Capillary Back Pressure Research Articles

Experiments and phase-field simulation of counter-current imbibition in porous media with different pore structure

Spontaneous imbibition is relevant to many processes in nature and industry. In this work, the effect of pore structure of porous media on counter-current imbibition is studied. The one-dimensional counter-current imbibition experiments were conducted in packed porous media with different pore structure. Experimental results showed that counter-current imbibition can only proceed for a short time in homogeneous porous media for all fluids. In heterogeneous porous media, counter-current imbibition can only proceed a short time for water–air experiments as well. However, imbibition can proceed continuously until the imbibition front reaches the end of packed porous media for water–oil experiments and the mass of water infiltration is proportional to the square root of time. The efficiency of water infiltration behind the imbibition front decreases with increase in viscosity of non-wetting phase fluid. In addition, the numerical simulation of counter-current imbibition in porous media with different pore structure were conducted using phase-field method. Simulation results showed that very little oil was produced in homogeneous porous media and more oil was produced in heterogeneous porous media. It is indicated that the difference between capillary driving pressure and capillary back pressure, which are closely related to pore structure and pore size distribution of porous media, has important influence on counter-current imbibition. Furthermore, the snap-off of oil or gas production channels in narrow pore throats may lead to termination of imbibition when the water saturation behind the imbibition front is higher.

Experiments on imbibition mechanisms of fractured reservoirs by microfluidic chips

To solve the problems of long experiment period and difficult measurement in core imbibition experiments, fracture—matrix microfluidic chips of different sizes, boundary conditions and wettability regulated by surface property modification were designed to research the imbibition mechanisms of oil-water, oil-surfactant solution and oil-Winsor III type surfactant solution. In the oil-water, and oil-wettability modification system imbibition process, oil was replaced from the matrix through Haines jump, the capillary back pressure was the main resistance blocking the flow of oil, the reduction of interfacial tension caused the weakening of Haines jump, reduction of oil discharge rate, and increase of oil recovery. The imbibition of oil-water or oil-surfactant solution with low interfacial tension was a counter- current imbibition process dominated by capillary force, in which all boundaries had similar contribution to imbibition, and the recovery data obtained from this experiment fit well with the classic imbibition scaling equation. The imbibition of oil and Winsor III type surfactant solution was a co-current imbibition process dominated by gravity under super-low interfacial tension, and is essentially the formation and re-balance of neutral microemulsion. The imbibition dynamics obtained from this experiment fit well with the modified imbibition scaling equation.

Simulation study of wettability alteration enhanced oil recovery during co-current spontaneous imbibition

Naturally fractured reservoirs are highly dependent on capillary forces to recover hydrocarbons during water injection. Water can spontaneously imbibe and expel oil if positive capillary forces exist; purely counter-current if all sides of the matrix blocks are exposed to water; and predominantly co-current with some counter-current production if the blocks are exposed to water and oil simultaneously. The latter is referred to as a co-current spontaneous imbibition (SI) setup. Wettability alteration (WA) has been identified as a key mechanism to improve oil recovery from naturally fractured reservoirs, however almost all experimental and modeling studies on WA during SI have focused on counter-current SI. Our review indicates limited systematic experimental work on co-current SI using nonzero initial saturation, mixed wettability or WA processes and This modeling study will investigate enhanced oil recovery by WA during co-current SI where a brine with a general WA component imbibes and causes the system to become more water-wet. We model a 1D oil-saturated core exposed to water at one end (inlet) and oil at the other end (outlet), thus facilitating co-current SI. The core is initially preferentially (not strongly) oil-wet with low SI potential. The component is both transported by the imbibing brine and diffuses towards the imbibition front. Adsorption of the component is assumed to improve the water-wetness of the porous medium and hence the SI potential. The model is parameterized using consistent capillary pressure and relative permeabilities from previous history matching of brine-dependent porous disc experiments. The behavior of co-current SI at mixed-wet state is examined and compared to that of literature strongly water-wet behavior. Both secondary and tertiary enhanced recovery by SI with WA component is then considered in the simulations. Important parameters such as mobility ratio (as via oil viscosity), capillary back pressure, WA component concentration, adsorption and time of WA component exposure are investigated. Under mixed-wet conditions, favorable and unfavorable mobility ratios do not limit oil production as can be the case for strongly wetted media at unfavorable mobility ratio. This is due to oil preserving mobility at all obtained saturations. A third or more of the total production was counter-current, which is high compared to strongly wetted media. It was shown that half the oil could be produced counter-currently as an upper limit. High oil mobility is preserved in the twophase region near the inlet and was found to ensure a high minimum fraction of counter-current production. Twice as much of the incremental oil from WA was produced counter-currently as co-currently, explained by increased oil relative permeability in the WA affected inlet region. Sensitivity analysis revealed that an opposite shift would reduce the incremental counter-current production despite raised local capillary forces. Capillary back pressure resists oil production at the inlet without limiting water from imbibing. As a result, capillary back pressure had significant impact on co-current SI simulations with fixed and changing wettability. The trends discovered in this study, both for mixed-wet and wettability alternating systems, are hoped to inspire future experimental measurements.

