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NEW IN-SITU MEASUREMENTS OF THE VISCOSITY OF GAS CLATHRATE HYDRATE SLURRIES FORMED FROM MODEL WATER-IN-OIL EMULSIONS Ahmad Majid, David T. Wu, and Carolyn A. Koh Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02642 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017
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Langmuir
NEW IN-SITU MEASUREMENTS OF THE VISCOSITY OF GAS CLATHRATE
2
HYDRATE SLURRIES FORMED FROM MODEL WATER-IN-OIL EMULSIONS
3
Ahmad A.A Majid 1,2 , David T. Wu 1,3 , Carolyn A. Koh 1 *
4
1. Center for Hydrate Research, Department of Chemical and Biological
5
Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
6
2. Faculty of Chemical & Natural Resources Engineering, Universiti Malaysia
7
Pahang, Lebuhraya Tun Razak, 26300 Gambang, Malaysia
8
3. Department of Chemistry, Colorado School of Mines, Golden, Colorado 80401,
9
United States
10
ABSTRACT
11
In-situ rheological measurements for clathrate hydrate slurries were performed using a high
12
pressure rheometer to determine the effect of hydrate particles on the viscosity and
13
transportability of these slurries. These measurements were conducted using a well-characterized
14
model water-in-oil emulsion1. The emulsion consists of a model liquid hydrocarbon, water, and a
15
surfactant
16
ethylhexylsulfosuccinate (Aerosol OT, AOT). This emulsion was used as an analog to water-in-
17
crude oil (w/o) emulsions and provides reproducible results. The flow properties of the model
18
w/o emulsion prior to hydrate formation were investigated in terms of several parameters
19
including water percentage, temperature and pressure. A general equation that describes the
20
viscosity of the emulsion as a function of the aforementioned parameters was developed. This
21
general equation was able to predict the viscosity of a saturated emulsion at various temperatures
22
and water percentages to within ± 13% error. The general equation was then used to analyze the
mixture
of
sorbitane
monooleate
1
80
(Span
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and
sodium
di-2-
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effect of hydrate formation on the transportability of gas hydrate slurries. As for hydrate slurries
2
investigation, measurements were performed using methane gas as the hydrate former and a
3
straight vane impeller as a stirring system. Tests were conducted at constant temperature and
4
pressure (1 °C and 1500 psig of methane) and water percentages ranging from 5 to 30 vol.%.
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Results of this work were analyzed and presented in terms of relative values, i.e., viscosities of
6
the slurries relative to the viscosities of the emulsion at similar temperature and pressure. In this
7
work, a correlation to predict the relative viscosity of a hydrate slurry at various hydrate volume
8
fractions was developed. Analysis of the developed correlation showed that the model was able
9
to predict the relative viscosity of a hydrate slurry to within ± 17% error.
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INTRODUCTION
11
Gas hydrates, commonly known as clathrate hydrates, are crystalline compounds where small
12
gas molecules, such as methane, ethane and propane, are enclathrated by water cages that
13
comprise a network of hydrogen-bonded water molecules 2. Gas hydrates typically form at high
14
pressure and low temperature (e.g. 10 MPa, 277 K for methane). As such, they can form in and
15
plug subsea oil/gas flowlines, and thus hydrates are considered to be a major flow assurance
16
problem for the oil and gas industry 2,3.
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The current practice in dealing with gas hydrate in flowlines is called “hydrate management”
18
where gas hydrates are allowed to form, but a hydrate plug is prevented by controlling the slurry
19
properties with the injection of small quantities (1-2 vol.%) of Low Dosage Hydrate Inhibitors
20
(LDHIs). As gas hydrates are allowed to form in the flowline, fundamental properties at the
21
micro-scale such as cohesive forces between hydrate particles, particle size distribution, as well
22
as particle rearrangement and breakup need to be investigated in order to evaluate the
2
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transportability of hydrates in flowlines. The rheological behavior of a gas hydrate slurry at
2
various conditions could provide insight into gas hydrate slurry properties and behavior.
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In a rheological investigation, it is known that the viscosity of a solid suspension that includes
4
gas hydrates depends on several variables such as the concentration, size and distribution of solid
5
particles, as well as the viscosity of the suspending fluid. In the case of gas hydrate slurries, the
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aforementioned variables are affected by both the temperature and pressure of the system. Thus,
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this work focuses on applying the knowledge of the rheology of solid suspensions to
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understanding and quantifying the rheology of gas hydrate slurries.
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Several attempts have been made to understand the rheology of gas hydrate slurries, including
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flowloop tests 4–9 and atmospheric and high pressure rheometer measurements 10–16. In this work,
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the viscosity of the hydrate slurry was measured using a high pressure rheometer. The
12
measurements involved up to 30 vol.% water concentration, using a well-characterized model
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water-in-oil (w/o) emulsion. Measurements were conducted using a systematic approach with
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baseline viscosity measurements performed. This allows for a better understanding of all
15
variables and their effect on the viscosity of the slurry. The current approach can provide
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accurate viscosity values that are representative of gas hydrate slurries in flowlines and
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decouples the effect of hydrate slurries.
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MATERIALS AND METHODS
19
Emulsion Preparation
20
Model water-in-oil emulsions were prepared using a model liquid hydrocarbon Crystal Plus
21
Mineral Oil 350T (STE Oil Company, Inc.; see Table S1 in supporting information for the
22
composition). All emulsions in this work were prepared using 5 wt.% surfactant mixtures with
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respect to the total mass of the emulsion. This concentration is higher than the Critical Micelle
2
Concentration (CMC). However, our prior investigation on the characterization of the emulsion
3
showed that emulsion water coalescence was observed within 24 hours at low temperature 1.
4
Water coalescence at low temperature was prevented by increasing the concentration of the
5
surfactant. Further discussion is described in our previous work 1. The surfactant mixture
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consists
7
Ethylhexylsulfosuccinate (AOT, Fisher Scientific) at a ratio of 75 wt.% to 25 wt.% respectively.
8
A surfactant mixture was used in this work in order to satisfy the criteria of a model emulsion.
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These criteria include: (1) be an oil continuous emulsion, (2) have similar physical properties
10
(viscosity and density) to typical flowlines fluids, (3) have well-defined surface active
11
components, (4) have water droplets in the range of 1-100 µm, and (5) be stable for ~one week.
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In our previous work, it was concluded that a surfactant mixture is required to satisfy all the
13
criteria. The emulsion preparation process is similar to the method described in our previous
14
work 1. However, in this work the stirring time was 5 min (instead of 3 min) and the water was
15
added slowly during the first 2 minutes (instead of 1 min). Due to the high viscosity of mineral
16
oil 350T, longer mixing times and water addition times were required. By providing longer
17
times, there was then sufficient time for the surfactant to transport to the water/oil interface and
18
thereby form a stable emulsion.
19
Viscosity Measurements
of
Sorbitan
Monooleate
(Span
80,
Sigma
Aldrich)
and
Sodium
Di-2-
20
Viscosity measurements were performed using a TA Instruments Discovery Hybrid
21
Rheometer -2 (TA DHR-2). The rheometer is equipped with a pressure cell with an inner
22
diameter of 28 mm and a height of 50 mm. The cell has a pressure rating of 2000 psia. In the
23
work reported here, measurements were conducted using a four-blade straight vane impeller
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purchased from TA Instruments. Each of the blades is 13 mm in width, 48 mm in height and are
2
at a 90° angle to each other. This vane impeller is connected to a rotor with a magnet. There is
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another magnet attachable to the rheometer spindle. Due to the small gap between the tip of the
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impeller and the wall of the rheometer cell, a temperature probe to measure the temperature of
5
the slurry could not be installed. The temperatures in this paper are those reported by the Peltier
6
system. It is assumed that the temperature of the Peltier and fluid are relatively similar. The
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viscosity values in this paper are reported to within a 10% tolerance. The pressure cell is
8
connected to a high pressure ISCO 500D syringe pump to maintain the system pressure. A
9
schematic diagram of the high pressure rheometer setup is shown in Figure 1.
10 11 12
Figure 1. Schematic diagram of the high pressure rheometer setup used in this work 17,18. In this work, the torque, volume of the high pressure ISCO syringe pump, temperature and
13
pressure of the system were constantly monitored and recorded.
14
Viscosity Measurements for Baseline Studies without Hydrate
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As the objective of the study is to understand the effect on viscosity due to the presence of
16
hydrate particles in the flowline, it is thus necessary to determine and understand the torque of
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the system in the absence of hydrate. It is known that the viscosity of a liquid is dependent on
2
several variables including the water percentage of the system, temperature and amount of gas
3
dissolved (saturation). Our analysis of the results in this work, specifically the mass balance at
4
steady state, show that the amount of methane dissolved in the liquid reaches a steady state after
5
the hydrate crystal growth stabilizes (with no further formation occurs under this condition). As
6
such, baseline measurements (viscosity without hydrate formation) are needed to analyze the
7
effect of hydrate particles. This can be evaluated by performing baseline studies, and it will help
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decouple the effect of the aforementioned variables from the effect of hydrate on the viscosity of
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the system. In this study, ~27 ml of sample (pure model liquid hydrocarbon or model emulsions)
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was added into the pressure cell. The sample was then cooled to the desired temperature, while
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stirring at 50 rad/s. Once the sample temperature reached the desired temperature (5°C, 10°C and
12
20°C), the sample was stirred at 50 rad/s for 30 min. Next, the cell was slowly pressurized with
13
methane gas (General Air, 99.97% purity) to 800 psig. The sample was then stirred until the
14
model liquid hydrocarbon was fully saturated with gas at this temperature and pressure and the
15
system has achieved steady state. This step was repeated at different pressures ranging from 900
16
to 1500 psig in 100 psig increments. In this work, tests were only conducted for pressures
17
between 800 to 1500 psig. In this work, hydrate does not form below 800 psig, due to either a
18
low drivsiing force or the system being outside the hydrate equilibrium condition (depending on
19
the temperature). Additionally, for tests conducted at low temperatures (5°C and 10°C), the
20
system is within hydrate stability region. For the baseline tests, hydrate nucleation did not occur
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as evidence by the high pressure ISCO syringe pump data. Hydrate formation is detected by a
22
rapid decrease in the volume of the ISCO pump, since hydrate formation consumes the gas. This
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change in volume of the ISCO pump was not detected in our baseline tests. (If hydrate formed
2
during these baseline tests, the results would not be included in the baseline investigations).
