Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for ...Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for shut-in time after horizontal well volume fracturing with the goal of shortening oil breakthrough time and achieving rapid oil breakthrough, and analyzes the influences of permeability, porosity, fracture half-length and fracturing fluid volume on the shut-in time. The oil and water imbibition displacement in the matrix and fractures occurs during the shut-in process of wells after fracturing. If the shut-in time is too short, the oil-water displacement is not sufficient, and the oil breakthrough time is long after the well is put into production. If the shut-in time is too long, the oil and water displacement is sufficient, but the energy dissipation in the formation near the bottom of the well is severe, and the flowing period is short and the production is low after the well is put into production. A rational shut-in time can help shorten the oil breakthrough time, extend the flowing period and increase the production of the well. The rational shut-in time is influenced by factors such as permeability, porosity, fracture half-length and fracturing fluid volume. The shortest and longest shut-in times are negatively correlated with porosity, permeability, and fracture half-length, and positively correlated with fracturing fluid volume. The pilot test in tight oil horizontal wells in the Songliao Basin, NE China, has confirmed that the proposed optimization method can effectively improve the development effect of horizontal well volume fracturing.展开更多
A multi-process(fracturing,shut-in and production)multi-phase flow model was derived considering the osmotic pressure,membrane effect,elastic energy and capillary force,to determine the optimal shut-in time after mult...A multi-process(fracturing,shut-in and production)multi-phase flow model was derived considering the osmotic pressure,membrane effect,elastic energy and capillary force,to determine the optimal shut-in time after multi-cluster staged hydraulic fracturing in shale reservoirs for the maximum production.The accuracy of the model was verified by using production data and commercial software.Based on this model and method,a physical model was made based on the inversion of fracture parameters from fracturing pressure data,to simulate the dynamic changes of pore pressure and oil saturation during fracturing,soaking and production,examine effects of 7 factors on the optimal shut-in time,and find out the main factors affecting the optimal shut-in time through orthogonal experiments.With the increase of shut-in time,the increment of cumulative production increases rapidly first and then tended to a stable value,and the shut-in time corresponding to the inflection point of the change was the optimal shut-in time.The optimal shut-in time has a nonlinear negative correlation with matrix permeability,porosity,capillary pressure multiple and fracture length,a nonlinear positive correlation with the membrane efficiency and total volume of injected fluid,and a nearly linear positive correlation with displacement.The seven factors in descending order of influence degree on optimal shut-in time are total volume of injected fluid,capillary force multiple,matrix permeability,porosity,membrane efficiency,salinity of fracturing fluid,fracturing fluid displacement.展开更多
The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk wit...The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.展开更多
This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is ...This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.展开更多
基金Supported by China National Major Project of Science and Technology(2016ZX05046-004)PetroChina Major Project of Science and Technology(2017B-4905)PetroChina Jilin Oilfield Company Major Project of Science and Technology(JY21A2-12).
文摘Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for shut-in time after horizontal well volume fracturing with the goal of shortening oil breakthrough time and achieving rapid oil breakthrough, and analyzes the influences of permeability, porosity, fracture half-length and fracturing fluid volume on the shut-in time. The oil and water imbibition displacement in the matrix and fractures occurs during the shut-in process of wells after fracturing. If the shut-in time is too short, the oil-water displacement is not sufficient, and the oil breakthrough time is long after the well is put into production. If the shut-in time is too long, the oil and water displacement is sufficient, but the energy dissipation in the formation near the bottom of the well is severe, and the flowing period is short and the production is low after the well is put into production. A rational shut-in time can help shorten the oil breakthrough time, extend the flowing period and increase the production of the well. The rational shut-in time is influenced by factors such as permeability, porosity, fracture half-length and fracturing fluid volume. The shortest and longest shut-in times are negatively correlated with porosity, permeability, and fracture half-length, and positively correlated with fracturing fluid volume. The pilot test in tight oil horizontal wells in the Songliao Basin, NE China, has confirmed that the proposed optimization method can effectively improve the development effect of horizontal well volume fracturing.
基金Supported by the National Natural Science Foundation of China Joint Fund Project(U1562217,U21B2701)。
文摘A multi-process(fracturing,shut-in and production)multi-phase flow model was derived considering the osmotic pressure,membrane effect,elastic energy and capillary force,to determine the optimal shut-in time after multi-cluster staged hydraulic fracturing in shale reservoirs for the maximum production.The accuracy of the model was verified by using production data and commercial software.Based on this model and method,a physical model was made based on the inversion of fracture parameters from fracturing pressure data,to simulate the dynamic changes of pore pressure and oil saturation during fracturing,soaking and production,examine effects of 7 factors on the optimal shut-in time,and find out the main factors affecting the optimal shut-in time through orthogonal experiments.With the increase of shut-in time,the increment of cumulative production increases rapidly first and then tended to a stable value,and the shut-in time corresponding to the inflection point of the change was the optimal shut-in time.The optimal shut-in time has a nonlinear negative correlation with matrix permeability,porosity,capillary pressure multiple and fracture length,a nonlinear positive correlation with the membrane efficiency and total volume of injected fluid,and a nearly linear positive correlation with displacement.The seven factors in descending order of influence degree on optimal shut-in time are total volume of injected fluid,capillary force multiple,matrix permeability,porosity,membrane efficiency,salinity of fracturing fluid,fracturing fluid displacement.
文摘The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.
文摘This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.
