Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour

Pore-to-continuum Multiscale Modeling of Two-phase Flow in Porous Media

Abstract Pore-scale network modeling using 3D X-ray computed tomographic images (digital rock technology) has become integral to both research and commercial simulations in recent years. While this technology provides tremendous insight into pore-scale behavior, computational methods for integrating the results into practical, continuum-scale models remain fairly primitive. The general approach is to run pore-scale models and continuum models sequentially, where macroscopic parameters are simulated using the pore-scale models and then used in the continuum models as if they have been obtained from laboratory experiments. While a sequential coupling approach is appealing in some cases, an inability to run the two models concurrently (exchanging parameters and boundary conditions in real numerical time) will prevent using pore-scale image-based modeling to its full potential. In this work, an algorithm for direct coupling of a dynamic pore-network model for multiphase flow with a traditional continuum-scale simulator is presented. The ability to run the two models concurrently is made possible by a novel dynamic pore-network model that allows simultaneous injection of immiscible fluids under either transient or steady-state conditions. The dynamic network algorithm can simulate both drainage and imbibition. Consequently, the network algorithm can be used to model a complete time-dependent injection process that comprises a steady-state relative permeability test, and also allows for coupling to a continuum model via exchange of information between the two models. Results also include the sensitivity analysis of relative permeability to pore-level physics and simulation algorithms. A concurrent multiscale modeling approach is presented. It allows the pore-scale properties to evolve naturally during the simulated reservoir time step and provide a unique method for reconciling the dramatically different time and length scales across the coupled models. The model is tested for examples associated with oil production and groundwater transport in which relative permeability depends on flowrate, thus demonstrating a situation that cannot be modeled using a traditional approach. This work is significant because it represents a fundamental change in the way we might obtain continuum-scale parameters in a reservoir simulation

