Inflow and pressure drawdown profiles along a horizontal well can be estimated given the geological reservoir model (including rock and fluid parameters) and the geometry of the well. These profiles should be taken into consideration when planning both the length of the well and the completion of the well. This especially applies for wells in high productivity reservoirs, where the frictional pressure loss in the well has a significant influence on the well inflow.
In this thesis a new mathematical model for calculating inflow and pressure profiles in horizontal oil wells has been developed, described and evaluated. The model is developed for single phase fluid in a horizontal well with open-hole completion (like Troll wells). The model is available in two different versions, both using the same algorithm. Both versions calculate the rate and pressure profile along the well. The difference between them is that one version calculate the pressure drawdown in the heel point of the well, given the target liquid rate, whereas the other version calculate the total liquid rate given the pressure drawdown in the heel point.
The modelling of the horizontal well inflow problem is based on the works by Dikken (1991), which is here extended by including acceleration pressure drop along the well. Quadratic functions are applied as influence functions for calculating the unknown variables along the well. The idea behind this model comes from dr.sc. Sverre Thomas Holte, Norsk Hydro ASA. The model has been checked for convergence and consistency, and is found to be a robust, simple model. The model is implemented in LOTUS 1-2-3 spreadsheet.
Different analytical equations for productivity index in horizontal wells (Butler, Darcy, Asheim, Goode and Kuchuk) are compared to each other and evaluated against results from interpreted production logs from the Troll Oil Field. The calculations are performed with the new mathematical model. This work has shown that none of the analytical equations describe the actual productivity. Effects of relative permeability are assumed to be one reason for this. It should also be noted that the analytical equations are derived from a line source assumption; that the pressure loss along the well is negligible.
The model is also used in a qualitative study of the effects on pressure drawdown and well inflow when shutting off an interval in the well or reducing the inflow in an interval. Reduction of inflow can be beneficial in highly productive intervals of the well, where the potential for water and gas coning is high. It is also useful for wells in homogenous reservoirs, where the effect of frictional pressure loss can be reduced. The reduction of the inflow is thought to be either mechanical with an internal sleeve/straddle, or hydraulic by forcing an extra frictional pressure drop on the inflowing fluid using ICD (Inflow Control Device). The calculations show that gas/water coning potential can be significantly reduced, and that the well can drain the reservoir in a better way. At the same time lifting capacity of the well will be reduced when shutting off an interval or reducing the inflow.
Comparison between calculations and measured data show that available analytical equations for productivity do not describe the actual productivity of the reservoir.
The acceleration pressure loss, the way it has been modelled in these calculations, can be neglected.
The frictional pressure loss in the well increases when the inflow to an interval of the well is either restricted or shut off. This results in a loss of lifting capacity. Restriction of inflow to intervals in the well can reduce the potential for gas/water coning.
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