Aace factored cost estimation

AACE International Recommended Practice No. 59R-10

DEVELOPMENT OF FACTORED COST ESTIMATES –
AS APPLIED IN ENGINEERING, PROCUREMENT, AND
CONSTRUCTION FOR THE PROCESS INDUSTRIES
TCM Framework: 7.3 – Cost Estimating and Budgeting

Acknowledgments:
Rashmi Prasad (Author) Peter R Bredehoeft Jr., CEP
Kul B. Uppal, PE CEP Larry R. Dysert, CCC CEP
A. Larry Aaron, CCE CEP PSP James D. Whiteside II, PE

Copyright 2011 AACE® International, Inc. AACE® International Recommended Practices

AACE International Recommended Practice No. 59R-10
DEVELOPMENT OF FACTORED COST ESTIMATES –
AS APPLIED IN ENGINEERING, PROCUREMENT, AND
CONSTRUCTION FOR THE PROCESS INDUSTRIES
TCM Framework: 7.3 – Cost Estimating and Budgeting
June 18, 2011
INTRODUCTION

As identified in the AACE International Recommended Practice No. 18R-97 Cost Estimate Classification
System – As Applied in Engineering, Procurement, and Construction for the Process Industries, the
estimating methodology tends to progress from stochastic or factored to deterministic methods with
increase in the level of project definition.

Factored estimating techniques are proven to be reliable methods in the preparation of conceptual
estimates (Class 5 or 4 based on block flow diagrams (BFDs) or process flow diagrams (PFDs)) during
the feasibility stage in the process industries, and generally involves simple or complex modeling (or
factoring) based on inferred or statistical relationships between costs and other, usually design related,
parameters. The process industry being equipment-centric and process equipment being the cost driver
serves as the key independent variable in applicable cost estimating relationships.

This recommended practice outlines the common methodologies, techniques and data used to prepare
factored capital cost estimates in the process industries using estimating techniques such as: capacity
factored estimates (CFE), equipment factored estimates (EFE), and parametric cost estimates. However,
it does not cover the development of cost data and cost estimating relationships used in the estimating
process.

All data presented in this document is only for illustrative purposes to demonstrate principles. Although
the data has been derived from industry sources, it is not intended to be used for commercial purposes.
The user of this document should use current data derived from other commercial data subscription
services or their own project data.

CAPACITY FACTORED ESTIMATES (CFE)

Capacity factored estimates are used to provide a relatively quick and sufficiently accurate means of
determining whether a proposed project should be continued or to decide between alternative designs or
plant sizes. This early screening method is often used to estimate the cost of battery-limit process
facilities, but can also be applied to individual equipment items. The cost of a new plant is derived from
the cost of a similar plant of a known capacity with a similar production route (such as both are batch
processes), but not necessarily the same end products. It relies on the nonlinear relationship between
capacity and cost as per equation 1:

CostB/CostA = (CapB/CapA)r

where CostA and CostB are the costs of the two similar plants, CapA and CapB are the capacities of the
two plants and r is the exponent, or proration factor.
(equation 1)

The value of the exponent typically lies between 0.5 and 0.85, depending on the type of plant and must
be analyzed carefully for its applicability to each estimating situation. It is also the slope of the logarithmic
curve that reflects the change in the cost plotted against the change in capacity. It can be determined by
plotting cost estimates for several different operating capacities where the slope of the best line through
the points is r, which can also be calculated from two points as per equation 2:

r = ln(CapB/CapA)/ln(CostB/CostA)
(equation 2)


Development of Factored Cost Estimates – As Applied in Engineering, Procurement, and
December 28, 2011 2 of 20
Construction for the Process Industries

June 18, 2011
The curves are typically drawn from the data points of the known costs of completed plants. With an
exponent less than 1, scales of economy are achieved wherein as plant capacity increases by a
percentage (say, by 20 percent), the costs to build the larger plant increases by less than 20 percent.
With more than two points, r is calculated by a least-squares regression analysis. A plot of the ratios on
log-log scale produces a straight line for values of r from 0.2 to 1.1.
This methodology of using capacity factors is also sometimes referred to as the “scale of operations”
method or the “six-tenths factor” method because of the reliance on an exponent of 0.6 if no other
information is available. With an exponent of 0.6, doubling the capacity of a plant increases costs by
approximately 50 percent, and tripling the capacity of a plant increases costs by approximately 100
percent. In reality, as plant capacity increases, the exponent tends to increase as per figure 1. The
capacity factor exponent between plants A and B may have a value of 0.6, between plants B and C a
value of 0.65, and between C and D, the exponent may have risen to 0.72. As plant capacity increases to
the limits of existing technology, the exponent approaches a value of one where it becomes as
economical to build two plants of a smaller size, rather than one large plant.

Figure 1 – The capacity factored relationships shown here are logarithmic. Exponents differ
across capacity ranges.

Usually companies should have indigenous capacity factors for several chemical process plants that must
be updated with regular studies. However, the above factors should be used with caution regarding their
applicability to any particular situation.

If the capacity factor used in the estimating algorithm is relatively close to the actual value, and if the plant
being estimated is relatively close in size to the similar plant of known cost, then the potential error from a
CFE is certainly well within the level of accuracy that would be expected from a stochastic method. Table
1 shows the typical capacity factors for some process plants. However, differences in scope, location, and
time should be accounted for where each of these adjustments also adds additional uncertainty and
potential error to the estimate. If the new plant is triple the size of an existing plant and the actual capacity
factor is 0.80 instead of the assumed 0.70, one will have underestimated the cost of the new plant by only
10 percent. Similarly, for the same three-fold scale-up in plant size, if the capacity factor should be 0.60
instead of the assumed 0.70, one will have overestimated the plant cost by only 12 percent. The capacity-
increase multiplier is CapB/CapA and in the base, r is 0.7. The error occurs as r varies from 0.7. Further,
table 2 shows percent error when 0.7 is the factor used for the estimate instead of the actual factor.

The CFE method should be used prudently. Making sure the new and existing known plants are near-
duplicates, include the risk in case of dissimilar process and size. Apply location and escalation
adjustments to normalize costs and use the capacity factor algorithm to adjust for plant size. In addition,
apply appropriate cost indices to accommodate the inflationary impact of time and adjustments for



June 18, 2011
location. Finally, add any additional costs that are required for the new plant, but were not included in the
known plant.

COST INDICES

A cost index relates the costs of specific items at various dates to a specific time in the past and is useful
to adjust costs for inflation over time. Chemical Engineering (CE) publishes several useful cost indices
each month such as the CE Plant Cost Index and the Marshall & Swift Equipment Cost Index. The CE
Cost Index provides values for several plant-related costs including various types of equipment,
buildings, construction labor and engineering fees. These values relate costs of complete plants over
time, using the 1957–1959 timeframe as the base period (value = 100). The Marshall & Swift indices
provide equipment cost index values arranged in accordance to the process industry in which the unit is
used, using 1926 as the base period.

