Simulating Hydrate Growth and Transport Behavior in Gas-Dominant

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Simulating Hydrate Growth and Transport Behaviour in Gas-Dominant Flow Thomas B Charlton, Mauricio Di Lorenzo, Luis E. Zerpa, Carolyn A. Koh, Michael L. Johns, Eric F May, and Zachary M. Aman Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 14 Dec 2017 Downloaded from http://pubs.acs.org on December 14, 2017

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Simulating Hydrate Growth and Transport Behaviour in GasDominant Flow Thomas B. Charltona,b, Mauricio Di Lorenzoc,a, Luis E. Zerpad, Carolyn A. Kohb, Michael L. Johnsa, Eric F. Maya, Zachary M. Amana,* a

Fluid Science and Resources Division, School of Mechanical & Chemical Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia b Center for Hydrate Research, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States c CSIRO-Energy, 26 Dick Perry Ave, Kensington, WA 6151, Australia d Department of Petroleum Engineering, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States

ABSTRACT. The current hydrate kinetics model implemented in the multiphase flow simulator OLGA® treats hydrate growth in oil-continuous systems by considering the solidification of emulsified water droplets to form a hydrate-in-oil slurry that is assumed to be stable. To date, the validity of this model has not been established for gas-dominant systems, where gas void fractions may exceed 90 vol%. Here, six experimental datasets, collected using a 40 m single-pass gas-dominant flowloop operating in the annular flow regime, were compared with predictions made using the current hydrate kinetics model. The comparison identified discrepancies in the predicted flow regime and the gas-water interfacial area, which significantly affect kinetic hydrate growth rate calculations; these discrepancies may in part be due to differences in dynamic similarity between flowloop experiments and industrial-scale simulations. By adjusting only the kinetic rate scaling factor, it was not possible to match the pressure drop observed experimentally, illustrating that the formation of a viscous hydrate slurry alone cannot account for the resistance-to-flow observed in gas-dominant systems. We demonstrate that it is possible to emulate deposition in the current model by adjusting the slip ratio between hydrate particles and the condensed phases; this approach allowed stenosis-type restrictions to occur in the simulation, and similar pressure drop behaviour to that observed experimentally. Utilising a simple in-house model, with empirical correlations to predict the hydrodynamics, it is possible to match relatively closely the measured growth rate and pressure drop simultaneously. Such agreement could not be reached using the curACS Paragon Plus Environment

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rent hydrate implementation available in OLGA®, highlighting the need for a gas-specific hydrate growth model that is capable of capturing both hydrate growth from suspended droplets in the gas phase and solid growth at the flowline wall, as well as the extent of hydrate deposition on the wall.

INTRODUCTION Clathrate hydrates are ice-like solids where light hydrocarbon guest molecules are trapped in a crystalline water network.1 Hydrates readily form in high-pressure oil and gas flowlines when process fluids cool to within the thermodynamic stability region, caused by heat exchange with the environment or Joule-Thompson cooling, or a combination of both. Once formed, hydrate particles may deposit on the flowline wall or aggregate in the continuous phase, presenting a considerable flow assurance risk due to potential flowline blockage.2 The discovery of petroleum reservoirs in deep water that require long tiebacks for the transport of produced fluids has introduced considerable engineering challenges in maintaining economic viability while minimizing hydrate blockage risk.3 Current hydrate management techniques either (i) eliminate the likelihood of hydrate formation by removing the flowline from the thermodynamic hydrate stability region or (ii) manage the risk of hydrate formation using low-dosage hydrate inhibitors. Passive hydrate prevention methods include insulation or pipeline burial to maintain the fluid temperature above the hydrate formation temperature. Active prevention methods include the injection of thermodynamic hydrate inhibitors (e.g. monoethylene glycol) or the use of active pipeline heating (e.g. direct electrical heating).2 The economic viability of complete hydrate avoidance in long-distance tiebacks has encouraged a new hydrate “risk management” paradigm,4 which relies on accurate predictions of hydrate growth rate and transportability. A model describing hydrate formation in oil-continuous systems has been successfully implemented into the transient multiphase flow simulator OLGA®.5 The current approximation used in the simulation treats condensed phases as a homogenous mixture, with hydrate formation augmenting the apparent oil

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phase viscosity.6 For oil-dominant systems, the increase in apparent oil-phase viscosity may be used as a proxy for hydrate blockage severity;7 this approximation derives from a physical balance between the pressure differential across the flowline and the increasing frictional loss due to the hydrate slurry. A constant mean water droplet diameter governs the interfacial area available for hydrate formation.

