Semi-Analytical Modeling of Fluid Flow and Solid Deformation in Heterogeneous Reservoirs Using Universal Boundary Integral Approaches


Book Description

In the Canadian oil and gas industry, heavy oil and unconventional reservoirs play a vital role in sustaining the production of crude oil and face tremendous technical challenges of enhancing recovery while reducing environmental footprints. Among various development technologies, the cold heavy oil production with sand (CHOPS) and hydraulic fracturing techniques have been widely applied in Western Canadian basins to unlock the unconsolidated heavy oil and tight formation reservoirs, respectively. Both technologies are proved to be efficient during the primary production period; however, they suffer sharp production decline and low recovery factor. Moreover, during the enhanced oil recovery (EOR) phase, the existence of wormholes and fractures will cause conformance problems and early polymer injection breakthrough. Therefore, better understanding of the wormholes distributions in CHOPS reservoirs and more reliable description of fractures in tight formations become crucial for Canadian operators to design EOR pilots and operate full field applications. Reservoir characterization and modeling of CHOPS reservoirs with wormholes and fractured tight formations face numerous technical issues due to the existence of wormholes and fractures, which make the system no longer homogeneous and cause more complex problems in fluid flow and solid deformation. The boundary element method (BEM), which has been widely applied to solve for fluid flow and solid deformation problems, however, is limited to homogeneous systems. To inherit the merits of BEM such as near-analytical accuracy and negligible space and time subdivision, this research aims at developing boundary integral approaches, as extensions of BEM, to heterogeneous reservoirs with arbitrary wormhole distributions, realistic fracture morphologies, and variation of geological facies. Moreover, field operators have observed that the in-situ stress state will be altered during hydraulic fracturing with associated stress shadow effects. The depletion-induced stress changes will also cause fracture closure and stress reorientation. Accordingly, the boundary integral approaches are further extended to solve for depletion-induced stress change due to poroelastic and mechanical effects in a heterogeneous reservoir with arbitrary distribution of porosity and permeability. The universal boundary integral approaches, which include the integration of various fundamental solutions along boundaries, have been proposed in this study. The developed boundary integral approaches are benchmarked by comparing with analytical solutions and numerical simulations. Representative cases are also presented to analyze complicated heterogeneous problems. Applications of the universal boundary integral approaches for heterogeneous systems are exemplified in the areas of wormhole coverage estimation, pressure and rate transient analysis of heterogeneous reservoirs, spatial-temporal stress evolution of multi-stage fractured horizontal wells, and evaluation of refracturing upside.




Unsteady-state Fluid Flow


Book Description

The ubiquitous examples of unsteady-state fluid flow pertain to the production or depletion of oil and gas reservoirs. After introductory information about petroleum-bearing formations and fields, reservoirs, and geologic codes, empirical methods for correlating and predicting unsteady-state behavior are presented. This is followed by a more theoretical presentation based on the classical partial differential equations for flow through porous media.Whereas these equations can be simplified for the flow of (compressible) fluids, and idealized solutions exist in terms of Fourier series for linear flow and Bessel functions for radial flow, the flow of compressible gases requires computer solutions, read approximations. An analysis of computer solutions indicates, fortuitously, that the unsteady-state behavior can be reproduced by steady-state density or pressure profiles at successive times. This will demark draw down and the transition to long-term depletion for reservoirs with closed outer boundaries.As an alternative, unsteady-state flow may be presented in terms of volume and surface integrals, and the methodology is fully developed with examples furnished. Among other things, permeability and reserves can be estimated from well flow tests.The foregoing leads to an examination of boundary conditions and degrees of freedom and raises arguments that the classical partial differential equations of mathematical physics may not be allowable representations. For so-called open petroleum reservoirs where say water-drive exists, the simplifications based on successive steady-state profiles provide a useful means of representation, which is detailed in the form of material balances.Unsteady-State Fluid Flow provides:• empirical and classical methods for correlating and predicting the unsteady-state behavior of petroleum reservoirs• analysis of unsteady-state behavior, both in terms of the classical partial differential equations, and in terms of volume and surface integrals• simplifications based on successive steady-state profiles which permit application to the depletion of both closed reservoirs and open reservoirs, and serves to distinguish drawdown, transition and long-term depletion performance.




Mathematical Modeling for Flow and Transport Through Porous Media


Book Description

This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'. The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media. The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.




Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs


Book Description

This investigation is an outgrowth of my doctoral dissertation at Princeton University. I am particularly grateful to Professors George F. Pinder and William G. Gray of Princeton for their advice during both my research and my writing. I believe that finite-element collocation holds promise as a numer ical scheme for modeling complicated flows in porous media. However, there seems to be a "conventional wisdom" maintaining that collocation is hopelessly beset by oscillations and is, in some way, fundamentally inappropriate for multiphase flows. I hope to dispel these objections, realizing that others will remain for further work. The U. S. National Science Foundation funded much of this study through grant number NSF-CEE-8111240. TABLE OF CONTENTS ABSTRACT ;; FOREWORD ;; ; CHAPTER ONE. THE PHYSICAL SYSTEM. 1.1 Introduction. 1 1.2 The reservoir and its contents. 5 1.3 Reservoir mechanics. 9 1.4 Supplementary constraints. 18 1.5 Governing equations. 26 CHAPTER TWO. REPRESENTING FLUID-PHASE BEHAVIOR. 39 2.1 Thermodynamics of the fluid system. 40 2.2 Standard equation-of-state methods. 45 2.3 Maxwell-set interpolation.




Semi-analytical Modelling of Fluid Flow in Unconventional Fractured Reservoirs Including Branch-fracture Permeability Field


Book Description

Growing demand for energy and unavailability of new viable energy resources have played a crucial role in the persistent exploitation of unconventional resources through multistage hydraulic fracturing. Currently, standard modelling approaches idealize a fractured media as an interplay of several homogeneous continuum of normal diffusive characteristics. However, evolved branch-fractures generate a space with extreme heterogeneity around primary fracture plane. The precise characterization of these branch-fractures is imperative for well performance analysis along with subdiffusive behaviour of unconventional matrices. This study presents two semi-analytical models that account for the branch-fracture permeability field and subdiffusion. The first model, Induced Branch-fracture Subdiffusive Flow model (SIBFF), accounts for exponential permeability field concept and subdiffusive transport behaviour of matrices. Compared to the earlier analytical models, the SIBFF model accounts for more comprehensive transport mechanisms and medium properties. The other model, Fractal Branch-fracture model, couples fractal porosity/permeability distribution of branch-fracture and subdiffusion to account for more detailed description of stimulated reservoir volume (SRV) and unfractured inner region. The wellbore pressure solution is derived by discretizing the reservoir into several flow regions and imposing both flux and pressure continuity at the interface between contiguous segments. The inclusion of permeability field and fractional flux law introduces important complexities to the mathematical model that are carefully resolved by implementing Bessel functions and Laplace transformation (LT). Finally, the solution is inverted to time domain using Gaver-Wynn-Rho (GWR) algorithm. This study also assessed the applicability of four numerical inversion methods and found GWR method more suitable and predictive. The sensitivity of important model parameters is presented. Results were verified analytically and validated against Niobrara and Eagleford field data. It is shown that the models could be implemented to quantify the efficiency of a stimulation job, to decide on the necessity of re-fracturing a formation and to analyze horizontal well performance with better predictive capability. The proposed models could further be employed to characterize different flow regimes for unconventional reservoirs.




Multi-scale Phenomena in Complex Fluids


Book Description

Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the ªrst two series of mini-courses from "Shanghai Summer School on Analysis and Numerics in Modern Sciences," which was held in 2004 and 2006 at Fudan University, Shanghai, China. This review volume of 5 chapters, covering various fields in complex fluids, places emphasis on multi-scale modeling, analyses and simulations. It will be of special interest to researchers and graduate students who want to work in the field of complex fluids.




Computer Modeling of Free-Surface and Pressurized Flows


Book Description

Computers are widely used for the analysis, design, and operation of water resource projects. This gives accurate results, allowing the analysis of complex systems which may not have been possible otherwise, and the investigation and comparison of several different alternatives in a short time, thereby reducing the project costs, optimizing design, and efficient utilization of resources. This volume compiles an edited version of the lecture notes specially prepared by 14 well-known European and North American researchers. Part I deals with free-surface flows. Governing equations are derived and their solution by the finite-difference, finite-element, and boundary-integral methods are discussed. Then, turbulence models, three-dimensional models, dam-break flow models, sediment transport models, and flood routing models are presented. Part II is related to the modeling of steady and transient pressurized flows. Governing equations for both single and two-component flows are derived and numerical methods for their solution are presented. The modeling of water quality in pipe networks, of cooling water systems, and slow and rapid transients is then discussed.




