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Research on Rumor Spreading Model with Time Delay and Control Effect

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Journal of Systems Science and Information 2019年第4期10卷 373-389页

作者： Hongxing YAO yushi zou School of Finance and Economics Jiangsu UniversityZhenjiang 212013China Faculty of Science Jiangsu UniversityZhenjiang 212013China

Information flow retains a critical role in decision making among investors. In this paper,we employ a diffusion model based on epidemiology theory to study the rumor spreading process within investors. The paper introduce the feedback mechanism of classical control theory into the model, which helps to reflect the interaction between rumor spreaders and information *** we apply a time delay factor to give investors access to transparent information and change their behavior. Subsequently, the stability of the rumor disappearance equilibrium and the rumor existence equilibrium are analyzed and the condition for the system undergoes a Hopf-bifurcation is given. The mathematical arguments are subjected to numerical simulations to present the ideal case scenarios. The results suggest that, increase the general strength of information supervision and the proportion coefficient associated with the infected population in the short-term delay are conducive to better control.

关键词： epidemic model rumor spreading Hopf-bifurcation control effect

A numerical method for simulating planar 3D multi-fracture propagation in multi-stage fracturing of horizontal wells

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Petroleum Exploration and Development 2020年第1期47卷 171-183页

作者： CHEN Ming ZHANG Shicheng XU Yun MA Xinfang zou yushi China University of Petroleum Beijing 102249China Texas A&M University College Station 77840USA PetroChina Research Institute of Petroleum Exploration&Development Beijing 100083China The Key Laboratory of Research Stimulation PetroChinaLangfang 065007China

To resolve the issue of design for multi-stage and multi-cluster fracturing in multi-zone reservoirs, a new efficient algorithm for the planar 3 D multi-fracture propagation model was proposed. The model considers fluid flow in the wellbore-perforation-fracture system and fluid leak-off into the rock matrix, and uses a 3 D boundary integral equation to describe the solid deformation. The solid-fluid coupling equation is solved by an explicit integration algorithm, and the fracture front is determined by the uniform tip asymptotic solutions and shortest path algorithm. The accuracy of the algorithm is verified by the analytical solution of radial fracture, results of the implicit level set algorithm, and results of organic glass fracturing experiment. Compared with the implicit level set algorithm(ILSA), the new algorithm is much higher in computation speed. The numerical case study is conducted based on a horizontal well in shale gas formation of Zhejiang oilfield. The impact of stress heterogeneity among multiple clusters and perforation number distribution on multi-fracture growth and fluid distribution among multiple fractures are analyzed by numerical simulation. The results show that reducing perforation number in each cluster can counteract the effect of stress contrast among perforation clusters. Adjusting perforation number in each cluster can promote uniform flux among clusters, and the perforation number difference should better be 1-2 among clusters. Increasing perforation number in the cluster with high in situ stress is conducive to uniform fluid partitioning. However, uniform fluid partitioning is not equivalent to uniform fracture geometry. The fracture geometry is controlled by the stress interference and horizontal principal stress profile jointly.

关键词： horizontal well multi-stage fracturing multi-fracture growth 3D boundary element planar stress heterogeneity perforation optimization

Hydraulic fracture geometry and proppant distribution in thin interbedded shale oil reservoirs

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Petroleum Exploration and Development 2022年第5期49卷 1185-1194页

作者： zou yushi SHI Shanzhi ZHANG Shicheng LI Jianmin WANG Fei WANG Junchao ZHANG Xiaohuan State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China Engineering Technology Research Institute PetroChina Xinjiang Oilfield CompanyKaramay 834000China

Small-scale true triaxial sand fracturing experiments are conducted on thin interbedded shale samples made from cores of Permian Lucaogou Formation shale oil reservoir in Jimsar sag, Junggar Basin, NW China. Combined with high-precision CT scanning digital core model reconstruction technology, hydraulic fracture geometry and proppant distribution in thin interbedded shale oil reservoirs are studied. The research shows that: In thin interbedded shale oil reservoir, the interlayer difference of rock mechanics and the interlayer interface near the wellbore cannot restrain the growth of fracture height effectively, but has a significant impact on the fracture width distribution in the fracture height direction. Hydraulic fractures in these reservoirs tend to penetrate into the adjacent layer in “step-like” form, but have a smaller width at the interface deflection, which hinders the transport of proppant in vertical direction, resulting in a poor effect of layer-crossing growth. In shale layers with dense laminae, hydraulic fractures tend to form “丰” or “井” shapes. If the perforated interval is large in rock strength and high in breakdown pressure, the main fracture is fully developed initially, large in width, and supported by enough sand. In contrast, if the perforated interval is low in strength and rich in laminae, the fracturing fluid filtration loss is large, the breakdown pressure is low, the main fracture will not open wide initially, and likely to have sand plugging. Proppant is mainly concentrated in the main hydraulic fractures with large width near the perforated layer, activated laminae, branch fractures and fractures in adjacent layers contain only a small amount of(or zero) proppant. The proppant is placed in a limited range on the whole. The limit width of fracture that proppant can enter is about 2.7 times the proppant particle size.

关键词： shale oil thin interbedded reservoir rock mechanics lithologic interface hydraulic fracturing fracture shape proppant distribution

An analysis of the uniformity of multi-fracture initiation based on downhole video imaging technology: A case study of Mahu tight conglomerate in Junggar Basin, NW China

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Petroleum Exploration and Development 2022年第2期49卷 448-457页

作者： ZANG Chuanzhen JIANG Hanqiao SHI Shanzhi LI Jianmin zou yushi ZHANG Shicheng TIAN Gang YANG Peng State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China Engineering Technology Research Institute PetroChina Xinjiang Oilfield CompanyKaramay 834000China

To solve the problem that the production of Mahu conglomerate reservoir is not up to expectation after the multi-cluster plus temporary plugging fracturing technology is applied in horizontal wells, stages 2–6 in the test well MaHW6285 are selected to carry out erosion tests with different pumping parameters. The downhole video imaging technology is used to monitor the degree of perforations erosion, and then the fracture initiation and proppant distribution of each cluster are analyzed. The results showed that proppant entered 76.7% of the perforations. The proppant was mainly distributed in a few perforation clusters, and the amount of proppant entered in most of the clusters was limited. The proppant distribution in Stage 4 was relatively uniform, and the fracture initiation of each cluster in the stage is more uniform. The proppant distribution in stages 2, 3, 5, and 6 was significantly uneven, and the uniform degree of fracture initiation in each cluster is low. More than 70% of the proppant dose in the stage entered clusters near the heel end, so the addition of diverters did not promote the uniform initiation of hydraulic fractures. There was a positive correlation between the amount of proppant added and the degree of perforations erosion, and the degree of perforations erosion ranged from 15% to 352%, with an average value of 74.5%, which was far higher than the statistical results of shale reservoir tests in North America. The use of 180° phase perforation(horizontal direction) can reduce the “Phase Bias” of perforations erosion, promote uniform perforations erosion and fluid inflow. The research results provide the basis for optimizing the pumping procedure, reducing the perforation erosion and improving the success rate of diversion.

关键词： tight conglomerate temporary plugging fracturing perforation erosion fracture initiation downhole video imaging technology Junggar Basin Mahu sag

Fracture propagation,proppant transport and parameter optimization of multi-well pad fracturing treatment

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Petroleum Exploration and Development 2023年第5期50卷 1225-1235页

作者： YANG Peng ZHANG Shicheng zou yushi LI Jianmin MA Xinfang TIAN Gang WANG Junchao State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China Engineering Technology Research Institute PetroChina Xinjiang Oilfield CompanyKaramay 834000China

