co sequestration simulations: a comparison study … · 2 sequestration simulations: a comparison...

Universitat Stuttgart - Institut fur WasserbauLehrstuhl fur Hydromechanik und Hydrosystemmodellierung

Prof. Dr.-Ing. Rainer Helmig

Diplomarbeit

CO2 sequestration simulations:

A comparison study between DuMuX and

Eclipse

Submitted by

Walter Vogel

Matrikelnummer 2203193

Stuttgart, July 2nd, 2009

Examiners: Prof. Dr.-Ing. Rainer Helmig

Dr.-Ing. Holger Class

Supervisor: Dipl.-Ing. Melanie Darcis

Dipl.-Ing. Felix Leicht (RWE Dea)

Contents

1 Introduction 1

1.1 CO2 sequestration - the solution for intermediate term clean energy? . 1

1.2 Current work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1 Schlumberger ECLIPSE . . . . . . . . . . . . . . . . . . . . . . 4

1.3.2 DuMuX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Structure of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Physical properties 7

2.1 Fluid properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Carbon dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.2 Brine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.3 Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Capillary pressure and permeability . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Capillary pressure-saturation relationship . . . . . . . . . . . . . 14

2.2.2 Relative permeability-saturation relationship . . . . . . . . . . . 15

2.2.3 Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Flow and transport processes . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.1 Advection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.3 Diffusion and Dispersion . . . . . . . . . . . . . . . . . . . . . . 19

2.3.4 Thermal conduction and convection . . . . . . . . . . . . . . . . 19

2.4 Trapping mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Model concept 22

3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.1 Scales, the representative elementary volume . . . . . . . . . . . 22

3.1.2 Phases and components . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Multiphase multi-component system . . . . . . . . . . . . . . . . . . . 23

3.3 Conceptual model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4.1 Momentum and continuity equation . . . . . . . . . . . . . . . . 25

CONTENTS i

3.4.2 Conservation of energy . . . . . . . . . . . . . . . . . . . . . . . 26

3.4.3 Mass balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.4 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.5 Closure conditions . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4.6 Primary variables . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 Numerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5.1 Time discretization . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.5.2 Space discretization . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Simulations with ECLIPSE E300 35

4.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Basic case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.1 Benchmark variables . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 Effect of hysteresis model . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 Influence of the injection schedule and hysteresis (additionally) . . . . . 45

4.5 Influence of the injection rate . . . . . . . . . . . . . . . . . . . . . . . 50

4.6 Effect of rock compressibility . . . . . . . . . . . . . . . . . . . . . . . . 55

4.7 Injection of CO2 in pure water . . . . . . . . . . . . . . . . . . . . . . . 55

4.8 Different reservoir temperatures . . . . . . . . . . . . . . . . . . . . . . 60

5 Simulations with DuMuX 67

5.1 Two-phase model (isothermal) . . . . . . . . . . . . . . . . . . . . . . . 67

5.2 Two-phase non-isothermal . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.3 Two-phase two-component non-isothermal . . . . . . . . . . . . . . . . 84

6 Summary and outlook 98

List of Figures

2.1 p,T-diagram for CO2 [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Carbon dioxide density with increasing temperature at p = 257.5 bar.

Data from [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Carbon dioxide viscosity with increasing temperature at p = 257.5 bar.

Data from [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Brine density with increasing temperature at p = 257.5 bar. The dia-

gram also shows the effect of dissolved CO2 on brine. Data from [19]. . 12

2.5 CO2 solubility with temperature at a constant pressure of 257.5 bar.

Data from [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6 CO2 solubility with depth (dependent on temperature, pressure and

salinity for a possible reservoir). Data from [19]. . . . . . . . . . . . . . 13

2.7 Capillary pressure-saturation relation (entry pressure: 0.05 bar, λ = 2,

Swr = 0.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.8 Relative permeability-saturation relation (entry pressure: 0.05 bar, λ =

2, Swr = 0.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.9 Trapping mechanisms on different time-scales (from [13], modified from

[6]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1 Definition of the size of a representative elementary volume (REV) after

[8] from [13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Two phase two-component model concept for the system CO2-water [9]. 25

3.3 Basis function Nj (from [9]). . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Finite element and finite volume mesh of the BOX method (from [9]). . 34

4.1 Geometry of the model (ECLIPSE), enlarged in z-direction . . . . . . . 37

4.2 Grid with control points (ECLIPSE). . . . . . . . . . . . . . . . . . . . 40

4.3 Example of scanning curves (from [26]). . . . . . . . . . . . . . . . . . . 41

4.4 Basic case: Bottom hole pressure at the injection well. . . . . . . . . . 42

4.5 Non-wetting phase saturation at control point three (cell 25-2-10, 115 m

from the injection well) with hysteresis option turned on. . . . . . . . . 43

4.6 Non-wetting phase saturation at control point four (cell 35-2-1, 422 m

from the injection well) with hysteresis option turned on. . . . . . . . . 44

ii

LIST OF FIGURES iii

4.7 Non-wetting phase saturation front, about 115 m away from the injection

well, directly after the injection. . . . . . . . . . . . . . . . . . . . . . . 44


well, 10 years after the injection. . . . . . . . . . . . . . . . . . . . . . . 45

4.9 Bottom hole pressure at the injection well (cell 1-1-1) with modified

injection schedule and hysteresis option turned on. . . . . . . . . . . . . 47


from the injection well) with hysteresis option turned on and changed

injection schedule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47


from the injection well) with hysteresis option turned on and changed

injection schedule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48


well, directly after the injection with hysteresis option turned on and

changed injection schedule. . . . . . . . . . . . . . . . . . . . . . . . . . 49


well, 10 years after the injection with hysteresis option turned on and

changed injection schedule. . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.14 Bottom hole pressure at injection well (cell 1-1-1) with modified injection

rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.15 Non-wetting phase saturation at control point two (cell 25-2-1, 115 m

from the injection well) with modified injection rate. . . . . . . . . . . 52






well,directly after the injection. . . . . . . . . . . . . . . . . . . . . . . 54


well, 10 years after the injection. . . . . . . . . . . . . . . . . . . . . . . 54

4.20 Bottom hole pressure at control point four (cell 35-2-1, 422 m from the

injection well) with compressibility model turned on. . . . . . . . . . . 55

4.21 Bottom hole pressure at injection well (cell 1-1-1), injection into water. 56

4.22 Wetting phase density at control point two (cell 25-2-1, 115 m from the

injection well), injection into water. . . . . . . . . . . . . . . . . . . . . 57

4.23 CO2 mole fraction in the wetting phase at control point two (cell 25-2-1,

115 m from the injection well), injection into water. . . . . . . . . . . . 57


from the injection well), injection into water. . . . . . . . . . . . . . . . 58


well, directly after the injection, injection into water. . . . . . . . . . . 59

LIST OF FIGURES iv


well, 10 years after the injection, injection into water. . . . . . . . . . . 59

4.27 Bottom hole pressure at injection well (cell 1-1-1), different reservoir

temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.28 Wetting phase density at control point two (cell 25-2-1, 115 m from the

injection well), different reservoir temperatures. . . . . . . . . . . . . . 62

4.29 Non-wetting phase density at control point two (cell 25-2-1, 115 m from

the injection well), different reservoir temperatures. . . . . . . . . . . . 62

4.30 Non-wetting phase mobility at control point one (cell 25-1-1, 115 m from

the injection well), different reservoir temperatures. . . . . . . . . . . . 63

4.31 Non-wetting phase saturation at control point two (cell 25-1-1, 115 m

from the injection well), different reservoir temperatures. . . . . . . . . 64


from the injection well), different reservoir temperatures. . . . . . . . . 64

4.33 CO2 mole fraction in the wetting phase at control point two (cell 25-2-1,

115 m from the injection well), different reservoir temperatures. . . . . 65


well, directly after the injection, different reservoir temperatures. . . . . 65


well, 10 years after the injection, different reservoir temperatures. . . . 66

5.1 Bottom hole pressure at injection well (cell 1-1-1), DuMuX isothermal

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.2 Non-wetting phase density (cell 25-1-1), DuMuX isothermal model. . . 70

5.3 Wetting phase density (cell 25-1-1), DuMuX isothermal model. . . . . . 70

5.4 Non-wetting phase Mobility (cell 25-1-1), DuMuX isothermal model. . . 71

5.5 Non-wetting phase saturation (cell 19-1-1), DuMuX isothermal model. . 72

5.6 Non-wetting phase saturation (cell 35-1-1), DuMuX isothermal model. . 73

5.7 Non-wetting phase saturation (cell 25-2-10), DuMuX isothermal model. 73

5.8 Non-wetting phase saturation front (directly after injection about 115

m away from the injection well), DuMuX isothermal model. . . . . . . 74

5.9 Non-wetting phase saturation front (10 years after injection about 115

m away from the injection well), DuMuX isothermal model. . . . . . . 74

5.10 Bottom hole pressure at injection well (cell 1-1-1), DuMuX 2pni model. 76

5.11 Temperature at cell 19-1-1 (51 m away from injection), DuMuX 2pni

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.12 Temperature at cell 25-1-1 (115 m away from the injection), DuMuX

2pni model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.13 Non-wetting phase density (cell 19-1-1), DuMuX 2pni model. . . . . . . 79

5.14 Wetting phase density (cell 19-1-1), DuMuX 2pni model. . . . . . . . . 79

5.15 Non-wetting phase mobility (cell 19-1-1), DuMuX 2pni model. . . . . . 80

5.16 Non-wetting phase mobility (cell 25-1-1), DuMuX 2pni model. . . . . . 80

LIST OF FIGURES v

5.17 Non-wetting phase saturation (about 51 m away from the injection well,

cell 19-1-1), DuMuX 2pni model. . . . . . . . . . . . . . . . . . . . . . 81

5.18 Non-wetting phase mass per m3 (about 115 m away from the injection

well, cell 25-2-10), DuMuX 2pni model. . . . . . . . . . . . . . . . . . . 82

5.19 Non-wetting phase saturation (about 115 m away from the injection

well, cell 25-2-10), DuMuX 2pni model. . . . . . . . . . . . . . . . . . . 82

5.20 Non-wetting phase saturation front, directly after injection (about 115

m away from the injection well) - DuMuX 2pni model. . . . . . . . . . 83

5.21 Non-wetting phase saturation front, 10 years after injection stop (about

115 m away from the injection well) - DuMuX 2pni model. . . . . . . . 84

5.22 Model concept for the DuMuX two-phase non-isothermal model. . . . . 85

5.23 Bottom hole pressure at injection well (cell 1-1-1), DuMuX 2p2cni model. 86

5.24 Temperature (about 51 m away from the injection well, cell 19-1-1),

DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.25 Wetting phase density (about 51 m away from the injection well, cell

19-1-1), DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . . . . . . 87

5.26 Non-wetting phase density (about 51 m away from the injection well,

cell 19-1-1), DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . . . . 88

5.27 Non-wetting phase mobility (about 51 m away from the injection well,


5.28 Non-wetting phase saturation (about 51 m away from the injection well,


5.29 Non-wetting phase saturation (about 115 m away from the injection

well, cell 25-2-10), DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . 90

5.30 Mole fraction CO2 in water (about 51 m away from the injection well,


5.31 Mole fraction water in CO2 (about 51 m away from the injection well,


5.32 Temperature in r-direction, directly after injection - DuMuX 2p2cni model. 92

5.33 Temperature in r-direction, 10 years after injection stop - DuMuX 2p2cni

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.34 Temperature front, directly after injection (about 51 m away from the

injection well) - DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . . 93

5.35 Temperature front, 10 years after injection stop (about 51 m away from

the injection well) - DuMuX 2p2cni model. . . . . . . . . . . . . . . . . 93

5.36 Non-wetting phase saturation in r-direction, directly after injection -

DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.37 Non-wetting phase saturation in r-direction, 10 years after injection stop

- DuMuX 2p2cni model. . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.38 Non-wetting phase saturation front, directly after injection (about 115

m away from the injection well) - DuMuX 2p2cni model. . . . . . . . . 96

LIST OF FIGURES vi

5.39 Non-wetting phase saturation front, 10 years after injection stop (about

115 m away from the injection well) - DuMuX 2p2cni model. . . . . . . 97

List of Tables

2.1 Physico-Chemical properties of carbon dioxide [21] . . . . . . . . . . . 8

2.2 Physico-Chemical properties of carbon dioxide at reservoir (353 K, 257.5

bar) and injection conditions (308 K, 257.5 bar). Data from [19]. . . . . 9

2.3 Physico-Chemical properties of pure brine at 353 K and 308 K (injec-

tion), 257.5 bar [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Physico-Chemical properties of CO2-saturated brine at 353 K and 308

K (injection), 257.5 bar [19] . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Wetting and non-wetting fluids . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Primary variables and corresponding phase states [9]. . . . . . . . . . . 29

4.1 Overview of all simulations . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Model parameters for the basic case . . . . . . . . . . . . . . . . . . . . 38

4.3 Benchmark variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Hysteresis: Model parameters that differ from basic case . . . . . . . . 40

4.6 Injection schedule: Model parameters that differ from the basic case . . 46

4.7 Injection rate: Model parameters that differ from the basic case . . . . 50

4.8 Injection into water: Model parameters that differ from basic case . . . 56

4.9 Temperature: Model parameters that differ from basic case . . . . . . . 60

4.10 Viscosity values in the ECLIPSE E300 model for various temperatures. 61

5.1 Model parameters for the DuMuX isothermal case . . . . . . . . . . . . 68

5.2 Model parameters that differ from the DuMuX isothermal case . . . . . 76

0

Chapter 1

Introduction

Currently the energy that we use in our daily life comes from 4 major sources:

− Fossil fuels (oil, coal, gas)

− Nuclear power

− Hydropower

− New regenerative power (wind, solar, waste)

The question which source should be preferred cannot be answered so quickly. Re-

generative power sources are probably the most clean sources of energy but currently

cannot support major industries mainly due to energy storage problems. Hydropower

is also very clean and a favorable source of energy, but its availability is quite limited,

too and major dams have already been built where possible. The problem with nuclear

power is the unsolved question of where to store the waste safely for a couple of thou-

sand years. That leaves fossil fuels: While there is a lot of coal available in Germany,

oil and gas have to be imported from foreign countries, thus various political factors

can influence this source of energy supply. However, coal is also not a perfect source

of energy because the product of the combustion process - mainly CO2 - is one of the

greenhouse gases that are said to be responsible for climate change. The consequences

and gravity of a changing climate are currently not well understood, however the price

of the worst scenarios to come true is seen to be so high that politicians have agreed

on a system of trading CO2 emission certificates which will make the emission of CO2

expensive and hopefully will help to avoid major environmental changes.

1.1 CO2 sequestration - the solution for intermedi-

ate term clean energy?

One idea of avoiding CO2 emissions into the atmosphere is to capture it at large point

sources, for example fossil fuel power plants and store it underground. This process is

1.2 Current work 2

known as CO2 Capture and Storage (CCS). The idea behind this process is to capture

the CO2 directly before or after the combustion of hydrocarbon fuel (pre-combustion or

post-combustion capture), transport it under high pressure to a storage site and trap

it beneath an impermeable rock layer deep underground. Due to the high pressure, the

CO2 is not actually a gas but a supercritical fluid with a higher density. However, it

is still lighter than water which means that it migrates upwards due to buoyancy. The

various trapping mechanisms that occur during sequestration are explained in more

detail in section 2.4. During injection and the first approximately 100 years of storage

the most important mechanism is structural and stratigraphic trapping below the cap

rock (an impermeable stratigraphic layer). Simulations have shown that the CO2 will

rise up to this impermeable layer and accumulate there. In this work, the results of

simulations that cover the first 5-20 years of storage will be presented.

To conclude this short introduction: If the storage site is safe, this might be a solution

for intermediate term ”clean” energy where the CO2 is kept out of the atmosphere.

While the legal framework for regulating CO2 storage sites is not yet in place, major

pilot plants are already being planned and suitable storage sites (for example deep

saline formations) are examined.

1.2 Current work

This work is part of the research made to understand the thermal effects on the spread-

ing of CO2 in the subsurface, the rock matrix and in particular the effects of thermally

induced shrinkage. The background for this work is that several effects that are related

to temperature changes are expected during and after the injection of CO2:

− When the density decreases, the volume increases. This can lead to an increase

in pressure if the space is limited;

− When the temperature of the soil decreases too quickly, stresses are induced that

could lead to fractures which could become preferred pathways;

− With the decrease of viscosity, the fluid will spread more quickly as it heats up.

The contribution to this research is to model the heat and fluid flow from the well

perforation into the reservoir with two different numerical simulators: Schlumberger

ECLIPSE, a well known commercial finite differences simulator that is widely used

in the oil industry and DuMuX [4], a vertex centered finite volume simulator and

research project for multiphase multicomponent flow processes based on the dune-

project [5]. The first simulations with ECLIPSE were done at RWE Dea in Hamburg,

the second part at the department of Hydromechanics and Modeling of Hydrosystems

at the University of Stuttgart.

Currently a lot of research regarding CO2 sequestration is being done due to the risk

of global warming. In the following few paragraphs I want to mention and give a very

1.2 Current work 3

brief summary of related research, however, I have no intention of giving a complete

list.

Numerical simulations of CO2 injection:

A very good introduction into the topic of CO2 sequestration and numerical simulation

gives the dissertation [9]. In this work a physico-mathematical model concept is devel-

oped for the description of CO2 storage in deep saline formations. A. Bielinski describes

non-isothermal flow and transport processes and presents example problems concerning

long term storage. Simulations were carried out with MUFTE-UG (Multiphase Flow

Transport and Energy Model on Unstructured Grids).

In [18] numerical simulations of CO2 sequestration are compared to semi-analytical

results. The aim of this paper is to ”set up problem-oriented benchmark examples that

allow a comparison of different modeling approaches to the problem of CO2 leakage”.

After the isothermal simulation results were matched to the semi-analytical solutions,

more complex processes like variable fluid properties, non-isothermal and compositional

effects were included. In the present work a similar approach is chosen to compare the

two simulators.

[14] gives an overview of recent developments. In short, the authors describe the

involved physical processes advection, dissolution, diffusion and dispersion, density

driven current, geochemical reactions and non-isothermal effects. Multiple simulations

are presented and address current challenges, for example the influence of phase com-

position.

