MAC-Kaust Project P1 – CO2 Sequestration Modeling of CO2 sequestration including parameter

identification and numerical simulation

M. Brokate, O. A. Pykhteev Hysteresis aspects of CO2 sequestration modeling

K-H. Hoffmann, N. D. Botkin

Objectives and methods of CO2 sequestration

There is a popular belief that the global warming is caused by the

growing concentration of carbon dioxide (CO2) in the

atmosphere. The objective of CO2 sequestration is disposal of

CO2 by deep injection into a naturally occurring repository.

Among the most important options are injection in saline

aquifers, abandoned oil fields, reservoirs, ocean water, or other

carbon sinks. Numerical simulations are necessary to predict e.g.

the upward leakage of CO2 . They involve mathematical modeling

and optimization of multiphase flows in porous media including

chemical reactions, phase transitions, hysteresis behavior, etc.

CO2 injection well Pumping wells

Platform

Utsira formation

Sleipner gas field

An artist's rendering of the Utsira

CO2 injection (from the thesis of

J. M. Nordbotten)‏

Gas is being produced from the

Sleipner field and separated from

CO2. The last component is being

injected into the Utsira formation.

Norway

An example of CO2 sequestration

are the saturation, density, velocity,

pressure, and stress tensor of phase

respectively.

Sketch of phase velocity equations

,

Simulations Light phase: supercritical CO2

Middle phase: brine (water)

Heavy phase: CO2 dissolved in water

gravity

Spatial separation of phases due to the gravity Transition of supercritical CO2 and

water into dissolved CO2

Play-type hysteresis operator .

Hysteresis behavior of the capillary pessure

Pressure

1st phase is injected

2nd phase is injected,

1st phase gets replaced

1st phase is injected again

2nd phase is injected,

1st phase gets replaced

is the saturation of phase .

Internal auxiliary variable governed by:

Are finite differences OK?

KAUST internship student Luiz Faria has to

prove the feasibility of finite differences

flux

PDE constrained optimization in CO2 sequestration M. Ulbrich, M. Simon

Objective: maximize the amount of trapped carbon dioxide in the reservoir

Structural trapping by impermeable cap rock Residual trapping dependent on porosity

(pictures taken from http://www.co2captureproject.org/co2_trapping.html)‏

State Variables y Conservation of Mass: PDE Constraints Control Parameters u Optimization Criteria

Model Setup Physical Agreements

drainage/imbibition curves

obtained values

Saturation

Capilla

ry p

ress

ure