Effects of flow history on oil entrapment in porous media: An experimental study

The effect of flow history on fluid phase entrapment during immiscible two‐phase flow in Hele‐Shaw cells packed with spherical and crushed glass beads is investigated. The wetting fluid is injected into an initially oil saturated cell at a well‐defined capillary number. It is observed that the size and shape of the trapped clusters strongly depend on the history of flooding such that less oil was trapped in the medium when the injecting capillary number gradually increased to the final maximum capillary number compared to the case when the injection was started and maintained constant at the maximum capillary number. In addition, a comprehensive series of experiments were conducted to delineate the effects of the capillary number on the phase entrapment. Contrary to previously published data, our experimental data reveal that the residual oil saturation depends on capillary number nonmonotonically. A physically based relationship to scale the capillary desaturation curve is proposed. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1385–1390, 2015     

Some aspects of wetting/dewetting of a porous medium

Various features of wetting/dewetting of porous media are examined. The phenomenon of capillary hysteresis is illustrated by a vertical capillary tube which consists of an alternating sequence of convergent—divergent conical sections. A study of the kinetics of wetting of this tube by a liquid shows that when the velocity of the liquid/vapour meniscus is plotted against the height of penetration, it oscillates about the Washburn velocity—distance curve and performs Haines jumps. A general macroscopic equation is derived for the rate of wetting/dewetting of a porous medium having randomly distributed, finely divided particles or pores. Use is made of the Forchheimer equation, which is an extension of Darcy's equation to higher Reynolds numbers. Dissipative energy terms due to internal fluid calculaton and to irreversible movements of the meniscus strongly affect the initial rate of imbibition, but as the wetting progresses the Reynolds number decreases and Washburn's equation prevails.The application of percolation theory to wetting/dewetting phenomena in porous media is studied. The use of percolation theory by Kirkpatrick and Stinchcombe to find the electrical conductivity of inhomogeneous solid mixtures is adapted to determining the permeability of a porous medium to fluid flow. It is also shown how the relation between the “precolation probability” and the concentration of “unblocked” channels or pores can be applied in calculating the capillary pressure—desaturation curve in drainage. In particular, percolation theory predicts that a threshold pressure or break-through pressure is required before a non-wetting fluid can displace a wetting fluid in a porous medium. It is often convenient to use tree-like or branching lattice networks as models of a porous medium, because these are amenable to exact solutions in regard to percolation probability and permeability. The percolation properties of porous medium models which consist of lattice networks of cylindrical channels with a distribution of cross-sections and also of randomly packed rotund particles are examined and their relevance to wetting/dewetting phenomena discussed.     

Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Slow immiscible displacement flow in disordered porous media

The immiscible displacement of a wetting fluid by a non-wetting fluid in a disordered porous medium is studied in the capillary region, i.e. when capillary forces are dominant, by using the invasion percolation model to describe the displacement mechanism. The porous medium is represented by a two-dimensional network of interconnected capillaries whose radii follow a uniform size distribution. Disorder is assigned to the medium by considering the probabilities of occurrence of inaccessible pores, p_s, and non-conductive capillaries, p_b. It is found that the dynamic behaviour of the displacing fluid and the fraction of invaded pores depend on the degree of disorder of the medium. The results can provide an interpretation of the effects of the dead-end pore volume on the oil recovery and the displacement behaviour.     

Using NMR displacement measurements to probe CO2 entrapment in porous media

Carbon dioxide sequestration in aquifers is seen as a potential climate change mitigation technique. One physical mechanism by which this could occur is capillary trapping of discrete pore‐scale CO₂ bubbles (referred to as ganglia) in the pore space. Nuclear magnetic resonance (NMR) techniques were used to quantify the spatial distribution and pore environment of such CO₂ entrapment in a model porous medium (random glass bead packing). 3D images revealed a relatively macroscopically homogeneous CO₂ entrapment, even though the image resolution is insufficient to resolve individual CO₂ ganglia. Quantification of the pore environment of the CO₂ ganglia was achieved using NMR displacement propagators (displacement probability distributions), acquired both before and after CO₂ entrapment. Lattice Boltzmann (LB) simulations were used to facilitate interpretation of the propagator statistics by considering various pore environments in which CO₂ could become trapped. Comparison with the experimental data suggests that CO₂ is preferentially entrapped in comparatively larger pores. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Experimental investigation of different brines imbibition influences on co-and counter-current oil flows in carbonate reservoirs

