Dinámica de sistemas: Recursos Economicos

8/19/2019 Dinámica de sistemas: Recursos Economicos

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Resource Economics:

Discovery and Production of Natural Gas in the USA

These exercises provide an opportunity to use system dynamics to study the life cycle of a non-renewable resource. Natural gas may be the most important source of energy in the United States today.It has many traditional uses in homes and industries; it may emerge as an important fuel for cleanvehicles. Natural gas was also the most popular fuel for new power generation during the construction boom of 1999-2000. The exercise collection begins with some historical background on this importantresource. Then we'll develop a simple model to help us understand its longevity. We conclude with adescription of a system dynamics model developed by Roger Naill (1973).

Background on Natural Gas in the United States

Natural gas is a surprisingly important source of energy in the United States today. It has alwaysenjoyed traditional uses in homes and industries. But it is now emerging as a potentially important fuelfor clean vehicles (see chapter 20),and it has already emerged as the most important fuel for new powergeneration (see chapter 23). Today's interest in gas-fired power generation is quite surprising since power companies were prohibited from investing in gas fired generation only two decades ago.

System dynamics was used by Roger Naill to simulate the life cycle in natural gas exploration.He published his results in 1973, the year in which the Arab oil embargo made the industrialized worldaware of the "energy crisis." To some, the energy crisis was an "oil crisis" -- we were too dependent onimported oil. But many experts spoke of an "oil and gas crisis." They feared that the United States was

Andrew Ford BWeb for Modeling the Environment 1


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running low on both oil and gas reserves. In the well-known "Harvard Energy Study," Stobaugh andYergin (1979) described gas policy as a debate over "how to slice a shrinking pie." They cautioned that"it will be a challenge to find enough new gas reserves to maintain production at current levels." Naill(1973, 215) held a similar view.

The natural gas industry seems to be facing the most imminent crisis of fossil fuel depletion. Although it has been estimated that from 400 to 900 trillion cubic feet of natural gas

still remain undiscovered in the United States, proven reserves are falling rapidly.

The discovery rate, currently less than the production rate,

is decreasing, while the production of natural gas is rising at almost 7 percent per year.

Naill (1973, 248) simulated gas production and exploration over a time period from 1900 to 2020. Thesimulations led him to conclude that:

The normal behavior mode is an initial period of unrestricted growth in supply,

a transition period when growth is slowed, and finally a decline in supply.

This is a natural result of the assumption of a finite amount of initial unproven reserves--at some point in time, growth will be limited by rising costs due to scarcity of the resource ...

the time of transition is remarkably insensitive to changes in these [parameter] values.

For example, an increase by a factor of two in the actual quantity of initial unproven reserves

results in postponing the transition in supply for only ten years

The natural gas model was the first of many modeling contributions to support policy making in the USenergy sector. Naill and his colleagues developed several models, including COAL2 (Naill 1977),FOSSIL2 (used in the 1991 National Energy Strategy), and IDEAS (AES 1993).

The history of these projects is reported in two articles in the System Dynamics Review (Naill1992A,B). The first article explains the models' use for policy analysis at the US Department of Energy.The second article describes the results of a simulation search for a cost effective combination of energy policies to mitigate the US contribution to global warming. Although the 1973 gas model is datedrelative to FOSSIL2 and IDEAS, it is better suited for student exercises by virtue of its small size and itsdetailed documentation.

A Simple Model of Natural Gas Discovery and Production

Figure 1 shows a simple model to introduce the combination of stocks and flows to study thelifecycle of discovery and production. The model has two stocks and two flows. The stocks aremeasured in trillion cubic feet (TCF); the flows are measured in TCF/yr. Proven reserves refer to previously discovered gas that is available for production. Unproven reserves are a larger, morespeculative quantity. It stands for total resources that might be discovered in the future.