To use either of these indices to adjust for cost escalation, multiply the un-escalated cost by the ratio of
the index values for the years in question. For example, to determine the cost of a new chlorine plant in
February 2001 using capacity factored estimates where the cost of a similar chlorine plant built in 1994
was $25M, first the cost of the 1994 must be normalized for 2001. The CE index value for 1994 is 368.1.
The February 2001 value is 395.1. The escalated cost of the chlorine plant is therefore: $25M x
(395.1/368.1) = $25M x 1.073 = $26.8M.

Product Factor
Acrolynitrile 0.60
Butadiene 0.68
Chlorine 0.45
Ethanol 0.73
Ethylene Oxide 0.78
Hydrochloric Acid 0.68
Hydrogen Peroxide 0.75
Methanol 0.60
Nitric Acid 0.60
Phenol 0.75
Polymerization 0.58
Polypropylene 0.70
Polyvinyl Chloride 0.60
Sulfuric Acid 0.65
Styrene 0.60
Thermal Cracking 0.70
Urea 0.70
Vinyl Acetate 0.65
Vinyl Chloride 0.80
Table 1 – Capacity Factors for Process Plants[8]



June 18, 2011

Actual Capacity-Increase Multiplier (CapB/CapA)
Exponent 1.5 2 2.5 3 3.5 4 4.5 5
0.20 23% 41% 58% 73% 88% 100% 113% 124%
0.25 20% 36% 51% 64% 75% 87% 97% 106%
0.30 18% 32% 44% 55% 64% 74% 83% 91%
0.35 16% 28% 38% 47% 55% 63% 70% 76%
0.40 13% 23% 32% 39% 46% 52% 57% 63%
0.45 11% 18% 26% 32% 36% 41% 46% 50%
0.50 9% 15% 20% 25% 28% 32% 35% 38%
0.55 6% 11% 15% 18% 21% 23% 25% 28%
0.60 4% 7% 10% 12% 13% 15% 16% 18%
0.65 2% 3% 5% 6% 6% 7% 8% 8%
0.70 0% 0% 0% 0% 0% 0% 0% 0%
0.75 -2% -4% -5% -5% -6% -7% -7% -8%
0.80 -4% -7% -9% -10% -12% -13% -14% -15%
0.85 -6% -10% -13% -15% -17% -19% -20% -21%
0.90 -8% -13% -17% -20% -22% -24% -26% -28%
0.95 -10% -16% -21% -24% -27% -29% -31% -33%
1.00 -11% -19% -24% -28% -31% -34% -36% -38%
1.05 -13% -22% -28% -32% -36% -39% -41% -43%
1.10 -15% -24% -31% -36% -40% -43% -45% -47%
1.15 -16% -27% -34% -39% -43% -46% -49% -52%
1.20 -18% -30% -37% -42% -47% -50% -53% -55%
Table 2 – % Error when factor r = 0.7 is used for estimate instead of actual exponent

Discrepancies are found in previously published factors due to variations in plant definition, scope, size
and other factors such as:

• Some of the data in the original sources covered a smaller range than what is now standard.
• Changes in processes and technology.
• Changes in regulations for environmental control and safety that was not required in earlier plants.

Exponents tend to be higher if the process involves equipment designed for high pressure or is
constructed of expensive alloys. As r approaches 1, cost becomes a linear function of capacity — that is,
doubling the capacity doubles the cost. The value of r may also approach 1 if product lines will be
duplicated rather than enlarged. Whereas a small plant may require only one reactor, a much larger plant
may need two or more operating in parallel.

Large capacity extrapolations must be done carefully because the maximum size of single-train process
plants may be restricted by the equipment's design and fabrication limitations. For example, single-train
methanol synthesis plants are now constrained mainly by the size of centrifugal compressors. Costs must
also be scaled down carefully from very large to very small plants because, in many cases the equipment
cost does not scale down but rather remains about the same regardless of plant capacity.

Despite these shortcomings, the r factor method represents a fast, easy and reliable way of arriving at
cost estimates at the predesigned stage. It is helpful for looking at the effect of plant size on profitability
when doing discounted cash-flow rate-of-return and payback-period calculations, and it is very useful for
making an economic sensitivity analysis involving a large number of variables.



June 18, 2011
EQUIPMENT FACTORED ESTIMATES (EFE)

Equipment factored estimates are used when the engineering is approximately 1 to 15 percent complete
to determine whether there is sufficient reason to pursue the project. If so, this estimate is used to justify
the funding required to complete additional engineering and design for a Class 3 or budget estimate. It
can be quite precise if the equipment factors are appropriate, if the correct adjustments have been
applied, and if the list of process equipment is complete and accurate. This estimating procedure relies on
the existence of a ratio between the cost of an equipment item and costs for the associated non-
equipment items (such as foundations, piping, and electrical components) needed when building a plant.
Its advantage over CFEs is its basis upon specific process design.

The first step is to estimate the cost for each piece of process equipment. The equipment list should be
examined carefully for completeness and compared against the PFDs and piping & instrumentation
diagrams (P&IDs). When the equipment list is in a preliminary stage with only the major equipment
identified, assume a cost percentage for auxiliary equipment that has not yet been defined. The
equipment sizing should be verified since equipment is often sized at 100 percent of normal operating
duty, but by the time the purchase orders are issued, some percentage of over-sizing has been added to
the design specifications. The percentage of over-sizing varies with the type of equipment as well as with
the organization’s procedures and guidelines. It is prudent to check with the process engineers and
determine if an allowance for over-sizing the equipment, as listed on the preliminary equipment list,
should be added before pricing the equipment. The purchase cost of the equipment is often obtained from
purchase orders, published equipment-cost data, and vendor quotations, and should include the
associated nozzles and appurtences, manways, internals, baffles, packing, trays, and process
instrumentation. Since the material cost of equipment can represent 20 to 40 percent of the total project
costs for process plants, it is extremely important to estimate the equipment costs as accurately as
possible. If historical purchase information is used, the costs should be escalated appropriately and
adjustments made for location and market conditions.

Once the equipment cost is established, the appropriate equipment factors should be generated and
applied with necessary adjustments for equipment size, metallurgy and operating conditions specific to
project or process conditions. For example, if the plot layout of the project requires much closer
equipment placement than is typical, one may want to make adjustments for the shorter runs of piping
and electrical than would be accommodated by the equipment factors. If a project is situated in an active
seismic zone, one may need to adjust the factors for foundations and support steel.

After developing equipment factored costs, account should be made for project costs that are not covered
by the equipment factors such as by generating indirect field costs (IFCs) and home-office costs (HOCs),
engineering costs and fees.
[23]
J.J. Lang proposed a simple set of multiplicative factors to estimate the total installed cost of a plant
from the total cost of its major equipment items (TME) based on whether the given facility is a ”solids”
plant handling mainly solid process streams, or a “solids-fluids” plant, or a ”fluids” plant, where the factors
are 3.89, 5.04, and 6.21 respectively. Since, this approach has only one element, the error of the product
is greater than that of either the TME figure or that of the multiplicative factor and the latter itself is an
average based on a large number of industries and products. Accordingly, the accuracy of this method is
not attractive. It is least reliable for outside battery limits (OSBL) and offsite costs which are highly
variable.



