Rheological properties of CO2 hydrate slurry produced in a stirred tank reactor and a secondary refrigeration loop

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Rheological properties of CO2 hydrate slurry produced in a stirred tank reactor and a secondary refrigeration loop Salem Jerbi a,*, Anthony Delahaye a, Je´re´my Oignet a, Laurence Fournaison a, Philippe Haberschill b a b

IRSTEA, Parc de Tourvoie BP 44, Antony 92163, France Universite´ de Lyon, INSA-Lyon, CETHIL, UMR 5008CNRS, Villeurbanne F-69621, France

article info

abstract

Article history:

The aim of this paper is to present the rheological properties of CO2 hydrate slurry for a use

Received 21 September 2012

as secondary fluids in refrigeration systems. A set-up composed of a stirred tank reactor

Received in revised form

and a circulation loop was used to study CO2 hydrate slurry formation and flowing.

18 December 2012

Rheological properties of CO2 hydrate slurries circulating in the loop were determined by

Accepted 22 December 2012

the capillary viscometer method. The results show a shear thinning behaviour of the CO2

Available online 12 January 2013

hydrate slurries for a solid fraction up to 22%. This behaviour is correlated by an Ostwaldde-Waele empirical equation, which takes into account the hydrate fraction of the slurry.

Keywords:

The apparent viscosity of CO2 hydrate slurry was estimated from the model and a good

Carbon dioxide hydrates

agreement was found with the experimental data. A comparison with literature shows the

Phase change

importance of using a stirred reactor for slurry homogenisation, which allows the decrease

Slurries

of the apparent viscosity of the slurry.

Rheology

ª 2013 Elsevier Ltd and IIR. All rights reserved.

Multiphase flow Refrigeration

Proprie´te´s rhe´ologiques d’un coulis d’hydrate de CO2 produit dans un bac sous agitation et une boucle secondaire Mots cle´s : hydrates de dioxyde de carbone ; changement de phase ; coulis ; rhe´ologie ; e´coulement multiphasique ; froid

1.

Introduction

The use of a secondary circuit for cold distribution is an alternative to reduce the quantity of traditional refrigerants.

The secondary refrigerant distributes cold using alternative environment-friendly fluids and the primary circuit using traditional greenhouse-effect refrigerants is then confined and minimized. However, secondary refrigeration requires

* Corresponding author. Tel.: þ33 (0)1 40 96 60 25; fax: þ33 (0)1 40 96 60 75. E-mail addresses: [email protected] (S. Jerbi), [email protected] (A. Delahaye), [email protected] (J. Oignet), [email protected] (L. Fournaison), [email protected] (P. Haberschill). 0140-7007/$ e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2012.12.017

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T U

Nomenclature Notation D k L n P Q R

Temperature (K) Fluid velocity (m s1)

Greek letters DP Pressure drop (Pa) Shear rate at the wall (s1) g_ w Volume fraction of hydrate (vol.%) fs Minimal shear or yield stress (Pa) s0 Shear stress at the wall (Pa) sw Apparent viscosity (Pa s) mapp

Pipe diameter (m) Consistency index (Pa s) Tube length (m) Behaviour index Pressure (MPa) Volume flow rate (m3 s1) Pipe radius (m)

the use of heat exchangers and additional circulating pumps which generate exergy losses in the system. In order to limit these losses, and thus to improve the system efficiency, it is possible to transport the cold via a two-phase (solideliquid) secondary refrigerant (TPSR), composed of solid particles in suspension able to store a large amount of energy by latent heat. Moreover, the temperatures of TPSR are stable, which minimizes the thermodynamic irreversibility in the exchangers. Ice slurries (suspension of ice crystals in a carrying liquid phase) are the most current TPSRs (Guilpart et al., 2006), but their industrial development is limited by the generators based on mechanical processes (scraped or brushed surface exchangers) which are often power-limited. Clathrate hydrate slurries (CHS) may also be used as TPSRs. Gas hydrates are crystalline solids resulting from the arrangement of water molecules linked by hydrogen bonds constituting cages

around stabilizing gas molecules. They were primarily studied in oil and gas industry since they could appear in the pipelines due to natural gas (methane, ethane) and water coexistence under appropriate pressure and temperature conditions and then provoke pipeline plugging. Studies on hydrate formation, remediation, and prevention are still numerous (Sloan, 2005). CHS are also investigated for natural gas capture processes, where gas is injected in liquid water-oil emulsion to form hydrates (Fouconnier et al., 2002; Huang et al., 2009), and for CO2 capture and sequestration (Li et al., 2009a, 2009b; 2011). The first studies on rheology for hydrate slurries were performed by Pinder (1964) on a suspension of hydrogen sulfide hydrate and tetrahydrofuran (H2S-2THF-17H2O). Using a rotational viscometer, the author showed the thixotropic behaviour of the slurry with a gel structure at very low hydrate concentration. Later, hydrate-slurry flow properties were

Table 1 e Work on rheology of hydrate slurries. *work for refrigeration applications; in bold: our work; HC: hydrocarbon; TA: surfactant; AA: antiagglomerant; fs: hydrate volume fraction [ Vsolid/(Vsolid D Vliquid); R141b: refrigerant HCFC 141-b; OdW: Ostwald-de-Waele; S-thin.: Shear thinning; S-thicken.: Shear thickening; HB: Herschel-Bulkley. Authors

Hydrate

Liquid

fs

Viscometer

Behaviour

Pinder (1964)

H2S þ THF

Aqueous

Rotating

<0.01

Austvik and Bjorn (1992) Fukushima et al. (1999)* Andersson and Gudmundsson (1999) Andersson and Gudmundsson, 2000 Oyama et al. (2002)

HC TBAB HC

Organic Aqueous Organic þ AA

Rotating Capillary Capillary

e 0.22e0.31 0e0.1

Thixotropic gel, in 76 h mapp: decrease to 60 at 23 mPa s No measure of sw OdW S-thin.: mapp: 30e2000 mPa s Bingham: k: 3.4e5.5 mPa s

CH4

Aqueous

Capillary

0.01e0.1

Bingham: k: 1e3.5 mPa s

CO2

Aqueous

e

mapp increase before nucleation, decrease after

Fidel-Dufour and Herri (2002) Peysson et al. (2003) Darbouret et al. (2005)* Xiao et al. (2006)* Fidel-Dufour et al. (2006) Delahaye et al. (2008)*

HC HC TBAB TBAB CH4 CO2

Organic þ TA Organic Aqueous Aqueous Organic þ AA Aqueous

Magnetic (Stress) Capillary Capillary Capillary Capillary Capillary Capillary

e 0.1e0.3 0.04e0.53 0e0.16 0.07e0.18 0.04e0.1 0.1e0.2

Wang et al. (2008)* Delahaye et al. (2011)* Ma et al. (2010)* Kumano et al. (2011)* Hashimoto et al. (2011)*

R141b CO2 TBAB TBAB TBAB TBAF TBPB HC

Aqueous Aqueous D TA Aqueous Aqueous Aqueous Aqueous Aqueous Organic

Capillary Capillary Capillary Ubbelohde Plate Plate Capillary Rotating

mapp increase before nucleation, decrease after OdW S-thicken. n z 2, k z 2.103 mPa s Bingham: k: 8e170 mPa s OdW S-thin.: mapp: 4e42 mPa s Newtonian: 2.5e3.5 mPa s w OdW S-thicken. HB S-thin.: mapp: 4e42 mPa s (at 400 sL1) OdW S-thicken.: mapp: 1.1e1.7 mPa s (at 400 s1) Newtonian: mapp: 3.3e16.6 mPa s OdW S-thin.: mapp: 3e100 mPa s OdW S-thin.: mapp: 2e5 mPa s OdW S-thin.: mapp: 3.5e1000 mPa s OdW S-thin.: mapp: 10e750 mPa s OdW S-thin.: mapp: 4-41 mPa s HB S-thin.: mapp: 500e3000 mPa s

Clain et al. (2012)* Webb et al. (2012)