This paper establishes a 3D multi-well pad fracturing numerical model coupled with fracture propagation and proppant migration based on the displacement discontinuity method and Eulerian-Eulerian frameworks,and the fracture propagation and proppant distribution during multi-well fracturing are investigated by taking the actual multi-well pad parameters as an *** initiation and propagation during multi-well pad fracturing are jointly affected by a variety of stress interference mechanisms such as inter-cluster,inter-stage,and inter-well,and the fracture extension is unbalanced among clusters,asymmetric on both wings,and dipping at *** to the significant influence of fracture morphology and width on the migration capacity of proppant in the fracture,proppant is mainly placed in the area near the wellbore with large fracture width,while a high-concentration sandwash may easily occur in the area with narrow fracture width as a result of quick *** the whole,the proppant placement range is *** the well-spacing can reduce the stress interference of adjacent wells and promote the uniform distribution of fractures and proppant on both *** maximum stimulated reservoir volume or multi-fracture uniform propagation can be achieved by optimizing the well *** reducing the perforation-cluster spacing also can improve the stimulated reservoir area,a too low cluster spacing is not conducive to effectively increasing the propped fracture *** increasing the stage time lag is beneficial to reduce inter-stage stress interference,zipper fracturing produces more uniform fracture propagation and proppant distribution.

关键词： multi-well pad multi-well fracturing fracture propagation proppant transport coupled numerical model fracturing parameter optimization

Micro-mechanical properties of shale due to water/supercritical carbon dioxide-rock interaction

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石油勘探与开发:英文版 2023年第4期50卷 1001-1012页

作者： LI Ning JIN Zhijun ZHANG Shicheng WANG Haibo YANG Peng zou yushi ZHOU Tong State Key Laboratory of Shale Oil and Gas Enhancement Mechanisms and Effective Development Beijing 100083China SINOPEC Key Laboratory of Shale Oil/Gas Exploration and Production Technology Beijing 100083China State Energy Center for Shale Oil Research and Development Beijing 100083China SINOPEC Petroleum Exploration and Production Research Institute Beijing 100083China Institute of Energy Peking UniversityBeijing 100871China State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China

To investigate the impacts of water/supercritical CO_(2)-rock interaction on the micro-mechanical properties of shale,a series of high-temperature and high-pressure immersion experiments were performed on the calcareous laminated shale samples mined from the lower submember of the third member of Paleogene Shahejie Formation in the Jiyang Depression,Bohai Bay *** that,grid nanoindentation tests were conducted to analyze the influence of immersion time,pressure,and temperature on micro-mechanical *** results show that the damage of shale caused by the water/supercritical CO_(2)-rock interaction was mainly featured by the generation of induced fractures in the clay-rich *** the case of soaking with supercritical CO_(2),the aperture of induced fracture was *** to the existence of induced fractures,the statistical averages of elastic modulus and hardness both ***,compaction and stress-induced tensile fractures could be observed around the ***,the longer the soaking time,the higher the soaking pressure and temperature,the more significant the degradation of micro-mechanical parameters *** with water-rock interaction,the supercritical CO_(2)-rock interaction caused a lower degree of mechanical damage on the shale ***,supercritical CO_(2)can be used as a fracturing fluid to prevent the surface softening of induced fractures in shale reservoirs.

关键词： shale hydration supercritical CO_(2) micro-mechanical properties nanoindentation shale damage

Numerical simulation of hydraulic fracture propagation in laminated shale reservoirs

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Petroleum Exploration and Development 2020年第5期47卷 1117-1130页

作者： ZHOU Tong WANG Haibo LI Fengxia LI Yuanzhao zou yushi ZHANG Chi Research Institute of Petroleum Exploration and Development SinopecBeijing 100083China Shale Gas Exploration and Development Co. Ltd.SinopecChongqing 408014China China University of Petroleum Beijing 102249China

The main area of the Jiaoshiba anticline of the Fuling shale gas field was taken as the research object,laboratory rock mechanical experiments and direct shear experiments were conducted to clarify the mechanical anisotropy characteristics and parameters of rock samples with rich *** on the experimental results,a 3D fracture propagation model of the target reservoir taking mechanical anisotropy,weak bedding plane and vertical stress difference into account was established by the discrete element method to analyze distribution patterns of hydraulic fractures under different bedding densities,mechanical properties,and fracturing engineering parameters(including perforation clusters,injection rates and fracturing fluid viscosity).The research results show that considering the influence of the weak bedding plane and longitudinal stress difference,the interlayer stress difference 3–4 MPa in the study area can control the fracture height within the zone of stress barrier,and the fracture height is less than 40 *** the influence of the weak bedding plane is not considered,the simulation result of fracture height is obviously *** the opening of high-density bedding fractures increases the complexity of hydraulic fractures,it significantly limited the propagation of fracture *** reducing the number of clusters,increasing the injection rate,and increasing the volume and proportion of high-viscosity fracturing fluid in the pad stage,the restriction on fracture height due to the bedding plane and vertical stress difference can be reduced,and the longitudinal propagation of fractures can be *** fracture propagation model was used to simulate one stage of Well A in Fuling shale gas field,and the simulation results were consistent with the micro-seismic monitoring results.

关键词： shale lamina hydraulic fracturing fracture propagation law longitudinal stress difference Jiaoshiba anticline shale gas reservoir

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天然页岩压裂裂缝扩展机理试验

石油学报 2014年第3期35卷 496-503,518页

作者：张士诚郭天魁周彤邹雨时牟松茹中国石油大学石油工程学院北京102249

采用大尺寸真三轴试验系统对页岩露头开展了水力压裂裂缝扩展模拟试验,并利用高能CT扫描观测压后岩心内部裂缝形态,研究了多种因素对页岩水平井压裂裂缝扩展规律的影响。试验条件下的研究结果表明:排量对裂缝复杂度的影响存在一定的范围... 详细信息

采用大尺寸真三轴试验系统对页岩露头开展了水力压裂裂缝扩展模拟试验,并利用高能CT扫描观测压后岩心内部裂缝形态,研究了多种因素对页岩水平井压裂裂缝扩展规律的影响。试验条件下的研究结果表明:排量对裂缝复杂度的影响存在一定的范围;当水平地应力差小于9 MPa时,水力裂缝易沿天然裂缝转向,形成网状缝。随着应力差的增加,主裂缝(横切缝)的产生有利于沟通更多的天然裂缝,形成相对更复杂的裂缝;相同水平应力差条件下,水平应力差系数大于0.25时,有明显形成单一主裂缝的趋势;排量和压裂液黏度对水力裂缝几何形状的影响可用参数qμ表达,该值较低或较高都不利于缝网的产生;页岩层理的发育和胶结强度严重影响压裂缝网的复杂度。

关键词：页岩水力压裂裂缝扩展水平地应力差排量

水平井分段压裂平面三维多裂缝扩展模型求解算法

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石油勘探与开发 2020年第1期47卷 163-174页

作者：陈铭张士诚胥云马新仿邹雨时中国石油大学(北京) 北京102249 Texas A&M University College Station 77840USA 中国石油勘探开发研究院北京100083 中国石油油气藏改造重点实验室河北廊坊065007

针对多层油气藏水平井分段多簇压裂设计问题,提出平面三维多裂缝扩展模型高效解法。采用三维边界积分方程计算固体变形,考虑井筒-射孔-裂缝耦合流动及缝内流体滤失。利用显式积分算法求解流固耦合方程,根据尖端统一解析解和最短路径算... 详细信息

针对多层油气藏水平井分段多簇压裂设计问题,提出平面三维多裂缝扩展模型高效解法。采用三维边界积分方程计算固体变形,考虑井筒-射孔-裂缝耦合流动及缝内流体滤失。利用显式积分算法求解流固耦合方程,根据尖端统一解析解和最短路径算法计算裂缝扩展边界。方法的准确性通过与径向裂缝解析解、隐式水平集算法和有机玻璃压裂实验对比得到全面验证。与隐式水平集算法相比,新算法计算速度大幅提高。以浙江油田页岩气水平井为例,重点分析了平面应力分布、射孔数分布等对多簇裂缝扩展与进液的影响。研究表明,减小单簇射孔数可以平衡簇间应力非均质分布的影响;调整各簇射孔数量可以实现均衡进液,各簇射孔数差别应控制在1~2孔;增加高应力簇的射孔数有利于均匀进液,但进液均匀并不等于裂缝形态一致,裂缝形态受应力干扰和层间应力剖面共同控制。

关键词：水平井分段压裂多裂缝扩展三维边界元平面应力非均质射孔优化