A Nonempirical Relative Permeability Model for Hydrate-Bearing Sediments
- Harpreet Singh (National Energy Technology Laboratory) | Evgeniy M. Myshakin (National Energy Technology Laboratory and AECOM) | Yongkoo Seol (National Energy Technology Laboratory)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2019
- Document Type
- Journal Paper
- 547 - 562
- 2019.Society of Petroleum Engineers
- two-phase flow, gas hydrates, relative permeability, non-empirical
- 11 in the last 30 days
- 162 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
There are currently two types of relative permeability models that are used to model gas production from hydrate-bearing sediments: fully empirical parameter-fitting models [such as the University of Tokyo model (Masuda et al. 1997) and the Brooks and Corey model (Brooks and Corey 1964)] and partially empirical models [such as the Kozeny and Carman model (Wyllie and Gardner 1958) and capillary-tube-based models that assume only a single phase]. This study proposes an analytical model to estimate relative permeability of gas and water in a hydrate-bearing porous medium without curve fitting or use of any empirical parameters. The model is derived by conserving the momentum balance with the steady-state form of the Navier-Stokes equation for gas/water flow in a hydrate-bearing porous medium. The model is validated against a number of laboratory studies and is shown to perform better than most empirical models over a full range of experimental data. The proposed model is an analytical function of rock properties (average pore size and shape, porosity, irreducible water saturation, and saturation of hydrate), fluid properties (gas/water saturations and viscosities), and the hydrate-growth pattern [pore filling (PF), wall coating (WC), and a combination of PF and WC]. The benefits of the proposed model include sensitivity analysis of relevant physical parameters on relative permeability and estimation of rock parameters (such as porosity, pore size, and residual water saturation) using inverse modeling. The model can also be used to estimate two-phase permeability in a permeable medium without hydrates.
The proposed model was used to analyze the effects of pore shapes, the hydrate-growth pattern, variable gas saturation, and wettability on relative permeability. The sensitivity results produced by the proposed model were verified using observations from other studies that investigated similar problems using either experiments or computationally expensive pore-scale simulations.
|File Size||824 KB||Number of Pages||16|
Andris, R. G. 2016. The Effect of Restrictive Diffusion on Hydrate Growth. Master’s thesis, University of Texas at Austin, Austin, Texas (May 2016).
Buleiko, V. M., Grigoriev, B. A., and Istomin, V. A. 2017. Capillary Effects on Phase Behavior of Liquid and Gaseous Propane and Dynamics of Hydrate Formation and Dissociation in Porous Media. Fluid Phase Equilibr 441 (15 June): 64–71. https://doi.org/10.1016/j.fluid.2017.01.026.
Brooks, R. H. and Corey, A. T. 1964. Hydraulic Properties of Porous Media. Hydrology Papers, No. 3, Hydrology and Water Resources Program, Colorado State University, Fort Collins, Colorado.
Cai, J., Perfect, E., Cheng, C.-L. et al. 2014. Generalized Modeling of Spontaneous Imbibition Based on Hagen–Poiseuille Flow in Tortuous Capillaries With Variably Shaped Apertures. Langmuir 30 (18): 5142–5151. https://doi.org/10.1021/la5007204.
Chen, X. and Espinoza, D. N. 2018. Ostwald Ripening Changes the Pore Habit and Spatial Variability of Clathrate Hydrate. Fuel 214 (15 February): 614–622. https://doi.org/10.1016/j.fuel.2017.11.065.
Coates, R., Kane, M., Chang, C. et al. 2000. Single-Well Sonic Imaging: High-Definition Reservoir Cross-Sections From Horizontal Wells. Presented at the SPE/CIM International Conference on Horizontal Well Technology, Calgary, 6–8 November. SPE-65457-MS. https://doi.org/10.2118/65457-MS.
Dai, S. and Seol, Y. 2014. Water Permeability in Hydrate-Bearing Sediments: A Pore-Scale Study. Geophys. Res. Lett. 41 (12): 4176–4184. https://doi.org/10.1002/2014GL060535.
Daigle, H. 2016. Relative Permeability to Water or Gas in the Presence of Hydrates in Porous Media From Critical Path Analysis. J. Pet. Sci. Eng. 146 (October): 526–535. https://doi.org/10.1016/j.petrol.2016.07.011.
