The objective of this paper is to incorporate a more detailed description of flow in shale matrix to improve modeling of production from fractured shale-gas reservoirs. Currently, most modeling approaches for shale-gas and -oil production are based on the dominance of Darcy flow in both natural fractures and matrix. We improve the description of matrix flow by considering diffusive (Knudsen) flow in nanopores. In our dual-mechanism approach, when Darcy flow becomes insignificant due to nanodarcy matrix permeability, Knudsen flow takes over and contributes, substantially, to the transfer of fluids from matrix to fracture network. Furthermore, we consider stress-dependent permeability in the fracture network. Therefore, incorporating Darcy and diffusive flows in the matrix and stress-dependent permeability in the fractures, we develop a dual-mechanism dual-porosity naturally fractured reservoir formulation and derive a new transfer function for fractured shale-gas reservoirs. The dual-mechanism dualporosity formulation presented in this paper can be used for numerical or analytical modeling purposes. We use the new formulation of matrix to fracture fluid transfer with an analytical model and demonstrate the differences from the conventional formulation.

This paper presents an investigation of the effect of pressuredependent natural-fracture permeability on production from shale-gas wells. The motivation of the study is to provide data for the discussion of whether it is crucial to pump proppant into natural fractures in shale plays. Experiments have been conducted on Bakken-shale core samples to select appropriate correlations to represent fracture conductivity as a function of pressure (the actual characterization of fracture conductivity under stress for a specific formation is not an objective of the study). Correlations have been used in a flow model to demonstrate the potential impact of natural-fracture closure as pressure drops during production. Although the correlations indicate up to an 80% reduction in fracture permeability over practical ranges of pressure, the results of the flow model do not warrant the claims that fracture closing plays a significant role in the productivity losses of shalegas wells. A history match of the performances of two wells in the Barnett and Haynesville formations also indicates that the effect of pressure-dependent natural-fracture permeability on shale-gas-well production is a function of the permeability of the matrix system. If the matrix system is too tight, then the retained permeability of the natural fractures may still be sufficient for the available volume of the fluid when the system pressure drops.

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Summary Previous experimental studies of foam generation and transport were conducted, mainly, in one-dimensional and homogeneous porous media. However, the field situation is primarily heterogeneous and multidimensional. To begin to bridge this gap, we have studied foam formation and propagation in an annularly heterogeneous porous medium. The experimental system was constructed by centering a 0.050 m diam cylindrical Fontainebleau sandstone core inside an 0.089 m acrylic tube and packing clean Ottawa sand in the annular region. The sandstone permeability is roughly 0.1 ?m2 while the unconsolidated sand permeability is 6.7 ?m2. Experiments with and without cross flow between the two porous media were conducted. To prevent cross flow, the cylindrical face of the sandstone was encased in a heat-shrink Teflon sleeve and the annular region packed with sand as before. Nitrogen is the gas phase and an alpha olefin sulfonate (AOS 1416) in brine is the foamer. The aqueous phase saturation distribution is garnered using X-ray computed tomography (CT). Results from this study are striking. When the heterogeneous layers are in capillary communication and cross flow is allowed, foam fronts move at identical rates in each porous medium as quantified by the CT-scan images. Desaturation by foam is efficient and typically complete in about 1 PV of gas injection. When cross flow is prohibited, foam partially plugs the high permeability sand and diverts flow into the low permeability sandstone. The foam front moves through the low permeability region faster than in the high permeability region. Introduction Foam is applied broadly as a mobility-control and profile modification agent for flow in porous media. Foams are usually formed by nonwetting gases such as steam, carbon dioxide (CO2) or nitrogen (N2) dispersed within a continuous surfactant-laden liquid phase. Typical applications include aqueous foams for improving steam-drive1–3 and CO2 -flood performance,4 gelled foams for plugging high permeability channels,5 foams for prevention or delay of gas or water coning,6 and surfactant-alternating-gas processes for clean up of ground-water aquifers.7,8 All of these methods have been tested in both the laboratory and the field. An unfoamed gas displays low viscosity relative to water or crude oil and is thereby very mobile in porous media. However, dispersing the gas phase within a surfactant solution where the surfactant stabilizes the gas/liquid interface can substantially reduce gas mobility in porous media. Mobility is reduced because pore-spanning liquid films (foam lamellae) and lenses block some of the flow channels. Additionally, flowing lamellae encounter significant drag because of the presence of pore walls and constrictions. One aspect of foams that makes them attractive is that a relatively small amount of surfactant chemical can affect the flow properties of a very large volume of gas. The volume fraction of gas in a foam frequently exceeds 80% and stable foams up to 99% volume fraction are not uncommon. Recent reviews of foam flow phenomena and mechanisms are given in Refs. 9-11. Laboratory studies of foam generation and transport have aided greatly in formulating and improving both our microscopic and macroscopic understanding of foam flow in porous media. They have focused, for the most part, on one-dimensional and homogeneous porous media. These studies, however, leave gaps in our knowledge of foam behavior because the field situation is primarily heterogeneous and multidimensional. While much work has been conducted in homogeneous systems, the literature on flow in stratified systems is sparse. Notable experiments in stratified systems include Casteel and Djabbarah who performed steam and CO2 displacements with foaming agents in two parallel porous media.12 Robin studied foam generation and transport in layered beadpacks that simulated reservoir strata.13 In these experiments he surmised that foam blocked the high permeability layer. Llave et al. observed that foam can divert gas flow from high permeability layers to low permeability layers when the layers are isolated.14 Yaghoobi and Heller studied CO2 foam in short composite cores composed of sand and sandstone.15 They reported diversion of CO2 to the low permeability section and delay in CO2 breakthrough from the high permeability section. More recently, Hirasaki et al. performed foam displacements in layered porous media to study the removal of organic liquids from groundwater aquifers.7 Gas was injected at a fixed pressure gradient rather than at a specified rate. By dyeing the various fluids, they observed displacement patterns directly. They found that injection of gas slugs into a porous medium containing surfactant resulted in foam generation and selective mobility reduction in the high permeability layers. In turn, recovery of the organic liquid was greatly enhanced. For the most part, the effect of flow among parallel layers in capillary communication has not been investigated. We denote this as cross flow. To bridge this gap, we perform foam flow experiments in an axially symmetric, cylindrical, heterogeneous porous medium. A sandstone core fills the center of the heterogeneous pack and a uniform sand fills the annular region between the core and the pressure vessel wall. By the use or absence of a heat-shrink Teflon jacket around the sandstone, fluid communication, or cross flow, is prohibited or allowed. The sandstone is about two orders of magnitude less permeable than the sand to provide a strong permeability and capillary pressure contrast. We interpret the experiments in terms of the evolution of in situ water saturation as a function of time. In the following sections we first discuss the construction and characterization of the porous medium, characterization of our foamer solution, and then experimental determination of water saturation via X-ray computed tomography (CT) scanning. CT provides accurate resolution of the progress of displacement fronts as well as the in situ displacement efficiency. Next, we outline the experimental program and give results. A discussion and conclusions complete the article.

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