Figure 1: Conceptual picture for hydrate formation in oil-dominant systems8, based on the mechanistic steps discussed by Turner et al.5 in collaboration with J. Abrahamson (U. Canterbury). As large-scale gas assets are projected to become a staple of the energy economy over the coming two decades,9 a predictive hydrate growth rate model for gas-continuous systems is critical for safe and reliable operations. No such model currently exists within a transient simulation framework, although significant effort has focussed on developing a comprehensive model to describe hydrate particle interactions and the formation of a viscous hydrate slurry in oil-continuous flowlines. While the conceptual descriptions of oil-continuous and gas-dominant hydrate blockage mechanisms differ, it is possible to draw some analogies between the physical behaviour of both systems so that, potentially, engineers may be able to deploy the current generation of tools developed for oil flowlines to deliver a first approximation of hydrate blockage severity in gas flowlines. To test the validity of this hypothesis, it is first necessary to develop a comprehensive understanding of hydrate growth and transport in gas flowlines. Lingelem et al.10 proposed a conceptual hydrate growth and deposition mechanism for systems with low liquid holdup, which was originally based on the formation of ice plugs in water pipelines. There are four primary stages in this mechanism that are explained in detail by Zerpa et al.11 First, hydrate blockages in gas-continuous flowlines may begin with cross-entrainment between the gas and water ACS Paragon Plus Environment

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phases, increasing the contact area between hydrate guest molecules and water. At sufficient subcooling (e.g. 3.6 K, Matthews et al.12), hydrate may form at available gas-liquid interfaces. Film growth in multiphase flows typically begins at the gas-liquid-wall interface where both hydrate guest and host molecules are readily available; however, water condensation on the wall may also cause deposits to form well above this interface. Near the final stages of hydrate blockage, the continued inward growth of the hydrate deposit may severely inhibit the space available for gas/water flow, leading to high frictional pressure losses. Rao et al.13 investigated single-phase hydrate film growth in laboratory-scale systems by analysing hydrate growth on the exterior of a cold pipe exposed to flowing water-saturated methane. Rao et al.13 observed that, following water condensation, a thin hydrate film developed uniformly along the pipe. The initially porous deposit annealed over time due to the insulating effect of the hydrate film, resulting in an estimated minimum porosity of 5% after the annealing stage. Dorstewitz and Mewes14 also investigated the influence of heat transfer on the formation of hydrate layers in pipes, observing a similar self-limiting hydrate growth rate due to the insulating effect of the hydrate deposit. Nicholas et al.15 similarly observed single-phase hydrate film growth using water-saturated cyclopentane in a single pass flowloop, showing that, when the water concentration was below the saturation limit, a uniform hydrate deposit formed along the length of the flowline resulting in a gradual increase in the measured pressure drop. Nicholas et al.15 also reported increased rates of film growth after increasing the water concentration to above the saturation limit at the experimental conditions; upon doing so, free water formed, and a rapid increase in the pressure drop was detected. This was attributed to coalescence of the free water, which quickly converted to hydrates and formed a local orifice-like restriction. More recently, Di Lorenzo et al.16 performed gas-dominant experiments using a high-pressure flowloop to observe hydrate formation. A number of experiments were completed using domestic natural gas and deionised water, operating in the annular flow regime. The turbulent nature of the flow ACS Paragon Plus Environment

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field resulted in a significant portion of the free water being entrained in the gas phase as small water droplets. Given sufficient subcooling, hydrate formation occurred quickly and the experiments ceased within an hour after the start of water injection to prevent a blockage. Using multiple viewing windows, Di Lorenzo et al.16 observed both hydrate film growth on the pipeline wall, and hydrate deposition from entrained particles. The increasing pressure drop measured across the flowloop with time was attributed to the stenosis-type accumulation of hydrates on the flowloop wall, due to both film growth and deposition of entrained particles. As deposition decreases the effective flowline diameter, the increase in flowing shear stress may be sufficient to slough some portion of the hydrate deposit from the flowline wall. This process rapidly increases the cross-sectional area for flow, corresponding to a sharp decrease in the frictional pressure drop signal.16 As the sloughed hydrate agglomerate enters the flowing gas or liquid phases, the increased momentum required to transport the solid hydrate may exceed the energy available in the system. This constitutes one mechanism by which solid hydrate masses may accumulate downstream of the original hydrate deposit, and was observed in flowloop studies by Di Lorenzo et al.16. The above reported experimental observations of hydrate growth in gas-dominant systems were used to generate a revised conceptual picture for the stages of hydrate blockage in gas flowlines (Figure 2). This picture is developed from the suggestions of Lingelem et al.10, incorporating all observed behaviour.

Figure 2. Conceptual picture for hydrate growth and plugging phenomena in gas-dominant flowlines.


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Significant effort has focussed on developing a comprehensive model to describe hydrate particle interactions and the formation of a viscous hydrate slurry in oil-continuous flowlines, but there remains uncertainty as to whether this model may be applied to gas-continuous systems. Models proposed by Di Lorenzo et al.17, and further extended by Wang et al.18, address some of the newly observed behaviour in gas-dominant systems; however, empirical parameters are used to match the growth and deposition rates observed experimentally. This paper investigates whether adjustment of two intrinsically-linked parameters (the kinetic rate constant and hydrate phase velocity) can usefully approximate hydrate growth rate and frictional pressure drop behaviour in gas-dominant systems. EXPERIMENTAL METHODS AND MODEL BASIS Gas-Dominant Flowloop. Hydrate growth rates and frictional pressure drop were captured on the Hytra gas-dominant flowloop as reported in detail by Di Lorenzo et al.16, who investigated the effect of subcooling for gas-dominant flows in the annular flow regime. The flowloop (Figure 3) included a 20.3 mm inner diameter test section arranged in a single-pass configuration at 40 m, with a stainless-steel wall thickness of 2.54 mm. The wall temperature was controlled externally with a co-current glycol jacket. Dry, domestic natural gas and deionised water were injected at the entrance to the flowloop (“PT0” in Figure 3), and were received from the test section in a gravimetric separator. A second cyclone separator ensured minimal liquid entrainment in the recovered gas stream, which was re-compressed and re-circulated with fresh water at the inlet. Liquid water was injected continuously, leading to a build-up in the separators and decreased total volume available for gas flow. As a consequence, the static pressure in the gas phase increased over the course of each experiment without hydrate formation. The water and gas flow rates were controlled by an injection pump and a compressor, respectively, and six pressure and temperature transducers were used to monitor the local conditions in the gas phase (along the loop). Three viewing windows were used to visually confirm hydrate formation, flow behaviour, deposition and sloughing.


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Experimental Flowloop

OLGA® Model

Figure 3. A schematic of the Hytra gas-dominant flowloop (Di Lorenzo et al.16) and the corresponding OLGA® simulation layout. Six experiments were performed with different amounts of subcooling within the hydrate formation region. In all experiments, the actual gas and water flowrates were controlled at 0.17 m3/min (~8.7 m/s superficial velocity) and 2 L/min (~0.1 m/s superficial velocity), respectively. The average hydrate subcooling ranged between 3.8 °C and 11.2 °C. Each experiment was halted when the pressure drop across the entire flowloop reached a preset maximum of 20 bar, which usually occurred within an hour of operating time within the hydrate-forming region. The maximum pressure drop condition is set as a safety limitation to reduce the risk of a hydrate blockage forming in the test section. The final hydrate volume formed was calculated by Di Lorenzo et al.16 from the difference in static pressure before and after hydrate formation, accounting for the effect of injecting a known volume of liquid water. Hydrate formation resulted in a significant increase in frictional pressure drop between the transducers bounding the test section (“P-T1” and “P-T6”, which were 33.4 m apart). All flowloop experiments resulted in a monotonic increase in the pressure drop after liquid water injection was initiated; the flowloop remained well inside the hydrate region at all times indicating no significant heat transfer limitation to growth. Model Setup. Two models were used to simulate flow behaviour and hydrate formation for the six flowloop experiments: (i) the default transient hydrodynamic model implemented in OLGA®, and, (ii) an in-house implementation of a simple pseudo-steady-state model based on empirical multiphase flow correlations, and similar in nature to the models described by Norris et al.19 and Baker et al.20 in different but related contexts. OLGA® uses the CSMHyK module (discussed in more detail below) to predict hydrate formation. To assess better the hydrate growth rate predictions for gas-dominant ACS Paragon Plus Environment

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systems, and the extent to which hydrate deposition affects the experimental pressure drop, the in-house tool uses the same kinetic hydrate growth rate equation employed in CSMHyK/OLGA®. However, predictions of surface area and temperature (required inputs of the kinetic equation) may vary due to differences in the underlying assumptions of each model. The closed-loop model in OLGA® 721 was designed to mimic the experimental apparatus (Figure 3), with identical inner diameter and wall thickness. The simulation’s flowloop length was extended to 43.45 m, using equivalent lengths to account for the various fitting losses along the line.22 A simple differential pressure unit on the gas recycle stream provided the driving force for fluid flow. The gas flow rate was maintained using a control valve and proportional integral controller. A constant mass flow rate of water was injected at the entrance of the flowloop, and the wall temperature was set to the experimental glycol coolant temperature. A constant overall heat transfer coefficient was applied and adjusted to match to baseline experiments without the formation of hydrates. The use of a separator allowed water to accumulate in the simulation, mimicking the static pressure increase with continued operation. The gas recycle loop implemented in the simulation was short in length (2 m), adiabatic and smooth. The purpose of this section was not to emulate the physical system precisely, but rather to allow matching of the temperature of the recirculated gas phase to the recorded experimental data prior to reinjection in the flowloop. Two (over-sized) 20 kW heat exchangers were used to match the inlet gas temperature with measured values (“P-T1” in Figure 3). Check valves on the gas recycle line were used to prevent back flow. The temperature of the injected water was set to match to the experimentally recorded values at “P-T1”. The flowloop was initially filled with gas at the experimental pressure, and simulations began with the injection of water and circulation of gas. The loop in the in-house model had an identical length, inner diameter and wall thickness to the OLGA® model. The separator and gas recycle stream were ignored, and therefore the effect of a steady static increase in the overall flowloop pressure with water injection was not considered. Inlet gas and ACS Paragon Plus Environment

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water flow rates were set to the experimental values (0.17 m3/min and 2 L/min, respectively). The inlet fluid temperature and pressure were held constant at the average experimental values (from sensor “PT1”) over the course of each simulation. The external wall temperature was also held constant at the experimental set-point. The flowloop was divided into 100 equal-length control volumes; calculations were made sequentially along the line to determine the subsequent control volume’s pressure and temperature under the assumption of steady-state flow. The Beggs and Brill23 empirical correlation was used to predict the flow regime, water holdup and pressure drop along the line. The heat balance for each control volume considered contributions from Joule-Thompson cooling, hydrate formation, and heat transfer to the external cooling jacket. Internal and external convective heat transport coefficients were based on the Dittus-Boelter24 equation for turbulent flow in a pipe. Local hydrate formation resulted in the consumption of water and gas along the line; although deposition mechanisms were not incorporated, it was possible to specify the quantity of hydrate formed in each control volume that remained on the wall as a non-porous deposit. The quantity of hydrate on the wall therefore affected frictional pressure drop and heat transfer predictions. The Multiflash® software package25 was used to generate the required fluid property tables and hydrate equilibrium curve using the gas composition reported by Di Lorenzo et al.16. The RKSAdvanced model set26 and CPA-Infochem model set25 were used to calculate the fluid properties and hydrate equilibrium curve, respectively. Both OLGA® and in-house models use the tabular property files generated using Multiflash® to calculate fluid properties in each control volume. OLGA® HD was used to simulate transient hydrodynamic behaviour at all times, as it contains an improved friction model for stratified flow, designed to provide more stable and accurate predictions of pressure drop and liquid holdup in this regime.27


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Table 1: Simulation parameters used in the OLGA® and in-house models for all experiments considered in this study. Initial Pressure [bara]

Inlet Temperature [°C]

Gas Flow Rate [m3/d (actual)]

Water Flow Rate [L/min (actual)]

Coolant Temperature [°C]

Experiment

Run Time [min]

OLGA®

In-House

OLGA®

In-House

OLGA®

In-House

OLGA®

In-House

OLGA®

In-House

Low vel.

40.0

104.1

104.4

20.6-22.1

21.6

129.3

120

0.97

1.0

20.5-21.9

21.1

High vel.

28.0

103.9

104.4

29.9-31.7

30.4

242.9

240

1.52

1.5

26.6-31.6

29.9

1

48.2

89.3

87.2

13.8-16.8

15.5

241.9

240

1.82

2.0

12.0

12.0

2

45.2

88.7

87.2

13.8-16.6

15.4

241.1

240

1.83

2.0

10.0

10.0

3

22.6

83.7

87.2

8.7-13.4

12.6

244.1

240

2.02

2.0

4.0

4.0

4

39.5

88.7

87.2

10.7-14.7

13.6

227.8

240

1.78

2.0

8.0

8.0

5

22.7

104.1

104.4

9.4-12.5

11.4

231.5

240

2.40

2.0

4.0

4.0

6

20.7

106.8

104.4

17.1-19.5

18.4

240.5

240

2.03

2.0

16.0

16.0

Model Tuning. Two system parameters were required to tune the OLGA® simulation to best represent the real system; the overall heat transfer coefficient (U) and the separator volume (Vsep). The value of U accounts for inefficiencies in the glycol cooling jacket, while Vsep accounts for the majority of the system’s total volume. Previous studies have shown that hydrate formation can significantly affect heat transport to the environment.14, 28 However, increased transport resistance due to hydrate deposition is not currently implemented in OLGA®. Future modelling efforts using this platform might consider altering the internal convective and conductive heat transport coefficients to account for hydrate deposit formation on the wall to obtain a more accurate estimate of U. Two experimental datasets in which no hydrates formed were used to tune and then validate the OLGA® model using the new parameters. Both experiments were at an initial (non-flowing) pressure of 104.4 bara. The ‘high’ and ‘low’ gas velocity experiments were set respectively to 0.17 and 0.085 m3/min gas flow, with 1.5 and 1 L/min water injection. As a first approximation, the OLGA® model was tuned to the data from the low gas velocity experiment, and its predictions at high gas velocity were then compared with the corresponding experimental results. Predictions using the in-house model, which requires no tuning as empirical correlations were used to determine the overall heat transport coefficient and the static increase in pressure with time was neglected, are also provided for both hydrate-free systems. ACS Paragon Plus Environment

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U = 300 W/m2/K 1.5 U = 100 W/m2/K

0.5

U = 30

W/m2/K

0

(a)

Experimental Data (Low Gas Velocity) OLGA® Simulations In-House Model

22

U = 30 W/m2/K U = 100 W/m2/K

1 0.5 0

71

U = 300 W/m2/K 70

21

(b) 0

10

20

30

40

69

Temperature Drop [°F]

2

Experimental Data (Low Gas Velocity) OLGA® Simulations In-House Model

1

Average Temperature [°F]

Average Temperature [°C]

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

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Temperature Drop [°C]

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50

Time After Water Injection [min]

