Mass fraction

The current calculation methods are based on the hypothesis that each mixture whose properties are sought can be characterized by a set of pure components and petroleum fractions of a narrow boiling point range and by a composition expressed in mass fractions. 

When oil and gas are produced simultaneously into a separator a certain amount (mass fraction) of each component (e.g. butane) will be in the vapour phase and the rest in the liquid phase. This can be described using phase diagrams (such as those described in section 4.2) which describe the behaviour of multi-component mixtures at various temperatures and pressures. However to determine how much of each component goes into the gas or liquid phase the equilibrium constants (or equilibrium vapour liquid ratios) K must be known. 

Barnes cautions about using the appropriate units (molecular area with mole fraction, or area per unit mass with mass fraction) when analyzing area data [244]. 

Throughout this discussion we have used the numerical fraction of molecules in a class as the weighting factor for that portion of the population. This restriction is not necessary some other weighting factor could be used equally well. As a matter of fact, one important type of average encountered in polymer chemistry is the case where the mass fraction of the ith component is used as the weighting factor. Defining the mass of material in the ith class as mj, we write... 

Referring to Figure 2, by considering solute mass balances over n, (n — 1),. .. 2, 1 units in turn and eliminating intermediate solute mass fractions and flow rates, the amount of solute associated with the leached sohd may be calculated in terms of the composition of the sohd and solvent streams fed to the system. The resulting equation is (2)... 

The solute mass fraction in the overflow solution from the first unit (n = 1) is... 

The particle mass retained by each sieve is determined by weighing after drying when necessary, and each fraction is designated by the sieve size it passed and the size on which it was retained. The sieve diameter of a particle is therefore defined as the size of the sieve aperture through which the particle in question just passes through. Mass fractions of the particles are then presented in tabular or graphical form. 

Refractive Index. The refractometric value of sugar solutions is used as a rapid method for the approximate determination of the soHds content (also known as dry substance), because it is assumed that the nonsugars present have a similar influence on the refractive index as sucrose. Measurement is usually carried out on a Brix refractometer, which is graduated in percentage of sucrose on a wt/wt basis (g sucrose/100 g solution) according to ICUMSA tables of refractive index at 20.0°C and 589 nm. Tables are available that give mass fraction corrections to refractometric values at temperatures different from 20°C. 

Fig. 1. Solidification of differential mass fraction dgoi 2l melt. Mass fraction of impurity in melt is and in soHd freezing out is...

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

This quantity, which is often referred to as magma density or soHds concentration (mass of crystals per unit system volume), is often an important process variable. A cumulative mass fraction of crystals having a size less than U can also be defined as... 

Equation (4-49) is merely a special case of Eq. (4-48) however, Eq. (4-50) is a vital new relation. Known as the summahility equation, it provides for the calculation of solution properties from partial properties. Thus, a solution property apportioned according to the recipe of Eq. (4-47) may be recovered simply by adding the properties attributed to the individual species, each weighted oy its mole fraction in solution. The equations for partial molar properties are also valid for partial specific properties, in which case m replaces n and the x, are mass fractions. Equation (4-47) applied to the definitions of Eqs. (4-11) through (4-13) yields the partial-property relations ... 

For theJth. component, my = m iDy is the component mass flow rate in stream i is the mass fraction of component j in stream i and q is the net reaction rate (mass generation minus consumption) per unit volume V that contains mass M. If it is inconvenient to measure mass flow rates, the product of density and volumetric flow rate is used instead. 

Three examples of simple multivariable control problems are shown in Fig. 8-40. The in-line blending system blends pure components A and B to produce a product stream with flow rate w and mass fraction of A, x. Adjusting either inlet flow rate or Wg affects both of the controlled variables andi. For the pH neutrahzation process in Figure 8-40(Z ), liquid level h and the pH of the exit stream are to be controlled by adjusting the acid and base flow rates and w>b. Each of the manipulated variables affects both of the controlled variables. Thus, both the blending system and the pH neutralization process are said to exhibit strong process interacHons. In contrast, the process interactions for the gas-liquid separator in Fig. 8-40(c) are not as strong because one manipulated variable, liquid flow rate L, has only a small and indirec t effect on one controlled variable, pressure P. 

Definitions Following the practice presented under Gas-Separation Membranes, distillation notation is used. Literature articles often use mass fraction instead of mole fraction, but the substitution of one to the other is easily made. 

Regime 3. If the punc ture is above the initial liquid level but becomes covered by the swell, there will be noncondensables mixed with the liquid (ot, > 0). If also T, < T no flashing occurs. This is called a. frozen flow situation, since the mass fraction of compressible component X, is constant during discharge. 

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