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A stability criterion for gas-hydrate slurry stratified flow was developed. The model was based on one-dimensional gas-liquid two-fluid model and perturbation method, considering unstable factors including shear stress, gravity, and surface tension. In addition, mass transfer between gas and liquid phase caused by hydrate formation was taken into account by implementing an inward and outward natural gas hydrates growth shell model for water-in-oil emulsion. A series of gas-hydrate slurry flow experiments were carried out in a high-pressure (>10 MPa) horizontal flow loop. The transition criterion of smooth stratified flow to other flow patterns for gas-hydrate slurry flow was established and validated and combined with experimental data at different water cuts. Meanwhile, parameters of this stability criterion were defined. This stability criterion was proved to be efficient for predicting the transition from smooth to nonsmooth stratified flow for gas-hydrate slurry.

Gas hydrates are ice-like crystals formed by inclosing gas molecules (guests) in clathrates of water molecules (host) under high pressure and low temperature [

Conventionally, chemical-based injection and insulation are two major techniques to prevent hydrate plugging in offshore production pipelines. However, these two techniques are of high capital expenditure and technical limitations [

Flow pattern is the key issue in characterizing multiphase flow. There are two generally recognized methods for flow pattern determination: plotting flow pattern map according to the experimental data [

Though lots of investigations have been made on thermodynamic and kinetic of gas-hydrate formation and decomposition [_{2} hydrate slurry flow patterns in CO_{2}-water two-phase flow using different types of static mixers. Zerpa et al. [

In this paper, gas-hydrate slurry interface stability was analyzed by deriving dispersion function of the interface wave, and then the transition criterion from smooth stratified flow to other flow patterns was obtained. Thereafter, a set of gas-hydrate slurry flow experiments in high-pressure (>10 MPa) horizontal flow loop were carried out to investigate the flow pattern characteristics of gas-hydrate slurry flow. The transition criterion of smooth stratified flow to other flow patterns for gas-hydrate slurry flow was established and validated, combined with experimental data at different water cuts.

A one-dimensional two-fluid model describing gas-hydrate slurry stratified flow was developed. The schematic description is shown in Figure

Sectional geometry of gas-hydrate slurry stratified flow.

In Figure

For the gas-hydrate slurry stratified flow shown in Figure

By introducing slurry phase height

Momentum balance for each phase can be described as follows:

Interfacial shear stress

Substituting (

Gas and hydrate slurry shear stresses at the pipe wall can be expressed as (

Substituting (

Referring to the method used in interface stability analysis, where the steady-state contribution and perturbation contribution are separated,

Substituting (

Analytically solve quadratic equations (

Imaginary part:

Real part:

Neglecting interfacial tension, viscous shear stress, and interface shear stress, (

Algorithm to determine the stratified flow boundary by calculating liquid superficial velocity

To analyze stability transition criterion for stratified smooth flow using (

A double-pass high-pressure horizontal flow loop shown in Figure ^{3}/h) and a magnetic centrifugal pump (12.0 m^{3}/h). Gas is injected at the inlet of the test section. At the outlet of the test section, gas and liquid flow into an insulated separator and are redirected towards the test section after pressurization.

Sketch of high-pressure hydrate flow loop.

Thermocouples are placed along the pipe, inside the separator, inside the water-glycol system, and on different gas utilities. A Coriolis flow meter is stalled to measure liquid mixture density and flow rate. Two FM1000 gamma ray densitometers are available to measure the mean density of the multiphase fluid. Differential pressure sensors are installed to follow the evolution of pressure. Rapid data acquisition system permits the detection of quickly occurring events. A Focused Beam Reflectance Measurements (FBRM) probe and Particle Video Microscope (PVM) are installed to capture the evolution of the droplets, bubbles, or solid particles in fluid.

Deionized water, civil natural gas, and −20# diesel (compositions listed in Table

Compositions of civil natural gas and −20# diesel oil.

