please show all work from a to e.
3. The equations given above give very specific information about the system. Write an equation or set of equations, chosen only from the equations given above, that is equivalent to each of the following statements: a. The feed consists of 4 components, labeled A, B, C, and D. b. The system operates at steady state. c. There is no accumulation of component B in the system. d. In this process, Nc = 3, Nr = 1, and Np = 2, and the process is running at steady state. e. This process has 2 input streams and 3 output streams, and operates at steady state, with no chemical reaction. (ie inlet, outlet, generation, and consumption): NE NP ZAF, - . k=1 j=1 + + (mass of i generated by chemical reaction) - (mass of i consumed by chemical reaction) = 0 (2.1, 2.2, ...,2.Nc) In processes where there is no chemical reaction, only the first 2 types of terms are needed. 3 - General stream balances (one for each feed streams, and one for each product stream, with a term for each component in each equation), so N + Ny equations: NC Ezx=1 written once for each value of k i=1 (t.e. each feed stream) (3.1, 3.2...3.N) 5 NC (4.1, 4.2.4.N.) Ex=1 written once for each value of (1.e. each product stream) in 1 A note about zeroes here: It's not uncommon to see cases where some of the composition variables, Zix or xare = 0, and this information is known from the problem statement. But here's a pro tip-write out the full equations anyway, and then cross off the terms that are = 0 afterward. You'll see that this way you're always starting from the same set of equations, which will build "muscle memory" for writing and checking this work and also enables you to analyze different cases for the system without having to start over. Now practicel Draw a schematic diagram below of a mixing process with 2 feed streams and 1 product stream, operating at steady state at constant temperature and pressure. Let's say that there are 3 components, called A, B, and C, and you don't know how much of each is in each stream. Label all your streams with the appropriate variables, and define all the variables at the right of the diagram. operation, there should be one stream balance written for each stream into and out of the process, for a total of N + Ne balances. These equations say, "There are Nc possible components in this stream, and their names are A, B, ....etc." So it's best to include a term for each component in the system in each stream balance, and then cross off any "zero" terms later. Summation notation: Let N EM indicate the summation from a=1 to N of M." a=1 which means the sum Mi + M2 + M3 + ... + MN where M is any arbitrary variable with a total of N possible values And finally, the mass balance equations (for steady state operation)! In terms of the symbols defined above: 1 - General overall balance for a flow system operating at steady state (1 independent equation: 2 types of terms (inlet and outlet)): NF NP EFk = EP k=1 j=1 (1) Note that the way F and P, were defined above, they have units of (mass/time). Yet what "balances" is mass in and mass out. So what does Equation (1) really say? Well , when the system is operating at steady state, the amount of mass entering is given by the sum of all the feed flow rates multiplied by the time of operation, At, being analyzed. And at steady state, product streams are withdrawn from the unit during that same time interval. Thus the same At is a factor on both sides of Equation (1). and can be left out for clarity. 2- General steady state component balances (N-1 independent equations; 4 types of terms in each (i.e. inlet, outlet, generation, and consumption): NF NP Ez Fx - EXP k=1 j=1 + (mass of i generated by chemical reaction) - (mass of consumed by chemical reaction) = 0 (2.1.2.2...., 2.Nc) In processes where there is no chemical reaction, only the first 2 types of terms are needed. There are 3 types of equations that can be written for this system, and taken together, they are all required to describe the system completely. They are, 1 - Overall mass balance equation (there is only 1 overall mass balance equation per control volume) The overall mass balance equation (also called material balance or Equation of Continuity) for a system operating at steady state is in fact a mathematical statement of the Law of Conservation of Mass. The equation tells how many feed.streams enter the system and how many product streams leave the system that is, it has one term for every feed stream and one term for every product stream, for a total of Ny + Np terms. So for a system operating at steady state, the overall mass balance equation says, in total mass units, mass in = mass out (@) Note that this can also be read as "there is no net accumulation of mass in a system during steady state operation." Written in terms of rates, this is equivalent to (rate of mass entering) x (time of operation) = (rate of mass leaving) x (time of operation) 6) Note that this is not true during unsteady state operation. In that case there is an imbalance between the total mass entering and leaving over some time interval, so additional information is needed about the initial conditions of the system (specifically, how much material was in there at the start of the process) and the total capacity of the system in order to fully specify the process. (What information will that give you? Ans: It will tell you how long it will take to fill the system to capacity at the given feed flow rates, which also tells when you will start making product) 2 - Component balance equations (Nc equations, but only N.-1 are independent if written along with the overall material balance and stream balances (why? The component balances also have one term for everything that can happen to a component in the control volume, namely, it can enter in a feed, it can leave in a product stream, it can be generated by a chemical reaction, or it can be consumed by a chemical reaction. So while the overall balance takes the same form for all steady state processes, the component balances may be different for different components in the same system. In mass units, for componenti in a system operating at steady state: mass of componenti in- mass of component i out + mass of i generated - mass of i consumed = 0 or, alternatively: "rate of mass of i..." (in-out + generated - consumed) = 0 at steady state. In a non-reacting system, the generation and consumption terms are both = 0, but you still need a separate component balance for each species in the system (Why?). In a reacting system, the generation term will be zero for reactants, and the consumption term will be zero for products (Why?). 3 - Stream balances (N+Ne equations. Noterms added together in cach). A stream balance describes the contents of a given stream on its own, independent of the system or process as a whole (think about it does the composition of Feed 1 in any way depend on the composition of Feed 2? These are completely separate inputs, so each needs to be presented on its own. It identifies all of the components in each stream, and tells how much of each component is present. For steady state
