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Chapter 4: Problem 39

The hormone estrogen is produced in the ovaries of females and elsewhere in the body in men and postmenopausal women, and it is also administered in estrogen replacement therapy, a common treatment for women who have undergone a hysterectomy. Unfortunately, it also binds to estrogen receptors in breast tissue and can activate cells to become cancerous. Tamoxifen is a drug that also binds to estrogen receptors but does not activate cells, in effect blocking the receptors from access to estrogen and inhibiting the growth of breast-cancer cells. Tamoxifen is administered in tablet form. In the manufacturing process, a finely ground powder contains tamoxifen (tam) and two inactive fillers- -lactose monohydrate (lac) and corn starch (cs). The powder is mixed with a second stream containing water and suspended solid particles of polyvinylpymolidone (pvp) binder, which keeps the tablets from easily crumbling. The slurry leaving the mixer goes to a dryer, in which 94.2\% of the water fed to the process is vaporized. The wet powder leaving the dryer contains 8.80 wr\% tam, 66.8\% lac, 21.4\% cs, 2.00\% pvp, and 1.00\% water. After some additional processing, the powder is molded into tablets. To produce a hundred thousand tablets, 17.13 kg of wet powder is required. (a) Taking a basis of 100,000 tablets produced, draw and label a process flowchart, labeling masses of individual components rather than total masses and component mass fractions. It is unnecessary to label the stream between the mixer and the dryer. Carry out a degree-of-freedom analysis of the overall two-unit process. (b) Calculate the masses and compositions of the streams that must enter the mixer to make 100,000 tablets. (c) Why was it unnecessary to label the stream between the mixer and the dryer? Under what circumstances would it have been necessary? (d) Go back to the flowchart of Part (a). Without using the mass of the wet powder (17.13 kg) or any of the results from Part (b) in your calculations, determine the mass fractions of the stream components in the powder fed to the mixer and verify that they match your solution to Part (b). (Hint: Take a basis of \(100 \mathrm{kg}\) of wet powder.) (e) Suppose a student does Part (d) before Part (b), and re-labels the powder feed to the mixer on the flowchart of Part (a) with an unknown total mass ( \(m_{1}\) ) and the three now known mole fractions. (Sketch the resulting flowchart.) The student then does a degree-of-freedom analysis, counts four unknowns (the masses of the powder, pvp, and water fed to the mixer, and the mass of water evaporated in the dryer), and six equations (five material balances for five species and the percentage evaporation), for a net of -2 degrees of freedom. since there are more equations than unknowns, it should not be possible to get a unique solution for the four unknowns. Nevertheless, the student writes four equations, solves for the four unknowns, and verifies that all of the balance equations are satisfied. There must have been a mistake in the degree-of-freedom calculation. What was it?

Short Answer

Expert verified
The process involves mixing tam, lac, cs with pvp and water. After the drying process where 94.2% of water is evaporated, the product is a wet powder that is then molded into tablets. The masses and compositions of streams entering the mixer are calculated by using material balances and the composition of the wet powder. The stream between the mixer and dryer does not need to be labeled because its mass does not affect the calculations. The mass fractions of the mixer feed are verified by taking a new basis. A student's degree-of-freedom analysis was incorrect due to miscounting the number of unknowns; the individual masses of the mixer components were actually dependent on the total mass of the powder feed, not independent.

Step by step solution

01

Drawing a Process Flowchart

First, draw a flowchart of the process: the tamoxifen (tam), lactose monohydrate (lac), and corn starch (cs) enter the mixer, get mixed with polyvinylpyrrolidone (pvp) and water, go through a dryer where 94.2% of the water is evaporated, and leaves the dryer as wet powder (containing 8.80% tam, 66.8% lac, 21.4% cs, 2.00% pvp, and 1.00% water) that is then processed into tablets.
02

Degree-of-freedom Analysis

For the degree-of-freedom analysis, first identify the number of unknowns and equations. In this case, there are five material balances (for tam, lac, cs, pvp, and water) and one additional equation from the percentage evaporation of water, making a total of six equations. The number of unknowns can be determined from the flowchart: each stream entering the mixer has an unknown mass, the mass of water evaporated is unknown, and the total mass of the exit stream from the mixer to the dryer is also unknown. This gives a total of four unknowns. Subtracting the number of equations from the number of unknowns (\(degrees\ of\ freedom = unknowns - equations\)) gives -2 degrees of freedom, meaning that the equations are overdetermined and there is no unique solution.
03

Calculation of the Masses and Compositions of Streams

To calculate the masses and compositions of the streams that enter the mixer to make 100,000 tablets, you need to use the material balances and the composition of the wet powder that leaves the dryer. First, calculate the mass of each component in the wet powder by multiplying the total mass of the wet powder used to produce 100,000 tablets (\(17.13\ kg\)) by the mass fraction of each component. Then, set up material balances for each component to solve for the masses of the components in the streams that enter the mixer. Note that for water, you have to account for the 94.2% that is evaporated in the dryer. The composition of each stream can then be calculated by dividing the mass of each component in a stream by the total mass of that stream.
04

Explanation for Unlabeled Stream

The stream between the mixer and the dryer was not labeled as its mass was not necessary for the calculations. It would have been necessary to label it and know its mass if the problem asked for the total mass balance around the mixer or the dryer, or if the water evaporation was not given as a percentage of the water fed to the process, but as a percentage of the mass of this stream.
05

Verification of Powder Feed to the Mixer

With a new basis of 100 kg of wet powder, calculate the mass of each component in the wet powder based on their mass fractions and then use the material balances as before to solve for the masses of the components in the stream entering the mixer. The mass fractions of the components in the stream entering the mixer are then calculated by dividing the mass of each component in this stream by the total mass of this stream. Compare these mass fractions with those obtained in Step 3 to verify that they are the same.
06

Analysis of Student's Mistake

Upon re-examining the degree-of-freedom analysis on the basis set by the student in step (e), it appears that the mistake lies in counting the degrees of freedom. While it's correct to count five material balances for five species and the percentage evaporation as six equations, the count of four unknowns is incorrect. The student didn't consider that once the mass fractions are known, the individual masses of the powder, pvp, and water fed to the mixer are not independent unknowns anymore, but are dependent on the unknown total mass of the powder feed to the mixer. Therefore, there are in fact only two independent unknowns in this case: the mass of the powder feed to the mixer and the mass of water evaporated in the dryer. This gives a total of four degrees of freedom (six equations - two unknowns= four), revealing that the student's calculation of -2 degrees of freedom was indeed an error.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Material Balances in Chemical Processes
Material balances are fundamental in chemical process analysis. These balances involve calculating the input, output, and accumulation of materials within a process. Understanding material balances allows engineers to determine the flow rates of all substances at various points in a system.

In the context of the tamoxifen tablet manufacturing process, material balances help track each ingredient, including tamoxifen, lactose monohydrate, corn starch, polyvinylpyrrolidone (pvp), and water. By knowing the amounts of these materials entering and leaving different sections of the process, engineers can maintain optimal production conditions and ensure the final formulation meets specifications.

**How to Apply a Material Balance:**
  • Identify each component that enters or leaves the system.
  • Set up an equation where the total inflow equals the total outflow for each component.
  • Use known mass fractions and total mass to calculate unknown quantities.
In the given exercise, such balances are crucial for determining the precise quantity of each raw material feeds into the mixer and the composition of the exiting product.
Degree-of-Freedom Analysis Explained
Degree-of-freedom analysis is an essential technique in chemical engineering used to determine how many properties or variables in a process can be independently set. It reveals whether a process is well-defined and if there are enough equations available to solve for the unknowns.

In the tamoxifen production problem, the degree-of-freedom analysis was used to assess the overall two-unit process involving mixing and drying. The analysis determined there were more equations than unknowns, leading to equations being overdetermined, which typically means a unique solution is not possible. However, this apparent contradiction occurred due to not correctly identifying the independent variables.

**Steps in Degree-of-Freedom Analysis:**
  • List all equations available for the system (material balances, additional relationships like percentage evaporation).
  • Count all unknowns in the process.
  • Calculate degrees of freedom by subtracting the number of equations from the number of unknowns.
  • If the result is zero, the problem may be theoretically solvable; a negative result suggests an error in the setup or analysis.
Accurate degree-of-freedom analysis is crucial for ensuring each variable in the process is appropriately accounted for and can be used effectively.
Estrogen, Tamoxifen, and Cancer Treatment
Estrogen plays a significant role in various bodily functions, but it can also be a double-edged sword by potentially triggering breast cancer cells. Tamoxifen is a widely used drug in cancer treatment because it binds to estrogen receptors without activating cancer cell proliferation.

This mode of action makes tamoxifen an effective agent in inhibiting the growth of estrogen-receptor-positive breast-cancer cells. It essentially competes with estrogen, blocking its access and thereby reducing the risk of cancer progression. Such treatments are critical for patients who are particularly vulnerable to estrogen-fueled cancers, including those undergoing estrogen replacement therapy post-hysterectomy.

Understanding this balance between beneficial hormone functions and potential cancer activation is vital for developing successful treatment strategies.
Principles of Flowchart Design
Flowchart design in chemical engineering visually represents processes to help understand and optimize them. A well-designed flowchart simplifies complex data and illustrates the pathway of materials and energy through the system.

For instance, in designing a flowchart for the tamoxifen production process, the crucial components like mixers, dryers, and streams of materials (like tamoxifen, fillers, and binders) are clearly detailed. Key information, such as mass fractions and compositions, can be annotated on the flowchart to provide a clear snapshot of what is happening in the process.

**Best Practices for Effective Flowchart Design:**
  • Clearly label all streams and components.
  • Indicate directions of material flow accurately.
  • Use consistent symbols for units and equipment to avoid confusion.
  • Provide necessary detail to allow for easy understanding without overcrowding for clarity.
By adhering to these principles, engineers can use flowcharts to diagnose process issues, facilitate communication among teams, and ultimately enhance process efficiency.

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Most popular questions from this chapter

Two streams flow into a 500 -gallon tank. The first stream is 10.0 wt\% ethanol and \(90.0 \%\) hexane (the mixture density, \(\rho_{1},\) is \(0.68 \mathrm{g} / \mathrm{cm}^{3}\) ) and the second is \(90.0 \mathrm{wt} \%\) ethanol, \(10.0 \%\) hexane \(\left(\rho_{2}=0.78 \mathrm{g} / \mathrm{cm}^{3}\right) .\) After the tank has been filled, which takes 22 \(\mathrm{min}\), an analysis of its contents determines that the mixture is 60.0 wt\% ethanol, \(40.0 \%\) hexane. You wish to estimate the density of the final mixture and the mass and volumetric flow rates of the two feed streams. (a) Draw and label a flowchart of the mixing process and do the degree-of- freedom analysis. (b) Perform the calculations and state what you assumed.

Carbon nanotubes (CNT) are among the most versatile building blocks in nanotechnology. These unique pure carbon materials resemble rolled-up sheets of graphite with diameters of several nanometers and lengths up to several micrometers. They are stronger than steel, have higher thermal conductivities than most known materials, and have electrical conductivities like that of copper but with higher currentcarrying capacity. Molecular transistors and biosensors are among their many applications. While most carbon nanotube research has been based on laboratory-scale synthesis, commercial applications involve large industrial-scale processes. In one such process, carbon monoxide saturated with an organo-metallic compound (iron penta-carbonyl) is decomposed at high temperature and pressure to form CNT, amorphous carbon, and CO_. Each "molecule" of CNT contains roughly 3000 carbon atoms. The reactions by which such molecules are formed are: In the process to be analyzed, a fresh feed of CO saturated with \(\mathrm{Fe}(\mathrm{CO})_{5}(\mathrm{v})\) contains \(19.2 \mathrm{wt} \%\) of the latter component. The feed is joined by a recycle stream of pure CO and fed to the reactor, where all of the iron penta-carbonyl decomposes. Based on laboratory data, \(20.0 \%\) of the CO fed to the reactor is converted, and the selectivity of CNT to amorphous carbon production is (9.00 kmol CNT/kmol C). The reactor effluent passes through a complex separation process that yields three product streams: one consists of solid \(\mathrm{CNT}, \mathrm{C},\) and \(\mathrm{Fe} ;\) a second is \(\mathrm{CO}_{2} ;\) and the third is the recycled \(\mathrm{CO}\). You wish to determine the flow rate of the fresh feed (SCM/h), the total CO_ generated in the process ( \(\mathrm{kg} / \mathrm{h}\) ), and the ratio (kmol CO recycled/kmol CO in fresh feed). (a) Take a basis of \(100 \mathrm{kmol}\) fresh feed. Draw and fully label a process flow chart and do degree-offreedom analyses for the overall process, the fresh-feed/recycle mixing point, the reactor, and the separation process. Base the analyses for reactive systems on atomic balances. (b) Write and solve overall balances, and then scale the process to calculate the flow rate (SCM/h) of fresh feed required to produce \(1000 \mathrm{kg} \mathrm{CNT} / \mathrm{h}\) and the mass flow rate of \(\mathrm{CO}_{2}\) that would be produced. (c) In your degree-of-freedom analysis of the reactor, you might have counted separate balances for C (atomic carbon) and O (atomic oxygen). In fact, those two balances are not independent, so one but not both of them should be counted. Revise your analysis if necessary, and then calculate the ratio (kmol CO recycled/kmol CO in fresh feed). (d) Prove that the atomic carbon and oxygen balances on the reactor are not independent equations.

