用超幂构造力迫扩充

设M是ZFC的可数标准传递模型,B是M上的完全布尔代数,I是B的单位元,G是B上的generic超滤,则有:1) 若A=■M_i(■i∈I(M_i≡M)),A上定义关系R,E,L(A)={∈,=}∪{f|f∈A}(f是f的名)是力迫语言,那么<A,R,E>是L(A)的布尔值模型;2) 若A/G上定义关系∈■,则<A/G,∈■>是M的力迫扩充M[G];3) M[G]=ZFC+ CH。

Numerical simulation of hydraulic fracture propagation in weakly consolidated sandstone reservoirs

Frac-packing technology has been introduced to improve the development effect of weakly consolidated sandstone.It has double effects on increasing production and sand control.However,determining operation parameters of frac-packing is the key factor due to the particularity of weakly consolidated sandstone.In order to study the mechanisms of hydraulic fracture propagation and reveal the effect of fracturing parameters on fracture morphology in weakly consolidated sandstone,finite element numerical model of fluid-solid coupling is established to carry out numerical simulation to analyze influences of mechanical characteristics,formation permeability,fracturing fluid injection rate and viscosity on fracture propagation.The result shows that lower elastic modulus is favorable for inducing short and wide fractures and controls the fracture length while Poisson ratio has almost no effect.Large injection rate and high viscosity of fracturing fluid are advantageous to fracture initiation and propagation.Suitable fractures are produced when the injection rate is approximate to3–4m3/min and fluid viscosity is over100mPa?s.The leak-off of fracturing fluid to formation is rising with the increase of formation permeability,which is adverse to fracture propagation.The work provides theoretical reference to determine the construction parameters for the frac-packing design in weakly consolidated reservoirs.

论语文教学中学生审美想象能力的培养

审美想象力是审美能力的核心内容,培养审美想象力是提高审美鉴赏力和创造力的关键环节,是提高语文核心素养的重要途径。语文教学培养学生的审美想象力应从这样几方面入手：训练审美想象联想力、发展审美想象再现力、培养审美想象扩充力、提升审美想象整合力。