496 research outputs found
Numerical modelling of multi-phase multi-component reactive transport in the Earth's interior
This is a pre-copyedited, author-produced PDF of an article accepted for publication in
Geophysical journal international following peer review. The version of record Oliveira, B.,
Afonso, J., Zlotnik, S., Diez, P. Numerical modelling of multi-phase multi-component reactive transport in the Earth's interior. "Geophysical journal international", 1 Gener 2018, vol. 212, nĂşm. 1, p. 345-388 is available online at: https://doi.org/10.1093/gji/ggx399.We present a conceptual and numerical approach to model processes in the Earth's interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multi-component in the sense that the compositions of the system and its constituent thermodynamic phases are expressed by a full set of fundamental chemical components (e.g. SiO, AlO, MgO, etc) rather than proxies. In contrast to previous approaches these chemical components evolve, react with, and partition into, different phases with different physical properties according to an internally-consistent thermodynamic model. This enables a thermodynamically-consistent coupling of the governing set of balance equations. Interfacial processes such as surface tensions and/or surface energy contributions to the dynamics and energetics of the system are also taken into account. The model presented here describes the evolution of systems governed by Multi-Phase Multi-Component Reactive Transport (MPMCRT) based on Ensemble Averaging and Classical Irreversible Thermodynamics principles. This novel approach provides a flexible platform to study the dynamics and non-linear feedbacks occurring within various natural systems at different scales. This notably includes major-and trace-element transport, diffusion-controlled trace-element re-equilibration or rheological changes associated with melt generation and migration in the Earth's mantle.Peer ReviewedPostprint (author's final draft
Reactive Flows in Deformable, Complex Media
Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today
Reactive Flows in Deformable, Complex Media
Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above
Numerical simulation of fluid flow, proppant transport and fracture propagation in hydraulic fractures for unconventional reservoirs.
The distribution of proppant injected in hydraulic fractures significantly affects fracture-conductivity and well-performance. The proppant transport and suspension in thin fracturing fluid used in unconventional reservoirs are considerably different from those of fracturing fluids in conventional reservoirs, due to the very low viscosity of fracturing fluids used in the unconventional reservoirs, poor ability to suspend proppants and hence quick deposition of the proppants. This research presents the development of a three-dimensional computational fluid dynamics (CFD) modelling technique for the prediction of proppant-fluid multiphase flow in hydraulic fractures for unconventional reservoirs. The Eulerian-Lagrangian multiphase modelling approach has been applied to model the fluid flow and proppant transport, and the kinetic theory of granular flow is used to model the inter-proppant, fluid-proppant and proppantwall interactions. The existing proppant transport models ignore the fluid leak-off effect from the fracture side wall and the effect of fracture roughness. Thus, at the interface between the fracture and surrounding porous medium, the mass flow rate from the fracture to porous rock is calculated based on the permeability and porosity of the rock. The leakage mass flow rate is then used to define the mass and momentum source term at the fracture wall as a user-defined function, to investigate the proppant transport in hydraulic fractures with fluid leak-off effect. Furthermore, the hydrodynamic and mechanical behaviour of proppant transport on fracture roughness was studied in detail using different rough fracture profiles, and a relationship between the fracture roughness and proppant transport velocity is proposed. Lastly, an integrated model is developed, which simulates the proppant transport in dynamically propagating hydraulic fractures. The existing models either model the proppant transport physics in static predefined fracture geometry or account for the analytical models for defining the fracture propagation using linear elastic fracture mechanics. This limits the fracture propagation model to brittle rocks and neglect plastic deformations. Thus, in the present study, the fracture propagation was modelled using the extended finite element method (XFEM) and cohesive zone model (CZM), which can model the plastic deformations in the ductile rock. The fracture propagation was coupled with the CFD based proppant transport model, to model the fluid flow and proppant transport. The parametric study was then performed to investigate the effect of variation in proppant properties, fracturing fluid properties and geomechanical properties on the proppant transport. This study has enhanced the understanding of the flow and interaction phenomenon between proppant and fracturing fluid, and provides a technique with potential application in fracturing design for increasing well-productivity. The model can accurately simulate the proppant transport dynamics in hydraulic fracture and the present study proposes a solution to a frequent fracture tip screen out challenge faced in the petroleum industry. Thus, the developed modelling techniques provide petroleum engineers with a more suitable option for designing hydraulic fracturing operations, simultaneously modelling fracture propagation and fluid flow with proppant transport, and improves confidence by accurately tracking the distribution of proppants inside the fracture
New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid
Seismic imaging of the mantle has revealed large and small scale
heterogeneities in the lower mantle; specifically structures known as large low
shear velocity provinces (LLSVP) below Africa and the South Pacific. Most
interpretations propose that the heterogeneities are compositional in nature,
differing in composition from the overlying mantle, an interpretation that
would be consistent with chemical geodynamic models. Numerical modeling of
persistent compositional interfaces presents challenges, even to
state-of-the-art numerical methodology. For example, some numerical algorithms
for advecting the compositional interface cannot maintain a sharp compositional
boundary as the fluid migrates and distorts with time dependent fingering due
to the numerical diffusion that has been added in order to maintain the upper
and lower bounds on the composition variable and the stability of the advection
method. In this work we present two new algorithms for maintaining a sharper
computational boundary than the advection methods that are currently openly
available to the computational mantle convection community; namely, a
Discontinuous Galerkin method with a Bound Preserving limiter and a
Volume-of-Fluid interface tracking algorithm. We compare these two new methods
with two approaches commonly used for modeling the advection of two distinct,
thermally driven, compositional fields in mantle convection problems; namely,
an approach based on a high-order accurate finite element method advection
algorithm that employs an artificial viscosity technique to maintain the upper
and lower bounds on the composition variable as well as the stability of the
advection algorithm and the advection of particles that carry a scalar quantity
representing the location of each compositional field. All four of these
algorithms are implemented in the open source FEM code ASPECT
Application of Streamline Simulation for Gas Displacement Processes
Performance evaluation of miscible and near-miscible gas injection processes is available through conventional finite difference (FD) compositional simulation, which is widely used for solving large-scale multiphase displacement problems that always require large computation time. A step can be taken to reduce the time needed by considering low-resolution compositional simulation. The model can be adversely affected by numerical dispersion and may fail to represent geological heterogeneities adequately. The number of fluid components can possibly be reduced at the price of less accurate representation of phase behaviour. Streamline methods have been developed in which fluid is transported along the streamlines instead of the finite difference grid. In streamline-based simulation, a 3D flow problem is decoupled into a set of 1D problems solved along streamlines, reducing simulation time and suppressing any numerical dispersion. Larger time steps and higher spatial resolution can be achieved in these simulations, particularly when sensitivity runs are needed to reduce study uncertainties. Streamline-based reservoir simulation, being orders of magnitude faster than the conventional finite difference methods, may mitigate many of the challenges noted above. For gas injection, the streamline approach could not provide a high resolution or adequate representation for the multiphase displacement.
In this work, the streamline simulations for both compositional and miscible gas injection were tested. In addition, the conventional gas injection scheme and detailed comparison between the FD simulation and the streamline approach are illustrated. A detailed comparison is given between the results of conventional FD simulation and the streamline approach for gas displacement processes. Finally, some guidelines are given on how the streamline method can potentially be used to enhance for gas displacement processes
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A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation
textThis dissertations focuses on solving the advection problem with the motivation of simulating transport in porous media. A quadrature based Eulerian-Lagrangian scheme is developed to solve the nonlinear advection problem in multiple spatial dimensions. The schemes combines the ideas of Lagrangian traceline methods with high order WENO reconstructions to compute the mass that flows into a given cell over a time step. These schemes are important since they have a relaxed CFL constraint, and can be run in parallel. In this thesis we provide two improvements to Eulerian-Lagrangian schemes. To do this an integration based WENO (IWENO) interpolation technique is derived by reconstructing the primitive function and differentiating. This technique gives a high order reconstruction of the mass at an arbitrary point. This WENO scheme is used to solve the linear advection problem. A scheme is derived by backwards tracing of quadrature points located on mesh elements. The mass at these tracepoints is used to compute the mass in the trace region, without resolving its boundary. This process defines a high order quadrature Eulerian-Lagrangian WENO (QEL-WENO) scheme that solves the multi-dimensional problem without the need for a spatial splitting technique. The second improvement is for solving the nonlinear advection problem using an approximate velocity field. The velocity field is used to transport mass in the manner of a standard Eulerian-Lagrangian scheme. Then a flux correction is applied to compute the flow across the tracelines. The contribution is to use a variation of the IWENO technique to reduce the stencil size of this computation. Numerical results are presented demonstrating the capabilities of the scheme. An application to two-phase flow in porous media is provided.Mathematic
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