To predict fracture height in hydraulic fracturing, we developed and solved a hydraulic fracture height mathematical model aiming at high stress and multi-layered complex formations based on studying the effect of pla...To predict fracture height in hydraulic fracturing, we developed and solved a hydraulic fracture height mathematical model aiming at high stress and multi-layered complex formations based on studying the effect of plastic region generated by stress concentration at fracture tip on the growth of fracture height. Moreover, we compared the results from this model with results from two other fracture height prediction models(MFEH, Frac Pro) to verify the accuracy of the model. Sensitivity analysis by case computation of the model shows that the hydraulic fracture growth in ladder pattern, and the larger the fracture height, the more obvious the ladder growth pattern is. Fracture height growth is mainly influenced by the in-situ stresses. Fracture toughness of rock can prohibit the growth of fracture height to some extent. Moreover, the increase of fracturing fluid density can facilitate the propagation of the lower fracture tip.展开更多
Performance of Mellapak 250Y and 350Y corrugated structured packing in distillation applications at pressures ranging from 0.3 to 2.0MPa is analysed by using HTU-NTU method. These data are obtained in a distillation c...Performance of Mellapak 250Y and 350Y corrugated structured packing in distillation applications at pressures ranging from 0.3 to 2.0MPa is analysed by using HTU-NTU method. These data are obtained in a distillation column with 0.15 m diameter op-erated with n-butane/n-pentane system at total reflux. In considering the axial backmixing effects, the height of an overall gas phase transfer unit, HTUOG , is divided into two parts. One part represents the height of an overall gas phase transfer unit, without backmixing, designated as*OGHTU, and the other part, designated as the height of a backmixing unit (HBUO), accounts for the backmixing effects. The HTUOG is evaluated from the measured concentration profile of n-butane in liquid phase. The HBUO obtained experimentally is correlated in terms of the properties of the materials being separated and the equivalent diameter of the structured packing. Our result shows that HBUO varies from 0.12 to 0.34 m as pressure increases from 1.0 to 1.9 MPa. It indicates that the overall efficiency of the structured packing decreases gradually at high pressure, as a result of the vapor backmixing.展开更多
A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120<SUP></SUP> do...A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120<SUP></SUP> down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokess formula, F<SUP>2</SUP>= tan , relating the wave speed (the Froude number F) and the logarithmic decrement of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokess basic term (singular in ), such that 2M is just somewhat beyond unity, i.e. 2M1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio =a/h, especially about 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined here to give the maximum height <SUB>hst</SUB>=0.8331990, and speed F<SUB>hst</SUB>=1.290890, accurate to the last significant figure, which seems to be a new record.展开更多
基金Supported by the Natural Science Foundation of Heilongjiang Province of China(YQ2019E007).
文摘To predict fracture height in hydraulic fracturing, we developed and solved a hydraulic fracture height mathematical model aiming at high stress and multi-layered complex formations based on studying the effect of plastic region generated by stress concentration at fracture tip on the growth of fracture height. Moreover, we compared the results from this model with results from two other fracture height prediction models(MFEH, Frac Pro) to verify the accuracy of the model. Sensitivity analysis by case computation of the model shows that the hydraulic fracture growth in ladder pattern, and the larger the fracture height, the more obvious the ladder growth pattern is. Fracture height growth is mainly influenced by the in-situ stresses. Fracture toughness of rock can prohibit the growth of fracture height to some extent. Moreover, the increase of fracturing fluid density can facilitate the propagation of the lower fracture tip.
基金Supported by the National Natural Science Foundation of China (No. 20136010).
文摘Performance of Mellapak 250Y and 350Y corrugated structured packing in distillation applications at pressures ranging from 0.3 to 2.0MPa is analysed by using HTU-NTU method. These data are obtained in a distillation column with 0.15 m diameter op-erated with n-butane/n-pentane system at total reflux. In considering the axial backmixing effects, the height of an overall gas phase transfer unit, HTUOG , is divided into two parts. One part represents the height of an overall gas phase transfer unit, without backmixing, designated as*OGHTU, and the other part, designated as the height of a backmixing unit (HBUO), accounts for the backmixing effects. The HTUOG is evaluated from the measured concentration profile of n-butane in liquid phase. The HBUO obtained experimentally is correlated in terms of the properties of the materials being separated and the equivalent diameter of the structured packing. Our result shows that HBUO varies from 0.12 to 0.34 m as pressure increases from 1.0 to 1.9 MPa. It indicates that the overall efficiency of the structured packing decreases gradually at high pressure, as a result of the vapor backmixing.
文摘A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120<SUP></SUP> down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokess formula, F<SUP>2</SUP>= tan , relating the wave speed (the Froude number F) and the logarithmic decrement of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokess basic term (singular in ), such that 2M is just somewhat beyond unity, i.e. 2M1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio =a/h, especially about 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined here to give the maximum height <SUB>hst</SUB>=0.8331990, and speed F<SUB>hst</SUB>=1.290890, accurate to the last significant figure, which seems to be a new record.
