Energy Fuels 2010, 24, 2999–3002 Published on Web 04/14/2010
: DOI:10.1021/ef901612t
Predictive Tool for the Estimation of Methanol Loss in Condensate Phase during Gas Hydrate Inhibition Alireza Bahadori* and Hari B. Vuthaluru School of Chemical and Petroleum Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia Received December 30, 2009. Revised Manuscript Received March 25, 2010
In this work, a simple Arrhenius-type function that is easier than existing approaches, because it is less complicated and has fewer computations, and is suitable for process engineers, is presented here for the estimation of methanol loss in paraffinic hydrocarbons, as a function of temperature and methanol concentration in the water phase. The solubility of methanol in paraffin hydrocarbons is calculated for temperatures between -30 °C and 50 °C and methanol concentrations in the water phase up to a mass fraction of 0.70. Estimations are found to be in excellent agreement with reliable data in the literature, with the average absolute deviation being ∼2.12%. The tool developed in this study can be of immense practical value for the engineers and scientists to have a quick check on the loss of methanol in paraffinic hydrocarbons phase under various conditions without opting for any experimental measurements. In particular, chemical and process engineers would find the approach to be user-friendly with transparent calculations that involve no complex expressions.
of temperature and methanol concentration in the water phase. The paper discusses the formulation of such predictive tool in a systematic manner, along with a sample example to show the simplicity of the model and the usefulness of such tools. The proposed method is an Arrhenius-type function, and this is the distinct advantage of the proposed method, in comparison with previously developed numerical and empirical methods.10,11
1. Introduction An inherent problem with natural gas production or transmission is the formation of gas hydrates, which can lead to safety hazards with regard to production/transportation systems and to substantial economic risks.1 Therefore, an understanding of conditions where hydrates form is necessary to overcome hydrate-related issues.2,3 Traditionally, the most common chemical additives to control hydrates in gas production systems are methanol, ethylene glycol, or triethylene glycol, which are employed at sufficiently high concentration.4,5 Often, when applying methanol as a hydrate inhibitor, there is a significant expense associated with the cost of lost methanol, so it is important to know how much methanol is lost to the hydrocarbon liquid phase in the pipeline. Prediction of inhibitor losses to the hydrocarbon liquid phase requires rigorous calculations.6-9 In view of the above-mentioned issues, it is necessary to develop an accurate and simple predictive tool that is easier than existing approaches;less complicated, with fewer computations;for predicting the loss of methanol in paraffinic hydrocarbons, as a function
2. Methodology for the Development of Novel Predictive Tool The primary purpose of the present study is to accurately correlate the solubility of methanol in the liquid hydrocarbon phase (mole fraction), as a function of temperature and methanol concentration in aqueous phase (mass fraction). This is done by applying a simple predictive tool that uses an Arrhenius-type asymptotic exponential function with a small modification of the Vogel-Tammann-Fulcher (VTF) equation.12-14 This is important, because such an accurate and mathematically simple correlation of the loss of methanol into liquid hydrocarbon phase (mole fraction), as a function of temperature and methanol mass fraction in the aqueous phase, is frequently required for quick engineering calculations, to avoid the additional computational burden of complicated calculations. The VTF equation12-14 is an asymptotic exponential function that is given in the following general form:
*Author to whom all correspondence should be addressed. Tel.: 61-89266 1782. Fax: 61-8-9266 2681. E-mail: alireza.bahadori@postgrad. curtin.edu.au. (1) Bahadori, A.; Vuthaluru, H. B. J. Nat. Gas Chem. 2009, 18 (4), 453–457. (2) Bahadori, A. J. Can. Pet. Technol. 2008, 47 (2), 13–16. (3) Bahadori, A. J. Nat. Gas Chem. 2007, 16 (1), 16–21. (4) Sloan, E. D., Jr. Hydrate Engineering; Bloys, J. B., Ed.; SPE Monograph 21; Society of Petroleum Engineers (SPE): Richardson, TX, 2000. (5) Sloan, E. D., Jr. J. Pet. Technol. 1991, 43, 1414. (6) Bahadori, A; Vuthaluru, H. B.; Mokhatab, S.; Tade, M. O. J. Nat. Gas Chem. 2008, 17 (3), 249–255. (7) Lundstrøm, C.; Michelsen, M. L.; Kontogeorgis, G. M.; Pedersen, K. S.; Sørensen, H. Fluid Phase Equilib. 2006, 247, 149–157. (8) GPSA Engineering Data Book, 12th Ed.; Gas Processors Suppliers Association: Tulsa, OK, 2004. (9) Bahadori, A.; Vuthaluru, H. B.; Mokhatab, S. Oil Gas Eur. Mag. 2008, 34 (3), 149–151. r 2010 American Chemical Society
ln f ¼ lnð fc Þ -
E RðT - Tc Þ
ð1Þ
In eq 1, f is a properly defined temperature-dependent parameter, the units for which are determined individually for a (10) (11) (12) (13) 257. (14)
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Elgibaly, A.; Elkamel, A. Energy Fuels 1999, 13, 105–113. Bahadori, A. Pet. Sci. Technol. 2009, 27, 943–951. Vogel, H. Phys. Z. 1921, 22, 645–646. Tammann, G.; Hesse, W. Z. Anorg. Allg. Chem. 1926, 156, 245– Fulcher, G. S. J. Am. Ceram. Soc. 1925, 8, 339–355.
