UNIVERSIDAD NACIONAL DE COLOMBIA SEDE MEDELLN FACULTAD DE MINAS DEPARTAMENTO DE PROCESOS Y ENERGA

MASS AND ENERGY BALANCES: 3007811-1 WORKSHOP I

Please give answer to the following problems. This set of problems has been taken from: Elementary Principles of Chemical Processes, 3rd edition, R. Felder; R. Rousseau, John Wiley & Sons, Inc. 2000

4.6 A distillation column is a process unit in which a feed mixture is separated by multiple partial vaporizations and condensations to form two or more product to streams. The overhead product stream is rich in the most volatile components of the feed mixture (the ones that vaporize most readily), and the bottom product stream is rich in the least volatile components.

The following flowchart shows a distillation column with two feed streams and three product streams:

(a) How many independent material balances may be written for this system? (b) How many of the unknown flow rates and/or mole fractions must be specified before the others may be calculated? (See Example 4.3-4. Also remember what you know about the component mole fractions of a mixture-for example, the relationship between 2x and 2y .) Briefly explain your answer. (c) Suppose values are given for 1m& and 2x . Give a series of equations, each involving only a single unknown, for the remaining variables. Circle the variable for which you would solve. (Once a variable has been calculated in one of these equations, it may appear in subsequent equations without being counted as an unknown.)

4.7 Liquid extraction is an operation used to separate the components of a liquid mixture of two or more species. In the simplest case, the mixture contains two components: a solute (A) and a liquid solvent (B). The mixture is contacted in an agitated vessel with a second liquid solvent (C) that has two key properties: A dissolves in it, and B is immiscible or nearly immiscible with it. (For example, B may be a water, C a hydrocarbon oil, and A a species that dissolves en both water and oil.) Some of the A transfers from B to C, and then the B-rich phase (the raffinate) and C-rich phase (the extract) separate from each other in a settling tank. If the raffinate is then contacted with fresh C in another stage, more A will be transferred from it. This process can be repeated until essentially all of the A has been extracted from the B.

Shown below is a flowchart of a process in which acetic acid (A) is extracted from a mixture of acetic acid and water (B) into 1-hexanol (C), a liquid immiscible with water.

(a) What is the maximum number of independent material balances that can be written for this process? (b) Calculate ,, EC mm && and Rm& , using the given mixture feed rate as a basis and writing balances in an order such that you never have an equation that involves more than one unknown variable. (c) Calculate the difference between the amount of acetic acid in the feed mixture and that in the %5.0 mixture and show that it equals amount that leaves in the %6.9 mixture. (d) Acetic acid is relatively difficult to separate completely from water by distillation (see problem 4.6) and relatively easy to separate from hexanol by distillation. Sketch a flowchart of a two-unit process the might be used to recover nearly pure acetic acid from an acetic acid-water mixture.

4.9 Strawberries contain about %15 wt solids and %85 wt water. To make strawberry jam, crushed strawberries and sugar are mixed in a 55:45 mass ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass.

(a) Draw and label a flowchart of this process. (b) Do the degree-of-freedom analysis and show that the system has zero degrees of freedom (i.e., the number of unknown process variables equals the number of equations relating them). If you have too many unknowns, think about what you might have forgotten to do.

(c) Calculate how many pounds of strawberries are needed to make a pound of jam.

4.10 Three hundred gallons of a mixture containing %75 wt ethanol (ethyl alcohol) and %25 water (mixture specific gravity 877.0= ) and a quantity of a %0.40 wt ethanol-

%0.60 water mixture (SG 952.0= ) are blended to produce a mixture containing %0.60 wt ethanol. The object of this problem is to determine 40V , the required volume

of the %40 mixture.

(a) Draw and label a flowchart of the mixing process and do the degree-of-freedom analysis. (b) Calculate 40V .

4.11 If the percentage of fuel in a fuel-air mixture falls below a certain value called the lower flammability limit (LFL), the mixture cannot be ignited. For example, the LFL of propane in air is 83%05.2 HCmole . If the percentage of propane in a propane-air mixture is greater than %05.2 mole , the gas mixture can ignite if it is exposed to a flame or spark; if the percentage is lower than LFL, the mixture will not ignite. (There is also an upper flammability limit, which for propane in air is %4.11 .) A mixture of propane in air containing 83%03.4 HCmole (fuel gas) is the feed to a combustion furnace. If there is a problem in the furnace, a stream of pure air (dilution air) is added to the fuel mixture prior to the furnace inlet to make sure that ignition is not possible.

(a) Draw and label a flowchart of the fuel gas-dilution air mixing unit, presuming that the gas entering the furnace contains propane at the LFL, and do degree-of-freedom analysis. (b) If propane flows at a rate of sHCmol /150 83 in the original fuel-air mixture, what is the minimum molar flow rate of the dilution air? (c) How would the actual dilution air feed rate probably compare with the value calculated in part (b)? ),,( = Explain.

4.12 One thousand kilograms per hour of a mixture containing equal parts by mass of methanol and water is distilled. Product streams leave the top and the bottom of the distillation column. The flow rate of the bottom stream is measured and found to be hKg /673 , and the overhead stream is analyzed and found to contain %0.96 wt methanol.

