Extended Roof snap-off for a continuous nonwetting fluid and an example case for supercritical CO2

A dominant mechanism for residual trapping of a nonwetting fluid in porous media during imbibition is snap-off or the disconnection of a continuous stream of the nonwetting fluid when it passes through pore constrictions and when a criterion based on capillary pressure imbalance is met. While quasi-static criteria for Roof snap-off have been defined for pores based on the imbalance between capillary pressure across the front/tail meniscus and local capillary pressure at the pore throat, and expressed in terms of pore body to pore throat ratio for simplification, we extended the previous quasi-static snap-off criterion by considering the local capillary pressure imbalance between the pore body and the pore throat for both circular and noncircular pores when the wetting film exists. We then used the criterion to analyze results from computational fluid dynamics (CFD) simulations of multi-phase flow with supercritical CO₂ as the nonwetting fluid and water as the wetting fluid. The extended criterion successfully described most situations we modeled. Furthermore, we compared fluid interface shape for a noncircular 3D pore predicted by the minimum surface energy (MSE) theory against 3D CFD simulations. While the fluid interface shape at the pore throat for 3D simulation was consistent with the shape predicted by MSE theory, the shape could not be successfully predicted by the MSE theory at the upstream and downstream pore body. Moreover, film flow existed for the noncircular pore at the downstream pore body.     

Modeling the velocity field during Haines jumps in porous media

When nonwetting fluid displaces wetting fluid in a porous rock many rapid pore-scale displacement events occur. These events are often referred to as Haines jumps and any drainage process in porous media is an ensemble of such events. However, the relevance of Haines jumps for larger scale models is often questioned. A common counter argument is that the high fluid velocities caused by a Haines jump would average-out when a bulk representative volume is considered. In this work, we examine this counter argument in detail and investigate the transient dynamics that occur during a Haines jump. In order to obtain fluid–fluid displacement data in a porous geometry, we use a micromodel system equipped with a high speed camera and couple the results to a pore-scale modeling tool called the Direct HydroDynamic (DHD) simulator. We measure the duration of a Haines jump and the distance over which fluid velocities are influenced because this sets characteristic time and length scales for fluid–fluid displacement. The simulation results are validated against experimental data and then used to explore the influence of interfacial tension and nonwetting phase viscosity on the speed of a Haines jump. We find that the speed decreases with increasing nonwetting phase viscosity or decreasing interfacial tension; however, for the same capillary number the reduction in speed can differ by an order of magnitude or more depending on whether viscosity is increased or interfacial tension is reduced. Therefore, the results suggest that capillary number alone cannot explain pore-scale displacement. One reason for this is that the interfacial and viscous forces associated with fluid–fluid displacement act over different length scales, which are not accounted for in the pore-scale definition of capillary number. We also find by analyzing different pore morphologies that the characteristic time scale of a Haines jump is dependent on the spatial configuration of fluid prior to an event. Simulation results are then used to measure the velocity field surrounding a Haines jump and thus, measure the zone of influence, which extends over a distance greater than a single pore. Overall, we find that the time and length scales of a Haines jump are inversely proportional, which is important to consider when calculating the spatial and temporal averages of pore-scale parameters during fluid–fluid displacement.     

Pore-scale imbibition experiments in dry and prewetted porous media

Two-phase imbibition behavior of immiscible fluids was studied in dry and prewetted porous media using a laser-induced fluorescence technique. Imbibition was first investigated in two-dimensional (2-D) systems under conditions comparable to those for a study of drainage [Ovdat H, Berkowitz B. Pore-scale study of drainage displacement under combined capillary and gravity effects in index-matched porous media. Water Resources Research 2006;42:W06411. doi:10.1029/2005WR004553] in the capillary-dominated regime. The effect of initial wetting saturation (IWS) was then explored in 2-D and 3-D porous media under the combined effect of gravity, capillary and viscous forces, within and outside the capillary-dominated regime. Parameters that describe maximum vertical advance, volumetric fraction, total surface area and specific surface area of the invading fluid were used to quantify the behavior. Comparison of 2-D drainage and imbibition patterns demonstrates significant qualitative differences under analogous viscosity ratio, buoyancy number, and capillary number values. However, quantitative analyses show strong pore-scale similarities between these patterns. Invasion structures in 3-D, prewetted (IWS ≈ 8% of the pore volume) porous media are ramified, with lateral branching and regions containing trapped residual fluid. These structures are qualitatively and quantitatively different from the compact, branchless structures that develop in dry (IWS = 0) porous media.     

