Velocity distribution characteristics and parametric sensitivity analysis of liquid nitrogen jet

Liquid nitrogen is expected to be used as a jet medium in petroleum engineering because of its cryogenic and non-polluting characteristics. To identify the velocity distribution characteristics of liquid nitrogen jet, a computational fluid dynamics model was built by coupling the equations for nitrogen properties. The velocity and pressure distributions of liquid nitrogen jet were analyzed by comparing them with water jet ones. Meanwhile, the influences of relevant parameters on the centerline velocity distributions of liquid nitrogen jet were researched as well. The simulation results showed that the liquid nitrogen jet not only displayed higher velocity but also presented fewer kinetic energy losses than the water jet during jetting process. The nozzle outlet velocity of liquid nitrogen jet was increased by increasing the nozzle pressure drop, and was slightly influenced by confining pressure and nozzle diameter. In the external space of the nozzle, the attenuation amplitude of centerline velocity was decreased with the growth of nozzle diameter, and was slightly influenced by nozzle pressure drop and confining pressure. This study is expected to provide a theoretical guide for parametric design of liquid nitrogen jet

Velocity distribution characteristics and parametric sensitivity analysis of liquid nitrogen jet

Liquid nitrogen is expected to be used as a jet medium in petroleum engineering because of its cryogenic and non-polluting characteristics. To identify the velocity distribution characteristics of liquid nitrogen jet, a computational fluid dynamics model was built by coupling the equations for nitrogen properties. The velocity and pressure distributions of liquid nitrogen jet were analyzed by comparing them with water jet ones. Meanwhile, the influences of relevant parameters on the centerline velocity distributions of liquid nitrogen jet were researched as well. The simulation results showed that the liquid nitrogen jet not only displayed higher velocity but also presented fewer kinetic energy losses than the water jet during jetting process. The nozzle outlet velocity of liquid nitrogen jet was increased by increasing the nozzle pressure drop, and was slightly influenced by confining pressure and nozzle diameter. In the external space of the nozzle, the attenuation amplitude of centerline velocity was decreased with the growth of nozzle diameter, and was slightly influenced by nozzle pressure drop and confining pressure. This study is expected to provide a theoretical guide for parametric design of liquid nitrogen jet

Experimental research on rock fracture failure characteristics under liquid nitrogen cooling conditions

As liquid nitrogen is injected into a wellbore as fracturing fluid, it can rapidly absorb heat from warmer rock and generate cryogenic condition in downhole region. This will alter the physical conditions of reservoir rocks and further affect rock failure characteristics. To investigate rock fracture failure characteristics under liquid nitrogen cooling conditions, the fracture features of four types of sandstones and one type of marble were tested on original samples (the sample without any treatment) and cryogenic samples (the samples just taken out from the liquid nitrogen), respectively. The differences between original samples and cryogenic samples in load-displacement curves, fracture toughness, energy evolution and the crack density of ruptured samples were compared and analyzed. The results showed that at elastic deformation stage, cryogenic samples presented less plastic deformation and more obvious brittle failure characteristics than original ones. The average fracture toughness of cryogenic samples was 10.47%–158.33% greater than that of original ones, indicating that the mechanical strength of rocks used were enhanced under cooling conditions. When the samples ruptured, the cryogenic ones were required to absorb more energy and reserve more elastic energy. In general, the fracture degree of cryogenic samples was higher than that of original ones. As the samples were entirely fractured, the crack density of cryogenic samples was about 536.67% at most larger than that of original ones. This indicated that under liquid nitrogen cooling conditions, the stimulation reservoir volume is expected to be improved during fracturing. This work could provide a reference to the research on the mechanical properties and fracture failure of rock during liquid nitrogen fracturing. Keywords: Liquid nitrogen, Fracturing, Cooling conditions, Rock, Fracture failur

Analytical solutions of linear diffusion and wave equations in semi-infinite domains by using a new integral transform

Recently, a new integral transform similar to Sumudu transform has been proposed by Yang [1]. Some of the properties of the integral transform are expanded in the present article. Meanwhile, new applications to the linear wave and diffusion equations in semi-infinite domains are discussed in detail. The proposed method provides an alternative approach to solve the partial differential equations in mathematical physics

The Modelling of Freezing Process in Saturated Soil Based on the Thermal-Hydro-Mechanical Multi-Physics Field Coupling Theory

The freezing process of saturated soil is studied under the condition of water replenishment. The process of soil freezing was simulated based on the theory of the energy and mass conservation equations and the equation of mechanical equilibrium. The accuracy of the model was verified by comparison with the experimental results of soil freezing. One-side freezing of a saturated 10-cm-high soil column in an open system with different parameters was simulated, and the effects of the initial void ratio, hydraulic conductivity, and thermal conductivity of soil particles on soil frost heave, freezing depth, and ice lenses distribution during soil freezing were explored. During the freezing process, water migrates from the warm end to the frozen fringe under the actions of the temperature gradient and pore pressure. During the initial period of freezing, the frozen front quickly moves downward, the freezing depth is about 5 cm after freezing for 30 h, and the final freezing depth remains about 6 cm. The freezing depth of the soil column is affected by soil porosity and thermal conductivity, but the final freezing depth mainly depends on the temperatures of the top and lower surfaces. The frost heave is mainly related to the amount of water migration. The relationship between the amount of frost heave and the hydraulic conductivity is positively correlated, and the thickness of the stable ice lens is greatly affected by the hydraulic conductivity. With the increase of the hydraulic conductivity and initial void ratio, the formation of ice lenses in the soil become easier. With the increase of the initial void ratio and thermal conductivity of soil particles, the frost heave of the soil column also increases. With high-thermal-conductivity soil, the formation of ice lenses become difficult