Broad-Band Permittivity Measurements of Formation of Gas Hydrate

Subscriber access provided by Northern Illinois University

Article

Broad-band permittivity measurements of formation of gas hydrate layers using open-ended coaxial probes Kjetil Haukalid, and Kjetil Folgerø Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b01534 • Publication Date (Web): 16 Aug 2016 Downloaded from http://pubs.acs.org on August 17, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Broad-band permittivity measurements of formation of gas hydrate layers using open-ended coaxial probes Kjetil Haukalid*†# and Kjetil Folgerø, ‡ † Department of Physics and Technology, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway, E-mail: [email protected], Fax: +47 55 58 94 40 ‡Christian Michelsen Research AS, P.O. Box 6031, NO-5892 Bergen, Norway

ABSTRACT

Careful measures are taken in the oil and gas industry to avoid the formation of gas hydrate plugs. However, the risk of inhibitor failure, unexpected process changes and more frequent transport of under-inhibited well streams calls for methods to monitor gas hydrate formation. In gas-dominated systems, hydrate plug formation is believed to be initiated by formation of hydrate layers on the pipeline wall. The permittivity spectra of gas hydrates differ from those of water, oil and gas. Hence, a potential approach to detect early stages of plug formation in gasdominated systems (i.e.: before hydrates become a threat to flow assurance) is to monitor the permittivity of the flow close to the pipeline wall. Such technology is also valuable for lab-scale studies on plug formation mechanisms in gas-dominated systems. This paper presents broad-

ACS Paragon Plus Environment

1

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 37

band permittivity measurements on gas hydrate layers using open-ended coaxial probes. Experiments are conducted both at atmospheric conditions, using tetrahydrofuran as the hydrate former, and at high pressures, using a mix of methane and propane as the hydrate former. Measurements on ice layers are included for comparison. Formation of hydrate layers thinner than 1 mm is shown to be easily detected.

INTRODUCTION Gas hydrates are ice-like clathrate compounds where hydrogen bonded water molecules form a lattice of polyhedral cages trapping small gas molecules.1 Hydrates are stable at high pressures and low temperatures and are therefore likely to form in oil and gas production pipelines. If formed, hydrates may eventually plug a pipeline, a scenario that the oil and gas industry takes careful measures to avoid. Hydrate formation is normally inhibited through thermodynamic means, i.e., by keeping the pressure and temperature conditions in the pipeline outside the hydrate stability zone. Hydrate inhibition represent a considerable expense and might ruin the profitability for marginal oil fields.2 Although the formation of hydrate plugs is a rare operational event, the risk of inhibition failure, abrupt process changes and more frequent transport of underinhibited well streams calls for methods for monitoring hydrate formation and build-up. Such technology would also be valuable to the hydrate research community, keeping in mind that hydrate deposition on pipeline walls is still a poorly understood phenomenon.3-8 This paper describes a permittivity based measurement system for the detection and characterization of hydrate deposits on pipeline walls. To the best of our knowledge, no on-line applications of permittivity measurements on hydrate build-up or similar deposits (like wax, scale or asphaltenes) are reported in the literature. However, techniques for the detection and


2

Page 3 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

characterization of pipeline deposits based on other measurement principles have been reported. These include gamma-ray methods,9 radioisotope tracer injection,10 acoustic techniques,11-14 pressure drop methods,15 heat transfer methods16,17 and neutron backscatter methods.18 Permittivity measurements are complementary to these techniques and can even be used for stand-alone sensors. The permittivity spectrum of gas hydrates differs significantly from that of crude oil, gas and water (see Figure 1). Thus, dielectric spectroscopy is considered to be an adequate measurement method for the detection and characterization of hydrate formation. Hydrate formation in oildominated emulsified systems has previously been studied by permittivity measurements with open-ended coaxial probes,19-21 but no work has been reported for gas-dominated systems. Formation of hydrate plugs in gas-dominated pipelines is believed to be initiated by the formation of hydrate layers on the pipeline wall, either through annular growth or through adhesion of hydrate particles originally formed in the bulk.22 The hydrate layer is believed to eventually collapse into large hydrate aggregates, which might form a plug downstream. Thus, early detection of plug formation risk might be achieved by monitoring the permittivity close to the pipeline wall. Open-ended coaxial probes are well suited to do this as they can be mounted non-intrusively in the pipeline wall and sense the permittivity in a limited volume close to the wall. Moreover, broad-band permittivity measurements can be obtained with open-ended coaxial probes. This is important, as the permittivity spectra contain valuable information not obtainable from single-frequency measurements. Due to its simple design, open-ended coaxial probes can be made very robust and thus suitable for on-line measurements under rough conditions (e.g. high pressures and high temperatures23-27). These features make the probes suitable for use at


3

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 37

petroleum installations. The probes used in this work are currently designed to withstand pressures up to 150 bar. The potential of using open-ended coaxial probes for the detection and characterization (e.g. estimation of hydrate fraction and layer thickness) of hydrate deposit layers is verified in this paper by measurements on ice and gas hydrate layers. The build-up of hydrate layers is similar to build-up of ice layers. A series of experiments are therefore done on ice layers for comparison with the hydrate experiments. Using ice, it is also quite easy to produce dense and well defined layers. Hence, these measurements are adequate for the characterization of the measurement system. A second series of experiments are done with tetrahydrofuran (THF) as the hydrate former. THF is water soluble and forms hydrates that are stable below 4.4 °C at atmospheric pressure. This property makes it possible to produce repeatable and well-defined experiments including well-defined layer thicknesses. A final experiment is done in a pressurized pipe, using a mix of methane and propane as hydrate former. This experiment verifies the capability of the measurement system to detect and characterize gas hydrate layers under realistic conditions. THEORY In general, the permittivity is a complex variable and is normally defined relative to the permittivity of vacuum ∗ = − (1) where is the permittivity of vacuum, ∗ is the complex relative permittivity with real ( ) and imaginary ( ) parts, and is the imaginary unit. In literature, and are normally referred to as the dielectric constant and the loss factor, respectively. In this work the term complex permittivity is used to refer to the complex relative permittivity ( ∗ ), while the term permittivity


4

Page 5 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

is used as a more general term. The complex permittivity is a frequency dependent parameter. Typical variation with frequency are shown for gas hydrates, ice, water, oil and gas in Figure 1. For oil and gas, the variation with frequency is negligible compared to the scale. The huge drops in the dielectric constant with increasing frequency, which are accompanied by an increase in the loss factor, are referred to as dielectric dispersions. The frequency where the loss factor reaches a maximum is referred to as the dispersion frequency. The magnitude of the drop the dielectric constant experiences during a dielectric dispersion is referred to as the dispersion strength. For many materials, the frequency behavior of the complex permittivity is well described by the Cole-Cole equation28

∗ = + −

(2)

where is the low frequency (static) dielectric constant, is the high frequency (optical) dielectric constant, is the relaxation time (s), is the distribution factor, is the direct current (dc) conductivity (S/m), and is the angular frequency (rad/s). The relaxation time is defined as = 1⁄2!"# , where "# is the dispersion frequency. The dispersion strength is defined as % = − . If a material experiences multiple dielectric dispersions equation (2) can be extended to &

&

&

∗ = + + ' ' + ⋯ + ) ) −

'

)

(3)

The effective permittivity of a mixture of materials or fluids can be estimated from composition information such as volume fraction. In this work, Hanai’s29 generalization of Bruggeman’s equation for two-phase mixtures is used to model the mixture of hydrates and liquid, where the liquid is either water or a solution of water and tetrahydrofuran. In this model, the volume fraction, *, of the dispersed phase is given as


5

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

* = 1−

∗ ∗ +, .,/

∗ ∗ +, 01)2

∗ 01)2

3

∗ .,/

⁄5

4

Page 6 of 37

(4)

∗ ∗ where 6789 is the complex permittivity of the continuous phase, #: is the complex ∗ permittivity of the dispersed phase, and ;< is the effective complex permittivity of the mixture.

EXPERIMENTAL An open-ended coaxial probe is basically composed of a coaxial transmission line with an electrically open end (see Figure 2). The material under test (MUT) is placed in front of the probe aperture. Signals transmitted to the probe are almost totally reflected at the probe aperture due to the severe impedance mismatch. Thus, only a fringing field penetrates the MUT. The amplitude and phase of the reflected signal are dependent on the permittivity of the MUT, making the probe suitable for permittivity measurements. The fringing field decays rapidly in strength with distance from the probe aperture. Consequently, the probe is decreasingly sensitive to changes in the MUT’s permittivity with increasing distance from probe aperture. This feature makes the probe suitable for measurements on thin layers. The term sensitivity depth is often used to denote the distance from the probe aperture beyond which changes in the MUT’s permittivity is not sensed by the probe. Depending on definition, the sensitivity depth is about the size of the outer conductor radius. Two custom-built open-ended coaxial probes (see Figure 3) designed to withstand pressures up to 150 bar were used in the experiments. The probe aperture dimensions are summarized in Table 1. The probes were connected through high quality coaxial cables to a vector network analyzer (VNA) for measurement. The reflection coefficient was measured over a broad frequency range (typically 1 MHz – 13.6 GHz). The effective permittivity of the MUT was calculated from the measured reflection coefficient using the method described by Folgerø and


6

Page 7 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Tjomsland.30 This method necessitates reference measurements on three fluids with known permittivity in order to characterize the probe. Laboratory measurements of air, methanol and doubly distilled water were used for reference. The VNA was calibrated prior to each experiment, after allowing temperature of probes, cables, etc. to stabilize at the experimental temperature. Measurements on ice layers. The two probes were mounted in a flange at the end of a short pipeline section (see Figure 4) and placed inside an environmental chamber. The VNA was placed outside the chamber with the coaxial cables led through the chamber wall. The chamber temperature was set to -17 °C. Tap water was sprayed inside the flange using a squirt bottle with a fine misting nozzle. The water was allowed to freeze completely to ice between each spray. The ice layer was very dense as judged by visual observations. The amount of trapped air in the layer is assumed to be negligible. The thickness of ice layer in front of each probe was estimated after each spray series by measuring the thickness of the flange plus the ice layer with a caliper, at several positions near each probe. The mean values are used as reference thickness for the ice layer. Hydrate experiments at atmospheric conditions. Natural gases occurring in oil and gas reservoirs do not form hydrates at atmospheric conditions if the temperature is above 0 °C. Tetrahydrofuran (THF), a water miscible colorless liquid that forms hydrates that are stable below 4.4 °C at atmospheric pressure, was therefore used as hydrate former in the measurements performed at atmospheric conditions. THF forms structure II hydrates with 17 water molecules per THF molecule if the large cages in the structure are fully occupied. Solutions of water (doubly distilled) and THF with molar ratio 17:1 were therefore used to minimize the amount of excess fluid. THF (>99%) was purchased from Sigma Aldrich and used as is. In one experiment,


