Low Pressures

Compilation of physical properties for 321 heavy hydrocarbons. Vapor pressures at low pressures. ... 

Correlation and compilation of vapor-pressure data for pure fluids. Normal and low pressure region. 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

If the vapor mixture contains only ideal gases, the integrals in Equations (3) and (6) are zero, z is unity for all compositions, and ()i equals 1 for each component i. At low pressures, typically less than 1 bar, it is frequently a good assumption to set ( ) = 1, but even at moderately low pressures, say in the vicinity of 1 to 10 bars, (f) is often significantly different from unity, especially if i is a polar component. 

While vapor-phase corrections may be small for nonpolar molecules at low pressure, such corrections are usually not negligible for mixtures containing polar molecules. Vapor-phase corrections are extremely important for mixtures containing one or more carboxylic acids. 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

At low pressures, it is often permissible to neglect nonidealities of the vapor phase. If these nonidealities are not negligible, they can have the effect of introducing a nonrandom trend into the plotted residuals similar to that introduced by systematic error. Experience here has shown that application of vapor-phase corrections for nonidealities gives a better representation of the data by the model, oven when these corrections... 

The low-pressure extrapolated data points were generated by linear extrapolation of the lowest 4-6 points on a plot of... 

Large errors in the low-pressure points often have little effect on phase-equilibrium calculations e.g., when the pressure is a few millitorr, it usually does not matter if we are off by 100 or even 1000%. By contrast, the high-pressure end should be reliable large errors should be avoided when the data are extrapolated beyond the critical temperature. 

Finally, at low pressures, the liquid fugacity can be calculated using Equation (5), i.e. we can assume that <() = 1 and that the Poynting correction = 1. 

This is an endothermic reaction accompanied by an increase in the number of moles. High conversion is favored by high temperature and low pressure. The reduction in pressure is achieved in practice by the use of superheated steam as a diluent and by operating the reactor below atmospheric pressure. The steam in this case fulfills a dual purpose by also providing heat for the reaction. 

Supp. E., Technology of Lurgi s Low Pressure Methanol Process, Chem. Tech., 3 430, 1973. 

Figure 3.8a shows the temperature-composition diagram for a minimum-boiling azeotrope that is sensitive to changes in pressure. This azeotrope can be separated using two columns operating at different pressures, as shown in Fig. 3.86. Feed with mole fraction of A Ufa)) of, say, 0.3 is fed to the high-pressure column. The bottom product from this high-pressure column is relatively pure B, whereas the overhead is an azeotrope with jcda = 0-8, jcdb = 0.2. This azeotrope is fed to the low-pressure column, which produces relatively pure A in the bottom and in the overhead an azeotrope with jcda = 0.6, jcdb = 0.4. This azeotrope is added to the feed of the high-pressure column.

Figure 6.25a shows the same grand composite curve with two levels of saturated steam used as a hot utility. The steam system in Fig. 6.25a shows the low-pressure steam being desuperheated by injection of boiler feedwater after pressure reduction to maintain saturated conditions. Figure 6.256 shows again the same grand composite curve but with hot oil used as a hot utility. 

Low pressure. Low pressures are not in general as hazardous as the other extreme operating conditions. However, one particular hazard that does exist in low-pressure plants handling flammable materials is the possible ingress of air with the consequent formation of a flammable mixture. 

Following the pinch rules, there should be no heat transfer across either the process pinch or the utility pinch by process-to-process heat exchange. Also, there must be no use of inappropriate utilities. This means that above the utility pinch in Fig. 16.17a, high-pressure steam should be used and no low-pressure steam or cooling water. Between the utility pinch and the process pinch, low-pressure steam should be used and no high-pressure steam or cooling water. Below the process pinch in Fig. 16.17, only cooling water should be used. The appropriate utility streams have been included with the process streams in Fig. 16.17a. 

Given a network structure, it is possible to identify loops and paths for it, as discussed in Chap. 7. Within the context of optimization, it is only necessary to consider those paths which connect two different utilities. This could be a path from steam to cooling water or a path from high-pressure steam used as a hot utility to low-pressure steam also used as a hot utility. These paths between two different utilities will be designated utility paths. Loops and utility paths both provide degrees of freedom in the optimization. ... 

Steam costs vary with the price of fuel. If steam is only generated at low pressure and not used for power generation in steam turbines, then the cost can be estimated from local fuel costs assuming a boiler efficiency of around 75 percent (but can be significantly higher) and distribution losses of perhaps another 10 percent, giving an overall efficiency of around 65 percent. 

Exampie A.3.1 The pressures for three steam mains have been set to the conditions given in Table A.l. Medium- and low-pressure steam are generated by expanding high-pressure steam through a steam turbine with an isentropic efficiency of 80 percent. The cost of fuel is 4.00 GJ and the cost of electricity is 0.07 h. Boiler feedwater is available at 100°C with a heat capacity... 

The problem with this approach is that if the steam generated in the boilers is at a very high pressure and/or the ratio of power to fuel costs is high, then the value of low-pressure steam can be extremely low or even negative. This is not sensible and discourages efficient use of low-pressure steam, since it leads to low-pressure steam with a value considerably less than its fuel value. 

An alternative approach is to assume that the low-pressure steam... 

Adams catalyst, platinum oxide, Pt02 H20. Produced by fusion of H2PtCl6 with sodium nitrate at 500-550 C and leaching of the cooled melt with water. Stable in air, activated by hydrogen. Used as a hydrogenation catalyst for converting alkenes to alkanes at low pressure and temperature. Often used on Si02... 

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

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