FIG 11
Ultimate oil recovery factor as a function of injection velocity u inj for both the left-wide and the right-wide matrixes.
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Oil recovery from naturally fractured reservoirs with low permeability rock remains a challenge. To provide a better understanding of spontaneous imbibition, a key oil recovery mechanism in the fractured reservoir rocks, a pore-scale computational study of the water imbibition into an artificially generated dual-permeability porous matrix with a fr...
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Imbibition oil recovery in low permeability fractured reservoirs has been acknowledged as an efficient method to enhance oil recovery. However, the effects of the complex pore structure and the hydraulic pressure in fracture on the fluids transport were not considered comprehensively in any model at pore scale in literature. This paper aims to stud...
Citations
... 2 During oil recovery, water invasion into highly conductive fracture networks leads to fully immersed or partially submerged porous matrix blocks, resulting in a capillary dominant counter-current flow of oil and water where the wetting phase (water) is imbibed into the matrix block and non-wetting phase (oil) is expelled. [19][20][21] Another form of imbibition is the co-current capillary imbibition, where water and oil flow in a similar direction. The co-current capillary imbibition takes place in the presence of viscous forces and is not the focus of this work; details can be found elsewhere. ...
... 19 A tremendous number of studies have addressed capillary imbibition in a porous matrix block. [19][20][21][22][23][24] However, all these attempts have targeted one-dimensional capillary imbibition when the matrix block is fully submerged in water. In this work, it will be shown that the partial immersion of matrix blocks has a significant effect on the amount of water imbibed into a 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.
... By comparing the pore distribution of each core and its imbibition displacement rate, they found that in the early stage of imbibition, the core imbibition displacement rate and imbibition recovery degree are positively correlated with the pore throat radius and its proportion in the core; In the late stage of imbibition, imbibition displacement rate is negatively correlated with the proportion of pore throat in the core [12]. Gu et al. [15]. used LBM method to study the influence mechanism of water injection rate and double permeability layer geometry on countercurrent spontaneous imbibition, they carried out the simulation of injecting water into a fracture beside a porous medium with dual permeability, and it is found that the geometry configuration of high permeability zone and low permeability zone affects the oil recovery through countercurrent spontaneous imbibition in the fracture matrix system, and there is a critical velocity (about 0.78 mm/s), above which the model with higher permeability zone near the inlet shows higher recovery, and under this critical velocity, the model with lower permeability zone near the inlet shows higher recovery. ...
... With iIiI-type zone and IiIi-type zone, a further study of the effect of geometry configuration of pore arrays was performed on the countercurrent spontaneous imbibition. Considering that different capillary number Ca in the experiment may also affect the phenomenon in spontaneous imbibition [15], a series of Ca gradient (0.0062, 0.0186, 0.0372, 0.0558, 0.0743, 0.1115, 0.1487) were also set up for study. The definition of Ca is shown in Eq. (18), in which v in is the viscosity of the wetting phase entering the fracture from the inlet, and the u in is a representative velocity of this part of wetting phase. ...
Keywords: Countercurrent spontaneous imbibition Multi-scaled pore structures Selectivity of wetting phase to pore size Lattice Boltzmann method a b s t r a c t The multi-scaled pore networks of shale or tight reservoirs are considerably different from the conventional sandstone reservoirs. After hydraulic fracturing treatment, the spontaneous imbibition process plays an important role in the productivity of the horizontal wells. Applying the color-gradient model of Lattice Boltzmann Method (LBM) accelerated with parallel computing, we studied the countercurrent spontaneous imbibition process in two kinds of pore structures with different interlacing distributions of large and small pores. The effect of geometry configuration of pore arrays with different pore-scale and the capillary number Ca on the mechanism of counter-current spontaneous imbibition as well as the corresponding oil recovery factor are studied. We found that the wetting phase tends to invade the small pore array under small Ca in both types of geometry configurations of different pore arrays of four pore arrays zones. The wetting phase also tends to invade the pore array near the inlet for injecting the wetting phase no matter if it is a large pore array or small pore array except for the situation when the Ca is large to a certain value. In this situation, the small pore arrays show resistance to the wetting phase, so the wetting phase doesn't invade the small pore near the inlet, but invades the large pore preferentially. Both the geometry configurations of different pore arrays and Ca have a significant effect on the oil recovery factor. This work will help to solve the doubt about the selectivity of the multi-scaled pores of the wetting phase and the role of pores with different sizes in imbibition and oil draining in counter-current spontaneous imbibition processes.