7

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 37

saline water (NaCl solution) with concentration 0.1 mol/l was used instead of doubly distilled water. The probes were mounted in a brass plate through threaded holes (see Figure 5). A Plexiglas cylinder was glued to the brass plate to serve as liquid container. Layer thickness was controlled by adding known volumes of fluid to the cylinder, or by placing a plastic (polyoxymethylene) block on spacers on the brass plate (see Figure 5). The probe/brass plate/Plexiglas cylinder assembly was placed in an environmental chamber for temperature control. The chamber temperature was set to 0.5 °C unless otherwise is specified. An experiment was initiated by adding a known volume of water/THF solution to the cylinder. A plastic film was fitted to the top of the cylinder using a rubber band, in order to minimize evaporation. Hydrate formation eventually started spontaneously, but was expedited in some experiments by adding a small amount of ice to the water/THF solution. Hydrate experiments in high pressure system. A 1 m long 3’’ steel pipe is the main constituent of the high pressure system (see Figure 6). The apparatus has been designed by SINTEF Petroleum Research.31 Its primary use is to produce hydrate plugs for melting studies. The steel pipe can be pressurized and rotated about its axis. The maximum operational pressure is 100 bar. The apparatus is operated by first injecting a small amount of water and then pressurizing the pipe with a hydrate forming gas. Inlet lines are then decoupled, and the pipe is rotated while hydrate formation takes place. Rotation speed is approximately 60 rpm. The purpose of rotating the pipe is to ensure that the hydrates form a layer around the pipe wall. Eventually most of the injected water is converted into hydrates. This procedure is repeated until the desired layer thickness is achieved. Tap water and a mixture of methane and propane (92 %


8

Page 9 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

and 8 % by weight, respectively) were used in the experiments. Methane-propane mixtures form structure II hydrates.32 The apparatus was placed in an environmental chamber, and the chamber temperature was set to 2 °C. The apparatus is equipped with a gamma densitometer to monitor layer build-up during hydrate formation. Layer thickness is calculated assuming there is no free gas in the hydrate layer. The densitometer is mounted on rails to allow measurement along the pipe length. However, after mounting the probes in the pipe it was difficult to move the densitometer past the probes, and it was therefore kept stationary during the experiment. Previous experiments conducted in the apparatus have shown that the layer thickness initially increases faster at the outlet side of the pipe compared to the inlet side, and that a significant difference in layer thickness persists until the pipe approaches maximum filling.31 The two probes were mounted mid pipe (with the probe aperture aligned with the inner pipe wall). The densitometer was placed between the probes and the outlet end of the pipe. Hence, the hydrate layer in front of the probes is expected to be somewhat thinner than the layer seen by the densitometer. The apparatus has previously been applied for melting studies of hydrate plugs.31 Using the same experimental procedure as in the reported measurements, the gamma densitometer indicated negligible gas entrainment in the final plug. Thus, we assume that gas entrainment had small or negligible influence on the reported measurements. Hydrate formation can be a time consuming process even though the temperature and pressure conditions are within the stability range for hydrate formation. E.g., if some liquid water is trapped within the hydrate layer, further hydrate formation here is slowed or hindered due to the need of transport of gas molecules through the hydrate layer. The permittivity measurements


9

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 37

were conducted prior to each injection of water, i.e. when the amount of liquid water still present in the hydrate layer (after the former injections) is expected to be low. The coaxial cables were disconnected from the probes during rotation. Care must therefore be taken in order to ensure as good repeatability as possible. The probes are equipped with high quality connectors and a torque wrench is used for tightening the connectors. Cables are moved as little as possible between each measurement. However, the accuracy of the permittivity measurement system was reduced compared to the static set-up used at atmospheric pressures, and the lower operating frequency was therefore limited to 100 MHz for these experiments. RESULTS AND DISCUSSION Measurements on ice layers. Figure 7 shows measured dielectric constant ( ) at 1 GHz as function of ice layer thickness for both probes. For the permittivity measurement there are two main contributions to the uncertainty in this frequency range: Random errors attributed to the repeatability of the coaxial connectors fitted to the probes, the coaxial cables, the VNA and the VNA calibration kit, and systematic errors attributed to the three reference measurements. See e.g. Nyshadham et al.33 for a more detailed uncertainty analysis for open-ended coaxial probes. The uncertainty contributions from the random and systematic errors are estimated to 1,5 % and 2 %, respectively. The uncertainty evaluation is based on previous measurement data obtained with the applied (and similar) probes, and on experience with and general knowledge of the applied measurement technology (with reference to ISO GUM).34 The uncertainty of the layer thickness is attributed to the uncertainty of the caliper (estimated to 0.1 mm), the roughness of the layer (uncertainty contribution estimated to 0.1 mm) and to the averaging method (uncertainty contribution estimated to 10 % of the layer thickness), keeping in mind that the


10

Page 11 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

reference thickness is an average value of the measured thickness at several positions near the respective probes. The dashed lines show equation (5) fitted to the measured dielectric constants. The sensitivity depth of probe A and probe B is approximately 5 mm and 2.5 mm, respectively. Thus, for most measurements the layer thickness is within the sensitivity depth of both probes. ≈ 1) and more ice (6? ≈ 3.15) as the layer grows thicker. For The probes sense less air (=>

small layer thicknesses, the measured dielectric constant increases fast, demonstrating the capability of the probe to detect very thin layers. As the layer thicknesses approaches the probes’ respective sensitivity depths, the measured dielectric constants converge towards a value close to the dielectric constant of ice. Probe A has greater sensitivity depth than probe B, and it is therefore able to sense changes in layer thickness at greater depths. The characteristic variation with layer thickness results from the nature of the open-ended coaxial probe, being decreasingly sensitive to changes in the MUT’s permittivity with increasing distance from the probe aperture. This variation with layer thickness has previously been showed to be approximated by the following relation30 ?@@ = A1 − B #⁄C D + E ∙ B #⁄C

(5)

where ?@@ is the measured effective dielectric constant, is the layer dielectric constant, E is

the backing material dielectric constant, G is the layer thickness and H is an empirical constant that is proportional with the sensitivity depth. The dashed lines in Figure 7 shows agreement of equation (5) to the measured dielectric constants when using a fitted value for D. By isolating G from equation (5), it is possible to estimate the layer thickness, if the dielectric constant of the layer and the backing material is known. Figure 8 shows comparison of estimated layer thickness and the manually measured layer thickness. Good agreement is achieved. The uncertainty increases as the layer thickness approaches the respective sensitivity depths of the probes.


11

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 37

Hydrate experiments at atmospheric conditions. In the first part of this section, formation of a 3 mm thick THF-hydrate layer (the volume of water/THF solution added to the cylinder corresponds to 3 mm layer thickness) is studied. The second part of the section concerns variation of the complex permittivity of THF hydrates with temperature. In the last part of the section formation of hydrate layers with different thickness is studied. Figure 9(a) shows the measured dielectric constant ( ) at 100 MHz as function of time during hydrate formation in the 3 mm thick layer. Equation (3) has been fitted to the measured complex permittivity spectra, with two dielectric dispersions and with set to 0 S/m, hence &

&

∗ = + + ' '

'

(6)

Figure 9(b-f) shows the fitted dispersion strengths (∆ and ∆E), relaxation times ( and E ) and distribution factors ( and E ) corresponding to the single frequency measurements in Figure 9(a). Below, the single frequency measurements (Figure 9(a)) are discussed first. Then complex permittivity spectra obtained before, during and after hydrate formation are presented (Figure 10). The section continues with discussing the fitting of equation (6) to the complex permittivity spectra (Figure 9(b-f)). Finally, equation (4) is used to estimate the hydrate fraction in the layer as function of time (Figure 12). The dielectric constant at 100 MHz measured with probe A and probe C is initially (i.e.: before hydrate formation) 69 and 73, respectively. From the measurements on ice layers it can be observed that the layer thickness of 3 mm is within the sensitivity depth of probe A, but thicker than the sensitivity depth of probe B (see Figure 7). Thus, only probe A senses some of the air above the liquid layer. Probe A therefore measures a lower dielectric constant than the liquid dielectric constant, while probe B measures the liquid dielectric constant. When hydrates start to


12

Page 13 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

form in front of the probes, the measured dielectric constant drops markedly and eventually stabilizes at a much lower level (′ ≈ 5.2). At 100 MHz and 0.5 °C the dielectric constant of the water/THF solution (′ ≈ 73) is much higher than the dielectric constant of THF-hydrates (′ ≈ 4).35,36 Consequently, since hydrate formation consumes water/THF solution the measured dielectric constant drops upon hydrate formation. Figure 10 shows three complex permittivity spectra measured with probe B before hydrate formation, during hydrate formation and after complete hydrate formation, respectively. The three spectra correspond to the labels T1 (4 minutes after startup), T2 (10 minutes after startup) and T3 (45 minutes after startup) in Figure 9(a). The dashed black curves show fittings of equation (4) to the measured spectra. Equation (4) is used for hydrate fraction estimation below. The measured spectra become increasingly noisy with decreasing frequency. This is because the sensitivity of open-ended coaxial probes applied for reflection measurements decreases at low frequencies.19 In the measured permittivity spectrum obtained during hydrate formation (T2) two dielectric dispersions are observed: The dielectric dispersion around 9 GHz is due to the dielectric dispersion of water (water dispersion), while the dielectric dispersion around 3 MHz is due to the dielectric dispersion of THF-hydrates (hydrate dispersion). Before hydrate formation (T1), only the water dispersion is observed. After completion of hydrate formation (T3), only the hydrate dispersion can be observed. Figure 9(b-f) shows how the (fitted) dispersion strengths (∆ and ∆E), relaxation times ( and E ) and distribution factors ( and E ) vary as function of time. The uncertainty of the fitted parameters increases with decreasing dispersion strength of the respective dispersion. The fitted dispersion strength and the corresponding relaxation time and distribution factor are not shown in the figure if the fitted dispersion strength is lower than 10. The fitted parameters


13

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 37

corresponding to the hydrate dispersion (∆ , and ) are plotted with open circles, while open diamonds are used for the water dispersion (∆E , E and E ). The permittivity spectra obtained with probe A are erroneous in the frequency range of the water dispersion if thin layers are examined. This is due to reflections from the interface between the layer and the backing air. The smaller probe B radiates much less than the larger probe A, which reduces these reflections significantly. The large variations in the fitted relaxation time (E ) and distribution factor (E ) for probe A are caused by the erroneous spectra. The hydrate dispersion strength (∆) increases during hydrate formation, while the opposite is observed for the water dispersion (∆E). Thus, the broad-band permittivity measurements confirm what the single frequency measurements indicate, namely that the volume fraction of hydrates increases and the volume fraction of water decreases during hydrate formation. If only the single frequency measurements had been studied and if the layer thickness had been unknown and possibly varying, it would be hard to determine if the observed decrease in measured dielectric constant was due to hydrate formation or due to decreasing layer thickness. However, by studying the variation in the measured permittivity spectra over time it is revealed that hydrate formation is occurring. Figure 9(d) and 9(f) show how the (fitted) relaxation times vary through the experiment. The relaxation time of the water dispersion shows negligible variations within the experimental error. The hydrate dispersion relaxation time increases slightly during hydrate formation and seems to stabilize around 60 ns, which corresponds well with Hawkins’ and Davidson’s data36 for THFhydrates extrapolated to 0.5 °C. The observed variations are relatively small, and they are most likely caused by measurement error, keeping in mind that the permittivity spectra are noisy and prone to errors in the frequency range of the hydrate dispersion. The fitted distribution factor of


14

Page 15 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

the hydrate dispersion ( ) is zero within the experimental error through the entire experiment for both probes. For probe A, the water distribution factor (E ), deviates significantly from zero, but this is due to the erroneous spectra caused by the reflections from the interface between the layer and the backing air. By assuming that THF hydrates are dispersed in a continuous liquid phase of THF/watersolution, the volume fraction of hydrates can be estimated using equation (4). As shown in Figure 10, a volume fraction of 25 % hydrates in liquid gives a model spectrum (black dashed curve) that corresponds well with the measured permittivity spectra during hydrate formation (T2). The model spectrum is calculated assuming a liquid permittivity as measured before hydrate formation (T1) and hydrate permittivity given by Cole-Cole parameters = 60.7, = 4.0, = 55 ns and =0.01. These parameters were found by extrapolating Hawkins’ and Davidson’s data36 to 0.5 °C. Some small deviations between the model spectrum and the measured spectrum are observed at high frequencies. This is probably due to the afore mentioned reflections from layer – air interface, which are present but much weaker for the smaller probe B than the larger probe A. In the permittivity spectrum measured after completion of hydrate formation (T3), only the hydrate dispersion can be observed. However, the measured high frequency dielectric constant ( ≈ 5.2) is above the literature value for THF hydrates ( ≈ 4), indicating that a small amount of excess liquid is present in the hydrate layer. The volume fraction of remaining liquid is estimated to be approximately 5 % using equation (4). It can be questioned whether it is a valid assumption that the layer is liquid continuous when the liquid volume fraction is only 5%. Measurements on snow show that the transition from dry snow to liquid continuous wet snow (pendular to funicular transition) occurs at liquid volume fractions in the range 3-8 %.37,38


15

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 37

Although not directly transferable to hydrate layers, this observation supports the assumption that layers may be liquid-continuous even for small fractions of water. In addition, this assumption is supported by a similar experiment performed with saline water and THF (see Figure 11). Here, a dc-conductivity is observed as a very sharp increase in the loss factor (") with decreasing frequencies below 100 MHz (explained by the last term in equation (2)). By fitting the measured permittivity spectrum to the Cole-Cole model (equation (6)) and HanaiBruggeman’s model (equation (4)), the remaining liquid fraction and liquid conductivity are estimated to *NO ≈ 5 % and NO ≈2 S/m, respectively, in this experiment. A dc-conductivity in this range can only be explained by a liquid-continuous or bi-continuous layer. Figure 12 shows the calculated hydrate fraction in the 3 mm thick layer as function of time. The hydrate fraction has been calculated from the measured layer permittivity using equation (4). For probe B, the layer permittivity is equal to the measured permittivity, while probe A also senses the backing air. For probe A, the layer permittivity can be estimated by isolating from equation (5). The final hydrate fraction is around 95 % in front of both probes. In the second part of this section variation of the complex permittivity of THF-hydrates with temperature is studied. As already shown above, measuring the permittivity over a broad frequency range may reveal important information not obtainable from single frequency measurements. Figure 13 shows three complex permittivity spectra (1 MHz – 13.6 GHz) obtained with probe A for a 20 mm thick hydrate layer at three different temperatures (0.5 °C, 10 °C and -20 °C). The hydrate layer was initially formed at 0.5 °C, before the temperature was lowered to -10 °C and -20 °C. Only the hydrate dispersion can be observed, as most of the water has been converted to hydrates. By using equation (4), the amount of excess water is estimated to


16

Page 17 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

5 % at 0.5 °C. Figure 14 shows the fitted dispersion strength (% ) and relaxation time ( ) of the hydrate dispersion as function of time for the part of the experiment when the temperature was varied. The relaxation time increases with decreasing temperature. Hence, the hydrate dispersion moves towards lower frequencies with decreasing temperature. This can also be observed in Figure 13, and it is consistent with the findings of Hawkins and Davidson.36 The dispersion strength decreases with decreasing temperature, which is also in accordance with the literature.36 These results show that broad-band permittivity measurements might be a promising candidate to verify the existence of gas hydrates deposits in pipelines, or gas hydrates occurring in subsea sediments and permafrost regions for that matter. As indicated in Figure 1, the permittivity of gas hydrates is dependent on the hydrate former. This is especially the case for the dispersion frequency. The variation of the dielectric properties with the hydrate former shows the potential of using dielectric spectroscopy to determine the composition of the hydrate formers if unknown. Davidson39 found that the dispersion frequency seemed to be correlated with the dipole moment of the hydrate forming molecule. Most hydrate forming molecules relevant for the oil and gas industry have low dipole moment, which may limit the sensitivity of dielectric spectroscopy for determination of the hydrate former composition. In the last part of this section it is shown how open-ended coaxial probes can be used for permittivity measurements on thin layers. Figure 15 shows measured dielectric constant at 100 MHz and fitted dispersion strengths for both dispersions (∆ and ∆E) during hydrate formation in three layers with different thickness (1 mm, 2 mm and 3 mm). Thus, all layers are within the sensitivity depth of probe A, while the thickest layer is slightly thicker than the sensitivity depth of probe B. In these experiments, the layer thickness was controlled by placing a plastic block (polyoxymethylene) on spacers on the brass plate. The dielectric constant of polyoxymethylene


17

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 37

is approximately 3,40 which is lower than the dielectric constant of both THF-hydrates and the THF/water solution. Similar to the experiment discussed in the first part of this section, hydrate formation is detected by a huge drop in measured dielectric constant. The magnitude of this drop decreases with decreasing layer thickness, as the probes sense more of the backing plastic block. However, even for the thinnest layer hydrate formation is easily detected. The fitted dispersion strength for the hydrate dispersion increases during hydrate formation, while the opposite is observed for the water dispersion. Again, the benefit of the broad-band measurements is demonstrated. In general, and especially for the two thinnest layers, the measured dielectric constant decreases and stabilizes faster for probe B than probe A, indicating faster hydrate formation in front of probe B. Hydrate formation is an exothermic reaction, and heat transport may therefore limit hydrate formation.1 We speculate that heat transport might be less efficient away from the front the larger probe A, due to the larger size of its sealing plastic bead, which has significantly lower thermal conductivity than the probe steel housing (see photo of the two probes in Figure 3). Hydrate experiments in high pressure system. As far as the authors are aware, no measurements of the permittivity of methane-propane hydrates have been reported. The dielectric constant of natural gas hydrates is normally assumed to be close to that of ice (′ ≈ 3.15) in the frequency range under study in this work.41 To the best of our knowledge, this assumption has yet to be confirmed, but it is supported by earlier dielectric studies on dense hydrates, mainly performed by Davidson and his group.39 They found that if the guest molecules had a very small dipole moment (which is the case for both methane and propane), the


18

Page 19 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

permittivity of both structure I and structure II hydrates was close to that of ice in the MHz to GHz range. Figure 16 shows the measured dielectric constant at 1 GHz as function of the layer thickness estimated from gamma densitometer measurements, as more and more water is injected to the pipe and converted into hydrates (six injections in total). The final layer thickness in position of the densitometer is around 20 mm, which is thicker than the sensitivity depth of both probes (i.e.: thicker than 5 mm). As discussed in the experimental section, the layer is probably thinner in position of the probes. However, it is reasonable to assume that the final layer in the probes’ position is thicker than the sensitivity depth of both probes. The measured dielectric constant generally increases with increasing layer thickness, but the characteristic variation with layer thickness that was observed in the ice layer experiment is now only observed for probe A. The dielectric constant measured with probe A stabilizes at around 3.5. Some liquid water is probably still present in the hydrate layer in front of the probe, causing the measured dielectric constant to be slightly higher than the expected dielectric constant of methane-propane hydrates. Unlike THF, methane and propane dissolve poorly in water. If liquid water is trapped within the hydrate layer, further hydrate formation necessitates transport of gas through the layer, which may be a time-consuming process.1 Probe B measures significantly higher dielectric constant than probe A after the third injection. The measured dielectric constant also shows large variations for this probe. The measured permittivity spectra reveal that liquid water is trapped within the hydrate layer in front of probe B. Figure 17 shows the permittivity spectra (100 MHz – 13.6 GHz) measured with probe B after injection number 2, 3 and 5. A dielectric dispersion with dispersion frequency around 10 GHz


19

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 37

can be identified, which correspond well with literature values for liquid water at 2 °C.42 The dispersion strength increases considerably after the third injection, indicating higher concentration of water. The amount of free water is estimated to approximately 6 % and 17 % for injection number 3 and 5 respectively. Model spectra corresponding to these water fractions are also shown in Figure 17. CONCLUSION Formation of hydrate layers has been monitored using permittivity measurements with openended coaxial probes. It has been shown that this system can detect formation of hydrate deposit layers thinner than 1 mm. The probes ability to perform broad-band permittivity measurements has been proven to be valuable for characterization of the hydrate layers, as the permittivity spectra contain information not obtainable from single frequency measurements. By using appropriate electromagnetic mixing formulas, the amount of free water in hydrate layers can be estimated. We believe permittivity measurements with open-ended coaxial probes could become a valuable tool for hydrate deposition studies, for instance in flow loops and rocking cells, and especially in opaque systems and in experimental setups where visual inspection is excluded or limited. ACKNOWLEDGMENTS The authors would like thank Professor Tanja Barth at the Department of Chemistry at the University of Bergen for helpful discussions. Roar Larsen and colleagues at SINTEF Petroleum Research’s multiphase flow laboratory are acknowledged for assistance with the experiments conducted in the high pressure system. The experiments on ice layers were carried out at Southwest Research Institute as part of a DeepStar project. Adam Ufford and Kevin Supak at


20

Page 21 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Southwest Research Institute are thanked for help in carrying out these experiments. Design and production of the open-ended coaxial probes was funded by The Michelsen Centre for Industrial Measurement Science and Technology. The experiments at CMR and SINTEF were supported by the Norwegian Deepwater Programme. The Ph.D. position of Kjetil Haukalid was financed by Statoil. AUTHOR INFORMATION Present Addresses # Christian Michelsen Research AS, P.O. Box 6031, NO-5892 Bergen, Norway REFERENCES (1) Sloan, E. D.; Koh, C. A. Clathrate hydrates of natural gases, 3rd ed.; CRC Press (Taylor and Francis Group): Boca Raton, FL, 2007. (2) Borgund, A. E.; Høiland, S.; Barth, T.; Fotland, P.; Askvik, K. M. Appl. Geochem. 2009, 24, 777-786. (3) Rao, I.; Koh, C. A.; Sloan, E. D.; Sum, A. K. Ind. Eng. Chem. Res. 2013, 52, 6262-6269. (4) Grasso, G. A.; Vijayamohan, P.; Sloan, E. D.; Koh, C. A.; Sum, A. K. Gas Hydrate Deposition in Flowlines: A Challenging Problem in Flow Assurance. ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering, Nantes, France, 2013. (5) Di Lorenzo, M.; Aman, Z. M.; Soto, G. S.; Johns, M.; Kozielski, K. A.; May, E. F. Energy Fuels 2014, 28, 3043-3052. (6) Creek, J. L. Energy Fuels 2012, 26, 4112-4116.


