how to use barcode scanner in asp.net c# The Material Balance in Visual Studio .NET

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The Material Balance
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In the steady state, as much ma- Feed terial must be withdrawn as enters F,z a tower: F=D+B (11.1) 5
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where F = molal feed rate D = distillate flow B = bottoms Aow A material balance on each component must also be closed, using x, y, and
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FIG 11.1. Material and energy balances play key roles in distillation control.
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x to represent the mole fraction of the light component in F, D, and B: Fz = Dy + Bx (11.2)
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From the overall material balance it is evident that the flow of only one of the product streams can be set independently. The flow of the other is determined by the feed rate and is therefore a dependent variable. But one flow must be set by some criterion, since they cannot both be allowed to drift. For t,he moment, distillate flow will be chosen to be manipulated by the control system, either directly or indirectily. (The reason for this choice will be discussed later.) Bottoms flow must then be manipulated by a controller which senses liquid level at the bottom of the tower in order to close the material balance by maintaining constant liquid inventory. Bottoms flow is thus dependent on current values of feed and distillate: B = F - D Substituting for B in the material balance of the light component permits expressing the relationship between the quality of both products in,terms of distillate flow: Fz = Dy + (F - D)x The ratio D/F determines the relative composition of each product: z-x _ _ y-x D =F (11.3)
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Figure 11.2 shows one way in which this relationship might be pictured. Remember that x is an uncontrolled variable, like F. Therefore if z should change, D/F must be adjusted to maintain constant values of x and y,
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FIG 11.2. If x and g are to be controlled, D/F must vary proportionately to z.
Distillation
Unfortunately, however, the material-balance equation alone is insoluble. It is a single equation with two unknowns, x and y. To provide a solution, another equation of x and y must be found. The Fenske equation 4 was derived for the purpose of estimating the number of theoretical trays n required to effect a given separation between components whose relative volatility is a, at total reflux: (11.:) Equation (11.4) needs to be modified to allow extension to situations other than total reflux: (11.5) The term S is defined as the separation and is a function of o(, n, and the energy to feed ratio. Solving Eq. (11.5) for y in terms of x and for x in terms of y,
A direct solution of these equations with the material balance ca nnot be readily obtained. But through the use of a numerical example, the prevailing relationships will be demonstrated. Consider the example of a tower separating a feed material x = 0.5 into distillate y = 0.95 and bottoms x: = 0.05. The separation factor for this tower under these conditions is
s = @.95)@.W
(0.05) (0.05)
= 361
The distillate to feed ratio is D/F = 0.5 - 0.05 0.95 - 0.05 = o.5
Should any other value of x or y be desired at the prevailing conditions of feed composition and separation, it can be obtained by appropriate adjustment of D/F. A value for y, for example, is first selected, and a corresponding value of x is then calculated from the modified Fenske equation. With these values of x, y, and x, the required D/F can be found from t,he material balance. Figure 11.3 illustrates how distillate and bottoms compositions would vary with D/F for this example. The slope of each curve at D/F = 0.5 represents the process gain at that point. It happens that the two curves have identical slopes at
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.s 0 . 6 f B E 0 0 . 4
FIG 11.3. Increasing D/F reduces both x and g, but in different degrees.
0 0.2 0.4 D/F 0.6 0.8 1.0
that point: -0.9 at $ = 0.5
A 1 percent change in D/F will change distillate and bottoms composition by 0.9 percent. Three conclusions may be drawn from the foregoing discussion: 1. Composition of both product streams is profoundly affected by distillate to feed ratio. 2. Changes in feed composition can be offset by appropriate adjustment of D/F. 3. If separation is constant, control of composition of either product will also result in control of composition of the other product. (The relationship between x and y is fixed for a given separation.)
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