pubs.acs.org/EF
Energy Fuels 2010, 24, 2999–3002
: DOI:10.1021/ef901612t In brief, the following steps are repeated to tune the correlation’s coefficients:18,19 (1) Correlate the methanol solubilities in the liquid hydrocarbon phase (ω, in mole fraction), as a function of temperature (T) for a given methanol mass fraction in the aqueous phase. (2) Repeat step 1 for other methanol mass fractions in the aqueous phase (ψ). (3) Correlate the corresponding polynomial coefficients, which were obtained for different plots of temperature versus methanol mass fraction: a = f(ψ), b = f(ψ), c = f(ψ), d = f(ψ). [See eqs 5-8.]
Table 1. Tuned Coefficients Used in eqs 5-8 coefficient
value
A1 B1 C1 D1
1.6812339429025 103 -1.0803155907846 104 2.2311693912313 104 -1.4729301398400 104
A2 B2 C2 D2
-1.564777661431 106 9.9874920671076 106 -2.0506540953867 107 1.3479263861302 107
A3 B3 C3 D3
4.8553968051888 108 -3.0835714347230 109 6.2988799656686 109 -4.1248186297104 109
A4 B4 C4 D4
-5.0424809928302 1010 3.1810877336225 1011 -6.4667402344901 1011 4.220547048108 1011
Equation 4 represents the proposed governing equation in which four coefficients are used to correlate the methanol solubilities in the liquid hydrocarbon phase (ω, expressed in terms of mole fraction), as a function of temperature (T) for a given methanol mass fraction in the aqueous phase; the relevant coefficients are reported in Table 1. lnðωÞ ¼ a þ
certain property; fc is a pre-exponential coefficient, having the same unit as the property of interest; T and Tc are the actual temperature and the characteristic-limit temperature, respectively (both given in degrees Kelvin); E is referenced as the activation energy of the process causing parameter variation (given in units of J/kmol); and R is the universal gas constant (R = 8.314 J/(kmol K)). A special case of the VTF equation for Tc = 0 is the well-known Arrhenius equation.15 For the purpose of the present application, which involves the correlation of methanol solubility in a gas condensate, as a function of temperature, the VTF equation has been modified in the following form by adding second-order and third order terms:16,17 ln f ¼ ln fc þ
b c d þ þ T - Tc ðT - Tc Þ2 ðT - Tc Þ3
b c d þ 2 þ 3 T T T
ð4Þ
where a ¼ A1 þ B1 ψ þ C1 ψ2 þ D1 ψ3
ð5Þ
b ¼ A2 þ B2 ψ þ C2 ψ2 þ D2 ψ3
ð6Þ
c ¼ A3 þ B3 ψ þ C3 ψ2 þ D3 ψ3
ð7Þ
d ¼ A4 þ B4 ψ þ C4 ψ2 þ D4 ψ3
ð8Þ
These optimum tuned coefficients help to cover the temperatures in the range of -30 °C to 50 °C and methanol concentrations in the water phase up to a mass fraction of 0.70. The optimum tuned coefficients given in Table 1 can be further retuned quickly, according to the proposed approach, if more data are available in the future. The proposed novel tool developed in the present work is a simple and unique expression that is nonexistent in the literature. Furthermore, the selected exponential function to develop the tool leads to well-behaved (i.e., smooth and nonoscillatory) equations, enabling fast and more-accurate predictions.