Figure 4. Comparison of Hytra flowloop experimental data (circles) and OLGA®/In-House simulation results (solid/dashed lines) at low gas velocity without hydrate formation, as a function of time following the start of liquid water injection: (a) temperature drop across the flowloop test section; (b) average flowloop test section temperature; (c) average pressure in the flowloop test section; and (d) average pressure drop across the flowloop test section. A U value of 100 W/m2/K provided the best agreement with the measured temperature drop across the loop and average temperature of the loop, for the low gas velocity experimental data (Figure 4a and b). The temperature drop was defined as the difference in temperatures recorded between sensors “P-T1” and “P-T6” with time, while the average fluid temperature was defined as the mean of all temperatures from sensors “P-T1” to “P-T6”. A separator volume (Vsep) of 864 L provided the best match to the change in average flowloop pressure over time as liquid water was injected (Figure 4c). Using this separator volume, which also accounted for additional volumes within the physical recirculation loop, the simulated total system volume was 886 L. This is consistent, within the estimated experimental uncertainty, of the total system volume (800 L) reported by Di Lorenzo et al.17. The model parameters (U and Vsep) determined from the low velocity experiments were then used to simulate the flowloop experiments conducted at high gas velocity (with no hydrate formation). The results of the comparisons are shown in Figure 5. The average absolute deviation in pressure (using OLGA®) was 0.35 bar, which is comparable with the uncertainty of the pressure transducers (0.28 bar). The temperature drop and average temperature were both generally under-predicted, with average ACS Paragon Plus Environment

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absolute deviations of 0.50 °C and 0.45 °C, respectively. Although the temperature drop prediction could be improved by increasing U to 300 W/m2/K, this decreased the accuracy of the average fluid temperature prediction (Figure 5a and b); therefore, U was kept at the original tuned value for the remainder of the OLGA® simulations. Although heat transfer would be best simulated using a pipe-inpipe model, this model option was not available in the multiphase OLGA® simulation package

90

Experimental Data (High Gas Velocity) OLGA® Simulation In-House Model

32

0

88

31

30

86

(b)

U = 300 W/m2/K

29 0

5

10

15

20

25

84

112


110

1620

1580 108 1540

106

(c)

104

1500

4

60


3

40

2 20 1

(d)

0 0

5


10

15

20

Pressure Drop [psi]

(a)

0

Temperature Drop [°F]

2

1

Average Pressure [bara]

4

U = 300 W/m2/K

Pressure Drop [bar]

2

Average Temperature [°F]

Temperature Drop [°C]

6 Experimental Data (High Gas Velocity) OLGA® Simulation In-House Model

3

Average Pressure [psia]

employed.

Average Temperature [°C]

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

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0

25


Figure 5. Comparison of Hytra flowloop experimental data (circles) and previously tuned OLGA® simulation results (lines) at high gas velocity without hydrate formation, as a function of time following the start of liquid water injection: (a) temperature drop across the flowloop test section (including U = 300 W/m2/K for comparison); (b) average flowloop test section temperature (including U = 300 W/m2/K for comparison); (c) average pressure drop across the flowloop test section; and (d) average pressure in the flowloop test section. Predictions using the in-house model are also provided for comparison. OLGA® simulations under-predicted the average pressure drop for both the low and high gas velocity cases by approximately 15% (Figure 4d and Figure 5d). This may be a consequence of differences in dynamic similarity between hydrodynamic simulations (tuned to represent the industrial scale) and labscale experimental results, which may cause incorrect prediction of the flow regime, or inaccuracy in the dispersion predictions within the flow regime model. In contrast, the Beggs and Brill23 empirical correlation slightly over-predicted the pressure drop in both the hydrate-free experiments simulated with the in-house model.


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Hydrate Formation and Entrainment Models. Over the past three decades, both industrial and academic laboratories have focused on the development of predictive models to support hydrate risk management in oil flowlines. Vysniauskas and Bishnoi29 proposed a first-order kinetic rate equation to predict the formation of hydrates, based on a fugacity driving force and the surface area between the phase containing the guest molecules and water (AS). Hydrate growth is determined from the mass of gas consumed per unit time (dmgas/dt). Turner et al.5 proposed the replacement of the fugacity driving force with the subcooling (∆Tsub), which is the difference between the system temperature (Tsys) and the hydrate dissociation temperature at the pipeline pressure. The model included two tuning parameters, k1 and k2, which were regressed to experimental hydrate growth rates from gas-water systems measured in an autoclave. −

= exp −

∆

(1)

The values of k1 and k2 regressed to hydrate formation data from Vysniauskas and Bishnoi29 and Englezos et al.30 were k1VB = 2.608×1016 kg/m2/°C/s and k2VB = 13,600 K.5 When applied to oildominant systems, Boxall et al.31 recommended scaling the parameter k1 to account for heat and mass transport limitations, and suggested k1/k1VB = 0.002. Turner et al.5 incorporated equation (1) into a hydrate growth and transport model for oil and gas flowlines, known as CSM Hydrate Kinetics (CSMHyK), which was integrated within the multiphase flow software package OLGA®. The CSMHyK model is based on a four-step mechanism to describe hydrate growth and transportability in oildominant flow: entrainment, hydrate shell growth, agglomeration and plugging. The conceptual model currently used in OLGA® is presented in Figure 1 for reference. The prediction of hydrate growth rate relies on accurate prediction of the interfacial area between hydrate forming partners, which intrinsically relies on the correct prediction of flow regime. Using the three viewing windows, Di Lorenzo et al.16 visually confirmed that an annular flow regime existed during their experiments; this flow behaviour is also predicted using the correlations presented by


