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Furthermore, the nonlinearity of the pH curve is compensated, to some extent, by the dead zone. If the large valve is selected to be about 20 times the size of the small valve, the flow rangeability of the combination can exceed 700 : 1. If this is insuflicicnt for a particular application, neutralization must be conducted in more than one stage. Should influent pH vary on both sides of neutral, a duplicate conbrol system can be used to add the other reagent to the same vessel.
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Feedforward Control of pH
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Figure 10.14 showed a combined feedforward-feedback control syst em with a forward loop from flow only. In waste-treating systems, the pH of the stream to be neutralized often varies more than it s flow. But because t,he relationship between pH and reagent requirement is variable, adaptation of t he forward loop by feedback is essential, Reagent requirements are based on flow times the acid or base cont ent estimat,ed in Eqs. (10.30). For simplification, only the neutralization of an influent acid HA, of flow F, by a reagent base B, will be considered. The required base flow is
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B:cn = Fzn = FIOWH ( 1 + 9)
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If thr rcagcnt is admitted by an equal-percentage valve, the logarithmic characteristic between flow and position, 112, will be found useful: - In BK = 4(1 - 112) n,nx Conversion to base 10 logarithms and lumping of valve size and reagent concentration into a c~onstnnt b yields
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- l o g Bz,; = 1.73(1
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- I/L) + b
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Next, Eq. (10.31) can be converted to logarithms: -1.73(1 - 111) - b = log F - pH + log 1 + r ( [nnl> Once again the various constants can be lumped, producing a general fcedformard model : 71~ = log aF + 9 (1 - pH) where 1 = set point 100/P = forward loop gain a = required feedback adaptation (10.32)
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Reagent
FIG 10.16. Two forward loops and one feedback loop give this pH system maximum effectiveness.
Because of the equal-percentage characteristic, loop gain will change with position (hence flow) as well as with PH. In order to make loop gain independent of flow, the output of the feedback controller, here designated a, must be placed on the same terms as flow. Actually the feedback trim is the same as was shown in Fig. 10.14, using a nonlinear controller to compensate the pH curve. The function of using an equal-percentage valve is twofold: 1. To provide maximum rangeability 2. To generate the forward-loop pH function The control system is shown in Fig. 10.16. Note that the forward-loop summation is made conveniently in a proportional controller with remote bias. A positioner is indicated on the equal-percentage valve to ensure as accurate delivery of reagent as possible. 1.0 It is also necessary t o supply the reagent at a fixed head. If a single valve gives insufficient rangeability, two may be sequenced. Full flow from the smaller L 0 valve should equal about 3 percent of the $0.5 + capacity of the larger. The large valve should be set to open to 3 percent flow when the smaller is full open, at 50 percent output. The smaller must be closed at the same time the larger is opened in order to avoid upset ting t h e p r o c e s s . FIG 10.17. Generation of the A small differential gap in the switching logarithmic function over a full logic is needed to minimize cycling at decade of flow is more than sufthis point. ficient.
1 A&Gxxtions Figure 10.17 shows the function needed to include both flow and feedback in the system. It is necessary to add 1 to log aF to normalize the ordinate over a single decade. The curve is not especially difficult to generate and can be matched with a four-bar Iinkage.8fg
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