Multiple unit balances

Most processes consist of many interconnected units. In analysing such processes material balance equations may be written for each unit, for groups of units, or for the whole plant. To obtain a unique solution the number of equations describing a process must be equal to the number of unknown variables. If the analysis leads to fewer equations it is necessary to specify extra design variables. In the case of an actual plant where values of process variables are obtained by direct measurements the number of equations may exceed the number of unknowns. In such circumstances calculations should be based on the most reliable measurements. 

The notation Fj will be used to represent the total (mass) flowrate of stream j and Xj j denotes the mass fraction of component i in stream j. Component 1 is ethanol, 2, water, and 3, benzene. 

The overall balance does not give enough equations to solve for all the variables. Three more unknowns would have to be specified before this balance could be used. 

O95F3 + 001F 2 = 3 (ethanol) OO5F3 + O93F2 = 7 (water) 

Equations resulting from balance B may be solved immediately to give F2 = 7 39 kg, F3 = 2 61 kg. 

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It is assumed for the remainder of this entry that the same number of units is tested from each of the sampled locations (i.e., it is a balanced sampling plan). Regardless of what sampling plan is used to determine testing, multiple units are normally collected at each of the sample locations during validation to serve as contingency samples for possible later testing. 

Part Two of this book, which begins with this chapter, outlines procedures for writing material balances on individual process units and multiple-unit processes. In this chapter we present methods for organizing known information about process variables, setting up material balance equations, and solving these equations for unknown variables. In Chapters 5 and 6 we introduce various physical properties and laws that govern the behavior of process materials and indicate how these properties and laws are taken into account (as they must be) in formulating material balances. 

Given a process description, (a) draw and fully label a flowchart (b) choose a convenient basis of calculation (c) for a multiple-unit process, identify the subsystems for which balances might be written (d) perform the degree-of-freedom analysis for the overall system... 

The procedure for material balance calculations on multiple-unit processes is basically the same as that outlined in Section 4.3. The difference is that with multiple-unit processes you may have to isolate and write balances on several subsystems of the process to obtain enough equations to determine all unknown stream variables. When analyzing multiple-unit processes, carry out degree-of-freedom analyses on the overall process and on each subsystem, taking into account only the streams that intersect the boundary of the system under consideration. Do not begin to write and solve equations for a subsystem until you have verified that it has zero degrees of freedom. 

The rich solvent goes to a multiple-unit separation process from which three streams emerge. One—the product gas—contains 99.1 mole% C H , 0.059% HiO. and the balance CO i the... 

Set up a spreadsheet to perform material and energy balance calculations for single-unit and multiple-unit processes. 

Material balances on reactive multiple-unit processes (end of Chapter 4). 

In the next section we turn to the solution of material balance problems involving multiple units. 

Apply the first and second law to solve the material and energy balances in flow sheets that involve multiple units, and to analyze the operation of the process in terms of irreversible features and overall efficiency of energy utilization. 

Example 7.3 illustrated the technique of working forwards through a process, solving balance equations unit by unit. This is usually possible for processes without recycle streams provided that the feed is specified. If no individual balance yields enough equations it is necessary to solve simultaneously equations arising from balances on two or more units. Most multiple unit processes involve recycle streams but the treatment of these will be postponed until section 7.2.S.3. 

Additional considerations on the degrees of freedom. We already have all the tools to determine the values for NV, NMB, NSV and NK, then we can determine DF. Now we need to understand that its use has some limitations. For exampie if we have some degrees on freedom in your process, then, certainly you will be able to fix some unknown variables in your process but with some limitations. For example if a process-unit has three degrees of freedom and with one stream at the input and two streams at the output you cannot fix ail three streams arbitrarily, there is a mass balance equation that relates these three streams, then, in this case, you can fix two of these three streams. We are not implying that you cannot use all the DF, just to state that some constraints limit your freedom in the choices of values and variables used as DF. This concept wili be further analyzed and exemplified in tiie warm-up examples and reinforced in section 7.9. For example in warm-up example 2 we will show how to arralyze the degrees of freedom in a multiple unit process including a side-stream. 

Stoichiometry - Conversions Using Balanced Equations http //www.youtube.com/watch v=wySZDEbqbnM Two Continuous Stirred Tank Reactors in Series http //www.youtube.com/watch v=7RLQ9sHkdkk Balances on Multiple Units with Reaction https //www.youtube.com/watch v=tQyrSvll nc Extent of Reaction for Material Balances https //www.youtube.com/watch v=YusSUOjlOUk Three Methods for Solving Reactive Material Balances https //www.youtube.com/watch v=MSzTIRAv5io... 

Because each effect of an evaporator produces almost as much vapor as the amount it condenses, the total evaporation accompHshed per unit of prime steam, or steam economy, iacreases ia almost direct proportioa to the number of effects used. The total heat load is also spHt up betweea the effects so that each effect has a much lower heat duty than a single effect for the same total evaporation load. However, the total available AT is also spHt up similarly so that each effect of a multiple effect requites about as much heating surface as a single effect operating over the same total temperature difference. Thus ia selecting the number of effects to use ia any iastallatioa, steam cost savings and capital cost of effects have to be balanced. Even before... 

If the CH balance given by the CH multiplicities differs from the number of H atoms in the molecular formula, then the additional H atoms are bonded to heteroatoms. The C NMR spectra in Fig. 2.5 show, for example, for isopinocampheol (2), Cio// 0, a quaternary C atom (C), four CH units (C4//4), two CH2 units C2H4) and three CH3 groups (C3//5). In the C//balance, Cvfln, one H is missing when compared with the molecular formula, Cio// 0 to conclude, the compound contains one OH group. 

One would notice that there are a number of nonlinearities in the above constraints, more specifically in the contaminant mass balances around a unit and the central storage vessel. The nonlinearities arise due to the fact that the outlet concentration of each contaminant may not necessarily be at its respective maximum. Unlike the single contaminant case where one could replace the outlet concentration with the maximum outlet concentration, in the multiple contaminant case the outlet concentration of each contaminant remains a variable. Furthermore, the concentration within the central storage vessel is always variable, since the contaminant mass and mass of water within the vessel changes each time a stream enters or exits the vessel. To deal with this situation the following procedure is considered. 

Now we will return briefly to Sections 3.8-3.11 and 4.6-4.8 where we considered the general problem of multiple flows, here of H, C, N, O, S and P. We observe immediately that all the products are from the same small molecule environmental sources and are required to be formed in relatively fixed amounts using the same source of energy and a series of intermediates. Controlling all the processes to bring about optimum cellular production are feedbacks between them and linked with the code which generates proteins, and here we note particularly enzymes, i.e. catalysts. The catalysts are made from the amino acids, the synthesis of which they themselves manage, while the amino acids control the catalysts so as to maintain a restricted balanced set of reaction pathways in an autocatalytic assembly. It is also the feedback controls on both the DNA (RNA) from the same units used in the... 

One important component of any evaporator installation is the equipment for condensing the vapour leaving the last effect of a multiple-effect unit, achieved either by direct contact with a jet of water, or in a normal tubular exchanger. If M is the mass of cooling water used per unit mass of vapour in a jet condenser, and H is the enthalpy per unit mass of vapour, then a heat balance gives ... 

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