June 18, 2011

PROCESS Direct Costs ALL SOLID Process FLUID & SOLID Process (*) ALL FLUID Process
Mat’l Labor Total TC% Mat’l Labor Total TC% Mat’l Labor Total TC%
Purchased Equipment 1.000 N/A 1.00 26% 1.000 N/A 1.00 24% 1.000 N/A 1.00 20%
Equipment Setting 0.014 0.024 0.04 1% 0.014 0.024 0.04 1% 0.014 0.024 0.04 1%
Site Development 0.016 0.029 0.05 1% 0.016 0.029 0.05 1% 0.016 0.029 0.05 1%
Concrete 0.038 0.054 0.09 2% 0.031 0.059 0.09 2% 0.028 0.052 0.08 2%
Structural Steel 0.106 0.050 0.16 4% 0.103 0.040 0.14 3% 0.100 0.030 0.13 3%
Buildings 0.016 0.006 0.02 1% 0.016 0.006 0.02 1% 0.016 0.006 0.02 0%
Piping 0.200 0.160 0.36 9% 0.307 0.242 0.55 13% 0.520 0.450 0.97 19%
Instrumentation & Controls 0.100 0.200 0.30 8% 0.100 0.215 0.32 7% 0.140 0.280 0.42 8%
Electrical 0.109 0.086 0.20 5% 0.109 0.086 0.20 5% 0.088 0.072 0.16 3%
Insulation 0.020 0.004 0.02 1% 0.030 0.004 0.03 1% 0.060 0.012 0.07 1%
Painting 0.009 0.060 0.07 2% 0.009 0.060 0.07 2% 0.008 0.050 0.06 1%
Direct Costs = 1.63 0.67 2.30 59% 1.74 0.77 2.50 59% 1.99 1.01 3.00 59%

PROCESS Indirect Costs
Labor Indirects & Field Costs 0.160 0.392 0.55 14% 0.176 0.424 0.60 14% 0.220 0.500 0.72 14%
Contractor Engineering & Fee 0.015 0.703 0.72 18% 0.016 0.759 0.78 18% 0.020 0.890 0.91 18%
Owner Engineering & Oversight 0.080 0.242 0.32 8% 0.082 0.267 0.35 8% 0.085 0.330 0.42 8%

Total PROCESS Direct and Indirect = 1.88 2.01 3.89 100% 2.01 2.22 4.22 100% 2.32 2.73 5.04 100%

Excludes OSBL (non-process infrastructure), excludes land acquisition, excludes contingency, and assumes at-grade installations
(*) = Most reliable data
Assumed material equipment cost (MEC) factor for bulks and direct field labor (DFL) = 1.5
Labor is based on 1.0 labor productivity factor (LPF) @ $20.00 W2 rate + 91% for field indirects = $38.14 all in hourly composite labor rate
Table 3 – “Original” Lang factors (multipliers) of delivered equipment cost for capitalized costs
and % of total installed costs to construct large scale capacity US Gulf Coast process plants.

Happel[28] estimated purchase cost for all pieces of equipment (material), labor needed for installation
using factors for each class of equipment, extra material and labor for piping, insulation etc. from ratios
relative to sum of material and added installed cost of special equipment, overhead, engineering fees,
and contingency. A number of items given in table 4 below are prorated from the sum of key accounts G.
Material listing in the second column refers to delivered cost to the plant site ready for erection. The labor
items in the adjoining column are the direct labor involved in erecting each of the items noted. When
material items A through F are made of expensive material such as stainless steel, the labor percentage
will be much lower than shown in table 4 which is based on carbon steel items in material column.

Item Material Labor
Vessels A 10% of A
Towers, field fabricated B 30 to 35% of B
Towers, prefabricated C 10 to 15% of C
Exchangers D 10% of D
Pumps, compressors and other machinery E 10% of E
Instruments F 10 to 15% of F
Key accounts (Sum of A to F) G
Table 4 – Happel’s Method: Table 1

Item Material Labor
Key accounts (Sum of A to F) G
Insulation H = 5 to 10% of G 150% of H
Piping I = 40 to 50% of G 100% of I
Foundations J = 3 to 5% of G 150% of J
Buildings K = 4% of G 70% of K
Structures L = 4% of G 20% of L
Fireproofing M = 0.5 to 1% of G 500 to 800% of M
Electrical N = 3 to 6% of G 150% of N
Painting and cleanup O = 0.5 to 1% of G 500 to 800% of O
Sum of Material and Labor P



June 18, 2011

Sum of material and labor P
Installed cost of special equipment Q
Subtotal R = P+Q
Overheads S = 30% of R
Total erected cost T = R+S
Engineering fee U = 10% of T
Contingency fee V = 10% of T
Total investment W = T+U+V

It presents difficulties in piping estimation as it is time-consuming to detail the piping sufficiently to
estimate it directly. If a percentage of 40 to 50% on key equipment for piping material is employed as
suggested above, errors may result in the estimates of plants having a large proportion of investment in
machinery, compressors or other relatively expensive equipment. The use of “exotic” pipe material such
as Teflon or stainless will also naturally completely upset calculations made on the basis of a simple
percentage. A good check can be made on piping material by noting that valves will constitute 40% of
total. Another item that must be considered carefully is the allowance for profit and fees to the
engineering contractor. Prices are fixed by supply and demand rather than arbitrary percentages like
those noted above, so that equipment companies with a considerable backlog of orders may be able to
enjoy greater profits. Another important factor to bear in mind when estimating construction costs from
published data or company records is that these costs are not constant like the physical properties of
chemical compounds. It is necessary to correct them by the use of some type of construction index,
especially when all information has not been obtained at the same time. In addition tables 4, 5, and 6
above do not cover OSBL items so these should be included separately in the estimate.
[24]
Hand advanced the above approaches by applying individual factors to major equipment categories. At
a 50% error range for the quantity and for the cost of each category, the error range for each element
would be 70.7%. But when the elements are added up, the error range of the sum (representing total
installed cost) is only 39.8%.

Hackney[25,26] developed an equipment ratio method with factors for labor and materials applied to not
only major equipment but also auxiliary equipment, to installation, and to various crafts, such as piping,
electrical and building. The auxiliary equipment cost is usually estimated as a percent of the major
equipment; the costs of installation and craft activities are taken as percentages of the major and auxiliary
equipment summed. A checklist was included for numerically estimating the certainty with which the
individual aspects of the project are known. Examples include the amounts, physical forms and allowable
impurities in the raw materials and products and the extent to which the process design has been
reviewed. The sum of the individual ratings is an indication of how accurate the estimate is. In spite of its
more detailed attention to uncertainty and accuracy, it does not lend itself to direct transfer to a more
detailed budget estimate. It is preferable to employ methods that can successively ”advance” to the more
detailed estimates.
[27]
Guthrie developed a module method that applied the Hackney approach to individual equipment
accounts. It used individual material factors for various crafts but one overall labor factor. The total plant
cost is the sum of the individual equipment modules, costs of linking the modules and indirect costs. The
latter, including design engineering, project management and contractor's profit, can account for about 10
to 30% of the total plant cost, depending on site topography, the economic climate of the area, the time of
year (i.e., the weather) and the nature of the bidding process itself. The modules can also serve to
monitor costs during construction and to control the scheduling of labor since the factors are replaced
with material and labor prices and the latter are translated into labor hours. Because of the extensive
summing involved, the accuracy of this method is high. Assume for instance, that the technique is being
used for a definitive estimate and that each quantity factor and cost factor for the pump module has an
accuracy of 5%. Summing the individual pump-installation elements brings the total accuracy for the



June 18, 2011
module into the range of 3%, and when all the modules in the cost estimate for the plant are summed, the
accuracy of the plant estimate will improve to 2% or less.