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Viscosity Measurements for Slurries Systems (with Hydrate)
4
For hydrate slurry measurements, 27 ml of emulsion sample was added into the rheometer
5
pressure cell. Next, the rheometer cell was purged with methane gas to remove air in the system.
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The cell was then slowly pressurized with methane gas to a pressure of 1500 psig. The ISCO
7
pump was then set to operate at a constant pressure mode of 1500 psig. Subsequently, the sample
8
was stirred at 50 rad/s for 4 hours. This process is necessary for the saturation of the model liquid
9
hydrocarbon with methane gas. In the initial work of this project, it was determined that 4 hours
10
of stirring at 50 rad/s provides enough time for the emulsion to be fully saturated with methane
11
gas. Full saturation was confirmed by constant viscosity, as well as a constant volume of the
12
ISCO pump for a certain period of time (typically one hour).
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After the saturation process, the sample was cooled from 20 °C to 1 °C at a rate of 0.5 °C/min,
14
while maintaining the stirring at 50 rad/s and pressure at 1500 psig. The hydrate equilibrium
15
temperature for pure methane at 1500 psig is 14 °C. Thus, in this study, the subcooling for the
16
system, ∆Tsub, is 13°C. The system was left at this condition (1 °C, 50 rad/s of mixing and 1500
17
psig) until gas hydrates formed. In this work, gas hydrate formation was confirmed by a sudden
18
increase in the viscosity of the system, and was accompanied by a rapid decrease in the volume
19
of the ISCO pump. After hydrates have formed, the system was continuously stirred at 1 °C, 50
20
rad/s of mixing and 1500 psig until steady state. Steady state is defined as occurring when the
21
change in the viscosity and volume of ISCO pump readings were minimal (±5 vol.% in volume
22
of ISCO and ±10% in viscosity). This indicated that there was no further hydrate formation and
23
also there was minimum change in the flow pattern in the system. Due to the geometry of the
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rheometer used in this investigation, there may be some hydrate growth along the wall of the
2
rheometer cell. This could affect the overall reported viscosity of the slurry. However, since the
3
gap between the impeller and the wall of rheometer cell is small, it is assumed that hydrate
4
growth along the wall of the rheometer cell would have minimal effect on the overall reported
5
viscosity.
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Finally, after steady state was achieved, the system was heated back to 20 °C, at a rate of 0.5
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°C/min, while maintaining the pressure at 1500 psig and the mixing speed at 50 rad/s to
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dissociate the hydrate. A fresh emulsion sample was used for each run.
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1
RESULTS AND DISCUSSIONS
2
Results for Baseline Measurements
3 4 5 6 7
Figure 2. Experimental results for model liquid hydrocarbon baseline measurements of viscosity versus gas pressure and amount of dissolved methane, performed at three different temperatures, (a) 20 °C (b) 10 °C and (c) 5 °C for four different water percentages (0 vol.% brown, 10 vol.% red, 20 vol.% blue and 30 vol.% green)
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Figure 3 Experimental results for model liquid hydrocarbon baseline measurements showing viscosity as a function of temperature and dissolved methane for four different water percentages at 1500 psig. (0 vol.% brown, 10 vol.% red, 20 vol.% blue and 30 vol.% green)
5
The results of the baseline measurements performed using the model liquid hydrocarbon are
6
shown in Figure 2. As can be seen in this figure, at all water percentages investigated, the
7
viscosity of the emulsion decreases as the pressure of the system increases. Moreover, higher
8
system pressures correspond to higher equilibrated concentrations of methane dissolved in the
9
model liquid hydrocarbon phase. The amount of methane dissolved was measured based upon
10
the volume change of the ISCO pump. Additionally, it can be observed that the viscosity of the
11
model emulsion depends on three variables; temperature, water composition (water percentage)
12
and saturation of the model liquid hydrocarbon (that depends on both temperature and pressure
13
of the system). This observation is in agreement with investigations on the effect of saturation on
14
hydrocarbon viscosity, reported by other researchers 19.
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Development of a Generalized Equation for the Viscosity of Model Emulsion Systems
16 17
Viscosity dependence upon pressure, such as shown in Figure 2, is commonly fit by an exponential correlation 20 10
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η = A0 e B P .
(1)
0
1
In this equation, η is the viscosity of the emulsion, P is the gauge pressure of the system and
2
A0 is a pre-exponential factor and is the viscosity of the emulsion at atmospheric pressure. This
3
simple exponential dependence is commonly used to model the relationship between viscosity
4
and pressure20. In this equation, A0 depends on both the temperature and water percentage of the
5
system and has units of viscosity (cP in this work). The B0 term is interpreted to be related to the
6
interactions between the components in the model liquid hydrocarbon and gas molecules. This
7
term has units of inverse pressure (psig-1 in this work).