Darcy-Scale Simulation of Boundary-Condition Effects During Capillary-Dominated Flow in High-Permeability Systems

Summary We present numerical interpretations of two experimental sets of spontaneous-imbibition tests with combined cocurrent/countercurrent flow in high-permeability, unconsolidated sandpacks. The experiments were conducted using the two-ends-open free-spontaneous-imbibition (TEOFSI) boundary condition, in which one end face was in contact with the wetting (W) phase and the other with the nonwetting (NW) phase. The simulations quantified the impact from boundary-condition effects during capillary imbibition in the low-capillary sandpacks; the flow resistance in the outlet filter controlled imbibition rates, end recovery, and countercurrent production in tests with high NW-phase viscosity. A hydrostatic water column of a few centimeters at the W-phase end face also affected the imbibition process. Numerical and analytical solutions provided insight into when such boundary effects become important. In particular, the observed linear recovery with time and variations in time scale could not be explained by conventional modeling, but were captured by incorporating a thin, low-permeability filter into the models. For high-viscosity NW-phase tests with a low-permeability filter, countercurrent production is strongly enhanced and controlled by the capillary backpressure (CBP).

Cocurrent Spontaneous Imbibition In Porous Media With the Dynamics of Viscous Coupling and Capillary Backpressure

Summary This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy's law. The model is parameterized using experimental data from the literature. We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

Guidelines for Numerically Modeling Co- and Counter-current Spontaneous Imbibition

We present guidelines for accurately simulating both co- and counter-current spontaneous imbibition (SI) phenomenon in 1D systems. We first consider several cases for this study, which involve strongly water-wet, weakly water-wet and mixed-wet wettability states, to simulate co- and counter-current SI in an oil–water system. We create two separate 1D models on a numerical simulator to simulate and obtain saturation profiles for the different cases. We then match simulation results with saturation profiles obtained through the capillary dominated flow semi-analytical solution proposed by Schmid et al. (Water Resour Res 47(2), 2011, SPE J 21:2–308, 2016). The numerical study evaluates the effect of model orientation and co-ordinate system on the saturation profiles. Moreover, we perform grid sensitivity analysis to choose the optimal number of grid cells, as well as the optimal time steps for the model. We find that capturing 0.25% of core volume in each grid cell is sufficient to numerically model an SI experiment within the acceptable margin of error of 5%. Simulations are performed for 23 different cases based on the SI mode, wettability and mobility ratios. The simulation results in saturation profiles have a mean absolute percentage error from the profile obtained from the semi-analytical solution between 0.14 and 5.41% for counter-current SI for the different wettability states. For most wettability states for the co-current SI, however, we do not get a close match, indicating that the semi-analytical solution does not hold for co-current SI. The paper lists some useful guidelines for simulating SI phenomenon, such as selecting the optimum number of grid cells for the SI model and accounting for capillary backpressure, which could be extended to be applied for simulating coreflooding experiments. This paper also discusses current limitations of the semi-analytical solution. These calibration and sensitivity studies can significantly improve the accuracy of the simulation results.