The completion of any construction project yields cost data that can be valuable for future cost estimates
provided that these data are not time-indexed over an unreasonably large number of years. Cost data on
major pieces of equipment are readily available from computerized services whose databases are derived
from equipment vendor and vessel fabricator information. It is often possible to get better accuracy on the
factors for equipment installation by basing the installation outlays on the equipment size or design
available from the flow sheets for the plant. It often reveals circumstances affecting the installation cost
that are masked by the cost figures alone. The article “Sharpen Your Cost Estimating Skills” by Larry R.
[6]
Dysert , is a good source of process equipment factors. This document shows equipment factors for
process equipment range from 2.4 for columns to 3.4 for pumps and motors, based upon the raw
equipment costs.

Equipment costs must be estimated to gauge a project's economic viability, to evaluate alternative
investment opportunities, to choose from among several process designs the one likely to be the most
profitable, to plan capital appropriations, to budget and control expenditures or a competitive bid for
building a new plant or revamping an existing one. Shop fabricated costs including freight derived from
cost curves is suitable for making study estimates of total plant costs and is more than adequate for
making order-of magnitude ones. Since costs are changing and costs obtained from one source are likely
not to agree with those acquired from another, costs derived from the related graphs should not be
considered incontestable but rather should be adjusted in light of cost data from other sources according
to one's judgment and experience.

A good source of process equipment costs is DOE/NETL-2002/1169, “Process Equipment Cost
[10]
Estimation” report:

Cooling tower purchased equipment cost range from $4,000 for a 150 gal/min unit to $100,000 for a
6,000 gal/min. The cooling tower would consist of a factory assembled cooling tower including fans,
drivers and basins.
The design basis would be:
• Temperature Range: 15 °F
• Approach Gradient: 10 °F
• Wet Bulb Temperature: 75 °F

Air cooler purchased equipment cost range from $11,000 for a 100 sq/ft to $120,000 for a 10,000 sq/ft of
bare tube area. The air cooler would consist of variety of plenum chambers, louver arrangements, fin
types (or bare tubes), sizes, materials, free-standing or rack mounted, multiple bays and multiple services
within a single bay.
• Tube Material: A214
• Tube Length: 6 – 60 Feet
• Number of Bays: 1 – 3
• Power/ Fan: 2 – 25 HP
• Bay Width: 4 – 12 Feet
• Design Pressure: 150 psig
• Inlet Temperature: 300 °F
• Tube Diameter: 1 Inch
• Plenum Type: Transition shaped
• Louver Type: Face louvers only
• Fin Type: L-footed tension wound aluminum

Furnace/process heater purchased equipment cost range from $100,000 for 2 Million BTU/hour to
$5,000,000 for 500 Million BTU/hour of heat duty. The furnace heater would consist of gas or oil-fired



June 18, 2011
vertical cylindrical type for low heat duty range moderate temperature with long contact time. Walls of the
furnace are refractory lined.
• Tube Material: A214
• Design Temperature: 750 °F

Rotary pump purchased equipment cost range from $2,000 for 10 gal/min to $10,000 for 800 gal/min of
capacity. The rotary pump would consist of rotary (sliding vanes) pump including motor driver.
• Material: Cast Iron
• Temperature: 68 °F
• Power: 25 – 20 HP
• Speed: 1800 RPM
• Liquid Specific Gravity: 1
• Efficiency: 82%

Single stage centrifugal pump purchased equipment cost range from $3,000 for 100 gal/min to $600,000
for 10,000 gal/min of capacity. The single stage centrifugal pumps would consist for process or general
service when flow/head conditions exceed general service, split casing not a cartridge or barrel and
includes standard motor driver.
• Material: Carbon Steel
• Efficiency: <50 GPM = 60%, 50 – 199 GPM = 65%, 100 – 500 GPM = 75%, > 500 GPM = 82%
• Driver Type: Standard motor
• Seal Type: Single mechanical seal

Reciprocating pump (duplex) purchased equipment cost range from $4,000 for 2 HP to $30,000 for 100
HP driver power. Reciprocating pump (triplex) purchased equipment cost range from $8,000 for 2 HP to
$80,000 for 100 HP driver power. The reciprocating pump would consist of duplex with steam driver
having Triplex (plunger) with pump motor driver.
• Material: Carbon Steel
• Efficiency: 82%

The direct field cost (DFC) factor is an uplift applied to the free on board (FOB) cost of the equipment and
ranges between 2.4 - 4.3 (with instrument) and 2 - 3.5(without instrument) for different equipment.

Guthrie introduced a module costing method as a type of EFE where the main relation is as per equation
3:

CBM = CPFBM
(equation 3)

For other items the related relations are shown below:

Labor CL = αL(CP + CM) = (1 + αM)αLCP
Direct
Freight CFIT = αFIT(CP+CM) = (1 + αM)αFITCP


December 28, 2011 10 of 20

June 18, 2011
Overhead CO = αOCL = (1 + αM)αLαOCP
Indirect
Engineering CE = αE(CP + CM) = (1 + αM)αECP

Direct Field Labor Cost (DFL) = 0.25(DFC)
Indirect Field Cost (IFC) = 1.15(DFL)
Total Field Cost (TFC) = DFC + IFC
Home-Office Cost (HOC) = 0.3(DFC)
Other Project Cost (OTC) = 0.03(DFC) +0.15(TFC + HOC)
Total Project Cost (TPC) = OTC + TFC + HOC

where,
CBM = bare module cost of equipment (direct plus indirect costs)
CP = equipment cost in base case (carbon steel material at atmospheric pressure)
FBM = module factor (a factor that includes all direct and indirect costs)
CM = required material cost
CFIT = freight and insurance factor
αM = material factor
αL = labor factor
αO = overhead factor
αE = engineering factor

Each component of fixed capital investment can be considered as a factor of equipment cost. The
required material cost and the module factor are given in equations 4 and 5:

CM = αMCP
(equation 4)
FBM = (1+αM)(αL + αFIT + αLαO + αE)
(equation 5)

The bare module cost includes the direct and indirect cost only and doesn't include contingency and
auxiliary services costs. For example, if the cost of a heat exchanger in a base case (with carbon steel
material and operating at ambient pressure) equals to $10,000 then for (αM = 0.7, αL = 0.37, αFIT = 0.08,
α0 = 0.7, αE = 0.15) the bare module cost equals to $14,603. The equipment cost in a non-base case is
shown in equations 6 and 7:

FBM0 = B1 + B2FPFM
(equation 6)
CBM0 = CPFBM0
(equation 7)
where
FBM0 = module factor for non-base case;
FP = correction factor for pressure;
FM = correction factor for material.

