Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distributi...Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distribution of stimulated reservoir volume,the complex hydraulic fracture morphology was accurately described using heterogeneous node connection system.Then a new fracture connection element method(FCEM)for fluid flow in stimulated unconventional reservoirs with complex hydraulic fracture morphology was proposed.In the proposed FCEM,the arrangement of dense nodes in the stimulated area and sparse nodes in the unstimulated area ensures the calculation accuracy and efficiency.The key parameter,transmissibility,was also modified according to the strong heterogeneity of stimulated reservoirs.The finite difference and semi-analytical tracking were used to accurately solve the pressure and saturation distribution between nodes.The FCEM is validated by comparing with traditional numerical simulation method,and the results show that the bottom hole pressure simulated by the FCEM is consistent with the results from traditional numerical simulation method,and the matching rate is larger than 95%.The proposed FCEM was also used in the optimization of fracturing parameters by coupling the hydraulic fracture propagation method and intelligent optimization algorithm.The integrated intelligent optimization approach for multi-parameters,such as perforation number,perforation location,and displacement in hydraulic fracturing is proposed.The proposed approach was applied in a shale gas reservoir,and the result shows that the optimized perforation location and morphology distribution are related to the distribution of porosity/permeability.When the perforation location and displacement are optimized with the same fracture number,NPV increases by 70.58%,which greatly improves the economic benefits of unconventional reservoirs.This work provides a new way for flow simulation and optimization of hydraulic fracture morphology of multi-fractured horizontal wells in unconventional reservoirs.展开更多
As current calculation models for inter-well connectivity in oilfields can only account for vertical wells,an updated model is elaborated here that can predict the future production performance and evaluate the connec...As current calculation models for inter-well connectivity in oilfields can only account for vertical wells,an updated model is elaborated here that can predict the future production performance and evaluate the connectivity of horizontal wells(or horizontal and vertical wells).In this model,the injection-production system of the considered reservoir is simplified and represented with many connected units.Moreover,the horizontal well is modeled with multiple connected wells without considering the pressure loss in the horizontal direction.With this approach,the production performance for both injection and production wells can be obtained by calculating the bottom-hole flowing pressure and oil/water saturation according to the material balance equation and a saturation front-tracking equation.Some effort is also provided to optimize(to fit known historical production performances)the two characteristic problem parameters,namely,the interwell conductivity and connected volume by means of a SPSA gradient-free algorithm.In order to verify the validity of the model,considering a heterogenous reservoir,three conceptual examples are constructed,where the number ratio between injection and production wells are 1/4,4/1 and 4/5,respectively.It is shown that there is a high consistency between simulation results and field data.展开更多
In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carn...In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.展开更多
基金supported the National Natural Science Foundation of China(No.52004033,51922007,and 51874044).
文摘Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distribution of stimulated reservoir volume,the complex hydraulic fracture morphology was accurately described using heterogeneous node connection system.Then a new fracture connection element method(FCEM)for fluid flow in stimulated unconventional reservoirs with complex hydraulic fracture morphology was proposed.In the proposed FCEM,the arrangement of dense nodes in the stimulated area and sparse nodes in the unstimulated area ensures the calculation accuracy and efficiency.The key parameter,transmissibility,was also modified according to the strong heterogeneity of stimulated reservoirs.The finite difference and semi-analytical tracking were used to accurately solve the pressure and saturation distribution between nodes.The FCEM is validated by comparing with traditional numerical simulation method,and the results show that the bottom hole pressure simulated by the FCEM is consistent with the results from traditional numerical simulation method,and the matching rate is larger than 95%.The proposed FCEM was also used in the optimization of fracturing parameters by coupling the hydraulic fracture propagation method and intelligent optimization algorithm.The integrated intelligent optimization approach for multi-parameters,such as perforation number,perforation location,and displacement in hydraulic fracturing is proposed.The proposed approach was applied in a shale gas reservoir,and the result shows that the optimized perforation location and morphology distribution are related to the distribution of porosity/permeability.When the perforation location and displacement are optimized with the same fracture number,NPV increases by 70.58%,which greatly improves the economic benefits of unconventional reservoirs.This work provides a new way for flow simulation and optimization of hydraulic fracture morphology of multi-fractured horizontal wells in unconventional reservoirs.
基金This study was supported by the National Natural Science Foundation of China(52004033,51922007).
文摘As current calculation models for inter-well connectivity in oilfields can only account for vertical wells,an updated model is elaborated here that can predict the future production performance and evaluate the connectivity of horizontal wells(or horizontal and vertical wells).In this model,the injection-production system of the considered reservoir is simplified and represented with many connected units.Moreover,the horizontal well is modeled with multiple connected wells without considering the pressure loss in the horizontal direction.With this approach,the production performance for both injection and production wells can be obtained by calculating the bottom-hole flowing pressure and oil/water saturation according to the material balance equation and a saturation front-tracking equation.Some effort is also provided to optimize(to fit known historical production performances)the two characteristic problem parameters,namely,the interwell conductivity and connected volume by means of a SPSA gradient-free algorithm.In order to verify the validity of the model,considering a heterogenous reservoir,three conceptual examples are constructed,where the number ratio between injection and production wells are 1/4,4/1 and 4/5,respectively.It is shown that there is a high consistency between simulation results and field data.
基金supported by the National Natural Science Foundation of China(No.10471063)
文摘In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.
