0 105q0.6 0.02

Grass-roots plant 5.0104+ 2.5 105q0.6 0.02

Natural Water, Pumped and Screenedd, $/m3 (0.001 < q< 10 m3/s)

Process module 1.0104+ 3106q0.6 0.003

Grass-roots plant 7.0105+ 2106q0.6 0.003

Water Desalination< 500 ppm total dissolved solids (tds) in product

Can be applied to membrane purification of wastewater also

Brackishd(up to 5,000 ppm tds in feed), $/m3 (0.04 < q< 1.0 m3/s)

Process module 0.0014 + 4.0105q0.6 0.02


Seawaterd(35,00040,000 ppm tds in feed), $/m3 (0.001 < q< 1.0 m3/s)

Process module 0.0015 + 6.0105q0.6 0.13


Refrigerant, $/kJ cooling capacitye (1 < Qc< 1,000 kJ/s; 0 < T< 300 K)

Process module 0.6 Qc0.9(T3) 1.1106T5

Grass-roots plant 0.5 Qc0.9(T3) 1.1106T5

Hot Water, Hot Oil, or Molten-Salt Heat Transfer Media, $/kJ heating capacityf

(100 < QH < 20,000 kJ/s; 350 < T < 850 K)

Process module 7.0107QH0.9(T0.5) 6.0108T0.5

Grass-roots plant 6.0107QH0.9(T0.5) 6.0108T0.5

a. CS,f, the price of fuel that partners with Coefficient b, is based on thehigher or gross heating value. For electrical power, compressed air, refrig-erant, cooling water, and other auxiliary facilities where electricity is usedto drive pumps and compressors, it is the price of fuel at the electric powerstation. For steam, it is the price of boiler fuel at the plant. Historic valuesfor CS,fare plotted in Figure 1.

b. Coefficients apply to ranges of qandpindicated, where qis total auxil-iary airplant capacity (Nm3/s) andpis delivered pressure of air (bara).

c. Use price of fuel burned in the boiler for CS,f; msis total auxiliary boilersteam capacity (kg/s).

d. qis total water capacity (m3/s).

e. Qcis total auxiliary cooling capacity (kJ/s), Tis absolute temperature (K).

f. QHis total auxiliary heating capacity (kJ/s), Tis absolute temperature (K).

g. Use these numbers advisedly. Waste disposal costs depend on local pub-lic attitude and other political factors that are capricious and location-sen-sitive. See Perry [3], page 25-101 for typical U.S.-regional variations.

h. mis waste flowrate (kg/s). HHV is higher heating value of waste (MJ/kg). Note that bis negative in these instances, because waste burning as asupplementary fuel returns a credit.

i. qis total treatment system flow in normal (273 K, 1 atm) cubic metersper second (Nm3/s). LHV is lower or net heating value in MJ/Nm3. Notethat bis negative in these instances, because waste burning as a supple-mentary fuel returns a credit.

Cost coefficients

a b

Wastewater Treatmentd, $/m3 (0.01 < q< 10 m3/s)

Primary (filtration)

Process module 0.0001 + 2107q1 0.002

Grass-roots plant 0.00005 + 2107q1 0.002

Secondary (filtration and activated sludge processing)

Process module 0.0007 + 2106q1 0.003

Grass-roots plant 0.00035 + 2106q1 0.003

Tertiary (filtration, activated sludge,

and chemical processing)

(0.0003 < q< 10 m3/s)

Process module 0.001 + 2104q0.6 0.1

Grass-roots plant 0.0005 + 1104q0.6 0.1

Membrane Processes (see water desalination costs above)

Liquid/Solid Waste Disposalg, $/kg

Conventional solid or liquid wastes

Process module 4.0104

Grass-roots plant 3.0104

Toxic or hazardous solids and liquids

Process module 2.5103

Grass-roots plant 2103

Combustion as Supplementary Fuelh (1 < m HHV< 1,000 MJ/s)

Process module 3.0105(HHV)0.77(m0.23) 5104(HHV)

Grass-roots plant 2.5105(HHV)0.77(m0.23) 5104(HHV)

