- Email: [email protected]
Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance
EUROPEAN POLYMER JOURNAL
European Polymer Journal 41 (2005) 341–348
www.elsevier.com/locate/europolj
Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance Nicolas von Solms a, Nicoletta Zecchin a, Adam Rubin b, Simon I. Andersen a, Erling H. Stenby a,* a
Department of Chemical Engineering, Centre for Phase Equilibria and Separation Processes (IVC-SEP), Technical University of Denmark, Building 229 DTH, DK-2800 Lyngby, Denmark b NKT Flexibles I/S, Priorparken 510, DK-2605 Brøndby, Denmark Received 14 April 2004; received in revised form 27 September 2004; accepted 30 September 2004
Abstract We present solubility and diffusion data for the gases methane and carbon dioxide in the polymer poly(vinylidene fluoride). The polymer was cut from extruded piping intended for use in offshore oil and gas applications. Measurements were carried out using a purpose-built high-pressure microbalance. These properties were determined in the temperature range 80–120 C and in the pressure range 50–150 bar for methane and 20–40 bar for carbon dioxide. In general, good agreement was obtained for similar measurements reported in the literature. Solubility follows a HenryÕs law (linear) dependence with pressure. Diffusion coefficients for each of the gases in the polymer were also measured using the balance. Activation energies for diffusion and heats of solution for the two gases in the polymer were also determined. 2004 Elsevier Ltd. All rights reserved. Keywords: Gas permeation; Poly(vinylidene fluoride); Solubility; High-pressure microbalance; Diffusion
1. Introduction This paper is the third and final contribution in a series reporting on new measurements of solubility and diffusivity of gases in polymers employed as barrier membranes in flexible pipelines used as risers and flowlines in offshore oilwell production systems. The offshore oil and gas industry is increasingly turning to the use of flexible flowlines and risers for the development of mar-
* Corresponding author. Tel.: +45 4525 2875; fax: +45 4588 2258. E-mail address: [email protected] (E.H. Stenby).
ginal fields in mature regions and in locations without established infrastructure. A flexible flowline typically consists of an inner and outer polymer tube (inner lining and outer sheath) separated by helically wound steel armoring (see Fig. 1). In oil drilling operations materials have to be selected to withstand drilling mud, acid water and hydrocarbon liquids and gases at pressures up to 1000 bar and temperatures ranging from 4 C in deep sea to 180 C in some North Sea wells. The inner liner needs to be resistant to the passage of such gases as carbon dioxide, methane and hydrogen sulfide as well as the hydrocarbon process fluid, whereas the outer sheath protects the annulus from seawater as well as mechanical impact [1,2].
0014-3057/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2004.09.020
342
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
Fig. 1. Photograph of a cutaway section through a flexible pipe used in offshore oil and gas applications. The pipe-wall has been expanded in a cartoon for clarity. The polymer section labelled ‘‘inner liner’’ is the barrier membrane which is the subject of this study. Photograph courtesy of NKT Flexibles (I/S), Brøndby, Denmark.
In part I of this series [3] we determined the solubility and diffusivity of methane and carbon dioxide in highdensity polyethylene (HDPE) in the temperature range 25–50 C and pressures up to 150 bar (methane) and 40 bar (carbon dioxide). This work also contains a description of the experimental apparatus and method and the reader is referred there for details. Part II [4] contains results for the same gases in polyamide-11 (PA-11) at temperatures from 70 to 90 C and the same pressure ranges. Here we report results for the polymer poly(vinylidene fluoride) (PVDF) in the temperature range 80–120 C and the same pressure ranges. A PVDF polymer barrier is typically expected to operate at temperatures up to 130 C [5]. The temperature ranges under which these investigations were carried out are typical of the intended operating conditions for each of the three polymers. The susceptibility of a polymer to penetration by a gas is determined by its permeability. However, permeability is a two-step process, involving both the solution of the gas in the polymer and the diffusion of the gas through the polymer [6]. To understand the mechanisms of gas permeation through a polymer membrane, we must understand both of these processes. Typically, permeability is measured directly in experiments such as those of Flaconne`che et al. [7]. Diffusivity is then obtained from the permeability data, using the so-called ‘‘time-lag’’ method [8]. Finally, the solubility coefficient is inferred as the ratio of permeability to diffusivity. Using a balance, both the solubility and diffusivity are obtained directly. In general, when using a balance, the solubility results are more reliable than the diffusion measurements, since only initial and final values of the polymer mass during an experiment are required, while for diffusion coefficient it is necessary to know the time-dependent polymer mass. Although much of the thermodynamic and transport data of gases in polymers has been obtained from permeation measurement, solubility measurements have been reported before [9–12].
This paper is organized as follows: a brief discussion of materials and experimental procedures is given. Thereafter, the experimental results for solubility and diffusion coefficient of methane and carbon dioxide in PVDF are given. The results are compared with similar results from literature and discussed in terms of HenryÕs law and the Arrhenius temperature dependency. Some brief conclusions are then drawn.
2. Experimental The PVDF was a SOLEF VF2-CTFE copolymer grade 60512 with a reported density of 1.77 g/cm3. This was also the value measured by us. The polymer is an alloy consisting of 67% poly (vinylidene fluorideco-chloro trifluoro ethylene), 33% polyvinylidene fluoride and small amounts of high-density polyethylene. The sequence of measurements for PVDF is shown in Table 1. The crystallinity of the PVDF sample was estimated from differential scanning calorimetry to be about 45%. Polymer samples were cut from extruded pipe intended for offshore use. The polymer was machined down to the required thickness and then cut into circular discs. Enough discs are used to give a total sample weight of about 0.3 g. Two different polymer sheet thicknesses (about 0.2 and 0.5 mm, respectively) were used in this investigation, as listed in Table 1. The samples were annealed before an experiment at the temperature of interest for 24–48 h. Methane and carbon dioxide gas samples were supplied in industrial gas bottles by Air Liquide (Ballerup, Denmark). The purity of the gas samples was better than 99.99%. Gas densities over the range of pressure and temperature were obtained from a modified Benedict– Webb–Rubin (MBWR) equation of state, the parameters of which were obtained from P–v–T measurements up to 1000 bar [13]. The agreement with experimental density data is better than 0.1% over the whole range.
