Two-dimensional treesph simulations of choked flow systems

Abstract

It is well-known that the flow of gas, liquid, and their mixtures through restrictors installed in pipeline systems is of great practical importance in many industrial processes. In spite of its significance, numerical hydrodynamics simulations of such flows are almost non-existent in the literature. Here we present exploratory two-dimensional calculations of the flow of a viscous, single-phase fluid through a wellhead choke of real dimensions, using the method of Smoothed Particle Hydrodynamics (SPH) coupled with a simple isothermal equation of state for description of the flow. The results indicate that an approximately stationary mean flow pattern is rapidly established across the entire tube, with the density and pressure dropping and the flow velocity rising within the choke throat. If the downstream flow is inhibited at the outlet end of the tube, a pressure drop of about 12% occurs across the choke when the mean flow reaches an approximate steady state. If, on the other hand, the flow is not inhibited downstream, the pressure drop is reduced to about 8% or less. The flow across the choke throat remains subsonic with typical velocities of $\sim 0.1c$, where $c$ denotes the sound speed. In contrast, the flow velocities in the upstream and downstream sections of the pipe are on the average factors of $\sim 6$ and $\sim 3.5$ times lower, respectively. Correlation studies based on experimental data indicate that the pressure drop is only 3% or even less for gas flow through wellhead chokes at a speed of $0.1c$. This discrepancy reflects the inadequacy of the isothermal equation of state to describe realistic gas flows.