Delli, M. L. and Grozic, J. L. H. 2014. Experimental Determination of Permeability of Porous Media in the Presence of Gas Hydrates. J. Pet. Sci. Eng. 120 (August): 1–9. https://doi.org/10.1016/j.petrol.2014.05.011.
Demirbas, A. 2010. Methane Hydrates as Potential Energy Resource: Part 2—Methane Production Processes From Gas Hydrates. Energ. Convers. Manage. 51 (7): 1562–1571. https://doi.org/10.1016/j.enconman.2010.02.014.
Fang, H., Xu, M., Lin, Z. et al. 2017. Geophysical Characteristics of Gas Hydrate in the Muli Area, Qinghai Province. J. Nat. Gas Sci. Eng. 37 (January): 539–550. https://doi.org/10.1016/j.jngse.2016.12.001.
Feng, J.-C., Wang, Y., Li, X.-S. et al. 2015. Production Performance of Gas Hydrate Accumulation at the GMGS2-Site 16 of the Pearl River Mouth Basin in the South China Sea. J. Nat. Gas Sci. Eng. 27-1 (November): 306–320. https://doi.org/10.1016/j.jngse.2015.08.071.
Fenton, L. 1960. The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems. IRE Trans. Commun. Sys. 8 (1): 57–67. https://doi.org/10.1109/TCOM.1960.1097606.
Franken, A. C. M., Nolten, J. A. M., Mulder, M. H. V. et al. 1987. Wetting Criteria for the Applicability of Membrane Distillation. J. Membrane Sci. 33 (3): 315–328. https://doi.org/10.1016/S0376-7388(00)80288-4.
Friend, D. G., Ely, J. F., and Ingham, H. 1989. Thermophysical Properties of Methane. J. Phys. Chem. Ref. Data 18 (2): 583–638. https://doi.org/10.1063/1.555828.
Gabitto, J. F. and Tsouris, C. 2010. Physical Properties of Gas Hydrates: A Review. J. Thermodyn. 2010: 271291. https://doi.org/10.1155/2010/271291.
Gallage, C., Kodikara, J., and Uchimura, T. 2013. Laboratory Measurement of Hydraulic Conductivity Functions of Two Unsaturated Sandy Soils During Drying and Wetting Processes. Soils Found. 53 (3): 417–430. https://doi.org/10.1016/j.sandf.2013.04.004.
Gupta, S., Deusner, C., Haeckel, M. et al. 2017. Testing a Thermo-Chemo-Hydro-Geomechanical Model for Gas Hydrate-Bearing Sediments Using Triaxial Compression Laboratory Experiments. Geochem. Geophys. Geosys. 18 (9): 3419–3437. https://doi.org/10.1002/2017GC006901.
Gupta, S., Helmig, R., and Wohlmuth, B. 2015. Non-Isothermal, Multi-Phase, Multi-Component Flows Through Deformable Methane Hydrate Reservoirs. Computat. Geosci. 19 (5): 1063–1088. https://doi.org/10.1007/s10596-015-9520-9.
Jensen, J. L. and Currie, I. D. 1990. A New Method for Estimating the Dykstra-Parsons Coefficient To Characterize Reservoir Heterogeneity. SPE Res Eng 5 (3): 369–374. SPE-17364-PA. https://doi.org/10.2118/17364-PA.
Jensen, J. L., Hinkley, D. V., and Lake, L. W. 1987. A Statistical Study of Reservoir Permeability: Distributions, Correlations, and Averages. SPE Form Eval 2 (4): 461–468. SPE-14270-PA. https://doi.org/10.2118/14270-PA.
Johnson, A., Patil, S., and Dandekar, A. 2011. Experimental Investigation of Gas-Water Relative Permeability for Gas-Hydrate-Bearing Sediments From the Mount Elbert Gas Hydrate Stratigraphic Test Well, Alaska North Slope. Mar. Petrol. Geol. 28 (2): 419–426. https://doi.org/10.1016/j.marpetgeo.2009.10.013.
Joseph, J., Singh, D. N., Kumar, P. et al. 2016. State-of-the-Art of Gas Hydrates and Relative Permeability of Hydrate Bearing Sediments. Mar. Georesour. Geotec. 34 (5): 450–464. https://doi.org/10.1080/1064119X.2015.1025929.
