Conference Paper

NREL/CP-6A1-48582

July 2010

Further Developments on the 

Geothermal System Scoping 

Model

Preprint

M. Antkowiak, R. Sargent, and J.W. Geiger

To be presented at the Geothermal Resources Council 2010 

Annual Meeting 

Sacramento, California 

October 24-27, 2010
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1

Further Developments on the Geothermal System Scoping Model

Mark Antkowiak, Rosemary Sargent, and Jesse W. Geiger 

National Renewable Energy Laboratory

KEYWORDS: EGS, geothermal systems, geothermal modeling

ABSTRACT

The fields of well construction and engineering, power plant construction and engineering, and reservoir engineering 

often proceed independently of one another. Yet the subsystems of a geothermal plant with which each of these 

fields is concerned need to be integrated in order to create a viable geothermal power system and make enhanced (or 

engineered) geothermal systems (EGS) a technical and an economic reality. Furthermore, each of these subsystems 

need to be examined in the context of the overall power system to aid with plant construction, and–more salient to 

the U.S. Department of Energy–to help determine best investment of research dollars.

In further development of a high-level model begun in collaboration between the National Renewable Energy 

Laboratory (NREL) and Sandia National Laboratories (SNL), refinements of the Geothermal System Scoping Model 

(GSSM) are presented. GSSM uses a lumped-parameter approach to examine the interactions among the several 

subsystems of a putative EGS. This effort will provide a means for performing a variety of trade-off analyses of 

surface and subsurface parameters, sensitivity analyses, and other systems engineering studies in order to better 

inform R&D direction and investment for the development of geothermal power into a major contributor to the U.S.

energy supply.

GSSM is not a design tool, but rather is intended to search over broad parameter spaces to determine the technical, 

and to a more limited extent, economic feasibility of a wide range of geothermal power configurations. The model 

does not make any assumptions as to the type of geothermal power being used. Thus, whether the system 

considered is hydrothermal, EGS, or co-produced fluids is not explicitly considered, although the inputs to the 

model should be aligned with known characteristics of the type(s) of plant under consideration. This allows GSSM 

to be more broadly applied. The model is complementary to ongoing work at SNL, which is more strongly focused 

on EGS.

Early results of the application of GSSM to the Geothermal Technologies Program’s technical baseline are also 

presented.

INTRODUCTION

There has been an increased interest and investment in geothermal power in recent years. In some cases this 

increase has been dramatic. For example, the U.S. Department of Energy’s (DOE) Geothermal Technologies 

Program (GTP) has seen a striking increase in its omnibus funding from near zero in 2007 to some $50 million in 

fiscal year (FY) 2010. In addition, the American Re-investment and Recovery Act (ARRA) allotted $400 million to 

GTP in FY 2009, over and above its omnibus funding. This interest has in part been sparked by the publication of 

the seminal Massachusetts Institute of Technology (MIT) study sponsored by DOE, The Future of Geothermal 

Energy, which describes enhanced, or engineered, geothermal systems (EGS)1

.

The purpose of this work is to develop a simple, flexible, high-level geothermal systems model to enable the 

performance of trade studies and sensitivity analyses among the various components and parameters of a geothermal

power station. For example, questions such as “How does the efficiency of the power plant affect the total number 

of wells that need to be drilled in order to build a profitable plant from a given reservoir, and what is the optimal 

ratio of producers to injectors?” or “How does the shape of a reservoir affect the power it can deliver?” The

Geothermal Systems Scoping Model (GSSM), still under development, can help answer questions such as these, and 

can inform decision-making in order to achieve GTP programmatic and national goals. Portions of this work have 
2

already been incorporated into a more sophisticated systems dynamics-based model being developed by Sandia 

National Laboratories (SNL).

