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Chapter 4: Problem 76

Methanol is produced by reacting carbon monoxide and hydrogen. A fresh feed stream containing \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) joins a recycle stream and the combined stream is fed to a reactor. The reactor outlet stream flows at a rate of \(350 \mathrm{mol} / \mathrm{min}\) and contains \(10.6 \mathrm{wt} \% \mathrm{H}_{2}, 64.0 \mathrm{wt} \% \mathrm{CO},\) and \(25.4 \mathrm{wt} \% \mathrm{CH}_{3} \mathrm{OH} .\) (Notice that those are percentages by mass, not mole percents.) This stream enters a cooler in which most of the methanol is condensed. The liquid methanol condensate is withdrawn as a product, and the gas stream leaving the condenser- -which contains \(\mathrm{CO}, \mathrm{H}_{2},\) and \(0.40 \mathrm{mole} \%\) uncondensed \(\mathrm{CH}_{3} \mathrm{OH}\) vapor \(-\mathrm{is}\) the recycle stream that combines with the fresh feed. (a) Without doing any calculations, prove that you have enough information to determine (i) the molar flow rates of CO and \(\mathrm{H}_{2}\) in the fresh feed, (ii) the production rate of liquid methanol, and (iii) the single-pass and overall conversions of carbon monoxide. Then perform the calculations. (b) After several months of operation, the flow rate of liquid methanol leaving the condenser begins to decrease. List at least three possible explanations of this behavior and state how you might check the validity of each one. (What would you measure and what would you expect to find if the explanation is valid?)

Short Answer

Expert verified
The molar flow rates of CO and H2 in the fresh feed, the production rate of liquid methanol, and the single-pass and overall conversions of carbon monoxide can all be calculated from the provided information and the mass and energy balance relations. Possible explanations for decreasing methanol production could be reactor inefficiencies, condenser pipe blockages, or insufficient fresh feed content, which can be checked through reactor condition measurements, condenser inspections, and composition checks, respectively.

Step by step solution

01

Calculate the mole flow rate of each component in the reactor outlet stream

First, the individual mass rates of H2, CO, and CH3OH in the 350 mol/min reactor outlet stream are found using the given weight percentages. These mass rates are then converted into mole flow rates using the molar masses of the components. The sum of these molar flow rates should equal the total molar flow rate of 350 mol/min, validating the calculations.
02

Calculate the molar flow rate of CH3OH in recycled stream

The subsequent step is to calculate the molar flow rate of uncondensed CH3OH in the recycle stream. Given that this constitutes 0.40 mole % of the recycle stream, the overall molar flow rate of the recycle stream can be calculated. Now, subtracting this uncondensed CH3OH flow rate from the total CH3OH flow rate in the reactor outlet stream gives the molar flow rate of the liquid methanol product.
03

Calculate molar flow rates of CO and H2 in fresh feed

Knowing the molar flow rates of the recycle stream from Step 2 and the components in the reactor outlet stream from Step 1, the fresh feed molar flow rates of CO and H2 can be determined by subtraction. This is possible because the fresh feed and recycle stream combine to form the reactor inlet stream.
04

Calculate single-pass and overall conversions of CO

Finally, the single-pass conversion of CO can be determined from the molar flow rates of CO in the fresh feed and reactor outlet stream. The overall conversion can be found by comparing the molar flow rate of CO in the fresh feed to the total molar flow rate of CO entering the reactor (recycle + fresh feed).
05

Reasoning for decrease in liquid methanol production

The decrease in methanol production could be due to several reasons like decreased efficiency of the reactor, blocked condenser pipes reducing CH3OH condensation, or less availability of CO and H2. To verify these, measurements of reactor temperature, pressure, and catalyst activity, condenser pipe inspections, and fresh feed composition checks would be necessary. Expected results would include lower than normal reactor temperatures or pressures, blockages in the condenser, or lower fresh feed contents of CO and H2.

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Key Concepts

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

Reaction Stoichiometry
Reaction stoichiometry is about understanding the quantitative relationships between reactants and products in a chemical reaction. In the methanol production process, the main reaction is between carbon monoxide (CO) and hydrogen gas (\(\text{H}_2\)) to produce methanol (\(\text{CH}_3\text{OH}\)). This reaction can be written as follows:\[\text{CO} + 2\text{H}_2 \rightarrow \text{CH}_3\text{OH}\]To properly analyze this reaction, it's critical to understand that one mole of CO reacts with two moles of \(\text{H}_2\) to produce one mole of methanol. This stoichiometric relationship forms the basis for calculating various flow rates and conversion efficiencies in a chemical process. By knowing the stoichiometric coefficients, we can determine how much of each reactant is required to produce a desired amount of product. This helps to ensure optimal use of resources within a chemical plant.
  • 1 mole of CO produces 1 mole of \(\text{CH}_3\text{OH}\)
  • 2 moles of \(\text{H}_2\) are required for each mole of CO
Understanding stoichiometry helps in determining what should be measured or adjusted if production rates deviate from the expected outcomes based on these ratios.
Mass Balance
Mass balance is an essential concept in chemical engineering. It involves analyzing the input, output, and accumulation of materials within a chemical process to ensure conservation of mass. In the methanol production example, performing a mass balance allows us to track the flow rates of CO, \(\text{H}_2\), and methanol throughout the system.The mass balance in this context consists of:
  • Input: Fresh feed of CO and \(\text{H}_2\) and any additional components from the recycle stream.
  • Output: Reacted and unreacted components exiting the reactor, condensible methanol, and uncondensed gases leaving the condenser.
  • Accumulation: Typically zero for a steady-state system where input equals output.
By calculating these parameters, we can evaluate the molar flow rates of individual components in both fresh feed and recycle streams. The mass balance helps in determining any discrepancies in expected versus actual production rates and could highlight issues such as component losses or inefficiencies in the process.
Chemical Process Dynamics
Chemical process dynamics consider the behavior and changes in a chemical system over time. In methanol production, dynamics involve the interaction between chemical reactions, phase changes, and recycle streams. Dynamics are crucial when assessing the stability and performance of the process, especially if there are fluctuations in feed rates or operational conditions. Process dynamics are sensitive to several factors such as:
  • Reaction kinetics: Rates at which the reactants turn into products.
  • Mass and heat transfer: Efficiency of transferring reactants and heat within the reactor.
  • Recycle flow rates: The amount of unreacted components re-entering the system which affects the reactor's feed composition dynamically.
Considering dynamics allows engineers to develop strategies to maintain optimal production conditions. For example, if methanol production decreases, examining the dynamics can reveal issues such as potential changes in reaction rates or pressure along with the reactor systems. Adjustments can then be made to stabilize the production process.
Methanol Production
Methanol production using CO and \(\text{H}_2\) is a sophisticated process involving several engineering principles. The primary goal is to optimize the conversion of reactants to methanol while minimizing losses and inefficiencies.The process begins with the combination of a fresh feed and a recycle stream, which then feeds into a reactor where methanol is formed. Following this, the reaction mixture flows to a condenser where methanol separates by condensing into liquid. The remains, a mixture of CO and \(\text{H}_2\), along with small methanol amounts, form the recycle stream.Key components affecting methanol production include:
  • Reaction efficiency: Ensuring that the maximum possible amount of methanol is generated in each pass through the reactor.
  • Condenser performance: Vital for separating methanol from other components effectively.
  • Feedstock purity: High purity CO and \(\text{H}_2\) results in competitive conversion rates and reduced catalyst poisoning.
Failure in any part of this process can lead to decreased methanol output. That is why monitoring component efficiencies and maintaining equipment are crucial in favoring sustainable production and lowering operational costs.

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Most popular questions from this chapter

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.

A stream consisting of 44.6 mole \(\%\) benzene and \(55.4 \%\) toluene is fed at a constant rate to a process unit that produces two product streams, one a vapor and the other a liquid. The vapor flow rate is initially zero and asymptotically approaches half of the molar flow rate of the feed stream. Throughout this entire period, no material accumulates in the unit. When the vapor flow rate has become constant, the liquid is analyzed and found to be 28.0 mole\% benzene. (a) Sketch a plot of liquid and vapor flow rates versus time from startup to when the flow rates become constant. (b) Is this process batch or continuous? Is it transient or steady-state before the vapor flow rate reaches its asymptotic limit? What about after it becomes constant? (c) For a feed rate of 100 mol/min, draw and fully label a flowchart for the process after the vapor flow rate has reached its limiting value, and then use balances to calculate the molar flow rate of the liquid and the composition of the vapor in mole fractions.