Combustion as Supplementary Fuel (with flue gas cleaning)

Process module 5.0105(HHV)0.77(m0.23) 4104(HHV)

Grass-roots plant 4.0105(HHV)0.77(m0.23) 4104(HHV)

Gas Emissions Treatmenti, $/Nm3 (0.05 < q< 50 Nm3/s)

Endothermic Flaring

Process module 1106q0.23 0.004

Grass-roots plant 0.7106q0.23 0.004

Thermal or Catalytic Incineration

Process module 1105q0.23 0.002


Thermal or Catalytic Incineration (with flue gas cleaning)

Process module 1.5105q0.23 0.003


Combustion as Supplementary Fuel (1 < qLHV < 1,000 MJ/s)

Process module 3.0105(LHV)0.77(q0.23) 6104(LHV)

Grass-roots plant 2.5105(LHV)0.77(q0.23) 6104(LHV)

Combustion as Supplementary Fuel (with flue gas cleaning)

Process module 5.0105(LHV)0.77(q0.23) 5104(LHV)

Grass-roots plant 4.0105(LHV)0.77(q0.23) 5104(LHV)


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on fuel price.

This allows one to calcu-late values for aand b.We have donethat for a host of utilities.

Results arepresented in Table 1. Meanwhile, thehigher heating values for a number oftypical fuels are given in Table 2.

To cover all types of common CPIprojects, two additional factors must

be considered.

First, since capital andlabor expenses are not linear functionsof capacity, it is necessary to makeCoefficient adependent on plant size.

This reflects the simple fact that rela-tive capital and labor costs per unit ofcapacity decline as plant size increases.

We see this, for instance, in the entryfor cooling water in Table 1.

In a cool-ing system designed to handle 1 m3/s,water will be more expensive per cubicmeter than from a plant designed tohandle 10 m3/s, and the expression forCoefficient areflects that.

Use of Equation (1) calls for judg-ment.

If your module includes a heatexchanger that consumes 0.1 m3/sand there are no other uses of coolingwater on site, you will simply use 0.1m3/s for q in the equation for Coeffi-cient a.

If, on the other hand, the ex-changer is part of a larger plant wheretotal cooling-water needs are 6 m3/s,6 is the appropriate value forq in theequation (Table 1) for Coefficient a.

Wisdom also tells us there is a limiton practical plant size. In a largercomplex where total cooling-waterdemand is greater than 10 m3/s, thator a lesser value should be used for q,because standard cooling systems arelimited to 10 m3/s.

Greater needs aremet with multiple units.

A second consideration hinges onwhether your module is a part of agrass-roots facility or an existing plant.For example, water is cooled in what isdescribed as an offsite facility.3If theheat exchanger in question is part of anew project being built from scratch,

offsite capital is included in total proj-ect capital.

If, on the other hand, theexchanger is being added to a plantwhere adequate offsite facilities arealready in place, the costs of the off-site facility have already been paid.

Tobe fair and accurate in assigning costs,an addition should be treated like acustomer that purchases utilities fromthe grass-roots plant.4

Thus, there aretwo categories in Table 1; one for grass-roots plants and a second for process

modules.

Grass-roots utility prices arelower because the cost estimate for aheat exchanger in a grass-roots proj-ect has already accounted for its shareof the cooling-tower capital.

One might ask why equations forutilities like cooling water and com-pressed air contain a Coefficient bwhen no fuel is burned.

Consider thatelectricity is required to power thepumps and compressors involved indelivering these utilities.

Fuel is con-sumed to generate that electricity, andits cost5must be included in the pricefor cooling water or compressed air.

Meanwhile, one might also ask whycoefficients for self-generated electric-ity in Table 1 are larger than those forpurchased electricity.

In general, pur-chased power is cheaper than onsitepower, because large, free-standingelectric power plants tend to be moreefficient than onsite generating facili-ties.

This supports a rule of thumb thatself-generation of electricity is not at-

tractive unless cheap fuel is availableor electricity can be co-generated withprocess steam.

Putting the method to useTo illustrate the use of Equation (1),consider the cost of electricity gener-ated using Number 6 (residual) fuel oil.

