Operating diagrams

Figure 12. COz-EOR operation diagram. COz injection into reservoir to flood. Diagram courtesy of Dakota Gasification Company.

Operational diagram can be populated with simulation agents representing individual compounds in various developmental stages. 

Figure 7.82 Operating diagram for the blow molding of HDPE. Arrows indicate regions of acceptable operation. From Z. Tadmor and C. G. Gogos, Principles of Polymer Processing, Copyright 1979 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Figure 5.7 General operating diagram for a cooling tower.

Model predictive control operation diagram. (From the Instrumentation, Systems, and Automation Society, 2002. All rights reserved. Used with permission of ISA.)... 

It is not essential to actually construct the limiting operating line on the operating diagram. If desired, it can be constructed as shown below for the actual operating line, except that (L M/G u)min is used rather than L u/ G u. 

This differs from Eq. (11.19) for dilute solutions only by the ratio of yBM to Xbm- Based on the average values, Hg/Hi = 1.34/0.82 = 1.634. Values of the other quantities in Eq. (11.32) vary over the tower. X is the ratio of the slope of the equilibrium line to that of the operating line. Values of X can be obtained directly from the operating diagram by determining the slope of the operating line at one end of a particular tie line and the slope of the equilibrium line at the other end of the same tie line. Values of xBM and yBM can be determined with the values of x and Xj and y and y, at either end of the same tie line. 

The criterion for a reaction being effectively irreversible with respect to the absorption of a gas is that the concentration of the unreacted gas in the solution [e.g., NH3(a )] is so small that its partial pressure at the interface is much less than the partial pressure of the absorbing gas [e.g., NH3(g)] in the gas phase. When this criterion is satisfied, the interfacial mole fraction of the absorbing gas y, can be considered to be zero. This obviates the need for an equilibrium line or an x-y operating diagram. 

Figure 1. (a) Operating diagram of a four section SMB unit (b) Fluid flow rates schemes in the SMB and PowerFeed operations during one switching period, U... 

Competition in a modified gradostat was considered in Smith and Tang [STa], There the rate E between the vessels (called the communication rate) was allowed to differ from the rate D (the dilution rate) from the feed bottle and to the overflow vessel. This, of course, still maintains the assumption that the volume in each vessel is constant. It was shown that the outcome of competition can be sensitive to the ratio E/D in the following sense As E/D is increased, first one competitor wins the competition, then coexistence occurs, and finally the second competitor wins. The analysis in the case E D k entirely similar to the case E = D discussed in this chapter. In [STa], a number of operating diagrams were determined numerically. For fixed population parameters fly, these oper-... 

Figure 9.1. Operating diagram for two-species competition with a varying communication rate E different from the washout rate D. In region VI, Q = [foj in region V, Q = [ , 2]-, in region II, = l o. iU in regions I and IV, fi = f o, i, 2l in region III, Q, = q, , 2, . (From [STa], Copyright 1989, Journal of Mathematical Biology. Reproduced by permission.)...

The figure shows the operating diagram for the HCl absorber. Since the operating line is drawn at a stage efficiency of 0.68, the representation depicts real trays. More than 7 trays are needed, but 8 would overshoot the design point. This accounts for the way the stages are drawn. 

Figure 5. Continuous centrifuge operation diagram. 1, Frame 2, discharge channel 3, conicai basket 4, screen 5, helicoidai biades 6, reduction gear unit 7, eiectric motor. Courtesy of Guinard Centrifugation. (16).

The cluster operator diagrams are particularly simple to interpret as matrix elements the diagrams always involve the reference determinant on the right (because they contain no lines below the interaction line) and an excited determinant on the left, for example,... 

However, recall that the Vj and T2 operator diagrams from Figures 3 and 4 are antisymmetric with respect to permutation of either the pair of outgoing lines or the pair of incoming lines at the two vertices. Hence, we have the relations. 

---