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This paper presents a new triple-continuum conceptual model for simulating flow and transport processes in fractured rock. Field data collected from the unsaturated zone of Yucca Mountain, a potential repository site of high-level nuclear waste, show that there are significant numbers of small-scale fractures. Although these small fractures may not contribute to the global flow and transport within the fracture networks, they may have a considerable effect on solute transport and liquid flow between the fractures and the matrix. The effect of these small fractures has not been considered in previous modeling investigations within the context of a continuum approach. A new triple-continuum model (consisting of matrix, small-fracture and large-fracture continua) has been developed to investigate the effect of these small fractures. This paper derives the model formulation and discusses the basic triple-continuum behavior of flow and transport processes under different conditions, using both analytical solutions and numerical approaches. The simulation results from the site-scale model of the unsaturated zone of Yucca Mountain indicate that these small fractures may have an important effect on radionuclide transport within the mountain.Key Words: Naturally fractured reservoir, fractured porous media, double-porosity model, dual-permeability model, triple-continuum model, numerical reservoir simulation, and fractured unsaturated rock. 2 IntroductionThe study of flow and transport processes in fractured rock has recently received increased attention because of its importance to underground natural-resource recovery, waste storage, and environmental remediation. Since the 1960s, significant progress has been made towards the understanding and modeling of flow and transport processes in fractured rock (Barenblatt et al., 1960;Warren and Root, 1963;Kazemi, 1969;Pruess and Narasimhan, 1985). Despite these advances, modeling the coupled processes of multiphase fluid flow, heat transfer, and chemical migration in a fractured porous medium remains a conceptual and mathematical challenge. The difficulty stems primarily from (1) the nature of inherent heterogeneity, (2) the uncertainties associated with the characterization of a fracture-matrix system for any field-scale problem, and (3) the difficulties in conceptualizing, understanding, and describing flow and transport processes in such a system.Mathematical modeling using a continuum approach involves developing conceptual models, incorporating the geometrical information of a given fracture-matrix system, and setting up the general mass and energy conservation equations for overlapping fracturematrix domains. The majority of the computational effort is used to solve the governing equations that couple fluid and heat flow with chemical migration either analytically or numerically. The key issue for simulating flow and transport in fractured rock is how fracture-matrix interactions under different conditions involving multiple processes are handled. The commonly us...

