Variables in Separation

Kwauk, M. (1956) AIChE Jl 2, 240. A system for counting variables in separation processes. 

In Chapter 1 it was shown that the number of independent variables for any problem is equal to the difference between the total number of variables and the number of linking equations and other relationships. Examples of the application of this formal procedure for determining the number of independent variables in separation process calculations are given by Gilliland and Reed (1942) and Kwauk (1956). For a multistage, multicomponent column, there will be a set of material and enthalpy balance equations and equilibrium relationships for each stage (the MESH equations) and for the reboiler and condenser, for each component. 

Clarke, R.P., Cosgrove, L.D., and Morse, E.H., 1966. Vitamin to creatinine ratios. Variability in separate voidings of urine of adolescents during a 24 hour period. The American Journal of Clinical Nutrition. 19 335-341. 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Ratio and Multiplicative Feedforward Control. In many physical and chemical processes and portions thereof, it is important to maintain a desired ratio between certain input (independent) variables in order to control certain output (dependent) variables (1,3,6). For example, it is important to maintain the ratio of reactants in certain chemical reactors to control conversion and selectivity the ratio of energy input to material input in a distillation column to control separation the ratio of energy input to material flow in a process heater to control the outlet temperature the fuel—air ratio to ensure proper combustion in a furnace and the ratio of blending components in a blending process. Indeed, the value of maintaining the ratio of independent variables in order more easily to control an output variable occurs in virtually every class of unit operation. 

A variable-speed drive is usually used on the feed and cross-belt drives to exercise control in separator operation, although the speed is not usually changed once the optimum operating condition is estabUshed. Feed rates and the selection of the number of magnetic poles are usually deterrnined by preliminary laboratory tests. The mineral types involved in the feed largely determine the number of poles selected. High intensity cross-belt separators are frequendy used in combination with induced-roU or electrostatic separators. 

The variables are separable, but an integration in closed form is not possible because of the odd exponent. Numerical integration followed by substitution into (4) will provide both A and B as functions of t. The plots, however, are of solutions of the original differential equations with ODE. 

Teirrperamre is often a forgotten variable in HPLC but ean influenee the robustness and seleetivity of many separations or if exploited eair provide novel high temperature separation eonditions with either high effieieney, a unique seleetivity or enable new deteetion methods to be applied. 

In reeent years, tire use of elevated temperatures has been reeognised as a potential variable in method development. Witlr inereased temperature, aqueous-organie mobile phases separations ean improve, viseosity deereases and diffusion inereases so baek pressures are redueed. At higher temperatures (usually with superheated water > 100 °C under modest pressures) water alone ean be used as the mobile phase and eair provide unique separation opportunities. The absenee of an organie solvent enables the use in HPLC of alternative deteetors sueh as FID or on-line LC-NMR using deuterium oxide as the eluent. 

A prominent part of many of the techniques is separation of variables. In that method, the deflection variables, or the variation In deflection variables, are arbitrarily separated into functions of plate coordinate x alone times functions of y alone. Wang [5-8] determined that separation of variables leads to exact solutions for some classes of plate problems, but does not for others, I.e., the deflections are not always separable. A specific example of an approximate use of separation of variables due to Ashton [5-9] will be discussed in Section 5.3.2. Other exact uses of the method abound throughout Section 5.3 through 5.5. 

Los Alamos National Laboratory performed separate statistical analyses using the Failure Rate Analysis Code (FRAC) on IPRDS failure data for pumps and valves. The major purpose of the study was to determine which environmental, system, and operating factors adequately explain the variability in the failure data. The results of the pump study are documented in NUREG/CR-3650. The valve study findings are presented in NUREG/CR-4217. 

Flame treatment is predominantly used with articles of relatively thick section, such as blow moulded bottles, although it has been applied to polyolefin films as well. The most important variables in the process are the air-gas ratio and their rate of flow, the nature of the gas, the separation between burner and surface, and the exposure time. 

In this chapter the different transformations of the reactive site F will be dealt with separately. Due to the potential variability in the chemical nature of this second reactive site it was possible to combine a wide variety of chemically unlike monomers with each other thus designing novel block copolymers. 

For land-based gas turbines, the overall plant output, efficiency, emissions, and reliability are the important variables. In a gas turbine, the processes of compression, combustion, and expansion do not occur in a single component, as they do in a diesel engine. They occur in components that can be developed separately. Therefore, other technologies and components can be added as needed to the basic components, or entirely new components can be substituted. 

---