Energy balances for a CSTR

Table 7.1.3 Energy Balance for a CSTR Producing Propylene Glycol...

The energy balance for a CSTR can be derived from Equation (9.2.7) by again carrying out the reaction isothermally at the inlet temperature and then evaluating sensible heat effects at reactor outlet conditions, that is. 

The dimensionless steady-state equations of mass and energy balance for a CSTR are reproduced here ... 

Forms of Ihe energy balance for a CSTR with heat exchange... 

Example (h) In terms of fractional conversion,/ = 1 — C/Cj, the material and energy balances for a first-order CSTR are ... 

The energy balance for a PFR, as an enthalpy balance, may be developed in a manner similar to that for a CSTR in Section 14.3.1.2, except that the control volume is a differential volume. This is illustrated in Figure 15.3, together with the symbols used. 

We first derive the energy balance in a CSTR. For the mass balance in a constant-density reactor we wrote an integral balance on the rate of change of the number of moles Nj of species j in the reactor to obtain... 

For the corresponding energy balance in a CSTR we write an analogous expression [accumulation of heat] = [heat flow in] — [heat flow out]... 

For a CSTR, recall that —F/ s)X = r y and therefore the steady-state energy balance for a single reaction is... 

Equation (8.15) gave the mass balance for a CSTR. A similar equation can be written as an energy balance. This example considers a CSTR in which a first-order reaction occurs. 

The steady-state mass and energy balances in a CSTR are given by Equations (2.20) and (2.21), respectively, which are reproduced here for ready reference ... 

For the first-order reaction, the steady-state equations for mass and energy balance in a CSTR can be combined into a single equation represented as... 

Consideration of the coupled mass and energy balances for the CSTR have led to possible behaviors that may seem surprisingly complex for even the simplest kinetic mechanism, an irreversible first-order reaction. Just because these behaviors are possible does not mean that they are normally observed in reactor operation for something as simple as A goes to B. 

Multiple Steady States and Local Stability in CSTR.—In the two decades since the seminal work of van Heerden and Amimdson, there has been vast output of papers conoemed with the dynamic behaviour of stirred-tank reactors. Bilous and Amundson put the van He den analysis of local stability of the equilibrium state on a rigorous basis by use of linear stability theory. Their method is similar to the phase-plane treatments of thermokinetic ignitions and oscillations discussed here in Sections 4 and 3 (and preceded them dironologically). The mass and energy balance for the CSTR having a single reactant as feedstock may be expressed as ... 

The dynamics of temperature and conversion within a cooled continuous-flow stirred tank reactor (CSTR) can be obtained from the material and energy balances. For a simple first order chemical reaction they are in a dimensionless form... 

Figure 14.8 Illustration of solution of material and energy balances for an endothermic reaction in a CSTR (no multiple stationary-states possible)...

In Example 9-4 we saw how a 500-gal CSTR used for the production of propylene glycol approached steady-state. For the flow rates and conditions (e.g., Tq = 75°F, = 60° ), the steady-state temperature was 138°Fand the corresponding conversion was 75.5%. Determine the steady-state temperature and conversion that would result if the entering temperature were to drop from 75°F to 70°F, assuming that all other conditions remain the same. First, sketch the steady state conversions calculated from the mole and energy balances as a function of temperature before and after the drop in entering temperature occurred. Next, plot the "conversion,"concentration of A, and the temperature in the reactor as a function of time after the entering temperature drops from 75°F to 70°F. 

To derive the dimensionless energy balance equation for a CSTR, the integral form of the energy balance equation, Eq. 5.2.48 is used. Since the temperature in the reactor is uniform, T = the rate heat is transferred to flie reactor is... 

This is the dimensionless energy balance equation for a CSTR, relating the outlet temperature, 0 ut, to the inlet temperature, 0,n, and the extents of the independent reactions in the reactor,... 

The analysis of multiplicity for a tubular reactor is involved because its mass and energy balances are governed by nonlinear boundary-value problems. The uniqueness conditions for a tubular reactor are more conservative than those for a CSTR. The exact bounds for the uniqueness require numerical solutions. 

Figure 6.1 illustrates the fact that for various ranges of kinetic and reactor parameters it is possible for the mass and energy conservation relations for a CSTR to be in stable balance at more than one condition. This may imply that there are other balance conditions that are unstable the point needs to be examined. Which of the stable balances is attained in actual operation may be dependent on the details of startup procedure, for example, which are not subject to the control of the designer. Thus, it is important to investigate reactor stability using unsteady-state rather than steady-state models. 

Coupled mass and thermal energy balances are required to analyze the nonisother-mal response of a well-mixed continuous-stirred tank reactor. These balances can be obtained by employing a macroscopic control volume that includes the entire contents of the CSTR, or by integrating plug-flow balances for a differential reactor under the assumption that temperature and concentrations are not a function of spatial coordinates in the macroscopic CSTR. The macroscopic approach is used for the mass balance, and the differential approach is employed for the thermal energy balance. At high-mass-transfer Peclet numbers, the steady-state macroscopic mass balance on reactant A with axial convection and one chemical reaction, and units of moles per time, is... 

CSTR For a CSTR, the energy balance for material in the reactor can be written as follows, where we have assumed heat transfer to both a jacket and losses to the atmosphere. In the case of additional coils in the reactor, a further term can be added ... 

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