2001 International Gas Research Conference
Amsterdam, The Netherlands
November 5-8, 2001
HYDRATE FORMATION RATE IN A CONTINUOUS
STIRRED TANK REACTOR
TAUX DE FORMATION D'HYDRATES DANS UN RÉACTEUR
PARFAITEMENT AGITÉ CONTINU
M. Mork and J. S. Gudmundsson
Department of Petroleum Engineering and Applied Geophysics
Norwegian University of Science and Technology, Norway
M. Parlaktuna
Department of Petroleum and Natural Gas Engineering
Middle East Technical University, Turkey
Abstract
The rate of hydrate formation plays an important role in the deposition of solids in pipelines, and in the making of hydrates for the storage and transport of natural gas. An extensive experimental program was carried out in the hydrate facilities at NTNU, where natural gas hydrate was produced in a Continuous Stirred Tank Reactor (CSTR). The reactor was operated at conditions planned in the manufacture of natural gas hydrates offshore for the capture of stranded gas. A semi-empirical rate of hydrate formation model was established and compared to experimental data obtained in batch reactors. The model includes the effects of temperature driving force, reactor pressure, stirring rate and gas superficial velocity. It was found that the rate of hydrate formation in CSTR reactors is 1-3 orders of magnitude larger than in batch reactors operated at the same temperature and pressure.
Resumé
Le taux de formation d'hydrate joue un rôle important dans la déposition de solides dans les pipelines et dans la formation d'hydrates pour le stockage et le transport de gaz naturel. Un important programme expérimental a été mene au laboratoire d'hydrate du NTNU, où un hydrate de gaz naturel a été produit dans un Réacteur Parfaitement Agité Continu (RPAC). Le réacteur a été utilise dans des conditions proches de celles intervanant dans l’exploitation offshore des champs gaziers marginaux. Un modele semi-empirique du taux de formation d'hydrate a été établi et comparé aux données expérimentales obtenues dans des réacteurs fermé. Le modèle inclut les effets de la température, la pression dans le réacteur, le taux d’agitation et la vitesse superficielle du gaz. Il a été trouvé que le taux de formation d'hydrate dans des réacteurs CSTR est 2-3 ordres de grandeur plus eleve que dans les réacteurs sans entrée ni sortie de matiere opérés aux mêmes conditions de température et de pression.
Introduction
Natural gas hydrates are solids that form when liquid water and natural gas are brought in contact at ambient temperature and high pressure, typically 5-15 °C and 50-100 bar. Such conditions are readily found in the natural gas industry and in oil and gas production operations. The formation of solid hydrates can lead to blockage of pipelines and equipment, causing major operational and safety problems. The oil and gas industries spend large sums of money to prevent hydrate formation [1].
Natural gas hydrates are crystals that typically contain 85 wt. % water and 15 wt. % natural gas. When referred to standard conditions, natural gas hydrates contain 150-180 volumes of gas per volume of water. Such large volumes make natural gas hydrates interesting for the storage of natural gas; also for the transport of natural gas. As the temperature is lowered, natural gas hydrates are stable at lower pressures. The refrigeration of natural gas hydrates to temperatures below the freezing point of water, makes it possible to store and transport natural gas hydrates at ambient pressure conditions [2].
R&D on the formation of natural gas hydrates in oil and gas production systems, and in land-based and offshore process plants for natural gas storage and transport purposes, has been reported at three international conferences [3,4,5]. The hydrate formation rate is important in both oil and gas production systems and in process plants for storage and transport purposes. Experimental results on the hydrate formation rate in a Continuous Stirred Tank Reactor (CSTR) are reported in this paper. The work was carried out to better understand the design of reactor systems in on-land and offshore plants for natural gas storage and transport. The results are also relevant in understanding the rate of hydrate formation in pipelines [6].
Hydrate Formation
The formation rate of natural gas hydrate is governed by a multitude of factors, including the pressure, temperature and gas composition, also called PVT-effects. Also, the rate of hydrate formation is determined by the combined effects of heat and mass transfer. Cooling is required to remove the hydrate heat of formation. Mass transport is required to dissolve the natural gas in liquid water, and to bring the dissolved gas molecules in contact with a growing hydrate crystal.
