A semi-analytical model for predicting the flow into a wellbore completed by inflow control devices

A method to predict the detailed flow into horizontal wellbores completed by inflow control devices is presented. In this work, the inflow control device (ICD) is a sequence of pipes lining the wellbore and perforated by many holes to enable the inflow of hydrocarbons. The reservoir is assumed to be infinite in the radial and axial directions and its permeability is assumed to be uniform. The pore pressure at infinity and inside the wellbore, is constant. To solve the problem of the flow into a single hole, we first treat it as if the pressure field is singular at the hole acting like an unknown point source. In this way we produce an outer approximation of the problem. We then examine the region where the singularity occurs and find a regular solution for this region only. Finally we match the two asymptotic solutions in the overlap zone, where they are both valid. Beginning with the problem of a single hole on the ICD, we use the superposition principle to add the pressure produced by the flow from the other holes at position i. We are left with a linear system of N equations relating the N unknown point sources of the N holes, with the given pressure drawdown. This system is inverted to give the strength of the point sources. This method is potentially very CPU demanding and an approximate method is also developed to deal with a lot of holes. The two methods are compared and the performance of a realistic ICD is compared against an open-hole.