Phase Behaviour,Fluid Properties and Recovery Efficiency of Immiscible and Miscible Condensate Displacements by SCCO<Subscript>2</Subscript> Injection: Experimental Investigation

This paper presents a quantitative investigation of the interfacial tension dependent relative permeability (IFT-DRP) and displacement efficiency of supercritical CO₂ injection into gas-condensate reservoirs. A high-pressure high-temperature experimental laboratory was established to simulate reservoir conditions and to perform relative permeability measurements on sandstone cores at a constant reservoir temperature of 95°C and displacement velocity of 10 cm/h. This investigation covers immiscible displacements (1100 and 2100 psi), near-miscible displacement (3000 psi) and miscible displacements (4500 and 5900 psi). The coreflooding results demonstrated that displacement pressure is a key factor governing the attainment of optimum sweep efficiency. The ultimate condensate recovery increased by almost threefold when CO₂ was injected at near-miscible conditions (i.e., 23.40% ultimate recovery at 1100 psi compared to 69.70% at 3000 psi). Miscible flooding was found to give the optimum condensate recovery (9% extra ultimate recovery compared to near-miscible injection). Besides improving the ultimate recovery, miscible floods provided better mobility ratios and delayed gas breakthrough (0.62 PV BT at 5900 psi compared to 0.21 PV BT at 1100 psi). In addition to the elimination of IFT forces in miscible displacements, favourable ratios of fluid properties and phase behaviour relationships between the SCCO₂ and condensate were believed to be the driving force for the improved recovery as they provided a stabilising effect on the displacement front and stimulated swelling of the condensate volume. This paper incorporates the theoretical aspects of phase behaviour and fluid properties that largely affect the microscopic displacement efficiency and serves as a practical guideline for operators to aid their project designs and enhance their recovery capabilities.     

Mixing and Mass Transfer in Multicontact Miscible Displacements

In this work, we investigate the accuracy of some physical models that are frequently used to describe and interpret dispersive mixing and mass transfer in compositional reservoir simulation. We have designed a quaternary analog fluid system (alcohol?Cwater?Chydrocarbon) that mimics the phase behavior of CO₂-hydrocarbon mixtures at high pressure and temperature. A porous medium was designed using PolyTetraFlouroEthylene (PTFE) materials to ensure that the analog oil acts as the wetting phase, and the properties of the porous medium were characterized in terms of porosity, permeability and dispersivity. Relative permeability and interfacial tension (IFT) measurements were also performed to delineate interactions between the fluid system and the porous medium. The effluent concentrations from two-component first-contact miscible (FCM) displacement experiments exhibit a tailing behavior that is attributed to imperfect sweep of the porous medium: A feature that is not captured by normal dispersion models. To represent this behavior in displacement calculations, we use dual-porosity (DP) models including mass transfer between flowing and stagnant porosities. Two 4-component two-phase displacement experiments were performed at near-miscible and multicontact miscible (MCM) conditions and the effluent concentrations were interpreted by numerical calculations. We demonstrate that the accuracy of our displacement calculations relative to the experimental observations is sensitive to the selected models for dispersive mixing, mass transfer between flowing and stagnant porosities, and IFT scaling of relative permeability functions. We also demonstrate that numerical calculations substantially agree with the experimental observations for some physical models with limited need for model parameter adjustment. The combined experimental and modeling effort presented in this work identifies and explores the impact of a set of physical mechanisms (dispersion and mass transfer) that must be upscaled adequately for field-scale displacement calculations in DP systems.     

Visualisation of Residual Oil Recovery by Near-miscible Gas and SWAG Injection Using High-pressure Micromodels

