Concentration outlet

Most dynamic adsorption data are obtained in the form of outlet concentrations as a function of time as shown in Figure 18a. The area iebai measures the removal of the adsorbate, as would the stoichiometric area idcai, and is used to calculate equiUbrium loading. For constant pattern adsorption, the breakthrough time and the stoichiometric time ( g), are used to calculate LUB as (1 — (107). This LUB concept is commonly used... 

In an alternative procedure (84), the electrolyte is pumped through the cells at such a rate that the outlet concentration is 50 g/L MnSO and 67 g/L H2SO4. This spent electrolyte is then mixed with equal parts of make-up solution containing 150 g/L MnSO and the mixture returned to the electrolysis step. The electrolysis is continued over a period of days and terrninated when the EMD layer deposited on the anode reaches a specific thickness, usually on the order of 1—3 or 6—8 mm. Following completion of the electrolysis cycle, the entire electrode assembly is removed from the cell for removal of the deposited EMD, either manually or by an automated system (85). The product is repeatedly washed with water to extract the occluded acid (83) and dried at about 85°C in air. 

Nonreacdive substances that can be used in small concentrations and that can easily be detected by analysis are the most useful tracers. When making a test, tracer is injected at the inlet of the vessel along with the normal charge of process or carrier fluid, according to some definite time sequence. The progress of both the inlet and outlet concentrations with time is noted. Those data are converted to a residence time distribution (RTD) that tells how much time each fracdion of the charge spends in the vessel. 

Fig. 6. Breakthrough curves for aqueous acetone (10 mg 1" in feed) flowing through exnutshell granular active carbon, GAC, and PAN-based active carbon fibers, ACF, in a continuous flow reactor (see Fig. 5) at 10 ml min" and 293 K [64]. C/Cq is the outlet concentration relative to the feed concentration. Reprinted from Ind. Eng. Chem. Res., Volume 34, Lin, S. H. and Hsu, F. M., Liquid phase adsorption of organic compounds by granular activated carbon and activated carbon fibers, pp. 2110-2116, Copyright 1995, with permission from the American Chemical Society.

Other Considerations For organic vapor HAP control applications, low outlet concentrations will typically be required, leading to impractically tall absorption towers, long contact times, and high liquid-gas ratios that may not be cost-effective. Wet scrubbers will generally be effective for HAP control when they are used in combination with other control devices such as incinerators or carbon adsorbers. 

Calculate the outlet concentration and temperature of the reactor with the following data. 

Modeling of Chemioal Kinetios and Reaotor Design Table 6-1 The reactor outlet concentration and temperature of a CFSTR with constant heat input ... 

A CONTINUOUS FLOW STIRRED TANK REACTOR OUTLET CONCENTRATION VERSUS TIME... 

Advantages (a) Low outlet concentrations possible. (b) Dilute mixtures can be treated. (c) Lots of operating data available. 

Now substitute the outlet concentration of substrate, resulting in the following equation ... 

Only the notation is different from the initial condition used for batch reactors. The subscripts in and out are used for flow reactors. The outlet concentration is found by setting z = L. 

Example 1.3 Find the outlet concentration of component A from a piston flow reactor assuming that A is consumed by a first-order reaction. 

There are only two possible values for concentration in a CSTR. The inlet stream has concentration and everywhere else has concentration The reaction rate will be the same throughout the vessel and is evaluated at the outlet concentration, SIa = A(ctout,bout, ) For the single reactions considered in this chapter, continues to be related to by the stoichiometric coefficient and Equation (1.13). With SS a known, the integral component balance, Equation (1.6), now gives useful information. For component A,... 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant cross-section) piston flow reactors. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition t = L/u. For example, the solution for component B in the competitive reaction sequence of... 

Equations (4.1) or (4.2) are a set of N simultaneous equations in iV+1 unknowns, the unknowns being the N outlet concentrations aout,bout, , and the one volumetric flow rate Qout- Note that Qom is evaluated at the conditions within the reactor. If the mass density of the fluid is constant, as is approximately true for liquid systems, then Qout=Qm- This allows Equations (4.1) to be solved for the outlet compositions. If Qout is unknown, then the component balances must be supplemented by an equation of state for the system. Perhaps surprisingly, the algebraic equations governing the steady-state performance of a CSTR are usually more difficult to solve than the sets of simultaneous, first-order ODEs encountered in Chapters 2 and 3. We start with an example that is easy but important. 

Determine all outlet concentrations, assuming constant density. 

Compare these results with those of Equation (2.22) for the same reactions in a batch reactor. The CSTR solutions do not require special forms when some of the rate constants are equal. A plot of outlet concentrations versus t is qualitatively similar to the behavior shown in Figure 2.2, and i can be chosen to maximize bout or Cout- However, the best values for t are different in a CSTR than in a PFR. For the normal case of bi = 0, the t that maximizes bout is a root-mean, t ix = rather than the log-mean of... 

Example 4.6 Use the kinetic model of Example 4.5 to determine the outlet concentration for the loop reactor if the operating conditions are the same as in Run 1. 

Compare this result with that for a single, ideal reactor having the same input concentration, throughput, and total volume. Specifically, compare the outlet concentration of the composite reactor with that from a single CSTR having a... 

Numerical calculations are the easiest way to determine the performance of CSTRs in series. Simply analyze them one at a time, beginning at the inlet. However, there is a neat analytical solution for the special case of first-order reactions. The outlet concentration from the nth reactor in the series of CSTRs is... 

Example 4.13 Determine the outlet concentration from a loop reactor as a function of Qi and q for the case where the reactor element is a PFR and the reaction is first order. Assume constant density and isothermal operation. 

The outlet concentration from the stirred tank, assuming constant physical properties and bin = 0, is given by... 

We turn now to the issue of material balance closure. Material balances can be perfect when one of the flow rates and one of the components is unmeasured. The keen experimenter for Examples 7.1 and 7.2 measured the outlet concentration of both reactive components and consequently obtained a less-than-perfect balance. Should the measured concentrations be adjusted to achieve closure and, if so, how should the adjustment be done The general rule is that a material balance should be closed if it is reasonably possible to do so. It is necessary to know the number of inlet and outlet flow streams and the various components in these streams. The present example has one inlet stream, one outlet stream, and three components. The components are A, B, and I, where I represents all inerts. 

One other type of reactor allows this in principle. Dijferential reactors are so short that concentrations and temperatures do not change appreciably from their inlet values. However, the small change in concentration makes it very hard to determine an accurate rate. The use of dilferential reactors is not recommended. If a CSTR cannot be used, a batch or piston flow reactor is preferred over a dilferential reactor even though the reaction rate is not measured directly but must be inferred from measured outlet concentrations. 

Suppose Equation (8.2) is solved either analytically or numerically to give air, z). It remains to find the average outlet concentration when the flows from all the... 

Example 8.1 Find the mixing-cup average outlet concentration for an isothermal, first-order reaction with rate constant k that is occurring in a laminar flow reactor with a parabolic velocity profile as given by Equation (8.1). 

Example 8.1 derived a specific example of a powerful result of residence time theory. The residence time associated with a streamline is t = LIVz. The outlet concentration for this streamline is ahatchit)- This is a general result applicable to diffusion-free laminar flow. Example 8.1 treated the case of a... 

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