8
Further analysis of the experimental baseline measurements, however, indicates that the
9
viscosity of the model liquid hydrocarbon also decreases exponentially with the gas saturation in
10
the liquid. In this way, and as stated earlier, the viscosity implictly depends on both the
11
temperature and pressure of the system through the gas saturation in the liquid. This suggests that
12
a higher order interaction of the gas and hydrocarbon molecules needs to be taken into account.
13
As such, a viscosity model for a mixture proposed by Grunberg and Nissan that takes into
14
account the non-ideality of the mixture was used as the basis for the improvement of Equation
15
(1) 21,22. Therefore, Equation (1) was generalized to Equation (2) shown below.
η = A0 e B n(T ,P )+B n(T ,P) 1
2
(2)
16
In this equation, B1 and B2 are the first and second order interaction parameters between the
17
gas and model liquid hydrocarbon molecules respectively. n (T, P ) is the number of moles of
18
methane dissolved in the model liquid hydrocarbon phase per unit volume of model liquid
19
hydrocarbon.
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1
As stated earlier, the generalized equation for the viscosity of the saturated emulsion is a
2
function of saturation, temperature and composition/water percentage . As can be seen in
3
Equation (2), the saturation variable has been taken into account. In order to take into account the
4
other two variables (temperature and water percentage), an assumption was made in which it is
5
assumed that the effect of gas saturation, which affects the viscosity of the continuous
6
hydrocarbon phase, and water percentage are independent. As such, the A0 function can be
7
expressed in terms of two separate functions as shown in Equation (3).
η = A1 (T ) A2 (φ ) e B n(T ,P)+B n(T,P) 1
2
(3)
8
In Equation (3), A1 (T ) describes changes in the viscosity of the model liquid hydrocarbon
9
phase with changes in the temperature of the system, at constant model liquid hydrocarbon
10
composition. The function A2 (φ ) describes the effect of water content on the viscosity of the
11
system, for a given viscosity of the model liquid hydrocarbon.
12
Obtaining Functions and Parameters in the Generalized Equation for Emulsion Viscosity
13
A1 (T ) Function
14
In order to obtain the A1 (T ) function, we examined the limiting case of an unsaturated (i.e,
15
n(T,P) = 0) model liquid hydrocarbon phase without any water (i.e., A2 (φ ) = 1). In this case,
16
Equation (3) simplifies to
η = A1 (T )
(4)
17
which is simply the dependence of temperature on the viscosity of the pure continuous phase. It
18
is known that the viscosity of a fluid is well-described as being inversely proportional to the
19
absolute temperature of the system
23,24
. Thus, the viscosity of the model liquid hydrocarbon
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phase at three different temperatures was plotted in order to determine the relationship between
2
viscosity and temperature, and the plot is shown in Figure 4. Note here that the temperature
3
chosen in this work is in a narrow temperature range and is based on the experimental
4
temperatures used for the hydrate slurry experiments. Additionally, from results obtained in this
5
work, the A1 (T ) function is observed to be valid even in the presence of a water phase.
6 7
Figure 4: Relationship between viscosity and temperature for the model liquid hydrocarbon.
8
From Figure 4 it can be seen that the viscosity of the model liquid hydrocarbon used in this
9
work can be adequately modeled as being linearly proportional to the inverse temperature of the
10
fluid within the temperature range studied in this work. While a linear correlation is adequate for
11
the small temperature range used in this work, we note that extrapolations to greater temperature
12
ranges may require refinement of this correlation to include nonlinear behavior. Based on the
13
analysis conducted, the linear correlation developed, shown in Equation (5), has a coefficient of
14
determination, R2 of 0.97.
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1 A1 (T ) = 6.81×10 5 − 2.27 ×10 3 T 1
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(5)
A2 (φ ) Function
2
The A2 (φ ) function describes the effect of composition/water percentage on the viscosity of
3
the model emulsion. This function expresses the viscosity relative to that of the continuous phase
4
of the emulsion. Currently, there are several widely used models to describe the increase in
5
viscosity with an increase in composition/water percentage. Among the common relative
6
viscosity models available in the literature are the Einstein, Krieger Daugherty, and Mooney
7
models25–28.
8 9
In the study of emulsion rheology, the relative viscosity of an emulsion can be divided into two regions: dilute and concentrated regimes
27
. The Einstein model is typically used for
10
emulsion systems in the dilute regime, where the water volume fraction, φ , is less than 0.01.
11
Since, in our work we investigated the effect of composition/water percentage up to 30 vol.% of
12
water, the Einstein model is not suitable to be used. On the other hand, for emulsions at higher
13
water fraction, most researchers describe the increase in relative viscosity using either the
14
Krieger Daugherty or Mooney equation.
15
However, in analyzing the results obtained in these measurements, all the models described
16
earlier (Einstein, Krieger Daugherty and Mooney) fail to predict the increase in relative viscosity
17
over the entire range of water volume fractions. Thus, an improvement to the relative viscosity
18
model, specifically for this emulsion system, needs to be made. The improvement to the relative
19
viscosity model was made based on the work performed by Sudduth 29.
20
From the work conducted by Sudduth, the relative viscosity model can be expressed in terms
21
of a differential equation, as shown in Equation (6). In this equation, the variable B is the
14
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25–28
1
“Einstein Coefficient” and usually taken to be a value of 2.5
. The second variable in the
2
equation is σ , which can be taken as an interaction/fitting parameter. Based on Equation (6), if
3
σ has a value of 1, the differential equation will yield Krieger-Dougherty equation while if σ
4
has a value of 2, the differential equation will yield Mooney equation. Accordingly, the value of
5
σ is not necessarily a whole number. Finally, the third variable in Equation (6) is φmax , which
6
is the maximum packing fraction for the particles and is taken to be either 0.74 or 0.64 25–27,30. In
7
this work, the maximum packing fraction, φmax was set to 0.74. This value was chosen since it is
8
near the inversion point of the model emulsion. −σ
φ = B 1− dφ η φmax
dη
(6)
9
Using Equation (6), the value of σ was determined by minimization of error between the
10
experimental data and the model. The value of σ obtained in this work was calculated to be 1.78
11
± 0.3 and a plot of the comparison between the experimental data and the predicted value from
12
the model is shown in Figure 5.
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1 2 3 4
Figure 5: Comparison between the experimental data and model developed in this work for the effect of water percentage on viscosity. Methane Saturation in Liquid Hydrocarbon, n (T , P ) Function
5
The moles of methane gas dissolved in the model liquid hydrocarbon phase were determined
6
at various temperatures and pressures. The composition analysis of the mineral oil 350T was
7
conducted by Weatherford lab and the composition is listed in Table S1 in the Supporting
8
Documentation. The error in this analysis is believed to be within 15%. For a given composition
9
of the model liquid hydrocarbon, the moles of methane dissolved in the model liquid
10
hydrocarbon was determined by performing a Multiflash® calculation for equilibrium
11
compositions and confirmed by experimental data. In this simulation, the amount of methane
12
dissolved in the model liquid hydrocarbon is reported in terms of per unit volume of model liquid
13
hydrocarbon [mol/cm3].
14
B1 and B2 constants
15
As described earlier and shown in Equation (3), there are two constants that describe the
16
interactions between the gas and molecules in the model liquid hydrocarbon. In this work, these
16
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1
constants B1 and B2 were determined by minimization of error between the experimental data
2
and the predicted result from the model. The values of B1 and B2 so determined are -95 ± 2.5
3
cm3/mol and 990 ± 123 cm6/mol2 respectively.
4
Comparison Between Emulsion Viscosity Data with Model
5 6 7
Figure 6: Comparison between the experimental value of the viscosity for model emulsions with the viscosities predicted by the model at (a) 20 ° C, (b) 10 °C and (c) 5 °C for four different
17
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1 2
water percentages (also showing amount of dissolved methane, 0 vol.% brown, 10 vol.% red, 20 vol.% blue and 30 vol.% green).
3
Figure 6 shows the comparison between the viscosity of the emulsion obtained from
4
experimental data and predicted by the model at two different temperatures. As can be seen here,
5
within the small temperature range chosen in this work; there is up to a ± 13% deviation between
6
the predicted viscosity from the model and the actual viscosity.
7
Hydrate Slurry Viscosity Profiles
Page 18 of 36
8
The next set of experiments to be conducted were hydrate slurry investigations. The results of
9
the hydrate slurry viscosity measurements at 1 °C, 1500 psig of methane and water percentages
10
ranging from 5 – 30 vol.% are presented in Figure 6. Repeat tests were conducted using different
11
batches of model liquid hydrocarbon, and the results were reproducible even with different
12
batches of model liquid hydrocarbon. For water percentage of ≥ 10 vol.%, two repeat
13
experiments were conducted at similar experimental conditions (water percentage, temperature
14
and pressure). Results at steady state are reproducible on average within 10% deviation. All data
15
(with repeats) were used for further analysis. The results of these repeat tests are presented in
16
Figure S1 of the supplementary document. It should be noted that for Figure S1, the data plotted
17
are those that show the most deviation between tests. From Figure 7, it can be seen that the
18
viscosity profile of gas hydrate slurries typically consists of four different regions: (1) initial and
19
gradual viscosity increase region, (2) constant viscosity region, (3) sudden and rapid viscosity
20
increase region and (4) gradual viscosity decrease region.
18
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1 2 3 4
Figure 7: Viscosity profiles of methane hydrate slurries formed in-situ at 1 °C, 1500 psig and water percentage ranges from 5 – 30 vol.% for model liquid hydrocarbon. Inset: expanded view illustrating the different viscosity regions for 20 vol.% water percentage test.
5
As shown in Figure 7, there is a gradual increase in viscosity of the system in the time frame
6
of 0 to ~0.5 hr. The increase in viscosity of the system is due to the cooling process, whereby the
7
emulsion is being cooled from 20 °C to 1 °C, reflecting the increasing model liquid hydrocarbon
8
phase viscosity with decreasing temperature
9
viscosity after the temperature and saturation have stabilized at the experimental condition (1 °C
10
and 1500 psig), but before hydrate formation. It should be noted that the formation/onset of gas
11
hydrate is stochastic and may take several hours 2. On the other hand, region (2) may be absent in
12
the cases where hydrate nucleation and formation could occur during the cooling process in
13
region (1). If this is the case, the system immediately enters region (3). We note that in this
14
investigation, hydrate nucleation and formation only occurred after the system was stabilized at
15
1500 psig and 1 °C.
23,24
19
. The system then enters a region of constant
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1
Upon hydrate formation, the system enters the third region wherein there is a sudden and
2
rapid increase in the viscosity. Hydrate formation was also confirmed by the decrease in volume
3
of the ISCO pump indicating that methane gas was being consumed. Currently, there are two
4
hypothesized factors for the increase in viscosity of the system upon hydrate formation. The first
5
factor is the increase in viscosity due to the formation of solid in the system. Studies have shown
6
that the viscosity of a solid suspension is higher than the viscosity of the corresponding liquid-
7
liquid emulsion
8
emulsion into a solid suspension and this increases the viscosity of the system. The second factor
9
reflects the depletion of methane in the liquid hydrocarbon phase. It is reported that for an oil-
10
dominated system, the gas for hydrate formation comes from the dissolved gas in the model
11
liquid hydrocarbon phase 2. As such, when gas hydrates start to form in the system, the
12
concentration of dissolved gas in the model liquid hydrocarbon phase will decrease
13
depletion of methane in the model liquid hydrocarbon will increase the viscosity of the
14
(continuous) model liquid hydrocarbon phase leading to a corresponding increase in the viscosity
15
of the slurry. However, it is believed that the main contribution to the increase in the overall
16
viscosity is likely due to the solidification (hydrate formation) 31. Additionally, previous studies
17
have also suggested that the interaction (capillary bridging) between solid hydrate particles could
18
cause the rapid increase in the viscosity 10,32. It should also be noted that since hydrate formation
19
is an exothermic process, the temperature of the slurry should increase during hydrate formation.
20
Thus, during hydrate formation there are competing effects of increasing viscosity due to solid
21
hydrate formation and decreasing viscosity due to increases in temperature. However, based
22
upon the results presented here, the increase in viscosity due to solid formation was dominant
23
compared to the decrease in viscosity due to increases in temperature.
25
.
Thus, when gas hydrates form, the system changes from being a w/o
20
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. This
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1
After region (3), the system enters region (4), where there is a gradual decrease in the
2
viscosity of the hydrate slurry. Similarly, in this region, there are currently two hypotheses for
3
the decrease in the viscosity. As stated earlier, when gas hydrates form in the system, dissolved
4
methane is consumed. Since there is still a gas phase in the system, the depletion of dissolved
5
methane creates a driving force for the methane in the gas phase to dissolve in and resaturate the
6
model liquid hydrocarbon phase. This resaturation decreases the viscosity of the liquid
7
hydrocarbon continuous phase, and thus the viscosity of the hydrate slurry. A second hypothesis
8
to explain the decrease in the viscosity is one based on gas hydrate particle break-up and
9
rearrangement. During hydrate formation, gas hydrate particles might agglomerate into large
10
hydrate aggregates. As the system continues to be stirred at high speed, these large aggregates
11
could break into smaller hydrate particles and re-arrange in the system. Consequently, the
12
effective volume fraction decreases and this decreases the viscosity of the hydrate slurry 33,34.
13
Further analyses of the hydrate slurries viscosity profile show that the viscosity increases with
14
increasing water percentage of the emulsion. In this work, it was hypothesized that the increase
15
in the viscosity of the slurry is due to the increase in the amount of gas hydrate particles in the
16
system (cf.
17
for the system as shown in Table 1.
26,27,35
). This hypothesis was confirmed by the mass balance calculations conducted
18
As described in the MATERIALS AND METHODS section, the rheometer setup that was
19
developed for this work13,18 is a closed system. Therefore, a mass balance on the system was
20
performed by calculating the total consumption of methane in the system; i.e., calculating the
21
difference between the moles of methane at the beginning and at the end of the experiment. The
22
value determined from this calculation is the experimental consumption of methane.
21
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1
In performing the mass balance of the system, it should be noted that the consumption of
2
methane is due to two separate phenomena: (1) saturation of the model liquid hydrocarbon phase
3
and (2) formation of gas hydrates. The moles of methane needed for the saturation was
4
determined from Multiflash® calculations and baseline measurements, while the moles of
5
methane needed for hydrate formation was determined using the in-house phase equilibrium
6
software, CSMGem 2. Using these values, the volume fraction of gas hydrates formed in the
7
slurry was then calculated and the results are shown in Table 1.
