Volumetric flow tubular reactors

For plug flow, only the flow and the processes other than mixing, diffusion, and conduction are considered. These have been studied in Chapter 4. In a plug flow tubular reactor model we consider only the convective one-dimensional flow and the chemical reaction as shown in Figure 5.1, where n is the convective molar flow rate for the constant volumetric flow rate g of component i. These two rates are connected by the equation rq = q Ci for the concentration Cj. 

One of the simplest models used to describe the performance of tubular reactors is the well-known isothermal one-dimensional plug flow tubular reactor (PFTR) model. The mass balance of this model for steady-state conditions, the simultaneous occurrence of M reactions and a constant volumetric flow rate V is ... 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

Step 24. Calculate the outlet conversion of reactant A in an ideal plug-flow tubular reactor with pseudo-volumetric first-order kinetics and no residence-time distribution effects ... 

For a batch reactor, the reaction time t is the natural performance measure. For flow reactors, the residence time r is used, which is defined as the ratio of the reactor volume to the volumetric flow rate at reaction conditions. In mixed flow reactors, r represents a mean value because the residence time of the fluid elements is distributed. Only for plug flow tubular reactors is the residence time the same for all fluid elements. For heterogeneously catalyzed or gas-solid reactions it is convenient to use a (mean) modified residence time related to the mass of catalyst or solid. 

Set the volumetric flow rate and feed concentration for the tank and tubular reactors to desired values. Set also the order of reaction to n = 1.01. Run for a range of fraction conversions from 0 to 0.99. Compare the required volumes for the two reactor types. 

The molar flow rate of a species in a flow reactor is Fj = vCj. The batch reactor is a closed system in which v = 0. The volumetric flow rate is ti, while thelinear velocity in a tubular reactor is u, We usually assume that the density of the fluid in the reactor does not change with conversion or position in the reactor (the constant-density reactor) because the equations for a constant-density reactor are easier to solve. 

The volumetric flow rate into the reactor system (tubular reactor and associated pipes for recycle) is Vg and the feed concentration is C q as before. However, a portion of the exit stream from the reactor is fed back and mixed with the feed stream. We call this portion R the recycle ratio. (Note that in this section we use R as recycle ratio while everywhere else R means tube radius.) The volumetric flow rate into the reactor is now... 

There is, however, another way of looking at a tubular reactor in which plug flow occurs (Fig. 1.15). If we imagine that a small volume of reaction mixture is encapsulated by a membrane in which it is free to expand or contract at constant pressure, it will behave as a miniature batch reactor, spending a time r, said to be the residence time, in the reactor, and emerging with the conversion aA/. If there is no expansion or contraction of the element, i.e. the volumetric rate of flow is constant and equal to v throughout the reactor, the residence time or contact time... 

The tubular reactor will be modelled like a PFR and for simplicity we are going to consider no change in volumetric flow rate due to reaction in other words, the inlet volumetric flow rate and the outlet volumetric flow rate are considered the same, V. Again we are going to consider first-order kinetics. We are going to represent the recycle volumetric flow by (RV), where R = (recycle volumetric flow/outlet volumetric flow) and is called recycle ratio . 

The feed to the reactor consists of two streams. One. stream is an equivolu-mctric mixture of propylene oxide and mcihanoU and the other stream is water containing 0.1 wt % sulfuric acid. The water is fed at a volumetric rate 2.5 limes larger than the propylene oxide-methanol feed. The molar flow rate of propylene oxide fed to the tubular reactor is 0.1 mol/s. 

It is possible to use solid catalysts in particulate forms in tubular reactors through the use of fluidised or fluid bed reactors, where the upward flow of the feed is sufficient to suspend the particulate catalyst in such a way that it seems to behave like a liquid (Figure 1.3). It is however preferable to use more structured catalysts, since better flow characteristics can be achieved, thus minimising hydrodynamic uncertainties and maximising volumetric reaction rates. 

Suppose an inert material is transpired into a tubular reactor in an attempt to achieve isothermal operation. Suppose the transpiration rate q is independent of z and that qL = Qtrims- Assume all fluid densities to be constant and equal. Find the fraction unreacted for a first-order reaction. Express your final answer as a function of the two dimensionless parameters Qaans/Qin and kV/gm, where k is the rate constant and gin is the volumetric flow rate at z = 0 (i.e., gout = gin + gtims)- Hint The correct formula gives aout/ in =... 

The reactions were performed in a vapour phase tubular quartz reactor packed with the catalyst (stationary bed) and heated in a shell oven under nitrogen at the test temperature. After thermal equilibria had been reached, nitrogen and HCFC were introduced via volumetric flow meters. Water was introduced with the aid of a syringe. The reaction products were collected after an initial 30 minute period of conditioning and were analysed by gas chromatography. The stationary phase used for analysis was a poraplot Q on silica (column length 10 m, diameter 0,32 mm). 

