Co-current Spontaneous Imbibition Research Articles

Pore-scale experimental investigation on the co-current spontaneous imbibition of gas–water two-phase with gravity force

Gravity and capillary forces play pivotal roles in the natural capillary-driven spontaneous imbibition process. The opacity of the medium and the intricate pore structure make it challenging to elucidate the influence of gravity force on co-current gas–water imbibition. A series of pore-scale visualization experiments were conducted using capillary tubes of five different diameters (100, 300, 400, 500, and 1000 μm). The vector concept, represented by the interaction angle with the horizontal direction, was employed to quantify the varying levels of gravity force in the imbibition process, and its impact on imbibition recovery was assessed quantitatively. The findings revealed that the primary influence of gravity on gas–water spontaneous imbibition recovery was predominantly observed in the early stage. Due to the water blocking effect, the gas–water spontaneous imbibition process temporarily halted and resumed when the capillary diameter was 300 μm (at an angle of 60°). For capillary diameters between 100 and 500 μm, the water blocking effect induced a wave-like variation in gas–water spontaneous imbibition recovery as the interaction angle increased. Conversely, for a capillary diameter of 1000 μm, imbibition recovery exponentially decreased with the interaction angle, and no water blocking effect was observed. Consequently, the critical range of pore sizes for the water blocking effect in the gas–water spontaneous imbibition process was determined to be between 500 and 1000 μm. This research offers valuable theoretical insights into understanding capillary-driven flow phenomena in porous media.

Further Study on the Effect of Interfacial Tension on Cocurrent Spontaneous Imbibition Based on Direct Simulation and NMR

Further Study on the Effect of Interfacial Tension on Cocurrent Spontaneous Imbibition Based on Direct Simulation and NMR

A novel method for evaluation of the spontaneous imbibition process in tight reservoir rocks: Mathematical model and experimental verification

Spontaneous imbibition driven by capillary forces is essential for the development of oil and gas resources because it can significantly influence the oil recovery of tight reservoirs. But limited by traditional experimental methods, the existing mathematical models lack applicability to complex tight reservoir rocks. Therefore, to better predict water imbibition in tight reservoirs, this paper proposes a new spontaneous imbibition model based on modifications of the classical Handy model. Two important parameters, the average capillary pressure, and the imbibition permeability are derived using a nuclear magnetic resonance spectroscopy method to quantify the macroscopic driving force and percolation ability of the complex pore network. Furthermore, combined experiments of co-current spontaneous imbibition experiments and transverse relaxation time analysis on four shale core plug samples are conducted to verify the new model. Results show the imbibition process can be modeled successfully before the imbibition volume reaches 85% of the maximum imbibition volume, and two continuous stages: the early/free imbibition stage and the later/limited imbibition stage, are then subdivided according to the applicability of our model. Considering the heterogeneity of the pore network in shale samples, it can be inferred that an uneven imbibition front occurred during the imbibition process. In all, this model enriches the classical imbibition theory and provides a new approach to analyzing the imbibition of fracturing fluids in complex tight reservoirs.

Water-Gas Imbibition Relative Permeability: Literature Review, Direct versus Indirect Methods and Experimental Recommendations

When an active aquifer encroaches into a gas bearing reservoir or when an oil rim sweeps gas during late depletion of the gas cap, gas displacement by liquid is important for estimating the gas recovery. In the water displacing gas condition, the viscosity ratio is extremely favorable, resulting in a sharp waterfront in the reservoir matrix: it results that changing the relative permeability Kr shape has negligible effect, while endpoints water relative permeability Krw Max and residual gas saturation Sgr are much more important to understand gas flow performance for estimation of gas recovery with active aquifer or productivity decline after water breakthrough. Three main methods are used to determine water/gas relative permeability curves: imbibition unsteady-state, imbibition steady-state or indirect approaches such as co-current spontaneous imbibition if transient data are available. One of the other popular indirect methods is called Brooks-Corey approach: by measuring the drainage Pc curve using centrifuge or porous plate methods, it is possible to calculate a pore size distribution index c. This coefficient is used in a Brooks-Corey model to determine the drainage Kr curve. It is also required to measure and determine the relationship between the residual gas saturation Sgr and the initial gas saturation Sgi relationship. Finally, it is accepted that there is no hysteresis on the water relative permeability Krw curve, as water is always the wetting phase in the gas/water couple. As non-wetting phase, gas exhibits strong hysteresis between drainage and imbibition curves: it is therefore necessary to apply a correction on the drainage Krg curve to build the imbibition one using correcting models. The aim of this paper is to compare gas/water relative permeability of clastic rocks using direct waterflooding information and indirect approach using Brooks-Corey model. It is shown that using the indirect approach leads to results like those experimentally obtained. Also, additional numerical simulations are proposed to discuss the relevance of measuring the entire water-gas imbibition relative permeability curve using the steady-state approach.

