Differential packed-bed reactor

Rostrup-Nielsen and Pedersen (209) recently studied sulfur poisoning of supported nickel catalysts in both methanation and Boudouard reactions by means of gravimetric and differential packed-bed reactor experiments. In their gravimetric experiments a synthesis mixture (H2/CO/He = 5/7/3) containing 1-2 ppm H2S was passed over a catalyst pellet of 13% Ni/Al203-MgO at 673 K and 1 atm. The rates of Boudouard and methanation reactions were determined from weight increases and exit methane concentrations respectively. In the presence of 2 ppm H2S a factor of 20 decrease was observed in both methanation and Boudouard rates over a period of 30-60 min. However, the selectivity or ratio of the rates for Boudouard and methanation reactions was constant with time. From these results the authors concluded that the methanation and Boudouard reactions involve the same intermediate, carbon, and that sulfur blocks the sites for the formation of this intermediate. 

An additional and important advantage of the recycle reactor, compared to the differential packed bed reactor, is that here flow uniformity through the bed is not required, so channeling is not a problem and one layer of catalyst or even separate particles can be used in the reactor. For packed bed reactors, flow nonuniformity would inhibit the application of the plug flow model. 

P5-15c The thermal decomposition of isopropyl isocyanate was studied in a differential packed-bed reactor. From the data in Table P5-15, determine the reaction law parameters. 

Stefuca et al. (1990) proposed an ET method offering a rapid, convenient, and general approach to determine kinetic constants of immobilized biocatalysts. Here, a differential reactor (DR) was used for the measurement of the initial reaction rate of sucrose hydrolysis (Vallat et al. 1986). The enzyme column of the ET has been considered as a differential packed-bed reactor, and with a mathematical model, intrinsic kinetic constants of immobilized invertase were calculated from experimental DR and ET data. 

If we consider a differential length element of our packed bed reactor (AX) and neglect the... 

Material and energy balances on plug flow and packed bed reactors are summarized in Tables 2.5 and 2.6. They are formulated on a differential reactor volume. When na is the molal flow rate of reactant A the flow reactor equation is... 

In order to illustrate this approach, we next consider the optimization of an ammonia synthesis reactor. Formulation of the reactor optimization problem includes the discretized modeling equations for a packed bed reactor, along with the set of knot placement constraints. The following case study illustrates how a differential-algebraic problem can be optimized efficiently using (27). In addition, suitable accuracy of the ODE model can be obtained at the optimum by directly enforcing error restrictions and adaptively adding elements. Finally, bounds on the continuous state profiles can be enforced directly in the optimization problem. 

Numerical Solution Techniques for Partial Differential Equations Arising in Packed Bed Reactor Modeling... 

Another potential solution technique appropriate for the packed bed reactor model is the method of characteristics. This procedure is suitable for hyperbolic partial differential equations of the form obtained from the energy balance for the gas and catalyst and the mass balances if axial dispersion is neglected and if the radial dimension is first discretized by a technique such as orthogonal collocation. The thermal well energy balance would still require a numerical technique that is not limited to hyperbolic systems since axial conduction in the well is expected to be significant. 

In simplifying the packed bed reactor model, it is advantageous for control system design if the equations can be reduced to lit into the framework of modern multivariable control theory, which usually requires a model expressed as a set of linear first-order ordinary differential equations in the so-called state-space form ... 

Continuously operated, fixed bed reactors are frequently used for kinetic measurements. Here the reactor is usually a cylindrical tube filled with catalyst particles. Feed of a known composition passes though the catalyst bed at a measured, constant flow rate. The temperature of the reactor wall is usually kept constant to facilitate an isothermal reactor operation. The main advantage of this reactor type is the wealth of experience with their operation and description. If heat and mass transfer resistances cannot be eliminated, they can usually be evaluated more accurately for packed bed reactors than for other reactor types. The reactor may be operated either at very low conversions as a differential reactor or at higher conversions as an integral reactor. 

