Natural Gas Discovery Model: Reference Modes
It is often argued that system dynamics modeling is mis-named because system dynamicists model problems, not systems. The reason that problems, rather than systems, are focused on is because they direct the system dynamicist away from the "kitchen sink approach" to modeling, which usually yields a model containing so much detail that it is no more easy to understand than the actual system itself.
The principle way that system dynamicists force themselves to focus on problems is through the use of reference modes. Reference modes are time series graphs of important system variables that exhibit patterns of behavior (e.g., exponential growth, exponential decay, oscillation, s-shaped growth, overshoot and collapse ) that are either problematic or not well understood. They also define the time horizon of a model, which involves the specification of both its time units (years, quarters, months, weeks, days, etc.) and time span (the modelís start time and stop time). The task of the system dynamicist is to identify, and include in the model, only those variables that help to explain (i.e., help the model to mimic) the reference modes.
The reference modes originally used by Roger Naill in the construction of his natural gas model were drawn from the oil and gas life cycle theory of M. King Hubbert. Hubbert based his theory on the knowledge of the physical structure of the oil and gas system and hence on the assumption that there is a finite amount of oil and gas in the earth. According to Hubbertís theory, the discovery and production flows of natural gas, as well as the stock of proven reserves of natural gas rise, peak and fall over time, and the stock of unproven resources falls monotonically due to depletion.
Although a theory can be used to provide reference modes for a system dynamics model, actual numerical time series data, if available, can also be used. Figure 1 presents some actual data from the U.S. natural gas system. It includes the actual discovery rate, usage (production) rate, proven reserves, and reserve-production ratio. Clearly, these data do not span the entire life cycle of the natural gas system (roughly the years 1900 to 2050) a la Hubbert, so they are of limited use in specifying reference modes for the natural gas depletion problem. On the other hand, they can be used to complement the reference modes resulting from Hubbertís theory and to calibrate the model.
Figure 1: Actual Data from the U.S. Natural Gas Discovery and Production System