Two-phase reactor model

Chemical Reactor Modeling 905 The van Deemter Two-Phase Reactor Model... 

All of these approaches end up as two-phase reactor models by the way in which the reaction kinetics are handled, but are also sort of back door methods in that the diffusion/reaction results are added on to the reactor model. We hasten to say that there is nothing wrong with this (indeed, why is the elfectiveness factor defined in the way that it is), but separate analytical expressions will not always be available for the effectiveness factor. In such a case one has to solve the intraparticle diffusion reaction problem along with the reactor continuity equations. If one wishes a lesson in humility, this is a good place to start. 

MACRO SCALE MODELING (TWO-PHASE REACTOR MODELS)... 

This intermediate scale affords a preliminary validation of the intrinsic kinetics determined on the basis of microreactor runs. For this purpose, the rate expressions must be incorporated into a transient two-phase mathematical model of monolith reactors, such as those described in Section III. In case a 2D (1D+ ID) model is adopted, predictive account is possible in principle also for internal diffusion of the reacting species within the porous washcoat or the catalytic walls of the honeycomb matrix. 

Most of the dynamic reactor relief simulation codes, described in A4.2 above, incorporate two-phase flow models. The models vary in their ease-of-use for stand-alone calculation. The use of complex two-phase flow models within a dynamic simulation can lead to very long run-times. 

Extensive experimental determinations of overall heat transfer coefficients over packed reactor tubes suitable for selective oxidation are presented. The scope of the experiments covers the effects of tube diameter, coolant temperature, air mass velocity, packing size, shape and thermal conductivity. Various predictive models of heat transfer in packed beds are tested with the data. The best results (to within 10%) are obtained from a recently developed two-phase continuum model, incorporating combined conduction, convection and radiation, the latter being found to be significant under commercial operating conditions. 

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

Ricker, N. L. Model Predictive Control of a Continuous. Nonlinear, Two-Phase Reactor," /. Proc. Cont., 3, 109-123 (1993),... 

However, there are some situations where the one-dimensional descriptions do not work well. For example, with highly exothermic reactions, a fixed-bed reactor may contain several thousand tubes packed with catalyst particles such that djdp 5 in order to provide a high surface area per reaction volume for heat transfer. Since the heat capacities of gases are small, radial temperature gradients can still exist for highly exothermic gas-phase reactions, and these radial variations in temperature produce large changes in reaction rate across the radius of the tube. In this case, a two-dimensional reactor model is required. 

Fligner, M. Schipper, P.H. Sapre, A.V. Krambeck, F.J. Two-phase cluster model in riser reactors impact of radial density distribution on yields. Chem. Eng. Sci. 1994, 49, 5813-5818. Derouin, C. Nevicato, D. Forissier, M. Wild, G. Bernard, J. Hydrodynamics of riser units and their impact on FCC operation. Ind. Eng. Chem. Res. 1997, 36, 4504-4515. 

Cichy, P.T. Russell, T.W.F. Two-phase reactor design tubular reactors—reactor model parameters. Ind. Eng. Chem. Res. 1969, 61, 15. 

Delhaye JM, Achard JL (1978) On the use of averaging operators in two phase flow modeling Thermal and Aspects of Nuclear Reactor Safty, 1 Light Water Reactors. ASME Winter Meeting... 

Spalding DB (1981) IPSA 1981 New Developments and Computed Results. HTS/81/2, Imperial College of Science and Technology, London, 1981. Spalding DB (1985) Computer Simulation of Two-Phase Flows, with Special Reference to Nuclear-Reactor Systems. In Lewis RW, Morgan K, Johanson JA, Smith WR (eds) Computational Techniques in heat Transfer, pp. 1-44. Stewart HB, Wendroff B (1984) Two-Phase Flow Models and Methods. J Comput Phys 56 363-409... 

In spite of this enticing come-on, we will not solve this problem for the moment, being content with its illustration of a typical two-phase reactor balance formulation using the PFR model. We hasten to add, however, that the solution to the set of equations (7-140) and (7-141) with the initial and boundary conditions given is identical to that for the much simpler set of (7-54) and (7-139). In the following sections we shall pursue in detail the developments using the by-now familiar dispersion model for tubular reactors, and in Chapter 8 will treat a number of other multiphase reactor models. 

