Modeling of multicomponent diffusions and natural convection in unfractured and fractured media by discontinuous Galerkin and mixed methods

Computation of the distribution of species in hydrocarbon reservoirs from diffusions (thermal, molecular, and pressure) and natural convection is an important step in reservoir initialization. Current methods, which are mainly based on the conventional finite‐difference approach, may not be numerically efficient in fractured and other media with complex heterogeneities. In this work, the discontinuous Galerkin (DG) method combined with the mixed finite element (MFE) method is used for the calculation of compositional variation in fractured hydrocarbon reservoirs. The use of unstructured gridding allows efficient computations for fractured media when the cross flow equilibrium concept is invoked. The DG method has less numerical dispersion than the upwind finite‐difference methods. The MFE method ensures continuity of fluxes at the interface of the grid elements. We also use the local DG (LDG) method instead of the MFE to calculate the diffusion fluxes. Results from several numerical examples are presented to demonstrate the efficiency, robustness, and accuracy of the model. Various features of convection and diffusion in homogeneous, layered, and fractured media are also discussed.     

An efficient preconditioner for the fast simulation of a 2D stokes flow in porous media

We consider an efficient preconditioner for a boundary integral equation (BIE) formulation of the two‐dimensional Stokes equations in porous media. While BIEs are well‐suited for resolving the complex porous geometry, they lead to a dense linear system of equations that is computationally expensive to solve for large problems. This expense is further amplified when a significant number of iterations is required in an iterative Krylov solver such as generalized minimial residual method (GMRES). In this paper, we apply a fast inexact direct solver, the inverse fast multipole method, as an efficient preconditioner for GMRES. This solver is based on the framework of ‐matrices and uses low‐rank compressions to approximate certain matrix blocks. It has a tunable accuracy ε and a computational cost that scales as . We discuss various numerical benchmarks that validate the accuracy and confirm the efficiency of the proposed method. We demonstrate with several types of boundary conditions that the preconditioner is capable of significantly accelerating the convergence of GMRES when compared to a simple block‐diagonal preconditioner, especially for pipe flow problems involving many pores.     

Modelling and simulation of automated manufacturing systems for evaluation of complex schedules

Automated manufacturing systems have been studied widely in terms of scheduling. As technology evolves, the behaviour of tools in automated manufacturing systems has become complicated. Therefore, mathematical approaches to the analysis of complex schedules no longer reflect reality. In this paper, we propose a systematic way of conducting simulation experiments to evaluate the complex operating schedules of automated manufacturing systems. A simulation model is based on a timed Petri net to take advantage of its mathematical strength. Since a Petri net cannot itself have token firing rules, we introduce additional states called operational states. Operational states are not directly related to a Petri net, and are only used for decision making. In addition, a decision function that is responsible for the conflict resolution of a Petri net model and an operational state transition function are introduced. The parallel simulation concept is also suggested by dividing a Petri net into several independent decision sub-nets. A multi-cluster tool system for semiconductor manufacturing is analysed as an application.     

Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay

Adaptive control techniques can be applied to dynamical systems whose parameters are unknown. We propose a technique based on control and numerical analysis approaches to the study of the stability and accuracy of adaptive control algorithms affected by time delay. In particular, we consider the adaptive minimal control synthesis (MCS) algorithm applied to linear time‐invariant plants, due to which, the whole controlled system generated from state and control equations discretized by the zero‐order‐hold (ZOH) sampling is nonlinear. Hence, we propose two linearization procedures for it: the first is via what we term as physical insight and the second is via Taylor series expansion. The physical insight scheme results in useful methods for a priori selection of the controller parameters and of the discrete‐time step. As there is an inherent sampling delay in the process, a fixed one‐step delay in the discrete‐time MCS controller is introduced. This results in a reduction of both the absolute stability regions and the controller performance. Owing to the shortcomings of ZOH sampling in coping with high‐frequency disturbances, a linearly implicit L‐stable integrator is also used within a two degree‐of‐freedom controlled system. The effectiveness of the methodology is confirmed both by simulations and by experimental tests. Copyright © 2009 John Wiley & Sons, Ltd.     

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

This paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows:

• A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework.
• An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated.
• An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem.
• The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.

All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN ²L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of tertiary treatment by nanofiltration and reverse osmosis for water reuse in denim textile industry

The wastewaters resulting from different baths of a dyeing factory specialized in denim fabric are collected and treated by an activated sludge plant. This study investigated the coupling of activated sludge treatment with either nanofiltration (NF) or reverse osmosis (RO) to recycle water and reuse it in the process. We first conducted NF experiments with a HL membrane in different configurations: dead end and cross-flow for flat sheets and also in spiral wound form. Results on water permeation and salt rejection show that performances are configuration dependent. Then, for the study of the NF/RO textile wastewater treatment, experiments were conducted with spiral wound membranes in order to be closest to the industrial configuration. After analyzing the removal efficiencies of suspended solids and chemical oxygen demand (COD) of the treatment plant, we conducted NF experiments using an HL2514TF spiral wound membrane preceded by ultrafiltration (UF) treatment. We used as well an RO membrane (AG2514TF) to compare performances in water yield and quality for the same pumping costs. The results show that NF allows higher yield, while respecting the Tunisian standard of water reuse (COD < 90 mg L⁻¹). Above 9 bar, the TDS rejection reaches 60% and the hardness is lower than the factory constraint (100 mg L⁻¹ CaCO₃), allowing the reuse of the water in the process.     

Analytical approximation for invasion and endemic thresholds,and the optimal control of epidemics in spatially explicit individual-based models

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial'' and ‘non-spatial'' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.