8 9 10 11
Table 1: Results of Mass Balance Calculations performed for Model Liquid Hydrocarbon Hydrate Slurry Experiments. Volume Fraction of Hydrates is determined by Experimental Gas Consumption. Theoretical Consumption of Experimental
Experimental Total
Volume
Consumption of
Fraction of
Methane
Hydrates
[mol]
[vol.%]
Methane for Liquid Water Saturation and Hydrate Percentage Formation [vol. %] [mol] 5
0.051
0.053
5.9
7
0.055
0.064
8.15
10
0.061
0.055
8.79
15
0.072
0.060
12.02
20
0.082
0.085
20.21
25
0.092
0.097
24.05
30
0.102
0.088
24.33
12
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1
As the water content of the emulsion increases, the amount of methane dissolved in the model
2
liquid hydrocarbon phase decreases, since there is less liquid hydrocarbon in the system.
3
However, Table 1 shows that as the water percentage of the system increases (from 5 to 25
4
vol.%), the consumption of methane increases. This increase in the amount of methane
5
consumed in the system indicates that there are more hydrates formed as the water content of the
6
emulsion increases. However, it should be noted that the consumption of methane decreases
7
when the water content increases from 25 vol.% to 30 vol.%. It is believed that this decrease in
8
methane consumption is due to the water in the 30 vol.% water percentage not fully converting
9
to hydrates. These calculations suggest that only 86% of the water converted to hydrates for the
10
30 vol.% water percentage emulsion, compared to 100% conversion for the 25 vol.% water
11
percentage emulsion.
12
Relative Viscosity of Hydrate Slurries at Steady State
13 14
Equation (7) defines a relative viscosity of a hydrate slurry to allow comparison and investigation of the effect of hydrate particles across all water percentages.
ηr =
η (T, P, ϕ hyd ) η (T, P, φWC=0 )
(7)
15
The numerator is the viscosity of the hydrate slurry at the experimental conditions (1500 psig
16
and 1 °C) and the calculated (from gas consumption) amount of hydrate in the system. The
17
denominator of the equation is the viscosity of the continuous phase at similar conditions (1500
18
psig and 1 °C); i.e. the viscosity of the saturated model liquid hydrocarbon at 1500 psig and 1 °C.
19
The value for the denominator was determined based on our baseline measurements.
20
The relative viscosity of hydrate slurries was analyzed only at steady state conditions, where
21
there are minimal changes in the system. This allows fewer assumptions to be made and
23
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Page 24 of 36
1
simplifies development of the model to predict relative viscosity. Steady state conditions were
2
defined as occurring when there are minimal change in both the viscosity of the slurry and the
3
volume of the ISCO pump for a period of one hour (±5 vol.% in volume of ISCO and ±10% in
4
viscosity). Minimal change in both values indicates that there is no further formation of hydrates
5
and there is also no change in the flow pattern. The average viscosity values during the one-hour
6
period is then calculated and used for the relative viscosity analysis.
7
Figure 8 shows the steady state relative viscosity of gas hydrate slurries at various hydrate
8
volume fractions. As can be seen in this figure, the relative viscosity of the system increases with
9
an increase in hydrate volume fraction. This is as expected since as the amount of solid in a
10
suspension increases, the absolute viscosity of the system increases and thus the relative
11
viscosity also increases 25,26,35,36.
12 13 14
Figure 8: Steady state relative viscosity of gas hydrate slurries formed from model liquid hydrocarbon at various hydrate volume fractions.
15
In addition to studying the viscosity of the hydrate slurry, the aggregation phenomenon in the
16
hydrate slurry was investigated. Hydrate particle aggregation was investigated by evaluating the
24
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1
average water droplet size of the emulsion at the beginning of the experiment (before hydrate
2
formation) as well as at the end of the experiment (after hydrate dissociation). It is believed that
3
if hydrate particle aggregation occurs in the system, the sizes of the water droplets will be larger
4
after hydrate dissociation compared to before hydrate formation
5
individual hydrate particles will adhere to one another and as such, during hydrate dissociation
6
the hydrate aggregates will dissociate into larger water droplets as depicted in Figure 9 37.
1,37
. In hydrate aggregation, the
7 8 9
Figure 9 Conceptual picture of water droplet size (a) without hydrate aggregation and (b) with hydrate aggregation. (redrawn from 18,37)
10
The average size of water droplets was determined using optical microscopy images of the
11
emulsion before and after hydrate formation, as illustrated in Figure 10. It should be stated that in
12
order to get a good representation of the water droplet size distribution, microscopic images were
13
taken immediately after hydrate dissociation and depressurization of the system. Coalescence of
14
water droplets may occur if image analysis is delayed. As a result of this process, the emulsion is
15
still partially saturated, and thus gas pockets cannot be prevented while taking the images, since
25
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Page 26 of 36
1
the emulsion is still releasing gas in the process. In this work, approximately 300 water droplets
2
per condition were measured for these analyses. This provides a representative of the average
3
droplet size. Thus, in Figure 10(b), it can be seen that there are large and irregular shaped circles
4
with a clear interior (marked in red). These are gas bubbles and were not taken into account
5
when calculating the average droplet size after hydrate formation. In this figure, examples of
6
water droplets are marked with yellow circles.
7 8 9 10
Figure 10: Microscopic image of water-in-oil emulsion (a) before and (b) after hydrate formation. Large and irregular red circles are selected gas bubbles and small yellow circles are selected water droplets.