Representing the group [kgl,a/(kgl,a + hy i, the following conclusions may be drawn for a(jo < MFR performs better for alx, > PFR performs better and for a jo = the models predict identical results this is a significant conclusion because PFR is always superior to MFR in two-phase reactors. 

With the reasonable assumption that the phases in a heterogeneous mixture are in phase (physical) equilibrium for a given reactor effluent composition at the temperature and pressure to which the effluent is brought, process simulators can readily estimate the amounts and compositions of the phases in equilibrium by an isothermal (two-phase)-flash calculation, provided that solids are not present. When the possibility of two liquid phases exists, it is necessary to employ a three-phase flash model, rather than the usual two-phase flash model. The three-phase model considers the possibility that a vapor phase may also be present, together with two liquid phases. 

A pseudo-homogeneous, two-dimensional reactor model for membrane reactors consists of the total gas-phase continuity and Navier-Stokes equations augmented with gas-phase component mass balances and the overall energy balance. 

Fligner, M., Schipper, P. H., Sapre, A. V., and Krambeck, F. J., Two Phase Cluster Model in Riser Reactors Impact of Radial Density Distribution on Yields , presented at ISCRE 13, Baltimore, September 1994. 

Remarks. Close inspection of the nonequilibrium model outputs reveals that assumption of nonequilibrium capillary pressure in the studied range of experimental conditions was not necessary and static equilibrium described by PcxPg-Pe was sufficient to account for the interfacial forces [54], However, recourse to empirical capillary relationships, such as the Leverett /-function, is unnecessary as the nonequilibrium two-phase flow model enables access to capillary pressure via entropy-consistent constitutive expressions for the macroscopic Helmholtz free energies. Also, the role of mass exchange between bulk fluid phase holdups and gas-liquid interfacial area was shown to play a nonnegligible role in the dynamics of trickle-bed reactor [ 54]. By accounting for the production/destruction of interfacial area, they prompted much briefer response times for the system to attain steady state compared to the case without inclusion of these mass exchange rates. 

Hydrodynamics, mass, and heat transfer in the commonly used three-phase fixed-bed reactors were briefly outlined. Also, scale-up rules and alternative ways to scale down trickle-bed reactors are discussed. In spite of the extensive studies on the hydrodynamics, mass, and heat transfer in three-phase fixed-bed reactors, clearly, a lot of work remains to be done in providing a fundamentally based description of the effect of pressure on the parameters of importance in three-phase fixed-bed reactors operation, design, and scale-up or scale-down. It is evident that atmospheric data and models/correlations cannot, in general, be extrapolated to operation at elevated pressures. The physics conveyed by the standard two-phase flow models is minimalistic because it insufficiently describes the role and presence of interfaces and their thermodynamic properties. The explicit inclusion of interfaces and interfacial properties is essential because they are known to have a significant role in determining the thermodynamic state of the whole system. 

Roy S, Dudukovic MP, Mills PL A two-phase compartments model for the selective oxidation of n-butane in a circulating fluidized bed reactor, Catal Today 61 73—85, 2000. http //dx.doi.org/10.1016/S0920-5861 (00)00352-7. 

Fligner M, Schipper PH, Sapre AV, Krambeck FJ. Two phase cluster model in riser reactors impact of radial density distribution on yields. Chem Eng Sd 49 5813-5818, 1994. 

Hence, for deep desulfurization, a two-phase reactor (oil externally pre-saturated with H2 and solid catalyst) could be an alternative to the trickle bed. The H2-recycle is then redundant, and scale-up problems do not occur. In addition, the two-phase technology utilizes the maximum intrinsic chemical reaction rate as pore diffusion does not play a role in the slow desulfurization of refractory compounds left in predesulfurized feedstocks. For a trickle bed this rate is an upper limit, which caimot, or only hardly, be reached with regard to improper gas-liquid distribution and/or wetting of the catalyst. A laboratory-scale tricHe-bed and two-phase reactor with pre-saturation are compared in Figure 6.8.10 for a model oil. 

Cichy, P.T., J.S. Ultman and T.W.F. Russel. Two-Phase Reactor Design Tubular Reactors - Reactor Model Development 61 (1969) (No. 8) 6-26. 

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