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Chapter 4: Problem 19

L-Serine is an amino acid that often is provided when intravenous feeding solutions are used to maintain the health of a patient. It has a molecular weight of \(105,\) is produced by fermentation and recovered and purified by crystallization at \(10^{\circ} \mathrm{C}\). Yield is enhanced by adding methanol to the system, thereby reducing serine solubility in aqueous solutions. An aqueous serine solution containing 30 wt\% serine and \(70 \%\) water is added along with methanol to a batch crystallizer that is allowed to equilibrate at \(10^{\circ} \mathrm{C}\). The resulting crystals are recovered by filtration; liquid passing through the filter is known as filtrate, and the recovered crystals may be assumed in this problem to be free of adhering filtrate. The crystals contain a mole of water for every mole of serine and are known as a monohydrate. The crystal mass recovered in a particular laboratory run is \(500 \mathrm{g},\) and the filtrate is determined to be \(2.4 \mathrm{wt} \%\) serine, \(48.8 \%\) water, and \(48.8 \%\) methanol. (a) Draw and label a flowchart for the operation and carry out a degree-of- freedom analysis. Determine the ratio of mass of methanol added per unit mass of feed. (b) The laboratory process is to be scaled to produce \(750 \mathrm{kg} / \mathrm{h}\) of product crystals. Determine the required aqueous serine solution rates of aqueous serine solution and methanol.

Short Answer

Expert verified
To determine the unknowns, M/F and the scaled feed and methanol rates, the mass balances for the three components and the total mass balance need to be considered. After setting up and solving these four equations for the four unknowns, short answers can be given for the two parts of the problem. Note these depend on the numerical solutions found and will vary for different problem parameters.

Step by step solution

01

Understanding the problem and labeling

A diagram should be constructed to represent the system. The system should be divided into three main streams labelled as Feed (F), Product recuperated crystals (P) and Filtrate (E). The quantities provided by the problem should now be inserted in the-block diagram. Methanol (M) is only present in the feed and the effluent. The feed is 30 wt% amino acid (serine), 70 wt% water; the product is serine monohydrate (combination of one molecule of serine with one molecule of water; i.e., it is half serine by moles); the effluent is 2.4 wt% serine, 48.8 wt% water, and 48.8 wt% methanol.
02

Degree-of-freedom Analysis

The degree of freedom for this problem can be determined by the formula DOF = C 鈥� E + 2; where C = number of components and E = Equations linking variables in the system. In this case, we have three components (Serine, Water, Methanol). We have 2 independent balance equations (Serine and Water) plus one extra equation that Total feed = Total output. Therefore, DOF = 3 鈥� 3 + 2 = 2. This means two independent variables must be specified or two pieces of information are needed to solve this problem completely.
03

Solving for methanol addition per feed mass.

Write mass balance equations for serine and water, and solve for the methanol requirement M. The general form would be (Mass of serine or water in feed) + (Mass of serine or water in methanol) = (Mass of serine or water in filtrate) + (Mass of serine or water in product). Since there is no methanol in the product and filtrate, its mass balance will be (Mass of methanol in feed) = (Mass of methanol in filtrate). From solving these equations, you can find M/F, the ratio of mass of methanol added per unit feed.
04

Scaling and flow rate calculations.

To determine the flow rate of the aqueous serine solution and methanol for a production target of \(750 \mathrm{kg} / \mathrm{h}\), the results from the laboratory run need to be scaled up. This can be done by finding the mass percentages of product, feed and methanol from the lab run and assuming these ratios will be the same at the larger scale. Use the known target output rate to calculate the mass flow rate of aqueous serine solution and methanol required.

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Key Concepts

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

Amino Acid Crystallization
Amino acid crystallization is an essential process in chemical engineering, especially for producing high-purity L-Serine, an amino acid utilized in intravenous feeding solutions. The crystallization process here involves separating L-Serine from an aqueous mixture by including methanol, which reduces the solubility of serine. Lower solubility means serine can easily crystallize out of the solution when the temperature is reduced. In our example, the process takes place at a low temperature of 10掳C. This temperature facilitates the formation of crystals by slowing down molecular movements, permitting serine molecules to arrange themselves into a crystalline structure.