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
343
Table 1 Experimental sequence for gas solubility/diffusivity measurements in PVDF Gas
Temperature (C)
Pressure (bar)
No. of discs
Diameter (mm)
Sample mass (g)
Thickness (mm)
CH4
80
50 100 150
18 18 18
7.70 7.70 7.70
0.2669 0.2669 0.2669
0.18 0.18 0.18
CO2
80
20 30 40
18 18 18
7.70 7.70 7.70
0.2669 0.2669 0.2669
0.18 0.18 0.18
CH4
100
50 50 100 150
18 16 16 16
7.70 8.02 8.02 8.02
0.2669 0.2600 0.2600 0.2600
0.18 0.18 0.18 0.18
CO2
100
20 30 40
9 9 9
6.39 6.39 6.39
0.2706 0.2706 0.2706
0.53 0.53 0.53
CH4
120
50 100 150
5 5 5
8.72 8.72 8.72
0.2802 0.2802 0.2802
0.53 0.53 0.53
CO2
120
20 30 40
5 5 5
8.72 8.72 8.72
0.2802 0.2802 0.2802
0.53 0.53 0.53
30
29 mass loss
mass (mg)
Pure gas densities obtained from this equation of state within the range of applicability may be considered to be pseudo-experimental data. For conversion of solubility between mass and volume units the gas densities at STP are required. These were calculated to be 0.7175 kg/m3 for methane and 1.9777 kg/m3 for carbon dioxide. All measurements were done using a S3D-P highpressure microbalance provided by Sartorius AG (Go¨ttingen, Germany). The equipment and method are described in detail in von Solms et al. [3]. The experimental principle is described here in brief. The polymer sample is placed on one arm of a microbalance, with quartz spheres placed on the other as counterweights. Gas is admitted rapidly to the whole balance at the pressure of interest (or evacuated rapidly in the case of an evacuation run), after the whole apparatus, including the sample has been at the temperature of interest for at least 24 h. Fig. 2 shows the course of a single experiment, showing both a pressurization (solid curve) and an evacuation (dotted curve) run. The difference in the reading on the balance before and after a run, is the amount of gas adsorbed or desorbed. This value divided by the known mass of polymer gives the solubility of the gas in the polymer. The diffusion coefficient can also be obtained by studying the time-dependent behaviour of the adsorbed/desorbed mass of gas. Figs. 3 and 4 show typical results obtained. The solid curve is the theoretical solution to the diffusion equation [14] over the whole time of the experiment. However, in the calculation of
28
27
mass gain
evacuation pressurization
26
25 0
20
40
60 1/2
time
80
100
1/2
(s )
Fig. 2. Pressurization and evacuation experiments for carbon dioxide in PVDF at 20 bar and 120 C. The mass output from the balance is plotted against the square-root of time. The difference between the initial and final mass reading is the amount of gas absorbed on or desorbed from the polymer. In the figure the two lines are superimposed on the same time scale. In fact, the evacuation experiment follows the pressurization experiment. Thus the final value on the pressurization curve (solid line) is the initial value on the evacuation curve (dotted line).
the diffusion coefficient, only the initial part of the curve is used. At relatively short times, a plot of mass adsorbed/desorbed against square-root of time is linear, as discussed in [3].
344
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
0.9
also show solubility correlations with HenryÕs law as follows:
0.8
SðT ,P Þ ¼ PH ðT Þ
1
where S is solubility in ggas/gpolymer, P is pressure in bar and H is HenryÕs constant in ggas/gpolymer bar. The HenryÕs constant is assumed to have an Arrhenius temperature dependency DH S ð2Þ H ¼ H 0 exp RT
0.7 0.6 Mt M∞
ð1Þ
0.5 0.4 0.3 0.2 0.1 0 0
0.5
1
1.5
Dt l2
Fig. 3. Mass uptake of carbon dioxide in the polymer as a function of square-root of dimensionless time at 80 C and 20 bar. The y-axis shows the mass increase as a fraction of the equilibrium value. The time is non-dimensionalized by the measured diffusivity (D) and the sample thickness (2l). The curve shows the non-linearity at short times.
1 0.9 0.8 0.7 0.6 Mt M∞
Plotting the natural log of the solubility coefficient S/ P against reciprocal temperature we can obtain H0 and DHS. These values are reported in Table 4. Figs. 7 (methane in PVDF) and 8 (carbon dioxide in PVDF) show solubility coefficient in cm3 gas(STP)/cm3 polymer bar compared with results of other authors. The lines are correlations of the data measured in this work averaged over all pressures. While the solubility of methane in PVDF measured by us is similar to that measured by Flaconne`che et al. [7] and El-Hibri and Paul [15], the solubility of carbon dioxide is lower by about 40%, although the slope of the line is comparable. The low-temperature data of El-Hibri and Paul [15] agrees well with the data of Flaconne`che et al. [7]. The disparity in carbon dioxide solubility may be attributable to the fact that the polymer used in this study is an alloy (see experimental section) and not a pure grade of PVDF. 3.2. Diffusion coefficient
0.5 0.4 0.3 0.2 0.1 0 0
0.5
1
1.5
Dt l2
Fig. 4. Mass uptake of carbon dioxide in the polymer as a function of square-root of dimensionless time at 120 C and 20 bar. The y-axis shows the mass increase as a fraction of the equilibrium value. The time is non-dimensionalized by the measured diffusivity (D) and the sample thickness (2l). At the higher temperature the non-linearity is not as severe as that observed in Fig. 3.
