Co-current and counter-current imbibition in independent tubes of non-axisymmetric geometry

Experiments that illustrate and quantify the basics of co- and counter-current spontaneous imbibition have been conducted in a series of simple model pore systems. The fundamental pore geometry is a rod in an angled round-bottomed slot with the rod touching a capping glass plate. The capillaries thus formed by the surfaces of the slot, rod and plate do not have circular cross-sections but more complicated geometric structures with angular corners. The tubes formed at each side of the rod connect at both ends. A viscous, refined oil was applied from one end. For co-current experiments, the opposite end was left open to the atmosphere and oil imbibed into both tubes. For counter-current experiments the opposite end was sealed and connected to a sensitive pressure transducer. Oil imbibed into the smaller capillary and expelled air as a series of bubbles from the end of the larger capillary. Bubble snap-off was observed to be rate-dependent and occurred at a lower curvature than that of the cylindrical meniscus that just fits inside the tube. Only the corners of the larger capillary filled with oil during counter-current imbibition. Meniscus curvatures were calculated using the Mayer and Stowe-Princen method and were compared with actual values by measuring the capillary rise in the tubes; agreement was close. A simple model for co-current and counter-current imbibition has also been developed and the predictions compared with the experimental results. The model results were in agreement with the experiments. The experiments demonstrate that the capillary back pressure generated by the interfaces and bubbles in counter-current imbibition can slow the process significantly.     

Prediction of imbibition in unconsolidated granular materials

A new way of modeling imbibition is proposed in this paper. It combines two elements. One is a physically consistent, dynamic criterion for the imbibition of an individual pore originally suggested by Melrose (SPEJ (November 1965) 259-271). The other is the use of a simple but physically representative model of porous media: a dense random packing of spheres that is geometrically predetermined. This approach allows truly a priori predictions of imbibition curves (saturation vs capillary pressure) for different values of contact angle, different initial conditions (e.g., different drainage endpoints), and different macroscopic sample geometries (the ratio of external to internal pores). It also provides a mechanistic basis for understanding the influence of pore-scale phenomena such as "snap-off" of nonwetting phase in the pore throats due to the coalescence of pendular rings. The simulations show that the capillary pressure curve for this unconsolidated packing is very sensitive to the wettability parameters (such as contact angle), whereas the influence of different initial conditions and snap-off is almost negligible. Predicted capillary pressure curves are compared to experimental data presented in the literature, and are consistent with them.     

Spontaneous Penetration of Liquids into Capillaries and Porous Membranes Revisited

A critical review of the problem of spontaneous penetration of a wetting liquid into pore channels shows that no theory exists to quantitatively predict the initial stage of imbibition. Since C. H. Bosanquet (1923, Phil. Mag. 45, 525), the theory operates with an universal velocity U(Bosanquet)=(2gammacosstraight thetarhor(1/2), with gamma being the surface tension, straight theta the contact angle, r the capillary/pore radius, and rho the fluid density. It is assumed that the initial impulse of the liquid entering the pore is insignificant for the penetration dynamics. Though the importance of the outside flow pattern has been noted in many papers, a thorough mathematical analysis of this effect is lacking in the literature. We derived a generalized equation of the fluid front motion by averaging the Euler equations of flow inside and outside the pore space. This analysis shows the significance of the flow patterns at the pore entrance. The initial stage of liquid imbibition is studied in the inviscid approximation using the methods of dynamic systems. The phase portrait of the dynamic system reveals a multiplicity of penetration regimes. Remarkably, the Bosanquet solution represents a particular regime, with the apparent mass being set zero. The Bosanquet trajectory refers to a separatrix of the phase portrait. It is shown that the initial conditions affect the rate of uptake significantly. The initial conditions stem from the prehistory of the fluid motion outside the pores prior to the liquid-solid contact. The phase portrait method allows us to distinguish two groups of solutions for the capillary rise dynamics of an inviscid fluid. The first group of trajectories corresponds to the liquid front rebound; the second group includes cyclic trajectories which correspond to the periodic regimes with liquid front oscillations at the equilibrium position. The upper estimate of the oscillation amplitude is found. Copyright 2001 Academic Press.     

