Spontaneous imbibition in porous media is ubiquitous in natural and industrial applications. It is of great value to probe into the microscopic and macroscopic multiphase flow mechanisms of spontaneous imbibition in science and engineering aspects. However, due to the multi-influencing factors such as petrophysical properties, fluid properties and boundary conditions in porous media, the microscopic and macroscopic flow mechanisms in spontaneous imbibition are difficult to be understood thoroughly. Currently, the spontaneous imbibition process under the influence of multiple factors is widely studied and mainly focused on laboratory experiments, theoretical analysis and numerical simulations. In this paper, the key issues and recent progress in spontaneous imbibition are analyzed, and some suggestions and an in-depth understanding of capillarity in porous media are provided for future work.
Mathematical models of imbibition under different boundary conditions were built with piston-like displacement assumption. Effect of gravity and capillary pressure on imbibition under OEO (single boundary) and TEO-OW (mixed boundary) boundary conditions are studied. It shows that oil is produced only by counter-current imbibition under OEO boundary conditions. Gravity inhibits imbibition as the open face is at the lower end face of core and gravity promotes imbibition as the open face is at the upper end face of core. Oil is produced by combination of co-and counter-current imbibition under TEO-OW boundary condition. Gravity inhibits counter-current imbibition and promotes co-current imbibition under TEO-OW boundary condition. Gravity is dominant driving force as the inverse Bond number is smaller and capillary pressure is dominant driving force as inverse Bond number is greater. In addition, effect of gravity and capillary pressure on imbibition under OEO and TEO-OW boundary conditions are studied. It shows that oil production by gravity under OEO boundary condition is greater than that under TEO-OW boundary condition with same inverse Bond number. The rate of oil production under OEO boundary condition is faster than that under TEO-OW boundary condition as inverse Bond number is smaller and opposite phenomena is observed as inverse Bond number is greater.
The classical Lucas-Washburn (L-W) capillary-driven model calculates capillary pressure using the Young-Laplace equation, which leads to a deviation from the real values for a pipe with small diameter. In this work we use Tolman length to improve the Young-Laplace equation, and propose an improved L-W model. Moreover, circular pipes with rough and variable sections are considered rather than the circular pipe with a constant diameter. Relation between time and wetting fluid injection length in the circular pipe with variable sections is established. The mathematical model is described as a second-order nonlinear ordinary differential equation, which cannot be solved analytically, and thus an efficient numerical method is developed. A concrete pipe with variable cross-section is selected, and the relation between water length and time is calulated with numerical simulation. Numerical results are analyzed, and the effectiveness of Tolman length is verified. It shows that the local shrinkage of circular pipe changes the states of water motion significantly, and there are three kinds of movement modes. The local expansion of circular pipe changes slowly the state of seepage and water absorption, and only one single movement mode takes place.
A random four-parameter method is used to reconstruct pore structure of heterogeneous sandy conglomerate. Imbibition behavior of wetting fluid in porous media is studied with an improved SC-LBM (Shan-Chen lattice Boltzmann) model. It shows that interfacial dynamics at the initial stage is closely related to the arrangement of pore skeleton, and the imbibition interface is mainly formed by matrix. As fluid flows through the pore throat, the flow cross section shrinked instantly, leading to a rapid increase in pressure gradient and flow resistance. The presence of hole roar pressure leads to the flow cross section shrinked instantly, which increases the flow resistance, indicating that the change of pore radius has a great influence on imbibition rate. In the later stage, the wetting fluid forms a dominant imbibition channel, which reduces the swept area and greatly reduces the imbibition displacement rate. This study is helpful to understand the spontaneous imbibition of fluid in heterogeneous pores, and is of great significance to imbibition and oil displacement in fractured tight reservoirs.
We investigated spontaneous imbibition behavior in a basic bifurcated channel. The rupture and convergence of the two-phase interface in a bifurcated channel is strongly unsteady, which is hard to be described accurately with classical theories and conventional numerical calculation methods. An improved two-component pseudopotential lattice Boltzmann method was employed in simulating the unsteady spontaneous process. It shows that the width of inlet/outlet channel controls the competitive imbibition behavior in the bifurcated channel. Whereas the viscosity ratio between the wetting phase and the non-wetting phase controls the overall spontaneous imbibition behavior. The results provide a basis for quantitative characterization of spontaneous imbibition in complex pore structures.