The article [22] presents simulations of CO2 injection scenarios with Schlumberger

ECLIPSE. It addresses complex processes such as dry-out, salting out and chemical

reactions related to CO2 injections in water/brine1 aquifers. The properties of the

modeled reservoir are taken from the CO2SINK project in Ketzin [29]. Since the depth

(and therefore the hydrostatic pressure) is considerably lower than in this study the

results cannot be compared directly.

Thermal effects:

In [25] the author presents simulations of CO2 leakage through an idealized fault from

an underground storage reservoir. Since the amounts of CO2, that will have to be

stored will spread over large areas, faults in the cap rock will likely be encountered.

The aim of the paper is to study heat transfer effects and phase changes of the CO2.

The simulations were carried out with the TOUGH2 simulator [1] of the Lawrence

Berkeley National Laboratory.

An introduction on reasons for the consideration of thermal effects in the simulations

gives [15]. This paper presents a way ”to simulate the possible effects of water-induced

rock compaction” as a chalk formation is flooded by cold seawater. The effects of rock

compaction can also - to a smaller extent - occur when cold CO2 is injected into the

storage area. Fractures may lead to preferred pathways and influence expected arrival

times.

1salt-water

1.3 Software 4

Several major projects on nearly all continents are already operating and monitoring

CO2 injection and its flow through the subsurface. I have picked 3 examples of well

known projects. More about these and other projects can be found on [3].

− Sleipner in Norway: This project is well known as it is the first commercial-scale

operation for storing CO2. It has been operational since August 1996, long before

the general discussion about climate change has directed much attention to the

idea of CO2 storage. From the Sleipner field below this storage area, natural gas

is produced and contains about 9% CO2. The exported gas however may only

contain about 2.5% which results in about 1 million tonne CO2/year that has

to be dealt with. To avoid high taxes this CO2 is stored in the saline aquifer

(called the Utsira formation) which is located above the field and about 800 m

below the bed of the North Sea. The CO2 movement is monitored by 3D seismic

examination (data was aquired 1994, prior to injection and in later years) [10].

− CLEAN in Germany is a study related to enhanced gas recovery (EGR). Aban-

doned gas reservoirs are a convenient storage area for CO2: The accumulation

of natural gas is a proof for a secure storage area where the CO2 can be stored

for several hundreds of years. The CLEAN project (see [2]) is a research project

that investigates the CO2 injection technology, geological processes, process moni-

toring and public acceptance.

− CO2SINK in northern Germany: This project is located at Ketzin, about 25

km west of Berlin. The storage formation lies about 700 m below the surface

which is the minimum depth to insure supercritical pressure. The project was

initiated to ”address and alleviate potential public concerns about the safety

and environmental impact of geological storage” [29] and to fill the gap between

numerical simulations and actual CO2 injections. The aim of the case study is in

particular to monitor the migration of CO2 in the storage formation, to observe

at which rate CO2 dissolves in brine and how chemical reactions lead to mineral-

bound CO2, to assess the possibility of leakage and to develop a risk assessment

for long term CO2 storage.

1.3 Software

To introduce the software that has been used in this study, a short overview will be

given for both ECLIPSE and DuMuX without going into much detail. Later in chapter

4 the options that have been used will be described.

1.3.1 Schlumberger ECLIPSE

The Schlumberger ECLIPSE reservoir simulation software is a well established com-

mercial software package that has been used by the oil industry for about 25 years. The

1.3 Software 5

version that I was allowed to use at RWE Dea was 2006.2 which is about 2 years old and

still widely used. There are two different types of simulators: The ECLIPSE E100 has

an integrated black oil simulator and ECLIPSE E300 is specialized in compositional

modeling. In this study ECLIPSE E300 was used and in the following paragraphs a

short description of its features will be given.

E300

The ECLIPSE E300 is a numerical simulator written in FORTRAN77 which uses a

finite differences (FD) method to discretize and solve multiphase multicomponent flow

equations. Since it is a commercial software not much is known about how this is done

but of course it is well documented what it can do.

The ECLIPSE E300 can use 3 calculation methods for the next time step: fully implicit,

adaptive implicit and IMPES. The fully implicit method provides the best stability for

long time steps, while the adaptive implicit method tries to save computation time

and memory by ”making cells implicit only when necessary” [26]. IMPES stands for

”implicit pressure explicit saturation”. For the simulations related to this work the

fully implicit method was used.

ECLIPSE 2006.2 can simulate various CO2 storage scenarios:

− Storage in aquifers: Using the keyword CO2SEQ a two-phase (CO2 rich and H2O

rich) two-component simulation can be calculated. Using the GASWAT keyword,

other gases can be used instead of CO2 however the mole fraction of H2O in the

gas is not as accurate as with the CO2SEQ option. In this work the CO2SEQ

keyword was used.

− Storage in oil depleted reservoirs and enhanced oil recovery using the CO2SOL

keyword. With this keyword, the mole fraction of H2O in non-wetting phase is

not considered.

− Storage in gas depleted reservoirs using the GASWAT keyword.

− Enhanced coal bed methane recovery using the COAL keyword.

Grids for ECLIPSE E300 can be 3-dimensional with Cartesian or radial coordinates.

Sections can be refined via local grid refinement to focus on a relevant area. Several

other options are possible which I will not describe further since in this study only a

very simple 3-D grid with radial coordinates has been used.

Finally, I want to mention several options which probably should be used but were not

for comparison reasons, since they are not (yet) implemented in DuMuX:

− Hysteresis: Multiphase flow in porous media is generally affected by Hysteresis,

which is described in more detail in section 2.2.3 on page 17. ECLIPSE E300

supports the simulation of hysteresis via the HYSTER and EHYSTER keyword

1.4 Structure of this work 6

for both relative permeability and capillary pressure - saturation relations. Dif-

ferent tables for the drainage and imbibition processes can be specified. In the

future DuMuX will also be able to simulate this effect.

− Rock compaction: Via the ROCK keyword the compaction of the rock during

drainage can be simulated. The rock compaction can be either reversible or

irreversible. A hysteretic model is also implemented.

− Composition of injected gas stream: The composition of the injected gas stream

can be specified. With this option it is possible to simulate the effect of wet gas.

1.3.2 DuMuX

DuMuX is a multi-scale, multi-phase, multi-component simulation program based on

the DUNE framework (see [5]) which can simulate flow and transport processes in

porous media. DuMuX has the capability to model non-isothermal compositional mul-

tiphase flow which is an advantage to the previously presented ECLIPSE since the

effects of heat transfer could influence the outcome of the flow simulation due to den-

sity, mobility and solubility changes.

DUNE (Distributed and Unified Numerics Environment) is a framework for solving

partial differential equations programmed in C++. It consists of several modules with

the core modules dune-common (basic classes used by all modules), dune-grid (grids in

arbitrary space dimensions), dune-istl (Iterative Solver Template Library) and dune-

disc (discretization algorithms and shape functions).

DuMuX is an additional module to this framework (dune-mux ) and provides a frame-

work for the implementation of porous media flow problems. Several models are avail-

able, including among others ”fully coupled two-phase flow”. DuMuX is open source -

the user has therefore complete control over the calculation. It is, however, a research

project and currently still under development. For more information about DuMuX

please see [20], the projects’ website can be found under [4].

1.4 Structure of this work

In the first part of this work, the relevant fluid properties for brine and CO2, fluid-soil-

relationships (capillary pressure- and relative permeability-saturation relationships)

and transport processes (advection, buoyancy, diffusion) are described.

In the second part the model concept, the mathematical and numerical model are

explained.

The third part will contain the actual description and comparison of numerical

simulations with ECLIPSE and DuMuX including an investigation of the effect of

several ECLIPSE options and 3 DuMuX models (two-phase isothermal, two-phase

non-isothermal and two-phase two-component non-isothermal).

Chapter 2

Physical properties

2.1 Fluid properties

The thermodynamic properties pressure (p) and temperature (T) at suitable storage

sites differ from the conditions on the surface that we are used to. To understand the

fluid properties at these storage sites, it is helpful to look at phase diagrams and the

equations of state for carbon dioxide and water.

An equation of state describes the relationship between pressure, volume and

temperature for a substance. Over the years several equations of state have been

developed. Simple ones are for example the ideal gas law or the Van-der-Waals cubic

equation of state. The equations of state used today have become more and more

complex and can cover broader pressure and temperature ranges. This is especially of

interest when phase changes are expected to occur during a simulation, because fluid

properties will then change abruptly. However not only phase changes are of interest:

Every change in temperature and pressure will influence the density and viscosity of a

substance, which then influences the fluid flow.

Figure 2.1 shows a phase diagram of CO2 with marked triple and critical point.

When temperature and pressure exceed the critical values (the values of the critical

point) the fluid is neither liquid nor gaseous but called a supercritical fluid. It has

the density of a liquid and the viscosity of a gas. Fluid properties change continually

and no phase change occurs when temperature and pressure change from super- to

subcritical values (or from sub- to supercritical).

In multiphase flow simulations viscosity and density play an important role. The

viscosity characterizes the fluids’ resistance with respect to deformation: µ = τdudy

,

where τ is the shear stress and dudy

is the velocity gradient. The lower a fluids’ viscosity,

the lower is its resistance to flow (the higher is its maximum velocity). The viscosity

influences the advective flow and the displacement of one fluid by another: If the

viscosity of the injected fluid is higher than the viscosity of the fluid that is in the

reservoir, the displacement front is stable. On the other hand if the viscosity of the

injected fluid is lower, the displacement front can become unstable [13].

2.1 Fluid properties 8

The relative density between the injected and the resident fluid determines how gravity

effects like buoyancy influence the flow process, the displacement front and whether

the injected fluid will ultimately (even after the injection has stopped) rise to the top

of the reservoir or sink to the bottom.

As mentioned before, density and viscosity can be strongly influenced by temperature

changes. As we will see later in section 2.1.1 and 2.1.2, the temperature does not affect

water and carbon dioxide in the same way and therefore the fluid flow will be influenced

by temperature effects.

In general, density and viscosity of liquids increase with increasing pressure and de-

crease with increasing temperature. However in a gaseous fluid, viscosity increases with

increasing temperature (more friction due to faster moving particles). At supercritical

conditions viscosity decreases with increasing temperature.

2.1.1 Carbon dioxide

Carbon dioxide is a colorless and odorless gas and a natural component of air. The

pre-industrial concentration in the air was about 0.026 %, however, the current con-

centration is at about 0.038 % and climbing due to combustion of fossil fuels and

possibly deforestation. The carbon dioxide concentration rises and falls also in a sea-

sonal pattern by about 0.0006 %. Carbon dioxide is used as the reference greenhouse

gas and has therefore by definition a greenhouse gas potential of 1.

2.1.1.1 Physico-Chemical properties

In order to become familiar with carbon dioxide, it is a good idea to first look at its

physico-chemical properties which are listed in table 2.1.

Property Value

Molar mass 44.01 gmol

Appearance (273.15 K, 1.013 bar) colorless and odorless gas

Density 1.9767 kgm3

Relative density to air 1.53

Sublimation temperature at 1.013 bar 194.65 K (-78.5 C)

Triplepoint 216.58 K (-56.57 C), 5.185 bar

Critical point 304.08 K (30.95 C), 73.77 bar

Viscosity at normal conditions 17.5 µPas [27]

Table 2.1: Physico-Chemical properties of carbon dioxide [21]

Reservoir conditions differ strongly from the conditions on the surface. To get an idea

about the conditions in a possible reservoir (approx. 353 K, 257.5 bar, brine salinity

0.173 kg/kg) and during injection (308.15 K) the approximate density and viscosity


reservoir injection

Density 697 kgm3 907 kg

m3

Relative density to brine 0.63 0.80

Viscosity 57.3 µPas 93.2 µPas

Relative viscosity to brine 0.11 0.087

Solubility in brine 27.36 gkg

27.83 gkg

Table 2.2: Physico-Chemical properties of carbon dioxide at reservoir (353 K, 257.5

bar) and injection conditions (308 K, 257.5 bar). Data from [19].

values for these temperature and pressure values are also mentioned at this point. The

values are listed in table 2.2.

The phase diagram for carbon dioxide is shown in figure 2.1

Figure 2.1: p,T-diagram for CO2 [9].

The estimated temperature and pressure for the reservoir and the values that have been

used in the present simulations are 353.15 K (80 C) and 257.5 bar (25.75 MPa). Both

values are clearly above the values of the critical point for CO2. Therefore the super-

critical properties of CO2 and the change of density and viscosity with temperature

are of particular interest.

The assumed temperature of the carbon dioxide prior to injection is at about 308.15

K (35 C). As the fluid is injected, its temperature will increase gradually, however at

the same time the temperature of the soil (and brine) will decrease. With changing


temperature, density and viscosity of both carbon dioxide and brine are expected to

change. In figure 2.2 the change of carbon dioxide density with increasing temperature

is shown. The data has been calculated with the online tool at [19] (Ennis King),

expected reservoir conditions for pressure, temperature and salinity have been applied.

0,6

0,7

0,8

0,9

1

1,1

CO

2 d

en

sity

[g

/cm

³]

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 20 40 60 80 100 120

CO

2 d

en

sity

[g

/cm

³]

Temperture [°C]

CO2 density Linear (CO2 density)

Figure 2.2: Carbon dioxide density with increasing temperature at p = 257.5 bar. Data

from [19].

In figure 2.3 the change of carbon dioxide viscosity is shown.

2.1.2 Brine

The pores of the storage area are not empty but filled with brine. This brine will have

to be displaced by the injected carbon dioxide. Its physical properties are therefore

also of interest, again especially its density, viscosity and its ability to dissolve CO2.

The density of the water changes not only with temperature and pressure but also with

the amount of dissolved salt and ultimately when CO2 gets dissolved. The property

changes of brine will not be as obvious as the property changes of carbon dioxide but

they will still be measurable and will be considered in the calculations.

First a tabular overview of the important physico-chemical properties of brine is pre-

sented and later diagrams are shown in which the effects can be seen more easily. Table

2.3 shows values for pure brine, while table 2.4 shows values for fully CO2 saturated

brine.


40

60

80

100

120

140

160

Vis

cosi

ty [

µP

as]

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120

Vis

cosi

ty [

µP

as]

Temp [°C]

Viscosity [µPas] Poly. (Viscosity [µPas])

Figure 2.3: Carbon dioxide viscosity with increasing temperature at p = 257.5 bar.

Data from [19].

reservoir injection

Density 1103 kgm3 1130.2 kg

m3

Relative density to carbon dioxide 1.59 1.25

Viscosity 540.9 µPas 1066 µPas

Relative viscosity to carbon dioxide 9.47 11.44

Table 2.3: Physico-Chemical properties of pure brine at 353 K and 308 K (injection),

257.5 bar [19]

reservoir injection

Density 1107.3 kgm3 1134.1 kg

m3

Relative density to pure brine 1.0039 1.0035

Relative density to carbon dioxide 1.59 1.25

Table 2.4: Physico-Chemical properties of CO2-saturated brine at 353 K and 308 K

(injection), 257.5 bar [19]


1,07

1,09

1,11

1,13

1,15B

rin

e d

en

sity

[g

/cm

³]

1,05

1,07

1,09

1,11

1,13

1,15

0 20 40 60 80 100 120

Bri

ne

de

nsi

ty [

g/c

m³]

Temperature [°C]

CO2-saturated Unsaturated

Figure 2.4: Brine density with increasing temperature at p = 257.5 bar. The diagram

also shows the effect of dissolved CO2 on brine. Data from [19].

2.1.3 Solubility

One of the storage mechanisms which is expected to ensure that the CO2 will not

escape from the reservoir is its dissolution in water/brine. The amount of dissolved

CO2 may be small but it still has to be considered especially for long-term models.

Dissolved CO2 is the precondition to form carbonates, the most secure form of CO2

storage (which is not considered in this work and is only expected to be of any relevant

effect after several hundreds or thousands of years). The ECLIPSE model considers

CO2 dissolution, in DuMuX it is only considered in the two-phase two-component

model.

The solubility of CO2 in brine is not constant but changes with temperature and

pressure as can be seen in figure 2.5. At the relatively hot reservoir temperature,

the solubility is lower than at the colder injection temperature. The cooling effect of

the injected (cold) carbon dioxide has therefore a (small) positive effect on its solu-

bility. However as mentioned before the amount of dissolved CO2 is small compared

to the total mass of injected carbon dioxide. In figure 2.6 both effects of pressure and

temperature change on the solubility can be observed.

The dissolved carbon dioxide has another effect which has already been shown in table

2.4: It slightly changes the density of brine. This will also help - over time - to secure

the stored carbon dioxide, because water saturated with CO2 will ultimately sink to the

bottom of the reservoir, while non-saturated water will rise and can dissolve more CO2.

It should not be overseen, however, that these effects are very small and it will take

long time until they become relevant. See also section 2.4 on trapping mechanisms.


28

28,5

29

29,5

30

30,5

CO

2 s

olu

bil

ity

[g

/kg

bri

ne

]

27

27,5

28

28,5

29

29,5

30

30,5

0 10 20 30 40 50 60 70 80 90 100

CO

2 s

olu

bil

ity

[g

/kg

bri

ne

]

Temperature [°C]

CO2 solubility Poly. (CO2 solubility )

Figure 2.5: CO2 solubility with temperature at a constant pressure of 257.5 bar. Data

from [19].

0

1000

2000

0 10 20 30 40 50 60

De

pth

[m

]

CO2 solubility [g/kg brine]

0

1000

2000

3000

4000

0 10 20 30 40 50 60

De

pth

[m

]

CO2 solubility [g/kg brine]

CO2 solubility

Figure 2.6: CO2 solubility with depth (dependent on temperature, pressure and salinity

for a possible reservoir). Data from [19].

2.2 Capillary pressure and permeability 14

2.2 Capillary pressure and permeability

Capillarity is the result of cohesive and adhesive forces. While cohesion describes inter-

molecular forces between particles of the same type and results in surface tension and

the usually curved surface, adhesion describes intermolecular forces between particles

of different type e.g. between a solid and a liquid.

The fluids in the tiny pores of a porous medium are also affected by capillarity and

thus also have curved surfaces. The pressure on the concave side is higher than on the

convex side - the pressure difference is the capillary pressure.

Depending on the angle that exists between fluid and solid, we can differentiate between

wetting and non-wetting fluids (see table 2.5) [9].

0 ≤ θ < 90 wetting fluid

90 < θ ≥ 180 non-wetting fluid

θ = 90 no capillary forces

Table 2.5: Wetting and non-wetting fluids

While the wetting fluid will occupy smaller pores first, because of its affinity to the

solid, the non-wetting fluid will fill larger pores and possibly never enter the smallest

ones. Capillarity and whether a fluid is wetting or non-wetting is therefore important

for porous media flow. As will be explained in section 2.4, this is another mechanism

that helps to trap the CO2 in the reservoir.

2.2.1 Capillary pressure-saturation relationship

The capillary pressure for each pore depends on its radius, the contact angle and the

surface tension. Since the wetting phase tends to fill smaller pores first, smaller pores

are occupied when the saturation level is low. Therefore the average radius of the

filled pores is smaller at low saturation levels and consequently the capillary pressure

is higher.

In multiphase simulations however usually a representative elementary volume (REV)

is defined where the pore volume is averaged. In this REV the capillary pressure

depends on the saturation level. An exact description of the relationship between

capillary pressure and saturation level has not yet been found. However there are two

well-known parametrizations for the capillary pressure-saturation relationship which

are implemented in DuMuX (van Genuchten and Brooks & Corey, the latter will be

explained in the following paragraph). In ECLIPSE this problem is solved with tables

where data from core samples or from other simulation programs can be entered. In

the simulations for this work however, tables were generated with a Brooks & Corey

approach, since the original data for the soil is usually classified and was not available.

In the Brooks & Corey equation (2.1) the λ represents again an empirical parameter for

the uniformity of the soil (the greater the λ, the more uniform is the soil). The capillary


pressure pc is depending on the effective saturation Se. The effective saturation can

be calculated with the wetting-phase saturation Sw and the residual wetting-phase

saturation Swr.

pc = pd S− 1λ

e (2.1)

pc capillary pressure

pd entry pressure

Se effective saturation (definition see below)

Se =Sw − Swr1− Swr

(2.2)

Se effective saturation

Sw wetting phase saturation

Swr wetting phase residual saturation

In the Brooks & Corey formulation, the capillary pressure approaches the so called

entry pressure pd when the soil is fully saturated with water. The entry pressure is

the minimum pressure that the non-wetting fluid must have to enter the largest pores.

As the saturation of the wetting phase Sw approaches its minimum value Swr (and

thus Se is close to 0), the capillary pressure approaches infinity asymptotically. This

corresponds to the definition of the residual saturation Swr: The (wetting) fluid that

occupies the smallest pores becomes trapped and cannot be removed by further increase

of the non-wetting phase pressure. The Brooks & Corey function is visualized in figure

2.7.

2.2.2 Relative permeability-saturation relationship

Studies about permeability of porous media for fluid flow go back to Henry Darcy [16].

He studied single-phase flow through porous media and found that the flow rate is

proportional to the hydraulic conductivity k (equation 2.3).

k =qµl

∆p ∗ A[Darcy] (2.3)

q flow rate

µ dynamic viscosity

l length

∆p pressure gradient

A area

1 Darcy = 9.86923 ∗ 10−13 m2

The general Darcy equation (2.4) is named after Henry Darcy [16] and is still used in

single phase flow calculations:

v = −kf ∇h (2.4)


1

1,5

2

2,5

3

3,5

4

Pc

[ba

r]

0

0,5

1

1,5

2

2,5

3

3,5

4

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Pc

[ba

r]

Sw [-]

Capillary Pressure

Figure 2.7: Capillary pressure-saturation relation (entry pressure: 0.05 bar, λ = 2,

Swr = 0.25

For multiphase flow calculations this equation has to be extended and the relative

permeability has to be introduced (equation 2.5).

va = −kraµa

K (∇pa − ρg) (2.5)

kra relative permeability

K intrinsic permeability tensorkrαµα

:= λα Mobility of phase α

µα dynamic viscosity

In the extended Darcy equation, the mobility is multiplied by the intrinsic permeability

tensor K. The mobility accounts for the effect that other fluids add to the resistance

of the solid medium. It is therefore obvious that the relative permeability of one phase

is depending on its saturation.

As before with the capillary pressure, only the approach of Brooks & Corey is presented.

Further information about the van Genuchten approach can for example be found in

[13].

The Brooks & Corey functions for krw(S) and krn(S) are given by equations 2.6 and

2.7

krw = S2+3λλ

e (2.6)


krn = (1− Se)2(

1− S2+λλ

e

)(2.7)

Figure 2.8 shows a graph of the Brooks & Corey functions in which the krw(Sw) function

is not very steep for low water saturations compared to high water saturations (and

therefore low non-wetting phase saturations). Since the wetting phase tends to occupy

smaller pores first (and these pores have a lower permeability) the increase in relative

permeability is lower until larger pores are filled. As the medium becomes filled with a

non-wetting phase, the curve should consequently flatten, because at this point smaller

pores will get filled and the increase in relative permeability is smaller.

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Rela

tive p

erm

eabili

ty [

-]

Drain Gas Corey

Imbibition: Gas Corey

Drain Water Corey

Imbibition Water Corey

0

0,1

0,2

0,3

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Sw [-]

Figure 2.8: Relative permeability-saturation relation (entry pressure: 0.05 bar, λ = 2,

Swr = 0.25

2.2.3 Hysteresis

A hysteretic behavior can be observed in many technical and natural processes. Simply

put, it means that the state of a system is not independent of its history.

The capillary pressure-saturation and relative permeability-saturation relationships

also show a hysteretic behavior: The values of pc and kr are dependent on whether the

system is going through an imbibition (the increase of the wetting phase) or through

a drainage process (the decrease of the wetting phase) and how many times the sys-

tem already changed between imbibition and drainage. The reason for this behavior

is that small amounts of e.g. the wetting phase become trapped in the small pores.

2.3 Flow and transport processes 18

This amount of fluid - called the residual saturation Sr - cannot be removed by viscous

forces. As mentioned in section 2.2.1 the capillary pressure takes very high values as the

saturation reaches low levels. This residual saturation changes the available pore space

and the initial saturation for the first imbibition cycle. The main imbibition curve of

the capillary pressure-saturation relationship ends at a saturation smaller 1, because

some of the pores are partly filled with the non-wetting phase that has become trapped

during the previous drainage cycle (the residual saturation Snr). The next drainage

cycle (beginning at Swr = 1 - Snr) will follow the path of the main drainage curve and

close the hysteresis cycle. If the drainage/imbibition cycle gets reversed before it is

complete, the capillary pressure follows the path of the secondary drainage/imbibition

scanning curves (see also [13]).

In ECLIPSE several models can be chosen to simulate these scanning curves, however

the hysteretic behavior is not yet implemented in DuMuX and the HYSTER option

has therefore been turned off in the basic case of the ECLIPSE models. In one set-up

for ECLIPSE, the HYSTER option has been turned on in order to evaluate its effect.

The results can be found in section 4.3.

2.3 Flow and transport processes

Several processes can affect the movement of a fluid. In the following sections the most

important ones will be described: Advection, buoyancy, diffusion and dispersion. For

the energy transport the main processes are thermal conduction and convection.

2.3.1 Advection

Advective flow is the driving process during the injection. It describes the movement of

the fluid resulting from the pressure difference between the well and the reservoir. The

advective flow is strongly influenced by the viscosity of the fluid and since the viscosity

varies with temperature, a change in temperature will also affect the advective flow.

At the well there is a pressure gradient in all directions, the carbon dioxide will therefore

flow from the well (more or less a point source) in all directions of the reservoir. This

is one of the reasons why a radial geometry represents the actual physical system best

(also see section 4.2).

2.3.2 Buoyancy

Buoyancy is the effect of density differences between fluid phases or within a phase. As

we would naturally expect, the phase with the higher density will sink and the phase

with the lower density will rise and displace the other phase. These effects do not only

exist between two phases like CO2 and water but also within one phase: As CO2 and/or

salt get dissolved in water, its density rises as can be seen in figure 2.5. The water

with dissolved CO2 therefore should slowly but steadily sink and fresh (CO2-free) water

2.3 Flow and transport processes 19

will rise and can dissolve more carbon dioxide. However since the density differences

between CO2-saturated and unsaturated water are small, this process is very slow.

The density of the CO2-phase is strongly dependent on temperature. Consequently

the buoyant flow also depends on the temperature of the fluid.

2.3.3 Diffusion and Dispersion

The concept of diffusion represents the Brownian movement of particles. This Brownian

movement of particles occurs at all temperatures above absolute zero (0 K) and is

driven by concentration and temperature gradients [9]. Diffusion occurs randomly and

in all spatial direction (the particle movement can be fast and particles will collide

and change direction). To describe diffusion mathematically, Fick’s law can be used

(equation 2.8 [9]).

jκα = −ρα Dκpm ∇Xκ

α (2.8)

jκα mass flux of a dissolved substance

α phase index

∇Xκα composition gradient

ρα density of phase α

Dκpm = τ φ Dκ

α diffusion coefficient

Dispersion is similar to diffusion but represents the interaction of the particles with

the solid medium: The fluid flowing in the porous medium is forced to move around

solid particles and follow a certain flow path. Often there is not only one path but

several and the fluid will more or less randomly choose one of the paths. One can differ-

entiate between micro and macro dispersion and between longitudinal and transverse

dispersion.

Micro-dispersion is the process that takes places on the pore scale. It is caused by

the friction between solid and fluid or between two phases and the resulting parabolic

velocity profile between the grains of the soil. Macro-dispersion is caused by hetero-

geneities on the macro-scale [9]. Longitudinal dispersion is caused by differences in

flow time, if flow lines starting at the same origin take different paths around a solid

particle. Transverse dispersion is dispersion perpendicular to the flow direction (see

also [7]).

Currently dispersion cannot be easily described mathematically for multiphase systems

and is therefore not implemented in the simulation programs.

2.3.4 Thermal conduction and convection

Heat can be transferred by conduction and by convection. An energy transfer occurs

when a temperature gradient in the system or between two phases exists. The amount

of energy that is transferred is proportional to the temperature difference and is depen-

2.4 Trapping mechanisms 20

ding on the heat conductivity λ, which is a measure for the ability of a material to

transport heat. The Fourier law describes this relationship:

q = −λ ∇T (2.9)

q heat flux density

λ heat conductivity

∇T temperature gradient

While the transport of heat between stagnant phases is called heat conduction, the

heat transport due to the flow of a fluid is called heat convection [23] and [9].

For a multiphase system, it is possible to describe the heat transfer for each phase sep-

arately. However in the simulations for this study a local thermodynamical equilibrium

was assumed.

2.4 Trapping mechanisms

The possible trapping mechanisms and its related time scales have been described in

detail in [6] and [13] p. 28-30.

Depending on the time scale (which reaches from 1 to 10000 years or even more)

different processes dominate the capture process:

2time after stop of CO −injection (years)

10,0001,000100101

structural and stratigraphic

trapping

residual

trapping

solubility

trappingmineral

trapping

tra

pp

ing

co

ntr

ibu

tio

n %

100

0

do

min

atin

g p

roce

sse

s

increasing storage security

Figure 2.9: Trapping mechanisms on different time-scales (from [13], modified from [6])

2.4 Trapping mechanisms 21

− During the injection and in the first couple of years when the CO2 is moving

in a discrete phase, structural and stratigraphic trapping are most important

to keep the CO2 from escaping the reservoir. As has been mentioned in section

2.1.1, CO2 has a lower density than water even in its supercritical state. During

the injection the carbon dioxide phase will move laterally away from the injection

well due to advective flow and vertically up due to buoyancy. It is important that

the cap rock (the stratigraphic layer which is impermeable for CO2) is at a depth

where pressure and temperature are high enough to keep the carbon dioxide in its

supercritical state. Otherwise the density would decrease abruptly and it would

be much harder to keep the same amount of gas inside the reservoir due to the

largely increased volume.

− As the carbon dioxide phase moves towards an impermeable barrier and finally

stops moving because the saturation drops below the residual saturation, another

mechanism, the so-called residual trapping, secures the CO2 storage. Accor-

ding to considerations explained in section 2.2.3, small amounts of carbon dioxide

can become trapped as they get separated from the rest of the non-wetting phase.

This effect is described by the relative permeability hysteresis. A combination of

several imbibition/drainage cycles in the injection schedule and thus maximizing

residual trapping could be used to optimize this effect.

− Starting at the beginning of the injection but becoming more relevant in the long

term is the solubility trapping. Carbon dioxide is soluble in water and even

changes the waters density in a favorable way (see section 2.1.1). Once the CO2

is dissolved in the water, the water will slowly but steadily sink and be replaced

with unsaturated water that can take up more CO2. This process however is

rather slow and the dissolution depends on the contact between the water phase

and the carbon dioxide phase.

− The final but most secure form of carbon dioxide storage is the mineral trap-

ping. This process is expected to become relevant only after more than 1000

years. First the dissolved carbon dioxide has to form ionic species that can react

to carbonate minerals. As this process is very slow and only becomes relevant

after a long time it is not implemented in the model and not being simulated by

ECLIPSE or DuMuX.

Chapter 3

Model concept

3.1 Terminology

3.1.1 Scales, the representative elementary volume

In the field of numerical simulations it is important to consider the scale on which

the physical processes of the system will be simulated. Not all processes are equally

important on all scales. Capillary pressure for example is quite important on a small

scale but might be irrelevant on a large scale. The transition between scales is gradual

and the length of each scale level is not clearly defined in general. In [13] p.43, several

scale levels have been outlined, namely

− The molecular scale, molecules are considered

− The continuum scale, averaged fluid properties like density can be obtained

− The micro scale or pore scale, individual pore spaces can be resolved. Description

is possible with the Navier-Stokes equations

− The local scale or REV scale, the flow description is based on a representative

elementary volume (REV)

− Larger scales from meso scale, macro scale to the field scale

A model concept and the physical processes that are represented within it, is based on a

certain scale. Processes that occur on a smaller scale but are relevant to the considered

scale have to be taken into account by effective parameters [13] (e.g. capillary pressure

- saturation relationship).

The size of the above mentioned REV is restricted by the minimum control volume,

that allows an averaging of system properties with unique non-oscillating values (see

figure 3.1). For example the porosity can be used for the minimum required volume.

It is defined by φ = volume of pore space in REVtotal volume of REV

. After the REV has been defined, other

parameters e.g. the saturation, density and viscosity for this REV can be introduced

[13].

3.2 Multiphase multi-component system 23

po

micro scale REV scale (local scale)

medium

homogeneous

heterogeneous

medium

φ

0

0

= (

V

) /

V1

volume Vmin REV=0V

Figure 3.1: Definition of the size of a representative elementary volume (REV) after

[8] from [13]

3.1.2 Phases and components

”A phase is a well-defined region where there are no discontinuities in material prop-

erties” [9]. On the edge of the phases the surface tension results in a usually sharp

interface and on a small scale, the pressure difference between two phases becomes

important as the capillary pressure. Commonly there are three phase states: Solid,

liquid and gaseous.

One phase can contain several components: A component is a chemical substance,

that can be transferred from one phase to another. For example salt or CO2 can

dissolve in water, water can dissolve in CO2, salt can fall out and become solid etc.

Gas mixtures can be considered as one component if the distinction is not important

for the calculation. Air is the most prominent example for such a pseudo-component.

If a substance is in its supercritical state (pressure and temperature are then above the

critical values of this substance), it also forms a separate phase with the density closer

to the liquid phase and the viscosity closer to the gaseous phase. A substance in its

supercritical state can dissolve other components like a liquid. Therefore the process

that is commonly referred to as ”evaporation” of water is more likely a dissolution of

water (in the supercritical CO2).

3.2 Multiphase multi-component system

For the simulation of CO2 sequestration in deep saline formations at least the phases

water (fluid), CO2 (supercritical/fluid) and the porous rock (solid) have to be consid-

ered. Several components should also be recognized by the model however the more

3.3 Conceptual model 24

components are included, the more complex the model will be. Components that could

be relevant for the simulation are:

− CO2

− Water

− NaCl in water

− HCO−3 , CO2−3 in water, CaCO3 as solid

− NaCl as solid

For this study a two-phase and a two-phase two-component model concept were chosen.

The salinity of the water is considered but the solubility of NaCl in water is constant.

Carbonates will only become relevant after several hundred years and are therefore not

considered since the simulations in this study will only cover the first couple of years

after the injection. In general chemical reactions are not part of this model. In the

two-component model the dissolution of CO2 in water and the dissolution of water in

the supercritical (liquid like) CO2 phase are considered. The solubility of CO2 in water

is depending on pressure, temperature and salinity but the dissolution of water in CO2

is again only a constant.

The rock matrix in this study is homogeneous and values for porosity, permeability,

entry pressure, heat conductivity, residual wetting and non-wetting phase saturations

are set to standard values and are assumed to be time-independent. The rock matrix

is assumed to be incompressible (except for the simulations in the chapter 4.6).

3.3 Conceptual model

In this section the model concept that has been developed for DuMuX with its mathe-

matical and numerical model are described. In principal, the same equations have to

be solved by ECLIPSE but since DuMuX is an open source project, more information

is available about the exact equations and algorithms that have been used. Figure 3.2

shows a graphical representation of the model concept.

3.4 Mathematical model

In this section the mathematical equations are presented that are relevant for the

simulation of the physical processes influencing the CO2 sequestration and that have

been used for the DuMuX code.

The important processes are the conservation of mass, momentum and energy. In fluid

mechanics usually an Eulerian approach is used to balance mass, momentum and en-

ergy over a stationary control volume. A mathematical representation of these balance

3.4 Mathematical model 25

CO −rich phase

dissolution

degassing

evaporation

condensation

water

water−rich phase2

CO2CO2

water

Figure 3.2: Two phase two-component model concept for the system CO2-water [9].

equations is possible using the Reynold’s transport theorem which states that the tem-

poral change of an extensive fluid property Esys is equal to the storage/accumulation of

the fluid property plus the fluxes over the surface of the control volume. See equation

3.2. [9]

A very good description of all these equations can be found in [9], p.55-58 and most of

the following descriptions are taken from this reference.

Esys =

∫Ω

ρ ε dΩ (3.1)

where ε is the corresponding intensive property of E.

dEsysdt

=

∫V

∂

∂t(ρε) dV +

∮Γ

(ρε)(v · n) dΓ (3.2)

In the following sections, Reynolds transport theorem is applied to mass, momentum

and energy.

3.4.1 Momentum and continuity equation

For the continuity equation or the conservation of mass, the extensive fluid property

Esys = m is chosen. The corresponding intensive fluid property is consequently

ε = mm

= 1. Mass is conserved and therefore it does not change over time:

dEsysdt

!= 0 (3.3)

When inserted in equation 3.2 this results in the integral form of the mass balance

equation:


∫V

∂ρ

∂tdV +

∮Γ

ρ(v · n) dΓ = 0 (3.4)

With the Gaussian integral rule, the surface integral can be converted to a volume

integral. Rewritten in differential this results in equation 3.5.

∂ρ

∂t+∇ · (ρv) = 0 (3.5)

For the momentum equation, the extensive property is the momentum p = mv with

the intensive property ε = v. The change of momentum is caused by external forces

(gravity), the pressure gradient and viscous forces (equation 3.6).

dEsysdt

=dpsysdt

= ρg−∇ p+∇ · τij (3.6)

Application of the Reynold’s transport theorem results in∫V

∂

∂t(ρv) dV +

∮Γ

(ρv)(v · n) dΓ =∑

f (3.7)

or in differential form

∂(ρv)

∂t+∇ · (ρv · v) = ρg−∇ p+∇ · τij (3.8)

For Reynolds numbers ¡¡ 1, Darcy’s equation can be used on the macro scale - here it

is shown in the extended form for multiphase flow where the relative permeability krαis divided by the dynamic viscosity µα and multiplied with the intrinsic permeability

of the porous medium:

vα =krαµα

K(∇pα − ραg) (3.9)

krαµα

:= λα Mobility of phase α

3.4.2 Conservation of energy

Reynold’s transport theorem can also be applied to energy. Energy is conserved accor-

ding to the first law of thermodynamics and the change of internal energy in a closed

system is the result of a heat flux or of work that has been done. For the application

of Reynold’s transport theorem, the extensive system variable is Esys = U and the

intensive system variable is ε = u (specific internal energy).

After the application of the Green-Gaussian integral rule, the result is equation 3.10


dU

dt=

∫V

∂(uρ)

∂tdV +

∫V

∇ · (uρv)dV

=

∫V

∇ · λ∇TdV −∫V

∇ · (pv)dV

(3.10)

u specific internal energy

λ heat conductivity

and the equation can also be written in differential form:

∂(uρ)

∂t+∇ · (uρv) +∇ · (pv)−∇ · (λ∇T )

=∂(uρ)

∂t+∇ · (ρhv)−∇ · (λ∇T )

(3.11)

h = u+ pv = u+ pρ

specific enthalpy

where the first term describes the energy storage, the second term energy transport

due to convection and the third term heat conduction.

3.4.3 Mass balance

The differential form of the general mass balance equation was described in equation

3.5 and will be used for the formulation of the multiphase mass balance equation. In

the following equation the index α stands for either the wetting phase (water) or the

non-wetting phase (CO2). With the extended version of Darcy’s law, the result is a

system of differential equations.

The components of a two-phase two-component system can also be directly included

in the system of equations resulting in equation 3.12.


φ

∂

(∑α

ραxκαSα

)∂t

−∑α

∇ ·krαµα

ρα xκα K (∇pα − ραg)

−∑α

∇ ·Dκpm ρα ∇xκα

− qκ = 0

(3.12)

κ ∈ w,CO2 component

α ∈ brine, CO2 phase

In this study, the components are either water or CO2. Salt is not considered as a

separate component in DuMuX but in ECLIPSE it is.

3.4.4 Energy balance

In the current version of DuMuX local thermal equilibrium is assumed to simplify the

energy balance equation. In this way only one equation for all fluid phases and the

rock matrix has to be set up because they locally have the same temperature. The

energy equation looks similar to the mass balance equation:

φ

∂

(∑α

ραuαSα

)∂t

+ (1− φ)∂(ρscsT )

∂t−∇ · (λpm ∇T )

−∑α

∇ ·krαµα

ρα hα K (∇pα − ραg)

− qh = 0

(3.13)


u specific internal energy

h specific enthalpy

λpm heat conductivity of the porous medium

K permeability tensor

The energy storage of the porous matrix is considered in part 2 of the storage term

(1-φ is the rock matrix) with the specific heat capacity of the solid cs.

3.5 Numerical model 29

3.4.5 Closure conditions

The three balance equations with three primary unknown variables are constrained by

the following closure conditions:

pw + pc(Sw) = pnw (3.14)

Sw + Snw = 1 (3.15)

∑C

XCα = 1 (3.16)

3.4.6 Primary variables

During a CO2 sequestration scenario several phase states can appear in the model. In

the beginning of the injection, the aquifer is completely filled with brine, during the

injection the CO2 advances and mixes with the brine. If there is only one phase present,

the dissolved amount of water (in CO2) and CO2 (in water) may become greater than

the corresponding solubility and the corresponding phase will appear again. Depending

on the phases present, different primary variables have to be chosen in order to solve

the differential equations, because not all primary variables are available all the time.

In the DuMuX model applied here, the primary variables given in table 3.1 were used:

Both phases Water phase CO2 phase

Present phases w, CO2 w CO2

Primary variables SCO2 , pw, T XCO2w , pw, T Xw

CO2, pw, T

Water phase appears - - XCO2w ≥ (XCO2

w )maxCO2 phase appears - Xw

CO2≥ (Xw

CO2)max -

Table 3.1: Primary variables and corresponding phase states [9].

For isothermal problems, the temperature is obviously not needed as a primary variable.

3.5 Numerical model

The mathematical equations can usually not be solved analytically. A numerical model

is necessary to transfer the equations to numerical algorithms where they can be solved

by a computer. There are several methods to discretize a model domain: The finite

differences (FD), finite element (FE) or finite volume method (FV) or a combination of

the FV and the FE method, the BOX method. While ECLIPSE uses finite differences

for time and space discretization, DuMuX uses a finite differences approach for the time

discretization but the BOX method for space discretization. The numerical model for

DuMuX are described shortly in the following sections.


3.5.1 Time discretization

For the time discretization a fully implicit finite difference method is used, which is

unconditionally stable (no conditions on the step size for stability reasons). With this

method, the time derivative of an unknown u looks as follows:

∂u

∂t≈ ut+∆t − ut

∆t(3.17)

The terms ut+∆t represent the values at time t+ ∆t.

3.5.2 Space discretization

For the space discretization in DuMuX, the BOX method is used, which is a combina-

tion of the finite volume and the finite element methods with the advantages that it is

locally mass conservative and can be used for unstructured grids. In this section the

BOX method is explained for the mass balance equation (see also [12]).

Finite elements / The BOX method

The integration of equation 3.12 over a Volume Ω yields the weak form of the mass

balance equation:

∫Ω

φ

∂(∑α

ρmol,α xκα Sα)

∂tdΩ

−∑α

∫Ω

∇ ·krαµα

ρmol,α xκα K (∇pα − ρmass,α g)

dΩ

−∑α

∫Ω

∇ ·Dκpm ρmol,α ∇ xκα

dΩ

−∫Ω

qκ dΩ = 0

(3.18)


κ ∈ CO2, w component

xκα mole-fraction

Sα saturation of phase α

Dκpm diffusion coefficient

In the discretized domain exact values of the primary variables (pressure, saturation,

mole fraction, temperature) are only assigned to the nodes. In between the nodes they

are interpolated using a linear function Nj (equation 3.19). All secondary variables


(e.g. density, enthalpy, ...) are also computed at the nodes.

pα =n∑j=1

pα,j ·Nj, Sα =n∑j=1

Sα,j ·Nj, xκα =

n∑j=1

xκα,j ·Nj, T =n∑j=1

Tj ·Nj (3.19)

The functions Nj are C0 Lagrange polynomials (continuous but not necessarily contin-

uously differentiable). The values of Nj are 1 for node j and 0 everywhere else: 3.20

(also see figure 3.3).

Nj(uk) = δjk =

1 for j = k

0 for j 6= k(3.20)

Figure 3.3: Basis function Nj (from [9]).

Insertion of the functions 3.19 into equation 3.18 results in an error ε. With the

method of the weighted residuals and the weighting functions Wi, the average error of

the domain Ω has to become zero, while the sum of the weighting functions Wi inside

the domain has to be one: ∫Ω

Wi ε dΩ!

= 0 (3.21)

∑i

Wi = 1 (3.22)

For the so called mass matrix Mij =∫Ω

WiNjdΩ a mass-lumping is implemented. The

matrix Mij can then be rewritten as

M lumpij =

∫Ωi

Wi dΩi =∫Ωi

Ni dΩi =: Vi for i = j

0 for i 6= j(3.23)

With this mass lumping, all sources and sinks and the storage in one domain are

concentrated on the node in order to prevent non-physical oscillations.


With an implicit Euler scheme for the time discretization, the storage term for one

node is discretized as in equation 3.24 [9].

∫Ω

Wi φ

∂(∑α

ραxκαSα)

∂tdΩ

≈∑j∈ηi

Mij φ1

∆t

[∑

α

ραxκαSα

]t+∆t

j

−

[∑α

ραxκαSα

]tj

(3.24)

ηi are the neighboring nodes of i and Mij =∫Ω

WiNjdΩ.

For the discretization of the advective term (the diffusive term is similar and will not

be shown separately), the Green-Gaussian integral rule is applied ([9]):

∫Ω

Wi∇ · F dΩ =

∫Ω

∇ · (Wi · F) dΩ−∫Ω

(∇Wi) · F dΩ

=

∮Γ

(Wi · F) · n dΓ−∫Ω

(∇Wi) · F dΩ

(3.25)


∫Ω

Wi∇ · F dΩ

=

∫Ω

Wi

∑α

∇ ·krαµα

ραxκα K (∇pα − ραg)

dΩ

≈∫Ω

Wi

∑α

∇ ·

krαµα

ραxκα K

(∑j∈ηi

(pαj − pαi)− ραg∑j∈ηi

(zαj − zαi)

)∇Nj

dΩ

=

∫Ω

Wi

∑α

∇ ·

krαµα

ραxκα K

∑j∈ηi

(ψαj − ψαi) ∇Nj

dΩ

=

∮Γ

Wi

∑α

krαµα

ραxκα K

∑j∈ηi

(ψαj − ψαi) ∇Nj

· n dΓ

=∑l∈Ei

∑j∈ηi

∑α

[krαµα

ραxκα

]t+∆t

upw

∮Γi

Kl[ψαj − ψαi

]t+∆t

∇Nj · n dΓ

=∑l∈Ei

∑j∈ηi

∑α

[krαµα

ραxκα

]t+∆t

upw

Kl[ψαj − ψαi

]t+∆t

∇Nj · nIP AIP

(3.26)

ψαi = pαi − ρmass,αi g z the total potential at node i

index upw upstream node

upw(i, j) =

i for (ψαj − ψαi) ≤ 0

j for (ψαj − ψαi) > 0

Figure 3.4 shows a finite element and a finite volume net for the BOX method. The

finite element mesh divides the model domain into sections (can have various forms e.g.

tetrahedra or hexahedra). The intersections of the elements edges are the nodes (where

the variables have exact values). Then a finite volume net is constructed by connecting

the midpoints of the finite elements’ edges with the barycenters of the elements. Each

finite element is divided into sub control volumes that can be associated with a certain

box and each box is associated with a certain node. For the BOX method, the weighting

functions Wi are one inside the box or zero otherwise:

Wi =

1 inside box Bi

0 outside box Bi(3.27)

where Bi is the box at node i.

The complete discretization of equation 3.18 for the BOX method is shown in equation

3.28 ([9]).


Vi φ1

∆t

[∑

α

ραxκαSα

]t+∆t

i

−

[∑α

ραxκαSα

]ti

−∑l∈Ei

∑j∈ηi

∑α

[krαµα

ραxκα

]t+∆t

upw

Kl[ψαj − ψαi

]t+∆t

∇Nj · nIP AIP

−∑l∈Ei

∑j∈ηi

∑α

[Dκpmρα

]t+∆t

ij

((xκα,j − xκα,i)t+∆t ∇Nj · nIP

)· AIP

− (Vi qκi )t+∆t

= 0

(3.28)

κ ∈ w,CO2 component


Figure 3.4: Finite element and finite volume mesh of the BOX method (from [9]).

Chapter 4

Simulations with ECLIPSE E300

As mentioned in the introduction, two numerical simulators have been applied for

this study. In this section the results of the simulations with Schlumberger ECLIPSE

E300, a compositional simulator with an integrated CO2 sequestration model will be

presented.

4.1 Objective

The objective of the first part of this study was to set up a simple model of a storage

reservoir with ECLIPSE E300 at RWE Dea in Hamburg. The model was intended to

be as realistic as possible, however, it was also important that it could be compared to

results from DuMuX, so that DuMuX could be benchmarked against ECLIPSE E300.

Since the two programs have different functionalities, several compromises had to be

made in order to insure comparability. The compromises are reflected in the ECLIPSE

E300 options that have not been used for the basic case.

The main objective of this work is to find out whether non-isothermal effects play an

important role in the simulation of CO2 sequestration. Temperature changes are not

only expected to have an effect on density and viscosity but also on the solid matrix,

similar to water induced rock compaction, where fractures appear in the rock after the

reservoir is flooded with cold water (more information about this matter can be found

in [15]). However the simulation of the effects on the rock are not part of this study.

In the following sections a basic case as reference and several other cases with various

additional ECLIPSE E300 options will be described to evaluate their effect on the

simulation. Table 4.1 gives an overview of all simulations.

4.2 Basic case 36

ECLIPSE

E300

DuMuX

iso

DuMuX

2pni

DuMuX

2p2cni

Basic case√ √

Compositional model√ √

Non-isothermal model√ √

Hysteresis√

Injection schedule√

Injection rate√

Rock compressibility√

Injection into pure water√

Variation of the reservoir

temperature

√

Table 4.1: Overview of all simulations

4.2 Basic case

For the basic case the chosen options will be described in more detail, while table 4.2

summarizes the most important options.

Figure 4.1 shows the geometry of the model. It has been kept as simple as possible: The

grid is set up as a radial grid with an inner radius of 0.05 m (the well diameter being 0.1

m) and an outer radius of 800 m + 1 m for the ECLIPSE E300 model. This additional

meter has been added in the ECLIPSE E300 model for the boundary condition which

will be explained in the next paragraph. From the inner to the outer ring of the model,

the grid spacing increases exponentially so that there are smaller distances between

nodes near the well, where the fastest flow changes are expected. Near the outer

boundary the distance between grid nodes is broader, to keep the simulation time at

a minimum. Since the radial flow is expected to be more or less the same in all lateral

directions, not a whole circle but only a 30 piece has been set up. It is divided in 4

pieces, each being 7.5 wide. In vertical direction, there are 20 layers, each 1 m high.

The grid has been made so fine to get a nice picture of the fluid front as it replaces the

brine and mixes with it.

The boundary conditions made some difficulties: The ECLIPSE E300 is a reservoir

simulator and does not know the concept of a constant head boundary condition. A

constant head boundary condition usually represents an ”infinite” reservoir, where

the volume is so big that the pressure can stay constant even during an injection.

DuMuX on the other hand knows only constant head or flux boundary conditions.

The objective was to keep the models as comparable as possible, so two ideas came up

of how to simulate a constant head boundary in ECLIPSE E300. One option was to

integrate wells, that would only flow if a certain pressure was reached. The pressure

curve, however, showed unrealistic results and another idea was developed: The pore

volume of the outermost (1 m) ring of the model was increased artificially to a number

4.2 Basic case 37

Figure 4.1: Geometry of the model (ECLIPSE), enlarged in z-direction

very big relative to the total pore volume of the rest of the model. With this set-up

the pressure at the outermost ring of the model could be kept very close to a constant

value of 257.5 bar (in the uppermost layer). All other boundaries (except for the well)

were set to no-flow.

The reservoir temperature was set to 80.3C and the initial pressure to 257.5 bar.

These values are about realistic for a considered reservoir in 2250 m depth.

Since data about a realistic relative permeability - and capillary pressure - saturation

relation was not available to be used in this study, a Brooks-Corey function was set

up and its tabulated values were used for this simulation. The residual gas saturation

Snr was set to 0.025 and the residual brine saturation Swr was set to 0.25. The entry

pressure for the non-wetting phase was set to 0.05 bar. These values strongly influence

the outcome of the simulation. For example if the entry pressure was 0.1 bar, the

pressure curve would look very different. The values that were used are not based on

measurements or other calculations, but arbitrary. For the comparison of ECLIPSE

E300 and DuMuX this should not have a negative effect since the same values were

used for both calculations. The soil properties were also kept at standard values:

The porosity was set to 20% and the permeability was set to 200 mDarcy (=1.9738 ∗10−13m2) in lateral and 20 mDarcy (=1.9738 ∗ 10−14m2) in vertical direction.

Values that are close to real data were used for the composition of the brine: The NaCl

mole fraction was set to 0.0624 which equals about 172800ppmw. No other molecular

species besides NaCl and water were used, the mole fraction of H2O was therefore

4.2 Basic case 38

0.9376. The injection stream was set to 100% CO2.

The injection time was set to one year, which is a random value that would allow a

reasonable amount of fluid with a reasonable pressure to flow into the reservoir. In

one simulation the injection time was also changed but the amount of fluid was kept

constant to see the effect of a faster or slower injection. After the injection the reservoir

was let to relax for 20 years.

As the results of the basic case are not too exciting by themselves, I will present them

along with the results of the modifications, so that differences can be seen more easily.

Table 4.2 gives an overview of all important parameters that have been used for the

basic case.