Short timescale inkjet ink component diffusion: an active part of the absorption mechanism into inkjet coatings

The structures of inkjet coatings commonly contain a high concentration of fine diameter pores together with a large pore volume capacity. To clarify the interactive role of the porous structure and the coincidentally occurring swelling of binder during inkjet ink vehicle imbibition, coating structures were studied in respect to their absorption behaviour for polar and non-polar liquid. The absorption measurement was performed using compressed pigment tablets, based on a range of pigment types and surface charge polarity, containing either polyvinyl alcohol (PVOH) or styrene acrylic latex (SA) as the binder, by recording the liquid uptake with a microbalance. The results indicate that, at the beginning of liquid uptake, at times less than 2 s, the small pores play the dominant role with respect to the inkjet ink vehicle imbibition. Simultaneously, water molecules diffuse into and within the hydrophilic PVOH binder causing binder swelling, which diminishes the number of active small pores and reduces the diameter of remaining pores, thus slowing the capillary flow as a function of time. The SA latex does not absorb the vehicle, and therefore the dominating phenomenon is then capillary absorption. However, the diffusion coefficient of the water vapour across separately prepared PVOH and SA latex films seems to be quite similar. In the PVOH, the polar liquid diffuses into the polymer network, whereas in the SA latex the hydrophobic nature prevents the diffusion into the polymer matrix and there exists surface diffusion. At longer timescale, permeation flow into the porous coating dominates as the resistive term controlling the capillary driven liquid imbibition rate.     

Dynamics of capillary imbibition when surfactant, polymer, and hot water are used as aqueous phase for oil recovery

Capillary imbibition is an oil recovery mechanism in naturally fractured reservoirs if rock matrix is water wet and there is enough water in fractures in contact with matrix. It, however, may not yield an effective recovery under certain circumstances even if these conditions are maintained. Heavy matrix oil, high interfacial tension (IFT), oil-wet matrix sample, and limited contact area of matrix with water in fractures require additional effort to enhance the oil recovery by capillary imbibition. Chemicals and heat can be injected into naturally fractured reservoirs to improve the capillary imbibition recovery performance. With the involvement of low IFT fluid, heat, and polymer solution in the process, capillary imbibition dynamics may change and this entails an identification of the dynamics of the process through laboratory experiments before injection of these expensive fluids into oil reservoirs. In this study, the dynamics of capillary imbibition was studied experimentally. Static imbibition experiments were conducted on oil- and water-wet rock samples under different boundary conditions and saturated with different types of oil. The analyses were conducted using three indicators, namely the capillary imbibition rate, ultimate oil recovery, and shape of the recovery profile. Based on these indicators, the dynamics of capillary imbibition of different aqueous phases were evaluated for different oil types and matrix properties. The conditions that cause weak or strong capillary imbibition were identified.     

Shape Factor Correlations of Hydraulic Conductance in Noncircular Capillaries

In Part I of this paper, we introduced the Mason-Morrow shape factor and the corner half-angles to capture the part of geometry of angular capillaries essential in pore network calculations of single- and two-phase flow in drainage and imbibition. We then used this shape factor to obtain simple expressions for the hydraulic conductance in single-phase flow through triangular, rectangular, and oval capillaries. In Part II, we study two-phase fluid flow along angular capillaries. The nonwetting fluid occupies the central part of the capillary, whereas the wetting liquid fills the corners. First, we verify the numerical solution obtained by Ransohoff-Radke for concave corner menisci by using a high-resolution finite element method with zero and infinite surface shear viscosity. We present new numerical results for corner flow domains bounded by convex menisci, i.e., for pinned contact lines and forced imbibition. We also present numerical solutions for two-phase flow with momentum transfer across the interface. We introduce a dimensionless hydraulic conductance of wetting fluid in the corners and correlate it with the corner filament shape factor, corner half-angle, and contact angle. By appropriate scaling, we obtain an accurate universal curve for flow conductance in the corners of an arbitrary angular capillary and for arbitrary contact angles. We give error estimates of the Ransohoff-Radke flow resistance factors, of the Zhou et al. analytical expressions for the resistance factors, and of our universal curves for the hydraulic conductance with no-slip and perfect-slip boundary conditions at the interface. Our expressions for the hydraulic conductance in corner flow of wetting liquid not only are valid for both concave and convex fluid interfaces but also are more accurate than any other published correlation. Copyright 2001 Academic Press.     

