This book addresses the problems involved in the modelling and simulation of shale gas reservoirs at pore scale, and details recent advances in the field. It presents the construction of simulation methods, mainly using the lattice Boltzmann method (LBM), that describe sorption, flow, and transport in nanoporous shale with some case studies. This book highlights the nanoscale effects, ascribed to the large surface-to-volume ratio, on fluids occurrence and transport physics. It discusses some interesting phenomena occurs at nanoporous shale, such as absorbed water film, water condensation, sorption hysteresis, surface excess adsorption, Knudsen diffusion, surface diffusion, structural fluid density, no-slip boundary, etc. The key techniques and methods introduced in this book provide the basis for accurate prediction of gas-well productivity. The basic principles and modeling methods are also relevant to many other nanoporous applications in science and engineering. The book aims to provide a valuable reference resource for researchers and professional scientists and engineers working on shale gas development and nanoporous media research.

Shale gas production accounts for about 70% of the total natural gas production in the US. Yet it remains a nontrivial task to characterize the petrophysical properties of shale core samples either by experimental analysis or numerical simulations. Shale matrix has low porosity and permeability resulting from nanometer-scale pore sizes. Surface properties of shale can be quite inhomogeneous arising from complex mineralogy and diagenesis. Heterogeneous morphology and topology of the pore structure poses significant challenges on understanding fluid distribution and flow capacity. Pore scale simulations provide insight into the fundamental mechanisms of thermodynamics and hydrodynamics in tight porous materials, and can supplement experimental characterization of shale petrophysical properties (e.g. absolute/relative permeability, capillary pressure curves). However, challenges exist in creating representative pore structures tailored for specific simulation tools, incorporating the appropriate and relevant physics for the problems to be simulated, and interpreting, calibrating, or validating the simulation results. In this work, we used two types of pore scale simulation tools, namely pore network modeling (PNM) and lattice Boltzmann method (LBM), to study gas adsorption/desorption and transport behavior in shale matrix. For the first part of the work, a dual-scale PNM was integrated with lattice density functional theory (LDFT) to study nitrogen adsorption/desorption in mesoporous materials with pore sizes smaller than 200 nm. Critical pore structure parameters (i.e. porosity, pore size distribution, and pore throat connectivity) were characterized by calibrating the simulated nitrogen sorption isotherms to experimental results, and were then used to construct PNMs to study supercritical methane transport. We found that the pore structure characterization results were nonunique and highly dependent on the assumed pore shape. Scanning electron microscope (SEM) images were used to further constrain the description of pore shapes. Advection and diffusion of methane at reservoir conditions were simulated and compared, and suggestions were made regarding the choice of representative pore shape in PNMs for single phase advection/diffusion calculations. We next used LBM to study two-phase thermodynamic and hydrodynamic problems in nanopore systems in shale. Both 2D and 3D LBM models were developed with consideration of mesoscale fluid-fluid and solid-fluid interactions to model gas adsorption in complex geometries, and phase separation occurs automatically without the need to track the interface. This overcomes the pore shape deficiency of PNMs in cases where nanoporous media reconstruction exists. LBM models were then calibrated to LDFT and validated against experimental adsorption data for both subcritical and supercritical gases for the first time. We studied and compared nitrogen sorption hysteresis in two model nanopore system reconstructions representing the interparticle and intraparticle pores in shale. As another example of many possible applications of our developed model, we studied water adsorption and condensation in a reconstructed clay pore structure based on SEM image analysis, and explored the effect of surface wettability on adsorbed/condensed water distribution and connectivity. Supercritical methane flow simulations with the existence of condensed water were conducted using a 3D hydrodynamic LBM model that considers nanoscale flow physics for high Knudsen number flow. The relative permeability of methane as a function of water saturation and surface wettability was calculated and compared to available experimental data measured on geosynthetic clay liners. We demonstrated the wide applicability of our model and suggested future applications

Geothermal energy is the thermal energy generated and stored in the Earth's core, mantle, and crust. Geothermal technologies are used to generate electricity and to heat and cool buildings. To develop accurate models for heat and mass transfer applications involving fluid flow in geothermal applications or reservoir engineering and petroleum industries, a basic knowledge of the rheological and transport properties of the materials involved (drilling fluid, rock properties, etc.)—especially in high-temperature and high-pressure environments—are needed. This Special Issue considers all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction and convection in porous media. The emphasis here is on mathematical and computational aspects of fluid flow in conventional and unconventional reservoirs, geothermal engineering, fluid flow, and heat transfer in drilling engineering and enhanced oil recovery (hydraulic fracturing, CO2 injection, etc.) applications.

