Richard Graham (University Of Nottingham) - Tractable Equations of State for CO2 Mixtures in CCS:...
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![Page 1: Richard Graham (University Of Nottingham) - Tractable Equations of State for CO2 Mixtures in CCS: Algorithms for Automated Generation and Optimisation, Tailored to End-User - UKCCSRC](https://reader033.fdocuments.in/reader033/viewer/2022051617/55a5429d1a28abb2478b457c/html5/thumbnails/1.jpg)
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.
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Potential applications: Avoiding pipeline issues
Two-phase flow
Jet
Snow/ dry ice
Pipe rupture
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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
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Mixture modelling CO2+N2
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Uncertainty quantification
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Uncertainty quantification
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Uncertainty quantification
Economic recovery!
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Uncertainty quantification
Huge uncertainty!
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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
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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
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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?
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Bubble point comparison CO2 + 5%H2
Phase boundary measurements by Jie Ke, Mike
George et al