Uncertainty associated with rates

PSCs are agreed with a schedule for exploration, appraisal and development, and production periods. During these times the terms of the PSC are usually fixed, thus reducing some of the uncertainties associated with tax and royalty systems where the royalty and tax rates may vary over the field lifetime. 

Risk and uncertainty associated with each venture should translate, ia theory, iato a minimum acceptable net return rate for that venture. Whereas this translation is often accompHshed implicitly by an experienced manager, any formal procedure suffers from the lack of an equation relating the NRR to risk, as well as the lack of suitable risk data. A weaker alternative is the selection of a minimum acceptable net return rate averaged for a class of proposed ventures. The needed database, from a collection of previous process ventures, consists of NPV, iavestment, venture life, inflation, process novelty, decision (acceptance or rejection), and result data. 

However, the data that are contributed to a generic failure rate data base are rarely for identical equipment and may represent many different circumstances. Generic data must be chosen carefully because aggregating generic and plant-specific data may not improve the statistical uncertainty associated with the final data point, owing to change in tolerance. 

The values of sA and. ru are not well defined by kinetic data.59 61 The wide variation in. vA and for MMA-S copolymerization shown in Table 7.5 reflects the large uncertainties associated with these values, rather than differences in the rate data for the various experiments. Partly in response to this, various simplifications to the implicit penultimate model have been used (e.g. rA3rBA= W- and -Va=- h)- These problems also prevent trends in the values with monomer structure from being established. 

Capital costs can be estimated by applying installation factors to the purchase costs of individual items of equipment. However, there is considerable uncertainty associated with cost estimates obtained in this way, as equipment costs are typically only 20 to 40% of the total installed costs, with the remainder based on factors. Utility investment, off-site investment and working capital are also needed to complete the capital investment. The capital cost can be annualized by considering it as a loan over a fixed period at a fixed rate of interest. 

Overall, there are always considerable uncertainties associated with an economic evaluation. In addition to the errors associated with the estimation of capital and operating costs, the project life or interest rates are not known with any certainty. The important thing is that different projects, and options within projects, are compared on the basis of consistent assumptions. Thus, even though the evaluation will be uncertain in an absolute sense, it will still be meaningful in a relative sense for choosing between options. 

An additional comphcating factor with respect to air samphng rate calibration is the uncertainty associated with determinations of vapor-phase and particle sorbed concentrations of analytes by HiVol sampling. These systems suffer from artifacts such as the volatilization of particle-bound contaminants, insufficient retention of small particles, and adsorption of vapor-phase contaminants on the GFFs (Ockenden et al., 1998 Lohman et al., 2001). These artifacts may cause concentrations in the vapor-phase to be overestimated or underestimated, which results in sampling rates that are too low or too high. 

Information on death rates from automobile or other types of accidents or activities is generally much more solid than that pertaining to most chemical risks. Statistical data, compiled by actuaries, are used to derive such risk information. There is uncertainty associated with these actuarial figures, but most are fairly reliable. Most of the risk information about various cancers, presented in Chapter 5, is of this type. 

When the uncertainty associated with AHf is 5 kcal/mol, rate and equilibrium constants can be estimated within a factor of 10 at process temperatures, i.e., 500-1,500 K. This level of accuracy may be acceptable for preliminary mechanism development work and for the identification of important reactions in a DCKM. However, it would clearly be desirable to know AHf within 1 kcal/mol, which would lead to the determination of rate and equilibrium constants that are accurate within a factor of two. Since this level of accuracy is very close to the limits of accuracy of most experimental measurements, improvements in AHf are often difficult. Consequently, computational quantum chemistry holds a great promise for the accurate determination of AHf. 

Molecular descriptors may provide fundamental and scientific explanations of variations in the activity mechanism due to the structure of molecules. QSAR models can provide insight into kinetic mechanisms of organic compounds, and some of the design uncertainty associated with SCWO kinetics can be reduced. By using appropriate molecular descriptors, then, the results of QSAR models for SCWO could be used to determine the oxidation rate constants of organic compounds of structure similar to the training set chemicals of the QSAR model without experiments. 

If only about the first 1% of a slow reaction is monitored, a plot of the concentration versus time plot is virtually linear, so the initial rate can be measured with little of the uncertainty associated with fitting a tangent to a curve. 

The resultant ions (both primary and produced) are mass-selected using a quadruple mass analyzer and measured as count rates by an electron multiplier detector. Count rates of the MH+ species are subsequently converted to ionic densities and then to mixing ratios of constituent M after consideration of instrumental transmission coefficients, temperature, and DT pressure. Instrumental accuracy, which is largely determined by the uncertainties associated with the reported proton transfer reaction rate coefficients (k), is estimated to be better than 30% (Hayward et al, 2002 Lindinger, Hansel and Jordan, 1998). 

The development of a natural sulfur emissions inventory for the contiguous U. S. is a necessary step toward understanding the natural component or acid deposition on a regional and national scale. A county length scale and a monthly time scale constitute appropriate levels of resolution for regional modeling. Emission estimates are based on the emission rate data described by Lamb et al. (1) which are limited to measurements of natural sulfur emissions in Ohio, Iowa, North Carolina, Washington and Idaho. The uncertainty associated with this inventory is carefully considered by analyses of model sensitivity. 

Deterministic sensitivity analysis performed during modelling of population exposures to ambient fine particulate matter by using high (H), medium (M) and low (L) values during the analysis of the impact of uncertainties associated with key inputs and parameters on model predictions (e.g. time spent outdoors [H = 95%, M = 80%, L = 50%], residential building infiltration fractions [H = 0.7, M = 0.5, L = 0.2], deposition rates [H = 0.4, M = 0.3, L = 0.1]). 

Owing to the uncertainties associated with substrate or reagent partitioning into various sub-sites of micelles, the quantitative predictions about the course of reactions and observed changes in the rates of such reactions often become difficult. Consequently attention has been directed toward the design and synthesis of amphiphiles in which either substrate or reagent functions are covalently attached. 

The low-pressure rate has never been adequately accounted for because of the difficulties that arise from surface contamination and heterogeneity. While the rate constant is not in too serious error, the activation energy has great uncertainty associated with it. Perrine and Johnston (Zoc. cit) report for the low-pressure limit... 

To better evaluate pollution prevention options, the project attempted to assess the risks posed to individuals and populations exposed to chemical contaminants released from the refinery. An initial risk assessment analysis was performed to identify chemicals requiring further study, and to establish a baseline by which to judge potential risk reduction opportunities. Since change in exposure to benzene was used as a proxy for evaluating relative risk reductions associated with alternative pollution prevention options, the usual uncertainty associated with risk assessments was not a factor in the option analysis. The uncertainty in absolute risk assessments can arise from multiple sources the use of animal study results, difficulties with human studies, variation in individual responses to chemical exposures, the impact of differing dose rates, multiple simultaneous exposure to chem-... 

When the heterogeneous electron-transfer process at the electrode becomes slow and irreversible, the use of the direct OTTLE/Nernst experiment is inconvenient because of the uncertainties associated with a slow equilibration process. A mediated OTTLE/Nernst experiment should rather be considered, where a redox mediator Mox/Mred characterized by a high heterogeneous rate constant is added to the cell (Eq. 111). The concentration ratio of the mediator couple will be adjusted quickly to the applied electrode potential E and, furthermore, it will be in a redox equilibrium (Eq. 112) with the redox pair O/R in the bulk solution, according to Eq. 113. 

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