Rheological and Flow Properties of Gas Hydrate Suspensions
Oil & Gas Science and Technology - Rev. IFP, Vol.
Rheological and Flow Properties of Gas Hydrate Suspensions
- Rheological and Flow Properties of Gas Hydrate Suspensions - The problem of hydrate blockage of pipelines in offshore production is becoming more and more severe with the increase of the water depth. Conventional prevention techniques like insulation or methanol injection are reaching their limits. Injection of antiagglomerant additives and/or presence of natural surfactants in crude oils give us a new insight into hydrate prevention methods. Hydrate crystals are allowed to form but size of the particles is limited and transportation within the hydrocarbon phase is possible as a suspension. Solid particles formation in the liquid modifies the flowing properties. The pressure drop is controlled by the friction factor under turbulent flow conditions or by the apparent viscosity in the case of laminar flow regime. In a first part, the rheological properties of hydrate suspension are analysed depending on the oil phase. Results of flow loop experiments are then reported and allow us to determine the modification of the friction factor under turbulent conditions. Effect of hydrate particles is analysed in terms of rheological properties of the system in the laminar regime and in terms of friction factor modification in the turbulent regime.
Hydrates are clathrate type crystals in which cages of water
molecules are stabilized by host molecules. Discovered in
1810, they stayed a laboratory curiosity until Hammerschmit
in 1934 highlighted the fact that light hydrocarbon molecules
at high pressure can stabilise these crystals as host molecules.
He determined that natural gas hydrates might block gas
transmission lines at temperature above the ice point. This
discovery marked the beginning of a more pragmatic interest
in gas hydrates and the beginning of the modern research era.
Since 1970, as oil companies have been producing in more
and more unusual environments, such as the north slope of
Alaska, Siberia, the North Sea and deeper and deeper ocean
(Gulf of Mexico, West Africa or Brazil), hydrate problems
have become more and more dreaded.
This article presents first some general properties of
hydrate and a rapid overview of the industrial context: the
methods used today to predict, prevent and eventually
remediate pipeline hydrate blockage. In terms of prevention of
hydrate blockage, some new options start to be deployed on
field. Among these new ways to control hydrates, the
possibility to solve the hydrate problem only by avoiding
their agglomeration either by adding some dispersant or
antiagglomerant additives or by taking advantage of natural
dispersing properties of some crude oils are mentioned.
Influence of hydrate particles in the fluid on rheological
properties and on friction factor modifications is then widely
developed in the rest of this article. In a first Section, the
viscosity modification caused by the hydrate particles is
analyzed and comparisons with hard sphere models are
presented. The last Section concerns experimental work on
the friction factor determination in turbulent flow regime and
the modification of the friction factor due to the presence of
1 HYDRATE PROPERTIES
For several decades, the problem of hydrates in petroleum
production have been studied worldwide in laboratory and
loop test facilities. The objectives were and still are to better
understand the mechanism of formation, to characterize the
physical properties of hydrates but also to try to develop
methods to prevent formation of hydrate plugs. This question
has become all the more crucial since deepwater fields have
been discovered or brought in production. These fields are
perfect candidates to encounter hydrate forming conditions.
Structure I 46 water molecules
Structure of hydrates (from Sloan [
Structure H 34 water molecules 8
Structure II 136 water molecules
1.1 Hydrate Structure
Gas hydrates are ice-like crystalline compounds that form
whenever water molecules contacts molecules of gas such as
low weight molecular hydrocarbon molecules (C1, C2, etc.) or
others: N2, CO2 or H2S. The hydrate crystals can be thought
as a network of hydrogen-bonded water molecules forming
cages with gas constituents trapped within. Three different
structures have been identified: I, II and H. These structures
are illustrated in Figure 1. Structure I and II are constituted
by two kinds of cavity: a small one (512) found in these both
structures and a larger one: 512 62 and 512 64 for the structure I
and II, respectively. These two structures can be stabilized by
molecules of gas having the molecular size in the range
3.57.5 Å. For example, the structure I can be stabilized by small
gas molecules such as pure methane and pure ethane, but the
presence of a small amount of a larger molecule like propane
(0.5 mol.%) with methane would result in the formation of
structure II. Structure H contains three cavities: the small
cage 512 and two large cavities. Molecules as large as
cyclopentane can stabilize the larger cavity. However, there
is no proof that such structure H hydrates exists in production
lines. Consequently, mainly structure II is expected to form
with natural gas under production conditions.
1.2 Hydrate Formation
Contrary to ice crystals, gas hydrate crystals are able to form
at temperatures higher than 0°C as soon as the pressure is
higher than a few 10 bar. Conditions promoting hydrate
formation are high pressure (typically > 30 bar) and low
temperature (typically < 20°C). Precise conditions in terms of
pressure and temperature depend on composition of the
fluids. Hydrate formation can occur for all the produced
fluids if required P-T conditions are reached: natural gas, gas
condensate and crude with associated gas, with condensed or
Figure 2 shows curves of dissociation for a natural gas
with water and different thermodynamic additives. The
dissociation curve delimits, in a P-T diagram, the region
where hydrate crystals are thermodynamically stable
(stability region on the left side, no hydrate on the right side). The
inhibiting effect of salt and methanol at typical concentration
used on fields is illustrated. Injection of thermodynamic
inhibitor results in a shift of the dissociation curve to the left.