2

 This paper is a follow-up to work presented previously.3

DEFINITIONS AND ASSUMPTIONS

In order to construct the GSSM, a geothermal power plant design is divided into four basic design blocs based on the 

major subsystems of a geothermal power plant – the reservoir, the wells, which are further divided into producers 

and injectors, and the surface facility. The producing wells are treated separately from the injectors. The model 

uses a readily accessible spreadsheet program (MS Excel) and makes extensive use of lumped parameters. Thus the 

individual blocs are interconnected but many engineering details of each are left unspecified; the interactions among 

them are what are important. This is not to say that the model does not include considerable detail, but rather that 

the model lumps parameters together in such a way as to maximize flexibility when trying different scenarios. In 

this sense, GSSM is more concerned with interface engineering among the various subsystems. The idea is not to 

develop a complete geothermal power plant specification, but rather to study the effects of varying parameters of 

one part of a geothermal plant on the other parts. This enables a high-level plant description that can serve as a 

starting point for plant design and as a benchmark for the determination of best investment of RD&D dollars. In 

fact, the development of various scenarios for the latter is one of the prime motivators for this work.

The blocs indicated previously are briefly described below. This is followed by a discussion of the various 

simplifying assumptions for GSSM and a work-up of a 20 MWe EGS power plant scenario.

Power Plant

For the purposes of GSSM, this is defined as all heat exchangers, flash vessels, condensers, turbines and generators, 

plus all pumps required to move fluid internally among these components. It can be thought of as that portion of the 

geothermal plant between the vaporizer inlet and the condenser outlet when following the circuit of the geothermal 

fluid. This specifically excludes pumping requirements from the well systems (see below). The power plant 

efficiencies used in GSSM calculations factor in all losses between these points, including frictional and form losses, 

turbine efficiencies, heat loss through component exposure to atmosphere, etc.

The power plant is assumed to be located at a point very near the center of the footprint of the reservoir projected to 

the surface.

Injector Wells

This is the simpler set of wells for modeling purposes. The design of the well(s) is a simplified version of a well 

design given in a report from SNL.

4 Each is broken into three sections for the purposes of hydraulic calculations –

production liners 1, 2 and 3, with a standard diameter for each section. Liner 1 is assumed to be 13 5/8 inches, or 

0.346075 m, in diameter. Production liners 2 and 3 are 0.244475 and 0.1778 m, respectively. The top portion of the 

well is liner 1, the bottom is liner 3. Pumping requirements are calculated for the injector wells separately from the 

producers, but no assumption is made as to the actual location of these well pumps (well head at the injectors, 

downhole in the producer, etc.) It is only necessary to calculate the pumping needed.

The heads of the injector wells are assumed to be co-located with the power plant for calculation purposes.

Reservoir

This is the rock mass from which heat is drawn as well as the pore and fracture system within this mass through 

which the water actually passes. In terms of the system circuit, it is that portion of the system between the bottom(s) 

of the injector well(s) and the bottom(s) of the producer(s). For the sake of simplicity, the water is assumed to pass 

through the entire volume of the reservoir, and heat is also assumed to be withdrawn uniformly from the entire 

volume. There is no assumption as to the form of the flow circuits through the reservoir, but rather these are 

characterized with a bulk hydraulic conductivity, and the model for the reservoir is similar to that of a confined 

aquifer. Pumping requirements are calculated based on a standard formulation of bulk flow through a confined 

aquifer, with the density based on the average (midpoint) temperature of the fluid in the reservoir.
3

Producer Wells

This includes both producer wells and the overland travelers that ultimately connect the producers to the power 

plant. Pumping requirements for both the producer wells and the travelers are calculated in this bloc. As in the case 

of the injectors, no assumption is made as to the specific location(s) of the pump(s). 

These blocs are conceptually arranged as shown in Figure 1. In earlier versions of GSSM, either the power plant 

could be selected to impose requirements on the reservoir, or the reservoir could be selected to impose constraints on 

the power plant, with the requirements and the constraints being mediated by the wells. This version streamlines the 

input while allowing both the power plant and the reservoir to be manipulated separately.

INJECTOR

WELLS

PRODUCER

WELLS

POWER 

PLANT

RESERVOIR

Figure 1: Conceptual layout of a geothermal power system

Thus, GSSM can be used to determine the general requirements that a potential reservoir formation must meet. 

However, since the actual reservoir created imposes constraints on the power plant that can be built, the reservoir 

can also be described and input to the model to help define the parameters of the desired power plant.

KEY ASSUMPTIONS

1) The resource type, whether it is hydrothermal, EGS, co-produced fluid with re-injection or other, is not 

specified in the model. However, the model does assume that the mass of the fluid brought up in the producer wells 

is equal to the mass of the fluid re-injected. Also, since the fluid is assumed to be re-injected, this excludes a broad 

swath of co-produced fluid from some oil and natural gas fields.

