K-Factor Charts

The K-factor method is designed for hand calculations. The GPSA Engineering Data Bookc ontainsaseriesofK-factorchartsforestimating 

The charts provide estimates of the K-factors given the temperature and the pressure, but the engineer must do iterative calculations in order to obtain actual estimates of the equilibrium. A single calculation is quite time-consuming thus repeated calculations are frustrating and take a considerable amount of time. The 

Phase equilibrium is also important in the design of an acid gas injection scheme. In fact, the first step in the design process is the construction of a phase envelope for the acid gas under consideration. This provides the engineer with a map indicating which phases will be encountered and under which conditions. These calculations are tedious fortunately, software packages are available for the calculations. 

Design engineers are responsible for verifying the models selected for their project - and this is true for the calculation of acid gas mixtures. Appendix A lists references to several experimental measures for systems related to acid gas. Design engineers should seek these data in order to verify their choice of models. 

Bierlein, J.A. and W.B. Kay. 1953. Phase-equilibrium properties of system carbon dioxide-hydrogen sulfide. Ind. Eng. Chem. 45 618-24. 

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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 ... 

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. 

The dimensionless K. is regarded as a function of system T and P only and not of phase compositions. It must be exfjerimentally determined. Reference 64 provides charts of R (T,P) for a number of paraffinic hydrocarbons. K. is found to increase with an increase in system T and decrease with an increase in P. Away from the critical point, it is invariably assumed that the K, values of component i are independent of the other components present in the system. In the absence of experimental data, caution must be exercised in the use of K-factor charts for a given application. The term distribution coefficient is also used in the context of a solute (solid or liquid) distributed between two immiscible liquid phases yj and x. are then the equilibrium mole fractions of solute i in each liquid phase. 

Notice that the K-factor charts in Appendix A apply to petroleum mixtures which have convergence pressure of 5000 psia. The other charts of this correlation (not reproduced in Appendix A) are for use with mixtures with other convergence pressures. A value of convergence pressure applicable to the fluid of interest must be estimated in order to select the correct set of graphs. 

The second is a K-factor approach. This method is slightly more rigorous but also requires more time to perform the calculations. Using the K-factor charts requires an iterative procedure. This method should not be used for acid gas. Carroll (2004) showed that this method is not very accurate for sour gas mixtures. It predicts the real hydrate temperature to within 1.7 Celsius degrees (3 Fahrenheit degrees) only 40% of the time. It is anticipated that this method would be significantly worse for acid gas. 

FIGURE 8.20 DePreister s K-factor chart, for low temperatures. There is a similar chart for higher temperatures. An SI equivalent is in [16]. This nomograph is intended only for preliminary estimates, but is widely used because it is simple. (From DePreister, C. L. Light hydrocarbon vapor-liquid distribution coefficients. Applied Thermodynamics, CEP Symp Ser. 7-49 1-43 (1953). Reproduced with permission of the American Institute of Chemical Engineers.)... 

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]. 

Equilibrium Basic Consideration, 1 Ideal Systems, 2 K-Factor Hydrocarbon Equilibrium Charts, 4 Non-Ideal Systems, 5 Example 8-1 Raoult s Law, 14 Binary System Material Balance Constant Molal Overflow Tray to Tray,... 

At a pressure of 10 bar, determine the bubble and dew point of a mixture of hydrocarbons, composition, mol per cent n-butane 21, n-pentane 48, n-hexane 31. The equilibrium K factors can be estimated using the De Priester charts in Chapter 8. 

A large number of K-factor correlations have been proposed.1 We will present only two one graphical, the other in equation form.2,3 A partial set of K-factor curves is given in Appendix A.2 Only 14 charts out of a total of 90 of this correlation are given. These should suffice for illustrative exercises in this text. 

The equilibrium K factors can be estimated using the De Priester charts in Chapter 8. 

For hydrocarbons, these equilibrium relations are often represented by y, = K,x, where K, = Ps,/P = K-factor for component i. K-factors are functions of both pressure and temperature but assumed to be independent of composition. Also, for a multi-component mixture, a relative volatility (a,) can be defined for each component with one of the components, say 3, as a basis such that a, = K/K . Charts for K-factors for various components are available in Handbooks. 

In the same year, one of the annual review articles in Industrial and Engineering Chemistry 2) mentioned that the BWR equation of state seemed to provide the most accurate method thus far developed for estimating K-factors for hydrocarbon systems. Use of the equation was deemed tedious, and a procedure for using the equation in a simplified form suitable for rapid equilibrium calculations was to be presented. Charts based on the procedure were available from the M, W. Kellogg Co., New York. 

The standard friction factor chart (Fig. 48.6) can also be used with Romr- Please note that two liquids having similar k and n values in laminar flow may not necessarily behave similarly to one another in turbulent flow, as would be the case if you compared a flocculated clay suspension with a polymer solution. 

DePriester charts Nomographs that present the complex relationships between pressure, temperamre, and K-factor for various light and heavy hydrocarbons. They are used to determine the bubble point and dew points of hydrocarbon mixtures and were first published in 1953 as an improvement on earlier charts known as Kellogg charts. 

FIGURE A.4 Compressibility factor chart. (From Hougen, O. A., K. M. Watson, and R. A. Ragatz, Chemical Process Principles, Part II Thermodynamics, ed. 2. 1959. New York Wiley. Reprinted by permission of the estate of O. A. Hongen.)... 

When flanges are attached to one or both ends, the values of k and shall be corrected by the factors Ci, which can be read directly from Chart B, entering with the computed h. 

Figure 4.4 shows the Moody chart for tubes when k = 0.03 mm, which is the case for steel tubes. Friction factors for other values of k can be attained by using the following ratio ... 

A peak on a chromatogram is usually identified by some measure of retention, for example retention time or chart length where the length or time is measured from the injection point to the peak apex. A useful quantity to locate or identify a peak is the capacity factor (k ) which is defined as follows ... 

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