Packed Bed Reactors The commonest vessels are cylindrical. They will have gradients of composition and temperature in the radial and axial directions. The partial differential equations of the material and energy balances are summarized in Table 7-10. Example 4 of Modeling of Chemical Reactions in Sec. 23 is an application of such equations. 

The packed bed reactors section of this volume presents topics of catalyst deactivation and radial flow reactors, along with numerical techniques for solving the differential mass and energy balances in packed bed reactors. The advantages and limitations of various models (e.g., pseudo-homogeneous vs. heterogeneous) used to describe packed bed reactors are also presented in this section. 

Packed-Bed Reactor. The derivation of the differential and integral forms of the design equations for a packed-bed reactor are analogous to those for a PFR [cf. Equations (2-15) and (2-16)). That is, substituting for Fa Equation (1-11) gives... 

The differential form of the design equation [i.e,. Equation (2-17)] must be u d when analyzing reactors that have a pressure drop along the length of the reactor. We discuss pressure drop in packed-bed reactors in Chapter 4. Integrating with the limits W = 0 at 2( = 0 gives... 

When using an ordinary differential equation (ODE) solver such as POLYMATH or MATLAB, it is usually easier to leave the mole balances, rate laws, and concentrations as separate equations rather than combining them into a single equation as we did to obtain an analytical solution. Writing She equations separately leaves it to the computer to combine them and produce a solution. The formulations for a packed-bed reactor with pressure drop and a semibatch reactor are given below for two elementary reactions. 

When one is being caixied out in a packed-bed reactor, the differential form of the mole... 

The exit volumetric flow rate from a differential packed bed containing 10 g of catalyst was maintained at 300 dmVmin for each run. The partial pressures of and CO were determined at the entrance to the reactor, and the methane concentration was measured at the reactor exit. 

For an isothermal plug flow packed bed reactor the following system of differential equations can be obtained... 

The condition of a small controlled amount of the IMB in the column allows description of the column as a reactor with a differential packed bed, which means that the reaction rate does not change along the bed. Then, the balance Eqs. (1) — (3) take the form of following difference equations ... 

Closure After completing this chapter, the reader should be able to derive differential equations describing diffusion and reaction, discuss the meaning of the effectiveness factor and its relationship to the Thiele modulus, and identify the regions of mass transfer control and reaction rate control. The reader should be able to apply the Weisz-Prater and Mears criteria to identify gradients and diffusion limitations. These principles should be able to be applied to catalyst particles as well as biomaierial tissue engineering. The reader should be able to apply the overall effectiveness factor to a packed bed reactor to calculate the conversion at the exit of the reactor. The reader should be able to describe the reaction and transport steps in slurry reactors, trickle bed reactors, fluidized-besd reactors, and CVD boat reactors and to make calculations for each reactor. 

An important embellishment to the foregoing treatment of packed-bed reactors is to allow for temperature and concentration gradients within the catalyst pellets. Intrapellet diffusion of heat and mass is governed by differential equations that are about as complex as those governing the bulk properties of the bed. See Section... 

Reaction rates were measured in the absence of MTBE in a thermostated packed-bed reactor. The reactor was fed with pure isobutene (IB) and methanol (MeOH), with a molar ratio IB/MeOH (Ri/a) between 0.5 and 2. It was operated isothermically in a differential regime, in the absence of mass transfer control. The experiments were carried out at four different temperatures in the range 318-363 K, and the pressure was kept at 1.6 MPa to assure that all the compounds involved in the reaction are in the liquid state. The sulfonic macroporous resin with a styrene-divinylbenzene matrix Bayer K2631 was used as the catalyst. The reactor inlet and outlet were analyzed by a gas chromatograph with a FID detector. Reaction rates were determined from these compositions at the steady state. 

For a heterogeneous catalytic reaction in an ideal packed-bed reactor, the material balance is written for a differential mass of catalyst, dW. The basic equation for the conversion of the key reactant A is the same as for any type of reaction, or combination of reactions, including reversible reactions. For A B-l-CorA B-l-CorA-l-B C-l-D,... 

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