Phase-fitted Discrete Lagrangian Integrators

Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian integrators. The results show improved accuracy and total energy behaviour in Hamiltonian systems. Numerical tests on the long term integration (100000 periods) of the 2-body problem with eccentricity even up to 0.95 show the efficiency of the proposed approach. Finally, based on a geometrical evaluation of the frequency of the problem, a new technique for adaptive error control is presented

Production Data Analysis by Machine Learning

In this dissertation, I will present my research work on two different topics. The first topic is production data analysis of low-permeability well. The second topic is a quantitative evaluation of key completion controls on shale oil production. In Topic 1, I propose and investigate two novel methodologies that can be applied to improve the results of low-permeability well decline curve analysis. Specifically, I first proposed an iterative two-stage optimization algorithm for decline curve parameter estimation on the basis of two-segment hyperbolic model. This algorithm can be applied to find optimal parameter results from the production history data. By making use of a useful relation that exits between material balance time (MBT) and the original production profile, we propose a three-step diagnostic approach for the preliminary analysis of production history data, which can effectively assist us in identifying fluid flow regimes and increase our confidence in the estimation of decline curve parameters. The second approach is a data-driven method for primary phase production forecasting. Functional principal component analysis (fPCA) is applied to extract key features of production decline patterns on basis of multiple wells with sufficiently long production histories. A predictive model is then built using principal component functions obtained from the training production data set. Finally, we make predictions for the test wells to assess the quality of prediction with reference to true production data. Both methods are validated using field data and the accuracy of production forecasts gives us confidence in the new approaches. In Topic 2, generalized additive model (GAM) is applied to investigate possibly nonlinear associations between production and key completion parameters (e.g., completed lateral length, proppant volume per stage, fluid volume per stage) while accounting for the influence of different geological environments on hydrocarbon production. The geological cofounding effect is treated as a random clustered effect and incorporated in the GAM model by means of a state-of-the-art statistical machine learning method graphic fused LASSO. We provide several key findings on the relation between completion parameters and hydrocarbon production, which provide guidance in the development of efficient completion practices

Production Data Analysis by Machine Learning

In this dissertation, I will present my research work on two different topics. The first topic is production data analysis of low-permeability well. The second topic is a quantitative evaluation of key completion controls on shale oil production. In Topic 1, I propose and investigate two novel methodologies that can be applied to improve the results of low-permeability well decline curve analysis. Specifically, I first proposed an iterative two-stage optimization algorithm for decline curve parameter estimation on the basis of two-segment hyperbolic model. This algorithm can be applied to find optimal parameter results from the production history data. By making use of a useful relation that exits between material balance time (MBT) and the original production profile, we propose a three-step diagnostic approach for the preliminary analysis of production history data, which can effectively assist us in identifying fluid flow regimes and increase our confidence in the estimation of decline curve parameters. The second approach is a data-driven method for primary phase production forecasting. Functional principal component analysis (fPCA) is applied to extract key features of production decline patterns on basis of multiple wells with sufficiently long production histories. A predictive model is then built using principal component functions obtained from the training production data set. Finally, we make predictions for the test wells to assess the quality of prediction with reference to true production data. Both methods are validated using field data and the accuracy of production forecasts gives us confidence in the new approaches. In Topic 2, generalized additive model (GAM) is applied to investigate possibly nonlinear associations between production and key completion parameters (e.g., completed lateral length, proppant volume per stage, fluid volume per stage) while accounting for the influence of different geological environments on hydrocarbon production. The geological cofounding effect is treated as a random clustered effect and incorporated in the GAM model by means of a state-of-the-art statistical machine learning method graphic fused LASSO. We provide several key findings on the relation between completion parameters and hydrocarbon production, which provide guidance in the development of efficient completion practices

Dynamic threshold policy for delaying and breaking commitments in transportation auctions

In this paper we consider a transportation procurement auction consisting of shippers and carriers. Shippers offer time sensitive pickup and delivery jobs and carriers bid on these jobs. We focus on revenue maximizing strategies for shippers in sequential auctions. For this purpose we propose two strategies, namely delaying and breaking commitments. The idea of delaying commitments is that a shipper will not agree with the best bid whenever it is above a certain reserve price. The idea of breaking commitments is that the shipper allows the carriers to break commitments against certain penalties. The benefits of both strategies are evaluated with simulation. In addition we provide insight in the distribution of the lowest bid, which is estimated by the shippers

Simulations of Unsteady Shocks via a Finite-Element Solver with High-Order Spatial and Temporal Accuracy

This research aims to improve the modeling of stationary and moving shock waves by adding an unsteady capability to an existing high-spatial-order, finite-element, streamline upwind/Petrov-Galerkin (SU/PG), steady-state solver and using it to examine a novel shock capturing technique. Six L-stable, first- through fourth-order time-integration methods were introduced into the solver, and the resulting unsteady code was employed on three canonical test cases for verification and validation purposes: the two-dimensional convecting inviscid isentropic vortex, the two-dimensional circular cylinder in cross ow, and the Taylor-Green vortex. Shock capturing is accomplished in the baseline solver through the application of artificial diffusion in supersonic cases. When applied to inviscid problems, especially those with blunt bodies, numerical errors from the baseline shock sensor accumulated in stagnation regions, resulting in non-physical wall heating. Modifications were made to the solver\u27s shock capturing approach that changed the calculation of the artificial diffusion flux term (Fad) and the shock sensor. The changes to Fadwere designed to vary the application of artificial diffusion directionally within the momentum equations. A novel discontinuity sensor, derived from the entropy gradient, was developed for use on inviscid cases. The new sensor activates for shocks, rapid expansions, and other ow features where the grid is insufficient to resolve the high-gradient phenomena. This modified shock capturing technique was applied to three inviscid test cases: the blunt-body bow shock of Murman, the planar Noh problem, and the Mach 3 forward-facing step of Colella and Woodward

Point-actuated feedback control of multidimensional interfaces

We consider the application of feedback control strategies with point actuators to stabilise desired interface shapes. We take a multidimensional Kuramoto--Sivashinsky equation as a test case; this equation arises in the study of thin liquid films, exhibiting a wide range of dynamics in different parameter regimes, including unbounded growth and full spatiotemporal chaos. In the case of limited observability, we utilise a proportional control strategy where forcing at a point depends only on the local observation. We find that point-actuated controls may inhibit unbounded growth of a solution, if they are sufficient in number and in strength, and can exponentially stabilise the desired state. We investigate actuator arrangements, and find that the equidistant case is optimal, with heavy penalties for poorly arranged actuators. We additionally consider the problem of synchronising two chaotic solutions using proportional controls. In the case when the full interface is observable, we construct feedback gain matrices using the linearised dynamics. Such controls improve on the proportional case, and are applied to stabilise non-trivial steady and travelling wave solutions

Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells

This article is an attempt to provide a self consistent picture, including existence analysis and numerical solution algorithms, of the mathematical problems arising from modeling photocurrent transients in Organic-polymer Solar Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear diffusion-reaction partial differential equations (PDEs) with electrostatic convection, coupled to a kinetic ordinary differential equation (ODE). We propose a suitable reformulation of the model that allows us to prove the existence of a solution in both stationary and transient conditions and to better highlight the role of exciton dynamics in determining the device turn-on time. For the numerical treatment of the problem, we carry out a temporal semi-discretization using an implicit adaptive method, and the resulting sequence of differential subproblems is linearized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then, we use exponentially fitted finite elements for the spatial discretization, and we carry out a thorough validation of the computational model by extensively investigating the impact of the model parameters on photocurrent transient times.Comment: 20 pages, 11 figure

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation