For liquid-phase PFRs

Computational Scheme for Liquid-Phase PFRs. The following is a procedure for solving the reactor design equations for a moderate-pressure, liquid-phase, piston flow reactor using the marching-ahead technique (Euler s method) ... 

Thus, we can make a reasonably accurate initial guess for Qp. This guess is used to calculate the conversion in a tubular reactor of the given dimensions. When the right guess is made, the mean residence time will be 2h and the fraction unreacted will be 20%. The following code follows the general procedure for liquid-phase PFRs. The fraction unreacted is calculated as the ratio of which is denoted as Phi/Philn in... 

Solution of the design equations for liquid phase PFRs is usually easier than for gas phase reactors because pressure typically has little effect on the fluid density or the reaction kinetics. Extreme pressures are an exception that theoretically can be handled by the same methods used for gas phase systems. The difficulty will be finding an equation of state. For ordinary pressures, the mass density can usually be estimated as a simple function of composition. This leads to easy and direct use of Equation 3.2. 

In this chapter, we develop the basis for design and performance analysis for a plug flow reactor (PFR). Like a CSTR. a PFR is usually operated continuously at steady-state, apart from startup and shutdown periods. Unlike a CSTR, which is used primarily for liquid-phase reactions, a PFR may be used for either gas-phase or liquid-phase reactions. 

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. 

Substituting for the given parameters k, Cao, and a, we can now use the tech niques in Chapter 2 to size the CSTRs and PFRs for liquid-phase reactions. 

TTie two reactors with recycle shown in (i) and (j) can be used for highly exothermic reactions. Here the recycle stream is cooled and returned to the reactor to dilute and cool the inlet stream thereby avoiding hot spots and runaway reactions. The PFR with recycle is used for gas-phase reactions, and the CSTR is used for liquid-phase reactions. The last (wo reactors, (k) and (I), are used for thermodynamically limited reactions where the equilibrium lies far to the left (reactant side)... 

CSTRs are generally more useful for liquid-phase reactions than PFRs since less transport power is required. However, gas-phase reactions are harder to control in a CSTR. 

For liquid-phase reactions, a single PFR or CSTR reactor is often used. For a single reaction at isothermal conditions, the volume of a PI is smaller than that of a CSTR for the same conversion and temperature. However, for (1) autocatalytic reactions, where the reaction rate depends on the concentration of a product, or (2) autothermal reactions, where the feed is cold, but the reaction is highly exothermic, the volume of a CSTR can be smaller than a PFR, such that axial dispersion in a tubular reactor may actually be beneficial. In general, a... 

The CSTR is also a hypothetical system in which there is perfect mixing so that tenperature, pressure, concentration, and reaction rate are constant over the reactor volume. Reactors approximating CSTRs are used for liquid-phase reactions. This represents a theoretical limit because perfect mixing can only be approached. Transit time for fluid elements varies. The exit stream is at the same tenperature, pressure, and conversion as the reactor contents. Feed is mixed with the reactor contents that have a high conversion. As a result, the CSTR requires a higher volume than a PFR when operated isothermally at the same tenperature and conversion for sinple, elementary reactions. 

A plug-flow reactor (PFR) may be used for both liquid-phase and gas-phase reactions, and for both laboratory-scale investigations of kinetics and large-scale production. The reactor itself may consist of an empty tube or vessel, or it may contain packing or a fixed bed of particles (e.g., catalyst particles). The former is illustrated in Figure 2.4, in which concentration profiles are also shown with respect to position in the vessel. 

Suppose the liquid-phase reaction A products is second-order, with ( rA) = kAcA, and takes place in a PFR. Show that the SFM gives the same result for 1 - fA = cAlcAo as does the integration of equation 15.2-16, the material balance. 

An exothermic first-order liquid-phase reaction A - R is conducted in a PFR. Determine the volume required for 90% conversion of A, if the process is adiabatic. 

Calculate the ratio of the volumes of a CSTR and a PFR ( Vst pf) required to achieve, for a given feed rate in each reactor, a fractional conversion (/A) of (i) 0.5 and (ii) 0.99 for the reactant A, if the liquid-phase reaction A - products is (a) first-order, and (b) second-order with respect to A. What conclusions can be drawn Assume the PFR operates isothermally at the same T as that in the CSTR. 

Using the SFM and the data from Example 19-8(b), calculate fA for the first-order, liquid-phase, isothermal reaction A - products, if kA = 0.05 s. For comparison, calculate /A for the reactor as a PFR and as a CSTR. 

Figure 6.16 displays the temperature profile and liquid-phase molar fractions for cumene and DIPB. It may be observed that the temperature is practically constant over the reactive sections with a first plateau at 200 °C and a second one at 210 °C. The top temperature is at 198 °C while the bottom temperature climbs to 242 °C. The explanation may be found in the variation of concentrations for cumene and DIPB in the liquid phase. The maximum reaction rate takes place on the stages where propylene is injected. The cumene concentration increases rapidly and reaches a flat trend corresponding to the exhaustion of the propylene in liquid phase. It may be seen that the amount of DIPB increases considerably in the second reaction zone. This variation is very different from that with a cocurrent PFR. The above variations suggest that the productivity could be improved by providing several side-stream injections and/or optimizing the distribution of catalyst activity. 

In order to approach idea PFR behavior, the flow must be turbulent. For example, with an open tube, the Reynolds number must be greater than 2100 for turbulence to occur. This flow regime is attainable in many practical situations. However, for laboratory reactors conducting liquid-phase reactions, high flow rates may not be achievable. In this case, laminar flow will occur. Calculate the mean outlet concentration of a species A undergoing a first-order reaction in a tubular reactor with laminar flow and compare the value to that obtained in a PFR when kV)/u = 1 ( = average linear flow velocity). 

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