Streamline modeling of fluid transport in naturally fractured porous medium
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摘要
To better understand the roles natural fractures play in porous media, an embedded discrete fracture model and streamline modeling method were combined to model natural fractures and compute the flow trajectory and time of fluid in matrix and fractures systems. The effects of fracture conductivity, number of fractures and fracture locations on fluid flow trajectory and time were examined through analyzing the differences in water breakthrough time and sweeping volume of reservoirs with different fracture networks. When other conditions are the same, compared with homogeneous reservoir without fractures, the fractured reservoir has water breakthrough time 30% sooner and swept volume 10% smaller. Although increase of single fracture can lead to faster water breakthrough and smaller swept volume, adding more fractures wouldn't necessarily reach the same effect. The effect of water flooding is also related to the strike and position of fractures. Fractures in different strikes and positions can result in 20% discrepancy in water breakthrough time and 9% gap in swept volume. The shorter the fracture, the less its effect on fluid flow trajectory and time will be. The position of fracture has a strong influence on sweeping efficiency, and the change of one fracture position could bring about 1% variation in swept volume.
To better understand the roles natural fractures play in porous media, an embedded discrete fracture model and streamline modeling method were combined to model natural fractures and compute the flow trajectory and time of fluid in matrix and fractures systems. The effects of fracture conductivity, number of fractures and fracture locations on fluid flow trajectory and time were examined through analyzing the differences in water breakthrough time and sweeping volume of reservoirs with different fracture networks. When other conditions are the same, compared with homogeneous reservoir without fractures, the fractured reservoir has water breakthrough time 30% sooner and swept volume 10% smaller. Although increase of single fracture can lead to faster water breakthrough and smaller swept volume, adding more fractures wouldn't necessarily reach the same effect. The effect of water flooding is also related to the strike and position of fractures. Fractures in different strikes and positions can result in 20% discrepancy in water breakthrough time and 9% gap in swept volume. The shorter the fracture, the less its effect on fluid flow trajectory and time will be. The position of fracture has a strong influence on sweeping efficiency, and the change of one fracture position could bring about 1% variation in swept volume.
To better understand the roles natural fractures play in porous media, an embedded discrete fracture model and streamline modeling method were combined to model natural fractures and compute the flow trajectory and time of fluid in matrix and fractures systems. The effects of fracture conductivity, number of fractures and fracture locations on fluid flow trajectory and time were examined through analyzing the differences in water breakthrough time and sweeping volume of reservoirs with different fracture networks. When other conditions are the same, compared with homogeneous reservoir without fractures, the fractured reservoir has water breakthrough time 30% sooner and swept volume 10% smaller. Although increase of single fracture can lead to faster water breakthrough and smaller swept volume, adding more fractures wouldn't necessarily reach the same effect. The effect of water flooding is also related to the strike and position of fractures. Fractures in different strikes and positions can result in 20% discrepancy in water breakthrough time and 9% gap in swept volume. The shorter the fracture, the less its effect on fluid flow trajectory and time will be. The position of fracture has a strong influence on sweeping efficiency, and the change of one fracture position could bring about 1% variation in swept volume.
引文
[1]AL-HARBL M,CHENG H,ZHONG H,et al.Streamlinebased production data integration in naturally fractured reservoirs.SPE 89914-PA,2005.
[2]BLAIR P M.Calculation of oil displacement by countercurrent water imbibition.Texas:The Fourth Biennial Secondary Recovery Symposium of SPE in Wichita Falls,1960.
[3]CHEN Z,LIAO X,ZHAO X,et al.Appraising carbon geological-stroage potential in unconventional reservoirs:Engineering-parameters analysis.SPE 189442-PA,2018.
[4]DATTA-GUPTA A,KING M J.A semianalytic approach to tracer flow modelling in heterogeneous permeable media.Advances in Water Resources,1995,18(1):9-24.
[5]DATTA-GUPTA A,KING M.Streamline simulation:Theory and practice.Texas:Society of Petroleum Engineers,2007.
[6]DONATO G D,HUANG W,BLUNT M.Streamline-based dual porosity simulation of fractured reservoirs.SPE 84036-MS,2003.
[7]DOUGLAS J J,ARBOGAST T,PAES L.Two models for the waterflooding of naturally fractured reservoirs.SPE 18425,1989.
[8]FAY C H,PRATTS M.The application of numerical methods to cycling and flooding problems.Hague,Netherlands:The3rd World Petroleum Congress,1951.
[9]GU S,LIU Y,CHEN Z,et al.A method for evaluation of water flooding performance in fractured reservoirs.Journal of Petroleum Science and Engineering,2014,120(8):130-140.
[10]GU Xiaoyu,PU Chunsheng,HUANG Hai,et al.Microinfluencing mechanism of permeability on spontaneous imbibition recovery for tight sandstone reservoirs.Petroleum Exploration and Development,2017,44(6):948-954.
[11]QU Guanzheng,QU Zhanqing,HAZLETT R D,et al.Geometrical description and permeability calculation about shale tensile micro-fractures.Petroleum Exploration and Development,2016,43(1):115-120.
