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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 The liquid methanol condensate is withdrawn as a product, and the gas stream leaving the condenser- -which contains \(\mathrm{CO}, \mathrm{H}_{2},\) and \(0.40 \mathrm{mole} \%\) uncondensed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

A drug (D) is produced in a three-stage extraction from the leaves of a tropical plant. About 1000 kg of leaf is required to produce 1 kg of the drug. The extraction solvent (S) is a mixture containing 16.5 wt\% ethanol (E) and the balance water (W). The following process is carried out to extract the drug and recover the solvent. 1\. A mixing tank is charged with \(3300 \mathrm{kg}\) of \(\mathrm{S}\) and \(620 \mathrm{kg}\) of leaf. The mixer contents are stirred for several hours, during which a portion of the drug contained in the leaf goes into solution. The contents of the mixer are then discharged through a filter. The liquid filtrate, which carries over roughly \(1 \%\) of the leaf fed to the mixer, is pumped to a holding tank, and the solid cake (spent leaf and entrained liquid) is sent to a second mixer. The entrained liquid has the same composition as the filtrate and a mass equal to \(15 \%\) of the mass of liquid charged to the mixer. The extracted drug has a negligible effect on the total mass and volume of the spent leaf and the filtrate. 2\. The second mixer is charged with the spent leaf from the first mixer and with the filtrate from the previous batch in the third mixer. The leaf is extracted for several more hours, and the contents of the mixer are then discharged to a second filter. The filtrate, which contains \(1 \%\) of the leaf fed to the second mixer, is pumped to the same holding tank that received the filtrate from the first mixer, and the solid cake- -spent leaf and entrained liquid - is sent to the third mixer. The entrained liquid mass is \(15 \%\) of the mass of liquid charged to the second mixer. 3\. The third mixer is charged with the spent leaf from the second mixer and with \(2720 \mathrm{kg}\) of solvent \(\mathrm{S}\). The mixer contents are filtered; the filtrate, which contains \(1 \%\) of the leaf fed to the third mixer, is recycled to the second mixer; and the solid cake is discarded. As before, the mass of the entrained liquid in the solid cake is \(15 \%\) of the mass of liquid charged to the mixer. 4\. The contents of the filtrate holding tank are filtered to remove the carried-over spent leaf, and the wet cake is pressed to recover entrained liquid, which is combined with the filtrate. A negligible amount of liquid remains in the wet cake. The filtrate, which contains \(\mathrm{D}, \mathrm{E},\) and \(\mathrm{W},\) is pumped to an extraction unit (another mixer). 5\. In the extraction unit, the alcohol-water-drug solution is contacted with another solvent (F), which is almost but not completely immiscible with ethanol and water. Essentially all of the drug (D) is extracted into the second solvent, from which it is eventually separated by a process of no concern in this problem. Some ethanol but no water is also contained in the extract. The solution from which the drug has been extracted (the raffinate) contains \(13.0 \mathrm{wt} \% \mathrm{E}, 1.5 \% \mathrm{F},\) and \(85.5 \%\) W. It is fed to a stripping column for recovery of the ethanol. 6\. The feeds to the stripping column are the solution just described and steam. The two streams are fed in a ratio such that the overhead product stream from the column contains \(20.0 \mathrm{wt} \% \mathrm{E}\) and \(2.6 \% \mathrm{F},\) and the bottom product stream contains \(1.3 \mathrm{wt} \% \mathrm{E}\) and the balance \(\mathrm{W}\). Draw and label a flowchart of the process, taking as a basis one batch of leaf processed. Then calculate (a) the masses of the components of the filtrate holding tank. (b) the masses of the components \(D\) and \(E\) in the extract stream leaving the extraction unit. (c) the mass of steam fed to the stripping column, and the masses of the column overhead and bottoms products.

A paint mixture containing \(25.0 \%\) of a pigment and the balance binders (which help the pigment stick to the surface) and solvents (which ensure that the paint stays in liquid form) sells for 18.00 dollar/kg, and a mixture containing 12.0\% sells for 10.00 dollar /kg. (a) If a paint retailer produces a blend containing \(17.0 \%\) pigment, for how much (S/kg) should it be sold to yield a 10\% profit? (b) Paint manufacturers have begun to market "low VOC" paint as a more environmentally friendly product. What are VOCs? List some ways in which paint products can be altered to lower the VOC content.

