12^th International Oil Field Chemistry Symposium

Geilo, April 1-4, 2001

M. Mork and J. S. Gudmundsson

Department of Petroleum Engineering and Applied Geophysics

Norwegian University of Science and Technology

7491 Trondheim

The NGH (natural gas hydrate) laboratory at NTNU is described, including the continuous-stirred tank reactor (CSTR) and the Tube Viscometer. The laboratory can be operated at temperature and pressure conditions found in subsea production of oil and gas. Experimental results from the stirred tank reactor were used to find an empirical correlation for the rate of methane hydrate formation. The concept of energy dissipation was introduced for the stirred tank reactor and for fluid flow in pipelines. As a result, the empirical correlation for the rate of hydrate formation in the reactor was used to make a new empirical correlation for the rate of methane hydrate formation in pipelines. This correlation gives the maximum rate of hydrate formation in flowing mixtures of oil, gas and water in subsea pipelines. A comparison with experimental data found in the literature, shows that the new correlation gives much higher rates of hydrate formation. It is postulated that the large difference between the maximum rates given by the correlation and the measured rates reported in the literature, is the large difference in gas-liquid interfacial area. The interfacial area in a CSTR is much larger than the interfacial area in a multiphase subsea pipeline.

The formation of hydrates is a fundamental hindrance in the production of oil and gas through subsea pipelines. The oil, gas and water mixture produced at the wellhead, will normally be at a high pressure and at a moderate temperature. As the mixture flows through the subsea production system and flowlines, it cools down gradually and sometimes rapidly. The mixture will enter the hydrate formation region and the flow path may become restricted or even blocked.

To prevent hydrate problems in subsea production systems, several methods can be used. First, the freezing point of the water phase can be lowered by injecting large volumes of chemicals such as methanol. Second, small volumes of additives can be injected to prevent the agglomeration of hydrate crystals. Third, the flowline can be insulated or even heated to maintain the flowing mixture outside the hydrate formation region. In the petroleum industry, methods have been developed to determine the volume of freezing point depressant required, the volume of additive required, and the insulation and degree of heating required.

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, mass and momentum transport. 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. Momentum transport influences the overall rate of hydrate formation.

In addition to the above factors, the rate of hydrate formation depends on the - difficult to describe - nature of crystal growth, also referred to as chemical reaction kinetics. The overall rate of hydrate formation in subsea production systems, 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.

NTNU has carried out extensive studies on hydrate technology for the storage and transport of natural gas, with stranded gas in focus (Gudmundsson et al., 1999a, 1999b, 1999c). As a part of this work, the rate of hydrate formation in a continuous-stirred tank reactor has been studied. The experiments were performed at conditions planned in FPSO-based and land-based process plants for production of natural gas hydrate, at pressure from 60 to 90 bar and temperature from 5 to 15 °C. In this paper, we have applied the experimental results to hydrate formation in subsea equipment and flowlines.

The Natural Gas Hydrate laboratory at NTNU was built to study the 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 rate 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.

Figure 1: Flow diagram of the hydrate production rig.

Figure 2: Flow diagram of the Tube Viscometer.

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. The Tube Viscometer is shown schematically in Figure 2. It consists of two horizontal pipes connected in series. With differential pressure transducers, the pressure drop is measured over the two pipe sections of 4 meters each. Combining the Tube Viscometer with the hydrate production rig enables "in-line" pressure drop measurement at the same conditions as in the hydrate flow loop of both oil-continuous and water-continuous hydrate slurries. Andersson (1999) and Andersson and Gudmundsson (1999a, 1999b) measured various flow properties of hydrate slurries using the tube viscometer. 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 stirred tank reactor, the rotating impeller dissipates power. First, mechanical energy is transferred from the impeller to the fluid causing fluid motion, then the energy dissipates in the fluid. For a reactor of standard geometry and at ideal conditions, power consumption in a liquid is (Oldshue, 1983):

( 1 )

giving power consumption in terms of W.

For a stirred tank reactor, Davies (1987) defines the volume where energy dissipation occurs as one-half of the swept-out volume of the impeller:

( 2 )

Then, the power consumption in a stirred tank reactor in terms of W/kg becomes:

( 3 )

Similarly, in a pipeline the energy dissipation is mainly due to frictional pressure drop. Assuming steady state flow, power loss is related to frictional pressure drop as:

( 4 )

and in terms of W/kg:

( 5 )

The pressure loss can be expressed by the Darcy-Weisbach equation:

( 6 )

Substituting into the power loss equation (5), the following relationship for the energy dissipated in a pipe in terms of W/kg emerges:

( 7 )

Experiments have been carried out to investigate the effect of pressure, temperature driving force, power consumption and gas injection rate on the methane hydrate formation rate (Parlaktuna and Gudmundsson, 1998a, 1998b). In the experiments, water was contacted with methane gas in the stirred tank reactor. Prior to the experiments, the hydrate rig was filled with deaerated tap water, where the water was saturated with methane gas at the experimental conditions. Therefore, the rate of gas consumed by the system, the gas consumption rate, is equal to the rate of gas included in hydrate cages, the hydrate formation rate. From the experimental data, we derived an empirical correlation for the gas consumption rate.

