Vapor pressure simulations error

Figure 9. Distribution of relative error for the three vapor pressure simulations (true value = 0.00).

The process of choosing a random number and calculation of cascading error is repeated 10,000 times, generating a distribution of solubility values relative to the "true" value which can be characterized mathematically, plotted, and used to furnish the likelihood or probability of any particular solubility value in the range being exceeded. Essentially the same steps were followed in simulations for other parameters investigated, even for those on vapor pressure, where effects of temperature variation are compound-specific. 

The results of isoteniscope simulations show a slight overprediction for all three compounds with a skewed distribution in each case (Figures 6, 7, and 8). Predictably, the lower the vapor pressure, the larger the relative standard deviation. On the other hand, the absolute standard deviation is relatively unchanged over the range of vapor pressures examined, varying between about 0.72 and 0.77 torr for the extreme cases. The maximum skewedness of the distribution is found for toluene, the medium-vapor pressure case. The standard deviation of 2.7 percent found for toluene corresponds quite well to the 3 percent error estimate made by MacKay et al. (4). The 6 percent standard deviation for the chlorobenzene case shows it to be at the lower end of the range recommended for reliable measurement. 

Column and high performance liquid chromatography (HPLC) methods for measurement of solubility, octanol-water partition coefficient, and vapor pressure which are replacing the older equilibrium methods tend to underestimate aqueous solubility and vapor pressure and tend to overestimate the octanol-water partition coefficient. The standard deviation for both the equilibrium and dynamic systems are similar, but calibration between systems is necessary to insure that they agree. The range of errors for both types of measurement as mentioned in the literature are well within the range predicted by the computer-simulated error distributions generated in this report. The measurement error... 

Van der Waals interactions are proportional to 1/Rfj at large distances and so are short range. A van der Waals cutoff distance of 8 A is typically used and was believed to produce little error. However, molecular-dynamics simulations of liquid alkanes using the GROMOS force field found that the enthalpies of vaporization and the vapor pressures changed very substantially when the van der Waals cutoff distance was varied within the range 8 to 14 A, and so a van der Waals cutoff radius of 16 A is much more justifiable than the traditional one of 8 A [X. Daura et al., J. Comput. Chem., 19, 535 (1998)]. 

Sometimes, users of process simulation programs calculate vapor pressures beyond the critical point, although it is physically meaningless. If the Wagner equation is applied above the critical temperature, it will yield a mathematical error. Therefore, the simulation program must provide an extrapolation function that continues the vapor pressure line with the same slope [26]. 

The application of the Clausius-Clapeyron equation should be restricted to a certain temperature range. The first term dP/dT can be considered as quite exact, as a reliable vapor pressure equation is a necessary requirement for process simulation. The limitation is that the common vapor pressure equations like Wagner and Antoine badly extrapolate to low temperatures. Furthermore, even if measured data at low temperatures are available, the relative errors are quite high. As a rule of thumb, it is recommended not to use the Clausius-Clapeyron equation... 

Care is needed when modeling compressible gas flows, flows of vapor-liquid mixtures, slurry flows, and flows of non-Newtonian liquids. Some simulators use different pipe models for compressible flow. The prediction of pressure drop in multiphase flow is inexact at best and can be subject to very large errors if the extent of vaporization is unknown. In most of these cases, the simulation model should be replaced by a computational fluid dynamics (CFD) model of the important parts of the plant. 

In many flash processes, the feed stream is at a higher pressure than the flash pressure, and the heat for vaporization is provided by the enthalpy of the feed. In this situation the flash temperature will not be known and must be found by trial and error. A temperature must be found at which both the material and energy balances are satisfied. This is easily carried out using commercial simulation software. 

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