As the main absorption mode of fracturing fluid in reservoir, imbibition is an important driving force to improve shale gas productivity. In this paper, the Longmaxi formation shale in Pengshui area of Chongqing is studied. Mercury intrusion porosimetry, imbibition under different conditions and NMR tests were carried out successively. It shows that: ① The permeability and porosity of shale are very low, mainly micropores and mesopcres, almost no macropores, and the pore structure is poor; ② The process of shale imbibition can be divided into three stages. With the increase of pressure and temperature, imbibition behavior is enhanced. The imbibition effect of gel breaking fracturing fluid is slightly stronger than that of non-gel breaking fracturing fluid. Surfactant and KCl solution can reduce the imbibition ability of shale; ③ In the process of imbibition, the medium and large pores and fractures are filled with liquid in the initial stage, while the very small pores and fractures are filled first, and then the liquid enters into the slightly larger micropores and microcracks, resulting in a large number of microcracks on the surface of shale.
Based on characteristics of multiple pores in the shale of Longmaxi formation (LF) in the south of Sichuan Basin, an analytical model of imbibition was established. Imbibition depths of different pore types were quantitatively calculated. Water imbibition experiments under conditions of formation temperature, confining pressure, and fluid pressure were carried out. Water imbibition law in shale was analyzed. It shows that according to imbibition saturation, the shale forcible imbibition can be divided into 3 periods. They are imbibition diffusion, imbibition transition and imbibition balance periods, respectrvely. Among them, the imbibition diffusion period is the main period for imbibition capacity rise. In the early period of shut-in, the imbibition capacity of shale increases significantly under the action of fluid pressure, providing a large amount of imbibition fluid for the spontaneous imbibition later. The reservoir confining pressure has prohibition on shale imbibition, but even under reservoir confining pressure, imbibition can improve fracturing effect of reservoir, resulting in the increase of porosity of 0.42-1.63 times and increase of permeability of 17.6-67.3 times. The imbibition depth of clay pore is much greater than that of brittle mineral pore and organic pore. Clay minerals are the main controlling factor of microfractures induced by shale hydration. An appropriate shut-in treatment enhances dramatically fracturing performance in shale gas reservoirs of LF in southern Sichuan Basin. The study provides scientific basis for the optimization of flowback regime of shale gas well.
Accurate understanding of the microscopic occurrence state of water flooding residual oil in porous media is of great significance for improving the development effect of water flooding and enhancing the recovery factor of water flooding in high water cut oil fields. Based on the verification of the Volume of Fluid (VOF) method, influence of physical property conditions and displacement modes on the microscopic occurrence characteristics and recovery factor of remaining oil in ultra-high water cut sandstone reservoir was studied by making full use of its advantages of tracking the dynamic change of two-phase interface and reproducing the physical process of microscopic seepage. By analyzing the microscopic seepage characteristics of typical pore structures and the stress of remaining oil, mechanism and law of different types of microscopic remaining oil are revealed: The increase of displacement velocity and the change of displacement direction make the distribution of microscopic remaining oil dispersed and the recovery efficiency is improved in different degrees under the condition of water and humidity; As the oil is wet and the viscosity ratio is high, the capillary resistance and viscosity are great, the remaining oil is mostly clustered and porous, and the recovery degree is relatively low.
The pore throat structure of low permeability tight sandstone gas reservoir is complex. It is difficult to characterize the flow and distribution of gas and water in it. Based on real low-permeability sandstone core, micro-CT scanning technology was used to construct three-dimensional digital core of the reservoir. Connected pore structure was extracted and unstructured tetrahedral mesh model was established. With level-set method and N-S equation, a mathematical model of gas-water two-phase flow is established which is solved by finite element method. Water drive gas process, residual gas distribution, influence of rock wettability on two-phase flow in low-permeability sandstone gas-water two-phase flow, and interflow characteristics in parallel channels are studied. It shows that level-set method provides clearly gas-water two-phase distribution and migration of the displacement front. Rock wettability has great influence on two-phase flow process, and production degree is higher under water-wet conditions. Interflow phenomenon is obvious in parallel channels. Water phase in the large channel breaks through first and forms a dominant flow channel, while flow in the narrow channel is affected by capillary phenomenon and has great additional resistance.