2) The power plant type–flash, binary, hybrid, etc. is assumed not to matter and is also not specified. In both 

conventional hydrothermal plants and EGS, the produced geofluid is re-injected into the reservoir, and some 

inventory tends to be lost, even in EGS where a binary plant is used. This latter condition is due to losses through 

other cracks and fissures that intersect the flow-path from the injector(s) to the producer(s), or bleed inventory away 

from the reservoir at the edges. However, since the re-injection flow rate is assumed equal to the production flow 

rate, this implies a binary plant. Furthermore, no geofluid phase change is assumed for the wells or reservoir.

3) For simplicity, it is assumed that the specific heat of the brine is constant throughout the plant, 

corresponding to the average temperature of the brine in the plant.

4) Reservoir geometry is assumed to be reasonably well described with a simple solid geometry; in this case a 

hybrid geometry between an elliptical disk and a rectangular slab. Currently the reservoir is assumed to be 

horizontal, although there are plans to allow various angles of inclination in future versions.

5) The reservoir is assumed to be essentially homogeneous and isotropic, and is modeled as a confined aquifer 

with constant bulk hydraulic conductivity throughout6

. Thus, there is no need to define the fracture width, spacing 

or geometry. These will be incorporated in later versions.

6) All wells are assumed to penetrate vertically to the same depth and are of identical size. This assumption 

follows in part from the reservoir lying horizontally, and will likely change in the future.
4

7) Injector wells are assumed to be located a negligible distance from the power plant(s); this results in 

overland traveler lines associated only with production wells.

DISCUSSION

GSSM allows the analysis of the impact of manipulating various parameters of a geothermal power system on other 

parts of the system. The user can approach the problem from the perspective of desiring to build a plant of a 

specified size, and can then impose requirements on the reservoir to be created. This allows more of a scoping level 

type of analysis. Alternatively, the user can input known parameters of the reservoir and determine characteristics 

of the power plant. This approach lends itself to trade-off analyses. 

There are a total of 31 input parameters for GSSM, broken down into five blocs: ambient conditions (one 

parameter), reservoir (nine parameters), power plant (13parameters), wells (seven parameters), and financial (one 

parameter).Note that the system is broken into four blocs for calculation purposes, but the wells are treated in 

generally the same way, with the difference being the inclusion of the overland traveling lines from the producers. 

Many of the input parameters are straightforward; those needing somewhat more explanation are described below.

Reservoir

Average geothermal gradient –the rate at which the temperature of the underlying rock increases with depth in units 

of °C/ km.

Reservoir "rectangularity” –refers to the degree to which the surface footprint of the reservoir tends toward 

rectangular rather than elliptical. This number is dimensionless and varies between 0 and 1, being a weighting 

factor used to calculate an average of the areas of a rectangle and an ellipse with the same length and width. Thus, 

the surface footprint is described as part ellipse, part rectangle, and can vary from a circle to a square. This allows 

somewhat more descriptiveness for the geometry of the reservoir. An example is shown in Figure 2.

Figure 2: Example of ellipse with approximately 1/3 rectangularity (red dashed lines) showing its 

circumscribed ellipse and the rectangle which inscribes it

Portion of reservoir Energy Remaining if Extraction is Complete – the remaining portion of exergy in the reservoir 

after the desired amount of energy is extracted.

Input - Power Plant

Reject ∆T above ambient –the excess temperature relative to ambient at which the power plant rejects waste heat.

Efficiency coefficient –the fraction of Carnot efficiency at which the power plant actually operates.

Total dissolved solids - start up and finish are the amounts, in ppm, of dissolved formation and other material 

traveling in the geothermal fluid at the beginning and end of plant life.

Specific gravity adjustment - start up and finish represents the effects on the geothermal brine for such measures as 

brine density, viscosity, etc.
5

Lifetime average capacity factor – the ratio of the actual total energy produced by the plant over the rated lifetime to 

the total energy that could have been produced had the plant been running at full rated capacity continuously over its 

lifetime, this is a dimensionless number.

Efficiency coefficient – this dimensionless number is the proportion of the Carnot efficiency actually achieved by 

the plant.

