Methanol is synthesized from carbon monoxide and hydrogen in the reaction
$$\mathrm{CO}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{3}
\mathrm{OH}$$
The fresh feed to the system, which contains only \(\mathrm{CO}\) and
\(\mathrm{H}_{2},\) is blended with a recycle stream containing the same
species. The combined stream is heated and compressed to a temperature
\(T(\mathrm{K})\) and a pressure \(P(\mathrm{kPa})\) and fed to the reactor. The
percentage excess hydrogen in this stream is \(H_{\mathrm{xs}}\). The reactor
effluent \(-\) also at \(T\) and \(P-\) goes to a scparation unit where essentially
all of the methanol produced in the reactor is condensed and removed as
product. The unreacted \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) constitute the
recycle stream blended with the fresh feed.
Provided that the reaction temperature (and hence the rate of reaction) is
high enough and the idealgas equation of state is a reasonable approximation
at the reactor outlet conditions (a questionable assumption), the ratio
$$K_{p c}=\frac{p_{\mathrm{CH}, \mathrm{OH}}}{p_{\mathrm{CO}}
p_{\mathrm{H}}^{2}}$$
approaches the equilibrium value, which is given by the expression
$$K_{p}(\mathrm{T})=1.390 \times 10^{-4} \exp
\left(21.225+\frac{9143.6}{T}-7.492 \ln T+4.076 \times 10^{-3} T-7.161 \times
10^{-8} T^{2}\right)$$
In these equations, \(p_{i}\) is the partial pressure of species \(i\) in
kilopascals \(\left(i=\mathrm{CH}_{3} \mathrm{OH}, \mathrm{CO},
\mathrm{H}_{2}\right)\) and \(T\) is in Kelvin.
(a) Suppose \(P=5000 \mathrm{kPa}, T=500 \mathrm{K},\) and the percentage excess
of hydrogen in the feed to the reactor \(\left(H_{\mathrm{xz}}\right)=5.0 \% .\)
Calculate \(\dot{n}_{4}, \dot{n}_{5},\) and \(\dot{n}_{6},\) the component flow
rates \((\mathrm{kmol} / \mathrm{h})\) in the reactor effluent. [Suggestion: Use
the known value of \(H_{x s}\), atomic balances around the reactor, and the
equilibrium relationship, \(K_{p c}=K_{p}(T),\) to write four equations in the
four variables \(\dot{n}_{3}\) to \(\dot{n}_{6} ;\) use algebra to eliminate all
but \(\dot{n}_{6} ;\) and use Goal Seck or Solver in Excel to solve the
remaining nonlinear equation for \(\dot{n}_{6} .\) J Then calculate component
fresh feed rates \(\left(\dot{n}_{1} \text { and } \dot{n}_{2}\right)\) and the
flow rate (SCMH) of the recycle stream.
(b) Prepare a spreadsheet to perform the calculations of Part (a) for the same
basis of calculation (100 kmol CO/h fed to the reactor) and different
specified values of \(P(\mathrm{kPa}), T(\mathrm{K}),\) and
\(H_{\mathrm{xs}}(\%)\) The spreadsheet should have the following columns:
A. \(P(\mathrm{kPa})\)
B. \(T(\mathrm{K})\)
C. \(H_{x s}(\%)\)
D. \(K_{p}(T) \times 10^{8} .\) (The given function of \(T\) multiplied by \(10^{8}
.\) When \(T=500 \mathrm{K}\), the value in this column should be 91.113.)
E. \(K_{p} P^{2}\)
F. \(\dot{n}_{3} .\) The rate (kmol/h) at which \(\mathrm{H}_{2}\) enters the
reactor.
G. \(\dot{n}_{4}\). The rate ( \(\mathrm{kmol} / \mathrm{h}\) ) at which CO leaves
the reactor.
H. \(\dot{n}_{5}\). The rate (kmol/h) at which \(\mathrm{H}_{2}\) leaves the
reactor.
I. \(\dot{n}_{6}\). The rate \((\mathrm{kmol} / \mathrm{h})\) at which methanol
leaves the reactor.
J. \(\dot{n}_{\text {lot. The total molar flow rate }(\mathrm{kmol} /
\mathrm{h}) \text { of the reactor effluent. }}\)
K. \(K_{p c} \times 10^{8} .\) The ratio \(y_{\mathrm{M}} /\left(y_{\mathrm{CO}}
y_{\mathrm{H}_{2}}^{2}\right)\) multiplied by \(10^{8} .\) When the correct
solution has been attained, this value should equal the one in Column E.
L. \(K_{p} P^{2}-K_{p r} P^{2} .\) Column E-Column K, which equals zero for the
correct solution.
M. \(\dot{n}_{1}\). The molar flow rate \((\mathrm{kmol} / \mathrm{h})\) of
\(\mathrm{CO}\) in the fresh feed.
N. \(\dot{n}_{2}\). The molar flow rate \((\mathrm{kmol} / \mathrm{h})\) of
\(\mathrm{H}_{2}\) in the fresh feed.
O. \(\dot{V}_{\text {rec }}(\text { SCMH })\). The flow rate of the recycle
stream in \(\mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\).
When the correct formulas have been entered, the value in Column I should be
varied until the value in Column L equals 0 . Run the program for the
following nine conditions (three of which are the same):
\(\cdot\) \(T=500 \mathrm{K}, H_{\mathrm{xs}}=5 \%,\) and \(P=1000 \mathrm{kPa},
5000 \mathrm{kPa},\) and \(10,000 \mathrm{kPa}\)
\(\cdot\) \(P=5000 \mathrm{kPa}, H_{x s}=5 \%,\) and \(T=400 \mathrm{K}, 500
\mathrm{K},\) and \(600 \mathrm{K}\)
\(\cdot\) \(T=500 \mathrm{K}, P=5000 \mathrm{kPa},\) and \(H_{\mathrm{xs}}=0 \%, 5
\%,\) and \(10 \%\)
Summarize the effects of reactor pressure, reactor temperature, and excess
hydrogen on the yield of methanol (kmol M produced per \(100 \mathrm{kmol}\) CO
fed to the reactor).
(c) You should find that the methanol yield increases with increasing pressure
and decreasing temperature. What cost is associated with increasing the
pressure?
(d) Why might the yield be much lower than the calculated value if the
temperature is too low?
(e) If you actually ran the reaction at the given conditions and analyzed the
reactor effluent, why might the spreadsheet values in Columns
\(\mathrm{F}-\mathrm{M}\) be significantly different from the measured values of
these quantities? (Give several reasons, including assumptions made in
obtaining the spreadsheet values.)
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine 
