Example CHEE C 8 : C 10 : lb-moles/h C 8 : C 10 : C 8 : C 10 : 0.854

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Miles Chapman
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1 Eample A feed stream containing C 8 and C hdrocarbons is split into 3 product streams: an overhead fraction, a middle cut and a bottom fraction, whose mole fraction compositions are shown below. Sevent per cent of the C 8 entering the column in the feed is recovered in the overhead. On the basis of lb-moles/h of feed determine the molar flow rates of the 3 product streams. C 8 :.56 C :.484 lb-moles/h C 8 :.35 C :.648 C 8 :.3 C :.7 C 8 :.46 C :.854 CHEE

2 Degree-of-Freedom Analsis A degree-of-freedom analsis (DFA) is a determination of the number of unknowns in a problem, and the number of independent equations that can be written. The difference between the number of unknowns and the number of independent equations is the number of degrees-offreedom, DF or n df, of the process. n df n unknowns n independent equations Possible outcomes of a DFA: n df =, there are n independent equations and n unknowns. The problem can be solved. n df >, there are more unknowns that independent equations. The problem is underspecified. n df more independent equations or specifications are needed to solve the problem. n df <, there are more independent equations than unknowns. The problem is overspecified with redundant and possibl inconsistent relations. CHEE

3 Sources of Equations Sources of equations that relate unknown process variables include:. Material balances for a nonreactive process, usuall but not alwas, the maimum number of independent equations that can be written equals the number of chemical species in the process. Process constraints given in the problem statement. Phsical constraints e.g., mass or mole fractions must add to 3. Stoichiometric relations sstems with reaction. Energ balances nd half of course CHEE 3

4 Eample F&R 4.3- An eperiment on the growth rate of certain organisms requires an environment of humid air enriched in ogen. Three input streams are fed into an evaporation chamber to produce an output stream with the desired composition. A: Liquid water, fed at a rate of. cm 3 /min B: Air ( mole% O, the balance N ) C: Pure ogen, with a molar flow rate one-fifth of the molar flow rate of stream B. The output gas is analed and is found to contain.5 mole% water. Draw and label a PFD, and calculate all unknown stream variables (i.e. flows and compositions). CHEE 4

5 CHEE 5 Independent Equations A set of equations are independent if ou cannot derive one b adding and subtracting combinations of the others. Is this set of equations independent? row reduce Rank = 3. No non-ero rows in reduced form

6 CHEE 6 Independent Equations Are these sets of equations independent?

7 Notes on DFA There are two common situations where ou will find fewer independent equations than species, and the are:. Balance around a splitter Single input two or more outputs with same composition Onl independent balance equation, since: m = m + m 3 (Overall Balance) and m = m + 3 m 3 (Balance on A) but since = = 3, these balances are not independent Splitters are used for: Purge streams (reactor sstems with reccle) Total condensers at the top of distillation columns m kg/h kg A/kg (- ) kg B/kg m kg/h Splitter kg A/kg (- ) kg B/kg m 3 kg/h 3 kg A/kg (- 3 ) kg B/kg CHEE 7

8 Notes on DFA. If two species are in the same ratio to each other wherever the appear in a process and this ratio is incorporated in the flowchart labeling, balances on those species will not be independent equations. Situation occurs frequentl when air is present in a nonreactive process ( mol% O ; 79 mol% N ) E.g., vapouriation of liquid carbon tetrachloride into an air stream n mol O /s 3.76n mol N /s n 3 mol O /s 3.76n 3 mol N /s n 4 mol CCl 4(v) /s Best to treat air as a single species in this situation n mol CCl 4(v) /s n 5 mol CCl 4(v) /s CHEE 8

9 Eample Hot soap is chilled on a roller and scraped continuousl from the roller onto a moving conveor belt which carries the soap into a drer (see below). The entering soap contains 5% water b weight. It is desired to reduce the water content to 5% b weight and to produce lb/h of nearl dr soap chips. The entering air contains.3 mole % water vapour. The drer manufacturer suggests that the drer operates efficientl when the nearl dr air/wet soap flow ratio is 3.. Calculate the unknown flowrates and compositions. Air is % ogen and 79% nitrogen (mole basis) and has a molecular weight of 9.. moist air hot, nearl dr air Soap Drer wet soap chips dried soap chips CHEE 9

10 Eample Five hundred kg/h of ternar miture (A, B, C) is being fractionated into 3 streams (Overhead, Middle and Bottom fractions ) in a distillation column. The mass fractions of components A and B in the feed are both.4, while the mass fraction of component A in the Overhead is.6, as is component C in the Bottoms. The flowrate of the Middle stream (whose mass fraction composition is.33,.6,.7 for A, B and C, respectivel) leaving the column is kg/h, while the flow of the Overhead stream is twice that of the Bottom stream. Perform a DFA on this sstem and solve the material balance. CHEE

11 Eample: Qui 9 A continuous distillation column is to be used to separate a 3-component miture of acetic acid (AA), water (W) and Benene (B), and a trial run gave the data below (mass basis). The data for the benene in the feed (which consists of AA, W and B) was not taken because of an instrument malfunction. Use a degree of freedom analsis, and then calculate the benene flow in the feed in kg/h. Waste.9% AA.7% W 67.4% B Aqueous Solution (containing 8% AA + % W) + B (data not available) Product 35 kg/h pure AA CHEE

12 Interactive Tutorial This is a good time to tr Interactive Tutorial # on the CD CHEE

Comprehend and execute the 10 elements of effective problem

Lecture 8, 3/9/2012 Chapter 7: A GENERAL Strategy for Solving Material Balance Problems Objectives: Comprehend and execute the 10 elements of effective problem Drive a flow chart and Place labels on the