The impact of capillary backpressure on spontaneous counter-current imbibition in porous media

We investigate the impact of capillary backpressure on spontaneous counter-current imbibition. For such displacements in strongly water-wet systems, the non-wetting phase is forced out through the inlet boundary as the wetting phase imbibes into the rock, creating a finite capillary backpressure. Under the assumption that capillary backpressure depends on the water saturation applied at the inlet boundary of the porous medium, its impact is determined using the continuum modelling approach by varying the imposed inlet saturation in the analytical solution.We present analytical solutions for the one-dimensional incompressible horizontal displacement of a non-wetting phase by a wetting phase in a porous medium. There exists an inlet saturation value above which any change in capillary backpressure has a negligible impact on the solutions. Above this threshold value, imbibition rates and front positions are largely invariant. A method for identifying this inlet saturation is proposed using an analytical procedure and we explore how varying multiphase flow properties affects the analytical solutions and this threshold saturation. We show the value of this analytical approach through the analysis of previously published experimental data.

Analytical and numerical investigations of spontaneous imbibition in porous media

AbstractWe present semianalytical solutions for cocurrent displacements with some degree of countercurrent flow. The solution assumes a one‐dimensional horizontal displacement of two immiscible incompressible fluids with arbitrary viscosities and saturation‐dependent relative permeability and capillary pressures. We address the impact of the system length on the degree of countercurrent flow when there is no pressure drop in the nonwetting phase across the system, assuming negligible capillary back pressure at the inlet boundary of the system. It is shown that in such displacements, the fractional flow can be used to determine a critical water saturation, from which regions of both cocurrent and countercurrent flow are identified. This critical saturation changes with time as the saturation front moves into the porous medium. Furthermore, the saturation profile in the approach presented here is not necessarily a function of distance divided by the square root of time. We also present approximate solutions using a perturbative approach, which is valid for a wide range of flow conditions. This approach requires less computational power and is much easier to implement than the implicit integral solutions used in previous work. Finally, a comprehensive comparison between analytical and numerical solutions is presented. Numerical computations are performed using traditional finite‐difference formulations and convergence analysis shows a generally slow convergence rate for water imbibition rates and saturation profiles. This suggests that most coarsely gridded simulations give a poor estimate of imbibition rates, while demonstrating the value of these analytical solutions as benchmarks for numerical studies, complementing Buckley‐Leverett analysis.

Asymmetry Characteristics of Oil Production by Spontaneous Imbibition from Cores with Two Ends Open

Spontaneous imbibition experiments with two ends open (TEO) boundary condition showed that oil production from each open face of core is asymmetrical while the invasion of water is symmetrical. Investigating the asymmetry characteristics of oil production is helpful to understand the imbibition displacement mechanisms. In this paper, a mathematical model considering the difference in capillary back pressure for TEO imbibition is established by assuming piston-like advance of the imbibition front. Based on the model, the reason for asymmetry in oil production is discussed and the effect of the viscosity ratio, relative permeability ratio, average capillary back pressure and the difference in capillary back pressure on the asymmetry in oil production is investigated as well. The simulated results show that asymmetry in oil production depends on the ratio of the difference in capillary back pressure to the pressure drop in oil between the imbibition front and the open face of the core. As capillary driving pressure dissipated in oil is very small, a small difference in capillary back pressure will cause a significant asymmetric production of oil. Furthermore, the asymmetry in oil production decreases with increasing viscosity ratio (\(\mu _{\mathrm{o}}/ \mu _{\mathrm{w}})\) and relative permeability ratio \((k_{\mathrm{rw}}/k_{\mathrm{rnw}})\) and increases with increasing average capillary back pressure and the difference in capillary back pressure. This work gives us a comprehensive insight into the spontaneous imbibition with TEO boundary condition.

The Effect of Viscosity on Relative Permeabilities Derived from Spontaneous Imbibition Tests

Spontaneous imbibition experiments are usually carried out on All Faces Open or One End Open cores and this severely limits the information that can be obtained because imbibition can be approximately described with a square root of time function, which involves only a single variable. Two Ends Open with one end in contact with the brine and the other end in contact with oil (at the same pressure) offers much more varied behaviour because imbibition is partly co-current and partly counter-current. Previously, an analysis and experiments were described for primarily co-current imbibition when the viscosities of the oil and brine were close to equal. Small deviations from the square root of time relationship allowed parameters such as the capillary back pressure (bubble pressure) to be determined. In the present paper, the situation when the oil is significantly more viscous than the brine is analysed and compared with experiments. The results show that counter-current imbibition continues for almost the entire imbibition period. They also show that the relative permeability to oil behind the front varies as the viscosity ratio is changed. Very viscous oil gives higher relative permeability than less viscous oil.

Capillary pressure and relative permeability estimated from a single spontaneous imbibition test

Under certain boundary conditions during spontaneous brine imbibition into oil-saturated porous rocks, it is possible for co- and counter-current flow to occur simultaneously. These circumstances are formalized into a special Two-Ends-Open (TEO) boundary condition; one end face of the core is exposed to brine and the other end face is exposed to oil. The behavior of imbibition with the new boundary condition (termed TEO-free spontaneous imbibition) is analyzed using a simple piston-like displacement model. The model allows interpretation of properly conducted experiments and the determination of the pressure, referred to as the capillary back pressure, which resists oil production at the water-wetted face where limited spontaneous countercurrent imbibition occurs. The opposite end face (in contact with oil) has zero capillary back pressure and oil is produced from this end as well, but co-currently. In experiments, oil production was monitored at each core end face to quantify oil production by counter-current imbibition from the face contacted by brine versus co-current imbibition from the face in contact with oil. In the experiments, oil production by counter-current flow only occurred in the very early stage of imbibition. This was because the counter-current imbibition contribution to oil production was curtailed by the action of the capillary back pressure. The influence of the capillary back pressure on the imbibition mechanism for variations in rock permeability and core length was investigated. For 9 tests in all, an average of 96% of total recovery was produced co-currently. The simple theory was used to analyze the co-current-only stage of imbibition. The theory gave an estimate of the relative permeability to brine behind the front and also of the effective capillary pressure generated at the imbibition front. In some experiments, the pressure in the core was monitored in addition to production and this enabled the absolute permeability and the capillary back pressure at the open face to be calculated directly.

Developments in spontaneous imbibition and possibilities for future work

Abstract Spontaneous imbibition controls many processes of practical importance. The subject is undergoing rapid growth in terms of the number of publications. This paper is a selective review of the literature which concentrates on the last ten years or so but also highlights, as necessary, earlier work. Insight into the mechanism of spontaneous imbibition is provided through consideration of the behavior of strongly wetted uniform tubes of any cross-section. The significance of cross-flow on the mechanism of advance of interfaces in tubes is related to imbibition in much more complex pore spaces. Details of the mechanism of imbibition by rocks and correlation of data for very strongly wetted conditions are discussed with respect to the numerous variables. Correlation of spontaneous imbibition data for a wide range of viscosity ratios demonstrates unequivocally that the operative relative permeabilities during counter current imbibition are not unique as is commonly assumed. They depend on viscosity ratio. This dependence points to the limitations of analytic models of spontaneous imbibition that also include the choice of specific boundary conditions at the open face. Experiments in which both the wetting and non-wetting phase are located at separate areas of the rock face demonstrate simultaneous co- and counter-current imbibition. This new configuration offers certain interpretive advantages, especially with respect to estimating operative relative permeabilities. The effective capillary pressure at the imbibition front drives the imbibition process. Imbibition is opposed by viscous resistance and the capillary back-pressure at the open face. Modeling advance of the imbibition front as a leaky piston gives agreement with experimental data for a range of scenarios. The piston model provides a consistent and more easily understood mechanistic account of frontal behavior than current network models. Experiment and theory for examples of when imbibition rate is and is not proportional to square root of time are explained. The predictive capability often claimed for network modeling with respect to spontaneous imbibition for very strongly wetted and other wetting states is questioned. Network modeling is now commonly tied to micro-CT images of small rock samples. Spontaneous imbibition is fundamentally a dynamic process and meaningful progress depends on it being modeled as such. There is a trend within the modeling community of reaching questionable conclusions based on so called quasistatic mechanisms while under-utilizing the versatility and predictive capabilities of network modeling with respect to dynamic processes. Topics for further investigations of spontaneous imbibition are suggested. They include several opportunities for testing network models against experimental data.

Bubble Snap-off and Capillary-Back Pressure during Counter-Current Spontaneous Imbibition into Model Pores

A previous paper (Unsal, E.; Mason, G.; Ruth, D. W.; Morrow, N. R. J. Colloid Interface Sci. 2007, 315, 200-209) reported experiments involving counter-current spontaneous imbibition into a model pore system consisting of a rod in an angled slot covered by a glass plate. Such an arrangement gives two tubes with different cross-sections (both size and shape) with an interconnection through the gap between the rod and the plate. In the previous experiments, the wetting phase advanced in the small tube and nonwetting phase retreated in the large tube. No bubbles were formed. In this paper, we study experimentally and theoretically the formation of bubbles at the open end of the large tube and their subsequent snap-off. Such bubbles reduce the capillary back pressure produced by the larger tube and can thus have an effect on the local rate of imbibition. In the model pore system, the rod was either in contact with the glass, forming two independent tubes, or the rod was spaced from the glass to allow cross-flow between the tubes. For small gaps, there were three distinct menisci. The one with the highest curvature was between the rod and the plate. The next most highly curved was in the smaller tube, and the least highly curved meniscus was in the large tube and this was the tube from which the bubbles developed. The pressure in the dead end of the system was recorded during imbibition. Once the bubble starts to form outside of the tube, the pressure drops rapidly and then steadies. After the bubble snaps off, the pressure rises to almost the initial value and stays essentially constant until the next bubble starts to form. After snap-off, the meniscus in the large tube appears to invade the large tube for some distance. The snap-off is the result of capillary instability; it takes place significantly inside the large tube with flow of wetting phase moving in the angular corners. As imbibition into the small tube progresses, the rate of imbibition decreases and the time taken for each bubble to form increases, slightly increasing the pressure at which snap-off occurs. The snap-off curvature is only about two-thirds of the curvature of a theoretical cylindrical meniscus within the large tube and about 40% of the curvature of the actual meniscus spanning the large tube.

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.

Pressures acting in counter-current spontaneous imbibition

Four water/oil and four oil/air linear counter-current spontaneous imbibition experiments were performed on Berea sandstone cores with permeabilities ranging from 0.065 to 1.094 μm 2. The cores were initially 100% saturated with non-wetting phase and all faces except one end were sealed. The experiments showed a clear frontal displacement mechanism. Capillary pressure was the driving force of the imbibition process. As well as viscous drag in both phases between the imbibition front and the open face, there is a significant opposing capillary back pressure associated with production of non-wetting phase at the open face. The location of the imbibition front, the overall changes in core saturation, and the pressure in the nonwetting phase in the dead end space ahead of the imbibition front, were monitored during the course of imbibition. The dead end pressure was essentially constant after a short start-up period. The distance advanced by the imbibition front was proportional to the square root of time. Based on the assumption that the properties of Berea sandstone of different permeabilities can be scaled, the experimental data were matched by numerical simulation to predict the saturation and pressure profiles, the saturation and capillary pressure at the imbibition front, and the capillary back pressure at the open face. The ratio of the capillary back pressure to the estimated capillary pressure at the imbibition front ranged from approximately 1/3 to 2/5, for oil displacing air, to approximately 1/9 to 1/4, for water displacing oil.

On the prediction of pulmonary diffusing capacity with a steady state carbon monoxide method in chronic lung diseases.

In 25 patients with chronic obstructive pulmonary diseases, DLCO was estimated under steady state conditions during mild to moderate exercise. The values calculated according to Filley et al. were significantly lower than values corrected for CO capillary back pressure as suggested by Linderholm, but values predicted according to Holmgren's equation given for normal individuals were significantly higher. A new equation is proposed for the prediction of DLCO, which is derived from the high correlation between Filley's and Linderholm's values. Its precision was demonstrated in 35 patients with different lung diseases. The equation is written DLCO corrected for CO back pressure'=—0.528 + 1.095 x DLCO uncorrected, SD ± 0.367.

ON THE SIGNIFICANCE OF PULMONARY MEAN CAPILLARY CO BACK PRESSURE CORRECTIONS FOR REPEATED MEASUREMENTS OF DLCO DURING EXERCISE IN MAN.

ON THE SIGNIFICANCE OF PULMONARY MEAN CAPILLARY CO BACK PRESSURE CORRECTIONS FOR REPEATED MEASUREMENTS OF DLCO DURING EXERCISE IN MAN.

On The Significance of Pulmonary Mean Capillary Co Back Pressure Corrections for Repeated Measurements of DLCODuring Exercise in Man

On The Significance of Pulmonary Mean Capillary Co Back Pressure Corrections for Repeated Measurements of DLCODuring Exercise in Man