A New Framework for Compositional Simulation Using Reduced Order Modeling Based on POD-DEIM

2020 ◽  
Author(s):  
Jae Wook Lee ◽  
Eduardo Gildin
Keyword(s):  
Reduced Order Modeling ◽  
Compositional Simulation ◽  
Reduced Order ◽  
New Framework

Reduced-Order Modeling for Compositional Simulation by Use of Trajectory Piecewise Linearization

SPE Journal ◽  
2014 ◽  
Vol 19 (05) ◽  
pp. 858-872 ◽  
Author(s):  
Jincong He ◽  
Louis J. Durlofsky
Keyword(s):  
Oil And Gas ◽  
Dimensional Subspace ◽  
Reduced Order Modeling ◽  
Galerkin Projection ◽  
Compositional Simulation ◽  
Piecewise Linearization ◽  
Reduced Order ◽  
Computational Optimization ◽  
Trajectory Piecewise Linearization ◽  
Low Dimensional

Summary Compositional simulation can be very demanding computationally as a result of the potentially large number of system unknowns and the intrinsic nonlinearity of typical problems. In this work, we develop a reduced-order modeling procedure for compositional simulation. The technique combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide a highly efficient surrogate model. The compositional POD-TPWL method expresses new solutions in terms of linearizations around states generated (and saved) during previously simulated “training” runs. High-dimensional states are projected (optimally) into a low-dimensional subspace by use of POD. The compositional POD-TPWL model is based on a molar formulation that uses pressure and overall component mole fractions as the primary unknowns. Several new POD-TPWL treatments, including the use of a Petrov-Galerkin projection to reduce the number of equations (rather than the Galerkin projection, which was applied previously), and a new procedure for determining which saved state to use for linearization are incorporated into the method. Results are presented for heterogeneous 3D reservoir models containing oil and gas phases with up to six hydrocarbon components. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations is demonstrated for the cases considered. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to approximately three or four full-order runs. Runtime speedups by use of POD-TPWL are, however, very significant—up to a factor of 800 for the cases considered. The POD-TPWL model is thus well suited for use in computational optimization, in which many simulations must be performed, and we present an example demonstrating its application for such a problem.

Lattice Boltzmann Flow Simulations With Applications of Reduced Order Modeling Techniques.

2014 ◽  
Author(s):  
Donald L. Brown ◽  
Jun Li ◽  
Victor M. Calo ◽  
Mehdi Ghommem ◽  
Yalchin Efendiev
Keyword(s):  
Lattice Boltzmann ◽  
Reduced Order Modeling ◽  
Reduced Order ◽  
Flow Simulations ◽  
Modeling Techniques
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