richard graham (university of nottingham) - tractable equations of state for co2 mixtures in ccs:...
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Understanding and predicting CO2 properties
Richard Graham Tom Demetriades, Alex Cresswell, Martin Nelson,
Richard Wilkinson and Simon Preston School of Mathematical Sciences, University of Nottingham.
Potential applications: Avoiding pipeline issues
Two-phase flow
Jet
Snow/ dry ice
Pipe rupture
10-4 10-3
Molar volume [m^3/mol]
2
4
6
8
10
12
Pre
ssur
e [M
Pa]
304.3K (Tc)294K285K
Predictions (pure CO2)
10-4
Molar volume [m^3/mol]
4
6
8
Pre
ssur
e [M
Pa]
Coexisting liquidCoexisting vapour
R
Mixture modelling CO2+N2
Uncertainty quantification
Uncertainty quantification
Uncertainty quantification
Economic recovery!
Uncertainty quantification
Huge uncertainty!
0 0.2 0.4 0.6 0.8 1x0
0.2
0.4
0.6
0.8
1
f(x)
Introduction to non-parametric methods
•Model for pressure against volume, as with an equation of state. •However, no need to specify terms or parameters •Model ‘learns’ the P(v) functional form from the measurements
0.2 0.4 0.6 0.8 1.0
−2
−1
01
2
volume
pressure
0.2 0.4 0.6 0.8 1.0
−2
−1
01
2
volume
pressure
A Gaussian process for pure CO2P
ress
ure/
(Crit
ical
Pre
ssur
e)
Molar volume/(Ideal gas volume)
Temperature=290K
CO2 data Gaussian Process mean. 95% confidence interval Individual Gaussian Processes
Gaussian Process accurately captures the data
Uncertainty is only significant in the coexistence region
Generalisation to mixtures is ongoing
Molecular simulationComputer model of individual molecules within a small box of fluid.
Can predict: •Pressure-‐volume •Coexistence •Effect of impurity •Most other quanBBes of interest
Can be used where experiments are unavailable?
Can be used to derive an EquaBon of State?
Bubble point comparison CO2 + 5%H2
Phase boundary measurements by Jie Ke, Mike
George et al