0.1e0.68 0.04e0.1 0.06e0.2 0.02e0.25 0.12e0.7 0e0.42 0e0.28 0.2e0.45

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investigated due to the problems of agglomeration and transportability in pipelines. Various studies in circulation loop were carried out on systems composed of natural gas hydrates suspended in organic (Austvik and Bjorn, 1992; Andersson and Gudmundsson, 1999; Austvik et al., 2000; Camargo et al., 2000; Camargo and Palermo, 2002; FidelDufour and Herri, 2002; Peysson et al., 2003, 2004; Sinquin et al., 2004; Fidel-Dufour et al., 2006) or aqueous (Nygaard, 1989; Andersson and Gudmundsson, 2000) carrying phases. The flow properties of hydrate slurries were also studied for refrigeration applications. Various studies concern the rheology of suspensions in aqueous phase for salt hydrates (Fukushima et al., 1999; Darbouret et al., 2005; Xiao et al., 2006; Ma et al., 2010; Hashimoto et al., 2011; Kumano et al., 2011; Clain et al., 2012; Webb et al., 2012) or gas hydrates (Delahaye et al., 2008, 2011; Wang et al., 2008; Delahaye et al., 2011). Table 1 includes all the rheological studies on hydrate slurries in refrigeration and some studies about oil and gas field and the work of Pinder (1964) and Oyama et al., 2002. According to Table 1, unlike ice slurry (Ayel et al., 2003), it is noted that most of hydrate slurries appear to be nonNewtonian even at low solid fraction. However, the authors do not agree on the type of rheological behaviour of slurries (Bingham, Ostwald-de-Waele, Herschel-Bulkey, Shear thinning, Shear thickening, thixotropic.). The work achieved at IRSTEA showed the interest of using CO2 hydrate slurries (CO2-HS) in secondary refrigeration, in particular due to their high energy content related to the high latent heat of melting of hydrates (374 kJ kg1). The latter can be formed under temperature conditions adapted to airconditioning applications (5e20  C). Furthermore hydrates can be generated by CO2 injection in a cooled aqueous solution, avoiding the use of mechanical processes. A simple loop was designed in previous work (Marinhas et al., 2006; Delahaye et al., 2008) to provide a first approach of CO2-HS formation and flow characterization. Thermodynamic and flow conditions (formation, instability.) were also studied in presence of dispersive additives to improve the rheological properties of CO2-HS (Delahaye et al., 2011). Nevertheless, this loop cannot be considered as a pilot loop since the system runs in isothermal condition and is not equipped with heat exchangers allowing heat transfer study. Moreover, this previous loop was not conceived to recover and to manage CO2 gaseous emissions involved during heat restitution by hydrate melting. A second loop was then implemented with heat exchangers and a tank reactor to optimize hydrate slurry formation (Jerbi et al., 2010a,b,c). The major objective of this paper is to present new rheological data related to CO2 hydrate slurry flowing in this new set-up. These results allow the conception of an empirical rheological model based on a Herschel-Bulkley-type equation. The results of this model are compared to rheological data from literature on hydrate slurry.

2.

Material and methods

The dynamic loop used for the generation and melting of CO2HS is presented Fig. 1. The system is composed of two parts, one for the formation of CO2-HS (storage) in the tank and

Separator gas/liquid

Heat Exchanger

Liquid Gas

Differential Pressure Gauge

Compressor

Pump

Coriolis Flowmeter Injection Gas

Slurry Tank Reactor

Fig. 1 e Design of the loop D tank reactor refrigeration system.

another part for its circulation and dissociation. The second part corresponds to the circulation loop. This loop allows CO2HS flow and heat transfer to be studied. In this paper, only rheological data are presented.

2.1.

Description of the experimental tank reactor

The tank reactor has a capacity of 26.47 L and can resist to a pressure of 4.5 MPa. It is made out of stainless steel and equipped with two glass windows in order to observe CO2 hydrate formation (Fig. 2). The top of the tank is equipped with PT 100 (0.3 K) and pressure transducers (0e5 MPa, 0.05% of full scale) and a mixer. This mixer (Burgmann MAK, power: 0.55 kW) operates with magnetic entrainment and has a double helix adjustable (diameter 100 mm). It is used to increase the rate of CO2 hydrate slurry formation by breaking hydrate barrier or crust which can form at the gaseliquid interface and prevent gas propagation into water during hydrate formation. The bottom of the tank is also equipped with thermocouples.

Mixer Water inlet

Windows

Gas injection

Inlet/Outel of double shell

Fig. 2 e Design of the tank reactor.

Slurry/water outlet

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One exit at the bottom is used for hydrate slurry outlet. Moreover, the tank is equipped with two inlets for water or slurry, and two inlets for gas, one on the cover for gas injection in the free part of the tank and another one for gas injection into water (Fig. 2). The gas injection is controlled by mass flow controllers (model SLAA5850S, flow rate: 0e1.5 L mn1. The cooling of the slurry inside the tank reactor is achieved thanks to a chiller (263.15e293.5 K) connected to the double shell of the tank.