It should be noted that P-T values on the dissociation
curve do not necessarily correspond to hydrate formation
conditions. At a given pressure, due to “kinetic” effects, the
temperature of formation may be shifted down by a few
degrees Celsius. This kinetic effect is time dependant, so
hydrate will not form at a given pressure and temperature
inside the metastable zone during a certain period of time. A
more or less wide metastable zone can be drawn (Fig. 2).
This temperature offset normally refers as subcooling. The
magnitude of the subcooling depends on the time, the
pressure, the flow conditions as well as the composition of the
fluids. The higher the subcooling, the shorter the time of
hydrate formation and the faster hydrate crystals will grow.
Formation of hydrate particles generally leads, by forming
solid plugs, to the blockage of pipelines and thus to the
shutdown of production facilities. Hydrate plugs can be the
result of growth of deposits on the inner wall and/or
agglomeration of hydrate crystals in the bulk. The removal of hydrate
plugs is generally difficult to achieve. A shutdown of several
days may be necessary prior to the restarting of the production
and, indeed, pipeline abandonment may occur. General
discussions on hydrate properties can be found in the literature [
2 INDUSTRIAL CONTEXT
To anticipate and solve potential production problems related
to hydrate blockages, operators dispose of tools and means
with respect to:
2.1 Prediction Methods
Prediction methods essentially consist in performing
thermodynamic calculations that enable dissociation curve of
hydrates to be determined (Fig. 2). Even if hydrate formation
may actually occur at a lower temperature (or at a higher
pressure), from a more practical point of view, the
dissociation curve is usually considered as the boundary that must not
be passed through. Today, computer models are
commercially available on the market and are considered as relatively
reliable. However, they necessitate an accurate compositional
analysis of the fluids. Risk of hydrate formation can then be
definitively evaluated according to pressure and temperature
in the lines. It should be noted that accuracy of temperature
prediction in pipes is often questionable. This may cause an
under or over-estimate of the jeopardy.
2.2 Prevention Methods
2.2.1 To Produce Outside the Hydrate Stability Zone
One way to prevent hydrate blockages is to maintain the
pressure and temperature conditions outside the hydrate
formation region (delimited by the dissociation curve). This
can be accomplished by insulating, burying or heating
pipelines to reduce heat losses between the hot produced
fluids and the cold environment of the pipeline. This can also
be accomplished by shifting the dissociation curve toward
the lowest temperatures with the injection of thermodynamic
inhibitors such as methanol or glycol (Fig. 2).
The most common methods presently used or foreseen by
operators are the insulation and the injection of
thermodynamic inhibitors. However, both of these solutions have a
significant economical impact and a technical limitation.
In addition to its high Capex level and the technical
challenge faced by the design and installation of high
performance insulation, it will not prevent entering the hydrate
formation region during a long-term shutdown. Consequently,
additional methods have to be anticipated for
shutdown/restart procedures. Nevertheless, it generally prevents
hydrate formation during normal operation conditions and
simultaneously avoids potential wax deposit formation.
Injection of thermodynamic inhibitors is only effective at
high concentration with respect to the water amount (30 to
50 wt%). Methanol injection leads to a high Opex level and
also needs large size storage facilities. As for glycol
injection, it needs installation of reboilers for glycol regeneration
as well as storage requirements accounting for typical loss
]. Moreover in Gulf of Mexico, the refineries tends now
to limit the methanol concentration allowed in the oil and
condensate which cause serious problem in desalting
operation and water management. Similarly, severe penalties are
now applied on the gas containing too much methanol.
2.2.2 New Options: LDHI and/or Natural Surfactants
A new option would be the injection of the so-called “low
dosage hydrate inhibitors” (LDHI). Injection of LDHI in
place of thermodynamic inhibitors has been considered as the
most interesting option regarding new methods to prevent
hydrate blockages and has been subjected to a lot of research
works for the last ten years [
]. The required
concentration for these additives is expected to be less than 1 wt%
(with respect to the water amount). Although low
concentration can lead to a significant reduction of processing costs,
the most interesting issue would probably be the reduction of
size storage facilities.
There are two types of LDHI: the “kinetic inhibitors” (KI)
and the “dispersant additives” also called “antiagglomerant
Kinetic inhibitors act by delaying hydrate nucleation and
by slowing down crystal growth. Therefore, they do not have
any effect on the dissociation curve but avoid, during a finite
period, the formation of large hydrate crystals inside the
hydrate stability envelope. The applicability of KI is limited
by a maximum subcooling at a given residence time in the
system. For the last generation of KI, it is commonly
admitted that the maximum subcooling temperature is around
10°C for a residence time of 2 days. This limitation appears
to be close to the theoretical limit for most KI.
Contrary to thermodynamic inhibitors and kinetic
inhibitors, the concept of dispersant additives or AA [
not prevent the formation of hydrate crystals but make their
transport in suspension feasible by preventing hydrate
deposition and formation of large aggregates. Today, AA have
mainly limitations in terms of water cut. The maximum water
cut is expected to be between 40 and 50%. This limitation is
caused by the rheological properties of suspensions with high
solid fraction and may depend on flow regime conditions.
Potentiality of LDHI has been highlighted under field
]. Three fields of the Eastern Trough Area
Project (ETAP) in the United Kingdom Central North Sea
are currently operating using KI . The Popeye field has
used the AA technology [
] and several other projects of
AA are studied in Gulf of Mexico and North Sea [
one or two years a growing interested has been noted for the
LDHI technologies even if they are not yet extensively used.
In case of black crude oils, instead of injecting additives, it
is also expected to have benefits of the presence of “natural
surfactants”, such as resins and asphaltenes. Indeed, these
compounds are suspected to be able to transport hydrate
particles in suspension as dispersant additives or AA do
]. Consequently, up to moderate water cut, treatment
for hydrate control would not be necessary.
2.2.3 Remediation Method
Even if new methods to remove hydrate blockages have been
discussed in the literature [
], the method successfully
implemented so far by operators is two-sided
depressurization  (eventually made more effective by injecting
methanol or external heating). However, this method may
be very time consuming and necessitates preinvestment of
facilities to access plugs from both sides. It may be not
practical to depressurize both sides of a hydrate blockage
(particularly when several plugs are formed simultaneously in the
line). Thus, a one-sided depressurization procedure, resulting
in a substantial pressure drop across the plug, has to be
]. In such a case, two extreme events can occur:
firstly, the plug can be extended because of a cooling effect
(Joule-Thompson effect) possibly generated by the gas flow
through the plug. Secondly, the plug can be suddenly broken
off from the pipe wall and flies down the flowline, thus
injuring persons or damaging downstream facilities [
Since remediation methods are still too much hazardous,
efforts are mainly focused on the deployment of prevention
methods. From these, the study of the rheological behaviour
of real produced fluids in the hydrate stability zone and the
influence of hydrate particles on the flow properties become
3 HYDRATE SUSPENSIONS RHEOLOGY
In this Section, we will discuss the rheological behaviour of
hydrate suspensions. Such systems are defined, here, as
composed of hydrate particles dispersed in a hydrocarbon liquid
phase (oil or condensate).
Hydrate formation in a pipeline generally leads to an
increase of the pressure drop. In worst situations, it is
associated with the growth of plugs and/or deposits, which can lead
to a complete blockage of the line. In this case, the system is
not homogeneous and an investigation in terms of rheology
cannot be achieved. In best situations, in particular thanks to
natural surfactants or AA-type LDHI’s as previously
mentioned, hydrates can be dispersed in the hydrocarbon liquid
phase. In this case, the pressure drop may be controlled by
the friction factor under turbulent flow conditions (this point
will be discussed in the next Section), or by the apparent
viscosity of the suspension under laminar flow conditions.
Mainly in collaboration with oil companies as Petrobras
in Brazil and Total in France, IFP has been investigating for
some years the rheological properties of hydrate suspensions
formed in different hydrocarbon liquid phases such as
asphaltenic crude oils, acidic crude oils, or condensate +
AA’s. These investigations have been performed in two
homemade devices: a laboratory rheological P-T cell [
and a multiphase pilot loop [
]. The pilot loop will be
briefly described later. Depending on the oil phase system,
different results have been obtained. Systems exhibit
shearthinning properties whereas others can be well described as
Newtonian suspensions. The relative viscosity, defined as the
apparent viscosity divided by the viscosity of the oil phase,
can also vary by one or two orders of magnitude from a
system to another one.
In the following, we will remind results obtained for
hydrate suspensions in an asphaltenic crude oil as well as a
phenomenological model developed in order to describe
rheological properties of such suspensions. These results
have been presented in several former papers [
the reader is invited to refer for more details. Based on an
analysis of forces of interaction between hydrate particles as
well as results obtained with other systems, a general
discussion on expected rheological properties of hydrate
suspensions is then presented.
3.1 Hydrate Suspensions in an Asphaltenic
3.1.1 General Properties
This crude oil is a rich asphaltenes-containing crude (around
5 wt%). It allowed us to form very stable water in oil
emulsions. Under typical shear stress conditions encountered in
real transportation conditions, water droplet diameters have
been measured in the range of 0.5 to 3 µ m. Moreover, no
significant change in size has been noticed before hydrate
formation and after hydrate dissociation. The crude oil also
showed a very good capability in transporting hydrate
particles as a suspension and made rheological investigations
feasible. As showed by Camargo et al. [
and time-dependant (thixotropy) properties were observed
for hydrate suspensions for a volume fraction of 0.27 and
above. On the other hand, suspensions formed at a volume
fraction of 0.134 behaved roughly like Newtonian fluids.
For this system, it was expected, in first approximation,
that a hydrate particle was formed from an individual water
droplet without any significant change neither in size (the
volume expansion due to hydrate formation is neglected) nor
in form (roughly spherical). Thus, based on general theories
related to rheology of hard-sphere dispersions, a
phenomenological model has been developed by Camargo and Palermo
] as an attempt for understanding and predicting
rheological properties of hydrate suspensions.
3.1.2 Phenomenological Model
Up to a particle volume fraction Φ around 0.5, a monodisperse
hard-sphere suspension is a fluid for which the viscosity is a
function of Φ as well as the dimensionless shear stress:
d p 3
where τ is the actual shear stress, dp/2 the particle radius and
kBT the thermal energy. In the limits of both low stresses and
high stresses, the viscosity depends only on the volume
fraction. For stresses conditions around Pe = 1, shear thinning
occurs and the viscosity depends also on the size of the
particles. By considering radius of hydrate particles larger than
1 µ m and typical shear stresses in realistic flow conditions
Φ eff = Φ dA
much larger than 1 Pa for the hydrate/crude .oil system
(suspension viscosity µ >> 0. 01 Pa·s; shear rate γ >100 s–1),
we have Pe ≈ 102 >> 1. We can then consider that, in our
case, the contribution of hydrodynamic interactions
dominates with respect to the contribution of the Brownian motion
and should confer to the hydrate suspension a Newtonian
behaviour (high stresses limit).
However, shear thinning is frequently observed for
concentrated suspensions. This phenomenon, particularly when
it is associated with a thixotropic behaviour, is generally
attributed to a reversible aggregation process that takes place
between particles under shear flow.
Let us first consider viscosity laws of concentrated
suspensions. Generally, equations are expressed as relationships
between the relative viscosity µ r and the couple (Φ, Φmax).
The relative viscosity is the ratio between the apparent
viscosity µ of the suspension and the viscosity of the dispersing
liquid µ 0. Φ is the particle volume fraction and Φmax is
physically interpreted as the maximum volume fraction to which
particles can pack. We will use the equation proposed by
], well adapted to hard spheres of equal size and
accounted only for hydrodynamic interactions:
µ r =
1 − Φ
Φ 2 ;Φ max =
Φmax is taken as the packing concentration of randomly
packed spheres of same diameter.
Let us now consider aggregated suspensions. Several
theoretical models have been proposed in the literature [
to describe the growth of particle clusters either by
perikinetic aggregation (caused by Brownian motion) or by
orthokinetic aggregation (caused by medium flow). The
porosity of the resulting aggregates is taken into account by
introducing a fractal dimension fr, relating the number of
particles N per fractal aggregate to characteristic lengths of
the system (dA: aggregate diameter; dp: particle diameter):
N = dA
It is well accepted that the fractal dimension, for perikinetic
aggregation, ranges from about 1.7 to 2.1. Under shear
conditions, it is generally reported that aggregates are more compact
with fractal dimension larger than 2 and up to 2.7 [
Because of viscous forces applied on aggregates in the
flow, they cannot growth indefinitely. A maximum size is
reached depending on the balance between the shear stress
and the force of adhesion Fa between particles. By
considering a mechanism of destruction based on the erosion of
], the maximum size of aggregates for laminar
flow is given by:
2− fr 4 − fr
dA,max = Fa (d p )
µ γ0 ˙
where γ is the shear rate.
In Equation (5), the shear stress exerted to aggregates is
related to the viscosity µ 0 of the dispersing liquid. It is only
correct when aggregates do not interact, i.e., Φ→0. However,
for finite Φ, hydrodynamic interaction of aggregates can be
taken into account, as proposed by Potanin [
substituting in Equation (5) the viscosity µ 0 by the apparent viscosity
of the suspension µ . Finally, we have:
dA,max = Fa (d p )
2− fr 4 − fr
At the equilibrium, we consider that dA ∼ dA,max.
Combining Equations (3, 4 and 6) dA/dp can be determined
by solving the following equation:
d (4 − fr)
Depending on the type of the characteristic length dA, a
prefactor can be introduced in the former relationship. As
demonstrated by Gmachowski [
], this prefactor is equal to
unity if dA corresponds to the “dynamic” diameter, the one
that should be taken into account with respect to
hydrodynamic phenomena. Due to the fractal structure of
aggregates, it has been proposed that an effective particle volume
fraction Φeff should be considered instead of the real volume
fraction in the expression for the viscosity [
µ r =
1 − Φ eff
1 − ΦΦmefafx 2 ;Φ max =
If the solution of Equation (7) is dA/dp < 1, dA is fixed
equal to dp. The relative viscosity is then determined by using
3.1.3 Comparison between Model and Experiment
Results obtained from the phenomenological model are
compared in Figure 3 with some experimental results obtained for
hydrate suspensions formed with the asphaltenic crude oil.
Except for the force of attraction Fa, all the parameters
have been set to their assumed or measured value.
According to the discussions above, the fractal dimension has
been set to fr = 2.5, the maximum packing concentration to
Φmax = 4/7, and the particle diameter to dp = 1.5 µ m. The
viscosity of the continuous oil phase corresponding to the
experimental conditions (pressure: 7.5 MPa; temperature:
7.5 °C) is µ 0 ≈ 60 cP.
Experimental results are presented for two particle volume
fractions: Φ = 0.134 and Φ = 0.274. Due to time-dependant
properties of suspensions, only results obtained during the
increase of the shear rate are shown. Indeed, it is expected that
the destruction of aggregates is a more rapid process than
formation. Consequently, the relative viscosity measured under
such conditions is probably closer to the equilibrium state
than the one measured during a decrease of the shear rate.
Results of calculation correspond to a force of attraction:
Fa = 1.2 10–9 N. Expressed with respect to the radius of
curvature of the surface dp/2, we have 2Fa/dp =1.6 mN/m.
Globally, the evolution of the relative viscosity with the
shear rate, depending on the particle volume fraction, is well
described by the aggregation model. At low volume fraction
(Φ = 0.134), calculation indicates that the increase of the
relative viscosity should be only significant at low shear rates
(below 50 s–1). Experimentally, in the range of shear rates
investigated (50 to 600 s–1) neither shear thinning nor
thixotropic behaviour have been observed. At Φ = 0.274, we
have a good agreement between calculation and experimental
data with a shear-thinning behaviour well described.
For such aggregated suspensions, it has been showed that
the rheological behaviour can be well described by a
Casson’s like equation of the form: τ1/2 = τ1/2 + (αγ.)1/2 where
τ is the shear stress, τ0 the yield stress, and α a constant,
which slightly depends on Φ.
3.2 Forces of Interaction between Hydrate Particles
Camargo and Palermo [
] also discussed the origin of forces
involved in hydrate particle interactions. The authors argued
that van der Waals forces were too weak to explain
aggregation in the asphaltenic crude oil. On the other hand, they
suggested that, due to adsorption of asphaltenes, interactions
between hydrate particles in the asphaltenic crude oil might
be similar in nature to the ones encountered between
3.2.1 Effect of van der Waals Forces on Rheological
Behaviour of Hydrate Suspensions
As van der Waals forces always exist in disperse systems, it
is of interest to analyse how they are able, in the absence of
other forces, to promote aggregation, and consequently
promote a shear thinning behaviour, depending on the
characteristics of the system.
The van der Waals forces between two spheres of same
radius dp/2 is given by the relation [
Comparison between calculation and experimental data obtained for hydrate suspensions in the asphaltenic crude oil. Lines: calculated from
the model; marks: experimental data obtained in the loop (•) and in the cell (×) - (from Camargo and Palermo [
Calculation of the relative viscosity as a function of the shear rate for two expected limit cases corresponding to condensate and oil phase
A(d p / 2)
where A is the Hamaker constant and dS the distance which
separates the two spheres. For hydrate particles dispersed in
an oil phase, A has been estimated around 5.2 10–21 J [
Accounting for a surface roughness of particles larger than
50 Å which maintain particles at a distance dS > 50 Å, 2Fa/dp
falls down rapidly below 0.01 mN/m.
Calculation of the relative viscosity as a function of the
shear rate is illustrated in Figure 4 depending on the volume
fraction Φ, the viscosity of the oil phase µ 0 and the diameter
of hydrate particles dp. The term related to van der Waals
forces has been set to 2Fa/dp = 0.01 mN/m, that is expected
to correspond to the upper limit. The more uncertainties are
about the size of hydrate particles. Few data have been
reported in the literature. Measurement of size of hydrate
crystals formed in a water continuous phase indicates that
crystals rapidly growth above 10 µ m [
]. In case size of
hydrate particles are limited to the size of water droplets
dispersed in the oil phase, it is expected to have a radius in the
range of some µ m (viscous or rich surfactant-containing
crude oil) to tens of µ m (light crude oil, condensate).
Two expected limit cases are illustrated: dp = 2 µ m,
µ 0 = 50 cP at Φ = 0.3, and dp = 20 µ m, µ 0 = 1 cP at Φ = 0.15,
0.3 and 0.35, corresponding to a crude oil system and a
condensate system, respectively. For the condensate system,
we can see that a shear-thinning behaviour, associated with
an aggregation process of hydrate particles, might be only
visible at low shear rate (< 100 s–1). As the volume fraction
increases, deviation from the Newtonian regime occurs at
lower shear rates and shear thinning increases in magnitude.
For the crude system, even for smaller particles, the increase
in viscosity of the oil phase keep the suspension as
Newtonian down to a shear rate of 10 s–1.
The actual wall shear rate in real conditions can be
estimated from . the Hagen-Poiseuille law (Newtonian
approximation): γw = 8U/D where U is the real mean liquid
velocity and D is the pipe diameter. U is usually in the range
of 2 to 5 m/s for oil production and even larger for.
condensate. By taking D of the order of 0.1 m, we have γw ≥ 100
s–1. Let us remind that numerical values chosen above
correspond to limit cases. It is consequently expected that hydrate
suspensions behave as Newtonian fluids under normal
conditions of production if only van der Waals forces are involved
in the interaction between hydrate particles. Only for extreme
limit cases gathering small particle radius, low oil viscosity,
high particle volume fraction, large pipe radius and low
velocity, shear-thinning behaviour should be expected. Note
that in this case, particularly for low viscosity and low
velocity, other phenomena as particle sedimentation might occur
which make rheology a nonpertinent approach to predict
3.3 Hydrate Suspensions in Other Systems
3.3.1 Rheological Behaviour
We present below results obtained for two other systems.
The first one (Fig. 5) concerns a hydrate suspension formed
in an acidic crude oil (Dalia 3) at a water cut of 27 vol%. It
should be noticed that, in contrast to the previous crude oil,
Dalia 3 crude oil contains less than 1 wt% of asphaltenes.
The second one (Fig. 6) corresponds to a hydrate suspension
formed with a condensate + AA-type LDHI at a water cut of
40 vol%. Results are presented in terms of nondimensional
friction factor f = (∆ P/L) ⁄ 2ρU 2 and Reynolds number
Re = ρUD⁄ µ 0 where ρ, U et µ 0 are respectively the density,
the velocity and the dynamic viscosity of the crude, ∆ P/L the
pressure gradient, and D the pipe diameter.
In the laminar regime, it can be seen that the two systems
exhibit a Newtonian behaviour. This confirms that a
Newtonian behaviour should be expected for hydrate suspensions as
far as other forces than van der Waals forces are not involved
in the interaction between hydrate particles.
3.3.2 Relative Viscosity
In Table 1, relative viscosities of hydrate suspensions are
reported for the different oil systems mentioned above and at
different volume fractions. Results for the asphaltenic crude
oil are also indicated. In this last case, the relative viscosity
corresponds to the one measured at high shear rate (700 s–1)
for which it is predicted that aggregates consist of a few
hydrate particles. Moreover, experimental values are
compared with calculated values according to Equation (1)
for the Newtonian suspensions and Equation (3) for the
For hydrate suspensions formed in the asphaltenic crude
oil, the relative viscosity remains at the same order of
magnitude as the calculated one. This confirms that hydrate
suspensions can be considered, in first approximation, as
hardsphere dispersions. Discrepancies between experimental and
calculated values are in the range of experimental error but
may also be the result of the volume expansion of particles
associated with hydrate formation and a slight deviation from
the ideal spherical shape.
On the other hand, for the other systems, discrepancies of
one or two orders of magnitude between experimental and
theoretical values indicate that the former assumption is no
longer valid. Note that the higher the initial water cut, the
larger the discrepancy. It is suspected, for such systems, that
hydrate particles are strongly different in shape and size from
initial water droplets. Particles probably stem from the
agglomeration of primary particles, such a process occurring
during hydrate formation. It has been suggested by some
] that capillary forces, associated with the
presence of free water during this stage, are responsible for
this agglomeration process. Resulting hydrate particles are
therefore large and porous particles, contributing to an
increase of the effective volume fraction. Contrary to the
reversible aggregation mechanism observed with the
asphaltenic crude oil, such an agglomeration process is not
reversible. The effective volume fraction does not depend on
the shear rate and the relative viscosity remains at a high
level whatever the flow rate.
15°C; W/O emulsion
4°C; hydrate suspension
Characterization of emulsion and hydrate suspension
at 30 wt% of water cut for Dalia 3 crude oil (from Maurel
et al. [
Characterization of hydrate suspension at 40 wt% of water
cut for condensate + AA additive (from Camargo [
Condensate + AA
Asphaltenic crude oil
(at high shear rate)
Because of the large size of hydrate particles (larger than
1 µ m) and the weakness of van der Waals forces, hydrate
suspensions are non-Brownian dispersions for which a
Newtonian behaviour is expected. In some particular cases,
for which heavy compounds as asphaltenes are able to adsorb
on hydrate surface and generate polymer-like interactions, a
reversible aggregation process can take place and a
shearthinning behaviour can be observed.
Prediction of viscosity of hydrate suspensions could be
achieved with the help of hard-sphere dispersion models.
However, difficulty in quantitatively predicting the viscosity
arises from the fact that hydrate particles may form from the
agglomeration of primary particles during the hydrate
formation stage. This agglomeration process promotes the
formation of large and porous particles and results in a strong
increase of the effective particle volume fraction.
4 TRANSPORT OF HYDRATE DISPERSED IN PIPE
In field conditions, the single phase or multiphase flow in
pipelines leads to pressure drops controlled by the friction
factor of the fluids. In the laminar case, the friction factor is
related to the viscosity and determination of the rheology
allows the pressure drop estimation. The previous Section
discussed in details this issue. In this Section, we will focus
on turbulent friction factor and the effect of hydrate particle
on their determination. This determination is only possible
through flow loop experiments.
The experimental procedure consists of the study of
different oils flowing in a large flow loop and aims at analysing the
modification of the pressure drop when water is added and
turned into hydrates in presence of AA-type LDHI’s. The
modification of the pressure drop for different mean flow
rates can be related to the presence of particles.
Experiments were conducted in a multiphase flow loop
specially built by the Institute to study at a large scale oil and gas
flow. A picture of this loop is presented in Figure 7.
4.1.1 Flow Loop Characteristics
This flow loop is a horizontal, 2" internal diameter, carbon
steel flow line of 140 m long. It has been designed to work in
controlled thermodynamics conditions. The temperature can
vary from 0 to 50°C and pressure from 1 to 100 bar. A
positive displacement pump (flow rate up to 20 m3/h) allows
fluid circulation for the liquid phase. A membrane
compressor (flow rates up to 2000 Nm3/h) is provided for circulation
of the gas phase. In order to keep the pressure constant in the
loop, gas is added to it from a gas tank.
Flow rates of each phase, pressures and temperatures at
different locations in the flow loop are controlled. More
details of the system can be found in Camargo [
] or in
Peysson et al. [
4.2 Flow Characterization
4.2.1 Flow Regime
Flow conditions in pipelines for oil production are dependent
on the rheological characteristic of the hydrocarbon phase.
In the laminar regime, pressure drop calculation is related
to the determination of the apparent shear viscosity of the oil.
When viscosity is known (or complete rheology if the fluid is
non-Newtonian), pressure drop calculation can be made
using the equation of motion (Eq. 9). The problem is to have
the rheological knowledge of the system as discussed in the
The stress at the wall have a different form when flow
regime is laminar or turbulent. But a common expression can
be written when introducing the friction factor f.
The pressure drop (∆ P/L) in a pipe is then:
U is the average velocity of the flow. R is the pipe radius,
ρ the flowing phase volume mass. f is only dependent upon
the Reynolds number of the flow define as:
µ is the dynamic viscosity of the liquid phase. For Reynolds
number less than 2000-3000 the flow is laminar and friction
factor can be easily calculated from the Poiseuille velocity
profile. We get for Newtonian fluids:
f is difficult to estimate in turbulent flow, but different
correlations have been proposed with a very good agreement with
Laminar or turbulent flow regime can be found depending on
the apparent shear viscosity.
Typically, pipe diameters are around ~0.1 m and liquid
velocity are between 1 and 5 m/s. At 1m/s, a viscosity of
100 cP (0.1 Pa·s) leads to a Reynolds number of the order of
magnitude 1000 and flow can be considered laminar. But
when viscosity is around 10 cP (0.01 Pa·s), Reynolds number
is up to 10 000. So for light oil and condensate, flow regime
will be mainly turbulent.
4.2.2 Pressure Drop Calculation
Force balance in steady state for pipe flow (Fig. 8) give the
following relation between stress at the wall and imposed
pressure drop in the system:
τw = ∂z 2
Note that this relation is not dependent on the rheology of
p (z + dz)
ooth pipe, Rek = 3
The Moody chart: f versus Re (from Govier and Aziz [
], p. 167).
= f ⋅
the data. The Moody chart of f versus Re is represented in
Figure 9. This is the most accepted correlation for f.
As it can be seen in the Moody chart, f is quasi constant
for highly turbulent flow. Its value depends essentially from
the pipe roughness ε (the mean size of the surface texture).
For high Re, f is given by the Nikuradse correlation (see for
example Govier and Aziz [
Between Reynolds number Re = 3000 and 10 000,
f exhibits a small dependence with velocity. This dependence
of f can be estimated from the Wood-Colebrook law for pipe
with intermediate roughness:
1f = 4 log 2Dε + 3.48 − 4 log1 + 9.35 2Dε ⋅ Re1 f (14)
In the following, we will focus on flow at large Reynolds
number, which is the most encounter flow regime for light oil
Different types of fluid have been tested in the “lyre” flow
loop. We will focus now on experiments on light oils. Two
sets of data will be used. The first one was recorded with a
naphtha oil in a large study in collaboration with IFP, IFE,
BP, Total, NorskHydro, Shell and Conoco. More details on
these experiments can be found in References [37 and 39].
The second was conducted with condensate oil during the
PhD, work conducted by Camargo [
4.3 Hydrate in Naphtha Oil
The first set of experiments was done with light naphtha oil
with low viscosity and density. The density of the Naphtha
oil saturated with gas (which is the case in the loop) is about
733 kg/m3 at 25°C and 737 kg/m3 at 4°C. Naphtha oil
viscosity has been measured with a low shear rheometer at
atmospheric pressure. The naphtha had a dynamic viscosity
of 0.6 mPa·s at 25°C and 0.8 mPa·s at 4°C. Under pressure
conditions (4 MPa), viscosity is expected to be two or three
Natural gas delivered by the domestic gas network is
used in the loop. This gas allows formation of hydrates of
4.3.2 Hydrate Formation
flow conditions become stable in time. After formation of the
emulsion in the loop, the loop is cooled down to form
hydrates while temperature and gas consumption are
monitored. Hydrate formation is detected by the temperature
increase as expected from hydrate formation exothermic
reaction. Water droplets in the oil phase are turned into
hydrate particles. The reaction continues until all accessible
water is converted into hydrates.
The flow regime during the hydrate formation period is
slug flow. The flow conditions are maintained until the
parameters like pressure, temperature are stable with time.
In the loop, the pressure is maintained by addition of gas
in the separator. During the hydrate formation stage, gas is
used to form hydrate, so gas is injected in the loop to adjust
pressure. The monitoring of this consumption can give an
indication on the water conversion in the system. This
calculation was done, and we get a conversion of roughly 50% of
the amount of water in the system. This can be explained by
the fact that water droplet are turned into solid particles
starting from the outside of the droplet. So a crust is formed, but
we can imagine that the core of the solid particles is filled
with free water.
At this stage, after a period of mixing, the pressure drop
versus velocity is measured at 4°C for the naphtha oil with
hydrate particles. No gas is injected in the loop. The results
are shown in Figure 10.
We add on the measurement represented in Figure 10, the
calculation of the pressure drop:
= f ⋅
with a fixed value of f determined experimentally.
4.4 Hydrate in Condensate
The hydrocarbon liquid phase chosen is a condensate. Its
density is ρ = 800 kg/m3. The viscosity is Newtonian and
was determined at ambient conditions at 2.8 mPa·s. But
pressurised with gas in the loop, the viscosity of the condensate
with saturated gas is around 1 mPa·s (this determination is
done by considering the pressure drop at low velocities and
comparison with Poiseuille law). The same gas as for the
naphtha measurements was used.
Naphtha oil and water are mixed together in the test flow
loop at 25°C and the AA additive is added. Circulation is
done at constant flow rate. Emulsion is quickly formed and
The pressure drop versus velocity is also measured at 4°C
when hydrate particles are formed. The results are shown in
Mean velocity (m/s)
Pressure drop (mbar/m) versus mean velocity (m/s) for naphtha
and hydrate particles at different water cut. Line: calculation
of the pressure drop in the system with friction factor adjusted.
Pressure drop (Pa/m) versus mean velocity (m/s) for condensate
and hydrate particles at different water cut. Line: calculation
of the pressure drop in the system with friction factor adjusted.
The black line in Figure 11 is:
∆ p ρU 2
= f ⋅
with a fixed value of f adjusted by best fit on the
4.5.1 Friction Factor and Flow Regime
For both systems, naphtha and condensate, we observe a
good agreement between the data and the calculation
especially for velocities more than 1 m/s confirming that the flow
regime is turbulent and f is constant. This is confirmed in
Reynolds number calculation. Indeed, in the two system, the
viscosity of the fluid is very low (0.5 mPa·s for naphtha oil
and 2.8 mPa·s for condensate or more close to 0.2 and
1 mPa·s, respectively, in the pressured case). The difficulty in
Reynolds number calculation with hydrates in the fluid is that
the viscosity of the effective media (hydrate suspension) is
not so well defined.
In order to get rid of this difficulty, we can plot the
pressure drop versus velocity in a log-log plot. Indeed, linear
increase with velocity is characteristic of laminar flow and
square like dependency is the one of turbulent flow.
Equation (10) shows that for turbulent flow, ∆ P/L scales as
U2 (f does not depend on velocity). In laminar flow, ∆ P/L
scale as U (Poiseuille flow ∆ P/L = µ ·(8/π)·U/R2).
4.5.2 Variation of f with Water Cut
As discussed in the former section, particularly for the
condensate + AA system, hydrate particles may form from
Mean velocity (m/s)
Mean velocity (m/s)
Mean velocity (m/s)
Mean velocity (m/s)
Pressure drop versus velocities in a log-log representation. Grey line is a line of slope 1 and dark line is a line of slope 2.
the agglomeration of primary droplets leading to an increase
of the effective particle volume fraction. As the two systems
(condensate and naphtha) are very similar, we can consider
that the evolution of the effective volume fraction depending
on the initial water cut is equivalent. Because of a lack of
accuracy in its determination, we will present in the
following results in terms of initial water cuts (defined as the
volume fraction of hydrate particles) for practical reasons.
For the two systems tested, we see that a large part of the
liquid flow rate imposed creates a turbulent flow. For that
velocity range, roughly between 1 m/s and the maximum
velocity in the loop the friction factor is constant and does
not depend on velocity.
This is completely in agreement with Nikuradse work and
its correlation showing that for large velocity, the friction
factor is imposed by the pipe roughness:
1f = 4 log 2Dε + 3.48
In the two sets of experiments, the same flow loop is used
with the same test tube. In this condition, the roughness of
the pipe wall is the same or at least quite close and so f
should be the same or very close for all the experiments
done. But we observe that when more and more hydrate are
formed the friction factor increases with the initial water cut.
In the Figure 13, we have plotted the value of f that has
been obtained from the experiments (Figs 10 and 11) with
naphtha oil and condensate for the different water cut that
were investigated. For the two systems, the evolution as well
as the order of magnitude of f with the initial water cut seems
to be equivalent.
Variation of the friction factor f with the water cut for the two
sets of experiments. White dots: naphtha oil, black dots:
Two explanations can be put forward to interpret this
increase. First, we can imagine that change of the roughness
at the pipe wall occurs during the hydrate formation stage as
a result of a sticking process at the wall. Therefore, the
pressure drop can be estimated from Nikuradse correlation if
roughness is determined. But, we were not able to measure
the modification of roughness at the pipe wall and we did not
see, neither, any modification at the wall through the
different windows of the flow loop, so this first mechanism has to
A second interpretation can be done related to the
presence of solid particles in the fluid. These particles can
contribute to the force balance and play a role in the pressure
drop evaluation via friction or collisions of the particles at the
wall. In that case, f should depend on the amount of particles
in the system, and this is in good agreement with Figure 13.
More experimental investigations should be done to
confirm the first or the second explanation. However a first
conclusion is that formation of hydrate particles modify the
turbulent friction factor and this modification does depend on
solid amount. At high water cut the friction factor diverges.
The same variation of f with the water cut for two systems
seems to indicate a close mechanism, which depend only
slightly on the based fluid.
Hydrate issue becomes critical with the development of deep
and ultra deep-water fields. As mentioned, conventional
prevention methods reached their limits and the new options like
“kinetic inhibitors” or “antiagglomerant” additives seem to
be a reliable alternative in the near future. The concentration
required is very low and so storage facilities and processing
costs will be much lower with these techniques. But then,
studies of the influence of hydrate particles on the flow
properties become essential to control the flow assurance with
The increase of pressure drop that occurs when hydrates
are formed in pipelines is controlled by the friction factor
under turbulent flow conditions or by apparent viscosity of
the suspension in the laminar flow regime. We have tried in
this article to characterize flowing properties of hydrate
particles dispersed in oils in both regimes to consider the whole
range of transport velocities.
In the laminar flow regime, predictions of the viscosity
can be done based on hard sphere models with interactions.
We showed that Newtonian behaviour is expected in most
cases, and the relative viscosity of the suspension increases
with the volume fraction of hydrate. In some specific cases, if
interparticle forces can be high enough, shear thinning
behaviour can be observed and modeled by introducing an
effective volume fraction depending on aggregation rate.
However, the agglomeration process which can occur during
the formation stage is complex and makes difficult the
prediction of the size, shape and porosity of the hydrate
In turbulent flow regime, the pressure drop is
characterized by a friction factor that does not depend on velocity. For
two different oils, naphtha oil and condensate, we measured
experimentally the friction factor for the suspensions. We
observed an increase of the friction factor with the water cut
and very close values have been found for both systems. This
seems to indicate that particles of hydrate play an equivalent
role in both systems. This role could be an increase of the
apparent roughness at the wall due to particle deposition at
the formation stage or it could be an effect of the solid
particles itself in modifying the force balance by hitting or
moving at the wall.
We stressed also that for low viscosity oil, like
condensate, settling process might occur at low velocities before we
reach the laminar regime. So rheology become a
nonpertinent approach to predict the flow properties. A stratified
model with a bed of particles and a layer of fluid above is a
better description of that situation.
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Final manuscript received in December 2003