Counter-current Imbibition Research Articles

Nonlinear diffusion mechanism of porous media and countercurrent imbibition distance of fracturing fluids

Fracturing fluids countercurrent imbibition is a significant method to enhance recovery during hydraulic fracturing and soaking in shale reservoirs. Most investigations have primarily focused on the fracturing fluids imbibition recovery. In this work, an on-line computed tomography device was employed for the first time to conduct experiments on the imbibition distance of fracturing fluids, quantifying the imbibition distance of fracturing fluids, establishing the model of fracturing fluids imbibition, and clarifying the mechanism of countercurrent imbibition for fracturing fluids. The findings demonstrated that the imbibition distance was 2.625 cm for high mass fraction fracturing fluid and 2.375 cm for low mass fraction fluid. For formation water with viscoelastic fracturing fluids, the imbibition distances were 1.125 and 0.875 cm. Compared to the permeability of 0.082 × 10−3 μm2, the imbibition distance increased by 2.625 times at 0.217 × 10−3μm2 and by 3.25 times at 0.760 × 10−3μm2. At injection pressures of 20 and 15 MPa, the imbibition distance increased by 1.7 and 1.61 times, compared to 5 MPa. Parameter sensitivity analysis demonstrated that crude oil and fracturing fluids viscosity were negatively correlated with imbibition distance. Low interfacial tension boosts imbibition power, extending the imbibition distance. High interfacial tension raises flow resistance, shortening the imbibition distance. Reducing the contact angle improves hydrophilicity and capillary force, extending the imbibition distance. When the permeability is below 1 × 10−3μm2, the imbibition distance increases significantly with rising permeability. When the permeability exceeds 1 × 10−3μm2, the rate of increase diminishes. The investigation in this paper provides guidance for the efficient development of shale oil.

Phase-Field Simulation of Counter-Current Imbibition and Factors Influencing Recovery Efficiency

Phase-Field Simulation of Counter-Current Imbibition and Factors Influencing Recovery Efficiency

Displacement-imbibition coupling mechanisms between matrix and complex fracture during injecting-shut in-production process using pore-scale simulation and NMR experiment

Displacement-imbibition coupling oil production, which involves adjusting the operations of a well group (water injection huff and puff in one well, continuous oil production in another well), is an effective technique for enhancing oil recovery (EOR) for tight oil reservoirs. However, the research on displacement-imbibition coupling mechanisms is still missing, especially the combination of pore-scale numerical simulations and physical experiments. In this paper, a novel self-designed displacement-imbibition online nuclear magnetic resonance (NMR) experiment technique is developed. The effect of changes in fracture morphology on the mechanism of displacement-imbibition (oil saturation field and oil displacement efficiency) has been investigated. Based on the fracture morphology of physical experiments, a pore-scale model is established and solved by the finite element method. The pore-scale oil-water two-phase displacement-imbibition during the injecting-shut in-production process is simulated. The results show that the pressure oscillation makes the counter-current imbibition and co-current imbibition occur simultaneously in the matrix pores, which promotes oil recovery in matrix-fracture systems. The strength of displacement and imbibition effects is affected by the complexity of fractures. When the fracture complexity increases, the imbibition of the dense part of the fracture is stronger, while the displacement effect is weakened.

Understanding the Dynamics of Matrix-Fracture Interaction: The First Step Toward Modeling Chemical EOR and Selecting Suitable Fracturing Fluid in Unconventional Oil/Gas Recovery

Summary The effects of chemical additives on mitigating water blocking and improving oil recovery were experimentally examined for gas-water and oil-water systems in spontaneous imbibition cells. In these attempts, two factors are critically important: (1) understanding the physics of the interaction, whether it is co- or countercurrent, and (2) characteristics of the chemical additives to suitably orient the interaction for specific purposes (accelerate/decelerate matrix-fracture interactions). Co- and countercurrent imbibition experiments were conducted on sandstone rock samples using various oil samples (viscosities between 1.37 cp and 54.61 cp) as well as gas (air). The selected new-generation chemical additives included deep eutectic solvents, cationic/anionic/nonionic surfactants, and inorganic and organic alkalis. We observed that the functionality of the chemicals varied depending on the fluid type, interaction type (co- or countercurrent), and application purposes. For instance, chemicals such as the cationic surfactant cetyltrimethylammonium bromide (CTAB) significantly reduced water invasion into the gas-saturated sandstone cores during fracturing, while chemicals such as the nonionic surfactant Tween® 80 provided considerable oil recovery improvement in the oil-saturated sandstone cores. The surface tension and wettability of the rock surface are crucial factors in determining the suitability of chemicals for mitigating water blockage. In terms of oil recovery, certain chemical additives, such as O342 and Tween 80, may result in a lower recovery rate in the early stage because of their strong ability in interfacial tension (IFT) reduction but could lead to a higher ultimate recovery factor by altering the wettability. Additionally, the introduction of chemicals resulted in notable spontaneous emulsification, especially in countercurrent imbibition, thereby enhancing oil recovery. The spontaneous emulsification and its stability are influenced by factors such as oil drop size, boundary condition, interaction type, IFT, wettability, as well as rock surface charges. The results have implications for understanding the physics and dynamics of matrix-fracture interactions in co- and countercurrent conditions. In addition, they serve as the first step toward selecting appropriate chemical additives in hydraulic fracturing fluid design and enhancing oil recovery in unconventional reservoirs.

Investigating the Feasibility of EOR While Preloading Parent Wells to Mitigate Fracture Hits: An Experimental and Modeling Study

Summary During a fracturing operation in an infill (child) well, pressure and fluid communication between this well and a nearby parent well, known as fracture hits (FHs), can impair the production performance of both wells. A cost-effective strategy to mitigate the FH is to preload the parent well with water during the fracturing of the child well. It has been hypothesized that the production performance of the parent well can be enhanced by the preloading process if proper additives are used in the injected water. We develop a laboratory protocol to physically simulate primary production and surfactant preloading stages using Montney core and fluid samples under reservoir conditions. We investigate the role of wettability alteration, interfacial tension (IFT) reduction, and surfactant’s chemical stability on the performance of enhanced oil recovery (EOR) during the preloading process. An analytical model is developed to predict the volume of leaked-off surfactant and recovered oil using measured pressure-decline data from the preloading stage. This study only focuses on the interactions of preloading fluid with the parent well’s matrix and does not consider the child-parent well interference. Our results demonstrate that 31.8% of the oil is recovered during primary production from large inorganic pores under solution-gas drive mechanism. Under countercurrent imbibition, a nonionic surfactant leaks off into the smaller organic and inorganic pores and recovers an additional 11.8% oil from a depleted core during preloading. The analytical model estimates oil recovery factors close to the experimental data determined by material balance. Core visualizations demonstrate a population of small oil droplets on the rock surface under reservoir conditions. While IFT is reduced to nearly the same extent by either surfactant, only the wettability-altering surfactant yields incremental oil recovery. Zeta-potential measurements indicate that while neither surfactant alters the rock-water surface charge, the wettability alteration is achieved by modifying the oil-water surface charge even at concentrations above the critical micelle concentration (CMC). Based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, the repulsive electrostatic double-layer (EDL) forces are intensified with an increase in surfactant concentration, resulting in enhanced stability of the water film on the rock surface and increased hydrophilicity. Under elevated temperatures, we observe two phenomena, which can adversely affect the performance of a nonionic surfactant: (a) agglomeration of surfactant particles due to reduced solubility in water, reducing pore accessibility, and (b) chemical decomposition of the surfactant, affecting its ability for IFT reduction and wettability alteration.

