Mole balances batch reactors

The corresponding combined batch reactor mole balances and rate laws are For the initiator ... 

We call Equation (2-6) the dit ferential form of the design equation for batch reactor because we have written the mole balance in terms of converstor The difTereniial forms of the batch reactor mole balances. Equations (2-5) ani (2-6). are often used in the interpretation of reaction rate data (Chapter 5) atu for reactors with heat effects (Chapter 9), respectively. Batch reactors are fre qiiently used in industry for both gas-phase and liquid-phase reactions. Thi laboratory bomb calorimeter reactor is widely used for obtaining reaction raa data (see Section 9.3). Liquid-phase reactions are frequently carried out it batch reactors when small-scale production is desired or operating diflicultie rule out the use of continuous (low. systems. 

This method is the quickest method to use to determine the rate law if (he order turns out to zero, first, or second order. In the integral method, we guess the reaction order, a, in the combined batch reactor mole balance and rate law equation... 

The feed composition variation with conversion gives the instantaneous composition of the copolymer as a function of conversion. It is also useful to know the overall average composition for a given conversion. This can be obtained through a material balance, say, for M, in a batch reactor. Moles Mj in feed = moles of Mj in polymer + moles of unreacted M,. 

For a batch reactor, a balance on moles of monomer can be written as... 

Since the volume depends on conversion or time in a constant pressure batch reactor, consider the mole balance in relation to the fractional conversion X. From the stoichiometry. 

The component balance for a variable-volume but otherwise ideal batch reactor can be written using moles rather than concentrations ... 

Stoichacmetry and reaction equilibria. Homogeneous reactions kinetics. Mole balances batch, continuous-shn-ed tank and plug flow reactors. Collection and analysis of rate data. Catalytic reaction kinetics and isothermal catalytic radar desttpi. Diffusion effects. 

Consider a mole balance on a constant volume batch reactor represented by... 

From the above mole balance equation we can develop the design equation for various reactor types. By solving the design equation we can then determine the time required for a batch reactor system or a reactor volume for a continuous flow system to reach a specific conversion of the reactant to products. 

Batch Reactor. In a batch reactor there are no inlet or outlet streams In = Out = 0. The total feed is charged into the reactor at the beginning and no withdrawal is made until the desired conversion level has been reached. Hence a reaction process occurring in a batch reactor is an unsteady one. All variables change with time. In addition, we assume that it is a perfectly mixed batch reactor, so that the concentrations of the reaction components, reactants or products are the same over the whole reactor volume. This assumption allows us to consider applying the mole balance equation across the whole reactor. With the term reactor we mean the space where the reaction(s) take place. For liquid phase reactions the reactor volume is smaller than the size of the physical reactor. It is the volume of the liquid phase, where the reaction ) take(s) place. 

Eqs. 1 to 3 relate the rate of production Rj of the balanced reaction component y to the molar amounts or their derivatives with respect to the time variable (reaction time or space time, see above). From the algebraic eq. 2 for the CSTR reactor the rate of production, Rj, may be calculated very simply by introducing the molar flow rates at the inlet and outlet of the reactor these quantities are easily derived from the known flow rate and the analytically determined composition of the reaction mixture. With a plug-flow or with a batch reactor we either have to limit the changes of conversion X or mole amount n7 to very low values so that the derivatives or dAy/d( //y,0) or dn7/d/ could be approximated by differences AXj/ (Q/Fj,0) or An7/A, (differential mode of operation), or to measure experimentally the dependence of Xj or nj on the space or reaction time in a broader region this dependence is then differentiated graphically or numerically. 

Develop a batch-reactor design equation from the mass balance. To find the required holding time, a relationship between reaction time and the rate of conversion of acetylene must be developed. This may be developed from a mass balance on the batch reactor. Since the molar density of the reacting mixture is not constant (there is a net change in the number of moles due to reaction), the pressure of the reactor will have to change accordingly. 

Related Calculations. For a batch reactor, the material balance is Rate of accumulation of species A = rate of generation of species A, or dNA/dt = rA, where N is number of moles at time t and r is rate of reaction (which can be, for example, per unit of catalyst mass in the reactor, in which case it must be multiplied by the number of such units present). The rate at any given time can be found by plotting Na against residence time and measuring the slope, but this technique can lead to large errors. A better approach is to use the Taylor-series interpolation formula (see mathematics handbooks for details). 

In batch photocatalytic reactors working in liquid-solid regime, the depletion of a species is the combined result of photoadsorption and photoconversion processes. To describe this depletion, a mole balance applied to the species at whatever time (de Lasa et al., 2005) can be represented as... 

From this general mole balance equation we can develop the design equations for the various types of industrial reactors batch, semibatch, and continuous-flow. Upon, evaluation of these equations we cau determine the time (batch) or reactor volume (continuous-flow) necessary to convert a specified amount of the reactants to products. 

A batch reactor has neither inflow nor outflow of reactants or products while the reaction is being carried out Fjo = Fj 0. The resulting general mole balance on species j is... 

Figure 1-3 shows two different types of batch reactors used for gas-phase reactions. Reactor A is a constant-volume (variable-pressure) reactor and Reactor B is a constant-pressure (variable-volume) reactor. At time r = 0, the reactants are injected into the reactor and the reaction is initiated. To see clearly the different forms the mole balance will take for eadi type of reactor, consider the follovring examples, in which the gas-phase decomposition of dimethyl ether is taking place to form methane, hydrogen, and carbon monoxide ... 

A mole balance on a batch reactor that is well mixed is... 

Recalling Example 5-1, the combined mole balance and rate law for a constant-volume batch reactor can be expressed in the form... 

We can also use nonlinear regression to determine the rate law parameters from concentr on-time data obtained in batch experiments. We recall that the combined rate law-stoichiometty-mole balance for a constant-volume batch reactor is... 

The Genera Mole Balance Equation 6 Batch Reactors 8 Continuous-Flow Reactors 10... 

Write the mole balance for dimethyl ether in terms of the reactor voluine, concentration, and rate of formation of dimethyl ether for both a constant-pressure and a constant-volume batch reactor. 

In writing the mole balance for dimethyl ether for a batch reactor, the only assumption made is that there are no spatial vatMons in r. ... 

Constant-volume batch reactor. The reactor is perfectly mixed so that the concentration of die reacting species is spatially uniform. Because die volume is constant we can take V inside the difierenlial and write the mole balance in terms of the concentration of A ... 

Constant-pressure batch reactor. To write the mole balance for this reactor in terms of concentration, we again use the feet that... 

CDP1-Aa Calculate the time to consume 80% of species A in a constant-volume batch reactor for a first- and a second-order reaction. (Includes Solution] CDPl-B Derive the differential mole balance equation for a foam reactor. [2nd Ed. P1-10b]... 

For batch reactors we are interested in deterjnining how long to leave the reactants in the reactor to achieve a certain conversion X To determine this length of time, we transform the mole balance. Equation (2-5), in terms of conversion by differentiating Equation (2-4),... 

Liquid Phase. For liquid-phase reactions in which there is no volume change, concentration is the preferred variable. The mole balances are shown in Table 4-5 in terms of concentration for the four reactor types we have been discussing. We see from Table 4-5 that we have only to specify the parameter values for the system (CAo,Uo,etc.) and for the rate law (i.e., ifcyv. .3) to solve the coupled ordiaaiy differential equations for either PFR, PBR, or batch reactors or to solve the coupled algebraic equations for a CSTR. 

To outline the procedure used in the differential method of analysis, we consider a reaction carded out isothermally in a constant-volume batch reactor and the concentration recorded as a function of time. By combining the mole balance with the rate law given by Equation (5-1), we obtain... 

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