Centre for Energy CHPR4531 & CHPR8501: Advanced Prediction of Fluid Properties Assignment 2 Issued 30th March 2011 Due 5pm 15th April, 2011 Submit an electronic copy of your assignment by the due date. Electronic copies are to be submitted through the WebCT assignment interface. Excel spreadsheets are to be combined into a single, well labelled file. Students enrolled in CHPR4531 will be assessed on their answers to Q1 to Q3. Students enrolled in CHPR8501 will be assessed on their answers to all questions. The solution to some of these problems requires numerical values for material, atomic or molecular properties. Where they are not given, you are expected to obtain their values from reputable sources, which you should cite.

1. In a gas-fired furnace, a CH4 molecule and an O2 molecule find themselves on a head-on collision course. When they are separated by a distance of 1 nm, their relative kinetic energy is equivalent to a temperature of 1000 K. Answer the following questions by assuming the interaction between these two molecules can be described by a LennardJones potential. (a) What is the minimum separation between the centres of the two molecules achieved during the collision? Comment on the likelihood of an elastic collision occurring under these conditions. (b) What is the maximum relative speed between the two molecules and at what separation is it achieved? Note to convert relative kinetic energy to a relative speed, the reduced mass  of the two molecules must be used. It is given in terms of the masses of the two molecules, m1 and m2 via: mm  1 2 m1  m2 2. Ownership of the natural gas contained in a pipeline at 20oC and 7 MPa is being transferred, and the buyer and seller are both keen to determine the properties of the gas as accurately as possible. Compositional measurements show that the natural gas is essentially a ternary mixture of 80.8 % CH4 + 11.8 % C2H6 + 7.4 % C3H8 by mass. Set-up and present the following calculations in a spreadsheet. (a) Use the virial EOS to determine the mixture’s density at this condition. (b) Calculate the total enthalpy of 1 cubic metre of the mixture. The molar enthalpy should be calculated, relative to a datum of (0oC, 1 atm), using correlations for the perfect gas heat capacity together with the virial EOS. 3. A cryogenic storage tank contains 48 % by volume of LNG (liquid phase) at (-162oC, 120 kPa). The space above the liquid is occupied by the equilibrium vapour. The total mass in the tank is 28,590 tonnes and the overall composition of the fluid in the tank is 0.990 CH4 + 0.010 N2 by mole. Composition measurements of the two phases have also

determined that the CH4 mole fractions in the vapour and liquid phases are 0.816 and 0.991, respectively. (a) What is the mass of the vapour-phase in the storage tank? (b) For each component, what is the ratio of the partial fugacity coefficients of the vapour and liquid phases? The reference fluids used in the Lee-Kesler Corresponding States method are argon (simple fluid) and n-octane (asymmetric fluid). PVT data for these two pure fluids are provided in the table in the Appendix. Use these PVT data, together with the Lee-Kesler Corresponding States method and the VDW-1 mixing rules to answer the following. (You should present your calculations in a spreadsheet.) (c) Calculate the volume occupied by the vapour phase in the storage tank and, also, the total volume of the storage tank. (Hint: Treat the vapour phase as one mixture and the liquid phase as a second mixture. Apply the Lee-Kesler scheme independently to both mixtures.) (d) Use equations (5.28) and (5.29) from Trusler to calculate the fugacities of the vapour phase and the liquid phase mixtures. (Note that there is a typographical error in equation (5.29) – the symbol b should be .) Compare the two fugacities and comment on whether or not these values violate the requirements of phase equilibrium.

4. For this question you will need to log-on to one of the computers in a Mechanical Engineering computing laboratory (LABMECH domain). Once you have logged on, run the executable file refprop.exe in the directory T:\software\minirefprop\ The executable runs an abbreviated version (miniREFPROP) of the software REFPROP produced by the U.S. National Institute of Standards and Technology. This abbreviated version contains reference equations of state for seven pure fluids, three of which will be used in this question. The full REFPROP software, which contains reference equations of state (EOS) for 80 pure fluids and mixtures with up to 20 components, can be obtained from http://www.nist.gov/srd/nist23.htm . The user’s guide for this software can be found at http://www.nist.gov/srd/WebGuide/REFPROP8_manua3.htm and additional information is available at http://www.boulder.nist.gov/div838/theory/refprop/Frequently_asked_questions.htm For this assignment question, calculations will be done with three pure fluids: methane, dodecane and the refrigerant R134a (1,1,1,2-tetrafluroethane). To select a pure fluid, go to the ‘Substance’ menu and choose ‘Pure Fluid’. In the pop-up window select the desired pure fluid and then press ‘OK’. Next go to the ‘Options’ menu and select ‘Properties’. Ensure that the radio button for ‘Comp. Factor’ is on. This will ensure the compressibility factor is evaluated and displayed when you input a pressure and temperature. Then go to the ‘Calculate’ menu and choose ‘Specified State Points’. An editable table will appear – if you type in values for two independent thermodynamic properties (e.g. T and P) then the program will use the reference equation of state for that pure fluid to calculate the other physical properties listed in the table.

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In this question you will use miniREFPROP to construct a corresponding states scheme similar to the Lee-Kesler and Lee-Kesler-Wu-Stiel schemes. However, because miniREFPROP does not include reference equations of state for argon or for n-octane, the simple and asymmetric reference fluids will be chosen as methane and dodecane instead. The acentric factors for all the fluids in this question are tabulated in Trusler or can be obtained by selecting ‘Fluid Information’ from the ‘Substance’ menu. (a) Calculate Z for R134a at (336.8 K, 3.65 MPa) and at (392.9 K, 5.68 MPa) using the reference EOS for this fluid contained in miniREFPROP. (b) Calculate Z for methane and for dodecane at the same reduced temperatures and pressures for R134a in (a), using the respective reference EOS for these two fluids contained in miniREFPROP. (c) Use the results from (b) to calculate the term Z1 = (ZR – Z0) / R , where the subscripts R and 0 refer to the asymmetric and simple reference fluids, respectively, in the new corresponding states scheme. (d) Use the acentric factor for R134a to estimate its Z at (336.8 K, 3.65 MPa) and at (392.9 K, 5.68 MPa) using the results of (b) and (c). Compare these values with the ones calculated in (a), and comment as to how the corresponding states scheme might be extended to improve the agreement.

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APPENDIX Argon

n-Octane

T [K]

P [MPa]

V [L/mol]

T [K]

P [MPa]

V [L/mol]

T [K]

P [MPa]

V [L/mol]

84 84 84 84 84 84 85 85 85 85 85 85 86 86 86 86 86 86 87 87 87 87 87 87 88 88 88 88 88 88 89 89 89 89 89

0.120 0.122 0.124 0.126 0.128 0.130 0.120 0.122 0.124 0.126 0.128 0.130 0.120 0.122 0.124 0.126 0.128 0.130 0.120 0.122 0.124 0.126 0.128 0.130 0.120 0.122 0.124 0.126 0.128 0.130 0.122 0.124 0.126 0.128 0.130

0.028217 0.028217 0.028217 0.028217 0.028217 0.028217 0.028339 0.028339 0.028339 0.028339 0.028339 0.028339 0.028463 0.028463 0.028463 0.028463 0.028463 0.028463 0.028589 0.028589 0.028589 0.028589 0.028588 0.028588 0.028717 0.028716 0.028716 0.028716 0.028716 0.028716 0.028846 0.028846 0.028846 0.028845 0.028845

93 93 93 93 93 93 94 94 94 94 94 94 95 95 95 95 95 95 96 96 96 96 96 96 97 97 97 97 97 97 98 98 98 98 98

0.130 0.132 0.134 0.136 0.138 0.140 0.130 0.132 0.134 0.136 0.138 0.140 0.130 0.132 0.134 0.136 0.138 0.140 0.130 0.132 0.134 0.136 0.138 0.140 0.130 0.132 0.134 0.136 0.138 0.140 0.132 0.134 0.136 0.138 0.140

5.7305 5.6402 5.5526 5.4676 5.3851 5.3049 5.7991 5.7078 5.6193 5.5334 5.4500 5.3690 5.8675 5.7753 5.6859 5.5991 5.5147 5.4329 5.9358 5.8426 5.7522 5.6645 5.5793 5.4966 6.0039 5.9097 5.8184 5.7298 5.6438 5.5602 5.9768 5.8845 5.7950 5.7081 5.6236

330 330 330 330 330 330 331 331 331 331 331 331 332 332 332 332 332 332 333 333 333 333 333 333 334 334 334 334 334 334 335 335 335 335 335

0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.062 0.064 0.066 0.068 0.070

0.16991 0.16991 0.16991 0.16991 0.16991 0.16991 0.17012 0.17012 0.17012 0.17012 0.17012 0.17012 0.17033 0.17033 0.17033 0.17033 0.17033 0.17033 0.17054 0.17054 0.17054 0.17054 0.17054 0.17054 0.17076 0.17076 0.17076 0.17075 0.17075 0.17075 0.17097 0.17097 0.17097 0.17097 0.17097

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T [K]

P [MPa]

V [L/mol]

353 353 353 353 353 353 354 354 354 354 354 354 355 355 355 355 355 355 356 356 356 356 356 356 357 357 357 357 357 357 358 358 358 358 358

0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.060 0.062 0.064 0.066 0.068 0.070 0.062 0.064 0.066 0.068 0.070

0.17494 0.17494 0.17494 0.17494 0.17494 0.17493 0.17517 0.17517 0.17517 0.17517 0.17516 0.17516 0.17540 0.17540 0.17540 0.17540 0.17539 0.17539 0.17563 0.17563 0.17563 0.17563 0.17563 0.17562 0.17586 0.17586 0.17586 0.17586 0.17586 0.17586 0.17609 0.17609 0.17609 0.17609 0.17609

ADVANCE FLUID PREDICTION TUT 2
ADVANCE FLUID PREDICTION TUT 2

This is really the worse unit ever. FML