... It can effectively capture the interface dynamic phenomena (e.g., DCA) with a well-defined physical background. [36][37][38] The LBM simulating imbibition processes include two-phase flow models based on diffusion interfaces [39][40][41][42][43][44][45][46][47][48] and free surface flow models based on sharp interfaces. 49 Among these models, the Shan-Chen model has a well-defined physical background and has been widely used to simulate gas-liquid [50][51][52] and liquid-liquid capillary imbibition. ...
Spontaneous liquid–liquid imbibition in capillaries with irregular axial geometries is common in the petroleum industry. Monitoring the real-time dynamic contact angle (DCA) of the meniscus is crucial during such processes. In this work, we extend the Bell–Cameron–Lucas–Washburn (BCLW) equation by considering the axial shape of the capillaries, inertial force, and non-wetting fluid viscosity. We also develop a cascaded multi-component Shan–Chen lattice Boltzmann method (CLBM) with a modified mass-conservative curved boundary scheme to accurately simulate imbibition processes in sinusoidal capillaries. The results indicate that the DCA is highly sensitive to variations in the axial geometry of the capillary during imbibition, displaying a periodic time evolution pattern. When the axial geometry diverges, the DCA increases, and when it converges, the DCA decreases. The viscosity ratio affects the imbibition velocity, controlling the evolution period and extreme values of the DCA. A critical contact angle exists for a fixed capillary axial geometry and viscosity ratio. Continuous spontaneous imbibition occurs if the static contact angle is smaller than this critical value. However, if it exceeds this threshold, imbibition ceases within regions where axial geometry divergence. Moreover, we noticed a discrepancy in imbibition lengths predicted by the extended BCLW equation that ignores the DCA compared to those computed through the CLBM. To address this issue, we employed CLBM to monitor the DCA in real time and used the gathered data to refine the extended BCLW equation. As a result, the prediction of imbibition lengths by the extended BCLW equation for coupling the DCA became more accurate.
... Due to the great difference between the permeability of rock fractures and rock blocks, fractures are the main channels for fluid flow and pollutant migration in rock masses. [1][2][3][4][5][6] The geological storage of carbon dioxide, 7 the development of oil 8,9 and shale gas, 10 and the treatment and disposal of nuclear waste 11 are inseparable from the help of fracture seepage which are also the main causes of water inrush in foundation pits 12 and underground tunnels. 13 Seepage in fractures will reduce the stability of slopes and lead to landslides, 14 and the displacement of people and huge losses of financial resources caused by landslides are not uncommon. ...
The cross section of a fracture along the streamwise direction determines the water-passing capacity of the fracture. The seepage fields in four fracture models with different contact conditions are analyzed and investigated via computational fluid dynamics simulations. The main results are as follows: (1) a kind of low-velocity region is formed under small local aperture conditions; (2) the blocking degree of the contact area to the fracture seepage depends on the local flow channels compressed by it (flow angle and local aperture); (3) on a cross section, the interference of the contact area and roughness on the fluid flow make the average flow velocity (Uavg) greater than its streamwise component (uavg) except for seepage inlet, which increases with the decrease in the average mechanical aperture and the expansion of the contact area [C = 17.90%, compared to lower C, the whole average flow velocity (1.88 m/s) is the maximum]; (4) there may be an upward trend of pressure along the streamwise direction: where the cross-sectional area increases, the additional kinetic energy generated by the reduced flow velocity will be converted into pressure potential energy if it is not fully consumed by the viscous force; (5) along the streamwise direction, there is a linear correlation between the change rate in uavg (∂uavg/∂x) and that of average pressure on a cross section (∂P/∂x), which is affected by the interference of the contact area and roughness (R2 = 0.25 at C = 17.90%), a conceptual model derived from this linear correlation can describe the relation between the hydraulic characteristics of a fracture and streamwise cross section.
... [27][28][29] The fractures are embedded within the matrix and exhibit interconnectedness, while the matrix pores and fractures serve as the primary channels for fluid flow. [30][31][32][33][34] Traditionally, fractures in the petroleum industry and the field of elasticity are often represented as smooth, parallel plates. [35][36][37][38] In this study, we adopt a dimension reduction technique to simplify the fractures, as depicted in Fig. 1, transforming them into one-dimensional line elements for computational Physics of Fluids ARTICLE pubs.aip.org/aip/pof ...
Fractures in low and ultra-low permeability reservoirs create a complex network, affecting fluid flow patterns and pressure propagation. However, limited research exists on fluid flow patterns and the impact of fracture properties on pressure within these networks. To address this, we introduce fracture shadow area and fracture penetration ratio concepts derived from studying single fracture reservoirs. Using a sophisticated model of a complex fracture network, we analyze how various fracture properties influence fluid flow patterns and reservoir pressure. Fractures are classified into five categories based on the development level. Through orthogonal experiments and multiple regression methods, we derive a formula that quantifies the pressure influence. We find that longer and denser cracks enhance fluid exchange and pressure propagation capacity. Moreover, increasing crack opening expands the area of pressure drop. Notably, fractures aligned with pressure propagation significantly decrease reservoir pressure. The hierarchical sequence of crack traits with the greatest influence is identified as crack length, crack opening, crack density, and crack angle. Our findings shed light on the intricate relationship between fracture properties and pressure dynamics.