ð2Þ
In eq 2, Tc has been considered zero to convert eq 2 to the wellknown Arrhenius-type equation.15 (See eq 3.) ln f ¼ ln fc þ
b c d þ 2 þ 3 T T T
ð3Þ
The required data to develop this correlation includes the reported data8 for the loss of methanol into a liquid hydrocarbon phase (ω, expressed in terms of mole fraction), as a function of temperature (in Kelvin) and methanol mass fraction in the aqueous phase (ψ). The following methodology has been applied to develop this correlation. 2.1. Developing the Predictive Tool. First, methanol solubilities in the liquid hydrocarbon phase (ω, given in terms of mole fraction) are correlated as a function of temperature for several methanol mass fractions in the aqueous phase (ψ). Then, the calculated coefficients for these equations are correlated as a function of the methanol mass fractions in the aqueous phase (ψ). The derived equations are applied to calculate new coefficients for eq 4 to predict methanol solubilities in liquid hydrocarbon phase (ω) in mole fraction. Later in this paper, Table 1 shows the tuned coefficients for eqs 5-8 for predicting methanol solubilities in the liquid hydrocarbon phase (ω, expressed in terms of mole fraction).
3. Results Figure 1 illustrates the solubility of methanol in paraffinic hydrocarbons for temperatures between -30 °C and 50 °C and methanol contents in hydrocarbons up to 0.70 mass fraction. Figure 2 shows the proposed numerical method results and excellent performance in the prediction of methanol solubility in the hydrocarbon liquid phase in gas hydrate inhibition for a wide range of conditions. It shows that high temperatures and more injected methanol in the water phase cause greater solubility of methanol in the liquid phase. Table 2 illustrates the accuracy of the proposed correlation for predicting the solubility of methanol in paraffinic hydrocarbons, in comparison with some reported data.8 The accuracy of the correlation, in terms of average absolute deviations, is ∼2.12%. (18) Bahadori, A., Vuthaluru, H. B. J. Loss Prev. Process Ind. 2010, in press (DOI:10.1016/j.jlp.2010.01.002). (19) Bahadori, A. Korean J. Chem. Eng. 2007, 24 (3), 418–425.
(15) Arrhenius, S. Z. Phys. Chem. 1889, 4, 226–248. (16) Civan, F. Chem. Eng. Progress 2008, 104 (7), 46–52. (17) Civan, F. Ind. Eng. Chem. Res. 2007, 46 (17), 5810–5814.
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Energy Fuels 2010, 24, 2999–3002
: DOI:10.1021/ef901612t
Figure 1. Prediction of the solubility of methanol in a paraffinic hydrocarbon liquid phase, using the new proposed correlation, in comparison with literature data.8
Figure 2. Performance of the proposed predictive tool for predicting the solubility of methanol in a hydrocarbon condensate phase. Table 2. Comparison of Calculated Solubility of Methanol in Hydrocarbons with Reported Data temperature (°C)
methanol mass fraction
calculated solubility of methanol in hydrocarbons (mole fraction)
reported solubility of methanol in hydrocarbons (mole fraction)a
relative error (%)
absolute deviation (%)
12 30 50 21 47 -10 2 43 -40 0 50
0.20 0.20 0.20 0.35 0.35 0.60 0.60 0.60 0.70 0.70 0.70
0.00099 0.00294 0.006 0.0044 0.01035 0.00295 0.00514 0.02034 0.0021 0.0073 0.0265
0.001 0.003 0.006 0.004 0.01 0.003 0.005 0.02 0.002 0.0071 0.027
-1 -2 0 10 3.5 -1.66 2.8 1.7 5 2.81 -1.85
1 2 0 10 3.5 1.66 2.8 1.7 5 2.8 1.9
Average deviation: a
2.12%
Data taken from ref 8.
In this study, our efforts have been directed at formulating a simple-to-use method that can help engineers and researchers. It is expected that our efforts in this investigation will pave the way for determining an accurate prediction of methanol loss in the liquid hydrocarbon phase (ω, expressed in terms of mole fraction) under various conditions, which can be used by engineers and scientists to monitor the key parameters periodically. A typical example8 is given below to illustrate the simplicity associated with the use of the proposed predictive tool
for rapid estimation of methanol loss in a condensate liquid phase. 3.1. Example. Assume that 2.83 106 Sm3/day of natural gas leaves an offshore platform at 38 °C and 8300 kPa (absolute pressure) (the water content is 850 mg/Sm3). [Note: The term Sm3 denotes standard cubic meters.] The gas comes onshore at 4 °C and 6200 kPa (absolute pressure) (the water content is now 152 m/Sm3). The hydrate temperature of the gas is 18 °C. The associated condensate production is 56 m3/(106 Sm3). 3001
Energy Fuels 2010, 24, 2999–3002
: DOI:10.1021/ef901612t
The condensate has a density of 778 kg/m3 and a molecular mass of 140. The methanol inhibitor concentration in the water phase required to avoid hydrate formation is 27.5%. Calculate the mass rate of inhibitor in the water phase and the amount of methanol loss in the hydrocarbon liquid phase. 3.1.1. Solution. (1) Identify the variables.
4. Conclusions In this work, a simple-to-use and Arrhenius-type predictive tool is presented here to estimate methanol loss in a liquid paraffinic hydrocarbon phase, as a function of temperature and methanol concentration in the water phase. Unlike complex mathematical approaches that have been used to estimate methanol loss in liquid paraffinic hydrocarbon phases, the proposed predictive tool is simple to use and would be of immense help for process engineers, especially those dealing with natural gas transmission and processing. In addition, the level of mathematical formulations associated with the estimation of methanol loss in the condensate phase can be easily handled by an oil and gas practitioner without any in-depth mathematical abilities. The example that has been shown for the benefit of engineers clearly demonstrates the usefulness of the proposed tools. Furthermore, the estimations are quite accurate, as evidenced from the comparisons with literature data (with average absolute deviations being ∼2.12%) and would help in attempting design and operations modifications in a shorter time.
Win ¼ 850 mg=Sm3 Wout ¼ 152 mg=Sm3 ΔW ¼ 698 mg=Sm3 amount of water condensed ¼ ð2:83 106 Þ ð698Þ ¼ 1975 106 mg=day ¼ 1975 kg=day (2) Calculate the mass rate of inhibitor in the water phase. 0:275 1975 ¼ 749 kg=day mi ¼ 1 - 0:275
b ¼ - 8:869793699719 104
ðfrom eq 6Þ
Acknowledgment. The lead author acknowledges the Australian Department of Education, Science and Training for Endeavour International Postgraduate Research Scholarship (EIPRS), the Office of Research & Development at Curtin University of Technology, Perth, Western Australia for providing Curtin University Postgraduate Research Scholarship and the State Government of Western Australia for providing top up scholarship through Western Australian Energy Research Alliance (WA:ERA).
c ¼ 2:8126995933983 107
ðfrom eq 7Þ
Nomenclature
d ¼ - 3:0722013379 10
ðfrom eq 8Þ
(3) Estimate the losses to the hydrocarbon liquid phase from the proposed method at 4 °C and 27.5 wt % methanol. a ¼ 9:136448034367 101
9
ðfrom eq 5Þ
Parameters A, B, C, D = tuned coefficients E = activation energy of the process causing parameter variation (J/kmol) f = a properly defined temperature-dependent parameter; the units for this term are determined individually for a certain property fc = pre-exponential coefficient; has the same unit of the property of interest T = temperature (K) Tc = characteristic-limit temperature (K) R = universal gas constant; R = 8.314 J/(kmol K)
From eq 4, the solubility of methanol in the hydrocarbon phase is estimated to be ∼0.0011 (or 0.11 mol %). Therefore, 2:83 106 Sm3 56 m3 778 kg 1 kmol Þ Þ ð 6 Þ ð Þ ð ð m3 140 kg day 10 Sm3 ¼ 881 kmol=day amount of methanol loss ðin terms of kmolÞ : 881 ð0:0011Þ ¼ 0:97 mol=day amount of methanol loss ðin terms of kgÞ :
Greek Symbols
0:97 32 ¼ 31:04 kg=day
ψ = amount of methanol in water phase (mass fraction) ω = solubility of methanol in hydrocarbon condensate (mole fraction)
The methanol in the condensate phase can be recovered by downstream water washing.
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