We present results of high-pressure micromodel visualizations of pore-scale fluid distribution and displacement mechanisms during the recovery of residual oil by near-miscible hydrocarbon gas and SWAG (simultaneous water and gas) injection under conditions of very low gas–oil IFT (interfacial tension), negligible gravity forces and water-wet porous medium. We demonstrate that a significant amount of residual oil left behind after waterflooding can be recovered by both near-miscible gas and SWAG injection. In particular, we show that in both processes, the recovery of the contacted residual oil continues behind the main gas front and ultimately all of the oil that can be contacted by the gas will be recovered. This oil is recovered by a microscopic mechanism, which is strongly linked to the low IFT between the oil and gas and to the perfect spreading of the oil over water, both of which occur as the critical point of the gas–oil system is approached. Ultimate oil recovery by near-miscible SWAG injection was as high as near-miscible gas injection with SWAG injection using much less gas compared to gas injection. Comparison of the results of SWAG experiments with two different gas fractional flow values (SWAG ratio) of 0.5 and 0.2 shows that fractional flow of the near-miscible gas injected simultaneously with water is not a crucial factor for ultimate oil recovery. This makes SWAG injection an attractive IOR (improved oil recovery) process especially for reservoirs, where continuous and high-rate gas injection is not possible (e.g. due to supply constraint).     

Microscopic Mechanisms of Oil Recovery By Near-Miscible Gas Injection

As gas flooding becomes a more viable means of enhanced oil recovery, it is important to identify and understand the pore-scale flow mechanisms, both for the development of improved gas flooding applications and for the predicting phase mobilisation under secondary and tertiary gas flooding. The purpose of this study was to visually investigate the pore-level mechanisms of oil recovery by near-miscible secondary and tertiary gas floods. High-pressure glass micromodels and model fluids representing a near-miscible fluid system were used for the flow experiments. A new pore-scale recovery mechanism was identified which significantly contributed to oil recovery through enhanced flow and cross-flow between the bypassed pores and the injected gas. This mechanism is strongly related to a very low gas/oil interfacial tension (IFT), perfect wetting conditions and simultaneous flow of gas and oil in the same pore, all of which occur as the gas/oil critical point is approached. The results of this study helps us to better understand the pore-scale mechanisms of oil recovery in very low-IFT (near-miscible) systems. In particular we show that in near-miscible gas floods, behind the main gas front, the recovery of the oil continues by cross-flow from the bypassed pores into the main flow stream and as a result almost all of the oil, which has been contacted by the gas, could be recovered. Our observations in high-pressure micromodel experiments have demonstrated that this mechanism can only occur in near-miscible processes (as opposed to immiscible and completely miscible processes), which makes oil displacement by near-miscible gas floods a very effective process.     

Relative Permeability Analysis of Tube Bundle Models

The analytical solution for calculating two-phase immiscible flow through a bundle of parallel capillary tubes of uniform diametral probability distribution is developed and employed to calculate the relative permeabilities of both phases. Also, expressions for calculating two-phase flow through bundles of serial tubes (tubes in which the diameter varies along the direction of flow) are obtained and utilized to study relative permeability characteristics using a lognormal tube diameter distribution. The effect of viscosity ratio on conventional relative permeability was investigated and it was found to have a significant effect for both the parallel and serial tube models. General agreement was observed between trends of relative permeability ratios found in this work and those from experimental results of Singhal et al. (1976) using porous media consisting of mixtures of Teflon powder and glass beads. It was concluded that neglecting the difference between the average pressure of the non-wetting phase and the average pressure of the wetting phase (the macro-scale capillary pressure) – a necessary assumption underlying the popular analysis methods of Johnson et al. (1959) and Jones and Roszelle (1978) – was responsible for the disparity in the relative permeability curves for various viscosity ratios. The methods therefore do not account for non-local viscous effects when applied to tube bundle models. It was contended that average pressure differences between two immiscible phases can arise from either capillary interfaces (micro-scale capillary pressures) or due to disparate pressure gradients that are maintained for a flow of two fluids of viscosity ratio that is different from unity.     

Structure and stability of the interface in a magnetizable fluid

The problems of interface stability in magnetizable and polarizable fluids are considered in the case of the surface tension tensor dependent on the electromagnetic field strength. For describing this dependence the model proposed by A.N. Golubyatnikov (1986) is used. The investigation of the internal interface structure showed that for single-component systems, as a rule, the dependence of the surface tension on the field strength corresponds to surface phase properties paramagnetic in the normal and diamagnetic in the tangential direction. It is shown that within the framework of the model adopted the thermodynamic stability of the surface depends on the thickness of the interphase layer. Necessary stability conditions are obtained for plane interfaces in media with a constant magnetic permeability outside the interphase layer. The problem of stability of the horizontal free surface of an ideal magnetic field in an external magnetic field (similar to the problem of stability of the horizontal interface of two polarizable fluids in an external electric field) is solved for an arbitrary orientation of the external field relative to the interface. The stability loss is now accompanied by qualitative effects absent in the case of the surface tension tensor independent of the electromagnetic field strength.     