B1 and B2 are calculated on the basis of fixed investment components, which obtained for different
equipments in specified ranges. The equipment cost (CP) is obtained by parametric models with a cost
relation shown in equation 8:

log10(CP) = K1 + K2log10(A) + K3log10(A)2

where A is a key parameter of equipment.
(equation 8)


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June 18, 2011
The pressure correction factor (FP) is described in equation 9:

log10(FP) = C1 + C2 log10(P) + C3log10(P)2

The coefficients K1, K2, K3, C1, C2, C3 are given for different equipment.
(equation 9)

By totaling the above module cost for equipments, the total module cost can be obtained. To calculate the
total plant cost one needs to add the auxiliary services and contingency costs, so 15 percent of the
module cost is considered for contingency, 3 percent for contractors, and 35 percent for auxiliary services.

Finally, the cost of a grass root plant can be calculated through equation 10:

0
CGR =1.18 CBM,i +0.35 CBM,i

where CGR = grass roots cost
(equation 10)

The auxiliary services and utilities do not depend on the pressure or material of the battery limit and
usually its cost is 35 percent of the module cost, at a base case of (CBM,i).

The capital cost, which includes all the capital, needed to ready a plant for startup is derived from:

• Direct project expenses include equipment FOB cost (CP), material (CM) required for installation,
and labor (CL) to install that equipment and material.
• Indirect project expenses include freight, insurance, and taxes (CFIT), construction overhead (CO)
and contractor engineering expenses (CE).
• Contingency and fees includes contractor fees (CFEE) and overall contingency (CCONT).
• Auxiliary facilities includes site development (CSITE), auxiliary buildings (CAUX) and off sites and
utilities (COFF).

TOTAL CAPITAL INVESTMENT COST BREAKDOWN

Total bare-module cost equipment CFE
Total bare-module cost machinery CPM
Total bare-module cost spares CSPARE
Total bare-module cost storage tanks CSTORAGE
Total bare-module cost initial catalyst CCATAL __________
Sums to total bare module investment CTBM
Cost of site preparation CSITE
Cost of service facilities (auxiliary buildings) CAUX
Cost of utility plant and related facilities COFF __________
Sums to cost of direct permanent investment CDPI
Cost of contingencies and contractors fees CCONT __________
Sums to total depreciable capital CTDC
Cost of land CLAND
Cost of royalties CROYALTY
Cost of plant startup CSTART__________
Sums to total permanent investment CTPI
Working capital CWC__________
Sums to total capital investment CTCI


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June 18, 2011
CSITE = (0.10 - 0.20) CTBM FOR GRASS ROOTS, (0.04 - 0.06) CTBM FOR INTEGRATED COMPLEX
CAUX = (0.1)CTBM FOR HOUSED OR INSIDE

Indirect on labor is based on U.S. Gulf Coast (USGC) as the suggested choice which is 115% to 180% of
direct labor cost. All other locations are compared with the USGC to establish their indirect percentages.
A typical make-up for all indirect on labor is shown below:

Proposed Ranges
Field Supervision & Field Office Expenses 25.0% to 41.0%
Temporary Facilities & Structures 9.0% to 18.0%
(Includes Temporary Support Systems & Utilities)
Construction Equipment & Tools 20.0% to 35.0%
Construction Consumables & Small Tools 9.0% to 15.0%
Statutory Burdens & Benefits 40.0% to 50.0%
Misc. Overhead & Indirects 2.5% to 6.0%
Profit/Fees for Construction Management 1.5% to 2.5%
Mobilization/Demobilization 4.0% to 6.5%
Scaffolding 4.0% to 6.0%
Total 115% to 180%

For international locations the field indirect and overheads (FIOH) percentage is identified through local
contacts or personal visits or through contacts with joint venture partners or from published information
from different sources. FIOH refers to a contractor’s construction costs necessary to support the direct
work and is a function of the project’s planned duration of need, as extended by a definable estimated
rate per hour, together with an estimated cost associated with site mobilization/transport and final
demobilization, relative size of project, type of project (grassroots or retrofit), local labor and construction
practices, site specific location and conditions (such as extremely remote site requiring daily transport of
workers to/from jobsite or special allowances for seasonal weather conditions). To compare the indirect
costs from different contractors, the multipliers should be on a similar basis and include field supervision
and indirect support staff, travel/relocation/subsistence, field per diems and relocation, temporary facilities
and structures, temporary support systems and utilities, construction equipment and tools, safety and first
aid, field office furnishings and supplies, communications, construction consumables, insurance/taxes,
statutory payroll burdens and benefits, miscellaneous overhead and indirects (home office overheads,
home office equipment, computers, purchasing services), and profit/fees. Statutory burdens should
include social security, medical insurance, unemployment benefits, worker’s compensation insurance,
general liability insurance, health and welfare, pension, education fund, industry fund, vacation, etc.

Temporary construction and consumables (TC&C) are the material, labor, and subcontract costs
associated with establishing and operating a temporary infrastructure to support construction work.
Examples of TC&Cs include: temporary facilities (such as trailers and temporary buildings, field offices,
furniture for temporary buildings, field shops including shop machinery, field warehouses, and worker
camps, temporary roads, and fencing), scaffolding materials and labor, site clean-up, temporary utility
costs, fuel, gas, welding rods, protective clothing and personal protective equipment, etc.

Field supervision/field office costs are the material, labor, and subcontract costs associated with
supervising the construction work. Examples of these costs include: wages, salaries, benefits, relocation
costs, travel expenses for assigned and local field staff (such as construction managers, superintendents,
area supervisors, craft supervisors, warehouse supervisors, field project controls, trainers, field
buyers/expediters, safety officers, etc.), and ongoing expenses for a field office such as personal
computers, telephone, fax machines, copiers, etc.


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June 18, 2011
Construction equipment/tools are material, labor, and subcontract costs necessary for providing tools and
machines to support the construction work. Examples include: cranes, trucks, welding machines, jacking
equipment, small tools, rigging devices, etc.

The contractor engineering is based on total equipment items:
• Small projects: 650 to 950 work-hours per equipment item
• Grassroots projects: 1,100 to 1,550 work-hours per equipment item
• Retrofits: 30% to 45% of all direct costs (included in direct cost is equipment, material, and labor)

The individual item count includes all numbered equipment, any numbered spares, and the individually
numbered pieces of equipment on a packaged unit.

A secondary check for grassroots projects for contractor engineering will be a cost range of 12% to 25%
of all direct costs or 8% to 14% of total project costs. The owner engineering cost is estimated as 10% to
12% of all direct costs or 25% to 45% of contractor engineering.