Input - Wells

Brine-well heat loss coefficient –a lumped parameter to describe the heat lost by the geothermal brine in transit from 

the reservoir to the power plant. It is estimated here as a simple proportionality constant relating the distance 

traveled by the brine to the plant to the temperature decrease it experiences. It is not a physics-based parameter 

because there is no accounting for the differences between the well casing temperature and the free stream fluid 

temperature, not between the top and bottom of the well. It is intended to provide a somewhat more realistic 

description than simply assuming the plant inlet sees the bottom-hole temperature; units are in °C/m.

Fraction of length for production liner 1 - the fraction of the well that is of the widest diameter, Production liner 2 

is the intermediate section diameter.

Input - Financial

Assumed lifetime average cost per kWh is a simple measure to convert plant output to financial return. It is 

intended only as a benchmark.

There are 33 outputs, although several of these are expressed in multiple different units so that there are 41 output 

lines in all. Most of these are self-explanatory. Others are described below.

Output – Reservoir

Initial reservoir temperature –the product of the well depth and the average geothermal gradient, units are in °C.

Final reservoir (abandonment) temperature –the lowest temperature reached by the reservoir just before that 

reservoir is abandoned, units are in °C. It is calculated from the initial reservoir temperature and the portion of 

energy remaining after extraction from the inputs, and has an error flag built in case this calculation goes below the 

re-injection temperature.

Extractable Initial Reservoir Energy Content - the amount of thermal energy that can be extracted from the reservoir 

based on specific heat, reservoir mass, and the difference between the initial and final reservoir temperatures.

Total Thermal Energy Extracted over Planned Lifetime of Plant - the total energy that is actually extracted from the 

reservoir over the course of the plant life. This is set to flag an error message if this value exceeds the Extractable 

Initial Reservoir Energy Content, above.

Output - Power Plant

Essentially all of the power plant output parameters are self-explanatory. Most are calculated at start up and finish 

to account for the effect of the changing temperature of the reservoir over the course of the plant life.

Time to complete extraction is the time it would hypothetically take if the reservoir were allowed to run all the way 

down to the final temperature. This must always be greater than or equal to the inputted planned plant life 

parameter.

Output - Wells

The length of production liner 3 is calculated from the remaining portion of the well depth that is not taken up by 

liners 1 and 2.
6

Distance from producers to power plant - represents a compromise for a very complicated well spacing scheme. It is 

equal to the distance between foci of the ellipse in the case of one producer and one injector, half that if there are 

two producers per injector. In cases where there are more than two producers, calculations pertaining to wellfield 

layout were much more difficult to contend with. Even with the simplifying assumptions that all wells penetrate 

vertically and to the same depth, a great deal depends on the positions of the wells relative to one another, and there 

are far too many ways that multiple wells can be arranged for a given number of wells and a given surface footprint. 

Several approaches were attempted, including tessellation of a surface with regular polygons. In the end, a simple 

scheme was adopted based on the average footprint area per well and the perimeter of the surface footprint.

Well catchment facing represents the flow width through the reservoir (as it is modeled as a confined aquifer). It is 

normal to the flow direction and is set equal to four times the square root of the average surface (footprint) area per 

producer.

Table 1: Inputs for a 20 MWe plant

Average geothermal gradient 45 °C/ km Average Annual Ambient Temperature 10 °C

Average reservoir specific heat capacity 0.8 kJ/kg-K

Average reservoir rock density 2700 kg/m3 mass flow rate 292.6 kg/s

Reservoir Bulk Hydraulic Conductivity 8.00E-07 m/s Reject ∆T above Ambient 2 °C

Reservoir length 5,600 m Lifetime Average Capacity Factor 0.9

Reservoir width 4,020 m Efficiency coefficient (power plant fraction of 

Carnot) 0.2

Reservoir thickness 100 m Re-Injection Temperature, start up 10 °C

Reservoir "rectangularity" 0.5 Re-Injection Temperature, finish 10 °C

Portion of Reservoir Energy Remaining if Extraction is 

Complete 0.89 Re-Injection temperature change over plant lifetime 0 °C

WELLS Total Dissolved Solids, start up 0 ppm

# INJECTORS 3 Specific gravity adjustment, start up 1

PRODUCER/ INJECTOR RATIO 2 Total Dissolved Solids, finish 50,000 ppm

well pump efficiency 0.67 Specific gravity adjustment, finish 1.05

WELL DEPTH 5 km Planned Plant Lifetime 30 yrs

Brine-Well heat loss coefficient 0.001 °C/m

Fraction of length for Production Liner 1 0.5 Assumed lifetime average cost per kWh 0.100 $

Fraction of length for Production Liner 2 0.35

Diameter of traveling Lines from producers to power 

plant 0.254 MWe

FINANCIAL

AMBIENT CONDITIONS

INPUTS

RESERVOIR

POWER PLANT

In all well calculations, Reynolds numbers and friction factors (the latter from Petukhov) were calculated for each 

section.5

 Head losses and concomitant power losses were calculated. The same was done for the overland travelers. 

The head loss experienced by the geothermal fluid as it crossed the reservoir was calculated from Darcy’s Law.6

Output - Financial

Well optimization - the geometric mean of the total return of the plant over its lifetime and the average total return 

per well. Since the total return will generally increase with the number of wells drilled, this provides a means of 

finding an optimum number of wells to drill, since real wells represent a significant investment and drive a 

significant portion of power plant cost.

Earlier versions of GSSM specified the size of the power plant as an input variable. This has been removed and now 

the power output appears only as an output variable. Also, drawdown has been removed as an input variable. It has 

been replaced with the related variable Portion of Reservoir Energy Remaining if Extraction is Complete. A brief 

example of the use of GSSM follows.

Example

A 20 MWe plant is considered. It is desired to find the effect of varying the flow rate on the average lifetime output 

and total return. The input as shown in Table 1.

In the base case, where the plant is a nominal 20 MWe, the output looks like Table 2.
7

Table 2: Outputs for a 20 MWe plant

Initial Reservoir Temperature 225 °C Carnot efficiency, start up 42.18%

Final Reservoir Temperature 170.2 °C Carnot efficiency, finish 34.95%

Ratio of minor:major axes 0.718 Plant thermal efficiency, start up 8.44%

Distance between Foci 3,899 m Plant thermal efficiency, finish 6.99%

Area of Surface Footprint of Reservoir 20,096,442 m2 Plant Output, start up 20.384 MWe

20.0964 km2 Plant Output, finish 5.451 MWe

Reservoir Volume 2,009,644,173 m3 Plant Output, end of planned lifetime 19.617 MWe

2.010 km3 Plant Output, average over planned lifetime 20.000 MWe

Total Initial Reservoir Energy Content (relative to 

surface) 9.333E+14 kJ TOTAL ELECTRIC ENERGY PRODUCED 540.0 MW-yrs

2.592E+11 kW-hrs Time to complete extraction 583.51 years

29,573.8 MW-yrs

Extractable Initial Reservoir Energy Content 2.379E+14 kJ # PRODUCERS 6

6.607E+10 kW-hrs TOTAL # WELLS 9

7,537.4 MW-yrs Distance from producers to power plant 1830 m

Total Thermal Energy Extracted over Planned Lifetime 

of Plant 7,001.5 MW-yrs Fraction of length for Production Liner 3 0.15

6.138E+10 kW-hrs Length of Production Liner 1 2,500 m

2.210E+14 kJ Length of Production Liner 2 1,750 m

Approach to complete extraction 92.89% Length of Production Liner 3 750 m

Well catchment facing ('width') 7,321 m

Total Return over planned life of plant $473,373,837 $

Average annual return $15,779,128 $

Lifetime: extraction time ratio 5.1%

Produced: extractable energy ratio 7.2%

WELL OPTIMIZATION $157,791,279 $

FINANCIAL

RESERVOIR

OUTPUTS

POWER PLANT

WELLS

GSSM allows us to examine the impact of varying input parameters on this base case. Figure 3 graphically shows 

the impact of flow rate on the average power delivered over the lifetime of the plant and the well optimization 

parameter. Calculations of the correlation coefficients shows that these are each actually sections of parabolas rather 

than straight lines. Note that this plant was designed such that the flow rate is at a maximum when it is producing 

20 MWe. If the flow rate is raised even slightly, the Power Unsustainable under Given Parameters error message 

will appear since the lifetime energy extraction exceeds the Extractable Initial Reservoir Energy Content.