Co-sequestration of SO2 with supercritical CO2 in carbonates: An experimental study of capillary trapping,relative permeability,and capillary pressure

In this study we performed three categories of steady- and unsteady-state core-flooding experiments to investigate capillary trapping, relative permeability, and capillary pressure, in a scCO₂ + SO₂/brine/limestone system at elevated temperature and pressure conditions, i.e., 60 °C and 19.16 MPa. We used a Madison limestone core sample acquired from the Rock Springs Uplift in southwest Wyoming. We carried out two sets of steady-state drainage-imbibition relative permeability experiments with different initial brine saturations to study hysteresis. We found that the final scCO₂ + SO₂ drainage relative permeability was very low, i.e., 0.04. We also observed a rapid reduction in the scCO₂-rich phase imbibition relative permeability curve, which resulted in a high residual trapping. The results showed that between 62.8% and more than 76% of the initial scCO₂ + SO₂ at the end of drainage was trapped by capillary trapping mechanism (trapping efficiency). We found that at higher initial brine saturations, the trapping efficiency was higher. The maximum initial and residual scCO₂-rich phase saturations at the end of primary drainage and imbibition were 0.525 and 0.329, respectively. Each drainage-imbibition cycle was followed by a dissolution process to re-establish S_w = 1. The dissolution brine relative permeabilities for both cycles were also obtained. We characterized the scCO₂ + SO₂/brine capillary pressure hysteresis behavior through unsteady-state primary drainage, imbibition, and secondary drainage experiments. We observed negative imbibition capillary pressure curve indicative of possible wettability alteration throughout the experiments due to contact with scCO₂ + SO₂/brine fluid system. The trapping results were compared to those reported in literature for other carbonate core samples. We noticed slightly more residual trapping in our sample, which might be attributed to heterogeneity, different viscosity ratio, and pore-space topologies. The impact of dynamic effects, i.e., high brine flow rate imbibition tests, on trapping of the scCO₂-rich phase was also explored. We performed two imbibition experiments with relatively high brine flow rates. The residual scCO₂ saturation dropped to 0.291 and 0.262 at the end of the first and second imbibition tests, i.e., 11.5% and 20.4%, respectively, compared to 0.329 under capillary-dominated regime.     

Petrophysical characterization of porous media starting from micro-tomographic images

A quasi-static scheme based on pore space spatial statistics is presented to simulate pore-scale two-phase capillary-dominant displacement processes. The algorithm is coupled with computational fluid dynamics in order to evaluate saturation functions. Wettability heterogeneity in partial and fractional/mixed-wet media is implemented using a contact angle map. The simulation process is pixel-wised and performed directly on binary images. Bypassing and snap-off are tackled as non-wetting phase trapping mechanisms. Post-processing results include residual saturations, effective permeability and capillary pressure curves for drainage and imbibition scenarios. The primary advantages of the proposed workflow are eliminating pore space skeletisation/ discretization, superior time efficiency and minimal numerical drawbacks when compared to other direct or network-based simulation techniques.     

The effect of wettability on capillary trapping in carbonates

We use an organic acid (cyclohexanepentanoic acid) to alter the wettability of three carbonates: Estaillades, Ketton and Portland limestones, and observe the relationship between the initial oil saturation and the residual saturation. We take cores containing oil and a specified initial water saturation and waterflood until 10 pore volumes have been injected. We record the remaining oil saturation as a function of the amount of water injected. In the water-wet case, with no wettability alteration, we observe, as expected, a monotonic increase in the remaining oil saturation with initial saturation. However, when the wettability is altered, we observe an increase, then a decrease, and finally an increase in the trapping curve for Estaillades limestone with a small, but continued, decrease in the remaining saturation as more water is injected. This behavior is indicative of mixed-wet or intermediate-wet conditions, as there is no spontaneous imbibition of oil and water. In contrast, Ketton did not show indications of a significant wettability alteration with a similar observed trapping profile to that observed in the water-wet case. Portland limestone also showed a monotonic increasing trend in remaining saturation with initial saturation but with a higher recovery, and less trapping, than the water-wet case. Again, this is intermediate-wet behavior with no spontaneous imbibition of either oil or water, and slow production of oil after water breakthrough. Finally, we repeat the same experiments but instead we age the three carbonates with a high asphaltenic content and high viscosity crude oil at 70 °C mimicking reservoir conditions. The results show a monotonic increase in residual saturation as a function of initial saturation but with higher recovery than the water-wet cases for Estaillades and Portland, with again no indication of wettability alteration for Ketton. We discuss the results in terms of pore-scale recovery process and contact angle hysteresis. In these experiments, water-saturated micro-porosity appears to protect the solid surfaces from a strong wettability alteration, particularly in Ketton.     

Computation of three-phase capillary entry pressures and arc menisci configurations in pore geometries from 2D rock images: A combinatorial approach

We present a semi-analytical, combinatorial approach to compute three-phase capillary entry pressures for gas invasion into pore throats with constant cross-sections of arbitrary shapes that are occupied by oil and/or water. For a specific set of three-phase capillary pressures, geometrically allowed gas/oil, oil/water and gas/water arc menisci are determined by moving two circles in opposite directions along the pore/solid boundary for each fluid pair such that the contact angle is defined at the front circular arcs. Intersections of the two circles determine the geometrically allowed arc menisci for each fluid pair. The resulting interfaces are combined systematically to allow for all geometrically possible three-phase configuration changes. The three-phase extension of the Mayer and Stowe – Princen method is adopted to calculate capillary entry pressures for all determined configuration candidates, from which the most favorable gas invasion configuration is determined. The model is validated by comparing computed three-phase capillary entry pressures and corresponding fluid configurations with analytical solutions in idealized triangular star-shaped pores. It is demonstrated that the model accounts for all scenarios that have been analyzed previously in these shapes. Finally, three-phase capillary entry pressures and associated fluid configurations are computed in throat cross-sections extracted from segmented SEM images of Bentheim sandstone. The computed gas/oil capillary entry pressures account for the expected dependence of oil/water capillary pressure in spreading and non-spreading fluid systems at the considered wetting conditions. Because these geometries are irregular and include constrictions, we introduce three-phase displacements that have not been identified previously in pore-network models that are based on idealized pore shapes. However, in the limited number of pore geometries considered in this work, we find that the favorable displacements are not generically different from those already encountered in network models previously, except that the size and shape of oil layers that are surrounded by gas and water are described more realistically. The significance of the results for describing oil connectivity in porous media accurately can only be evaluated by including throats with more complex cross-sections in three-phase pore-network models.     

Identifying the representative flow unit for capillary dominated two-phase flow in porous media using morphology-based pore-scale modeling

In this paper, we extend pore-morphology-based methods proposed by Hazlett (1995) and Hilpert and Miller (2001) to simulate drainage and imbibition in uniformly wetting porous media and add an (optional) entrapment of the (non-)wetting phase. By improving implementation, this method allows us to identify the statistical representative elementary volume and estimate uncertainty by computing fluid flow properties and saturation distributions of hundreds of subsamples within a reasonable time-frame. The method was utilized to study three different porous medium systems and results demonstrate that morphology-based pore-scale modeling is a viable approach to assess the representative elementary volume with respect to capillary dominated two-phase flow. The focus of this paper is the determination of the representative elementary volume for multiphase-flow properties for a digital representation of a rock.     

A semi-analytical model for computation of capillary entry pressures and fluid configurations in uniformly-wet pore spaces from 2D rock images

A novel semi-analytical model for computation of capillary entry pressures and associated fluid configurations in arbitrary, potentially non-convex, 2D pore space geometries at uniform wettability is developed. The model computes all possible centre positions of circular arcs, and physically sound criteria are implemented to determine the set of these arcs that correspond to geometrically allowed interfaces. Interfaces and pore boundary segments are connected to form closed boundaries of identified geometrical regions. These regions are classified as either oil regions, located in the wider parts of the pore space, or as water regions located in pore space constrictions. All possible region combinations are identified and evaluated for each radius value in an iterative procedure to determine the favourable entry radius and corresponding configuration based on minimisation of free energy. The model has been validated by comparison with known analytical solutions in idealised pore geometries. In cases where different analytical solutions are geometrically possible, the model generates several oil and water regions, and the valid solution is determined by the region combination that corresponds to the most favourable entry pressure, consistent with the analytical solution. Entry pressure radii and configurations are computed in strongly non-convex pore spaces extracted from an image of Bentheimer sandstone, which demonstrates that the model captures successfully well-known characteristics of capillary behaviour at different wetting conditions. The computations also demonstrate the importance of selecting the fluid configuration of minimum change in free energy. In some cases, a merged region formed by a combination of oil and water regions corresponds to the favourable entry configuration of oil, whereas in other cases, an individual oil region may correspond to the favourable oil entry configuration. It is also demonstrated that oil entry configurations may constitute merged regions for weakly water-wet conditions and individual oil regions for strongly water-wet conditions in the same pore space. The computations show that the ratio of pore area to perimeter multiplied by the cosine of the contact angle under-predicts the entry pressure radii in Bentheimer sandstone pore spaces. An alternative formula is proposed for prediction of entry radii for nonzero contact angles based on the entry radii obtained for zero contact angles.     

Effects of fluid displacement pattern on complex electrical impedance in Berea sandstone over frequency range 104–106 Hz

To better understand the effect of fluid distribution on the electric response of rocks saturated with oil and brine, we conducted experimental studies on the complex electrical impedance in a Berea sandstone, together with in situ acquisitions of oil distribution images employing a high‐resolution medical X‐ray computed tomography. We performed two tests of brine displacement by oil under high (10 MPa) and low (5 MPa) pressures, which were accompanied by fingering and stable displacement patterns, respectively. The measured complex impedance data were fitted to the Cole model to obtain the resistance, capacitance, peak frequency of the imaginary impedance, and the exponent α of the rock–fluid system. With increasing oil saturation, the resistance showed an increasing trend, whereas the other three parameters decreased. The fingering displacement exhibited lower resistance and capacitance than the stable displacement. The analysis of the resistance changes using a simple parallel connection model indicates that there are more components of residual brine in parallel connections in the fingering pattern than in the stable displacement pattern at the same saturation. We also interpreted the normalised changes in the capacitance (or apparent dielectric constant) with respect to the oil saturation via an analysis of the shape factor of fluid distribution based on the Maxwell–Wagner–Brugermann–Hanai model. The changes in the shape factor suggest that the pinch‐off of the brine in parallel connection by the oil is a dominant mechanism reducing the capacitance. In the stable displacement, most of the connections in the brine phase are immediately pinched off by oil displacement front at a local oil saturation of 65%. Conversely, in the fingering displacement, there is a transition from the bulk or layered brine to the pinched‐off at a local oil saturation below 60%. The analyses indicate that the difference in the fluid distribution under different fluid conditions is responsible for the non‐Archie behaviour.     

Theoretical estimation of free and entrapped nonwetting–wetting fluid interfacial areas in porous media

Fluid–fluid interfacial areas play important roles in numerous subsurface processes such as dissolution, volatilization, and adsorption. Integral expressions have been derived to estimate both entrapped (discontinuous) and free (continuous) nonwetting fluid–wetting fluid specific interfacial areas in porous media. The expressions, compatible with widely used capillary head-saturation and entrapment models, require information on capillary head-saturation relation parameters, porosity, and fluid-pair interfacial tension. In addition, information on the maximum entrapped nonwetting fluid saturation as well as the main drainage branch reversal point for water and total liquid saturations is necessary to estimate entrapped fluid interfacial areas. Implementation of the interfacial area equations in continuum-based multifluid flow simulators is straightforward since no additional parameters are needed than those required by the simulators to complete the multifluid flow computations. A limited sensitivity analysis, based on experimentally obtained parameter values, showed that imposed variations resulted in logical and consistent changes in predicted specific interfacial areas for both entrapped and free nonwetting fluid–wetting fluid systems. A direct comparison with published experimental work to test the derived expressions was limited to free air–water systems and yielded reasonable results. Such comparisons are often not possible because of the lack of information given on retention parameters, and variables used to determine nonwetting fluid entrapment. This contribution is dedicated to John W. Cary.     

When 4D seismic is not applicable: Alternative monitoring scenarios for the Arab-D reservoir in the Ghawar Field

Ghawar, the largest oilfield in the world, produces oil from the Upper Jurassic Arab‐D carbonate reservoir. The high rigidity of the limestone–dolomite reservoir rock matrix and the small contrast between the elastic properties of the pore fluids, i.e. oil and water, are responsible for the weak 4D seismic effect due to oil production. A feasibility study was recently completed to quantify the 4D seismic response of reservoir saturation changes as brine replaced oil. The study consisted of analysing reservoir rock physics, petro‐acoustic data and seismic modelling. A seismic model of flow simulation using fluid substitution concluded that time‐lapse surface seismic or conventional 4D seismic is unlikely to detect the floodfront within the repeatability of surface seismic measurements. Thus, an alternative approach to 4D seismic for reservoir fluid monitoring is proposed. Permanent seismic sensors could be installed in a borehole and on the surface for passive monitoring of microseismic activity from reservoir pore‐pressure perturbations. Reservoir production and injection operations create these pressure or stress perturbations. Reservoir heterogeneities affecting the fluid flow could be mapped by recording the distribution of epicentre locations of these microseisms or small earthquakes. The permanent borehole sensors could also record repeated offset vertical seismic profiling surveys using a surface source at a fixed location to ensure repeatability. The repeated vertical seismic profiling could image the change in reservoir properties with production.     

Dissolution of residual non-aqueous phase liquids in porous media: pore-scale mechanisms and mass transfer rates

Experiments designed to elucidate the pore-scale mechanisms of the dissolution of a residual non-aqueous phase liquid (NAPL), trapped in the form of ganglia within a porous medium, are discussed. These experiments were conducted using transparent glass micromodels with controlled pore geometry, so that the evolution of the size and shape of individual NAPL ganglia and, hence, the pore-scale mass transfer rates and mass transfer coefficients could be determined by image analysis. The micromodel design permitted reasonably accurate control of the pore water velocity, so that the mass transfer coefficients could be correlated in terms of a local (pore-scale) Peclet number. A simple mathematical model, incorporating convection and diffusion in a slit geometry was developed and used successfully to predict the observed mass transfer rates. For the case of non-wetting NAPL ganglia, water flow through the corners in the pore walls was seen to control the rate of NAPL dissolution, as recently postulated by Dillard and Blunt [Water Resour. Res. 36 (2000) 439–454]. Break-up of doublet non-wetting phase ganglia into singlet ganglia by snap-off in pore throats was also observed, confirming the interplay between capillarity and mass transfer. Additionally, the effect of wettability on dissolution mass transfer was demonstrated. Under conditions of preferential NAPL wettability, mass transfer from NAPL films covering the solid surfaces was seen to control the dissolution process. Supply of NAPL from the trapped ganglia to these films by capillary flow along pore corners was observed to result in a sequence of pore drainage events that increase the interfacial area for mass transfer. These observations provide new experimental evidence for the role of capillarity, wettability and corner flow on NAPL ganglia dissolution.     

Prediction of imbibition from grain-scale interface movement

Processes in porous media governed by capillary forces, such as drainage or imbibition of wetting phase, are of great importance in different branches of soil science, petroleum engineering and hydrology. In this work we describe a new way of modeling imbibition by considering the movement and merger of interfaces at the pore level. The model is based upon a physically consistent dynamic criterion for the imbibition of a single pore originally proposed by Melrose.     

致密砂岩储层CO2驱油特征的核磁共振实验研究

利用核磁共振技术对致密砂岩储层不同渗透率级别基质岩心和裂缝基质岩心不同驱替压力下CO2驱油特征进行了研究,简述核磁共振原理及实验方法。表明:致密砂岩储层特低、超低渗透基质岩心在初始CO2驱替压力下,岩心毛细孔隙和微毛细孔隙区间的油不同程度被采出,随着CO2驱替压力增大,特低、超低渗透基质岩心毛细孔隙区间油的采出程度不断增加且累积采出程度不同。裂缝致密砂岩储层岩心,裂缝和毛细孔隙区间的油在初始CO2驱替压力下,岩心裂缝中的油及毛细孔隙中的部分油被驱替出来,CO2驱替压力提高毛细孔隙、微毛细区间油的采出程度和累积采收程度较小。致密砂岩储层特低、超低渗透基质岩心和裂缝致密砂岩储层岩心,随着CO2驱替压力增大毛细孔隙区间的部分剩余油成正比增加进入到微毛细孔隙区间改变储层剩余油分布。核磁共振技术能够深入研究致密砂岩储层CO2不同驱替压力阶段,岩心裂缝、毛细孔隙区间、微毛细孔隙区间油的采出程度和剩余油分布情况,对于研究致密砂岩储层微观驱油机理具有较重要的价值。      

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier–Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid–fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.     

Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations

A significant body of current research is aimed at developing methods for numerical simulation of flow and transport in porous media that explicitly resolve complex pore and solid geometries, and at utilizing such models to study the relationships between fundamental pore-scale processes and macroscopic manifestations at larger (i.e., Darcy) scales. A number of different numerical methods for pore-scale simulation have been developed, and have been extensively tested and validated for simplified geometries. However, validation of pore-scale simulations of fluid velocity for complex, three-dimensional (3D) pore geometries that are representative of natural porous media is challenging due to our limited ability to measure pore-scale velocity in such systems. Recent advances in magnetic resonance imaging (MRI) offer the opportunity to measure not only the pore geometry, but also local fluid velocities under steady-state flow conditions in 3D and with high spatial resolution. In this paper, we present a 3D velocity field measured at sub-pore resolution (tens of micrometers) over a centimeter-scale 3D domain using MRI methods. We have utilized the measured pore geometry to perform 3D simulations of Navier–Stokes flow over the same domain using direct numerical simulation techniques. We present a comparison of the numerical simulation results with the measured velocity field. It is shown that the numerical results match the observed velocity patterns well overall except for a variance and small systematic scaling which can be attributed to the known experimental uncertainty in the MRI measurements. The comparisons presented here provide strong validation of the pore-scale simulation methods and new insights for interpretation of uncertainty in MRI measurements of pore-scale velocity. This study also provides a potential benchmark for future comparison of other pore-scale simulation methods. © 2012 Elsevier Science. All rights reserved.     

Efficient flow and transport simulations in reconstructed 3D pore geometries

Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element–finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection–diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion D_m of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated.