A Numerical Model of Tracer Transport in a Non-isothermal Two-Phase Flow System for {\text{ CO}}_2 Geological Storage Characterization

For the purpose of characterizing geologically stored $\text{ CO}_{2}Air sparging is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air through air sparging well below the zone of contamination. To investigate the rate-dependent flow properties during multistep air sparging, a rule-based dynamic two-phase flow model was developed and applied to a 3D pore network which is employed to characterize the void structure of porous media. The simulated dynamic two-phase flow at the pore scale or microscale was translated into functional relationships at the continuum-scale of capillary pressure?Csaturation (P ^c?CS) and relative permeability??saturation (K _r?CS) relationships. A significant contribution from the air injection pressure step and duration time of each air injection pressure on both of the above relationships was observed during the multistep air sparging tests. It is observed from the simulation that at a given matric potential, larger amount of water is retained during transient flow than that during steady flow. Shorter the duration of each air injection pressure step, there is higher fraction of retained water. The relative air/water permeability values are also greatly affected by the pressure step. With large air injection pressure step, the air/water relative permeability is much higher than that with a smaller air injection pressure step at the same water saturation level. However, the impact of pressure step on relative permeability is not consistent for flows with different capillary numbers (N _ca). When compared with relative air permeability, relative water permeability has a higher scatter. It was further observed that the dynamic effects on the relative permeability curve are more apparent for networks with larger pore sizes than that with smaller pore sizes. In addition, the effect of pore size on relative water permeability is higher than that on relative air permeability.     

Simulation of compressibility of entrapped air in an incompressible free surface flow using a pressure-based method for unified equations

A pressure-based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single-pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction,which limits their capability for increased predictive accuracy relative to experimental data.This is partly because of the nature of slug flow pneumatic conveying system,which,as a dynamic system,never becomes stable.By utilising conservation of mass (airflow),a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour.The rate of air permeation through slug,one of the important factors in the conservation model,is expressed as a function of a slug permeability factor.Other factors such as slug velocity,slug length and the fraction of stationary layer were also considered.Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model,showing good agreement between the model and experimental results.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

Measurement of the relative air permeability of compacted earth in the hygroscopic regime of saturation

The hygroscopic behavior of earthen materials has been extensively studied in the past decades. However, while the air flow within their porous network may significantly affect the kinetics of vapor transfer and thus their hygroscopic performances, few studies have focused on its assessment. For that purpose, a key parameter would be the gas permeability of the material, and its evolution with the relative humidity of the air. Indeed, due to the sorption properties of earthen material, an evolution of the water content, and thus of relative permeability, are foreseeable if the humidity of in-pore air changes. To fill this gap, this paper presents the measurement of relative permeabilities of a compacted earth sample with a new experimental set-up. The air flow through the sample is induced with an air generator at controlled flow rate, temperature, and humidity. The sample geometry was chosen in order to reduce, as much as possible, its heterogeneity in water content, and the tests were realized for several flow rates. The results, which show the evolution of gas permeability with the relative humidity of the injected air and with the water content of the material, either in adsorption or in desorption, were eventually successfully compared to predictions of the well-known Corey's law.     

Effect of gap and flow orientation on two-phase flow in an oil-wet gap: Relative permeability curves and flow structures

Naturally fractured reservoirs contain about 25–30% of the world supply of oil. In these reservoirs, fractures are the dominant flow path. Therefore, a good understanding of transfer parameters such as relative permeability as well as flow regimes occurring in a fracture plays an important role in developing and improving oil production from such complex systems. However, in contrast with gas–liquid flow in a single fracture, the flow of heavy oil and water has received less attention. In this research, a Hele-Shaw apparatus was built to study the flow of water in presence of heavy oil and display different flow patterns under different flow rates and analyze the effect of fracture orientations on relative permeability curves as well as flow regimes. The phase flow rates versus phase saturation results were converted to experimental relative permeability curves. The results of the experiments demonstrate that, depending on fracture and flow orientation, there could be a significant interference between the phases flowing through the fracture. The results also reveal that both phases can flow in both continuous and discontinuous forms. The relative permeability curves show that the oil–water relative permeability not only depends on fluid saturations and flow patterns but also fracture orientation.     