Theoretical Approach to the Onset of Convection in a Porous Layer

We examine the effect of viscous forces on the displacement of one fluid by a second, immiscible fluid along parallel layers of contrasting porosity, absolute permeability and relative permeability. Flow is characterized using five dimensionless numbers and the dimensionless storage efficiency, so results are directly applicable, regardless of scale, to geologic carbon storage. The storage efficiency is numerically equivalent to the recovery efficiency, applicable to hydrocarbon production. We quantify the shock-front velocities at the leading edge of the displacing phase using asymptotic flow solutions obtained in the limits of no crossflow and equilibrium crossflow. The shock-front velocities can be used to identify a fast layer and a slow layer, although in some cases the shock-front velocities are identical even though the layers have contrasting properties. Three crossflow regimes are identified and defined with respect to the fast and slow shock-front mobility ratios, using both theoretical predictions and confirmation from numerical flow simulations. Previous studies have identified only two crossflow regimes. Contrasts in porosity and relative permeability exert a significant influence on contrasts in the shock-front velocities and on storage efficiency, in addition to previously examined contrasts in absolute permeability. Previous studies concluded that the maximum storage efficiency is obtained for unit permeability ratio; this is true only if there are no contrasts in porosity and relative permeability. The impact of crossflow on storage efficiency depends on the mobility ratio evaluated across the fast shock-front and on the time at which the efficiency is measured.     

Models for Ground Water Flow: A Numerical Comparison Between Richards' Model and the Fractional Flow Model

In this paper we compare two models for flow in porous media. The first is the well known Richards' equation, which is based on the assumption that the air in the unsaturated zone has infinite mobility. This means that it models a single phase. In the second and more general full two-phase approach, the air is considered as a separate phase. Here, we use the fractional flow equation.We study the difference between the two models numerically by varying the relative contribution of the different physical terms (the gravity and the total velocity) in the fractional flow equation. Richards' equation is considered as the limit of the fractional flow approach when the mobility of the air-phase tends to infinity. In particular, we are interested in determining the parameter intervals where the two models differ significantly, and we will quantify the asymptotic behavior.The equations are studied in the two-dimensional (2D) case. The study is based on a relative permeability depending quadratically on the saturation, and a capillary pressure expressed by a cubic function of the saturation.     

Anisotropy effects in two-phase flows through porous media

Effects manifested in two-phase flows through anisotropic porous reservoirs with monoclinic and triclinic characteristics are analyzed. It is shown that in two-phase flows through media with monoclinic and triclinic symmetries of flow characteristics the position of the principal axes of the phase permeability tensors depends on the saturation and does not coincide with the position of the principal axes of the absolute permeability tensor in single-phase flows and that going over from single-to two-phase flow may lead to a change in the symmetry group of the flow characteristics. A general representation of the phase permeability tensor components is presented and formulas are given for the diagonal and nondiagonal components of the relative phase permeabilities, which are universal and can be used for anisotropic media with any type of anisotropy (symmetry) of flow characteristics. A complex of laboratory tests for finding the nondiagonal components of the phase and relative phase permeability tensors is discussed.     

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.     

Percolation model of two-phase equilibrium flow in a porous medium with microheterogeneous wettability

The percolation model of two-phase flow described in [1, 2] is used as a basis for examining the problem of the behavior of the characteristics of two-phase equilibrium flow in a porous medium when the capillaries have a radius distribution and differ with respect to the wettability properties of their surfaces. Analytic expressions describing the dependence of the relative phase permeability coefficients on the saturation of the medium by the displacing phase and the microinhomogeneous wettability parameters are obtained. A qualitative comparison shows the theoretical results to be consistent with the data of a direct numerical computer calculation of a grid model [3]. The effect of the microinhomogeneity parameters and the form of the capillary radius distribution function on the phase permeabilities is analyzed within the framework of the approach developed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 86–93, September–October, 1989.     

