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A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of the main complexities related to efficient and effective simulations in realistic DFMs. [ABSTRACT FROM AUTHOR]

Controlled-source electromagnetic (CSEM) surveying becomes a widespread method for oil and gas exploration, which requires fast and efficient software for inverting large-scale EM datasets. In this context, one often needs to solve sparse systems of linear equations with a large number of sparse right-hand sides, each corresponding to a given transmitter position. Sparse direct solvers are very attractive for these problems, especially when combined with low-rank approximations which significantly reduce the complexity and the cost of the factorization. In the case of thousands of right-hand sides, the time spent in the sparse triangular solve tends to dominate the total simulation time, and here we propose several approaches to reduce it. A significant reduction is demonstrated for marine CSEM application by utilizing the sparsity of the right-hand sides (RHS) and of the solutions that results from the geometry of the problem. Large gains are achieved by restricting computations at the forward substitution stage to exploit the fact that the RHS matrix might have empty rows (vertical sparsity) and/or empty blocks of columns within a non-empty row (horizontal sparsity). We also adapt the parallel algorithms that were designed for the factorization to solve-oriented algorithms and describe performance optimizations particularly relevant for the very large numbers of right-hand sides of the CSEM application. We show that both the operation count and the elapsed time for the solution phase can be significantly reduced. The total time of CSEM simulation can be divided by approximately a factor of 3 on all the matrices from our set (from 3 to 30 million unknowns, and from 4 to 12 thousands RHSs). [ABSTRACT FROM AUTHOR]

Methane gas hydrates have increasingly become a topic of interest because of their potential as a future energy resource. There are significant economical and environmental risks associated with extraction from hydrate reservoirs, so a variety of multiphysics models have been developed to analyze prospective risks and benefits. These models generally have a large number of empirical parameters which are not known a priori. Traditional optimization-based parameter estimation frameworks may be ill-posed or computationally prohibitive. Bayesian inference methods have increasingly been found effective for estimating parameters in complex geophysical systems. These methods often are not viable in cases of computationally expensive models and high-dimensional parameter spaces. Recently, methods have been developed to effectively reduce the dimension of Bayesian inverse problems by identifying low-dimensional structures that are most informed by data. Active subspaces is one of the most generally applicable methods of performing this dimension reduction. In this paper, Bayesian inference of the parameters of a state-of-the-art mathematical model for methane hydrates based on experimental data from a triaxial compression test with gas hydrate-bearing sand is performed in an efficient way by utilizing active subspaces. Active subspaces are used to identify low-dimensional structure in the parameter space which is exploited by generating a cheap regression-based surrogate model and implementing a modified Markov chain Monte Carlo algorithm. Posterior densities having means that match the experimental data are approximated in a computationally efficient way. [ABSTRACT FROM AUTHOR]

In many applications in flows through porous media, one needs to determine the properties of subsurface to detect, monitor, or predict the actions of natural or induced forces. Here, we focus on two important subsurface properties: rock permeability and porosity. A Bayesian approach using a Markov Chain Monte Carlo (MCMC) algorithm is well suited for reconstructing the spatial distribution of permeability and porosity, and quantifying associated uncertainty in these properties. A crucial step in this approach is the computation of a likelihood function, which involves solving a possibly nonlinear system of partial differential equations. The computation time for the likelihood function limits the number of MCMC iterations that can be performed in a practical period of time. This affects the consistency of the posterior distribution of permeability and porosity obtained by MCMC exploration. To speed-up the posterior exploration, we can use a prefetching technique, which relies on the fact that multiple likelihoods of possible states into the future in an MCMC chain can be computed ahead of time. In this paper, we show that the prefetching technique implemented on multiple processors can make the Bayesian approach computationally tractable for subsurface characterization and prediction of porous media flows. [ABSTRACT FROM AUTHOR]

In geosciences, complex forward problems met in geophysics, petroleum system analysis, and reservoir engineering problems often require replacing these forward problems by proxies, and these proxies are used for optimizations problems. For instance, history matching of observed field data requires a so large number of reservoir simulation runs (especially when using geostatistical geological models) that it is often impossible to use the full reservoir simulator. Therefore, several techniques have been proposed to mimic the reservoir simulations using proxies. Due to the use of experimental approach, most authors propose to use second-order polynomials. In this paper, we demonstrate that (1) neural networks can also be second-order polynomials. Therefore, the use of a neural network as a proxy is much more flexible and adaptable to the nonlinearity of the problem to be solved; (2) first-order and second-order derivatives of the neural network can be obtained providing gradients and Hessian for optimizers. For inverse problems met in seismic inversion, well by well production data, optimal well locations, source rock generation, etc., most of the time, gradient methods are used for finding an optimal solution. The paper will describe how to calculate these gradients from a neural network built as a proxy. When needed, the Hessian can also be obtained from the neural network approach. On a real case study, the ability of neural networks to reproduce complex phenomena (water cuts, production rates, etc.) is shown. Comparisons with second polynomials (and kriging methods) will be done demonstrating the superiority of the neural network approach as soon as nonlinearity behaviors are present in the responses of the simulator. The gradients and the Hessian of the neural network will be compared to those of the real response function. [ABSTRACT FROM AUTHOR]

We present a network flow model to compute transport, through a pore network, of a compositional fluid consisting of water with a dissolved hydrocarbon gas. The model captures single-phase flow (below local bubble point conditions) as well as the genesis and migration of the gas phase when bubble point conditions are achieved locally. Constant temperature computational tests were run on simulated 2D and 3D micro-networks near bubble point pressure conditions. In the 2D simulations which employed a homogeneous network, negligible capillary pressure, and linear relative permeability relations, the observed concentration of CO dissolved in the liquid phase throughout the medium was linearly related to the liquid pressure. In the case of no gravity, the saturation of the gas phase throughout the medium was also linearly related to the liquid pressure; under gravity, the relationship became nonlinear in regions where buoyancy forces were significant. The 3D heterogeneous network model had nonnegligible capillary pressure and nonlinear relative permeability functions. While 100 % of the CO entered the 3D network dissolved in the liquid phase, 25 % of the void space was occupied by gas phase and 47 % of the CO exiting the outlet face did so via the gaseous phase after 500 s of simulation time. [ABSTRACT FROM AUTHOR]

The increasing use of unstructured grids for reservoir modeling motivates the development of geostatistical techniques to populate them with properties such as facies proportions, porosity and permeability. Unstructured grids are often populated by upscaling high-resolution regular grid models, but the size of the regular grid becomes unreasonably large to ensure that there is sufficient resolution for small unstructured grid elements. The properties could be modeled directly on the unstructured grid, which leads to an irregular configuration of points in the three-dimensional reservoir volume. Current implementations of Gaussian simulation for geostatistics are for regular grids. This paper addresses important implementation details involved in adapting sequential Gaussian simulation to populate irregular point configurations including general storage and computation issues, generating random paths for improved long range variogram reproduction, and search strategies including the superblock search and the k-dimensional tree. An efficient algorithm for computing the variogram of very large irregular point sets is developed for model checking. [ABSTRACT FROM AUTHOR]

This paper presents an object-oriented programming approach for the design of numerical homogenization programs, called JHomogenizer. It currently includes five functional modules to compute effective permeability and simple codes for computing solutions for flow in porous media. Examples with graphical output are shown to illustrate some functionalities of the program. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. The software is freely available, and the open architecture of the program facilitates further development and can adapt to suit specific needs easily and quickly. [ABSTRACT FROM AUTHOR]