Countercurrent Imbibition in Porous Media with Dense and Parallel Microfractures: Numerical and Analytical Study

Summary Countercurrent imbibition is the process in which the wetting fluid spontaneously displaces the nonwetting fluid, while the nonwetting fluid is recovered at the wetting fluid inlet. It is a major mechanism for the recovery of shale oil, shale gas, and tight oil. In shale and tight formations, microfractures are highly developed. Specifically, some typical formations, such as continental shales, consist of dense and parallel microfractures (DPFs). In DPF systems, microfractures are segregated by low-permeability matrix layers, while the very close distance betwen neighboring microfractures results in strong capillary correlation. The underlying assumptions of the classical dual-porosity (DP) model break down. Despite extensive studies on layered media, there is still no suitable model to describe imbibition in the DPF system at the representative elementary volume (REV) scale. In this study, we first numerically simulate countercurrent imbibition in DPF systems with fine grids, adopting typical continental shale parameters. For imbibition parallel to microfractures, two distinct stages are identified: an early stage where fractures are not correlated and a late stage where neighboring fractures are strongly correlated by capillarity. In both stages, cumulative oil production (Q) is proportional to the square root of imbibition time (t1/2), while the prefactors are very different. The late stage is the dominant stage in oil recovery. We note that the matrix permeability rarely contributes to imbibition parallel to microfractures at the late time, indicating that the matrix’s role here is to store fluid rather than to provide flow resistance. In addition, we rationalize the failure of the classical DP model, as it significantly overestimates fracture-matrix fluid exchange near the displacement front. Similarly, for imbibition perpendicular to microfractures, Q is also proportional to t1/2 in the late stage. After elucidating the mechanisms of fracture-fracture capillary interaction, we successfully derive analytical solutions for uni-directional countercurrent imbibition kinetics in DPF systems at the late stage, for imbibition parrallel and perpendicular to microfractures, respectively. We accordingly propose an equivalent REV scale model and examine it with fine-grid simulations. We highlight the importance of adopting anisotropic relative permeability in this DPF system at REV scale for reservoir simulation rather than simply adopting anisotropic absolute permeability. This presents a new challenge for numerical simulations at reservoir scale.

Lattice Boltzmann simulation of counter-current imbibition of oil and water in porous media at the equivalent capillarity

The characterization of oil and water displacement in porous media often relies on the capillary number (Ca = μv/σ cos θ). However, limited investigations have been conducted to explore the relative significance of interfacial tension and wettability in determining oil recovery, particularly under the imbibition mode. To address this research gap, the modified color gradient lattice Boltzmann method has been employed. This study aims to systematically investigate the transient imbibition characteristics, pore-scale events, and morphological features of the two-phase distribution in the matrix, all under the same capillarity but varying capillary numbers. The obtained results indicate that, for a given capillary number, a more water–wet condition generally leads to a higher imbibition recovery. Conversely, the influence of capillary number on oil recovery is complex and contingent upon the capillarity value, i.e., the interfacial tension between oil and water. Additionally, the oil recovery data from all cases have been effectively fitted using the Minkowski functionals, demonstrating a linear correlation. Moreover, an attempt has been made to elucidate the mechanism behind the varying oil recovery observed in different capillarity combinations. This analysis considers factors such as energy conversion, the transient change of the ratio of viscous force over capillarity, and the capillary valve effect. The findings of this study contribute to our understanding of the use of chemical agents to enhance oil recovery and provide valuable insights for determining key two-phase parameters in reservoir simulations.

Improved Amott Method to Determine Oil Recovery Dynamics from Water-Wet Limestone Using GEV Statistics

