A numerical well model considering capillary end effect for the low-permeability gas reservoir

Abstract

In the recovery of low permeability reservoir, the capillary pressure has an important effect, which may reduce gas production. Due to the capillary end effect, there are two flow patterns in the vicinity of the production well: both water and gas phases can flow into the production well and only gas phase can enter the production well. Based on the analytical equations of one-dimensional radial flow considering the capillary end effect, an alternative numerical well model for low permeability gas reservoir is constructed. Numerical examples show that the proposed model can reflect the dramatic change for saturation and gas-phase pressure in the vicinity of the production well both for two flow patterns, and therefore can predict the gas and water productions accurately at different grid scales. In contrast, the original Peaceman well model for multi-phase flow, which is directly extended from that for single-phase flow, only can provide good prediction under the condition of that the grid size is enough small. Especially, for the original Peaceman well model, this problem is out of control since it is difficult to estimate a suitable grid size.