In mid-2000, the CEPCI was 392, theequivalent price of energy from resid-ual oil was $4/GJ ($27/barrel), and thecost of purchased electricity (estimated

from Equation [1] with coefficientstaken from Table 1) is calculated to be:

CS,e,2000= 1.3104(392) + 0.010 (4.0)= $0.091/kWh

This agrees closely with the price ofelectricity charged to large industrialcustomers in the northeastern U.S.,where residual fuel oil was a promi-nent utility fuel in 2000.

Coal is an important resource in theU.S. because it is abundant and rela-tively inexpensive. Its use is limited,however, to large power plants wherecombustion is efficient and clean.

Withcoal at $1.20/GJ, the price of electric-ity generated from this source in 2000would have been

6.4 cents per kWh,about two-thirds the price of electric-ity generated from No. 6 fuel oil thatyear. Historical price data for coal, oil,and other important fuels are plottedin Figure 1.

Escalating prices for the futureContinuing with the No. 6 fuel-oil ex-ample, what will the price of electric-ity be in 2010?

Inflation, estimated at3. See Chapter 5 of Reference [2].4. Even though owned by the same company.5. In these instances, CS,fin Equation [1] is theprice paid for fuel by the electric power plant.

68 CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2006

UTILITY COST ESTIMATION EXAMPLE

Estimate the annual andunit costs of utilities foran alkylate splitter modulethat consumes 23.5 kW ofelectricity, 0.10 m3/s ofcooling water, and 3.0 kg/sof 32 barg steam. Assumethat the operating or on-line

factor is 94% and that elec-tricity is purchased from anoutside utility plant that usesNo. 6 fuel oil at a price of$4.50/GJ.

Based on a CEPlant CostIndex in the range of 460to 480, the unit price ofelectricity isCS,e= 1.3 104(470) +0.010 (4.5)= $0.106/kWh

Annual cost of electricity forthe alkylate splitter moduleis given by the power con-sumption rate multiplied

by number of seconds peryear, operation factor, priceof electricity in dollars perkilowatt hour, and dividedby 3,600 seconds per hour:

Ae= P(31.5 106s/yr)foCS,e(1 h/3,600 s)Ae= (23.5 kW)(31.5

106s/yr)(0.94)($0.106/kWh)(1 h/3,600 s)

Ae= $20,500/yr

Since this module is part ofa large refinery, total plantcooling water consumptionis undoubtedly 10 m3/s orgreater. Using that value forqand grass-roots figuresfrom Table 1, the first coef-ficient ain Equation [1], iscalculated as follows:a= 0.00007 + (2.5 105) 101= 0.000073and CS,cwis

CS,cw= 0.000073 (470) +0.003 (4.5) = $0.048/m3

Annual cooling water cost iscalculated as was done forelectricity.

Ae= (0.10m3/s)(31.5106s/yr) (0.94)($0.048/m3)

Ae= $140,000/yrFor steam, auxiliary plantcapacity is assumed to be themaximum and residual oil at$4.50/GJ is the postulatedenergy source. From data inTable 1, we can solve:CS,s-32= [(2.3 105)(40)0.9(470)] +[(0.0034)(32)0.05] (4.50)CS,s-32= $0.019/kgand

AS= (3.0kg/s)(31.5 106s/yr)(0.94)($0.019/kg))

AS= $1,700,000/yr

TABLE 2.

PROPERTIES OF TYPICAL FUELS

Fuel Higher (Gross)

Heating Value

Density

Bituminous and an-

thracite coals

27-33 MJ/kg 670-930 kg/

m3(bulk)

Lignite 15-19 MJ/kg 640-860 kg/

m3(bulk)

Wood (bone dry) 19-22 MJ/kg

Number 2 fuel oil 38 GJ/m3 870 kg/m3

Number 6 (residual)fuel oil

42 GJ/m3 970 kg/m3

Gasoline 37 GJ/m3 700 kg/m3

Natural gas 38.1-40.7 MJ/Nm3 0.715 kg/Nm3

For more detailed information, see Perry [3],Section 27


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3 to 3.5% per year, foreshadows a CEPCI of 550.

