Leaving Radiator Springs
in the Dust
Just the Facts
DOFPro Team
Bypass
- Less common than recycle
- Common example is fruit-juice concentrator.
Simplifying PFDs
Flowsheets can be simplified by drawing a surrounding box and only dealing with the inputs and outputs. For example, the process flowsheet for the dehydrogenation of propane to propene.
propane
hydrogen
methane
propane
propene
Simplifying PFDs
Flowsheets can be simplified by drawing a surrounding box and only dealing with the inputs and outputs. For example, the process flowsheet for the dehydrogenation of propane to propene.
propane
hydrogen
methane
propane
propene
Simplifying PFDs (cont.)
The absorber and stripper can be combined into one separator for calculation purposes.
propane
hydrogen
methane
propane
propene
Simplifying PFDs (cont.)
The absorber and stripper can be combined into one separator for calculation purposes.
propane
hydrogen
methane
propane
propene
Simplifying PFDs (cont.)
The reactor, separator, distillation column, and recycle loop can be combined into an overall process block for calculation purposes.
propane
hydrogen
methane
propane
propene
Simplifying PFDs (cont.)
The reactor, separator, distillation column, and recycle loop can be combined into an overall process block for calculation purposes.
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propane
hydrogen
methane
propane
propene
Example of Simplifying
propane
hydrogen
methane
propane
propene
Let’s look at the calculations for this slightly more realistic dehydrogenation process.
Product flow rate – \(100\ \mathrm{mol/s}\)
Product stream 6 – \(98\%\) propene
Recycle stream 5 – \(97\%\) propane
\(\mathrm{C_3H_8 - A}\)
\(\mathrm{C_3H_6 - B}\)
\(\mathrm{CH_4 - C}\)
\(\mathrm{H_2 - D}\)
\(\mathrm{C_3H_8 \rightarrow C_3H_6 + H_2}\)
\(\mathrm{C_3H_8 + 2H_2 \rightarrow 3CH_4}\)
\(f_\mathrm{C_3H_8} = 0.35\) (in reactor)
\(S = \frac{\dot{n}_{\mathrm{C_3H_6}_\text{–gen}}}{\dot{n}_{\mathrm{CH_3}_\text{–gen}}} = 2\) (in reactor)
Example of Simplifying (cont.)
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propane
hydrogen
methane
propane
propene
\(\mathrm{C_3H_8 - A}\)
\(\mathrm{C_3H_6 - B}\)
\(\mathrm{CH_4 - C}\)
\(\mathrm{H_2 - D}\)
If there is only one reactor in the process, the extents of reaction overall have to be the same as the extents of reaction in the reactor.
Propene is produced by reaction 1 only, so
\(\dot{\xi}_1 = (0.98)(100\ \mathrm{mol/s}) = 98\ \mathrm{mol/s}\)
\(\dot{n}_\text{B–gen} =\dot{n}_\mathrm{B6} - \dot{n}_\mathrm{B1} = \dot{n}_\mathrm{B6}\)
\(\dot{n}_\text{C–gen} =\dot{n}_\mathrm{C7} - \dot{n}_\mathrm{C1} = \dot{n}_\mathrm{C7}\)
\(S = \frac{\dot{n}_\text{B–gen}}{\dot{n}_\text{C–gen}} = \frac{\dot{n}_\mathrm{B6}}{\dot{n}_\mathrm{C7}} = \frac{\nu_\mathrm{B,1} \dot{\xi}_1}{\nu_\mathrm{C,2} \dot{\xi}_2} = \frac{\dot{\xi}_1}{3 \dot{\xi}_2} = 2\)
\(\dot{\xi}_2 = \frac{\dot{\xi}_1}{6} = \frac{98}{6}\)
Example of Simplifying (cont.)
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\(\mathrm{A,\ B}\)
\(\mathrm{A,\ B,\ C,\ D}\)
Reactor
propane
hydrogen
methane
propane
propene
\(\mathrm{C_3H_8 - A}\)
\(\mathrm{C_3H_6 - B}\)
\(\mathrm{CH_4 - C}\)
\(\mathrm{H_2 - D}\)
Mole balance on \(\mathrm{A}\)
\(\dot{n}_\mathrm{A6} = \dot{n}_\mathrm{A1} + \nu_\mathrm{A1} \dot{\xi}_1 + \nu_\mathrm{A2} \dot{\xi}_2\)
\(2 = \dot{n}_\mathrm{A1} - 98 - 16.3\)
\(\implies \dot{n}_\mathrm{A1} = 116.3\ \mathrm{mol/s}\)
\(f_\mathrm{A} = 1 - \frac{\dot{n}_\mathrm{A3}}{\dot{n}_\mathrm{A2}}\)
\(\implies \dot{n}_\mathrm{A3} = \dot{n}_\mathrm{A2}(1-f_\mathrm{A})\)
\(\dot{n}_\mathrm{A3} = \dot{n}_\mathrm{A2} + \nu_\mathrm{A1} \dot{\xi}_1 + \nu_\mathrm{A2} \dot{\xi}_2 = \dot{n}_\mathrm{A2} - \dot{\xi}_1 - \dot{\xi}_2\)
\(\dot{n}_\mathrm{A2}(1-f_\mathrm{A}) = \dot{n}_\mathrm{A2} - \dot{\xi}_1 - \dot{\xi}_2\)
\(\dot{n}_\mathrm{A2} = \frac{\dot{\xi}_1 + \dot{\xi}_2}{f_\mathrm{A}} = \frac{98 + \frac{98}{6}}{0.35} = 326.7\)
Example of Simplifying (cont.)
propane
hydrogen
methane
propane
propene
\(\mathrm{C_3H_8 - A}\)
\(\mathrm{C_3H_6 - B}\)
\(\mathrm{CH_4 - C}\)
\(\mathrm{H_2 - D}\)
Material Balance on \(\mathrm{A}\) around each element
M: \(\dot{n}_\mathrm{A2} = 116.3 + \dot{n}_\mathrm{A5}\)
R: \(\dot{n}_\mathrm{A3} = 0.65 \dot{n}_\mathrm{A2}\)
S1: \(\dot{n}_\mathrm{A4} = \dot{n}_\mathrm{A3} - \dot{n}_\mathrm{A7} = \dot{n}_\mathrm{A3}\)
S2: \(2 = \dot{n}_\mathrm{A4} - \dot{n}_\mathrm{A5}\)
Solution
\(\dot{n}_\mathrm{A2} = 326.6\ \mathrm{mol/s}\)
\(\dot{n}_\mathrm{A3} = 212.3\ \mathrm{mol/s}\)
\(\dot{n}_\mathrm{A4} = 212.3\ \mathrm{mol/s}\)
\(\dot{n}_\mathrm{A5} = 210.3\ \mathrm{mol/s}\)
Recycle \(97\%\ \mathrm{A}\)
\(\therefore\ \dot{n}_5 = \frac{210.3}{0.97} = 216.8\ \mathrm{mol/s}\)
Example of Simplifying Spreadsheet
propane
hydrogen
methane
propane
propene
\(\mathrm{C_3H_8 - A}\)
\(\mathrm{C_3H_6 - B}\)
\(\mathrm{CH_4 - C}\)
\(\mathrm{H_2 - D}\)
Thanks for watching!
The Full Story companion video is in the link in the upper left. The companion video in the series, The Symbolic Meaning of Recycling, is in the upper right. To learn more about Chemical and Thermal Processes, visit the website linked in the description.