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Figure 1. A simple model of natural gas production

The gas demand is a user specified variable which will grow over time. Near the start of the 20thcentury, gas demand was around 1 TCF/yr. Demand is satisfied by gas production which drains thestock of proven reserves. The reserve production ratio is used to measure the adequacy of provenreserves. If there were 20 TCF of reserves at the start of the century, for example, the ratio would have been 20 years. In other words, demand could be satisfied for 20 years even if there were no furtherdiscoveries.

To explain the discovery of gas, we need to know the industry rational for investing inexploration and the likelihood that the investments will lead to new discoveries. Naill assumed that theindustry strives to keep the proven reserves at an adequate level, as measured by the reserve productionratio. He selected 20 years as the target value. Figure 2 expands the introductory model to simulate thediscovery of gas based on this target. Let's initialize the model with 20 TCF of proven reserves, 1,000TCF of unproven reserves and a gas demand of 1 TCF/yr. The initial value of the reserve productionratio is 20 years, and the target ratio is set at 20 years.

Figure 2. Simple model to experiment with a "thousand year supply" of natural gas.

The model assumes that the discovery of gas is identical to the discovery required to keep the proven reserves sufficiently large to provide "20 years of gas." If gas demand were to remain constantover time, the discovery of gas need only be 1 TCF/yr to replace gas production. With 1,000 TCF ofunproven reserves, it appears that we are creating what might be called the

thousand year model.That is, if demand were to remain constant, natural gas supplies would last for a thousand years!



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Testing the Thousand Year Model

To test the simple model, let's set the gas demand to grow exponentially over time. The first test will bequite simple since the rate of growth is zero:

gas_demand = demand_in_1900*EXP(growth_rate_for_exercise*(time-1900))growth_rate_for_exercise = .00

Then we set the gas production to serve the gas demand:

gas_production = gas_demand

And then set the discovery of gas to match the required discovery:

discovery_of_gas = required_discoveryrequired_discovery = (gas_demand*target_ratio-proven_reserves)+gas_demand

With a growth rate at zero, the simulations will show that discoveries will continually replenish thestock of proven reserves, and the reserve production ratio will be maintained near 20 years over theentire simulation.

But if you experiment with high growth rates (i.e., 50%/yr) ,you will see that the stock ofunproven reserves will be driven rapidly toward zero. When we reach a point where the rule fordiscoveries calls on more gas than remains in unproven reserves, the exercise is terminated.

A simple trick to get the software to stop the simulation is to write an equation that forcesdivision by zero:

stop_the_exercise = 1/MAX(0,unproven_reserves-required_discovery)

When unproven reserves are below the required discovery, the MAX function chooses 0 rather than thenegative number. When Stella attempts to divide 1 by 0, the software will complain about the variable“stop_the_exercise.” When we see this complaint, we will know that it is time to stop the simulation.

Your Expectation with 4% Annual Growth in Demand?

Let’s now simulate the model with exponential growth in the demand for natural gas. An annualgrowth of 4% is a reasonable number for the historical period, so we can repeat the simulation with thegrowth rate at 0.04/yr. Now, before looking ahead at the simulation results, you should guess how manyyears will pass before the model runs out of unproven reserves. What is your expectation --- will thesimulation stop in a thousand years? in 500 years? in 250 years? Try to do the simulation in your head,(or by taking notes on a piece of paper). Then write your expectation for the longevity of the natural gasresource in the box below:

The simulation with 4% annual growth in demand will stop after ____________________ years.



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Figure 3 shows the "thousand year model" in a simulation with 4%/yr growth in demand.Unproven reserves are at 1,000 TCF in 1900, and they decline slowly during the first 20 years of thesimulation. The rate of decline accelerates, however, as growing demand forces higher and higherdiscoveries to replenish the stock of proven reserves. The decline is especially dramatic in the 1960s and1970s. The exercise is terminated in the late 1970s because the remaining stock of unproven reserves is

too small. Even if the industry were to discover the last cubic foot of gas, discoveries would not besufficient to maintain the proven reserves at the target value.