In an absorption tower (or absorber), a gas is contacted with a liquid under conditions such that one or more species in the gas dissolve in the liquid. A stripping tower (or stripper) also involves a gas contacting a liquid, but under conditions such that one or more components of the feed liquid come out of solution and exit in the gas leaving the tower. A process consisting of an absorption tower and a stripping tower is used to separate the components of a gas containing 30.0 mole \(\%\) carbon dioxide and the balance methane. A stream of this gas is fed to the bottom of the absorber. A liquid containing 0.500 mole\% dissolved \(\mathrm{CO}_{2}\) and the balance methanol is recycled from the bottom of the stripper and fed to the top of the absorber. The product gas leaving the top of the absorber contains 1.00 mole \(\% \mathrm{CO}_{2}\) and essentially all of the methane fed to the unit. The CO_-rich liquid solvent leaving the bottom of the absorber is fed to the top of the stripper and a stream of nitrogen gas is fed to the bottom. Ninety percent of the \(\mathrm{CO}_{2}\) in the liquid feed to the stripper comes out of solution in the column, and the nitrogen/CO_stream leaving the column passes out to the atmosphere through a stack. The liquid stream leaving the stripping tower is the \(0.500 \% \mathrm{CO}_{2}\) solution recycled to the absorber. The absorber operates at temperature \(T_{\mathrm{a}}\) and pressure \(P_{\mathrm{a}}\) and the stripper operates at \(T_{\mathrm{s}}\) and \(P_{\mathrm{s}}\) Methanol may be assumed to be nonvolatile- -that is, none enters the vapor phase in either column and \(\mathrm{N}_{2}\), may be assumed insoluble in methanol. (a) In your own words, explain the overall objective of this two-unit process and the functions of the absorber and stripper in the process. (b) The streams fed to the tops of each tower have something in common, as do the streams fed to the bottoms of each tower. What are these commonalities and what is the probable reason for them? (c) Taking a basis of 100 mol/h of gas fed to the absorber, draw and label a flowchart of the process. For the stripper outlet gas, label the component molar flow rates rather than the total flow rate and mole fractions. Do the degree-of-freedom analysis and write in order the equations you would solve to determine all unknown stream variables except the nitrogen flow rate entering and leaving the stripper. Circle the variable(s) for which you would solve each equation (or set of simultaneous equations), but don't do any of the calculations yet. (d) Calculate the fractional \(\mathrm{CO}_{2}\) removal in the absorber (moles absorbed/mole in gas feed) and the molar flow rate and composition of the liquid feed to the stripping tower. (e) Calculate the molar feed rate of gas to the absorber required to produce an absorber product gas flow rate of \(1000 \mathrm{kg} / \mathrm{h}\). (f) Would you guess that \(T_{\mathrm{s}}\) would be higher or lower than \(T_{\mathrm{a}} ?\) Explain. (Hint: Think about what happens when you heat a carbonated soft drink and what you want to happen in the stripper.) What about the relationship of \(P_{\mathrm{s}}\) to \(P_{\mathrm{a}} ?\) (g) What properties of methanol would you guess make it the solvent of choice for this process? (In more general terms, what would you look for when choosing a solvent for an absorption-stripping process to separate one gas from another?)

Oxygen consumed by a living organism in aerobic reactions is used in adding mass to the organism and/or the production of chemicals and carbon dioxide. since we may not know the molecular compositions of all species in such a reaction, it is common to define the ratio of moles of \(\mathrm{CO}_{2}\) produced per mole of \(\mathrm{O}_{2}\) consumed as the respiratory quotient, \(R Q,\) where $$R Q=\frac{n_{\mathrm{CO}_{2}}}{n_{\mathrm{O}_{2}}}\left(\text { or } \frac{\dot{n}_{\mathrm{CO}_{2}}}{\dot{n}_{\mathrm{O}_{2}}}\right)$$ since it generally is impossible to predict values of \(R Q\), they must be determined from operating data. Mammalian cells are used in a bioreactor to convert glucose to glutamic acid by the reaction $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+a \mathrm{NH}_{3}+b \mathrm{O}_{2} \rightarrow p \mathrm{C}_{5} \mathrm{H}_{9} \mathrm{NO}_{4}+q \mathrm{CO}_{2}+r \mathrm{H}_{2} \mathrm{O}$$ The feed to the bioreactor comprises \(1.00 \times 10^{2} \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} / \mathrm{day}, 1.20 \times 10^{2} \mathrm{mol} \mathrm{NH}_{3} / \mathrm{day},\) and \(1.10 \times\) \(10^{2}\) mol \(\mathrm{O}_{2} /\) day. Data on the system show that \(R Q=0.45 \mathrm{mol} \mathrm{CO}_{2}\) produced/mol \(\mathrm{O}_{2}\) consumed. (a) Determine the five stoichiometric coefficients and the limiting reactant. (b) Assuming that the limiting reactant is consumed completely, calculate the molar and mass flow rates of all species leaving the reactor and the fractional conversions of the non-limiting reactants.

Solid calcium fluoride (CaF, \(_{2}\) ) reacts with sulfuric acid to form solid calcium sulfate and gaseous hydrogen fluoride (HF). The HF is then dissolved in water to form hydrofluoric acid. A source of calcium fluoride is fluorite ore containing \(96.0 \mathrm{wt} \% \mathrm{CaF}_{2}\) and \(4.0 \% \mathrm{SiO}_{2}\) In a typical hydrofluoric acid manufacturing process, fluorite ore is reacted with 93 wt\% aqueous sulfuric acid, supplied 15\% in excess of the stoichiometric amount. Ninety-five percent of the ore dissolves in the acid. Some of the HF formed reacts with the dissolved silica in the reaction $$6 \mathrm{HF}+\mathrm{SiO}_{2}(\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{SiF}_{6}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$$ The hydrogen fluoride exiting from the reactor is subsequently dissolved in enough water to produce 60.0 wt\% hydrofluoric acid. Calculate the quantity of fluorite ore needed to produce a metric ton of aqueous hydrofluoric acid. Note: Some of the given data are not needed to solve the problem.
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