5,401 research outputs found
Modelling and quantification of structural uncertainties in petroleum reservoirs assisted by a hybrid cartesian cut cell/enriched multipoint flux approximation approach
Efficient and profitable oil production is subject to make reliable predictions about
reservoir performance. However, restricted knowledge about reservoir distributed
properties and reservoir structure calls for History Matching in which the reservoir
model is calibrated to emulate the field observed history. Such an inverse problem
yields multiple history-matched models which might result in different predictions of
reservoir performance. Uncertainty Quantification restricts the raised model
uncertainties and boosts the model reliability for the forecasts of future reservoir
behaviour. Conventional approaches of Uncertainty Quantification ignore large scale
uncertainties related to reservoir structure, while structural uncertainties can influence
the reservoir forecasts more intensely compared with petrophysical uncertainty.
What makes the quantification of structural uncertainty impracticable is the need for
global regridding at each step of History Matching process. To resolve this obstacle, we
develop an efficient methodology based on Cartesian Cut Cell Method which decouples
the model from its representation onto the grid and allows uncertain structures to be
varied as a part of History Matching process. Reduced numerical accuracy due to cell
degeneracies in the vicinity of geological structures is adequately compensated with an
enhanced scheme of class Locally Conservative Flux Continuous Methods (Extended
Enriched Multipoint Flux Approximation Method abbreviated to extended EMPFA).
The robustness and consistency of proposed Hybrid Cartesian Cut Cell/extended
EMPFA approach are demonstrated in terms of true representation of geological
structures influence on flow behaviour. In this research, the general framework of
Uncertainty Quantification is extended and well-equipped by proposed approach to
tackle uncertainties of different structures such as reservoir horizons, bedding layers,
faults and pinchouts. Significant improvements in the quality of reservoir recovery
forecasts and reservoir volume estimation are presented for synthetic models of
uncertain structures. Also this thesis provides a comparative study of structural
uncertainty influence on reservoir forecasts among various geological structures
Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins
In this work we propose an Uncertainty Quantification methodology for
sedimentary basins evolution under mechanical and geochemical compaction
processes, which we model as a coupled, time-dependent, non-linear,
monodimensional (depth-only) system of PDEs with uncertain parameters. While in
previous works (Formaggia et al. 2013, Porta et al., 2014) we assumed a
simplified depositional history with only one material, in this work we
consider multi-layered basins, in which each layer is characterized by a
different material, and hence by different properties. This setting requires
several improvements with respect to our earlier works, both concerning the
deterministic solver and the stochastic discretization. On the deterministic
side, we replace the previous fixed-point iterative solver with a more
efficient Newton solver at each step of the time-discretization. On the
stochastic side, the multi-layered structure gives rise to discontinuities in
the dependence of the state variables on the uncertain parameters, that need an
appropriate treatment for surrogate modeling techniques, such as sparse grids,
to be effective. We propose an innovative methodology to this end which relies
on a change of coordinate system to align the discontinuities of the target
function within the random parameter space. The reference coordinate system is
built upon exploiting physical features of the problem at hand. We employ the
locations of material interfaces, which display a smooth dependence on the
random parameters and are therefore amenable to sparse grid polynomial
approximations. We showcase the capabilities of our numerical methodologies
through two synthetic test cases. In particular, we show that our methodology
reproduces with high accuracy multi-modal probability density functions
displayed by target state variables (e.g., porosity).Comment: 25 pages, 30 figure
Postprocessing of Non-Conservative Flux for Compatibility with Transport in Heterogeneous Media
A conservative flux postprocessing algorithm is presented for both
steady-state and dynamic flow models. The postprocessed flux is shown to have
the same convergence order as the original flux. An arbitrary flux
approximation is projected into a conservative subspace by adding a piecewise
constant correction that is minimized in a weighted norm. The application
of a weighted norm appears to yield better results for heterogeneous media than
the standard norm which has been considered in earlier works. We also
study the effect of different flux calculations on the domain boundary. In
particular we consider the continuous Galerkin finite element method for
solving Darcy flow and couple it with a discontinuous Galerkin finite element
method for an advective transport problem.Comment: 34 pages, 17 figures, 11 table
Finite volume schemes for diffusion equations: introduction to and review of modern methods
We present Finite Volume methods for diffusion equations on generic meshes,
that received important coverage in the last decade or so. After introducing
the main ideas and construction principles of the methods, we review some
literature results, focusing on two important properties of schemes (discrete
versions of well-known properties of the continuous equation): coercivity and
minimum-maximum principles. Coercivity ensures the stability of the method as
well as its convergence under assumptions compatible with real-world
applications, whereas minimum-maximum principles are crucial in case of strong
anisotropy to obtain physically meaningful approximate solutions
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