In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hy...In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.展开更多
The maximum effective hole-diameter mathematical modei describing the flow of slightly compressible fluid through a commingled reservoir was solved rigorously with consideration of wellbore storage and different skin ...The maximum effective hole-diameter mathematical modei describing the flow of slightly compressible fluid through a commingled reservoir was solved rigorously with consideration of wellbore storage and different skin factors. The exact solutions for wellbore pressure and the production rate obtained from layer j for a well production at a constant rate from a radial drainage area with infinite and constant pressure and no flow outer boundary condition were expressed in terms of ordinary Bessel functions. These solutions were computed numerically by the Crump's numerical inversion method and the behavior of systems was studied as a function of various reservoir parameters. The modei was compared with the real wellbore radii modei. The new modei is numerically stable when the skin factor is positive and negative, but the real wellbore radii modei is numerically stable only when the skin factor is positive.展开更多
Reservoir deposition occurs over geologic periods of time. Although reservoirs are assumed to be homogenous for simplicity of analysis, most reservoirs are heterogeneous in nature. Some common forms of hetergeneity ar...Reservoir deposition occurs over geologic periods of time. Although reservoirs are assumed to be homogenous for simplicity of analysis, most reservoirs are heterogeneous in nature. Some common forms of hetergeneity are the presence of layers and the presence of different zones of fluids and/or rock in the formation. A modified semi-permeable model for multi-layered gas reservoirs with pseudo-steady state interlayer crossflow was developed. The model accounted for the effect of skin and wellbore storage, considers all layers open to a single well, which flows at constant total rate. This new numerical solution was proved to be computationally very efficient, and it has been validated by comparing the results with those of some simple, well known models in the well testing literature. The effects of the reservoir parameters such as permeability, vertical permeability, skin, wellbore storage on the wellbore response, pressure and layer production rate were investigated. Numerical solutions of the problem for the modified semi-permeable model were used to find the structure of crossflow in typical cases.展开更多
文摘In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.
基金National Natural Science Foundation of China(No.50206016)Special Funds for Major State Basic Research Program of China(973 Program,No.1999022308)
文摘The maximum effective hole-diameter mathematical modei describing the flow of slightly compressible fluid through a commingled reservoir was solved rigorously with consideration of wellbore storage and different skin factors. The exact solutions for wellbore pressure and the production rate obtained from layer j for a well production at a constant rate from a radial drainage area with infinite and constant pressure and no flow outer boundary condition were expressed in terms of ordinary Bessel functions. These solutions were computed numerically by the Crump's numerical inversion method and the behavior of systems was studied as a function of various reservoir parameters. The modei was compared with the real wellbore radii modei. The new modei is numerically stable when the skin factor is positive and negative, but the real wellbore radii modei is numerically stable only when the skin factor is positive.
文摘Reservoir deposition occurs over geologic periods of time. Although reservoirs are assumed to be homogenous for simplicity of analysis, most reservoirs are heterogeneous in nature. Some common forms of hetergeneity are the presence of layers and the presence of different zones of fluids and/or rock in the formation. A modified semi-permeable model for multi-layered gas reservoirs with pseudo-steady state interlayer crossflow was developed. The model accounted for the effect of skin and wellbore storage, considers all layers open to a single well, which flows at constant total rate. This new numerical solution was proved to be computationally very efficient, and it has been validated by comparing the results with those of some simple, well known models in the well testing literature. The effects of the reservoir parameters such as permeability, vertical permeability, skin, wellbore storage on the wellbore response, pressure and layer production rate were investigated. Numerical solutions of the problem for the modified semi-permeable model were used to find the structure of crossflow in typical cases.