2.2.

Description of the experimental dynamic loop

The experimental loop is composed of 316 L stainless pipes with an internal diameter of 7.74 mm and an external diameter of 9.52 mm. The inner volume of the loop was approximately determined at 0.75 L. The experimental loop is equipped with a 220-type Axflow Micro Pump (adjustable speed, differential pressure of 0.4 MPa, static pressure of 10 MPa, flow rate pump max of 200 L h1). The pump is controlled by a Leroy Somer speed variator. The flow rate is measured by an Emerson CMF050 Coriolis Flow and Density Meters (0e250 L h1, 0.2% of reading) with two parallel tubes of measurement. This flowmeter is placed at the outlet of the tank to measure the mass flow, the density and the temperature of the CO2 HS. A differential pressure gauge (0e400 mbar adjustable, 0.04% of full scale) is placed on a linear part of the circuit to measure pressure drops generated by the displacement of the slurry. The device is also equipped with eight PT 100 (0.3 K) located at various positions and two pressure gauges (0e5 MPa, 0.05% of full scale). The dynamic loop is able to measure heat transfer with heat exchanger systems and to manage CO2 gaseous emissions involved during hydrate melting, but this part was not used for the present work and thus is not presented in this paper. Finally, the whole system (tank reactor þ loop) is placed in a temperaturecontrolled cold room (3.39  3.48  2.51 m).

2.3.

CO2-HS formation protocol

In this section, the protocol of CO2 hydrate formation by cooling is presented. The studied system is a watereCO2 mixture in the tank reactor and the loop prepared by dissolution of CO2 in water. The initial pressure and temperature are 3 MPa and 10  C in the tank (and 10  C in the temperaturecontrolled cold room). In this condition, the system is in liquidevapour (LweV) state (Delahaye et al., 2008). The mixer of the tank and the pump of the loop are used to mix and to circulate the solution. First, the temperature is maintained constant in order to reach CO2-in-water dissolution equilibrium (Fig. 3). Then, the cooling of the liquid solution is performed by the chiller in order to reach 275.15 K in the tank. Temperature and pressure in the tank decrease to cut the liquid-hydrate-vapour (Lw-HeV) equilibrium curve. The system is then in metastable liquidevapour equilibrium without hydrate. After several minutes of cooling in the metastable field, a rupture of metastability occurs and causes a temperature peak and a strong pressure drop. This temperature and pressure evolution is related to hydrate formation, which is an exothermic and gas-consuming phenomenon. Finally, pressure and temperature conditions reach the Lw-HeV

Fig. 3 e CO2 hydrate formation on the (P-T) diagram phase.

equilibrium curve and hydrates continue to form until temperature and pressure are constant (Fig. 3).

2.4.

Capillary viscosimeter method

The aim of the present work is to characterise the rheological behaviour of CO2 hydrate slurry, in order to determinate the apparent viscosity mapp of the slurry as a function of hydrate fraction. Indeed, the data are essential for the control of hydrate slurry flow. After hydrate formation and stabilisation, measurements on hydrate slurry flow in the loop are performed using the differential pressure gauge and the flow meter. This device represents can be considered as a capillary viscometer and used to evaluate hydrate slurry rheology based on various assumptions. Hydrate slurries must be considered as pseudo-homogeneous fluids, circulating in a laminar regime in cylindrical pipe without wall slip. Finally, flow rate, shear stress, and shear rate can be, represented at the wall by the Rabinowitsch and Mooney’s equation (Metzner and Reed, 1955) Q 1 ¼ pR3 s3w

Zsw _ s2 gds

(1)

0

Where sw is the shear stress at the wall, related to the pressure drop DP by friction: sw ¼

D DP 4 L

(2)

Derivation of the expression of Rabinowitsch and Mooney leads to an expression of the shear rate at the wall: g_ w ¼

8u 3n þ 1 D 4n

(3)

Where n is the behaviour index defined as: n¼

d lnsw 8u d ln D

(4)

Thus, measurements of pressure drops DP and flow velocities u combined to Eqs. (2) and (3) allow the rheological behaviour of the fluid to be established according to HerschelBulkley’s model : sw ¼ kg_ nw þ s0

(5)

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Finally, the apparent viscosity of the slurry is defined by (Andersson and Gudmundsson, 2000): (6)

Various studies reported by (Delahaye et al., 2011; Clain et al., 2012) show this method is the most widespread in literature to model the rheological behaviour of hydrate slurries in aqueous phase (Table 1).

