Hydraulic fracturing and commingle production of multiple layers are extensively adopted in unconventional tight gas reservoirs.Accurate determination of parameters of individual layers in multilayered tight gas reser...Hydraulic fracturing and commingle production of multiple layers are extensively adopted in unconventional tight gas reservoirs.Accurate determination of parameters of individual layers in multilayered tight gas reservoirs is essential for well performance evaluation and development strategy optimization.However,most analytical models for fractured vertical wells in stratified gas reservoirs focus on fully penetrated hydraulic fractures,neglecting the influence of partial penetration of hydraulic fractures.This paper presents a semi-analytical model to investigate the transient pressure behavior of vertically fractured wells in dual porosity multi-layered tight gas reservoirs.The partial penetration of hydraulic fracture,the vertical heterogeneities of layer properties,the differences between hydraulic fracture lengths in each layer and the stress sensitivity are all incorporated in the proposed model.The point-source solution,Laplace transformation,Fourier transformation,Pedrosa's transformation,perturbation technique,and the superposition principle are applied to obtain the analytical solution of transient pressure responses.The proposed model is validated against a commercial software,and the transient pressure behavior of vertically fractured wells in multi-layered tight gas reservoirs are analyzed.Based on the characteristics of the type curves,seven flow regimes can be identified,including wellbore storage,transitional flow period,reservoir linear flow period,vertical pseudo-radial flow in fracture system,inter-porosity flow period,late-time pseudo-radial flow period,and the boundary-dominated flow period.Sensitivity analyses reveal that the penetration ratio of hydraulic fracture has primary influence on early-time transient pressure behavior and production contribution,while the stress sensitivity mainly affects the late-time transient pressure behavior.Gas production at the initial stage is mainly contributed by the high-pressure/high-permeability layer,and gas backflow will occur during initial production stage for obviously unequal initial formation pressures.Finally,two field cases are conducted to illustrate the applicability of the proposed model.The model and corresponding conclusions can provide technical support for performance analysis of tight gas reservoirs.展开更多
Low-speed flow experiments in which ultra-fine copper tubes are used to simulate micro-fractures in carbonate strata are conducted to analyze the variations of gas flow state in fractures of different fracture heights...Low-speed flow experiments in which ultra-fine copper tubes are used to simulate micro-fractures in carbonate strata are conducted to analyze the variations of gas flow state in fractures of different fracture heights,determine flow state transition limit and transition interval,and establish the calculation method of flow state transition limit.The results show that the ideal Hagen-Poiseuille flow is the main form of gas flow in large fractures.Due to the decrease of fracture height,the gas flow in the fracture changes from Hagen-Poiseuille flow with ideal smooth seam surface to non-Hagen-Poiseuille flow,and the critical point of the transition is the boundary of flow state transition.After the fracture height continues to decrease to a certain extent below the boundary of the flow state transition fracture height,the form of gas flow gradually changes to the ideal Darcy flow,thus the transition interval of the gas flow state in the closing process of fracture can be determined.Based on the three-dimensional microconvex body scanning of the fracture surface,the material properties of fracture and properties of fluid in the fracture,a method for calculating the boundary of flow state transition is established.The experimental test and theoretical calculation show that the limit of the fracture height for the transition from pipe flow to Darcy flow is about twice the sum of the maximum height of the microconvex bodies on the upper and lower sides of the fracture.展开更多
Shale reservoirs are characterized by numerous geological discontinuities,such as bedding planes,and exhibit pronounced heterogeneity across rock layers separated by these planes.Bedding planes often possess distinct ...Shale reservoirs are characterized by numerous geological discontinuities,such as bedding planes,and exhibit pronounced heterogeneity across rock layers separated by these planes.Bedding planes often possess distinct mechanical properties compared to the surrounding rock matrix,particularly in terms of damage and fracture behavior.Consequently,vertical propagation of hydraulic fractures is influenced by both bedding planes and the heterogeneity.In this study,a numerical investigation into the height growth of hydraulic fractures was conducted using the finite element method,incorporating zero-thickness cohesive elements.The analysis explored the effects of bedding planes,toughness contrasts between layers,and variations in in-situ stress across different strata.The results reveal that hydraulic fractures are more likely to propagate along bedding planes instead of traversing them and extending vertically into barrier layers when(1)bedding strength is low,(2)stress contrast between layers is high,and(3)toughness contrast is significant.Furthermore,for a given bedding strength,increased stress contrast or higher toughness contrast between layers elevate hydraulic fracture extension pressure.When a substantial stress difference exists between layers(Lc 0.4),hydraulic=fractures preferentially propagate along bedding planes.Conversely,as bedding strength increases,the propagation distance along bedding planes decreases,accompanied by an amplified horizontal compressive stress field.Notably,when the stress difference is sufficiently small(SD a phenomenon termed“stress rolling”emerges,wherein<-0.2),hydraulic fractures deviate from vertical growth and instead extend along a near-horizontal trajectory.展开更多
In the process of using the original key stratum theory to predict the height of a water-flowing fractured zone(WFZ),the influence of rock strata outside the calculation range on the rock strata within the calculation...In the process of using the original key stratum theory to predict the height of a water-flowing fractured zone(WFZ),the influence of rock strata outside the calculation range on the rock strata within the calculation range as well as the fact that the shape of the overburden deformation area will change with the excavation length are ignored.In this paper,an improved key stratum theory(IKS theory)was proposed by fixing these two shortcomings.Then,a WFZ height prediction method based on IKS theory was established and applied.First,the range of overburden involved in the analysis was determined according to the tensile stress distribution range above the goaf.Second,the key stratum in the overburden involved in the analysis was identified through IKS theory.Finally,the tendency of the WFZ to develop upward was determined by judging whether or not the identified key stratum will break.The proposed method was applied and verified in a mining case study,and the reasons for the differences in the development patterns between the WFZs in coalfields in Northwest and East China were also fully explained by this method.展开更多
To study the heights of the caved zone and water-conducting fracture zone in backfill mining,the failure mechanism of strata during backfill mining was analyzed,and a method for determining the heights of the two zone...To study the heights of the caved zone and water-conducting fracture zone in backfill mining,the failure mechanism of strata during backfill mining was analyzed,and a method for determining the heights of the two zones was proposed based on key strata theory.The movement and failure regularity of the strata above the backfilling panel were revealed through numerical simulation.Considering the geologic conditions of the CT101 backfilling panel,the height of the fracture zone was determined using the proposed method along with empirical calculation,numerical simulation,and borehole detection.The results of the new calculation method were similar to in situ measurements.The traditional empirical formula,which is based on the equivalent mining height model,resulted in large errors during calculation.The findings indicate the reliability of the new method and demonstrate its significance for creating reference data for related studies.展开更多
Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on ...Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.展开更多
The focus of this study is to analyze a parametric space for the problem of a constant height hydraulic fracture driven by a power-law fluid.The interplay of physical mechanisms related to toughness,fluid resistance,a...The focus of this study is to analyze a parametric space for the problem of a constant height hydraulic fracture driven by a power-law fluid.The interplay of physical mechanisms related to toughness,fluid resistance,and leakoff is considered,but the model is restricted to local elasticity for simplicity.The problem of a semi-infinite constant height fracture is first analyzed:limiting solutions are obtained analytically and their locations inside the dimensionless parametric space are obtained.Then,the problem of a finite constant height fracture is investigated.Similarly,limiting vertex solutions are first outlined and then their locations in the parametric space are quantified.Results demonstrate that the effect of the power-law factor is relatively mild,as it does not significantly distort the parametric spaces.At the same time,there are quantitative differences,which are also determined by the obtained results.Numerical examples highlighting the effect of fracture regime on morphology of multiple fractures are presented at the end.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52174036,52234003)the Sichuan Province Science and Technology Program(Grant No.2024NSFSC0199)the Joint Fund for Innovation and Development of Chongqing Natural Science Foundation(Grant No.2023NSCQ-LZX0184).
文摘Hydraulic fracturing and commingle production of multiple layers are extensively adopted in unconventional tight gas reservoirs.Accurate determination of parameters of individual layers in multilayered tight gas reservoirs is essential for well performance evaluation and development strategy optimization.However,most analytical models for fractured vertical wells in stratified gas reservoirs focus on fully penetrated hydraulic fractures,neglecting the influence of partial penetration of hydraulic fractures.This paper presents a semi-analytical model to investigate the transient pressure behavior of vertically fractured wells in dual porosity multi-layered tight gas reservoirs.The partial penetration of hydraulic fracture,the vertical heterogeneities of layer properties,the differences between hydraulic fracture lengths in each layer and the stress sensitivity are all incorporated in the proposed model.The point-source solution,Laplace transformation,Fourier transformation,Pedrosa's transformation,perturbation technique,and the superposition principle are applied to obtain the analytical solution of transient pressure responses.The proposed model is validated against a commercial software,and the transient pressure behavior of vertically fractured wells in multi-layered tight gas reservoirs are analyzed.Based on the characteristics of the type curves,seven flow regimes can be identified,including wellbore storage,transitional flow period,reservoir linear flow period,vertical pseudo-radial flow in fracture system,inter-porosity flow period,late-time pseudo-radial flow period,and the boundary-dominated flow period.Sensitivity analyses reveal that the penetration ratio of hydraulic fracture has primary influence on early-time transient pressure behavior and production contribution,while the stress sensitivity mainly affects the late-time transient pressure behavior.Gas production at the initial stage is mainly contributed by the high-pressure/high-permeability layer,and gas backflow will occur during initial production stage for obviously unequal initial formation pressures.Finally,two field cases are conducted to illustrate the applicability of the proposed model.The model and corresponding conclusions can provide technical support for performance analysis of tight gas reservoirs.