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Barnea32 and Beggs and Brill23. In contrast, OLGA® predicted a stratified-wavy flow regime in all simulations. Discrepancies in the predicted flow regimes may be explained by differences in dynamic similarity. At the experimental conditions, the dimensionless Froude number (ratio of inertial to gravitational forces) is typically much larger than that encountered in gas-dominant flowlines, as a result of the smaller pipeline diameter and high gas velocities. When the fluid’s inertia dominates gravitational forces, the formation of an annular film on the wall is promoted.32 Barnea’s unified model was validated using experimental data from a two-inch flowline,32 which is nearer in diameter to the Hytra flowloop than the diameters of industrial flowlines. Given the underlying models in OLGA® were developed and validated as a tool for systems with industrial-scale dimensions, their application to smaller scales may lead to appreciable differences between predicted and observed behaviour. The interfacial gas-water area for gas-dominant annular flow consists of two parts: bulk water and entrained water droplets.17 The bulk water interface is defined as the area between the bulk liquid and gas phases, and depends on the liquid holdup and the extent to which the liquid covers the inner perimeter of the pipeline wall. For idealised annular flow, a liquid film is assumed to cover the entire pipe perimeter. In systems where both the Froude and Weber numbers are high (i.e. inertial forces dominate gravitational and interfacial forces, respectively), the rate of droplet entrainment may be similar to that found in vertical flow, becoming a strong function of the gas velocity.33 As observed in the flowloop experiments, the entrained water in the gas phase had a mist-like appearance and a volume fraction that may exceed 15%.17 These small water droplets significantly impact the calculated surface area available for hydrate formation. The predictions from OLGA® at various gas superficial velocities are compared to correlations derived by Pan and Hanratty33 and Paleev and Filippovich34 for liquid droplet entrainment in the dimensions of the Hytra flowloop system (Figure 6).


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Page 15 of 29 1 Liquid Entrainment [m3/m3]

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Paleev and Filippovich (1966) 0.8 OLGA® 7.3.2 (HD) 0.6 0.4 Pan and Hanratty (2002)

0.2 0

0

5

10

15

20

25

30

Superficial Gas Velocity [m/s]

Figure 6: Droplet entrainment calculated by OLGA® as a function of the gas superficial velocity in the dimensions of the Hytra flowloop. Relevant empirical predictions are also shown. The correlation from Pan and Hanratty33 was tuned to the high-pressure experimental data of Mantilla et al.35, for nitrogen and water in a 2-inch pipeline, as reported by Di Lorenzo et al.17. Equation (2) shows Pan and Hanratty’s correlation for entrainment in annular flow, which is a semiempirical formation that is based on a force balance between the rate of droplet atomisation and deposition.33 The entrainment fraction (E) is ratio of the mass flow of drops in the gas to the total mass flow of liquid, where EM is the maximum entrainment value. The equation is a function of A1, a dimensionless constant, the pipeline diameter (D), the gas superficial velocity (UG), the densities of the gas and liquid phases (ρG and ρL) and the interfacial tension (σ). ⁄

⁄

=

!" "# $%⁄ &

(2)

Predictions of droplet entrainment by Paleev and Filippovich34 were developed from an analytical description of the dynamic equilibrium between precipitated and entrained droplets. The correlation uses two dimensionless numbers to describe the interaction between gas and liquid phases, and a modified gas density to account for the separation of liquid between the film and the gas core. Data from numerous previous entrainment studies were used to develop the final expression. Limited experimental data exists for entrainment in high pressure systems, but the results from an investigation by Mantilla et al.35 using water and nitrogen at 1000 psia in a 2-inch pipeline was used to tune Pan and Hanratty’s model. The value of the A1 parameter in equation (2) for high-pressure systems was determined to be 3.6x10-5 by fitting to Mantilla’s data.17 Figure 6 illustrates that, as the gas flow ACS Paragon Plus Environment

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rate was increased in the flowloop, the predicted liquid droplet entrainment fraction increases; however, there are differences between the various correlations that significantly affect downstream hydrate growth rate calculations. Turner’s kinetic model (equation 1) was also used to predict hydrate formation rates in the in-house model, with the default values of k1 = k1VB and k2 = k2VB. The surface area for hydrate formation were derived from the bulk and droplet interfaces, incorporating Pan and Hanratty’s33 model (tuned to Mantilla’s data) to predict liquid droplet entrainment, and the following equation33 to predict the sautermean droplet diameter (d32). '

" ( &

)'

(

) = 0.0091

(3)

Dynamic similarity between the experimental data and simulation predictions should also be considered when assessing the accuracy of any scale-up from the observed behaviour to industrial applications, particularly if the reliability of available entrainment models for hydrate growth rate calculations is to be assessed. The in-house model is designed to emulate hydrate predictions using the OLGA® model with a better understanding of the individual contributions to growth rates and pressure drop. It is therefore not the aim of this investigation to capture hydrate growth rates precisely using OLGA®, but rather outline observed behaviours and discrepancies to aid future development of a gasdominant specific model. RESULTS AND DISCUSSION Surface Area Estimates. Empirical predictions using the in-house model to describe the experimental hydrodynamics were compared with OLGA® simulations, to estimate (i) the effective liquid holdup under steady-state conditions; (ii) the volume fraction of liquid entrained in the gas phase, labelled as entrainment; (iii) the water droplet diameter in the gas phase; and (iv) the total interfacial area between the gas and liquid phases. The results for Experiment 1 are shown in Table 2, which lists average values for each parameter over the course of the simulation. The results of simulations for the remaining


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Energy & Fuels

experiments did not diverge significantly from Experiment 1 as the gas and liquid flow rates were held approximately constant. Table 2. Comparison of average hydrodynamic properties predicted using the in-house model and with the OLGA® simulation for Experiment 1 (without adjustment of the kinetic rate factor k1/k1VB). Simulation Environment

Flow Regime

Holdup [vol.%]

Entrainment [vol.%]

Droplet Diameter [µm]

Bulk Area [m2/m3]

Droplet Area [m2/m3]

Total Area [m2/m3]

In-House Model

Annular

4.4%

16.2%

44.7

193

969

1162

Stratified

1.0%

48.1%

-

22.0*

-

27.7

®

OLGA

* estimated from holdup assuming a flat, stratified liquid layer along the length of the flowline

The largest deviation between the empirical correlations and OLGA® simulations arises in the estimates of total interfacial area, where the in-house model predicted 1162 m2/m3 and OLGA® predicted approximately 28 m2/m3. The total interfacial area is calculated from a combination of the bulk and droplet interfacial areas, where the latter corresponds to the contribution from entrained droplets. Although OLGA®’s predicted entrainment is higher than that predicted using the empirical correlations (Figure 6 and Table 2), this was not reflected in the total interfacial area. It is not possible to distinguish between droplet and film contributions in the total interfacial area used by OLGA®’s hydrate module, but a theoretical bulk area of 22 m2/m3 may be approximated from the predicted holdup (1 vol.%) under the assumption of a flat, stratified layer. Curvature in the stratified liquid phase, which is expected at higher gas velocities, would increase bulk area predictions and explain the difference between 22 and 28 m2/m3. Hydrate Growth Rate. Di Lorenzo et al.16 calculated the extent of hydrate formed at the end of each experiment from the moles of gas consumed. The average growth rates for the six flowloop experiments were compared to the simulated growth rates without modifying the kinetic rate constants (k1 = k1VB). Subcooling requirements for hydrate nucleation in the simulations were set to 0 °C, to ensure hydrate onset in all cases. No hydrate deposition was allowed in these simulations. The growth rates simulated using OLGA® were approximately one order of magnitude lower than the measured growth rates in all cases, whereas the in-house model over-predicted growth rates by up to one order of magnitude (Figure 7). ACS Paragon Plus Environment

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Average Hydrate Growth Rate [kg/m3/s]

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10 Experiments OLGA® Simulations In-House Model 1

0.1

0.01 0

2

4 6 8 Average Subcooling [°C]

10

12

Figure 7: Predicted and measured average hydrate growth rate for the six experiments. The dashed line through experimental results is for guidance only. The kinetic hydrate growth rate, as implemented by Turner et al.5, is a function of the fluid temperature, hydrate dissociation temperature and the surface area for hydrate formation. As the fluid temperature in each simulation does not diverge significantly from the experimental data, deviations between the model and experiment may – as a first approximation – be attributed primarily to discrepancies in the predicted surface area. The ratio of growth rates predicted using the in-house model and OLGA® are relatively consistent for all six experiments (Table 3), approximately 30 times higher using the in-house model. This aligns closely with the difference in predicted total surface area between the two models, further suggesting that the differences in growth rates may be due to discrepancies in predicted surface areas. Table 3: Ratios of growth rates predicted using OLGA® and the in-house model for each experiment. Experiment Number

Average Experimental Subcooling [°C]

1

Ratio of experimental to model growth rates [-] OLGA®

In-House

Ratio of model growth rates (In-House/OLGA®)

