Isothermal compressibility fluids

For an isothermal compressible fluid, the state law of the fluid links density with pressure. 

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 )-... 

Other Refrigeration Methods. Cryocoolers provide low temperature refrigeration on a smaller scale by a variety of thermodynamic cycles. The Stirling cycle foUows a path of isothermal compression, heat transfer to a regenerator matrix at constant volume, isothermal expansion with heat transfer from the external load at the refrigerator temperature, and finally heat transfer to the fluid from the regenerator at constant volume. 

For theoretical cycle work performed in an isothermal compression cycle (For ideal fluid case)... 

Compressible fluid flow occurs between the two extremes of isothermal and adiabatic conditions. For adiabatic flow the temperature decreases (normally) for decreases in pressure, and the condition is represented by p V (k) = constant. Adiabatic flow is often assumed in short and well-insulated pipe, supporting the assumption that no heat is transferred to or from the pipe contents, except for the small heat generated by fricdon during flow. Isothermal pVa = constant temperature, and is the mechanism usually (not always) assumed for most process piping design. This is in reality close to actual conditions for many process and utility service applications. 

Corollary.—A fluid emits or absorbs heat on isothermal compression according as it expands or contracts, respectively, with rise of temperature at constant pressure. 

An isothermal compression of the fluid is made at 91 from C3 to V4. Work is added to the system, and, to maintain isothermal conditions, a quantity of heat q is removed from the system and absorbed in a heat reservoir maintained at the temperature 9. ... 

Lawlb. C. . Trans. Am. Inst. Chem. Eng. 39 (1948) 385. Isothermal and adiabatic flow of compressible fluids. 

Little error is introduced if this expression is applied to the flow of a compressible fluid provided that the velocity is not greater than about 60 m/s. When the velocity is high, the equation of state must be used to give the relation between the pressure and the volume of the gas. For non-isothermal flow, Pvk = a constant,... 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

Figure 17. Specific volume Vt and isothermal compressibility (at the glass transition temperature Tg) calculated from the LCT as a function of the inverse number l/M of united atom groups in single chains for constant pressure (P = I atm 0.101325 MPa) F-F and F-S polymer fluids. Both quantities are normahzed by the corresponding high molar mass limits (i.e., by...

At temperatures much higher than Za, the polymer fluid formally undergoes a fluid-gas transition where the isothermal compressibility Kr diverges, but this high temperature regime is normally inaccessible in polymer systems because of thermal decomposition. 

R. ZwanzigandR. D. Mountain, J. Chem. Phys. 43,4464 (1965) show that the modulus Goo and the isothermal compressibility are determined by similar integrals containing the pair correlation function and the interparticle potential for simple Lennard-Jones fluids. The adiabatic (zero frequency) bulk modulus Ko equals —y(0P/0P) j, which clearly is a kind... 

TABLE 11.2 Measured Thermodynamic Properties (in SI Units) of Some Common Fluids at 20° C, 1 atm Molar Heat Capacity CP, Isothermal Compressibility jS7, Coefficient of Thermal Expansion otp, and Molar Volume V, with Monatomic Ideal Gas Values (cf. Sidebar 11.3) Shown for Comparison... 

The following physical properties can be determined from the results of a black oil reservoir fluid study bubble-point pressure, formation volume factor of oil, solution gas-oil ratio, total formation volume factor, coefficient of isothermal compressibility of oil, and oil viscosity,... 

The differential energy balances of Eqs. (6.10) and (6.15) with the friction term of Eq. (6.18) can be integrated for compressible fluid flow under certain restrictions. Three cases of particular importance are of isentropic or isothermal or adiabatic flows. Equations will be developed for them for ideal gases, and the procedure for nonidcal gases also will be indicated. 

Equation (3) is for the special case of an incompressible fluid. As an example of a compressible fluid, consider an isothermal or constant-temperature layer of gas. The equation of state for such a gas can be written ... 

Other properties that behave in a similar fashion include the isothermal compressibility of fluids and the magnetic susceptibility for magnetic transitions. 

A gaseous pure component can be defined as supercritical when its state is determined by values of temperature T and pressure P that are above its critical parameters (Tc and Pc). In the proximity of its critical point, a pure supercritical fluid (or a dense gas as it is alternatively known) has a very high isothermal compressibility, and this makes possible to change significantly the density of the fluid with relatively limited modifications of T and P. On the other hand, it has been shown that the thermodynamic and transport properties of supercritical fluids can be tuned simply by changing the density of the medium. This is particularly interesting for... 

The local density augmentation caused by the large isothermal compressibility of the fluid may conceivably influence k i or ka. We assume that the lifetime of the clusters is extremely short and thus there is no effect on kd, based on the molecular dynamics study of Petsche and Debenedetti (29) and experimental measurements of binary diffusion coefficients near the critical point. It seems more likely that a higher local density would affect k i due to an increase in the number of... 

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