Adaptive nonlinear solver for a discrete fracture model in operator-based linearization framework

K. Mansour Pour*, D. Voskov

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)
3 Downloads (Pure)


Simulation of compositional problems in hydrocarbon reservoirs with complex heterogeneous structure requires adopting stable numerical methods that rely on an implicit treatment of the flux term in the conservation equation. The discrete approximation of convection term in governing equations is highly nonlinear due to the complex properties complemented with a multiphase flash solution. Consequently, robust and efficient techniques are needed to solve the resulting nonlinear system of algebraic equations. The solution of the compositional problem often requires the propagation of the displacement front to multiple control volumes at simulation timestep. Coping with this issue is particularly challenging in complex subsurface formations such as fractured reservoirs. In this study, we present a robust nonlinear solver based on a generalization of the trust-region technique to compositional multiphase flows. The approach is designed to embed a newly introduced Operator-Based Linearization technique and is grounded on the analysis of multi-dimensional tables related to parameterized convection operators. We segment the parameter-space of the nonlinear problem into a set of trust regions where the convection operators maintain the second-order behaviour (i.e., they remain positive or negative definite). We approximate these trust regions in the solution process by detecting the boundary of convex regions via analysis of the directional derivative. This analysis is performed adaptively while tracking the nonlinear update trajectory in the parameter-space. The proposed nonlinear solver locally constraints the updating of the overall compositions across the boundaries of convex regions. Besides, we enhance the performance of the nonlinear solver by exploring diverse preconditioning strategies for compositional problems. The proposed nonlinear solution strategies have been validated for both miscible and immiscible gas injection problems of practical interest.

Original languageEnglish
Title of host publicationECMOR 2020
Subtitle of host publication17th European Conference on the Mathematics of Oil Recovery
Number of pages18
ISBN (Electronic)9789462823426
Publication statusPublished - 2020
Event17th European Conference on the Mathematics of Oil Recovery, ECMOR 2020 - Virtual, Online
Duration: 14 Sep 202017 Sep 2020


Conference17th European Conference on the Mathematics of Oil Recovery, ECMOR 2020
CityVirtual, Online

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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