Water isothermal compressibility

Reservoir fluids (oil, water, gas) and the rock matrix are contained under high temperatures and pressures they are compressed relative to their densities at standard temperature and pressure. Any reduction in pressure on the fluids or rock will result in an increase in the volume, according to the definition of compressibility. As discussed in Section 5.2, isothermal conditions are assumed in the reservoir. Isothermal compressibility is defined as ... 

Many of the unusual properties of the perfluorinated inert fluids are the result of the extremely low intermolecular interactions. This is manifested in, for example, the very low surface tensions of the perfluorinated materials (on the order of 9-19 mN jm. = dyn/cm) at 25°C which enables these Hquids to wet any surface including polytetrafluoroethene. Their refractive indexes are lower than those of any other organic Hquids, as are theh acoustic velocities. They have isothermal compressibilities almost twice as high as water. Densities range from 1.7 to 1.9 g/cm (l )-... 

The discussion of the last section is then useful in considering the evaporative cycles. We shall see that the effect of water injection downstream of the compressor (and possibly in the cold side of the heat exchanger) may lead towards the [CBTJiXr type of plant, with increased cold side effective specific heat and hence increased heat exchanger effectiveness. Water injection in the compressor may lead to a plant with isothermal compression. 

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

The theorem also applies to a heterogeneous system, such as a liquid in presence of its saturated vapour, or in presence of the solid. In the former case, vapour is liquefied by compression and gives out its latent heat. Under isothermal conditions this would escape as fast as produced, but if the heat is compelled to remain in the system, it raises the temperature and thereby increases the pressure. If, on the other hand, a mixture of ice and water is compressed, ice melts and the mass is cooled by abstraction of heat. If heat is allowed to enter from outside, so as to restore the original temperature, more ice melts, and the pressure falls by reason of the contraction. 

In an experimental study of a small air-lift pump(6), (25 mm. diameter and 13.8 m overall height) the results were expressed by plotting the efficiency of the pump, defined as the useful work done on the water divided by the energy required for isothermal compression of the air, to a basis of energy input in the air. In each case, the curve was found to rise sharply to a maximum and then to fall off more gradually. Typical results are shown in Figure 8.37. 

Despite the importance of mixtures containing steam as a component there is a shortage of thermodynamic data for such systems. At low densities the solubility of water in compressed gases has been used (J, 2 to obtain cross term second virial coefficients Bj2- At high densities the phase boundaries of several water + hydrocarbon systems have been determined (3,4). Data which would be of greatest value, pVT measurements, do not exist. Adsorption on the walls of a pVT apparatus causes such large errors that it has been a difficult task to determine the equation of state of pure steam, particularly at low densities. Flow calorimetric measurements, which are free from adsorption errors, offer an alternative route to thermodynamic information. Flow calorimetric measurements of the isothermal enthalpy-pressure coefficient pressure yield the quantity 4>c = B - TdB/dT where B is the second virial coefficient. From values of obtain values of B without recourse to pVT measurements. 

In the first, isothermal, step with this two-phase system, one mole of liquid water is vaporized at 400 K with an absorption of 39.3 kJ. In the second, adiabatic, step, the system is expanded even more, with an accompanying decrease in temperature to 300 K. At 300 K, an isothermal compression is carried out, which is followed by an adiabatic compression to return the system to its starting point. 

Assuming that this two-phase system obeys the first and second laws of thermodynamics, and given that the heat of vaporization of water at 300 K is 43.5 kJ mol, how many grams of liquid water must condense out of the vapor in the isothermal compression step Show your reasoning in your answer. 

It is found that, even a monolayer of lipid (on water), when compressed can undergo various states. In the following text, the various states of monomolecular films will be described as measured from the surface pressure, n, versus area, A, isotherms, in the case of simple amphiphile molecules. On the other hand, the Il-A isotherms of biopolymers will be described separately since these have a different nature. 

We saw in Chapter 8 that the coefficient of isothermal compressibility of oil has a discontinuity at the bubble point. The coefficient of isothermal compressibility of water has the same discontinuity for the same reason. Figure 8-7 is typical of the relationship between water... 

The Coefficient of Isothermal Compressibility of Water at Pressures Above the Bubble Point... 

Figure 16-12 gives the coefficient of isothermal compressibility of pure water. The figure is a combination of two sets of data which are in fair agreement in the region of overlap.6,7... 

Fig. 16-13. Effect of salinity on the coefficient of isothermal compressibility of water. (From an equation by Osif, SPE Res. Eng. 3, 1988, 175.)...

Estimate a value of the coefficient of isothermal compressibility of the reservoir water of Exercise 16-6 at 2300 psig and 140°F. 

Preliminary Thermodynamic Relations. Here it will be assumed that we are dealing with incompressible systems this is a very good assumption for aqueous solutions since the isothermal compressibility of water is so small. At constant temperature the equilibrium condition for any mixed association (see Equations 1 and 2 for example) is... 

Figure 3. Isothermal compressibility of water from data of Pena and McGlashan (117). Curve redrawn by present author...

The pressure dependence of equilibrium constants in this work are estimated with Eq. 2.29, which requires knowledge of the partial molar volumes and compressibilities for ions, water, and solid phases. For ions and water, molar volumes and compressibilities are known as a function of temperature (Table B.8 Eqs. 3.14 to 3.19). Molar volumes for solid phases are also known (Table B.9) unfortunately, the isothermal compressibilities for many solid phases are lacking (Millero 1983 Krumgalz et al. 1999). 

For a reaction with positive gas mole change, Eq. (47) indicates that Kx decreases with pressure. Because ce is a monotonically increasing function of Kx, the equilibrium extent of a reaction with positive Avgas always decreases as pressure is increased. This is an example of Le Chatelier s principle, which states that a reaction at equilibrium shifts in response to a change in external conditions in a way that moderates the change. In this case, because the reaction increases the number of moles of gas and thus the pressure, the reaction shifts back to reactants. The isothermal compressibility of a reactive system can, therefore, be much greater than that of a nonreactive system. This effect can be dramatic in systems with condensed phases. For example, in the calcium carbonate dissociation discussed in Example 12, if the external pressure is raised above the dissociation pressure of C02, the system will compress down to the volume of the solid. Of course, a similar effect is observed in simple vaporization or sublimation equilibrium. As the pressure on water at 100°C is increased above 1.0 atm, all vapor is removed from the system. 

The mixture dimethyl sulphoxide + water has attracted a great deal of interest. The excess function HE is negative for this mixture at 298 K (Clever and Piggott, 1971 Fox and Whittingham, 1975), as also are GE (Lam and Benoit, 1974 Philippe and Jambon, 1974) and FE-quantities (Lau et al., 1970). A set of smoothed thermodynamic excess functions is shown in Fig. 54 (Kenttamaa and Lindberg, 1960). The dependence on x2 of the isothermal compressibilities of DMSO + water mixtures is quite different from that for the TA monohydric alcohols + water mixtures. The curves for the latter systems show... 

---