Experimental investigation on spontaneous counter‐current imbibition in water‐wet natural reservoir sandstone core using MRI

Counter‐current imbibition is a process whereby a wetting phase spontaneously imbibes into a porous media, displacing the non‐wetting phase. This process is considered an important oil recovery mechanism during water flooding in fractured oil reservoirs. In this study, the dynamic process of counter‐current imbibition for a natural reservoir sandstone core with an all‐face‐open boundary condition was monitored using magnetic resonance imaging (MRI). A series of images and relaxation time T₁ spectra were acquired. The movement of water spontaneously entering the core sample while oil escapes, the spatial distribution of oil and water, and the in situ saturation change of oil and water in porous media can be accurately detected using MRI. MRI assists the direct evaluation of the basic mechanisms of imbibitions. Experimental results suggest the remaining oil was trapped in some large pores because of the capillary pressure, and the oil recovery in some large‐pore regions is lower than that in some small‐pore regions at the end of imbibition. Experimental findings show a close agreement between conventional material balance and oil recovery determined from MRI. The in situ oil recovery data agree well with the empirical models. The observations from MRI images could provide test cases to enable the development of mathematical models and to facilitate the evaluation of the proposed imbibition mechanisms. Copyright © 2016 John Wiley & Sons, Ltd.     

The possibility of different time scales in the dynamics of pore imbibition

To model the imbibition of liquids into porous solids, use is often made of the Lucas-Washburn equation, which relates the distance of penetration of a liquid at a given time to the pore radius, the viscosity and surface tension of the liquid, and the effective contact angle between the liquid and the solid. In this paper, we extend previous large-scale molecular dynamics simulations to show how this tool can be used to study the details of liquid imbibition, including the impact of the contact angle on the dynamics of penetration and the evolution of the internal flow field. In particular, we show that the asymptotic behavior of the contact angle versus time for a completely wetting liquid is given by approximately t(-1/4).     

An experimental study about the imbibition of aqueous solutions of low concentration of a non-adsorbable surfactant in a hydrophilic porous medium

The imbibition of aqueous solutions of Triton X-100 in calcium fluoride columns has been studied in order to determine the influence of the interfacial adsorption of the surfactant in the capillary rise of the solutions. This system has been chosen because this surfactant behaves as non-adsorbable at the surface of this solid when it is in aqueous solution. The experiments have consisted of the measurement of the increase in the weight of the porous columns caused by the capillary rise of the solutions. The analysis of the results has been made through a modified expression of Washburn's equation that takes into account that the experimental increase in the weight is caused by the imbibition as well as by the development of a liquid meniscus around the bottom base of the columns. From this analysis, it has been deduced that the surfactant concentration does not influence on the imbibition rate, it being equal to the observed for water. However, it has been also proved that the contact angle depends on the surfactant concentration, taking decreasing values as the surface tension of the solutions decreases. In order to justify these findings, a study about the influence of the interfacial adsorption on the imbibition has been carried out. By means of them, it has been proved that the absence of adsorption at the solid-liquid interface is the reason that explains both the independence of the imbibition rate from the surfactant concentration and the decrease of the contact angle. Moreover, this fact indicates that the depletion of the surfactant molecules from the advancing meniscus, which has been normally adduced as the phenomenon causing the observed behaviour, has to be ruled out as the physical cause that justifies the behaviour found from the analysis of the imbibition experiments. As a corollary, it has been also stated that only if the adsorption at the solid interfaces happened, the imbibition of aqueous solution of surfactant in hydrophilic media could be influenced by the surfactant concentration.     

Capillary imbibition of surfactant solutions in porous media and thin capillaries: partial wetting case

The capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting. Cylindrical capillaries are used as a model of porous media to study the problem. It is shown that if the mean pore size is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants whatever the value of the concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of pure water. The critical radius is determined by the adsorption of the surfactant molecules onto the inner surface of the pores. If the mean pore size is larger than the critical value, then the permeability increases with increasing surfactant concentration. These theoretical conclusions are in agreement with the experimental observations.     

Co- and counter-current spontaneous imbibition into groups of capillary tubes with lateral connections permitting cross-flow

A model for co- and counter-current imbibition through independent capillaries has already been developed and experiments conducted to verify the theory [E. Unsal, G. Mason, N.R. Morrow, D.W. Ruth, J. Colloid Interface Sci. 306 (2007) 105]. In this paper, the work is extended to capillaries which are connected laterally and in which cross-flow can take place. The fundamental pore geometry is a rod in an angled round-bottomed slot with a gap between the rod and a capping glass plate. The surfaces of the slot, rod and plate form capillaries and interconnecting passages which have non-axisymmetric cross-sections. Depending on the gap size either (i) a large single meniscus, (ii) two menisci one on each side of the rod, or (iii) three menisci, one between the rod and the glass additional to the ones on each side can be formed. A viscous refined oil was applied to one end of the capillaries and co-current and counter-current spontaneous imbibition experiments were performed. The opposite end was left open to the atmosphere for co-current experiments. When the gap between the rod and the plate was large, the imbibing oil advanced into the tubes with the meniscus in the largest capillary always lagging behind the two menisci in the other two smaller capillaries. For counter-current imbibition experiments the open end was sealed and connected to a sensitive pressure transducer. In some experiments, the oil imbibed into the smaller capillaries and expelled air as a series of bubbles from the end of the largest capillary. In other experiments, the oil was allowed to imbibe part way into the tubes before counter-current imbibition was started. The meniscus curvatures of the capillaries have been calculated using the Mayer and Stowe-Princen method for different cell slot angles and gap sizes using a value of zero for the contact angle. These values have been compared with actual values by measuring the capillary rise in the tubes; agreement was very close. A model for co-current and counter-current imbibition has also been developed. The significance of this model is that some hydraulic/capillary properties are common for both co-current and counter-current imbibition. The experiments give an illustration of behavior expected in a real porous material and verify the importance of the 'perfect cross-flow' modification to the 'bundle of parallel tubes' model.     

Improvement of the Kruk-Jaroniec-Sayari method for pore size analysis of ordered silicas with cylindrical mesopores

In this work, the X-ray diffraction structure modeling was employed for analysis of hexagonally ordered large-pore silicas, SBA-15, to determine their pore width independently of adsorption measurements. Nitrogen adsorption isotherms were used to evaluate the relative pressure of capillary condensation in cylindrical mesopores of these materials. This approach allowed us to extend the original Kruk-Jaroniec-Sayari (KJS) relation (Langmuir 1997, 13, 6267) between the pore width and capillary condensation pressure up to 10 nm instead of previously established range from 2 to 6.5 nm for a series of MCM-41 and to improve the KJS pore size analysis of large pore silicas.     

Partial Wetting in Capillary Liquid Absorption by Limestones

We report measurements of the capillary absorption (imbibition) of water, n-heptane, n-decane, n-dodecane, methanol, ethanol, propan-2-ol, and ethanol-water mixtures into a number of dry calcitic limestones. The data are analyzed on the basis of unsaturated flow theory to give values of sorptivity S for water and for each organic liquid at different temperatures. The results show that for the organic liquids S varies as (surface tension/viscosity)(1/2) but that for the water S is anomalously low, indicating partial wetting. The wettability of these limestones is discussed in relation to natural contamination of the pore surface. Copyright 2000 Academic Press.     

Optimization of a modified aerospray deposition device for the preparation of samples for quantitative analysis by MALDI-TOFMS

A modified aerospray apparatus was used to prepare a thin layer sample of matrix and analyte for quantitative analysis by MALDI-TOFMS. The apparatus consists of a set of coaxial tubing; the liquid sample is forced by a syringe pump through the inner capillary and it is nebulized by a flow of gas through the outer capillary. The small droplets of sample exiting the device are deposited onto a rotating plate, which serves as the sample surface for a time-of-flight mass spectrometer. An optimization was carried out after initial experiments with the device resulted in poorer than expected reproducibility of analyte signal. A two-level plus center point factorial experiment was performed investigating several factors, including the inner capillary internal diameter, gas pressure, liquid flow, spray distance, and time. After optimization the within-sample reproducibility of the analyte signal improved 3-fold, while the sample-to-sample reproducibility improved 4.5-fold.     

Device for filling of small diameter capillaries with stationary phase solutions in liquefied gases

This paper describes a high pressure device for filling small diameter capillaries with stationary phase solutions is described. A liquid is forced into the capillary column with the help of high pressure syringe whose needle (provided with a side opening) is tightened in a PTFE seal. The device allows use of liquefied gas as solvent. A detailed procedure is given for filling the capillary with stationary phase solution. The performance of the device was evaluated by filling 12 m × 15 μm i. d. glass capillary with 6.5 % (w/v) SE-54.     

Source-like solution for radial imbibition into a homogeneous semi-infinite porous medium

We describe the imbibition process from a point source into a homogeneous semi-infinite porous material. When body forces are negligible, the advance of the wetting front is driven by capillary pressure and resisted by viscous forces. With the assumption that the wetting front assumes a hemispherical shape, our analytical results show that the absorbed volume flow rate is approximately constant with respect to time, and that the radius of the wetting evolves in time as r ≈ t(1/3). This cube-root law for the long-time dynamics is confirmed by experiments using a packed cell of glass microspheres with average diameter of 42 μm. This result complements the classical one-dimensional imbibition result where the imbibition length l ≈ t(1/2), and studies in axisymmetric porous cones with small opening angles where l ≈ t(1/4) at long times.     

