Flow-balancing plugs

To write a force balance on the hquid stiU in the pipe as it is pushed out, we must take into account the changing mass of material. Assume the pig is weightless and fiictionless compared with the hquid in the hne. Let z be the axial position of the pig at any time. The hquid is incompressible (density p) and flows in plug flow. It exerts a frictional force proportional to the square of its velocity and to the length of pipe stiU containing hquid. 

The mass of solid catalyst is used because the amount of catalyst is what is important to the rate of product formation. For a packed tubular reactor the governing plug flow balance equations are [8] ... 

In Sec. 6-5 a non-steady-state mass balance for a tubular-flow reactor (plug flow except for axial dispersion) was used to evaluate an effective diffusivity. Now we consider the problem of calculating the conversion when a reaction occurs in a dispersion-model reactor operated at steady-state conditions. Again a mass balance is written, this time for steady state and including reaction and axial-dispersion terms. It is considered now that the axial diffusivity is known. 

Coupled mass and thermal energy balances are required to analyze the nonisother-mal response of a well-mixed continuous-stirred tank reactor. These balances can be obtained by employing a macroscopic control volume that includes the entire contents of the CSTR, or by integrating plug-flow balances for a differential reactor under the assumption that temperature and concentrations are not a function of spatial coordinates in the macroscopic CSTR. The macroscopic approach is used for the mass balance, and the differential approach is employed for the thermal energy balance. At high-mass-transfer Peclet numbers, the steady-state macroscopic mass balance on reactant A with axial convection and one chemical reaction, and units of moles per time, is... 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

DCL Axial dispersion Hydrogen mass balance Plug flow Partially backmixed Negligible Chemical (23) reaction... 

Axial dispersion Hydrogen mass and energy balance Plug-flow Partially backmixed Present Depends on the turbulence in the reactor (21) ... 

CCC Shrinking core model Sulfur balance Plug-flow Partially backmixed Absent Diffusion controlled (29) ... 

NOTE - This can be difficult as many BPCS valves are installed flow to open, and many SIS valves are installed flow to close. Actuator power requirements for an SIS valve may differ from that of a control valve. While control valves may be of double seat, balanced plug designs, SIS valves are often single seat, globe valves for reduced leakage. 

Heat Transfer in Rotary Kilns. Heat transfer in rotary kilns occurs by conduction, convection, and radiation. In a highly simplified model, the treatment of radiation can be explained by applying a one-dimensional furnace approximation (19). The gas is assumed to be in plug flow the absorptivity, a, and emissivity, S, of the gas are assumed equal (a = e ) and the presence of water in the soHds is taken into account. Energy balances are performed on both the gas and soHd streams. Parallel or countercurrent kilns can be specified. 

Product Recovery. Comparison of the electrochemical cell to a chemical reactor shows the electrochemical cell to have two general features that impact product recovery. CeU product is usuaUy Uquid, can be aqueous, and is likely to contain electrolyte. In addition, there is a second product from the counter electrode, even if this is only a gas. Electrolyte conservation and purity are usual requirements. Because product separation from the starting material may be difficult, use of reaction to completion is desirable ceUs would be mn batch or plug flow. The water balance over the whole flow sheet needs to be considered, especiaUy for divided ceUs where membranes transport a number of moles of water per Earaday. At the inception of a proposed electroorganic process, the product recovery and refining should be included in the evaluation to determine tme viabUity. Thus early ceU work needs to be carried out with the preferred electrolyte/solvent and conversion. The economic aspects of product recovery strategies have been discussed (89). Some process flow sheets are also available (61). 

Material and energy balances of a plug flow reactor are summarized in Table 7-7. 

TABLE 7-7 Material and Energy Balances of a Plug Flow Reactor (PFR)... 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

Plug Flow Reactor (PFR) The material balance over a differential vohime dV) is... 

Much of the basic theory of reaction kinetics presented in Sec. 7 of this Handbook deals with homogeneous reaclions in batch and continuous equipment, and that material will not be repeated here. Material and energy balances and sizing procedures are developed for batch operations in ideal stirred tanks—during startup, continuation, and shutdown—and for continuous operation in ideal stirred tank batteries and plug flow tubulars and towers. 

Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

Three basic fluid contacting patterns describe the majority of gas-liquid mixing operations. These are (1) mixed gas/mixed liquid - a stirred tank with continuous in and out gas and liquid flow (2) mixed gas/batch mixed liquid - a stirred tank with continuous in and out gas flow only (3) concurrent plug flow of gas and liquid - an inline mixer with continuous in and out flow. For these cases the material balance/rate expressions and resulting performance equations can be formalized as ... 

The volumetric flowrate into the plug flow is Uq and the feed concentration of A is C g- portion of A exiting from the reactor is fed back through a pump and mixed with the feed stream, referred to as R (i.e., the recycle ratio). The volumetric flowrate at the entrance of the reactor is u = UgCl + R). A balance at the mixing point M gives... 

Balanced bellows type valves are normally used where the relief valves are piped to a closed flare system and the back-pressure exceeds 10% of the set pressure, where conventional valves can t be used because back-pressure is too high. They are also used in flow lines, multiphase lines, or for ptu affinic or asphaltic crude, where pilot-operated valves can t be used due to possible plugging of the pilot line. An advantage of this type of relief valve is, for corrosive or dirty service, the bellows protects the spring from process fluid. A disadvantage is that the bellows can fatigue, which will allow process fluid to escape through the bonnet. For HjS service, the bonnet vent must be piped to a safe area. 

For a plug flow reactor, differential volume moves along the length. The following equation may express the material balance for a plug flow reactor ... 

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