5.8

9.98

0.314

31.8

2

6.0

11.5

0.311

36.8

3

10.3

26.2

0.754

34.7

4

8.7

13.6

0.408

33.4

5

11.2

20.4

0.641

31.8

6

3.8

7.52

0.209

35.9


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Pressure Drop. The formation of hydrate in a multiphase pipe invariably leads to an increased resistance-to-flow, thereby increasing the measured pressure drop across in the flowline; accurate predictions of pressure drop are, therefore, useful indicators of hydrate plugging severity. Pressure drop in oil-dominant pipelines may be ascribed primarily to the aggregation of hydrate particles in a viscous slurry, while pressure drop in gas-dominant pipelines may be primarily the consequence of hydrate film growth and particle deposition at the pipe wall. The characteristics of the liquid phase can influence the formation of a hydrate deposit, with the presence and type of natural surfactants being particularly important.36-38 Oils or condensates with a lower tendency to form stable emulsions generally have a higher likelihood of forming hydrate plugs.10 The oil-dominant model available in OLGA® currently accounts for the formation of a viscous slurry, but the simulator does not allow increases in apparent slurry viscosity to impact the momentum balance. As a consequence, OLGA® simulations of pressure drop can only be influenced only by (i) gas consumption to form hydrate or (ii) hydrate particle accumulation, which is controlled by decreasing the slip factor between hydrate particles and the continuous phase. It is also important to consider that changes in hydrate growth rates between simulations will also affect frictional pressure drop predictions, by affecting the amount of hydrate present in the slurry or on the wall. Figure 8a shows a comparison between the experimental and simulated pressure drop in Experiment 1, where OLGA® simulations were run for two different values of the kinetic rate factor, k1: (i) the intrinsic kinetic rate reported by Vysniauskas and Bishnoi29 (k1 = k1VB); and (ii) a theoretical rate that was 10 times higher than the intrinsic rate (k1/k1VB = 10), to artificially increase hydrate growth rates and identify the limiting behaviour of the simulation. In all cases, the homogenously-dispersed hydrate phase travelled at the same velocity as the water phase; this specification prevents deposition at any point in the flowloop. The results demonstrate that the simulation diverges from experimental results, suggesting that adjustment of a scaling factor for the kinetic rate alone is not sufficient to reproduce the experimental pressure drops. ACS Paragon Plus Environment

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Hydrate particle deposition on the flowline wall may be artificially enforced within OLGA® by imposing a low- or no-slip condition between the hydrate and oil/water phases6, as shown in equation (4). In calculating the hydrate particle velocity (uhyd), OLGA® allows the user to specify the hydrate-oil (Co) and hydrate-water (Cw) slip ratios, which depend on the oil (uo) and water phase (uw) velocities. ./0 = 12 .2 + 14 .4

(4)

In this work, the first term on the right side of equation (4) was ignored given the absence of any hydrocarbon liquid in any of the experiments. Figure 8b shows the comparison between Experiment 1 and the OLGA® simulations with k1/k1VB = 1, where CW was set to 0.01, 0.03 or 0.10. The simulation only returned a representative pressure drop behaviour for the lowest slip velocity (1% of the liquid water phase velocity), which enables severe hydrate build-up in the flowloop.

Figure 8. Simulation versus experimental pressure drop (Experiment 1) for (a) varying kinetic reaction rate coefficients k1, where the hydrate phase velocity is equal to the water phase velocity; (b) varying the hydrate-water velocity slip factors (Cw), where the kinetic rate coefficient k1 is equal to the value of k1VB and (c) 100% hydrate deposition; the kinetic rate was reduced by half to better match the flowloop data. Setting the hydrate slip factor, CW, to zero forces all hydrate particles formed in the simulation to deposit at the pipe wall (Figure 8c). One cannot choose the quantity of hydrates formed that remain on the wall in OLGA®, therefore it is not currently possible to match growth rates and pressure drop simultaneously. However, the condition of half the intrinsic kinetic rate of hydrate growth and 100% deposition provided a reasonable representation of the measured pressure drop across the flowloop. ACS Paragon Plus Environment

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With an understanding that the pressure drop behaviour in these experiments can be usefully approximated with hydrate deposition on the wall, predictions using the in-house model were compared against the six flowloop experiments described in Di Lorenzo et al.16. Figure 9 shows the pressure drop deviation between the experimental and simulated results as a function of run time for the experiments. Similar pressure drop behaviour was observed for all six simulations, generally showing a steady, monotonic increase in the pressure drop of the same order of magnitude as the experimental results.

18

Moderate Subcooling

Experiments In-House Model

16

High Subcooling


270


240

14

210

12

Experiment 6 (Tsub = 3.9°C)

10

180 Experiment 4 (Tsub = 8.6°C)

150

8


6

120 90

4


2

(a)

0 0

10

20

30

Time [min]

40

60


50 0

10

20

30

40

50 0

Time [min]

30


(b) 10

20

30

Pressure Drop [psi]

Low Subcooling

Pressure Drop [bar]

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(c) 40

0

50

Time [min]

Figure 9. Pressure drop predictions using the in-house model and kinetic hydrate formation (solid lines) for all six Hytra flowloop experiments (circles). The simulation was set to immediately deposit a frac9 tion of hydrate particles on the flowline wall (5/0,4788 ) upon formation after adjustment of the intrinsic VB kinetic rate (k1/k1 ). Parameters used in each model are given in Table 4. The in-house model is able to simulate the experimental data well because of its ability to match both hydrate growth rates and pressure drop through adjustment of the kinetic rate factor (k1/k1VB) and the fraction of hydrate formed that remains on the wall (5/0,4788 ). The values of the final parameters for each simulation are given in Table 4. The deposits were assumed to be non-porous, and changes in this assumption would affect the volume occupied by the hydrate deposits on the wall, and therefore the predicted pressure drop.


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Table 4: Required growth rate scaling (k1/k1VB) and fraction of hydrates that remain on the wall ;

Simulating Hydrate Growth and Transport Behavior in Gas-Dominant

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