Imbibition of water, as wetting phase in oil-wet fractured carbonate reservoirs, plays a key role in fluid flow be-tween matrix and fracture system. The type of injected seawater and its chemistry would profoundly influence the imbibition process. In this study, the impact of smart water (a brine that its ions have been adjusted to facil-itate oil recovery) and low salinity water on co-and counter-current imbibition processes for oil-wet carbonate cores has been experimentally investigated. The results show an increase of about 10％in oil recovery for co-and counter-currents for smart seawater imbibition compared to that of low salinity seawater. In addition, as a result of the influence of co-and counter-current on each other, by co-current removal from one core face, the counter-current in the other face would be intensified by as much as about 75％. A close examination of different lengths (5, 7 and 9 cm) of carbonate cores with the same permeability revealed that by decreasing porous medium length, the amount of counter-current producing oil would be decreased so that in the 5 cm core, counter current oil production will not happen. For similar core lengths by increasing permeability, the share of counter current flow would be decreased approximately 18％since the capillary pressure could not overcome non-wetting phase viscous forces. Considering the role of matrix length along with a modified brine (which is designed according to the matrix mixture) strengthen the relevant mechanisms to have more oil production so that the higher thick-ness of matrix causes the higher amount of co-current oil producing and consequently more total recovery.     

NETWORK SIMULATION OF RELATIVE PERMEABILITY CURVES USING A BOND CORRELATED-SITE PERCOLATION MODEL OF PORE STRUCTURE

This paper deals with the conductivity and relative conductivity properties of irregular 3-D networks of pores that represent the continua of the oil phase and the aqueous phase respectively, during steady slate two phase flow in porous media. The relative conductivity properties presented, correspond to the saturation history defined by the drainage, imbibition and secondary drainage capillary pressure curves respectively. Use has been made of the pore accessibility history of a 20 × 20 × 20 network and a 10 × 10 × 10 nodes core portion of the network is used to write the flow equations. A set of 1001 linear equations is solved using the Preconditioned Conjugate Gradients Method for the conductivities of the wetting phase and the non-wetting phase respectively, as a function of network saturation and saturation history. The effects of pore throat size distribution and pore body size distribution on relative permeability behaviour has been investigated. Furthermore, the effect of conductivity function q(D) proportional to Dⁿ (n = 0, 1, 2, 3, 4) on relative permeability behaviour was investigated, where D stands for pore throat diameter and n is an exponent depending on pore geometry.

The results of this work are very significant in elucidating the following points that are not clearly stated in the literature: 1) using the bypassing as the only trapping mechanism, the primary drainage and secondary drainage relative permeability curves are in agreement with experimental findings; 2) more realistic displacement mechanisms in secondary imbibition are required to have better agreement with experimental findings; 3) the correlated network models after the site type problem of percolation theory are realistic models of pore structure; 4) the conductivity function q(D) proportional to D³ is the most appropriate pore throat conductivity function because of lamelar like pore geometries; and 5) accurate prediction of the effective permeability requires knowledge of the porosity and the detailed pore geometry in the pore network, in addition to pore size distributions used in the network simulation.     