3. Results and discussion 3.1. Solubility The solubilities of methane and carbon dioxide in PVDF are given in Tables 2 and 3 respectively. The average solubilities are plotted in Figs. 5 and 6. These figures
Figs. 9 and 10 show results for diffusion coefficients of methane and carbon dioxide respectively in PVDF. The data are also reported in Tables 5 and 6. The error bars in Figs. 9 and 10 correspond to one standard deviation above and below the average. The lines are a correlation of the data based on an Arrhenius temperature dependency Ed D ¼ D0 exp ð3Þ RT where D0 is the pre-exponential factor and Ed is the activation energy of diffusion. Values of D0 and Ed can be obtained from plots such as those in Figs. 9 and 10 and are shown in Table 4. The values of Ed of 68 kJ/ mol for methane and 45 kJ/mol for carbon dioxide are similar to those obtained by Flaconne`che et al. [7] (59– 64 and 44–49 kJ/mol for methane and carbon dioxide respectively). Extrapolating Eq. (3) down to 35 C we may also compare our values with those of El-Hibri and Paul [15]. We obtain a diffusion coefficient of 4.0 · 109 cm2/s for methane, which is close to their value of 2.94 · 109 cm2/s. Our value of 1.91 ·108 cm2/s for carbon dioxide is also reasonably close to their value of 5.66 · 109 cm2/s.
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
345
Table 2 Solubilities of methane in PVDF T = 80 C
T = 100 C
T = 120 C
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
53.7 53.5
0.00148 0.00147
51.4 51.4 50 50
0.00131 0.00051 0.00157 0.00069
42.4 54.2 54.2 71.9
0.00116 0.00111 0.00061 0.00140
104.8 104.8
0.00388 0.00220
100.1 100.1
0.00256 0.00120
97.9 97.9
0.00217 0.00139
158 158.3
0.00476 0.00337
158.2 158.2
0.00342 0.00227
158.5 158.3
0.00332 0.00250
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
Table 3 Solubilities of carbon dioxide in PVDF T = 80 C
T = 100 C
T = 120 C
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
19.1 19.4
0.00637 0.00680
20.1 20.1
0.00717 0.00618
18.6 18.6
0.00573 0.00413
31.2 31
0.00855 0.00891
28.1 28.1
0.00898 0.00873
29 29 28.5 28.5
0.00765 0.00541 0.00738 0.00603
38.9 38.7
0.01042 0.01408
37.6 37.6
0.01110 0.01118
38.4 38.4
0.00941 0.00861
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
0.016
0.0045 0.0040
0.014
80 ˚C 100 ˚C 120 ˚C
0.0030
80 ˚C 100 ˚C
0.012
Solubility (ggas /gpolymer )
Solubility (ggas /gpolymer )
0.0035
increasing temperature
0.0025 0.0020 0.0015 0.0010
120 ˚C 0.010 0.008 0.006 increasing temperature
0.004 0.002
0.0005
0.000
0.0000 0
50
100
150
Pressure (bar)
Fig. 5. Solubility of methane in PVDF as a function of pressure at 80 C (squares), 100 C (triangles) and 120 C (diamonds). Lines are correlations with HenryÕs law.
0
10
20 Pressure (bar)
30
40
Fig. 6. Solubility of carbon dioxide in PVDF as a function of pressure at 80 C (squares), 100 C (triangles) and 120 C (diamonds). Lines are correlations with HenryÕs law.
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348 1
Gas
D0 (cm2/s)
Ed (kJ/mol)
H0 (ggas/gpolymer bar)
DHS (kJ/mol)
Methane Carbon dioxide
1533 0.7366
68 45
5.90e7 2.90e5
11 7
The pre-exponential factors (D0 and H0) are shown for completeness.
0.1
3
3
Table 4 Activation energies of diffusion (Ed) and heat of solution (DHS) for methane and carbon dioxide in PVDF
Solubility coefficient (cm (STP)/cm .bar)
346
this work El-Hibri Flaconnèche
Solubility coefficient (cm (STP)/cm .bar)
correlation 3
0.1 0.0024
0.0026
0.0028
0.003
0.0032
1/Temperature (1/K)
3
Fig. 8. Solubility coefficient (cm3 gas(STP)/cm3 polymer bar) of carbon dioxide in PVDF as a function of inverse temperature. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the data point of El-Hibri and Paul [15].
this work El-Hibri Flaconnèche correlation
1.E-05 0.01 0.0024
0.0026
0.0028
0.003
0.0032
this work El-Hibri
0.0034
1/Temperature (1/K)
Flaconnèche correlation
1.E-06
2
D (cm /s)
Fig. 7. Solubility coefficient (cm3 gas(STP)/cm3 polymer bar) of methane in PVDF as a function of inverse temperature. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the data point of El-Hibri and Paul [15].
