Carbon capture and storage (CCS) is broadly recognised as having the potential to play a key role in meeting climate change targets, delivering low carbon heat and power, decarbonising industry and, more recently, its ability to facilitate the net removal of CO2 from the atmosphere. However, despite this broad consensus and its technical maturity, CCS has not yet been deployed on a scale commensurate with the ambitions articulated a decade ago. Thus, in this paper we review the current state-of-the-art of CO2 capture, transport, utilisation and storage from a multi-scale perspective, moving from the global to molecular scales. In light of the COP21 commitments to limit warming to less than 2 °C, we extend the remit of this study to include the key negative emissions technologies (NETs) of bioenergy with CCS (BECCS), and direct air capture (DAC). Cognisant of the non-technical barriers to deploying CCS, we reflect on recent experience from the UK's CCS commercialisation programme and consider the commercial and political barriers to the large-scale deployment of CCS. In all areas, we focus on identifying and clearly articulating the key research challenges that could usefully be addressed in the coming decade.

/pdf/carbon-capture-and-storage-ccs-the-way-forward-11rgsqyer0.pdf

Carbon capture and storage (CCS): the way forward

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

A new and very general technique for simulating solid–fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in a companion paper (Part 2), extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.

Numerical simulations of particulate suspensions via a discretized boltzmann equation: part 1. theoretical foundation

A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs). In the presence of a general nonlinearity, the standard POD-Galerkin technique reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term remains that of the original problem. The original empirical interpolation method (EIM) is a modification of POD that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD. We propose a discrete empirical interpolation method (DEIM), a variant that is suitable for reducing the dimension of systems of ordinary differential equations (ODEs) of a certain type. As presented here, it is applicable to ODEs arising from finite difference discretization of time dependent PDEs and/or parametrically dependent steady state problems. However, the approach extends to arbitrary systems of nonlinear ODEs with minor modification. Our contribution is a greatly simplified description of the EIM in a finite-dimensional setting that possesses an error bound on the quality of approximation. An application of DEIM to a finite difference discretization of the one-dimensional FitzHugh-Nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long-time integration that fully captures nonlinear limit cycle behavior. We also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results.

/pdf/nonlinear-model-reduction-via-discrete-empirical-f3tjqvqhuf.pdf

Nonlinear Model Reduction via Discrete Empirical Interpolation

https://www.math.utah.edu/~epshteyn/selectedpapers.html/paperHou1.pdf

A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media

Upscaling Discrete Fracture Characterizations to Dual-Porosity, Dual-Permeability Models for Efficient Simulation of Flow With Strong Gravitational Effects

This paper (SPE 118958) was accepted for presentation at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 2–4 February 2009, and revised for publication. Original manuscript received for review 3 November 2008. Revised manuscript received for review 22 September 2009. Paper peer approved 30 September 2009. Summary Oil shale is a highly abundant energy resource, though commercial production has yet to be realized. Thermal in-situ upgrading processes for producing hydrocarbons from oil shale have gained attention recently, however, in part because of promising results reported by Shell using its in-situ conversion process (Crawford et al. 2008). This and similar processes entail heating the oil shale to approximately 700°F (371°C), where the kerogen in the shale decomposes through a series of chemical reactions into liquid and gas products. In this paper, we present a detailed numerical formulation of the in-situ upgrading process. Our model, which can be characterized as a thermal/compositional, chemical reaction, and flow formulation, is implemented into Stanford’s General Purpose Research Simulator (GPRS). The formulation includes strongly temperature-dependent kinetic reactions, fully compositional flow and transport, and a model for the introduction of heat into the formation through downhole heaters. We present detailed simulation results for representative systems. The model and heating patterns are based on information in Shell publications; chemical-reaction and thermodynamic data are from previously reported pyrolysis experiments. After a relatively modest degree of parameter adjustment (with parameters restricted to physically realistic ranges), our results for oil and gas production are in reasonable agreement with available field data. We also investigate various sensitivities and show how production is affected by heater temperature and location. The ability to model these effects will be essential for the eventual design and optimization of in-situ upgrading operations.

Numerical Simulation of the In-Situ Upgrading of Oil Shale

Deep-learning-based surrogate flow modeling and geological parameterization for data assimilation in 3D subsurface flow

Coarse scale equations applicable to two phase flow in heterogeneous reservoirs are developed via a volume average of the fine scale saturation equation. The resulting coarse scale description, in the form of an average saturation equation and a sequence of moment equations, is then used to assess several methods for the upscaling of detailed reservoir characterizations. The approaches considered are the use of pseudo‐relative permeabilities, the nonuniform coarsening of the fine grid geostatistical model, and the use of higher moments of the fine scale variables. Using the volume averaged equations as a framework, the underlying assumptions, strengths and limitations of each of these methods are discussed. Previous findings demonstrating the accuracy of coarse scale relative permeability functions based on higher moments are readily explained in terms of the volume average saturation and moment equations. Finally, the volume averaged equations are simplified for the unit mobility ratio case and applied to the direct solution of a model coarse scale problem.

Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to existing upscaling techniques

The relationship of the axisymmetric flow between large but finite coaxial rotating disks to the von Karman similarity solution is studied. By means of a combined asymptotic – numerical analysis, the flow between finite disks of arbitrarily large aspect ratio, where the aspect ratio is defined as the ratio of the disk radii to the gap width separating the disks, is examined for two different end conditions: a ‘closed’ end (shrouded disks) and an ‘open’ end (unshrouded or free disks). Complete velocity and pressure fields in the flow domain between the finite rotating disks, subject to both end conditions, are determined for Reynolds number (based on gap width) up to 500 and disk rotation ratios between 0 and – 1. It is shown that the finite-disk and similarity solutions generally coincide over increasingly smaller portions of the flow domain with increasing Reynolds number for both end conditions. In some parameter ranges, the finite-disk solution may not be of similarity form even near the axis of rotation. It is also seen that the type of end condition may determine which of the multiple similarity solutions the finite-disk flow resembles, and that temporally unstable similarity solutions may qualitatively describe steady finite-disk flows over a portion of the flow domain. The asymptotic – numerical method employed has potential application to related rotating-disk problems as well as to a broad class of problems involving flow in regions of large aspect ratio.

On rotating disk flow

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