Numerical studies of spontaneous imbibition in porous media: Model development and pore-scale perspectives

Spontaneous imbibition is a crucial two-phase flow process in a variety of subsurface and industrial applications. Due to the lack of an efficient and reliable pore-scale model, however, how pore-filling events in spontaneous imbibition influence average transport properties (i.e., capillary pressure and relative permeability curves) and entrapment of the nonwetting fluid has not been fully understood. In this work, we first experimentally verify an image-based dynamic pore-network model of spontaneous imbibition that is computationally efficient. Then, case studies of a Nubian sandstone are conducted. We demonstrate that average capillary pressure in cocurrent spontaneous imbibition is significantly overestimated by the widely used Young-Laplace equation. This is because the effects of dynamic pore-filling and air entrapment on average capillary pressure are not parameterized in the equation. Based on our pore-scale numerical results, we elaborate on the competition of pore-filling events under different viscosity ratios of the wetting to the nonwetting fluids. It is found that the filling mode evolves from the co-filling of neighboring pores to the preferential filling of small pores as the nonwetting viscosity increases. Our model will be a useful numerical tool for quantitatively predicting spontaneous imbibition in geological formations. Our findings will help us bridge the gap between pore-scale flow dynamics and the Darcy theory of spontaneous imbibition.

A semi-empirical modified geometry model for long-term co-current spontaneous imbibition of porous media based on convoluted, nonuniform and topological pore network

Hydraulic diffusivity or imbibition is a well-known unsaturated hydrodynamics phenomenon in water resources and geosciences study. Currently, there have been numerous analytical or numerical models describing the spontanneous imbibition of porous rock and soil. However, the most existing models do not consider hydrostatic pressure and elaborate pore geometry characteristics. Assuming that the penetration direction is one-dimensional and infinitely continuous, a long-term co-current spontaneous imbibition (SI) model is proposed by average and fractal geometries, respectively accordingly obtaining the general expression of dimensionless comprehensive parameter. The practicability and accuracy of the model are verified by experimental data and compared with other models. The influence mechanisms of tortuosity, pore-throat, fractal, shape and topological characteristics on initial and equilibrium SI behaviors are comprehensively revealed. The new models are applied to inversely predict the dimensionless comprehensive parameters, variations of which with porosity are analyzed along with their influence on long-term SI characteristics. The results are shown as follows. Compared with the existing classical models, the prediction accuracy of the new model consistent with experiment is greatly improved, generalizing the existing models. The dimensionless comprehensive parameters based on average and fractal geometries show the decreasing trend in power-law and increasing trend in linear with the increase of porosity, respectively. The equilibrium height or mass is only related to topology factor, fractal dimension and shape factor, whereas the equilibrium time is also correlated to pore-throat ratio and tortuosity. The sensitivities of fractal dimension, topological factor and shape factor to equilibrium time are stronger than that of equilibrium mass or height. The sensitivities of topological characteristics, pore-throat structure, tortuosity, pore geometry and fractal characteristics to SI reduce successively for porous media. The influences of dimensionless comprehensive parameter on evolution of SI mass with time go through four stages, i. e., no influence at initial stage, increasing influence at initial later stage, weakening influence at later stage and increasing influence at end, whereas on evolution of SI velocity versus time and recovery rate go through two stages, that is, significant influence at initial stage and no influence at later stage.

Wetting Dynamics of Spontaneous Imbibition in Porous Media: From Pore Scale to Darcy Scale

AbstractSpontaneous imbibition plays an important role in many subsurface and industrial applications. Unveiling pore‐scale wetting dynamics, and particularly its upscaling to the Darcy model, are still unresolved. We conduct image‐based pore‐network modeling of cocurrent spontaneous imbibition and the corresponding quasi‐static imbibition in homogeneous sintered glass beads and heterogeneous Estaillades carbonate. We find that pore‐scale heterogeneity significantly influences entrapment of the nonwetting fluid, which in Estaillades is mainly because of the poor connectivity of pores. We show that wetting dynamics significantly deviates capillary pressure and relative permeability away from their quasi‐static counterparts. Moreover, we propose a nonequilibrium model for wetting permeability that well incorporates flow dynamics. We implement the nonequilibrium model into two‐phase Darcy modeling of a 10 cm long medium. Sharp wetting fronts are numerically predicted, which are in good agreement with experimental observations. Our studies provide insights into developing a two‐phase imbibition model with measurable material properties.

Analytical Exact Solution for Co-Current Spontaneous Imbibition in Porous Media Considering Early- and Late-Time Effects

Analytical Exact Solution for Co-Current Spontaneous Imbibition in Porous Media Considering Early- and Late-Time Effects

Spontaneous imbibition in tight porous media with different wettability: Pore-scale simulation

Spontaneous imbibition is significantly influenced by rock wettability, and it has been extensively studied in core-based experiments and numerical simulations owing to its important role in the development of oil/gas reservoir. Due to the fine pore structure and complex wettability of tight sandstone, an in-depth exploration of the effects of wettability on the pore-scale flow physics during spontaneous imbibition is of great value to complement traditional experimental studies and enhance the understanding of microscopic flow mechanisms during the development of tight oil reservoirs. Based on a X-ray computed tomography scanning experiment and a lattice Boltzmann multiphase model, in this work, we systematically investigate the effects of different hydrophilic strengths on the evolution of the imbibition fronts within the micropores and the degree of nonwetting fluid recovery during spontaneous imbibition of tight sandstone. The results show that the wettability significantly affects the morphological characteristics of the imbibition fronts. Under strong hydrophilic conditions, the wetting fluid preferentially invades the pore corner in the form of angular flow. As the contact angle increases, the hysteresis effect at the main terminal interface decreases, and the two-phase interface becomes regular and compact. Wettability also significantly affects the imbibition rate and the nonwetting fluid recovery degree. The smaller the contact angle, the faster the imbibition rate and the higher the recovery degree of nonwetting fluids during the cocurrent spontaneous imbibition.

All-Time Modeling of Co-Current Spontaneous Water Imbibition Into Gas-Saturated Rocks Using a Novel Transition Time

Abstract Spontaneous imbibition (SI) into a porous medium is an important transport phenomenon in petroleum reservoir engineering. The study of spontaneous water imbibition is critical to predict the production performance in these reservoirs developed by waterflooding, especially in the fractured gas reservoirs with active aquifers. While some studies have been reported to characterize spontaneous water imbibition into gas-saturated rocks, they are either limited or inaccurate due to the fact that the existing models have specific assumptions that cannot be applied in other time intervals. To this end, we proposed a novel transition imbibition time t* and developed an all-time (including both early- and later-time SI) model to match the experimental SI data. Furthermore, we proposed a novel model to estimate capillary pressures at different water saturations and to characterize the water saturation profile in capillary-dominated stage. Comparison with the existing capillary pressure estimation models was performed to test the differences. The results demonstrated that the all-time model could fit the experimental imbibition data of the entire SI process satisfactorily. The new saturation model established in this paper can be well fitted with the water saturation profile measured by the X-ray computer tomography (CT) scanners. The results and findings from this work may be of great significance in many areas related to SI, particularly in the development of naturally fractured gas reservoirs with active aquifers.

Early- and Late-Time Analytical Solutions for Cocurrent Spontaneous Imbibition and Generalized Scaling