1.E-07
CH4 in PVDF 1.E-08
Figs. 3 and 4 show examples of the non-linearity observed in some of the plots of mass increase vs. squareroot of time. This effect is most severe in Fig. 3, where the sample is at 80 C. The uptake of carbon dioxide is apparently ‘‘activated’’ by a small concentration in the polymer at short times before normal Fickian (concentration-independent) diffusion takes over. Small amounts of carbon dioxide may serve to plasticize the sample, facilitating diffusion. This uptake may also be responsible for some swelling of the polymer, which would change the diffusion characteristics. However, it should be noted that if any swelling did occur, it was found to be reversible, based on the fact that consecutive experiments were reversible, as well as on visual inspection of the polymer at the end of a series of runs. In Fig. 4, the effect is not as pronounced at the higher temperature of 120 C. This is possibly because the polymer is already softened at the higher temperature. The non-linearity in the early part of the curve we do not believe to be caused by a Joule–Thomson cooling effect or by gradual increase in pressure. The gases are
1.E-09 0.0024
0.0026
0.0028
0.003
0.0032
1/Temperature (1/K)
Fig. 9. Diffusivity of methane in PVDF as a function of inverse temperature. The values calculated at each pressure have been averaged. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the single data point of ElHibri and Paul [15]. The error bars correspond to one standard deviation above and below the average.
admitted to the chamber in about a second. Also the mass of gas in the apparatus is small compared with the mass of the heated part of the apparatus. Finally, if the cooling of the carbon dioxide had an effect, it would be greater for experiments at higher temperature. However, we found the non-linearity to be greater at lower temperatures (80 C) and not as pronounced at
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
120 C (see Figs. 3 and 4). A preliminary calculation indicates that carbon dioxide at 40 bar and 25 C when released through a valve to 20 bar, will cool to about 0 C.
1.E-05 this work El-Hibri Flaconnèche correlation
4. Conclusions
2
D (cm /s)
1.E-06
347
1.E-07
1.E-08
1.E-09 0.0024
CO2 in PVDF
0.0026
0.0028
0.003
0.0032
1/Temperature (1/K)
Fig. 10. Diffusivity of carbon dioxide in PVDF as a function of inverse temperature. The values calculated at each pressure have been averaged. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the single data point of El-Hibri and Paul [15]. The error bars correspond to one standard deviation above and below the average.
Using a high-pressure microbalance we have measured solubility and diffusion coefficients for the two gases methane and carbon dioxide in PVDF over the temperature range 80–120 C and pressures up to 150 bar. The polymer was cut from piping intended for use in offshore oil and gas applications. The method is well suited to determining the solubility of these gases in PVDF. In general, good agreement is found with similar data for both solubility and diffusion over comparable ranges of temperature and pressure. The exception was carbon dioxide solubility, for which we measured values about 40% lower than those reported in literature. This effect may be a result of a difference in grade between the polymer used in this study and that used in previous work. Solubility data follow a HenryÕs law (linear) dependence on pressure. Based on our measurements
Table 5 Diffusivities of methane in PVDF T = 80 C
T = 100 C 2
7
T = 120 C 2
7
Diffusivity (cm /s) · 10
53.7 53.5
1.54 1.51
51.4 51.4 50
1.29 3.57 2.78
54.2 54.2 71.9
19.54 31.03 8.45
104.8 104.8
3.09 0.426
100.1 100.1
1.43 5.10
97.9 97.9
10.19 7.68
158 158.3
2.15 0.6
158.2 158.2
1.56 0.74
158.5 158.3
36.59 6.29
Pressure (bar)
Diffusivity (cm /s) · 10
Diffusivity (cm2/s) · 107
Pressure (bar)
Pressure (bar)
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
Table 6 Diffusivities of carbon dioxide in PVDF T = 80 C
T = 100 C
T = 120 C
Pressure (bar)
Diffusivity (cm2/s) · 107
Pressure (bar)
Diffusivity (cm2/s) · 107
Pressure (bar)
Diffusivity (cm2/s) · 107
19.1 19.4
1.53 1.40
20.1 20.1
3.30 1.90
18.6 18.6
6.15 10.06
31.2 31
2.43 1.69
28.1 28.1
4.09 3.77
29 29 28.5 28.5
10.74 11.86 6.58 6.78
38.9 38.7
2.67 1.62
37.6 37.6
4.27 3.09
38.4 38.4
9.41 10.39
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
348
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
we have also calculated activation energies of diffusion and heats of solution for these gases in PVDF, assuming an Arrhenius-type temperature dependence. Acknowledgement We thank the Danish Energy Research Program (EFP) for financial support. References [1] Jarrin J. Oil Gas Sci Tech Rev IFP 2001;56:219. [2] Dawans F, Jarrin J, Hardy J. SPE Prod Eng 1988:387. [3] von Solms N, Nielsen JK, Hassager O, Rubin A, Dandekar AY, Andersen SI, et al. J Appl Polym Sci 2004;91:1476. [4] von Solms N, Rubin A, Andersen SI, Stenby EH. Int J Thermophys, in press.
[5] Campion R, Morgan G, Samulak M. Polym Polym Compos 1997;5:451. [6] Klopffer MH, Flaconne`che B. Oil Gas Sci Tech Rev IFP 2001;56:223. [7] Flaconne`che B, Martin J, Klopffer MH. Oil Gas Sci Tech Rev IFP 2001;56:261. [8] Crank J, Park GS. Diffusion in polymers. New York: Academic Press; 1968. [9] Michaels AS, Bixler HJ. J Polym Sci 1961;50:393. [10] Lowell PN, McCrum NG. J Polym Sci Part A2 1971;9: 1935. [11] Kulkarni SS, Stern SA. J Polym Sci Polym Phys Ed 1983;21:441. [12] Aubert JH. J Supercrit Fluids 1998;11:163. [13] Younglove BA, Ely JF. J Phys Chem Ref Data 1987;16: 577. [14] Crank J. The mathematics of diffusion. Oxford: Clarendon Press; 1975. [15] El-Hibri MJ, Paul DR. J Appl Polym Sci 1986;31:2533.