Experimental investigation of hysteretic dynamic effect in capillary pressure–saturation relationship for two‐phase flow in porous media

Well‐defined laboratory experiments have been carried out to investigate hysteretic dynamic effect in capillary pressure–saturation relationships for two‐phase flow in homogeneous and heterogeneous (layered) porous media. Conceptually, the dependence of the capillary pressure curves on the rate of change of saturation (dS_w/dt) is defined as the dynamic effect in capillary pressure relationship, which is indicated by a dynamic coefficient, τ (Pa s) and it determines the rate at which two‐phase flow equilibrium is reached, i.e., dS_w/dt = 0 where S_w and t are the water saturation and time, respectively. The dependences of τ on various fluid and porous materials properties have been studied in the context of drainage; but, there is limited study for imbibition and the hysteresis of τ?S_w relationships. As such, the emphasis in this article is on reporting τ?S_w curves for imbibition while also demonstrating the hysteresis in the τ?S_w relationships by comparing τ?S_w curves for drainage (previously reported) and imbibition (this study) in carefully designed laboratory experiments. Homogeneous sand samples composed of either fine (small particle size and lower permeability) or coarse (larger particle size and higher permeability) sand have been used for these experiments. Furthermore, a layered domain made of a find sand layer sandwiched between two coarse sand layers is used as a model of heterogeneous domain. The results of the study confirm that the τ?S_w relationships are hysteretic in nature and, as such, the speed to flow equilibrium should vary depending on whether drainage or imbibition takes place. At a particular water saturation, the magnitudes of the dynamic coefficient (τ) are found to be generally higher for imbibition, which imply that the speed to flow equilibrium at the same saturation will be slower for imbibition. © 2013 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 59: 3958–3974, 2013     

Influence of the boundary conditions on capillary flow dynamics and liquid distribution in a porous medium

After depositing a wetting liquid onto a porous medium surface, and under the influence of the capillary pressure, the liquid is imbibed into the porous medium creating a wetted imprint. The flow within the porous medium does not cease once all the liquid is imbibed but continues as a secondary capillary flow, where the liquid flows from large pores into small pores along the liquid interface. The flow is solved using the capillary network model, and the influence of the boundary condition on the liquid distribution within the porous medium is investigated. The pores at the porous medium boundaries can be defined as open or closed pores, where an open pore is checked for the potential threshold condition for flow to take place. In contrast, the closed pore is defined as a static entity, in which the potential condition for flow to take place is never satisfied. By defining the pores at distinct porous medium boundaries as open or closed, one is able to obtain a very different liquid distribution within the porous medium. The liquid saturation profiles along the principal flow direction, ranging from constant to steadily decreasing, to the profile with a local maximum, are found numerically. It is shown that these saturation profiles are also related to the geometrical dimension that is perpendicular to the flow principal direction, and changing the boundary type from open to closed allows the liquid distribution within the porous medium to be controlled. In addition to the liquid distribution, the influence of the boundary conditions on capillary pressure and relative permeability is investigated, where both parameters are not influenced by variation of the boundary condition types. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Nonequilibrium thermomechanical modeling of liquid drainage/imbibition in trickle beds

We extend the macroscopic nonequilibrium thermomechanical multiphase flow theory proposed by Hassanizadeh and Gray for porous media to analyze a set of drainage and imbibition experiments in trickle beds. The nonequilibrium model rests on inclusion of mass and momentum conservations for the gas‐liquid interface, nonequilibrium capillary pressure, Helmholtz free energy gradients in the body supply of momentum for fluid bulk phases and gas‐liquid interface, and mass exchange rates between interface and fluid bulks accounting for production and destruction of gas‐liquid interfacial area. To solve the nonequilibrium model, entropy‐consistent constitutive relationships are derived and calibrated using liquid holdup and bed pressure drop measurements in drainage and imbibition. The model captures very well the decay (drainage), and breakthrough (imbibition) curvatures of liquid holdup and pressure drop kinetics, while model closer inspection allows assessing the role of nonequilibrium capillary pressure and of dynamic interfacial mass exchanges for the production/destruction of interfacial area. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3123–3134, 2012     

Two-phase flow in porous media

Two-phase flow in porous media depends on many factors, such as displacement vs steady two-phase flow, saturation, wettability conditions, wetting fluid vs non-wetting fluid is displacing, the capillary number, interfacial tension, viscosity ratio, pressure gradient, uniformly wetted vs mixed-wet pore surface, uniform vs distributed pore throats, small vs large pores, well-connected pores vs pores connected by small throats, etc. These parameters determine how the two fluids are distributed in the pores, e.g. whether they flow in seperate channels or side-by-side in the same channels, either with both fluids being continous or only one fluid being continous and the other discontinuous. In displacement, the capillary number and the viscosity ratio determine whether the displacement front is sharp, or if there is either capillary or viscous fingering.     

Trapping of the non-wetting phase in an interacting triangular tube bundle model

An interacting triangular tube bundle model is developed using capillaries of equilateral triangle cross sections. In addition to pressure equilibration among the capillaries, the non-circular tubes allow the wetting phase to reside in the corners and flow continuously in the entire model. An interacting-serial type model is constructed with step changes of tube size along the model, while the total cross-section of the model is kept constant. This model includes trapping of oil which is absent in traditional tube bundle models. Trapping of non-wetting phase in the model in imbibition processes is simulated. The relationship between the residual oil saturation and the complete capillary number CA is investigated. The simulation results obtained by this model are consistent with the results reported in literature of both experimental studies, using actual porous media, and simulations in pore-scale network models. The effects of the tube size, tube size distribution and viscosity ratio on the magnitude of entrapment are also studied using this tube bundle model.     

Pore-scale simulation of water/oil displacement in a water-wet channel

Water/oil flow characteristics in a water-wet capillary were simulated at the pore scale to increase our understanding on immiscible flow and enhanced oil recovery. Volume of fluid method was used to capture the interface between oil and water and a pore-throat connecting structure was established to investigate the effects of viscosity, interfacial tension (IFT) and capillary number (Ca). The results show that during a water displacement process, an initial continuous oil phase can be snapped off in the water-wet pore due to the capillary effect. By altering the viscosity of the displacing fluid and the IFT between the wetting and non-wetting phases, the snapped-off phenomenon can be eliminated or reduced during the displacement. A stable displacement can be obtained under high Ca number conditions. Different displacement effects can be obtained at the same Ca number due to its significant influence on the flow state, i.e., snapped-off flow, transient flow and stable flow, and ultralow IFT alone would not ensure a very high recovery rate due to the fingering flow occurrence. A flow chart relating flow states and the corresponding oil recovery factor is established.     

Vacuum‐assisted resin transfer molding model

A model of the vacuum‐assisted resin transfer molding (VARTM) process is developed that includes the most important aspects of the processing physics. The model consists of several submodels, such as preform mechanics, Darcy flow, wicking flow, and void formation. The preform mechanics model treats the preform as a linearly elastic, one‐dimensional (1D) solid. However, the key physical process is the lubrication of the preform due to fluid wetting, and this is modeled as a reduction in preform modulus, an easily measurable parameter. Residual stress, three‐dimensional (3D) structural behavior, and nonlinearity are neglected, but can all be included. The fluid flow model of capillary wicking is not tacked onto the Darcy equation as a modified boundary condition, as was previously done. The wicking is treated simply, but more realistically, by performing a force balance on the fluid in a pore. Balancing the capillary pressure and the viscous drag allows the development of a wicking front that precedes the main Darcy flow front to an extent that depends on several easily measurable factors. It is this wicking front that is responsible for the small void formation that reduces the quality of VARTM parts, relative to resin transfer molding (RTM) parts. POLYM. COMPOS. 26:477–485, 2005. © 2005 Society of Plastics Engineers     

Flow Kinetics in Porous Ceramics: Understanding with Non-Uniform Capillary Models

The present work describes the development of a two-parameter non-uniform capillary model to describe kinetics of flow in porous solids with complex tortuous varying paths. Experimentally, the rate of fluid flow in such a non-uniform capillary is found to be orders of magnitude slower compared with a corresponding average uniform capillary. This slow rate is explained in terms of an extremely small 'effective' hydrodynamic radius. The origin of such an 'unphysical' radius is rationalized based on geometrical considerations and effective driving forces for flow through a stepped capillary. Infiltration rate parameters are derived from the geometry of the porous medium for both wetting and non-wetting conditions.     