To study adsorption mechanism of polar substance of crude oil in water flooding reservoir and its influence on surface wettability of reservoir, a sandstone skeleton model represented by quartz, a non-polar substance model represented by hexane and polar substance models represented by toluene, resin and asphaltene are constructed. Competition adsorption process and wet condition of four crude oil components and water molecules on sandstone reservoir surface are studied with molecular simulation. It shows that non-polar substances of crude oil are more easily desorbed than the polar substances when water competes with the four components for adsorption on quartz mineral surface. And as time goes by, polar substances are gradually adsorbed on the rock mineral surface, while non-polar substances move away gradually. Electrostatic force acts as adsorption and van der Waals force acts as repulsion in adsorption process. Finally, based on wettability experiment results, influence of different crude oil compositions on wettability was explained in mechanism, that is, the more polar substance in the oil component, the more resin and asphaltene, the strong the oil wettability of rock surface is. And it is more difficult to change the wettability to hydrophilic during water flooding. The conclusions are of great significance in the understanding of contributing factors of the recovery in water flooding reservoirs.
Molecular dynamics simulations are utilized to systematically investigate the effects of wettability on capillary imbibition process at the nanoscale. We consider two sets of scenarios. In the first set, the two sidewalls of a nanochannel have the same wettability. We find that the capillary imbibition rate increases with the hydrophilicity of capillary and that the imbibition dynamics deviates from the Lucas-Washburn theory at the early stage but agrees with it at the late stage. In the second set where the two sidewalls have different wetting conditions, the liquid-vapor interface oscillates, and there exists a difference between the capillary height of the two sidewalls. The amplitude of the liquid-vapor interface oscillation and the capillary height difference increase with the wettability contrast between the two sidewalls. We determine the critical condition for the occurrence of capillary imbibition in the nanochannel with inhomogeneous wettability, and propose a method to estimate the evolution of the capillary height. Our findings deepen the understanding of capillary dynamics at the nanoscale and could be useful for relevant engineering applications.
Localized method of fundamental solutions is applied to the simulation and analysis of electrostatic field problems. The localized method of fundamental solutions is a meshless algorithm based on local theory and moving least square approximation, which uses fundamental solution of the governing equation. Compared with traditional mesh-type methods such as finite element method and finite difference method, this method needs discrete nodes only, and avoids troublesome mesh generation. As a semi-analytical numerical technique, fundamental solutions of physical problems are used as interpolation basis functions to establish a numerical discrete model, thus ensuring high accuracy of the algorithm. In addition, compared with meshless methods with global discretization scheme, the local fundamental method is more suitable for high-dimensional complex geometry and large-scale simulation. Two- and three-dimensional numerical tests show that this method is convenient, flexible, accurate and fast. It is a new way for electrostatic field simulation. It expands application of localized method of fundamental solutions.
According to the fractal scaling law of microstructures, the particle and pore structures of random porous media were reconstructed with Monte Carlo method. The seepage property of multiscale porous media was studied with a fractal capillary bundle model. A quantitative relation between macroscopic seepage properties and microscopic structures was addressed. It shows that microstructures of porous media reconstructed by the fractal Monte Carlo method are close to that of real media. Calculated results for gas flow through porous media agree well with those by lattice Boltzmann method. It is shown that gas permeability increases with the increment of Knudsen number. The pore fractal dimension takes important effect on the microscale effect of gas flow through porous media, while the influence of tortuosity fractal dimension on the ratio of apparent gas permeability to intrinsic permeability is marginal. The method shows advantages that the convergence speed is fast and the calculation error is independent of dimension. It is helpful in understanding seepage mechanisms of multiscale porous media.