1.2

Ln(DΔP/4L)

mapp

sw ¼ g_ w

1.4

1.0 0.8

y = 0.63x - 2.75

0.6 0.4 0.2 0.0

3.

Results and discussion

5.0

5.5

6.0

6.5

Ln(8Ud/D) The system was loaded for various CO2 concentrations in water in order to obtain hydrate solid fraction between 0 and 22 vol.%. The hydrate solid fraction is calculated from a model based on a mass balance on CO2 in its various phases (liquid, gas, hydrate), previously described in detail (Marinhas et al., 2006, 2007). For each solid fraction, the rheological properties of CO2 hydrate slurries circulating in the loop were determined from experimental measurements of pressure drop and flow rate (capillary viscometer method). Different flow rates were applied using the circulation pump and resulting pressure drops were measured. Fig. 4 shows an example of measurements representing various plateaus of flow rate and corresponding pressure drop. The first rheological property of CO2 hydrate slurry to be determined is the behaviour index n from Eq. (4). Fig. 5 represents an example of behaviour index determination for hydrate fraction of 18.14 vol.%. The experimental points can be approximated by a linear curve. Based on Eq. (4), the slope of the curve corresponds to the behaviour index n. In the present case, the behaviour index is lower than 1, corresponding to a non-Newtonian shear-thinning behaviour. Fig. 6 shows the behaviour index n obtained for various solid fractions between 0 and 22 vol.%. When the solid fraction increases from 0 to 22 vol.%, the behaviour index n decreases, indicating that the non-Newtonian (n s 1) and the shear-thinning (n < 1) tendency is increased. Consequently, the apparent viscosity of the slurry, deduced from Eq. (6), decreases as the applied shearing stress increases, like the majority of hydrate slurries in aqueous solution. Finally, the behaviour index data can be

Flow rate (l.h-1)

180

Flow rate Pressure drop

160

18 16

140

14

120

12

100

10

80

8

60

6

40

4

20

2

0

0

50

100

150

Time (s) Fig. 4 e Example of pressure drop and flow rate measurements.

0 200

Pressure drop (mbar)

20

200

Fig. 5 e Example of behaviour index determination from Eq. (4) for a CO2 hydrate fraction of 18.14%.

approximated by the following correlation (for hydrate fraction between 0% and 22%): n ¼ 1:82fs þ 1

(7)

The next step consists in determining the other parameters of the general model of Herschel-Bulkley, given by Eq. (5), i.e. the consistency index k and the yield stress s0. Fig. 7 represents the shear stress sw, deduced from Eq. (2), :n versus gw , deduced from Eqs. (3) and (4). The experimental point can be modelled by a linear curve where the consistency index k is the slope and the yield stress s0 is the ordinate at the origin, according to Herschel-Bulkley’s model. In our case, this curve can be adjusted by a linear curve which passes through the origin. This implies that the values of the yield stress for CO2 hydrate slurry can be considered null: s0 ¼ 0

(8)

Fig. 8 represents the values of k as a function of fs. The correlation of the consistency index as a function of solid fraction obtained from experimental data is given by: k ¼ 0:0018 expð17:976 fs Þ

(9)

The consistency index k increases strongly from 10 vol.% of solid fraction which means apparent viscosity increases significantly in the same conditions. In a first approach, since the yield stress was neglected, the rheological behaviour for CO2 hydrate slurry with solid fraction between 0 and 22 vol.% could be represented by an Ostwald-de-Waele’s model: sw ¼ kg_ n

(10)

Including Eqs. (7)e(9), the Ostwald-de-Waele’s model becomes: sw ¼ 0:0018 expð17:976fs Þ g_ ð1:82fs þ1Þ

(11)

The model of Ostwald-de-Waele was compared to experimental results for hydrate fractions between 0 and 20% (Fig. 9). This comparison shows a good agreement in the range of solid fraction between 0 and.22 vol. %. However at 21.66 vol.% discrepancies appear. In fact, above 20 vol.%, the flow in the loop is more difficult to maintain in laminar regime because the mixing in the tank was not sufficient to homogenise a slurry at high solid fraction. During the

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Consistency index , k (Pa s n)