Comp | Mol% |
---|---|

Civil natural gas | |

N_{2} | 1.5603 |

CO | 2.0911 |

CO_{2} | 0.9129 |

C_{1} | 90.6061 |

C_{2} | 3.1207 |

C_{3} | 3.1207 |

iC_{4} | 0.3291 |

iC_{5} | 0.0425 |

n | 0.0106 |

| |

−20# diesel oil | |

| 0.8863 |

| 3.3586 |

| 5.3886 |

| 6.1990 |

| 6.7780 |

C_{16} | 6.8310 |

C_{17} | 7.9890 |

C_{18} | 7.4618 |

C_{19} | 6.3752 |

| 48.7325 |

Four groups of experiments at different water cuts (15%, 20%, 25%, and 30%) were carried out with gas, −20# diesel oil, and deionized water. Experimental conditions are listed in Table

Vacuum the experimental system one hour before injecting the required amount of −20# diesel oil, deionized water, and antiagglomerates.

Start and set the temperature controller at 18°C, the magnetic centrifugal pump at 40 Hz, and the control valve at 100%, get the liquid phase well circulated for least 5 hours to form water-in-oil emulation, and then open FBRM to monitor changes of the particles in the fluid.

Open the gas injection valve and pressure the system up to experimental set point, after the temperature of the system stays constant at 18°C and particles size observed using FBRM becomes stable.

Set the system temperature to experimental set point and cool the flow loop; hydrate would form as the temperature drops below the hydrate equilibrium temperate at the system pressure.

Maintain temperature and pressure at experimental set point for at least 5 hours to ensure the fully hydrate formation, adjust compressor inlet valve and pump speed to attain a gas flow rate within 20~195 kg/h and liquid flow rate within 75~860 kg/h, and then observe the flow pattern and record the data; for each data point presented in this work, flow rate of both gas and slurry phase were controlled and flow pattern was observed when the flow rates, pressure, and temperature were stabilized.

Increase the system temperature, stop the compressor and pump, evacuate the residual gas, discharge the experiment liquid, clean and flush the flow loop with compressed air, and replace it with nitrogen.

Repeat the procedure at different water cuts.

Experimental conditions of gas-hydrate slurry flow.

Water cut | | | ^{3}) | |
---|---|---|---|---|

15 | 4.13 | 277.33 | 0.0777 | 34 |

20 | 4.26 | 279.82 | 0.0875 | 75 |

25 | 3.85 | 278.99 | 0.0933 | 96 |

30 | 4.20 | 278.99 | 0.1000 | 88 |

In the experiments, 293 smooth and nonsmooth stratified flow pattern data points at different water cuts were obtained under steady-state conditions (Tables S.1–S.4), which was visually observed through the sight glass of the loop. Four types of flow patterns were found, including two typical flow patterns (stratified smooth flow and slug flow) and two transitional flow patterns (stratified wavy flow and short slug flow). Distinct gas-liquid interface can be observed, and the interface was flat for the stratified smooth flow (Figure

Photos of stratified flow: (a) stratified smooth flow and (b) stratified wave flow.

Photos of slug flow: (a) liquid film zone before liquid slug, (b) liquid slug, and (c) liquid film zone after liquid slug.

The morphologies, sizes, and distributions of fully formed hydrate particles in the slurry were recorded by PVM as shown in Figure

Hydrate particles (marked in the red circles) in gas-liquid multiphase system.

Chord length distribution before and after hydrates formation.

Based on experimental conditions listed in Table

Hydrate growth parameters of different water cuts and gas consumed rate.

Water cut | ^{2}⋅Mpa⋅s) | ^{2}/s | | ^{3} | | ^{3}⋅s |
---|---|---|---|---|---|---|

15 | 4.364 | 1.149 | 1.489 | 14.66 | 0.2527 | 7.188 |

20 | 7.606 | 13.82 | 1.527 | 6.339 | 0.2679 | 9.575 |

25 | 8.980 | 30.62 | 1.546 | 4.891 | 0.2767 | 11.72 |

30 | 16.16 | 321.5 | 1.564 | 2.994 | 0.2820 | 13.88 |

To compare the transition criterion of smooth stratified flow to other flow patterns for gas-hydrate slurry flow developed in this work with the classical flow pattern distribution models, flow region boundaries calculated using this model as well as that calculated using Taitel-Dukler [

Flow pattern map and boundary for stratified flow of gas-slurry flow at different water cuts: (a) 15%, (b) 20%, (c) 25%, and (d) 30%.