The contingency amount will vary based on the type of unit under consideration:
• Well established process design (previously built): 5% to 10%
• Well established process designs, debottleneck type: 20% to 35%
• Any OSBL unit: 25% to 40%
• Brand new process design (never built before): 15% to 30%
• DCS implementation, any unit: 10% to 15%.

The escalation for equipment, materials, and construction activities is based on the most current
construction cost index. The freight cost for a typical project is 2% to 6% of equipment cost. For overseas
locations, the freight cost varies from 8% to 18% of equipment cost, depending upon the country under
consideration. The spare parts (capital spares only) for US installations are 4% to 8% of equipment costs.
The percentages are higher for overseas locations (8% to 12% of equipment cost) but should be looked
at on an individual basis.

PARAMETRIC COST ESTIMATES

Parametric cost estimates are used to estimate equipment cost and finally the total plant cost at an
acceptable error percentage when there is little technical data about equipment and other capital cost
items or engineering deliverables for submission to equipment manufacturers. It involves development of
parametric model based on data on equipment costs from specified time duration. Then, using statistical
methods, the models coefficients are obtained and their accuracy and estimation capabilities are studied.
The best reference for reliable cost data is the completed projects of an organization. Applying this data,
using regression methods and statistical tests, a final model is proposed.

A parametric model is a mathematical representation of cost relationships that provide a logical and
predictable correlation between the physical or functional characteristics of a plant and its resultant cost.
Capacity and equipment-factored estimates are simple parametric models. Sophisticated parametric
models involve several independent variables or cost drivers.

The first step in developing a parametric model is to establish its scope. This includes defining the end
use, physical characteristics, critical components and cost drivers of the model taking into consideration
the type of process to be covered, the type of costs to be estimated (such as TIC and TFC) and the
accuracy range.

The model should be based on actual costs from completed projects and reflect the company’s
engineering practices and technology. It should use key design parameters that can be defined with
reasonable accuracy early in the project scope development and provide the capability for the estimator


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to easily adjust the derived costs for specific factors affecting a particular project. Finally, the model
should generate current year costs or have the ability to escalate to current year costs.

Data collection and development for a parametric estimating model requires significant effort. Both cost
and scope information must be identified and collected. It is best to collect cost data at a fairly low level of
detail. The cost data can always be summarized later if an aggregate level of cost information provides a
better model. It is important to include the year for the cost data in order to normalize costs later. The type
of data to be collected is usually decided upon in cooperation with the engineering and project personnel.
It is best to create a formal data collection form that can be consistently used and revised if necessary.

After the data have been collected, it must be normalized. By doing this, we make adjustments to account
for escalation, location, site conditions, system specifications and cost scope. Data analysis, the next step
in the development of a parametric model, is achieved by a wide variety of techniques such as performing
regression of cost versus selected design parameters to determine the key drivers for the model. The
regression involves iterative experiments to find the best-fit algorithms or mathematical relationships that
describe how data behave. The result is a parametric model. Most spreadsheet applications provide
regression analysis and simulation functions that are reasonably simple to use. As an algorithm is
discovered that appears to provide good results, it must be tested to ensure that it properly explains the
data. Using advanced statistical tools can quicken the process but can be more difficult to use.
Sometimes erratic or outlying data points will need to be removed from the input data in order to avoid
distortions in the results. The algorithms will usually take one of the equations 11&12:

A linear relationship, such as,

Cost = a + bV1 + cV2 + ...
(equation 11)
or a nonlinear relationship, such as,

Cost = a + bV1x + cV2y + …
(equation 12)

where V1 and V2 are input variables; a, b, and c are constants derived from regression; and x and y are
exponents derived from regression.

The equation that is the best fit for the data will typically have the highest R-squared (R2) value, which
provides a measure of how well the algorithm predicts the calculated costs. However, a high value by
itself does not imply that the relationships between the data input and the resulting cost are statistically
significant. One still needs to examine the algorithm to ensure that it makes sense.

A cursory examination of the model can help identify the obvious relationships that are expected. If the
relationships from the model appear to be reasonable, then additional tests (such as the t-test and f-test)
can be run to determine statistical significance and to verify that the model is providing results with an
acceptable range of error. A quick check can be performed by running the regression results directly
against the input data to see the percent error for each of the inputs. This allows the estimator to
determine problems and refine the algorithms. After the individual algorithms have been developed and
assembled into a complete parametric cost model, it is important to test the model as a whole against
new data (data not used in the development of the model) for verification.

During the data application stage, a user interface and a presentation form for the parametric cost model
is established. Computer spreadsheets provide an excellent means of accepting estimator input,
calculating costs based upon algorithms, and displaying output.

Perhaps the most important effort in developing a parametric (and any other) cost model is making sure
the application is thoroughly documented. Record the actual data used to create the model, the resulting


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regression equations, test results and a discussion on how the data was adjusted or normalized for use in
the data analysis stage. Any assumptions and allowances designed into the cost model should be
documented, as should any exclusion. The range of applicable input values and the limitations of the
model’s algorithms should also be noted. Write a user manual to show the steps involved in preparing an
estimate using the cost model and to describe the required inputs to the cost model.

Induced-draft cooling towers are typically used in process plants to provide a recycle cooling-water loop.
These units are generally prefabricated and installed on a subcontract or turnkey basis by the vendor.
Key design parameters that appear to affect the costs of cooling towers are the cooling range, the
temperature approach and the water flow rate. The cooling range is the temperature difference between
the water entering the cooling tower and the water leaving it. The approach is the difference in the cold
water leaving the tower and the wet-bulb temperature of the ambient air.

Cooling Temperature Flow Rate, gal/min Actual Cost, $ Predicted Cost, $ % Error
Range, °F Approach, °F
30 15 50,000 1,040,200 1,014,000 -2.5%
30 15 40,000 787,100 843,000 7.1%
40 15 50,000 1,129,550 1,173,000 3.8%
40 20 50,000 868,200 830,000 -4.4%
25 10 30,000 926,400 914,000 -1.3%
35 8 35,000 1,332,400 1,314,000 -1.4%
Table 7 – Actual Costs versus Predicted Costs with Parametric Equation

Table 7 provides the actual costs and design parameters of six recently completed units whose costs
have been normalized (adjusted for location and time) to a Northeast US, year-2000 timeframe[6]. These
data are the input to a series of regression analyses that are run to determine an accurate algorithm for
estimating costs. Using a computer spreadsheet, the cost estimation algorithm was developed as per
equation 13:

Predicted Cost = $86,600 + $84,500(Cooling Range, °F)0.65 – $68,600(Approach, °F) +
+ $76,700(Flow Rate, 1,000 gal/min)0.7
(equation 13)

The above equation demonstrates that the cooling range and flow rates affect cost in a nonlinear fashion,
while the approach affects cost in a linear manner. Increasing the approach will result in a less costly
cooling tower, since it increases the efficiency of the heat transfer-taking place. These are reasonable
assumptions. The regression analysis resulted in an R2 value of 0.96, which indicates that the equation is
a “good fit” for explaining the variability in the data. The percentage of error varies from –4.4 percent to
7.1 percent. The estimating algorithm developed from regression analysis, can be used to develop cost
versus design parameters that can be represented graphically.