All 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 effect of power consumption was determined indirectly by varying the impeller stirring speed between 200 and 800 rpm. For liquids, power consumption is derived directly from equation (1). However, for gas-liquid systems the gassed power consumption P_G is related to the ungassed power consumption P_U as (Whitton, 1992):

( 8 )

for gas flow numbers Fl_G below 0.035. In all experiments, gas flow numbers were below 0.035. Gas flow number is defined as (Whitton, 1992):

( 9 )

The gassed power consumption was converted to energy dissipation rate in terms of W/kg given by equation (3).

Based on the experimental results from the CSTR, we propose an empirical correlation to represent the formation rate of methane hydrates in the reactor. The gas consumption rate was taken to be proportional to both pressure and superficial gas velocity at in-situ conditions. Increases in subcooling and power consumption result in an increase in gas consumption rate, but these effects seem to decline with increasing subcooling and power consumption. With a multiple non-linear regression program, we found the following correlation:

( 10 )

where k is 8.710·10^-5, a is 0.1299 and b is 0.1702. P_MG is the energy dissipation rate caused by the impeller in a gas-liquid system. P_O represents other sources of mixing in the reactor and the circulation system, such as gas sparging and liquid inlet velocity.

Figure 3 shows a plot of measured gas consumption rate vs. calculated gas consumption rate. The calculated gas consumption rates are found from equation (10) using the same conditions as in the appurtenant 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.

In Figure 4, the energy dissipation rate vs. gas consumption rate is shown. With increasing energy dissipation rate the gas consumption rate seems to approach an asymptotic value. Also, the figure shows how predicted values from equation (10) fit with the experimental data.

Figure 3: Comparison between measured gas consumption rate and calculated gas consumption rate from equation (10) for various experimental conditions.

Figure 4: The effect of energy dissipation rate on gas consumption rate. Experimental conditions are 90 bar and 5 °C.

Under certain conditions, the experimentally determined correlation for methane hydrate formation rate in a stirred tank reactor may be suitable for prediction of methane hydrate formation rate in a pipeline. In the reactor, turbulent mixing of the content occurs mainly due to stirring by the impeller. The same conditions are obtained in a pipeline with turbulent flow where the turbulent eddies cause mixing of oil, gas and water. Lippmann et al. (1995) indicate that hydrate formation rate in a pipeline increases strongly with flow velocity because enhanced gas entrainment into water takes place, and because subcritical hydrate nuclei agglomerate more easily.

We propose that the power supplied from an impeller is similar to the power supplied from friction loss in a pipeline, referring to equations (3) and (7), respectively. As a result, the following relationship emerges by substituting equation (7) into equation (10):

( 11 )

and by assuming that the power supplied to the turbulent eddies in the gas-liquid mixture in the pipeline is from the friction power loss only.

Ideally, in a CSTR gas and liquid are perfectly mixed, and we can therefore assume that gas and liquid is a homogeneous mixture. In a pipeline under conditions of bubbly flow, gas is homogeneously dispersed in the liquid and void fraction is normally less than 0.3 (Whalley, 1987). In all the reactor experiments, void fraction was well below this limit. Using a homogeneous two-phase flow model, we assume that both phases travel with equal velocity, and thus:

( 12 )

where u_M is the average velocity of the mixture and constants are the same as those for equation (10). From this equation it follows that the density of a gas, oil and water mixture is:

( 13 )

where is the density of the oil/water mixture. Equation (12) can be used for prediction of the methane hydrate formation rate in a pipeline with homogeneous bubbly flow. However, the use of this equation is also limited by other assumptions.

We assume that the hydrate formation rate is not heat transfer limited. Furthermore, pressure and temperature conditions must be within the hydrate formation region, and all the parameters in equation (12) must lie within the range of the experimental conditions on which the correlation in equation (10) is based.

In the reactor experiments, gas was supplied from an external gas reservoir. For a pipeline, both the oil phase and the water phase are saturated with methane gas. When hydrates are formed in the water phase or at the gas-water interface, the pressure is reduced. Then, gas is flashed from the oil and more gas is transported to the water phase and converted to hydrate. This will occur as long as water is saturated with gas, or as long as gas and water are available for further hydrate formation.

In Figure 5, we have used equation (12) to estimate the methane hydrate formation rate in a pipeline. The figure shows how the gas consumption rate will vary with both flow velocity and diameter of pipe in a multiphase pipeline assuming an average pressure of 90 bar, and an average temperature of 5°C. The gas consumption rate increases nearly proportionally with flow velocity, u_M, but decreases slightly with an increase in pipeline diameter, D.

