Jefferson L. M. A. Gomes

Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

Numerical simulation of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. The governing equations are the continuity equation and Darcy’s law. A novel control volume finite element (CVFE) approach is developed to discretize the governing equations in which a node-centered control volume approach is applied for the saturation equation, while a CVFE method is used for discretization of the pressure equation. We embed the discrete continuity equation into the pressure equation and ensure that the continuity equation is exactly enforced. Furthermore, the scheme is equipped with dynamic anisotropic mesh adaptivity which uses a metric tensor field approach, based on the curvature of fields of interest, to control the size and shape of elements in the metric space. This improves the resolution of the mesh in the zones of dynamic interest. Moreover, the mesh adaptivity algorithm employs multi-constraints on element size in different regions of the porous medium to resolve multi-scale transport phenomena. The advantages of mesh adaptivity and the capability of the scheme are demonstrated for simulation of flow in several challenging computational domains. The scheme captures the key features of flow while preserving the initial geometry and can be applied for efficient simulation of flow in heterogeneous porous media and geological formations.

Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles. The inverse problem is formulated as a sequential data integration problem. Gaussian process regression is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen–Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized EnKF algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models.

Space-dependent kinetics simulation of a gas-cooled fluidized bed nuclear reactor

In this paper we present numerical simulations of a conceptual helium-cooled fluidized bed thermal nuclear reactor. The simulations are performed using the coupled neutronics/multi-phase computational fluid dynamics code finite element transient criticality which is capable of modelling all the relevant non-linear feedback mechanisms. The conceptual reactor consists of an axi-symmetric bed surrounded by graphite moderator inside which 0.1 cm diameter TRISO-coated nuclear fuel particles are fluidized. Detailed spatial/temporal neutron flux and temperature profiles have been obtained providing valuable insight into the power distribution and fluid dynamics of this complex system. The numerical simulations show that the unique mixing ability of the fluidized bed gives rise, as expected, to uniform temperature and particle distribution. This uniformity enhances the heat transfer and therefore the power produced by the reactor.

Reservoir Modeling for Flow Simulation Using Surfaces, Adaptive Unstructured Meshes, and Control-Volume-Finite-Element Methods

We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multi-scale geological heterogeneity and the prediction of flow through that heterogeneity. The research builds on 20+ years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation. Geological heterogeneities, whether structural, stratigraphic, sedimentologic or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a pre-defined grid. Petrophysical properties are uniform within the geologically-defined rock volumes, rather than within grid-cells. The resulting model is discretized for flow simulation using an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured using fewer cells than conventional corner-point or unstructured grids. Multiphase flow is simulated using a novel mixed finite element formulation centered on a new family of tetrahedral element types, PN(DG)-PN+1, which has a discontinuous N-order polynomial representation for velocity and a continuous (order N+1) representation for pressure. This method exactly represents Darcy force balances on unstructured meshes and thus accurately calculates pressure, velocity and saturation fields throughout the domain. Computational costs are reduced through (i) automatic mesh adaptivity in time and space and (ii) efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes, whilst preserving the surface-based representation of geological heterogeneity. Computational effort is thus focused on regions of the model where it is most required. Having validated the approach against a set of benchmark problems, we demonstrate its capabilities using a number of test models which capture aspects of geological heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly non-orthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geological features that are typically lost. The approach may also be used to capture near wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations and, in future applications, geomechanical models with fracture propagation, opening and closing. Introduction Reservoir modelling and flow simulation have become ubiquitous in the hydrocarbon industry over the past 20 years and the development of flow simulation models now follows a widely accepted workflow that is surprisingly similar across companies and academic institutions, regardless of the software tools used (e.g. Bryant and Flint, 1993): 1. The reservoir volume is defined by surfaces representing the top and base of the reservoir and surfaces representing key reservoir bounding faults. 2. Additional faults within the reservoir are represented by additional surfaces, across which the top and base surfaces may be offset. 3. The reservoir is subdivided into geologically defined zones by one or more surfaces, which may be offset across the fault surfaces. These surfaces may be interpreted from seismic data, or correlated between wells, in which case the topography of the surfaces may be dictated by the top and/or base reservoir surfaces. Conventional reservoir models may contain 10s to 100s of these surfaces.

A model of heat transfer dynamics of coupled multiphase‐flow and neutron‐radiation

Purpose – To present dynamical analysis of axisymmetric and three‐dimensional (3D) simulations of a nuclear fluidized bed reactor. Also to determine the root cause of reactor power fluctuations.Design/methodology/approach – We have used a coupled neutron radiation (in full phase space) and high resolution multiphase gas‐solid Eulerian‐Eulerian model.Findings – The reactor can take over 5 min after start up to establish a quasi‐steady‐state and the mechanism for the long term oscillations of power have been established as a heat loss/generation mechanism. There is a clear need to parameterize the temperature of the reactor and, therefore, its power output for a given fissile mass or reactivity. The fission‐power fluctuates by an order of magnitude with a frequency of 0.5‐2 Hz. However, the thermal power output from gases is fairly steady.Research limitation/implications – The applications demonstrate that a simple surrogate of a complex model of a nuclear fluidised bed can have a predictive ability and has...

An Investigation of Power Stabilization and Space-Dependent Dynamics of a Nuclear Fluidized-Bed Reactor

Abstract Previous work into the space-dependent kinetics of the conceptual nuclear fluidized bed has highlighted the sensitivity of fission power to particle movements within the bed. The work presented in this paper investigates a method of stabilizing the fission power by making it less sensitive to fuel particle movement. Steady-state neutronic calculations are performed to obtain a suitable design that is stable to radial and axial fuel particle movements in the bed. Detailed spatial/temporal simulations performed using the finite element transient criticality (FETCH) code investigate the dynamics of the new reactor design. A dual requirement of the design is that it has a moderate power output of ˜300 MW(thermal).

On an improved design of a fluidized bed nuclear reactor-I: Design modifications and steady-state features

Abstract This paper describes several modifications to the design of a fluidized bed nuclear reactor in order to improve its performance. The goal of these modifications is to achieve a higher power output, requiring an excess reactivity of 4% at maximum expansion of the bed. The modifications are also intended to obtain a larger safety margin when the reactor does not operate; a shutdown margin of 4% is required when the bed is in a packed state. The modifications include installing an embedded side absorber, changing the reactor cross-section area, and modifying the moderator-to-fuel ratio. The new design based on the modifications related to the aforementioned parameters achieves the desired shutdown margin and the excess reactivity. A model describing the coupling of neutronics and thermal/fluid dynamics is developed, and it is used to study the behavior of the reactor at steady conditions. The results show that the reactor can achieve a high output temperature of 1163 K and produce a thermal power of ~120 MW. Further, the results indicate that the power level of the reactor can be controlled easily by adjusting the flow of helium into the core without any further use of control rods or other active control mechanisms.

A New Approach to Reservoir Modeling and Simulation Using Boundary Representation, Adaptive Unstructured Meshes and the Discontinuous Overlapping Control Volume Finite Element Method

We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous Nth-order representation for pressure and (N 1)th-order for velocity. The method conserves mass and ensures that the extended Darcy equations for multi-phase flow are exactly enforced, but does not require the use of control volumes (CVs) that span domain boundaries. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic features such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, in conjunction with dynamic mesh optimization, in which the mesh adapts in space and time to key solution fields such as pressure, velocity or saturation whilst honoring a surface-based representation of the underlying geologic heterogeneity, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The work presented is significant for two reasons. First, it resolves a long- standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media; second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization without compromising parallelization.

Asian Dust Transport in China: A Palaeoclimate and Modeling Study

We evaluate the ability of the regional chemistry/aerosol climate model REMOTE to simulate Asian dust transport over China in response to changing Asian monsoon conditions. Applied to years of different monsoon strength, model results are compared to dust fluxes measured in a 9.5 kyr peat core from NW Szechuan. This palaeoclimate archive provides an uninterrupted history of Holocene monsoon conditions and dust fluxes to the Eastern Tibetan Plateau and represents a solid long-term framework for evaluating model responses to climate change. We present preliminary model results for selected months of the year 1996, which displayed normal monsoon conditions. Simulation results suggest that dust deposition to the Eastern Tibetan Plateau is dominated by wet deposition during monsoon and pre-monsoon months. Model deposition fluxes agree within a factor of two with fluxes from relevant sections of the peat core, providing encouraging new data in the bid to assess future impacts of dust on climate. The yearly simulations must henceforth be carried out under dry and wet monsoon conditions and compared to relevant sections of the core.

Numerical Simulation of Air Flows in Street Canyons Using Mesh-Adaptive LES

In this study a novel approach for modelling urban atmospheric flows is presented. It uses a modified general purpose CFD model with anisotropic mesh adaptivity. The effect of traffic induced turbulence is modelled through a two-fluid approach giving the ability to explicitly model the movement of individual vehicles. Results are presented from the application of the model to a real urban area.