Use of Reduced-Order Modeling Procedures for Production Optimization

2009 ◽  
Author(s):  
Marco Antonio Cardoso ◽  
Louis J. Durlofsky
Keyword(s):  
Reduced Order Modeling ◽  
Production Optimization ◽  
Reduced Order

Use of Reduced-Order Modeling Procedures for Production Optimization

SPE Journal ◽  
2009 ◽  
Vol 15 (02) ◽  
pp. 426-435 ◽  
Author(s):  
M.A.. A. cardoso ◽  
L.J.. J. Durlofsky
Keyword(s):  
Optimization Problems ◽  
Dimensional Space ◽  
Reduced Order Modeling ◽  
Production Optimization ◽  
High Fidelity ◽  
Control Variables ◽  
Reduced Order ◽  
First Case ◽  
High Fidelity Simulations

Summary The determination of optimal well settings is very demanding computationally because the simulation model must be run many times during the course of the optimization. For this reason, reduced-order modeling procedures, which are a family of techniques that enable highly efficient simulations, may be very useful for optimization problems. In this paper, we describe a recently developed reduced-order modeling (ROM) technique that has been used in other application areas, the trajectory piecewise linearization (TPWL) procedure, and incorporate it in production-optimization computations. The TPWL methodology represents solutions encountered during the optimization runs in terms of Taylor-series expansions around previously simulated states. This requires a small number of preprocessing (training) simulations using the full (high-fidelity) model, during which pressure and saturation states and Jacobian matrices are saved. These states and matrices are then projected into a low-dimensional space using proper orthogonal decomposition (POD). Simulations in this reduced space can be performed very efficiently; in this work, we observe runtime speedups of a factor of 450. Overall speedups are, however, less because of the preprocessing overhead. We assess the TPWL representation for simulations of waterflood in a heterogeneous 3D model containing more than 20,000 gridblocks and six wells. The high degree of accuracy of the TPWL model is first demonstrated for several testing simulations in which producer- and injector-well settings differ from those used in the training runs. The TPWL representations are then used in optimizations involving the determination of optimal bottomhole pressures (BHPs) for a reservoir model with four production wells and two injection wells. A gradient-based algorithm is applied for the optimizations. In the first case, the BHPs of the producers and injectors are optimized at six different times (36 control variables) and in the second case at 15 different times (90 control variables). Results for optimized net present value (NPV) using TPWL are shown to be in consistently close agreement with those computed using high-fidelity simulations. Most significantly, when the optimal well settings obtained using the TPWL procedure are applied in high-fidelity models, the resulting NPVs are within approximately 0.5% of the values determined using the high-fidelity simulations. Our overall conclusion is that the TPWL representation may be quite useful in production-optimization problems.

Hyper-Reduced-Order Models for Subsurface Flow Simulation

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2128-2140 ◽  
Author(s):  
Seonkyoo Yoon ◽  
Zeid M. Alghareeb ◽  
John R. Williams
Keyword(s):  
Subsurface Flow ◽  
Flow Simulation ◽  
Reduced Order Modeling ◽  
Production Optimization ◽  
Galerkin Projection ◽  
Flow Modeling ◽  
State Reduction ◽  
Constraint Reduction ◽  
Reduced Order ◽  
Modeling Procedure

Summary Subsurface flow modeling is an indispensable task for reservoir management, but the associated computational cost is burdensome because of model complexity and the fact that many simulation runs are required for its applications such as production optimization, uncertainty quantification, and history matching. To relieve the computational burden in reservoir flow modeling, a reduced-order modeling procedure based on hyper-reduction is presented. The procedure consists of three components: state reduction, constraint reduction, and nonlinearity treatment. State reduction based on proper orthogonal decomposition (POD) is considered, and the impact of state reduction, with different strategies for collecting snapshots, on accuracy and predictability is investigated. Petrov-Galerkin projection is used for constraint reduction, and a hyper-reduction that couples the Petrov-Galerkin projection and a “gappy” reconstruction is applied for the nonlinearity treatment. The hyper-reduction method is a Gauss-Newton framework with approximated tensors (GNAT), and the main contribution of this study is the presentation of a procedure for applying the method to subsurface flow simulation. A fully implicit oil/water two-phase subsurface flow model in 3D space is considered, and the application of the proposed hyper-reduced-order modeling procedure achieves a runtime speedup of more than 300 relative to the full-order method, which cannot be achieved when only constraint reduction is adopted.

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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