European Polymer Journal 41 (2005) 341–348
www.elsevier.com/locate/europolj
Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance Nicolas von Solms a, Nicoletta Zecchin a, Adam Rubin b, Simon I. Andersen a, Erling H. Stenby a,* a
Department of Chemical Engineering, Centre for Phase Equilibria and Separation Processes (IVC-SEP), Technical University of Denmark, Building 229 DTH, DK-2800 Lyngby, Denmark b NKT Flexibles I/S, Priorparken 510, DK-2605 Brøndby, Denmark Received 14 April 2004; received in revised form 27 September 2004; accepted 30 September 2004
Abstract We present solubility and diffusion data for the gases methane and carbon dioxide in the polymer poly(vinylidene fluoride). The polymer was cut from extruded piping intended for use in offshore oil and gas applications. Measurements were carried out using a purpose-built high-pressure microbalance. These properties were determined in the temperature range 80–120 C and in the pressure range 50–150 bar for methane and 20–40 bar for carbon dioxide. In general, good agreement was obtained for similar measurements reported in the literature. Solubility follows a HenryÕs law (linear) dependence with pressure. Diffusion coefficients for each of the gases in the polymer were also measured using the balance. Activation energies for diffusion and heats of solution for the two gases in the polymer were also determined. 2004 Elsevier Ltd. All rights reserved. Keywords: Gas permeation; Poly(vinylidene fluoride); Solubility; High-pressure microbalance; Diffusion
1. Introduction This paper is the third and final contribution in a series reporting on new measurements of solubility and diffusivity of gases in polymers employed as barrier membranes in flexible pipelines used as risers and flowlines in offshore oilwell production systems. The offshore oil and gas industry is increasingly turning to the use of flexible flowlines and risers for the development of mar-
* Corresponding author. Tel.: +45 4525 2875; fax: +45 4588 2258. E-mail address: [email protected] (E.H. Stenby).
ginal fields in mature regions and in locations without established infrastructure. A flexible flowline typically consists of an inner and outer polymer tube (inner lining and outer sheath) separated by helically wound steel armoring (see Fig. 1). In oil drilling operations materials have to be selected to withstand drilling mud, acid water and hydrocarbon liquids and gases at pressures up to 1000 bar and temperatures ranging from 4 C in deep sea to 180 C in some North Sea wells. The inner liner needs to be resistant to the passage of such gases as carbon dioxide, methane and hydrogen sulfide as well as the hydrocarbon process fluid, whereas the outer sheath protects the annulus from seawater as well as mechanical impact [1,2].
0014-3057/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2004.09.020
342
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
Fig. 1. Photograph of a cutaway section through a flexible pipe used in offshore oil and gas applications. The pipe-wall has been expanded in a cartoon for clarity. The polymer section labelled ‘‘inner liner’’ is the barrier membrane which is the subject of this study. Photograph courtesy of NKT Flexibles (I/S), Brøndby, Denmark.
In part I of this series [3] we determined the solubility and diffusivity of methane and carbon dioxide in highdensity polyethylene (HDPE) in the temperature range 25–50 C and pressures up to 150 bar (methane) and 40 bar (carbon dioxide). This work also contains a description of the experimental apparatus and method and the reader is referred there for details. Part II [4] contains results for the same gases in polyamide-11 (PA-11) at temperatures from 70 to 90 C and the same pressure ranges. Here we report results for the polymer poly(vinylidene fluoride) (PVDF) in the temperature range 80–120 C and the same pressure ranges. A PVDF polymer barrier is typically expected to operate at temperatures up to 130 C [5]. The temperature ranges under which these investigations were carried out are typical of the intended operating conditions for each of the three polymers. The susceptibility of a polymer to penetration by a gas is determined by its permeability. However, permeability is a two-step process, involving both the solution of the gas in the polymer and the diffusion of the gas through the polymer [6]. To understand the mechanisms of gas permeation through a polymer membrane, we must understand both of these processes. Typically, permeability is measured directly in experiments such as those of Flaconne`che et al. [7]. Diffusivity is then obtained from the permeability data, using the so-called ‘‘time-lag’’ method [8]. Finally, the solubility coefficient is inferred as the ratio of permeability to diffusivity. Using a balance, both the solubility and diffusivity are obtained directly. In general, when using a balance, the solubility results are more reliable than the diffusion measurements, since only initial and final values of the polymer mass during an experiment are required, while for diffusion coefficient it is necessary to know the time-dependent polymer mass. Although much of the thermodynamic and transport data of gases in polymers has been obtained from permeation measurement, solubility measurements have been reported before [9–12].
This paper is organized as follows: a brief discussion of materials and experimental procedures is given. Thereafter, the experimental results for solubility and diffusion coefficient of methane and carbon dioxide in PVDF are given. The results are compared with similar results from literature and discussed in terms of HenryÕs law and the Arrhenius temperature dependency. Some brief conclusions are then drawn.
2. Experimental The PVDF was a SOLEF VF2-CTFE copolymer grade 60512 with a reported density of 1.77 g/cm3. This was also the value measured by us. The polymer is an alloy consisting of 67% poly (vinylidene fluorideco-chloro trifluoro ethylene), 33% polyvinylidene fluoride and small amounts of high-density polyethylene. The sequence of measurements for PVDF is shown in Table 1. The crystallinity of the PVDF sample was estimated from differential scanning calorimetry to be about 45%. Polymer samples were cut from extruded pipe intended for offshore use. The polymer was machined down to the required thickness and then cut into circular discs. Enough discs are used to give a total sample weight of about 0.3 g. Two different polymer sheet thicknesses (about 0.2 and 0.5 mm, respectively) were used in this investigation, as listed in Table 1. The samples were annealed before an experiment at the temperature of interest for 24–48 h. Methane and carbon dioxide gas samples were supplied in industrial gas bottles by Air Liquide (Ballerup, Denmark). The purity of the gas samples was better than 99.99%. Gas densities over the range of pressure and temperature were obtained from a modified Benedict– Webb–Rubin (MBWR) equation of state, the parameters of which were obtained from P–v–T measurements up to 1000 bar [13]. The agreement with experimental density data is better than 0.1% over the whole range.
