We developed and implemented a new first-stage preconditioning method for large-scale reservoir simulation as an alternative to the popular Algebraic Multi Grid (AMG) method. We used Proper Orthogonal Decomposition (POD) to derive a reduced-order model for the linearized pressure equation in a proprietary reservoir simulator. A small set of pre-computed pressure solutions are used to transform the equation into a lower-order system that can be solved economically yet provides a relatively accurate estimation of the solution of the original high-order system. We present results for a two-phase (oil-water) reservoir model under water flooding conditions. Use of the POD-based preconditioner lead to a significantly faster convergence of the overall simulation compared to AMG, and reduced the linear solver times between approximately 70 % and 80%, i.e. we obtained accelerations with factors between three and five. The highest speed up was achieved for a case in which the flow rates in the eight injection wells were changed frequently during the entire production period, using ten POD basis functions obtained from short training simulations in which the injectors were operated only once each. These first results are very encouraging, especially because there is room to optimize the trade-off between the number of basis functions used in the POD method and the required number of linear iterations. However, further research is required to assess the applicability of the POD-based preconditioner to more complex cases including e.g. strongly compressible flow or compositional effects. The overhead required to pre-compute the POD solutions implies that the new method will be particularly attractive when many solutions of near-similar simulation models are required such as in computer-assisted history matching or flooding optimization.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.