In addition to the above factors, the rate of hydrate formation depends on the nature of crystal growth, also referred to as chemical reaction kinetics. The overall rate of hydrate formation therefore, depends on PVT-effects, transport-effects and reaction-effects. One way to gain knowledge about the overall rate of hydrate formation, is to carry out experiments at conditions similar to the conditions found in subsea production systems and process plants.
Gas hydrate formation is usually described as a crystallization process with nucleation, growth, agglomeration and breakage [7]. Gas is dissolved in water, and nucleation starts primarily at the gas-water interface where the gas concentration is highest. The recently formed crystals disperse in the bulk liquid and start to grow as more gas is supplied to the liquid phase. Usually, after a while, agglomeration and breakage of the growing particles can be observed.
In the literature, the gas consumption rate and the particle size distribution of the formed hydrate crystals are used to describe the hydrate formation process quantitatively.In a model proposed by Vysniauskas and Bishnoi in 1983 [8], the rate of hydrate formation was modelled from the consumption rate of gas. Experiments were performed with methane and ethane gas and distilled water in a 0.5 litre semi-batch stirred reactor, and it was found that pressure, temperature driving force and gas-liquid interfacial area were the most important parameters affecting the gas consumption rate. I
ncreased stirring rate and pressure resulted in increased consumption rate of gas, while an increase in temperature resulted in decreased consumption rate. The effect of stirring was due to the increased gas-liquid interfacial area with increased stirring rate.In work done by Englezos et al. [9] published in 1987, the gas consumption rate was coupled to the hydrate crystal growth rate.
Experiments were carried out in the same equipment as used by Vysniauskas and Bishnoi [8]. The growth was modelled using crystallization theory, and a two-film theory was adapted for the gas-liquid interfacial mass transfer. Experimental results were modelled so that the number of moles of gas consumed per particle per second was proportional to the fugacity driving force and the surface area of the particle. This fugacity driving force was defined as the difference in the fugacity of the dissolved gas and the three-phase equilibrium fugacity at the experimental temperature. The rate constants indicated a weak dependence on the temperature.In 1994, Skovborg and Rasmussen [10] simplified the Englezos-model by assuming that the rate of hydrate formation was mass-transport limited. In that way, the need for information about the crystal size distribution was eliminated.
The experiments were performed in a semi-batch stirred reactor, and the gas consumption rate was modelled as a linear function of the difference in mole fraction of gas at the gas-liquid interface and the mole fraction in the liquid bulk phase. The rate constant was the product of the liquid side mass transfer coefficient and the total gas-liquid interfacial area in the reactor.In 1999, Herri and co-workers [7,11] published a comprehensive work based on both classical crystallization and mass transfer theory. The hydrate formation process was described by gas absorption, primary and secondary nucleation, growth, agglomeration and breakage. In a semi-batch stirred reactor of approximately 1 litre, consumption of methane gas and particle size distribution were measured with time. The influence of the stirring rate was measured and modelled, and found to be more complex than previously thought. In addition, the model predicts the development of the mean particle diameter and the total amount of particles.
An interesting study was published by Happel et al. in 1994 [12]. Hydrate equilibrium conditions, hydrate formation and melting of methane hydrates and methane-nitrogen hydrates in a CSTR of 1 litre were studied. Methane gas consumption rates were presented but no model was proposed for the hydrate formation rate. However, the experimental formation rates were found to be much higher than the experimental results of Vysniauskas and Bishnoi [8]. This led to the conclusion that applying results from batch reactors could prove difficult in design of a continuous hydrate formation reactor.
The above laboratory scale studies reveal the importance of knowing the effect of operational parameters on the gas consumption rate and the particle size distribution. However, as pointed out by Happel et al. [12], new results and new models may be necessary to describe the rate of hydrate formation for large-scale continuous reactors. In the present paper, the experimental results are presented as an empirical correlation for the rate of hydrate formation in a 9 litre CSTR. Selected results from the references reviewed above and from this study are compared, showing that there are large discrepancies between rates measured in batch reactors and in CSTRs.
