Tank blending

For all impellers with Newtonian fluids, dimensional analysis indicates 

for geometrically similar fully baffled (or with anti-swirl impeller positioning) 

The application of the presented power correlations are illustrated in Examples 10.1 and 10.2. 

It is important to understand the experimental measurement of blend time. The early experimental work was done by using the 

The time required to achieve a certain degree of uniformity after a material is added to a tank is one of the most frequently 

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This arrangement has proved satisfactory for the tank blending of oils. 

Propellers are frequently of the three-bladed marine type and are used for in-tank blending operations with low viscosity liquids, and may be arranged as angled side-entry units, as shown in Figure 7.22. Reavell 1 has shown that the fitting of a cruciform baffle at the bottom of the vessel enables much better dispersion to be obtained, as shown in... 

Example 14.2 Helical Ribbon Impeller. Determine the process-side heat transfer coefficient for the tank blending design example for a helical ribbon impeller (Bakker and Gates, 1995) ... 

A continuous, stirred-tank blending system is shown in Fig. 1.3. The control objective is to blend the two inlet streams to produce an outlet stream that has the desired composition. Stream 1 is a mixture of two chemical species, A and B. We assume that its mass flow rate w is constant, but the mass fraction of A, jci, varies with time. Stream 2 consists of pure A and thus X2 = 1 The mass flow rate of Stream 2, W2, can be manipulated using a control valve. The mass... 

Finally, Method 4 consists of a process design change and thus is not really a control strategy. The four strategies for the stirred-tank blending system are summarized in Table 1.1. 

In Chapter 1 we developed a steady-state model for a stirred-tank blending system based on mass and component balances. Now we develop an unsteady-state model that will allow us to analyze the more general situation where process variables vary with time. Dynamic models differ from steady-state models because they contain additional accumulation terms. 

As an illustrative example, we consider the isothermal stirred-tank blending system in Fig. 2.1. It is a more general version of the blending system in Fig. 1.3 because the overflow line has been omitted and inlet stream 2 is not necessarily pure A (that is, xi 1). Now the volume of liquid in the tank V can vary with time, and the exit flow rate is not necessarily equal to the sum of the inlet flow rates. An unsteady-state mass balance for the blending system in Fig. 2.1 has the form... 

Figure 2.2 Exit composition responses of a stirred-tank blending process to step changes in...

For the simple process discussed so far, the stirred-tank blending system, energy effects were not considered due to the assumed isothermal operation. Next, we illustrate how dynamic models can be developed for processes where energy balances are important. 

Example 2.1 plots responses for changes in input flows for the stirred tank blending system. Repeat part (b) and plot it. Next, relax the assumption that V is constant, and plot the response of x(t) and V(t) for the... 

A stirred-tank blending system initially is full of water and is being fed pure water at a constant flow rate, q. At a particular time, an operator shuts off the pure water flow and adds caustic solution at the same volumetric flow rate q but with concentration ci. If the liquid volume V is constant, the dynamic model for this process is... 

Again consider the stirred-tank blending system in Eqs. 2-17 and 2-18, written as... 

A stirred-tank blending system can be described by a first-order transfer function between the exit composition x and the inlet composition xi (both are mass fractions of solute) ... 

The transfer function representation makes it easy to compare the effects of different inputs. For example, the dynamic model for the constant-flow stirred-tank blending system was derived in Section 4.1. 

In Section 4.1, we developed a relation for the dynamic response of the simple stirred-tank blending system (Eq. 4-14). To find how the outlet composition changes when either of the inputs, X (5 ) or W s), is changed, we use the general first-order transfer function,... 

As noted in Chapter 4, a second-order transfer function can arise physically whenever two first-order processes are connected in series. For example, two stirred-tank blending processes, each with a first-order transfer function relating inlet to outlet mass fraction, might be physically connected so that the outflow stream of the first tank is used as the inflow stream of the second tank. Figure 5.7 illustrates the signal flow relation for such a process. Here... 

We introduce feedback control systems by again considering the stirred-tank blending process of Chapters 2 and 4. 

A schematic diagram of a stirred-tank blending process is shown in Fig. 8.1. The control objective is to keep the tank exit composition x at the desired value set point by adjusting W2, the flow rate of species A, via the control valve. The composition analyzer-transmitter (AT)... 

Figure 8.1 Schematic diagram for a stirred-tank blending system.

On the other hand, in analyzing control systems it can be more convenient to express the error signal in engineering units such as °C or mol/L. For these situations, Kc will not be dimensionless. As an example, consider the stirred-tank blending system. Suppose that e[=] mass fraction and p [=] mA then Eq. 8.2 implies that Kc[=] mA because mass fraction is a dimensionless quantity. If a controller gain is not dimensionless, it... 

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