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Merge pull request #13551 from cpgr/fixdocs

Fix up rendering in PorousFlow convective mixing example
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permcody committed Jun 12, 2019
2 parents 93c8b6d + e195ed0 commit 90b114b769da0a9bb8e28486c60ae0e429a50071
@@ -110,6 +110,16 @@ @article{duan2003
year={2003}
}

@article{emami,
title={Convective dissolution of CO2 in saline aquifers: Progress in modeling and experiments},
author={Emami-Meybodi, Hamid and Hassanzadeh, Hassan and Green, Christopher P and Ennis-King, Jonathan},
journal={International Journal of Greenhouse Gas Control},
volume={40},
pages={238--266},
year={2015},
publisher={Elsevier}
}

@techreport{garcia2001,
title={{Density of aqueous solutions of CO$_2$}},
author={J. E. Garcia},
@@ -1,22 +1,20 @@
# Density-driven convective mixing

PorousFlow may be used to study the convective mixing of fluids. In this page we discuss the density-driven convective mixing of CO$_{2}$ into brine. CO$_{2}$ exists initially in both the liquid and gas phase. As the CO$_{2} diffuses into the brine, the gaseous CO$_{2}$ disappears and the brine's density increases, which drives convective mixing of the two fluids. Input files for similar situations may be found [here](https://github.com/idaholab/moose/blob/master/modules/porous_flow/examples/lava_lamp).

A few years ago this type of simulation was explored by Chris Green when modelling CO$_{2}$ sequestration. He was particularly interested in quantifying the CO$_{2}$ flux into a brine-filled reservoir, and found that it was dominated by convective mixing rather than diffusion.
PorousFlow may be used to study the convective mixing of fluids. In this page we discuss the density-driven convective mixing of CO$_{2}$ into brine. CO$_{2}$ exists initially in both the liquid and gas phase. As the CO$_{2}$ diffuses into the brine, the gaseous CO$_{2}$ disappears and the brine's density increases, which drives convective mixing of the two fluids and accelerates the dissolution of the gas phase [citep!emami]. Input files for similar situations may be found [here](https://github.com/idaholab/moose/blob/master/modules/porous_flow/examples/lava_lamp).

Because this problem involves the disappearance of the gaseous phase, the simulation utilises persistent primary variables and a vapor-liquid flash.

!listing modules/porous_flow/examples/lava_lamp/2phase_convection.i start=[Variables] end=[]

Here {\tt pgas} is the gas-state pressure (the capillary pressure is zero, so this is also the brine porepressure) and {\tt zi} is the total mass fraction of the CO$_{2}$ summed over the two phases. In this input file, the salt content of the brine is fixed at 0.01:
Here `pgas` is the gas-state pressure (the capillary pressure is zero, so this is also the brine porepressure) and `zi` is the total mass fraction of the CO$_{2}$ summed over the two phases. In this input file, the salt content of the brine is fixed at 0.01:
!listing modules/porous_flow/examples/lava_lamp/2phase_convection.i start=[./xnacl] end=[../]
and the temperature at 45degC:
and the temperature at 45$^{\circ}$C:
!listing modules/porous_flow/examples/lava_lamp/2phase_convection.i start=[./temperature] end=[../]
The porepressure is initialised to approximate hydrostatic conditions, and the total mass fraction of CO$_{2}$ is zero except towards the top of the model domain where it is 0.2. This corresponds to a gas saturation of 0.29 (the gas is almost all CO$_{2}$ and only about 0.2\% brine) and the mass-fraction of CO$_{2}$ in the liquid phase is 0.048. The porosity is slightly randomised and this promotes initiation of the beautiful "fingers" of CO$_{2}$-rich brine seen in the results.
The porepressure is initialised to approximate hydrostatic conditions, and the total mass fraction of CO$_{2}$ is zero except towards the top of the model domain where it is 0.2. This corresponds to a gas saturation of 0.29 (the gas is almost all CO$_{2}$ and only about 0.2% brine) and the mass-fraction of CO$_{2}$ in the liquid phase is 0.048. The porosity is slightly randomised and this promotes initiation of the beautiful "fingers" of CO$_{2}$-rich brine seen in the results.
!listing modules/porous_flow/examples/lava_lamp/2phase_convection.i start=[ICs] end=[]
@@ -50,4 +48,4 @@ The evolution of the CO$_{2}$ mass fraction is shown in the animation below
!media porous_flow/2phase_convection.gif caption=Left: Mass fraction of CO2 in the liquid phase. Right: Saturation of gas. The adaptive mesh is overlayed on each figure. id=2phase_convection_anim
!bibtex bibliography

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