Hydrate Laboratory
The Natural Gas Hydrate laboratory at NTNU was built to study production of hydrates and their properties. The laboratory is designed to operate at pressures up to 120 bar and temperatures in the range 0-20 °C. It is Ex-II classified and situated in a temperature controlled room. A schematic drawing of the hydrate laboratory is shown in Figure 1. The laboratory has a flow loop consisting of four main units: a Continuous Stirred Tank Reactor (CSTR), a separator, a shell-and-tube heat exchanger and a centrifugal circulation pump. The main units are connected with 20 mm pipes. The reactor is of standard design with four baffles and a Rushton impeller with 6 blades. Maximum rotational speed of the impeller is 2500 rpm.
In hydrate formation experiments, the circulation loop is filled with water or a mixture of water and oil. Gas is injected into the flow loop through a sparger at the bottom of the reactor, and is vented out through a gas vent line from the top of the separator. The pressure in the flow loop is kept constant with a back pressure regulator on the gas vent line. Gas volume injection rate and gas volume vent rate are measured with gas flow meters. From the difference in injection rates and vent rates, the gas consumption rates can be calculated. Pressures and temperatures are measured at various locations around the loop. All instrument output signals are transferred to a PC-based data acquisition system for analysis.
A Coriolis mass flow meter measures density and mass flow of hydrate slurry produced in the loop. In a test unit downstream the separator, variable equipment such as filters and hydrate sampler can be mounted. Also, a Tube Viscometer can be connected to the flexible hoses of the test unit which enables "in-line" pressure drop measurement of the slurry at the same conditions as in the hydrate flow loop of both oil-continuous and water-continuous hydrate slurries. Also, the horizontal pipe section can be connected directly to a gas reservoir for pressure drop measurements with various gases at different flow rates.
In a high-pressure flow cell connected at the test unit, hydrate particles can be observed. Between two parallel sapphire windows the slurry passes and can be captured at any time. Using a microscope with a maximum magnification of 2500x and an image analysing computer, the size of the hydrate particles can be determined.
Figure 1 Flow diagram of the hydrate production rig.
Rate of Formation in CSTR
Experiments were carried out to investigate the effect of pressure, temperature driving force, power consumption and gas injection rate on the methane hydrate formation rate. Prior to the experiments, the hydrate rig was filled with deaerated tap water and the water saturated with methane gas at the experimental conditions. The rate of gas consumed by the system, the gas consumption rate, was assumed to be equal to the rate of gas included in hydrate cages, the hydrate formation rate.
The experiments were carried out at constant operational pressure in the range 70 to 90 bar. Subcooling ranged from 2 to 7.5 °C. The subcooling, or the temperature driving force, is the difference between operational temperature and equilibrium temperature for methane hydrate dissociation at the operational pressure. The superficial gas velocity in the reactor was varied between 0.059
× 10-3 m/s and 0.71× 10-3 m/s at in-situ conditions.The effect of power consumption was determined indirectly by varying the impeller stirring speed between 200 and 800 rpm. For a reactor of standard geometry and at ideal conditions, a CSTR, power consumption in a liquid is [13]:
( 1 )
giving power consumption in terms of W. The volume of liquid affected by the energy dissipation is one-half of the swept-out volume of the impeller Vs [14]. The power consumption in the reactor in terms of W/kg was calculated from:
( 2 )
However, for gas-liquid systems the energy consumption decreases compared to power consumption in liquid systems. The gassed power consumption PMG is related to the ungassed power consumption PM as [15]:
( 3 )
for gas flow numbers FlG below 0.035. In all experiments, gas flow numbers were below 0.035. Gas flow number is defined as [15]:
( 4 )
The power consumption found in equation (2) was corrected for the presence of gas using equation (3).
Based on 34 experimental results from the CSTR, an empirical correlation for the formation rate of methane hydrates in the reactor was found. The gas consumption rate was found to be proportional to both pressure and superficial gas velocity at in-situ conditions. The subcooling and the power consumption were non-linear functions of the gas consumption rate, and these effects declined with increasing subcooling and power consumption. With a multiple non-linear regression program, the following correlation was found:
( 5 )
where PMG is the power consumption caused by the impeller in a gas-liquid system. PO represents other sources of mixing in the reactor and the circulation system, such as gas sparging and liquid inlet velocity. The correlation constants are given in Table 1.