Counter-current spontaneous imbibition of water is a critical oil recovery mechanism. In the laboratory, the Amott test is a commonly used method to assess the efficacy of brine imbibition into oil-saturated core plugs. The classic Amott-cell experiment estimates ultimate oil recovery, but not the recovery dynamics that hold fundamental information about the imbibition mechanisms. Retention of oil droplets at the outer core surface and initial production delay are the two key artifacts of the classic Amott experiment. This retention, referred to here as the “external-surface oil holdup effect” or simply “oil holdup effect”, often results in stepwise recovery curves that obscure the true dynamics of spontaneous imbibition. To address these holdup drawbacks of the classic Amott method, we modified the Amott cell and experimental procedure. For the first time, using water-wet Indiana limestone cores saturated with brine and mineral oil, we showed that our improvements of the Amott method enabled accurate and reproducible measurements of oil recovery dynamics. Also for the first time, we used the generalized extreme value (GEV) statistics to describe oil production histories from water-wet heterogeneous limestone cores with finite initial water saturations. We demonstrated that our four-parameter GEV model accurately described the recovery dynamics, and that optimal GEV parameter values systematically reflected the key characteristics of the oil–rock system, such as oil viscosity and rock permeability. These findings gave us a more fundamental understanding of spontaneous, counter-current imbibition mechanisms and insights into what constitutes a predictive model of counter-current water imbibition into oil-saturated rocks with finite initial water saturation.

The Role of Core Sample Geometry on Countercurrent Spontaneous Imbibition: Mathematical Foundation, Examples, and Experiments Accounting for Realistic Geometries

Summary Countercurrent spontaneous imbibition (SI) experiments are among the most common multiphase experiments performed on porous rock samples. Although the samples rarely are designed to give linear flow, they are often modeled and interpreted using mathematical descriptions assuming linear flow. In this work, the goal is to derive general understanding of how imbibition into different sample geometries behaves compared with linear (1D) imbibition. Using the mathematical theory of N-volume spheres (N being the dimension), we consider core samples as N-spherical and quantify their geometry by a dimension N and length scale L. For the special cases, N=1,2,3, we obtain linear, radial, and spherical flow; however, we treat the dimension as an arbitrary real number for cases not adhering to either of these regimes. Particularly, for rectangular or cylindrical core plugs, a continuous range of dimensions is produced. Theoretical calculations of N and L of arbitrary sample shapes are derived based on relations with area per volume and derivative of area with respect to volume. They correctly produce limit cases and physically meaningful values for symmetrical, cylindrical, and rectangular geometries. The differential equation for countercurrent imbibition in N-dimensions is derived and solved with numerical examples. Also, a simplified analytical solution assuming piston-like displacement is derived to get illustrative relations between system parameters (including dimension) and recovery and front position. Predicted recovery profiles of the N-dimensional (N-D) solution overlap consistently with numerical simulations (by an alternative simulator) into cylindrical geometries with a wide range of height/diameter ratios and viscosity ratios. At early time, the saturation profiles are self-similar (look the same plotted against position divided by square root of time) and identical regardless of dimension. As long as the profiles are self-similar near the open boundary, recovery is proportional to the square root of time. For N=1, this lasts long after the front has reached the closed boundary, while for N >1, it can happen long before the boundary has been reached. The same time scale was applicable for all geometries, stating especially that doubling the length scale increased the time of the entire recovery profile by a factor 4. As long as recovery is proportional to square root of time, at a given time, it is also proportional to dimension over length, NL, and the time needed to reach same level of recovery is proportional to LN2. Permeability anisotropy (lower vertical than horizontal permeability) could effectively be modeled using an effective increased height, which further was captured by the dimension and length scale. Literature and in-house experimental data were matched by the model and used to validate model predictions such as the variation in time, shape of recovery curves with changes in dimension, and the importance of accounting for the dimension (geometry) during data interpretation. The model is valid for all wetting states but assumes negligible gravity and compressibility effects.

Two-dimensional counter-current capillary imbibition of a wetting phase into a partially submerged porous cylindrical matrix block

The purpose of this study is to address the two-dimensional counter-current capillary dominant imbibition of a wetting phase into a water-wet porous cylindrical matrix block partially submerged in the wetting phase. A two-dimensional unsteady-state diffusion equation is used to model the process. The governing equation is solved using a combination of the Laplace and the finite Fourier sine transforms to find and analyze the solutions for the normalized water saturation and the volume of the imbibed wetting phase. The results reveal that the volume of the imbibed wetting phase and the capillary diffusion shape factor for a partially submerged matrix block are significantly lower compared to those of a fully submerged matrix block, highlighting the overestimation of imbibed volume using available models based on full immersion in the wetting phase. It has been observed that the volume of the imbibed wetting phase increases over time until reaching a state of equilibrium. In the case of a partially submerged matrix block, the shape factor is inversely proportional to the square root of time (σ ∼ 1/t) during the early time and decreases sharply as the imbibed wetting phase reaches an equilibrium. In the case of a fully submerged matrix block, the shape factor is inversely proportional to the square root of time (σ ∼ 1/t) during the early time and later reaches a pseudo-steady-state value. The proposed model, along with the findings obtained, advances our understanding of capillary imbibition in porous media.

Quantitative characterization of imbibition in fractured porous media based on fractal theory

In low-permeability reservoirs, such as shale and tight sandstone, imbibition is an important mechanism for enhancing oil recovery. After hydraulic fracturing treatment, these reservoirs create a network of fracture pathways for fluid flow. Therefore, understanding the imbibition mechanisms in fractured porous media and quantitatively characterizing oil–water distribution are crucial for the development of low-permeability reservoirs. In this study, a mathematical model of two-phase flow in porous media with branching fractures was established. The phase-field method was employed to track the oil–water interface, and quantitative characterization of imbibition was conducted based on fractal theory, and the effects of wetting phase injection rate, the number of disconnected fractures, fracture spacing, and fracture morphology on imbibition in branched fracture porous media were discussed. The research findings indicate that in branched fracture porous media, both co-current and countercurrent imbibition processes occur simultaneously, and there exists a diffusion interface layer with a certain thickness at the oil–water interface. The hydraulic pressure generated by the wetting phase injection rate provides the driving force for imbibition oil recovery, but it also affects the contact time between the wetting and non-wetting phases. The presence of disconnected fractures hinders the propagation of hydraulic pressure, reducing the effectiveness of imbibition. The imbibition displacement zone is limited and occurs only within a certain range near the fractures. As the number of branching fractures increases, the channels for the wetting phase to enter matrix pores are enhanced, resulting in higher efficiency of imbibition displacement of the oil phase. The results of this research can provide guidance for the design of fracturing programs and recovery prediction in low-permeability reservoirs.

Counter-current spontaneous imbibition dynamics: Combined effects of wettability, fracture flow, and pore structure

Spontaneous imbibition plays a crucial role in various engineering and industrial applications, with its efficiency significantly influenced by a range of factors. To unravel the intricate mechanisms behind these factors, our study employs pore-scale numerical simulations. Utilizing a color gradient model within the framework of the lattice Boltzmann method, we delve into how pore structure, wettability, and flow velocity within fractures collectively impact spontaneous imbibition. Our findings reveal that the dynamics of drainage and imbibition interfaces during countercurrent spontaneous imbibition are key determinants of imbibition efficiency. Specifically, the synergy between wettability and pore structure markedly affects the penetration depth and distribution characteristics of the imbibition interface, which, in turn, influences the imbibition's speed and duration. Moreover, the interaction between the flow velocity inside fractures and the configuration of adjacent pore structures significantly shapes the evolution of the drainage interface. This interplay is crucial as it can either enhance or hinder countercurrent spontaneous imbibition. These insights deepen our understanding of the pore-scale processes governing countercurrent spontaneous imbibition, laying a solid theoretical foundation for optimizing its application in engineering and industrial settings.

Application of Physics-Informed Neural Networks for Estimation of Saturation Functions from Countercurrent Spontaneous Imbibition Tests

