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Partial Differential Equations. Control Engineering. With these principles? Fluidization: Unit Operations 1 1 Introduction Fluidized beds are used widely in chemical processing industries for separations, rapid mass and heat transfer. Perry's Chemical Engineers' Handbook, edited by R. Perry and D. Green The Knovel scientific and engineering online database www. Smallwood, Solvent Recovery Handbook?

Perry H. Fogler, Elements of Chemical Reaction Engineering? Other units of concentration can be used as well. Often, information about flow rates is not available quite in the form that we ultimately need e.

For example, suppose that you know the value of the mass flow rate of a chemical compound with known molecular weight within a mixture, and that you also know the volumetric flow rate of that mixture. You should be sufficiently familiar with the relations in Equation 4. Furthermore, you should also be very familiar with the relations and terms in Equation 4.

Make sure you understand the concepts and units of all variables in both equations and practice writing them until you can reproduce these equations without looking at the book. Based on this information and the answers in Example 4.

How many gmol of HCl are in 88 m3 of the solution? How many gmol of HCl are flowing from the process per minute i.

What is the mass fraction of HCl in the solution? In such cases, it is necessary to convert between the various types of fractions or percentages.

The steps outlined in Figures 4. You will note that when the given composi- tions are expressed as fractions or percentages, the most convenient basis of calculation is units of mass or moles e. Example 4. From the known Using the molecular mole fractions, weights, convert the Compute the desired Assume a basis calculate the mass fractions of moles moles into mass number of moles or percentages for each species of each species Figure 4. Strategy for Converting Mole Fractions or Percentages to Mass Fractions or Percentages From the known Using the molecular mass fractions, Compute the desired Assume a basis weights, convert the calculate the mass into moles mole fractions of mass units mass of each or percentages for each species species Figure 4.

As explained in the text, we select that number because it is convenient, and because it makes it easy to calculate how many gmol of each substance are present in those gmol. Check: 0. Terms that are added together or subtracted must have the same units. Exponents must be unitless. Thus, if an exponent consists of several terms, the units of all those terms must cancel. One that has already been mentioned is that it provides a way of safeguarding against the incorrect application of conversion factors.

It also provides a check on the equation being used for the calculation, because an error in that equation might produce erroneous units for the answer e. An error in the equation might also produce a violation of the rules of dimensional consistency, which would be discovered as units are carefully monitored. For these reasons, the habit of giving careful attention to units is vital to good engineering practice, and the reader should work hard to establish that habit in all technical calculations.

Part of the rea- from the United States because of the measurement system son is cultural inertia. The current U. Given these facts, why does is ingrained into the daily lives of its citizens, and the effort the United States continue to use an inferior system?

The United States was the first coun- would be to lift a lb bag of salt. A notable exception to the lack of in- in , when France first officially adopted the metric sys- tuition concerning metric measures is the present familiarity tem, the United States made no commitment to conversion.

Since , the yard, our culture. With that exception, the American engineering pound, and so forth, have actually been defined officially in system is such a natural part of our lives, it is not some- terms of the metric system3.

The Metric Conversion Act was thing that we are looking to change. Consequently, we as passed by Congress in ; this Act established the U. Why Metric Board to coordinate and plan the increasing use and would we want to go through a difficult change when things voluntary conversion to the metric system. However, no tar- are working just fine as they are now? The Omnibus Trade and Competitiveness A second major disincentive for the United States to Act of strengthened the Metric Conversion Act, des- switch completely to the metric system is the high cost as- ignated the metric system as the preferred system of mea- sociated with such a change.

The investment of U. In , President George H. Bush issued Executive Order , requiring all federal The financial burden associated with replacing that invest- government programs to use the metric system. While num- ment is difficult to justify as an alternative to just translating bers are converted to metric units to satisfy legal require- between the American and metric systems, even though such ments, it is unclear that day-to-day operations have been im- translation can be a nuisance.

Now suspended, September Finally, as far as cultural forces go, the forces at play in 30, was the deadline set for conversion of all feder- the metric conversion issue are relatively weak, as they are ally funded highway construction to the metric system. In not connected to either the basic values or beliefs of individ- spite of the fact that the United States has been talking about uals in United States society. Cultural forces have enormous a metric system for over years, and in spite of all the impact, and it is imperative that we understand cultural is- efforts of legislative bodies and boards, conversion to the sues when attempting to effect change across the globe.

Handbook of Chemistry and Physics, D. Lide, ed. Green and R. Perry, eds. Mendenhall, T. Reprinted in Barbrow, Louis E. Washington D. In a particular 9. Two compounds, one with a high density and one with a situation, the pressure exerted on a certain surface is found to low density, are flowing at the same mass flow rate.

Identify the following parts the greater volumetric flow rate? Which has the greater mass fraction in the all base units involved mixture? Solution 1 has a greater density than does solution 2, and solution 1 also has a greater concentration of species A than 2.

In this chapter, we mention that problems arise from hav- does solution 2. For these solutions, answer each of the follow- ing at least two systems of units in the industrialized world i. In more specific terms, describe at least two such problems that a. Which will occupy greater volume: 1 kg of solution 1, you think would arise.

The length of a specimen is determined and, in the cgs sys- b. Which will contain more molecules of species A: 1 gal- tem, is represented as 3. How would this same length be lon of solution 1, or 1 gallon of solution 2? If the two solutions flow with equal volumetric flow 4. Using the material in the beginning of the textbook after rate, which stream will have the table of contents and before Chapter 1 , find and report the i. The meaning and dimensions of the symbol w f as used iii.

The equivalent of 1 Btu a unit of energy when ex- pressed in Joules J A solution of salt dissolved in water is diluted with ad- ditional water.

With each of the following variables, indicate c. The definition of 1 lb f in terms of lbm , ft, and s whether the dilution process will cause the value of the variable d. The atomic weight and symbol for the element tungsten to increase, decrease, or stay the same. Support your answer. The weight of an astronaut is measured on a distant planet b. Is his mass different on that distant planet than on Earth? What does A solution of NaOH in water flows in a stream, and the the weight difference imply about the acceleration of gravity on mass flow rate of the stream is suddenly increased.

For each of the distant planet? In an attempt to compute the number of seconds equivalent crease in flow rate will cause the property to increase, decrease, to 36 minutes, your colleague obtains for an answer 0.

In each case, explain your answer. What did your colleague do wrong? Using water and air as examples, what is an approximate b. MWNaOH d. Two compounds, one with a high molecular weight and one with a low molecular weight, are flowing at the same mass flow rate. Which has the greater molar flow rate? Perform the following conversions by determining the equiv- 6. The exhaust gas coming from a coal-burning furnace flue alent value of the given number in the new units indicated: gas usually contains sulfur in the form of SO2 , and when the a.

The reaction is d. What is the composition: equivalent value in units of H2 SO4 : 0. O2 : H2 O: 1. A gas mixture has the following percentages by mass: of this air?

The density of the solution is 1. Determine of dimensional consistency? Support your answers the value of the items requested below show your work. For parts b - d , first write out the equation using symbols for the a. A piston is movable up and down inside a vertical cylin- a. The molecular weight of the sulfuric acid der as shown below. The pressure beneath the piston is greater b. The molar flow rate of H2 SO4 into the tank than the pressure on top of the piston, and this difference in pres- c.

The mass flow rate of H2 SO4 into the tank sure can support the mass and weight of the piston according to the equation d. A stream consisting of two organic chemicals: 1 benzene where g is the acceleration of gravity and the other pertinent val- C6 H6 and 2 toluene C7 H8 , enters a separation column. The ues are shown in the drawing. For these values, how much mass lbm can the piston ing for the stream: have and be supported by these pressures? The mass flow rate of benzene b. The total molar flow rate of the stream Piston e.

That determination will require an understanding of material balances. One important principle in dealing with material balances is that total mass is con- served. Ignoring the very small conversion of mass to energy in nuclear reactions, mass will never be created or destroyed.

In other words, all mass entering a system will either leave that same system or will accumulate build up in the system. If we try to add water to a half-filled tub with the drain open, the following situations are possible: situation 1: The water will enter faster than it leaves through the drain the water level will rise — hence the water will accumulate. Unlike total mass, total moles are not always conserved, because we sometimes have chem- ical reactions taking place that change the number of total moles e.

Hence, an equation similar to Equation 5. If the process with which we are dealing is also steady-state, then nothing changes with time. For such a process, there would be no accumulation of mass in the system, because an accumulation of mass would be a change with time. For such a steady-state process, Equation 5. A more general statement of this same principle is given in Equation 5. While this idea is straightforward and may seem too simple to write in such formal terms, it is important for you to practice thinking in terms of balances that have the form of Equation 5.

At what mass flow rate must the oil be withdrawn to maintain a constant scale reading? Therefore, Equation 5. For example, in Chapter 4, we learned that mass flow rate could also be expressed in terms of density and volumetric flow rate, as shown in Equation 5.

We can substitute the equivalent forms into the steady-state mass balance to produce many variations with Equation 5. This procedure of finding the algebraic solution first is recommended because it will help you 1.

Because of its general applicability, it is a universal basis for determining some unknown input or output flow rate or density from the other flow rates and densities. These first two examples are relatively simple, and the strategy for applying the gen- eral material balance equations is somewhat intuitive. However, material-balance problems can get sufficiently complex that our intuition may not be enough to get us through the so- lution.

Here, it becomes helpful to have a stepwise strategy for solving such problems. Such a strategy is outlined below. You should discipline yourself to develop the habit of following this approach even for simple problems, so that you will instinctively do so for more complex problems where the strategy will become particularly helpful — both for the problems presented in this book and in more advanced courses.

Draw a diagram if one is not already available. Write all known quantities flow rates, densities, etc. If symbols are used to designate known quantities, include Steps for Analyzing those symbols on the diagram. Material Balance Problems 3.

Identify and assign symbols to all unknown quantities and write them in the appropriate locations on the diagram. Select a basis if needed: If no flow rates are known, assume a convenient value for one of the flow rates as a basis of calculation e.

Determine the appropriate set of equations needed to solve for the unknown quantities. In order for the problem to be solved, the number of equations must equal the number of unknowns.

The steps below can be used to obtain the desired set of equations. Construct the material balance equation s : 1. Discard terms that equal zero in your specific problem 3. Replace remaining terms with more convenient forms because of given information or selected symbols b.

Construct equations to express other known relationships between variables remember, the total number of equations must equal the number of unknowns. Solve algebraically and then numerically: Solve algebraically for the desired parameters and then determine their values.

The input to the process is orange juice that has a density of 1. Two streams are output from the process. The first output stream is the orange juice concentrate. The second is an ice slurry that has a density of 0. The diagram is shown below with the pertinent values and symbols included: Ice. V unspecified Concentrate J Step 4: No flow rates are given, so we must choose a basis of calculation.

Thus, we have a single equation and three unknowns. Additional relationships are then required. We will now consider streams containing more than one chemical compound or species in situations where we need to keep track of one or more of those species individually. Thus, we will write an entire material balance on only one compound, and then, if needed, write another entire material balance on another compound, and so on. We will call each balance on an individual compound a species balance.

As just stated, a balance can be constructed for a particular chemical compound. In that case, the formation of a compound — e. Thus Equation 5. The following example illustrates the use of Equation 5.

Also, no methane is being formed in the burner, so the rate of formation of methane equals 0. Master these relationships! For example, suppose that we are constructing a mass balance Equation 5. Obviously, the mass balance for species A can take many forms, because the equivalent forms indicated in Equation 5.

You should note that this equation is written for only one species at a time! Material balances are the key to solving a wide range of problems, including complex problems involving multiple processing units, each with its own set of input and output streams. However, in this book, we will limit the focus to material balances performed on single units with only one set of input and output streams.

In contrast with total material balances as presented in Section 5. The following sections consider 1 simple material balance problems that include formation or consump- tion but where the chemical reaction stoichiometry is not given, 2 more complex material balance problems for multiple species that do not include formation or consumption, and 3 material balance problems that include formation or consumption and where the chem- ical reaction stoichiometry is given.

Words such as consumed, formed, converted, reacted, produced, generated, absorbed, destroyed, etc. The procedure for solving this type of problem is the same as that described in the summary table entitled Steps for Analyzing Material Balance Problems in Section 5. Per that table, after drawing and labeling a diagram, we construct step 5a the general form of the material balance Equation 5. These additional balances may include a total mass balance, which is especially useful for determining a missing flow rate.

The procedure is illustrated in the example below. One such method involves continuous steady-state production in a continuously stirred tank reac- tor, where optimum penicillin production has been reported1 when both of the following are true: 1. A product stream containing penicillin leaves the reactor the bacteria stay in the reactor, and the penicillin concentration in the product stream is the same as inside the reactor.

The densities of the nutrient and product streams can be assumed to be equal. What is the production rate of penicillin under these conditions? Note: The molecular weight of this penicillin can be taken as In this problem, the species for which we need information is penicillin, so a material balance is needed for this species.

Again, the production rate being requested equals the formation rate. Therefore, another equation is needed to solve this problem. Missing flow rates often can be determined from a total material balance. For example, separation problems involve the extraction of specific com- pounds from mixtures of chemicals. For this type of problem we avoid writing the for- mation and consumption terms in Equation 5. However, we still write mass balances for the individual species of interest.

What are the toluene flow rate in the overhead output stream, and the benzene flow rate in the bottoms output stream? Column mtol. Further, because there are no chemical reactions, the formation and consumption terms in the material balance equations equal 0. Thus, we need another equation, and the obvious choice is that mass fractions must add to equal 1. Sum of mass fractions: xben. Make sure to look for these types of relationships in the problem statement. However, in problems involving a chemical reaction and where the stoichiometry of the reaction is known, it is usually more convenient to use mole balances to solve the problem.

The result is that the molecular weight of species A appears in all the terms of the material balance and can be divided out. As we will restrict ourselves to a single chemical reaction, any one species is either consumed or formed, but not both. To use these relationships, select one of the species in the reaction to be a reference species and write the stoichiometric relation- ships relative to that reference, as is shown above where species A is used as the reference species.

Once one of the formation or consumption terms is known, stoichiometric rela- tionships can be used to find all of the other formation or consumption terms for species participating in the chemical reaction. The formation or consumption rate of a particular species can be found from the material balance for that species if both the inlet and outlet flow rates are known. The conversion is the fraction of a species that reacts. The following example illustrates how to solve a material balance problem where a chemical reaction is given.

Note that we will only consider problems with a single chemical reaction. Systems with multiple units and multiple reactions will be addressed in a later course.

Also, given a chemical reaction with known stoichiometry, we will follow the recommendation to use mole balances. Therefore, we need three more equations.

Mole fractions: yeth. We now have five equations and five unknowns and can solve those equations: From Equation c : ybut. MW but. One final note of caution. Therefore, you should not write a total mole balance for a reacting system. Guidelines helpful for solving problems involving multiple species are summarized below. Note: Problems involving multiple species require species information. If information on a particular species is required, write the balance for that species first.

It may be that a single-species equation will provide enough in- Guidelines for Solving formation to solve the problem. Material Balance 3. Use species mole balances rather than mass balances if the reaction stoichiometry Problems Involving is known. Multiple Species 4. Do not attempt to balance the total number of moles for reacting systems if the reaction changes the number of moles.

A total mass balance is frequently useful to determine a missing flow rate for systems where the densities of the input and output streams are approximately constant. The constant-density assumption is applicable to liquid systems that contain a small amount small concentration of a reactant or pollutant or dis- solved substance such as a salt. Words like consumed, formed, converted, reacted, produced, generated, absorbed, destroyed, and the like in the problem statement indicate that consumption or for- mation terms are required in the material balance.

If a single species balance does not provide sufficient information to solve the problem, write additional material balances up to the total number of species. If there are still more unknowns than equations, look for additional relationships among the unknowns, such as a.

Given flow rates or ratios e. Fractions mass or mole of all species in a stream must add up to 1. Carry units as you work the problem. Calculation mistakes are frequently dis- covered as you try to work out the units. When confronted with a new problem e. Once you have identified the type of problem, you can use the specific approach needed to address that type of problem.

Finally, when solving problems using material balance equations, it is frequently nec- essary to use more than one balance to solve a given problem. For example, a balance on total mass and a balance on one of the species may both be needed to arrive at a unique solution. Or balances on two separate species e.

Wilson, Gregory L. Fundamentals of Thermodynamics by Borgnakke. Chemical Process Control by George stephanopoulos.

Reynolds, John S. Jeris, Louis Theodore. Heat and Mass Transfer by Sudheer Siddapureddy. Missen, Charles A. Mims, Bradley A. Introduction to Fluid Mechanics by Y.