This paper discusses the implementation of a discretized wellbore simulator fully implicitly coupled with the grid cells in a thermal compositional simulator. The computational of pressure losses due to multiphase frictional effects and flow regimes in the wellbore cells is handled with the Beggs and Brill correlation but the formulation is general enough to use with any other correlation. Wellbore configurations such as partial or complete tubing in casing, uninsulated/insulated tubing, partial or complete casing perforations, variations in skin damage along the well, can be modelled.
The resulting simulator has been applied to simulate circulating startup in SAGD processes with steam trap control. The model calculated horizontal wellbore pressure losses compare very favourably with a process simulator. The simulator SAGD oil rates for 2D cases with steam trap control match published results from another simulator. The simulator can be used for SAGD well design to redirect tubing and annular flows to try to affect steam chamber development.
The effect of tubing insulation and pressure drop is shown in 3D cases. The simulation cases have very reasonable execution times showing the efficiency of the coupled wellbore model.
Most conventional simulators model well flow as source sink terms. For a well with a long perforation interval, several grid cells along the perforation path of the well will be used as well locations and a source-sink term allocated to each well location grid cell. The total well rate will then be the sum of the individual sourcesink terms allocated to the well. It will be assumed that there is infinite conductivity between the well locations, that is, there is no frictional pressure loss between the source-sink terms. Thus for horizontal wells, the wellbore pressure will be assumed to be equal among all the locations. For vertical wells, some simulators will compute an average density based on entering fluid from the locations and use this to compute a wellbore pressure gradient based on the vertical depth of the various locations.
This approach is simple, quick and sufficient for most problems in conventional recovery involving vertical wells. There is no consideration of frictional losses and what happens in the pipe or casing is ignored. When crossflow occurs in the tubing, simplifications have to be made to compute crossflow, based on averaged wellbore fluid contents.
In the Steam Assisted Gravity Drainage (SAGD) process, a long horizontal well is used to inject steam and a lower long horizontal well is used to produce hot oil draining from the resulting steam chamber. As sometimes the cold oil is immobile, it is necessary to circulate steam in both the upper horizontal injector and lower horizontal producer to preheat the oil before communication of temperature and pressure could be achieved between the well pairs. This is accomplished by using a tubing string inside the casing. To accurately model these startup conditions, it is not possible to use source-sink terms. If source-sink terms are used, the startup heating phase is modelled using heat injector source-sink terms at the well locations.