Summary In this work, physics-informed neural networks (PINNs) are used for history matching data from core-scale countercurrent spontaneous imbibition (COUCSI) tests. To our knowledge, this is the first work exploring the variation in saturation function solutions from COUCSI tests. 1D flow was considered, in which two phases flow in opposite directions driven by capillary forces with one boundary open to flow. The partial differential equation (PDE) depends only on a saturation-dependent capillary diffusion coefficient (CDC). Static properties such as porosity, permeability, interfacial tension, and fluid viscosities are considered known. In contrast, the CDC or its components [relative permeability (RP) and capillary pressure (PC)], are considered unknown. We investigate the range of functions (CDCs or RP/PC combinations) that explain different (synthetic or real) experimental COUCSI data: recovery from varying extents of early-time and late-time periods, pressure transducers, and in-situ saturation profiles. History matching was performed by training a PINN to minimize a loss function based on observational data and terms related to the PDE, boundary, and initial conditions. The PINN model was generated with feedforward neural networks, Fourier/inverse-Fourier transformation, and an adaptive tanh activation function, and trained using full batching. The trainable parameters of both the neural networks and saturation functions (parameters in RP and PC correlations) were initialized randomly. The PINN method successfully matched the observed data and returned a range of possible saturation function solutions. When a full observed recovery curve was provided (recovery data reaching close to its final value), unique and correct CDC functions and correct spatial saturation profiles were obtained. However, different RP/PC combinations composing the CDC were calculated. For limited amounts of recovery data, different CDCs matched the observations equally well but predicted different recovery behavior beyond the collected data period. With limited recovery data, when all points were still following a square root of time trend, a CDC with a low magnitude and peak shifted to high saturations gave the same match as a CDC with a high magnitude and peak shifted to low saturations. Recovery data with sufficient points not being proportional to the square root of time strongly constrained how future recovery would behave and thus which CDCs could explain the results. Limited recovery data combined with an observed in-situ profile of saturations allowed for accurate determination of CDC and prediction of future recovery, suggesting in-situ data allowed for shortened experiments. With full recovery data, in-situ PC data calibrated the PC toward unique solutions matching the input. The RPs were determined, where their phase had much lower mobility than the others. The CDC is virtually independent of the highest fluid mobility, and RPs could not be matched at their high values. Adding artificial noise in the recovery data increased the variation of the estimated CDCs.

Pore-scale imbibition patterns in layered porous media with fractures

The presence of fractures increases the difficulty of flow mechanisms analysis, and it remains unclear how fractures affect multiphase flow displacement in the layered rock matrix. Herein, a pore-scale imbibition model considering the layered matrix-fracture system is established using the phase-field method, where oil is displaced by a range of fluids with various properties. Two typical flow modes are carefully analyzed, depending on the locations of the fracture and the interfaces between different layers of the matrix: fracture is parallel to the interface (mode I), and it penetrates through the interface (mode II), which are dominated by the co-current imbibition and countercurrent imbibition mechanisms, respectively. Interestingly, the surface tension is found to be negatively correlated with the ultimate oil recovery rate for mode I and plays an opposite effect on that of mode II. For flow mode I, the conditions of lower injection rate, higher viscosity ratio, higher grain diameter ratio, and injection of the invading fluid from the larger pore throat size (positive direction flow) can improve oil recovery. For flow mode II, the fracture bifurcation angle has little effect on the positive direction flow, while it can significantly regulate the phase distribution in the negative direction flow. Based on scaling analysis of relating pore-filling events to displacement modes and the equilibrium relationship between capillary and viscous forces, two theoretical models are derived to predict the imbibition patterns, and the variation of the flow regime under various parameters in the typical layered matrix-fracture models is systematically concluded.

Study of imbibition phenomenon in homogeneous porous medium model for oil recovery with temporal-fractional approach

In this article, the phenomenon of countercurrent imbibition in a specific displacement method occurs within a dipping homogeneous porous medium. This phenomenon plays a vital role in the process of oil recovery, which motivates our analysis. To overcome the difficulties associated with the nonlinear partial differential equation governing the countercurrent imbibition phenomenon, we have been using two distinct methods: the natural transform decomposition method and the variational iteration transform method with their convergence analysis for solutions. These techniques give different perspectives and enable us to obtain approximate solutions. Notably, both the proposed methods demonstrate the potential for substantial production of oil during the secondary oil recovery process in the petroleum industry. The obtained results by the proposed methods show the efficiency in optimizing the oil recovery rate.

Shale Matrix Petrophysical Evolution due to Spontaneous Water Imbibition.

Shale matrix alteration resulting from fracturing water-rock interactions has become a major concern. It significantly affects economic production from shale gas formation. Previous studies mostly failed to investigate the thickness of the water intrusion zone and quantified its effects on shale geophysical alteration. As a result, we present a one-dimensional countercurrent water imbibition model in which capillary pressure and chemical osmosis stress are included. This model is used to predict water front movement with respect to soaking durations. Based on the simulation results and theory derivations, the matrix porosity-permeability and mechanical alteration models are set up to reveal shale geophysical variables change due to shale-water interactions. Our results show that during the water imbibition process, capillary pressure plays a more crucial role than osmosis pressure. Furthermore, both core-scaled porosity and permeability are negatively associated with water saturation, the extent of which depends on different driving forces and penetration depth. Finally, water soaking is quantitatively demonstrated to induce an increase in compressive strength and stress sensitivity but a reduction in the elastic modulus. These findings will provide efficient insights into driving mechanisms involved in the water-rock interactions. The study is useful to be incorporated into production models for predicting hydrocarbon production from shale reservoirs.

Experimental study on countercurrent imbibition in tight oil reservoirs using nuclear magnetic resonance and AFM: Influence of liquid–liquid/solid interface characteristics

Countercurrent imbibition of the fracturing fluid is of much significance for enhancing oil production in tight oil reservoirs during the shut-in period after hydraulic fracturing. The addition of enhanced imbibition agents such as surfactants and nanoparticles into the polymer-based fracturing fluid is conducive to oil production. How different types of imbibition agents affect oil recovery and the applicable conditions for different imbibition agents, however, still need to be clarified. In this article, we used low-field nuclear magnetic resonance (NMR) to measure the one-dimensional (1D) oil signal profiles along the imbibition direction during the countercurrent imbibition process and determine the imbibition distance and water saturation of different imbibition agents including polymer, surfactant, nano-silica (NS) and NS-surfactant complexes. Moreover, by measuring oil–water interfacial tension (IFT), and the adhesion forces between alkanes and the hydrophobic surfaces before/after the imbibition agent treatments by atomic force microscope (AFM), the IFT reduction and wettability alteration abilities of these agents were evaluated. After the NS-surfactant complexes treatment, the adhesion force which represents the force required to pull off oil from the rock surface became the lowest (15.81 pN), merely a quarter of that of NS (73.48 pN) and surfactant (70.01 pN), indicating a superior capability of NS-surfactant to improve wettability. The imbibition efficiency of the four systems in terms of imbibition distance and oil recovery was: NS-surfactant complexes: 38.43 mm 13.2 % > nonionic surfactant: 32.15 mm 9.0 % > NS: 25.88 mm 7.6 % > polymer: 17.64 mm 4.9 %. NS-surfactant nanofluid displayed the longest imbibition distance and highest water saturation, thus possessing the highest imbibition oil recovery. Nonionic surfactant with an IFT of 4.19 mN/m could greatly reduce the IFT compared with NS (35.98 mN/m), but the recovery enhancement induced by IFT reduction was not significant. In contrast, the increase in oil recovery by wettability alteration was distinctly higher than that by IFT reduction, as indicated by the recovery difference between NS-surfactant complexes and surfactant. Accordingly, wettability alteration is the primary mechanism to enhance imbibition oil recovery when ultralow IFT cannot be achieved. This research provides guidance on which type of imbibition agent should be selected to improve imbibition efficiency.

