Pressure-temperature-concentration phase

Equilibrium measurements of the solid hydrate phase have been previously avoided due to experimental difficulties such as water occlusion, solid phase inhomogeneity, and measurements of solid phase concentrations. Instead, researchers have traditionally measured fluid phase properties (i.e., pressure, temperature, gas phase composition, and aqueous inhibitor concentrations) and predicted hydrate formation conditions of the solid phase using a modified van der Waals and Platteeuw (1959) theory, specified in Chapter 5. 

The closed loop can be regarded as a vertical section through a nose in the concentration-temperature-pressure space at constant pressure (see Figure 3.13a). When the pressure increases, the surface covered in the temperature-concentration phase by the phase separation loop decreases and vanishes at a critical pressure P. ... 

The state of the system is given by a set of values of properly chosen physical variables. To determine unambiguously the state of the simplest system (a pure substance in one phase) one should know two properties (e.g. temperature and pressure) in addition to the quantity (moles). To describe the state of more complex systems one should know more properties (e.g. the concentrations of individual species). The thermodynamic properties of the system depending only on the state and not on the way by which the system has reached the given state, are called state functions. The typical fundamental state functions are temperature, pressure, volume and concentration of the individual components of the system. The thermodynamic properties are usually classified into extensive and intensive ones. The extensive properties are proportional to the quantity of the substance in the system. Therefore, they are additive, i.e. the total extensive property of the system equals the sum of the extensive properties of the individual parts of the system. Typical extensive quantities are weight, energy, volume, number of moles. On the other hand, the intensive properties do not depend on the quantity of the substance in the system (pressure, temperature, concentration, specific quantities, specific resistance, molar heat, etc.). 

F the degrees of freedom of the system at equilibrium (chosen from the state variables pressure, temperature, concentration of each component in each phase) number of variables describing the state of the system which may be varied independently without disturbing the system equilibrium... 

Pressure, temperature, concentration of the key component in the liquid phase... 

Figure 3. (a) Temperature-concentration phase diagram at P =0.15 and 0.20, for LJ polymer solutions, (b) Pressure-Temperature phase diagram predicted by coil-to-globule transition of a single chain (lines) compared to LCSTs from phase behavior simulations (points). Ref. [61]. 

At a second-order SmA-SmC phase transition, the symmetries are different but the layer spacing is the same. Fluctuations can drive a line of second-order SmA-SmC phase transitions to an N-SmA-SmC mul-ticritical point (see Fig. 4) [53]. Competing N-SmA and N-SmC fluctuations pull the N phase under the SmA phase in the temperature-concentration phase plane, leading to the Nj-e-SmA-SmC multicritical point [16]. High-resolution studies, as a function of both concentration and pressure, resolve the fluctuation-driven N-SmA/ N-SmC step (see, e.g. Fig. 5) into a universal spiral (Fig. 12) [16] around the N-SmA-SmC and the Nre-SmA-SmC multicritical points. Loosely speaking, the N-SmA transition line is dominated by N-SmA fluctuations, and the N-SmC transition line is dominated by Brazovskii fluctuations [54] that drive the N-SmC transition to lower temperatures compared to the N-SmA transition [18]. 

So far we have considered only a single component. However, reservoir fluids contain a mixture of hundreds of components, which adds to the complexity of the phase behaviour. Now consider the impact of adding one component to the ethane, say n-heptane (C7H.,g). We are now discussing a binary (two component) mixture, and will concentrate on the pressure-temperature phase diagram. 

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

Methanol is frequently used to inhibit hydrate formation in natural gas so we have included information on the effects of methanol on liquid phase equilibria. Shariat, Moshfeghian, and Erbar have used a relatively new equation of state and extensive caleulations to produce interesting results on the effeet of methanol. Their starting assumptions are the gas composition in Table 2, the pipeline pressure/temperature profile in Table 3 and methanol concentrations sufficient to produce a 24°F hydrate-formation-temperature depression. Resulting phase concentrations are shown in Tables 4, 5, and 6. Methanol effects on CO2 and hydrocarbon solubility in liquid water are shown in Figures 3 and 4. 