Once the crystals form, they are filtered off from the liquid phase, known as the filtrate. The fascinating aspect of this procedure is that the crystals formed contain water in a 1:1 ratio with serine molecules, classifying them as monohydrates. Understanding the nature of crystals and solubility behavior is paramount in optimizing this purification technique. This allows for maximizing the yield of serine crystals which are crucial for medical and biochemical applications.
Degree-of-Freedom Analysis
In chemical engineering, performing a degree-of-freedom (DOF) analysis is crucial for predicting whether a system can be solved or more data is needed. The DOF analysis uses the equation: \( \text{DOF} = C - E + 2 \), where \( C \) is the number of components and \( E \) is the number of independent equations. This equation tells us how many variables need to be specified to find a solution.

For our amino acid crystallization process, we consider three components: serine, water, and methanol. In the laboratory experiment, the balance includes two independent mass balance equations for serine and water. There鈥檚 also a total balance equation that assures the sum of all outputs equals the feed. The result, in this case, is that we have two degrees of freedom, meaning we need two additional pieces of information or specified variables to solve the problem entirely.

Approaching this analysis systematically helps when scaling up processes, such as determining if more methanol or other conditions need altering to refine production.
Mass Balance Equations
Understanding mass balance equations is fundamental because they ensure that mass entering a system equals mass leaving, accounting for any generation or consumption. This principle is the cornerstone of chemical engineering and is particularly useful in crystallization processes where we aim for reliability and precision.

In the L-Serine crystallization exercise, we write mass balance equations for each component. For instance, for serine, the equation would include its initial mass in the feed plus any interaction in the methanol stream equating to the mass in the filtrate and product (crystals). The balance is crucial because it outlines how much methanol should be added to achieve optimal crystallization and recovery.

Similarly, mass balance for water follows the same logic, keeping track of water in the feed, in the formed crystals, and the filtrate. Solving these equations provides insight into the system's dynamics, such as the quantity of methanol required, ensuring no methanol is left in the end product, refining both efficiency and purity in the crystallization process.

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Most popular questions from this chapter

A liquid mixture contains \(60.0 \mathrm{wt} \%\) ethanol \((\mathrm{E}), 5.0 \mathrm{wt} \%\) of a dissolved solute \((\mathrm{S}),\) and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Product 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 to contain 90.0 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 stream flows and compositions can be calculated. (Don't do any calculations yet.) (b) Calculate (i) the mass fraction of \(S\) in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., \(\mathrm{kg} \mathrm{E}\) in bottom stream/kg \(\mathrm{E}\) 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, \(x\) (kg E/kg mixture), versus analyzer reading, \(R\). The line passes through the points \((R=15, x=\) 0.100) and \((R=38, x=0.400)\). Derive an expression for \(x\) as a function of \(R(x=\cdots\) ) 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 top 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 followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between \(R_{\text {measured and }} R_{\text {prediced }}\), 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.

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.

Certain vegetables and fruits contain plant pigments called carotenoids that are metabolized in the body to produce Vitamin A. Lack of Vitamin A causes an estimated 250,000 to 500,000 children worldwide to become blind every year. An approach to reducing blindness and other childhood health problems resulting from this deficiency is to use genetic engineering of rice- -a food staple in developing countries and economically disadvantaged regions of the world \(-\) so that rice becomes a dietary source of Vitamin A. For example, a strain known as Golden Rice has been genetically engineered so that it can produce and store carotenoids such as \(\beta\) -carotene (which helps give carrots and squash their yellow-orange color). One type of Golden Rice contains approximately 30 micrograms of carotenoids (81\% \beta-carotene, 16\% \alpha- carotene, and 3\% \beta-cryptoxanthin) per gram of uncooked rice. A study has reported that when a person eats Golden Rice, their body metabolizes 1 microgram of Vitamin A for every 3.8 micrograms of \beta-carotene they consume. (a) It is recommended that children between 1 and 3 years of age should get 300 micrograms of Vitamin A per day. Considering only the metabolism of \(\beta\) -carotene given above, how many grams of Golden Rice would a child have to eat in order to obtain this much Vitamin A? Does this seem like a reasonable amount of rice to eat in one day, if one cup of cooked rice is approximately 175 g? (b) \(\alpha\) -carotene and \(\beta\) -cryptoxanthin can also be converted into Vitamin \(A\), but when compared to \beta-carotene, it takes twice as much of each of these compounds to produce one unit of Vitamin A. Considering all of the carotenoids in Golden Rice as potential sources of Vitamin A, how many grams of Golden Rice would a three-year-old child have to eat in order to obtain the recommended daily amount of Vitamin A? (c) Some individuals are not convinced that genetically modified foods are safe to grow or to eat. What kinds of risks or uncertainties are cited by these individuals? What kinds of measures are taken by farmers and suppliers of genetically modified seeds to minimize these risks? (d) Some people do not believe that Golden Rice is a practical, viable solution to Vitamin A deficiency around the world. Summarize the major arguments for and against production and distribution of Golden Rice.

