Operating lines

Figure Bl.7.9. (a) Stability diagram for ions near the central axis of a quadnipole mass filter. Stable trajectories occur only if the and values lie beneath tire curve, (b) Stability diagram (now as a fiinction of U and F) for six ions with different masses. The straight line miming tlirough the apex of each set of curves is the operating line, and conesponds to values of UIVthat will produce mass resolution (reproduced with pennission of Professor R March, Trent University, Peterborough, ON, Canada).

Open-arc furnaces Open-celled foam Open-circuit potential Open-mold processes Open-pit mining Operating line... 

Fig. 6. Operating lines for an absorption system line A, high -L /ratio soHd line, medium -L /G ratio line B, -L /G ratio at theoretical minimum...

Log arithmic-Mean Driving Force. As noted eadier, linear operating lines occur if all concentrations involved stay low. Where it is possible to assume that the equiUbrium line is linear, it can be shown that use of the logarithmic mean of the terminal driving forces is theoretically correct. When the overall gas-film coefficient is used to express the rate of absorption, the calculation reduces to solution of the equation... 

For cases in which the equiUbtium and operating lines may be assumed linear, having slopes E /and respectively, an algebraic expression for the integral of equation 55 has been developed (41) ... 

Simplified Design Procedure for Linear Equilibrium and Operating Lines. A straight operating line occurs when the concentrations are low such that and remain essentially constant. (The material balance is obtained from equation 35.) In cases where the... 

For linear equiHbrium and operating lines, an expHcit expression for the number of theoretical plates required for reducing the solute mole fraction... 

The iategral can be found graphically if the equiUbrium line is curved. An analytical expression for the iategral is available for the case where both the equihbrium and operating lines are linear (5) ... 

In extraction (qv), the distribution coefficient value is the slope of the equiUbrium line. In practice, the slope of the operating line is set at a value somewhat less than the distribution coefficient to provide driving force and fix the required theoretical extraction stages at some reasonable number. 

Intermediate Condenser. As shown in Figure 3, an intermediate condenser forces the operating line closer to the equiUbrium line, thus reducing the inherent inefficiencies in the tower. Using intermediate condensers and reboilers, it is possible to raise the efficiency above that for a simple reboder—condenser system, particularly when the feed composition is far from 50 50 in a binary mixture. 

Fig. 5. Adiabatic gas—Hquid contacting, graphical representation where point A is an arbitrary point along the column line CAB is the operating line having slope of F l / j point E represents the interface conditions corresponding to point A and the tie line AE has slope of h -al ky-a). The bold line...

The locus of corresponding Tj and points, the operating line for the column, can be obtained by assuming that V and change Htde and by integrating equation 27 along the length of the column. 

In the example developed herein fogging occurs at about the time the gas reaches the top of the column. That is far from inevitable and would not have occurred if the operating line had terminated at point U. 

Chlorinated by-products of ethylene oxychlorination typically include 1,1,2-trichloroethane chloral [75-87-6] (trichloroacetaldehyde) trichloroethylene [7901-6]-, 1,1-dichloroethane cis- and /n j -l,2-dichloroethylenes [156-59-2 and 156-60-5]-, 1,1-dichloroethylene [75-35-4] (vinyhdene chloride) 2-chloroethanol [107-07-3]-, ethyl chloride vinyl chloride mono-, di-, tri-, and tetrachloromethanes (methyl chloride [74-87-3], methylene chloride [75-09-2], chloroform, and carbon tetrachloride [56-23-5])-, and higher boiling compounds. The production of these compounds should be minimized to lower raw material costs, lessen the task of EDC purification, prevent fouling in the pyrolysis reactor, and minimize by-product handling and disposal. Of particular concern is chloral, because it polymerizes in the presence of strong acids. Chloral must be removed to prevent the formation of soflds which can foul and clog operating lines and controls (78). 

Equation 32 represents the upper (or rectifying) operating line equation and equation 33 represents the lower (or stripping) operating line equation. The slopes L jV and L jV can vary, depending on heat effects. 

The McCabe-Thiele method employs the simplifying assumption that the molal overflows in the stripping and the rectification sections are constant. This assumption reduces the rectifying and stripping operating line equations to ... 

Condition of Feed (q Fine). The q line, which marks the transition from rectifying to stripping operating lines, is determined by mass and enthalpy balances around the feed plate. These balances are detailed in distillation texts (15). 

Minimum Reilux with Pinch Zone. There are some distillations where the minimum reflux does not occur at the intersection of the upper and lower operating lines and the q line. These cases arise when the equiUbrium is skewed from positive activity coefficients and when the operating line intersects the equiUbrium line in a 2one of constant composition, a pinch 2one, which is not at the line intersection. Figure 14 illustrates such a case. An example of such a pinch 2one in an ethanol—water column is available (37). 

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