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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A PREDATOR-PREY SYSTEM WITH UNFORTUNATE PARAMETER VALUES

2.8 Easter Island as a Predator-Prey System

As reported in 1998 by Brander and Taylor, the understanding of Easter Island can be greatly advanced by using formal mathematical analysis. The formal description provided here relies on that analysis. One key point is that the Easter Island economy can be viewed as a ‘‘predator-prey’’ system. The forest resource can be considered as the prey and the Easter Islanders as the predators. One important aspect of even relatively simple predator-prey systems is that small to moderate changes in one or more key parameters can give rise to major qualitative changes in the dynamic pattern of population growth and decline...

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The Wells

The use of a geothermal resource depends entirely on the output from the wells. A well’s output can vary significantly from that of a typical well (Fig. 10). An example is the cycling wells that have fluctuating mass output with a cycle time as short as a few minutes. This type of well is not suitable for power production unless it can be balanced by stable output wells. Another type of problem well is one that continuously discharges solids with the well fluids. Sometimes this problem can be solved by throttling, but generally a dirty well is not used for production.

3.1 The Wellhead

A typical wellhead consists of several valves to provide service functions required (Fig. 11). The master valve is for completely shutting off the well...

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GEOTHERMAL STEAM PRODUCTION FIELDS

Geothermal wells need to undergo a test program before they are used. This is so that the baseline conditions of both the wells and the geothermal aquifers that they tap can be determined. This baseline data are critical because all future informa­tion is compared against them.

After drilling has been completed and before the initial discharge, the well downhole conditions are measured. The temperature and pressure are mea­sured by using a clockwork Kuster gauge or electronic logging tools. Standard practice is to initially do an injection (or completion) test, that is, sometime at a series of flows, where the temperature, pressure, and possibly flows using a spinner tool are

Подпись: 100GEOTHERMAL STEAM PRODUCTION FIELDSПодпись: о % 0 2 5 о Li ra га га Подпись: 50Подпись: CD —) measured at intervals down the open hole section of the well...

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