Hydrodynamics of Free Surface Flows


Book Description

A definitive guide for accurate state-of-the-art modelling of free surface flows Understanding the dynamics of free surface flows is the starting point of many environmental studies, impact studies, and waterworks design. Typical applications, once the flows are known, are water quality, dam impact and safety, pollutant control, and sediment transport. These studies used to be done in the past with scale models, but these are now being replaced by numerical simulation performed by software suites called “hydro-informatic systems”. The Telemac system is the leading software package worldwide, and has been developed by Electricité de France and Jean-Michel Hervouet, who is the head and main developer of the Telemac project. Written by a leading authority on Computational Fluid Dynamics, the book aims to provide environmentalists, hydrologists, and engineers using hydro-informatic systems such as Telemac and the finite element method, with the knowledge of the basic principles, capabilities, different hypotheses, and limitations. In particular this book: presents the theory for understanding hydrodynamics through an extensive array of case studies such as tides, tsunamis, storm surges, floods, bores, dam break flood waves, density driven currents, hydraulic jumps, making this a principal reference on the topic gives a detailed examination and analysis of the notorious Malpasset dam failure includes a coherent description of finite elements in shallow water delivers a significant treatment of the state-of-the-art flow modelling techniques using Telemac, developed by Electricité de France provides the fundamental physics and theory of free surface flows to be utilised by courses on environmental flows Hydrodynamics of Free Surface Flows is essential reading for those involved in computational fluid dynamics and environmental impact assessments, as well as hydrologists, and bridge, coastal and dam engineers. Guiding readers from fundamental theory to the more advanced topics in the application of the finite element method and the Telemac System, this book is a key reference for a broad audience of students, lecturers, researchers and consultants, right through to the community of users of hydro-informatics systems.




A Systems Description of Flow Through Porous Media


Book Description

This text forms part of material taught during a course in advanced reservoir simulation at Delft University of Technology over the past 10 years. The contents have also been presented at various short courses for industrial and academic researchers interested in background knowledge needed to perform research in the area of closed-loop reservoir management, also known as smart fields, related to e.g. model-based production optimization, data assimilation (or history matching), model reduction, or upscaling techniques. Each of these topics has connections to system-theoretical concepts. The introductory part of the course, i.e. the systems description of flow through porous media, forms the topic of this brief monograph. The main objective is to present the classic reservoir simulation equations in a notation that facilitates the use of concepts from the systems-and-control literature. Although the theory is limited to the relatively simple situation of horizontal two-phase (oil-water) flow, it covers several typical aspects of porous-media flow. The first chapter gives a brief review of the basic equations to represent single-phase and two-phase flow. It discusses the governing partial-differential equations, their physical interpretation, spatial discretization with finite differences, and the treatment of wells. It contains well-known theory and is primarily meant to form a basis for the next chapter where the equations will be reformulated in terms of systems-and-control notation. The second chapter develops representations in state-space notation of the porous-media flow equations. The systematic use of matrix partitioning to describe the different types of inputs leads to a description in terms of nonlinear ordinary-differential and algebraic equations with (state-dependent) system, input, output and direct-throughput matrices. Other topics include generalized state-space representations, linearization, elimination of prescribed pressures, the tracing of stream lines, lift tables, computational aspects, and the derivation of an energy balance for porous-media flow. The third chapter first treats the analytical solution of linear systems of ordinary differential equations for single-phase flow. Next it moves on to the numerical solution of the two-phase flow equations, covering various aspects like implicit, explicit or mixed (IMPES) time discretizations and associated stability issues, Newton-Raphson iteration, streamline simulation, automatic time-stepping, and other computational aspects. The chapter concludes with simple numerical examples to illustrate these and other aspects such as mobility effects, well-constraint switching, time-stepping statistics, and system-energy accounting. The contents of this brief should be of value to students and researchers interested in the application of systems-and-control concepts to oil and gas reservoir simulation and other applications of subsurface flow simulation such as CO2 storage, geothermal energy, or groundwater remediation.




New Trends In Fluid And Solid Models - Proceedings Of The International Conference In Honour Of Brian Straughan


Book Description

The Proceedings of the 1st Conference on New Trends in Fluid and Solid Models provide an overview of results and new models in fluid dynamics and, in general, in continuum mechanics. The contributions refer in particular to models in continuum mechanics, phase transitions, qualitative analysis for ODEs or PDEs models, Stability in fluids and solids, wave propagation, discontinuity and shock waves, and numerical simulations.