... Compared to other numerical methods for studying porous flows at pore scale, e.g., direct numerical simulation and pore-network method, 34 the lattice Boltzmann method is very popular because of its advantages, such as intrinsic parallelism, ease of implementation, and ability to handle complex geometries. [35][36][37][38] Additionally, an iterative source-correction immersed boundary method was used to describe the interaction between the fingering flow and the porous structure, the accuracy of which was verified in our previous study. 39 With this numerical model, we have conducted the first systematic study of salt finger convection in porous media in the non-Darcy regime. ...
We report a pore-scale numerical study of salt finger convection in porous media, with a focus on the influence of the porosity in the non-Darcy regime, which has received little attention in previous research. The numerical model is based on the lattice Boltzmann method with a multiple-relaxation-time scheme and employs an immersed boundary method to describe the fluid-solid interaction. The simulations are conducted in a two-dimensional, horizontally-periodic domain with an aspect ratio of 4, and the porosity is varied from 0.7 to 1, while the solute Rayleigh number ranges from 4*10^6 to 4*10^9. Our results show that, for all explored Rayleigh number, solute transport first enhances unexpectedly with decreasing porosity, and then decreases when porosity is smaller than a Rayleigh number-dependent value. On the other hand, while the flow strength decreases significantly as porosity decreases at low Rayleigh number, it varies weakly with decreasing porosity at high Rayleigh number and even increases counterintuitively for some porosities at moderate Rayleigh number. Detailed analysis of the salinity and velocity fields reveals that the fingered structures are blocked by the porous structure and can even be destroyed when their widths are larger than the pore scale, but become more ordered and coherent with the presence of porous media. This combination of opposing effects explains the complex porosity-dependencies of solute transport and flow strength. The influence of porous structure arrangement is also examined, with stronger effects observed for smaller porosity and higher Rayleigh number. These findings have important implications for passive control of mass/solute transport in engineering applications.
... Compared to other numerical methods for studying porous flows at pore scale, e.g., direct numerical simulation and pore-network method, 34 the lattice Boltzmann method is very popular because of its advantages, such as intrinsic parallelism, ease of implementation, and ability to handle complex geometries. [35][36][37][38] Additionally, an iterative source-correction immersed boundary method was used to describe the interaction between the fingering flow and the porous structure, the accuracy of which was verified in our previous study. 39 With this numerical model, we have conducted the first systematic study of salt finger convection in porous media in the non-Darcy regime. ...
We report a pore-scale numerical study of salt finger convection in porous media, with a focus on the influence of the porosity in the non-Darcy regime, which has received little attention in previous research. The numerical model is based on the lattice Boltzmann method with a multiple-relaxation-time scheme and employs an immersed boundary method to describe the fluid–solid interaction. The simulations are conducted in a two-dimensional, horizontally periodic domain with an aspect ratio of 4, and the porosity [Formula: see text] is varied from 0.7 to 1, while the solute Rayleigh number [Formula: see text] ranges from [Formula: see text] to [Formula: see text]. Our results show that, for all explored [Formula: see text], solute transport first enhances unexpectedly with decreasing [Formula: see text] and then decreases when [Formula: see text] is smaller than a [Formula: see text]-dependent value. On the other hand, while the flow strength decreases significantly as [Formula: see text] decreases at low [Formula: see text], it varies weakly with decreasing [Formula: see text] at high [Formula: see text] and even increases counterintuitively for some porosities at moderate [Formula: see text]. Detailed analysis of the salinity and velocity fields reveals that the fingered structures are blocked by the porous structure and can even be destroyed when their widths are larger than the pore scale, but become more ordered and coherent with the presence of porous media. This combination of opposing effects explains the complex porosity dependencies of solute transport and flow strength. The influence of porous structure arrangement is also examined, with stronger effects observed for smaller [Formula: see text] and higher [Formula: see text]. These findings have important implications for passive control of mass/solute transport in engineering applications.
... However, the 3D voxel is still approximately 10 nm, which is still not enough to fully identify the shale pores. Another challenge is the severe heterogeneity of shale pore structures; hence, the representative element volume (REV) is far larger than the pore sizes, which makes the REV of shale digital rock generally much larger than 1000 3 (Germanou et al., 2020), and the corresponding direct multiphase flow computational demand is overwhelming (Yu et al., 2017;Rokhforouz and Akhlaghi Amiri, 2017;Gu et al., 2019;and Zhu et al., 2021). To resolve this issue, a pore network modeling method is proposed to simulate multiphase flow in porous media. ...
