Mass Balances With Recycle Streams

Most processes involve a recycle stream. The reason is that all the reactants do not react, and businesses cannot afford to throw the rest away. Furthermore, any leftovers have to be disposed of in an environmentally friendly manner, which costs money. Thus, engineers take the unreacted reactants and put them back in the start of the process and try again. This makes the mass balances a little more complicated, and it leads to iterative methods of solution, which are described in this chapter. The hrst part of this chapter uses Excel to solve mass balances with recycle streams. Situations in which the energy balances affect the mass balance are treated in Chapters 6 and 7, because these are best done using a process simulator such as Aspen Plus . 

Introduction to Chemical Engineering Computing, by Bruce A. Finlayson Copyright 2006 John Wiley Sons, Inc. 

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Plug flow reactor (PFR) with recycle. The recycle reactor is characterized by a non-zero value of R, that is the ratio between the mass flow rate of the recycled stream and the feeding rate Q. The material balance reads for this case as... 

Mass balances are to be solved for this process. Perfect separation between methanol and the reactants is assumed. Unreacted reactants are recycled to the reactor to improve their utilization. The recycle stream within the process complicates solving the mass balances, for there is a circularity in the logic of the solution. The mass balance equations must be solved simultaneously rather than singly, or solved iteratively, as is done with a spread sheet. 

Several classification functions, C(L), are given in Figure 4.20. Here, the fraction of particles by mass reporting to the recycle stream is given as a function of particle size, L, for a screen and a cyclone. Several authors have used empirical classification functions instead of dassifier performance curves with reasonable results for the overall comminution-classification circuit control. The steady state (i.e., dmidt = 0) macroscopic population balance on a discrete mass basis over the grind-... 

If one or more unit operations have been given infeasible specifications, then the flowsheet will never converge. This problem also occurs with multicomponent distillation columns, particularly when purity specifications or flow rate specifications are used, or when nonadjacent key components are chosen. A quick manual mass balance around the column can usually determine whether the specifications are feasible. Remember that all the components in the feed must exit the column somewhere. The use of recovery specifications is usually more robust, but care is still needed to make sure that the reflux ratio and number of trays are greater than the minimum required. A similar problem is encountered in recycle loops if a component accumulates because of the separation specifications that have been set. Adding a purge stream usually solves this problem. 

Step 1 One way to solve this problem is to do a sequential solution. You start with the feed, and solve the mass balance for the mixer, labeled MIXR. Since you do not yet know the amount of A in stream S5, assume it is zero and go on. Then there is one mole of A fed to the reactor, 40 percent of it reacts, and the unreacted part is recycled into stream S5. 

The next example illustrates the use of Excel to solve mass balances for a process consisting of a feed stream, a mixer in which the feed stream is mixed with the recycle stream, and a reactor, followed by a separator where the product is removed and the reactants are recycled. In later examples and problems, there will be inerts, purge streams, and so on, but this problem uses a stoichiometric feed. The reactor is limited by chemical equilibrium considerations, which complicates the solution. 

The process is fed with three streams ethane, ethylene, and chlorine. The ethane and ethylene streams have the same molar flow rate, and the ratio of chlorine to ethane plus ethylene is 1.5. The ethane/ethylene stream also contains 1.5 percent acetylene and carbon dioxide. (For this problem, just use 1.5 percent carbon dioxide.) The feed streams are mixed with an ethylene recycle stream and go to the first reactor (chlorination reactor) where the ethane reacts with chlorine with a 95 percent conversion per pass. The product stream is cooled and ethyl chloride is condensed and separated. Assume that all the ethane and ethyl chloride go out in the condensate stream. The gases go to another reactor (hydrochlorination reactor) where the reaction with ethylene takes place with a 50 percent conversion per pass. The product stream is cooled to condense the ethyl chloride, and the gases (predominately ethylene and chlorine) are recycled. A purge or bleed stream takes off a fraction of the recycle stream (use 1 percent). Complete the mass balance for this process. 

Acrylonitrile/Butadiene/Styrene (ABS) Acry-lonitrile/butadiene/styrene (ABS) polymers are not true terpolymers. As HIPS they are multipolymer composite materials, also called polyblends. Continuous ABS is made by the copolymerization of styrene and acrylonitrile (SAN) in the presence of dissolved PB rubber. It is common to make further physical blends of ABS with different amounts of SAN copolymers to tailor product properties. Similar to the bulk continuous HIPS process, in the ABS process, high di-PB (>50%, >85% 1,4-addition) is dissolved in styrene monomer, or in the process solvent, and fed continuously to a CSTR where streams of AN monomer, recycled S/AN blends from the evaporator and separation stages, peroxide or azo initiators, antioxidants and additives are continuously metered according to the required mass balance to keep the copolymer composition constant over time at steady state. 

Next, the dichloroethane source from the chlorination operation is sent to its sink in the pyrolysis operation, which operates at 500°C. Here only 60% of the dichloroethane is converted to vinyl chloride with a byproduct of HCl, according to reaction (3.4). This conversion is within the 65% conversion claimed in the patent. To satisfy the overall material balance, 158,300 Ib/hr of dichloroethane must produce 100,000 Ib/hr of vinyl chloride and 58,300 Ib/hr of HCl. But a 60% conversion only produces 60,000 Ib/hr of vinyl chloride. The additional dichloroethane needed is computed by mass balance to equal [(1 - 0.6)/0.6] X 158,300 or 105,500 Ib/hr. Its source is a recycle stream from the separation of vinyl chlo-... 

Figure 3.40. Derivation of mass balance equations based on the concept of open loop reactors with a stream F through the whole system (balance line 2) and a recycle flow rate F. The concentration in the reactor inlet (cj is different from Ci due to recycle.

The purified isobutylene is then blended with a recycled methyl chloride stream containing a low level of isobutylene ( 5%). Finally, the comonomer, iso-prene or p-methylstyrene, is added. In this blending process, control of the ratio of comonomer to isobutylene is very important. This is because it has a significant impact on the composition of the polymer produced, the conversion of monomer, and the stability of reactor operation. For these reasons, a combination of both an analyzer and a mass balance control can be used to maintain the composition of the feed blend. The feed blend contains 20-40 wt% of isobutylene and 0.4-1.4 wt% of isoprene or 1-2 wt% of p-methylst5Tene, depending on the grade of butyl rubber to be produced the remainder is methyl chloride. 

The input/output structure defines the material balance boundary of the flowsheet Often it is referred as the inside battery limit envelope. A golden rule requires that the total mass flow of all components entering the process must be equal with the total mass flow of all components leaving it. It should be kept in mind that the recycles affect only the internal process streams, but not the input/output material balance. 

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