11 12
Using the microscopic images, it was determined that the numerical average size of water
13
droplets before hydrate formation is 2.7 ± 1.9 µm, while the average size of water droplets after
14
hydrate formation was determined to be 2.8 ± 1.0 µm. Since the average size of the water
15
droplets before and after hydrate formation is relatively unchanged, it can be said that there is
16
minimal hydrate particle aggregation in the system. For emulsion systems at low water
17
percentage (below 30 vol.%), it is believed that the minimal hydrate aggregation in the system
18
can be attributed to the high concentration of surfactant in the system 1,38.
26
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1 2
Langmuir
Development of a Relative Viscosity Model at Steady State In the study of hydrate slurry rheology, the most common relative viscosity model is the 39
3
model proposed by Camargo and Palermo in 2002
4
others
5
system. Thus, a simpler model needs to be developed and is the main focus of this work.
2,40
. Though widely used by our group and
, the model requires several parameters that may not be easily obtained in a flowline
6
Similar to the emulsion system, as discussed in the section on Obtaining Functions and
7
Parameters in the Generalized Equation for Emulsion Viscosity, work by Sudduth (Equation (6))
8
was used as the basis of this model development. However, for a hydrate slurry, both the B and
9
σ parameters need to be determined and these parameters are system specific. Thus, the values
10
of both the Einstein coefficient, B , and interaction parameter, σ , were determined by
11
performing minimization of error of predicted values compared to the experimental data
12
collected in this work. The values for both constants for the model emulsion system are 5.33 ±
13
0.73 for the Einstein Coefficient, B, and 1.98 ± 0.87 for the interaction parameter, σ.
14
Additionally, a comparison of the relative viscosities from experimental data and from the model
15
is shown in Figure 11.
27
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Page 28 of 36
1 2 3 4
Figure 11: Comparison of the model liquid hydrocarbon hydrate slurry relative viscosity at steady state from experiment and calculated using three different models, (this work, Mooney, and Krieger Dougherty).
5
From Figure 11, it can be seen that the model developed in this work can predict the relative
6
viscosity of a hydrate slurry at steady state, with a higher level of accuracy (± 17% error)
7
compared to the widely used models by Mooney and by Krieger Dougherty.
8
CONCLUSIONS
9
In this work, viscosity measurements of saturated emulsions and gas hydrate slurries at
10
various temperatures, pressures and water volume fractions were performed using a high
11
pressure rheometer (TA Instruments). Measurements were made using a four-blade straight vane
12
impeller as an agitator and with a mixing speed of 477 RPM. All tests were conducted using pure
13
methane as the hydrate former. Measurements were conducted using a model w/o emulsion that
14
has been proven to behave similarly to a crude oil1.
15
For the viscosity of saturated emulsions, measurements were performed over a relatively
16
small temperature range between 5 – 20 °C and pressures in the range of 0 – 1500 psig. This
28
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1
temperature and pressure range is the typical condition in oil and gas subsea flowlines. Since the
2
focus of the work is on oil-dominated systems, viscosity measurements were only conducted for
3
water percentages in the range of 0 to 30 vol.% water percentage. From the study of saturated
4
emulsions, a new generalized equation that is a function of temperature, pressure (saturation) and
5
water volume fraction (water percentage) was developed. Tests were conducted to determine the
6
accuracy of the equation. The results of the comparison between experimental data and
7
calculated values show that the model was able to predict the viscosity of saturated emulsion at
8
various conditions fairly accurately (to within ± 13% error). This generalized equation serves as
9
a baseline for the analysis of the effect of hydrate particles on the viscosity of slurries.
10
For the study of the viscosity of gas hydrate slurries, measurements were made at a constant
11
temperature of 1 °C and constant pressure of 1500 psig. The water percentage for experiments
12
was chosen to be between 5 and 30 vol.% water. Analyses of the viscosity of hydrate slurries
13
were conducted at steady state conditions, where there is no further formation of gas hydrates
14
and there is minimal change in the flow pattern. In order to compare the results across all water
15
percentages, results are presented in terms of relative viscosity. Using these results, a correlation
16
that predicts the relative viscosity of hydrate slurries as a function of hydrate volume fraction
17
was developed. Comparison of the experimental data and calculated values from the correlation
18
shows that the model was able to predict the relative viscosity relatively well to within ± 17%
19
error.
20
Acknowledgements
21
The authors would like to acknowledge past and current members of Center for Hydrate
22
Research Consortium consisting of BP, Chevron, ConocoPhillips, Petrobras, ENI, ExxonMobil,
23
Halliburton, IMP, Multi-Chem, Nalco Champion, Shell, SPT Group, OneSubsea, Schlumberger, 29
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Page 30 of 36
1
Statoil and Total for supporting this work. Ahmad A Abdul Majid would also like to
2
acknowledge Universiti Malaysia Pahang (UMP) under the Ministry of Education (MoE),
3
Malaysia for sponsoring his studies.
4
5
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Lv, X.; Shi, B.; Wang, Y.; Gong, J. Study on Gas Hydrate Formation and Hydrate Slurry
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Deen, W. M. Analysis of Transport Phenomena, First Edit.; Oxford University Press: New York, 1998.
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