21

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 37

(7) Di Lorenzo, M.; Aman, Z. M.; Kozielski, K. A.; Norris, B. W. E.; Johns, M.; May, E. F. Energy Fuels 2014, 28, 7274-7284. (8) Grasso, G. A.; Sloan, E. D.; Koh, C. A.; Sum, A. K.; Creek, J. L.; Kusinski, G. Hydrate Deposition Mechanisms on Pipe Walls. Offshore Technology Conference, Houston, TX, 2014. (9) Benson, D. Nonintrusive Pipeline-Inspection Techniques for Accurate Measurement of Hydrates and Waxes Within Operational Pipelines. Offshore Europe Oil and Gas Conference and Exhibition, Aberdeen, Scotland, 2007. (10) Hood, T. Verification of Flare Line Flows and Pipeline Deposit Measurement Using NonIntrusive Radioisotope Technology. Abu Dhabi International Conference and Exhibition, Abu Dhabi, United Arab Emirates, 2004. (11) Gunarathne, G. P. P. Measurement and monitoring techniques for scale deposits in petroleum pipelines. In Instrumentation and Measurement Technology Conference, 1997. IMTC/97. Proceedings. Sensing, Processing, Networking., IEEE, Ottawa, Canada, 1997, 841847. (12) Papadopoulou, K. A.; Shamout, M. N.; Lennox, B.; Mackay, D; Taylor, A. R.; Turner, J. T.; Wang, X. Proc. Inst. Mech. Eng., Part C, 2008, 222, 959-966. (13) Wang, X.; Lewis, K. M.; Papadopoulou, K. A.; Lennox, B.; Turner, J. T. Proc. Inst. Mech. Eng., Part C, 2012, 226, 1800-1810.


22

Page 23 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(14) Kippersund, R. A.; Lunde, P.; Frøysa, K. E. Hydrate deposit detection in pipes using ultrasonic guided waves. In Proceedings of the 34th Scandinavian Symposium on Physical Acoustics, Geilo, Norway, 2011. (15) Chen, X. T.; Butler, T.; Volk, M.; Brill, J. P. Techniques for Measuring Wax Thickness During Single and Multiphase Flow. SPE Annual Technical Conference and Exhibition, San Antonio, TX, 1997. (16) Cordoba A. J.; Schall, C. A. Fuel 2001, 80, 1285-1291. (17) Hoffmann, R.; Amundsen, L.; Schüller, R. Meas. Sci. Technol. 2011, 22, 075701. (18) Samir, A. M.; Abul-Faraj, W. Asphalt and Paraffin Scale Deposit Measurement by Neutron Back Diffusion Using 252 Cf and 241 Am-Be Sources. In Proceedings of the 3rd Middle East Nondestructive Testing Conference and Exhibition, Manama, Bahrain, 2005. (19) Jakobsen, T.; Folgerø, K. Meas. Sci. Technol. 1997, 8, 1006-1015. (20) Jakobsen, T.; Sjöblom, J.; Ruoff, P. Colloids Surf., A. 1996, 112, 73-84. (21) Haukalid, K.; Folgerø, K. Energy Fuels 2015, 29, 43-51. (22) Lingelem, M. N.; Majeed, A. I.; Stange, E. Ann. N. Y. Acad. Sci. 1994, 715, 75-93. (23) Dimitrakis, G. A.; George, M.; Poliakoff, M.; Harrison, I.; Robinson, J.; Kingman, S.; Lester, E.; Gregory, A. P.; Lees, K. Meas. Sci. Technol. 2009, 20, 045901. (24) Jannier, B.; Dubrunfaut, O.; Ossart, F. Meas. Sci. Technol. 2013, 24, 025304. (25) Kaatze, U. Metrologia 2010, 47, S91-S113.


23

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 37

(26) Lee, S. B.; Smith, R. L.; Inomata, H.; Arai, K. Rev. Sci. Instrum. 2000, 71, 4226-4230. (27) Smith Jr., R. L.; Saito, C.; Suzuki, S.; Lee, S. B.; Inomata, H.; Arai, K. Fluid Phase Equilib. 2002, 194-197, 869-877. (28) Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941, 9, 341-51. (29) Hanai, T. Bull. Inst. Chem. Res., Kyoto Univ. 1962, 39, 341-367. (30) Folgerø, K.; Tjomsland, T. Meas. Sci. Technol. 1996, 7, 1164-1173. (31) Larsen, R.; Wolden, M. Controlled production of hydrate plugs for test purposes. 23rd International Oil Field Chemistry Symposium, Geilo, Norway, 2012. (32) Holder, G. D.; Hand, J. H. AIChE J. 1982, 28, 440-447. (33) Nyshadham, A.; Sibbald, C. L.; Stuchly, S. S. IEEE Trans. Microwave Theory Tech. 1992, 40, 305-314. (34) International Organization for Standardization (ISO), ISO guide 98-3, Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM: 1995), ISO: Geneva, 2008. (34) Kumbharkhane, A. C.; Helambe, S. N.; Lokhande, M. P.; Doraiswamy, S.; Mehrotra, S. C. Pramana 1996, 46, 91-98. (35) Hawkins, R. E.; Davidson, D. W. J. Phys. Chem. 1966, 70, 1889-1894.