A fuel oil is fed to a furnace and burned with \(25 \%\) excess air. The oil contains \(87.0 \mathrm{wt} \% \mathrm{C}, 10.0 \% \mathrm{H},\) and 3.0\% S. Analysis of the furnace exhaust gas shows only \(\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{CO}_{2}, \mathrm{SO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\). The sulfur dioxide emission rate is to be controlled by passing the exhaust gas through a scrubber, in which most of the \(\mathrm{SO}_{2}\) is absorbed in an alkaline solution. The gases leaving the scrubber (all of the \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{CO}_{2}\), and some of the \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{SO}_{2}\) entering the unit) pass out to a stack. The scrubber has a limited capacity, however, so that a fraction of the furnace exhaust gas must be bypassed directly to the stack. At one point during the operation of the process, the scrubber removes \(90 \%\) of the \(\mathrm{SO}_{2}\) in the gas fed to it, and the combined stack gas contains 612.5 ppm (parts per million) \(\mathrm{SO}_{2}\) on a dry basis; that is, every million moles of dry stack gas contains 612.5 moles of \(\mathrm{SO}_{2}\). Calculate the fraction of the exhaust bypassing the scrubber at this moment.

A catalytic reactor is used to produce formaldehyde from methanol in the reaction $$\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2}$$ A single-pass conversion of \(60.0 \%\) is achieved in the reactor. The methanol in the reactor product is separated from the formaldehyde and hydrogen in a multiple-unit process. The production rate of formaldehyde is 900.0 kg/h. (a) Calculate the required feed rate of methanol to the process ( \(\mathrm{kmol} / \mathrm{h}\) ) if there is no recycle. (b) Suppose the unreacted methanol is recovered and recycled to the reactor and the single-pass conversion remains 60\%. Without doing any calculations, prove that you have enough information to determine the required fresh feed rate of methanol (kmol/h) and the rates (kmol/h) at which methanol enters and leaves the reactor. Then perform the calculations. (c) The single-pass conversion in the reactor, \(X_{\mathrm{sp}},\) affects the costs of the reactor \(\left(C_{\mathrm{r}}\right)\) and the separation process and recycle line \(\left(C_{\mathrm{s}}\right) .\) What effect would you expect an increased \(X_{\mathrm{sp}}\) would have on each of these costs for a fixed formaldehyde production rate? (Hint: To get a \(100 \%\) singlepass conversion you would need an infinitely large reactor, and lowering the single-pass conversion leads to a need to process greater amounts of fluid through both process units and the recycle line.) What would you expect a plot of \(\left(C_{\mathrm{r}}+C_{\mathrm{s}}\right)\) versus \(X_{\mathrm{sp}}\) to look like? What does the design specification \(X_{\mathrm{sp}}=60 \%\) probably represent?

Methane reacts with chlorine to produce methyl chloride and hydrogen chloride. Once formed, the methyl chloride may undergo further chlorination to form methylene chloride ( \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) ), chloroform, and carbon tetrachloride. A methyl chloride production process consists of a reactor, a condenser, a distillation column, and an absorption column. A gas stream containing 80.0 mole \(\%\) methane and the balance chlorine is fed to the reactor. In the reactor a single-pass chlorine conversion of essentially \(100 \%\) is attained, the mole ratio of methyl chloride to methylene chloride in the product is \(5: 1,\) and negligible amounts of chloroform and carbon tetrachloride are formed. The product stream flows to the condenser. Two streams emerge from the condenser: the liquid condensate, which contains essentially all of the methyl chloride and methylene chloride in the reactor effluent, and a gas containing the methane and hydrogen chloride. The condensate goes to the distillation column in which the two component species are separated. The gas leaving the condenser flows to the absorption column where it contacts an aqueous solution. The solution absorbs essentially all of the HCl and none of the \(\mathrm{CH}_{4}\) in the feed. The liquid leaving the absorber is pumped elsewhere in the plant for further processing, and the methane is recycled to join the fresh feed to the process (a mixture of methane and chlorine). The combined stream is the feed to the reactor. (a) Choose a quantity of the reactor feed as a basis of calculation, draw and label a flowchart, and determine the degrees of freedom for the overall process and each single unit and stream mixing point. Then write in order the equations you would use to calculate the molar flow rate and molar composition of the fresh feed, the rate at which HCI must be removed in the absorber, the methyl chloride production rate, and the molar flow rate of the recycle stream. Do no calculations. (b) Calculate the quantities specified in Part (a), either manually or with an equation-solving program. (c) What molar flow rates and compositions of the fresh feed and the recycle stream are required to achieve a methyl chloride production rate of \(1000 \mathrm{kg} / \mathrm{h} ?\)
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