Uncertainty in pressure

There is an uncertainty in pressure of an order of 0.1 MPa depending on whether classical or quantum partition function is used for vibrational motions. Clearly, equation (14) gives too low dissociation pressure. Therefore, the influence of the guest molecule on the host lattice is fairly large and cannot be neglected[22, 24, 33]. Comparison with experiment will be made below. 

Typical uncertainties in density are 0.02% in the liquid phase, 0.05% in the vapor phase and at supercritical temperatures, and 0.1% in the critical region, except very near the critical point, where the uncertainty in pressure is 0.1%. For vapor pressures, the uncertainty is 0.02% above 180 K, 0.05% above 1 Pa (115 K), and dropping to 0.001 mPa at the triple point. The uncertainty in heat capacity (isobaric, isochoric, and saturated) is 0.5% at temperatures above 125 K and 2% at temperatures below 125 K for the liquid, and is 0.5% for all vapor states. The uncertainty in the liquid-phase speed of sound is 0.5%, and that for the vapor phase is 0.05%. The uncertainties are higher for all properties very near the critical point except pressure (saturated vapor/liquid and single pliase). The uncertainty in viscosity varies from 0.4% in the dilute gas between room temperature and 600 K, to about 2.5% from 100 to 475 K up to about 30 MPa, and to about 4% outside this range. Uncertainty in thermal conductivity is 3%, except in the critical region and dilute gas which have an uncertainty of 5%. 

The Joule-Thomson inversion locus in P-T coordinates has been computed from the P-F-T data and first derivatives by Weber. Uncertainty in pressure on this locus increases monotonically from 0.1 atm at 27°K to 2.2 atm at 100°K. Figure 5 is an outline of these results. The densities on this locus also have been derived P]. 

The uncertainty in density of the equation of state is 0.0001% at 1 atm in the liquid phase, and 0.001% at other liquid states at pressures up to 10 MPa and temperatures to 423 K. In the vapor phase, the uncertainty is 0.05% or less. The uncertainties rise at higher temperatures and/or pressures, but are generally less than 0.1% in density except at extreme conditions. The uncertainty in pressure in the critical region is 0.1%. The uncertainty of the speed of sound is... 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

Although a torsion test is simple to carry out, it is not commonly accepted as an integral part of a material specification furthermore, few torsion data exist in handbooks. If, as is usually the case, the design needs to be based on tensile data, then a criterion of elastic failure has to be invoked, and this introduces some uncertainty in the calculated yield pressure (8). 

The first two examples show that the interaction of the model parameters and database parameters can lead to inaccurate estimates of the model parameters. Any use of the model outside the operating conditions (temperature, pressures, compositions, etc.) upon which the estimates are based will lead to errors in the extrapolation. These model parameters are effec tively no more than adjustable parameters such as those obtained in linear regression analysis. More comphcated models mav have more subtle interactions. Despite the parameter ties to theoiy, tliey embody not only the uncertainties in the plant data but also the uncertainties in the database. 

After some early uncertainty in the literature about the nature of the pressure sensitive bond, Dahlquist [5,6] related modulus data to tack-temperature studies and observed that the compression modulus of the adhesive had to be less than about 3 X 10 dyne/cm (3 x lO Pa) before any adhesive tack was observed. This was explained as the highest modulus that still allowed the adhesive to be sufficiently compliant to wet out or come into molecular contact with the substrate and form dispersive bonds. As other investigators [7-9] accepted this requirement it was termed the Dahlquist Criterion . 

The temperature at the observed transition is the initial temperature of the sample added to the shock-compression heating, which is only 3 °C. Uncertainties in the change in Curie temperature are principally due to the measurement of Curie temperature at atmospheric pressure, which was found to... 

It is conventional to take as the activation volume the value of AV when P = 0, namely —bRT. (This is essentially equal to the value at atmospheric pressure.) Pressure has usually been measured in kilobars (kbar), or 10 dyn cm 1 kbar = 986.92 atm. The currently preferred unit is the pascal (Pa), which is 1 N m 1 kbar = 0.1 GPa. Measurements of AV usually require pressures in the range 0-10 kbar. The units of AV are cubic centimeters per mole most AV values are in the range —30 to +30 cm moP, and the typical uncertainty is 1 cm moP. Rate constant measurements should be in pressure-independent units (mole fraction or molality), not molarity. ... 

Uncertainties in physical wocleling -Inappropriate model selection Incorrect or inadequate physical basis for model Inadequate validation Inaccurate model parameters Uncertainties in physical model data -Input data (composition, temperature, pressure)... 

Pressure losses through the shell side of exchangers are subject to much more uncertainty in evaluation than for tube side. In many instances, they should be considered as approximations or orders of magnitude. This is especially true for units operating under vacuum less than 7 psia. Very little data has been published to test the above-atmospheric pressure correlations at below-atmospheric pressures. The losses due to differences in construction, baffle clearances, tube clearances, etc., create indeterminate values for exact correlation. Also see the short-cut method of reference 279. 

The values of i calculated from (8) and (8) do not agree very closely, and it would appear, as Weinstein (loc. cit. 1068) remarks, that Although the calculations undoubtedly establish the legitimacy of the system of equations, the great uncertainty in the numerical determination of the decisive magnitudes forms a practical defect which will only be removed by observations over very wide intervals of the variables. Any discrepancy between the results of actual observations of equilibria, and those calculated by means of Nernst s chemical constants, need not, in the present state of uncertainty of the latter, cause any great alarm. Nernst himself apparently regards the constant < >, obtained from vapour-pressure measurements, as the most certain, and the others as more or less tentative. 

Detonation pressure may be computed theoretically or measured exptly. Both approaches are beset with formidable obstacles. Theoretical computations depend strongly on the choice of the equation of state (EOS) for the detonation products. Many forms of the EOS have been proposed (see Vol 4, D269—98). So.far none has proved to be unequivocally acceptable. Probably the EOS most commonly, used for pressure calcns are the polytropic EOS (Vol 4, D290-91) and the BKW EOS (Vol 4, D272-74 Ref 1). A modern variant of the Lennard Jones-Devonshire EOS, called JCZ-3, is now gaining some popularity (Refs -11. 14). Since there is uncertainty about the correct form of the detonation product EOS there is obviously uncertainty in the pressures computed via the various types of EOS ... 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

The major source of error In calculating the free energies of Pu0(g) and Pu02(g) from Battles et al. probably results from the derived equations for the partial pressures of 0(g) and Pu(g) as a consequence of uncertainties In Ionization cross sections. The thermodynamic assessments of Ackermann et al. Involve extrapolations of oxygen potentials reported by Markin and Rand (4) In temperature of the order of 500 K. However, a second and third... 

The uncertainties in the condensed-phase thermodynamic functions arise from (1) the possible existence of a solid-solid phase transition in the temperature range 2160 to 2370 K and (2) the uncertainty in the estimated value of the liquid heat capacity which is on the order of 40%. While these uncertainties affect the partial pressures of plutonium oxides by a factor of 10 at 4000 K, they are not limiting because, at that temperature, the total pressure is due essentially entirely to O2 and 0. 

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