Population Growth

To describe population growth, we adopt the linear form used by Lotka and Volterra in their original predator-prey formulations. The first component is a base net fertility rate, n, that would apply in the absence of a resource stock (and would presumably be negative in our environment). In addition, there is a second term that, from our point of view, captures the Malthusian idea that net fertility rises when per capita consumption rises. This implies that propor­tional net fertility should rise when, other things equal, the resource stock is larger. The effect follows because a higher stock (for a given population) would normally give rise to higher per capita consumption. This reasoning leads to the following population growth function:

dP/dt = nP + bPS, (2)

where b is a parameter that...

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GEOTHERMAL POWER STATIONS

The total installed geothermal power generating capacity in the world is approximately 9000 MWe from 21 countries, with the United States leading at nearly 3000 MWe and The Philippines with nearly 2000 MWe (Table II). Other major countries are Italy, Mexico, Indonesia, Japan, and New Zealand, with between 400 and 800 MWe each.

Geothermal power stations have very high avail­ability, load, and capacity factors (>90%). They are most suitable as base load power stations. Liquid – dominated reservoirs are not suitable for peak load generation because two-phase flow and the separa­tion process make their operations and control at changing flows difficult.

A geothermal power station that uses steam turbines to generate electricity is similar to a conventional fossil fuel-fired power station...

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Open Access, Property Rights, and Harvesting Behavior

The natural growth of the forest stock provides part of the story in characterizing the evolution of the forest stock. The other part of the story depends on the harvesting behavior of the Easter Islanders. The key economic point is that under conditions of incomplete property rights, it is natural to expect that, for any given stock, the amount harvested at any given time period, H(t), is increasing with population size. In other words, for any given set of external conditions and any given forest stock, we expect more harvesting to occur if there is a larger population seeking to use the forest stock. Similarly, for a given population, harvesting is easier if the stock is larger, and therefore more harvesting would be likely to occur...

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Other Growth Functions

The logistic growth function is no doubt far from being a perfect approximation to the growth of the Jubaea chilensis forest on Easter Island. Various extensions to the logistic growth function are possible. For example, it is quite possible that at very low values of the stock, the proportional growth rate actually tends to decline. This is referred to as ‘‘depensation’’ or the ‘‘Allee effect.’’ The logistic growth function can be augmented to allow for depensation, but that will not be pursued here. The basic logistic growth function does allow for the critical elements of biological renewable resource growth that are needed to capture at least the qualitative experience of Easter Island.

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The Silencer

A geothermal silencer is like a separator operating at atmospheric pressure. It is normally connected directly to a well and a separation plant for bypass or emergency discharge. The silencer reduces the high – frequency noise discharging from an open pipe to a low-frequency rumbling noise that is more bearable to human ears. The earlier Wairakei silencer design consisted of twin barrels, and the body was made of timber. The modern silencer design consists of a single barrel made of corrosion-resistant steel, sometimes internally lined with concrete (Fig. 13). Fiberglass barrels worked well for silencers not in constant use. Some new silencer designs have a cone fitted at the top of the barrel to increase the steam velocity so that it is dispersed farther away from the silencer area...

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The Flasher/Separator

Although sometimes a flasher is differentiated from a separator, the two are the same pressure vessel in practice. A flasher allows high-pressure geothermal water to flash at a lower pressure. In practice, the lower pressure is achieved by a throttling orifice or valve upstream of the flasher/separator. The vessel then separates the two phases by centrifugal and gravity effects.

The modern separators differ in many aspects from those first used at Wairakei during the 1950s. They differ in size, location, body arrangement, separated water vessel, two-phase inlet nozzle, water outlet nozzle, steam outlet nozzle, and efficiency. The original Wairakei separators were wellhead separa­tors. Each wellhead has its own small separator handling the capacity of a single well...

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Logistic Growth

The starting point for describing the evolution of a renewable resource stock is the logistic growth function. Using t to denote time, a simple logistic growth function has the form G(t) = rS(1—S/K). The variable r is the intrinsic growth rate and K is the environmental carrying capacity, or maximum pos­sible size of the resource stock. G(t) is the growth rate defined in biomass units and G/S is the proportional growth rate (i. e., a number such as 0.1 or 10%). If the forest stock S reaches a level equal to carrying capacity K, then G = 0 and no further growth occurs. Similarly, if there is no forest stock, then S = 0 and no growth occurs. If the forest stock is small relative to carrying capacity (but positive), then S/K is negligible and G = rS...

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Modeling the Renewable Resource Stock

The economy and ecology of Easter Island were relatively simple, but obtaining a tractable mathe­matical representation still requires significant ab­straction and approximation. At a minimum, it is necessary to model the behavior of two ‘‘stocks’’ or ‘‘state variables’’: the forest stock and the population. In fact, it is an oversimplification to focus just on the forest stock. Even in the absence of the forest stock, grass, shrubs, and certain vegetables could be grown and this biomass was sufficient to support a diminished but significant population. Rather than introduce a third ‘‘stock’’ representing other biomass, it is simpler to aggregate the renewable resource base growing on the land into a single resource stock, denoted as S...

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