Figure 3. Simulated reserves with 4%/yr exponential growth in demand.(Unproven reserves are far short of what is needed for a 1,000 years.

This experiment shows that the simulation is terminated in less than 80 years.)

Conclusion from the Simple Test

This experiment shows that an industry with a "thousand year resource" would find itself inserious trouble in less than 80 years. The simulation makes an important point about the discovery and production of a non-renewable resource like natural gas:

Exponential growth in demand is a powerful force

that will cause an industry to rapidly consumewhat appears to be a huge resource.

The simulation reveals that measuring resource adequacy based on current demand is terribly misleadingin an exponentially growing system.

1

The introductory model helps us understand how an industry could move from a period ofseeming abundance to a period of scarcity in a surprisingly short time interval, but it does not simulate



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the many changes when resources become scarce. One important change is the increase in explorationcosts as the stock of unproven reserves are depleted. Higher exploration costs would temper industryinvestment in exploration well before the "stop the exercise" warning. Another important changeinvolves the higher prices that will appear during a period of scarcity. As proven reserves fall belowtarget levels, gas prices would rise (in an unregulated industry). Higher prices could lead to higher

revenues and, perhaps, an increased investment in exploration. These are two of the counteractingeffects simulated in Naill's original model.

Roger Naill’s Model of Natural Gas Production

Naill's model was developed in Dynamo, the software described in Appendix C in the book. Themodel has been converted to Stella and is shown in Figure 4.

Figure 4. Stella version of Naill's 1973 model of the exploration and production of natural gas.

In adapting the model to Stella, I have taken the liberty of changing the units from cubic feet (CF) totrillion cubic feet (TCF). I have also changed the variable names from the short names that arecustomary with Dynamo to the longer names in Figure 4. Table 1 provides a comparison of the namesand units assigned to the stocks and flows in the two models. Table 2 provides a similar comparison forthe converters in the two models.



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Dynamo Names

OldUnits

Longer Names for the Stella model NewUnits

UPR CF unproven reserves TCF

PR CF proven reserves TCF

AUR CF/yr average usage rate over past few years TCF/yrUR CF/yr usage rate TCF/yr

DR CF/yr discovery rate TCF/yr

Table 1. Names and Units for the Stocks and Flows in the Two Models

Dynamo Names

OldUnits

Longer Names for the Stella model NewUnits

AURAD years average interval for the usage rate yrs

MAR Dim’less cost margin Dim’less

COE $/CF cost of exploration $/kcf

DD Years discovery delay years

EIIE $/yr effective investment in exploration B$/yr

FURR Dim’less fraction of unproven reserves remaining Dim’less

GC 1/yr growth constant 1/yr

UPRI CF Initial amount of unproven reserves TCF

URI CF/yr Initial usage rate TCF/yr

IIE $/yr Investment in exploration B$/yr

COEN $/CF Normal cost of exploration $/kcf

PIEE Dim’less Percent invested in exploration Dim’less

URP CF/yr Potential useable rate TCF/yr

P $/CF Price $/kcf

RPR Years Reserve-production ratio YearsSR $/yr Sales revenue B$/yr

STC $/CF Smoothed total cost $/kcf

TC $/cf Total cost $/kcf

TCSD Years Total cost smoothing delay Years

Cost of exploration multiplier Dim’less

DM Dim’less Demand multiplier Dim’less

Percent invested in exploration multiplier Dim’less

ROIM Dim’less Return on investment multiplier Dim’less

Table 2. Names and Units for the Converters in the Two Models



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Verifying Naill’s Results

Figure 5 shows a test simulation to verify that the Stella model generates the results reported by Naill (1973, 238) in a base line simulation without price regulation. The model is initialized in the year1900 with 1,040 TCF of unproven reserves and an initial demand of 0.4 TCF/yr. In this case, the

unproven reserves would appear to cover demand for 2,600 years! But you know this measure ismisleading if demand grows exponentially over time. Naill assumes that demand has the potential togrow exponentially at 6.6%/yr; the actual growth will be tempered by changes in the price of naturalgas.

