Reduced-Order Modeling for Compositional Simulation Using Trajectory Piecewise Linearization

2013 ◽  
Author(s):  
Jincong He ◽  
Louis J. Durlofsky
Keyword(s):  
Reduced Order Modeling ◽  
Compositional Simulation ◽  
Piecewise Linearization ◽  
Reduced Order ◽  
Trajectory Piecewise Linearization

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.

Reduced-Order Modeling of Coupled Flow and Quasistatic Geomechanics

SPE Journal ◽  
2019 ◽  
Vol 25 (01) ◽  
pp. 326-346 ◽  
Author(s):  
Zhaoyang Larry Jin ◽  
Timur Garipov ◽  
Oleg Volkov ◽  
Louis J. Durlofsky
Keyword(s):  
Automatic Differentiation ◽  
Dimensional Subspace ◽  
General Purpose ◽  
Reduced Order Modeling ◽  
Global Maximum ◽  
Test Case ◽  
Coupled Flow ◽  
Piecewise Linearization ◽  
Reduced Order ◽  
Low Dimensional

Summary A reduced-order-modeling (ROM) framework is developed and applied to simulate coupled flow/quasistatic-geomechanics problems. The reduced-order model is constructed using POD-TPWL, in which proper orthogonal decomposition (POD), which enables representation of the solution unknowns in a low-dimensional subspace, is combined with trajectory-piecewise linearization (TPWL), where solutions with new sets of well controls are represented by means of linearization around previously simulated (training) solutions. The overdetermined system of equations is projected into the low-dimensional subspace using a least-squares Petrov-Galerkin (LSPG) procedure, which has been shown to maintain numerical stability in POD-TPWL models. The states and derivative matrices required by POD-TPWL, generated by an extended version of the Stanford University Automatic Differentiation General Purpose Research Simulator (AD-GPRS), are provided in an offline (preprocessing or training) step. Offline computational requirements correspond to the equivalent of five to eight full-order simulations, depending on the number of training runs used. Run-time (online) speedups of O(100) or more are typically achieved for new POD-TPWL test-case simulations. The POD-TPWL model is tested extensively for a 2D coupled problem involving oil/water flow and geomechanics. It is shown that POD-TPWL provides predictions of reasonable accuracy, relative to full-order simulations, for well-rate quantities, global pressure and saturation fields, global maximum- and minimum-principal-stress fields, and the Mohr-Coulomb rock-failure criterion, for the cases considered. A systematic study of POD-TPWL error is conducted using various training procedures for different levels of perturbation between test and training cases. The use of randomness in the well-bottomhole-pressure (BHP) profiles used in training is shown to be beneficial in terms of POD-TPWL solution accuracy. The procedure is also successfully applied to a prototype 3D example case.

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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