Effective Relative Permeabilities Based on Momentum Equations with Brinkman Terms and Viscous Coupling

Summary The relative permeability expresses the mobility reduction factor when a fluid flows through a porous medium in the presence of another fluid and appears in Darcy’s law for multiphase flow. In this work, we replace Darcy’s law with more general momentum equations accounting for fluid-rock interaction (flow resistance), fluid-fluid interaction (drag), and Brinkman terms responding to gradients in fluid interstitial velocities. By coupling the momentum equations with phase transport equations, we study two important flow processes—forced imbibition (coreflooding) and countercurrent spontaneous imbibition. In the former, a constant water injection rate is applied and capillary forces are neglected, while in the latter, capillary forces drive the process and the total flux is zero. Our aim is to understand what relative permeabilities result from these systems and flow configurations. From previous work, when using momentum equations without Brinkman terms, unique saturation-dependent relative permeabilities are obtained for the two flow modes that depend on the flow mode. Now, with Brinkman terms included, the relative permeabilities depend on local spatial derivatives of interstitial velocity and pressure. Local relative permeabilities are calculated for both phases utilizing the ratio of phase Darcy velocity and phase pressure gradient. In addition, we use the Johnson-Bossler-Naumann (JBN) method for forced imbibition (with data simulated under the assumption of negligible capillary end effects) to calculate interpreted relative permeabilities from pressure drop and average saturation. Both flow setups are parameterized with literature data, and sensitivity analysis is performed. During coreflooding, Brinkman terms give a flatter saturation profile and higher front saturation. The saturation profile shape changes with time. Local water relative permeabilities are reduced, while they are slightly raised for oil. The saturation range where relative permeabilities can be evaluated locally is raised and made narrower with increased Brinkman terms. JBN relative permeabilities deviate from the local values: The trends in curves and saturation range are the same but more pronounced as they incorporate average measurements, including the strong impact at the inlet. Brinkman effects vanish after sufficient distance traveled, resulting in the unique saturation functions as a limit. Unsteady state (USS) relative permeabilities (based on transient data from single-phase injection) differ from steady-state (SS) relative permeabilities (based on SS data from coinjection of two fluids) because the Brinkman terms are zero at SS. During spontaneous imbibition, the higher effect from the Brinkman terms caused oil relative permeabilities to decrease at low water saturations and slightly increase at high saturations, while water relative permeability was only slightly reduced. The net effect was a delay in the imbibition profile. Local relative permeabilities approached the unique saturation functions without Brinkman terms deeper in the system because phase velocities (involved in the Brinkman terms) decreased with distance. In both systems, scaling and simulations demonstrate that the relative change in relative permeabilities due to Brinkman terms increases with the Brinkman coefficient, permeability, and inverse squared distance from the inlet.

Mathematical Model of Imbibition Replacement and Optimization of Soaking Time for Massively Fractured Tight Oil Reservoirs.

Due to the small pore throat characteristics of tight oil reservoirs, their strong capillary pressure makes imbibition replacement an effective development method. Field data has indicated that only a little fracture fluid can flow back and that there is an enhancement in oil recovery with shut-in periods after volume fracturing. A large number of scholars have carried out core-scale experiments on imbibition characteristics, but there has been limited research on the quantitative characterization of the differential pressure and imbibition replacement during counter-current imbibition. At the same time, there was also controversy on the calculation method of the optimal soaking time. In this paper, a mathematical model of oil-water two-phase flow is first established. Then, a mathematical model representing differential pressure and imbibition replacement in tight reservoirs is derived with a diversion function. Based on the saturation equation, Corey relative-permeability curve, and J function, the model is simplified to a mathematical model of spontaneous imbibition in the shut-in periods after volume fracturing. Second, based on the finite difference method, a dynamic solution method for the flow field considering the dynamic capillary force was established, and the variation law of the pressure field and the water saturation field during the soaking time was revealed. The simulation results show that imbibition characteristics are the core of flow field reconstruction, and the differential pressure action can ensure the advancing distance of the fracturing fluid; both of them are not a linear superposition on tight oil development but complement each other and promote each other. Third, according to the growth rate of the imbibition replacement between fractures and the matrix during the soaking time, the calculation method of optimal soaking time was established. Taking the development parameters of the volume fracturing development case in the Ordos Basin into account, a reasonable soaking time was optimized. Finally, we analyzed the optimal soaking time under different conditions, and a chart of optimal soaking time for different initializations was plotted. Such a chart has profound reference significance for engineers, and they can make quick and accurate decisions regarding development and adjustment.

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks