Pressure-temperature plot

In the production of hydrocarbon reservoirs, the process of isothermal depletion is normally assumed, that is reducing the pressure of the system while maintaining a constant temperature. Hence, a more realistic movement on the pressure-temperature plot is from point A to A . 

The pressure-temperature plot of Figure 2.1 extends all the way to the critical temperature and pressure, which has not been shown. Above the critical temperature, water strictly exists as a gas. The term saturated is used to describe the vapor-liquid portion of the curve. Basically, it implies the same thing as saying that vapor and liquid are in equilibrium with each other. The gas is said to be saturated if it is ready to condense the first drop of liquid. Conversely, the liquid is saturated if it is just about to vaporize. For the gas, this condition is called the dew point for the liquid, it is the bubble point. 

Roozeboom (1884, 1885) generated the first pressure-temperature plot for SO2 hydrate, similar to that in Figure 1.2 for several components of natural gases. In the figure, H is used to denote hydrates, I for ice, V for vapor, and Lw and Lhc for aqueous and hydrocarbon liquid phases, respectively. For each component,... 

The two calculation methods in Section 4.2 enable prediction of the three-phase (Lw-H-V) gas mixture region extending between the two quadruple points Qi and Q2 in Figure 4.1. Section 4.3 provides a method to use the techniques of Section 4.2 to locate both quadruple points on a pressure-temperature plot. Section 4.3 also discusses equilibrium of three condensed phases [aqueous liquid-hydrate-hydrocarbon liquid (Lw-H-Lhc)] Determination of equilibrium from condensed phases provides an answer to the question, Given a liquid... 

Figure 13.1 shows the process summary for an acid gas injection scheme on a pressure-temperature plot. The composition of the acid gas used to generate this and the next plot is H2S 75 mol% and C02 25% (on a water-free basis). 

Figure 13.1 Add gas injection summary on a pressure-temperature plot.

Figure A3 shows six isochores for the reduced density on a pressure-temperature plot. Note, this plot is the actual pressure and temperature, not reduced values. Also shown is the vapor pressure curve (broken line) in this case there is no two-phase dome. Note the p = 1 curve extends from the critical point (the black dot on the plot) so the combination of the vapor pressure curve and the = 1 separate the P-T plane into regions where the density is greater than the critical density cuid less than the critical density.

Figure 19. Pressure - temperature plot for the propane (l)/tripalmitin (2) system at various tripalmitin compositions (W2) K [30],...

Fig. 2.22 Adsorption isotherms of argon on graphitized carbon black at a number of temperatures," plotted as fractional coverage 0 against relative pressure p/p°. (Courtesy Prenzlow and Halsey.)...

The activation parameters for an initiator can be deterrnined at normal atmospheric pressure by plotting In vs 1/T using initiator decomposition rates obtained in dilute solution (0.2 M or lower) at several temperatures. Rate data from dilute solutions are requited in order to avoid higher order reactions such as induced decompositions. The intercept for the resulting straight line is In and the slope of the line is —E jR therefore both and E can be calculated. 

The most common a2eotropes (3,4) formed by the butanols are given in Table 2. Butyl alcohol Hquid vapor pressure/temperature responses (5,6), which are important parameters in direct solvent appHcations, are presented in Figure 1. Similarly, viscosity/temperature plots (1) for the four butanols are presented in Figure 2. 

Relation of gas volume (V) to number of moles (n) and temperature (7) at constant pressure (/ ). The volume of a gas at constant pressure is directly proportional to (a) the number of moles of gas and (b) the absolute temperature. The volume-temperature plot must be extrapolated to reach zero because most gases liquefy at low temperatures well above 0 K. 

The vapor pressure of water, which is 24 mm Hg at 25°C, becomes 92 mm Hg at 50°C and 1 atm (760 mm Hg) at 100°C. The data for water are plotted at the top of Figure 9.2. As you can see, the graph of vapor pressure versus temperature is not a straight line, as it would be if pressure were plotted versus temperature for an ideal gas. Instead, the slope increases steadily as temperature rises, reflecting the fact that more molecules vaporize at higher temperatures. At 100°C, the concentration of H20 molecules in the vapor in equilibrium with liquid is 25 times as great as at 25°C. 

Increasing the temperature increases the vapor pressures and moves the liquid and vapor curves to higher pressure. This effect can best be seen by referring to Figure 8.14, which is a schematic three-dimensional representation for a binary system that obeys Raoult s law, of the relationship between pressure, plotted as the ordinate, mole fraction plotted as abscissa, and temperature plotted as the third dimension perpendicular to the page. The liquid and vapor lines shown in Figure 8.13 in two dimensions (with Tconstant)... 

The stable phase of a substance depends on temperature and pressure. A phase diagram is a map of the pressure-temperature world showing the phase behavior of a substance. As Figure 11-38 shows, a phase diagram is aP-r graph that shows the ranges of temperature and pressure over which each phase is stable. Pressure is plotted along... 

P(x) U(x) we see that the variation in Du/Dm with (Fig. 14) is remarkably similar to that for clinopyroxene (Fig. 1). The fact that the plotted garnet partitioning data derive from a wide range of pressures, temperatures and compositions is particularly encouraging. 

For convenience, the vapour pressures are plotted on a logarithmic scale against the reciprocal of the temperature (1/K) given a straight line. The relative volatilities may then be calculated in tabular form as follows ... 

FIGURE 9.11 Vapor pressure-temperature relationships of various vaporization and combustion temperatures of various metal-oxygen/nitrogen systems as a function of total pressure, both plotted in the form log P versus 1 IT. 

The data in Table 8.4 [4] represent the vapor pressure of mercury as a function of temperature. Plot In P as a function of 1/T to a scale consistent with the precision of the data. If the resultant plot is linear, calculate AH Iz from the slope obtained by a least-squares fit to the line. If the plot is curved, use a numerical differentiation procedure to obtain the value of AHmjZ as a function of T, and calculate ACpm- See Appendix A for methods. 

Still we have to obtain relationship between half time or the slope of the lines and the operating conditions such as operational pressure, temperature and so on. But taking pilot plant data only for 1000 to 2000 hours at some designated conditions, this type of plot proved to be able to predict the flux decline over 10 000 hours quite accurately. 

One has to design the experiment to take a set of data designed to facilitate the task of parameter extraction. If a set of data is taken under constant volume conditions, and the pressure is plotted against the temperature, then there will be an intercept of —alV and a slope of R/ V — b). The van der Waals equation of state is the simplest of the equations of state beyond the perfect gas law, and the task of extracting parameter values from experimental data for the more complicated equations of state would require more ingenuity. The Redlich-Kwong equation has two parameters, A and B ... 

The amount of gas adsorbed at constant temperature plotted as a function of the equilibrium pressure (adsorption isotherm I). 

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