Flow regime kinetic

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

The Flow Reactor In flow reactor experiments designed for chemical kinetic interpretation, the objective is to achieve a plug-flow situation, where composition and temperature are uniform over the cross section of the reactor. This condition may be approximated both in the turbulent [442] and the laminar [233] flow regimes. In the turbulent flow regime, a high linear flow rate secures negligible recirculation flow. Each element of gas reacts as it moves, with the characteristic time scale for heat and mass transfer by... 

To understand and ultimately to forecast the performance of a reactor, it is essential to study the coupling of "true" (intrinsic) kinetics with mass and energy transport, and to determine the flow regimes of the three phases (hydrodynamics). Modelling... 

Finally, it has to be noted that the pressure limit between the LP-CVD regime (kinetics-limited) and the AP-CVD regime (diffusion-limited) is not identical for all CVD systems. Indeed, it strongly depends on the reactor geometry (e.g., gas inlet, gas shower, laminar flow), on the thermal emissivity of the chamber components (walls, substrate holder,. ..), and on the reactivity of the precursors used for the chemical deposition of ZnO. The limit of lOTorr has been chosen here based on the results published in the literature, and should be taken only as an indication. 

The research of Roy Jackson combines theory and experiment in a distinctive fashion. First, the theory incorporates, in a simple manner, inertial collisions through relations based on kinetic theory, contact friction via the classical treatment of Coulomb, and, in some cases, momentum exchange with the gas. The critical feature is a conservation equation for the pseudo-thermal temperature, the microscopic variable characterizing the state of the particle phase. Second, each of the basic flows relevant to processes or laboratory tests, such as plane shear, chutes, standpipes, hoppers, and transport lines, is addressed and the flow regimes and multiple steady states arising from the nonlinearities (Fig. 6) are explored in detail. Third, the experiments are scaled to explore appropriate ranges of parameter space and observe the multiple steady states (Fig. 7). One of the more striking results is the... 

In the rarefied flow regime, all of these collisional mechanisms can also occur. Due to the reduced number of intermolecular collisions, however, all of the energy distributions may be in a state of nonequilibrium. This means that the rates of the kinetic processes cannot be described by the temperature-dependent forms usually employed in continuum models. Instead, models are required that describe these processes at the individual collision level. 

According to reference [1] four flow regimes for gases exist continuum flow (0iKn<0.001), slip flow (0.00l Kn<0.1), transition flow (0.l SKn<10), and free molecular flow (lOsKn). Continuum equations are valid for Kn- >0, while kinetic theory is applicable for Kn>8. Slip flow occurs when gases are at low pressure or in micro conduits. The gas slip at the surface, while in continuum flow at the surface it is immobilized. 

It must be noted here that most industrial fluidized bed reactors operate in a turbulent flow regime. Trajectory simulations of individual particles in a turbulent field may become quite complicated and time consuming. Details of models used to account for the influence of turbulence on particle trajectories are discussed in Chapter 4. These complications and constraints on available computational resources may restrict the number of particles considered in DPM simulations. Eulerian-Eulerian approaches based on the kinetic theory of granular flows may be more suitable to model such cases. Application of this approach to simulations of fluidized beds is discussed below. 

The mass-transfer coefficient depends on the geometry of the solid surface, on the hydrodynamic conditions in the vicinity of the catalyst (which are a function, e.g., of the reactor type, geometry, operating conditions, flow regime), and it also depends on the dif-fusivity of the gas species. Correlations for the mass-transfer coefficient are a large topic and outside the scope of this section. For more details see Bird, Stewart, and Lightfoot, Transport Phenomena, 2d ed., John Wiley Sons, New York, 2002, and relevant sections in this handbook. For non-first-order kinetics a closed-form relationship such as the series of resistances cannot always be derived, but the steady-state assumption of the consecutive mass and reaction steps still applies. 

The first term on the RHS in the viscosity closure denotes the kinetic contribution and dominates in the dilute regime. The second term on the RHS denotes the collisional contribution and dominates in the dense flow regime. 

This model is supposed to capture the two extreme limits of granular flow, which are designating the rapid shear and quasi-static flow regimes. In the rapid shear flow regime the kinetic stress component dominates, whereas in the quasi-static flow regime the friction stress component dominates [127]. 

Steady states for flow and for chemistry are different concepts and are often confused steady-state flow means constant directions and magnitudes of velocities steady-state chemistry means constant concentration distributions. Local equilibrium can possibly maintain a chemical steady state for reactive constituents in a transient flow regime (e.g., Ca2+ and HCCTj" in a Karst aquifer). However, if kinetics plays a significant role, e.g., the dissolution rate of feldspars or oxidation of organic carbon, then the chemical state in a transient flow field depends on competing factors of kinetic rates and velocity changes. Thus, chemical steady state may be achieved for some constituents but not others. 

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