PRISM :: Browsing by Author "Liao, Wenyuan"

Browsing by Author "Liao, Wenyuan"

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Open Access
A Class of Stochastic Path-Dependent Models and Controls
(2024-09-19) Yang, Yang; Qiu, Jinniao; Ware, Antony; Sezer, Deniz; Swishchuk, Anatoliy; Liao, Wenyuan; Huang, Minyi
This thesis explores controlled stochastic path-dependent differential systems and their applications in stock and energy markets. We first focus on a class of path-dependent stochastic optimal control problems within an infinite-dimensional framework. Our primary contribution is proving that the value function serves as the unique viscosity solution to the corresponding infinite-dimensional stochastic path-dependent Hamilton-Jacobi equation. Then, we investigate the introduction of path-dependent features in stochastic volatility models. The price-storage dynamic is studied in natural gas markets. We propose a novel stochastic path-dependent volatility model that incorporates path-dependence into both price volatility and storage increments. Chapter 1 focuses on the stochastic optimal control problem for infinite-dimensional differential systems that incorporate both path-dependence and measurable randomness. Unlike deterministic path-dependent cases, the value function emerges as a random field over the path space, characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. We propose a notion of viscosity solution and demonstrate that the value function is the unique viscosity solution to the associated SPHJ equation. Chapter 2 and 3 explores price-storage dynamics in natural gas markets. We introduce a novel stochastic path-dependent volatility model that incorporates path-dependence in both price volatility and storage increments. Model calibrations are performed for both price and storage dynamics. Additionally, we address the pricing problem for discrete-time swing options using the dynamic programming principle and propose a deep learning-based method for numerical approximations. A numerical algorithm is presented, accompanied by a convergence analysis of the deep learning approach. Chapter 4 outlines future research directions in stochastic path-dependent Hamilton-Jacobi-Bellman (HJB) equations, stochastic volatility models, mean field games and stochastic path-dependent filtering problems.
Open Access
A Compact ADI Finite Difference Method for 2D Reaction-Diffusion Equations with Variable Diffusion Coefficients
(2023-08) He, Mingyu; Liao, Wenyuan; Braverman, Elena; Long, Quan
Reaction-diffusion systems on a spatially heterogeneous domain have been widely used to model various biological applications. However, it is rarely possible to solve such partial differential equations (PDEs) analytically. Therefore, efficient and accurate numerical methods for solving such PDEs are desired. In this paper, we apply the well-known Pad\'{e} approximation-based operator splitting (ADI) scheme. The new scheme is compact and fourth-order accurate in space. Combined with the Richardson extrapolation, the method can be improved to fourth-order accurate in time. Stability analysis shows that the method is unconditionally stable; thus, a large time step can be used to improve the overall computational efficiency further, Numerical examples have also demonstrated the new scheme's high efficiency and high-order accuracy.
Open Access
A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation
(2015-03-25) Liao, Wenyuan
The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly stiff. Therefore numerical time integration methods with stiff stability such as implicit Runge-Kutta methods and implicit multistep methods are required to solve the large-scale stiff ODE system. However those methods are computationally expensive, especially for nonlinear cases. Rosenbrock method is efficient since it is iteration-free; however it suffers from order reduction when it is used for nonlinear parabolic partial differential equation. In this work we construct a new fourth-order Rosenbrock method to solve the nonlinear parabolic partial differential equation supplemented with Dirichlet or Neumann boundary condition. We successfully resolved the phenomena of order reduction, so the new method is fourth-order in time when it is used for nonlinear parabolic partial differential equations. Moreover, it has been shown that the Rosenbrock method is strongly A-stable hence suitable for the stiff ODE system obtained from compact finite difference discretization of the nonlinear parabolic partial differential equation. Several numerical experiments have been conducted to demonstrate the efficiency, stability, and accuracy of the new method.