Based on the empirical correlation for rate of methane hydrate formation in a CSTR (equation 10), a new empirical correlation for the rate of methane hydrate formation in pipelines was found (equation 12). In a CSTR, ideal mixing conditions are approached. Usually, this is not obtained in a pipeline. Because of intensive stirring in a CSTR, the gas-liquid interfacial area is normally very large, enabling good mass transfer. Usually, mass transfer is the limiting step in hydrate formation (Skovborg and Rasmussen, 1994), and therefore, reduced mass transfer results in reduced overall rate of hydrate formation. Also, limited heat transfer will reduce the hydrate formation rate. Consequently, our empirical correlation for hydrate formation rate in pipeline represents the maximum attainable hydrate formation rate.

Figure 5: Gas consumption rate in pipeline vs. velocity of mixture and diameter of pipeline (from equation (12)). Void fraction of 0.01 and friction factor of 0.02 are assumed.

Lippmann et al. (1995) and Gaillard et al. (1999) have studied the rate of hydrate formation in equipment resembling a pipeline. Lippmann et al. (1995) performed experiments with natural gas and water in a rotating wheel simulating slug flow. Gaillard et al. (1999) investigated the hydrate formation rate in a flow loop with a mixture of gas, oil and water. A circulation pump and the turbulent eddies in the loop provided mixing. In both references, it is pointed out that velocity is an important mixing parameter. Our correlation for hydrate formation rate in a pipeline seems to overestimate the hydrate formation rate by 1 to 2 orders of magnitude compared to the results in the literature. However, the discrepancy depends on the values of void fraction and friction factor, which had to be assumed for the comparison. While we have assumed homogeneous flow, results from Lippmann et al. are for slug flow. For slug flow, the gas-liquid interfacial area is expected to be lower than the interfacial area for homogeneous bubbly flow. The type of flow regime may have a significant effect on the rate of hydrate formation.

We have found that the rate of hydrate formation in a pipeline is governed by the parameters shown in equation (12). Laboratory and field tests could confirm this result. With a calibration factor, which is probably less than 1, the correlation for rate of hydrate formation in a pipeline could be fitted with experimental data from a pipeline.

The NTNU natural gas hydrate laboratory can be used to study the formation rate of solid hydrates and their flowing properties at conditions similar to those found in subsea production systems. Based on experimental work carried out to study the production rate of hydrates for storage and transport of gas, an empirical correlation was obtained for the rate of methane hydrate formation in a stirred tank reactor.

The concept of energy dissipation in terms of W/kg was used to couple the rate of hydrate formation in a stirred tank reactor and the rate of formation in a subsea pipeline. The stirring action was considered equivalent to the effect of frictional pressure drop in a pipeline. An empirical correlation was obtained for the rate of methane hydrate formation in a pipeline. The assumptions used to arrive at the correlation denote that the rate of hydrate formation obtained is the maximum rate.

A comparison was made between the empirical correlation and the rate of hydrate formation in two independent experimental facilities. It was found that the empirical correlation overestimated the rate of hydrate formation by 1-2 orders of magnitude. The large discrepancy was explained by the large difference in contact area between small bubbles in a stirred reactor compared to bubbles in pipeline flow.

The Research Council of Norway supports the doctoral work of Marit Mork through the NATURGASS programme contract no. 125482/212.

Symbols –Roman letters

a correlation coefficient [-]

A area of pipeline [m]

b correlation coefficient [-]

D diameter of pipeline [m]

D_I diameter of impeller [m]

¦ friction factor [-]

Fl_G gas flow number [-]

k correlation constant [(m³ s²)/(kg °C^b)× ( s³/m²)^a], constant [-]

L length of pipeline [m]

N rotational speed of impeller [s^-1]

N_P power number [-]

p pressure [bar]

P power consumption/power loss [W]

P_G gassed power consumption [W]

P_M power consumption/energy dissipation rate [W/kg]

P_MG power consumption/energy dissipation rate, gassed conditions [W/kg]

P_O power consumption/energy dissipation rate, various other effects [W/kg]

P_U ungassed power consumption [W]

q gas consumption rate/hydrate formation rate [m³/s]

Q_G gas flow in reactor [m³/s]

u liquid velocity [m]

u_M velocity of homogeneous mixture [m/s]

v_SG superficial gas velocity [m/s]

v_SL superficial liquid velocity [m/s]

V_s swept-out volume by impeller [m³]

W impeller blade width [m]

Symbols -Greek letters

a void fraction [-]

D p frictional pressure drop [Pa]

r density [kg/m³]

r _G density of gas phase [kg/m³]

r _L density of liquid phase [kg/m³]

D T temperature driving force/subcooling [°C]

Abbreviations

CSTR Continuous-Stirred Tank Reactor

NGH Natural Gas Hydrate

NTNU Norwegian University of Science and Technology

rpm revolutions per minute

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