【正文】 its main plicated characteristic is the existence of deformable interfaces whose unknown shape and motion profoundly affect the structure of the flow field. These moving interfaces can distribute in the channel in many different ways. Changes in flow rates, fluid properties, geometry or inclination can alter the interfacial distribution. In addition, the phase to phase interactions are very important in controlling the flow structure and phase distribution. Other plicating aspects of gasliquid flow are time dependant and three dimensional effects, flow instabilities, turbulence and fluctuations of variables due to the irregular motion of the interfaces. In order to simplify the analysis of gasliquid flows, these are classified according to some types of idealized interfacial configurations called flow patterns. Within each flow pattern, the topology of the two phases is considered to be essentially the same.Consider a long vertical tube into which liquid and gas are flowing upward. Several flow patterns can be observed for particular binations of the gas and liquid flow rates. If the liquid rate is maintained constant and the gas is set at different increasing values, a sequence of flow patterns can be observed as shown in Figure : In bubble flow, the liquid phase is continuous and the gas is nearly uniformly distributed as discrete small bubbles in the liquid continuum. As the gas rate is increased, bubble coalescence occurs, and finally the bubble diameter approaches that of the pipe. When this happens, large axisymmetric bulletshaped gas bubbles are formed, which may be separated by regions c。M University by Weiner and Tolle (1976) and Tolle and Greenwood (1977). The material hardness factor for carbon steel materials is an empirical constant provided in Eq. (): The final and the most important term to pute erosion from Eq. is the particle impact velocity. The particle impact velocity is modeled using a simplified particle tracking model developed by Shirazi et al. (1995). The mechanistic and semi empirical algorithms wer developed based on a normal impingement scenario where the particle laden fluid strikes the metal surface at 90176。 fluid properties and rate。 there have been five revisions since its original release. The guideline states that severe erosion should not occur if production velocities are kept below the erosional velocity given by Eq. : Where Ve is the erosional velocity in ft/s, ρ m is the carrier fluid density in lb/ft 3 , and C is a constant. The API guideline remends that the value of C should be 100 for continuous service and 125 for intermittent service. According to API RP 14E, higher erosion can be tolerated for a less dense fluid. But, this has been shown not to be true experimentally. Also, this guideline does not account for many factors affecting erosion, such as particle properties, wall material mechanical properties, impact angle and geometry. Several investigators concluded that API RP 14E cannot be used in the presence of sand, and efforts were started to develop alternate erosion models. Based on experimental data from Rabinowicz (1979), Salama and Venkatesh (1983) proposed the following model for elbows:where h is the penetration rate in mils per year (mpy), W is the sand flow rate in bbl/month, V is the fluid flow velocity in ft/s, d is the pipe diameter in inches, P is the material hardness in psi. From Eq. , it can be understood that the penetration rate (erosion) increases with an increase in fluid impact velocity and decreases with an increase in pipe wall material hardness and the diameter of the pipe. It can be observed from the equation that the influence of the pipe diameter on erosion is greater than the effect of the wall material hardness. Bourgoyne (1989) also developed an erosion model for calculating penetration rates as a function of flow velocity, sand rate, densities of sand and eroded material, and crosssectional area of the fitting. However, this model relies on a specific erosion factor that depends on the type and material of the geometry that also varied if the flow was a dry gas, mist, or liquid. Svedeman and Arnold (1993) introduced an equation for erosional velocity that was similar in form to that of Salama and Venkatesh (1983) but also used a fitting erosion constant that was derived from Bourgoyne’s specific erosion factor. The fitting erosion constant depends on the fitting geometry type and material and the flow conditions. The erosional velocity models of Salama and Venkatesh (1983), Bourgoyne (1989), and Svedeman and Arnold (1993) were all improvements of API RP 14E。m, effect of size on erosion has been considered negligible (Finnie, 1972。 the function of theta ( θ ) is an angle term that demonstrates the sensitivity of erosion to the incidence angle of an impinging jet. The angle factor is usually dealt with by laboratory testing. A material under study should be impinged at various angles to establish maximum sensitivity. Thus, solid particle erosion models need to include the factors in the preceding equation. As shown in Eq. , particle impact velocity is probably the most important factor for erosion. The effect of particle velocity can easily overshadow the changes in 10 the other factors. Lindsley and Marder (1999) reported that the empirical constant n is independent of target material and erosion mechanism but governed by test conditions such as particle characteristics and erosion test apparatus. According to their work, erosion resulting from the brittle cracking mechanism and plastic deformation mechanism showed the exponent n to be for both cases even though the erosion mechanisms are pletely different. Finnie and McFadden (1978) examined the effect of particle velocity on erosion and found that the exponent n should increase with impact angle for a given range of velocities. He also pared the value of n from other literature and