This study was aimed at improving the accuracy of the model predictions for the minimum fluid and inner wall temperatures for cold, low-pressure start-up of wells that produce oil or gas. Due to the large pressure drop over the well head choke, the so-called Joule-Thomson cooling will give a very low temperature of the
expanding gas jet. Low-temperatures can give brittle fracture of the material in the piping downstream of the choke. Models are needed to verify whether the material temperature remains above the lower-design temperature. For the model validation, Imperial College in London (on request by Shell) has carried out lab experiments with argon gas that expands through an orifice from 120 bara to 1 bara. Awaiting the results of the lab experiments, detailed simulations were carried out in the present study using the Fluent CFD programme.

The 3D, steady, compressible Reynolds-Averaged Navier-Stokes equations were solved with the SST k −ω model for the turbulence. The considered configuration is the same as in the lab. It consists of an upstream chamber with argon at 120 bara, that expands through a 5 mm long orifice with 1.55 mm diameter, into a square outlet section with 50 mm sides and 500 mm length. The inlet temperature is -17 oC and the outlet pressure is 1 bara. The supersonic flow leaving the orifice reaches a maximum Mach number of about 9, just before a shock to subsonic flow is found. The jet reaches very low temperatures due to isentropic expansion, and reaches the isenthalpic expansion temperature of 196 K (or -77 oC) downstream of the shock. The jet reaches the sides of the outlet at a distance of about 100 mm.

The maximum Mach number of about 9 predicted by Fluent is higher than the value of about 6 found in a previous simulation study that used the STAR-CCM+ CFD programme. To verify the Fluent results, the distributions of grid cells was varied and the number of grid cells was increased. Also, a MATLAB programme was written that solved the inviscid compressible equations (Euler equations) for an axisymmetric jet.

This confirmed the Fluent results. In addition to the 3D square outlet section, also 3D and 2D Fluent simulations were carried out for a cylindrical outlet (using a hydraulic diameter of 50 mm). The maximum Mach number and the jet structure (velocity, temperature) are not affected by the side walls. This is because the side walls are sufficiently far from the jet.

Furthermore, the temperature and the heat transfer at the walls of the outlet section were investigated. Thereto both adiabatic and non-adiabatic walls were considered. The ambient temperature is 20 oC. Thermal boundary layers are formed along the side walls, that are exposed to a temperature of 196 K (the isenthalpic expansion temperature) in the centre of the pipe, up to a distance of about 1.5 m, where the outer edge of the boundary layer reaches the centre of the pipe. Thereafter the centre line temperature increases due to heat inflow from the ambient.