Estimating Near-Wellbore Permeability in Horizontal Wells From Distributed Pressure Measurements Using an Adjoint-Based Minimization Algorithm

Abstract

Recent developments in the deployment of distributed pressure measurement devices in horizontal wells carry the promise to lead to a new, cheap and reliable way of monitoring production and reservoir performance. We theoretically examine the identifiability of reservoir parameters from distributed pressure measurements in the well. The wellbore and near-wellbore are described by semi-analytical steady state models, and a gradient-based inversion method is applied to estimate the permeability of layers that are perpendicular to the wellbore axis. To obtain the derivative information we employ the adjoint method which results in a computationally very efficient inversion scheme. Through several synthetic examples we investigated the effects of well and reservoir parameters, sensor spacing, and measurement noise on the quality of the inversion results. In particular we considered a 2000 m long horizontal well passing through two 300 m long high-permeability streaks in a 10 times lower permeability background. The location of high-permeability zones could be detected with a fair accuracy using 20 unknown parameters (specific PI values) even when the number of measurements was four times less than the number of parameters. Moreover, with 0.01 MPa (1.5 psi) measurement noise (and an average wellbore pressure of approximately 20 MPa (3000 psi)) the estimated specific PI profiles were satisfactory and the high permeability streaks were still detectable. However, when the noise level increased to 0.1 MPa, only the high permeable zone close to the heel was detectable. The negative effects of measurement noise and low sensor/parameter ratios are strongest in those areas of the well where the influx is smallest (usually close to the toe). The inversions typically required less than 90 seconds on a standard laptop. This offers the opportunity to extend the algorithm to multi-phase flow and dynamic applications (pressure-transient testing) while still maintaining sufficient computational speed to perform the inversion online.