Figure 5. Verification that the Stella model matches theunregulated baseline simulation from Naill (1973, 238).

The test simulation shows a sixty year period of exponential growth in useage, discoveries, and proven reserves. But the growth phase of the simulated life cycle concludes during the late 1960s andearly 1970s. The remainder of the simulation shows the "down side" of the discovery life cycle. Themodel suggests that gas discovery would be the first variable to reach a peak and turn downward. Withina few years, the decline in discovery rate will cause discoveries to fall below the usage rate. When thishappens, proven reserves are forced downward.

Figure 5 verifies the first simulation appearing in Toward Global Equilibrium. Additionalsimulations in that book show the impact of ceiling price regulation imposed in 1960, changes in theestimate of unproven reserves and improvements in exploration technology.



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Exercises

The first four exercises are provided for the student with an introductory interest in resources. They may be completed with the simple model used to study a “thousand year supply” of natural gas.

1. Build and Verify

Build the introductory model in Figure 2 and verify that it generates the results in Figure 3.

2. Simulate Cumulative Production

Add a stock to the model in Figure 2 to keep track of "cumulative production." Define a new converternamed "total gas" as the sum of cumulative production, proven reserves and unproven reserves. Thensimulate the model to verify that "total gas" remains constant over the simulation.

3. Double the Resource Base

Naill assumes that unproven gas reserves in 1900 were around 1,000 TCF based on the work by Hubbert(1969), but he cautions that other estimates have ranged as high as 2,000 TCF. Run the model in Figure2 with 2,000 TCF of reserves. How much longer does the simulation run before termination?

4. Comparison with Naill's Conclusion

Recall Naill's (1973, 248) conclusion that a doubling of the unproven reserves would postpone thetransition in supply by only around ten years. Do your findings in the previous exercise match hisgeneral conclusion?

The next five exercises are provided for the student with advanced interest in resources. They challengeyou to build, verify and improve upon Naill's original model.

5. Build and Verify

Build the model in Figure 4 and verify that it behaves as shown in Figure 5. As further verification,generate a time graph of the cost of exploration, the price and the reserve production ratio. Do thesethree variables also match the results in Naill's unregulated baseline run?

6. Double the Resource Base

Change the initial value of the unproven reserves to 2,000 TCF and verify that the Stella model deliversthe same results as published by Naill. Do you agree with his conclusion that "an increase by a factor oftwo in the actual quantity of initial unproven reserves results in postponing the transition in supply foronly ten years"?



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7. Changing Estimates of Gas Resources During the Course of the Exploration Life Cycle

Naill describes a large range of uncertainty in the initial value assigned to the stock of unprovenreserves. Review his explanation of why geologists arrive at such widely ranging estimates. Then review

the work by Sterman and Richardson (1985) to simulate how geologists' estimates can change over time.Their model of the US petroleum industry is strikingly similar to Naill's model of natural gas, but their purpose is quite different. They wish to explain how geologists' estimates of a resource base change asmore and more information becomes available.

To appreciate their purpose, we might imagine three possibilities:

• The geologists get the estimate right early in the life cycle.

• The estimates are too low in the early years, but they gradually approach the correct value overtime.

• The estimates start out too low, but they increase rapidly as more information becomes available.

Unfortunately, they shoot past the correct amount, and downward corrections are needed later inthe life cycle.

Review the 1985 article to learn which of the possible patterns is most characteristic of the nation's petroleum industry. Review the updated study (Davidsen 1990) to learn if they held the same view fiveyears later. Do you agree with their characterization of oil resource estimation? Do you think theirreasoning would apply to natural gas as well?

