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Mechatronics, Computer Science and Applied Mathematics

More efficient flow simulations inspired by optimal control

Multiphase mixture (gas and liquid) flow simulation in porous media has a variety of applications in the field of geosciencesa but also in the fields of engineering and chemical processes.
In industrial simulators, globally implicit equation formulations are crucial for ensuring calculation robustness and performance, as well as maintaining close coupling between fluid flows and thermodynamics. However, mathematical and numerical difficulties remain, such as, for example, treating the appearance and disappearance of phases simultaneously with the transport of components. The numerical methods need to be adapted to take into account the variable structure of the system of equations and solve the associated inequalities.
A variety of different innovative solutions have been proposed in recent years, via a reformulation based on “complementarity constraints”b, used in optimization and optimal control. Drawing on these new ideas and its long-standing expertise, IFPEN has developed a unified approach and a general framework facilitating the development of algorithms and their computerization. These algorithms have been tested on prototypes(1) and then successfully deployed in operational simulators.
Using this approach, it is now possible to handle systems coupling flows with chemical(2) (figure), thermal and compaction(3) reactions.
Current research is aimed at integrating kinetic chemical reactions and adapting solvers used in the field of optimization.

a- CO2 storage, gas storage, the exploitation of oil and gas resources, geothermal energy, ground remediation.
b- Via which the positivity of two magnitudes and the nullity of at least one of them is concisely expressed.


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Published in Science@ifpen n°33 - June 2018


  1.  I. Ben Gharbia et al., Study of Compositional Multi-Phase Flow Formulations with Cubic EOS, SPE Reservoir Simulation Symposium 2015, Houston, USA, 23-25 February 2015.
    >> DOI: 10.2118/173249-MS
  2. T. Faney et al., Comparison of numerical schemes for multiphase reactive transport, Workshop “Reactive Transport Modeling in the Geological Sciences”, IHP, Paris, France, 17-18 November 2015.
  3. C. Meiller et al., Three-Phase Darcy Migration in Basin Modeling, AAPG ACE, 100th, Houston, USA, 2-5 April 2017

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