Natural Gas: Testing the Simple Model

Setting Up the Test

To test the simple model, let's set the gas demand to grow exponentially over time. But, for now, set the rate of exponential growth to zero.

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

Then set the gas production to serve the gas demand:
gas_production = gas_demand

Then set the discovery of gas to match the required discovery:
discovery_of_gas = required_discovery
required_discovery = (gas_demand*target_ratio-proven_reserves)+gas_demand

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

But if you experiment with high growth rates (i.e., 50%/yr) ,you will see that the stock of unproven reserves will be driven rapidly toward zero. When we reach a point where the rule for discoveries calls on more gas than remains in unproven reserves, the exercise is terminated. Let's stop the exercise by attempting to divide by zero:
stop_the_exercise = 1/Max(0,unproven_reserves-required_discovery)

Testing the Model

Figure 3 shows the "thousand year model" in an experiment 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 the simulation. The rate of decline accelerates, however, as growing demand forces higher and higher discoveries to replenish the stock of proven reserves. The decline is especially dramatic in the 1960s and 1970s. 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 be sufficient to maintain the proven reserves at the target value.

Figure 3. Simulated reserves with 4%/yr exponential growth in demand.
(The simulation is terminated prior to 1980.)

Conclusion from the "Thousand Year Model"
This experiment shows that an industry with a "thousand year resource" would find itself in serious trouble in less than 80 years. The simulation makes an important point about resources:

Exponential growth in demand is a powerful force that will cause an industry to rapidly consume what appears to be a huge resource.

The simulation reveals that measuring resource adequacy based on current demand is terribly misleading in an exponentially growing system. Behrens (1973) explains this problem in more detail and provides a different measure of resource longevity.

The introductory model helps us understand how an industry could move from a period of seeming abundance to a period of scarcity in a surprisingly short time interval, but it does not simulate the many changes when resources become scarce. One important change is the increase in exploration costs as the stock of unproven reserves are depleted. Higher exploration costs would temper industry investment in exploration well before the "stop the exercise" warning. Another important change involves the higher prices that will appear during a period of scarcity. As proven reserves fall below target 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 counteracting effects simulated in Naill's original model.