Batch heat balance

Batch Reactions For a batch reaction, the heat balance is... 

Batch with Constant Reflux Ratio, 48 Batch with Variable Reflux Rate Rectification, 50 Example 8-14 Batch Distillation, Constant Reflux Following the Procedure of Block, 51 Example 8-15 Vapor Boil-up Rate for Fixed Trays, 53 Example 8-16 Binary Batch Differential Distillation, 54 Example 8-17 Multicomponent Batch Distillation, 55 Steam Distillation, 57 Example 8-18 Multicomponent Steam Flash, 59 Example 8-18 Continuous Steam Flash Separation Process — Separation of Non-Volatile Component from Organics, 61 Example 8-20 Open Steam Stripping of Heavy Absorber Rich Oil of Light Hydrocarbon Content, 62 Distillation with Heat Balance,... 

The energy balance for the bioreactor is shown by the following equation. As the fermenter is used batch wise, the heat balance is mathematically expressed as stated in (4.4.1) ... 

There is one significant difference between batch and continuous-flow stirred tanks. The heat balance for a CSTR depends on the inlet temperature, and Tin can be adjusted to achieve a desired steady state. As discussed in Section 5.3.1, this can eliminate scaleup problems. 

A relatively simple example of a confounded reactor is a nonisothermal batch reactor where the assumption of perfect mixing is reasonable but the temperature varies with time or axial position. The experimental data are fit to a model using Equation (7.8), but the model now requires a heat balance to be solved simultaneously with the component balances. For a batch reactor. 

The component mass balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

The heat balance for a batch reactor, where Qin is zero, shows that heat accumulation is the difference between heat production and heat removal, from Equation (3-1), leading to Equation (3-7) ... 

Heat and material balances of a batch reactor are derived in Section 2.6.2. In the present instance, the differential heat balance is Heat of reaction + Heat tranfer = Sensible heat gain or... 

A first order reaction takes place in batch, starting with Ca0 = 2 gmol/liter. The specific rate is represented by k = exp 21-7500/T) and the heat balance by T - 350 + 25(2-Ca)... 

Ice Crystal Growth. In order to quantify these results for the production of large disc and spherical crystals, seversd batch experiments on 6% lactose solutions were undertaken. The experimental conditions and results are shown in Table II. In these experiments, nuclei were generated at -2.5 C (except for Run Sa at -4.0°C) and input to the batch crystallizer controlled at various refirigerant temperatures. As these crystals grew, the total crystal surface area was controlled manually in order to maintain a heat balance for a constant value of the refrigerant temperature. Slurry removal rate for these experiments... 

Figure 3. Changes in size distribution with time during growth of ice crystal seeds in 6% lactose under batch or semi-batch growth conditions, concentration processes based on suspension growth. In addition, the relation of this observed widening to the heat balance conditions needs to be further explored.

However, in most cases a simplified heat balance, which comprises the two first terms on the right-hand side of Equation 2.26, is sufficient for safety purposes. Let us consider a simplified heat balance, neglecting terms such as the heat input by the stirrer or heat losses. Then, the heat balance for a batch reactor can be written as... 

The differential equations governing a non-isothermal batch reaction describe the material balance coupled to the heat balance (see also Section 2.4.2) ... 

These points are explained in detail in this chapter. In a first section, the general aspects of reaction engineering for batch reactors are briefly presented. The mass and heat balances are analysed and it is shown that a reliable temperature control is central to the safety of batch reactors. The different strategies of temperature control and their consequences on reactor safety are explained in the following sections. For each strategy, the design criteria and the safety assessment procedure are introduced. The chapter is closed by recommendations for the design of thermally safe batch reactions. 

As with the batch reactor, the semi-batch reactor operates discontinuously. The difference with true batch operation is that for the semi-batch reactor, at least one of the reactants is added as the reaction proceeds (Figure 7.1). Consequently, the material balance as well as the heat balance will be affected by the progressive addition of one of the reactants. Also, as with the batch reactor, there is no steady state. There are essentially two advantages in using a semi-batch reactor instead of a batch reactor ... 

The overall heat balance of a semi-batch reactor can be written by using the three terms mentioned above. If the heat exchange does not compensate exactly, the other terms (heat production, effect of the feed, temperature) will vary as... 

The heat balance of an isothermal semi-batch reaction is represented graphically in Figure 7.2. The maximum heat exchange rate (qeXiialx) calculated for a constant temperature of the heat carrier is also represented in the diagram. It increases linearly with time until the upper limit of the jacket is reached. In this example, the upper limit of the jacket is not reached during the feed time of four hours. 

Figure 7.2 The different terms of the heat balance of an isothermal semi-batch reactor (in kW) as a function of time. The maximal cooling capacity of the reactor (qama,) obtained with cold water at 5°C is also represented. The difference between both curves q and qa represents the cooling effect by the feed. Its disappearance at the end of the feed at 4 hours is visible.

The condition for the practical implementation of such a feed control is the availability of a computer controlled feed system and of an on-line measurement of the accumulation. The later condition can be achieved either by an on-line measurement of the reactant concentration, using analytical methods or indirectly, by using a heat balance of the reactor. The amount of reactant fed to the reactor corresponds to a certain energy of reaction and can be compared to the heat removed from the reaction mass by the heat exchange system. For such a measurement, the required data are the mass flow rate of the cooling medium, its inlet temperature, and its outlet temperature. The feed profile can also be simplified into three constant feed rates, which approximate the ideal profile. This kind of semi-batch process shortens the time-cycle of the process and maintains safe conditions during the whole process time. This procedure was shown to work with different reaction schemes [16, 19, 20], as long as the fed compound B does not enter parallel reactions. 

We study the separation of 77-hexane-ethyl acetate mixture by using acetonitrile as a heavy heterogeneous entrainer. The simulation of the process is performed with the batch process simulator ProSimBatch [10]. It enables to evaluate operational parameters like the entrainer amount that are not provided by the feasibility and synthesis analysis The column model consists of usual plate by plate Material balance, Equilibrium, Summation of fractions and Heat balance... 

By renaming the two terms on the right-hand side of (4.12) as qr and qE, which represent the rate of heat production by reaction and of heat exchange with the cooling medium, respectively, the heat balance in the batch reactor can be rewritten as... 

When an agitated batch containing M of fluid with specific heat c and initial temperature t is heated using an isothermal condensing heating medium Tt, the batch temperature t2 at any time 0 can be derived by the differential heat balance. For an unsteady state operation as shown in Figure 7-27, the total number of heat transferred is q, and per unit time 0 is ... 

---