As is shown in Figure

All data points are summarized in Figure

Flow pattern distribution for gas-slurry stratified flow at different water cuts.

Hydrate fraction and water conversion rate at different water cuts.

The pattern experiment data of gas-hydrate slurry multiphase flow pattern in this work are not effectively enough to obtain more precise correlation parameters or investigate the flow pattern transition mechanism deeply. More experimental and theoretical research should be carried out in the future. Nevertheless, the good agreement with experimental data proved this work to be both feasible and significant.

In this work, a one-dimension two-fluid model for gas-hydrate slurry stratified flow was developed based on perturbation method, and a stability criterion for smooth stratified flow was proposed. In establishing the criterion, mass transfer between gas and slurry phase caused by hydrate formation was considered, and various mathematical techniques were applied in linearizing the equation sets. As the formation of hydrate would evidently complicate the flow, the influences of shear stress, gravity, surface tension, hydrate formation, and other unstable factors were considered. Compared with the classical two-phase gas-liquid stratified flow stability criteria proposed by Taitel-Dukler [

Groups of gas-hydrate slurry multiphase flow experiments were carried out on a most advanced high-pressure (>10 MPa) hydrate slurry flow loop in China, and 293 experimental data points of both smooth and nonsmooth stratified flow were obtained. Model parameters were generated in combining the experiment data with the gas-hydrate slurry stratified flow stability creation developed in this work, and the model was proved applicable in gas-hydrate slurry multiphase flow numerical simulation and characteristic study.

Cross area of the pipeline, m^{2}

Cross area of gas phase, m^{2}

Cross area of hydrate slurry phase, m^{2}

Viscosity critical wave velocity at the inception of instability, m s^{−1}

Nonviscosity critical wave velocity at the inception of instability, m s^{−1}

Correlated coefficient

Diameter of hydrates particle, m

Diameter of the wetted perimeter of hydrate slurry phase, m

Friction coefficient of interface gas-slurry phase

Friction coefficient of interface gas phase at pipe wall

Friction coefficient of interface slurry at pipe wall

Height of gas phase, m

Height of hydrate slurry phase, m

Parameter in wave equation

Pressure of gas phase

Pressure of hydrate slurry phase

Pressure at the interface

Relative pressure at the interface of gas phase

Relative pressure at the interface of hydrate slurry phase

Gas phase fraction of pipe cross area

Hydrate slurry phase fraction of pipe cross area

Reynolds number of gas phase

Wetted perimeter of gas phase, m

Wetted perimeter of interface gas-slurry phase, m

Wetted perimeter of hydrate slurry phase, m

Time, s

Velocity of gas phase, m·s^{−1}

Velocity of hydrate slurry phase, m·s^{−1}

Parameter in wave equation

Axial direction of the pipe, m

Distance to the infinitesimal segment, m

Radial direction of the pipe, m

Density of hydrates, kg/m^{3}

Density of oil phase, kg/m^{3}

Hydrate volume fraction

Maximum hydrate volume fraction

Mass transfer rate between gas phase and hydrate slurry phase, kg·s^{−1}·m^{−3}

Angle of inclination, rad

Interfacial tension, N/m

Density of gas phase, kg·m^{−3}

Density of hydrate slurry phase, kg·m^{−3}

Density of faster phase: subscript f represents the faster phase, kg·m^{−3}

Shear friction of interface gas phase at pipe wall, N

Shear friction of interface of gas-slurry phase, N

Shear friction of interface of slurry at pipe wall, N

Absolute roughness of the pipe wall, m

Friction calculated empirical parameter

Friction calculated empirical parameter

Parameter in wave equation.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (51306208, 51534007, and 51274218), National Science and Technology Major Project of China (2016ZX05028004-001), National Key Research and Development Plan of China (SQ2016YFSF010222), and Science Foundation of China University of Petroleum-Beijing (2462015YQ0404 and 201602), which are gratefully acknowledged.