CSTR system

SIMPLIFIED FLOW DIAGRAM — FRONT END OF SERIES CSTR SYSTEM... 

Equations 11 and 12 are only valid if the volumetric growth rate of particles is the same in both reactors a condition which would not hold true if the conversion were high or if the temperatures differ. Graphs of these size distributions are shown in Figure 3. They are all broader than the distributions one would expect in latex produced by batch reaction. The particle size distributions shown in Figure 3 are based on the assumption that steady-state particle generation can be achieved in the CSTR systems. Consequences of transients or limit-cycle behavior will be discussed later in this paper. 

In this short initial communication we wish to describe a general purpose continuous-flow stirred-tank reactor (CSTR) system which incorporates a digital computer for supervisory control purposes and which has been constructed for use with radical and other polymerization processes. The performance of the system has been tested by attempting to control the MWD of the product from free-radically initiated solution polymerizations of methyl methacrylate (MMA) using oscillatory feed-forward control strategies for the reagent feeds. This reaction has been selected for study because of the ease of experimentation which it affords and because the theoretical aspects of the control of MWD in radical polymerizations has attracted much attention in the scientific literature. 

Case 1 Anaerobic/Aerobic Treatment of Municipal Landfill Leachate in Sequential Two-Stage Up-Flow Anaerobic Sludge Blanket Reactor (UASB)/Aerobic Completely Stirred Tank Reactor (CSTR) Systems... 

Osman, N.A, and Sponza, D.T., Anaerobic/aerobic treatment of municipal landfill leachate in sequential two-stage up-flow anaerobic sludge blanket reactor (UASB)/completely stirred tank reactor (CSTR) system, Proc. Biochem., 40, 895-902, 2005. 

This example involves a continuous adiabatic nitration process for the manufacture of mono-nitrobenzene (MNB) [215] by the reaction of benzene with nitric acid in a CSTR system. The process is designed to be inherently safe. No external cooling is used, but the reaction mass is heated by the reaction itself to a temperature level controlled by the amount of sulfuric add-water mixture circulating through the system. This acid actually acts as both a heat sink and as a nitration enhancer. If the sulfuric add pumps fail, the nitric add and benzene pumps are automatically shut off. 

THERM and THERM PLOT - Thermal Stability of a CSTR System... 

THERMFF - Feedforward Control of an Exothermic CSTR System... 

Example 2.6. The CSTR system of Example 2.3 will be considered again, this time with a cooling coil inside the tank that can remove the exothermic heat of reaction 2 (Btu/lb. mol of A reacted or cal/g mol of A reacted). We use the normal convention that 2 is negative for an exothermic reaction and positive for an endothermic reaction. The rate of heat generation (energy per time) due to reaction is the rate of consumption of A times 2. 

Example 6 7, Suppose the feed concentration in the CSTR system considered above is ramped up with time ... 

Combine the three first-order ODEs describing the three-CSTR system of Sec. 3.2 into one third-order ODE in terms of Then solve for the response of to a unit step change in C 0 assuming all Jt s and t s are identical. 

Simulate the three-CSTR system on a digital computer with an on-off feedback controller. Assume the manipulated variable is limited to +1 mol of A/lt around the stcadystate value. Find the period of oscillation and the average value of for values of the load variable of 0.6 and 1. 

Examiik 9J. The isothermal three CSTR system is described by the three linear ODEs... 

A feedback controller is added to the three-CSTR system of Example 9.5. Now... 

Example 10.4. Consider again the three-CSTR system. We have already developed its doscdloop characteristic equation with a proportional controller [Equation (10.22)]. 

Example 10.10. Our thiee-CSTR system is an interesting one to explore via root locus. With the same process as shown in Fig. 10.4 we will use different types of feedback controllers and different settings and see how the root loci change. 

Root locus curves for a. three-CSTR system. 

Root locus results for three CSTR system... 

Load step response of a ihree-CSTR system with Ziegler-Nidiols and f = 0.316 controller settings. 

KU. Use the Routh stability criterion to find the ultimate gain of the closedloop three-CSTR system with a PI controller ... 

Example 11.3. The nonlinear ODEs describing the constant holdup, nonisothemial CSTR system are... 

The actual stability requirement for the nonisothermal CSTR system is a little more complex than Eq. (11.43) because the concentration C does change. 

Nyquist plots of thiee-CSTR system with pfoportioiul controller. 

Figure lillb is a Nichols chart with two G B curves plotted on it. They are from the three-CSTR system with a proportional controller. 

Nichols chart with a three-CSTR system openloop Gmho plotted. 

Openloop and dosedbop Bode plots for a three-CSTR system. 

Bode plots of openloop and dosedloop BG /(l + BG ) for a thiee-CSTR system and PI oon-tiollers. 

Bode plots of B three-CSTR system with proportional controller. 

We have also found it helpful to think of the rate equation for CSTR systems in terms of a flow rate L and a reaction rate R, and eqn (8.2) has the form... 

Each of the four plots in Figure 3.13 contains two graphs that of a solid line for the linear left-hand sides of equations (3.11) through (3.16) and that of the respective exponential function from the respective right-hand sides, in a dotted curve. The very shallow intersections in Figure 3.13 indicate the location of the multiple steady states of the given nonadiabatic CSTR system. 

To gain further and broader insights into the bifurcation behavior of nonadiabatic, nonisothermal CSTR systems, we again use the level-set method for nonalgebraic surfaces such as z = /(K,., y). This particular surface is defined via equation (3.14) as follows for a given constant value of yc with the bifurcation parameter Kc ... 

When viewing the graphs of Figure 3.15, please recall that multiple solutions of Fl(x) = 0 for x [0,1] signify bifurcation for the underlying CSTR system. 

Equation (3.17) allows a different interpretation of the underlying system s bifurcation behavior by taking Kc and yc as fixed and letting a vary, for example. We now study the bifurcation behavior of nonadiabatic and nonisothermal CSTR systems via their level-zero curves for the associated transcendental surface z = g(a,y). The surface is defined as before, except that here we treat Kc and yc as constants and vary a and y in the 3D surface equation... 

Thus far we have explored the bifurcation behavior of equation (3.14) with respect to Kc via equation (3.17) in Figures 3.14 through 3.16, and with respect to a via (3.19) in Figures 3.17 and 3.18. Since different Kc and a values can lead to bifurcation behavior for the same nonadiabatic, nonisothermal CSTR system, it is of interest and advantageous to be able to plot the joint bifurcation region for the parameters Kc and a as well. 

Nonadiabatic, nonisothermal CSTR system with disjoint multiplicity regions for Kc... 

Nonadiabatic CSTR system with a contiguous multiplicity region for Kc... 

We are made aware of the lively change in bifurcation behavior here just a third digit change in a can cause absolutely different bifurcation behavior of the associated CSTR system, as witnessed by Figures 3.20 to 3.22. 

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