A Mechanistic Model of Gas-Condensate Flow in Pores

Recent experimental results reported in the literature indicate that the relative permeability of gas-condensate systems increases with rate (velocity) at some conditions. To gain a better understanding of the nature of the flow and the prevailing mechanisms resulting in such behaviour flow visualisation experiments have been performed, using high pressure micromodels. The observed flow behaviour at the pore level has been employed to develop a mechanistic model describing the coupled flow of gas and condensate phases. The results of the model simulating the observed simultaneous flow of gas and condensate phases have been compared with reported core experimental results. Most features of the reported rate effect are predictable by the developed single pore model, nevertheless, its extension to include multiple pore interaction is recommended.     

Multiphase flow with a simplified model for oil entrapment

A computationally simple procedure is described to model effects of oil entrapment on three-phase permeability-saturation-capillary pressure relations. The model requires knowledge of airwater saturation-capillary pressure relations, which are assumed to be nonhysteretic and are characterized by Van Genuchten's parametric model; scaling factors equal to the ratio of water surface tension to oil surface tension and to oil-water interfacial tension; and the maximum oil (also referred to as nonwetting liquid in a three-phase medium) saturation which would occur following water flooding of oil saturated soil. Trapped nonwetting liquid saturation is predicted as a function of present oil-water and air-oil capillary pressures and minimum historical water saturation since the occurrence of oil at a given location using an empirically-based algorithm. Oil relative permeability is predicted as a simple function of apparent water saturation (sum of actual water saturation and trapped oil saturation) and free oil saturation (difference between total oil and trapped oil saturation), and water relative permeability is treated as a unique function of actual water saturation. The proposed method was implemented in a two-dimensional finite-element simulator for three-phase flow and component transport, MOFAT. The fluid entrapment model requires minimal additional computational effort and computer storage and is numerically robust. The applicability of the model is illustrated by a number of hypothetical one- and two-dimensional simulations involving infiltration and redistribution with changes in water-table elevations. Results of the simulations indicate that the fraction of a hydrocarbon spill that becomes trapped under given boundary conditions increases as a nonlinear function of the maximum trapped nonwetting liquid saturation. Dense organic liquid plumes may exhibit more pronounced effects of entrapment due to the more dynamic nature of flow, even under static water table conditions. Disregarding nonwetting fluid entrapment may lead to significant errors in predictions of immiscible plume migration.     

Numerical Analysis of Imbibition Front Evolution in Fractured Sandstone under Capillary-Dominated Conditions

Fractures serve as primary conduits having a great impact on the migration of injected fluid into fractured permeable media. Appropriate transport properties such as relative permeability and capillary pressure are essential for successful simulation and prediction of multi-phase flow in such systems. However, the lack of a thorough understanding of the dynamics governing immiscible displacement in fractured media, limits our ability to properly represent their macroscopic transport properties. Previous experimental observations of imbibition front evolution in fractured rocks are examined in the present study using an automated history-matching approach to obtain representative relative permeability and capillary pressure curves. Predicted imbibition front evolution under different flow conditions resulted in an excellent agreement with experimental observations. Sensitivity analyses, in combination with direct experimental observation, allowed exploring the competing effects of relative permeability and capillary pressure on the development of saturation distribution and imbibing front evolution in fractured porous media. Results show that residual saturations are most sensitive to matrix relative permeability to oil, while the ratio of oil and water relative permeability, rock heterogeneity, boundary condition, and matrix–fracture capillary pressure contrast, affect displacement shape, speed, and geometry of the imbibing front.     

Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps

The large-scale turbulence and high air content in a hydraulic jump restrict the application of many traditional flow measurement techniques. This paper presents a physical modelling of hydraulic jump, where the total pressure and air–water flow properties were measured simultaneously with intrusive probes, namely a miniature pressure transducer and a dual-tip phase-detection probe, in the jump roller. The total pressure data were compared to theoretical values calculated based upon void fraction, water depth and flow velocity measured by the phase-detection probe. The successful comparison showed valid pressure measurement results in the turbulent shear region with constant flow direction. The roller region was characterised by hydrostatic pressure distributions, taking into account the void fraction distributions. The total pressure fluctuations were related to both velocity fluctuations in the air–water flow and free-surface dynamics above the roller, though the time scales of these motions differed substantially.