Immiscible Displacement In Porous Media Research Articles

Microtomography of Imbibition Phenomena and Trapping Mechanism

Water imbibition during the waterflooding process of oil production only sweeps part of the oil present. After water disrupts the oil continuity, most oil blobs are trapped in porous rock by capillary forces. Developing an efficient waterflooding scheme is a difficult task; therefore, an understanding of the oil trapping mechanism in porous rock is necessary from a microscopic viewpoint. The development of microfocused X-ray CT scanner technology enables the three-dimensional visualization of multiphase phenomena in a pore-scale. We scanned packed glass beads filled with a nonwetting phase (NWP) and injected wetting phase (WP) in upward and downward injections to determine the microscopic mechanism of immiscible displacement in porous media and the effects of buoyancy forces. We observed the imbibition phenomena for small capillary numbers to understand the spontaneous imbibition mechanism in oil recovery. This study is one of the first attempts to use a microfocused X-ray CT scanner for observing the imbibition and trapping mechanisms. The trapping mechanism in spontaneous imbibition is determined by the pore configuration causing imbibition speed differences in each channel; these differences can disrupt the oil continuity. Gravity plays an important role in spontaneous imbibition. In upward injection, the WP flows evenly and oil is trapped in single or small clusters of pores. In downward injection, the fingering phenomena determine the amount of trapped oil, which is usually in a network scale. Water breakthrough causes dramatic decrease in the oil extraction rate, resulting in lower oil production efficiency.

Visual analysis of immiscible displacement processes in porous media under ultrasound effect

The effect of sonic waves, in particular, ultrasonic radiation, on immiscible displacement in porous media and enhanced oil recovery has been of interest for more than five decades. Attempts were made to investigate the effect through core scale experimental or theoretical models. Visual experiments are useful to scrutinize the reason for improved oil recovery under acoustic waves of different frequency but are not abundant in literature. In this paper, we report observations and analyses as to the effects of ultrasonic energy on immiscible displacement and interaction of the fluid matrix visually in porous media through two-dimensional (2D) sand pack experiments. 2D glass bead models with different wettabilities were saturated with different viscosity oils and water was injected into the models. The experiments were conducted with and without ultrasound. Dynamic water injection experiments were preferred as they had both viscous and capillary forces in effect. The displacement patterns were evaluated both in terms of their shape, size, and the interface characteristics quantitatively and qualitatively to account for the effects of ultrasonic waves on the displacement and the reason for increased oil production under this type of sonic wave. More compact clusters were observed when ultrasonic energy was present in water-wet systems. In the oil-wet cases, more oil was produced after breakthrough when ultrasound was applied and no compact clusters were formed in contrast to the water-wet cases.

Scaling miscible displacement in fractured porous media using dimensionless groups

Scaling of miscible and immiscible displacement in porous media using inspectorial analysis leads us to better understanding of the process. Less has been listed about fractured reservoirs especially with the fracture flow conditions taken into consideration. We derived dimensionless groups using Inspectional Analysis for the miscible displacement in fractured porous media when there is flow through fracture. The solvent–solute transfer between fracture and adjunct matrix is only due to diffusion/flux transfer. Based on the dimensionless groups derived we proposed a new dimensionless group for better defining the effectiveness of the process. The newly proposed group, Matrix-Fracture Diffusion Number ( N M-FD), will be critical in evaluating the performance of enhanced oil recovery, CO 2 sequestration and contaminant transport problems. Laboratory scale experiments were performed for validation and physical interpretation of the ( N M-FD).

On Capillary Slowdown of Viscous Fingering in Immiscible Displacement in Porous Media

Hydrodynamic instability in immiscible porous media flows in the presence of capillarity is investigated here. The analysis and arguments presented here show that the slowdown of instabilities due to capillarity is usually very rapid which makes the flow almost, but not entirely, stable. The profiles of the stable and unstable waves in the far-field are characterized using a novel but very simple approach.