Experimental study of the immiscible displacement of shear-thinning fluids in pore networks

The pore scale mechanisms and network scale transient pattern of the immiscible displacement of a shear-thinning nonwetting oil phase (NWP) by a Newtonian wetting aqueous phase (WP) are investigated. Visualization imbibition experiments are performed on transparent glass-etched pore networks at a constant unfavorable viscosity ratio and varying values of the capillary number (Ca), and equilibrium contact angle (theta(e)). Dispersions of ozokerite in paraffin oil are used as the shear-thinning NWP, and aqueous solutions of PEG colored with methylene blue are used as the Newtonian WP. At high Ca values, the tip splitting and lateral spreading of WP viscous fingers are suppressed; at intermediate Ca values, the primary viscous fingers expand laterally with the growth of smaller capillary fingers; at low Ca values, network spanning clusters of capillary fingers separated by hydraulically conductive noninvaded zones of NWP arise. The spatial distribution of the mobility of shear-thinning NWP over the pore network is very broad. Pore network regions of low NWP mobility are invaded through a precursor advancement/swelling mechanism even at relatively high Ca and theta(e) values; this mechanism leads to irregular interfacial configurations and retention of a substantial amount of NWP along pore walls; it becomes the dominant mechanism in displacements performed at low Ca and theta(e) values. The residual NWP saturation increases and the end WP relative permeability decreases as Ca increases and both become more sensitive to this parameter as the shear-thinning behavior strengthens. The shear-thinning NWP is primarily entrapped in individual pores of the network rather than in clusters of pores bypassed by the WP. At relatively high flow rates, the amplitude of the variations of pressure drop, caused by fluid redistribution in the pore network, increase with shear-thinning strengthening, whereas at low flow rates, the motion of stable and unstable menisci in pores is reflected in strong pressure drop fluctuations.     

The influence of pore wettability on the dynamics of imbibition and drainage

Using large-scale molecular-dynamic (MD) simulations, we have shown previously that the classical Lucas–Washburn equation commonly employed to describe capillary imbibition and drainage should be modified to include dynamic contact-angle effects. In addition, we have demonstrated how these effects can be accounted for using the molecular-kinetic theory of dynamic wetting. In a further publication, we presented theoretical arguments and experimental evidence that the velocity of wetting depends on the intrinsic wettability of the solid surface in such a way that there exists an optimum contact angle at which the velocity of wetting is a maximum. Here, we combine these ideas to show how the maximum speeds of capillary imbibition and drainage are affected both by the pore wettability and the pressures used to drive capillary displacement. In particular, we introduce the concept of dynamic wetting transitions (DWTs) and discuss how these limit displacement efficiency and can be manipulated by controlling pore wettability. The results of this work may be beneficial in optimising the performance of capillary processes such as those involved in oil recovery.     

Sensitivity of drainage and imbibition to pore structures as revealed by computer simulation of displacement process

This work concerns the effects of the properties of porous media on two phase fluid displacement at slow rates. These properties include the size frequency distributions, shape and connectivity of pores and throats, the size correlation of directly connected throats and pores and the spatial arrangement of pores and throats in porous media. Computer simulations using 3-dimensional networks of pores and throats were used to determine the effects of these properties on the form of primary and secondary drainage curves, imbibition curves and scanning loops of a capillary pressure diagram.The application of the results is in deriving information about the structure of a porous medium from capillary pressure curves and understanding how predictions about the form of relative permeability curves can be made from capillary pressure curves.The concepts of finite and infinite throat and pore controlled domains are applied during the filling and emptying of a network. These concepts are then combined with considerations of the accessibility of network sites to non-wetting phase or wetting phase sources and sinks to provide information about the amounts and distribution of continuous and discontinuous wetting phase (wp) and non-wetting phase (nwp) at any stage of a displacement. The distribution of fluids Is strictly controlled by the domains. It is shown that recognition of the types, abundance and distribution of domains provides a fundamental basis for understanding boundary effects, differences in tortuosity in porous systems containing two immiscible phases, breakthrough pressures, and saturations, differences in nwp withdrawal efficiency between uncorrelated and correlated pore-throat size models, differences in hysteresis between drainage and imbibition and differences in the shapes of capillary pressure and relative permeability curves for various types of porous structures.