This problem requires an analysis of coupled thermal energy and mass transport in a differential tubular reactor. In other words, the mass and energy balances should be expressed as coupled ordinary differential equations (ODEs). Since 3 mol of reactants produces 1 mol of product, the total number of moles is not conserved. Hence, this problem corresponds to a variable-volume gas-phase flow reactor and it is important to use reactor volume as the independent variable. Don t introduce average residence time because the gas-phase volumetric flow rate is not constant. If heat transfer across the wall of the reactor is neglected in the thermal energy balance for adiabatic operation, it... 

The heterogeneous rate law in (22-57) is dimensionalized with pseudo-volumetric nth-order kinetic rate constant k that has units of (volume/mol)" per time. k is typically obtained from equation (22-9) via surface science studies on porous catalysts that are not necessarily packed in a reactor with void space given by interpellet. Obviously, when axial dispersion (i.e., diffusion) is included in the mass balance, one must solve a second-order ODE instead of a first-order differential equation. Second-order chemical kinetics are responsible for the fact that the mass balance is nonlinear. To complicate matters further from the viewpoint of obtaining a numerical solution, one must solve a second-order ODE with split boundary conditions. By definition at the inlet to the plug-flow reactor, I a = 1 at = 0 via equation (22-58). The second boundary condition is d I A/df 0 as 1. This is known classically as the Danckwerts boundary condition in the exit stream (Danckwerts, 1953). For a closed-closed tubular reactor with no axial dispersion or radial variations in molar density upstream and downstream from the packed section of catalytic pellets, Bischoff (1961) has proved rigorously that the Danckwerts boundary condition at the reactor inlet is... 

The objective of this problem is to calculate reactant conversion in the exit stream of a packed catalytic tubular reactor. The chemical kinetics are irreversible and first-order. The reactor is packed with catalysts that are spherically symmetric. The following data are available. Be careful with units, because the kinetic rate constant and the volumetric flow rate are given in minutes, whereas the net intrapeiiet diffusivity is given in seconds. 

Total gas-phase volumetric flow rate = 10 L/min = 10,000 cm /min Diameter of the tubular reactor = 20 cm Interpellet porosity of the packed bed = 0.25... 

The dilemma can be summarized as follows. Plug-flow mass and thermal energy balances in a packed catalytic tubular reactor are written in terms of gas-phase concentrations and temperature of the bulk fluid phase. However, the volumetrically averaged rate of reactant consumption within catalytic pellets is calculated via concentrations and temperature on the external surface of the pellets. When external transport resistances are negligible, design of these reactors is simplified by equating bulk gas-phase conditions to those on the external catalytic surface. In this chapter, we address the dilemma when bulk gas-phase conditions are different from those on the external surface of the pellet. The logical sequence of calculations is as follows ... 

For plug flow reactors all fluid elements take the same length of time to travel from the reactor inlet to the reactor outlet. This time is the mean residence time 1. Consider the general case of a reaction accompanied by a volumetric expansion or contraction. The average time necessary for a plug to travel from inlet to outlet of a tubular reactor is given by... 

These researchers also indicated that for temperatures from 483 to 523 K, the activation energy for this reaction is 41.7 kcal/mol. Use these data to ascertain the temperature at which a plug flow reactor should be operated if one desires to decompose 98% of a pure barrelene feedstock when the barrelene enters the reactor at 2 atm. Barrelene is to be supplied at a volumetric flow rate of 10 / min to a tubular... 

Determine the volumetric flow rate that maximizes the effluent concentration of monoethyl adipate if the mbular reactor is operated at a temperature of 80°C. The feed stream is 0.018 M in diethyl adipate and 0.050 M in sodium hydroxide. The tubular reactor is 6 ft long and has an internal diameter of 1.25 in. Will the relative yield of monoethyl adipate increase or decrease if the reactor is operated at a higher temperature ... 

The irreversible enzyme-catalyzed reaction 2A B -I- C is to be carried out in the hquid phase in a tubular reactor. The feedstock contains A at a concentration of300 g/L and enters at a temperature of 25°C. The density of the feed stream is 0.95 kg/L and its volumetric flow rate is 0.8 m /h. Thermochemical data indicate that at 25°C, the standard heat of reaction is -200 cal/g of A reacting. Experimental measurements indicate that the heat capacity of the liquid is essentially 0.92 cal/(g-°C), regardless of the extent of reaction. Bench-scale measurements indicate that over the temperature range of interest, the dependence of the first-order rate constant on temperature is given by k = 3.0 -I- 0.6(r - 25) for k in h" and T in °C. 

Example 3.7 Determination of the volume of an ideal tubular flow reactor The reaction of Example 3.3 is to take place in a TER under adiabatic conditions. The volumetric flow amounts to Vq = 1 m. What is the necessary volume of the reactor It is assumed that the adiabatic temperature rise is constant in the entire reactor and amounts to AT = 27.13 K. 

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