Average Lifetime Power and Well Optimization as Functions of Mass Flow Rate

0.000

5.000

10.000

15.000

20.000

25.000

0 50 100 150 200 250 300 350

mass flow rate (kg/s)

MWe

$0

$20,000,000

$40,000,000

$60,000,000

$80,000,000

$100,000,000

$120,000,000

$140,000,000

$160,000,000

$180,000,000

$

Avg. Lifetime Power (MWe) Well Optimization

Figure 3: Average Lifetime Power and Well Optimization as Functions of Mass Flow Rate

Figure 4 shows the well optimization parameter and the plant power output as functions of the number of injector 

wells and producer to injector ratio. In contrast to the nearly linear relationship with flow rate, the optimizer clearly 

has a maximum at 2, from where it then decreases. However, if we look at the power output corresponding to the 

number of injectors, we see that the power production is clearly below its maximum. This is especially true in the 

case of the 1:1 producer-to-injector ratio. This would indicate that the design point for the best return on investment 

may not be 20 MWe with six producers and three injectors, but rather 18 MWe with three producers and two

injectors. At the very least, it indicates there may be cause for reconsideration.
8

Well optimization and average lifetime power output as a function of number of injector wells and 

producer to injector ratio

0.000

5.000

10.000

15.000

20.000

25.000

30.000

35.000

40.000

45.000

50.000

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

# injector wells

power (MWe)

$0

$20,000,000

$40,000,000

$60,000,000

$80,000,000

$100,000,000

$120,000,000

$140,000,000

$160,000,000

$180,000,000

$200,000,000

optimizer ($)

MWe, 1:1 P:I MWe, 3:2 P:I MWe, 2:1 P:I

WELL OPTIMIZATION 1:1 P:I WELL OPTIMIZATION, 3:2 P:I WELL OPTIMIZATION, 2:1 P:I

Figure 4: Power plant output and well optimization

CONCLUSION

GSSM is a product of DOE systems integration activities at NREL and is still a work in progress. It is intended for 

internal use, although this could conceivably change. When completed, it will be used to provide DOE with various 

scenarios to aid in making programmatic decisions.

Early efforts in the development of GSSM have already yielded some interesting results. However, because of the 

sheer number of variables, even with a large number of simplifying assumptions, there are no unique solutions. 

Nevertheless, improvements over earlier versions have been seen. Most notably, the reservoir’s characteristics can 

now dictate the power plant that is built, which is a more accurate reflection of reality.

REFERENCES

 1 MIT (2006). The Future of Geothermal Energy: Impact of Enhanced Geothermal Systems (EGS) on the United 

States in the 21st Century. Massachusetts Institute of Technology

2 Thomas S. Lowry, Vincent C. Tidwell, Peter H. Kobos, Mark Antkowiak, Charles Hickox (2010). "A System 

Dynamics Approach for EGS Scenario Analysis". 35th Stanford Geothermal Workshop, February 1-3, Stanford, CA

3 Mark Antkowiak, Neil K. Snyder and Thomas S. Lowry, “A High Level Geothermal System Scoping Model: A 

First Step Toward Enhanced Geothermal Systems Engineering”. 35th Stanford Geothermal Workshop, February 1-

3, Stanford, CA

4

Yarom Polsky, Louis Capuano Jr., John Finger, Michael Huh, Steve Knudsen, A.J. Chip Mansure, David Raymond 

and Robert Swanson, “Enhanced Geothermal Systems (EGS) Well Construction Technology Evaluation Report”. 

Sandia National Laboratories, Albuquerque, New Mexico 87185, and Livermore, California 94550

5 Incropera, Frank P., and DeWitt, David P. (1996). Introduction to Heat Transfer, 3rd Edition. John Wiley and 

Sons, Inc.

6 Fetter, C.W. (1988). Applied Hydrogeology, 2nd Edition. MacMillan Publishing Company, Inc.
F1147-E(10/2008)

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Further Developments on the Geothermal System Scoping Model: 

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This paper discusses further developments and refinements for the uses of the Geothermal System Scoping Model in 

an effort to provide a means for performing a variety of trade-off analyses of surface and subsurface parameters, 

sensitivity analyses, and other systems engineering studies in order to better inform R&D direction and investment for 

the development of geothermal power into a major contributor to the U.S. energy supply.

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Geothermal; modeling; enhanced geothermal systems 

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Unclassified 19b. TELEPHONE NUMBER (Include area code)

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18