应变局部化分析中两类不同材料模型的讨论

特定情况下单相固体材料率相关模型与多孔介质中的渗流作用均对问题的动力应变局部化分析产生内尺度律效应，对两类问题基本解之间的关系进行讨论，给出了两类不同材料模型解之间的若干联系．     

Generalized fourier analyses of the advection–diffusion equation—Part II: two‐dimensional domains

Part I of this work presents a detailed multi‐methods comparison of the spatial errors associated with the one‐dimensional finite difference, finite element and finite volume semi‐discretizations of the scalar advection–diffusion equation. In Part II we extend the analysis to two‐dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one‐dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control‐volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out‐perform their lumped mass counterparts and finite‐difference based schemes. While this work can only be considered a first step in a comprehensive multi‐methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.     

Pore-Scale Imaging and Analysis of Wettability Order,Trapping and Displacement in Three-Phase Flow in Porous Media with Various Wettabilities

Three-phase flow in porous media is encountered in many applications including subsurface carbon dioxide storage, enhanced oil recovery, groundwater remediation and the design of microfluidic devices. However, the pore-scale physics that controls three-phase flow under capillary dominated conditions is still not fully understood. Recent advances in three-dimensional pore-scale imaging have provided new insights into three-phase flow. Based on these findings, this paper describes the key pore-scale processes that control flow and trapping in a three-phase system, namely wettability order, spreading and wetting layers, and double/multiple displacement events. We show that in a porous medium containing water, oil and gas, the behaviour is controlled by wettability, which can either be water-wet, weakly oil-wet or strongly oil-wet, and by gas–oil miscibility. We provide evidence that, for the same wettability state, the three-phase pore-scale events are different under near-miscible conditions—where the gas–oil interfacial tension is ≤?1 mN/m—compared to immiscible conditions. In a water-wet system, at immiscible conditions, water is the most-wetting phase residing in the corners of the pore space, gas is the most non-wetting phase occupying the centres, while oil is the intermediate-wet phase spreading in layers sandwiched between water and gas. This fluid configuration allows for double capillary trapping, which can result in more gas trapping than for two-phase flow. At near-miscible conditions, oil and gas appear to become neutrally wetting to each other, preventing oil from spreading in layers; instead, gas and oil compete to occupy the centre of the larger pores, while water remains connected in wetting layers in the corners. This allows for the rapid production of oil since it is no longer confined to movement in thin layers. In a weakly oil-wet system, at immiscible conditions, the wettability order is oil–water–gas, from most to least wetting, promoting capillary trapping of gas in the pore centres by oil and water during water-alternating-gas injection. This wettability order is altered under near-miscible conditions as gas becomes the intermediate-wet phase, spreading in layers between water in the centres and oil in the corners. This fluid configuration allows for a high oil recovery factor while restricting gas flow in the reservoir. Moreover, we show evidence of the predicted, but hitherto not reported, wettability order in strongly oil-wet systems at immiscible conditions, oil–gas–water, from most to least wetting. At these conditions, gas progresses through the pore space in disconnected clusters by double and multiple displacements; therefore, the injection of large amounts of water to disconnect the gas phase is unnecessary. We place the analysis in a practical context by discussing implications for carbon dioxide storage combined with enhanced oil recovery before suggesting topics for future work.

     

Effects of Fines Migration on Low-Salinity Waterflooding: Analytical Modelling

We discuss the governing system for oil–water flow with varying water composition. The model accounts for wettability alteration, which affects the relative permeability, and for salinity-variation-induced fines migration, which reduces the relative permeability of water. The overall ionic strength represents the aqueous phase composition in the model. One-dimensional displacement of oil by high-salinity water followed by low-salinity-slug injection and high-salinity water chase drive allows for exact analytical solution. The solution is derived using the splitting method. The analytical model obtained analyses the effects of wettability alteration and fines migration on oil recovery as two distinct physical mechanisms. For typical reservoir conditions, the significant effects of both mechanisms are observed.     