基金Supported by the Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance(2020CX010401)。
文摘Low-speed flow experiments in which ultra-fine copper tubes are used to simulate micro-fractures in carbonate strata are conducted to analyze the variations of gas flow state in fractures of different fracture heights,determine flow state transition limit and transition interval,and establish the calculation method of flow state transition limit.The results show that the ideal Hagen-Poiseuille flow is the main form of gas flow in large fractures.Due to the decrease of fracture height,the gas flow in the fracture changes from Hagen-Poiseuille flow with ideal smooth seam surface to non-Hagen-Poiseuille flow,and the critical point of the transition is the boundary of flow state transition.After the fracture height continues to decrease to a certain extent below the boundary of the flow state transition fracture height,the form of gas flow gradually changes to the ideal Darcy flow,thus the transition interval of the gas flow state in the closing process of fracture can be determined.Based on the three-dimensional microconvex body scanning of the fracture surface,the material properties of fracture and properties of fluid in the fracture,a method for calculating the boundary of flow state transition is established.The experimental test and theoretical calculation show that the limit of the fracture height for the transition from pipe flow to Darcy flow is about twice the sum of the maximum height of the microconvex bodies on the upper and lower sides of the fracture.
基金the National Natural Science Foundation of China(No.52204052)the NationalNatural Science Foundation of China(No.U23B20156)the Sichuan Science and Technology Program(No.2023NSFSC0933).
文摘Shale reservoirs are characterized by numerous geological discontinuities,such as bedding planes,and exhibit pronounced heterogeneity across rock layers separated by these planes.Bedding planes often possess distinct mechanical properties compared to the surrounding rock matrix,particularly in terms of damage and fracture behavior.Consequently,vertical propagation of hydraulic fractures is influenced by both bedding planes and the heterogeneity.In this study,a numerical investigation into the height growth of hydraulic fractures was conducted using the finite element method,incorporating zero-thickness cohesive elements.The analysis explored the effects of bedding planes,toughness contrasts between layers,and variations in in-situ stress across different strata.The results reveal that hydraulic fractures are more likely to propagate along bedding planes instead of traversing them and extending vertically into barrier layers when(1)bedding strength is low,(2)stress contrast between layers is high,and(3)toughness contrast is significant.Furthermore,for a given bedding strength,increased stress contrast or higher toughness contrast between layers elevate hydraulic fracture extension pressure.When a substantial stress difference exists between layers(Lc 0.4),hydraulic=fractures preferentially propagate along bedding planes.Conversely,as bedding strength increases,the propagation distance along bedding planes decreases,accompanied by an amplified horizontal compressive stress field.Notably,when the stress difference is sufficiently small(SD a phenomenon termed“stress rolling”emerges,wherein<-0.2),hydraulic fractures deviate from vertical growth and instead extend along a near-horizontal trajectory.
基金supported by the Key Projects of Natural Science Foundation of China(No.41931284)the Scientific Research Start-Up Fund for High-Level Introduced Talents of Anhui University of Science and Technology(No.2022yjrc21).
文摘In the process of using the original key stratum theory to predict the height of a water-flowing fractured zone(WFZ),the influence of rock strata outside the calculation range on the rock strata within the calculation range as well as the fact that the shape of the overburden deformation area will change with the excavation length are ignored.In this paper,an improved key stratum theory(IKS theory)was proposed by fixing these two shortcomings.Then,a WFZ height prediction method based on IKS theory was established and applied.First,the range of overburden involved in the analysis was determined according to the tensile stress distribution range above the goaf.Second,the key stratum in the overburden involved in the analysis was identified through IKS theory.Finally,the tendency of the WFZ to develop upward was determined by judging whether or not the identified key stratum will break.The proposed method was applied and verified in a mining case study,and the reasons for the differences in the development patterns between the WFZs in coalfields in Northwest and East China were also fully explained by this method.
基金Supported by the National Key R&D Program(2018YFC0604501).
文摘To study the heights of the caved zone and water-conducting fracture zone in backfill mining,the failure mechanism of strata during backfill mining was analyzed,and a method for determining the heights of the two zones was proposed based on key strata theory.The movement and failure regularity of the strata above the backfilling panel were revealed through numerical simulation.Considering the geologic conditions of the CT101 backfilling panel,the height of the fracture zone was determined using the proposed method along with empirical calculation,numerical simulation,and borehole detection.The results of the new calculation method were similar to in situ measurements.The traditional empirical formula,which is based on the equivalent mining height model,resulted in large errors during calculation.The findings indicate the reliability of the new method and demonstrate its significance for creating reference data for related studies.
文摘Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.
文摘The focus of this study is to analyze a parametric space for the problem of a constant height hydraulic fracture driven by a power-law fluid.The interplay of physical mechanisms related to toughness,fluid resistance,and leakoff is considered,but the model is restricted to local elasticity for simplicity.The problem of a semi-infinite constant height fracture is first analyzed:limiting solutions are obtained analytically and their locations inside the dimensionless parametric space are obtained.Then,the problem of a finite constant height fracture is investigated.Similarly,limiting vertex solutions are first outlined and then their locations in the parametric space are quantified.Results demonstrate that the effect of the power-law factor is relatively mild,as it does not significantly distort the parametric spaces.At the same time,there are quantitative differences,which are also determined by the obtained results.Numerical examples highlighting the effect of fracture regime on morphology of multiple fractures are presented at the end.
