Pipeline Transport of CO2 Mixtures Models for Transient Simulation.pdf

Pipeline transport of CO2 mixtures:
Models for transient simulation
P. Aursand, M. Hammer, S. T. Munkejord∗
, Ø. Wilhelmsen
SINTEF Energy Research, P.O. Box 4761 Sluppen, NO-7465 Trondheim, Norway
Abstract
This paper reviews current research challenges related to the modelling of
transient flow of multiphase CO2-rich mixtures in pipes. This is relevant
not only for events like start-up, shutdown or planned or uncontrolled
depressurization of pipelines, but also for normal operation, and therefore
needs to be taken into account by simulation tools employed for design and
operation of CO2 pipelines. During transportation, CO2 will often be in a
dense liquid phase, whereas e.g. natural gas is in a dense gaseous phase. This
requires special attention to depressurization and the possible propagation
of cracks. In addition, we highlight and illustrate research challenges related
to thermodynamics, and the modelling of the wave-propagation velocity
(speed of sound) for two-phase flows. Further, some relevant currently
available simulation tools, and their applicability to CO2 transport, are
briefly discussed.
Keywords: CO2 transport, pipeline, transient simulation, CFD, fluid
dynamics, thermodynamics, transport properties, non-equilibrium,
depressurization, crack propagation
1. Introduction
CO2 capture and storage (CCS) is considered one of the most important
technologies for reducing the world’s emission of greenhouse gases. In the
International Energy Agency’s two-degree scenario (2DS), CCS will contribute
to reducing the global CO2 emissions by about seven gigatonnes per year in
2050 (IEA, 2012). This is a much larger amount than what is transported
in pipelines today for enhanced oil and gas recovery purposes (about 50
megatonnes per year in the USA (US DOE, 2010)), and a major part will
be transported in high-pressure pipelines. Therefore, existing knowledge
on models and simulation tools for multiphase flow of CO2 with relevant
impurities should be further developed to help improve safety and cost-
efficiency.
Multiphase flow modelling has been an active field of research for the
last half century (Slattery, 1967; Ishii, 1975; Drew, 1983; Drew and Passman,
∗Corresponding author.
Email address: svend.t.munkejord [a] sintef.no (S. T. Munkejord)
Preprint submitted to Elsevier 8th March 2013

Table 1: Natural gas composition (Aihara and Misawa, 2010).
Component (mol %)
CH4 88.9
C2H6 6.2
C3H8 2.5
iC4H10 0.4
nC4H10 0.6
iC5H12 0.1
nC5H12 0.1
nC6H14 0.1
N2 0.3
CO2 1.0
1999; Ellul et al., 2004; Ellul, 2010). This development has mainly been
driven by the energy sector. In the nuclear industry, two-phase flow is
important in reactor cooling systems. Herein, the RELAP model developed
by the US Nuclear Regulatory Commission has become the standard tool
for simulating transients and accidents in water-cooled reactors (Allison
and Hohorst, 2010). In the petroleum industry, there has been a need for
pipeline models enabling safe and cost-efficient transport of oil and gas.
This research has led to models and tools for dynamic pipeline simulation of
three-phase (oil-gas-water) mixtures (Bendiksen et al., 1991; Pauchon et al.,
1994; Larsen et al., 1997; Danielson et al., 2011). An example of such a tool
is the dynamic multiphase flow simulator OLGA (Bendiksen et al., 1991),
which has become industry standard for such applications.
There are a number of specific challenges related to CO2 transport that
makes it, from a modelling point of view, different from the transport of
oil and gas. First, the critical point (7.38 MPa at 31.1 ◦
C) and triple point
(about 518 kPa at −56.6 ◦
C) are different. This is illustrated in Figure 1, which
highlights that CO2 will normally be transported in a dense liquid state,
whereas natural gas is in a dense gaseous state. Second, CO2 transported in
a CCS chain will in general not be pure (de Visser et al., 2008). Depending
on the fuel source and capture process, CO2 might contain nitrogen, oxygen,
water, sulphur oxides, methane and other impurities. This will introduce
considerable modelling challenges since the presence of even minute quant-
ities of impurities may significantly affect the thermodynamic and transport
properties of the mixture (Li et al., 2011a,b). The equation of state by Span
and Wagner (1996) (SW EOS) is commonly considered to be the reference for
pure CO2. There are, however, significant gaps in knowledge when it comes
to CO2 with impurities. Furthermore, in pipeline transport of CO2, it is of
interest to predict the minimum water content where hydrates form at a
specified pressure, temperature and composition, both for economical and
safety reasons (Sloan and Koh, 2008). It is known that even small amounts
of impurities can change the equilibrium water content at which hydrates
are formed (Song and Kobayashi, 1987, 1990). In case of impurities like
water and hydrogen sulphide it is also possible to have multiple liquid
phases. When considering tools for simulating multiphase pipe transport,
one should distinguish between steady state and transient (time dependent)
models. Under normal operation, one scenario for pipeline transport is CO2
2

0.01
0.1
1
10
100
1000
180 200 220 240 260 280 300 320 340
Pressure
(MPa)
Temperature (K)
Solid
Liquid
Vapour
Isentropic path
(a) Pure CO2
0
2
4
6
8
10
12
200 220 240 260 280 300
Pressure
(MPa)
Temperature (K)
Phase envelope
Isentropic path
Critical point
(b) Natural gas
Figure 1: Isentropic depressurization from p = 12 MPa, T = 293 K. CO2 is in a dense
liquid state until it reaches the saturation line and then the triple point, whereas
the natural gas is in a dense gaseous state until it reaches the two-phase area. The
Span–Wagner EOS has been used for CO2 and the Peng–Robinson EOS for natural
gas. The natural gas composition is given in Table 1.
in a dense or liquid state, since this is the most energy-efficient condition
(Zhang et al., 2006; Jung and Nicot, 2010). For this case, pressure-drop
predictions for single-phase flow are believed to be satisfactory with the well
known correlations for friction factors (see e.g. White, 1994). This is also the
case for Nusselt number heat-transfer correlations like the Dittus–Boelter
equation (see e.g. Bejan, 1993, Ch. 6). Under such conditions, steady-state
analysis to calculate pressure drop, compression work and mass flow might
be sufficient for flow assurance. It should be noted, however, that some
sources of CO2, such as coal- or gas-fired powerplants, will be fluctuating,
since they are operated in response to external demands. This will cause a
transient flow of CO2 in the pipeline, and moreover, due to the fluctuating
mass flow, the pressure will change, and the state in the pipeline may change
between single- and two-phase (Klinkby et al., 2011).
There are also other transient events, related to start-up, shutdown and
accidents for which the steady-state methodology will be inadequate. One
example is pipe depressurization, either accidental or as a part of planned
maintenance. The decompression wave associated with such an event will
cause the initially dense or liquid CO2 to undergo phase change. The sub-
sequent cooling might render the pipe material, and any coatings, brittle and
vulnerable to cracks. Also, CO2 has a relatively high triple-point pressure,
which means that dry-ice might form during such a depressurization event
(Jäger and Span, 2012; Trusler, 2011, 2012). Accurate predictions of the
velocity and magnitude of the depressurization and cooling is therefore
crucial for assuring safe and reliable operation of a CCS pipeline.
In a transport model, depressurization waves will propagate at the speed
of sound of the mixture. In order to accurately resolve transient events,
it is therefore essential to model the speed of sound in a physically reas-
onable way. The multiphase speed of sound is, however, very sensitive to
various physical equilibrium assumptions (Flåtten and Lund, 2011). Also,
the presence of impurities will affect the propagation velocities of the model
(Munkejord et al., 2010). Even in a pure single-phase case, CO2 mixtures
3

from different capture technologies will give different dynamic behaviour
during pipeline transport. This includes compressor power and hence fuel
consumption (Chaczykowski and Osiadacz, 2012).
Widespread implementation of CCS will in some cases require onshore
CO2 transport pipelines running through populated areas. This may require
strict safety guidelines due to the pipeline pressure and since CO2 is toxic
at high concentrations. Developing such guidelines will require accurate
models for predicting both the occurrence and evolution of pipeline cracks
(Nordhagen et al., 2012). Pipelines can then be designed specifically to avoid
the significant hazards and financial costs associated with the formation
of a running ductile fracture – while reducing the need for safety factors.
Existing models for predicting cracks in pipes are semi-empirically-based
and were mainly developed for natural gas transport. Such models will need
re-calibration when applied to CO2 with impurities transported in pipes
made of modern steel materials.
It should be emphasized that the accuracy of a simulation depends not
only on the accuracy of the physical model, but also on the ability of the
numerical scheme to correctly resolve the underlying model. It has been
shown that numerical diffusion associated with certain numerical methods
can adversely affect the resolution of a depressurization wave in a pipeline
(Clausen and Munkejord, 2012; Morin et al., 2009). This is, however, outside
the scope of this paper.
Race et al. (2007) reviewed key technical challenges for anthropogenic
CO2 offshore pipeline transport. Fracture propagation and transient flow
were mentioned among the subjects requiring further attention. The purpose
of this paper is to review the challenges which should be addressed in the
development of models and tools for transient simulation of pipeline flow of
CO2. It should be noted that the subject of this article is composed of several
research areas, each with their abundant literature. This is a reflection of the
fact that the problem at hand is multifaceted. In particular, in this article,
we will focus on leaks and crack propagation as highly relevant examples of
transient events for which currently available models may not be sufficient
for the application to CO2 transport.
The outline of this paper is as follows: In Section 2 we discuss the most
common approaches for modelling multiphase flow in pipelines. Section
3 is devoted to the modelling of closure relations, thermodynamics and
transport properties of CO2 mixtures, as well as issues associated with the
formation of hydrates. In Section 4 we consider the modelling of leaks and
crack propagation in pipelines. Different scenarios where such modelling
is essential as well as specific challenges related to CO2 are discussed. In
Section 5 we review some common commercially available tools for simulat-
ing transient multiphase flow in pipelines, and discuss their applicability to
CO2 transport. Section 6 concludes the paper and highlights topics in which
more research is needed.
2. Averaged 1D models for pipeline flow
It is not uncommon to state that two-phase flow should be avoided in
CO2 pipelines (see e.g. Race et al., 2007). However, this requirement may not
always be realistic. Klinkby et al. (2011) performed a modelling study of the
4

CO2 transport chain from a coal-fired power plant, including injection into a
reservoir. Due to the transient operation of the power plant, the CO2 supply
will vary. As a result of this, Klinkby et al. found that the CO2 will change
phase from dense phase to two-phase gas and liquid in the upper part of
the well and in the pipeline. It is also interesting to note that two-phase
conditions have been documented in a demonstration well at the Ketzin site
in Germany (Henninges et al., 2011). There are also indications of two-phase
flow at the wellhead at the Sleipner field in the North Sea (Munkejord et al.,
2012). In addition to this, phase change will occur during situations like first
fill and depressurization. This motivates the study of transient multi-phase
flow of CO2-rich mixtures.
In this section we discuss some of the most common formulations of the
governing dynamics of multi-phase pipeline flow. Note that most of these
topics will be generic with regard to the transported medium and impurities.
Issues specific to CO2 transport will be most apparent when introducing
equations of state and closure relations for the averaged model, which will
be the topic of the subsequent sections.
2.1. The two-fluid model
For a real-scale pipeline, fully resolving the governing equations of the
multiphase flow is computationally intractable. The usual way to get around
this problem is to consider averaged models (see e.g. Drew and Passman,
1999). For a pipeline, a commonly used approach is to consider transport
equations for mass, momentum and energy averaged across the cross sec-
tion of the pipe. For two-phase flow, the resulting 1D model takes a form
often referred to as the two-fluid model. A common formulation is given by
Conservation of mass:
∂
∂t
(ρgαg) +
∂
∂x
(ρgαgug) = Γ, (1)
∂
∂t
(ρ`α`) +
∂
∂x
(ρ`αù`) = −Γ. (2)
Conservation of momentum:
∂
∂t
(ρgαgug) +
∂
∂x
(ρgαgu2
g + αgpg) − pi ∂αg
∂x
= ρgαgfx − Mw,g − Mi
+ ui
Γ Γ, (3)
∂
∂t
(ρ`αù`) +
∂
∂x
(ρ`αù2
` + α`p`) − pi ∂α`
∂x
= ρ`α`fx − Mw,` + Mi
− ui
Γ Γ. (4)
Conservation of energy:
∂
∂t
(ρgαgEg) +
∂
∂x
ρgαgug