Table 1 Correlation constants in equation (5)
|
Parameter |
Converged value |
95% confidence interval |
|
k |
87.60 ·10-6 |
16.37 ·10-6 |
|
a |
0.1299 |
0.03237 |
|
b |
0.1702 |
0.05910 |
Measured gas consumption rate vs. calculated gas consumption rate is shown in Figure 2. The calculated gas consumption rates are found from equation (5) using the same conditions as in the measured gas consumption rate. The resulting non-linear regression coefficient R2 is 0.9888, and nearly all the calculated consumption rates are within 20% of the measured value.
The effect of power consumption on gas consumption rate is shown in Figure 3. With increasing power consumption the gas consumption rate approaches an asymptotic value. Also, the figure shows how predicted values from equation (5) fit with the experimental data.
Comparison between measured gas consumption rate and calculated gas consumption rate from equation (5) for various experimental conditions.
Figure 3 The effect of power consumption on gas consumption rate. Experimental conditions are 90 bar and 5 °C.
Reactors compared
As reviewed above, the rate of hydrate formation, given as gas consumption rate, was measured in different laboratory facilities. The units of the experimental results were inconsistent, and had to be recalculated before they could be compared. The results could be represented in terms of normal volume of gas per time and volume of liquid [12], or in terms of amount of gas per time and volume of liquid.
Choosing the latter alternative and using the real gas law, the experimental results reported in this study were recalculated in terms of moles per second and cubic meters of water in the reactor. The Z-factor in real gas law was calculated using PVTsim 9.0 [16]. The NTNU reactor was completely filled with water, resulting in a maximum liquid volume of 0.0095m3.
Vysniauskas and Bishnoi [8] reported the accumulated consumed gas volume with time. During the first minutes of an experiment performed at 5500 kPa, 274.3 K and 400 rpm, the volume of gas consumed increased almost linearly with time. The volume of gas was converted to the amount of gas in terms of moles by using real gas law and a Z-factor calculated from PVTsim. The slope of the curve gave the gas consumption rate in terms of moles per second. This value was divided by the reactor volume, and the result is given in Table 2.
In the work by Englezos et al. [9], the accumulated number of moles of consumed gas per minute was measured. At 6.60 MPa and 1°C, the number of moles of consumed gas increased linearly with time. Thus, the gas consumption rate was found as the slope of the curve divided by the reactor volume. The result is given in Table 2.
Herri et al. [11] measure the total amount of gas consumed with time. The consumption rate at 45 bar and 1°C was given directly in the reference. The volume of liquid in the reactor was between 0.0008 and 0.0012 m3 for all experiments [1]. The volume in this experiment was assumed to be the average volume, 0.001 m3.
In the work by Happel et al. [12], the methane hydrate formation rate was given in terms of cubic centimetres at normal conditions per minute and litres of water. The rate was recalculated using real gas law with Z-factor calculated from PVTsim [16]. The temperature was given indirectly through the value of the subcooling. The equilibrium temperature at 782.7 psia was calculated using PVTsim, and the operational temperature was found by subtracting the subcooling from the equilibrium temperature.
Table 2 Rate of methane gas consumption in reactors
|
Reference |
Reactor |
Reactor volume [m3] |
Pressure [bar] |
Temper-ature [°C] |
Stirring rate [rpm] |
Gas consumption rate [mol/m3s] |
|
Vysniauskas & Bishnoi [8] |
Semi-batch |
0.0005 |
55 |
1.3 |
400 |
0.096 |
|
Englezos et al. [9] |
Semi-batch |
0.0005 |
66 |
1 |
400 |
0.078 |
|
Herri et al. [11] |
Semi-batch |
0.001 |
45 |
1 |
400 |
0.064 |
|
Happel et al. [12] |
CSTR |
0.001 |
54 |
5.3 |
* |
74.5 |
|
This study |
CSTR |
0.0095 |
70 |
6 |
400 |
1.14 |
*Somewhere in the range 400 rpm to 2250 rpm
Discussion
The gas consumption rates in the CSTRs are 1-3 orders of magnitude higher than the gas consumption rates in the semi-batch reactors, as shown in Table 2. The different consumption rates in the batch reactors and the CSTRs seem to be related primarily to the reactor system used. The CSTR is designed to promote good mixing. The gas is sparged from the bottom of the reactor resulting in high gas-liquid interfacial area, and the baffles on the inside walls increase the turbulent mixing. In addition, liquid flow into the reactor volume contributes to the mixing effect. Batch reactors usually do not have spargers and baffles, and often the impeller is not well designed. As a result, increased transfer of gas from gas phase to liquid bulk is obtained in a CSTR compared to a batch reactor, even if the stirring rates are identical.