1.2 1

n

0.8 0.6

y = -1.82x + 1.00

0.4 0.2

.1 0.1

0.05

0.15

s

0.2

(vol.%)

0.02

mapp ¼ 0:0018 expð17:976fs Þ g_ ð1:82fs Þ

(12)

Fig. 10 show that the apparent viscosity decreases as the shear rate increases and CO2 hydrate fraction decreases. This is an expected result and rather classical for the shearthinning fluids such as hydrate slurries. The present rheological characterisation of CO2 hydrate slurries is compared to the work of literature related to gas hydrates in flow in aqueous solutions. Our previous work (Delahaye et al., 2008, 2011) were carried out on CO2 hydrate slurries formed in a simple loop, for shear rates between 450

20%

y = 0.047x y = 0.036x y = 0.022x y = 0.015x y = 0.012x y = 0.009x

2 1

5.20% 9.00% 10.70% 12.04% 14.30% 16.56% 18.14% 19.70% 21.60%

5.20% 5.20% mod 9.00% 9.00% mod 10.70% 10.70% mod 12.04% 12.04% mod 14.30% 14.30% mod 16.56% 16.56% mod 18.14% 18.14% mod 19.70% 19.70% mod 21.66% 21.66% mod

4.0 3.5 3.0 2.5 2.0 1.5

y = 0.005x

1.0 0.5

0 0

50

100

150 w

:n

n

200

250

-1

(s )

Fig. 7 e swas a function gw for hydrate fraction between 0 and 22 vol. % (Points: experimental data; lines: model data).

25%

and 1050 s1 and solid fraction between 4 and 20 vol.%. According to these results, the CO2 hydrate slurries follows a Herschel-Bulkley’s model (Eq. (5)) close to a shear thickening Ostwald-de-Waele’s model for solid fration lower than 10%, reduced to a Bingham model for a solid fraction of 10%, and having a shear thinning tendency for fractions above 10%. A second study about CO2 hydrate slurries in the presence of antiagglomerant additives (Caflon, block copolymer) was performed in the simplified loop for shear rates between 450 and 1350 s1 and solid fractions ranging from 4 to 10 vol.% (Delahaye et al., 2008, 2011). According to these results, the presence of additives allows CO2 hydrate slurries to have a Newtonian behaviour. In the present study (tank reactor þ loop), the rheological behaviour of CO2 hydrate slurries follows a law of Ostwald-deWaele for a solid fraction between 0 and 22 vol.% with a behaviour index less than unity, reflecting a shear-thinning tendency, as CO2 hydrate slurries above 10 vol.% in the simple loop (Delahaye et al., 2008, 2011) behaviour difference observed at low concentrations of hydrate particle can be explained by the presence of a stirred tank reactor in the present study which allows the slurry homogenisation. In

(Pa)

y = 0.060x

5

15%

4.5

y = 0.087x

6

10%

φs (vol. %)

w

7

5%

Fig. 8 e Consistency index as a function of CO2 hydrate fraction (points: experimental; line: model).

measurements, some plugging could appear, which explain the disparity between the model and the experimental data above 20 vol.%. Nevertheless, our objective was to propose a predictive model related to the influence of solid fraction on the rheological behaviour of hydrate slurries, useful for comparison with data from literature at various hydrate fractions. To suggest an alternative reading, Fig. 10 is a representation of the apparent viscosity as a function of shear rate by applying Eq. (6). The apparent viscosity of CO2 hydrate slurry can be modelled from previous Eqs. (6) and (11):

(Pa)

0.04

0.25

Fig. 6 e Behaviour index n as a function of CO2 hydrate solid fraction.

w

y = 0.0018e17.976x

0.06

0% 0

3

0.08

0.00

0

4

0.10

300

0.0 100

200

300

400 w

500

600

700

800

-1

(s )

Fig. 9 e CO2 hydrate slurry rheograms for hydrate fraction between 0 and 22 vol. % (points: experimental; lines: model).