Eg +
pg
ρg
!
+ pi
ui
τ
∂αg
∂x
= ρgαgugfx + Qw,g − Qi
− ui
M Mi
+ Ei
Γ, (5)
5

∂
∂t
(ρ`αÈ`) +
∂
∂x
ρ`αù`

E` +
p`
ρ`
!
+ pi
ui
τ
∂α`
∂x
= ρ`αù`fx + Qw,` + Qi
+ ui
M Mi
− Ei
Γ, (6)
where the nomenclature is as follows:
αk Volume fraction of phase k
ρk Mass density of phase k
uk Velocity of phase k
pk Pressure of phase k
Ek Energy density for fluid k, Ek = ek + 1/2 u2
k
Qk Heat source for phase k
fx x-component of body force
In the cross-section averaged description above, the model does not con-
tain information about the internal moving interfaces between the phases.
Also, any information on local gradients along the cross section of the pipe is
lost in the averaging procedure. Closure relations are thus needed to model
the source terms representing transfer of heat, Q, mass, Γ, and momentum,
M, between the fields (denoted by the index i) and between the fields and the
pipe wall (denoted by the subscript w). In general, these closure relations will
depend on the detailed description of the flow, and they cannot be derived
from first principles based on averaged quantities (Stewart and Wendroff,
1984). The modelling of such terms is further discussed in Section 3.
2.2. The drift-flux model
In multiphase pipe flow, there are flow regimes where the velocities of
the individual phases are highly correlated. For two-phase flow, the relative
velocity between the phases can be expressed as a slip relation
u1 − u2 = Φ(α1, p, T, u1), (7)
see the work of e.g. Zuber and Findlay (1965), Ishii (1977) and Hibiki and
Ishii (2002).
A slip relation in the form (7) can be used to reduce the complexity of
the two-fluid model (1)–(6). In particular, if the pressures in both phases
are assumed to be equal, p1 = p2 = p, the momentum equations (3)–(4) can
be combined into a single mixture momentum equation. Likewise, with the
assumption of equal phasic temperatures, T1 = T2 = T, the energy equations
(5)–(6) can also be combined. The resulting drift-flux model is given by
Conservation of mass:
∂
∂t
(ρgαg) +
∂
∂x
(ρgαgug) = Γ, (8)
∂
∂t
(ρ`α`) +
∂
∂x
(ρ`αù`) = −Γ. (9)
Conservation of momentum:
∂
∂t
((ρgαgug + ρ`αù`) +
∂
∂x
(ρgαgu2
g + ρ`αù2
` + p)
= (ρgαg + ρ`α`)fx − Mw. (10)
6

Conservation of energy:
∂
∂t

ρgαgEg + ρ`αÈ`

+
∂
∂x

ρgαgug(Eg + p/ρg)

+ (ρ`αù`(E` + p/ρ`))

= (ρgαgug + ρ`αù`)fx + Qw. (11)
Besides being simpler and in conservation form, the drift-flux model also,
as discussed by Munkejord (2005), has some advantages over the two-fluid
model when it comes to stability and well-posedness. However, it may not
be appropriate to model all relevant flow regimes with a slip relation of the
form (7). The drift-flux model (8)–(11) with the additional assumptions of
no slip (ug = u`) and equal chemical potential in the two phases is often
referred to as the homogeneous equilibrium model.
For two-phase mixtures, the composition of the gas and the liquid will
in general differ. Hence, if there is slip between the phases, the flow model
needs to include a mass-conservation equation for each component.
2.3. Wave speeds in multifluid models
When studying transient events in CO2 pipelines, the speed with which
disturbances propagate along the pipe is an important factor. In any fluid,
pressure waves travel at the speed of sound relative to the local velocity.
It is therefore essential to include a realistic speed of sound to be able to
correctly simulate many transient events in pipes.
For the basic two-fluid model (1)–(6), the eigenvalues of the flux Jacobian
are not guaranteed to be real (Gidaspow, 1974). When this occurs, the
equation system is no longer hyperbolic, which causes problems related to
stability and well-posedness (Stuhmiller, 1977). To remedy this, regulariza-
tion terms are often introduced, forcing the eigenvalues to be real. In the
opposite case, robustness issues are typically encountered, unless the solver
has a high-enough numerical smearing.
2.3.1. Non-equilibrium fluid-dynamical models
In general, the wave speeds of a set of conservation laws are also influ-
enced by various source terms. Local source terms will not influence the
characteristics of the system but will introduce dispersion, i.e. wave-number
dependent sound velocities (Aursand and Flåtten, 2012).
Relaxation terms represent a class of local source terms that are of par-
ticular relevance to multiphase flow modelling (Baer and Nunziato, 1986;
Saurel et al., 2008; Flåtten and Lund, 2011). Chemical, thermal and mechan-
ical non-equilibrium are examples of processes that can be described with
relaxation terms. A hyperbolic relaxation model can be written in the form
∂
∂t
Q +
∂
∂x
F(Q) =
1
ε
R(Q), (12)
where R(Q) is a relaxation term representing the driving-force pulling the
system towards local equilibrium, characterized by R(Q) = 0. The relaxation
time ε can be seen as a characteristic time scale of the relaxation process.
7