SummaryWe propose an explicit analytical solution for 1D cocurrent (COC) spontaneous imbibition (SI) in which a core is exposed to water (inlet) and oil (outlet). The system is described using an advection-capillary diffusion transport equation combined with a pressure equation. By ignoring the capillary diffusion term in the transport equation, the analytical solution follows in terms of Buckley-Leverett (BL) saturation profiles. The capillary force appears in the pressure equation and determines the advective term of the transport equation. The time when the front reaches the outlet (critical time) is calculated and used for scaling. The solution is extended to after critical time (late time) by maintaining the BL profile inside the system, thus preserving continuity in recovery and spatial profiles. The solution is characterized by an effective total mobility and capillary pressure (incorporating the entire saturation functions), both constant at early time (before critical time). At late times, they change dynamically. The model states that the imbibition rate can increase, decrease, and stay constant with time based on a new mobility ratio being less than, more than, or equal to unity, respectively. The ratio also indicates effectiveness of oil displacement. The square root of time recovery is a special case only seen for a (very) favorable mobility ratio. The model predicts that COC imbibition scales with the square of length both at early and late times and that the solution can scale saturation functions.The analytical solution was compared against numerical simulations of the full system. The new mobility ratio reflected the evolution in COC recovery better than total recovery. The analytical solution showed a too-high imbibition rate at a favorable mobility ratio. The diffusion term is important then due to strong saturation gradients, and the resulting smoothened profile yields a lower imbibition rate from the pressure equation. The analytical solution showed a too-low imbibition rate at early times for unfavorable mobility ratio due to not accounting for rapid early countercurrent (COUC) production. The analytical solution predicted a too-high imbibition rate at late times because the BL profile does not capture the oil mobility restriction at the outlet at late times. The time of water reaching the outlet was underestimated by a factor ∼ 2 for strongly water-wet (SWW) simulations and ∼ 10 for mixed-wet (MW) simulations. Scaling recovery with length squared was exact for all times. Scaling recovery until water reaching the outlet demonstrated consistency across saturation functions and viscosities. The analytical solution could match literature experimental data and produce corresponding saturation functions.To our knowledge, previous analytical solutions have only considered infinite-acting systems (early time), assumed piston-like displacement (PLD) (uniform saturations on both sides of a saturation shock front) or are implicit, thus not providing more insight than numerical simulations.

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.

Effects of methanol and acetone as mutual solvents on wettability alteration of carbonate reservoir rock and imbibition of carbonated seawater

The enhanced oil recovery (EOR) methods combination is a way to simultaneously utilize the mechanisms of the combined methods. Besides, in chemical water injection, additives controlling the mechanisms by their mutual interactions also exert other effects on the system, known as synergistic effects. In the current study, acetone and methanol mutual solvents were utilized to enrich carbonated water and their effects on the mechanisms of carbonate reservoir rock wettability alteration and oil production in the imbibition process have been investigated at different conditions of salinity, the ratio of solvent to water and pressure. Also, various boundary conditions and fracture effects were considered in the imbibition experiments. Imbibition fluid optimization was performed based on the contact angle tests and reservoir rock wettability alteration. Seawater was used as the base fluid at various initial and diluted concentrations. According to the results, the contact angle magnitude depends on the parameters of salinity, the volume percent of the mutual solvents and the pressure so that as the solvents volume and pressure increase and the salinity decreases, the contact angle decreases when carbon dioxide (CO2) is present but in absence of CO2, the contact angle decreases with increasing base fluid salinity. The lowest contact angle values for methanol and acetone solvents were recorded at 10.342 MPa, initial seawater salinity, 15% volumetric solvent, and a constant temperature 75 °C in absence of dissolved CO2 at 60.95° and 58.43°, respectively. The lowest contact angle values were obtained in the presence of dissolved CO2 for methanol and acetone solvents at 15% volumetric pressure at 10.342 MPa, salinity resulting from 20 times seawater dilution and at a temperature of 75 °C at 36.31° and 32.92°. Final oil production of 66.29%, 28.44%, 85.42% and 91.38% of primary oil saturation for the imbibition of carbonated water containing 15%Vol of methanol and final oil production of 70.32%, 32.10%, 90.60% and 94.09% of primary oil saturation for the imbibition of carbonated water containing 15%Vol acetone were obtained which were performed as one-dimensional co-current spontaneous imbibition (COCSI), one-dimensional counter-current spontaneous imbibition (COUCSI), multi-dimensional COUCSI and imbibition in the fractured plug, respectively.

Modeling of Co-current Spontaneous Imbibition Oil Recovery from Partially Covered Homogeneous Hydrocarbon Reservoir

In this paper, an approximate integral equation solution for a horizontal, unsteady flow of two viscous incompressible fluids is derived. Wettability variation of the porous medium is also considered in the present study. The non-wetting phase recovery fraction is obtained in terms of dimensionless time for 1D model from the derived solution. The derived approximate recovery fraction has been compared with the existing experimental data and empirical correlations for spontaneous imbibition from water-wet medium. It is observed that the normalized water saturation profiles show sharp gradients indicating some instability of the water front. Hence, a linear stability analysis is developed to study viscous instability of the co-current spontaneous imbibition. Viscous instability phenomenon for a two-phase oil–water system is also discussed. The corresponding instability number related to co-current imbibition recovery is estimated. The present study clearly spells out the effect of the instability number on the recovery process and estimates a critical instability number for co-current spontaneous imbibition.

