Volumetric relations

Hayes M. J. and Boles J. R. (1992) Volumetric relations between dissolved plagioclase and kaohnite in sandstones imphcations for aluminum mass transfer in the San Joaquin Basin, Cahfomia. In Origin, Diagenesis, and Petrophysics of Clay Minerals in Sandstones (eds. D. W. Houseknecht and... 

Volumetric Relations. The fluid-filled porosity is not a primary unknown because it is determined by the Pkjk=l,...,Np. In the iterative Newton-Raphson solution scheme, values of 6/ are updated based on new values of the Pjt s at the end of each iteration. 

The initial substanees are two fluid monomers (for example, methyl methacrylate or ethyl methaerylate and styrene), which at separate polymerization form transparent homopolymers with different values of the refi active indices, ti and ti2, in which we take ri2> ri. The same monomers at any volumetric relation form transparent copolymers. It is also necessary for shrinkage eoefficients PmoJp ow to be equal or to be of close values, because this situation affeets the degree to which the theoretical calculations can be realized. 

A rigorous relation exists between the fugacity of a component in a vapor phase and the volumetric properties of that phase these properties are conveniently expressed in the form of an equation of state. There are two common types of equations of state one of these expresses the volume as a function of... 

Finally, by volumetric imaging Three-dimensional information was obtained by stacking reflection tomograms from multiple planes. Using this stacking technique, cubic voxels were obtained and could be numerically dissected in any plane. Although there are several attractive features related to this technique, there are also several questions which need to be addressed before it can be used for industrial applications. For example, the applied sound field must be further characterized. 

E. Interrelationships in Electrokinetic Phenomena In electroosmosis, the volumetric flow and current are related through... 

Polymer Flooding. Even in the absence of fractures and thief 2ones, the volumetric sweep efficiency of injected fluids can be quite low. The poor volumetric sweep efficiency exhibited in waterfloods is related to the mobiUty ratio, Af, the mobiUty of the injected water in the highly flooded (low oil saturation) rock, divided by the mobiUty of the oil in oil-bearing portions of the reservoir, (72,73). The mobiUty ratio is related to the rock permeabihty to oil, and injected water, and to the viscosity of these fluids by the following equation ... 

In any gas burner some mechanism or device (flame holder or pilot) must be provided to stabilize the flame against the flow of the unbumed mixture. This device should fix the position of the flame at the burner port. Although gas burners vary greatly in form and complexity, the distribution mechanisms in most cases are fundamentally the same. By keeping the linear velocity of a small fraction of the mixture flow equal to or less than the burning velocity, a steady flame is formed. From this pilot flame, the main flame spreads to consume the main gas flow at a much higher velocity. The area of the steady flame is related to the volumetric flow rate of the mixture by equation 18 (81,82)... 

Both catalyst space velocity and bed geometry play a role. The gas hourly space velocity (GHSV) is used to relate the volumetric flow rate to the catalyst volume. GHSV has units of inverse hour and is defined as the volume flow rate per catalyst volume. 

The volume fraction, sometimes called holdup, of each phase in two-phase flow is generally not equal to its volumetric flow rate fraction, because of velocity differences, or slip, between the phases. For each phase, denoted by subscript i, the relations among superficial velocity V, in situ velocity Vj, volume fraclion Rj, total volumetric flow rate Qj, and pipe area A are... 

When a gas is blown steadily through an orifice into an essentially inviscid liquid, a regular stream of bubbles is formed. A theoretical expression that relates the bubble volume V to volumetric gas flow rate G and gravitational acceleration g is the following ... 

Volumetric Flow Rate The equipment size is normally dictated by its capacity and is therefore directly related to investment costs. Incineration systems are capable of handling large amounts of waste gases and are often the most cost-effective method when handling large flows. Adsorption systems can handle large volumes of gases, provided that the gas stream is fairly dilute. Absorption will... 

The transition from a ferromagnetic to a paramagnetic state is normally considered to be a classic second-order phase transition that is, there are no discontinuous changes in volume V or entropy S, but there are discontinuous changes in the volumetric thermal expansion compressibility k, and specific heat Cp. The relation among the variables changing at the transition is given by the Ehrenfest relations. 

The appearance of spontaneous polarization in the case of LuTaO is related to volumetric irregularities and ordering of the Li+ - Ta5+ dipoles, as is in the case of the similar niobium-containing compound Li4Nb04F. It can be assumed that the main difference between the two compounds is that the irregularities and the Li+ - Ta5+ dipoles are thermally more stable compared to the niobium-containing system. This increased stability of the dipoles leads to the reversible phase transition at 660°C. 

The fugacity coefficient is a function of pressure, temperature, and gas composition. It has the useful property that for a mixture of ideal gases (Pi = 1 for all i. The fugacity coefficient is related to the volumetric properties of the gas mixture by either of the exact relations (B3, P5, R6) ... 

The chemical literature is rich with empirical equations of state and every year new ones are added to the already large list. Every equation of state contains a certain number of constants which depend on the nature of the gas and which must be evaluated by reduction of experimental data. Since volumetric data for pure components are much more plentiful than for mixtures, it is necessary to estimate mixture properties by relating the constants of a mixture to those for the pure components in that mixture. In most cases, these relations, commonly known as mixing rules, are arbitrary because the empirical constants lack precise physical significance. Unfortunately, the fugacity coefficients are often very sensitive to the mixing rules used. 

Empirical void fraction correlations, relating to the Lockhart-Martinelli factor X and from there to volumetric quality x, have been provided by Lockhart and Mar-tinelli (1949), Baroczy (1963), Wallis (1969), and have been discussed by Butter-worth (1975) and Chen and Spedding (1983). Butterworth (1975) showed that Lockhart and Martinelli s correlation (1949) for void fraction, as well as several other void fraction correlations, can be represented in the following generic form ... 

Hydrogen chemisorption Static H2 chemisorption at 100°C on the reduced cobalt catalysts was used to determine the number of reduced surface cobalt metal atoms. This is related to the overall activity of the catalysts during CO hydrogenation. Gas volumetric chemisorption at 100°C was performed using the method described by Reuel and Bartholomew [6]. The experiment was performed in a Micromeritics ASAP 2010 using ASAP 2010C V3.00 software. 

Variation of bubble size, bubble frequency, and the standard deviation of -APbed with variation of Ug in the conical fluidized beds with a uniform gas distributor (Fopen = 3.87 %) is shown in Fig. 7. As can be seen, the standard deviation of - APbed and the bubble size increase with increasing Ug in the fully fluidized region. However, bubble frequency remains unchanged with variation of Ug that may imply the bubble size will increase as much as the volumetric gas flow increases. As shown, the bubble size dramatically increases with increasing Ug. Also, it is confirmed that the increase of standard deviation of -APbed is closely related to bubble size. 

Pe, coj, and fio are dimensionless parametas relating to the opoating conditions Pe is Peclet number denoting the inverse of axial mixing intensity, coj denotes the inverse of volumetric loading rate per mass of granules, and ySo daiotes the dimensionless inlet substrate concentration as respectively defined as follows ... 

The area required for processing A = Qo — QVJ, where Qo Q is the perrneate volumetric flow, can be estimated by using the approximation / = 0.33/initiai + 0.67/finai (Cheryan, Ultrafiltration Handbook, Technomic, Lancaster, Pa., 1986) and a suitable flux model. An appropriate model relating flux to crossflow, concentration, and pressure is then applied. Pressure profiles along the retentate channel are empirically correlated with flow for spacer-filled channels to obtain A = APfQ/AT. 

---