Volumetric behavior of a gas

Historical. About a century ago, experimentalists and theoreticians independently popularized the use of various forms of polynomial expressions for the mathematical description of physical behavior, e.g., the volumetric behavior of a gas. The early use was based solely on convenience, especially for interpolation of data. Theoretical significance was later established for many cases. For the volumetric behavior of a gas, each term of an infinite series expansion in density was given specific significance in terms of intermolecular forces. 

The first major contribution was made in 1901 by Kamerlingh Onnes, who described the isothermal volumetric behavior of a gas by the finite polynomial series... 

The early application of volumetric data for hydrocarbons made use of the perfect gas laws. They were not sufficiently descriptive of the actual behavior to permit their widespread use at pressures in excess of several hundred pounds per square inch. The need for accurate metering aroused interest in the volumetric behavior of petroleum and its products at elevated pressures. Table II reviews references relating to the volumetric behavior of a number of components of petroleum and their mixtures. For many purposes the ratio of the actual volume to the volume of a perfect gas at the same pressure and temperature has been considered to be a single-valued function of the reduced pressure and temperature or of the pseudo-reduced (38) pressure and temperature. The proposals of Dodge (15), Lewis (12), and Brown (8) with their coworkers serve as examples of the nature of these correlations. The Beattie-Bridgeman (2) and Benedict (4) equations of state describe the volumetric behavior of many pure substances and their mixtures with an accuracy adequate (31) for most purposes. However, at pressures above 3000 pounds per square inch the accuracy of representation with existing constants leaves something to be desired. 

A mathematician would write P = f(T, V, n) for the functional relation in Eq. (1.1-4), using the letter P for the variable and the letter / for the function. Chemists have too many variables to use two letters for each variable, so we use the same letter for the variable and the function. A functional relation that relates P, V, T, and n for a gas or a liquid at equilibrium is called an equation of state and is said to represent the volumetric behavior of the gas or liquid. We will introduce several equations of state later in this chapter. 

With reference to the estimation of the volumetric behavior of a pure fluid (gas or liquid) ... 

Figure 32.27 shows how a centrifugal pump is affected, particularly at low flow rates, and the behavior is typical of conventional centrifugal pumps. Figures 32.28 and 32.29 present well-known information on the effects of dissolved and entrained gas on the volumetric efficiency of a positive displacement pump. 

Three thousand cubic meters per day of a gas mixture containing methane and n-butane at 21 C enters an absorber tower. The partial pressures at these conditions are 103 kPa for methane and 586 kPa for -butane. In the absorber, 80% of the butane is removed and the remaining gas leaves the tower at 38°C and a total pressure of 550 kPa. What is the volumetric flow rate of gas at the exit How many moles per day of butane are removed from the gas in this process Assume ideal behavior. 

The effects of SCFs on the catalytic activity of methanol synthesis are shown in Table 3. It is obvious that the gas phase (He) exhibited the lowest total carbon conversion (about 16.4%). As methanol synthesis is a highly exothermic reaction, the low conversion in gas phase possibly resulted from the heat of reaction which cannot be removed rapidly from the catalyst bed. The total carbon conversion increased to 45.6% when SC-Ce was introduced into the reaction. This illustrates that the SCF enhanced the reaction activity of methanol synthesis. The rate of reaction was possibly enhanced while the experiment was operated in the mixture critical region because of a favorable pressure dependence of the reaction rate constant as well as the imusual volumetric behavior of heavy solutes solubilized in an SCF solvent [16]. 

We will start with a description of the volumetric behavior of pure fluids, by considering first gases and then vapors and liquids. (The difference between gases and vapors is that a gas cannot be condensed when compressed isothermally a vapor, can. The two terms are often used interchangeably, however.)... 

The WAG process has been used extensively in the field, particularly in supercritical CO2 injection, with considerable success (22,157,158). However, a method to further reduce the viscosity of injected gas or supercritical fluid is desired. One means of increasing the viscosity of CO2 is through the use of supercritical C02-soluble polymers and other additives (159). The use of surfactants to form low mobihty foams or supercritical CO2 dispersions within the formation has received more attention (160—162). Foam has also been used to reduce mobihty of hydrocarbon gases and nitrogen. The behavior of foam in porous media has been the subject of extensive study (4). X-ray computerized tomographic analysis of core floods indicate that addition of 500 ppm of an alcohol ethoxyglycerylsulfonate increased volumetric sweep efficiency substantially over that obtained in a WAG process (156). 

Fig. 14-7. Effects of errors in equilibrium ratios on the calculated quantity of liquid of a retrograde gas at reservoir conditions. (Standing, Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, SPE, Dallas, 1951. Copyright 1951 SPE-AIME.

Given a description of a process system in which a volumetric flow rate is either specified or requested for any process stream, (a) carry out the degree-of-ffeedom analysis, including density estimates for liquid and solid streams and equations of state for gas streams (b) write the system equations and outline the procedure you would use to solve for all requested quantities (c) carry out the calculations (d) list all your assumptions (e.g., volume additivity for liquids or ideal gas behavior) and state whether or not they are reasonable for the given process conditions. 

Estimate the liquid-phase volumetric coefficient of oxygen transfer for a stirred-tank fermentor with a diameter of 1.8 m, containing a viscous non-Newtonian broth, with consistency index K — 0.39, flow behavior index n — 0.74, density p = 1020 kg m-3, superficial gas velocity UG — 25 m h, stirred by a flat-blade turbine of diameter d — 0.6 m, with a rotational speed N of 1 s. ... 

The purity of the SCF is an important consideration in the planning of a synthesis. Low concentrations of impurities can have noticeable effects on the volumetric and phase behavior of SCFs. For example, helium can be present in commercial CO2 because it is sometimes added as a head-gas to ensure nearly-complete delivery of the cylinder contents and this has been found to affect the use of SCCO2 as a solvent for analytical and prepeu-ative purposes [51-53]. The He head-gas is unnecessary if a cooled pump is used for CO2 delivery. 

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