Numerical simulation of two phase flow in vertical pipes

Abstract

The procedure for predicting pressure drops in vertical pipes for oil/gas field work has been handled to date by empirical and experimental correlations applied to a steady-state energy equation often called the Pressure Drop Model. Analyses of these correlations have shown undue dependence on the data used for the derivation of the correlations thus limiting their general application. This study describes the development and application of a one-dimensional fully implicit numerical model for simulating the transient and equilibrium conditions of a flowing oil/gas well. By modifying the diffusivity equation with a turbulence factor, different flow patterns from bubble to mist flow are simulated including liquid build-up, start-up or shut-in of a producing well. Pseudo-relative permeability-data are used to replace the flow regime map used in the correlation methods. The insitu foam densities are found to be velocity dependent when liquid is entrained as dispersed droplets in the gas phase. The densities are also saturation dependent when gas is entrained as dispersed bubbles in the liquid phase. By coupling the tubing model to a one-cell depletion type gas reservoir, flu id flow problems from the reservoir into the tubing and the sequential liquid build-up in the tubing up to the cessation of flow and subsequent unloading of the well can be monitored. Results of the pressure losses predicted by the tubing model compared very favorably and in many cases improved on those from the correlation-type models..