DFA, Multiunit Process

For more complex processes, those consisting of a single operation, it is of utmost importance that you have a method of determining if a problem is solvable at all, given the information that you have at hand. The DFA for a

100% Ethanol

96% Ethanol 4% Water

Decanter

Process flow sheet of the ethanol–water–benzene separation process.

single-unit process can be easily extended to multiunit processes. There are three ways to describe a problem in terms of its solvability:

1. If the problem has a unique set of solutions then it is called well-defined.

2. The problem is over-specified; that is, you have too much informa-tion and it is either redundant or inconsistent. It could be fixed by removing an assumption about the system that one had made.

3. The problem is under-specified; that is, you do not have enough information to solve for all your unknowns. There are several ways to deal with this. The most obvious is to gather additional infor-mation, such as measuring additional process variables (e.g., tem-peratures, flow rates, etc.), until you have a well-defined problem.

Another way is to use additional equations or information about what we want to achieve out of a process (e.g., conversion level of a reaction, efficiency of a separation unit, etc.). Finally, we can make assumptions in order to simplify the equations, and perhaps they will simplify enough that they become solvable.

Multiunit process systems are more involved in their analysis than single-unit systems, but they can be analyzed, provided a structured approach is followed. The next few steps can prove to be extremely useful:

1. Label a flowchart completely with all the relevant unknowns for all units and streams.

2. Perform a DFA on each unit operation.

3. Determine the NDF for each unit and the overall system.

Example 2.14 DFA for a Multiunit Process Problem

An absorber–stripper system is used to remove carbon dioxide and hydrogen sulfide from a feed consisting of 30% CO2 and 10% H2S in nitrogen. In the absorber, a solvent selectively absorbs hydrogen sul-fide and carbon dioxide. The absorber overhead contains only 1% CO₂ and no H₂S. N₂ is insoluble in the solvent. The rich solvent stream leav-ing the absorber is flashed, and the overhead stream consists of 20%

solvent, and contains 25% of the CO2 and 15% of the H2S in the raw feed to the absorber. The liquid stream leaving the flash unit is split into equal portions, one being returned to the absorber. The other portion, which contains 5% CO₂, is fed to the stripper. The liquid stream leav-ing the stripper consistleav-ing of pure solvent is returned to the absorber along with makeup solvent. The stripper overhead contains 30% sol-vent. Draw and completely label a flow sheet of the process and per-form a DFA.

Solution

The labeled process flow sheet is shown here (Example Figure 2.14.1).

The DFA is demonstrated in the following table:

System

Absorber Flash Stripper Splitter Mixer Overall Number of

The lowest degrees of freedom value is for the overall process. Specifying a basis will reduce its NDF to zero. There are two common situations where you will find fewer independent equations than species. They bal-ance around a divider, since the single input and two or more output streams have the same composition, thus resulting in only one indepen-dent equation (mass balance). If two species are in the same ratio to each other wherever they appear in a process and this ratio is incorporated in the flowchart labeling, balances on those species will not be indepen-dent equations. This situation occurs frequently when air is present in a nonreactive process (21 mol% O₂; 79 mol% N₂ ).

Process flow sheet of the acid gas absorption process.

Homework Problems

2.1 An ethanol–methanol–propanol stream is fed at a rate of 2000 kg/h to a distillation column. Feed is 20% methanol. Ninety percent of the methanol is to be recovered in the distillate along with 60% of ethanol.

All of the 400 kg/h of propanol fed to the process must be sent to the bottom. Draw and label the PFD and perform a DFA.

2.2 An ethanol–methanol stream fed at a rate of 100 kg/h is to be separated in a distillation column. The feed has 40 wt% ethanol and the distillate has 80% methanol by weight. Note that 80 wt% of methanol in the feed is to be recovered as distillate. Perform a DFA (Problem Figure 2.2.1).

2.3 A stream of aqueous hydrochloric acid, 57.3 wt% HCl, is mixed with pure water to produce a stream of 16.5% acid. Perform a DFA (Problem Figure 2.3.1).

Feed, F = 100 kg/h 1

2 Distillate, D = ?

3 40% Ethanol

20 wt% Ethanol

Bottom, B (kg/h) Xe Ethanol X^m Methanol 80% of methanol in

the feed is to be recovered as

distillate 60% Methanol

80 wt% Methanol

PROBLEM FIGURE 2.2.1

Ethanol–methanol separation process.

57.3% HCl

16.5% HCl Water

1 2

3

PROBLEM FIGURE 2.3.1 Mixing process.

2.4 An absorber is used to remove acetone from a nitrogen carrier gas. The feed, with acetone weight fraction 0.213, enters at a rate of 200 kg/h.

The absorbing liquid is water, which enters at a rate of 1000  kg/h.

The exit gas stream is 0.8 wt% acetone and 2.9% water vapor. Perform a DFA (Problem Figure 2.4.1).

2.5 Air containing 3% acetone and 2% water is fed to an absorber column.

The mass flow rate of air is 1000 kg/h. Pure water is used as absor-bent to absorb acetone from air. The air leaving the absorber should be free of acetone. The air leaving the absorber was found to contain 0.5% water. The bottom product of the absorber is sent to a distillation column to separate acetone from water. The bottom of the distillation column was found to contain 4% acetone, and the balance is water.

The vapor from the head of the absorber is condensed. The concentra-tion of the condensate is 99% acetone and the balance is water. Draw and label a process flowchart, and perform a DFA.

2.6 A liquid mixture containing 38 mol% benzene (B), 35.0 mol% toluene (T), and 27.0 mol% xylene (X) is fed to a distillation column. The bot-tom product contains 97.0 mol% X and the balance is T, bearing in mind that 93.0% of X in the feed is recovered in this stream. The over-head product is fed to a second column. The overover-head product from the second column contains 95 mol% B and 5.0 mol% T, bearing in mind that 96.0 mol% of the benzene fed to the system is recovered in this stream. Draw and completely label a flow sheet of the process, and perform a DFA.

2.7 A copper ore contains 1.00 wt% copper and 99.0 wt% rock. The crushed ore is mixed with a stream of fresh acid plus a recycled stream. The rock is allowed to settle out of the copper/acid solution completely.

The rock leaving this stage contains all of the rock in the ore as well

(CH₃)₂CO 0.008

as some of the copper/acid solution produced in this stage. Every 3.00 lb of rock that leaves this stage contains 1.00 lb of the copper/acid solution. It is desired that only 10% of the copper originally contained in the ore be lost in this stream. The remaining copper/acid solution, containing no rock, is sent to an electrical recovery process where pure copper is separated and a solution containing copper and acid is gen-erated. In the electrical recovery process, 90% of the copper that enters the electrical recovery process is recovered as the pure copper product.

The copper/acid solution generated in the electrical recovery process is recycled and mixed with the fresh acid stream entering the mixing stage. For every 2000 lb of ore that enters this process, draw and label the PFD.

2.8 A chemical A is to be removed from its ore. Hundred kilograms per