Spontaneous imbibition of liquids in glass‐fiber wicks. Part I: Usefulness of a sharp‐front approach

Spontaneous imbibition of a liquid into glass‐fiber wicks is modeled using the single‐phase Darcy's law after assuming a sharp flow‐front marked by full saturation behind the front occurring in a transversely isotropic porous medium. An analytical expression for the height of the wicking flow‐front as a function of time is tested through comprehensive experiments involving using eight different wicks and one oil as the wicking liquid. A good fit with experimental data is obtained without using any fitting parameter. The contact‐angle is observed to be important for the success of the model—lower contact angle cases marked by higher capillary pressures were predicted the best. The proposed model provides a nice upper bound for all the wicks, thereby establishing its potential as a good tool to predict liquid absorption in glass‐fiber wicks. However, the sharp‐front model is unable to explain region of partial saturation, thereby necessitating the development of part II of this article series (Zarandi and Pillai, Spontaneous Imbibition of Liquid in Glass fiber wicks. Part II: Validation of a Diffuse‐Front Model. AIChE J, 64: 306–315, 2018) using Richard's equation. © 2017 American Institute of Chemical Engineers AIChE J, 63: 294–305, 2018     

Scale-up of pore-level relative permeability from micro- to macro-scale

Scaling up relative permeability curves of wetting and nonwetting phase of drainage and imbibition processes from pore scale to macro scale is a challenge. A new method for scaling up relative permeability from micro- to macro-scale is proposed based on electrical analogy of multiphase fluid flow at pore scale. The method is validated against four synthetic porous media generated using homogeneous and heterogeneous grain size distributions, each of which were cut into eight sub-segments. Single-phase and two-phase flow properties were calculated for the main blocks and the subsequent sub-segments using random network modelling technique. Then, the subsegments were randomly distributed in space to reconstruct the main blocks and the proposed scale-up method was employed to calculate the relative permeability curves of the reconstructed blocks. Results were compared to the ones obtained directly from the network model of the original blocks and show good agreement between the calculated and scaled-up relative permeability curves of primary drainage and secondary imbibition. Furthermore, the model was tested on real media. Eight network models were extracted from pore size distribution of core samples obtained from the Green River basin located in the Mesaverde Formation. Flow properties obtained from the network models were validated against experimental data and good agreement was observed. These network models show a higher level of heterogeneity at micro-scale. Then, the scale-up methods were employed in order to reconstruct the macro-scale sample and predict its properties. Scale-up methods successfully predict the single-phase and two-phase flow properties of the sample.     

Snap‐off of a liquid drop immersed in another liquid flowing through a constricted capillary

Emulsions are encountered at different stages of oil production processes, often impacting many aspects of oilfield operations. Emulsions may form as oil and water come in contact inside the reservoir rock, valves, pumps, and other equipments. Snap‐off is a possible mechanism to explain emulsion formation in two‐phase flow in porous media. Quartz capillary tubes with a constriction (pore neck) served to analyze snap‐off of long (“infinite”) oil droplets as a function of capillary number and oil‐water viscosity ratio. The flow of large oil drops through the constriction and the drop break‐up process were visualized using an optical microscope. Snap‐off occurrence was mapped as a function of flow parameters. High oil viscosity suppresses the breakup process, whereas snap‐up was always observed at low dispersed‐phase viscosity. At moderate viscosity oil/water ratio, snap‐off was observed only at low capillary number. Mechanistic explanations based on competing forces in the liquid phases were proposed. © 2009 American Institute of Chemical Engineers AIChE J, 2009