Open Access
Compact High-order Finite Difference Schemes for Acoustic Wave Equations
(2021-01-05) Li, Keran; Liao, Wenyuan; Lamoureux, Michael P.; Liao, Wenyuan; Braverman, Elena; Liang, Dong; Ware, Antony Frank
This study developed three compact high-order finite difference schemes for acoustic wave equations. Benefiting from the compactness, the new schemes require less layers of boundary conditions than conventional finite difference schemes. All the three schemes work for acoustic wave equations with variable coefficients in homogeneous media, with the third one also being applicable to the case of heterogeneous density media. The first scheme is based on Padé approximation which is formally a product of the inverse of a finite difference operator and the conventional 2nd-order finite difference operator, thus some algebraic manipulation is necessary to discuss the product of operators. The second scheme is based on so-called combined finite difference method, which needs the boundary conditions for the second spatial derivatives and the needed boundary conditions can be derived by using the wave equation and usual Dirichlet boundary conditions themselves. The third scheme is also based on combined finite difference method, and it generalizes the second scheme so that it can also work in heterogeneous density media case, i.e., the Laplacian in the wave equations being divergence form. The stability of the first two schemes are established by an energy method, while the stability of the last scheme is obtained by an analogy of von Neumann analysis. All of these new schemes are proven to be conditionally stable with given Courant-Friedrichs-Lewy (CFL) numbers. Numerical experiments are conducted to verify the efficiency, accuracy and stability of the new schemes. It is expected that these new schemes will find extensive applications in both research and engineering areas.
Open Access
Credit Risk Pricing based on Epstein-Zin Preference
(2019-12-20) Ma, Junchi; Sezer, Deniz; Qiu, Jinniao; Swishchuk, Anatoliy V.; Liao, Wenyuan
We present a consumption-based equilibrium framework for credit risk pricing in an Epstein-Zin setting. The default time is modeled as the first hitting time of a default boundary. Bond investors have imperfect information about the firm value which is unobservable. The state variables, consumption and volatility are modeled as affine diffusion processes. Using the Epstein-Zin equilibrium solution as the pricing kernel, the price of a zero-coupon bond is expressed as the solution of a system of a two-dimensional parabolic partial differential equation (PDE) which is solved numerically. The price under the imperfect information is derived based on the solution of a stochastic partial differential equation (SPDE). Finally, We analyze the implications of imperfect information and firm parameters on the yield spreads.
Open Access
Credit Risk Pricing via Epstein-Zin Pricing Kernel
(2017) Ogunsolu, Mobolaji; Sezer, Deniz; Frei, Christoph; Badescu, Alexandru; Ware, Antony; David, Alexander; Liao, Wenyuan
We present an equilibrium framework for pricing corporate bonds with information delay in an Epstein-Zin setting. As in structural models of credit risk, the default time is modeled as the first hitting time of a default boundary by the unobservable process; the firm's asset value. The observable state variables; log consumption and volatility are affine processes which drive the unobservable firm's value process. The stochastic pricing kernel is expressed in terms of the state variables. The price of a zero-coupon bond is expressed as the solution of a multidimensional partial differential equation which is solved numerically. Our equilibrium price model is also calibrated to fit available corporate bond and consumption data. Finally, we analyze the implications of investor’s preferences and information delay on the credit yield spreads.
Open Access
Development of a New Parallel Thermal Reservoir Simulator
(2016-01-08) Zhong, He; Chen, Zhangxing (John); Liang, Dong; Azaiez, Jalel; Gates, Ian Donald; Liao, Wenyuan
Thermal reservoir simulation is the most complex of all reservoir simulators and thus the most computationally intensive. With the advent of computer science, today's commodity PC clusters consist of a large number of discrete computer processors distributed across a network. Improving robustness and performance of parallel reservoir simulators on new high performance computing architectures remains a key issue to address. New numerical difficulties and performance problems appear because computing architecture is very sensible to memory distribution and load balance. This project proposes a new domain partition algorithm based on a fully-distributed graph framework. A reservoir is divided into multiple subregions, where connections, defined by geometry and well perforation information, are weighted by transmissibility and well indices. The continuity of fluxes and better load balance are guaranteed. Different strategies with different message passing frequency and accuracy are proposed for high performance computation. The subregion coupling effects are released or distracted into a linear system according to the physical principles. Subregions are coupled dramatically at flooding fronts and high frequency phase-changing regions, which enhances messages passing through processors. An analytical Jacobian calculation method and a variable alignment scheme are developed in this thesis. They have the ability to simulate three-dimensional multi-component three-phase thermal processes, and are capable of determining different property estimation approaches, such as correlations or table interpolations. An automatic time step algorithm, different variable-ordering algorithms and a Gauss elimination technique are implemented to reduce the intensive computation of linear iterations and to speedup the simulation process. The simulator is validated by analytical and numerical experiments, which include the Buckley-Leverett problem and the fourth SPE comparative solution project. The capability of this simulator is demonstrated through cyclic steam stimulation, steam flooding and steam-assisted gravity drainage processes. Three different parallelism strategies are tested in this thesis. A highly scalability implementation is achieved. This efficient, accurate, and parallel thermal simulator is applicable to highly complex reservoir systems.
Open Access
Difference population equation with the variable Allee effect and periodic carrying capacity
(2018-08-09) Chugunova, Marina Alexandrovna; Bates, Larry M.; Badescu, Alexandru M.; Liao, Wenyuan; Chruchill, Richard C.
The subject of this research is the location, stability, and the basin of attraction for the equilibrium points and periodic solutions for the Ricker equation enhanced with the mechanism for both weak and strong types of the Allee effect and periodic carrying capacity. The research has shown that just an addition of one biological phenomenon to Ricker equation, namely, the Allee effect, significantly changes the necessary conditions for the equilibrium point of the equation to obtain stability. This also increases the range of the parameters which allow for the equilibrium solution or a cycle to remain globally asymptotically stable. It was shown that the p-periodic carrying capacity always generates the p-periodic solutions which can be global attractors. Embedding the mechanism for the strong Allee effect generates several basins of attraction with either an equilibrium point or a stable cycle as an attractor. Concavity was proven not necessary for the attenuant property of the cycle.
Open Access
Distributionally robust binary classifier under Wasserstein distance
(2024-09-08) Huang, Qian; Wu, Jingjing; Zhang, Qingrun; Liao, Wenyuan; Swishchuk, Anatoliy
The robustification of statistical models has been a popular topic for decades. Statistical robustification and robust optimization are the two main approaches in the literature, where the former stabilizes the model output by removing the outlier points while the latter concerns more the outlier points in making the conservative decisions. This thesis develops a novel robust optimization perspective to robustify a class of binary classifiers. Our model considers the worst-case distribution within a pre-determined uncertainty ball that centers at the given benchmark distribution with the radius calculated as per the Wasserstein distance. We derive the tractable formulation for the general problem. When focusing on the support vector machine (SVM), the general problem boils down to an easy-to-solve second- order cone programming problem. The robustified SVM is then applied to synthetic data with and without contamination, and our simulation studies show that our robustified SVM model can outperform the classical SVM and the extreme empirical loss SVM models under many circumstances.
Open Access
Explainable Autoencoder Deciphering Key Pathways Underlying Cancer Expression Patterns
(2021-09) Yu, Yang; Liao, Wenyuan; Zhang, Qingrun; Thierry Chekouo, Tekougang; Xuewen, Lu
Modern machine learning methods have been extensively utilized in gene expression data analysis. In particular, autoencoders (AE) have been employed in processing noisy and heterogenous RNA-Seq data. However, AEs usually lead to “black-box” hidden variables difficult to interpret, hindering downstream experimental validations and clinical translation. To bridge the gap between complicat-ed models and the biological interpretations, we developed a tool, XAE4Exp (eXplainable AutoEn-coder for Expression data), which integrates AE and SHapley Additive exPlanations (SHAP), a flagship technique in the field of eXplainable AI (XAI). It quantitatively evaluates the contributions of each gene to the hidden structure learned by an AE, substantially improving the expandability of AE outcomes. By applying XAE4Exp to The Cancer Genome Atlas (TCGA) breast cancer gene ex-pression data, we revealed intriguing pathways including cell damage management, cell cycle, immune system related pathways underlying breast cancer. This tool will enable researchers and practitioners to analyze high-dimensional expression data intuitively, paving the way towards broad-er uses of deep learning.
Open Access
Full waveform inversion combining rock physics for seismic reservoir characterization and monitoring
(2023-10-27) Hu, Qi; Innanen, Kristopher A.H.; Grana, Dario; Trad, Daniel Osvaldo; Liao, Wenyuan; Zheng, Yingcai
Quantitative estimation of rock physics properties, such as porosity, lithology, and fluid saturation, is an important part of reservoir characterization. Most current seismic workflows in this field are based on amplitude variation with offset (AVO). Full waveform inversion (FWI) methods, although computationally more complex than AVO approaches, can produce more accurate elastic models by extracting the full information content in the seismogram. Progress has been reported in using elastic FWI results as intermediate quantities to derive rock properties from seismic data. However, the question of whether FWI can be geared towards the direct determination of rock physics properties remains open. In this thesis, I formulate FWI with rock physics model parameterizations to directly estimate parameters of immediate interest in reservoir characterization. This approach allows examination of any rock physics property that has a well-defined relationship with elastic parameters. It also shares the same numerical structure as the conventional elastic FWI, allowing various existing inversion strategies to be used. The reliability of the approach is systematically examined using different synthetic examples and is quantified by comparing it to conventional two-step inversions. Building on this approach, I formulate a time-lapse FWI framework for quantitative seismic monitoring CO2 storage. The method is tested on synthetic data generated for the Johansen formation model. The results demonstrate this approach's robustness for retrieving static properties, such as porosity and mineral volumes, and dynamic reservoir properties, such as CO2 saturation. Moreover, with a joint rock physics model combining Gassmann’s equation with empirical pressure relations, I illustrate the potential of this approach for the simultaneous prediction of CO2 saturation and pore pressure. Finally, I apply a sequential inversion scheme combining elastic FWI and Bayesian rock physics inversion to a vertical seismic profile (VSP) dataset acquired with accelerometers and a collocated distributed acoustic sensing (DAS) fiber at the Carbon Management Canada’s Newell County Facility. The inverted porosity and lithology models are reasonably accurate at the well location and are geologically meaningful in spatial distribution. This baseline (before injection) study can be used to support later monitoring of CO2 storage.
Open Access
Inferences for Two-Component Mixture Models with Stochastic Dominance
(2018-01-18) Abedin, Tasnima; Wu, Jingjing; Lu, Xuewen; Leon, Alexander de; Liao, Wenyuan; Nettleton, Dan
In this thesis, we studied a two-component nonparametric mixture model with a stochastic dominance constraint, which is a model that arises naturally from genetic studies. For this model, we proposed and studied nonparametric estimation based on cumulative distribution functions (c.d.f.s) and maximum likelihood estimation (MLE) through multinomial approximation. In order to incorporate the stochastic dominance constraint, we introduced a semiparametric model structure for which we proposed and investigated both MLE and minimum Hellinger distance estimation (MHDE). We also proposed a hypothesis testing to test the validity of the semiparametric model. For the proposed methods, we investigated their asymptotic properties such as consistency and asymptotic normality theoretically and through simulation studies. Our numerical studies demonstrated that (1) all the proposed estimation methods work well; (2) the semiparametric model structure incorporates nicely the stochastic dominance constraint and thus the MLE and MHDE based on it are superior in terms of efficiency than the two estimation techniques that do not use this model structure; (3) the MHDE is much more robust than the MLE. To demonstrate the use of these methods, we applied them to several real data including publicly available grain data (Smith et al., 1986) and malaria data (Vonatsou et al., 1998).
Open Access
Local Factorization of Multidimensional Differential Operators to Optimize Implicit Solution Methods
(2021-05-14) Vestrum, Robert J.; Lamoureux, Michael P.; Trad, Daniel Osvaldo; Liao, Wenyuan
Solving multidimensional differential operators using implicit finite-difference methods involves a computationally intensive step of calculating the solution to a system that involves both the current and future state of the system. If a linear operator can be expressed as an affine combination of sufficiently many orthogonal finite-difference approximations, then it is possible to factor the operator as product of an upper triangular matrix and that matrix's adjoint. Using the factor calculated in this Affine Local Grid Factorization (ALG-F), it is possible to solve the system by simple back substitution followed by forward substitution resulting in an implicit scheme that is O(N) rather than O(N^2) typical in implicit finite-difference schemes. Included are the equations to calculate the ALG Factorization for the wave equation in two and three dimensions to demonstrate the method provides robust and accurate results.
Open Access
Merton Problem in Insurance
(2022-03) Fooladamoli, Ehsan; Swishchuk, Anatoliy; Swishchuk, Anatoliy; Liao, Wenyuan; Ambagaspitiya, Rohana
The goal of Insurance companies, like that of any other financial institution, is to maximize their wealth. In doing so, there are different parameters they have to consider, such as premium rate, number of claim arrivals, size of claim arrival, etc. Moreover, they can invest their money in risk-free and risky asset to earn some income from those resources as well. This thesis discusses the application of Merton problem in insurance and risk and how to solve it. That is, we design a trading strategy for an insurance company such that its utility is maximized over a given time horizon. We use General Compound Hawkes Process to model the insurance’s risk and use the corresponding diffusion approximation to approximate the risk using a diffusion process. Then, we proceed with solving the problem by Hamilton- Jacobi-Bellman equation. Finally, we show some simulation results based on the calibration on data from insurance companies in Germany and their interpretations.
Open Access
Model checking optimal finite-horizon control for probabilistic gene regulatory networks
(2017-12-14) Wei, Ou; Guo, Zonghao; Niu, Yun; Liao, Wenyuan
Abstract Background Probabilistic Boolean networks (PBNs) have been proposed for analyzing external control in gene regulatory networks with incorporation of uncertainty. A context-sensitive PBN with perturbation (CS-PBNp), extending a PBN with context-sensitivity to reflect the inherent biological stability and random perturbations to express the impact of external stimuli, is considered to be more suitable for modeling small biological systems intervened by conditions from the outside. In this paper, we apply probabilistic model checking, a formal verification technique, to optimal control for a CS-PBNp that minimizes the expected cost over a finite control horizon. Results We first describe a procedure of modeling a CS-PBNp using the language provided by a widely used probabilistic model checker PRISM. We then analyze the reward-based temporal properties and the computation in probabilistic model checking; based on the analysis, we provide a method to formulate the optimal control problem as minimum reachability reward properties. Furthermore, we incorporate control and state cost information into the PRISM code of a CS-PBNp such that automated model checking a minimum reachability reward property on the code gives the solution to the optimal control problem. We conduct experiments on two examples, an apoptosis network and a WNT5A network. Preliminary experiment results show the feasibility and effectiveness of our approach. Conclusions The approach based on probabilistic model checking for optimal control avoids explicit computation of large-size state transition relations associated with PBNs. It enables a natural depiction of the dynamics of gene regulatory networks, and provides a canonical form to formulate optimal control problems using temporal properties that can be automated solved by leveraging the analysis power of underlying model checking engines. This work will be helpful for further utilization of the advances in formal verification techniques in system biology.
Open Access
Near surface investigation with DAS for CO2 sequestration and monitoring
(2024-01-11) Qu, Luping; Innanen, Kris; Dettmer, Jan; Martin, Eileen; Liao, Wenyuan; Trad, Daniel
In this thesis, I investigate near-surface seismic properties and several geophysical methods mainly including surface wave dispersion inversion (SWDI) and full waveform inversion (FWI) for CO2 monitoring, focusing on the capabilities of Distributed Acoustic Sensing (DAS) technology. The study is underpinned by data collected from Newell County Facility, Alberta, Canada, employing seismic data acquired from both surface-deployed and vertical seismic profi le (VSP) DAS fiber. DAS data, characterized by broadband and dense spatial sampling, facilitate the extraction of high-resolution near-surface velocity pro les due to their enhanced signal-to-noise ratio and resolution in low-frequency components and multimode dispersion curves. The first segment of the study introduced several types of dispersion curves, explores trans-dimensional (TD) inversion, employing multimode dispersion curves and reversible-jump Markov Chain Monte Carlo (MCMC) sampling to generate probabilistic posterior density (PPD) estimates of model parameters. This approach yields inversion results that align well with known lithological data. This research showcases the potential of horizontal DAS data in high-resolution, near-surface investigations. Additionally, I developed a multi-step multiscale surface wave FWI. Utilizing DAS recorded surface waves, high-resolution S-wave velocity (Vs) and attenuation (quality factor Qs) models of the near-surface are obtained through FWI, offering improved lateral resolution and depth penetration compared to conventional surface-wave analysis. The inclusion of low-frequency components in DAS data effectively mitigates the cycle skipping challenge commonly associated with FWI, leading to high-resolution VS models that capture lateral variations effectively. I also addressed the challenge of noise in seismic data, particularly its impact on acoustic and elastic FWI models. By incorporating the data covariance matrix into the mis t function, this approach mitigates the effects of noise, improving the accuracy of the FWI models. Building on these methods, I applied anisotropic FWI with variable density to DAS recorded walk-away VSP data for characterizing subsurface velocity, anisotropy, and density structures. This technique, essential for time-lapse studies of CO2 injection and storage, proved effective in providing more accurate P-wave velocity, density models, and anisotropy parameters compared to isotropic FWI. In conclusion, this thesis demonstrates the potential of using DAS technology and advanced geophysical methods for near-surface investigation and CO2 monitoring. The integration of DAS data with trans-dimensional and varied FWI approaches, alongside noise mitigation strategies, offers a signi cant step forward in accurate and e cient subsurface characterization, crucial for environmental monitoring and carbon capture and storage initiatives.
Open Access
Novel Optimization Schemes for Full Waveform Inversion: Optimal Transport and Inexact Gradient Projection
(2021-03-09) Li, Da; Lamoureux, Michael P.; Liao, Wenyuan; Lamoureux, Michael P.; Liao, Wenyuan; Braverman, Elena; Innanen, Kristopher A.; Fear, Elise C.; Haber, Eldad
Full waveform inversion (FWI) is an important seismic inversion technique that provides high-resolution estimates of underground physical parameters. However, high-accuracy inverse results are not guaranteed due to the essential non-convexity characteristics of the FWI problem. This thesis focuses on designing novel optimization schemes for the FWI problem which improve the inverse results. Applying optimal transport (OT) based distances to the FWI problem is popular because they provide additional geometric information. The OT distances are designed for positive measures with equal mass, and the unbalanced optimal transport (UOT) distance can overcome the mass equality condition. A mixed distance is constructed which can also overcome the mass equality condition, and the convex properties for the shift, dilation, and amplitude change are proved. Both UOT distance and the proposed distance are applied to the FWI problem with normalization methods transforming the signals into positive functions. Numerical examples show that the optimal transport based distances outperform the traditional L2 distance in certain cases. The gradient projection methods are often used to solve constrained optimization problems, and the closed-form projection function is necessary since the projection has to be evaluated exactly. A constraint set expanding strategy is designed for the gradient projection methods such that the projection can be evaluated inexactly, which extends the application scope of the gradient projection methods. The convergence analysis is provided with proper assumptions. A priori information of the model is important to improve the inverse result, and an optimization scheme is proposed for incorporating multiple a priori information into the FWI problem. The optimization scheme is a combination of the scaled gradient projection method and a projection onto convex sets algorithm. Also, the L-BFGS Hessian approximation and the above constraint set expanding strategy are used. Numerical examples show that the proposed optimization scheme is flexible for integrating multiple types of constraint sets such as total variation constraint, sparsity constraint, box constraint, and hyperplane constraint into the FWI problem.
