Steady state continuously stirred tank

Figure 3.14. Heat loss, Hl, and heat gain, Hq, in a steady-state, continuous stirred-tank reactor.

Fig. 3.12 Heat loss HL and heat gain Hc in a steady-state continuous stirred-tank reactor.

The experimental unit, shown on the previous page, is the simplest assembly that can be used for high-pressure kinetic studies and catalyst testing. The experimental method is measurement of the rate of reaction in a CSTR (Continuous Stirred Tank Reactor) by a steady-state method. 

Table 11.4 lists reactors used for systems with two fluid phases. The gas-liquid case is typical, but most of these reactors can be used for liquid-liquid systems as well. Stirred tanks and packed columns are also used for three-phase systems where the third phase is a catal5hic solid. The equipment listed in Table 11.4 is also used for separation processes, but our interest is on reactions and on steady-state, continuous flow. 

Continuous Stirred Tanks with Biomass Recycle. When the desired product is excreted, closing the system with respect to biomass offers a substantial reduction in the cost of nutrients. The idea is to force the cells into a sustained stationary or maintenance period where there is relatively little substrate used to grow biomass and where production of the desired product is maximized. One approach is to withhold some key nutrient so that cell growth is restricted, but to supply a carbon source and other components needed for the desired product. It is sometimes possible to maintain this state for weeks or months and to achieve high-volumetric productivities. There will be spontaneous cell loss (i.e., kd > 0), and true steady-state operation requires continuous purging and makeup. The purge can be achieved by incomplete separation and recycle... 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

For steady-state operation of a continuous stirred-tank reactor or continuous stirred-tank reactor cascade, there is no change in conditions with respect to time, and therefore the accumulation term is zero. Under transient conditions, the full form of the equation, involving all four terms, must be employed. 

Although continuous stirred-tank reactors (Fig. 3.12) normally operate at steady-state conditions, a derivation of the full dynamic equation for the system, is necessary to cover the instances of plant start up, shut down and the application of reactor control. 

The following reactions take place in the liquid phase in a continuous stirred tank reactor operating at steady state. 

The steady-state form of the energy balance for a continuous stirred tank reactor is given by equation 10.1.4. 

The kinetics of a liquid-phase chemical reaction are investigated in a laboratory-scale continuous stirred-tank reactor. The stoichiometric equation for the reaction is A 2P and it is irreversible. The reactor is a single vessel which contains 3.25 x 10 3 m3 of liquid when it is filled just to the level of the outflow. In operation, the contents of the reactor are well stirred and uniform in composition. The concentration of the reactant A in the feed stream is 0.5 kmol/m3. Results of three steady-state runs are ... 

For the continuous stirred-tank reactor of volume Vc A steady-state balance on reactant A gives ... 

Data obtained in continuous stirred tank reactors have the merits of isothermicity and of an algebraic relation between the variables rather than a differential one. At steady state In a CSTR the material balance on a reactant A is... 

A system of N continuous stirred-tank reactors is used to carry out a first-order isothermal reaction. A simulated pulse tracer experiment can be made on the reactor system, and the results can be used to evaluate the steady state conversion from the residence time distribution function (E-curve). A comparison can be made between reactor performance and that calculated from the simulated tracer data. 

Steady-State Absorption Column Design 471 Oxidation of O-Xylene to Phthalic Anhydride 324 Continuous Stirred Tank Reactor Model of Activated 577... 

The chemical reactor is the unif in which chemical reactions occur. Reactors can be operated in batch (no mass flow into or out of the reactor) or flow modes. Flow reactors operate between hmits of completely unmixed contents (the plug-flow tubular reactor or PFTR) and completely mixed contents (the continuous stirred tank reactor or CSTR). A flow reactor may be operated in steady state (no variables vary with time) or transient modes. The properties of continuous flow reactors wiU be the main subject of this course, and an alternate title of this book could be Continuous Chemical Reactors. The next two chapters will deal with the characteristics of these reactors operated isothermaUy. We can categorize chemical reactors as shown in Figure 2-8. 

Many reviews and several books [61,62] have appeared on the theoretical and experimental aspects of the continuous, stirred tank reactor - the so-called chemostat. Properties of the chemostat are not discussed here. The concentrations of the reagents and products can not be calculated by the algebraic equations obtained for steady-state conditions, when ji = D (the left-hand sides of Eqs. 27-29 are equal to zero), because of the double-substrate-limitation model (Eq. 26) used. These values were obtained from the time course of the concentrations obtained by simulation of the fermentation. It was assumed that the dispersed organic phase remains in the reactor and the dispersed phase holdup does not change during the process. The inlet liquid phase does not contain either organic phase or biomass. 

The mass balance over a continuous stirred-tank reactor (CSTR) in the steady state yields for the average residence T... 

Continuous-stirred tank reactor (CSTR) This reactor is operated under steady-state condition. The reactants flow continuously in and out of the vessel at a constant flow rate and are perfectly mixed by mechanical means, and thus the composition is the same throughout the reactor. The result is that the exit concentration is the same as the one in the reactor. The concentration is constant, i.e. is not time-dependent. 

All chemical reactions are accompanied by some heat effects so that the temperature will tend to change, a serious result in view of the sensitivity of most reaction rates to temperature. Factors of equipment size, controllability, and possibly unfavorable product distribution of complex reactions often necessitate provision of means of heat transfer to keep the temperature within bounds. In practical operation of nonflow or tubular flow reactors, truly isothermal conditions are not feasible even if they were desirable. Individual continuous stirred tanks, however, do maintain substantially uniform temperatures at steady state when the mixing is intense enough the level is determined by the heat of reaction as well as the rate of heat transfer provided. 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

Fig. 1.9. Continuous stirred-tank reactor showing steady state operation (a) and two modes of unsteady state operation (b) and (c)...

Fig. 1.17. Continuous stirred-tank reactor material balance over rth tank in steady state...

Continuous Stirred-Tank Reactor — One Tank Taking material balances in the steady state as shown in Fig. 1.26 ... 

The fluidised bed will be considered as a continuous stirred tank reactor in which ideal macromixing of the particles occurs. As shown in the section on mixing (Chapter 2, Section 2.1.3), in the steady state the required exit age distribution is the same as the C-curve obtained using a single shot of tracer. In fact the desired C-curve is identical with that derived in Chapter 2, Fig. 2.3, for a tank containing a liquid with ideal micromixing, but now the argument is applied to particles as follows ... 

The shape of the performance curve for a continuous stirred-tank fermenter is dependent on the kinetic behaviour of the micro-organism used. In the case where the specific growth rate is described by the Monod kinetic equation, then the productivity versus dilution rate curve is given by equation 5.137 and has the general shape shown by the curve in Fig. 5.58. However, if the specific growth rate follows substrate inhibition kinetics and equation 5.65 is applicable then, at steady state, equation 5.131 becomes ... 

Two continuous stirred-tank fermenters are connected in series, the first having an operational volume of 100 1 and that of the second being 50 1. The feed to the first fermenter is sterile and contains 5000 mg/1 of substrate, being delivered to the fermenter at 18 1/h. If the microbial growth can be described by the Monod kinetic model with /x, = 0.25 h l and Ks = 120 mg/l, calculate the steady-state substrate concentration in the second vessel. What would happen if the flow were from the 50 I fermenter to the 100 1 fermenter ... 

In contrast to the batch fermentation based methods of determining kinetic constants, the use of a continuous fermenter (Fig. 3.71) requires more experiments to be performed, but the analysis tends to be more straightforward. In essence, the experimental method involves setting up a continuous stirred-tank fermenter to grow the micro-organisms on a sterile feed of the required substrate. The feed flowrate is adjusted to the desired value which, of course, must produce a dilution rate below the critical value for washout, and the system is allowed to reach steady state. Careful measurements of the microbial density X, the substrate concentration S, and the flowrate F are made when a steady state has been achieved, and the operation is then repeated at a series of suitable dilution rates. 

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