24

Page 25 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(36) Mitterer, C; Techel, F.; Fierz, C.; Schweizer, J. An operational supporting tool for assessing wet-snow avalanche danger. In Proceedings International Snow Science Workshop, Grenoble, France, 2013, 334-338. (37) Denoth, A. J. Glaciol. 1980, 25, 93-97. (38) Davidson, D.W. Clathrate Hydrates. Water in Crystalline Hydrates Aqueous Solutions of Simple Nonelectrolytes, F. Franks, Ed. Springer US, 1973, pp 115-234. (39) Tkadlec, R.; Raida, Z.; Keskilammi, M.; Kettunen, L. A Novel Design of the Sample Holder for Broadband Complex Permittivity Measurements. In Proceedings of the 4th WSEAS International Conference on Applied Informatics and Communications, Stevens Point, WI, 2004, 33:1-33:4. (40) Kliner, J. R.; Grozic, J. L. Can. Geotech. J. 2006, 43, 551-562. (41) Kaatze, U. J. Chem. Eng. Data. 1989, 34, 371-374.


25

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 37

Figure 1. Typical complex permittivity spectra of gas, oil, water, ice and gas hydrates. The dielectric constant ( ) is shown in the upper plot and the loss factor ( ) in the lower plot. The loss factor of oil and gas is negligible compared to the scale. The dielectric properties of gas hydrates are dependent on the hydrate former, in particular the dispersion frequency. This is illustrated by plotting several lines in the dispersion region. Compared to water and ice, the dielectric properties of gas hydrates are rather sparsely documented in the literature.


26

Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 2. Sketch of an open-ended coaxial probe mounted in a pipe wall.

Figure 3. The two open-ended coaxial probes used in the experiments.

Figure 4. The experimental setup used in the ice layer experiment.


27

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 37

Figure 5. Sketch of the experimental setup used in the THF-experiments. A plastic block and spacers was used to control layer thickness in some experiments.

Figure 6. The high pressure test setup with the coaxial cables connected to the probes.


28

Page 29 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 7. Measured dielectric constant at 1 GHz of ice layer as function of layer thickness. Blue data points correspond to probe A and red data points to probe B. The dashed lines show fitting of equation (5) to the measurements.

Figure 8. Measured layer thickness of ice layer compared with reference thickness. Blue data points correspond to probe A and red data points to probe B.


29

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 37

Figure 9. Figure 9(a): Measured dielectric constant at 100 MHz during formation of a 3 mm thick THF hydrate layer. Figure 9(b-f): Fitting parameters (dispersion strength, relaxation time and distribution factor) to equation (6), corresponding to the data points in Figure 9(a). Blue data points correspond to probe A and red data points to probe B. Open circles correspond to the hydrate dispersion (% , and ), and open diamonds correspond to the water dispersion (%E,E and E ).


30

Page 31 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 10. Measured complex permittivity spectra obtained with probe B before hydrate formation (T1), during hydrate formation (T2) and after completion of hydrate formation (T3). The dashed lines are model spectra corresponding to 0 %, 25 % and 95 % hydrate volume fraction, respectively.


31

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 37

Figure 11. Measured complex permittivity spectra of a mixture of THF and saline water before (blue data points) and after (red data points) hydrate formation.


32

Page 33 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 12. Calculated hydrate fraction during hydrate formation in 3 mm thick water/THF layer.


33

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 37

Figure 13. Complex permittivity spectra of a 20 mm thick hydrate layer at three different temperatures measured with probe A.

Figure 14. Fitted dispersion strength (∆) and relaxation time ( ) for the hydrate dispersion for a thick THF hydrate layer during variation of temperature. Three set temperatures were used. The extent of the periods where the chamber temperature has stabilized at the set temperature is shaded with uniform shading. Gradient shading is used between the stable periods.


34

Page 35 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 15. Figure 15 (a), (c) and (e): Measured dielectric constant ( ) at 100 MHz as function of time for three hydrate layers with thickness 1mm, 2 mm and 3 mm, respectively. Figure 15 (b), (d) and (f) show the corresponding fitting parameters (∆ and ∆E) to equation (6). Blue and red data points correspond to probe A and probe B, respectively. Open circles correspond to the hydrate dispersion (∆), and open diamonds correspond to the water dispersion (∆E).


35

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 37

Figure 16. Measured dielectric constant at 1 GHz during hydrate layer build-up in the pressurized pipe. The measurements obtained with probe B after injection number 2, 3 and 5 are marked with arrows. The corresponding complex permittivity spectra are shown in Figure 16.


36

Page 37 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 17. Complex permittivity spectra measured with probe B after injection number 2, 3 and 5. The dashed lines are model spectra corresponding to 83 %, 94 % and 97 % hydrate volume fraction, respectively. Table 1. Inner conductor radius (Ra) and outer conductor radius (Rb) at the probe aperture for the two open-ended coaxial probes used in the reported experiments. Ra [mm]

Rb [mm]

Probe A

1.50

5.00

Probe B

1.00

2.35


37

Broad-Band Permittivity Measurements of Formation of Gas Hydrate

Recommend Documents