Coupled pressure-driven (viscous) flow and spontaneous imbibition are the main regimes during shale oil production. Revealing the unclear mechanisms of this coupled flow is a major concern for scholars and field engineers. In this work, the oil–water flow mechanisms within shale pore structures are investigated by pore-scale modeling methods in focused ion beam scanning electron microscopy digital rocks enhanced by applying super-resolution reconstruction (SRR). More small pores are identified with SRR, and the connectivity is improved. The enhanced pore size distribution is consistent with the nitrogen adsorption measurement; hence, more representative capillary pressure and relative permeability curves are obtained with essential experimental measurements. Then, an analytical solution of coupled pressure-driven (viscous) flow and spontaneous imbibition is derived, and a corresponding algorithm is proposed. Based on the pore-scale calculated relative permeability and capillary pressure curves, the analytical solution is applied to investigate the variations in water saturation profiles and conductance of the oil phase during the shale reservoir development. The results demonstrate that most of the shale oil is recovered by pressure dropdown-induced viscous flow and that imbibition is a minor factor. The overall oil-relative permeability decreases due to imbibition invasion. When the fracture spacing increases, the impairment of the overall oil-relative permeability decreases.
... Spontaneous imbibition is a capillary-driven, self-propelled phenomenon of great potential for use in oil/gas recovery operations. [34][35][36][37][38][39][40][41][42] It is also the basis of paper-based microfluidic devices, such as rapiddiagnostic kits, flow batteries, and disposable viscometers. [43][44][45][46][47] The classic Richards equation is well capable of accurately predicting dynamic imbibition of the working fluids in these applications provided that they are Newtonian. ...
A new generalized Richards equation (GRE) valid for highly shear-thinning liquids obeying the power-law model is developed using the concept of the effective viscosity. The mathematical model developed this way is validated against experimental data reported recently for one-dimensional spontaneous imbibition of two pusher liquids by a tight sandstone. The GRE model was then used for evaluating the applicability of shear-thinning liquids for enhanced gas recovery (EGR). For a homogenous tight sandstone, it is shown that shear-thinning can dramatically shorten the time needed for the gas recovery to reach equilibrium. Based on the obtained numerical results, the mass of the gas recovered using spontaneous imbibition is increased if use is made of highly shear-thinning liquids. At prolonged times, however, it is predicted that gas recovery might slightly drop below its Newtonian counterpart even for highly shear-thinning fluids. The effect was attributed to the fact that, in spontaneous imbibition, the viscosity of power-law fluids increases with time and can eventually become larger than its Newtonian counterpart. For a two-layered non-homogeneous system, numerical results suggest that depending on the microstructure of the two layers, the liquid mass uptake can be smaller than that of the homogenous case. It is predicted that if the liquid is sufficiently shear-thinning, gas recovery can reach levels much above the homogeneous case.
... In addition, it can be used for large-scale oil/gas recovery operations when polymer-extended pusher fluids are used as a displacing liquid to enhance sweep efficiency. [30][31][32][33][34][35][36][37][38][39] Work is currently ongoing in our research group to investigate the effect of yield stress or viscoelasticity of physiological fluids on the quasi-steady regime. Physiological fluids are known to exhibit viscoplastic and/or viscoelastic behavior, 23 and such behavior are speculated to affect liquid imbibition in paper-based diagnostic kits. ...
In the present work, spontaneous imbibition of shear-dependent fluids is numerically investigated in a two-layered, rectangular/fan-shaped, paper-based diagnostic kit using the modified Richards equation. It is shown that the average velocity at the test line of the kit is strongly influenced by the absorbent pad's microstructure with its contact angle playing a predominant role. Assuming that the test fluid is shear-thinning, a generalized version of the Richards equation, valid for power-law fluids, was used to investigate the effect of shear-thinning on the quasi-steady regime. The shear-thinning behavior of the test fluid is predicted to shorten the duration of the constant-velocity regime on the nitrocellulose membrane used as the test cell. By manipulating the contact angle and/or choosing appropriate microstructure for the absorbent pad, it is still possible to establish a constant velocity regime at the test line for nearly five minutes even for such fluids. A comparison between our numerical results and published numerical results obtained using simplistic theories has revealed the key role played by the transition, partially-saturated zone near the advancing front during the liquid imbibition. The general conclusion is that use should preferably be made of robust models such as Richards equation for the design of lateral-flow, paper-based assays.
