辅导案例-GENG4405 2019-Assignment 2

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GENG4405 2019 - Assignment 2, Part 2
Part 2 of the Assignment: What is the fluid volume?

The geothermal fluid from the reservoir reaches the surface as a two-phase fluid. As previously
mentioned, the vapor fraction will be separated off and run through a turbine and the liquid
fraction will be reinjected to the reservoir. For the purposes of sizing pipes and equipment it is
necessary to know the specific volume (on a mass basis) of the liquid and vapor phases. Your
team has been tasked with developing code to calculate the volumes based on the pressure to be
used in the separator and turbine inlet. While the final pressure has yet to be determined,
through some optimization procedure, you can demonstrate that your code works by using 8 bar
absolute pressure. The geothermal fluid may be approximated as pure water.
Since the system being modeled is two-phase the pressure and temperature are linked. It is
suggested that you think of your code as containing two loops. On the outer loop you guess a
value for the temperature, starting from a temperature that should correspond to a super-heated
vapor. On the inner loop you run your algorithm(s) for finding a value of v (the specific volume)
that will be a root for the equation of state. By stepping down in temperature on the outer loop
you should eventually cross the saturation temperature and the value of the root, corresponding
to the specific volume, should become much smaller (~2 orders of magnitude). You can check if
this has happened by taking the ratio of specific volumes from successive temperature steps.
A chemical engineer suggests using the volume-translated Peng-Robinson equation of state1
(EOS) to model the properties of water; the EOS is “translated” meaning that the expected
physical volume is corrected from the volume in the EOS by ா௫௣௘௖௧௘ௗ = ாைௌ + , where t is a
correction parameter in the EOS. The volume used in the EOS is the molar volume,
temperatures are in K and pressure is in Pa. The EOS is as follows:

=

+ −


( + )( + + ) + ( + − )

= 0.45724
ଶ௖ଶ


= 0.07780



= [1 + (1 − ோ) + (1 − ோ)(0.7 − ோ)]ଶ
ோ =



= 0.20473 + 0.83548 − 0.18470ଶ + 0.16675ଷ − 0.09881ସ
=


ൣଵ + ଶ൫1 − ோଶ ଷ
⁄ ൯ + ଷ(1 − ோଶ ଷ
⁄ )ଶ൧
ଵ = 0.00185 + 0.00438 + 0.36322ଶ − 0.90831ଷ + 0.55885ସ
ଶ = −0.00542 − 0.51112ଷ + 0.04533ଷ
ଶ + 0.07447ଷ
ଷ − 0.03831ଷ

Specific to water in the EOS
= 0.11560
ଷ = 0.01471
General properties of water
௖ = 647.1 K
௖ = 22.0664 MPa
= 0.344
= 18.015 g/mol
Ideal Gas Constant
= 8.314
J
mol K



Assignment Questions:
1. (25%) Write MATLAB code to determine the saturation temperature and specific
volumes of the saturated vapor and saturated liquid. In your report, please give the
saturation temperature (to be found to within a range of half a degree) and the specific
volume (on a mass basis) for the saturated liquid and saturated vapor along with some
statement about the accuracy or relative error in the values. You may use any of the
methods for finding zeros and roots discussed in class but may not use in built MATLAB
functions (such as fzero) in your code (of course you can use that function as a means of
checking your code).


Fig. 1 The saturation dome for water on a T-v plot along with the 0.8 MPa isobar.








Ref.
1. J.C. Tsai, Y.P. Chen, Application of a volume-translated Peng-Robinson equation of state
on vapor-liquid equilibrium calculations, Fluid Phase Equilibr. 145 (1998) 193-215
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