Yuan Di

A Generalized Framework Model for Simulation of Gas Production in Unconventional Gas Reservoirs

Unconventional gas resources from tight-sand and shale gas reservoirs have received great attention in the past decade around the world because of their large reserves and technical advances in developing these resources. As a result of improved horizontaldrilling and hydraulic-fracturing technologies, progress is being made toward commercial gas production from such reservoirs, as demonstrated in the US. However, understandings and technologies needed for the effective development of unconventional reservoirs are far behind the industry needs (e.g., gas-recovery rates from those unconventional resources remain very low). There are some efforts in the literature on how to model gas flow in shale gas reservoirs by use of various approaches—from modified commercial simulators to simplified analytical solutions—leading to limited success. Compared with conventional reservoirs, gas flow in ultralow-permeability unconventional reservoirs is subject to more nonlinear, coupled processes, including nonlinear adsorption/ desorption, non-Darcy flow (at both high flow rate and low flow rate), strong rock/fluid interaction, and rock deformation within nanopores or microfractures, coexisting with complex flow geometry and multiscaled heterogeneity. Therefore, quantifying flow in unconventional gas reservoirs has been a significant challenge, and the traditional representative-elementary-volume(REV) based Darcy’s law, for example, may not be generally applicable. In this paper, we discuss a generalized mathematical framework model and numerical approach for unconventional-gas-reservoir simulation. We present a unified framework model able to incorporate known mechanisms and processes for two-phase gas flow and transport in shale gas or tight gas formations. The model and numerical scheme are based on generalized flow models with unstructured grids. We discuss the numerical implementation of the mathematical model and show results of our model-verification effort. Specifically, we discuss a multidomain, multicontinuum concept for handling multiscaled heterogeneity and fractures [i.e., the use of hybrid modeling approaches to describe different types and scales of fractures or heterogeneous pores—from the explicit modeling of hydraulic fractures and the fracture network in stimulated reservoir volume (SRV) to distributed natural fractures, microfractures, and tight matrix]. We demonstrate model application to quantify hydraulic fractures and transient flow behavior in shale gas reservoirs.

A Generalized Framework Model for the Simulation of Gas Production in Unconventional Gas Reservoirs

Unconventional gas resources from tight-sand and shale gas reservoirs have received great attention in the past decade around the world because of their large reserves and technical advances in developing these resources. As a result of improved horizontaldrilling and hydraulic-fracturing technologies, progress is being made toward commercial gas production from such reservoirs, as demonstrated in the US. However, understandings and technologies needed for the effective development of unconventional reservoirs are far behind the industry needs (e.g., gas-recovery rates from those unconventional resources remain very low). There are some efforts in the literature on how to model gas flow in shale gas reservoirs by use of various approaches—from modified commercial simulators to simplified analytical solutions—leading to limited success. Compared with conventional reservoirs, gas flow in ultralow-permeability unconventional reservoirs is subject to more nonlinear, coupled processes, including nonlinear adsorption/ desorption, non-Darcy flow (at both high flow rate and low flow rate), strong rock/fluid interaction, and rock deformation within nanopores or microfractures, coexisting with complex flow geometry and multiscaled heterogeneity. Therefore, quantifying flow in unconventional gas reservoirs has been a significant challenge, and the traditional representative-elementary-volume(REV) based Darcy’s law, for example, may not be generally applicable. In this paper, we discuss a generalized mathematical framework model and numerical approach for unconventional-gas-reservoir simulation. We present a unified framework model able to incorporate known mechanisms and processes for two-phase gas flow and transport in shale gas or tight gas formations. The model and numerical scheme are based on generalized flow models with unstructured grids. We discuss the numerical implementation of the mathematical model and show results of our model-verification effort. Specifically, we discuss a multidomain, multicontinuum concept for handling multiscaled heterogeneity and fractures [i.e., the use of hybrid modeling approaches to describe different types and scales of fractures or heterogeneous pores—from the explicit modeling of hydraulic fractures and the fracture network in stimulated reservoir volume (SRV) to distributed natural fractures, microfractures, and tight matrix]. We demonstrate model application to quantify hydraulic fractures and transient flow behavior in shale gas reservoirs.

A Comprehensive Numerical Model for Simulating Fluid Transport in Nanopores

Since a large amount of nanopores exist in tight oil reservoirs, fluid transport in nanopores is complex due to large capillary pressure. Recent studies only focus on the effect of nanopore confinement on single-well performance with simple planar fractures in tight oil reservoirs. Its impacts on multi-well performance with complex fracture geometries have not been reported. In this study, a numerical model was developed to investigate the effect of confined phase behavior on cumulative oil and gas production of four horizontal wells with different fracture geometries. Its pore sizes were divided into five regions based on nanopore size distribution. Then, fluid properties were evaluated under different levels of capillary pressure using Peng-Robinson equation of state. Afterwards, an efficient approach of Embedded Discrete Fracture Model (EDFM) was applied to explicitly model hydraulic and natural fractures in the reservoirs. Finally, three fracture geometries, i.e. non-planar hydraulic fractures, non-planar hydraulic fractures with one set natural fractures, and non-planar hydraulic fractures with two sets natural fractures, are evaluated. The multi-well performance with confined phase behavior is analyzed with permeabilities of 0.01 md and 0.1 md. This work improves the analysis of capillarity effect on multi-well performance with complex fracture geometries in tight oil reservoirs.

Liquefaction analysis of saturated soils taking into account variation in porosity and permeability with large deformation

Abstract A numerical method for liquefaction analysis of saturated soils with large deformation is presented. Formulations are based on Biots two-phase mixture theory and the updated Lagrangian method. Governing equations consist of an equilibrium equation and one for mass conservation. Based on the u-p formulation, displacement of the soil skeleton and pore pressure are the two basic unknown variables. Governing equations are discretized by the FE-FD coupled method. A cyclic elasto-plastic constitutive model is used to describe the liquefaction behavior of saturated soils under dynamic loading. The coefficient of porosity is considered to vary with large deformation. The coefficient of permeability is assumed to be a function of the void ratio. The examples show the flexibility and applicability of the proposed method. Comparison is made between large and small strain solutions. The large deformation analysis shows that liquefaction occurs earlier in seabed deposits under wave action and deeper in the soil surrounding an embankment subjected to strong earthquake motion than it does in small strain analysis.

A Practical Compositional Method for Simulation of CO2 Flooding in Porous and Fractured Petroleum Reservoirs

CO2 flooding is one of the most effective and used methods for enhanced oil recovery (EOR) approaches. The number of CO2 flooding projects has increased rapidly in China and around the world. Compositional simulation is required for evaluating CO2 flooding in EOR operations, especially for miscible or nearly miscible flooding when black-oil simulation is no longer adequate. The simulation method proposed here is a multi-dimensional, three-phase, and compositional modeling approach, which is applicable to both porous and fractured reservoirs. In the model formulation, a generalized multi-continuum approach is adopted to handle flow and transport in naturally fractured reservoirs and the mass flux of each mass component is contributed by advection and diffusion processes. In addition, precipitation of heavy oil components and absorption of CO2 on the solid grains are modeled based on reversible linear or nonlinear isotherms. The governing partial differential equations for conservation of each component are discretized using a finite volume method and the resulting discrete equations are solved fully implicitly by Newton-Raphson iteration. The equation of state (EOS) by Soave-Redlich-Kwong is used to calculate the physical properties of fluids. Research has shown that the flash calculations with EOS in compositional simulation are computationally intensive and may not be reliable at near critical conditions. Therefore, a K-value based approach, improved by Almehaideb et al. (2002), is used for partitioning of oil components and CO2 between oil and CO2 phases. In addition, the laboratory measured oil and CO2 phase compositional data can be used alternatively to account for compositional effect in this model. Two numerical examples are presented to show that the proposed modeling method is efficient for simulation of CO2 flooding processes in EOR operations. Introduction CO2 flooding has been used as a commercial process for enhanced oil recovery (EOR) for over 40 years and is the secondmost applied EOR process in the world (Jarrell et al., 2002). Both laboratory studies and field applications have established that CO2 can be an efficient oil-displacing agent. CO2 injection in mature hydrocarbon fields has also been considered as a favourable option to reduce accumulation of atmospheric CO2 and thus mitigate greenhouse effects on climate (Bradshaw and Cook, 2001). As the results, a number of CO2 flooding projects has increased rapidly in China and around the world. Numerical simulation is the most common technique in the oil industry to better understand, predict, design, and manage a CO2-EOR project. Miscibility between oil and CO2 will occur when pressure is high enough to compress the CO2 to a density at which it becomes a good solvent for the lighter hydrocarbons in the crude oil. Compositional simulation is required for modeling the complex interaction of flow in CO2-EOR operations, especially for miscible or nearly miscible flooding when black-oil simulation is no longer adequate. In recent years, we have seen more CO2 application in naturally fractured reservoirs. Due to the large permeability contrast between the matrix and the fracture in fractured reservoirs, injected fluids such as CO2 or water easily move toward the production well and result in bypassing of the matrix oil and poor sweep efficiency. Early gas or water breakthrough becomes problematic in the secondary oil recovery stage in most fractured reservoirs. Among the commonly used conceptual models for analyzing flow through fractured rock, dual-continuum models, i.e., doubleand multi-porosity, and dual-permeability, are perhaps the most popular approaches used in fractured reservoir modeling studies (Barenblatt et al., 1960; Warren and Root, 1963; Kazemi, 1969). A more general and efficient method for multi-continuum, named multiple-interacting-continua (MINC) method, was proposed (Pruess and Narasimhan, 1985; Wu and Pruess, 1988). The TOUGH2 family of multiphase flow numerical simulators (Pruess, 2004) has a long recognized record of

Simulation of Multiphase Non Darcy Flow in Porous and Fractured Media

A Buckley and Leverett type analytical solution is derived for non-Darcy displacement of immiscible fluids in porous media, in which non-Darcy flow is described using the general model proposed by Barree and Conway. Recent laboratory studies and analyses have shown that the Barree and Conway model is able to describe the entire range of relationships between rate and potential gradient from lowto high-flow rates through porous media, including those in transitional zones. We also present a general mathematical and numerical model for incorporating the Barree and Conway model to simulate multiphase non-Darcy flow in porous and fractured media, while flow in fractured rock is handled using a general multi-continuum approach. The numerical solution of the proposed multiphase, non-Darcy flow model is based on a discretization scheme using an unstructured grid with regular or irregular meshes for multi-dimensional simulation. The final discretized nonlinear equations are handled fully implicitly with the Newton iteration. As an application example, we use the analytical solution to verify the numerical solution for and to obtain some insight into one-dimensional non-Darcy displacement of two immiscible fluids according to the Barree and Conway model. Overall, this work provides an improved platform for modeling multiphase non-Darcy flow in oil and gas reservoirs, including complex fractured systems such as shale gas reservoirs.