Property Value / Setting

Geometry Length 800 m + 1 m, Width 400 m / 30, Thick-

ness: 20 m. Well diameter: 0.1 m

Matrix/Soil Porosity 20 %

Permeability: 200 mDarcy (in r and θ direction)

20 mDarcy in z direction

Grid r-direction 41 cells, θ-direction: 4 slices, z-

direction: 20 layers

Boundary conditions Constant head at the outer ring (very large pore

volume), source at the well, noflow at all other

boundaries

Initial values Temperature 80.3C (constant, isotherm)

Pressure at the top of the reservoir: 257.5 bar

Fluid properties 3 components (H2O, NaCl, CO2)

Salinity: 172800ppmw (molefraction: 0.0624)

Injection schedule 365 days injection at a rate of 50 Rm3

d(= about

0.403 kgs

, 20 years relaxation)

S−kr, S−pc relations Artificial Brooks-Corey functions

Hysteresis Model off

Rock Compaction 0.0

Simulator and dis-

cretization scheme

ECLIPSE E300, Finite Differences

Table 4.2: Model parameters for the basic case

4.2.1 Benchmark variables

Several benchmark variables have been chosen for the comparison (see table 4.3). In

table 4.4 the measurement points for ECLIPSE E300 and DuMuX are listed.

The measurement points have to be set up slightly differently for ECLIPSE E300

and DuMuX: In ECLIPSE E300, the data is written for a certain cell e.g. 25 1 1

4.3 Effect of hysteresis model 39

Benchmark variable

Pressure (BPR)

Viscosity of brine (BVWAT)

Density of brine (BDENW)

CO2 saturation (BGSAT)

Density of CO2 (BDENG)

Mobility of CO2 ( BGKRBV GAS

)

Capillary pressure of CO2 (BGPC)

Molefraction of CO2 in brine (BXMF)

Molefraction of H2O in CO2 (BYMF)

Table 4.3: Benchmark variables

would be the 25th cell in r-direction, 1 in θ-direction in the uppermost layer. The

grid in DuMuX is set up with the same grid spacing, however, variables are written

at certain (Cartesian) coordinates. That means that while the distance from the well

should be approximately the same for both measurement points, the coordinates for

the measurement look very different as can be seen in table 4.4. As has been explained

they are not exactly the same, since the values are averaged for one cell in ECLIPSE

E300.

Another small difference is that in DuMuX, the z coordinate is 0 at the bottom, while

in ECLIPSE E300 the cells in the top layer have the z-coordinate 01.

Distance from well [m] Coordinates ECLIPSE E300 Coordinates DuMuX [m]

0.05 01 01 01 0.0433013 0.025 20

0.05 01 01 10 0.0433013 0.025 10

51.17 19 01 01 44.3119 25.5835 20

115.19 25 01 01 99.7547 57.5934 20

115.14 25 01 10 99.7547 57.5934 10

422.00 35 02 01 365.51 211.027 20

799.95 40 02 01 739.104 306.147 20

Table 4.4: Coordinates

4.3 Effect of hysteresis model

The hysteresis model has been turned off in the basic case because DuMuX does not

yet support it. However, the effect of hysteresis is well known and studies have shown

that it can have a significant effect on the prediction of CO2 flow in a reservoir. In [28]

for example the authors demonstrate, that ”physical trapping mechanisms during the

simultaneous flow of two fluid phases through the porous medium, such as snap-off, have

a huge impact on the migration and distribution of CO2”. These trapping mechanisms


Figure 4.2: Grid with control points (ECLIPSE).

act already during the relaxation and therefore in a much smaller time period than for

example the dissolution process. ”Therefore, relative permeability hysteresis becomes

an order-one factor in the assessment of CO2 sequestration projects” [28].

During each imbibition/drainage cycle a bit more of the injected fluid should stay in

the pores as residual saturation (see section 2.2.3). Pores that do not go through a

complete cycle should trap larger amounts of non-wetting phase due to snap-off of iso-

lated CO2 bubbles. Figure 4.3 shows an example of the relative permeability function

with drainage, imbibition and scanning curves. A complete drainage and imbibition

process would go from point 1 over 2 to 3, which denotes the imbibition critical satu-

ration. If the drainage process is however reversed at point 4, the scanning curve from

4 to 5 would be used to model the imbibition process. Point 5 denotes the trapped

critical saturation ([26], page 434). However the important trapping mechanism is that

a path of residual CO2 is left behind during its upward migration and the simultaneous

imbibition process. This mechanism is already integrated into the DuMuX model as

the residual gas saturation Sgr.


Hysteresis Model on (Killough’s model)

Simulator and discretization scheme ECLIPSE E300, Finite Differences

Table 4.5: Hysteresis: Model parameters that differ from basic case


krn

Snmax Sncri Sncrt Sncrd

2

3

4

5

Non-Wetting PhaseSaturationWetting Phase

Saturation

1

Imbibitioncurve

Drainagecurve

Relativepermeability

Scanningcurve

Figure 4.3: Example of scanning curves (from [26]).

Evaluation

The driving force for fluid flow during the injection is the pressure. The wells for all

simulations are on ”volume control”. That means that the well will always use as much

pressure as is needed to inject a certain volume (here 50m3

dat reservoir conditions) of

CO2.

In order to see how the system reacts to this pressure we can look at the pressure

curve in figure 5.1 on page 69, since the pressure curve of the basic case is identical

to the pressure curve of the simulation with the hysteresis option turned on: When

the injection well is turned on, the pressure immediately jumps to about 266 bar, but

almost immediately after this spike it drops steadily. The reason for this behavior

is mainly the entry pressure. The pressure by the well has to be higher than the

entry pressure of the pores in order to inject fluid. As the pores become saturated the

pressure that is needed to inject a constant 50m3

dof CO2 drops since the viscous forces

drop due to an increase in relative permeability. The pressure curve for the basic case

and this test case where the hysteresis option is turned on are close to identical. The

pressure curve of the basic case can be seen in figure 4.4).

As mentioned above, the highest pressure during the injection is reached immediately

after the start: about 266 bar and it drops to 261.58 bar just before the injection

stops. After injection stop, the pressure drops almost immediately to 258 bar and then

continues to fall very slowly to the initial pressure of 257.5 bar.

The saturation curves at various control points can be useful to determine the arrival

time of the non-wetting phase and to determine how quickly it reaches fully saturated

conditions.


258

260

262

264

266

268

P [

ba

r]

Bottom hole pressure (1 1 1)

256

258

260

262

264

266

268

-1 1 3 5 7 9 11 13

P [

ba

r]

Time [years]


WV_1-REFERENZ

Figure 4.4: Basic case: Bottom hole pressure at the injection well.

The first two control points (19-1-1 and 25-1-1) on the upper layer show almost no

effect of the hysteresis options.

In the middle layer (in 10 m depth of the reservoir), a first major difference of this

simulation to the basic case can be observed. During the injection, the saturation

curves (figure 4.5) are identical. But after the well is shut off, it becomes obvious that

less CO2 has reached this control point: The maximum saturation is only slightly below

the reference value (0.436 compared to 0.448), but it is reached much earlier (472 days

after injection start compared to 532 days).

The capillary pressure and relative permeability hysteresis have the effect of a higher

residual saturation and more mass of the non-wetting phase is trapped in the pores

that have been drained. This behavior can also be seen in figure 4.5: The saturation

of the non-wetting phase does not return to a value near the residual saturation but a

much larger value of about 0.178. This value is of course dependent on the hysteresis

model parameters but it shows that more CO2 will be trapped compared to the basic

case. The CO2 saturation level also returns more quickly to a constant value making

the migration of the CO2 less dynamic.

In figure 4.6 we can see that the hysteresis of the capillary pressure and relative perme-

ability also has an effect on the maximum extent of the plume or the saturation in the

topmost layer of the reservoir. The effect that can be seen at this control point, about

422 m away from the injection well is still small but it gives an idea about the propaga-

tion of the plume and the additional trapping effect. As the plume moves forward and

upward, the same saturation value (e.g. 0.4) is reached eventually in both simulations.

With the hysteresis option turned on, this saturation however is reached at a later date

(1446 days after injection start compared to 1355 days). Another way to look at this


0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

Sg

[-]

CO2 saturation (25 2 10)

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

-1 0 1 2 3 4 5

Sg

[-]

Time [years]


WV_2-HYSTERESE Basic case (Eclipse)

Figure 4.5: Non-wetting phase saturation at control point three (cell 25-2-10, 115 m

from the injection well) with hysteresis option turned on.

is that on the same date, the saturation in this case is lower than in the basic case.

This means that when the non-wetting phase comes to rest (after several decades) the

simulation with no consideration of the hysteresis effect will have predicted a further

extent of the plume.

In figure 4.5 we could see that the effects of the hysteresis become most obvious in

regions of the reservoir that go through a drainage and an imbibition cycle or in other

words, where pores become (partly) saturated with the non-wetting phase and as time

progresses and the CO2 moves upwards, they become saturated with brine again. So

another way to examine the differences between the two simulations is to look at the

front of the plume. In order to get a snapshot of the front, two dates were chosen, the

first directly after the injection is completed, the other date 10 years later when the

system had time to return to static conditions with respect to pressure.

In figure 4.7 we see the saturation of the non-wetting phase over the depth of the

reservoir 115 m away from the well (cell 25-2-1 through 20). The two curves are

again almost identical. This is expected since the system has not yet gone through

a drainage/imbibition cycle. Figure 4.8 shows the same section 10 years later. The

lighter non-wetting phase had time to move upward and also a bit in radial direction

due to the remaining small pressure gradient. As can be seen on the graph, more CO2

becomes trapped in the lower layers of the reservoir. The saturation in these layers

does not drop to the residual saturation of 0.025 as in the basic case.


0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

Sg

[-]


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

-1 0 1 2 3 4 5

Sg

[-]

Time [years]


WV_2-HYSTERESE Basic case (Eclipse)

Figure 4.6: Non-wetting phase saturation at control point four (cell 35-2-1, 422 m from

the injection well) with hysteresis option turned on.

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front

(directly after injection)

0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


WV_2-HYSTERESE.xls Basic case (Eclipse)

Figure 4.7: Non-wetting phase saturation front, about 115 m away from the injection

well, directly after the injection.

4.4 Influence of the injection schedule and hysteresis (additionally) 45

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front

(10 years after injection stop)

0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


WV_2-HYSTERESE.xls Basic case (Eclipse)


well, 10 years after the injection.

Conclusion

The comparison of the basic case simulation and the simulation with the hysteresis

option turned on showed two things: A correct simulation of the hysteresis effect will

influence the prediction of available storage and the propagation of the plume. Since

more CO2 becomes trapped in the pores and will consequently not rise to the top of

the reservoir, the available storage space is used more effectively. However, to simulate

this effect correctly, more information about the storage area has to be collected and

analyzed. The other thing that became clear during this comparison is that the effect

is small at the control points in the top layer. The mass of trapped CO2 is too small

in this model in order to see effects on the extension of the plume at these points.

Only figure 4.6 gives a hint that the hysteresis effect will eventually also influence the

prediction of the extent of the plume. To investigate this, a larger model, where the

control points are further away from the injection well, would be more suitable.

4.4 Influence of the injection schedule and hyster-

esis (additionally)

In this simulation set-up the same amount of CO2 as in the basic case is injected

into the reservoir but the injection is split into three parts: The first two injections

are 2/5th, the third injection is 1/5th of a year long (the basic case injection time is

exactly one year). In between each injection there is a relaxation time of two years.

The injection schedule might have an effect on the flow path of the plume since the


advective flow is interrupted several times and the system has time to relax in between

injections. At the second cycle the pores are already partly saturated with the non-

wetting phase and the relative permeability will therefore be higher. Also will the

injection pressure be lower for the same reason.

During the relaxation, a path of residual saturation will stay behind and could increase

the relative permeability. This is especially the case for the simulation with the hyster-

esis model. As the system goes through several drainage/imbibition cycles this effect

should be more obvious and more CO2 should eventually become trapped.


Injection schedule injection 2/5th of a year - 2 years relaxation,

2/5th of a year injection, 2 years relaxation -

1/5th of a year injection

Hysteresis Model off or on (Killough’s model)

Simulator and dis-

cretization scheme


Table 4.6: Injection schedule: Model parameters that differ from the basic case

Evaluation

In figure 4.9 the procedure explained above with three injections becomes clear. In the

simulation with the changed injection schedule and the hysteresis option turned on,

the pressure for the second injection is not lower than for the first injection. In fact

the pressure needed for the second injection is even higher. Only in the third injection

it is lower.

The saturation curves for the control points in cells 19-1-1 and 25-1-1 (topmost layer)

again show no significant difference to the basic case, but in the middle layer (figure

4.10) the effect of the changed injection schedule can be observed: Most obvious are the

2 respectively 3 spikes that indicate that the well has been turned on. In comparison to

the basic case, the pores become less saturated with the non-wetting phase. However

this does not necessarily mean that less CO2 flows through this layer. Since during the

first injection only 40% of the total volume is injected, it is logical that the pores in

this layer become less saturated, because less CO2 is available at this time.

The combined effect of the hysteresis option and the injection schedule is, besides the

effects that arise from the hysteresis model only (section 4.3), almost negligible. If the

hysteresis option is turned on a very small difference can be noticed after the second

injection: The saturation does not return to the same value as before but to a slightly

higher value. This may be the expected effect, that more CO2 becomes trapped when

the system goes through several imbibition/drainage cycles. The effect is very small

but for a larger area it could become significant.


258

260

262

264

266

268

270

P [

ba

r]


256

258

260

262

264

266

268

270

-1 0 1 2 3 4 5 6 7

P [

ba

r]

Time [years]


WV_2A-HYSTERESE-SCHED Basic case (Eclipse)

Figure 4.9: Bottom hole pressure at the injection well (cell 1-1-1) with modified injec-

tion schedule and hysteresis option turned on.

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

Sg

[-]


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

-1 0 1 2 3 4 5 6

Sg

[-]

Time [years]


WV_2A-HYSTERESE-SCHED Basic case (Eclipse) WV_2-HYSTERESE

Figure 4.10: Non-wetting phase saturation at control point three (cell 25-2-10, 115

m from the injection well) with hysteresis option turned on and changed injection

schedule.


In figure 4.11 we can see the effect of the hysteresis option about 400 m away from

the injection well: A significant amount of CO2 has been trapped due to hysteresis

with the result that it arrives later at the control point. The arrival time is, however,

also influenced by the injection time and the changed relative permeability due to the

hysteresis.

0,1

0,2

0,3

0,4

0,5

0,6

Sg

[-]


0

0,1

0,2

0,3

0,4

0,5

0,6

-1 0 1 2 3 4 5 6

Sg

[-]

Time [years]


WV_2A-HYSTERESE-SCHED Basic case (Eclipse) WV_2-HYSTERESE

Figure 4.11: Non-wetting phase saturation at control point four (cell 35-2-1, 422 m from

the injection well) with hysteresis option turned on and changed injection schedule.

Figure 4.12 shows the saturation distribution directly after the last injection, that

means including 4 years of relaxation. The curve from the basic case that is shown in

the same diagram has therefore been taken four years after the injection stop so that

in total both systems had the same relaxation time.

What can be seen in figure 4.12 is that the non-wetting phase has not advanced as

much in deeper layers as in the case where it was injected in several intervals.

In the case where injection schedule was changed (and the hysteresis option was turned

on), one can see that the CO2 has not advanced in a depth below 18 m. In comparison

to the case that has been discussed in section 4.3, the saturation is lower in deeper

layers.

Figure 4.13 shows the curves of the cases with hysteresis option turned on and the

curve of the basic case 10 years after injection stop of the basic case. It can be seen

that in the case with an injection schedule and the hysteresis option turned on, the

CO2 has not spread as far as in the case with only the hysteresis option.


0

2

4

6

8

10

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front

0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front

WV_2A-HYSTERESE-SCHED.xls Basic case (Eclipse) WV_2-HYSTERESE


well, directly after the injection with hysteresis option turned on and changed injection

schedule.

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


WV_2A-HYSTERESE-SCHED.xls Basic case (Eclipse) WV_2-HYSTERESE


well, 10 years after the injection with hysteresis option turned on and changed injection

schedule.

4.5 Influence of the injection rate 50

Conclusion

The simulation results show that it seems more favorable to inject large amounts at

once in order to use as much of the storage space as possible. This is especially the

case when the hysteresis effect is also considered as can be seen in figure 4.10. The

trapped amount of CO2 is significantly larger in the simulation where it was injected

all at once.

4.5 Influence of the injection rate

In these two sets of simulations the injection rate was modified. In one simulation the

rate was lower, in the other it was higher than in the basic case. In order to inject

the same amount of CO2 into the reservoir the injection time consequently had to be

modified as well. The higher the injection rate, the more pressure is needed in the

beginning. That means that the injection rate is limited by the maximum pressure

that the rock can withstand without fracturing.

The change of injection rate is interesting for several reasons: On the one hand it is

favorable to have high injection rates, so that large volumes of carbon dioxide can be

processed quickly. On the other hand it is possible that fractures appear if the pressure

is too high. Fractures are preferred flow paths and could threaten the safety of the

storage area when perforating the seal.

In [28] the authors have also shown that ”trapping of CO2 can be enhanced by: [...]

operating at high injection rates”. The combined effect of different injection rate and

the hysteresis option were not part of this study but the injection rate and the different

pressure will still have consequences for the flow and distribution of the non-wetting

phase.


Injection rate Low rate: 25 m3

d(= about 0.201 kg

s)

High rate: 75 m3

d(= about 0.606 kg

s)

Table 4.7: Injection rate: Model parameters that differ from the basic case

Evaluation

In figure 4.14 the bottom hole pressure at the bore hole is shown for the basic case

and the two injection rate variations. As mentioned in the introduction to this section,

the same amount of CO2 is injected in each simulation. The higher injection rate has

therefore a smaller, the lower injection rate a longer injection time. To inject more fluid

in a shorter time, a higher initial pressure is needed, but as the fluid is distributed more

quickly, the relative permeability (or rather the mobility) also rises more quickly and

less pressure is needed to inject more fluid. This is also reflected in the pressure curve:


From injection start to injection stop, the curve is steeper the higher the injection rate

is.

256

258

260

262

264

266

268

270

272

P [

ba

r]


254

256

258

260

262

264

266

268

270

272

-1 0 1 2 3 4 5 6

P [

ba

r]

Time [years]


WV_1A-LOWINJRATE Basic case (Eclipse) WV_1B-HIGHINJRATE

Figure 4.14: Bottom hole pressure at injection well (cell 1-1-1) with modified injection

rate.

The pressure of the injection also has a (very small but measurable) effect on the

density of brine and CO2 but this effect is not permanent: After the injection stops,

the density is the same in all cases.