Fuel prices, on the otherhand, are capricious. Assume thatpressure from coal and nuclear energymoderate the recent escapades in oilprices.

Extrapolating from the rela-tively stable 1990s at an annual rateof 4 to 5%, we arrive at a price of about$6/GJ for No. 6 fuel oil.

Accordingly,

the 2010 price of electricity from thissource is projected to be:

CS,e,2010= 1.3104(550) + 0.010 (6.0)= $0.132/kWh

Any projection so many years in thefuture is highly speculative.

Based onhistorical data for capital costs, the

projected CE PCI is reasonable, butthere is little evidence to support theprojected fuel price. One could eas-ily argue for an energy price that isdouble or triple that calculated above.

This would mean electricity prices of19 to 25 cents per kWh.

Edited by Rebekkah Marshall

AuthorsGael D. Ulrich (34R Pren-tiss St., Cambridge, MA02140-2241; Email: [email protected]) is pro-fessor emeritus of chemicalengineering at the University

of New Hampshire, where hejoined the faculty in 1970. Heworked at Atomics Interna-tional Div. of North Americanaviation and Cabot Corp. priorto entering teaching. He holds

a B.S.Ch.E. and an M.S.Ch.E. from the Universityof Utah and an Sc.D. from the Massachusetts In-stitute of Technology. For the past thirty years, hehas consulted for a number of corporations andpresided over a small contract research firm forten. Material in this article was extracted fromReference [2] published with coauthor P. T. Va-sudevan in 2004.

Palligarnai T. Vasudevanis professor of chemical en-gineering at the Universityof New Hampshire (Chemi-cal Engineering Department,Kingsbury Hall, Rm W301, 33College Road, Durham, NH03824; Phone: 603-862-2298;

Email: [email protected]) wherehe joined the faculty in 1988.He worked for a large petro-chemical company for seven

years prior to entering teaching. For the past 15years, he has worked in the areas of catalysis andbiocatalysis. He is currently collaborating withresearchers in Spain in the areas of hydrode-sulfurization and enzyme catalysis. Vasudevanholds a B.S.Ch.E. from Madras India, a M.S.Ch.E. from SUNY at Buffalo and a Ph.D. in chemicalengineering from Clarkson University.

References1. Vatavuk, W.M., How to Estimate Operating

Costs, Chem. Eng., pp. 33-37, July 2005.

2. Ulrich, G.D. and P.T. Vasudevan, ChemicalEngineering Process Design and Economics,

A Practical Guide, 2nd edition, Process Pub-lishing, 2004, ulrichvasudesign.com.

3. Perry, J. H., Green, D.W., and Maloney, J.O.,Perrys Chemical Engineers Handbook,7th Edition, McGraw-Hill, New York, 1997.

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CHEMICAL ENGINEERING WWW.CHE.COM APRIL 2006 69

REFRIGERANT AND WASTEWATER TREATMENT EXAMPLE

Calculate the cost of provid-ing 1.2 109kJ/yr of5C refrigerant and treating35,000 m3of wastewater per

year in a grass-roots biotech-nology manufacturing process.The maximum refrigerantdemand rate is 40 kJ/s, andmaximum plant wastewaterflowrate is 0.01 m3/s. The

waste stream contains both or-ganics and inorganic salts, sotertiary treatment is necessary.

Based on Table 1, assuming a CEPCI = 470 and Cs,f= $4.50/GJ, the same inflation index and fuel valuesas in the utility cost estimation illustration on p. 68,CS,refrig= [0.5(40)0.9(268)3] (470) + (1.1 106)(268)5(4.50) = $4.0 106/kJCS,waste treat= [0.0005 +(1 104) (0.01)0.6] (470) +(0.1) (4.50) = $1.43/m3

Annual expenses for refrigerant are

Arefrig= (1.2 109 kJ/yr)($4.0106/kJ) =$4,800/yr

And, for wastewater treatment the annual expenses areAwaste treat= (35,000m3/yr)($1.43/m3) = $50,050/yr

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