Richard Graham (University Of Nottingham) - Tractable Equations of State for CO2 Mixtures in CCS:...

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