The procedures used in the different batch experiments are similar, but differ from the procedures used for the CSTRs. The procedure used by Happel et al. [12] is similar to the procedure used in this study. Thus, the discrepancy in consumption rates may also be related to the different procedures.
In the selected results in Table 2, the temperatures in batch experiments were lower than the temperatures in the CSTR experiments. Lowering the temperature results in increased temperature driving force and thus increased hydrate formation rate. However, the formation rates in batch are much lower than the formation rates in the CSTRs, indicating that the discrepancy between the two systems is not related to temperature or temperature driving force.
The pressure in the experiment reported from the present study was higher than the pressure in the experiments reported in the literature. As shown in the empirical correlation (equation 5), the hydrate formation rate is proportional to the operational pressure. A rough extrapolation of the data down to 55 bars still gives a gas consumption rate of one order of magnitude higher than the one in reference [8]. Therefore, the high consumption rate in the present study is not primarily related to the high pressure. The result of Happel et al. at 54 bar confirms this statement.
The volume of the reactor seems to have a minor effect, because the batch experiments of Herri et al. [1] were performed with the same liquid volume as the experiments of Happel et al.. Moreover, in the present study, the reactor volume was much larger, still giving a lower consumption rate than the ones reported by Happel et al..
Summarized, the stirring and the geometry inside the reactor seem to be important while temperature and pressure can not explain the differences between the formation rates in batch reactors and CSTRs. As a consequence, models based on batch reactor experiments cannot be applicable to CSTRs because they are based on different procedures and different equipment.
The gas consumption rate reported by Happel et al. [12] is much higher than the gas consumption rate reported in the present study. There is a large uncertainty related to the value of the stirring rate in Happel’s experiments, but it was indicated that the stirring rate was much higher than 400 rpm. Also, it was pointed out that the sparger used gave optimal bubble size, and that the baffle configuration gave a more effective gas-liquid contact. However, the 9 litre reactor used in the present study had a sparger and four baffles.
In a CSTR, the superficial gas velocity is affecting the gas consumption rate, as indicated in equation (5). According to the correlation, a tenfold increase in superficial gas velocity increases the consumption rate with one order of magnitude. In this study, the in-situ superficial gas velocities were very low, and the impeller was operated in the complete dispersion regime or in the recirculating regime [15]. Under these conditions, more gas can effectively be dispersed in the liquid volume, and therefore most CSTRs are operated with higher superficial gas velocities. Most likely, the experiments reported by Happel et al. were carried out at higher superficial gas velocities, explaining the order of magnitude difference, together with the stirring rate, between the gas consumption rate in this study and in the article by Happel et al..
Conclusions
Acknowledgement
The Research Council of Norway supports the doctoral work of Marit Mork through the NATURGASS programme contract no. 125482/212.
Nomenclature
Symbols –Roman Letters
a correlation coefficient [-]
b correlation coefficient [-]
DI diameter of impeller [m]
FlG gas flow number [-]
k correlation constant [(m3 s2)/(kg °Cb)
× ( s3/m2)a], constant [-]N rotational speed of impeller [s-1]
NP power number [-]
p pressure [bar]
P power consumption/power loss [W]
PM power consumption [W/kg]
PMG power consumption, gassed conditions [W/kg]
PO power consumption, various other effects [W/kg]
q gas consumption rate/hydrate formation rate [m3/s]
QG gas flow in reactor [m3/s]
vSG superficial gas velocity [m/s]
Vs swept-out volume by impeller [m3]
Symbols -Greek Letters
r density [kg/m3]
D
T temperature driving force/subcooling [°C]Abbreviations
CSTR Continuous Stirred Tank Reactor
NTNU Norwegian University of Science and Technology
rpm revolutions per minute
References
Sloan, E.D. and Bloys, J.B. (2000). Hydrate Engineering, SPE, 21.