When a gas comes in contact with a solid surface, under suitable conditions of temperature and pressure, the concentration of the gas (the adsorbate) is always found to be greater near the surface (the adsorbent) than in the bulk of the gas phase. This process is known as adsorption. In all solids, the surface atoms are influenced by unbalanced attractive forces normal to the surface plane adsorption of gas molecules at the interface partially restores the balance of forces. Adsorption is spontaneous and is accompanied by a decrease in the free energy of the system. In the gas phase the adsorbate has three degrees of freedom in the adsorbed phase it has only two. This decrease in entropy means that the adsorption process is always exothermic. Adsorption may be either physical or chemical in nature. In the former, the process is dominated by molecular interaction forces, e.g., van der Waals and dispersion forces. The formation of the physically adsorbed layer is analogous to the condensation of a vapor into a liquid in fret, the heat of adsorption for this process is similar to that of liquefoction. 

Process Desialions Pressure. Temperature, Flow rate. Concentration, Phase/statc change. 

Two situations are found in leaching. In the first, the solvent available is more than sufficient to solubilize all the solute, and, at equilibrium, all the solute is in solution. There are, then, two phases, the solid and the solution. The number of components is 3, and F = 3. The variables are temperature, pressure, and concentration of the solution. All are independently variable. In the second case, the solvent available is insufficient to solubilize all the solute, and the excess solute remains as a solid phase at equilibrium. Then the number of phases is 3, and F = 2. The variables are pressure, temperature and concentration of the saturated solution. If the pressure is fixed, the concentration depends on the temperature. This relationship is the ordinary solubility curve. 

Given the temperature and pressure, the concentration of any component in the vapour phase can be obtained from the concentration in the liquid phase, from the vapour-liquid equilibrium data for the system. 

The equilibrium conversion can be calculated from knowledge of the free energy, together with physical properties to account for vapor and liquid-phase nonidealities. The equilibrium conversion can be changed by appropriate changes to the reactor temperature, pressure and concentration. The general trends for reaction equilibrium are summarized in Figure 6.8. 

Process simulators contain the model of the process and thus contain the bulk of the constraints in an optimization problem. The equality constraints ( hard constraints ) include all the mathematical relations that constitute the material and energy balances, the rate equations, the phase relations, the controls, connecting variables, and methods of computing the physical properties used in any of the relations in the model. The inequality constraints ( soft constraints ) include material flow limits maximum heat exchanger areas pressure, temperature, and concentration upper and lower bounds environmental stipulations vessel hold-ups safety constraints and so on. A module is a model of an individual element in a flowsheet (e.g., a reactor) that can be coded, analyzed, debugged, and interpreted by itself. Examine Figure 15.3a and b. 

The liquid phase activity coefficients y and y2 depend upon temperature, pressure and concentration. Typical values taken from Perry s Chemical Engineers Handbook114) are shown in Figure 11.8 for the systems m-propanol-water and acetone-chloroform. In the former, the activity coefficients are considered positive, that is greater than unity, whilst in the latter, they are fractional so that the logarithms of the values are negative. In both cases, y approaches unity as the liquid concentration approaches unity and the highest values of y occur as the concentration approaches zero. 

Temperature, pressure, and concentration can affect phase equilibria in a two-component or binary system, although the effect of pressure is usually negligible and data can be shown on a two-dimensional temperature-concentration plot. Three basic types of binary system — eutectics, solid solutions, and systems with compound formation—are considered and, although the terminology used is specific to melt systems, the types of behaviour described may also be exhibited by aqueous solutions of salts, since, as Mullin 3-1 points out, there is no fundamental difference in behaviour between a melt and a solution. 

In terms of concentrations of species indicated by [] s (these may be pressures for gas phase equilibria), the high temperature equilibrium constant is given by... 

Phase occurring over a definite range of temperature, pressure or concentration within the... 

Simple component exchange between solid phases is accomplished by diffusion. If only two components (such as Fe " and Mg) are exchanging, the diffusion is binary. The boundary condition is often such that the exchange coefficient between the surfaces of two phases is constant at constant temperature and pressure. The concentrations of the components on the adjacent surfaces may be constant assuming interface equilibrium. The solution to the diffusion equation... 

It is also important to maintain the same gas and liquid used in the bench scale BSCR, the same physical and transport properties, pressure, temperature, and the concentration of reagents in the gas and liquid phases. 

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