Leakage Flow of Gas in a Standpipe

Standpipes are used in the gas-solid circulating flow systems in which a cyclone-standpipe-valve configuration for the separation and reintroduction of particles, as shown in Fig. 8.18, is constantly encountered. The satisfactory operation of the cyclone-standpipe system depends on a small leakage flow of gas up the standpipe. A simple method to estimate 

Consider the flow of cohesionless material in the system. The particle mass flow through a valve can be modeled as the flow of solids through an orifice where the Bernoulli relation holds [Li et al., 1982], Thus the particle mass flow in the standpipe can be expressed as 

The validity of Eq. (8.95) is subjected to the condition that n + wp is less than the terminal velocity of the particles. Equation (8.95) further indicates the condition at which the leakage flow of gas downward along the standpipe occurs when 

The typical pressure profile of the standpipe and the valve is shown in Fig. 8.18. As can be seen in the figure, the pressure head over the standpipe Aps, in the absolute sense, is equal to the sum of the overall pressure head, Apt, and the pressure drop over the valve, Ap0. From Eq. (8.92), the particle volume fraction in the standpipe can be estimated from the measured height of the bulk particles. Thus, given the particle mass flow rate, the leakage flow of gas in the standpipe can be estimated from Eq. (8.95). 

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