This information can then be used to prepare estimates for future cooling towers. It is fairly easy to
develop a spreadsheet model that will accept the design parameters as input variables, and calculate the
costs based on the parametric estimating algorithm.

To derive the models, one needs to suppose that a linear relationship exists between the cost of the
equipment and its key parameters as per equation 14:
2
ln(CE) = A + Bln(KP) + Cln(KP)

Where CE is equipment cost and KP is a key parameter. The models for other equipment are given in
Table 8 calculated using the linear regression method along with the coefficients.
(equation 14)


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June 18, 2011

.
Figure 2 – Graph developed from regression data for tower cost that can be used for future
cooling towers.

Equipment Proposed Models Parameter Ranges %AAD Coefficients
Pressure Vessels (Carbon Steel) CE = exp[A1 + B1ln(W) + C1ln(W)^2] 180 < W < 621,000 21%
A1 = -1.731737
2 < P < 20 B1 = 0.5598
C1 = 0.024773
Pressure Vessels (Stainless Steel) CE = exp[A2 + B2ln(W)] 168 < W < 108,849 27.6% A2 = -2.788577
2<P<5 B2 = 0.94935
Atmospheric Storage Tanks CE = exp[A3 + B3ln(W)] 2,800 < W < 1,540,000 4.2% A3 = -4.619487
(Carbon Steel) B3 = 0.9892
Separation Tower (Carbon Steel) CE = exp[A4 + B4ln(W) + C4ln(W)^2] 5,360 < W < 178,000 12.8% A4 = 13.271536
3.5 < P < 30 B4 = -2.253712
C4 = 0.154118
Separation Tower (Stainless Steel) CE = exp[A5 + B5ln(W) + C5(L/D)] 6,400 < W < 39,000 37% A5 = -2.484312
1.4 < (L/D) < 21.3 B5 = 0.964302
3.5 < P < 37 C5 = 0.04109
Shell and Tube Heat Exchangers – CE = exp[A6 + B6ln(W)] 4,400 < W < 77,400 3.2% A6 = -2.910474
BEU Type (Carbon Steel) 7 < P < 85 B6 = 1.016550
Oil Injected Screw Compressor CE = exp[A7 + B7WP + C7WP^0.5] 7 < WP < 315 9.2% A7 = 2.193159320
7 < P < 85 B7 = -0.01059287
C7 = 0.450875824
Where: W(weight, kg), P(operating pressure, bar), L(length, m), D(diameter, m), CE(equipment cost, Millions Iranian Rials),
WP(power, kW). Note: The above costs are related to year 2004 in the Iranian market.
Table 8 – Obtained models for some equipment

The parametric models for the above equipment were prepared using a provided data bank including the
cost and some specifications of equipment. Because of limitations, both in the number of projects and in
the type of equipment, the defined models are in specified limited domains. To increase these domains,
additional cost data in broader ranges are needed.

To increase these domains, additional cost data in broader ranges are needed. The achieved results can
be used as initial data to develop more complete models.

In the above table, the obtained models are shown, as well as the applicable ranges and absolute
average deviation percentages, which are listed as %AAD. The %AAD can be defined as per equation
15:

1 ABS Y − Y
%AAD = 100x
n Y

where Y is the estimated value and Yi is the cost value from data bank and n is the number of data.

(equation 15)


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For example, the cost of a BEU type heat exchanger (carbon steel) with a weight of 10,000 kg can be
calculated as:

CE = exp(-2.910474 + 1.01655 ln(10000)) = 631.15 MRls = $71253.60

(For exchange rate in 2004 use: 8900 Rials = 1 $)

The confidence interval method also provides a means of quantifying uncertainty. For each coefficient (Bi)
is as per equation 16:

Bi = B ± tSE

where B is estimated coefficients, t is t-student from the distribution table and depends on degree of
freedom and statistical significance. SE is the standard error for coefficients.
(equation 16)

The confidence interval was determined at 95 percent statistical significance for coefficients of the six first
models and 90 percent statistical significance for the last model for a compressor.

Table 9 shows the related confidence intervals and standard errors for coefficients in the proposed
models. Since none of the intervals straddle zero, then none of the coefficients are zero, and therefore,
they are acceptable.
2 2
The goodness of fit is explained by R-square in regression. R = 1 is a perfect score. R = 0.99 is a very
good score that shows the goodness of fit.
2
Equipment Coefficients t Standard Confidence Interval R
Error
Pressure Vessels (Carbon Steel) B1 = 0.5598 1.98 0.135254 0.292005 < B1 < 0.827595 0.99
C1 = 0.024773 1.98 0.007028 0.0108576 < C1 < 0.0386884 0.99
Pressure Vessels (Stainless Steel) B2 = 0.94935 2.074 0.035066 0.876623 < B2 < 1.022077 0.98
Atmospheric Storage Tanks (Carbon Steel) B3 = 0.9892 2.074 0.007508 0.97362 < B3 < 1.00477 0.99
Separation Tower (Carbon Steel) B4 = -2.253712 2.179 0.696337 -3.77103 < B4 < -0.73639 0.99
C4 = 0.154118 2.179 0.032736 0.082786 < C4 < 0.22545 0.99
Separation Tower (Stainless Steel) B5 = 0.964302 2.776 0.011674 0.640231 < B5 < 1.288372 0.99
C5 = 0.04109 2.776 0.001323 0.0004363 < C5 < 0.0077816 0.99
Shell and Tube Heat Exchangers – BEU B6 = 1.016550 2.131 0.006779 1.002104 < B6 < 1.030996 0.99
Type (Carbon Steel)
Oil Injected Screw Compressor B7 = -0.01059287 1.697 0.000939 -0.00624 < B7 < -0.00899 0.99
C7 = 0.450875824 1.697 0.025139 0.0024 < C7 < 0.087 0.99
Table 9 – Confidence Intervals

Cost estimation accuracy by parametric models in the feasibility study stages ranges between 20 to 50
percent (upper limit) and -15 to -30 percent (lower limit). These models can be accepted with accuracy
ranges between ±3 percent to ±37 percent. The obtained models are related to a specific year. Because
of inflation, they must be re-evaluated for use in following years.

ACCURACY OF FACTORED ESTIMATE

There are different kinds of cost estimates prepared in the conceptual arena depending on their purpose
or the amount of time and information available with an accuracy of plus or minus X %, implying that the
true value lies between (100 + X)% and (100 - X)%. However, that range is biased, because the largest
possible positive deviation theoretically approaches infinity whereas the largest possible negative
deviation is only 100%. So, a value of (100 - X) is a more significant departure from X than is the value
(100 + X).