This book addresses the problems involved in the modelling and simulation of shale gas reservoirs, and details recent advances in the field. It discusses various modelling and simulation challenges, such as the complexity of fracture networks, adsorption phenomena, non-Darcy flow, and natural fracture networks, presenting the latest findings in these areas. It also discusses the difficulties of developing shale gas models, and compares analytical modelling and numerical simulations of shale gas reservoirs with those of conventional reservoirs. Offering a comprehensive review of the state-of-the-art in developing shale gas models and simulators in the upstream oil industry, it allows readers to gain a better understanding of these reservoirs and encourages more systematic research on efficient exploitation of shale gas plays. It is a valuable resource for researchers interested in the modelling of unconventional reservoirs and graduate students studying reservoir engineering. It is also of interest to practising reservoir and production engineers.

Phase Behavior provides the reader with the tools needed to solve problems requiring a description of phase behavior and specific pressure/volume/temperature (PVT) properties.

Shale gas accounts for an increasing proportion in the world,Äôs oil and gas supply, with the properties of low carbon, clean production, and huge potential for the compensation for the gradually depleted conventional resources. Due to the ubiquitous nanopores in shale matrix, the nanoscale gas flow becomes one of the most vital themes that are directly related to the formulation of shale gas development schemes, including the optimization of hydraulic fracturing, horizontal well spacing, etc. With regard to the gas flow in shale matrix, no commonly accepted consensus has been reached about the flow mechanisms to be considered, the coupled flow model in nanopores, and the upscaling method for its macroscopic form. In this chapter, the propositions of wall-associated diffusion, a physically sound flow mechanism scheme, a new coupled flow model in nanopores, the upscaling form of the proposed model, and the translation of lab-scale results into field-scale ones aim to solve the aforementioned issues. It is expected that this work will contribute to a deeper understanding of the intrinsic relationship among various flow mechanisms and the extension of the flow model to full flow regimes and to upscaling shale matrix, thus establishing a unified model for better guiding shale gas development.

A fascinating and instructive guide to Markov chains for experienced users and newcomers alike This unique guide to Markov chains approaches the subject along the four convergent lines of mathematics, implementation, simulation, and experimentation. It introduces readers to the art of stochastic modeling, shows how to design computer implementations, and provides extensive worked examples with case studies. Markov Chains: From Theory to Implementation and Experimentation begins with a general introduction to the history of probability theory in which the author uses quantifiable examples to illustrate how probability theory arrived at the concept of discrete-time and the Markov model from experiments involving independent variables. An introduction to simple stochastic matrices and transition probabilities is followed by a simulation of a two-state Markov chain. The notion of steady state is explored in connection with the long-run distribution behavior of the Markov chain. Predictions based on Markov chains with more than two states are examined, followed by a discussion of the notion of absorbing Markov chains. Also covered in detail are topics relating to the average time spent in a state, various chain configurations, and n-state Markov chain simulations used for verifying experiments involving various diagram configurations. • Fascinating historical notes shed light on the key ideas that led to the development of the Markov model and its variants • Various configurations of Markov Chains and their limitations are explored at length • Numerous examples—from basic to complex—are presented in a comparative manner using a variety of color graphics • All algorithms presented can be analyzed in either Visual Basic, Java Script, or PHP • Designed to be useful to professional statisticians as well as readers without extensive knowledge of probability theory Covering both the theory underlying the Markov model and an array of Markov chain implementations, within a common conceptual framework, Markov Chains: From Theory to Implementation and Experimentation is a stimulating introduction to and a valuable reference for those wishing to deepen their understanding of this extremely valuable statistical tool. Paul A. Gagniuc, PhD, is Associate Professor at Polytechnic University of Bucharest, Romania. He obtained his MS and his PhD in genetics at the University of Bucharest. Dr. Gagniuc’s work has been published in numerous high profile scientific journals, ranging from the Public Library of Science to BioMed Central and Nature journals. He is the recipient of several awards for exceptional scientific results and a highly active figure in the review process for different scientific areas.