Open Access
Numerical Analysis of Enhanced Heavy Oil Recovery (EHOR) by Chemical Injection
(2016) GUO, ZIQIANG; CHEN, JOHN (ZHANGXIN); Dong, Mingzhe; Azaiez, Jalel; Maini, Brij; Liao, Wenyuan; Bai, Baojun
Chemical flooding has been proved to be technically feasible and economically affordable to increase oil recovery in western Canada heavy oil reservoirs. Numerical studies of experimental results are carried out to improve the understanding of EOR mechanism of chemical flooding of heavy oil. Polymer flooding of heavy oil on the lab scale shows appreciable incremental oil recovery. However, when it is extended to field scale, the high recovery efficiency usually cannot be achieved. Scaling-up analysis of polymer flooding of heavy oil is conducted in this research. Twenty-eight dimensionless scaling groups are derived using inspectional analysis and validated by numerical simulation. The effect of each scaling group on oil recovery is examined by sensitivity analysis. Nine scaling groups dominating the process are identified. These dominant scaling groups can be used to design scaled experiments to predict field-scale oil recovery by polymer flooding in heavy oil reservoirs. A fast and effective method to examine the potential of enhanced heavy oil recovery by polymer flooding is developed in this study. Experimental results of sand-pack polymer flooding tests, for heavy oil samples with different viscosities, are analyzed. For each heavy oil sample, the polymer viscosity-sensitive range, within which the incremental recovery increases dramatically with increasing polymer viscosity, is different. To facilitate the evaluation of polymer flooding potential for heavy oils with various viscosities, the oil-water mobility ratio at the end of waterflooding is chosen as a normalization factor. Using normalization, an identical oil-water mobility ratio-sensitive range can be obtained for heavy oils with different viscosities. Based on the normalized relationship, the potential of enhanced heavy oil recovery by polymer injection can be quickly and effectively evaluated. Experimental results of chemical flooding of heavy oil suggested that lower interfacial tension resulted in lower heavy oil recovery. Theoretical analysis is conducted to give a reasonable explanation to the detrimental effect of interfacial tension reduction on heavy oil displacement. The effect of interfacial tension reduction induced by surfactant during heavy oil displacement is further studied by carrying out linear stability analysis, tube bundle calculation and numerical simulations.
Open Access
Numerical Schemes for the Fractional Calculus and their Application to Image Feature Detection
(2018-06-08) Adams, Matthew Paul; Liao, Wenyuan; Boyd, Jeffrey Edwin; Aiffa, Mohammed; Rios, Cristian
Fractional calculus is an extension of integer-order differentiation and integration which explains many natural physical processes. New applications of the fractional calculus are in constant development. The current thesis introduces fractional differentiation to feature detection in digital images. The Harris-Laplace feature detector is adapted to use the non-local properties of the fractional derivative to include more information about image pixel perturbations when quantifying features. Numerical schemes for the computation of fractional derivatives and integrals are also presented, and methods for increasing their computational efficiency are discussed. An implementation of some numerical algorithms is introduced in this thesis as the Python software package differint. The geometric and physical interpretations of fractional derivatives are also included. The work in this thesis shows that the use of fractional derivatives in the Harris-Laplace detector leads to higher repeatability when detecting features in grayscale images. Applications of this development are suggested.
Open Access
Optimal Finite Difference Schemes for the Helmholtz Equation with PML
(2019-12-17) Dastour, Hatef; Liao, Wenyuan; Ware, Antony Frank; Lamoureux, Michael P.; Zinchenko, Yuriy
An efficient and accurate numerical scheme for solving the seismic wave equations is a key part in seismic wave propagation modeling. The pollution effect of high wavenumbers (the accuracy of the numerical results often deteriorates as the wavenumber increases) plays a critical role in the accuracy of these numerical schemes and it is inevitable in two and three dimensional Helmholtz equations. Optimal finite difference methods can offer a remedy to this problem; however, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome when the perfectly matched layer (PML) boundary condition is implemented. This study develops a number of optimal finite difference schemes for solving the Helmholtz equation in the presence of PML. In doing so, we implement two common strategies, derivative-weighting and point-weighting strategies, for constructing these schemes. Furthermore, a challenge for developing such methods is being consistent with the Helmholtz equation with PML. Thus, analytical and numerical proofs are provided to show the consistency of the schemes. Moreover, for each developed optimal finite difference method, error analysis for the numerical approximation of the exact wavenumber is provided. Based on minimizing the numerical dispersion, some optimal parameters strategies for each optimal finite difference schemes are recommended. Furthermore, several examples are provided to illustrate the accuracy and effectiveness of the new methods in reducing numerical dispersion.