Balanced lines

Solution Evolution. It is often beneficial to re-examine a completed flow sheet and look for opportunities for simplification and consoHdation of unit operations. A compHcated series of unit operations can sometimes be replaced by a simpler stmcture that has equivalent material balance lines. 

Because a material balance on water must be satisfied during the drydown as well as afterward, the path from the initial concentration to equihbrium can be represented graphically by a material balance line and an equihbrium curve. The coordinates of the starting point on the material balance line are the initial water contents of the fluid to be dried and the desiccant. The slope of the line is the ratio of fluid mass to desiccant mass. The line terminates at its intersection with the equihbrium curve (Eig. 4). 

Fig. 4. Drydown path to equilibrium ia a closed system. A represents the equiUbrium curve and B, the material balance line.

Fig. 4. Column sequences and material balance lines for the (a) direct and (b) indirect sequences for separating nonazeotropic...

Fig. 5. The acetone—2-propanol—water system where I represents the 2-propanol—water azeotrope, (a) Residue curve map (34) (b) material balance lines...

Fig. 11. Separation of nitric acid, HNO, and water, H2O, using sulfuric acid, H2SO4, as the solvent, (a) Residue curve map and material balance lines where...

Fig. 18. Separation of ethanol from an ethanol—water—benzene mixture using benzene as the entrainer. (a) Schematic representation of the azeo-column (b) material balance lines where I denotes the homogeneous and the heterogeneous azeotropes D, the end points of the Hquid tie-line and A, the overhead vapor leaving the top of the column. The distillate regions, I, II, and III, and the boundaries are marked. Other terms are defined in text.

Fig. 19. Separation of ethanol and water from an ethanol—water—benzene mixture. Bottoms and are water, B is ethanol, (a) Kubierschky three-column sequence where columns 1, 2, and 3 represent the preconcentration, azeotropic, and entrainer recovery columns, respectively, (b) Material balance lines from the azeotropic and the entrainer recovery columns, A and E, respectively, where represents the overall vapor composition from the azeo-column, 2 1SP Hquid in equiUbrium with overhead vapor composition from the azeo-column, Xj, distillate composition from entrainer...

The entrainer recovery column takes the distillate stream, from the azeo-column and separates it into a bottoms stream of pure water, and a ternary distillate stream for recycle to column 2. The overall material balance line for column 3 is shown in Figure 19b. This sequence was one of two original continuous processes disclosed in 1915 (106). More recendy, it has been appHed to other azeotropic separations (38,107,108). 

Fig. 20. Three sets of material balance lines for the Kubierschky three-column sequence where design 1 corresponds to the upper tie-line having Tmin = 8.78 design 2, to the subcooled upper tie-line having = 12.23 and design 3, to the lower tie-line having = 17.31 represents overall decanter composition , the overall feed composition to the azeo-column , the distillate composition from the entrainer recovery column and O, the...

Since residue cur ves do not by definition cross separatrices, the distillate and bottoms compositions must be in the same distillation region with the mass balance line intersecting a residue cur ve in two places. Mass balance lines for mixing and for other separations not involving vapor-hquid equihbria, such as extraction and decantation, are of course not hmited by distiUation boundaries. 

Our example system has a flow-controlled feed, and the reboiler heat is controlled by cascade from a stripping section tray temperature. Steam is the heating medium, with the condensate pumped to condensate recovery. Bottom product is pumped to storage on column level control overhead pressure is controlled by varying level in the overhead condenser the balancing line assures sufficient receiver pressure at all times overhead product is pumped to storage on receiver level control and reflux is on flow control. 

For a known reactor and kinetics, and at a given feed temperature Tq, the intersection of the energy balance line with the S-shaped mass... 

Flooded evaporators require a constant liquid level, so that the tubes remain wetted. A simple float valve suffices, but must be located with the float outside the evaporator shell, since the surface of the boiling liquid is agitated and the constant movement would cause excessive wear in the mechanism. The float is therefore contained within a separate chamber, coupled with balance lines to the shell (see Figure 8.1). 

Figure 25.2 A balancing line can prevent VOC emissions when filling and emptying tankers.

Numerical Solution for Orifice Flow With orifice flow, the last two terms of the momentum balance (line resistance and potential energy change) are negligible. The momentum balance, Eq. (23-40), reduces to... 

P4.10.02 has a case where the energy balance line is not quite straight, as it need not be. 

Auxiliary process fluid piping inclndes vent and drain lines, balance lines, product flushing lines, and lines for injection of external fluid. 

Mass balance lines such as AF are important and are known as operating lines in countercurrent cascades. Clearly, an operating line ean-not eross an equilibrium line. Wherever an operating line approaehes an... 

With heat input proportional to AT = T2 — the energy balance line rotates about T. This change is shown in Fig. 9.11. Other modes of heat addition or removal yield corresponding shifts in the energy balance line. 

First, the energy balance line T A represents the situation where insufficient heat is liberated by reaction to raise the temperature to a high enough level for the reaction to be self-sustaining. Hence, conversion is negligible. At the other extreme, if we have more than enough heat liberated, the fluid will be hot and conversion essentially complete. This is shown as line T B. Finally, line T C indicates an intermediate situation which has three solutions to the material and... 

The type of behavior described here occurs in systems where the slope of the energy balance line, CpZ-Ai/ is small thus, large liberation of heat and pure reactants which leads to far from isothermal operations, van Heerden (1953, 1958) discusses and gives examples of this type of reacting system. In addition, though it is a much more complex situation, a gas flame illustrates well the... 

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