Ethanol can be produced commercially by the hydration of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$$ Some of the product is converted to diethyl ether in the side reaction $$2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}$$ The feed to the reactor contains ethylene, steam, and an inert gas. A sample of the reactor effluent gas is analyzed and found to contain 43.3 mole\% ethylene, 2.5\% ethanol, 0.14\% ether, 9.3\% inerts, and the balance water. (a) Take as a basis 100 mol of effluent gas, draw and label a flowchart, and do a degree-of-freedom analysis based on atomic species to prove that the system has zero degrees of freedom. (b) Calculate the molar composition of the reactor feed, the percentage conversion of ethylene, the fractional yield of ethanol, and the selectivity of ethanol production relative to ether production. (c) The percentage conversion of ethylene you calculated should be very low. Why do you think the reactor would be designed to consume so little of the reactant? (Hint: If the reaction mixture remained in the reactor long enough to use up most of the ethylene, what would the main product constituent probably be?) What additional processing steps are likely to take place downstream from the reactor?

The fresh feed to an ammonia production process contains nitrogen and hydrogen in stoichiometric proportion, along with an inert gas (I). The feed is combined with a recycle stream containing the same three species, and the combined stream is fed to a reactor in which a low single-pass conversion of nitrogen is achieved. The reactor effluent flows to a condenser. A liquid stream containing essentially all of the ammonia formed in the reactor and a gas stream containing all the inerts and the unreacted nitrogen and hydrogen leave the condenser. The gas stream is split into two fractions with the same composition: one is removed from the process as a purge stream, and the other is the recycle stream combined with the fresh feed. In every stream containing nitrogen and hydrogen, the two species are in stoichiometric proportion. (a) Let \(x_{10}\) be the mole fraction of inerts in the fresh feed, \(f_{\mathrm{sp}}\) the single-pass conversion of nitrogen (and of hydrogen) in the reactor, and \(y_{p}\) the fraction of the gas leaving the condenser that is purged (mol purged/mol total). Taking a basis of 1 mol fresh feed, draw and fully label a process flowchart, incorporating \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}}\) in the labeling to the greatest possible extent. Then, assuming that the values of these three variables are given, write a set of equations for the total moles fed to the reactor \(\left(n_{\mathrm{r}}\right),\) moles of ammonia produced \(\left(n_{\mathrm{p}}\right),\) and overall nitrogen conversion \(\left(f_{\mathrm{ov}}\right) .\) Each equation should involve only one unknown variable, which should be circled. (b) Solve the equations of Part (a) for \(x_{10}=0.01, f_{\mathrm{sp}}=0.20,\) and \(y_{\mathrm{p}}=0.10\) (c) Briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the process design. (d) Prepare a spreadsheet to perform the calculations of Part (a) for given values of \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}} .\) Test it with the values in Part (b). Then in successive rows of the spreadsheet, vary each of the three input variables two or three times, holding the other two constant. The first six columns and first five rows of the spreadsheet should appear as follows:Summarize the effects on ammonia production \(\left(n_{\mathrm{P}}\right)\) and reactor throughput \(\left(n_{\mathrm{r}}\right)\) of changing each of the three input variables.
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