scholarly journals Multigrid Reduction for Coupled Flow Problems with Application to Reservoir Simulation

2017 ◽  
Author(s):  
Lu Wang ◽  
Daniel Osei-Kuffuor ◽  
Rob Falgout ◽  
Ilya Mishev ◽  
Jizhou Li
Keyword(s):  
Reservoir Simulation ◽  
Coupled Flow ◽  
Flow Problems

scholarly journals Well-posed Stokes/Brinkman and Stokes/Darcy coupling revisited with new jump interface conditions

2018 ◽  
Vol 52 (5) ◽  
pp. 1875-1911 ◽  
Author(s):  
Philippe Angot
Keyword(s):  
Tangential Velocity ◽  
Cross Flow ◽  
Jump Condition ◽  
Force Balance ◽  
Pressure Jump ◽  
Interface Conditions ◽  
Coupled Flow ◽  
Flow Problems ◽  
Porous Interface ◽  
Well Posed

The global well-posedness in time is proved, with no restriction on the size of the data, for the Stokes/Brinkman and Stokes/Darcy coupled flow problems with new jump interface conditions recently derived by Angot et al. [Phys. Rev. E 95 (2017) 063302-1–063302-16] using asymptotic modelling and shown to be physically relevant. These original conditions include jumps of both stress and tangential velocity vectors at the fluid–porous interface. They can be viewed as generalizations for the multi-dimensional flow of Beavers and Joseph’s jump condition of tangential velocity and Ochoa-Tapia and Whitaker’s jump condition of shear stress. Therefore, they are different from those most commonly used in the literature. The case of Saffman’s approximation is also studied, but with a force balance for the cross-flow including the Darcy drag and inducing a law of pressure jump different from the usual one. The proof of these results follows the general framework briefly introduced by Angot [C. R. Math. Acad. Sci. Paris, Ser. I 348 (2010) 697–702; Appl. Math. Lett. 24 (2011) 803–810.] for the steady flow.

Efficient Uncertainty Quantification and Data Assimilation via Theory-Guided Convolutional Neural Network

SPE Journal ◽  
1900 ◽  
pp. 1-29
Author(s):  
Nanzhe Wang ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Neural Network ◽  
Data Assimilation ◽  
Convolutional Neural Network ◽  
Uncertainty Quantification ◽  
Reservoir Simulation ◽  
High Accuracy ◽  
Training Data ◽  
Flow Problems ◽  
Stochastic Parameter ◽  
Reservoir Flow

Summary A deep learning framework, called the theory-guided convolutional neural network (TgCNN), is developed for efficient uncertainty quantification and data assimilation of reservoir flow with uncertain model parameters. The performance of the proposed framework in terms of accuracy and computational efficiency is assessed by comparing it to classical approaches in reservoir simulation. The essence of the TgCNN is to take into consideration both the available data and underlying physical/engineering principles. The stochastic parameter fields and time matrix comprise the input of the convolutional neural network (CNN), whereas the output is the quantity of interest (e.g., pressure, saturation, etc.). The TgCNN is trained with available data while being simultaneously guided by theory (e.g., governing equations, other physical constraints, and engineering controls) of the underlying problem. The trained TgCNN serves as a surrogate that can predict the solutions of the reservoir flow problem with new stochastic parameter fields. Such approaches, including the Monte Carlo (MC) method and the iterative ensemble smoother (IES) method, can then be used to perform uncertainty quantification and data assimilation efficiently based on the TgCNN surrogate, respectively. The proposed paradigm is evaluated with dynamic reservoir flow problems. The results demonstrate that the TgCNN surrogate can be built with a relatively small number of training data and even in a label-free manner, which can approximate the relationship between model inputs and outputs with high accuracy. The TgCNN surrogate is then used for uncertainty quantification and data assimilation of reservoir flow problems, which achieves satisfactory accuracy and higher efficiency compared with state-of-the-art approaches. The novelty of the work lies in the ability to incorporate physical laws and domain knowledge into the deep learning process and achieve high accuracy with limited training data. The trained surrogate can significantly improve the efficiency of uncertainty quantification and data assimilation processes. NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Finite Difference Simulation of Geologically Complex Reservoirs With Tensor Permeabilities

1998 ◽  
Vol 1 (06) ◽  
pp. 567-574 ◽  
Author(s):  
S.H. Lee ◽  
L.J. Durlofsky ◽  
M.F. Lough ◽  
W.H. Chen
Keyword(s):  
Finite Difference ◽  
Reservoir Simulation ◽  
Reservoir Characterization ◽  
Heterogeneous Systems ◽  
General Purpose ◽  
Flow Problems ◽  
Continuous Approach ◽  
Original Manuscript ◽  
Element Approach ◽  
Reservoir Description

This paper (SPE 52637) was revised for publication from paper SPE 38002, first presented at the 1997 SPE Reservoir Simulation Symposium, Dallas, 8-11 June. Original manuscript received for review 1 July 1997. Revised manuscript received 5 August 1998. Paper peer approved 3 September 1998. Summary The gridblock permeabilities used in reservoir simulation are commonly determined through the upscaling of a fine scale geostatistical reservoir description. Though it is well established that permeabilities computed in this manner are, in general, full tensor quantities, most finite difference reservoir simulators still treat permeability as a diagonal tensor. In this paper, we implement a capability to handle full tensor permeabilities in a general purpose finite difference simulator and apply this capability to the modeling of several complex geological systems. We formulate a flux continuous approach for the pressure equation by use of a method analogous to that of previous researchers (Edwards and Rogers; Aavatsmark et al.), consider methods for upwinding in multiphase flow problems, and additionally discuss some relevant implementation and reservoir characterization issues. The accuracy of the finite difference formulation, assessed through comparisons to an accurate finite element approach, is shown to be generally good, particularly for immiscible displacements in heterogeneous systems. The formulation is then applied to the simulation of upscaled descriptions of several geologically complex reservoirs involving crossbedding and extensive fracturing. The method performs quite well for these systems and is shown to capture the effects of the underlying geology accurately. Finally, the significant errors that can be incurred through inaccurate representation of the full permeability tensor are demonstrated for several cases. P. 567

Domain Decomposition Methods Applied To Coupled Flow-Geomechanics Reservoir Simulation

2011 ◽  
Author(s):  
Horacio Florez ◽  
Mary Fanett Wheeler ◽  
Adolfo Antonio Rodriguez ◽  
Jorge Eduardo Palomino Monteagudo
Keyword(s):  
Domain Decomposition ◽  
Reservoir Simulation ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Coupled Flow

An implicit 2D hydrodynamic numerical model for free surface-subsurface coupled flow problems

2018 ◽  
Vol 87 (7) ◽  
pp. 343-357 ◽  
Author(s):  
Naser Shokri ◽  
Masoud Montazeri Namin ◽  
Javad Farhoudi
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Coupled Flow ◽  
Flow Problems
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