Gas transfer through clay barriers

Gas transport through clay-rocks can occur by different processes that can be basically subdivided into pressure-driven flow of a bulk gas phase and transport of dissolved gas either by molecular diffusion or advective water flow (Figure 1, Marschall et al., 2005). The relative importance of these transport mechanisms depends on the boundary conditions and the scale of the system. Pressure-driven volume flow (“Darcy flow”) of gas is the most efficient transport mechanism. It requires, however, pressure gradients that are sufficiently large to overcome capillary forces in the typically water-saturated rocks (purely gas-saturated argillaceous rocks are not considered in the present context). These pressure gradients may form as a consequence of the gravity field (buoyancy, compaction) or by gas generation processes (thermogenic, microbial, radiolytic). Dissolved gas may be transported by water flow along a hydraulic gradient. This process is not affected by capillary forces but constrained by the solubility of the gas. It has much lower transport efficiency than bulk gas phase flow. Molecular diffusion of dissolved gas, finally, is occurring essentially without constraints, ubiquitously and perpetually. Effective diffusion distances are, however, proportional to the square root of time, which limits the relevance of this transport process to the range of tens to hundreds of metres on a geological time scale (millions of years). 2 Process understanding and the quantification of the controlling parameters, like diffusion coefficients, capillary gas breakthrough pressures and effective gas permeability coefficients, is of great importance for up-scaling purposes in different research disciplines and applications. During the past decades, gas migration through fully water-saturated geological clay-rich barriers has been investigated extensively (Thomas et al., 1968, Pusch and Forsberg, 1983; Horseman et al., 1999; Galle, 2000; Hildenbrand et al., 2002; Marschall et al., 2005; Davy et al., 2009; Harrington et al., 2009, 2012a, 2014). All of these studies aimed at the analysis of experimental data determined for different materials (rocks of different lithotype, composition, compaction state) and pressure/temperature conditions. The clay-rocks investigated in these studies, ranged from unconsolidated to indurated clays and shales, all characterised by small pores (2-100 nm) and very low hydraulic conductivity (K < 10-12 m·s-1) or permeability coefficients (k < 10-19 m²). Studies concerning radioactive waste disposal include investigations of both the natural host rock formation and synthetic/engineered backfill material at a depth of a few hundred meters (IAEA, 2003, 2009). Within a geological disposal facility, hydrogen is generated by anaerobic corrosion of metals and through radiolysis of water (Rodwell et al., 1999; Yu and Weetjens, 2009). Additionally, methane and carbon dioxide are generated by microbial degradation of organic wastes (Rodwell et al., 1999; Ortiz et al., 2002; Johnson, 2006; Yu and Weetjens, 2009). The focus of carbon capture and storage (CCS) studies is on the analysis of the long-term sealing efficiency of lithologies above depleted reservoirs or saline aquifers, typically at larger depths (hundreds to thousands of meters). During the last decade, several studies were published on the sealing integrity of clay-rocks to carbon dioxide (Hildenbrand et al., 2004; Li et al., 2005; Hangx et al., 2009; Harrington et al., 2009; Skurtveit et al., 2012; Amann-Hildenbrand et al., 2013). In the context of petroleum system analysis, a significant volume of research has been undertaken regarding gas/oil expulsion mechanisms from sources rocks during burial history (Tissot & Pellet, 1971; Appold & Nunn, 2002), secondary migration (Luo et al., 2008) and the capillary sealing capacity of caprocks overlying natural gas accumulations (Berg, 1975; Schowalter, 1979; Krooss, 1992; Schlömer and Kross, 2004; Li et al., 2005; Berne et al., 2010). Recently, more attention has been paid to investigations of the transport efficiency of shales in the context of oil/gas shale production (Bustin et al., 2008; Eseme et al., 2012; Amann-Hildenbrand et al., 2012; Ghanizadeh et al., 2013, 2014). Analysis of the migration mechanisms within partly unlithified strata becomes important when explaining the 3 origin of overpressure zones, sub-seafloor gas domes and gas seepages (Hovland & Judd, 1988; Boudreau, 2012). The conduction of experiments and data evaluation/interpretation requires a profound process understanding and a high level of experience. The acquisition and preparation of adequate samples for laboratory experiments usually constitutes a major challenge and may have serious impact on the representativeness of the experimental results. Information on the success/failure rate of the sample preparation procedure should therefore be provided. Sample specimens “surviving” this procedure are subjected to various experimental protocols to derive information on their gas transport properties. The present overview first presents the theoretical background of gas diffusion and advective flow, each followed by a literature review (sections 2 and 3). Different experimental methods are described in sections 4.1 and 4.2. Details are provided on selected experiments performed at the Belgian Nuclear Research Centre (SCK-CEN, Belgium), Ecole Centrale de Lille (France), British Geological Survey (UK), and at RWTH-Aachen University (Germany) (section 4.3). Experimental data are discussed with respect to different petrophysical parameters outlined above: i) gas diffusion, ii) evolution of gas breakthrough, iii) dilation-controlled flow, and iv) effective gas permeability after breakthrough. These experiments were conducted under different pressure and temperature conditions, depending on sample type, burial depth and research focus (e.g. radioactive waste disposal, natural gas exploration, or carbon dioxide storage). The interpretation of the experimental results can be difficult and sometimes a clear discrimination between different mechanisms (and the controlling parameters) is not possible. This holds, for instance, for gas breakthrough experiments where the observed transport can be interpreted as intermittent, continuous, capillary- or dilation-controlled flow. Also, low gas flow rates through samples on the length-scale of centimetres can be equally explained by effective two-phase flow or diffusion of dissolved gas

Artificial neural network to determine dynamic effect in capillary pressure relationship for two-phase flow in porous media with micro-heterogeneities

Open access articleAn artificial neural network (ANN) is presented for computing a parameter of dynamic two-phase flow in porous media with water as wetting phase, namely, dynamic coefficient (τ), by considering micro-heterogeneity in porous media as a key parameter. τ quantifies the dependence of time derivative of water saturation on the capillary pressures and indicates the rates at which a two-phase flow system may reach flow equilibrium. Therefore, τ is of importance in the study of dynamic two-phase flow in porous media. An attempt has been made in this work to reduce computational and experimental effort by developing and applying an ANN which can predict the dynamic coefficient through the “learning” from available data. The data employed for testing and training the ANN have been obtained from computational flow physics-based studies. Six input parameters have been used for the training, performance testing and validation of the ANN which include water saturation, intensity of heterogeneity, average permeability depending on this intensity, fluid density ratio, fluid viscosity ratio and temperature. It is found that a 15 neuron, single hidden layer ANN can characterize the relationship between media heterogeneity and dynamic coefficient and it ensures a reliable prediction of the dynamic coefficient as a function of water saturation