In the production of a bean oil, beans containing 13.0 wt\% oil and \(87.0 \%\) solids are ground and fed to a stirred tank (the extractor) along with a recycled stream of liquid \(n\) -hexane. The feed ratio is \(3 \mathrm{kg}\) hexane/kg beans. The ground beans are suspended in the liquid, and essentially all of the oil in the beans is extracted into the hexane. The extractor effluent passes to a filter where the solids are collected and form a filter cake. The filter cake contains 75.0 wt\% bean solids and the balance bean oil and hexane, the latter two in the same ratio in which they emerge from the extractor. The filter cake is discarded and the liquid filtrate is fed to a heated evaporator in which the hexane is vaporized and the oil remains as a liquid. The oil is stored in drums and shipped. The hexane vapor is subsequently cooled and condensed, and the liquid hexane condensate is recycled to the extractor. (a) Draw and label a flowchart of the process, do the degree-of-freedom analysis, and write in an efficient order the equations you would solve to determine all unknown stream variables, circling the variables for which you would solve. (b) Calculate the yield of bean oil product (kg oil/kg beans fed), the required fresh hexane feed \(\left(\mathrm{kg} \mathrm{C}_{6} \mathrm{H}_{14} / \mathrm{kg} \text { beans fed }\right),\) and the recycle to fresh feed ratio (kg hexane recycled/kg fresh feed). (c) It has been suggested that a heat exchanger might be added to the process. This process unit would consist of a bundle of parallel metal tubes contained in an outer shell. The liquid filtrate would pass from the filter through the inside of the tubes and then go on to the evaporator. The hot hexane vapor on its way from the evaporator to the extractor would flow through the shell, passing over the outside of the tubes and heating the filtrate. How might the inclusion of this unit lead to a reduction in the operating cost of the process? (d) Suggest additional steps that might improve the process economics.

A mixture of 75 mole \(\%\) methane and 25 mole \(\%\) hydrogen is burned with \(25 \%\) excess air. Fractional conversions of \(90 \%\) of the methane and \(85 \%\) of the hydrogen are achieved; of the methane that reacts, \(95 \%\) reacts to form \(\mathrm{CO}_{2}\) and the balance reacts to form CO. The hot combustion product gas passes through a boiler in which heat transferred from the gas converts boiler feedwater into steam. (a) Calculate the concentration of \(\mathrm{CO}\) (ppm) in the stack gas. (b) The CO in the stack gas is a pollutant. Its concentration can be decreased by increasing the percent excess air fed to the furnace. Think of at least two costs of doing so. (Hint: The heat released by the combustion goes into heating the combustion products; the higher the combustion product temperature, the more steam is produced.)

A liquid-phase chemical reaction \(\mathrm{A} \rightarrow \mathrm{B}\) takes place in a well-stirred tank. The concentration of \(\mathrm{A}\) in the feed is \(C_{\mathrm{A} 0}\left(\operatorname{mol} / \mathrm{m}^{3}\right),\) and that in the tank and outlet stream is \(C_{\mathrm{A}}\left(\mathrm{mol} / \mathrm{m}^{3}\right) .\) Neither concentration varies with time. The volume of the tank contents is \(V\left(\mathrm{m}^{3}\right)\) and the volumetric flow rate of the inlet and outlet streams is \(\dot{V}\left(\mathrm{m}^{3} / \mathrm{s}\right)\). The reaction rate (the rate at which \(\mathrm{A}\) is consumed by reaction in the tank) is given by the expression $$r(\text { mol } A \text { consumed } / \mathrm{s})=k V C_{\mathrm{A}}$$ (a) Is this process continuous, batch, or semibatch? Is it transient or steady-state? (b) What would you expect the reactant concentration \(C_{\mathrm{A}}\) to equal if \(k=0\) (no reaction)? What should it approach if \(k \rightarrow \infty\) (infinitely rapid reaction)? (c) Write a differential balance on \(A,\) stating which terms in the general balance equation (accumulation = input + generation - output - consumption) you discarded and why you discarded them. Use the balance to derive the following relation between the inlet and outlet reactant concentrations: $$C_{\mathrm{A}}=\frac{C_{\mathrm{A} 0}}{1+k V / \dot{V}}$$ Verify that this relation predicts the results in Part (b).
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