While the different arrival times are difficult to distinguish for the first control point,

about 51 m away from the injection well, it is easier to see the differences at the second

control point, 115 m away from the injection well (figure 4.15). More CO2 has entered

the system in the simulation with a high injection rate. The plume has therefore

already a larger extent than in the other two cases (the saturation is higher at the

same point in time).

The saturation curves at the fourth control point (figure 4.16) show an interesting

result: Two years after the beginning of the injections, the injection of the simulation

with a low rate has also stopped. The CO2 plume in the simulation with a lower

injection rate has now spread further than in the other two cases. A likely explanation

is that during the injection, the CO2 spreads further (especially in deeper layers) the

higher the injection rate is, because the influence of the viscous forces become more

dominant (relative to the gravitational forces). In the case with a lower injection rate,

most of the CO2 accumulates only in the top layers with the result that it flows through

a smaller cross-section and therefore advances faster. Another reason for the slower

advancing of the plume in the case with a higher injection rate is that the more pores

become saturated during the injection, (the more CO2 is held back stored by residual

trapping), the less CO2 reaches the control point (at the same point in time).


0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Sg

[-]


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

-1 0 1 2 3 4 5 6

Sg

[-]

Time [years]



Figure 4.15: Non-wetting phase saturation at control point two (cell 25-2-1, 115 m

from the injection well) with modified injection rate.

0,1

0,2

0,3

0,4

0,5

0,6

0,7

Sg

[-]


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

-1 0 1 2 3 4 5 6

Sg

[-]

Time [years]



Figure 4.16: Non-wetting phase saturation at control point four (cell 35-2-1, 422 m



When comparing the results of control point three (figure 4.17), which is located about

115 m away from the well but in the middle of the reservoir, we can see that the

saturation curve for the low injection rate differs significantly from the other two curves.

The maximum saturation is not only lower but it also drops faster than in the basic

case and in the case with a high injection rate. As mentioned before it was also found

in [28] that a higher injection rate has a positive influence on the calculation of the

available storage space.

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

Sg

[-]


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

-1 0 1 2 3 4 5 6

Sg

[-]

Time [years]





The saturation distribution in figure 4.18 shows the effect of the injection rate more

clearly: In case of a higher rate the deep layers become much more saturated than in

the basic case. In case of a lower injection rate there is no saturation below a depth of

about 13m.

10 years after the injection the curves look similar to the basic case (see figure 4.19)

except for the layers that have previously not been reached by the CO2 plume. If the

hysteresis effect had been considered one could imagine that a higher injection rate

would have a positive effect on the amount of trapped CO2 since more pores would be

affected.

Conclusion

A high injection rate is necessary in order to process large amounts of CO2 quickly.

The present simulation has shown that a high injection rate is also better in terms of

efficient usage of the available storage space. Since the CO2 will rise eventually to the

impermeable barrier at the top of the reservoir, it is a good idea to use as much of the


0

2

4

6

8

10

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front (directly after injection)

0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]




well,directly after the injection.

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front (10 years after injection stop)

0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


WV_1A-LOWINJRATE.xls Basic case (Eclipse) WV_1B-HIGHINJRATE


well, 10 years after the injection.

4.6 Effect of rock compressibility 55

storage potential of the deeper layers as possible so that the residual trapping of the

pores in these layers is also available.

4.6 Effect of rock compressibility

Rock compressibility denotes the ability of the matrix to consolidate when pressure is

applied with the result of an increase in pore space. The rock compressibility can not

yet be simulated by DuMuX and has therefore been set to 0 (rigid, no compressibility)

in all simulations except this one. In this set-up the effects of the rock compressibility

were investigated but there is barely any noticeable effect on the benchmark variables

and most curves are identical to the basic case. At control point four (figure 4.20)

there is a very small difference in the pressure curves: The pressure of this simulation

stays slightly below the pressure of the basic case.

257,6

257,8

258

258,2

258,4

258,6

258,8

P [

ba

r]


257,4

257,6

257,8

258

258,2

258,4

258,6

258,8

-1 0 1 2 3 4 5

P [

ba

r]

Time [years]


WV_4-COMPRESS Basic case (Eclipse)

Figure 4.20: Bottom hole pressure at control point four (cell 35-2-1, 422 m from the

injection well) with compressibility model turned on.

For a larger model this effect could become more relevant.

4.7 Injection of CO2 in pure water

In this simulation the effect of the salinity is investigated. Saltwater has a higher density

than pure water (see section 2.1.2), meaning that the density difference between the

wetting and the non-wetting phase in this set-up is reduced. As the buoyant forces are

reduced due to the reduced density difference between CO2 and brine, the advective

forces become more dominant.

4.7 Injection of CO2 in pure water 56

The solubility of CO2 in water is also depending on the salinity.


Fluid properties 2 components (H2O, CO2)

Simulator and dis-

cretization scheme


Table 4.8: Injection into water: Model parameters that differ from basic case

Evaluation

It was shown in section 2.1.2 how the salinity changes the density of water. In this

simulation there is no salt dissolved in the water - its density is therefore lower and

only dependent on pressure, temperature and dissolved CO2. Especially the solution

of CO2 can be seen in figure 4.22: As the CO2 arrives at cell 25-1-1, the density rises

from initially 982 kgm3 to 989 kg

m3 .

To replace the water with CO2, less pressure needs to be used than for the injection into

brine due to the waters’ lower density (and the resulting lower hydrostatic pressure).

The effect of the salinity can thus also be seen in the pressure curve (figure 4.21).

258

260

262

264

266

268

P [

ba

r]


256

258

260

262

264

266

268

-1 0 1 2 3 4 5

P [

ba

r]

Time [years]


WV_8-2KOMP Basic case (Eclipse)

Figure 4.21: Bottom hole pressure at injection well (cell 1-1-1), injection into water.

Figure 4.23 shows a significant difference of the CO2 mole fraction in water indicating

that the solubility of CO2 in fresh water is much higher than in brine (see also [9] p.

40-42). Aquifers that are relevant for CO2 sequestration do often have high salinities.

It is therefore important that the salinity and its effects on density and solubility are

included in the simulation.

While the density of the CO2 is the same as in the basic case, the water density is

lower. With a smaller difference in density, the buoyancy is not as strong as before


980

1000

1020

1040

1060

1080

1100

1120

1140

De

nsi

ty [

kg

/m³]

Brine density (25 2 1)

960

980

1000

1020

1040

1060

1080

1100

1120

1140

-1 0 1 2 3 4 5

De

nsi

ty [

kg

/m³]

Time [years]



Figure 4.22: Wetting phase density at control point two (cell 25-2-1, 115 m from the

injection well), injection into water.

0,005

0,01

0,015

0,02

0,025

[-]

Molefraction CO2 (25 1 1)

0

0,005

0,01

0,015

0,02

0,025

-1 0 1 2 3 4 5

[-]

Time [years]



Figure 4.23: CO2 mole fraction in the wetting phase at control point two (cell 25-2-1,

115 m from the injection well), injection into water.


and the advective forces are more dominant. This can be seen in figure 4.24 where the

saturation levels of CO2 stay at high values for a longer time than in the basic case.

Eventually of course the CO2 will rise and the saturation will return to the residual

saturation.

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

Sg

[-]


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

-1 0 1 2 3 4 5

Sg

[-]

Time [years]




from the injection well), injection into water.

The same effect can be seen in the saturation distribution over the depth of the reservoir

in figure 4.25. The non-wetting phase advances for a longer time in deep layers of the

reservoir. The long term saturation as can be seen in figure 4.26, however, is very

similar to the basic case except for the saturation in the layers between 16m and 18m,

that have not been reached by the CO2 in the basic case simulation. We can see also

a slightly lower saturation at the top layer. This is probably due to the fact that the

CO2 rises slower from the deeper layers to the top of the reservoir.

Conclusion

Many reservoirs that are considered as a potential storage for CO2 are saline aquifers.

The salinity of the brine can be very high (in the basic case a salinity of about

173000ppmw or 2.96molkg

brine was used). The maximum solubility of NaCl at 80

is about 303076 ppmw, calculated with equation 4.1, maximum NaCl solubility, [24]

and [26]

%(weight)[NaCl] = 26.218 + 0.0072 · T + 0.000106 · T 2 (4.1)

The salinity does not only influence the density of water but also has a significant

influence on the solubility of CO2. Compared to the basic case more than double the

amount of CO2 dissolves in pure water. The salinity should therefore be considered in

every simulation.


0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


WV_8-2KOMP.xls Basic case (Eclipse)


well, directly after the injection, injection into water.

0

5

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


0

5

10

15

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]

Saturation front


WV_8-2KOMP.xls Basic case (Eclipse)


well, 10 years after the injection, injection into water.

4.8 Different reservoir temperatures 60

Another effect that the salt can have on the outcome of the simulation (not considered

in this set-up) is that the wetting phase can disappear near the injection well causing

the salt to fall out as a solid and changing the permeability of the matrix around the

well. This effect is known as ”salting-out” and has been described for example in [14].

4.8 Different reservoir temperatures

Since the ECLIPSE E300 can only be used with a constant, isothermal reservoir

temperature, viscosity and density cannot change with respect to temperature. The

injected carbon dioxide will most likely not have the same temperature as the reservoir

in all sequestration projects. Changes in density and viscosity for both carbon dioxide

and brine as well as effects for the solid matrix are therefore very likely.

Under real conditions (considering the sequestration project of RWE Dea), the in-

jected fluid will be cooler than the reservoir: As it enters the reservoir it will probably

have a temperature of about 35C, while the reservoir temperature is expected to be

around 80C. The basic case simulation was carried out with a constant temperature

of 80.3C, viscosity and density for brine and CO2 were calculated for this temperature.

As has been shown in figures 2.2 and 2.3 both density and viscosity of CO2 will change

significantly in the temperature range of 35C to 80C. The changes are not so obvious

for brine as they are for CO2 but the relative density and viscosity of CO2 to brine will

be changed.

In two simulations with ECLIPSE E300, the reservoir temperature was set to 35C

and 60C. Still this will not properly simulate the non-isothermal effects, as the

temperature is set constant. At lower temperatures, the CO2 density and viscosity

will be higher. A lower temperature will therefore mean that the fluid rises and ad-

vances slower.


Initial values Temperature 35C and 60C (constant,

isotherm)

Pressure at the top of the reservoir: 257.5 bar

Simulator and dis-

cretization scheme


Table 4.9: Temperature: Model parameters that differ from basic case

Evaluation

Density and even more viscosity are strongly depending on temperature. As will be

seen in the following graphs, both influence the fluid flow and lead to different results,

indicating that temperature effects should be considered in the simulation.


In figure 4.27 we see three pressure curves for three reservoir temperatures. The reser-

voir temperature for the basic case was 80.3C, in the two other simulations the (con-

stant) temperature was set to 35C and 60C respectively. The lower the temperature,

the higher the viscosity of CO2. If the viscosity is higher, a higher injection pressure

is needed to inject the same amount of CO2. (The highest pressure is needed in the

simulation with 35C, medium for the simulation with 60C).

258

260

262

264

266

268

270

272

P [

ba

r]


256

258

260

262

264

266

268

270

272

-1 0 1 2 3 4 5 6

P [

ba

r]

Time [years]


WV_10-TEMP35 Basic case (Eclipse) WV_10A-TEMP60

Figure 4.27: Bottom hole pressure at injection well (cell 1-1-1), different reservoir

temperatures.

Figures 4.28 and 4.29 also show that the densities of brine and CO2 do not change in

the same way: The increase for brine from 35C to 80.3C is only about 2.4% while

the increase for CO2 is about 23%. The relative density changes by a factor of 10. As

the CO2 arrives at the control point and dissolves it also changes the brines’ density,

which explains the small spike several days after the beginning of the injection.

The viscosity (and therefore the mobility) are even more depending on the temperature.

As we can see in figure 4.30, the mobility decreases as the temperature decreases. With

decreasing temperature, the viscosity of CO2 increases: see table 4.10

Temperature Viscosity

80 C 0.056 cP (1 cP = 10−3Pas)

60 C 0.068 cP

35 C 0.090 cP

Table 4.10: Viscosity values in the ECLIPSE E300 model for various temperatures.

A higher viscosity results in higher friction within the fluid and a slower advancing of

the fluid (lower mobility). Figure 4.31 shows that for lower temperatures the saturation


1115

1120

1125

1130

1135

1140

1145

De

nsi

ty [

kg

/m³]


1110

1115

1120

1125

1130

1135

1140

1145

-1 0 1 2 3 4 5 6

De

nsi

ty [

kg

/m³]

Time [years]



Figure 4.28: Wetting phase density at control point two (cell 25-2-1, 115 m from the

injection well), different reservoir temperatures.

200

400

600

800

1000

1200

De

nsi

ty [

kg

/m³]

CO2 density (25 1 1)

0

200

400

600

800

1000

1200

-1 0 1 2 3 4 5 6

De

nsi

ty [

kg

/m³]

Time [years]

CO2 density (25 1 1)


Figure 4.29: Non-wetting phase density at control point two (cell 25-2-1, 115 m from

the injection well), different reservoir temperatures.


4000

6000

8000

10000

12000

14000

16000

Mo

bil

ity

[1

/Pa

s]

Mobility non-wetting phase (25 1 1)

0

2000

4000

6000

8000

10000

12000

14000

16000

-1 0 1 2 3 4 5 6

Mo

bil

ity

[1

/Pa

s]

Time [years]

Mobility non-wetting phase (25 1 1)

WV_10-TEMP35 Base case WV_10A-TEMP60

Figure 4.30: Non-wetting phase mobility at control point one (cell 25-1-1, 115 m from

the injection well), different reservoir temperatures.

does not increase as quickly as for higher temperatures. While there is only a small

difference in arrival time up to a saturation of 30%, the same values for higher saturation

in the top layer are more than a year apart. The effect becomes more obvious further

away from the injection well, where different arrival times can be better distinguished.

In the middle layer, the saturation curves look even more different. As the injection

well is turned off, the buoyant forces become more dominant. The decline of non-

wetting phase saturation is not as steep for lower temperatures, meaning that it does

not rise as quickly to upper layers due to the smaller density difference between CO2

and brine.

Figure 4.33 shows the variation of solubility of CO2 in brine. As mentioned in section

2.1.3, the solubility increases with decreasing temperature. While the absolute increase

in solubility is not very large, the percent increase is about 10%.

The graph showing the saturation distribution over the depth of the reservoir directly

after the injection (figure 4.34) confirms the impression given by the saturation curve

in figure 4.32, that the colder the temperature, the slower does the fluid advance.

In deep layers (between 16m and 20m), the saturation is higher for the simulation

with a low temperature, while above 16m it is higher for high temperatures. Both are

related to the changed relative density and viscosity between CO2 and brine. A phase

with a lower density will push itself above the denser phase resulting in a flatter front,

while the front is steeper when the densities are more similar.

A higher viscosity causes a slower movement of the fluid, which can also be seen in

figure 4.34: The average saturation over the depth is lower for lower temperatures.

Figure 4.35 shows the saturation front 10 years after the injection. As we can see, the

front of the simulation at 35C has not yet advanced as far to the top layers as the

front of the other two simulations. The saturation values for the simulation at 60C


0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Sg

[-]


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

-1 0 1 2 3 4 5 6

Sg

[-]

Time [years]



Figure 4.31: Non-wetting phase saturation at control point two (cell 25-1-1, 115 m

from the injection well), different reservoir temperatures.

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

Sg

[-]


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

-1 1 3 5 7 9

Sg

[-]

Time [years]




from the injection well), different reservoir temperatures.


0,002

0,004

0,006

0,008

0,01

0,012

0,014

Mo

lefr

act

ion

[-]


0

0,002

0,004

0,006

0,008

0,01

0,012

0,014

-1 0 1 2 3 4 5 6

Mo

lefr

act

ion

[-]

Time [years]



Figure 4.33: CO2 mole fraction in the wetting phase at control point two (cell 25-2-1,

115 m from the injection well), different reservoir temperatures.

0

2

4

6

8

10

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]




well, directly after the injection, different reservoir temperatures.


above 6m depth are even lower as in the basic case simulation at 80.3C. A larger

amount of the non-wetting phase has been trapped in the layers below 16 m and less

is still flowing and ”available” for the top layers.

0

2

4

6

8

10

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]




well, 10 years after the injection, different reservoir temperatures.

Conclusion

This simulation set-up has shown that the potential influence of temperature effects on

the CO2 injection and flow can be significant. While all simulations in this set-up where

carried out at isothermal conditions, the question that hopefully can be answered by

DuMuX is, how big the influence radius of the temperature will be before it equilibrates

with the reservoir temperature.

The values for density and viscosity of both CO2 and brine were as expected, and the

saturation and pressure curves showed that the change in temperature significantly

changes the spreading of the CO2 plume in the underground. Only a non-isothermal

model will, however, correctly show how important the temperature effects really are

and in which area other possible effects (like fractures in the rock) could appear.

Chapter 5

Simulations with DuMuX

5.1 Two-phase model (isothermal)

The simulation with the isothermal model in DuMuX will be the first step for the

comparison and evaluation of non-isothermal effects. In order to evaluate these effects

that can currently only be simulated with DuMuX, the same parameters as in the

basic case for ECLIPSE E300 will be used, to see what the basic differences of the two

programs are and what effect they will have on the results.

In theory, since the grid, the boundary conditions, the matrix properties etc. are

close to identical for both DuMuX and E300 simulations, the results should be very

similar and identical at best. Of course there are still some differences between the two

models: This DuMuX model is a two-phase model which does not take dissolution of

the components in the other phase into account. However, as will be shown in chapter

5.3 the differences also exist with the two-phase two-component model and therefore

have a different origin. Table 5.1 summarizes the settings.

Evaluation

Pressure

Figure 5.1 shows the pressure curve at the injection well: While the curves for the

ECLIPSE E300 basic case and the DuMuX isothermal case look quite similar at first

sight, some differences can be noticed when the curves are examined more closely.

The most obvious difference is the higher pressure in the DuMuX simulation during

injection. The peak pressure is at about 268.1 bar compared to 266.0 bar in the basic

case.

The second difference is not so obvious: The curves are not quite parallel during the

injection and the pressure values at the end of the injection don’t differ that much

anymore. The pressure in the DuMuX simulation is now 262.0 compared to 261.6 bar

in the basic case. This could indicate a slightly different modeling of the capillary

pressure and relative permeability-saturation relation, since the increase in relative

5.1 Two-phase model (isothermal) 68


Geometry Length 800 m

Width 400 m / 30

Thickness: 20 m.

Radius of the segment where the well would be located:

0.05 m

Matrix properties Porosity 20 %

Permeability: 200 mDarcy (in r and θ direction) 20

mDarcy in z direction

Grid r-direction: 40 cells

θ-direction: 4 slices

z-direction: 20 layers

Boundary conditions Dirichlet (constant head) at the outer ring

Neumann at the well (source)

no-flow at all other boundaries

Initial values Temperature 80.3C (353.15 K) (constant)

Bottom of reservoir: 2397.6183 m = hydrostatic pressure

at the top of the reservoir: approximately 257.5 bar

(brine density is assumed to be 1100 kgm3 , g = 9.81 m

s2)

Fluid properties Salinity: 172800ppmw (constant)

Injection schedule 365 days injection at a rate of 0.403125 kgs

and rate = 0.769912044 kgs·m2 with

A = 16· π · 0.05 · 20 m = 0.523598776 m2

Q = 50RM3

d= 0.000578703704 m3

s

(ρ assumed to be 696.6 kgm3 )

20 years relaxation

Hysteresis Model N/A

Rock Compaction N/A

Simulator and dis-

cretization scheme

DuMuX, BOX method

Table 5.1: Model parameters for the DuMuX isothermal case


permeability is mainly responsible for the pressure drop during injection. A slightly

higher injection rate in the DuMuX simulation due to an imprecise conversion is also

possible: The injection rate in DuMuX is set as a mass-value, while in ECLIPSE it is

a volume-value (for the conversion a density value had to be estimated).

The third difference is very small: After the injection stop, there is still a pressure

difference even though the hydrostatic conditions should be the same. Reasons for this

behavior could be a difference in water density or the not quite equal calculation of the

depth of the reservoir (and thus the pressure). The calculation is shown in table 5.1.

260,0

262,0

264,0

266,0

268,0

270,0

P [

ba

r]

Pressure nwPhase 1 1 1

256,0

258,0

260,0

262,0

264,0

266,0

268,0

270,0

-1 0 1 2 3 4 5 6

P [

ba

r]

Time [years]


DuMuX isothermal Basic case (Eclipse)

Figure 5.1: Bottom hole pressure at injection well (cell 1-1-1), DuMuX isothermal

model.

The pressure curves at the other control points show a similar behavior, with the same

already mentioned differences.

Fluid properties

As can be seen in figure 5.2, the density for the non-wetting phase is calculated differ-

ently in the two simulators. While in DuMuX an equation of state from Span and

Wagner [27] is used, ECLIPSE E300 uses an equation of state from Peng and Robin-

son, which is explained in more detail on page 223 of the ECLIPSE E300 technical

description [26].

Basically the same explanation is also valid for the brine density, which is shown in

figure 5.3. The matching of the initial conditions between the two programs might also

play a role. The water density in ECLIPSE E300 (basic case) is also influenced by the

dissolution of CO2 while in DuMuX the dissolution of CO2 is not accounted for.


690,0

695,0

700,0

705,0

710,0

715,0

720,0

De

nsi

ty [

kg

/m³]

Density nwPhase 25 2 1

680,0

685,0

690,0

695,0

700,0

705,0

710,0

715,0

720,0

-1 0 1 2 3 4 5 6

De

nsi

ty [

kg

/m³]

Time [years]



Figure 5.2: Non-wetting phase density (cell 25-1-1), DuMuX isothermal model.

1104,0

1106,0

1108,0

1110,0

1112,0

1114,0

1116,0

De

nsi

ty [

kg

/m³]

Density wPhase 25 2 1

1098,0

1100,0

1102,0

1104,0

1106,0

1108,0

1110,0

1112,0

1114,0

1116,0

-1 0 1 2 3 4 5 6

De

nsi

ty [

kg

/m³]

Time [years]



Figure 5.3: Wetting phase density (cell 25-1-1), DuMuX isothermal model.


The graph of the mobility at control point 25-1-1 can be seen in figure 5.4. The mobility

is defined as the relative permeability divided by the viscosity. Here, the arrival time

at this control point is almost identical for both models. The increase in mobility in

the DuMuX model is slightly faster during the injection but about 1 year after the

injection, the values are slightly higher in the ECLIPSE E300 model. The calculation

of the fluids viscosity is related to the equation of state that is being used, which might

be the source for the differences.

4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

Mo

bil

ity

[1

/Pa

s]

Mobility nPhase 25 2 1

0,0

2000,0

4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

-1 0 1 2 3 4 5 6

Mo

bil

ity

[1

/Pa

s]

Time [years]

Mobility nPhase 25 2 1


Figure 5.4: Non-wetting phase Mobility (cell 25-1-1), DuMuX isothermal model.

Non-wetting phase saturation

A difference in density and viscosity of the fluids and possibly small differences in

the capillary pressure and relative permeability-saturation relation result in a different

spreading of the CO2 plume. The further away from the injection well, the more obvious

is the effect. Figure 5.5 shows the saturation curve at the control point 19-1-1, 51 m

away from the injection well and figure 5.6 shows the saturation curve at 35-2-1, about

400 m away from the injection well. Clearly, the differences become larger. While

the curves in the first two diagrams still seem to be quite similar, major differences

can be seen in the second diagram. The arrival times of the plume at point 19-1-1 is

still within the injection period. The arrival time at point 35-2-1 is after the injection

stopped. The CO2 had time to move upward and the effects of the fluid flow in lower

layers are reflected in this diagram. The differences in the arrival times of the plumes

could also be the result of slightly different injection rates and the resulting differences

in mass that is in the system. The injection mass had to be manually calculated for


DuMuX, because in ECLIPSE a volume-value was used. In the next paragraph we will

look at the saturation curves in the lower layers.

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Sn

[-]

Saturation nwPhase 19 1 1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

-1 0 1 2 3 4 5 6

Sn

[-]

Time [years]



Figure 5.5: Non-wetting phase saturation (cell 19-1-1), DuMuX isothermal model.

Figure 5.7 shows the saturation curve in a medium layer of the model (cell 25-2-10).

The characteristics of the curve are very similar in the beginning, however, a couple

of months after injection start they begin to diverge. The saturation curve of the

basic case increases faster and reaches a slightly higher maximum saturation than the

DuMuX isotherm case (about 0.45 compared to 0.44). This diagram also shows the

behavior during the relaxation (note the longer time period on the x-axis). In ECLIPSE

E300, the saturation values return faster to the residual saturation than in DuMuX.

Figures 5.8 and 5.9 illustrate again the saturation ”front” at control point 25-1-1 di-

rectly after injection and 10 years later.

Figure 5.8 shows that the saturation values in DuMuX are slightly lower between 2 m

and 14 m and slightly higher in the region below 14 m. The general ”shape” of the

front is however quite similar: Both saturation levels have a significant bend in a depth

of about 14 m. Reasons for the differences could be slightly different density values for

brine and the not quite equal location of the measurement point: While the DuMuX

values are measured at the node, the ECLIPSE E300 values are averaged for one cell.

Figure 5.9 shows that even ten years after the injection, the saturation level is not yet

at the residual saturation (in the DuMuX simulation).


0,2

0,3

0,4

0,5

0,6

0,7

Sn

[-]


0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

-1 0 1 2 3 4 5 6 7 8 9 10

Sn

[-]

Time [years]




0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,5

Sn

[-]


0,0

0,1

0,1

0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,5

-1 0 1 2 3 4 5 6 7 8 9 10

Sn

[-]

Time [years]





0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]



Figure 5.8: Non-wetting phase saturation front (directly after injection about 115 m

away from the injection well), DuMuX isothermal model.

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]



Figure 5.9: Non-wetting phase saturation front (10 years after injection about 115 m

away from the injection well), DuMuX isothermal model.

5.2 Two-phase non-isothermal 75

Conclusion

In general it can be said that the simulation results of both the ECLIPSE E300 simu-

lation and the DuMuX isothermal model are fairly similar. However, the further away

from the injection well, the more the results vary. As mentioned in section 5.1, the

discussed DuMuX model is only a two-phase model. Compositional effects as the dis-

solution of CO2 in water have not been included. Some of the differences do also exist

with the two-phase two-component model (2p2cni, described in section 5.3). Other

differences, however, (especially the saturation levels at the control points that are fur-

ther away from the injection well) are most likely related to these compositional effects

since the results from the two-phase two-component (2p2cni) model are more similar

to the ECLIPSE E300 results as will be shown in section 5.3.

For further comparison and especially the influence of the non-isothermal effect, it can

be stated that the saturation values in the DuMuX model at control points close to the

injection well have a good correlation with the values of the ECLIPSE E300 model.

Even the saturation ”front” (the saturation distribution over depth) is similar. Main

differences exist at the pressure curves and the values of control points further away

from the well.

In the following chapter the isothermal model will first be compared with a two-phase

(non-compositional) non-isothermal model. The differences between these two models

will directly show the effect of the temperature on the simulation. In a second step a

two-phase two-component model will be used which can also account for compositional

effects.

5.2 Two-phase non-isothermal

The two-phase non-isothermal model [2pni] can simulate effects that are related to heat

transfer within the model domain. In section 2.1 it was already shown that density and

viscosity are highly dependent on temperature. The question that should be answered

by this simulation is how fast the temperature difference between the area that has

been cooled by the injected CO2 and the rest of the matrix equilibrates and how big

the radius of influence is (in which area these temperature effects can be expected).

For the matrix, an estimated heat capacity of 1696 kJm3 K

was used. In section 2.1.1 it

has also been pointed out that the fluid properties do not change in the same way,

meaning that the relative density and viscosity of water and CO2 will change.

The graphs that will be presented in the following sections show comparisons between

this model, the DuMuX isothermal model (described in section 5.1) and the ECLIPSE

E300 basic case. In this chapter more data from cell 19-1-1 was used because it is

located in the area that is influenced by temperature effects. Only in this area the

non-isothermal effects can be seen clearly.

Table 5.2 shows the initial conditions that differ from the isothermal model.



Initial values Matrix temperature 80.3C (353.15 K) (at the

top of the reservoir)

Fluid temperature 35C (308.15 K)

Simulator and dis-

cretization scheme

DuMuX, Finite Elements (BOX method)

Table 5.2: Model parameters that differ from the DuMuX isothermal case

Evaluation

Pressure

As before we will first have a look at the bottom hole pressure near the injection well

(figure 5.10). Three graphs are shown in the diagram: The solid line illustrates the

pressure curve from the 2pni simulation, the dashed line is from the DuMuX isothermal

model and the dotted line is from the ECLIPSE E300 basic case. It can be seen, that

the values from the two DuMuX simulations are very similar. With a closer look,

small differences can be observed: During the injection, the pressure in the 2pni model

is slightly higher than in the isothermal model. After injection stop, the pressure is

slightly lower and closer to values from the ECLIPSE E300 simulation.

260,0

262,0

264,0

266,0

268,0

270,0

272,0

P [

ba

r]


256,0

258,0

260,0

262,0

264,0

266,0

268,0

270,0

272,0

-1 0 1 2 3 4 5 6

P [

ba

r]

Time [years]


DuMuX 2pni Basic case (Eclipse) DuMuX isothermal

Figure 5.10: Bottom hole pressure at injection well (cell 1-1-1), DuMuX 2pni model.


Temperature

Control point 19-1-1 is right in the zone where the temperature variations due to the

injection take place. Figure 5.11 shows the temperature at 19-1-1. Note that the graph

depicts values up to 20 years after the beginning of the injection. As mentioned in table

5.2, the initial (matrix) temperature was 353.15 K or about 80C. This temperature

value was set for a layer in the middle of the reservoir (small differences result from

a temperature gradient). The beginning of the injection first causes a small increase

- probably due to the increase in pressure - but as soon as the cold CO2 reaches the

control point, the temperature begins to drop until injection stop. The injection stop

causes the fluid flow to slow down and thus slowing down the cooling of the matrix

temperature. However, the fluid flow has not stopped completely so that cold CO2 still

advances. Together these processes cause the noticeable rise and fall of the temperature

curve.

344,0

346,0

348,0

350,0

352,0

354,0

356,0

Te

mp

era

ture

[K

]

Temperature 19 1 1

338,0

340,0

342,0

344,0

346,0

348,0

350,0

352,0

354,0

356,0

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Te

mp

era

ture

[K

]

Time [years]

Temperature 19 1 1

DuMuX 2pni

Figure 5.11: Temperature at cell 19-1-1 (51 m away from injection), DuMuX 2pni

model.


353,0

353,2

353,4

353,6

353,8

354,0

354,2

Te

mp

era

ture

[K

]Temperature 25 1 1

352,4

352,6

352,8

353,0

353,2

353,4

353,6

353,8

354,0

354,2

-1 0 1 2 3 4 5 6

Te

mp

era

ture

[K

]

Time [years]

Temperature 25 1 1

DuMuX 2pni

Figure 5.12: Temperature at cell 25-1-1 (115 m away from the injection), DuMuX 2pni

model.

Fluid properties

As mentioned before, the fluid properties are highly dependent on the temperature.

Figures 5.13 (CO2 density), 5.14 (brine density) and 5.15 (CO2 mobility) also reflect

the temperature changes. Unfortunately, density and relative permeability data has

not been collected in ECLIPSE E300 for this control point. However data is available

for cell 25-1-1.

Even though both the density of brine and CO2 show the same temperature depen-

dence, the changes are more significant for CO2 (see also section 2.1.1).

The control point 25-1-1 (115 m from injection) is not located in the zone where strong

temperature effects occur (the temperature range as can be seen in figure 5.12 is only

about 2K). The fluid properties consequently do not change as much as at point 19-1-1

(51 m from injection, figure 5.13). The temperature starts at a value slightly below

353.15 K, because this value was set for a middle layer (the difference is the result of

a temperature gradient in the reservoir). At the beginning of the injection, a small

increase of the temperature can be noticed, which is probably due to the injection

pressure. The density changes are still obvious, the mobility changes however are

so small that almost no difference can be seen between the non-isothermal and the

isothermal (DuMuX) model.

The capillary pressure is also not affected at all by the temperature.


700,0

710,0

720,0

730,0

740,0

750,0

760,0

770,0

De

nsi

ty [

kg

/m³]


670,0

680,0

690,0

700,0

710,0

720,0

730,0

740,0

750,0

760,0

770,0

-1 0 1 2 3 4 5 6 7 8 9 10

De

nsi

ty [

kg

/m³]

Time [years]


DuMuX 2pni Basic case (Eclipse, estimated) DuMuX isothermal

Figure 5.13: Non-wetting phase density (cell 19-1-1), DuMuX 2pni model.

1104,0

1106,0

1108,0

1110,0

1112,0

1114,0

1116,0

De

nsi

ty [

kg

/m³]


1098,0

1100,0

1102,0

1104,0

1106,0

1108,0

1110,0

1112,0

1114,0

1116,0

-1 0 1 2 3 4 5 6 7 8 9 10

De

nsi

ty [

kg

/m³]

Time [years]


DuMuX 2pni Basic case (Eclipse, estimated) DuMuX isothermal

Figure 5.14: Wetting phase density (cell 19-1-1), DuMuX 2pni model.


4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

Mo

bil

ity

[1

/Pa

s]

Mobility nwPhase 19 1 1

0,0

2000,0

4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

-1 0 1 2 3 4 5 6

Mo

bil

ity

[1

/Pa

s]

Time [years]


DuMuX 2pni DuMuX isothermal

Figure 5.15: Non-wetting phase mobility (cell 19-1-1), DuMuX 2pni model.

4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

Mo

bil

ity

[1

/Pa

s]


0,0

2000,0

4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

-1 0 1 2 3 4 5 6

Mo

bil

ity

[1

/Pa

s]

Time [years]



Figure 5.16: Non-wetting phase mobility (cell 25-1-1), DuMuX 2pni model.



The CO2 saturation curve (figure 5.17) shows a (very small) difference between the

DuMuX isothermal and the 2pni model. In the 2pni model, the saturation is slightly

lower, which is a result of the higher density and thus mass accumulation in the cool

zone near the injection well. At the injection well, a certain mass of CO2 is injected.

At low temperatures, the density is higher and the volume lower. A larger amount of

mass is stored in the zone near the well. The saturation therefore rises more slowly.

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Sa

tura

tio

n [

-]


0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

-1 0 1 2 3 4 5 6

Sa

tura

tio

n [

-]

Time [years]



Figure 5.17: Non-wetting phase saturation (about 51 m away from the injection well,

cell 19-1-1), DuMuX 2pni model.

In deeper layers of the reservoir, deviations between the models become more obvious.

Figure 5.19 shows the non-wetting phase saturation in a medium layer. It can be seen

that in the 2pni model less CO2 reaches this control point compared to the other models

and saturation levels drop earlier than in the DuMuX isothermal model. A reason for

this could be the already mentioned mass storage due to a higher density in the cooled

zone of the reservoir. Figure 5.18 shows saturation levels multiplied with the density.

Even though saturation levels (figure 5.17) are lower at control point 19-1-1, the actual

mass is higher. This would explain why less CO2 arrives at the control point 25-1-1.

On the other hand the density difference between brine and CO2 in the 2pni model

is lower than in the other two models. The non-wetting phase should therefore rise

slower and remain for a longer time in deeper layers of the reservoir.

The saturation distribution of CO2 over the depth of the reservoir in the 2pni model


200,0

300,0

400,0

500,0

600,0

Ma

ss [

kg

/m³]

Mass per m³ nwPhase 19 1 1

0,0

100,0

200,0

300,0

400,0

500,0

600,0

-1 0 1 2 3 4 5 6 7 8 9 10

Ma

ss [

kg

/m³]

Time [years]

Mass per m³ nwPhase 19 1 1


Figure 5.18: Non-wetting phase mass per m3 (about 115 m away from the injection

well, cell 25-2-10), DuMuX 2pni model.

0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,5

Sa

tura

tio

n [

-]


0,0

0,1

0,1

0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,5

-1 0 1 2 3 4 5 6

Sa

tura

tio

n [

-]

Time [years]




cell 25-2-10), DuMuX 2pni model.


is surprisingly similar to the distribution of the isothermal model with slightly lower

values in the layers between 4 m and 14 m and slightly higher values between 16 m and

18 m. These values are collected about 115 m away from the well i.e. outside the area

where the reservoir is cooled. The only very small differences between the isothermal

and the non-isothermal model indicate that the effect of the cooler temperature on the

propagation of the CO2 plume is very small.

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]



Figure 5.20: Non-wetting phase saturation front, directly after injection (about 115 m

away from the injection well) - DuMuX 2pni model.

Conclusion

The comparison between the DuMuX 2pni and the isothermal model have shown only

small differences. In the area around the well that is influenced by the change in

temperature, major differences in the fluid properties can be observed. The den-

sity change also results in a temporary storage which, however, lasts only as long

as the temperature is cooler than the reservoir. With time and the equilibration of

temperature, the CO2 in this area will also expand and contribute to the expansion

of the plume. This behavior could be unfortunate in the long term: The ECLIPSE

E300 simulations in section 4.5 have shown that a high injection rate is favorable due

to its better use of the depth of the reservoir. A later release of the temporarily stored

CO2 could result in a further expansion of the plume in the top layers of the reservoir,

because less pores are used for residual storage.

5.3 Two-phase two-component non-isothermal 84

0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]



Figure 5.21: Non-wetting phase saturation front, 10 years after injection stop (about

115 m away from the injection well) - DuMuX 2pni model.

The exact radius of influence for the temperature changes and the extension of the

plume will be shown in the following section about the two-phase two-component

model.

5.3 Two-phase two-component non-isothermal

The two-phase two-component model (2p2cni) is the most complex DuMuX model. In

this model the solubility of CO2 in water and water in CO2 is simulated. The density

is also dependent on the dissolved CO2. Figure 5.22 shows the model concept for the

two-phase two-component model.

The influence of dissolved CO2 on the density of brine has been described in section

2.1.1: The density of brine will become slightly higher than before. The dissolution of

CO2 is also a desired trapping mechanism (see section 2.4). In the following evaluation,

the results from the 2p2cni simulation are compared with the results of the ECLIPSE

E300 basic case and the DuMuX 2pni simulation.

The boundary and initial conditions are the same as for the previously discussed 2pni

model.


CO −rich phase

dissolution

degassing

evaporation

condensation

water

water−rich phase2

CO2CO2

water

Figure 5.22: Model concept for the DuMuX two-phase non-isothermal model.

Evaluation

Pressure

The bottom hole pressure at the injection well shows some anomalies (figure 5.23)

which are related to the dissolution of CO2. The fluctuations are most likely the result

of an error in the (now outdated) DuMuX version that has been used here.

Besides that, the pressure curve is closer to the curve from the ECLIPSE E300 sim-

ulation during injection. The maximum pressure is not as high as in the 2pni model.

After injection stop, the values from the 2p2cni and from the 2pni model are almost

identical, while the values from the ECLIPSE E300 model are slightly higher for about

1 year.

Temperature

Figure 5.24 shows the temperature at control point 19-1-1 from the beginning of the

injection until 20 years after injection stop. In comparison with the 2pni model, the

values for the 2p2cni model are very similar, the consideration of the dissolution of

components in the phases has only small effects on the temperature: The values in the

2p2cni model are slightly lower especially during the injection and several years after

injection stop probably due to the evaporation/dissolution of water in the non-wetting

phase.

Fluid properties

The density of the phases are now dependent on the amount of dissolved components.

As mentioned before we can see a higher water density in this simulation than in the

2pni model (figure 5.25). Besides that and the ”anomaly” at the injection start, the

curves of the 2p2cni and 2pni model run parallel. An updated version of DuMuX does


260,0

262,0

264,0

266,0

268,0

270,0

272,0

P [

ba

r]Pressure nwPhase 1 1 1

256,0

258,0

260,0

262,0

264,0

266,0

268,0

270,0

272,0

-1 0 1 2 3 4 5 6

P [

ba

r]

Time [years]


DuMuX 2p2cni Basic case (Eclipse) DuMuX 2pni

Figure 5.23: Bottom hole pressure at injection well (cell 1-1-1), DuMuX 2p2cni model.

344,0

346,0

348,0

350,0

352,0

354,0

356,0

Te

mp

era

ture

[K

]

Temperature 19 1 1

338,0

340,0

342,0

344,0

346,0

348,0

350,0

352,0

354,0

356,0

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Te

mp

era

ture

[K

]

Time [years]

Temperature 19 1 1

DuMuX 2p2cni DuMuX 2pni

Figure 5.24: Temperature (about 51 m away from the injection well, cell 19-1-1),

DuMuX 2p2cni model.


not show this spike at the beginning of the injection, indicating that it was a bug in

the version that has been used here.

1100,0

1110,0

1120,0

1130,0

1140,0

De

nsi

ty [

kg

/m³]


1080,0

1090,0

1100,0

1110,0

1120,0

1130,0

1140,0

-1 0 1 2 3 4 5 6 7 8 9 10

De

nsi

ty [

kg

/m³]

Time [years]


DuMuX 2p2cni Basic case (Eclipse, estimated) DuMuX 2pni

Figure 5.25: Wetting phase density (about 51 m away from the injection well, cell

19-1-1), DuMuX 2p2cni model.

In DuMuX, the CO2 density is not influenced by the dissolution of water. It has to be

mentioned, however, that the solubility of water in CO2 is a constant in this (2p2cni)

simulation and is therefore only an approximation. In fact as we will see in the mass

fraction graph (figure 5.31), ECLIPSE E300 calculates a much higher solubility for

water in CO2.

The mobility at point 19-1-1 (figure 5.27) shows no difference between the 2pni and

the 2p2cni model. The viscosity is influenced by the temperature (comparison between

isothermal and non-isothermal model) but neither the relative permeability nor the

viscosity are affected by the dissolution of the components. The DuMuX isothermal

model was used as comparison, because no density data was collected in the ECLIPSE

E300 model for this control point. The general characteristics should, however, be

similar.


Figure 5.28 shows the saturation at cell 19-1-1 over time. As can be seen in the

graph, no difference between the 2pni and the 2p2cni model can be noticed at this


700,0

710,0

720,0

730,0

740,0

750,0

760,0

770,0

De

nsi

ty [

kg

/m³]


670,0

680,0

690,0

700,0

710,0

720,0

730,0

740,0

750,0

760,0

770,0

-1 0 1 2 3 4 5 6 7 8 9 10

De

nsi

ty [

kg

/m³]

Time [years]


DuMuX 2p2cni Basic case (Eclipse, estimated) DuMuX 2pni

Figure 5.26: Non-wetting phase density (about 51 m away from the injection well, cell


4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

Mo

bil

ity

[1

/Pa

s]


0,0

2000,0

4000,0

6000,0

8000,0

10000,0

12000,0

14000,0

16000,0

-1 0 1 2 3 4 5 6 7 8 9 10

Mo

bil

ity

[1

/Pa

s]

Time [years]


DuMuX 2p2cni Dumux isothermal DuMuX 2pni

Figure 5.27: Non-wetting phase mobility (about 51 m away from the injection well,

cell 19-1-1), DuMuX 2p2cni model.


cell. However, significant differences in saturation can be seen further away from the

injection well, as will be shown in figure 5.36.

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Sa

tura

tio

n [

-]


0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

-1 0 1 2 3 4 5 6

Sa

tura

tio

n [

-]

Time [years]





Figure 5.29 already shows a tiny difference between the 2pni and the 2p2cni model with

a slightly lower saturation in the 2p2cni simulation. As explained in the introduction

and in section 2.4, the dissolution of CO2 in brine stores mass in areas that have already

been drained by the non-wetting phase, resulting in less fluid present in the phase.

Compositional effects

Figures 5.30 and 5.31 finally show the effect of the 2p2cni model, the mole fraction

of the components in the respective phases. While the solubility of CO2 in brine

is dependent on temperature and pressure, the solubility of water in CO2 is not (a

constant mass fraction of 0.001 in the non-wetting phase is assumed). In comparison

with the ECLIPSE E300 model the solubility of water in CO2 is significantly lower

(by a factor of 11). The solubility of CO2 in water on the other hand is higher (by a

factor of 3) which can not be explained by temperature effects (see figure 2.5 on page

13). In DuMuX an approach of Duan and Sun [17] has been used, while in ECLIPSE

a different approach by Chang et al. [11], which could be responsible for the different

results.


0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,5

Sa

tura

tio

n [

-]Saturation nwPhase 25 2 10

0,0

0,1

0,1

0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,5

-1 0 1 2 3 4 5 6

Sa

tura

tio

n [

-]

Time [years]





0,015

0,020

0,025

0,030

0,035

0,040

0,045

0,050

Mo

lefr

act

ion

[-]

Molefraction CO2 in water 19 1 1

0,000

0,005

0,010

0,015

0,020

0,025

0,030

0,035

0,040

0,045

0,050

-1 0 1 2 3 4 5 6

Mo

lefr

act

ion

[-]

Time [years]

Molefraction CO2 in water 19 1 1

DuMuX 2p2cni Basic case (Eclipse)

Figure 5.30: Mole fraction CO2 in water (about 51 m away from the injection well, cell



0,004

0,006

0,008

0,010

0,012

Mo

lefr

act

ion

[-]

Molefraction water in CO2 19 1 1

0,000

0,002

0,004

0,006

0,008

0,010

0,012

-1 0 1 2 3 4 5 6

Mo

lefr

act

ion

[-]

Time [years]

Molefraction water in CO2 19 1 1

DuMuX 2p2cni Basic case (Eclipse)

Figure 5.31: Mole fraction water in CO2 (about 51 m away from the injection well, cell


Plume extension and temperature distribution in the reservoir

The graphs in figures 5.32 and 5.33 show in which distance from the well the

temperature effects will take place. About 80 m away from the well the temperature is

already at the initial reservoir temperature. This would mean that less than 1 % of the

models area experiences the density/viscosity effects that are caused by the injection

of cold CO2. However in this small area the density changes are significant (see also

figure 5.18) and since the equilibration of the temperature in the reservoir is very slow

(figure 5.33 shows the temperature 10 years after injection stop), still large amounts

of mass are temporarily stored in the area around the well. The CO2 will however be

”released” as soon as the reservoir warms up and the density drops.

In section 5.2 it has already become clear that the non-isothermal effects do not seem

to have a big influence on the propagation of the plume. The amount of temporarily

stored CO2 will be related to the injection rate and the amount of injected fluid. The

more fluid is injected per time, the larger the cooled area around the well will be.

Figures 5.34 and 5.35 illustrate the temperature front at cell 19-1-1 directly after in-

jection and 10 years later. While the general form is similar in the 2pni and 2p2cni

model, the temperatures are slightly different (note the small temperature range on

the x-axis of the graph).

Figures 5.36 and 5.37 show the non-wetting phase saturation in the top layer of the


320

330

340

350

360

Te

mp

era

ture

[K

]Temperature in r-direction (directly after injection)

300

310

320

330

340

350

360

0 100 200 300 400 500 600 700 800

Te

mp

era

ture

[K

]

Distance from well [m]

Temperature in r-direction (directly after injection)


Figure 5.32: Temperature in r-direction, directly after injection - DuMuX 2p2cni model.

320

330

340

350

360

Te

mp

era

ture

[K

]

Temperature in r-direction (10 years after injection)

300

310

320

330

340

350

360

0 100 200 300 400 500 600 700 800

Te

mp

era

ture

[K

]


Temperature in r-direction (10 years after injection)


Figure 5.33: Temperature in r-direction, 10 years after injection stop - DuMuX 2p2cni

model.


0

2

4

6

8

10

340,2 340,4 340,6 340,8 341 341,2 341,4 341,6

De

pth

[m

]

Temperature [K]

Temperature front (directly after injection)

0

2

4

6

8

10

12

14

16

18

20

340,2 340,4 340,6 340,8 341 341,2 341,4 341,6

De

pth

[m

]

Temperature [K]

Temperature front (directly after injection)


Figure 5.34: Temperature front, directly after injection (about 51 m away from the

injection well) - DuMuX 2p2cni model.

0

2

4

6

8

10

339,25 339,3 339,35 339,4 339,45 339,5 339,55 339,6

De

pth

[m

]

Temperature [K]

Temperature front (10 years after injection stop)

0

2

4

6

8

10

12

14

16

18

20

339,25 339,3 339,35 339,4 339,45 339,5 339,55 339,6

De

pth

[m

]

Temperature [K]

Temperature front (10 years after injection stop)


Figure 5.35: Temperature front, 10 years after injection stop (about 51 m away from

the injection well) - DuMuX 2p2cni model.


reservoir over the length of the reservoir directly after injection and 10 years later.

Several differences between the models can be observed in the two diagrams:

In a small area around the injection well (up to a radius of about 5 m), the dry-out-

effect that is a result of the solubility of water in CO2 can be noticed in the 2p2cni

model simulation: The non-wetting phase saturation reaches values of 1.0 with no

residual water saturation left. The evaporation/dissolution of the residual water into

the injected CO2 can result in ”salt-out”. Since the dissolved salt is left behind when

the water vanishes, the pores around the well can become clogged with the salt-crystals.

In the area with a radius of up to 60 m, the thermal effects can be noticed. Both

the 2pni and the 2p2cni model simulation show identical results with a lower non-

wetting phase saturation in the top layer. The CO2 density is higher due to the lower

temperature and therefore accumulates not as fast in the top layers as in the isothermal

simulation.

In these two diagrams, the values of the ECLIPSE E300 control points were also added.

The saturation levels are slightly lower than the values of the other simulations but it

can be noticed that they are close to the values of the 2p2cni model.

In the area with a radius between 60 and 230 m, all three DuMuX saturation levels

are close to identical but from this point on, the effects of the 2p2cni model and the

difference between the isothermal and the non-isothermal model become quite obvious.

In the 2p2cni model, some of the injected CO2 has been stored by dissolution in the

wetting phase with the result that the extension of the plume is lower than in the other

models. The ECLIPSE E300 values of this (3 component: CO2, water and NaCl) model

are still close to the values from the 2p2cni model.

The results from the 2pni and the isothermal model show the effect from the low-

ered temperature: In the 2pni model, the plume has not advanced quite as far as in

the isothermal model. As described in section 5.2, some of the CO2 will be stored

temporarily due to the higher density. However, the effect is small compared to the

dissolution of CO2. In figure 5.37 the values from the 2pni model and the isothermal

model are very similar.

Figures 5.38 and 5.39 show the non-wetting phase saturation over the depth of the

reservoir about 115 m away from the injection well. It can be seen in the diagram

that illustrates the saturation directly after injection stop (figure 5.38), that the non-

isothermal models (2pni and 2p2cni) have higher saturation levels in deep layers (14 m

to 20 m) but lower saturation levels in the upper layers of the reservoir. With the

changed relative density due to the lower temperature of the injected CO2, the fluid

does not rise as quickly as in the isothermal model. Between the 2pni and the 2p2cni

model only small differences can be noticed: In the 2pni model, the lowest layer of

the reservoir also becomes saturated, which is not the case in the other simulations.

Between 12 m and 20 m, saturation levels are slightly higher in the 2pni model than

in the 2p2cni model - above 12 m the curves are almost identical.

Figure 5.39 shows the saturation curve 10 years after injection stop. While the gen-

eral form of all three models is similar, the non-isothermal models still have higher


0,4

0,6

0,8

1

1,2

Sg

[-]

Saturation in r-direction (directly after injection)

0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600 700 800

Sg

[-]


Saturation in r-direction (directly after injection)

DuMuX 2p2cni DuMuX iso DuMuX 2pni Basic case (Eclipse)

Figure 5.36: Non-wetting phase saturation in r-direction, directly after injection -

DuMuX 2p2cni model.

0,4

0,6

0,8

1

1,2

Sg

[-]

Saturation in r-direction (10 years after injection stop)

0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600 700 800

Sg

[-]


Saturation in r-direction (10 years after injection stop)

DuMuX 2p2cni DuMuX iso DuMuX 2pni Basic case (Eclipse)

Figure 5.37: Non-wetting phase saturation in r-direction, 10 years after injection stop

- DuMuX 2p2cni model.


0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]



Figure 5.38: Non-wetting phase saturation front, directly after injection (about 115 m

away from the injection well) - DuMuX 2p2cni model.

saturation levels in all but the uppermost layer.

Conclusion

The compositional effects have a major influence on the prediction for the extension

of the plume, differences between the 2p2cni and the 2pni model become obvious at

the control points that are furthest away from the well. The solubility storage is an

important trapping mechanism and the prediction of the mutual solubility of CO2 and

water is therefore important for the simulation of CO2 reservoirs. The comparison

has shown that major differences exist between DuMuX and ECLIPSE E300 in the

calculation of the components mass fraction.

In this section, the area of influence of the temperature effect was also analyzed and it

became clear that the area of the reservoir that is influenced by the lower temperature

of the injected fluid is quite small. The lower temperature has the effect of a temporary

storage, but the CO2 will be released eventually when the reservoir warms up.


0

2

4

6

8

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]


0

2

4

6

8

10

12

14

16

18

20

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

De

pth

[m

]

Sg [-]



Figure 5.39: Non-wetting phase saturation front, 10 years after injection stop (about

115 m away from the injection well) - DuMuX 2p2cni model.

Chapter 6

Summary and outlook

CO2 sequestration is meant to be a transition technology on the way to clean power-

generation. While many political and technological questions yet have to be solved,

lots of research is already being done in this field.

This study is part of the research that investigates the propagation of CO2 in the sub-

surface. Experimental data is rare, since drilling is very expensive and the prospective

storage areas are very deep underground (some of them are over 2000 m below the

surface). Therefore, numerical simulation programs have been developed in order to

predict the behavior of fluids under various conditions. The main focus of this study

are the non-isothermal effects that can be simulated with DuMuX [4].

The simulation results show that the temperature does have a significant influence

on the fluid properties, the fluid flow and eventually the storage of the CO2. The

simulations, however, also show that the radius of influence, where the temperature of

the rock changes due to the injected CO2, is small. The temperature effects could still

be important: It is expected that if the rock matrix is cooled abruptly, fractures might

appear that would lead to preferred flow paths.

CO2 sequestration is currently the only technology that could reduce the emitted CO2

quickly in order to take fast measures against climate change. Since not much is known

about the subsurface, research has to be done to clear the way for a safe and accepted

way to dispose of the CO2.

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