THERMAL SCIENCE
International Scientific Journal
ANALYTICAL SOLUTIONS OF FRACTAL-HYDRO-THERMAL MODEL FOR TWO-PHASE FLOW IN THERMAL STIMULATION ENHANCED COALBED METHANE RECOVERY
ABSTRACT
Thermal stimulation is a useful supplementary mining technique for the enhancement of coalbed methane recovery. This technique couples the temperature change with gas-water two-phase flow in the mining process. Many integer dimension hydro-thermal models have been proposed but cannot well describe this coupling because two-phase flow and heat conduction are usually non-linear, tortuous and fractal. In this study, a fractal-hydro-thermal coupling model is proposed to describe the coupling between heat conduction and two-phase flow behaviors in terms of fractional time and space derivatives. This model is analytically solved through the fractal travelling-wave method for pore pressure and production rate of gas and water. The analytical solutions are compared with the in-situ coalbed methane production rate. Results show that our proposed fractal-hydro-thermal model can describe both heat and mass transfers in thermal stimulation enhanced coalbed methane recovery.
KEYWORDS
PAPER SUBMITTED: 2018-06-20
PAPER REVISED: 2018-09-10
PAPER ACCEPTED: 2018-11-15
PUBLISHED ONLINE: 2019-04-14
THERMAL SCIENCE YEAR
2019, VOLUME
23, ISSUE
Issue 3, PAGES [1345 - 1353]
- Wang, H., et al., Enhance hydraulic fractured coalbed methane recovery by thermal stimulation, Society of Petroleum Engineers, SPE175927 (2015).
- Salmachi, A., Haghighi, M., Feasibility study of thermally enhanced gas recovery of coal seam gas reservoirs using geothermal resources, Energy Fuels, 26 (2012), pp. 5048-5059.
- Zhou, F., et al., Injecting pure N2 and CO2 to coal for enhanced coalbed methane: experimental observations and numerical simulation, International Journal of Coal Geology, 116 (2013), pp. 53-62.
- Qu, H., et al., Complex evolution of coal permeability during CO2 injection under variable temperatures, International Journal of Greenhouse Gas Control, 9 (2012), pp. 281-293.
- Lewis, R.W., et al., Finite element modelling of two-phase heat and fluid Flow in deforming porous media, Transport in Porous Media, 4 (1989), 4, pp. 319-334.
- Wang, J.G., Peng, Y., Numerical modeling for the combined effects of two-phase flow, Deformation, gas diffusion and CO2 sorption on caprock sealing efficiency, Journal of Geochemical Exploration, 144 (2014), pp. 154-167.
- Wang, J.G., Wang, H.M., Sealing efficiency analysis for shallow-layer caprocks in CO2 geological storage, Environmental Earth Sciences, 77 (2018), 738.
- Teng, T., et al., A thermally sensitive permeability model for coal-gas interactions including thermal fracturing and volatilization, Journal of Natural Gas Science and Engineering, 32(2016), pp. 319-333.
- Shang, X.J., et al., Fractal analysis for heat extraction in geothermal system, Thermal Science, 21(2017), Suppl. 1, pp. S25-S31.
- Teng, T., et al., Complex thermal coal gas interactions in heat injection enhanced CBM recovery, Journal of Natural Gas Science and Engineering, 34 (2017), pp.1174-1190.
- Li, S., et al., A fully coupled thermal-hydraulic-mechanical model with two-phase flow for coalbed methane extraction, Journal of Natural Gas Science and Engineering, 33 (2016), pp. 324-336.
- Kang, J. H., et al., Numerical modeling and experimental validation of anomalous time and space subdiffusion for gas transport in porous coal matrix, International Journal of Heat and Mass Transfer, 100 (2016), pp. 747-757.
- Yang, X. J., Baleanu, D., Local fractional integral transforms and their applications, Academic Press, New York, USA, 2015.
- Yang, X. J., et al., Systems of Navier-Stokes equations on cantor sets, Mathematical Problems in Engineering, 2013, Article ID 769724, pp.1-8.
- Liu, H. Y., et al., Fractional calculus for nanoscale flow and heat transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250.
- Cao, W., et al., Analysis on coalbed methane with heat injection based on COMSOL Multiphysics, Chinese Journal of Underground Space and Engineering, 10(2014), 5, pp. 1139-1145. (in Chinese)
- Xue, Y.C., et al., Mathematical model study on gas and water two-phase of early-time flowback in shale gas wells, Science Technology and Engineering, 17(2017), 24, pp. 213-217.
- Mora, C.A., Wattenbarger, R.A., Comparison of computation methods for CBM performance, Journal of Canadian Petroleum Technology, 48 (2009), pp. 42-48.