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17.12 Energy Balances for Reactions Click here. 20 1

Equilibrium constants and adiabatic reactor calculations with Excel (uakron.edu, 6 min) We previously discussed adiabatic reactor calculations in Section 3.6 with application to the dimethyl ether process. At that time, we accepted the expression for equilibrium constant as given. In Chapter 17, we must recognize how to compute the equilibrium constant for ourselves. This presentation illustrates the calculations for Example 17.9. These kinds of calculations often occur in the context of an overall process, rather than in isolation. Therefore, the presentation shows how to apply Eqn 3.5b with pathway 2.6c to characterize the enthalpies of process streams and solve for the extent of reaction and adiabatic outlet temperature simultaneously.

Comprehension Questions:

1. Suppose the reactor inlet feed was: kmol/hr of 110 N2, 300 H2, 15NH3 and 16 CH4. Solve for the adiabatic reactor temperature and extent of reaction in that case.
2. Suppose the actual conversion was only 80% of the equilibrium conversion and the inlet feed was the same as given in part 1. Solve for the adiabatic reactor temperature and extent of reaction in that case.
3. Compute the stream attributes for this entire process assuming 85% of the equilibrium conversion and a feed (kmol/h) of 105 N2, 300 H2, 20 CH4 at 10bars and 200C. The distillation column operates at 10 bars with a partial condenser and splits of 99.99% on N2 and 2% on NH3. The recycle ratio is 19:1. Assume the compressors are 100% efficient and the reactor operates adiabatically with an inlet temperature of 400K and a pressure of 100bars. Report the molar flow rates of all outlet stream components.

07.08 Matching The Critical Point Click here. 20 1

Visualizing the vdW EOS (uakron.edu, 16min) Building on solving for density, describes plotting dimensionless isotherms of the vdW EOS for methane at 5 temperatures, two subcritical, two supercritical, and one at the critical condition. From these isotherms in dimensionless form, it is possible to identify the critical point as the location of the inflection point where the temperature first exits the 3-root region. This method can be adapted to any equation of state, whether it is cubic or not. The illustration was adapted from a sample test problem. This screencast also addresses the meaning of the region where the pressure goes negative, with a (possibly disturbing) story about a blood-sucking octopus.

Comprehension Questions:

1. What are the dimensions of the quantity (bP/RT)?
2. Starting with the expression for Z(ρ,T), rewrite the vdW EOS to solve for the quantity (bP/RT) in terms of () and (a/bRT).
3. Consider the following EOS: Z = 1 + 2/(1-2) - (a/bRT) /(1-)2. Estimate the value of bPc/(RTc) for this EOS.
4. Consider the following EOS: Z = 1 + 2/(1-2) - (a/bRT) /(1-)2. Estimate the value of (a/bRTc) for this EOS.
5. Compute the values of a(J-cm3/mol2) and b(cm3/mol) for methane according to this new EOS.

09.10 - Saturation Conditions from an Equation of State Click here. 20 1

Solving for the saturation pressure using PREOS.xls simply involves setting the temperature and guessing pressure until the fugacities in vapor and liquid are equal. (5min, learncheme.com) It is not shown, but it would also be easy to set the pressure and guess temperature until the fugacities were equal in order to solve for saturation temperature. One added suggestion would be to type in the shortcut vapor pressure (SCVP) equation to give an initial estimate of the pressure. Rearranging the SCVP can also give an initial guess for Tsat when given P. This presentation illustrates a sample calculation for toluene to explore when the vapor is the stable, when the liquid is the stable phase, and when the phases are roughly in equilibrium.

Comprehension Questions:

1. Estimate the vapor pressure (MPa) of n-pentane at 450K according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
2. Estimate the saturation temperature (K) of n-pentane at 3.3 MPa according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
3. Estimate the vapor pressure (MPa) of n-pentane at 223K according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
4. Estimate the saturation temperature (K) of n-pentane at 3.3 kPa according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?

06.2 Derivative Relations Click here. 20 1

Assembling your derivative toolbox including the triple product rule, (uakron.edu, 13min) Beginning with the fundamental property relation, substitutions lead to Eqns. 6.4-6.7. Differentiating these and equating through exact differentials leads to Eqns. 6.29-6.32 (aka. Maxwell's Relations). Combining Maxwell's Relations with Eqns. 6.4-6.7 leads to Eqns. 6.37-6.41. With these tools in hand, and Eqn. 6.15 (aka. Triple Product Rule), you have all the tools you need to quickly transform any derivative into "expressions involving Cp, Cv, P, V, T, and their derivatives." This capability is fundamental to obtaining expressions for U, H, and S from any given equation of state for any chemical of interest. Four sample derivations are illustrated: (∂U/∂V)T, (∂T/∂S)V, (∂T/∂V)S, (∂S/∂V)A,

Comprehension Questions:

1. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives:" (∂T/∂V)S.

2. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives." Your expression may involve absolute values of S as long as they are not associated with any derivative. (∂T/∂U)P.

06.2 Derivative Relations Click here. 20 3

Heat Capacity Volume Dependence (uakron.edu, 10min) This example derives how the heat capacity of the gas depends on volume, ie. (∂Cv/∂V)T. It may seem paradoxical that a quantity defined at constant volume can change with respect to volume. The discussion here shows how to solve this puzzle. The sample derivation presented here follows an alternative approach to what is illustrated in Example 6.9 of the textbook.

Comprehension Questions:

1. The van der Waals (vdW) equation of state (EOS) is: P = RT/(V-b) - a/V2.  Evaluate (∂Cv/∂V)T for the vdW EOS.
2. The Soave-Redlich-Kwong (SRK) EOS is: P = RT/(V-b) - a/[V(V+b)]
where a=[1+K*(1-sqrt(T/Tc))]2.  Evaluate (∂Cv/∂V)T for the SRK EOS.
3. Comment on the differences between the results for 1 and 2 above. Do these results change the way you look at the vdW EOS?

03.6 - Energy Balance for Reacting Systems Click here. 20 1

In case you need a little extra help on energy balances after iterating mass balances, this video walks you through the process. (8min, uakron.edu) for the same process flow diagram related to dimethyl ether synthesis.

Comprehension Questions:

1. Choose any process flow diagram from your material and energy balances (MEB) textbook that has a recycle stream. Solve the problem using this technique and compare to the answer you obtained in MEB class. Estimate stream enthalpies for every stream and compute the overall energy balance of all product streams to all feed streams. Does the process require net heat addition or removal?
2. Suggest limitations of this approach. What are the assumptions? Which assumptions seem most suspect?

05.2 - The Rankine cycle Click here. 20 1

Rankine Example Using Steam.xls (uakron.edu, 15min) High pressure steam (254C,4.2MPa, Saturated vapor) is being considered for application in a Rankine cycle dropping the pressure to 0.1MPa; compute the Rankine efficiency. This demonstration applies the Steam.xls spreadsheet to get as many properties as possible.

Comprehension Questions:

1. Why does the proposed process turn out to be impractical?

2. What would you need to change in the process to make it work? Assume the high and low temperature limits are the same. Be quantitative.

3. What would be the thermal efficiency of your modified process?

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