Fluid transfer between tubes in interacting capillary bundle models

The interacting capillary bundle model proposed by Dong et al. [Dong, M., Dullien, F.A.L., Zhou, J.: Trans. Porous Media 31, 213–237 (1998); Dong, M., Dullien, F.A.L., Dai, L., Li, D.: Trans. Porous Media 59, 1–18 (2005); Dong, M., Dullien, F.A.L., Dai, L., Li, D.: Trans. Porous Media 63, 289–304 (2006)] has simulated correctly various aspects of immiscible displacement in porous media, such as oil production histories at different viscosity ratios, the effects of water injection rate and of the oil–water viscosity ratio on the shape of the displacement front and the independence of relative permeabilities of the viscosity ratio. In the interacting capillary bundle model pressure equilibrium was assumed at any distance x measured along the bundle. Interaction between the capillaries also results in transfer of fluids across the capillaries. In the first part of this paper the process of fluid transfer between two capillaries is analysed and an algebraic expression for this flow is derived. Consistency with the assumption of pressure equilibration requires that all transfer must take place at the positions of the oil/water menisci in the tubes without any pressure drop. It is shown that fluid transfer between the tubes has no effect on the predictions obtained with the model. In the second part of the paper the interacting tube bundle model is made more realistic by assuming fluid transfer between the tubes all along the single phase flow regions across a uniform resistance, resulting in pressure differences throughout the single phase regions between the fluids present in the different tubes. The results of numerical simulations obtained with this improved interacting capillary bundle model show only small differences in the positions of the displacement front as compared with the predictions of the idealized model.

A Lagrangian Approach for Oil Recovery in Two-Phase Porous Media Flow

Abstract This paper deals with a fully implicit finite difference scheme for the numerical solution of the Lagrangian form of the porous media fractional flow equation. It covers the theoretical background, description of mathematical formulations, basic assumptions in the models, normalization and transformation between Lagrangian and Eulerian formulations, specification of boundary conditions, discretization and solution method. Some numerical examples are described and the results compared favourably with co-current immiscible displacement data. The solution presented is more efficient than the finite element solution method in terms of requiring less matrix computation effort and it is much more stable than the explicit finite difference solution methods that have been presented in the literature. Due to the ease of formulation and use, the simulation algorithm presented can be used to formulate laboratory numerical simulators that can be used routinely for co-current flow numerical studies. Introduction An equation of the form: Equation (1) (Available In Full Paper) is one of the various Lagrangian forms of the fractional flow equation for two-phase, immiscible displacement in porous media. It is Lagrangian because this configuration allows the equation to be solved as a function of saturation and time. The Eulerian configuration enables the equation to be solved as a function of space and time. Bentsen(1) first derived Equation (1), also called the Bentsen equation(2,3). It was subsequently re-derived by Shen and Ruth(2,3) using a different derivation approach. The equation was derived by combining Darcy's equation for two-phase flow with the continuity equation and by transforming the resulting fractional flow Eulerian form to Lagrangian form. A summary of this derivation is presented later in the paper. This equation, together with normalized forms of the displacement (frontal advance) equation, can be solved to produce a numerical description of a two-phase, incompressible, immiscible displacement process in porous media. The main aim of using the Lagrangian approaches is to enable a more computationally efficient scheme and eliminate the need for space discretization as distance is eliminated from the resulting equation. The form presented in Equation (1) is particularly useful because it is very compact. Theoretical Background Douglas et al.(4) presented an Eulerian technique for solving linear waterflooding problems which involved using a transformed saturation variable and the use of a small mobile water saturation ahead of the flood front to enable the base of the flood front to move forward. Fayers and Sheldon(5) obtained solutions to the one-dimensional displacement equation using both the Lagrangian and the Eulerian approaches. McEwen(6) used the method of characteristics for a numerical solution of the linear displacement equation with capillary pressure. Hovanessian and Fayers(7) also solved numerically the equations describing waterflooding experiments that include both gravity and capillary effects. Their method is similar to that of Douglas et al.(4) because it involves the use of the Eulerian form of the fractional flow equation and the transformation of the resulting second-order non-linear partial differential equations. Hovanessian and Fayers(7) solution differs from those of Douglas et al.(4) because it includes the effect of gravity, allows for the calculation of pressure profiles and makes use of a tabular format for the input of relative permeability and capillary pressure values instead of the u

Linking drainage front morphology with gaseous diffusion in unsaturated porous media: A lattice Boltzmann study

The effect of drainage front morphology on gaseous diffusion through partially saturated porous media is analyzed using the lattice Boltzmann method (LBM). Flow regimes for immiscible displacement in porous media have been characterized as stable displacement, capillary fingering, and viscous fingering. The dominance of a flow regime is associated with the relative magnitudes of gravity, viscous, and capillary forces, quantifiable via the Bond number Bo, capillary number Ca, and their difference, Bo-Ca . Forced drainage from an initially saturated two-dimensional (2D) porous medium was simulated and the resulting flow patterns were analyzed and compared with theoretical predictions and experimental results. The LBM simulations reproduced expected flow morphologies for a range of drainage velocities and gravitational forces (i.e., a range of capillary and Bond numbers). Furthermore, measures of drainage front width as a function of the dimensionless difference Bo-Ca correspond well with scaling laws derived from percolation theory. Effects of flow morphology on residual fluid entrapment and gaseous diffusion were assessed by running LBM diffusion simulations through the partially saturated domain for a range of water contents. The effective diffusion coefficient as a function of water content was estimated for three regimes: stable drainage front, capillary fingering, and viscous fingering. Significant reductions in gaseous diffusion coefficient were found for viscous fingering relative to stable displacement, and to a lesser extent for capillary fingering, indicating that wetting phase distribution with a high degree of fingering in the 2D domain severely restricts connectivity of gas diffusion pathways through the medium. The study lends support for the use of LBM in design and management of fluids in porous media under variable gravity, and enhances the understanding of the role of dynamic fluid behavior on macroscopic transport properties of partially saturated porous media.

Scaling Immiscible Displacements in Porous Media with Horizontal Wells

Despite the increase in horizontal well applications, scaling fluid displacement in porous medium with horizontal wells is yet to be fully investigated. Determining the conditions under which horizontal wells may lead to better oil recovery is of great importance to the petroleum industry. In this paper, a numerical sensitivity study was performed for several well configurations. The study is performed in order to reveal the functional relationships between the scaling groups governing the displacement and the performance of immiscible displacements in homogeneous reservoirs produced by horizontal wells. These relationships can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. In addition, they provide the condition under which a horizontal well configuration may yield better recovery performance. These results have potential applications in modeling immiscible displacements and in the scaling of laboratory displacements to field conditions.

Influence of Relative Permeability on the Stability Characteristics of Immiscible Flow in Porous Media

Relative permeability functions for immiscible displacements in porous media show a wide range of profiles. Although, this behavior is well known, its impact on the stability of the displacement process is unexplored. Our analysis clearly demonstrates for the first time that the viscous instability characteristics of two-phase flows are governed not only by their end point values, but are strongly dependent on the actual profile of relative permeability functions. Linear stability analysis predicts the capacity of the flow to develop large scale fingers which can result in substantial bypassing of the resident fluid. It is observed that relative permeability functions attributed to drainage processes yield a more unstable displacement as compared to functions related to imbibition processes. Moreover, instability is observed to increase for those relative permeability functions which result from increased wettability of the wetting fluid. High accuracy numerical simulations show agreement with these predictions and demonstrate how large amplitude viscous fingers result in significant bypassing for certain relative permeability functions. In the nonlinear regime, the finger amplitude grows at a rate ∝ t1/2 initially, drops to t1/4 at a later time and finally grows ∝ t. The basic mechanisms of finger interaction, however, are not substantially influenced by relative permeability functions.

Macroscopic capillarity without a constitutive capillary pressure function

This paper challenges the foundations of the macroscopic capillary pressure concept. The capillary pressure function, as it is traditionally assumed in the constitutive theory of two-phase immiscible displacement in porous media, relates the pressure difference between nonwetting and wetting fluid to the saturation of the wetting fluid. The traditional capillary pressure function neglects the fundamental difference between percolating and nonpercolating fluid regions as first emphasized in R. Hilfer [Macroscopic equations of motion for two phase flow in porous media, Phys. Rev. E 58 (1998) 2090]. The theoretical approach proposed here starts from residual saturations as the volume fractions of nonpercolating phases. The resulting equations of motion open the possibility to describe flow processes where drainage and imbibition occur simultaneously. The theory predicts hysteresis and process dependence of capillary phenomena. The traditional theory is recovered as a special case in the residual decoupling approximation. Explicit calculations are presented for quasistatic equilibrium profiles near hydrostatic equilibrium. The results are found to agree with experiment.

A New Technique to Measure the Breakthrough Capillary Pressure

Abstract The breakthrough capillary pressure is an important macroscopic property of porous media that is used to predict permeability and to correlate capillary pressure curves. It is normally determined using the porous plate method, where the non-wetting phase is introduced into the medium in increasing steps of pressure until it establishes a continuous pathway through the sample. In mercury porosimetry, breakthrough capillary pressure is identified as the pressure corresponding to about 10 - 20% non-wetting phase saturation or the point of inflection in the drainage capillary pressure curve. A new method for measuring the breakthrough capillary pressure has been developed, involving a constant rate injection process as opposed to constant injection pressure. The scope of this paper is to report the accuracy and reliability of the new technique in measuring the breakthrough capillary pressure by reporting test results on transparent micromodels and Berea sandstone core samples. Air or mercury was used as the non-wetting phase while water (or brine, in the case of core samples) was the wetting phase. Constant rate injection was provided by means of a syringe pump, using water to displace a slug of either air or mercury in a tube connected to the porous medium at rates of about 1.8 × 10−2 cm3/min. Pressure was measured at the sample inlet using a pressure transducer and data were recorded using a data acquisition system. The injection pressure vs. time plot reveals the highest pressure established in such a test, which is identified as the breakthrough capillary pressure. It was concluded that the new test enables the determination of the breakthrough capillary pressure in micromodels with excellent accuracy. The new test was also validated using a sandstone core sample. Introduction In the literature of immiscible displacement in porous media, the terms "breakthrough capillary pressure," "threshold pressure," "entry pressure," and "bubbling pressure" are frequently encountered. It has been observed, for example, that in order to make a non-wetting phase, such as air, flow through a porous medium saturated with brine, the applied capillary pressure on the air side has to exceed a critical limiting value, Pc °, at which air can flow through the medium (i.e., can break through and emerge as bubbles from the outlet face of the sample). The pore channels in the medium used by the air to break through the sample are made up of pore sizes greater than or equal to the pore size De °, defined by Equation (Available In Full Paper) Where γ is the interfacial tension, θ is the contact angle, and De ° is the (equivalent) diameter of a capillary tube of circular cross-section which requires the same capillary pressure, Pc °, for penetration as that measured at breakthrough capillary pressure in the porous medium. The value of De ° calculated using Equation (1) is the minimum capillary size that is necessary for the non-wetting phase to invade and break through the medium.

Characterisation of Gas Transport Properties of the Opalinus Clay, a Potential Host Rock Formation for Radioactive Waste Disposal

The Opalinus Clay in Northern Switzerland has been identified as a potential host rock formation for the disposal of radioactive waste. Comprehensive understanding of gas transport processes through this low-permeability formation forms a key issue in the assessment of repository performance. Field investigations and laboratory experiments suggest an intrinsic permeability of the Opalinus Clay in the order of 10-20 to 10-21 m2 and a moderate anisotropy ratio 25 nm. The determined entry pressures are in the range of 0.4-10 MPa and exhibit a marked dependence on intrinsic permeability. Both in situ gas tests and gas permeameter tests on drillcores demonstrate that gas transport through the rock is accompanied by porewater displacement, suggesting that classical flow concepts of immiscible displacement in porous media can be applied when the gas entry pressure (i.e. capillary threshold pressure) is less than the minimum principal stress acting within the rock. Essentially, the pore space accessible to gas flow is restricted to the network of connected macropores, which implies a very low degree of desaturation of the rock during the gas imbibition process. At elevated gas pressures (i.e. when gas pressure approaches the level of total stress that acts on the rock body), evidence was seen for dilatancy controlled gas transport mechanisms. Further field experiments were aimed at creating extended tensile fractures with high fracture transmissivity (hydro- or gasfracs). The test results lead to the conclusion that gas fracturing can be largely ruled out as a risk for post-closure repository performance.

On the Numerical Simulation of Three‐Phase Reservoir Transport Problems

We introduce a new method for the numerical solution of three‐phase immiscible displacement in porous media. An operator splitting technique allows for the use of distinct time steps for the solution of advection and diffusion problems defined by the procedure. A nonlinear system of conservation laws is approximated by a nonoscillatory, second order, conservative central difference scheme in the advection step. Locally conservative mixed finite elements are used to discretize the nonlinear diffusion system. A simulator was developed to solve one‐dimensional problems and it was shown to be accurate and efficient through a set of numerical experiments. The numerical solutions are in very good agreement with semi‐analytic results available in the literature. In these numerical solutions transitional waves, which have a strong dependency upon the physical diffusion being modeled, have been captured.

Recent advances in pore-scale models for drying of porous media

This paper presents a review of the recent advances in pore-scale modelling of drying in capillary porous media. The development of pore network models in drying has been first motivated by several fundamental features of drying that cannot be fully explained within the framework of continuum models. These features include the dry patch phenomenon and the constant drying rate period. A second source of motivation has been the advances made in pore-scale modelling of immiscible displacements in porous media and the increasing conviction that concepts developed in this area could be utilised to model drying. These concepts are recalled. We describe how they have been used for developing a pore network model of drying driven by mass transfer. A review of the main results is made, including pattern formation, drying rates and some recent results regarding drying of a porous medium containing a binary mixture and the influence of heat transfer. The use of network models for computing effective transport properties is discussed. Open problems are discussed.

Concentration profiles of reactant in a viscous finger formed during the interfacially reactive immiscible displacements in porous media

A simple unsteady-state convective-diffusion model was employed to simulate reactant concentration profiles in a viscous finger, which is created during interfacially reactive displacement of two immiscible fluids in porous media. A two-dimensional system was considered. It was assumed that the finger grew in one direction at a constant flow rate and that a fast chemical reaction was taking place at the oil–water interface layer. Interaction with reservoir rock was also taken into account. Two types of convective flow were studied: steady-state laminar flow with a parabolic velocity profile and plug flow with a flat velocity profile. The numerical method of lines was used to solve the model equation. A significant decrease of reactant concentration in the water phase, especially in the fingertip area was observed. This can cause important changes in interfacial behavior and influence the efficiency of fluid displacement. The model numerically confirmed previous visual observations of displacing patterns during the displacement of acidified oil by alkaline solutions.

Macroscopic two-phase flow in porous media

A system of macroscopic equations for two-phase immiscible displacement in porous media is presented. The equations are based on continuum mixture theory. The pairwise character of interfacial energies is explicitly taken into account. The equations incorporate the spatiotemporal variation of interfacial energies and residual saturations. The connection between these equations and relative permeabilities is established, and found to be in qualitative agreement with experiment.

Convergence analysis of a mass-conserving approximation of immiscible displacement in porous media by mixed finite elements and a modified method of characteristics with adjusted advection

The MMOC procedure for approximating the solutions of transport-dominated diffusion problems does not automatically preserve integral conservation laws, leading to (mass) balance errors in many kinds of flow problems. The variant, called the MMOCAA, discussed herein preserves the conservation law at a minor additional computational cost. The application of the MMOCAA to a problem in two-phase, immiscible flow in porous media is discussed.

Scaling theory of drying in porous media

Concepts of immiscible displacements in porous media driven by mass transfer are utilized to model drying of porous media. Visualization experiments of drying in two-dimensional glass micromodels are conducted to identify pore-scale mechanisms. Then, a pore network approach is used to analyze the advancing drying front. It is shown that in a porous medium, capillarity induces a flow that effectively limits the extent of the front, which would otherwise be of the percolation type, to a finite width. In conjuction with the predictions of a macroscale stable front, obtained from a linear stability analysis, the process is shown to be equivalent to invasion percolation in a stabilizing gradient. A power-law scaling relation of the front width with a diffusion-based capillary number is also obtained. This capillary number reflects the fact that drying is controlled by diffusion in contrast to external drainage. The scaling exponent predicted is compatible with the experimental results of Shaw [Phys Rev. Lett. 59, 1671 (1987)]. A framework for a continuum description of the upstream drying regimes is also developed.

Macroscopic equations of motion for two-phase flow in porous media

The usual macroscopic equations of motion for two-phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore, a more general system of macroscopic equations is derived here that incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach that exhibit a complex dependence on the state variables. A capillary pressure function can be identified in equilibrium that shows the qualitative saturation dependence known from experiment. In addition, the proposed equations include a description of the spatiotemporal changes of residual saturations during immiscible displacement.

Stochastic analysis of immiscible displacement in porous media

The interface of two immiscible fluids flowing in porous media may behave in an unstable fashion. This instability is governed by the pore distribution, differential viscosity and interface tension between the two immiscible fluids. This study investigates the factors that control the interface instability at the wetting front. The development of the flow equation is based on the mass balance principle, with boundary conditions such as the velocity continuity and capillary pressure balance at the interface. By assuming that the two-phase fluids in porous media are saturated, a covariance function of the wetting front position is derived by stochastic theory. According to those results, the unstable interface between two immiscible fluids is governed by the fluid velocity and properties such as viscosity and density. The fluid properties that affect the interface instability are expressed as dimensionless parameters, mobility ratio, capillary number and Bond number. If the fluid flow is driven by gravitational force, whether the interface undergoes upward displacement or downward displacement, the variance of the unstable interface decreases with an increasing mobility ratio, increases with increasing capillary number, and decreases with increasing Bond number. For a circumstance in which fluid flow is horizontal, our results demonstrate that the capillary number does not influence the generation of the unstable interface.