Effect of petrophysical matrix properties on bypassed oil recovery from a matrix-fracture system during CO2 near-miscible injection: Experimental investigation

The effects of petrophysical matrix properties such as porosity and permeability on bypassed oil recovery were investigated during CO₂ injection in fractures at different miscibility regimes (first-contact miscibility, near-miscibility, and immiscibility). A special experimental setup was designed for this purpose and a series of CO₂ injection experiments were performed using two different types of porous media, sandstones and carbonates. To confirm the analysis, some tests were repeated in the presence of irreducible water saturation. In addition, dimensional analysis was used to capture the dominant forces and mechanisms.The results demonstrated that the highest oil recovery was achieved within near-miscible regime for the both rock types. Furthermore, in all miscibility regimes, the oil recovery factor decreased with the increase of the rock complexity and frequency of dead-end pores, whereas it declined as the permeability decreased. However, differences in recovery factors of near-critical and super-critical tests grew. Considering the analytical calculations and the results of experiments including initial water saturation, it can be concluded that near-critical point wetting and the number of dead-end pores have significant effects on variations of the oil recovery factor. With near-critical point wetting, maximum recovery was achieved at near-critical state, and the presence of dead-end pores caused the role of this mechanism to be more noticeable. As a result, differences in the recovery factor of near-critical and super-critical tests grew.     

Effect of Network Topology on Relative Permeability

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res. 105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.     

Capillary Heterogeneity Trapping and Crossflow in Layered Porous Media

We examine the effect of capillary and viscous forces on the displacement of one fluid by a second, immiscible fluid across and along parallel layers of contrasting porosity, and relative permeability, as well as previously explored contrasts in absolute permeability and capillary pressure. We consider displacements with wetting, intermediate-wetting and non-wetting injected phases. Flow is characterized using six independent dimensionless numbers and a dimensionless storage efficiency, which is numerically equivalent to the recovery efficiency. Results are directly applicable to geologic carbon storage and hydrocarbon production. We predict how the capillary–viscous force balance influences storage efficiency as a function of a small number of key dimensionless parameters, and provide a framework to support mechanistic interpretations of complex field or experimental data, and numerical model predictions, through the use of simple dimensionless models. When flow is directed across layers, we find that capillary heterogeneity traps the non-wetting phase, regardless of whether it is the injected or displaced phase. However, minimal trapping occurs when the injected phase is intermediate-wetting or when high-permeability layers contain a smaller moveable volume of fluid than low-permeability layers. A dimensionless capillary-to-viscous number defined using the layer thickness rather than the more commonly used system length is most relevant to predict capillary heterogeneity trapping. When flow is directed along layers, we show that, regardless of wettability, increasing capillary crossflow reduces the distance between the leading edges of the injected phase in each layer and increases storage efficiency. This may be counter-intuitive when the injected phase is non-wetting. Crossflow has a significant impact on storage efficiency only when high-permeability layers contain a smaller moveable volume of fluid than low-permeability layers. In that case, capillary heterogeneity traps the wetting phase, regardless of whether it is the injected or displaced phase.     

Investigation of Generalized Relative Permeability Coefficients for Electrically Assisted Oil Recovery in Oil Formations

Evaluation of relative permeability coefficients is one of the key steps in reliable simulation of two-phase flow in porous media. An extensive body of work exists on evaluation of these coefficients for two-phase flow under pressure gradient. Oil transport under an applied electrical gradient in porous media is also governed by the principles of two-phase flow, but is less understood. In this paper, relative permeability coefficients under applied electric field are evaluated for a specific case of two- phase fluid flow in water-wet porous media, where the second fluid phase is oil. It is postulated that the viscous drag on the oil phase, exerted by the electro-osmotic flow of the water phase, is responsible for the transport of oil in the absence of a pressure gradient. Reliable prediction of the flow patterns necessitates accurate representation and determination of the relative permeability coefficients under the electrical gradient. The contribution of each phase to the flow is represented mathematically, and the relative permeability coefficients are evaluated through electro-osmotic flow measurements conducted on oil bearing rock cores.