K factors

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

Subroutine VPLQK. VPLQK calculates K factors (K = for given values of pressure, temperature, liquid and vapor compositions, and the adjustable parameters. The K factors are calculated from the following relation (Prausnitz, 1969) ... 

CALCULATION USING K-FACTORS CALCULATED IN SUBROUTINE VPLOK... 

This relation is used only for temperatures greater than 0°C. The average error is about 5 kJ/kg. Figure 4.5 gives the enthalpy for petroleum fractions whose is 11.8 as a function of temperature. For K, factors different from 11.8, a correction identical to that used for Cpi is used (to... 

The K factors in (C3.4.1) represent another very important facet of tire energy transfer [4, H]. These factors depend on tire orientations of tire donor and acceptor. For certain orientations tliey can reduce tire rate of energy transfer to zero—for otliers tliey effect an enhancement of tire energy transfer to its maximum possible rate. Figure C3.4.1 exhibits tire angles which define tire mutual orientation of a donor and acceptor pair in tenns of Arose angles the orientation factors and are given by [6, 7]... 

K Factor, ratio of temperature difference across retaining waU to overaU mean temperature difference between bulk fluids Dimensionless Dimensionless... 

Thermal Conductivity (K Factor) Depending on the type of insulation, the thermal conductivity K factor) can vary with age, manufacturer, moisture content, and temperature. Typical published values are shown in Fig. 11-65. Mean temperature is equal to the arithmetic average of me temperatures on both sides of the insulating material. 

K = factor to account for the lower p.f. at higher negative slips, when working as an induction generator... 

Rq = re-lubricating interval in hours of operation K = factor as noted below... 

The API, with help from gear manufacturers, has a 1977 standard (API 613) for rating gears. (See Chapter 4.) A common procedure for comparing and sizing gear is based on the tooth pitting index, the K factor... 

The minimum liquid head above the drawoff nozzle must be greater than the nozzle exit resistance. Based on a safety factor of 4 and a velocity head K factor of 0.5 ... 

This K factor is approximately proportional to the roughness of pipe (friction factor) and inversely proportional to the pipe diameter ... 

Venable, H. Dean, The K Factor A New Mathematical Tool for Stability Analysis and Synthesis, POWERCON March 1983. 

In the analysis of trace elements or thin films on substrate using electrons, however, one finds that the MDL, may be increased by choosing Eq such that Uis just greater than 1. The reason for this is that the k factor, which is the ratio of the intensity from the sample to that from the standard, increases as Uapproaches 1 for thin films. Thus, by maximizing the k factor, the sensitivity is increased. For bulk sample analysis, however, the k factor will usually be a maximum ax. U- 2.5. 

K = factor for unequal fragments from which Vi can be calculated. 

Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions... 

K Factor Table Representative Resistance coefficients (K) for Valves and Fittings... 

Formulas for Calculating K Factors for Valves and Rttings with Reduced Port... 

Lo.ss through discharge fittings, valves, connections, using K factors using Table 2-2 ... 

Figure 4-17C. Pressure drop vs K-factor for standard York-Vane mist eliminators, air-water system. By permission, Otto H. York Co., Inc.

II BalanSeal valve construction is used and variable back pressure conditions exist, use the maximum back pressure to determine Pn in equation and correct K factor (see graph page 44)... 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

Values of K-equilibrium factors are usually associated with hydrocarbon systems for which most data have been developed. See following paragraph on K-factor charts. For systems of chemical components where such factors are not developed, the basic relation is ... 

K-factors for vapor-liquid equilibrium ratios are usually associated with various hydrocarbons and some common impurities as nitrogen, carbon dioxide, and hydrogen sulfide [48]. The K-factor is the equilibrium ratio of the mole fraction of a component in the vapor phase divided by the mole fraction of the same component in the liquid phase. K is generally considered a function of the mixture composition in which a specific component occurs, plus the temperature and pressure of the system at equilibrium. 

The Gas Processors Suppliers Association [79] provides a more detailed background development of the K-factors and the use of convergence pressure. Convergence pressure alone does not represent a system s composition effects in hydrocarbon mixtures, but the concept does provide a rather rapid approach for systems calculations and is used for many industrial calculations. These are not well adapted for very low temperature separation systems. 

Interpolation between charts of convergence pressure can be calculated, depending on how close the operating pressure is to the convergence pressure. The K-factor (or K-values) do not change rapidly with convergence pressure, (psia) [79]. 

The use of the K-factor charts represents pure components and pseudo binary systems of a light hydrocarbon plus a calculated pseudo heavy component in a mixture, when several components are present. It is necessary to determine the average molecular weight of the system on a methane-free basis, and then interpolate the K-value between the two binarys whose heavy component lies on either side of the pseudo-components. If nitrogen is present by more than 3-5 mol%, the accuracy becomes poor. See Reference 79 to obtain more detailed explanation and a more complete set of charts. 

FsR,k = factor for contribution of sidestream k flow to minimum reflux HK = heavy key component L = liquid flo Tate, mol/h LK = light key component nf = number of feeds ns = number of sidestreams m = number of sidestreams above feed n qp = thermal condition of feed qs = thermal condition of sidestream R = reflux ratio... 

FsR,k = Factor for contribution of sidestream, k, flow to minimum reflux... 

Com- Mols Rich Absoiption K Factors Eai, Frac. Mols... 

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