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[1]
In line with this logic, the listing of cost estimates classes sanctioned by AACE typically uses ranges
with the positive deviation being larger than the negative:

Primary
Secondary Characteristic
Characteristic
DEGREE OF
EXPECTED
ESTIMATE PROJECT END USAGE METHODOLOGY
Typical purpose of ACCURACY RANGE
CLASS DEFINITION Typical estimating method Typical variation in low and
Expressed as % of estimate [a]
high ranges
complete definition
Capacity factored,
Concept L: -20% to -50%
Class 5 0% to 2% parametric models,
screening H: +30% to +100%
judgment, or analogy
Study or Equipment factored or L: -15% to -30%
Class 4 1% to 15%
feasibility parametric models H: +20% to +50%
Budget Semi-detailed unit costs
L: -10% to -20%
Class 3 10% to 40% authorization or with assembly level line
H: +10% to +30%
control items
Control or Detailed unit cost with L: -5% to -15%
Class 2 30% to 70%
bid/tender forced detailed take-off H: +5% to +20%
Check estimate Detailed unit cost with L: -3% to -10%
Class 1 70% to 100%
or bid/tender detailed take-off H: +3% to +15%
Notes: [a] The state of process technology and availability of applicable reference cost data affect the range markedly.
The +/- value represents typical percentage variation of actual costs from the cost estimate after application of
contingency (typically at a 50% level of confidence) for given scope.
Table 1 – Cost Estimate Classification Matrix for Process Industries[1]

It is important to understand how uncertainties propagate in cost estimates involving the four arithmetic
manipulations (being the sum of multiplicative products or requiring subtraction and division during its
calculation) since the values of the quantities, unit costs and other numbers being thus manipulated
typically are uncertain.

Consider an estimate to be a summation of elements with each element being the product of two
variables or factors: a) Quantity Factor: the number of units - individual pieces as reactors, areas as
surfaces to be insulated, volumes as cubic meters of concrete to be poured or other units that enumerate
the entity being priced, and b) Cost Factor: the corresponding unit cost. When two or more independent
variables A and B are multiplied together, any inaccuracies in the individual variables are amplified in their
product:
2 2 2 2 1/2
(A ± a)(B ± b) = AB ± (A b + B a )

If a is a symmetric accuracy range for A, and b is a symmetric accuracy range for B

For instance, consider a cost estimate element consisting of a tank. Its required volume A is expected to
be 21,000 gal with an uncertainty of ± 20%, and its anticipated unit capital cost B is $2/gal with an
uncertainty of ± 30%. Thus, a equals (21,000)(0.20) or 4,200, and b is (2)(0.30) or $0.60. Then their
product P becomes: P = (21,000)(2.00) ± (21,0002 x 0.602 + 22 x 4,2002)1/2 = 42,000 ± 15,143, or ± 36.1%
between the percent ranges corresponding to the product of two independent variables, each having its
own accuracy range. The range of the product is at the intersection of the row and column appropriate for
the two variables. The ± 20% quantity factor would be accurate enough for budgeting purposes under the
aforementioned conventional listing, and the ± 30% cost factor would qualify for study or factored
estimates, but their product qualifies only for use as a conventional order-of-magnitude or conceptual


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estimate. If the quantity and cost factors each were instead ± 50% accurate, their product would be ±
70.7%, unacceptable even for order-of-magnitude purposes.

Division has the same effect as multiplication, increasing the range of inaccuracy whereby the product or
quotient is less accurate than the more uncertain of the two factors involved.

When two or more independent variables are added, any inaccuracies in the individual variables are
decreased in their sums. The expression for two numbers A and B having symmetric accuracy ranges a
and b is:
2 2 1/2
(A ± a) + (B ± b) = A + B ± (a + b )

Consider, for instance, summing the costs of 10-in. and 8-in. flanges, respectively costing $120 with an
accuracy of 10% and $80 with an accuracy of ± 10%. Then a = (120)(0.10) = $12, and b = (80)(0.20) =
$16, and their sum S becomes: S = (120 + 80) ± (122 + 162)1/2 = 200 ± 20 = 200 ± 10%

The expected error range of the total will be less than the error in either of the individual numbers or, at
most, equal to the lower of them.

This decrease in accuracies is not limited to the summation of two variables. The inaccuracies of the
seven cost-estimating elements such as list of process equipment that is needed for a distillation unit
become far less significant when the associated costs are summed. This demonstrates that the more
detail in which we define the scope of our project, the more accurate our estimate becomes.

In subtraction, the same formula is used as for addition. The expected absolute range is the same as
when adding, but the percentage range is much greater. Consider again the two flanges mentioned
1/2
above and take the difference D in their costs: D = (120 - 80) ± (122 + 162) = 40 ± 20, or ± 50%

These uncertainty-propagation rules have significant implications for the accuracies that we can expect
from any given estimating method.

CONCLUSION

Factored cost estimation is proposed as sample methods to organizations and engineering companies to
derive their own cost relations by referring to their past project cost archives. When deciding upon
potential investment opportunities, management must employ a cost screening process that requires
various estimates to support key decision points. At each of these points, the level of engineering and
technical information needed to prepare the estimate will change. Accordingly, the techniques used
prepare the estimates will vary depending upon the information available at the time of preparation, the
end use of the estimate, and its desired accuracy. The challenge for the engineer is to know what is
needed to prepare these estimates, and to ensure they are well documented, consistent, reliable,
accurate and supportive of the decision-making process.

REFERENCES

1. AACE International Recommended Practice No. 18R-97, Cost Estimate Classification System – As
Applied in Engineering, Procurement, and Construction for the Process Industries, AACE
International, Morgantown, WV, (latest revision)
2. Black, Dr. J. H., “Application of Parametric Estimating to Cost Engineering”, 1984 AACE
Transactions, AACE International, 1984
3. Mohammed Reza Shabani and Reza Behradi Yekta, “Chemical Processes Equipment Cost
Estimation Using Parametric Models”, AACE International, May 2006


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June 18, 2011
4. Chilton, C. H., “Six Tenths Factor Applies to Complete Plant Costs”, Chemical Engineering, April
1950
5. Dysert, L. R., “Developing a Parametric Model for Estimating Process Control Costs”, 1999 AACE
6. Dysert, L. R., “Sharpen Your Cost Estimating Skills”, Cost Engineering, Vol. 45, No.6, AACE
International , Morgantown, WV, 2003
7. Guthrie, K. M., “Data and Techniques for Preliminary Capital Cost Estimating”, Chemical Engineering,
March 1969
8. Guthrie, K.M., Capital and Operating Costs for 54 Chemical Processes, Chem. Eng., June 1970.
9. Mohammed Reza Shabani and Reza Behradi Yekta, “Suitable Method for Capital cost estimation in
Chemical Process Industries”, AACE International, May 2006
10. Loh, H.P., Jennifer Lyons, and Charles W. White III, Process Equipment Cost Estimation Final
Report, DOE/NETL-2002/1169, U.S. Department of Energy/National Energy Technology Laboratory,
January 2002
11. Hand, W. E., “Estimating Capital Costs from Process Flow Sheets”, Cost Engineer’s Notebook, AACE
International, January 1964
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CONTRIBUTORS

Rashmi Prasad (Author)
Kul B. Uppal, PE CEP
A. Larry Aaron, CCE CEP PSP
Peter R Bredehoeft Jr., CEP
Larry R. Dysert, CCC CEP
James D. Whiteside II, PE


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