Kang, D. H., Yun, T. S., Kim, K. Y. et al. 2016. Effect of Hydrate Nucleation Mechanisms and Capillarity on Permeability Reduction in Granular Media. Geophys. Res. Lett. 43 (17): 9018–9025. https://doi.org/10.1002/2016GL070511.
Kang, S.-P., Lee, J.-W., and Ryu, H.-J. 2008. Phase Behavior of Methane and Carbon Dioxide Hydrates in Meso- and Macro-Sized Porous Media. Fluid Phase Equilibr. 274 (1–2): 68–72. https://doi.org/10.1016/j.fluid.2008.09.003.
Kleinberg, R. L. 2009. Exploration Strategy for Economically Significant Accumulations of Marine Gas Hydrate. Geol. Soc. London Spec. Pub. 319: 21–28. https://doi.org/10.1144/SP319.3.
Kleinberg, R. L., Flaum, C., Griffin, D. D. et al. 2003. Deep Sea NMR: Methane Hydrate Growth Habit in Porous Media and Its Relationship To Hydraulic Permeability, Deposit Accumulation, and Submarine Slope Stability. J. Geophys. Res. 108 (B10): 2508. https://doi.org/10.1029/2003JB002389.
Kumar, A., Maini, B., Bishnoi, P. R. et al. 2010. Experimental Determination of Permeability in the Presence of Hydrates and Its Effect on the Dissociation Characteristics of Gas Hydrates in Porous Media. J. Pet. Sci. Eng. 70 (1–2): 114–122. https://doi.org/10.1016/j.petrol.2009.10.005.
Li, C.-H., Zhao, Q., Xu, H.-J. et al. 2014. Relation Between Relative Permeability and Hydrate Saturation in Shenhu Area, South China Sea. Appl. Geophys. 11 (2): 207–214. https://doi.org/10.1007/s11770-014-0432-6.
Liang, H., Song, Y., Chen, Y. et al. 2011. The Measurement of Permeability of Porous Media With Methane Hydrate. Petrol. Sci. Technol. 29 (1): 79–87. https://doi.org/10.1080/10916460903096871.
Liu, X. and Flemings, P. B. 2011. Capillary Effects on Hydrate Stability in Marine Sediments. J. Geophys. Res. 116 (B7): B07102. https://doi.org/10.1029/2010JB008143.
Mahabadi, N., Zheng, X., and Jang, J. 2016a. The Effect of Hydrate Saturation on Water Retention Curves in Hydrate-Bearing Sediments. Geophys. Res. Lett. 43 (9): 4279–4287. https://doi.org/10.1002/2016GL068656.
Mahabadi, N., Dai, S., Seol, Y. et al. 2016b. The Water Retention Curve and Relative Permeability for Gas Production From Hydrate-Bearing Sediments: Pore-Network Model Simulation. Geochem. Geophys. Geosyst. 17 (8): 3099–3110. https://doi.org/10.1002/2016GC006372.
Masuda, Y., Naganawa, S., Ando, S. et al. 1997. Numerical Calculation of Gas-Production Performance From Reservoirs Containing Natural Gas Hydrates. Presented at SPE Asia Pacific Oil and Gas Conference.
Merey, S. and Sinayuc, C. 2017. Numerical Simulations for Short-Term Depressurization Production Test of Two Gas Hydrate Sections in the Black Sea. J. Nat. Gas Sci. Eng. 44 (August): 77–95. https://doi.org/10.1016/j.jngse.2017.04.011.
Millington, R. J. and Quirk, J. P. 1961. Permeability of Porous Solids. Trans. Faraday Soc. 57: 1200–1207. https://doi.org/10.1039/TF9615701200.
Misyura, S. Y. 2016. The Influence of Porosity and Structural Parameters on Different Kinds of Gas Hydrate Dissociation. Scientific Reports 6: 30324. https://doi.org/10.1038/srep30324.
Misyura, S. Y., Donskoy, I. G., and Morozov, V. S. 2017. Dissociation of Methane Hydrate Granules. J. Phys. Conf. Ser. 899: 032014. https://doi.org/10.1088/1742-6596/899/3/032014.
Murray, D. R., Fukuhara, M., Osawa, O. et al. 2006. Saturation, Acoustic Properties, Growth Habit, and State of Stress of a Gas Hydrate Reservoir From Well Logs. Petrophysics 47 (2). SPWLA-2006-v47n2a2.
Myshakin, E. M., Ajayi, T., Anderson, B. J. et al. 2016. Numerical Simulations of Depressurization-Induced Gas Production From Gas Hydrates Using 3-D Heterogeneous Models of L-Pad, Prudhoe Bay Unit, North Slope Alaska. J. Nat. Gas Sci. Eng. 35A (September): 1336–1352. https://doi.org/10.1016/j.jngse.2016.09.070.
Nimblett, J. and Ruppel, C. 2003. Permeability Evolution During the Formation of Gas Hydrates in Marine Sediments. J. Geophys. Res. 108 (B9): 2420. https://doi.org/10.1029/2001JB001650.
Pesaran, A. and Shariati, A. 2013. Effect of Capillary Term Parameters on the Thermodynamic Modeling of Methane Hydrate Formation in Porous Media. J. Nat. Gas Sci. Eng. 14 (September): 192–203. https://doi.org/10.1016/j.jngse.2013.06.003.
Rose, K., Boswell, R., and Collett, T. 2011. Mount Elbert Gas Hydrate Stratigraphic Test Well, Alaska North Slope: Coring Operations, Core Sedimentology, and Lithostratigraphy. Mar. Petrol. Geol. 28 (2): 311–331. https://doi.org/10.1016/j.marpetgeo.2010.02.001.
Singh, H. 2017. Representative Elementary Volume (REV) in Spatio-Temporal Domain: A Method to Find REV for Dynamic Pores. J. Earth Sci. 28 (2): 391–403. https://doi.org/10.1007/s12583-017-0726-8.
Singh, H. and Srinivasan, S. 2014a. Some Perspectives on Scale-Up of Flow and Transport in Heterogeneous Media. Oral presentation given at the 2014 Gussow Geosciences Conference, Closing the Gap II: Advances in Applied Geomodeling for Hydrocarbon Reservoirs, Banff, Canada, 22–24 September.
Singh, H. and Srinivasan, S. 2014b. Scale Up of Reactive Processes in Heterogeneous Media—Numerical Experiments and Semi-Analytical Modeling. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, 12–16 April. SPE-169133-MS. https://doi.org/10.2118/169133-MS.
Singh, H., Javadpour, F., Ettehadtavakkol, A. et al. 2014. Nonempirical Apparent Permeability of Shale. SPE Res Eval & Eng 17 (3): 414–424. SPE-170243-PA. https://doi.org/10.2118/170243-PA.
Sloan, E. D. Jr. 2003. Fundamental Principles and Applications of Natural Gas Hydrates. Nature 426: 353–363. https://doi.org/10.1038/nature02135.
Sun, J., Ning, F., Zhang, L. et al. 2016. Numerical Simulation on Gas Production From Hydrate Reservoir at the 1st Offshore Test Site in the Eastern Nankai Trough. J. Nat. Gas Sci. Eng. 30 (March): 64–76. https://doi.org/10.1016/j.jngse.2016.01.036.
Uchida, T., Ebinuma, T., Takeya, S. et al. 2002. Effects of Pore Sizes on Dissociation Temperatures and Pressures of Methane, Carbon Dioxide, and Propane Hydrates in Porous Media. J. Phys. Chem. B 106 (4): 820–826. https://doi.org/10.1021/jp012823w.
Wagner, W. and Kretzschmar, H.-J. 2008. IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. In International Steam Tables—Properties of Water and Steam based on the Industrial Formulation IAPWS-IF97, 7–150. Berlin: Springer.
Waite, W. F., Santamarina, J. C., Cortes, D. D. et al. 2009. Physical Properties of Hydrate-Bearing Sediments. Rev. Geophys. 47 (4): RG4003. https://doi.org/10.1029/2008RG000279.
Wang, J., Zhao, J., Zhang, Y. et al. 2015. Analysis of the Influence of Wettability on Permeability in Hydrate-Bearing Porous Media Using Pore Network Models Combined With Computed Tomography. J. Nat. Gas Sci. Eng. 26 (September): 1372–1379. https://doi.org/10.1016/j.jngse.2015.08.021.
Wyllie, M. R. J. and Gerdner, G. H. F. 1958. The Generalized Kozeny-Carman Equations: Its Application to Problems of Multiphase Flow in Porous Media: Part 2—A Novel Approach to Problems of Fluid Flow. World Oil. 146 (5): 8–16.