Time horizon

ODP values are relative to R-11 GWP values relative to CO2 and given for 100 years iategrated time horizon. Atmospheric lifetimes are based on an -folding decay. 

A variety of data sources are available to inform interactive programs, including prospective data sets, retrospective databases, expert opinion, and unpub-lished/published literature. Time horizon, that is, the length of time into the future considered in the analysis over which costs and outcomes are projected, is very important here [26]. For example, if a clinical trial or the published literature only report short-term results for a chronic condition, the outcomes may come into question. This is where decision-analytic models may come... 

Kleine Reaktoren mit grower Zukunji, Chemische Rundschau, April 2002 PAMIR study large commercial potential large industrial interest market volume standardization strategic cooperations time horizon potential for pharmaceuticals and fine chemistry Clariant pilot with caterpillar mixer [211],... 

Approximate equipment sizing. There are many combinations of equipment units that meet the requirements concerning the functions of all equipment units and the time horizons for all products. Based on the Flatz (1980) concept, a simple procedure is presented to determine feasible equipment sizes that meet all requirements for plants operated in a single-product campaign mode (no process overlapping). The procedure is illustrated in Fig. 7.4-10. 

Production planning includes considerations on production objectives over a certain time horizon given marketing forecasts for prices and product demands, equipment availability, and inventories. This is a macrolevel problem of the allocation of production capacity, time, product inventories, and labour and energy resources, so as to determine the production goals that maximize the total profit over an extended period of time into the future (e.g. a few months to a few years). 

A particular problem is the number of events that should be simulated before the results are stabilized about a mean value. This problem is comparable to the question of how many runs are required to simulate a Gaussian distribution within a certain precision. Experience shows that at least 1000 sample arrivals should be simulated to obtain reliable simulation results. The sample load (samples/day) therefore determines the time horizon of the simulation, which for low sample loads may be as long as several years. It means also that in practice many laboratories never reach a stationary state which makes forecasting difficult. However, one may assume that on the average the best long term decision will also be the best in the short run. One should be careful to tune a simulator based on results obtained before equilibrium is reached. 

Because of the different properties and lifetimes in the atmosphere associated with each of the GHGs, emissions are typically reported as teragrams (Tg), or million metric tons, of carbon dioxide equivalent, C02eq-The 100-year time horizon global warming potential (GWP) of CH4 is 25 times as potent as CO2, N2O is 298 times as potent as CO2, and the halocar-bons range from 124 to 14,800 times as potent as CO2 (IPCC, 2007). 

In single-scale filtering, basis functions are of a fixed resolution and all basis functions have the same localization in the time-frequency domain. For example, frequency domain filtering relies on basis functions localized in frequency but global in time, as shown in Fig. 7b. Other popular filters, such as those based on a windowed Fourier transform, mean filtering, and exponential smoothing, are localized in both time and frequency, but their resolution is fixed, as shown in Fig. 7c. Single-scale filters are linear because the measured data or basis function coefficients are transformed as their linear sum over a time horizon. A finite time horizon results infinite impulse response (FIR) and an infinite time horizon creates infinite impulse response (HR) filters. A linear filter can be represented as... 

Combining these two profiles across the space or time horizon allows virtually all types of continuous curves to be produced that can be implemented in a practical design. When the two profiles are combined, two additional variables are needed. The value of tinter indicates the point in space or time where the two curves meet and xinter is the corresponding value of the control variable where the curves meet. Figure 3.14c illustrates the form of Type I followed by Type II and Figure 3.14d the form of Type II followed by Type I. 

In formulating profiles, emphasis should be placed on searching for profiles that are continuous and easily implemented in practice. Therefore, curves that include serious discontinuities should normally be avoided. It is meaningless to have a global optimum solution with complex and practically unrealizable profiles. Curve combinations from the above equations such as Type I + Type I or Type II + Type II should not normally be considered as there would be a prominent discontinuity at the intermediate point. The profile generator can be easily extended to combine three or more curves across the space or time horizon instead of two. However, there is little practical use to employ more than two different curves for the majority of problems. The complexity of the profiles increases with the number of curves generated. It should not be forgotten that a way must be found to realize the profile in practice. For a continuous process, the equipment must somehow be... 

Figure 4. Comparison of GHG emissions from shale gas and conventional natural gas with low and high estimates of fugitive methane emissions, surface-mined coal, deep-mined coal, and diesel oil time horizon equal to 100 years [27]...

Data on the waste management phase those are really difficult to obtain. Measurements of additive emissions are scarce. Material specific emissions data are always modelled. Estimates can only be based on rough assumptions. Especially in cases of unprotected landfills, the leaching from landfill sites may be important here, too, it is better to use crude estimates than nothing at all. Assumptions on emission rates together with an assumed time horizon should be made. 

The ZW, FW, and UW are in most instances a consequence of product stability. In a situation where the intermediates are unstable, it is always advisable to proceed with the subsequent step(s) in the recipe as soon as the intermediates are formed, hence the ZW operational philosophy. Due to its nature, ZW does not require any dedicated storage for the intermediates and could be depicted by a flowsheet similar to that shown in Fig. 1.3. On the other hand, the intermediate could be partially stable and only commence decomposition after a certain period. In this case storage time has to be finite in order to prevent formation of unwanted material, hence the FW operational philosophy. The UW operational philosophy is applicable whenever the intermediates are stable over a significantly longer time than the time horizon of interest. In both FW and UW operational philosophies, storage of intermediates can either be within the processing equipment or dedicated storage unit. 

Needless to mention, the exact capturing of time presents further challenges in the analysis. Fundamentally, a decision has to be made on how the time horizon has to be represented. Early methods relied on even discretization of the time horizon (Kondili et al., 1993), although there are still methods published to date that still employ this concept. The first drawback of even time discretization is that it inherently results in a very large number of binary variables, particularly when the granularity of the problem is too small compared to the time horizon of interest. The second drawback is that accurate representation of time might necessitate even smaller time intervals with more binary variables. Even discretization of time is depicted in Fig. 1.8a. 

Recent approaches tend to adopt the uneven discretization of the time horizon of interest wherein each time point along the time horizon coincides with either the start or the end of a task (Schilling and Pantelides, 1996). In addition to accurate representation of time this approach results in much smaller number of time points, hence fewer binary variables, as shown in Fig. 1.8b. 

Q[/ (s) maximum amount of state s stored within the time horizon of interest CP (.v) Selling price of product s, s = product... 

Constraints (2.17) and (2.18) respectively stipulate that the usage or production of state should be within the time horizon of interest. 

In this section, the above mathematical model is applied to a literature example shown in Fig. 2.2 (Ierapetritou and Floudas, 1998). The SSN representation is given in Fig. 2.3b. Table 2.1 gives data for this example. 5 time points and a 12-h time horizon were used. Using less time points leads to a suboptimal solution with an objective value of 50, and using more time points than 5 did not improve the solution. It is worthy of note that, in this particular example, constraint (2.13) is redundant as mentioned earlier, since each unit is only performing one task. 

Five time points and a 12-h time horizon were used for this example. The results from this proposed method and from the methods proposed by Ierapetritou and Floudas (1998), Zhang (1995), and Schilling and Pantelides (1996) are shown in Table 2.2. 

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