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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.

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?

Thermodynamic pathways of EOS's for arbitrary reference states (uakron.edu, 20min) The development of a thermodynamic pathway from an arbitrary reference state to a given state condition is independent of the thermodynamic model. It depends only on (1a) identifying the condition of the reference state (e.g. ideal gas, real vapor, or liquid) (1b) transforming from the reference state to the ideal gas, if necessary (2) transforming from the ideal gas at the condition of the reference state to the ideal gas at the given state condition (3a) identifying the condition at the given state (3b) transforming from the ideal gas at the given state to the real fluid at the given state. The methodology is illustrated for two thermodynamic models: the Psat/Hvap model of Figure 2.6c,Eqs 2.45,47 vs. the PR EOS. The screencast is a bit long, but it covers 16 sample calculations (8 for H and 8 for S) and comparisons between PREOS vs Psat/Hvap. You might like to refer back to Sections 2.10 and 3.6 to review the Psat/Hvap model and the elemental reference state. Push pause before each sample calculation and check whether you can predict the next answer.

Comprehension Questions:

1. Compute "H" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the PR EOS. You may use PREOS.xlsx to compute H-Hig, but you must show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
2. Compute "S" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the PR EOS. You may use PREOS.xlsx to compute S-Sig, but you must show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
3. Compute "H" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the Psat/Hvap model. Show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
4. Compute "S" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cpig/R = 8.85 and the Psat/Hvap model. Show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.

11.05 - Modified Raoult's Law and Excess Gibbs Energy Click here. 20 1

Extending the M1 derivation of the activity coefficient to multicomponent mixtures  (uakron.edu, 14min) is straightforward but requires careful attention to the meaning of the subscripts and notation. It is a good warmup for derivations of more sophisticated activity models. This presentation begins with a brief review of the M1 model and its relation to the Gibbs excess function, then systematically explains the notation as it extends from the binary case to multiple components.

Comprehension Questions
1. Derive the activity coefficient for the multicomponent M2 model.
2. Derive the activity coefficient for the multicomponent Redlich-Kister model.

Helmholtz Energy - Mother of All Departure Functions. (uakron.edu, 10min) This screencast begins with a brief perspective on energy and free energy as they relate to concepts from Chapter 1 and through to the end of the course. Then it focuses on how the Helmholtz departure function is one of the most powerful due to the relations that can be developed from it. The Helmholtz departure is relatively easy to develop from a density integral of the compressibility factor. Then the internal energy departure can be derived from a temperature derivative. Alternatively, if the internal energy departure is given, the Helmholtz energy can be inferred by integration, and the compressibility factor can be derived from a density derivative.
Comprehension Questions: (Hint: some of the following may be answered in later videos below.)
1. Write an equation that takes you from the Helmholtz energy departure function to Z.
2. Write an equation that takes you from the Helmholtz energy departure function to (U-Uig)/RT.
3. Derive the internal energy departure function for the vdW EOS using Eqn. 8.22.
4. Derive the Helmholtz energy departure function for the vdW EOS using Eqn. 8.25.
5. Use the result of #4 to derive the internal energy departure function for the vdW EOS.

Helmholtz Example - vdW EOS (uakron.edu, 18min) This video begins with a brief review of the connection of the Helmholtz departure with all other departures then shows four sample derivations assuming that Z is given by the vdW EOS: (1) the Helmholtz departure , (2) the internal energy departure from the Helmholtz departure. (3) the Helmholtz energy from the internal energy (4) the Z factor from the Helmholtz departure. The procedures illustrated here can be applied to any EOS starting with any part (U, A, or Z) as given to derive any other departure: ZUHAGS.
Comprehension Questions: The virial EOS for SW fluids can be written as: Z = 1 + Bρ/RT where B = 4b+[4b(λ^3-1)] [exp(βε)-1], b = πNAσ^3/6.
1. Derive an expression for the Helmholtz departure.
2. Use the result of #1 to derive the internal energy departure.
3. Use the result of #2 to derive the Helmholtz departure. What is the integration constant in this case?