Pressurization paths

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Figure A2.5.12. Typical temperatxire T versus mole fraction v diagrams for the constant-pressure paths shown in figure A2.5.11. Note the critical points (x) and the horizontal tliree-phase lines.

Restriction Orifice - In general a restriction orifice should not be used as a means of limiting the capacity of a pressurization path. In special cases, where large incentives apply (such as reducing die size of a flare system), a restriction orifice may be used, provided that all the following conditions are satisfied ... 

Control Valve - A control valve with a limit stop to restrict the maximum opening is not normally acceptable as a means of limiting the capacity of a pressurizing path, since the stop may later be removed or the valve changed. Credit for the limiting capacity of a control valve in the wide open position may be taken only if all of the following conditions apply ... 

A rough rule of thumb can be set forth to help avoid having your deconvolved spectral lines exhibit saturation effects. Reduce the pressure path (and thus apparent absorption) until you are sure that it is actually too low then cut it in half again. As an alternative, one could easily generate a dictionary of simulations based on the ratio of the FWHM of the true line to the equivalent FWHM characterizing specific instrumental resolution. In our laboratory we have simply developed experience in evaluating the requirements. Our instrumental resolution of 0.009 cm-1 makes that fairly easy. 

The reservoir pressure path on the phase diagram, Figure 5-3, indicates that at some low pressure the liquid begins to revaporize. This occurs in the laboratory however, it probably does not occur to much extent in the reservoir because during production the overall composition of the reservoir fluid changes. 

A wet gas exists solely as a gas in the reservoir throughout the reduction in reservoir pressure. The pressure path, line 12, does not enter the phase envelope. Thus, no liquid is formed in the reservoir. However, separator conditions lie within the phase envelope, causing some liquid to be formed at the surface. 

Since H, Cp, and T are all state functions, Eq. (2.26) applies to any process for which P2 = Pi whether or not it is actually carried out at constant pressure. However, it is only for the mechanically reversible, constant-pressure path that heat and work can be calculated by the equations Q = n AH, Q = n f CPdT, and W = PnAV,... 

Moldenhauer, H., Htinerbein, B., and Kala, H. (1972), Recording of pressure-path diagrams from an eccentric press using piezoelectric measurement, Pharmazie, 27, 417—418. 

Verbally, the absorptivity computed from Eq. (5-141) by using the correlations in Table 5-5 is based on a value for gas emissivity Eg calculated at a temperature 7 and at a partial-pressure path-length product of (pc+pw)L7y77. The absorptivity is then equal to this value of gas emissivity multiplied by (Tg/Tj). It is recommended that spectrally based models such as RADCAL (loc. cit.) be used particularly when extrapolating beyond the temperature, pressure, or partial-pressure-length product ranges presented in Table 5-5. 

The phase behavior of a pure substance may be depicted schematically on a pressure-temperature diagram as shown in Figure 1.1. The curve OC, the vapor pressure curve, separates the vapor and liquid phases. At any point on this curve, the two phases can coexist at equilibrium, both phases having the same temperature and pressure. Phase transition takes place as the curve is crossed along any path. Figure 1.1 shows two possible paths at constant pressure (path AB) and at constant temperature (path DE). At the critical point, C, the properties of the two phases are indistinguishable and no phase transition takes place. In the entire region above the critical temperature or above the critical pressure, only one phase can exist. 

A typical integration path is illustrated in Fig. 1. The point O is an arbitrary reference state while the path AB is a constant-pressure path along which Cp is known. The equation of state is considered to be explicit in pressure. The application of (9) and (10) to the isothermal paths OA and BC and (11) and (12) to AB results in the following relations giving Sy Hf and U at the point C with respect to the reference values Hq, and 7o, respectively ... 

The amount of heat depends on the path of the heating process. We have encountered two simple paths, the constant-volume and the constant-pressure path. Each is characterized by its own heat capacity. 

Constant-pressure path The constant-pressure path connects state A to the saturation line at the same isobar (state C) at Tc = 212.38 °C. We express the enthalpy at C in terms of the enthalpy at C plus the change from C to A ... 

Consider the constant-pressure path AB in Figure -10 The initial state is compressed liquid and the final state is superheated vapor. The enthalpy change between initial and final state is AHab = Hb — Ha- (3.29)... 

In Chapter c we will learn how to calculate properties between any two states without the limitation of constant-volume or constant-pressure paths. A special case of practical importance is the ideal-gas state. In this special limit, internal energy and enthalpy are functions of temperature only and changes between any two states are given by... 

Calculation of Entropy Constant-Pressure Path, No Phase Change... 

A rather simple problem is the calculation of AS between two states at the same pressure. To perform this calculation we devise a reversible constant-pressure path between the two states. If no phase change occurs, the heat along this path the heat is... 

Constant-Pressure Path. Drawing a line of constant pressure from state Ta = 100 Pa = 20 bar to the saturated... 

This result agrees very well with the one obtained using the constant-pressure path. 

---