50
100
150
200
250
300
350
0 0.2 0.4 0.6 0.8 1
Speed
of
sound
(m/s)
αg (-)
chem
ctf,µg=µ`
ctf
cg
c`
Figure 2: Speed of sound of pure CO2 in the gas-liquid two-phase area as a function
of gas volume fraction for various two-phase flow models. T = 250 K, SW EOS. ‘hem’
denotes the homogeneous equilibrium model, ‘tf’ denotes the two-fluid model with
no phase change and no slip, ‘tf µg = µ`’ is the two-fluid model with full chemical
equilibrium and no slip, ‘g’ is gas and ‘`’ is liquid.
For a given relaxation process there is a corresponding local equilibrium
approximation. The characteristic velocities of the equilibrium model are in
general different from those of the relaxation model. Flåtten and Lund (2011)
analysed two-phase drift-flux models with and without thermal, mechanical
and chemical equilibrium. They showed that imposing equilibrium will
always reduce the speed of sound for such models, i.e., the characteristic
velocities of the local equilibrium model are smaller than those of the
non-equilibrium (relaxation) model. In general, this concept is known as
the sub-characteristic condition and is closely related to the stability and
well-posedness of the model (Chen et al., 1994).
In the modelling of multiphase flow, the assumption of thermal, mechan-
ical or chemical equilibrium is ubiquitous. While these assumptions often
simplify the model in question, it is important to be aware that they will
directly influence the wave dynamics of the model. For example, assuming
chemical, thermal and mechanical equilibrium may lead to a significant un-
derestimation of the rate of which disturbances will propagate in a pipeline,
compared to a non-equilibrium model. This is illustrated in Figure 2, where
the speed of sound of pure CO2 is calculated for different two-phase flow
models as a function of gas volume fraction. The graphs are plotted for a
temperature of T = 250 K using the Span–Wagner equation of state (SW EOS).
It can be seen that models with the assumption of full chemical equilibrium
(instantaneous phase transfer) have the artifact of a discontinuous speed of
sound in the limit of single-phase flow. This is not believed to be physical.
Further, it can be seen from the figure that allowing phase transfer lowers
the predicted speed of sound in almost the entire volume-fraction range.
This highlights how tightly intertwined thermo and fluid dynamics are for
two-phase flow.
In Figure 2, we have plotted analytical expressions for the speed of sound.
The speed of sound in the homogeneous equilibrium model is also referred
to as the ‘Wood speed of sound’, and it can e.g. be found in Martínez Ferrer
8

et al. (2012, eq. (3.7)). The speed of sound in the two-fluid model with no
phase change and no slip can be found in Martínez Ferrer et al. (2012, eq.
(3.74)). Finally, the speed of sound in the two-fluid model with full chemical
equilibrium and no slip can be found in Morin and Flåtten (2012), see also
Morin (2012).
Since decompressions of CO2 will often pass through the triple point, it
is interesting to note that at the triple point, for full equilibrium, the speed
of sound is zero (Henderson, 2000, Sec. 2.8.1).
3. Closure relations and thermophysical models
For an averaged multifluid model such as (1)–(6), closure relations are
needed for terms depending on transversal gradients and the detailed
phase configuration. Since these relations cannot be derived from the
same first principles as the averaged flow model, they need to be modelled.
Moreover, thermodynamic relations are needed for calculating the pressures,
temperatures and compositions, as a function of the variables of the fluid-
dynamic transport model.
3.1. Closure relations for CO2
While the field of multiphase flow modelling is mature, there exists
no general way of modelling closures valid for all fluids. Flow maps and
correlations must be validated, adjusted or developed for each new working
fluid or composition of fluids. This presents one of the main challenges in
the modelling of CO2 flow in pipelines. Existing correlations and models
used by research and industry for oil-gas-water mixtures cannot necessarily
be assumed to be valid for CO2 with impurities. These models need to be
adapted to these new applications, a process needing experimental input
for validation.
For CO2, there exist flow maps and pressure-drop measurements for
tubes and channels with a hydraulic diameter in the millimetre range. Most
of them are developed for heat exchanger applications, see e.g. (Bredesen
et al., 1997; Pettersen, 2002; Yun and Kim, 2003; Cheng et al., 2008).
Aakenes (2012) compared experimental data for frictional pressure-drop
for steady-state two-phase flow of pure CO2 (see also de Koeijer et al., 2011)
to data calculated using the model of Friedel (1979) and that of Cheng et al.
(2008). Although the latter was developed specifically for CO2, the former
fitted the data better, most likely to its broader experimental base.
Since the existing small-scale data may not be representative for real
pipelines, there is a need for medium and large-scale data. Presently, there
exist some initiatives towards this end, such as the OXYCFB300 Compostilla
Project (CIUDEN, 2012) and the multiphase CO2 lab at the Institute for
Energy Technology (IFE) (SPT Group, 2012).
3.2. Thermophysical models for pure CO2
For pure CO2, a large amount of experiments have been conducted for
thermodynamic properties such as densities, heat capacities and liquid-
vapour coexisting curves, as well as for transport properties. The accurate
single-component equation of state (EOS) by Span and Wagner (1996) is
9

considered the reference EOS for pure CO2. The EOS is valid for temperat-
ures from 216 to 1100 K and pressures up to 800 MPa, which is more than
sufficient for pipeline transport of CO2. Accurate models for the viscos-
ity and the thermal conductivity were developed by Vesovic et al. (1990).
Fenghour and Wakeman (1998) presented an improved viscosity model. The
resulting overall viscosity model for pure CO2 covers the temperature range
of 200 K–1500 K and pressures up to 300 MPa.
3.3. Thermophysical models for CO2 mixtures
For CO2 mixtures relevant for CCS, the amount of available data is
more scarce than for single-component CO2. This is true both for the
thermodynamic properties (Li et al., 2011a; Hu et al., 2007) and for the
transport properties (Li et al., 2011b). Consequently the development of
comprehensive reference models has not yet been possible.
Li et al. (2011a) argue in their review that there is no equation of state
which shows any clear advantages in CCS applications. The cubic equations
of state have a simple structure and are capable of giving reasonable results
for the thermodynamic properties, but are inaccurate in the dense phase and
around the critical point (Wilhelmsen et al., 2012). More complex equations
of state such as Lee-Kesler (Lee and Kesler, 1975), SAFT (Wertheim, 1984a,b,
1986a,b) and GERG (Kunz et al., 2007) typically give better results for the
density, but not necessarily for the vapour-liquid equilibrium. See also
Dauber and Span (2012). Wilhelmsen et al. (2012) have recently shown
evaluations with the SPUNG EOS (Jørstad, 1993). They found that the SPUNG
equation represents a good compromise between accuracy, versatility and
computational time-use for calculations with CO2 mixtures.
It is well known that the EOS must be equipped with suitable interaction
parameters to give reliable phase-equilibrium predictions (Wilhelmsen et al.,
2012). These are available for cubic EOS’es and several CO2 mixtures (Li and
Yan, 2009), but for other EOS’es, regression of new interaction parameters
is needed (Wilhelmsen et al., 2012).
For the viscosities and thermal conductivities of CO2 mixtures, the gas
phase is well investigated for many impurities. Accurate models are avail-
able in the literature, for instance through Chapman-Enskog theory or
corresponding-state relations (Reid et al., 1987). For the liquid phase, how-
ever, no experimental data are available except for mixtures of CO2/H2O/NaCl,
which makes development and validation of models difficult (Li et al., 2011b).
One should therefore expect large uncertainties in empirical closure rela-
tions which rely heavily on the prediction of viscosities or thermal conduct-
ivities in liquid phase CO2 mixtures.
Currently, some experimental work is being carried out towards obtaining
properties for CO2 mixtures (Sanchez-Vicente et al., 2013; Stang et al., 2012).
It should also be noted that pseudo-experimental data of vapour-liquid
equilibrium and transport properties for CO2 mixtures can be calculated
using molecular simulations based on Monte Carlo and Molecular Dynamics.
CO2 + N2O and CO2 + NO are investigated by Lachet et al. (2012).
Water is a common impurity in the CO2 stream, which is the key com-
ponent in several undesired phenomena, such as hydrate formation, ice
formation and corrosion. The CO2 will have a significant solubility in the
10

water phase, which changes its properties. In addition, water and CO2 can
form mixtures with more than two phases, which necessitates more than
two phases in the fluid-dynamical model formulation. Extensive reviews
have been presented in the literature on the mutual solubility of water, CO2
and other impurities (Chapoy et al., 2004; Austegard et al., 2006; Hu et al.,
2007).
3.4. Implementation in fluid-dynamic pipeline models
Equations of state are usually not written in a form suitable for fluid-
dynamic simulations. For example, a pressure-temperature state function
cannot be directly employed in model formulations of the form presented
in Section 2. Rather, a density-energy function is more appropriate. This
necessitates the development of fast and robust numerical algorithms for
solution phase-equilibrium equations with specification of energy and dens-
ity (Michelsen and Mollerup, 2007). Giljarhus et al. (2012) studied such
a method for the Span–Wagner EOS for pure CO2. With CO2 containing
impurities, robust and time efficient solution of the phase equilibrium is a
considerable challenge (Wilhelmsen et al., 2013).
3.5. Hydrate formation, solid CO2 and non-equilibrium effects
For economic and safety reasons, it is of interest to predict the minimum
water content where hydrates form at a specified pressure, temperature and
composition (Sloan and Koh, 2008). The equilibrium of hydrate formation is
a well investigated issue for natural gas mixtures, but few data are available
for pure CO2 (Tohidi et al., 2010), and even fewer for CO2 mixtures. Song
and Kobayashi (1987, 1990) show that even small amounts of impurities
can change the equilibrium water content at which hydrates are formed.
Reliable prediction of the hydrate equilibrium depends on equations of
state which are able to provide accurate estimates of the chemical potential
in CO2 mixtures with small water concentrations. This is not trivial, and
often requires tailored EOS’es and interaction parameters, such as the CPA
equation, or SRK with Huron–Vidal mixing rules (Austegard et al., 2006). See
also Chapoy et al. (2004). Jäger et al. (2013) employed accurate equations of
state to predict hydrate formation in pure CO2 with water.
Several commercial codes predict hydrate equilibrium properties also
for CO2 with impurities. However, without an EOS tailormade to provide an
accurate estimate of the chemical potentials of water in CO2 mixtures, the
results may not be reliable. During depressurization events or formation of
cracks in pipelines, there is a risk of formation of solid CO2. Zhang (2012)
shows models which are capable of providing accurate predictions of the
CO2 freeze-out temperature of several CO2-CH4 mixtures, and experimental
data are also available for systems with N2 (Argwal and Laverman, 1974).
A comprehensive evaluation solid-phase equilibria for CO2 mixtures with
impurities is currently not available. Uncertainties in the models should
be expected for CO2-rich mixtures with other impurities than CH4 and N2
(Zhang, 2012).
In fluid-dynamical simulations, it is common to assume mechanical,
thermal and chemical equilibrium between the coexisting phases. Flåtten
and Lund (2011) argue that this is insufficient in many applications. In
11

dynamic simulations of depressurization of pipelines for instance, the
transients in the systems will be so fast that the coexisting phases are not
in equilibrium. The metastable sections of an equations of state where
subcooling or overheating occurs, are well defined mathematically and may
be used to a certain extent to account for situations away from equilibrium.
However, the rate at which transfer of heat, mass and momentum between
the phases occurs is not easily described by thermodynamics alone, since
it is about how the transport across the interface separating the gas and
liquid evolves over time. Theories for this are currently being developed
(Kjelstrup and Bedeaux, 2008), but these theories have yet to be used in
existing fluid-dynamical simulations of CO2 transport.
The presence of free water is the principal influence on corrosion rate
in pipes (see e.g. Cole et al., 2011). However, since the present subject is
transient effects, this will not be further discussed here.
4. Flow through valves and cracks
Simulating transient events related to depressurization or crack forma-
tion in CO2 pipelines requires modelling of multiphase critical flow through
an orifice. For homogeneous flows, critical flow occurs at the sonic point. By
assuming isentropic flow, we can integrate the differential relations
d (ρuA) = 0 (13)
d

h +
1
2
u2

= 0 (14)
ds = 0, (15)
along a streamline going through the valve or crack. In the above, A is the
cross-section area, h is the specific enthalpy and s is the specific entropy.
For multiphase flow, phase transfer needs to be taken into account when
integrating (13)–(15). Herein, there are two different assumption in common
use, each representing an extreme case:
Homogeneous equilibrium model The choke flow is assumed to remain
in equilibrium. Equations (13)–(15) are integrated along a path of
chemical equilibrium.
Frozen model The phase composition is assumed to remain constant through
the choke. Equations (13)–(15) are integrated along a path where the
mass fractions are constant and where the chemical potentials of the
phases are not equal.
In addition to the two extreme cases described above, there exists a number
of empirical correlations in common use (Auria and Vigni, 1980). One of the
most cited is the Henry–Fauske model (Henry and Fauske, 1971), which can
be seen as a correction to the frozen approximation.
In general, different assumptions of phase equilibrium will lead to differ-
ent choke pressures, and consequently different mass-flow rates. A typical
situation is illustrated in Figure 3. A homogeneous equilibrium model will
give choked flow at a lower pressure difference than a non-equilibrium
model. For many cases the resulting difference in predicted mass flow will
12

∆p
M
Frozen
Henry–Fauske
HEM
Figure 3: Illustration of the two-phase mass-flow rate M through an orifice as a
function of the pressure difference ∆p, for different equilibrium assumptions.
be significant. The assumption of phase equilibrium in valves and cracks
can therefore strongly influence transient multiphase pipeline simulations.
For multiphase flow, the assumption of homogeneous flow though a valve
or crack might not be valid. Depending on the flow regime, the acceleration
of the denser phases might be significantly lower than that of the less dense
phases.
4.1. Running ductile fractures in CO2 pipelines
For CO2 transport, pipeline crack modelling represents a particularly
relevant example of an application of critical flow. CO2 is toxic at high con-
centrations; predicting the occurrence and evolution of cracks is therefore
essential for designing and operating a safe CCS pipeline. For high-pressure
pipelines, including CO2 lines (Maxey, 1986), a concern is also the formation
of running ductile fractures. In order to prevent hazardous situations and
potentially significant costs, high-pressure pipelines must be designed both
to avoid the formation of cracks and to ensure the quick arrest of any cracks
that might still form.
Running ductile fracture is commonly assessed using semi-empirical
methods like the Battelle method (Maxey, 1974). Herein, the fluid decom-
pression and the fracture propagation in the pipeline are assumed to be
uncoupled processes. The fracture velocity is correlated to the fracture en-
ergy (e.g. Charpy energy). As long as the fracture velocity is smaller than the
decompression wave velocity, crack arrest is assured. In the HLP approach
(Sugie et al., 1982), the final crack length is also predicted. There exists a
large body of work in the field, see e.g. Ives et al. (1974); Parks and Freund
(1978); Picard and Bishnoi (1988); Leis and Eiber (1998); Makino et al. (2001);
Hashemi (2009). Recalibration is needed for new fluids and new material
qualities. In particular, for modern steel types with high toughness, the
relationship between fracture velocity and Charpy energy is less certain
(Leis et al., 2005). Thus it is challenging to predict the pressure at which a
running fracture will arrest.
Although the saturation pressure and arrest pressure are key parameters
(Cosham and Eiber, 2008), the evolution of a pipeline crack is a coupled
material-fluid problem (Mahgerefteh and Atti, 2006). The fracture speed
depends on the forces caused by the pressure difference through the crack,
13

while the pressure in the pipe depends on the rate of escaping mass flow
which again depends on the crack size. The arrest or continued propagation
of a crack will depend on the difference between the speed of the depres-
surization wave in the fluid and the speed of the crack tip. If the depres-
surization propagates faster than the crack, the driving forces maintaining
the crack propagation will vanish and the crack will arrest; if not, the crack
might form a running fracture. The crack arrest length will therefore also
depend on the fluid inside the pipe (Aihara and Misawa, 2010; Mahgerefteh
et al., 2012a). This is important because the existing semi-empirical models
for evaluating running fractures in pipes were mainly developed for natural
gas transport. Such models will need costly recalibration before they can
be applied to CO2 transported in pipes made of modern steel materials
(Nordhagen et al., 2012).
Running ductile fracture in gas-transport pipelines consists of three main
phenomena, namely, the large-scale elasto-plastic deformation of pipe walls,
the three-dimensional nonsteady fluid dynamics and the inelastic dynamic
crack-extension process (O’Donoghue et al., 1991). Due to the complexity of
these factors, and their interaction, there exist relatively few fully coupled
models for the prediction running ductile fracture.
O’Donoghue et al. (1991, 1997) developed a fluid-structure interaction
model in which a three-dimensional finite-difference fluid-dynamics code
was linked with a shell finite-element code. O’Donoghue et al. (1997) con-
sidered crack arrestors, which are steel rings employed to prevent long
running axial cracks. The effect of dissipation of plastic work for high-
toughness steels was studied by You et al. (2003). Greenshields et al. (2000)
investigated fast brittle fracture in plastic pipes, employing a finite-volume
discretization both for the pipe and the fluid. Herein, the pipe material was
represented in 3D, while the fluid flow was calculated in 1D.
Several authors have considered the behaviour of a gas escaping through
a crack or nozzle, but few have coupled the structural failure with the fluid
behaviour. In the work by Rabczuk et al. (2010), a meshfree method for
treating fluid-structure interaction of fracturing structures under impulsive
loads was described. Terenzi (2005) emphasized that it is necessary to take
care of real fluid behaviour when analyzing the decompression properties
of dense natural gas mixtures. It was found that friction hinders crack
propagation, while condensation promotes it. Mahgerefteh et al. (2006)
simulated outflow after rupture in pipeline networks. It was found that
bends, branches and couplings could have significant effects on the fluid
flow. Cumber (2007) described a methodology for predicting outflow from
a rupture in a pipeline transporting supercritical ethylene. The flow was
modelled without solving a full two-phase flow model, but phase change
was accounted for.
Berstad et al. (2011); Nordhagen et al. (2012) used a coupled material-
fluid methodology in order to predict crack arrest for natural gas and
hydrogen. Good agreement with full-scale tests (Aihara et al., 2008) was
obtained. A similar modelling approach was used by Misawa et al. (2010).
In an experimental and computational study, Yang et al. (2008) found that
as the amount of heavier hydrocarbons increased in the natural gas, steels
of higher toughness were required. Mahgerefteh et al. (2012a) evaluated
the effect of some stream impurities on ductile fractures in CO2 pipelines,
14

0
2
4
6
8
10
12
0 100 200 300 400 500 600
Pressure
(MPa)
Decompression velocity (m/s)
HEM CO2
Two-Fluid CO2
HEM NG
HEM 4% N2
Figure 4: Fluid pressure versus decompression velocity for the homogeneous
equilibrium model (HEM) and the two-fluid model with full chemical equilibrium. NG
denotes the natural gas from Table 1.
while Aursand et al. (2012) took into account dry-ice formation in pure
CO2. Both of the two latter studies found that CO2 pipelines might be more
susceptible to running ductile fracture than natural gas pipelines. Regarding
the validation of these predictions, to our knowledge, no experimental data
for running fractures in CO2 pipelines have been published, but work is
under way, see e.g. Lucci et al. (2011). It can therefore be said that the
development of coupled fluid-structure models for crack behaviour in CO2
pipelines is at an early stage.
To illustrate the effect of fluid flow modelling and fluid properties, we
have plotted pressure versus decompression velocity in Figure 4. The
decompression velocity is the speed of sound minus the flow velocity (c − u)
as the decompression wave travels through a ‘long’ pipe. In the figure, we
have plotted the decompression velocity using the homogeneous equilibrium
model for pure CO2 (using the SW EOS), for CO2 with 4 % N2 (using the EOS
by Peng and Robinson (1976) (PR)) and for a natural gas (using the PR EOS
with the composition given in Table 1). The plots have been made for
an initial state of p = 12 MPa and T = 293 K. In e.g. the Battelle method,
similar plots are generated, and a curve for the arrest pressure of the pipe
is added. In the left region, the CO2 curves lie above the one for the natural
gas. This indicates that CO2 gives a lower decompression speed in this
region, which means that the pipe filled with CO2 may be more vulnerable
to running ductile fracture, see e.g. Cosham and Eiber (2008); Aihara and
Misawa (2010). It is clear from the figure that the addition of N2 to the CO2
stream aggravates the situation.
Figure 4 also shows a curve calculated using the two-fluid model with full
chemical equilibrium. In contrast to the case in Figure 2, here, there is slip
between the phases. Hence the decompression speed has been calculated
numerically. For cases like the emptying of a pipe, it is quite clear that the
assumption of slip or no slip has a large influence. On the other hand, the
present plot indicates that for the fast process of crack propagation, the
slip modelling may be of less importance. However, it is interesting to note
that in this case, the homogeneous equilibrium model would prescribe a
15

more conservative design than would the two-fluid model.
4.2. Depressurization through valves
For planned maintenance, or in case of emergency shutdown, a CO2
pipeline might need to be quickly depressurized through one or more valves.
If this depressurization is performed too fast, the pipeline might be cooled
to the point where the material becomes brittle and cracks might occur.
Moreover, if the CO2 reaches it triple point (518 kPa and −56.6 ◦
C) dry ice
will be formed, potentially causing blockages.
The development of reliable simulation tools requires validation of mod-
els using experimental data. There is, however, a limited amount of publicly
available experimental data for the depressurization of CO2 pipelines. As
a consequence, there is also a limited amount of work along the lines of
validating standard models for such applications. Clausen et al. (2012) con-
sidered the depressurization of a 50 km onshore CO2 pipeline and compared
it to a simulation performed using OLGA®
. The results showed reasonable
agreement for the pressure, while there were significant discrepancies in
the predicted cooling of the pipe. A similar conclusion was reached by
de Koeijer et al. (2011).
Mahgerefteh et al. (2012b) simulated depressurizations of a pipe employ-
ing the homogeneous equilibrium model and comparing with experimental
data. It was found that for depressurizations from the gaseous phase, the
addition of impurities lowered the phase transition pressure plateau, as
opposed to depressurizations from the dense phase, where the effect was
the opposite.
5. Available simulation tools
The industrial relevance of oil and gas transport has lead to the devel-
opment of commercial tools for the simulation of pipeline transport. From
the point of view of CCS, it is of interest to establish if some of these tools
might be applicable and sufficiently accurate for simulating the transport of
CO2 with impurities.
Detailed information on commercial simulation tools is usually not public
information. However, the underlying transport model if often published
and can be put in context with the technical topics of this paper. In the
following, we consider some of the most common commercial tools and
briefly discuss their potential for simulating pipeline transport of CO2.
5.1. OLGA
The development of the dynamic two-fluid model OLGA®
was started in
the early 80s by Statoil in order to meet the two-phase modelling challenges
specific to pipelines (Bendiksen et al., 1991). The tool has since then been
under continuous development supported by the oil industry, and is today
considered an industry standard for such applications.
Today, the standard OLGA tool solves for a three-phase mixture of gas,
oil and water (Håvelsrud, 2012b). The model contains nine conservation
equations: Five equations describe conservation of mass in the bulk of the
phases as well as oil droplets immersed in gas and gas bubbles immersed in
16

oil. There are three momentum equations and one mixture energy equation.
Standard OLGA can handle impurities through externally supplied thermo-
dynamic data tables. In this case, the phase envelope must be sufficiently
wide.
A recent addition to OLGA which makes it more suitable for CO2 trans-
port is the single-component two-phase module (Håvelsrud, 2012a). This
model contains six conservation equations: Three equations describe con-
servation of mass. There are two momentum equations and one mixture
energy equation. For pure CO2, the Span–Wagner equation of state is used.
At present, single-component OLGA cannot take the presence of impurities
in CO2 into account. Future versions might, however, have this capability.
The formation of dry-ice is also not supported.
5.2. LedaFlow
LedaFlow®
is a transient multiphase flow simulation tool developed in the
early 2000s by Total, ConocoPhilips and SINTEF. Today, it is being further
developed for the commercial market by Kongsberg Oil Gas Technologies.
The LedaFlow model is mainly developed for three-phase oil-gas-water
mixtures, and the basic model solves 15 transport equations for nine fluids
(Danielson et al., 2011; Johansen, 2012): Nine mass equations govern the
conservation of the mass in the bulk phases as well as immersed droplets
and bubbles in each. Also, three momentum and energy equations are used.
For thermodynamics, the model uses the SRK and Peng–Robinson equations
of state.
While the standard LedaFlow described above applies to oil-gas-water
mixtures, the framework and formulation is generally applicable for mul-
tiphase flow, and can in principle be applied to CO2 transport. This, however,
requires the implementation of closure relations relevant to CO2 and the
relevant impurities.
5.3. TACITE/PIPEPHASE
TACITE is a transient multicomponent, multiphase flow simulation tool
developed by Elf Aquitaine/Total in the early 1990s. The tool has been
developed mainly for simulating natural gas transport. TACITE is currently
licensed as an add-on module to PIPEPHASE (Cos, 2012).
The underlying multifluid model of TACITE is described by Pauchon et al.
(1994). It is a drift-flux model with one mass-conservation equation for
each phase, one mixture momentum conservation equation and one mixture
energy conservation equation. In addition, the model contains a flow-regime
dependent closure law governing the momentum exchange between phases.
For thermodynamics, TACITE uses tabulated values for the fluid properties
as a function of pressure and temperature.
While the basic formulation of the model in TACITE is quite general,
it uses closure relations and thermodynamics based of flow regimes and
tabulated properties. TACITE considers eight types of flow regimes: Single-
phase liquid, dispersed, slug, annular dispersed, stratified smooth, stratified
wavy, annular and single-phase gas. The characterization of – and transition
between – these flow regimes is highly dependent on the fluid. The models
of TACITE have been developed and validated for natural gas transport, and
their validity to CO2 is not clear.
17

5.4. PipeTech
PipeTech is a transient multicomponent simulation tool developed and
maintained by professor Haroun Mahgerefteh at Interglobe ltd. The main
focus of PipeTech is the simulation of transient behaviour related to acci-
dental depressurization and catastrophic failure of pipelines. The tool is
used by the petroleum industry for safety assessment.
The PipeTech model employs the homogeneous equilibrium formulation
of the transport equations (Mahgerefteh and Atti, 2006; Mahgerefteh et al.,
2011). It solves one mass equation, one momentum equation and one energy
equation for the homogeneous mixture. A feature of this tool is the ability
to model the evolution of pipeline cracks via a coupled fluid-fracture model.
This enables the study of running ductile fractures.
PipeTech has a thermodynamics module taking account of CO2 with
impurities (Mahgerefteh et al., 2012a).
6. Conclusion
In this paper, we have reviewed the state of the art for the modelling of
transient flow of CO2 mixtures in pipes. A main point of interest has been the
modelling of the depressurization related to running ductile fracture, since
this forms an important part of safety and design analyses. Running ductile
fracture is a coupled fluid-structure problem, since the pipe influences the
fluid flow, and vice versa.
The transport of CO2 will often take place at a supercritical pressure.
Therefore, in most cases, phase transfer will occur during a depressuriza-
tion. In coupled fluid-structure simulations of running ductile fractures, it
is important to correctly capture the wave-propagation speed in the fluid,
as well as the crack-propagation speed in the pipe material. In two- or mul-
tiphase flow, the wave-propagation speed (speed of sound) is not a purely
thermodynamic function, but it is also a function of the flow topology. In
particular, the predicted two-phase speed of sound is a function of the
assumptions regarding equilibrium in velocity, pressure, temperature and
chemical potential. It should be noted that the common assumption of full
equilibrium gives a discontinuous speed of sound in the limit of single-phase
flow. Experimental data for the two-phase wave-propagation speed of relev-
ant CO2 mixtures would be useful not only for model validation, but also to
gain insight into the applicability of different mathematical formulations of
two-phase flow models, such as the homogeneous equilibrium model versus
the two-fluid model, etc.
The thermodynamic properties of pure CO2 at equilibrium are well de-
scribed e.g. using the Span–Wagner reference EOS. Similar reference EOS’es
for CCS-relevant impurities are under development. Further insight into the
proper modelling of departure from thermodynamic equilibrium is needed
in order to avoid such non-physical model features as a discontinuous speed
of sound at phase boundaries.
The gas and liquid in a CO2 mixture will in general have different compos-
itions. In addition, the gas and liquid are likely to have different velocities
during a depressurization. Therefore, flow models intended to describe
depressurization of CO2 mixtures will need to include component tracking.
18

In some cases, the amount of impurities will be small. Therefore, the flow
models should also be able to handle the situation when a phase envelope
turns into a line for a vanishing fraction of impurities.
Due to the high triple-point pressure of CO2 (518 kPa), models intended
to accurately simulate depressurization down to atmospheric pressure will
need to take into account the formation of dry ice.
Some commonly used commercial tools for simulating transient mul-
tiphase pipeline transport have been screened. The tools available today
have been developed for natural gas transport. The multifluid transport
models used in such tools can in principle be generalized to model any
liquid with impurities. However, the closure terms that are employed are
often based on empirical models highly adapted to the original oil-gas-water
application.
Acknowledgements
This publication has been produced with support from the NORDICCS
Centre, performed under the Top-level Research Initiative CO2 Capture
and Storage program, and Nordic Innovation. The authors acknowledge
the following partners for their contributions: Statoil, Gassco, Norcem,
Reykjavik Energy, and the Top-level Research Initiative (Project number
11029).
We thank Sigmund Clausen (Gassco), Gelein de Koeijer (Statoil) and our
colleagues Michael Drescher, Tore Flåtten, Jana P. Jakobsen, Alexandre Morin,
Geir Skaugen and Jacob Stang for fruitful discussions.
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