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12

5.20% 5.20% mod 9.00% 9.00% mod 10.70% 10.70% mod 12.04% 12.04% mod 14.30% 14.30% mod 16.56% 16.56% mod 18.14% 18.14% mod 19.70% 19.70% mod 21.66% 21.66% mod

app

(mPa.s)

10 8 6 4 2 0 100

200

300

400

500

600

(1999). It may be emphasized that both studies were carried out in systems involving a tank reactor and a circulation loop, which confirms the interest of slurry stirring. Nevertheless, the rheogram of CH4 hydrate slurries was modelled by a Bingham model, while the CO2 hydrate slurries studied in the present work shear thin following an Ostwald-de-Waele’s model. The similarity of results can be explained however by the fact that the Bingham model can provide data close to that obtained with a model of Ostwald-de-Waele on a narrow range of shear rate.

700

-1

(s )

4.

Fig. 10 e Apparent viscosity of CO2 hydrates slurries for hydrate fraction between 0 and 22 vol. % (points: experimental; lines: model).

fact, the stirred reactor can limit agglomeration phenomena, more frequent in a simple loop without mechanical stirring. Fig. 11 proposes a comparison between various viscosity results obtained for CO2 hydrate slurries with or without surfactant (Delahaye et al., 2008, 2011), and for CH4 hydrate slurries calculated from a Bingham model (Andersson and Gudmundsson, 2000). First of all, the overall results confirm that the apparent viscosity increases with hydrate solid fraction. The apparent viscosity calculated according to the expression of Thomas (1965) is well below the viscosity determined on hydrate slurries, which were already pointed out by Kauffeld on ice slurries (2005). This representation shows that the CO2 hydrate slurries formed in the new system (tank reactor þ loop) present viscosity values significantly lower than those of CO2 hydrate slurries formed in a simple loop (Delahaye et al., 2008, 2011) with or without surfactant. This difference confirms the ability of the stirred tank reactor to homogenise the slurry, and then to limit agglomeration phenomena and fluid flow resistance. It can be noticed that viscosity values, and consequently rheograms, obtained in the present study are nearly identical to those of CH4 hydrate slurries obtained in the work of Andersson and Gudmunsson

25

CO2 hydrate slurry with tank (present work) CH4 hydrate slurry with tank [20] CO2 hydrate slurry without tank [29] CO2 hydrate slurry without tank with surfactant [31] Thomas [40]

μapp (mPa.s)

20 15 10 5

Conclusion

Characterization of CO2 hydrate slurries flowing in a dynamics loop associated to a stirred tank reactor showed that the slurry had a non-Newtonian behaviour with a shear thinning tendency and can be described by a law of Ostwald-de-Waele for concentrations of CO2 hydrate solid fractions from 0 to 22 vol.%. Beyond 22% of solid fraction, problems of heterogeneity limited the rheological study. The study shows that the apparent viscosity of CO2 hydrate slurries increases with increasing solid fraction, but decreases with increasing shear rate. This observation is consistent with results generally obtained on the shear-thinning slurry. Comparison of rheological properties of CO2 hydrate slurries in this system (tank reactor þ loop) compared with literature data shows that the slurry behaviour is very close to the CH4 hydrate slurries, itself studied in a system composed of both tank reactor and loop. The comparison with previous studies on CO2 hydrate slurries in simple loop without tank (with or without surfactant) also shows the importance of using a stirred reactor for the homogenisation of slurry. In fact, a decreasing of the shear stress and therefore of the apparent viscosity of the slurry was observed in the system including a stirred tank. This dependence could be explained by the impact of the experimental device on the fluid structure (liquideparticle interactions, fluid flow resistance, agglomeration phenomena). In the context of refrigeration applications, the interest of reducing slurry viscosity can be related to the limitation of the pumping energy for the secondary loop. Viscosity reduction could also be related to the improvement of heat transfer coefficients for energy restitution. This hypothesis should be tested in future work. Nevertheless, if the presence of a stirred reactor could improve fluid flow properties, the gain due to this improvement (mainly related to the pump) must be weighed against the energy required by the agitation system. A further work could then consist in modelling the energy efficiency of the system including hydrate formation in a stirred tank reactor, pumping of the slurry, and heat restitution by hydrate melting in heat exchanger.

0 0

0.05

0.1

0.15

φs (vol. %) Fig. 11 e Comparison between apparent viscosity vs. solid fraction for CO2 hydrate slurry with and without surfactant (Delahaye et al., 2008, 2011) and CH4 hydrate slurry (Andersson and Gudmundsson, 2000).

Acknowledgement The authors would like to acknowledge financial support from ADEME (Agence pour le De´veloppement et la Maıˆtrise de l’Energie).

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 2 9 4 e1 3 0 1

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