Summary. This paper describes the application of the method of "Multiple Interacting Continua" (MINC) to the simulation of oil recovery in naturally fractured reservoirs. A generalization of the double-porosity technique, the MINC method permits a fully transient description of interporosity flow by numerical methods. We present examples to demonstrate the utility of the MINC method for modeling oil-recovery mechanisms by water imbibition and field applications for five-spot waterflooding and water coning problems in fractured reservoirs. All results show that the MINC method problems in fractured reservoirs. All results show that the MINC method provides accurate predictions of the behavior of naturally fractured provides accurate predictions of the behavior of naturally fractured reservoirs, while requiring only a modest increase in computation work compared with the double-porosity method. The double-porosity method may result in large errors for matrix blocks of low permeability or large size. Introduction The study of fluid flow in naturally fractured petroleum reservoirs has been a challenging task. Considerable progress has been made since the 1960's because many fractured hydrocarbon reservoirs have been discovered and put into development in the past decades. Most papers treating flow in fractured reservoirs consider that global flow occurs primarily through the high-permeability, low-effective-porosity fracture system surrounding matrix rock blocks. The matrix blocks contain the majority of the reservoir storage volume and act as local source or sink terms to the fracture system. The fractures are interconnected and provide the main fluid flow path to injection and production wells. Because of the complexity of the pore structure of fractured reservoirs, no universal method for the simulation of reservoir behavior exists. Several different double-porosity models (DPM's) have been developed to describe single-phase and multiphase flow in fractured media. Usually, analytic approximations are introduced for the coupling between fracture and matrix continua. For example, it is commonly assumed that a quasisteady state exists in the primary-porosity matrix elements at all times. Very little work has been done so far in studying transient flow in the matrix blocks or between matrix and fracture systems either numerically or experimentally. As a generalization of the double-porosity concept, Pruess and Narasimhan developed the MINC method, which treats the multiphase and multidimensional transient flow in both fractures and matrix blocks by a numerical approach. This method was successfully applied to a number of geothermal reservoir problems. The MINC method of Pruess and Narasimhan involves discretization of matrix blocks into a sequence of nested volume elements, which are defined on the basis of distance from the block surface (Fig. 1a). In this way, it is possible to resolve in detail the gradients (of pressure, possible to resolve in detail the gradients (of pressure, temperature, etc.) that drive interporosity flow. This discretization technique was later adopted by Gilman for flow in fractured hydrocarbon reservoirs and by Neretnieks and Rasmuson for chemical transport in fractured groundwater systems. In the present paper, we apply the MINC method to study oil- recovery mechanisms in fractured reservoirs and to obtain insight into the behavior of water/oil flow during the imbibition process. Imbibition is regarded as a very important mechanism of oil production in waterflooding or water coning of fractured production in waterflooding or water coning of fractured reservoirs. For multiphase flow, pressure, viscous, gravitational, and capillary forces should all be taken into account. To understand the roles played by the three kinds of forces, we have studied the imbibition process with the MINC method, the conventional DPM, and with a detailed explicit discretization of matrix blocks. The comparison of the results from the three methods shows that the MINC method can give an accuracy of better than 1% at all times, while the DPM approximation with quasisteady interporosity flow can produce large errors, especially for matrix blocks with low permeability or large size. We also apply the MINC method to match published data of a five-spot waterfloods and the observed coning behavior of a well with bottomwater drive in a fractured oil reservoir. Satisfactory results have been obtained for the two examples. In both the imbibition study of individual matrix blocks and field-scale applications, the MINC method is found to give more reliable history matching and behavior predictions for the simulation of fractured reservoir than the conventional DPM. In most previous analytical or numerical studies of multiphase flow in porous media, it has been taken for granted that the matrix system can be treated as a single continuum with (locally) uniform pressure and fluid saturation distributions. To the best of our pressure and fluid saturation distributions. To the best of our knowledge, no studies for multiphase flow have been published concerning how much error will be introduced by this treatment and under what conditions the quasisteady approximation for interporosity flow is acceptable for engineering applications. The applicability of the DPM method is discussed by analyzing the results from individual block imbibition studies and field-scale examples with MINC and DPM in this paper. Through the work of this paper, it is found that the DPM method is often unsuitable for the paper, it is found that the DPM method is often unsuitable for the simulation of oil/water imbibition processes in naturally fractured reservoirs. Depending on reservoir fluid and rock properties, DPM may either overestimate or underestimate imbibition oil recovery from matrix blocks, especially for matrix blocks with low permeability and large size or for high oil viscosity. In some permeability and large size or for high oil viscosity. In some special cases, the results from MINC and DPM calculations are very close, either because of similarities in individual block response predicted from either method or because of the compensatory effect predicted from either method or because of the compensatory effect of global flow in the fractures on individual block imbibition response in field-scale modeling. In general, it will be difficult to determine the suitability of DPM for a given reservoir problem. It is suggested that individual matrix imbibition studies be carried out with various possible reservoir parameters with DPM approximation as well as explicit discretization before DPM is applied to actual reservoir simulation. Comparison between DPM and EDM results for individual matrix blocks may provide clues for the accuracy to be expected from the DPM approximation in field studies. When changes in water saturation in the fractures are rapid, as may often happen in coning problems or in response to rate changes, it is usually necessary to account for the transient flow inside the matrix blocks and between matrix and fractures. SPERE P. 327

Shale swelling during drilling is attributed to osmotic pressure, where low-salinity water enters the shale pores to cause swelling. Low-salinity water injected into high-salinity Bakken formation could similarly enter the matrix pores to displace oil by counter-current flow observed in core experiments. As a result, we believe, low-salinity water can potentially enhance oil recovery from oil-wet Bakken formation.In this paper, we report experimental and numerical modeling studies we conducted to evaluate the potential of lowsalinity waterflooding in Bakken. For laboratory experiments, we used horizontal core plugs drilled parallel to the bedding plane.The mathematical included osmotic pressure, gravity and capillary effects. In the mathematical model, the osmotic pressure mass transfer equations were calibrated by matching time-dependent salinities in a published laboratory osmotic pressure experiment. We also modeled oil recovery for a Bakken core using our osmotic pressure mass transport model. The results indicate that osmotic pressure promotes counter-current flow of oil from both the water-wet and oil-wet segments of the core.

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Summary 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 horizontal-drilling 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.