An Analytical Solution for One-dimensional Horizontal Imbibition in a Cocurrent Flow

Cocurrent spontaneous imbibition (COCSI) of an aqueous phase into matrix blocks arising from capillary forces is an important mechanism for petroleum recovery from fractured petroleum reservoirs. In this work, the modeling of countercurrent imbibition is used to develop the appropriate scaling equations. Considering the imbibition process and the water and oil movement respectively as the wet phase and the non-wet phase in a block saturated by oil and surrounded by two vertical fractures full of water, a differential equation having partial and nonlinear derivatives is introduced using Darcy and mass balance equations. On the other hand, as there is no analytical solution for this equation, a new equation is introduced by considering the different intervals of the wet and non-wet phase viscosity and by selecting the best suitable functions for relative permeability and capillary pressure. Considering the boundary conditions governing the countercurrent imbibition, an analytical solution (equation) is developed. Finally, the developed equation is validated. The results of this research can be very important for a better understanding of the imbibition process and the water and oil movement in the fractured environments.

A mathematical model for co-current spontaneous water imbibition into oil-saturated tight sandstone: Upscaling from pore-scale to core-scale with fractal approach

Spontaneous Imbibition (SI) is an important mechanism of enhancing oil recovery in tight oil reservoirs. Predicting core-scale oil flow rate by water imbibition from the pore-scale SI modelling is challenging due to the wide distributions of nano- and micro-pores in tight sandstone and huge amount of calculation of upscaling pore-scale modelling results for core-scale prediction. A semi-analytical mathematical model of characterizing co-current SI of water into oil-saturated tight sandstone has been proposed in this paper based on the capillary tube model and fractal theory. The non-uniform of water imbibition front due to the different imbibition rate in different sizes of pores can be dynamically characterized. Connate water and residual oil are considered and treated as immovable boundary-layers and coupled into the tortuous capillary tube model. The proposed model has been validated with the experiments results of core imbibition tests from literature. The key parameters of pore structures and fluid properties influencing imbibition flow rate have been quantitatively analyzed and identified.

Mathematical modeling of co-current spontaneous imbibition in heterogeneous porous medium

Abstract Fractured carbonate reservoirs are principal crude oil and natural gas resources. These reservoirs are composed of matrix block with interconnected network of fractures. Oil or gas recovery from such low porous and low permeable reservoirs is important because a large amount of such hydrocarbon fluids are trapped inside those reservoir formulations. Water-flooding or more specifically spontaneous imbibition is one of the most effective recovery mechanisms to increase the production from fractured reservoirs. However, the performance of water-flooding mainly depends on the wettability of the reservoirs. In co-current imbibition, wetting phase displaces the non-wetting phase in such a way that the non-wetting phase moves in the same direction of the wetting phase. Hence the corresponding mathematical model requires a total flux condition. This study deals with the mathematical modeling of co-current spontaneous imbibition from heterogeneous porous reservoirs. The resulting governing equations are highly non-linear in nature. We solve these equations numerically and show that the co-current imbibition recovery is very much sensitive to the viscosity ratio, porosity variation models and the wettability of the reservoir. The impact of the viscosity ratio on the water saturation gradient and the end point mobility ratio is also analyzed. In addition, the variations in the heterogeneity and wettability of the medium and the corresponding influence on the sweeping efficiency of the co-current imbibition is investigated.

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.

A modified model for spontaneous imbibition of wetting phase into fractal porous media

Fractal theory has been applied to characterize complex pore structure of sedimentary rocks and to model fluid flow through porous media. In recent years, several analytical models have been developed to simulate spontaneous imbibition of wetting phase into porous media with fractal geometry. In previous studies, spontaneous imbibition of wetting phase is considered as a piston-like displacement phenomenon which leads to similar rates of imbibition in capillaries with different diameters. However, imbibition rate of wetting phase is positively proportional to the square root of pore diameter based on the Lucas-Washburn equation. Therefore, we should expect faster imbibition of wetting phase in larger capillaries compared with smaller capillaries.In this paper, we extend the previous model by assuming non-piston-like imbibition in capillaries with different diameters. In our model, first the larger capillaries are filled by wetting phase, followed by smaller capillaries. We develop an analytical equation without considering hydrostatic pressure and a semi-analytical equation with considering hydrostatic pressure. We can apply actual boundary conditions in the proposed model, while the previous piston-like models are only valid before the wetting phase reaches top of the porous media in co-current spontaneous imbibition test. Moreover, the proposed model can be used to determine the minimum pore diameter of rock sample according to the equilibrium time in spontaneous imbibition tests.