Overview of numerical models for interactions between hydraulic fractures and natural fractures: Challenges and limitations

The intersection of natural fractures with hydraulic fractures results in formation of complex fracture networks, including non-planar fractures or multi-stranded fractures. On one hand, opening of these natural fractures improves productivity of the formation; on the other hand, coalescence of these fractures into a hydraulic fracture makes pressure analysis and prediction of fracture growth very complicated. Overall, interactions between natural fractures and hydraulic fractures pose more challenges in the fracturing design and its execution. Investigation and understanding of their interaction are crucial in achieving successful fracture treatments in formations with pre-existing natural fracture network. In this paper, we will review the numerical works that have been done in the last decade to model opening of natural fractures during hydraulic fracturing, focusing especially on mechanical models that address propagation of hydraulic fractures in naturally fractures reservoirs. Linear elastic fracture mechanics, cohesive element methods and continuum damage mechanics techniques utilized to understand interaction of hydraulic fractures with natural fractures are discussed here based on their capability to reproduce experimental results and field observations.     

A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation

A three-phase hydro-mechanical model for hydraulic fracturing is proposed. Three phases include: porous solid, fracturing fluid and host fluid. Discontinuity is handled using extended finite element method (XFEM) while cohesive crack model is used as fracturing criterion. Flow through fracture is defined as one-dimensional laminar flow, and flow through porous medium (host reservoir) is defined as two-dimensional Darcy flow. Coupling between two fluids in each space, fracture and pore, is captured through capillary pressure–saturation relationship, while the identical fluids in fracture and pore are coupled through a so-called leak-off mass transfer term. Coupling between fluids and deformation is captured through compatibility of volumetric strain of fluids within fracture and pore, and volumetric strain of the matrix. Spatial and temporal discretisation is achieved using the standard Galerkin method and the finite difference technique, respectively. The model is verified against analytical solutions available from literature. The leaking of fracturing fluid into the medium and suction of porous fluid into the fracture around the tip, are investigated. Sensitivity analyses are carried out for cases with slow and fast injection rates. It is shown that the results by single-phase flow may underestimate the leak-off.     

常州地区土的塑性指数与渗透系数的经验关系研究

粉土、粘性土的渗透系数受土的结构构造、矿物成分、颗粒级配等因素影响,而这些影响因素可在土性指标(尤其是塑性指数IP)上得到集中体现。基于常州地区土的室内渗透系数K与塑性指数IP试验数据,初步建立了粘性土、粉土渗透系数K与塑性指数IP间的地区经验关系,对常州地区土的渗透系数的确定具有参考意义。     

Modeling the erosion of cohesive clay coasts

A model was developed to study the erosion of cohesive clay coasts in macro- to non-tidal environments. The model shares some of the characteristics of previous models, including the erosion of bare clay surfaces by wave generated bottom shear stresses, and of mobile, sediment-covered surfaces by abrasion. It differs from previous models, however, in several important ways. The morphodynamics of beaches with clay foundations, under different wave conditions, are based on a previously developed model for beaches on rocky shore platforms. Sediment thickness along a beach profile is calculated at regular intervals and compared with the maximum thickness that could be moved at that location under prevailing wave conditions. Wave friction factors are determined, where necessary, according to the occurrence and morphology of ripples on the bottom. In addition to abrasion and the effect of wave induced shear stresses on the clay bottom, erosion by stresses generated by wave impact at the bluff foot and on the intertidal platform is calculated using an expression derived from hard rock coastal models. Tides are represented by their computed tidal duration values, the amount of time each year that the water level falls within each 0.1 m vertical interval. Water depths are modified by wave setup and set-down conditions. Several preliminary model runs were made. The profiles were concave in the submarine zone and roughly linear in the intertidal zone. Equilibrium profiles developed which were maintained as they migrated landwards.     

Three-dimensional numerical modeling of cohesive sediment transport and wind wave impact in a shallow oxbow lake

It was observed that in some closed inland lakes sediment transport was dominated by wind-induced currents, and the sediment resuspension was primarily driven by wind-induced waves. This paper presents the development and application of a three-dimensional numerical model for simulating cohesive sediment transport in water bodies where wind-induced currents and waves are important. In the model, the bottom shear stresses induced by currents and waves were calculated, and the processes of resuspension (erosion), deposition, settling, etc. were considered. This model was first verified by a simple test case consisting of the movement of a non-conservative tracer in a prismatic channel with uniform flow, and the model output agreed well with the analytical solution. Then it was applied to Deep Hollow Lake, a small oxbow lake in Mississippi. Simulated sediment concentrations were compared with available field observations, with generally good agreement. The transport and resuspension processes of cohesive sediment due to wind-induced current and wave in Deep Hollow Lake were also discussed.     

Erosion rate of sand and mud mixtures

Erosion of mixed cohesive and noncohesive sediments is studied using the erosion test instrument SEDFlume. The sediment mixtures are composed of well-sorted quartz sand (0.25–0.5 mm) and one of the three used muds: kaolinite, kaolinite-bentonite and Mississippi River muds. The mud contents cover from 0 to 100%. The measured data of erosion rate and bed shear stress are used to examine the segmented linear, nonlinear, and exponential erosion models. The parameters of each erosion model are related to the physical properties of sediment mixtures, including clay fraction, mud fraction, mixture dry density, and mud dry density. It is found that the three models can fit well with the data, and their parameters have strong relations with the mud fraction and mud dry density, to a less extent with the clay fraction, but not with the mixture dry density.     

灰色关联度分析及应用

研究报道了灰色关联度分析用来考察影响实际化学问题的各种因素 ,用以找出主要因素。以碱金属结合能的计算为例 ,说明灰色关联度分析作为新兴的化学计量学的有效方法和技术是很有应用前景的     

Fine sediment resuspension dynamics in a large semi-enclosed bay

A field study was conducted to investigate fine sediment resuspension dynamics in Moreton Bay, a large semi-enclosed bay situated in South East Queensland, Australia. One S4ADW current meter and three OBS sensors were used to collect the field data on tides, mean currents, waves and suspended sediment concentrations in a mean water depth of 6.1 m for about 3 weeks. Two small cleaning units were specially designed to automatically clean the OBS sensors several times every hour to avoid biological growth on the OBS sensors. Based on the collected field data, the main driving force for fine sediment resuspension is found to be the storm wind-waves generated locally in the Bay, not the tidal current or penetrated ocean swell. The critical wind-wave orbital velocity for sediment resuspension was determined to be U_rms=7 cm/s and the critical bed shear stress τ_cr=0.083–0.095 Pa at this study site.     

Rheological properties of dense natural cohesive sediments subject to shear loadings

Cohesive sediments exhibit complex rheological behaviors that are non-Newtonian and time-dependent when subjected to external loading. This paper presents the results of an investigation on the theological properties of three types of dense cohesive sediments, collected from the mouth of the Yangtze River, the shoal of the ttangzhou Bay, and the Yangcheng Lake in China. A set of rheological parameters （including viscosity, yield stress, etc.） was studied based on experiments that were conducted with a RheolabQC rheometer. Measurements of the flow curves, shear stress-time responses, and yield stresses were made. The solid-liquid transition of the dense cohesive sediments occurred both in the shear rate ramp tests and the shear stress ramp tests. This transition was not direct, but it was mediated by a transitional deformation regime or stress plateau. Both the Herschel-Bulkley model and Carreau model were able to describe the theological behavior of dense cohesive sediments, and the empirical expressions for calculating the parameters in these models were obtained by a dimensional and regression analysis. The yield stresses determined by the shear stress ramp test and by the vane method were compared and discussed. The influence of the water content on the rheological properties of dense cohesive sediments was considered.