[12]HE Y,CHENG S,RUI Z,et al.An improved rate-transient analysis model of multi-fractured horizontal wells with non-uniform hydraulic fracture properties.Energies,2018,11(2):393.
[13]HOTEIT H,FIROOZABADI A.Compositional modeling of discrete-fractured media without transfer functions by the discontinuous galerkin and mixed methods.SPE 90277-PA,2006.
[14]JIMENEZ E,DATTA-GUPTA A,KING M J.Full-field streamline tracing in complex faulted systems with non-neighbor connections.SPE 113425-PA,2010.
[15]KAZEMI H,GILMAN J R,EISHARKAWY A A.Analytical and numerical solution of oil recovery from fractured reservoirs with empirical transfer functions.SPE Reservoir Engineering,1992,72(2):219-227.
[16]KLAUSSEN R,RASMUSSEN A,STEPHANSEN A.Velocity interpolation and streamline tracing on irregular geometries.Computational Geosciences,2012,16(2):261-276.
[17]LIM J,ZUO L,KING M J.Development of data models and velocity interpolation methods for streamline trajectories on unstructured grids.Barcelona:The 11th World Congress on Computational Mechanics,2014.
[18]MARTIN J C,WEGNER R E.Numerical solution of multiphase two-dimensional incompressible flow using streamtube relationships.SPE Journal,1979,19(5):313-323.
[19]MOINFAR A,NARR W,HUI M H,et al.Comparison of discrete-fracture and dual-permeability models for multiphase flow in naturally fractured reservoirs.SPE 142295-MS,2011.
[20]MOINFAR A,VARAVEI A,SEPEHRNOORI K,et al.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs.SPE Journal,2014,19(2):289-303.
[21]MUSKAT M.Flow of homogeneous fluids.Boston:International Human Resources Development Corporation,1982.
[22]OLORODE O,FREEMAN C M,MORIDIS G,et al.Highresolution numerical modeling of complex and irregular fracture patterns in shale-gas reservoirs and tight gas reservoirs.SPE 152482-PA,2013.
[23]POLLOCK D.Semi-analytical computation of path lines for finite-difference models.Ground Water,1988,26(6):743-750.
[24]PU Chunsheng,JING Cheng,HE Yanlong,et al.Multistage interwell chemical tracing for step-by-step profile control of water channeling and flooding of fractured ultra-low permeability reservoirs.Petroleum Exploration and Development,2016,43(4):621-629.
[25]SHAKIBA M.Modeling and simulation of fluid flow in naturally and hydraulically fractured reservoirs using embedded discrete fracture model(EDFM).Austin:University of Texas,2014.
[26]THIELE M R.Modeling multiphase flow in heterogeneous media using streamtubes.Palo Alto:Stanford University,1994.
[27]WANG B,FENG Y.An embedded grid-free approach for near wellbore streamline simulation.SPE 182614-MS,2017.
[28]WARREN J E,ROOT P J.The behavior of naturally fractured reservoirs.SPE Journal,1963,3(3):245-255.
[29]WU Y S,BAI B.Efficient simulation for low-salinity waterflooding in porous and fractured reservoirs.SPE 118830,2009.
[30]XU Y,FILHO J C,YU W,et al.Discrete-fracture modeling of complex hydraulic-fracture geometries in reservoir simulators.SPE 183647-PA,2017.
[31]YANG R,HUANG Z,YU W,et al.A comprehensive model for real gas transport in shale formations with complex nonplanar fracture networks.Scientific Reports,2016,6:36673.
[32]ZHANG Y,KING M J,DATTA-GUPTA A.Robust streamline tracing using inter-cell fluxes in locally refined and unstructured grids.Water Resources Research,2012,48(6):116-120.
[33]ZHOU W,BANERJEE R,POE B,et al.Semianalytical production simulation of complex hydraulic-fracture networks.SPE 157367-PA,2014.
[34]ZUO L H,WEIJERMARS R.Rules for flight paths and time of flight for flows in porous media with heterogeneous permeability and porosity.Geofluids,2018(3):1-18.
[35]ZUO L,LIM J,CHEN R,et al.Efficient calculation of flux conservative streamline trajectories on complex and unstructured grids.Vienna:The 78th EAGE Conference&Exhibition,2016.
[2]BLAIR P M.Calculation of oil displacement by countercurrent water imbibition.Texas:The Fourth Biennial Secondary Recovery Symposium of SPE in Wichita Falls,1960.
[3]CHEN Z,LIAO X,ZHAO X,et al.Appraising carbon geological-stroage potential in unconventional reservoirs:Engineering-parameters analysis.SPE 189442-PA,2018.
[4]DATTA-GUPTA A,KING M J.A semianalytic approach to tracer flow modelling in heterogeneous permeable media.Advances in Water Resources,1995,18(1):9-24.
[5]DATTA-GUPTA A,KING M.Streamline simulation:Theory and practice.Texas:Society of Petroleum Engineers,2007.
[6]DONATO G D,HUANG W,BLUNT M.Streamline-based dual porosity simulation of fractured reservoirs.SPE 84036-MS,2003.
[7]DOUGLAS J J,ARBOGAST T,PAES L.Two models for the waterflooding of naturally fractured reservoirs.SPE 18425,1989.
[8]FAY C H,PRATTS M.The application of numerical methods to cycling and flooding problems.Hague,Netherlands:The3rd World Petroleum Congress,1951.
[9]GU S,LIU Y,CHEN Z,et al.A method for evaluation of water flooding performance in fractured reservoirs.Journal of Petroleum Science and Engineering,2014,120(8):130-140.
[10]GU Xiaoyu,PU Chunsheng,HUANG Hai,et al.Microinfluencing mechanism of permeability on spontaneous imbibition recovery for tight sandstone reservoirs.Petroleum Exploration and Development,2017,44(6):948-954.
[11]QU Guanzheng,QU Zhanqing,HAZLETT R D,et al.Geometrical description and permeability calculation about shale tensile micro-fractures.Petroleum Exploration and Development,2016,43(1):115-120.
[12]HE Y,CHENG S,RUI Z,et al.An improved rate-transient analysis model of multi-fractured horizontal wells with non-uniform hydraulic fracture properties.Energies,2018,11(2):393.
[13]HOTEIT H,FIROOZABADI A.Compositional modeling of discrete-fractured media without transfer functions by the discontinuous galerkin and mixed methods.SPE 90277-PA,2006.
[14]JIMENEZ E,DATTA-GUPTA A,KING M J.Full-field streamline tracing in complex faulted systems with non-neighbor connections.SPE 113425-PA,2010.
[15]KAZEMI H,GILMAN J R,EISHARKAWY A A.Analytical and numerical solution of oil recovery from fractured reservoirs with empirical transfer functions.SPE Reservoir Engineering,1992,72(2):219-227.
[16]KLAUSSEN R,RASMUSSEN A,STEPHANSEN A.Velocity interpolation and streamline tracing on irregular geometries.Computational Geosciences,2012,16(2):261-276.
[17]LIM J,ZUO L,KING M J.Development of data models and velocity interpolation methods for streamline trajectories on unstructured grids.Barcelona:The 11th World Congress on Computational Mechanics,2014.
[18]MARTIN J C,WEGNER R E.Numerical solution of multiphase two-dimensional incompressible flow using streamtube relationships.SPE Journal,1979,19(5):313-323.
[19]MOINFAR A,NARR W,HUI M H,et al.Comparison of discrete-fracture and dual-permeability models for multiphase flow in naturally fractured reservoirs.SPE 142295-MS,2011.
[20]MOINFAR A,VARAVEI A,SEPEHRNOORI K,et al.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs.SPE Journal,2014,19(2):289-303.
[21]MUSKAT M.Flow of homogeneous fluids.Boston:International Human Resources Development Corporation,1982.
[22]OLORODE O,FREEMAN C M,MORIDIS G,et al.Highresolution numerical modeling of complex and irregular fracture patterns in shale-gas reservoirs and tight gas reservoirs.SPE 152482-PA,2013.
[23]POLLOCK D.Semi-analytical computation of path lines for finite-difference models.Ground Water,1988,26(6):743-750.
[24]PU Chunsheng,JING Cheng,HE Yanlong,et al.Multistage interwell chemical tracing for step-by-step profile control of water channeling and flooding of fractured ultra-low permeability reservoirs.Petroleum Exploration and Development,2016,43(4):621-629.
[25]SHAKIBA M.Modeling and simulation of fluid flow in naturally and hydraulically fractured reservoirs using embedded discrete fracture model(EDFM).Austin:University of Texas,2014.
[26]THIELE M R.Modeling multiphase flow in heterogeneous media using streamtubes.Palo Alto:Stanford University,1994.
[27]WANG B,FENG Y.An embedded grid-free approach for near wellbore streamline simulation.SPE 182614-MS,2017.
[28]WARREN J E,ROOT P J.The behavior of naturally fractured reservoirs.SPE Journal,1963,3(3):245-255.
[29]WU Y S,BAI B.Efficient simulation for low-salinity waterflooding in porous and fractured reservoirs.SPE 118830,2009.
[30]XU Y,FILHO J C,YU W,et al.Discrete-fracture modeling of complex hydraulic-fracture geometries in reservoir simulators.SPE 183647-PA,2017.
[31]YANG R,HUANG Z,YU W,et al.A comprehensive model for real gas transport in shale formations with complex nonplanar fracture networks.Scientific Reports,2016,6:36673.
[32]ZHANG Y,KING M J,DATTA-GUPTA A.Robust streamline tracing using inter-cell fluxes in locally refined and unstructured grids.Water Resources Research,2012,48(6):116-120.
[33]ZHOU W,BANERJEE R,POE B,et al.Semianalytical production simulation of complex hydraulic-fracture networks.SPE 157367-PA,2014.
[34]ZUO L H,WEIJERMARS R.Rules for flight paths and time of flight for flows in porous media with heterogeneous permeability and porosity.Geofluids,2018(3):1-18.
[35]ZUO L,LIM J,CHEN R,et al.Efficient calculation of flux conservative streamline trajectories on complex and unstructured grids.Vienna:The 78th EAGE Conference&Exhibition,2016.