CSTRs energy balance

Material and energy balances of common types of reactors are summarized in several tables of Sec. 7. For review purposes some material balances are restated here. For the /ith stage of a CSTR batteiy,... 

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

For a continuous-flow reactor, such as a CSTR, the energy balance is an enthalpy (H) balance, if we neglect any differences in kinetic and potential energy of the flowing stream, and any shaft work between inlet and outlet. However, in comparison with a BR, the balance must include the input and output of H by the flowing stream, in addition to any heat transfer to or from the control volume, and generation or loss of enthalpy by reaction within the control volume. Then the energy (enthalpy) equation in words is... 

Figure 14.3 Quantities in energy-balance equation (14.3-8) for CSTR...

If feed at a specified rate and T0 enters a CSTR, the steady-state values of the operating temperature T and the fractional conversion fA (for A —> products) are not known a priori. In such a case, the material and energy balances must be solved simultaneously for T and fA. This can give rise to multiple stationary states for an exothermic reaction, but not for an endothermic reaction. 

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

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. 

Case (2) CSTR T0 for Vmin with adiabatic operation and specified fA, FAo and q The result given by 18.4-4 requires only that the operating temperature within the CSTR be Topt, and implies nothing about the mode of operation to obtain this, that is, nothing about the feed temperature (TJ, or heat transfer either within the reactor or upstream of it. If the CSTR is operated adiabatically without internal heat transfer, T0 must be adjusted accordingly to a value obtained from the energy balance, which, in its simplest integrated form, is, from equation 14.3-10,... 

For nonisothermal operation, the energy analysis, point (4) above, requires that the energy balance be developed for a complex system. The energy (enthalpy) balance previously developed for a BR, or CSTR, or PFR applies to a simple system (see equations 12.3-16,14.3-9, and 15.2-9). For a complex system, each reaction (i) in a specified network contributes to the energy balance (as (-AHRl)rt), and, thus, each must be accounted for in the equation. We illustrate this in the following example. 

Material and energy balances of CSTRs are derived by the general conservation rule,... 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

Eq.(l) and (9) can be utilized for modeling a CSTR considering the material and energy balances as well as the expression for the rate flow of heat removed, Q. This heat rate is obtained from the overall heat transfer coefficient U and the transmission area A by the equation Q = UA(T — Tj) [1], [9], [13], [14], [18], [22],... 

Figure 5-1 Energy balance in chemical reactors. The volume shown could be the total reactor volume in a CSTR or a differential volume in a PFTR.

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 steady state in the CSTR we set dHIdt = 0 and divide each term by vpCp to yield steady-state energy balance... 

We solved the mass- and energy-balance equations for the CSTR in the previous chapter. The mass balance on species A is... 

Now we substitute this expression for X(T) into the energy-balance equation to yield a combined energy- and mass-balance equation for a first-order irreversible reaction in a CSTR,... 

For a single reaction in the CSTR, the transient mass- and energy-balance equations are... 

Figure 6-15 Sketches of a CSTR with cooling either through a jacket (left) or a cooling coil (right). A separate energy balance must be solved for the coolant temperature if the temperature of the cooling fluid Tq is not constant and equal to the coolant feed temperature Tio-...

Note that now Tj is a variable that is a function of position Zc in the cooling coif while T, the reactor temperature in the CSTR reactor, is a constant. We can solve this differential equation separately to obtain an average coolant temperature to insert in the reactor energy-balance equation. However, the heat load on the cooling coil can be comphcated to calculate because the heat transfer coefficient may not be constant. 

Recall from Chapter 6 that the steady-state energy-balance equations in a CSTR can be reduced to a single equation, which we wrote by considering the rates of heat generation and removal. We wrote these as... 

The energy balance of ethanol in this type of reactor (CSTR type) is flux in - flux out = disappearance by reaction... 

Material and energy balances for batch, CSTR and PFR are in Tables... 

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