(a) Draw and label a flowchart of the process and do the degree-of-freedom analysis. (b) Calculate the mass and mole fractions of methanol and the molar flow rates of methanol and water in the bottom product stream. (c) Suppose the bottom product stream is analyzed and the mole fraction of methanol is found to be significantly higher than the value calculated in part (b). List as many possible reasons for the discrepancy as you can think of. Include in your list possible violations of assumptions made in part (b).

4.13 A pharmaceutical product, P, is made in a batch reactor. The reactor effluent goes through a purification process to yield a final product stream and a waste stream. The initial charge (feed) to the reactor and the final product are each weighed, and the reactor effluent, final product, and waste stream are each analyzed for P. The analyzer calibration is a series of meter readings, R, corresponding to known mass fractions of P,

px .

px 0.08 0.16 0.25 0.45 R 105 160 245 360

(a) Plot the analyzer calibration data on logarithmic axes and determine an expression for )(Rx p . (b) The data sheet for one run is shown below:

Batch #: 23601 Date: 10/4 Mass charged to reactor: 2253 Kg Mass of purified product: 1239 Kg Reactor effluent analysis: R=388 Final product analysis: R=583 Waste stream analysis: R=140

Calculate the mass fractions of P in all three streams. Then calculate the percentage yield of the purification process,

%100=effluentreactorinPKg

productfinalinPKgYp

(c) You are the engineer in charge of the process. You review the given run sheet and the calculations of part (b), perform additional balance calculations, and realize that all of the recorded run data cannot possibly be correct. State how you know, itemize possible causes of the problem, state which cause is most likely, and suggest a step to correct it.

4.15 A liquid mixture contains %0.60 wt ethanol (E) %0.5 wt of a dissolve solute (S), and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Products streams emerge at the top and bottom of the column. The column design calls for the product streams to have equal mass flow rates and for the top stream contain %0.90 wt ethanol and no S.

(a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown streams flows and compositions can be calculated. (Dont do any calculations yet.) (b) Calculate (i) la mass fraction of S in the bottom stream and (ii) the fraction of the ethanol in feed the leaves in the bottom product stream (i.e., Kg E in bottom stream/kg E in feed) if the process operates as designed. (c) An analyzer is available to determine the composition of ethanol-water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, )/( mixtureKgEKgx , versus analyzer reading, R. The line

passes through the points ( )100.0,15 == xR and )400.0,38( == xR . Derive an expression for x as a function of ...)( =xR based on the calibration, and use it to determine the value of R that should be obtained if the top product stream from the distillation column is analyzed. (d) Suppose a sample of the bottom stream is taken and analyzed and the reading obtained is not the one calculated in part (c). Assume that the calculation in part (c) is correct and that the plant operator fallowed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between

measuredR and predictedR , including several assumptions made when writing the balances of part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.

4.21 A dilute aqueous solution of 42SOH (Solution A) is to be mixed with a solution containing %0.90 wt 42SOH (Solution B) to produce a %0.75 wt solution (Solution C).

The flow rate and concentration of Solution A change periodically, so that it is necessary to adjust the flow rate of Solution B to keep the product 42SOH concentration constant. Flowmeters A and B have linear calibration plots of mass flow rate )(m& versus meter reading (R), which pass through the followings points:

Flowmeter A: 70,/50025,/150

==

==

AmA

AmA

RhlbmRhlbm

&

&

Flowmeter B: 60,/80020,/200

==

==

BmB

BmB

RhlbmRhlbm

&

&

The analyzer calibration is a straight line on a semilog plot of 42% SOH )(x on a logarithmic scale versus meter reading )( xR on a linear scale. The line passes through the points )0.4%,20( == xRx and ( )0.10%,100 == xRx .

(a) Calculate the flow rate of Solution B needed to process hlbm /300 of 42%55 SOH (Solution A), and the resulting flow rate of solution C. (The calibration data are not needed for this part). (b) Derive the calibration equations for )( AA Rm& , )( BB Rm& and )( xRx . Calculate the values of BA RR , , and xR corresponding to the flow rates and concentrations of part (a). (c) The process technicians job is to read Flowmeter A and the analyzer periodically, and then to adjust the flow rate of Solution B to its required value. Derive a formula that the technician can use for BR in terms of AR and xR , and then check it by substituting the values of part (a).

4.23 An artificial kidney is a device that removes water and waste metabolites from blood. In one such device, the hollow fiber hemodialyzer, blood flows from an artery through the insides of a bundle of hollow cellulose acetate fibers, and dialyzing fluid, which consists of water and various dissolved salts, flows on the outside of the fibers. Water and waste metabolites-principally urea, creatinine, uric acid and phosphate ions-pass through the fiber walls into the dialyzing fluid, and the purified blood is returned to a vein.

At some time during a dialysis the arterial and venous blood conditions are as follows:

Arterial (entering) blood

Venous (exiting) blood

Flow Rate 200,0 min/mL 195,0 min/mL Urea ( )22 NCONHH concentration 1,90 mLmg / 1,75 mLmg /

(a) Calculate the rates at which urea and water are being removed from the blood. (b) If the dialyzing fluid enters at a rate of min/1500ml and the exiting solution (dialysate) leaves at approximately the same rate, calculate the concentration of urea in the dialysate. (c) Suppose we want to reduce the patients urea level from an initial value of

mLmg /7.2 to a final value of mLmg /1.1 . If the total blood volume is 0.5 liters and the average rate of urea removal is that calculated in part (a), how long must the patient be dialyzed? (Neglect the loss in total blood volume due to the removal of water in the dialyzer.)