8. Gas Production in Recent Decades

Figure 5 shows natural gas usage peaking at over 20 TCF/yr in the year 1977 and declining rapidly

thereafter. By 1997, gas use is projected at less than 5% of the peak value! This projection does notmatch recent history due, in part, to the absence of price regulations which were imposed in the 1960s.Review Nail's simulations and compare them with the actual data on gas production during the 1970s,1980s and 1990s (CRA 1983; DOE 1996; Fisher 1994). You will learn that gas production did not climbas high in the 1970s, nor has it declined as rapidly in the 1980s and 1990s. Experiment with changes inthe model parameters based on information that has become available in the past 25 years. Can youobtain a reasonable match between simulated gas production and historical production?

9. Coflow Approach to the Embedded Discovery Costs

Richardson (1997) has developed an interesting exercise involving Naill's use of a smooth function to

approximate the total discovery cost of a cubic foot of gas when it reaches the retail market. Naill setsthe length of the smoothing delay to the reserve production ratio because the ratio "gives a measure ofthe average time gas remains in the proven reserve category" (Naill 1973, p. 224). In effect, he is usingthe simple smooth function to keep track of the embedded costs of discovery over time. Richardsonadvises that the "coflow" provides an improved method to track embedded costs. Coflow is short forcoincident flows which are useful to track an attribute associated with a material flow. In this case, themain flow is gas discovery. The attribute to be tracked is the cost of each discovery. Expand Naill'smodel by introducing a coflow. Introduce a new converter for the price based on the total cost calculated



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from the coflow structure. Simulate the new model and document your results with a time graph of totalcost and the price of natural gas. Does the improved simulation of embedded costs lead to significantchanges in the results in Figure 5?

References

AES 1993The AES Corp. (Applied Energy Services Corp), An Overview of the IDEAS Model, 1001 North 19

th

St. Arlington, VA 22209.

CRA 1983Charles River Associates, The Future Natural Gas Supply and Demand Balance, report EPRI EA-2840of the Electric Power Research Institute, 3412 Hillview Ave, Palo Alto, CA 94304, Jan 1983.

Davidsen 1990Pal Davidsen, John Sterman and George Richardson, A Petroleum Life Cycle Model for the United

States with Endogenous Technology, Exploration, Recovery and Demand, System Dynamics Review,Vol 6, Nu 1, Winter 1990, pages 66-93.

DOE 1996U.S. Department of Energy, Annual Energy Outlook, Government Printing Office, Washington DC.

Fisher 1994William Fisher, "How Technology Has Confounded US Gas Resource Estimators," Oil and Gas Journal,October 24, 1994, pages 100-107.

Hubbert 1969M. King Hubbert, Energy resources, in Resources and Man, Washington DC: National Academy ofSciences; New York: W.H. Freeman.

Naill 1973Roger Naill, The Discovery Life Cycle of a Finite Resource: A Case Study of U.S. Natural Gas, inToward Global Equilibrium, Dennis Meadows and Donella Meadows, editors, Waltham, MA: PegasusCommunications.

Naill 1977Roger Naill, Managing the Energy Transition: A System Dynamics Search for Alternatives to Oil andGas, Ballinger Publishing Co, Cambridge, MA

Naill 1992Roger Naill, Sharon Belanger, Adam Klinger and Eric Petersen, An Analysis of the Cost Effectivenessof U.S. Energy Policies to Mitigate Global Warming, System Dynamics Review 8, no 2.

Richardson 1997George Richardson, "PAD 724 Class Notes and Assignment Packet," Rockefeller College of PublicAffairs and Policy, State University of New York, Albany, NY 1002.



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Sterman and Richardson 1985John Sterman and George Richardson, An Experiment to Evaluate Methods for Estimating Fossil FuelResources, Journal of Forecasting, 4, no. 2: 197-226.

Stobaugh 1979Robert Stobaugh and Daniel Yergin, Energy Future, Random House, New York.

End Note

1 The problem with this measure of resource adequacy is explored in more detail by Behrens in a

separate chapter of Toward Global Equilibrium. He provides a better measure of resource

longevity.

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