Diminishing return

Scale kilotonnes/year Fixed capital million AFC million Cost + return /tonne AC -I- R /tonne 

Fixed capital million Variable cost /tonne Fixed capital dependent charges /tonne Other fixed costs /tonne Cost + return 

This diminishing effect on cost plus return resulting from a uniform incremental increase in capacity as the total capacity level is increased is usually referred to in the chemical industry as the law of diminishing returns. In classical economics the same law refers to the situation in which an increase in one of the factors of production (land, labour or capital) results in a reduction in output rather than an increase. 

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The PIF estimate is only a qualitative check on the potential benefit of a horizontal well. There is actually a diminishing return of production rate on the length of well drilled, due to increasing friction pressure drops with increasing well length, shown schematically in Figure 9.6. 

Most observations in chemistry come from ex periments If we do enough experiments we may see a pattern running through our observations A /aw is a mathematical (the law of gravity) or verbal (the law of diminishing returns) description of that pattern Establishing a law can lead to the framing of a rule that lets us predict the results of future experiments This IS what the 1870 version of Markovnikov s rule is a statement based on experimental observations that has predictive value... 

Temperature limits of flight engine alloys have been steadily inereasing about 20 °F (11 °C) per year sinee 1945. Transpiration and internally eooled metal blades have resulted in higher temperatures and more effieient operation. But the direet eorrelation between effieieney and fabrieation eost has resulted in a situation of diminishing returns for the superalloys. As more and more eooling air is needed for the superalloy eomponents, the effieieney of the engine drops to a point where turbine inlet temperatures around 2300 °F (1260 °C) are the optimum and, at that point, they are uneeonomie for automotive use. 

The law of diminishing returns ensures that heat exchangers near the end of the heat path require increasingly larger heating surfaces to extract heat from the lower temperature gases than those at the beginning of the heat path. 

Basicity also may be regarded as a measure of amine hydrolysis, and it governs the increase in pH level, per additional unit measure of amine. The law of diminishing returns applies of course, and beyond a certain point there is little further increase in system pH. Also, the basicity constant for individual amines varies considerably with temperature, so it is important to consider Kb at the relevant operating temperature, rather than simply at ambient temperature. 

Data for the model are given below in Table 4.6. The variable y represents yields of wheat corresponding to six rates of application of fertilizer, x, on a coded scale. The model equation is often called Mitcherlisch s law of diminishing returns. 

Larger and larger areas of copper do not help, especially with thinner copper. A point of diminishing returns is reached for a square copper area of size lin. x lin. Some improvement continues up to about 3in. (on either side), especially for 2-oz boards and better. But beyond that, external heatsinks are required. A reasonable practical value attainable for the thermal resistance (from the case of the power device to the ambient) is about 30°C/W. That means a 30°C rise for every Watt of dissipation inside the IC. 

The final consideration in operationalizing a taxon is the number of indicators. Generally, greater numbers are preferred. MAXCOV requires at least three indicators and simulations suggest that three may work reasonably well, but this number is far from ideal. In a large simulation study, Beauchaine and Beauchaine (2002) found that an increase in indicator numbers from three to four and from four to five produced considerable incremental improvement. However, six appeared to be a point of diminishing returns that is, five indicators performed almost as well as six. Moreover, MAXCOV outputs for six or more indicators are rather unwieldy. We believe it is better to have a few high quality indicators than to add low quality indicators to the set just to increase their number. 

This solution should be much cleaner than the original solution. If not, you ll have to add charcoal and filter again. There is a point of diminishing returns, however, and one or two treatments is usually all you should do. Get some guidance from your instructor. 

Extracting or washing a layer twice, perhaps thrice, is usually enough. Diminishing returns set in after that. 

The industry continues its efforts to reduce even these emissions still further. The law of diminishing returns does of course apply, and we are now reaching levels close to the limits of detection where it is difficult to be sure what measurements actually mean. At these very low levels there are also significant relative differences between... 

Effective operation of the bioslurp system manages the problem of diminishing returns. When liquid recovery declines due to decreased saturation, the percentage of the recovered flow is vapor. The airflow to the well can be continued until water and/or LNAPL again enters the well. Or the dip tube can be raised or lowered to... 

An important factor to keep in mind when designing reinjection wells or systems is that eventually they will have to be redeveloped. Reinjection wells and the redevelopment of these wells unfortunately follow the law of diminishing returns. Constant reinjection of coproduced groundwater without regular development results in irreversible clogging and ultimately the abandonment of the well. 

It is evident that the mean of n results is 4n times more reliable than any one of the individual results. Therefore, there exists a diminishing return from accumulating more and more replicate meaurements. In other words, the mean of 9 results is 3 times as reliable as 1 result in measuring central tendency (i.e., the value about which the individual results tend to cluster) the mean of 16 results is 4 times as reliable etc. 

Equation 19.14 also shows that resolution increases with increasing capacity factor k. Diminishing returns apply at high k and values of 1-5 are generally advocated. 

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