Ideal reactors laminar flow

Program to calculate conversion of second-order reaction in non-ideal reactor—-segregated flow reactor and laminar flow reactor... 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

Solution The approach is similar to that in Example 3.7. The unknowns are Sl and (Em)2. Set (Poudi = (Pout) - Equation (3.40) is used to calculate iPm)2 nd Equation (3.41) is used to calculate Sl- Results are given in Table 3.2. The results are qualitatively similar to those for the turbulent flow of a gas, but the scaled reactors are longer and the pressure drops are lower. In both cases, the reader should recall that the ideal gas law was assumed. This may become unrealistic for higher pressures. In Table 3.2 we make the additional assumption of laminar flow in both the large and small reactors. This assumption will be violated if the scaleup factor is large. 

As a general rule, scaled-down reactors will more closely approach isothermal operation but will less closely approach ideal piston flow when the large reactor is turbulent. Large scaledowns will lead to laminar flow. If the large system is laminar, the scaled-down version will be laminar as well and will more closely approach piston flow due to greater radial diffusion. 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

The final idealized flow situation that we will consider is laminar flow in a tubular reactor in the absence of either radial or longitudinal diffusion. The velocity profile in such a reactor is given by... 

The F(t) curve for a laminar flow tubular reactor with no diffusion is shown in Figure 11.6. Curves for the two other types of idealized flow patterns are shown for comparison. 

Ideal flow is introduced in Chapter 2 in connection with the investigation of kinetics in certain types of ideal reactor models, and in Chapter 11 in connection with chemical reactors as a contrast to nonideal flow. As its name implies, ideal flow is a model of flow which, in one of its various forms, may be closely approached, but is not actually achieved. In Chapter 2, three forms are described backmix flow (BMF), plug flow (PF), and laminar flow (LF). 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

For any more complex flow pattern we must solve the fluid mechanics to describe the fluid flow in each phase, along with the mass balances. The cases where we can still attempt to find descriptions are the nonideal reactor models considered previously in Chapter 8, where laminar flow, a series of CSTRs, a recycle TR, and dispersion in a TR allow us to modify the ideal mass-balance equations. 

In practice, there is always some degree of departure from the ideal plug flow condition of uniform velocity, temperature, and composition profiles. If the reactor is not packed and the flow is turbulent, the velocity profile is reasonably flat in the region of the turbulent core (Volume 1, Chapter 3), but in laminar flow, the velocity profile is parabolic. More serious however than departures from a uniform velocity profile are departures from a uniform temperature profile. If there are variations in temperature across the reactor, there will be local variations in reaction rate and therefore in the composition of the reaction mixture. These transverse variations in temperature may be particularly serious in the case of strongly exothermic catalytic reactions which are cooled at the wall (Chapter 3, Section 3.6.1). An excellent discussion on how deviations from plug flow arise is given by DENBIGH and TURNER 5 . 

M 39] [P 37] Using an azo-type competitive reaction, the mixing efficiency could be determined via the selectivity [41]. Using a P-type micro mixer, laminar flow mixing could be investigated (see Figure 1.104). The selectivities measured are far from the ideal behavior of a tubular reactor. 

A graphical representation of the cumulative residence time distribution function is given in Figure 4.97 for a structured well, a laminar flow reactor and an ideal plug flow reactor assuming the same average residence time and mean velocity in each reactor. 

Obviously the characteristic distribution of the structured square, as expected, is much closer to the ideal plug flow reactor than to the laminar flow reactor. This desired behavior is a result of the channel walls, which are flow-guiding elements and pressure resistors to the flow at the same time. Two of the streamlines are projecting with a residence time of more than 0.4 s. These are the streamlines passing the area close to the wall of the distribution area, which introduces a larger resistance to these particles due to wall friction. This could, for example, be accounted for by a different channel width between the near wall channels and the central channels. 

Figure 8-22 shows the F(0) curves for laminar flow in a tubular reactor and for other idealized flow patterns. 

Fig. 3-4 Deviations from ideal tubular-flow performance (a) longitudinal mixing due to vortices and turbulence, (b) laminar-flow (poor radial mixing), (c) bypassing in fixed-bed catalytic reactor...

For reactors with known mixing characteristics the response curve and the RTD can be predicted no experiments are necessary. As an illustration let us deyelop the RTD for the plug-flow reactor, a single ideal stirred-tank reactor, and a tubular reactor with laminar flow. 

A tubular reactor with laminar flow has been mentioned as a good approximation to segregated flow. If the dispersion due to molecular diffusion is neglected, the approximation is exact. Since the flow is segregated and the velocity profile is known, the RTD can be calculated. It is instruc- tive to compare the calculated results with those for the ideal forms given in Fig. 6-5. The velocity in the axial direction for laminar flow is parabolic,... 

J d) is plotted against d/d in Fig. 6-7 also shown are the curves for the two ideal reactors, taken from Fig. 6-5. The comparison brings out pertinent points about reactor behavior. Although the plug-flow reactor might be expected to be a better representation of the laminar case than the stirred-tank reactor, the RTD for the latter more closely follows the laminar-reactor curve for 6/6 from about 0.6 to 1.5. However, there is no possibility for 6 to be less than 0.5 in the laminar-flow case. Hence the stirred-tank form is not applicable at all in the low 6 region. At high 6 the three curves approach coincidence. Conversions for these reactors are compared in Sec. 6-7. 

Denbigh has provided useful guidelines for deciding when deviations (in conversion) from ideal tubular-flow performance are significant. In laminar flow, molecular diffusion in the axial direction causes little deviation if the reactor is reasonably long with respect to its diameter. Molecular diffusion in the radial direction may be important, particularly for gases, but it serves to offset the deviation from ideal performance caused by the velocity distribution. That is, radial diffusion tends to make the reactor... 

Overview In this chapter we learn about nonideal reactors, that is, reactors that do not follow the models we have developed for ideal CSTRs, PFRs, and PBRs. In Pan I we describe how to characterize these nonideal reactors using the residence time distribution function (/), the mean residence time the cumulative distribution function Fit), and the variance a. Next we evaluate E t), F(t), and for idea) reactors, so that we have a reference proint as to how far our real (i.e., nonideal) reactor is off the norm from an ideal reactor. The functions (f) and F(r) will be developed for ideal PPRs. CSTRs and laminar flow reactors, Examples are given for diagnosing problems with real reactors by comparing and E(i) with ideal reactors. We will then use these ideal curves to help diagnose and troubleshoot bypassing and dead volume in real reactors. 

We will now determine the mean conversion predicted by the segregation model for an ideal PFR, a CSTR, and a laminar flow reactor,... 

Example 13-4 Mean Conversian Is an Ideal PER, an Ideal CSTR, and a Laminar Flow Reactor... 

Derive the equation of a Srsi-order reaction using the segregation model when the RTD is equivalent to fa) an ideal PFR, (b) an idea CSTR, and (c) a laminar flow reactor. Compare these conversions with those obtained from the design equation. 

The integral in the second term is a form of the exponential integral, normally tabulated as Ei z) [M. Abramowitz and LA. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, (1965)]. Further discussion of the ideal laminar-flow reactor with a first-order reaction is given by Cleland and Wilhelm [F.A. Cleland and R.H. Wilhelm, Amer. Inst. Chem. Eng. J., 2, 489 (1956)]. 

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