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
343
Table 1 Experimental sequence for gas solubility/diffusivity measurements in PVDF Gas
Temperature (C)
Pressure (bar)
No. of discs
Diameter (mm)
Sample mass (g)
Thickness (mm)
CH4
80
50 100 150
18 18 18
7.70 7.70 7.70
0.2669 0.2669 0.2669
0.18 0.18 0.18
CO2
80
20 30 40
18 18 18
7.70 7.70 7.70
0.2669 0.2669 0.2669
0.18 0.18 0.18
CH4
100
50 50 100 150
18 16 16 16
7.70 8.02 8.02 8.02
0.2669 0.2600 0.2600 0.2600
0.18 0.18 0.18 0.18
CO2
100
20 30 40
9 9 9
6.39 6.39 6.39
0.2706 0.2706 0.2706
0.53 0.53 0.53
CH4
120
50 100 150
5 5 5
8.72 8.72 8.72
0.2802 0.2802 0.2802
0.53 0.53 0.53
CO2
120
20 30 40
5 5 5
8.72 8.72 8.72
0.2802 0.2802 0.2802
0.53 0.53 0.53
30
29 mass loss
mass (mg)
Pure gas densities obtained from this equation of state within the range of applicability may be considered to be pseudo-experimental data. For conversion of solubility between mass and volume units the gas densities at STP are required. These were calculated to be 0.7175 kg/m3 for methane and 1.9777 kg/m3 for carbon dioxide. All measurements were done using a S3D-P highpressure microbalance provided by Sartorius AG (Go¨ttingen, Germany). The equipment and method are described in detail in von Solms et al. [3]. The experimental principle is described here in brief. The polymer sample is placed on one arm of a microbalance, with quartz spheres placed on the other as counterweights. Gas is admitted rapidly to the whole balance at the pressure of interest (or evacuated rapidly in the case of an evacuation run), after the whole apparatus, including the sample has been at the temperature of interest for at least 24 h. Fig. 2 shows the course of a single experiment, showing both a pressurization (solid curve) and an evacuation (dotted curve) run. The difference in the reading on the balance before and after a run, is the amount of gas adsorbed or desorbed. This value divided by the known mass of polymer gives the solubility of the gas in the polymer. The diffusion coefficient can also be obtained by studying the time-dependent behaviour of the adsorbed/desorbed mass of gas. Figs. 3 and 4 show typical results obtained. The solid curve is the theoretical solution to the diffusion equation [14] over the whole time of the experiment. However, in the calculation of
28
27
mass gain
evacuation pressurization
26
25 0
20
40
60 1/2
time
80
100
1/2
(s )
Fig. 2. Pressurization and evacuation experiments for carbon dioxide in PVDF at 20 bar and 120 C. The mass output from the balance is plotted against the square-root of time. The difference between the initial and final mass reading is the amount of gas absorbed on or desorbed from the polymer. In the figure the two lines are superimposed on the same time scale. In fact, the evacuation experiment follows the pressurization experiment. Thus the final value on the pressurization curve (solid line) is the initial value on the evacuation curve (dotted line).
the diffusion coefficient, only the initial part of the curve is used. At relatively short times, a plot of mass adsorbed/desorbed against square-root of time is linear, as discussed in [3].
344
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
0.9
also show solubility correlations with HenryÕs law as follows:
0.8
SðT ,P Þ ¼ PH ðT Þ
1
where S is solubility in ggas/gpolymer, P is pressure in bar and H is HenryÕs constant in ggas/gpolymer bar. The HenryÕs constant is assumed to have an Arrhenius temperature dependency DH S ð2Þ H ¼ H 0 exp RT
0.7 0.6 Mt M∞
ð1Þ
0.5 0.4 0.3 0.2 0.1 0 0
0.5
1
1.5
Dt l2
Fig. 3. Mass uptake of carbon dioxide in the polymer as a function of square-root of dimensionless time at 80 C and 20 bar. The y-axis shows the mass increase as a fraction of the equilibrium value. The time is non-dimensionalized by the measured diffusivity (D) and the sample thickness (2l). The curve shows the non-linearity at short times.
1 0.9 0.8 0.7 0.6 Mt M∞
Plotting the natural log of the solubility coefficient S/ P against reciprocal temperature we can obtain H0 and DHS. These values are reported in Table 4. Figs. 7 (methane in PVDF) and 8 (carbon dioxide in PVDF) show solubility coefficient in cm3 gas(STP)/cm3 polymer bar compared with results of other authors. The lines are correlations of the data measured in this work averaged over all pressures. While the solubility of methane in PVDF measured by us is similar to that measured by Flaconne`che et al. [7] and El-Hibri and Paul [15], the solubility of carbon dioxide is lower by about 40%, although the slope of the line is comparable. The low-temperature data of El-Hibri and Paul [15] agrees well with the data of Flaconne`che et al. [7]. The disparity in carbon dioxide solubility may be attributable to the fact that the polymer used in this study is an alloy (see experimental section) and not a pure grade of PVDF. 3.2. Diffusion coefficient
0.5 0.4 0.3 0.2 0.1 0 0
0.5
1
1.5
Dt l2
Fig. 4. Mass uptake of carbon dioxide in the polymer as a function of square-root of dimensionless time at 120 C and 20 bar. The y-axis shows the mass increase as a fraction of the equilibrium value. The time is non-dimensionalized by the measured diffusivity (D) and the sample thickness (2l). At the higher temperature the non-linearity is not as severe as that observed in Fig. 3.
3. Results and discussion 3.1. Solubility The solubilities of methane and carbon dioxide in PVDF are given in Tables 2 and 3 respectively. The average solubilities are plotted in Figs. 5 and 6. These figures
Figs. 9 and 10 show results for diffusion coefficients of methane and carbon dioxide respectively in PVDF. The data are also reported in Tables 5 and 6. The error bars in Figs. 9 and 10 correspond to one standard deviation above and below the average. The lines are a correlation of the data based on an Arrhenius temperature dependency Ed D ¼ D0 exp ð3Þ RT where D0 is the pre-exponential factor and Ed is the activation energy of diffusion. Values of D0 and Ed can be obtained from plots such as those in Figs. 9 and 10 and are shown in Table 4. The values of Ed of 68 kJ/ mol for methane and 45 kJ/mol for carbon dioxide are similar to those obtained by Flaconne`che et al. [7] (59– 64 and 44–49 kJ/mol for methane and carbon dioxide respectively). Extrapolating Eq. (3) down to 35 C we may also compare our values with those of El-Hibri and Paul [15]. We obtain a diffusion coefficient of 4.0 · 109 cm2/s for methane, which is close to their value of 2.94 · 109 cm2/s. Our value of 1.91 ·108 cm2/s for carbon dioxide is also reasonably close to their value of 5.66 · 109 cm2/s.
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
345
Table 2 Solubilities of methane in PVDF T = 80 C
T = 100 C
T = 120 C
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
53.7 53.5
0.00148 0.00147
51.4 51.4 50 50
0.00131 0.00051 0.00157 0.00069
42.4 54.2 54.2 71.9
0.00116 0.00111 0.00061 0.00140
104.8 104.8
0.00388 0.00220
100.1 100.1
0.00256 0.00120
97.9 97.9
0.00217 0.00139
158 158.3
0.00476 0.00337
158.2 158.2
0.00342 0.00227
158.5 158.3
0.00332 0.00250
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
Table 3 Solubilities of carbon dioxide in PVDF T = 80 C
T = 100 C
T = 120 C
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
Pressure (bar)
Solubility (g gas/g polymer)
19.1 19.4
0.00637 0.00680
20.1 20.1
0.00717 0.00618
18.6 18.6
0.00573 0.00413
31.2 31
0.00855 0.00891
28.1 28.1
0.00898 0.00873
29 29 28.5 28.5
0.00765 0.00541 0.00738 0.00603
38.9 38.7
0.01042 0.01408
37.6 37.6
0.01110 0.01118
38.4 38.4
0.00941 0.00861
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
0.016
0.0045 0.0040
0.014
80 ˚C 100 ˚C 120 ˚C
0.0030
80 ˚C 100 ˚C
0.012
Solubility (ggas /gpolymer )
Solubility (ggas /gpolymer )
0.0035
increasing temperature
0.0025 0.0020 0.0015 0.0010
120 ˚C 0.010 0.008 0.006 increasing temperature
0.004 0.002
0.0005
0.000
0.0000 0
50
100
150
Pressure (bar)
Fig. 5. Solubility of methane in PVDF as a function of pressure at 80 C (squares), 100 C (triangles) and 120 C (diamonds). Lines are correlations with HenryÕs law.
0
10
20 Pressure (bar)
30
40
Fig. 6. Solubility of carbon dioxide in PVDF as a function of pressure at 80 C (squares), 100 C (triangles) and 120 C (diamonds). Lines are correlations with HenryÕs law.
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348 1
Gas
D0 (cm2/s)
Ed (kJ/mol)
H0 (ggas/gpolymer bar)
DHS (kJ/mol)
Methane Carbon dioxide
1533 0.7366
68 45
5.90e7 2.90e5
11 7
The pre-exponential factors (D0 and H0) are shown for completeness.
0.1
3
3
Table 4 Activation energies of diffusion (Ed) and heat of solution (DHS) for methane and carbon dioxide in PVDF
Solubility coefficient (cm (STP)/cm .bar)
346
this work El-Hibri Flaconnèche
Solubility coefficient (cm (STP)/cm .bar)
correlation 3
0.1 0.0024
0.0026
0.0028
0.003
0.0032
1/Temperature (1/K)
3
Fig. 8. Solubility coefficient (cm3 gas(STP)/cm3 polymer bar) of carbon dioxide in PVDF as a function of inverse temperature. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the data point of El-Hibri and Paul [15].
this work El-Hibri Flaconnèche correlation
1.E-05 0.01 0.0024
0.0026
0.0028
0.003
0.0032
this work El-Hibri
0.0034
1/Temperature (1/K)
Flaconnèche correlation
1.E-06
2
D (cm /s)
Fig. 7. Solubility coefficient (cm3 gas(STP)/cm3 polymer bar) of methane in PVDF as a function of inverse temperature. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the data point of El-Hibri and Paul [15].
1.E-07
CH4 in PVDF 1.E-08
Figs. 3 and 4 show examples of the non-linearity observed in some of the plots of mass increase vs. squareroot of time. This effect is most severe in Fig. 3, where the sample is at 80 C. The uptake of carbon dioxide is apparently ‘‘activated’’ by a small concentration in the polymer at short times before normal Fickian (concentration-independent) diffusion takes over. Small amounts of carbon dioxide may serve to plasticize the sample, facilitating diffusion. This uptake may also be responsible for some swelling of the polymer, which would change the diffusion characteristics. However, it should be noted that if any swelling did occur, it was found to be reversible, based on the fact that consecutive experiments were reversible, as well as on visual inspection of the polymer at the end of a series of runs. In Fig. 4, the effect is not as pronounced at the higher temperature of 120 C. This is possibly because the polymer is already softened at the higher temperature. The non-linearity in the early part of the curve we do not believe to be caused by a Joule–Thomson cooling effect or by gradual increase in pressure. The gases are
1.E-09 0.0024
0.0026
0.0028
0.003
0.0032
1/Temperature (1/K)
Fig. 9. Diffusivity of methane in PVDF as a function of inverse temperature. The values calculated at each pressure have been averaged. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the single data point of ElHibri and Paul [15]. The error bars correspond to one standard deviation above and below the average.
admitted to the chamber in about a second. Also the mass of gas in the apparatus is small compared with the mass of the heated part of the apparatus. Finally, if the cooling of the carbon dioxide had an effect, it would be greater for experiments at higher temperature. However, we found the non-linearity to be greater at lower temperatures (80 C) and not as pronounced at
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
120 C (see Figs. 3 and 4). A preliminary calculation indicates that carbon dioxide at 40 bar and 25 C when released through a valve to 20 bar, will cool to about 0 C.
1.E-05 this work El-Hibri Flaconnèche correlation
4. Conclusions
2
D (cm /s)
1.E-06
347
1.E-07
1.E-08
1.E-09 0.0024
CO2 in PVDF
0.0026
0.0028
0.003
0.0032
1/Temperature (1/K)
Fig. 10. Diffusivity of carbon dioxide in PVDF as a function of inverse temperature. The values calculated at each pressure have been averaged. The solid diamonds are the average values measured in this work. The line is the correlation based on these measurements. The open squares are the data of Flaconne`che et al. [7] and the open triangle is the single data point of El-Hibri and Paul [15]. The error bars correspond to one standard deviation above and below the average.
Using a high-pressure microbalance we have measured solubility and diffusion coefficients for the two gases methane and carbon dioxide in PVDF over the temperature range 80–120 C and pressures up to 150 bar. The polymer was cut from piping intended for use in offshore oil and gas applications. The method is well suited to determining the solubility of these gases in PVDF. In general, good agreement is found with similar data for both solubility and diffusion over comparable ranges of temperature and pressure. The exception was carbon dioxide solubility, for which we measured values about 40% lower than those reported in literature. This effect may be a result of a difference in grade between the polymer used in this study and that used in previous work. Solubility data follow a HenryÕs law (linear) dependence on pressure. Based on our measurements
Table 5 Diffusivities of methane in PVDF T = 80 C
T = 100 C 2
7
T = 120 C 2
7
Diffusivity (cm /s) · 10
53.7 53.5
1.54 1.51
51.4 51.4 50
1.29 3.57 2.78
54.2 54.2 71.9
19.54 31.03 8.45
104.8 104.8
3.09 0.426
100.1 100.1
1.43 5.10
97.9 97.9
10.19 7.68
158 158.3
2.15 0.6
158.2 158.2
1.56 0.74
158.5 158.3
36.59 6.29
Pressure (bar)
Diffusivity (cm /s) · 10
Diffusivity (cm2/s) · 107
Pressure (bar)
Pressure (bar)
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
Table 6 Diffusivities of carbon dioxide in PVDF T = 80 C
T = 100 C
T = 120 C
Pressure (bar)
Diffusivity (cm2/s) · 107
Pressure (bar)
Diffusivity (cm2/s) · 107
Pressure (bar)
Diffusivity (cm2/s) · 107
19.1 19.4
1.53 1.40
20.1 20.1
3.30 1.90
18.6 18.6
6.15 10.06
31.2 31
2.43 1.69
28.1 28.1
4.09 3.77
29 29 28.5 28.5
10.74 11.86 6.58 6.78
38.9 38.7
2.67 1.62
37.6 37.6
4.27 3.09
38.4 38.4
9.41 10.39
Pressure is either pressure applied during a pressurization run or equilibrium pressure immediately preceding an evacuation run.
348
N. von Solms et al. / European Polymer Journal 41 (2005) 341–348
we have also calculated activation energies of diffusion and heats of solution for these gases in PVDF, assuming an Arrhenius-type temperature dependence. Acknowledgement We thank the Danish Energy Research Program (EFP) for financial support. References [1] Jarrin J. Oil Gas Sci Tech Rev IFP 2001;56:219. [2] Dawans F, Jarrin J, Hardy J. SPE Prod Eng 1988:387. [3] von Solms N, Nielsen JK, Hassager O, Rubin A, Dandekar AY, Andersen SI, et al. J Appl Polym Sci 2004;91:1476. [4] von Solms N, Rubin A, Andersen SI, Stenby EH. Int J Thermophys, in press.
[5] Campion R, Morgan G, Samulak M. Polym Polym Compos 1997;5:451. [6] Klopffer MH, Flaconne`che B. Oil Gas Sci Tech Rev IFP 2001;56:223. [7] Flaconne`che B, Martin J, Klopffer MH. Oil Gas Sci Tech Rev IFP 2001;56:261. [8] Crank J, Park GS. Diffusion in polymers. New York: Academic Press; 1968. [9] Michaels AS, Bixler HJ. J Polym Sci 1961;50:393. [10] Lowell PN, McCrum NG. J Polym Sci Part A2 1971;9: 1935. [11] Kulkarni SS, Stern SA. J Polym Sci Polym Phys Ed 1983;21:441. [12] Aubert JH. J Supercrit Fluids 1998;11:163. [13] Younglove BA, Ely JF. J Phys Chem Ref Data 1987;16: 577. [14] Crank J. The mathematics of diffusion. Oxford: Clarendon Press; 1975. [15] El-Hibri MJ, Paul DR. J Appl Polym Sci 1986;31:2533.